Rethinking Input-Output Analysis: A Spatial Perspective 3030334465, 9783030334468, 9783030334475

Table of contents :
Preface: History and Acknowledgements......Page 6
Contents......Page 7
Variables and Coefficients......Page 10
1 Introduction: Importance Interindustry Relations and Overview......Page 11
References......Page 12
2.1 Single-region IO Tables and Their Descriptive Power......Page 14
2.2 Mathematics Versus Economics of the Closed Economy IO Model......Page 16
2.3.1 Distinguishing Technical and Trade Origin Coefficients......Page 20
2.3.2 Underestimation of Interregional Spillovers and Feedbacks......Page 25
References......Page 27
3.1.1 Most Non-Survey Methods Overestimate Intra-Regional Multipliers......Page 28
3.1.2 Non-Survey CC-RAS Method: Advantage of Using Multiple Comparable IOTs......Page 32
3.1.3 Semi-Survey DE-BRIOT Method: Advantage of Constructing Bi-Regional IO Tables......Page 34
3.2 Construction of Interregional Supply-Use Tables and Models......Page 37
3.2.1 Difficulty of Deriving an IO Model from a Supply-Use Table......Page 38
3.2.2 Family of Interregional Supply-Use Tables and Models......Page 41
3.3 Difference Between Constructing Interregional and International SUTs......Page 44
References......Page 46
4.1 Interregional Models with Endogenous Household Consumption......Page 49
4.2 Further Demo-Economic Model Extensions......Page 55
4.3 Where to End with Endogenizing Final Demand?......Page 60
References......Page 62
5.1 Forward Causality of the Single-Region IO Price Model......Page 64
5.2 Type II Interregional Price and Quantity Models Combined: Lower Multipliers......Page 67
References......Page 72
6.1.1 Basic Supply-Driven IO Model: How Factories May Work Without Labour......Page 74
6.1.2 Type II Supply-Driven IO Model: How More Private Cars May Run with Less Gasoline......Page 79
6.2 Revenue-Pull IO Price Model = Plausible Dual of the Ghosh Quantity Model......Page 81
6.3 Markets: Why All Four IO Models Overestimate Their Typical Impacts......Page 84
References......Page 87
7.1 Limited Usability of the IO Model in Case of Supply Shocks......Page 90
7.2 Nonlinear SU Programming Alternative: Much Smaller Disaster Multipliers......Page 94
References......Page 98
8.1 Key Sector and Linkage Analyses: A Half-Truth......Page 100
8.1.1 Analytical and Empirical Comparison of Key Sector Measures......Page 101
8.1.2 Cluster and Linkage Analysis for Three Dutch Spatial Policy Regions......Page 103
8.1.3 The Other, Cost Side of the Coin......Page 106
8.2 Structural Decomposition Analyses: Another Half-Truth......Page 108
8.2.1 Shift and Share Analysis of Regional Growth......Page 109
8.2.2 Structural Decomposition Analyses of National and Interregional Growth......Page 111
8.2.3 The Other, Supply Side of the Coin: Growth Accounting......Page 115
References......Page 116
9 Future: What to Forget, to Maintain and to Extend......Page 120
References......Page 122

Citation preview

SPRINGER BRIEFS IN REGIONAL SCIENCE

Jan Oosterhaven

Rethinking InputOutput Analysis A Spatial Perspective

SpringerBriefs in Regional Science Series Editors Henk Folmer, University of Groningen, Groningen, The Netherlands Mark Partridge, Ohio State University, Columbus, USA Daniel P. McMillen, University of Illinois, Urbana, USA Andrés Rodríguez-Pose, London School of Economics, London, UK Henry W. C. Yeung, National University of Singapore, Singapore, Singapore

SpringerBriefs present concise summaries of cutting-edge research and practical applications across a wide spectrum of fields. Featuring compact, authored volumes of 50 to 125 pages, the series covers a range of content from professional to academic. SpringerBriefs in Regional Science showcase emerging theory, empirical research and practical application, lecture notes and reviews in spatial and regional science from a global author community.

More information about this series at http://www.springer.com/series/10096

Jan Oosterhaven

Rethinking Input-Output Analysis A Spatial Perspective

123

Jan Oosterhaven University of Groningen Groningen, The Netherlands

ISSN 2192-0427 ISSN 2192-0435 (electronic) SpringerBriefs in Regional Science ISBN 978-3-030-33446-8 ISBN 978-3-030-33447-5 (eBook) https://doi.org/10.1007/978-3-030-33447-5 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface: History and Acknowledgements

The origin of this book dates back to my lecture notes for the first regional economics course at the University of Groningen, taught in 1976. The last revision of the resulting Dutch language Syllabus Ruimtelijke Economie appeared in 2003. An English language extension of its input-output (IO) part was written for the educational section of the website of the IIOA with my dear colleague Dirk Stelder in 2007. The theoretical parts of this book benefited further from the Handbook articles I wrote with Karen Polenske in 2009 for Edward Elgar and with Geoff Hewings in 2014 for Springer, while all of this book benefited from my cooperation with a series of colleagues and Ph.D.-students. In the order in which my work with them is used in this book, these are Fernando Escobedo (Sect. 3.1.2), Piet Boomsma (3.1.3), Jouke van Dijk and Henk Folmer (4.2), Bjarne Madsen (5.2), Maaike Bouwmeester and Johannes Többen (7.2), Umed Temursho (8.1.1), Gerard Eding and Dirk Stelder (8.1.2), Jan van der Linden, Jiansuo Pei and Erik Dietzenbacher (8.2.2). Finally, I thank an anonymous reviewer and Eva Mulder for useful comments on drafts for this book. Naturally, the final text is my sole responsibility. Groningen, The Netherlands August 2019

Jan Oosterhaven

v

Contents

1 Introduction: Importance Interindustry Relations and Overview . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2

2 Basic, Demand-Driven IO Quantity Models . . . . . . . . . . . . . . . . 2.1 Single-region IO Tables and Their Descriptive Power . . . . . . . 2.2 Mathematics Versus Economics of the Closed Economy IO Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Open Economy Interregional and Multi-regional IO Models . . 2.3.1 Distinguishing Technical and Trade Origin Coefficients 2.3.2 Underestimation of Interregional Spillovers and Feedbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

... ...

5 5

... ... ...

7 11 11

... ...

16 17

3 Data Construction: From IO Tables to Supply-Use Models . . . . . 3.1 Construction of Regional IO Tables: Towards Cost-Effective Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Most Non-Survey Methods Overestimate Intra-Regional Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Non-Survey CC-RAS Method: Advantage of Using Multiple Comparable IOTs . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Semi-Survey DE-BRIOT Method: Advantage of Constructing Bi-regional IO Tables . . . . . . . . . . . . . . . . 3.2 Construction of Interregional Supply-Use Tables and Models . . 3.2.1 Difficulty of Deriving an IO Model from a Supply-Use Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Family of Interregional Supply-Use Tables and Models . 3.3 Difference Between Constructing Interregional and International SUTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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19

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19

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19

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23

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25 28

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29 32

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35 37

vii

viii

4 From Basic IO and SU Models to Demo-Economic Models 4.1 Interregional Models with Endogenous Household Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Further Demo-Economic Model Extensions . . . . . . . . . . 4.3 Where to End with Endogenizing Final Demand? . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contents

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41

. . . .

. . . .

41 47 52 54

... ...

57 57

... ...

60 65

. . . .

. . . .

. . . .

5 Cost-Push IO Price Models and Their Relation with Quantities . 5.1 Forward Causality of the Single-Region IO Price Model . . . . . 5.2 Type II Interregional Price and Quantity Models Combined: Lower Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

.. ..

67 67

..

67

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72

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74

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77 80

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83 83

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87 91

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93 93

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model . . . 6.1 Plausibility of the Supply-Driven Input-Output Model . . . . . . . 6.1.1 Basic Supply-Driven IO Model: How Factories May Work Without Labour . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Type II Supply-Driven IO Model: How More Private Cars May Run with Less Gasoline . . . . . . . . . . . . . . . . 6.2 Revenue-Pull IO Price Model = Plausible Dual of the Ghosh Quantity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Markets: Why All Four IO Models Overestimate Their Typical Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Negative IO Supply Shock Analyses: A Disaster and a Solution . . 7.1 Limited Usability of the IO Model in Case of Supply Shocks . . 7.2 Nonlinear SU Programming Alternative: Much Smaller Disaster Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Other IO Applications with Complications . . . . . . . . . . . . . . . . . 8.1 Key Sector and Linkage Analyses: A Half-Truth . . . . . . . . . . 8.1.1 Analytical and Empirical Comparison of Key Sector Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Cluster and Linkage Analysis for Three Dutch Spatial Policy Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 The Other, Cost Side of the Coin . . . . . . . . . . . . . . . . 8.2 Structural Decomposition Analyses: Another Half-Truth . . . . . 8.2.1 Shift and Share Analysis of Regional Growth . . . . . . .

. . . .

. . . .

. . . .

. 96 . 99 . 101 . 102

Contents

ix

8.2.2 Structural Decomposition Analyses of National and Interregional Growth . . . . . . . . . . . . . . . . . . . . . . . . . 104 8.2.3 The Other, Supply Side of the Coin: Growth Accounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Future: What to Forget, to Maintain and to Extend . . . . . . . . . . . . . 113 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Variables and Coefficients

D a b c d e f g h i j k l m n o p q r s t u v w x y z

Absolute change (first order difference) Intermediate input coefficients by industry Intermediate output coefficients by industry, trade balance, final demand bridge coefficients Primary input coefficients by industry, commuting coefficients by industry Final output coefficients by industry, total demand External exports Local final demand by category, final demand preference (technical) coefficients Ghosh-inverse coefficients Household consumption, product heterogeneity Summation vector Employment (jobs) Consumption expenditure coefficients Leontief-inverse coefficients, employment (labour) coefficients Import and self-sufficiency ratios Inactive people without benefits Other value added Prices, industry product mix ratios Total product supply/demand, household consumption/industry output ratios Industry market shares in product supply Product supply by industry, industry sales ratios, savings rates Trade volumes, export coefficients, tax rates Product use by industry, unemployed people Primary inputs (value added) by industry Wage income, wage rate Total industry input/output Total final demand by category, gross income Intermediate inputs/outputs

xi

Chapter 1

Introduction: Importance Interindustry Relations and Overview

Keywords Globalization · Supply chains · Interindustry relations · Input–output analysis · Supply-use tables · Cumulative impacts · Exogenous final demand With the historic, continuous reduction of tariff and non-tariff barriers to international trade, firms became able to increasingly exploit international locational cost and revenue advantages. Fragmentation of production processes and lengthening of supply chains were the result, along with a globalization of the world economy and a steady increase in world welfare. International income differences predominantly declined (see Sala-i-Martin 2006, for before 2000, and ILO 2015, for after 2000), whereas interregional income differences often increased (see Silva and Leichenko 2004, for the USA, and Wan et al. 2007, for China); mainly because several regions in several countries lost their comparative advantages in the concomitant worldwide reorganisation of interindustry relations. In the late 2010s, tariff and non-tariff barriers were raised again, and again regions within and between countries won and lost comparative advantages in the again changing global supply chains they participated in. Analysing such processes requires detailed data on interindustry relations, such as offered by interregional and international input–output tables (IOTs), as these tables show the transactions between say the Russian natural gas industry and the German energy distribution industry. With an input–output (IO) model, based on such data (Leontief 1936) many questions can be answered, such as those about the amount of Chinese value-added embodied, both directly and indirectly, in American household consumption. Questions about consumer responsibility in environmental studies, such as the direct and indirect amount of CO2 emissions of the German car industry incorporated in French household investments, require comparable data and models. Besides, more mundane questions, such as those about the likely employment, income and environmental impacts of organizing the Olympic games or relocating national government offices, also require the information of such tables to build the models necessary to answer such questions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_1

1

2

1 Introduction: Importance Interindustry Relations and Overview

This book will help you to understand the social, economic and environmental importance of the relations between industries in the same and in different regions and countries, and how to model these relations by means of regional, interregional and international IO models. While presenting these models, it will be assumed that you are familiar with standard matrix algebra. You will also learn how to extend the basic IO models with endogenous household expenditures, which are especially important in case of smaller regions. Moreover, you will learn how to use the modern IO tables called supply-use tables (SUTs), which explicitly distinguish the products used and sold, per purchasing and per selling industry, respectively. Besides the standard demand-driven IO quantity model, this book will also carefully lay out the economic assumptions of its supply-driven mirror image, indicate its extremely limited usefulness and explain that its little known, accompanying revenue-pull IO price model is almost as useful as the much better known cost-push IO price model that is the dual of the standard IO quantity model. After the mainly theoretical first chapters, the two final chapters discuss three well-known applications of the IO model, namely (1) economic impact analysis of negative supply shocks caused by, for example, natural and man-made disasters, (2) regional and interregional forward and backward linkage analysis, better known as key sector analysis and (3) structural decomposition analysis of regional, national and interregional economic growth. In all three cases, the standard IO approach is shown along with its problematic implications, such as producing misleadingly high multipliers in the first case and presenting policy makers with only half of the truth in the other two cases. Of course, the necessary additions to and changes in the standard approach are presented as well. This book stands out with its emphasis on the behavioural foundations of the two IO quantity models and the two IO price models, and the plausibility of the causal mechanisms implied by the mathematics of the base models. This leads to a far more critical evaluation of the usefulness of IO analysis than found in standard textbooks. This book will thus be of relevance to both graduate and Ph.D. students, as well as to practitioners in research and consulting firms and agencies, as it provides a better understanding of the foundations, the power and the limitations of input–output analysis.

References ILO (2015) Global Wage Report 2014/15: wages and income inequality. International Labour Office, Geneva Leontief W (1936) Quantitative input and output relations in the economic system of the United States. Rev Econ Stat 18:105–125 Sala-i-Martin X (2006) The world distribution of income: falling poverty and… convergence, period. Q J Econ 121:351–397

References

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Silva J, Leichenko R (2004) Regional income inequality and international trade. Econ Geogr 80:261–286 Wan G, Lu M, Chen Z (2007) Globalization and regional income inequality: empirical evidence from within China. Rev Income Wealth 53:35–59

Chapter 2

Basic, Demand-Driven IO Quantity Models

Keywords Input–output tables · Technical coefficients · Trade coefficients · Leontief model · Normalized multipliers · Impact studies · Price elasticities · Interregional spillovers · Interregional feedbacks Notation In this and in all the following chapters, columns are indicated by small bold cases x, rows as transposed columns x , matrices by bold capitals X and scalars by small italic cases x. Diagonal matrices are indicated by putting a hat on the vector that fills up the diagonal xˆ . The summation vector with ones is indicated by i and the unity matrix by I = ˆi. With super- or subscripted symbols, a dot indicates a summation over the super- or subscript at hand. With deliveries between industries or regions, the first index indicates the origin, and the second index indicates the destination of the product flow.

2.1 Single-region IO Tables and Their Descriptive Power The core of any regional or national input–output table (IOT) consists of a matrix with, along its rows, the sales of all industries i to all industries j (i.e. zij in the first quadrant of Fig. 2.1, with i and j = 1, …, I). Looking along the columns of the IOT, these sales represent the purchases of intermediate inputs from industry i by industry j. The third quadrant of Fig. 2.1 contains the additional purchases of primary inputs of type p by industry j (i.e. vpj , with p = 1, …, P). For a closed economy, these consist of the payments for labour and capital, which is why they are called primary inputs. For an open economy, however, they also include imports of intermediate inputs from the Rest of the World (RoW). By including profits as payments for capital use, the overall column totals of the first and third quadrant equal the value of total production by purchasing industry, x j .

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_2

5

6

2 Basic, Demand-Driven IO Quantity Models Industry 1

Industry j

Industry I

Local final demand Exports

st

Total

nd

Industry 1

z11

1 quadrant …

z1I

y11

2 quadrant …

y1Q

x1

Industry i

…

zij

…

…

yiq

…

xi

Industry I

zI 1

…

z II

yI 1

…

yIQ

xI

y pq

… …

M Y

G

E

rd

Imports Value added

… …

Total

x1

3 quadrant …

th

v pj

… …

… …

xj

xI

C

4 quadrant … I

Fig. 2.1 Single-region input–output table, with four quadrants and macroeconomic totals. Legend zij = intermediate sales from industry i to industry j, yiq = final sales from industry i to final demand category q, x i = total output/input of industry i, vpj = primary input of type p by industry j, ypq = primary inputs of type p by final demand category q, C = consumption, I = investments, G = government expenditures, E = exports, M = imports, and Y = gross value added at market prices.

Along the rows of the IOT, the second quadrant complements the intermediate outputs of industry i with its sales to the various categories of final demand q (i.e. yiq in Fig. 2.1, with q = 1, …, Q). For a closed economy, these consist of the sales of consumer and investment goods to households, firms and government agencies, which is why they are called final outputs. For an open economy, however, they also include the exports of both intermediate and final outputs to the RoW. By adding changes in stocks as a separate category of final demand, the overall row sums of the first and second quadrant of the IOT equal the total production by selling industry, x i . The row totals by industry, in this way, equal the column totals by industry. The fourth quadrant with the purchases of primary inputs of type p by final demand category q completes the accounting framework of the IOT (i.e. ypq in Fig. 2.1). Summation along the columns of the second and the fourth quadrant gives the macroeconomic totals of consumption, investment, government expenditures and in case of an open economy also of exports to the RoW. Summation along the rows of the third and the fourth quadrant gives the totals for the gross domestic product and in case of an open economy also of imports from the RoW. Reorganising the row and column totals of the IOT produces the well-known macroeconomic accounting identity for the gross domestic product (GDP): Y = C + I + G + E−M

(2.1)

With (2.1), it becomes clear that an IOT essentially represents an industry-by-industry disaggregation of the accounting identity for gross regional or gross national domestic product. An IOT offers a series of interesting possibilities for descriptive research at the industry level. Taking percentages along the upper rows of an IOT, for instance,

2.1 Single-region IO Tables and Their Descriptive Power

7

enables you to make comparative analyses of the sales structures of various industries, while the lower rows of an IOT show the contributions of the various industries to total wage and capital income, and thus to GDP. Taking percentages along the first columns of an IOT enables you to analyse the differences in cost structures of various industries, while taking percentages along the last columns of an IOT allows for a comparative analysis of the purchase structures of the various categories of the final demand.

2.2 Mathematics Versus Economics of the Closed Economy IO Model The main use of IO tables, however, is to provide the data to build IO models; the first of which was formulated by Wassily Leontief (1941), who won the 1972 Nobel Prize in economics for the development of IO analysis. The economics of the basic, closed economy IO model, without imports and exports, may be complicated, and its mathematics is simple. It consists of only two equations. The first states that the production by industry is determined by the demand for its outputs, i.e. by the row totals of the matrices with intermediate and final demand:   zi j + yiq , ∀i, or in matrix notation: x = Zi + Yi = Zi + y (2.2) xi = j

q

The second equations state that the demand for intermediate and primary inputs is proportionally dependent on the size of total output: z i j = ai j x j , ∀i, j, or in matrix notation: Zi = Ax

(2.3a)

v pj = c pj x j , ∀ p, j, or in matrix notation: Vi = Cx

(2.3b)

This second assumption implies that economies of scale and substitution between inputs are absent. Instead, all inputs are assumed to be pure complements of one another. When only one single IOT is available, point estimates of the intermediate and primary input coefficients, aij and cpj , are made by simply dividing the cells of the columns with intermediate and primary inputs by their overall column total, i.e. by total production. Thus, A = Zˆx−1 and C = Vˆx−1 , which imply that i A + i C = i , i.e. the overall column total of the input coefficients by purchasing industry equals one. Only in case of a closed economy, the intermediate input coefficients may be called technical coefficients. In case of an open economy, however, the intermediate input coefficients equal the product of self-sufficiency trade coefficients and the above

8

2 Basic, Demand-Driven IO Quantity Models

·r defined technical coefficients, i.e. for any region or country r they equal airrj = m rr i j ai j , as will be further explained in the next section. Finally, note the power of (2.3b) in empirical applications. Instead of primary input coefficients, any other type of input or output that is technically linked to the production level by industry may be modelled in the same way. The impact variable vpj may thus equally well represent employment, CO2 emissions, energy use or water use of industry j, in which case the technical coefficients cpj will represent the employment, CO2 emissions, energy use or water use of industry j per unit of the output of industry j. The mathematical solution of the basic IO model is also simple: (2.3a) is substituted into (2.2) and then transferred from its right-hand side (RHS) to its left-hand side (LHS), after which (2.2) is pre-multiplied with the so-called Leontief-inverse, L = (I − A)−1 . This gives the following solution for total output by industry:

xi ∈ x = (I − A)−1 y = Ly

(2.4)

The subsequent substitution of (2.4) into (2.3a) and (2.3b) gives the solution for the matrices with intermediate and primary inputs: z i j ∈ Z = ALˆy and v pj ∈ V = CLˆy

(2.5)

This closes the mathematics of the IO model.1 The economic interpretation and practical application of (2.4) and (2.5) are straightforward. These equations have the general structure of the solution of any model: Endogenous variable A = model X  s A multiplier of B * exogenous variable B. Whenever that information is clear from the context at hand, the exogenous variable B and the type of model X do not need to be mentioned explicitly. In our case, it is most often not mentioned that the multipliers need to be applied to exogenous final demand nor that they are derived from an IO model. When value added is chosen as the impact variable of interest, the matrix with ci li j ∈ cˆ L contains the disaggregate income multipliers, indicating the value added of sector i embodied in (i.e. both directly and indirectly needed to produce) one unit of the final output of industry j. The column sums of this multiplier matrix,   i ci li j ∈ c L, subsequently, contain the aggregate income multipliers indicating the value added in the whole economy embodied in one unit of exogenous final demand of industry j. Employment, energy use, CO2 emission, etc., multipliers may be calculated analogously. Note that the total of all primary input multipliers equals one, as i C L = i (I − A)(I − A)−1 = i , which means that the value-added multipliers equal one in case 1 If

you have a problem with the interpretation of the matrix algebra of the above equations, please consult Miller and Blair (2009, Appendix A). If you want to calculate multipliers or any kind of impacts with several kinds of IO models, you may use the InterRegional Input–Output Software package IRIOS, which is downloadable at: https://www.rug.nl/research/reg/research/irios/ irios-download?lang=en (Stelder et al. 2000).

2.2 Mathematics Versus Economics of the Closed Economy IO Model

9

of a closed economy. For value added, it is, therefore, more informative to look that the direct and indirect income per unit of direct income embodied in the final demandof industry  j. We call this the standardized or normalized multiplier, which equals i c pi li j c pj ∈ cp L cˆ −1 p . Normalized multipliers typically have values of 1.1 to 2.2. Larger and more closed economies with smaller imports leakages tend to have the larger multipliers, while industries that are part of tightly interwoven local industrial complexes also tend to have the larger multipliers. Normalized multipliers are also very useful when the impact variable has a nonmonetary value. In those cases, ordinary multipliers are numbers with a dimension, such as the number of direct and indirect jobs per unit of the final demand in euros or the tons of directly and indirectly emitted CO2 per unit of final demand in dollars. These ordinary multipliers will inconveniently change over time, due to both price inflation and real labour productivity growth or real CO2 emission efficiency increases, in the case of ordinary employment or ordinary CO2 multipliers, respectively. Normalized multipliers, however, are dimensionless numbers and will therefore be relatively stable over time. They signify, for instance, the number of direct and indirect jobs per direct job embodied in the final output of industry j or the amount of direct and indirect tons of CO2 emitted per ton of CO2 directly embodied in the final output of industry j. Normalized multipliers have been used in a tremendous amount of impact analyses done with the single-region IO models (see Oosterhaven et al. 2019, for an overview). As the economics of the basic IO model is more complex than the mathematics, a further clarification is given in Fig. 2.2, which shows the economic causality of the model. The size of final demand y is exogenous, i.e. no arrows are coming in. That is, its size needs to be determined outside the IO model. Both the level and any change in the level of y then endogenously, within the model, lead to an equally large level or change in total output of I y, called the direct effect or direct impact of that change, as indicated by the arrow with the unity matrix I that leaving the box with exogenous final demand. This direct effect on total output x subsequently needs A times I y of intermediate inputs and C times I y of primary inputs, as indicated by the arrows accompanied by the matrices A and C in Fig. 2.2. The change in primary inputs leads to no further changes in the basic IO model, as indicated by the absence of outgoing arrows from the box with primary inputs. The change in intermediate inputs, however, leads to a further effect on total output, as these inputs need to be produced, which leads to the first round indirect effect of A y on total output. This

Final demand

I

C

Total output

A

I

Intermediate inputs Fig. 2.2 Causal structure of the basic IO quantity model

Primary inputs

10

2 Basic, Demand-Driven IO Quantity Models

middle circle of arrows in Fig. 2.2 goes on and on, leading to increasingly higher round indirect effects of A2 y + A3 y + A4 y + · · · on total output. In this way, the total cumulative effect on the production by industry may also be derived by means of: x = (I + A + A2 + A3 + A4 + · · · )y = (I − A)−1 y = Ly

(2.6)

A sufficient condition for this Taylor expansion of the Leontief-inverse to converge is that all column sums of A are smaller than one (Miller and Blair 2009, p. 33). Note the similarity of this matrix convergence condition with the condition under which the simply algebraic expansion (1 + a + a 2 + a 3 + · · · ) converges to (1 − a)−1 , namely a < 1. Since i C + i A = i , the sufficient condition for the Taylor expansion to converge is satisfied whenever the column sums of the primary input matrix are positive, i.e. whenever gross value added in market prices (plus the external imports in case of an open economy) is strictly positive for all industries. Although the above economic explanation of the equilibrium process of the Leontief model is offered by almost all IO texts, it needs to be emphasized that Eqs. 2.2, 2.3a and 2.3b neither specify the length nor the nature of the equilibrium process. The IO model is a purely comparative static model. When firms correctly predict and anticipate future changes in demand, adaptation may be quite fast. Most IO applications, however, work with year-to-year changes. From Fig. 2.2, two more things become clear. First, it is the demand that drives the model, while prices do not play a role. Second, the absence of price effects means that supply does not play an active role either. Its role is entirely passive: it follows any change in demand. This is why this model is further defined by labelling it the demand-driven IO quantity model. Demand is met without any restriction on the supply side, i.e. there are no capacity constraints nor shortages of any kind. Hence, by explicitly assuming that demand is always fully met, it is implicitly assumed that the supply of primary and intermediate inputs is perfectly price elastic. One important implication of this assumption is that the IO model will produce an overestimation of the production and employment effects of any increase in final demand whenever an economy is close to the top of its business cycle. Finally, consider the implied behaviour of industry j. The most general production function assumes heterogenous inputs and heterogenous outputs, as measured in column j and row j of an IOT. The basic IO model simplifies this by assuming that the outputs constitute a single homogenous product j, while the heterogeneous intermediate inputs i and primary inputs p are combined according to the following Walras–Leontief production function:   x j = min (z i j ai j , ∀i; v pj c pj , ∀ p)

(2.7)

Under full competition (i.e. at given market prices),  assuming  (2.7) for firms in industry j implies that maximizing profits ( p j x j − i pi z i j − p p p v pj ) is achieved by minimizing cost, which results in using the multiple inputs in the fixed proportions defined in (2.3a) and (2.3b). Under full competition, industry j will thus have a

2.2 Mathematics Versus Economics of the Closed Economy IO Model

11

perfectly elastic supply of its single homogenous output and a perfectly inelastic demand for its heterogenous intermediate and primary inputs (Oosterhaven 1996).

2.3 Open Economy Interregional and Multi-regional IO Models 2.3.1 Distinguishing Technical and Trade Origin Coefficients The mathematics of the IO model does not change when an open interregional or international economy is considered instead of a single, closed regional or national economy. The economic interpretation of the interregionally extended model, however, becomes more convoluted, as do the data required to construct such a model. Walter Isard (1951), the founder of the Regional Science Association, specified the “ideal” interregional input–output table (IRIOT) on which such an extension of the basic IO model might be based (see Fig. 2.3). Its first and main quadrant again contains the intermediate output of the industries of the interregional economy at hand. However, now, not only the intra-regional sales of intermediate outputs are part of this quadrant, but also the interregional exports of intermediate outputs to all included regions. The typical element of this matrix z ri js ∈ Zr s , with r and s = 1, …, R, indicates the sales of industry i in region r to industry j in region s. Intermediate demand

Final demand

Region 1

Region s

Region R

Region 1

…

Region R

Region 1

Z11

…

Z1R

F11

…

Region r

…

Zrs

…

…

Region R RoW imports Value added Total

ZR1

…

ZRR

…

Zms

V1 x1´

… xs´

Total

F1R

RoW exports e1

x1

Frs

…

er

xr

FR1

…

FRR

eR

xR

…

…

Fms

…

VR xR´

Y1 C I1 G1

… …

YR C IR GR

1

R

Transit

Mfor

0 Efor

Ynat

r s ∈ Fr s = IQFig. 2.3 “Ideal” interregional input–output table Legend Additional to Fig. 2.1: f iq matrix with final demand of type q of region s for products of industry i in region r, eir ∈ er = ms = II-matrix with foreign imports of I-column with foreign exports of industry i in r, z ims j ∈ Z ms ms intermediate inputs, and f iq ∈ F = IQ-matrix with foreign imports of final inputs of products of industry i for final demand of type q in region s

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2 Basic, Demand-Driven IO Quantity Models

The typical element of the second quadrant of the IRIOT, f iqr s ∈ Fr s , has a comparable interpretation, but now the second quadrant explicitly also contains eir ∈ er , ∀r, i.e. sub-columns with the combined export of both intermediate and final outputs to regions or nations external to the interregional economy at hand. This is done to clearly separate the local final demand of each region from the demand from outside the interregional economy at hand. The third and fourth quadrants have the same interpretation as in Fig. 2.1, but now mr matrices with intermediate imports from the RoW, z imr j ∈ Z , have explicitly been added to the third quadrant, while matrices with imports of final products from the RoW, f iqmr ∈ Fmr , have explicitly been added to the fourth quadrant. Again the last row and column totals contain the macroeconomic totals of the now R endogenous  The overall  sum of the column totals of the second and fourth  regions. quadrant ( r C r + r I r + r G r + E for ) again equals the overall sum of the row totals of the third and the fourth quadrant (Y nat + M for ), as total input equals total output for each regional industry (wherein the superscript for indicates foreign, while nat stands for nation). Although not directly clear from Fig. 2.3, a rearrangement of its elements produces the macroeconomic accounting identities of each of the R regions included, but now with much more detail than in Fig. 2.1: ⎛ Y r = i Vr i = C r + I r + G r + ⎝ ⎛ −⎝

 s=r

 s=r

i Zsr i + i Zmr i +



i Zr s i +



⎞ r i Fr s i + i e ⎠

s=r

⎞

i Fsr i + i Fmr i⎠ = C r + I r + G r + E r −M r

s=r

(2.8) The added detail, of course, relates to regional exports (i.e. the first term between brackets) and regional imports (i.e. the second term between brackets) of both intermediate and final outputs. Figure 2.3 represents the ideal IRIOT, but this amount of statistical detail is unavailable in practice. This is why a series of less data demanding interregional IO accounting frameworks has been developed (see Batten and Boyce 1986, for an overview). The most commonly used of these is the multi-regional input–output table (MRIOT, Chenery 1953; Moses 1955). A MRIOT is a straightforward aggregation of an IRIOT. Instead of the full block columns of Fig. 2.3, with intermediate and final use distinguished by region of origin, a MRIOT only contains  the vertical aggregation of their sub-matrices, i.e. Z·s =  rs ms ·s and F = r Fr s + Fms , ∀s. This type of information on the products r Z +Z needed by firms, consumers, investors and government agencies regardless of their spatial origin is relatively easily available from statistical surveys. To substitute for the lost information on the spatial origin of the intermediate and final inputs, a MRIOT additionally contains the horizontal aggregation of all bi-regional trade over

2.3 Open Economy Interregional and Multi-regional IO Models

13

the industries and the final demand categories within the region of destination, i.e. tir s ∈ tr s = Zr s i + Fr s i , ∀r, s. An IO model can be based on both sets of data; written with all sub-matrices of Fig. 2.3 separately, it reads as follows in case of the interregional IO model: ⎡

⎤ ⎡ 11 x1 A ⎢ .. ⎥ ⎢ .. x=⎣ . ⎦=⎣ . xR

A R1

⎤⎡ 1 ⎤ ⎡ 11 . . . A1R x F .. .. ⎥⎢ .. ⎥ + ⎢ .. . . ⎦⎣ . ⎦ ⎣ . . . . AR R xR F R1

⎤⎡ ⎤ ⎡ 1 ⎤ . . . F1R i e .. .. ⎥ ⎢ .. ⎥ + ⎢ .. ⎥ . . ⎦⎣.⎦ ⎣ . ⎦ . . . FR R eR i

= Ax + Fi + e

(2.9)

When only one single IRIOT is available, point estimates of the sub-matrices with intermediate input coefficients may be calculated directly column-wise from Fig. 2.3 by means of Ar s = Zr s (ˆxs )−1 . The multi-regional IO model has the same set-up and answers exactly the same set of research questions. It reads as follows: ⎡

⎤ ⎡ 1 ⎤ ⎡ 11 ·1 ˆ 1R A·R ˆ F ... m x m ⎥ ⎢ .. ⎥ ⎢ .. .. .. ⎦⎣ . ⎦ + ⎣ . . . R1 ·1 R R ·R ˆ A ... m ˆ R1 F·1 ˆ A m m xR ⎡ 1⎤ e ⎢ .. ⎥ + ⎣ . ⎦ = Ax + F i + e,

ˆ 11 A·1 m ⎢ .. x=⎣ .

e

⎤⎡ ⎤ ˆ 1R F·R ... m i ⎥⎢ .. ⎥ .. .. ⎦⎣ . ⎦ . . R R ·R ˆ F ... m i (2.10)

R

Note that the summation dots in (2.10) include imports from the RoW, which is why the input coefficients of the sub-matrices A·r may be called technical coefficients. They may be calculated directly from a MRIOT column-by-column by means of A·s = Z·s (ˆxs )−1 , while the diagonal sub-matrices with intra-regional purchase coefˆ r s (with r = s), may ˆ rr , and those with interregional import coefficients m ficients m rs ˆ r s , ∀r, s. also be calculated directly from a MRIOT by means of m i = tir s /ti·s ∈ m The position of the summation dot is crucial. It sums the overall regions of origin, which is why these two types of trade coefficients may best be labelled as trade origin ratios.2 The core difference between the interregional and the multi-regional IO model is found in the implicit assumptions about the trade origin ratios in both models: interregional IO model: airjs = m ri js ai·sj , multi-regional IO model: airjs = m ri·s ai·sj (2.11) 2 In the IO literature, these trade origin ratios are often referred to as column trade coefficients. Export

coefficients or trade destination ratios or row trade coefficients are used in the row coefficient IO model, which is shown to perform worse than the standard model (Polenske 1970) and has not been used since. See Oosterhaven (1984) for other members of the family of square interregional IO tables and models.

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Equation 2.11 explicitly shows that all intermediate input coefficients in an open economy IO model, in fact, consist of the product of a technical coefficient and a trade coefficient. The difference between the two models is that the interregional model assumes that each cell of an IRIOT has its own fixed trade origin ratio, whereas the multi-regional model assumes that all cells along each sub-row of an IRIOT have one and the same fixed trade origin ratio. The cell-specific interregional IO assumption better fits with the situation in which say agriculture in each region produces its own unique product, in which case the trade origin ratios m ri js may be assumed to be stable for technical reasons, as in the closed economy case of Eq. 2.7. The sub-row-specific multi-regional IO assumption better fits with the situation in which say again agriculture in each region produces about the same product mix or, alternatively, when agriculture in each region produces a close substitute. In these cases, one may assume the trade origin ratios m ri·s to be stable, as long as the relative prices of the products of different regions are more or less stable. In most multi-regional IOTs, however, the multi-regional trade ratio assumption is hidden, as almost all MRIOTs are published in an IRIOT format (see Sect. 3.3, for the reason why this is common practice). The mathematical solution of both models is derived in the same way as in the single-region case. The matrix with endogenous intermediate inputs is transferred from the RHS to the LHS of (2.9) and (2.10), whereupon both sides are pre-multiplied with the appropriate inverse. The solution of the interregional IO model then simply reads as follows: x = (I − A)−1 (Fi + e) = L∗ (Fi + e)

(2.12)

where airjs ∈ A and f iqr s ∈ F are equal to the corresponding block matrices in (2.9), and where L* indicates the interregional Leontief-inverse. The liss∗ j from the submatrices on its diagonal blocks indicate the intra-regional impact of exogenous final demand for the products from industry j in s on the production of industry i in the same region s, whereas the lirjs∗ from the sub-matrices on its off-diagonal blocks indicate the interregional spillover effect of the final demand for the products from industry j in s on the production of industry i in a different region r. In the same way, the solution of the multi-regional IO model may be derived as follows: 



x = (I − M ⊗ At )−1 (M ⊗ Ft i + e) 



(2.13)

where m ri·s ai·sj ∈ M ⊗ At and m ri·s f iq·s ∈ M ⊗ Ft equal the corresponding block matrices in (2.10), and where t stands for technical to indicate that the products at hand come from all over the world, while ⊗ indicates the Hadamard (cell-by-cell) matrix product. Note that (2.10) and (2.13) show that the multi-regional trade ratio assumption not only applies to intermediate demand, but also to local final demand. In case of international IOTs, it is shown that the trade ratios for local final demand significantly differ from those for intermediate demand (Dietzenbacher et al. 2013).

2.3 Open Economy Interregional and Multi-regional IO Models

15

The same is most likely true for interregional IOTs, but has not been reported in the literature, as such detailed internal trade data are lacking for almost all countries. For the base year IRIOT and MRIOT from which the model coefficients of (2.9) and (2.10) may be calculated, the two IO model solutions (2.12) and (2.13) will produce exactly the same endogenous column with total output per regional industry xir ∈ x. However, for any other year than the base year or for any non-proportional exogenous final demand impulse, both models will produce a different outcome. This difference is caused by the aggregation error that is made with the multi-regional IO model compared to the “ideal” interregional IO model. Using hypothetical IRIOTs, as real data are lacking, Vali (1988) reports mean average percentage errors (MAPEs) of about 13% at the aggregate industry level, 4% at the aggregate regional level and 0.4% at the national level. Vali (1993), additionally, reports no systematic under or overestimations, which was not to be expected, but does report average overestimations of aggregate trade flows of 20–30% and average underestimations of these flows of as much as 37–50%. To enhance the understanding of the working of the interregional IO model, Fig. 2.4 shows how two open economy single-region IO models are joined in one interregional IO model. The boxes and arrows with solid lines reproduce Fig. 2.2 for region r and region s, respectively. The boxes and arrows with dotted lines show the changes necessary to obtain the interregional model. We only discuss region r, as the changes for s are identical. The single difference for region r is that its exports of intermediate outputs to region s, Zr s i, which are exogenous in the single-region model, become endogenously determined by the production levels of region s in the interregional IO model, i.e. by Zr s i = Ar s xs , as indicated by the upper dotted box with dotted arrows. This means that the exogenous final demand of the interregional model is smaller than that of the single-region model, as indicated in the upper left solid box of Fig. 2.4. To see what this implies, remember that reality does not change. Only the way in which reality is modelled changes. Thus, to get the same endogenous level of output yr = f r +

Zrs i

ys = f s + Zrs

Zrr

Ars xs

xr Asr Vr

Zsr i

Zss

Zsr Vs

Fig. 2.4 Causal structure of the interregional IO model extension Legend y = vector with exogenous final demand of the single-region IO model, f = vector with exogenous final demand of interregional IO model, Zrs = interindustry matrix with intermediate exports from region r to region s, x = vector with total output by sector, and V = matrix with value added by type, by sector

16

2 Basic, Demand-Driven IO Quantity Models

in region r, the intra-regional part of the extended Leontief-inverse Lrr ∗ must become sufficiently larger to compensate for the smaller exogenous final demand. How is this possible? The answer is given by the circle of dotted arrows in the middle of Fig. 2.4. In the single-region model, the endogenous intermediate imports of region r, i.e. Zsr i, do not lead to any further endogenous effects, but in the interregional model they do. There, they constitute the endogenous intermediate exports of region s, which need to be produced there. This is called an interregional spillover effect. This production effect in region s in turn requires endogenous intermediate imports from r, i.e. Zr s i. This second, reverse, interregional spillover effect rounds the circle in the middle of Fig. 2.4. Together, these two spillover effects create what is called an interregional feedback effect. Following this circle shows that the size of the feedback effect in the two-region case can be determined as follows: interregional feedbackrr = interreg. spilloverr s ∗ intra-regional multiplierss ∗ interreg. spilloversr . See Oosterhaven and Hewings (2014, p. 886) for the proof of this two-region formula. Returning to the multiple region case of Eq. 2.12, the size of the interregional spillover effects of region s on say aggregate employment in region r can simply found by calculating the aggregate interregional employment multipliers  be r r s∗ c l ∈ (cr ) Lr s∗ . The size of the interregional feedback effects may, subi i ij sequently, be calculated by taking the difference between the intra-regional employment multipliers from the interregionally extended IO model and those from the single-region IO model, i.e. by calculating (cr ) [ Lrr ∗ − Lrr ], where the absence of * indicates that Lrr originates from the single-region or single-nation IO model.

2.3.2 Underestimation of Interregional Spillovers and Feedbacks Empirically, the size of these interregional feedback effects was extensively studied in the 1970s. Miller and Blair (1985, p. 127) concluded in an overview of the literature that they could be disregarded, as they only added between 1 and 2% to the value of intra-regional multipliers when moving from a single-region model to a multi-region model. However, earlier on, Yamada and Ihara (1969) already reported much larger errors of neglecting interregional feedbacks in case of Japan, while Greytak (1970) did the same in case of the USA. Unfortunately, the denominator of the percentages reported always included the direct production effect of one unit of final demand. For this direct effect of 1.00, however, one does not need a model at all. A model is only needed to estimate the indirect effects, which is why the error measure should only have the indirect effect in its denominator. Consequently, most errors percentages reported in the literature should be multiplied with a factor of 2.00–3.00, assuming a single-region multiplier of, respectively, 2.00 or 1.50.

2.3 Open Economy Interregional and Multi-regional IO Models

17

Comparing only the indirect effects, Oosterhaven (1981) found an underestimation of the regional indirect income effect of only 1.1% for the rural, peripheral Northern Netherlands and found a 3.4% underestimation for the urbanized greater Rotterdam area in the economic core of the Netherlands. When Type II income multipliers with endogenous consumption expenditures were compared, the underestimation increased to 3.1% in case of the Northern Netherlands and to as much as 6.6% in the case of the greater Rotterdam area. The reason for these larger interregional feedback effects was the inclusion of interregional commuting and interregional shopping in the Type II input–output model. Recently, using intercountry supply-use tables at the global level (see Chap. 3), Termursho (2018) reported a weighted average error of neglecting spillovers and feedbacks as large as 7.9% of the global output multiplier of 1.9 in 1995, increasing to 11.5% in 2008 and decreasing to 9.8% in 2009, due to the 2008–2009 global economic decline. Note that the relevant error in only the indirect part of the global multiplier is about two times larger than the percentages reported by Termursho. The second difference between the single-region model and the multi-region model is hardly discussed, but is at least as important. It appears in the interregional spillover effects of the own final demand f s on say the income vr of a different region. In the single-region model, the aggregate spillover effects equal (cr ) Ar s Lss , whereas they equal (cr ) Lrr ∗ Ar s Lss∗ in the two-region case (see Oosterhaven and Hewings 2014). Hence, not only the intra-regional impacts but also the interregional spillovers of an exogenous impulse are larger when estimated with a multi-region model compared to single-region model. Bouwmeester et al. (2014) estimated the income and CO2 effects of the exports to third countries for the 27 members of the European Union (EU), both with 27 separate national IO models and with a single consolidated IO model for the EU27 as a whole. They find an average first round intra-EU income spillover to the rest of the EU27 of 7.7%, when calculated with the 27 single-country models. The additional higherorder intra-EU spillovers, as calculated with the consolidated EU27 model, appeared to be as large as an additional 10.7% of the domestic direct and indirect income effect. Note that both percentages represent an underestimation of the importance of intraEU spillovers as their denominator includes the direct domestic income effect for which no model is needed to estimate it. In sum, the underestimation of interregional spillover effects as well as that of interregional feedback effects with a single-region or a single-nation IO model appears to be much more serious than suggested in the early literature.

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References Batten DF, Boyce DE (1986) Spatial interaction, transportation and interregional commodity flow models. In: Mills ES, Nijkamp P (eds) Handbook in Urban and regional economics, vol 1. North Holland, Amsterdam Bouwmeester MC, Oosterhaven J, Rueda-Cantuche JM (2014) A new SUT consolidation method tested by a decomposition of value added and CO2 embodied in EU27 exports. Econ Syst Res 26:511–541 Chenery HB (1953) Regional analysis. In: Clark PG, Vera VC (eds) Chenery HB. The structure and growth of the Italian economy. U.S. Mutual Security Agency, Rome Dietzenbacher E, Los B, Stehrer R, Timmer M, de Vries G (2013) The construction of world input-output tables in the WIOD project. Econ Syst Res 25:71–98 Greytak D (1970) Regional impact of interregional trade in input-output analysis. Pap Reg Sci Assoc 25:203–217 Isard W (1951) Interregional and regional input-output analysis, a model of the space economy. Rev Econ Stat 33:318–328 Leontief WW (1941) The structure of the American economy, 1919–1929: an empirical application of equilibrium analysis. Cambridge University Press, Cambridge Miller RE, Blair PD (1985) Input-output analysis: foundations and extensions. Prentice Hall, Englewood Cliffs, New Jersey Miller RE, Blair PD (2009) Input-output analysis: foundations and extensions, 2nd edn. Cambridge University Press, Cambridge Moses LN (1955) The stability of interregional trading pattern and input-output analysis. Am Econ Rev 45:803–832 Oosterhaven J (1981) Interregional input-output analysis and Dutch regional policy problems. Gower Publishing, Aldershot-Hampshire Oosterhaven J (1984) A family of square and rectangular interregional input-output tables and models. Reg Sci Urban Econ 14:565–582 Oosterhaven J (1996) Leontief versus Ghoshian price and quantity models. South Econ J 62:750–759 Oosterhaven J, Hewings GJD (2014) Interregional input-output models. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer-Verlag, Berlin/Heidenberg Oosterhaven J, Polenske KR, Hewings GJD (2019) Modern regional input-output and impact analysis. In: Capello R, Nijkamp P (eds) Handbook of regional growth and development theories: revised and extended, 2nd edn. Edward Elgar, Cheltenham Polenske KR (1970) An empirical test of interregional input-output models: estimate of 1963 Japanese production. Am Econ Rev 60:76–82 Stelder TM, Oosterhaven J, Eding GJ (2000) IRIOS: an interregional input-output software approach to generalised input-output endogenisation, linkage, multiplier and impact analysis. Paper 40th ERSA congress, Barcelona, August 2000, and 47th NARSC congress, Chicago, November 2000. https://www.rug.nl/research/reg/research/irios. Accessed 26 Aug 2019 Termursho U (2018) Intercountry feedback and spillover effects within the international supply and use framework: a Bayesian perspective. Econ Syst Res 30:337–358 Vali S (1988) Economic structure and errors in multiregional input-output model. Ric Econ 17:367– 390 Vali S (1993) Simulation evidence bearing on the structure of errors in MRIO analysis. Environ Plan A 25:159–178 Yamada H, Ihara T (1969) Input-output analysis of interregional repercussions. Pap Proc Third Far East Conf Reg Sci Assoc 3–31

Chapter 3

Data Construction: From IO Tables to Supply-Use Models

Keywords Location quotient methods · Cross-hauling · Cell-Corrected RAS · Bi-regional input–output table · Supply-use table · Product technology assumption · Industry sales structure assumption · Interregional supply-use model · International input–output tables

3.1 Construction of Regional IO Tables: Towards Cost-Effective Methods We start with a brief review of non-survey methods to estimate single-region IOTs and show that most of them minimize cross-hauling, i.e. they minimize the simultaneous import and export of comparable products, which leads to a systematic overestimation of all regional multipliers. Next, we discuss an easy to use non-survey method (CC-RAS) that avoids this problem and a semi-survey method (DE-BRIOT) that exploits the double-entry strength of a bi-regional IOT with the rest of a country when constructing a single-region IO table.

3.1.1 Most Non-Survey Methods Overestimate Intra-Regional Multipliers Depending on the amount of already available regional statistical data, surveys necessary to supplement the lacking data will be expensive or very expensive. This is why the search for non-survey construction methods started already early with Schaffer and Chu (1969).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_3

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3 Data Construction: From IO Tables to Supply-Use Models

The first generation of non-survey methods all start with the assumption that the unknown regional “technical” coefficients equal the corresponding national coefficients (see Miller and Blair 2009, Chap. 3). Since most of these methods were developed in the USA for the US regions, the rather small US foreign imports of that time were ignored. Doing this, implicitly assumes that, not only the regional real technical coefficients, but also the regional foreign import coefficients are equal to their national equivalents. In (3.1), these two base assumptions are shown together with the resulting, explicitly made assumption (consult Fig. 2.1 and 2.3 for the meaning of the symbols): mn mn n ˆ i∗rj = ai∗nj = z i∗nj /x nj aˆ i·rj = ai·nj = z i·nj /x nj and mˆ imr j = m i j = z i j /x j ⇒ a

(3.1)

where, additionally, ˆ = estimate, n = country at hand, m = foreign, · = summation over all regions in the whole world, and ∗ = summation over all regions in the country at hand. Multiplication of the coefficients of (3.1) with regional output per industry results in the desired estimate of the matrix with intermediate inputs of domestic products z i∗rj ∈ Z∗r . Equivalent assumptions are usually made to estimate the delivery of domestic products to local final demand f iq∗r ∈ F∗r .1 The most frequently applied second non-survey assumption uses the well-known location quotient (LQ) to estimate regional self-sufficiency ratios, also known as regional purchase coefficients (RPCs)2 :   r r xi /x· LQri if LQri < 1 r , ∀ j, with LQi = = r 1 if LQi ≥ 1 xin /x·n 

mˆ rr ij

(3.2)

The LQ indicates whether industry i is regionally overrepresented (LQ > 1) or underrepresented (LQ < 1). Note the asymmetry in the use of the LQ in (3.2). The amount of under-representation does matter, whereas the amount of overrepresentation does not. If an industry is absent in a region (LQ = 0), it is of course assumed that all inputs are imported, i.e. that self-sufficiency is zero. If the relative presence of a regional industry becomes larger, it is assumed that the self-sufficiency ratio increases proportionally, while the import ratios decrease proportionally. However, if the amount of overrepresentation (LQ > 1) increases, it does not have a further impact on the amount of imports. In that case, imports are always assumed to be zero. Equivalent assumptions are usually again made for local final demand. The core of the problem of using (3.2) is that the LQ represents a good approximation of the net exports of industry i, but not of its gross exports. Consider the equality of total regional supply and total regional demand of product i in region r: 1 If

countries only have statistical information on total employment by regional industry, regional output may be replaced with regional employment times national output per unit of national employment by industry. Using employment this way implies making a strong additional assumption, namely that regional labour productivity by industry equals its national equivalent. 2 Stevens and Trainer (1980), who coined this term, show how RPCs may be estimated econometrically by means of secondary data. Stevens et al. (1989) show that this results in more reliable RPCs than those estimated by LQ-type non-survey methods.

3.1 Construction of Regional IO Tables: Towards Cost-Effective …

xir + m ri = dir + eir ⇒ xir − dir = eir − m ri

21

(3.3)

wherein dir = total local intermediate plus local final demand for product i. Note that the production surplus over local demand, xir −dir , and thus also net exports, eir −m ri , is nonlinearly proportional to the LQ if the local demand for product i is proportional to the size of the region.3 In that case, if LQ > 1, Eq. (3.2) sets gross imports equal to zero and gross exports equal to net exports. However, in reality, gross exports will be larger than net exports, and imports will not be zero because of cross-hauling. A comparable conclusion holds if LQ < 1. In that case, (3.2) sets gross exports equal to zero and gross imports equal to net imports, but both will again be larger because of cross-hauling. Cross-hauling of the same product into - and out of - a region will, especially, be large for developed economies that produce and consume many close substitutes (e.g. different brands of the same product). Minimizing cross-hauling in this way results in a structural underestimation of both imports and exports and a subsequent overestimation of intra-regional transactions, and thus, of all regional multipliers. Willis (1987), while surveying the literature and adding own results for Staffordshire and Wales, reports the average multiplier overestimations of above 20%, which represents a misleadingly low percentage as it includes the direct effect for which no IO model would be needed. With reported average regional multipliers of about 1.5, a correct measure would report these overestimations to be above 60%. Moreover, rank correlations between survey and non-survey multipliers were reported to be as low as 0.10–0.70. Hence, almost any non-biased estimate of gross imports and gross exports will produce more reliable multipliers than applying the LQ method. Comparable conclusions hold for the purchases only LQ, the cross-industry quotient (CIQ), the semi-logarithmic quotient, the supply-demand pool and the commodity trade balance method, as they all share the asymmetric nature of the LQ method [see Round (1983) and Miller and Blair (2009, Chap. 8), for a further evaluation of the first generation non-survey methods]. The second generation non-survey methods more or less starts with Fleg’s et al. (1995) adaptation of the cross-industry quotient (CIQ):    δ  FLQri j = λr ∗ CIQri j = log2 1 + x·r /x·n ∗ LQri /LQrj

(3.4)

Note that the CIQ takes the ratio of the LQ of the selling industry i to that of the purchasing industry j and is thus different at the cell level of the IOT, whereas the ordinary LQ is uniformly applied to entire rows of the IOT. λr corrects the CIQ upwards with the size of the region. Since the FLQ replaces the LQ in (3.2), it inherits the asymmetric nature of LQ method: resulting in larger imports when FLQ declines below unity, but not resulting in smaller imports when FLQ increases above unity. Hence, the FLQ adds cross-hauling in case of industries that are regionally poorly represented, whereas it only partially adds cross-hauling for industries that 3 The

association between the two measures would be linear if the LQ would be measured in an additive way as ALQri = xir /x·r − xin /x·n instead of the standard multiplicative definition [see Hoen and Oosterhaven (2006), for more reasons to use the additive definition].

22

3 Data Construction: From IO Tables to Supply-Use Models

are regionally strongly represented. As expected, when tested on a Finnish survey regional IOT, the FLQ with δ = 0.3 in (3.4) is reported to outperform both the LQ and the CIQ (Thomo 2004). More recently, Kronenberg’s (2009) Cross-Hauling Adjusted Regionalization Method (CHARM) claims to explicitly take account of cross-hauling qir , which is assumed to increase with the heterogeneity hi of the products traded. His combined core formulas equal



qir = (eir + m ri ) − eir − m ri = ttir − bir = h i (xir + dir )

(3.5)

wherein tt = total trade volume and b = trade balance. His core assumption is that heterogeneity h i is product-specific and invariant to the region at hand. Consequently, he assumes that 0 ≤ h ri = h in ≤ ∞, where h in is measured by means of national IO data. Többen and Kronenberg (2015), however, show that the CHARM formula only allocates international cross-hauling to the regional level, but still assumes interregional cross-hauling to be zero. Not surprisingly, Flegg et al. (2015), when testing against a survey IOT for the Chinese province of Hubei, found that CHARM still systematically overestimates intra-regional transactions and regional multipliers. Even with an improved CHARM formula, Többen and Kronenberg (2015) come to the same conclusion.4 The last non-survey method we discuss is RAS. This is a bi-proportional, iterative matrix balancing technique, which sequentially scales and rescales the rows and columns of a base IOT until they equal the rows and columns totals (called margins) of the target IOT. RAS was initially developed to update an older national IOT such that it becomes consistent with more recent national margins (Stone 1961; Stone and Brown 1962). The product of the series of scalers for row i was denoted as ri ∈ rˆ , the product of the series of scalers for column j as s j ∈ sˆ and the initial matrix as A. The solution of the iterative scaling algorithm thus equals rˆ A sˆ, which explains the name of the method.5 Since RAS is very flexible, it may also be applied in situations wherein given regional margins are combined with either a national IOT or an IOT of a different region, from either the same year or a different year. Hewings (1977; Hewings and Janson 1980) experimented with different parent regional IOTs and with different regional margins and concluded that the errors made by choosing the “wrong” parent region were far less serious than the errors made by using the “wrong” margins. Using

4 In view of the poor performance of almost all these non-survey methods, we do not pay attention to

shortcut multiplier estimation methods that do not even use a non-survey IOT to calculate regional multipliers. See Burford and Katz (1981) for a typical shortcut method and Jensen and Hewings (1985) for a critical evaluation of a series of such methods. 5 RAS only works with semi-positive base matrices and semi-positive margins. When the base IOT also has negative cells, such as subsidies or negative stocks changes, which have to be updated or regionalized to become consistent with margins that may also be negative, the generalized RAS method (GRAS) has to be used (Junius and Oosterhaven 2003). See Termurshoev et al. (2013) for the algorithm.

3.1 Construction of Regional IO Tables: Towards Cost-Effective …

23

the “right” margins, however, requires the availability of a survey or at least a semisurvey regional IOT, and estimating the margins of such a table is precisely the problem that has to be solved. Hence, RAS only works well if that problem is solved beforehand.6 In practice, there will almost always be all kind of ad hoc, region-specific survey information that may be used to improve the outcomes of the above discussed nonsurvey methods. A systematic way to use this type of superior data is incorporated in the generation of regional input–output tables (GRIT) procedure [see West (1990), see also Lahr (1993)].

3.1.2 Non-Survey CC-RAS Method: Advantage of Using Multiple Comparable IOTs One way to solve the problem of estimating the internal margins of an IOT for a RAS procedure is to use the domestic import and export ratios of a comparable region. Nowadays with electronic access to all kind of data, a host of survey-based regional IOTs is readily available to estimate these unknown margins. But then, why would one only use these IOTs to estimate the unknown margins, why not also use them to improve the estimation of the unknown cells of the target IOT? The latter is exactly what the Cell-Corrected RAS method does (CC-RAS, Minguez et al. 2009). To understand how CC-RAS works, it is important to know that the iterative scaling solution of RAS can also be found by minimizing the information gain of the target IOT compared to the base IOT, subject to the margins of the target IOT (Bacharach 1970; Batten 1983, pp. 112–116): Minimize:



    z i j ln z i j /z ibj , subject to: z i j = z i·t and z i j = z ·t j

ij

j

(3.6)

i

where b = base matrix, t = target margins, and zij = matrix to be estimated. Note the nature of the information gain measure (Kullback 1959; Theil 1967). It minimizes the weighed logarithm of the relative (i.e. %) differences between of the two IOTs. In a typical non-survey construction situation, the target matrix will consist of the combination of the matrix with local intermediate demand, the matrix with local final demand, the column with domestic exports and the aggregate row or full matrix with domestic imports (see Fig. 2.1). The target row totals in that case equal the domestic sales of the regional industries followed by the regional total of all domestic imports (in case of an aggregate import row instead of a matrix). The target column totals 6 Unfortunately,

in the past, it has been assumed that these margins were known exactly when applying RAS, instead of having to be estimated by say LQ methods. As a consequence, it was unjustly reported that RAS outperformed several LQ methods (Czamanski and Malizia 1969; Sawyer and Miller 1983). RAS and LQ methods, however, serve different purposes and may thus not be compared one-to-one.

24

3 Data Construction: From IO Tables to Supply-Use Models

in that case equal the total use of domestically produced intermediate inputs by purchasing industry j, followed by the total use of domestically produced final inputs by purchasing type q and the regional total of all domestic exports. CC-RAS starts with calculating the errors εit j(b) made at the cell level of the IOT of region or year t when RAS is applied to the IOT of region or year b for all possible combinations of two survey-based IOTs that are considered to be comparable with the target IOT, followed by the calculation of the means μiεj and standard deviations σiεj of these errors: t (b) t (b) εi j = z it j /z i j , ∀t = b ⇒ μiεj =



T

  2

t (b) t (b) εi j /(T − 1) and σiεj =  εi j − μiεj /(T − 2) tb, t =b tb, t =b T 

(3.7)

where z it (b) j = estimate of the IOT of t made by applying (3.6) to the IOT of b with margins for t that are estimated by means of those of b (i.e. zˆ i·t (b) and zˆ ·t (b) j ), and T = number of comparable survey IOTs [see Oosterhaven and Escobedo-Cardeñoso (2011), for further details]. Consequently, there will be T values for each μiεj and σiεj , one for each target region or target year t. In the second stage of CC-RAS, the data from (3.7) are used to correct the projection of the IOT of t by means of the IOT of b by minimizing the weighted squared errors, subject to the estimated margins: Minimize:

 2   t (b)  t (b) t (b)  t (b) t (b) t (b) t (b) εi j z i j = zˆ i· and εi j z i j = zˆ · j εi j − μiεj /σiεj , subject to: ij

j

(3.8)

i

Note that the resulting optimal error corrections at the cell level for the target IOT of r (i.e. εit j(b) ) are crucially dependent upon the choice of the base IOT. The first application of CC-RAS was to test whether using a time series of national IOTs with CC-RAS would improve the traditional updates of IOTs made by applying RAS to the most recent survey IOT. In the case of the Netherlands, it was shown that CC-RAS clearly outperforms RAS in making projections of five years or more, which is the most relevant period in practical IO work (Minguez et al. 2009). However, when the large oil price hikes of 1973–74 and 1979–80 or the sharp oil price decline of 1985–86 had to be covered, RAS with the most recent IOT outperformed CC-RAS. In case of updating an IOT, the choice of the best base IOT is easy. That is, of course, the most recent survey IOT. Choosing the best base IOT in case of estimating a regional IOT is far more difficult, as space is two-dimensional, whereas time is one-dimensional. Moreover, time is uni-directional (from past to present), whereas space is bi-directional. However, the problem of choosing the best predictor in the regional case is not specific for CC-RAS. It also occurs when applying RAS as a non-survey method to estimate a regional IOT. Oosterhaven and Escobedo-Cardeñoso (2011) tested the performance of both RAS and CC-RAS by means of eleven semi-survey Spanish RIOTs. Even when with the best predicting region was chosen, RAS was reported to produce weighted average percentage errors (WAPEs) at the IO cell level between 20 and 40%, with outliers of

3.1 Construction of Regional IO Tables: Towards Cost-Effective …

25

about 50% for the Baleares Islands and the Madrid capital region, which both have a rather unique sector structure. When the fourth or fifth best base IOT was chosen, instead of the in practice unknown best base IOT, the WAPEs became about two times larger. Additionally, Oosterhaven and Escobedo-Cardeñoso (2011) report that CC-RAS with only the two best base IOTs has WAPEs that are between 50% and 80% smaller than those of RAS with the single best base IOT. The better performance of CC-RAS decreased when more next best base IOTs were added, but continued to outperform RAS until about the five best base IOTs were used. Adding more increasingly dissimilar IOTs, naturally, led to underperformance of CC-RAS compared to RAS with the single best base IOT, except for the Baleares and Madrid that are dissimilar from all other Spanish regions. A further advantage of CC-RAS is that selecting the, in practice unknown, first and second best base IOTs among a total of four to five base IOTS for CC-RAS is more likely than selecting the first or second best base region for RAS that only uses a single base IOT. Finally, note that the choice of the base IOT not only determines the size of the errors made in estimating the cell corrections of CC-RAS, but also the size of the errors made in estimating the margins of the target IOT, which according to Hewings represents the larger error. Hence, the only way to further improve the quality of the spatial projection of a regional IOT is by adding survey data on these margins; all of which are primarily determined by the domestic import and export ratios of the region at hand.

3.1.3 Semi-Survey DE-BRIOT Method: Advantage of Constructing Bi-Regional IO Tables With limited resources, the next question is what kind of additional trade information may most easily be derived from a limited survey among local industries or even only among local industry experts. The international tradition is to ask for domestic import ratios and regional purchase coefficients (RPCs) [see Miller and Blair (2009), for an overview, and Oosterhaven et al. (2019), especially for the USA]. Aside from tradition, this approach may be preferred for theoretical reasons, as it seems to better fit into the Leontief model, but it proved already early on to produce unsatisfactory results (Isard and Longford 1971, p. 121). The extensive experience in the construction of semi-survey regional IOTs in the Netherlands led to the conclusion that asking for domestic export ratios and regional sales coefficients (RSCs) produced higher response rates and higher quality data (Boomsma and Oosterhaven 1992). The reason is that firms, as a rule, are better informed about the spatial destination of most of their often few outputs than about the spatial origin of their often many inputs. This is even more the case, when firms sell and purchase through retail and wholesale channels. If they buy from wholesalers and, especially, if they buy from retailers, they have no idea about the primary spatial

26

3 Data Construction: From IO Tables to Supply-Use Models Intra- and interregional transactions

To region r

To region s

To nation

From region r

Zrr

Frr

Zrs

Frs

Zrn

Frn

From region s

Zsr

Fsr

Zss

Fss

Zsn

Fsn

From nation

Znr

Fnr

Zns

Fns

Znn

Fnn

Fig. 3.1 Components of the DE-BRIOT approach. Legend Z = matrix with intermediate demand, F = matrix with local final demand, r + s = n = nation at hand. The row totals equal domestic sales per industry, i.e. x − e, while the column totals equal the use of domestic inputs, i.e. x − v − m , per industry and per category of local final demand (see also Fig. 2.1)

origin of their inputs; whereas, they have a good idea about the final spatial destination of their outputs if they sell through wholesalers and, almost by definition, if they sell through retailers. In fact, one of the easiest questions for firms to answer is: what percentage of your output do you sell within your own region, what percentage in the Rest of the Country and what percentage abroad, given a pre-filled-in total of 100%? Having this type of survey sales data, however, requires a change in the set-up of the rest of the construction of a regional IOT. The most important  that the  change is . . construction process also needs a regional domestic sales table Zr n . Fr n , next to   . nr . nr the traditional regional domestic purchases table Z . F (see Fig. 3.1). But with

those two tables, it is only one extra step to construct a bi-regional IOT (BRIOT) with the Rest of the Country as a second region, as shown by bold lined rectangle in Fig. 3.1. Doing that has the additional advantage that the analyst can benefit from the double-entry (DE) accounting identities of the BRIOT to check and double-check all estimates. The DE-BRIOT approach has the following six major construction steps [see Boomsma and Oosterhaven (1992), for details]: 1. The  non-survey estimation of the domestic purchases table of region  traditional, . r, Znr .. Fnr , by means of Eq. (3.1) and the calculation of the comparable table for the Rest of the Country s as the residual from the national domestic purchases table (see Fig. 3.1):       . . . ns . ns nn . nn nr . nr Z .F = Z .F − Z .F

(3.9)

2. The non-traditional, non-survey estimation of the matrix with domestic sales ratios of region r as the weighted average of the demand structure of the

3.1 Construction of Regional IO Tables: Towards Cost-Effective …

27

  . region, i.e. (ˆxr − eˆ r )−1 Znr .. Fnr , and that of the rest of the nation, i.e.   . s s −1 ns . ns (ˆx − eˆ ) Z . F , where the survey-based aggregate self-sufficiency sales rr r r rr ratios, i.e. ti·rr = (z rr i· + f i· )/(x i − ei ) ∈ t , and the survey-based aggregate rs rs rs domestic export ratios, i.e. ti· = (z i· + f i· )/(xir − eir ) ∈ tr s , function as the weights per selling industry:

rn

S

    . . rr r r −1 nr . nr rs s s −1 ns . ns ˆ ˆ + t (ˆx − eˆ ) Z . F , = t (ˆx − eˆ ) Z . F with trr + tr s = i

(3.10)

3. The regional domestic sales table is then simply calculated row-by-row as:   . rn. rn Z .F = (ˆxr − eˆ r ) Sr n

(3.11)

and that of the Rest of the Country as the residual from the national table (see Fig. 3.1):       . . . Zsn .. Fsn = Znn .. Fnn − Zr n .. Fr n

(3.12)

4. The application of the survey-based domestic self-sufficiency sales ratios and domestic export ratios to the regional domestic sales table of Step 3 to obtain the core of the semi-survey IO table for region r, i.e. the intra-regional transactions table, and the domestic export table for region r: 

       . . . . Zrr .. Frr = tˆrr Zr n .. Fr n and Zr s .. Fr s = tˆr s Zr n .. Fr n

(3.13)

The combination of the above three tables for region r (see the light shaded part of Fig. 3.1), in fact, represents a rows only full information RIOT on which one may already base a similarly named IO model (Oosterhaven 1984). It is, however, advisable not to stop the IO table construction process after this step, but to continue with. 5. The estimation of the semi-survey regional domestic import table as the residual of the regional domestic purchases table of Step 1 and the intra-regional transactions table of Step 4:       . . . sr . sr nr . nr rr . rr = Z .F − Z .F Z .F

(3.14)

28

3 Data Construction: From IO Tables to Supply-Use Models

This residual domestic import table, together with the residual domestic exports table from Step 4, offers excellent opportunities for extensive checking for inconsistencies and improbabilities at the cell level of the RIOT [see Boomsma and Oosterhaven (1992), for details]. The total of the light and darker shaded tables in Fig. 3.3 is called a dogleg full information RIOT [see Bourque and Conway (1977), for a good empirical example]. Again, it is not advisable to stop here, but to continue with. 6. The calculation of the intra-regional transactions table for the Rest of the Country as the final residual:           . . . . . (3.15) Zss .. Fss = Znn .. Fnn − Zrr .. Frr − Zr s .. Fr s − Zsr .. Fsr With this last step, all sub-tables of Fig. 3.1 are estimated. This final result thus offers the possibility to simulate not only the intra-regional impacts, but also the interregional spillovers and interregional feedbacks of any change in exogenous final demand, as explained in Chap. 2. The DE-BRIOT construction method may already be implemented with the above used minimal survey information on only three sales percentages, namely one for intra-regional sales, one for exports to the Rest of the Country and one for exports the RoW. Collecting additional survey information is welcome, but will be difficult in the traditional industry-by-industry set-up of the IOT, as it would require firms to answer such questions as what industries in your own region are you selling your outputs to, or purchasing your inputs from? Far more easy are questions such as what products are you selling to which spatial markets or what products do you purchase from which spatial markets?

3.2 Construction of Interregional Supply-Use Tables and Models In fact, large-scale national statistical surveys among firms, households and government agencies do not ask for industries of origin or destination, as that is incomprehensible for most respondents, especially for households. Instead, they ask for products sold and products bought. When this type data are processed into an IO type of table, one gets a so-called supply-use table (SUT). First, we discuss the set-up of a national SUT and the options to derive an IO-type model from a national SUT. Next, we discuss the ways to estimate different types of interregional SUTs and which types of models belong to each of them.

3.2 Construction of Interregional Supply-Use Tables and Models

29

3.2.1 Difficulty of Deriving an IO Model from a Supply-Use Table The structure of a single-nation SUT, or a single-region SUT, for that matter, is shown in Fig. 3.2. The bold outlined block matrices represent four quadrants that are comparable with the four quadrants of the open economy IOT of Fig. 2.1. The macroeconomic totals, the industry totals and the value-added sub-matrices are   iden.. .. tical to those of Fig. 2.1. The first difference is that the use table U . F . e , with intermediate demand, u ci ∈ U, domestic final demand, f cq ∈ F, and exports to the RoW, ec ∈ e, has the use of separate products c on its rows instead of the product mix of a certain industry i. In the early IO literature, products were labelled commodities; hence, we use c. The second difference is that a SUT contains a new matrix, namely the supply table, containing the supply of product c by domestic industry i, sic ∈ S,

. The first rows of the supply table and the supply of c from the RoW, smc ∈ sm indicate the product mix of each domestic industry, whereas its last row indicates the product mix of foreign imports. The added product dimension means that a SUT has two accounting identities. The first, old identity states that total industry output equals total industry input xi : 

sic = xi =

c



u ci +



c

v pi , ∀i or in matrices: S i = x = (i U + i V)

p

(3.16) Products

Products

Industries Imports

Domestic final demand

Exports

Total

uci ∈ U

f cq ∈ F

ec ∈e

qc ∈q

sic ∈S

xi ∈ x

smc ∈ s m′

M

Value added Total

Industries

fpq

v pi ∈ V

qc ∈q′

xi ∈ x′

C

I

Y G

E

Fig. 3.2 Single-region or single-nation supply-use table. Legend See Fig. 2.1. Additional: sic = supply of product c by industry i, smc = import of c, uci = use of c by industry i, f cq = use of c by final demand category q, and ec = export of c

30

3 Data Construction: From IO Tables to Supply-Use Models

The second, new identity states that the total product supply equals total product demand qc :  i

sic + smc = qc =

 i

u ci +



f cq + ec , ∀c

q

= q = (Ui + Fi + e)

or in matrices: i S + sm

(3.17)

In (3.17), the sum of the output of domestic industries i S and foreign imports sm

equals total product supply q , which equals the sum of intermediate demand Ui, domestic final demand Fi and foreign export demand e. Note that the empty product-by-product square in Fig. 3.2 is larger than the empty industry-by-industry square. This reflects that a SUT usually distinguishes more products than industries. Hence, the industry part of both the supply table and the use table is usually rectangular; whereas, the industry part of an IO table is always square. The most simple way to build a supply-use (SU) model is to fill the shaded subtables with zeros and to then use the first two quadrants of Fig. 3.2 mathematically in the same way as the first two quadrants in Fig. 2.1. This leads to the following formulation and solution of the basic supply-use model:

             −1  Fi + e q 0 A q Fi + e q I0 0 A = + ⇒ = − 0 x R 0 x 0 x 0I R 0 (3.18) in which A = matrix with assumingly fixed industry technology coefficients, point  estimated by means of aci = u ci xi ∈ A = U xˆ −1 , and R = matrix with assumingly fixed industry market shares in the supply of product c, point estimated with ric = sic /qc ∈ R = S qˆ −1 . The solution in (3.18) serves to estimate the impact of any change in exogenous final product demand Fi + e on total supply of product c, on total output of industry i and on any impact variable that may be linked to one of them, such as foreign imports that may be linked to q, or value-added and CO2 emissions that may be linked to x. Additional insight may be gained by decomposing (3.18) in the two separate solutions for total supply and total output, respectively: q = (I − AR)−1 (F i + e) and

(3.19)

x = R (I − AR)−1 (F i + e) = (I − RA)−1 R (F i + e)

(3.20)

Most interesting are the two alternative solutions for total output in Eq. (3.20). Note that the two matrices AR and RA in the two Leontief-inverses of (3.20) have different dimensions, namely product-by-product in case of AR and industry-by-industry in case of RA. This implies that the two assumptions underlying these two matrix combinations may be used to construct the standard two types of square, symmetric

3.2 Construction of Interregional Supply-Use Tables and Models

31

IO tables, namely the not yet discussed product-by-product IOT by means of AR and the already familiar industry-by-industry IOT by means of RA. In most IO impact and scenario studies, the change in exogenous final demand is given by product. With only an i-by-i IOT available, which delivers (I − RA)−1 for the last part of (3.20), the analyst has to allocate the exogenous changes in product demand, by hand, to the domestic and foreign industries that are most likely to satisfy it. That is, the analyst needs to assemble the information that is contained in the industry market shares matrix R, which is absent in an i-by-i IOT. Many countries, however, only construct p-by-p IOTs and some construct them with AR. With only a p-by-p IOT available, (I − AR)−1 may be calculated for the first part of (3.20). Doing an IO impact or scenario study, however, additionally again requires the absent industry market shares matrix R. Only now, it is needed to allocate the predicted change in total supply to the domestic industries that supply part of that change. The use of the basic, rectangular SU model (3.18), instead of one of the two, mathematically identical, square IO models, provides the solution to both problems, as the industry market shares matrix R is part of the SU model. This straightforward use of (3.18) ignores the problematic nature of assuming fixed industry technology coefficients in Ui = Ax. However, fixing these coefficients implies making the assumption that each industry uses one and same technology for all of its different products, which is known as the industry technology assumption (model A, Eurostat 2008). The alternative product technology assumption, in contrast, states that each product has unique input requirements irrespective of the industry that produces it (model B, Eurostat 2008). Kop Jansen and ten Raa (1990) and ten Raa and Rueda-Cantuche (2003) show that the alternative assumption has superior theoretical properties, as it satisfies four desired axioms, namely material balance, financial balance, price invariance and scale invariance; whereas, the industry technology assumption used in (3.18)–(3.20) only satisfies the first axiom. Unfortunately, using this theoretically more plausible alternative assumption to construct a p-by-p IOT requires the domestic part of the supply table to be square instead of rectangular, because it requires calculating the inverse of the row ratios of the domestic supply table, i.e. it requires to calculate the inverse of the industry product mix ratios matrix, pic = sic /xi ∈ P = xˆ −1 S (Gigantes 1970). De Mesnard (2004), however, shows that the forward direction of causality of fixed product mix ratios is inconsistent with the backward direction of causality assumed in the demand-driven IO model; whereas, it perfectly fits within the forward causality of the implausible supply-driven IO model (see further, Chap. 6). Moreover, using P−1 may lead to inacceptable negative product technology coefficients, which may be solved by a series of ad hoc methods [see Rueda-Cantuche (2017), for an overview]. De Mesnard (2011), however, shows that even when no negatives occur in the product technology coefficients, negatives always occur in P−1 and claims that this makes this approach unacceptable.

32

3 Data Construction: From IO Tables to Supply-Use Models

To further complicate matters, there is not only a second way to construct a p-by-p IOT, there is also a second way to construct an i-by-i IOT. The first way is to combine the industry technology assumption with the fixed market share assumption, as done in (3.18)–(3.20) (labelled product sales structure assumption in Eurostat 2008, model D). The second way is to combine the product technology assumption with the product mix ratios assumption (labelled industry sales structure assumption in Eurostat 2008, model C). Again, the first combination, used in the first part of (3.20), is shown to satisfy only the first of the above four axions, whereas the second combination satisfies all four axioms (Rueda-Cantuche and ten Raa 2009). Again, unfortunately, using fixed product mix ratios is in contradiction with the direction of causality of the Leontief model, while it again requires a square domestic supply table to be able to invert the matrix with product mix ratios P, which again delivers negatives in each row and column of P−1 , which de Mesnard (2011) again claims to be unacceptable. After an extensive weighing of advantages and disadvantages, Eurostat favours industry-by-industry IO tables based on fixed industry market share ratios (model D, see Eurostat 2008, p. 310). Miller and Blair (2009, p. 208), in contrast, conclude that the literature up till now is undecisive on this issue. In practice, most countries nowadays construct SUTs far more regularly than symmetric IO tables, which may be the best reason to favour the basic SU model (3.18)–(3.20), as it may be based on more recent data.

3.2.2 Family of Interregional Supply-Use Tables and Models The obvious next question is how to regionalize the national SUT of Fig. 3.2. Oosterhaven (1984) discusses a whole family of regionalized national SUTs. Here, we only discuss the last phase of adding trade data to a national SUT that is already regionalized once. Adding trade data is required to obtain an interregional SU model. Being “already regionalized once” means that the national supply table Sn· is already regionalized along its rows into Sr · + Ss· + · · · , while the national use table U·n is already regionalized along its columns into U·r + U·s + · · · (see Fig. 3.3, where the relevant core of the national SUT is indicated with double lines). The smallest amount of trade data is required in case of constructing a multiregional SUT (see Table A in Fig. 3.3). It, additional to the one-sided split up of the national SUT, only requires aggregate bilateral trade data tcr s , which also represents the minimum trade data necessary to apply the DE-BRIOT approach: tcr s =

 i

rs sic =

 i

u rcis +



rs f cq ∈ tr s ∀r, s

(3.21)

q

The sales only interregional SUT (see Table B in Fig. 3.3) requires the next least amount of additional trade data. On top of the data of Table A, it requires that all regional supply tables are regionalized a second time, i.e. the data in the second term

3.2 Construction of Interregional Supply-Use Tables and Models

33

Fig. 3.3 Four regionalized national SUTs that each have a supply-use model. Legend t·cr s ∈ (tr s )

r s ∈ Sr s = sales of c by industry i in r to = total trade of product c from region r to region s, sic region s, and u rcqs ∈ Ur s = use of c from region r by producers and local final demand q in s. The national supply table Sn· is exclusive of foreign imports, and the national use table U·n is exclusive of foreign exports. Source Adapted from Oosterhaven (1984)

in (3.21) needs to be estimated for all combinations of r and s. If all industries have the same export ratios for their supply of product c, this seconds split up simply rs r· = (tcr s /tcr · ) sic , ∀i. requires applying sic The purchases only interregional SUT (see Table C in Fig. 3.3, called “useregionalized” by Jackson and Schwarm 2011), instead, requires that all regional use tables are regionalized a second time, i.e. the data in the third term of (3.21) need to be estimated for all combinations of r and s. This requires much more effort, as intermediate outputs, in general, have trade patterns different from those of final outputs. However, if all industries and all final demand categories have the same rs ·s = (tcr s /tc·s ) f cq , ∀q import ratios, this second split up simply requires to apply f cq for local final use of product c (analogous for intermediate use). The FI interregional SUT (see Table D of Fig. 3.3), at last, requires an estimate of all trade flows shown in Eq. (3.21). It is interesting to compare Fig. 3.3 with Fig. 3.1 and note that the first three bi-regional SUTs offer zero double-entry error checking possibilities and thus no data improvement opportunities, whereas bi-regional IOTs do. Only Table D of Fig. 3.3 offers a double-entry checking possibility, not at the cell

34

3 Data Construction: From IO Tables to Supply-Use Models

level as in Fig. 3.1, but at the level of the column sums and row sums of its supply and use tables, respectively, as Table D has to satisfy: i Sr s = (Ur s i) , ∀r, s. All four interregional SUTs of Fig. 3.3 would suffice to build an interregional version of (3.18). We only present the solution of the two extremes with regard to data requirements [see Oosterhaven (1984), for the remaining two models]. Without loss of generality as regards the number of regions, the multi-regional SU model reads as follows:  rr r s  ·r r   ·r   r   r   r· ˆ ˆ m R 0 m A x F i e x = + (3.22) + s ˆ sr m ˆ ss xs A·s xs e m 0 Rs· F·s i ˆ = diagonal matrix with trade origin where R = matrix with industry market shares, m ratios in total supply q, and A = matrix with technical coefficients; all coefficients may be point estimated directly from the data in Table A of Fig. 3.3. Note the rank order of the brackets used. Foreign export demand er is already specified by region of production. Hence, exports only need to be pre-multiplied with the regional industry market shares Rr · in order to determine which regional industry produces these exports. Intermediate and local final demand (Ax + Fi), on the other hand, are specified as the demand for products from anywhere, and thus, have to be preˆ to determine which regions satisfy multiplied first with the trade origin ratios m this demand, before they are pre-multiplied with the regional industry market shares Rr · to determine which industries in those regions will produce these products. The solution of (3.22) is straightforward: transfer the term with x from the RHS to the LHS of (3.22) and pre-multiply both sides with the appropriate inverse. Again without loss of generality as regards the number of regions, the FI interregional SU model reads as follows: 

xr xs



 =

Rrr Arr Rr s Ar s Rsr Asr Rss Ass



xr xs



 +

Rrr Frr Rr s Fr s Rsr Fsr Rss Fss

   rr r  i R e + Rss es i

(3.23)

All coefficient matrices of (3.23) may be point estimated directly from the data in Table D of Fig. 3.3. Note that the difference in the treatment of foreign exports and regional demand in (3.22) disappears in (3.23), as information on the regions that satisfy the intermediate and local final demand is now available at the product level. As a consequence, (3.23) has become far simpler than (3.22), while its solution is even more straightforward. The amount of data required, however, has grown significantly, as is also evident from comparing Table A with Table D in Fig. 3.3. When exogenous final demand (Fi + e) of the base year is used, both models will produce the same endogenous values for total industry output x and total product supply q. In case of a non-proportional change in exogenous final demand, however, both models will produce different endogenous outcomes. Such differences may be viewed as representing the aggregation error that is made by using the multi-regional SU model instead of the FI interregional model. Since the FI interregional SU model

3.2 Construction of Interregional Supply-Use Tables and Models

35

has not been constructed yet, it remains unknown how serious this aggregation error will be. The same holds for the FI international SU model for multiple countries.

3.3 Difference Between Constructing Interregional and International SUTs Although the mathematics and economics are exactly similar, the construction of international SUTs, noteworthy, requires a strategy that is quite different from the construction of within country interregional SUTs. The construction of interregional SUTs essentially follows a top-down process, which starts with the one-sided regionalisation of a national SUT and continues with adding trade data as discussed above.7 In most cases, aggregate survey or non-survey trade origin ratios are applied to the rows of the one-sidedly regionalized national use table resulting in the first estimate of a use-regionalized national SUT (see Table C of Fig. 3.3). Next, iterative bi-proportional scaling of this first estimate (RAS) is used to achieve consistency with the accounting identities. As a consequence of using RAS, each cell in the resulting table ends up with having its own different trade origin ratio. It is important to understand that this type of RAS-caused differentiation of trade ratios along the rows the resulting MRSUT does not have an empirical foundation. The resulting table, consequently, still suffers from the type of aggregation error that a survey-based MRIOT contains compared to a survey-based IRIOT, as discussed in Sect. 2.3. Unfortunately, most countries do not even have aggregate interregional trade data. Many countries, instead, have transport data, mostly by product group and single transport mode, ignoring multi-modal transport chains, while using a product classification with a mostly large, miscellaneous category, mainly covering container transport. Moreover, most transport data are primarily measured in tons and only partially or not at all in monetary values. Integrating such quite different physical transport data into the monetary data and product classifications of a use-regionalized national SUT is rather complex and is best done by using the maximum entropy model [see Többen (2017b), for a fine, recent example]. Since a world SUT is not available, the construction of international SUTs, in contrast to that of interregional SUTs, follows an entirely bottom-up process. The two main data sources for this bottom-up construction process are national SUTs and national foreign trade data. The core international construction problem is not the lack of trade data but the abundance of conflicting trade data, as for each international trade flow tcr s there are at least four values, namely the SUT and the export statistics of the origin country r, and the SUT and the import statistics of the destination 7 See Többen (2017a) for a state of the art construction of a purchases only interregional SUT, using

the KRAS algorithm of Lenzen et al. (2009). See Madsen and Jensen-Butler (1999) for a general discussion on constructing interregional SUTs and the actual construction of a Danish interregional SUT that has a more bottom-up character, due to the abundance of micro data in case of Denmark.

36

3 Data Construction: From IO Tables to Supply-Use Models

Table 3.1 Valuation of international commodity flows Country

Valuation layers

Statistical source

R

Basic price in R

Supply table

R

+ Taxes and subsidies

Supply table

R

+ Trade and transport margins

Supply table

R

= Purchaser price in R

Use table and export stats (f.o.b. price)

International

+ Trade and transport margins

S

= Basic price in S

Supply table and import stats (c.i.f. price)

S

+ Taxes and subsidies

Supply table

S

+ Trade and transport margins

Supply table

S

= Purchaser price in S

Use table and export stats (f.o.b. price)

International

+ Trade and transport margins

… and so on

Source Adapted from Bouwmeester (2014)

country s. The differences between the four values may be as large as 10–30%, with a maximum of more than 200% for beverages, due to excise taxes (van der Linden and Oosterhaven 1995). Aside from the measurement errors and transport-chain timing differences, these flows mainly differ rather systematically because they are measured in different prices, as shown in Table 3.1. Table 3.1 also shows a second problem, namely that most countries measure the values of the use table in purchasers’ prices, while the supply table is measured in basic prices. For modelling purposes, however, it is essential that the use table is also measured in basic prices, as only this valuation enables allocating economic and environmental impacts to the industries that actually produce them. Using purchasers’ prices would result in allocating impacts on taxes, subsidies and trade and transport margins unjustly to the industries that produce the goods and services that carry these payments, instead of to the government that receives the taxes and to the industries that produce the trade and transport margins. Van der Linden and Oosterhaven (1995) solved this problem probably for the first time. In case of the construction of the EU intercountry IOTs for 1965–1985, they applied RAS to an initial estimate of the off-diagonal blocks of their IRIOTs measured in purchasers’ prices, while using the exports to the rest of the EU measured in producers’ prices as row totals. Bouwmeester (2014) describes in great detail how this problem, along with several other problems, was solved in case of the EU Exiopol project (Tukker et al. 2013). In case of the EU WIOD project, Dietzenbacher et al. (2013) also favour to reprice the internationalized use table. A more demanding solution is to quantify the valuation layers specified in Fig. 3.4 at the cell level of either the use or the supply table, as is done in the Eora project (Lenzen et al. 2013). See the special issues of Economic Systems Research of March 2013 and September 2014, for other international SUT databases and for several analyses of their methodological and empirical differences.

References

37

References Bacharach M (1970) Biproportional matrices and input-output change. Cambridge University Press, Cambridge Batten D (1983) Spatial analysis of interacting economies. Kluwer-Nijhoff, Boston Boomsma P, Oosterhaven J (1992) A double-entry method for the construction of bi-regional inputoutput tables. J Reg Sci 32:269–284 Bourque PJ, Conway RS (1977) The 1972 Washington input-output study. Graduate School of Business Administration, Seattle Bouwmeester MC (2014) Economics and environment—modelling global linkages. Dissertation, SOM Research School, University of Groningen Burford RL, Katz JL (1981) A method for estimation of input-output-type output multipliers when no I-O model exists. J Reg Sci 21:151–1621 Czamanski S, Malizia E (1969) Applicability and limitations in the use of national input-output tables for regional studies. Pap Reg Sci 23:65–78 de Mesnard L (2004) Understanding the shortcomings of commodity-based technology in inputoutput models: an economic circuit approach. J Reg Sci 44:125–141 de Mesnard L (2011) Negatives in symmetric input–output tables: the impossible quest for the Holy Grail. Ann Reg Sci 46:427–454 Dietzenbacher E, Los B, Stehrer R, Timmer M, de Vries G (2013) The construction of world input-output tables in the WIOD project. Econ Syst Res 25:71–98 Eurostat (2008) Eurostat manual on supply, use and input-output tables. European Communities, Luxemburg Flegg AT, Webber CB, Elliot MV (1995) On the appropriate use of location quotients in generating regional input-output tables. Reg Stud 29:547–561 Flegg AT, Huang Y, Tohmo T (2015) Using charm to adjust for cross-hauling: the case of the province of Hubei, China. Econ Syst Res 27:391–413 Gigantes T (1970) The representation of technology in input-output systems. In: Carter AP, Bródy A (eds) Contributions to input-output analysis. North-Holland, Amsterdam Hewings GJD (1977) Evaluating the possibilities for exchanging regional input-output coefficients. Environ Plan A 9:927–944 Hewings GJD, Janson BN (1980) Exchanging regional input-output coefficients: a reply and further comments. Environ Plan A 12:843–854 Hoen AR, Oosterhaven J (2006) On the measurement of comparative advantage. Ann Reg Sci 40:677–691 Isard W, Langford TW (1971) Regional input-output study: recollections, reflections and diverse notes on the Philadelphia experience. M.I.T Press, Cambridge Jackson RW, Schwarm WR (2011) Accounting foundations for interregional commodity-byindustry input-output models. Lett Spat Resour Sci 4:187–196 Jansen PK, ten Raa T (1990) The choice of model in the construction of input-output coefficients matrices. Int Econ Rev 31:31–45 Jensen RC, Hewings GJD (1985) Shortcut ‘input-output’ multipliers: a requiem. Environ Plan A 17:747–759 Junius T, Oosterhaven J (2003) The solution of updating or regionalizing a matrix with both positive and negative entries. Econ Syst Res 15:87–96 Kronenberg T (2009) Construction of regional input-output tables using nonsurvey methods: the role of cross-hauling. Int Reg Sci Rev 32:40–64 Kullback S (1959) Information theory and statistics. Wiley, New York Lahr ML (1993) A review of literature supporting the hybrid approach to constructing regional input-output models. Econ Syst Res 5:277–293 Lenzen M, Gallego B, Wood R (2009) Matrix balancing under conflicting information. Econ Syst Res 21:23–44

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Lenzen M, Moran D, Kanemoto K, Geschke A (2013) Building EORA: a global multi-region input-output database at high country and sector resolution. Econ Syst Res 25:20–49 Madsen B, Jensen-Butler C (1999) Make and use approaches to regional and interregional accounts and models. Econ Syst Res 11:277–299 Miller RE, Blair PD (2009) Input-output analysis: foundations and extensions, 2nd edn. Cambridge University Press, Cambridge Minguez R, Oosterhaven J, Escobedo F (2009) Cell-Corrected RAS method (CRAS) for updating or regionalizing an input-output matrix. J Reg Sci 49:329–348 Oosterhaven J (1984) A family of square and rectangular interregional input-output tables and models. Reg Sci Urban Econ 14:565–582 Oosterhaven J, Escobedo-Cardeñoso F (2011) A new method to estimate input-output tables by means of structural lags, tested on Spanish regions. Pap Reg Sci 60:829–845 Oosterhaven J, Polenske KR, Hewings GJD (2019) Modern regional input-output and impact analysis. In: Capello R, Nijkamp P (eds) Handbook of regional growth and development theories: revised and extended, 2nd edn. Edward Elgar, Cheltenham Round JI (1983) Non-survey techniques: a critical review of the theory and the evidence. Int Reg Sci Rev 8:189–212 Rueda-Cantuche JM (2017) The construction of input-output coefficients. In: ten Raa T (ed) Handbook of input-output analysis. Edward Elgar, Cheltenham Rueda-Cantuche JM, ten Raa T (2009) The choice of model in the construction of industry inputoutput coefficient matrices. Econ Syst Res 21:363–376 Sawyer CH, Miller RE (1983) Experiments in the regionalization of national input-output table. Environ Plan A 15:1501–1520 Schaffer W, Chu K (1969) Nonsurvey techniques for constructing regional interindustry models. Pap Reg Sci 23:83–104 Stevens BH, Trainer GA (1980) Error generation in regional input-output analysis and its implications for nonsurvey models. In: Pleeter SP (ed) Economic impact analysis: methodology and applications. Martinus Nijhoff, Boston Stevens BH, Treyz GI, Lahr ML (1989) On the comparative accuracy of RPC estimation techniques. In: Miller RE, Polenske KR, Rose AZ (eds) Frontiers of input-output analysis. Oxford University Press, New York Stone R (1961) Input-output and national accounts. Organization for European Economic Cooperation, Paris Stone R, Brown A (1962) A computable model of economic growth. In: A programme for growth, vol. 1. Chapman and Hall, London Temurshoev U, Miller RE, Bouwmeester MC (2013) A note on the GRAS method. Econ Syst Res 25:361–367 ten Raa T, Rueda-Cantuche JM (2003) The construction of input-output coefficient matrices in an axiomatic context: some further considerations. Econ Syst Res 14:439–455 Theil H (1967) Economics and information theory. North-Holland, Amsterdam Thomo T (2004) New developments in the use of location quotients to estimate regional input-output coefficients and multipliers. Reg Stud 38:43–54 Többen J (2017a) Effects of energy- and climate policy in Germany: a multiregional analysis. Dissertation, SOM research school, University of Groningen Többen J (2017b) On the simultaneous estimation of physical and monetary commodity flows. Econ Syst Res 29:1–24 Többen J, Kronenberg TH (2015) Construction of multi-regional input–output tables using the charm method. Econ Syst Res 27:487–507 Tukker A, De Koning A, Wood R, Hawkins T, Lutter S, Acosta J, Rueda-Cantuche JM, Bouwmeester MC, Oosterhaven J, Drosdowski T, Kuenen J (2013) Exiopol—development and illustrative analyses of a detailed global MR EE SUT/IOT. Econ Syst Res 25:50–70

References

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van der Linden JA, Oosterhaven J (1995) European community intercountry input-output relations: construction method and main results for 1965–1985. Econ Syst Res 7:249–269 West GR (1990) Regional trade estimation: a hybrid approach. Int Reg Sc Rev 13:103–118 Willis KG (1987) Spatially disaggregated input-output tables: an evaluation and comparison of survey and non-survey results. Environ Plan A 19:107–116

Chapter 4

From Basic IO and SU Models to Demo-Economic Models

Keywords Endogenous household consumption · Social accounting matrices (SAMs) · Type II input–output model · Demo-economic models · Vacancy chains · Type IV multipliers · Infinite multipliers · Net multipliers Chapters 2 and 3 end with interregional input–output (IO) and interregional supply–use (SU) models, respectively. Extending single-region models into interregional models by endogenizing the export of intermediate outputs is shown to be methodologically interesting, but empirically—for most industries—it is much less important than endogenizing household expenditures. In this chapter, we explain the intricacies of endogenizing household consumption and conclude with a discussion of how far the analyst should go with endogenizing more and more components of exogenous final demand.

4.1 Interregional Models with Endogenous Household Consumption Figure 4.1 shows the causal nature of endogenizing that part of household consumption that may be tied directly to the size and growth of value added by industry. The solid arrows and boxes reproduce the causal structure of the interregional IO model shown in Fig. 2.4. The dotted separations in the top two boxes show which part of exogenous final demand of the basic (Type I) interregional IO model remains exogenous (f r,ex and f s,ex ) and which part is made endogenous, i.e. hrr and hsr in case of region r, and hss and hsr in case of region s, where h ri s ∈ hr s = endogenous consumption of products from industry i in region r by households in region s.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_4

41

42

4 From Basic IO and SU Models to Demo-Economic Models

fs = fs,ex +

fr = fr,ex + hrr + hrs

hss + hsr

Zrs i Zrr

r

x

xs

Zss

Vs

hss

Zsr i hrr

Vr

hrs hsr

Fig. 4.1 Causal structure of the endogenous consumption extension. Legend See Fig. 2.4. In addition: f r,ex = vector with remaining exogenous final demand of the Type II interregional IO model, hrs = vector with the endogenous delivery of consumption goods and services by industries in region r to households in region s

In the Type I single-region IO model for region r only the consumption expenditures on regionally produced goods and services out of regionally earned value added may be made endogenous, as shown for region r by the dotted arrows entering and leaving the dotted box with hrr . For region r this results in the so-called Type II single-region IO model, which has larger multipliers than the Type I model, because the additional causal loop (Vr ⇒ hrr ⇒ xr ) shown in the bottom-left part of Fig. 4.1 leads to additional impacts on regional total output, called intra-regional induced effects. As was the case with the interregional model extension, the larger multipliers of the single-region model extension, when multiplied with its smaller base year exogenous final demand, will reproduce the base year values for total output. Reality does not change, only the way in which it is modelled changes! In the Type II interregional IO model, not only to the intra-regional hrr and hss but also the interregional export of consumption goods and services that can directly be tied to the value added of other regions is made endogenous (i.e. hrs and hsr ). The result is that not only the intra-regional multipliers will be larger, but also the interregional spillover and feedback effects. These so-called induced spillovers and feedbacks will enhance the indirect spillovers and feedbacks of the Type I interregional IO model, as illustrated by the dotted boxes and arrows in the middle part of Fig. 4.1, which provide a second connection back and forth between the two single-region Type II models on the LHS and the RHS of Fig. 4.1. How, exactly, can household consumption expenditures be endogenized? The columns with household consumption in an IOT (see Fig. 2.1) or a SUT (see Fig. 3.2) usually relate to the consumption of all households living in the region or nation at hand. Only part of these expenditures will directly depend on the size and growth of the own value added of the region, and then especially on the size and growth of the labour income part of that value added, as assumed in Fig. 4.1. A large part of household consumption only indirectly depends on the value added of the own region and that of other regions via the redistribution of value added through interregional labour income flows (mainly via commuting), through interregional capital

4.1 Interregional Models with Endogenous Household Consumption

43

income flows (mainly via interregionally operating firms) and through central and local governments’ social security and taxation schemes. The empirical specification of the regional and interregional redistribution of value added requires the information that is available in interregional social accounting matrices (SAMs, see Pyatt and Thorbecke 1976, or Pyatt and Round 1977, for the original concept). The fundamental difference between IOTs and SUTs, on the one hand, and SAMs, on the other hand, is that for each and every SAM all accounts balance, i.e. all successive row totals (= incoming payments) and column totals (= outgoing payments) in a SAM are equal. Besides balancing industry and product accounts, SAMs usually have disaggregated, balancing household accounts, where all income sources and all expenditures are specified per type of household. Depending on the data, households may be disaggregated in many ways, but often they are disaggregated by income decile. When all household accounts balance, all household expenditures may be endogenized in exactly the same way as the commodity account in the basic SU model in Eq. 3.18. In that way, a SAM model may directly be derived from a SAM table. Figure 4.2 shows a simplified single-region or single-nation SAM with a disaggregated household account and an aggregated account for all other institutions (i.e. the total of the government, capital and RoW accounts). In the SAM of Fig. 4.2, additional to the accounting identities by industry (3.16) and by-product (3.17), total household expenditures equal total household receipts for each household type q: Products

Products

Industries

Total

Households

Other

Total

uci ∈ U

hcq ∈ H

ec ∈e

q

x

sic ∈S

Households Other

Industries

y ex

ht

tq ∈ t ′

T

E

hqt ∈ht ´

E

wqi ∈ W

smc ∈s m ´

qc ∈q′

oi ∈o′

xi ∈ x′

Fig. 4.2 Simplified single-region social accounting matrix. Legend See Fig. 3.2. In addition: hcq = expenditure on product c by household type q, ec = expenditure on c by other accounts, wqi = payments to q by industry i, yex = income from exogenous accounts, hqt = total income/expenditures of q, oi = other value added of i, t q = payments by q to other accounts, T = transactions between other accounts, E = total receipts/expenditures of other accounts

44

4 From Basic IO and SU Models to Demo-Economic Models

 c

h cq + tq = h qt =

 i

wqi + yqex ∈ i H + t = (ht ) = (W i + yex ) (4.1)

where hcq = expenditures on product c from everywhere by households q, t q = payments of households q to other accounts (mainly taxes, social security payments and savings, but not imports that are accounted for by smc in the supply table), hqt = total income/expenditures of households q, wqi = incomes paid to households q by industry i, yqex = other incomes of households q (mainly social security benefits, domestic capital incomes, pensions and incomes from the RoW). The SAM model that may directly be based on the data of Fig. 4.2 contains only three simple assumptions: 1. The expenditures e, yex and T of the “combined other accounts” are exogenous. 2. Any change in e and yex leads to an equally large change in the total receipts q and h of the endogenous product and household accounts. 3. Any change in the total receipts of any endogenous account leads to proportional changes in all the expenditures of that account. In other words: all expenditures in the heavily outlined part of the SAM in Fig. 4.2 are determined by the size of their column totals and assumingly fixed expenditure coefficients. With only one SAM available, the model coefficients may be point estimated by dividing all endogenous expenditures by their account’s base year column total.1 This delivers the technical coefficient matrix A and the market share matrix R, already known from the basic SUT model (3.18), as well as the new household income shares in total industry input (i.e. cqi = wqi /xi ∈ C = W xˆ −1 ) and the new product shares in total household expenditures (or consumption package coefficients, i.e. kcq = h cq / h qt ∈ K = H hˆ t−1 ). Summarized by means of block matrices and stacked columns, as in (3.18), the SAM model and its subsequent solution directly follow from Fig. 4.2: ⎤ ⎡ ⎤ ⎤⎡ ⎤ ⎡ 0 AK e q q ⎣ x ⎦ = ⎣ R 0 0 ⎦⎣ x ⎦ + ⎣ 0 ⎦ ⇒ 0 C 0 yex ht ht ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎤−1 ⎡ q I −A −K e LCC LC I LC Q e ⎣ x ⎦ = ⎣ −R I 0 ⎦ ⎣ 0 ⎦ = ⎣ L I C L I I L I Q ⎦⎣ 0 ⎦ L QC L Q I L Q Q ht 0 −C I yex yex ⎡

(4.2)

where the subscripts in the extended Leontief-inverse indicate the dimensions of the corresponding sub-matrices. LCC , for instance, indicates the impact of changes in exogenous demand for products e on the total supply of products q, while L I Q indicates the impact of changes in exogenous household income yex on total industry output x. 1 Note that this also makes the s  , o m

and t receipts of the “combined other accounts” endogenous. Also note that the column sums of the expenditure coefficients add to unity, as it is the case with the column sums of the input coefficients of the IO and the SU model.

4.1 Interregional Models with Endogenous Household Consumption

45

Pre-multiplication of the extended Leontief-inverse with a row vector with, for instance, employment coefficients [ 0 l I l Q ] delivers the ordinary employment multipliers indicating the employment impact of changes in the exogenous variables. lQ L QC , for instance, gives the total employment impact in the household sector, measured in say full-time equivalents (fte’s), due to changes in the exogenous demand for products, e, measured in say euros. These multipliers will not be constant, but will decrease due to nominal increases in labour productivity. Post-multiplication of the ordinary employment multipliers with the inverse of the employment coefficients (i.e. with nominal labour productivity levels), subsequently, gives the dimensionless normalized employment multipliers, which have the advantage to be relatively constant. lI L I C (ˆlC )−1 , for instance, gives the total increase of fte’s in all industries due to an increase in exogenous product demand that may be produced by one fte. The decomposing the solution of (4.2) gives additional insight into the working of this most basic SAM model: q = (I − AR − KCR)−1 (Kyex + e)

(4.3a)

x = Rq

(4.3b)

ht = Cx + yex

(4.3c)

In Eq. 4.3a, changes in exogenous household income yex and in exogenous final demand e lead through the regional multiplier mechanism (I − AR − KCR)−1 to changes in endogenous product demand q, which leads in (4.3b) to changes in endogenous industry output x, which leads in (4.3c) to a further, now endogenous change in total household income ht . The overall multiplier effect of (I − AR − KCR)−1 consists of the sum of the direct I, the indirect AR and the induced KCR effect of a change in exogenous demand on all of the three sets of endogenous variables. When a single-nation version of Fig. 4.2 is disaggregated by region, it directly provides the empirical basis for the coefficients of an interregional SAM model. However, in the interregional case there are at least four ways in which a national SAM may be disaggregated by region, similar to the split up of a national SUT into four different interregional SUTs shown in Fig. 3.3 (see Madsen and Jensen-Butler 2005, for more detailed spatial SAMs). Here we only discuss the multi-regional SAM, as it requires the least amount of additional data. The multi-regional SAM model, that may be derived directly from this data, reads as follows (see Eq. 3.22 for the comparable multi-regional SUT model): 

xr xs





 Rr · 0 = 0 Rs· rr r s  ·r r   ·r r r   ·r r,ex   r  m m A x K Cx K y e + s sr ss ·s s + ·s s s + ·s s,ex m m A x K Cx K y e 







(4.4)

46

4 From Basic IO and SU Models to Demo-Economic Models

The large term between {…} in (4.2) shows the four components of the total demand for product c from region r and s. Note that the demand of the combined exogenous accounts of region r is already specified by region of supply, er , whereas intermediate demand, A·r xr , endogenous household demand, K·r Cr xr , and exogenous household demand, K·r yr,ex , of region r need to be pre-multiplied with trade ˆ sr , to determine the region of supply. Finally, all four terms ˆ rr and m origin ratios, m are pre-multiplied with Rr · to determine which industry in r supplies product c. The solution of (4.4) is simple. The two terms with intermediate demand and endogenous household demand need to be moved from the RHS to the LHS of (4.4), and then both sides need to be pre-multiplied with the appropriate inverse. This gives: 

xr xs



 =

ˆ rr (A·r + K·r Cr ) I − Rr · m ˆ r s (A·s + K·s Cs ) I − Rr · m s· sr ·r ·r r s· ss ˆ (A + K C ) −R m ˆ (A·s + K·s Cs ) −R m  r·  rr ·r r,ex  r s ·s s,ex ˆ K y ˆ K y +m + er R 0 m ˆ sr K·r yr,ex + m ˆ ss K·s ys,ex + es 0 Rs· m

−1 (4.5)

The interpretation of (4.5) is relatively straightforward. Following the causal chain from the right to the left, the upper most right-hand term er describes the direct impact of exogenous final demand on the supply of products by region r. The second term ˆ r s K·s ys,ex describes the direct spillover of exogenous incomes of households in s on m ˆ rr K·r yr,ex describes the the supply of products by region r, whereas the third term m intra-regional impact of exogenous incomes of households in r on the same supply. Next, the matrix Rr · in the middle of (4.5) determines which industries in region r will satisfy these three types of exogenous product demand. Finally, the inverse matrix determines the direct, indirect and induced impact of these three sets direct effects. Take, for instance, its bottom left-hand term ˆ sr (A·r + K·r Cr ). Again along the causal chain from the right to the left, its Rs· m sub-term between brackets describes the impact of total output by industry in region r on intermediate demand A·r and endogenous household demand K·r Cr for prodˆ sr determine which part of that ucts from everywhere. Next, trade origin ratios m demand in region r is satisfied from region s, while market share ratios Rs· determine which part of those imports are delivered by which industry in s. When (4.5) is pre-multiplied with value-added coefficients, the pre-multiplied inverse strongly resembles the sectorally and regionally disaggregated Keynesian income multipliers of Miyazawa (1976).2 Note that the additional data required to estimate the multi-regional SAM model (4.4), compared to the multi-regional SUT model (3.21), is limited to a column-wise ·n n ·n = h ·n split up of the national consumption package coefficients kcq cq / h qt ∈ K 2 See

Miyazawa and Masegi (1963) for the original idea and Sonis and Hewings (1999) for an overview of Miyazawa-type IO model extensions. Pyatt (2001) shows that Miyazawa-type multipliers can be viewed as special cases of interregional SAM multipliers. The core difference is that Miyazawa-type multipliers relate the generation of income by production factor, industry and region, directly to the spending of that income on products produced by industry and region, whereas SAM multipliers offer additional detail and more understanding in that they add the spatial and governmental redistribution of income in-between its generation and its spending.

4.1 Interregional Models with Endogenous Household Consumption

47

per household type q into the regional package coefficient matrices K·r and K·s , along with a column-wise split up of the national labour income/output ratios for n n = wqi /xin ∈ Cn , into the corresponding regional households q per industry i, cqi r s matrices C and C . In both cases, this breakdown may be made by assuming that the regional coefficients equal the national coefficients, but using survey data is, of course, to be preferred. Also note that the interregional labour income redistribution through commuting easily fits in this multi-regional disaggregation of the national SAM of Fig. 4.2. It only requires that the regional labour income/output ratios are given a second spatial dimension that accounts for the share of the labour income earned in industry j in region s that accrues to in-commuters from region r, i.e. the regional labour income/output ratios then need to be disaggregated into cqr sj = wqr sj /x sj ∈ Cr s , wherein wqr sj = labour income earned by households q living in r and working in industry j in s. Finally, note that the other three types of interregional SAMs require a further split up of the simplified national SAM of Fig. 4.2, comparable to the further split up of the national SUT in Fig. 3.3. Hence, this requires the earlier discussed split up of the aggregate interregional trade data shown in Eq. 3.21, which is the most elusive interregional trade data to collect/construct with any degree of reliability.

4.2 Further Demo-Economic Model Extensions Unfortunately, there were and there still are only few single-region SAMs available, let alone interregional SAMs, which explains why most of the literature on endogenizing household consumption relates to single-region and interregional IO models. In the absence of an interregional SAM, the interregional IO model extension that specifies the endogenous part of the household expenditures needs to be build-up piece-by-piece: h ri js = qirjs x sj = m ri hs ki·sh (1 − shs )(1 − ths ) chs j x sj ∈ H i = Qa x

(4.6)

where reading backwards, following the causal chain, chs j = gross household income earned in industry j in region s per unit of output of j in s, ths = tax rate for households in s, shs = savings rate for households in s, ki·sh = consumption of products from industry i from everywhere per unit total endogenous household consumption in s, and m ri hs = share of consumption of i in s that originates from r. The columns of H thus represent the endogenous consumption expenditures by region of living s, while Qa contains average household consumption expenditures/industry output ratios.3 3 Note

that this specification does not endogenize the consumption of commuters, which would require separate data on their specific consumption behaviour with a large share of interregional shopping in their region of work (see Madsen and Jensen-Butler 2004, for a SAM model with both interregional commuting and shopping).

48

4 From Basic IO and SU Models to Demo-Economic Models

The addition of (4.6) to the interregional IO model of (2.9), as shown in Fig. 4.1, gives the Type II interregional IO model, followed by its straightforward solution: ⎤ ⎡ ⎤ ⎡ 1,ex ⎤ i h11 · · · h1R f x = Zi + ⎣ · · · · · · · · · ⎦ ⎣ · · · ⎦ + ⎣ · · · ⎦ = Ax + Qa x + f ex ⇒ h R1 · · · h R R f R,ex i ⎡

x = (I − A − Qa )−1 f ex = L∗∗ f ex

(4.7)

When (4.7) is used for impact studies, any increase in endogenous total output will lead to proportional increases in employment, labour incomes and endogenous consumption. This proportional increase models what would happen if all marginal coefficients would be equal to the corresponding average coefficients as point estimated from the base year IO table. This is a reasonable assumption for labour income coefficients, which equal one minus the total of the other input coefficients. It is, however, not a reasonable assumption for employment and consumption package coefficients, nor for tax and savings rates. Marginal employment coefficients are smaller than their average equivalents, whereas marginal tax and savings rates are larger, which together leads to marginal consumption/output ratios Qm that are much smaller than the Qa of (4.7). Miernyk et al. (1967) and Tiebout (1969) solved part of this problem by making a distinction between extensive income growth that accrues to people without an earlier income in the region (mainly school-leavers, non-active partners and new residents) and intensive income growth that accrues to people who stay with their jobs. To extensive income growth, they applied average consumption/output ratios, and to intensive income growth, they applied marginal consumption/output ratios. The indirect part of the resulting, so-called Type III multipliers, was roughly about 20% lower than the comparable Type II multipliers.4 Additionally, Blackwell (1988) considered that new jobs would also go to formerly unemployed residents who would lose their unemployment benefits, which he labelled redistributive income growth. To this type of income growth either marginal consumption/output ratios Qm need to be applied, or the difference between the average ratios of employed residents Qa and unemployed residents Qu , which delivers about the same result. Obviously, adding a negative feedback on unemployment benefits leads to substantially lower, so-called Type IV multipliers. Van Dijk and Oosterhaven (1986), with Dutch unemployment benefits and a vacancy chain submodel for the regional labour market, estimated Type IV multipliers to have values 4 The 20% is derived from Miller and Blair (2009), who report a ratio of Type III to Type II multipliers

of 0.87–0.91 on p. 255. Their ratio, however, includes the direct effect, which we exclude, as no model is needed for its estimation. In the older IO literature, there is quite some discussion about fixed multiplicative relations between Types I, II and III normalized income multipliers (see Miller and Blair 2009, ch. 6). If one defines total endogenous income per regional industry to be equal to that part of it that is paid to regional households, then a fixed relation exists (see Miller and Blair 2009, for proof and empirical ratios). In the old days, this presented an important computational advantage, but nowadays this advantage is outweighed by the disadvantage of having to use a definition of income that only covers the labour part of value added.

4.2 Further Demo-Economic Model Extensions

49

of 35% to 60% between the values of Type I and Type II multipliers per industry, which they therefore viewed as lower and upper limit for the true values of regional multipliers. Batey and Madden (1983) extended these models with a population block and labelled them demographic-economic or demo-economic models. Instead of the earlier ad hoc and iterative model specifications, they proposed the far more efficient commodity-activity framework to formulate them, which we already used in Eqs. 3.18 and 4.2 (see also Batey and Rose 1990). Batey (1985) gave an overview of ten such models with increasing complexity, with the integration of the three types of income changes by Oosterhaven (1981) as the tenth model. All ten models, however, still use a residual definition of intensive income growth, as these models do not make a distinction between the levels and the changes in the levels of variables, which is necessary to adequately distinguish between cases where marginal ratios are needed and cases that require the use of average ratios. With an interregional labour market model, which included vacancy chains for job-to-job hoppers, social security and population growth, Oosterhaven and Folmer (1985) show how the distinction between levels and changes solves this remaining problem. To illustrate the nature of this solution, we finish this overview of demoeconomic modelling with a simplified version of their interregional model, skipping the vacancy chain sub-model and most of the social security and population submodel details. Changes in levels of output are indicated with x, and lagged output levels with x−1 . Hence, x = x − x−1 . The nature of their approach is best understood by starting with endogenous employment growth, measured as the growth in the number of full-time equivalent (fte) jobs per industry per region,  jir ∈ j. For small changes, the growth of employment by definition equals: j = ˆl x + ˆl x−1

(4.8)

where lir = jir /xir ∈ ˆl = diagonal matrix with average employment coefficients, i.e. with inverse labour productivity levels, and ˆl = ˆl − ˆl−1 = diagonal matrix with the decrease in average employment coefficients, i.e. with the growth of nominal labour productivity. In general, the last term of (4.8), with lagged output, will only be relevant in case of a projection of a whole economy, but not in case of impact studies with only limited exogenous changes. Note that in case of impact studies, the average employment coefficients ˆl are better replaced with marginal employment coefficients that will be smaller, but positive, whereas ˆl will almost always be negative. Next, extensive wage income growth yext and intensive wage income growth yint by region of work may be defined using of the outcomes of (4.8): ˆ −1 j and yint = w ˆ j−1 yext = w

(4.9)

50

4 From Basic IO and SU Models to Demo-Economic Models

ˆ = diagonal matrix with wage rates per regional industry. Note that where w sj ∈ w the sum of extensive and intensive wage income growth equals total wage income ˆ ˆj−1 . Furthermore, note that in ˆ ˆj) = w ˆ −1 ˆj + w growth, as for small changes (w ˆ ˆl are case the wage income/production ratios chr i = (wir jir )/xir = wir lir ∈ cˆ h = w stable, the employment decreasing and wage increasing effects of labour productivity growth cancel out. Next, to obtain extensive and intensive wage income growth by region of living, the outcomes of (4.9) have to be pre-multiplied with crj s ∈ Co , which denotes a Rby-IR matrix with commuting origin ratios, indicating the proportion of workers in industry j in region s that commutes in from region r. Note that i Co = i , if external in-commuting is zero. To define redistributive income growth, first, the change in the number of unemployed people u and the number of inactive people without benefits n needs to be explained by region of living: u = −Mu j + uex and n = −Mn j + nex

(4.10)

where m rusj ∈ Mu = R-by-IR matrix with re-employment probabilities, indicating the probability that new jobs in industry j in region s, either directly or indirectly after a vacancy chain,5 are taken up by unemployed formerly living in region r, while uex = exogenous change in number of unemployed per region of living. Comparable definitions hold for the second part of (4.10) with inactive people without benefits (mainly school-leavers, non-working partners and immigrants). Note that i Mu + i Mn = i , if there are no external immigrants taking up part of the new jobs and if all job vacancies, either directly or indirectly after a vacancy chain, are filled up. Equation 4.10 makes explicit that only part of the new local jobs will be filled up by locally unemployed people, who will then lose their unemployment benefits and thus cause a negative feedback on employment in their own region. Another part will be filled up by unemployed from other regions, which will cause a negative feedback on unemployment benefits in those other regions! This will, especially, be the case for new jobs in industries that require relatively high-skilled workers or in the construction industry where workers are used to long commuting distances to work in often changing regions. The remainder of the new jobs, either directly or indirectly after a vacancy chain, will be filled up by either local or immigrating non-active people with no benefits to loose. Using the outcomes of (4.9)–(4.10), pre-multiplied with the commuting matrix Co , the change in total demand for products from industry i in region r may now be defined as: x = Ax + Ka Co yext + Km Co yint + Ku uˆ b u + f ex 5 With

(4.11)

twelve industries, nine occupations, males and females, in case of Queensland, Oosterhaven and Dewhurst (1990) report significant differences in re-employment and immigration probabilities when the vacancy chains of people moving between jobs are ignored.

4.2 Further Demo-Economic Model Extensions

51

rs where kia ∈ Ka = IR-by-R matrix with average consumption/gross income ratios, indicating the consumption of products from i in r per unit of gross income of households living in s, Km = comparable marginal consumption/gross income ratios, Ku = comparable average consumption/gross income ratios for unemployed, u sb ∈ uˆ b = diagonal matrix with unemployment benefits per region of living s and f ir, ex ∈ f ex = column with changes in exogenous final demand for products of i in r. Substitution of (4.8) in (4.9)–(4.10), and subsequent substitution of the results for yext , yint and u in (4.11) gives the following equation for the endogenous change in total output by industry and region:

ˆ ˆl x − Ku uˆ b ˆl x + Ku uˆ b uex ˆ −1 ˆl x + Km Co w x = A x + Ka Co w + lagged variables + f ex (4.12) ˆ −1 ˆl x−1 + Km Co w ˆ ˆl x−1 − Ku uˆ b ˆl x−1 . where lagged variables = Ka Co w After moving the terms with x from the RHS to the LHS of (4.12) and premultiplying the result with the appropriate Leontief-inverse, the resulting solution of (4.12) may be summarized as follows: x = (I − A − Qa − Qm + Qu )−1 (Ku uˆ b uex + lagged variables + f ex ) (4.13) In (4.13), the four coefficient matrices in the extended Leontief-inverse, when added cumulatively, represent the Types I, II, III and IV, direct, indirect and induced impacts of exogenous demand on total output, and thus also on more policy-relevant variables such as employment, value added and CO2 emissions. Note that the Type IV redistributive income growth effect (Qa − Qu )x is, in fact, estimated by taking the difference between the average consumption/output ratios of employed and unemployed people. Also note that (4.13), compared to the standard interregional IO model, has a much larger number of exogenous variables and most of them hidden in the lagged variables component. Finally, and most importantly, note that Eq. 4.10 for non-active people and the vacancy chain sub-model that is behind it, only indirectly influence the size of the Type IV regional multipliers and interregional spillovers. When more non-actives find jobs at the cost of local unemployed, the larger values for Mn and the consequently smaller values for Mu lead to smaller negative feedbacks of disappearing unemployment benefits, and consequently to larger Type IV multipliers and spillover effects. A somewhat different effect occurs when, either directly or indirectly after a vacancy chain, more unemployed from other regions fill up new jobs at the cost of local unemployed. This also leads to larger Type IV multipliers, but it leads to smaller rather than larger Type IV interregional spillovers, as the negative feedback of disappearing benefits shifts from the own region to other regions. These two positive effects on the size of the intra-regional multipliers, namely that of more inactive people and that of more unemployed from other regions taking up new local jobs, lead to an interesting policy dilemma. Often, the goal of regional

52

4 From Basic IO and SU Models to Demo-Economic Models

policy is to reduce local unemployment, while most policy instruments stimulate the growth of local employment (see van Dijk et al. 2019, for an overview of regional policy goals and instruments). The larger Type IV multipliers that result from the two effects, in this regard, have contradictory effects: more new jobs, but relatively less local unemployed taking them up. Also interesting from a policy point of view is the finding that in the case of Queensland, a unit increase in exogenous final demand for some industries generated increased tax receipts and reduced unemployment benefits that actually outweighed the unit cost of increasing final demand (Oosterhaven and Dewhurst 1990). The more extensive interregional labour market model of Oosterhaven and Folmer (1985), of which (4.8)–(4.11) is a simplification, uses the commodity-activity framework of Batey and Madden (1983) to summarize the model, instead of the more simple representation of (4.13). The advantage of (4.13) is that it nicely shows the three types of incomes growth and four types of multipliers that figure so prominently in the demo-economic literature. The disadvantage of this presentation is that it would result in incomprehensible set single equations if this notation and solution would be applied to the full model.6

4.3 Where to End with Endogenizing Final Demand? After endogenizing most of household consumption demand, the obvious next question is: How far should an analyst go with endogenizing more and more components of final demand? 7 Studying the regional impacts of plant close-downs with a singleregion SAM model, Cole (1989, 1997) advocates the fullest possible closure of the model to capture all possible short- and long-run impacts. The distinction between short-run and long-run impacts is made by means of expenditure lags, for which Cole introduces a very handy computational solution. The fullest possible closure is reached by linking the size of government expenditures to tax income, linking investment expenditures to the operating surplus and linking regional exports to regional imports. Especially adding that last causal relation, led to a fierce debate with Jackson et al. (1997) who claimed that closing a single-region model with regard to the RoW leads to inconsistencies, zero exogenous demand and infinitely large multipliers. Oosterhaven (2000) closed the debate on request of the editors of the journal at hand. Obviously, one cannot endogenize interregional feedbacks consistently without specifying the full interregional model. When that is done with regard to the whole RoW, as Cole advocates, the full closure of the extended model does result 6 See

van Dijk and Oosterhaven (1986) and Oosterhaven and Dewhurst (1990) for single-region applications of the above approach, and Oosterhaven et al. (2019) for an overview of extended IO models, especially for the USA. 7 Parts of this section were written earlier for Oosterhaven et al. (2019). I thank my transport economics colleague Jaap B. Polak for providing the data on the close-down of the Fokker aircraft company.

4.3 Where to End with Endogenizing Final Demand?

53

in zero exogenous demand and infinitely large multipliers, as in such a completely closed world model, only the model’s coefficients remain exogenous, whereas all its variables become endogenous. Consequently, such a model may no longer be used to evaluate the impacts of changes in demand, as all demand has become endogenous. For an entirely different reason, overestimation of impacts also occurs when total value added or total employment of an industry is multiplied by that industry’s already too large Type II normalized value added or employment multiplier, c (I − A − Qa )−1 cˆ −1 , in order to indicate its importance for the economy at hand. This is a misuse of impact analysis for public relations purposes, as a multiplier may only be applied to exogenous final demand and never to endogenous value added or endogenous employment. Imagine that the average normalized multiplier equals two and that the analyst would apply this estimation procedure to all industries and sum the results. In that case, the predicted size of the total economy would be twice its actual size, which also numerically shows that this procedure is not allowed. One solution to the overestimation problem is to correct the calculated “gross impact” of a certain industry with that part of that industry that is endogenously dependent on the rest of the economy, in order to obtain the net impact of that industry (see Oosterhaven et al. 2003, for an example of this solution). A second solution is to down-size the standard “gross multiplier” with that part of an industry’s output that is exogenous, that is, to multiply the normalized Type II multiplier with the exogenous final demand/total output ratio yiex, r /xir ∈ yex x such that it becomes a net multiplier (see Oosterhaven and Stelder 2002, for this solution).8 This c (I − A − Qa )−1 cˆ −1 yˆ ex x also solves the overestimation problem, because when the net multiplier is multiplied with an industry’s total employment or total value added, the weighted average of all industries’ net multipliers does become one, which does result in the precise size of the whole economy, as it should. Finally, it is important to understand that even with exogenous exports to the Rest of the World, the fullest possible closure of the remaining components of final demand in a single-region model exacerbates the theoretically already problematic one-sidedness of IO, SUT and SAM models. In case of the close-down of the Dutch aircraft producer Fokker, for instance, aside of the direct loss of 4500 jobs, not too much happened. After only three months, 60% of the mostly highly skilled former employees had found a new job, while most of Fokker’s many subcontractors suffered only a temporary setback in output growth. Some, in fact, were reported to have found new markets for their often high-tech goods and services; new markets that proved to grow much faster than the old secure, but low-growth Fokker demand. This illustrates that possible shortages on local labour markets, price and wage reactions, and pressure to supply to new markets and to develop new products may strongly reduce the demand-driven multiplier estimation of the impact of a negative output shock. In such cases, endogenizing price/wage effects and supply reactions is 8 Note that de Mesnard (2006) takes offence at the use of the word multiplier in this case. See Oost-

erhaven (2007) for a reply and Dietzenbacher (2005) for an independent evaluation. The conclusion of this debate is that the net multiplier is best viewed as a net key sector measure that takes into account the two-sided nature of an industry’s dependence on the rest of the economy versus the rest of the economy’s dependence on that industry. See further Sect. 8.1.

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4 From Basic IO and SU Models to Demo-Economic Models

more important than a further closure of the demand-side; that is, if the consultant is interested in the most probable estimation of the real impacts instead of in reporting maximally large multipliers to serve the special interests of his or her principal.

References Batey PWJ (1985) Input-output models for regional demographic-economic analysis: some structural comparisons. Environ Plan A 17:77–93 Batey PWJ, Madden M (1983) The modelling of demographic-economic change within the context of regional decline: analytical procedures and empirical results. Socio-Econ Plan Sci 17:315–328 Batey PWJ, Rose A (1990) Extended input-output models: progress and potential. Int Reg Sci Rev 13:27–49 Blackwell J (1988) Disaggregation of the household sector in regional input-output analysis: some models specifying previous residence of worker. Reg Stud 12:367–377 Cole S (1989) Expenditure lags in impact analysis. Reg Stud 23:105–116 Cole S (1997) Closure in Cole’s reformulated Leontief model: a response to R.W. Jackson, M. Madden, and H.A. Bowman. Pap Reg Sci 76:29–42 de Mesnard L (2006) A critical comment on Oosterhaven-Stelder net multipliers. Ann Reg Sci 41:249–271 Dietzenbacher E (2005) More on multipliers. J Reg Sci 45:421–426 Jackson RW, Madden M, Bowman HA (1997) Closure in Cole’s reformulated Leontief model. Pap Reg Sci 76:21–28 Madsen B, Jensen-Butler C (2004) Theoretical and operational issues in sub-regional economic modelling, illustrated through the development and application of the LINE model. Econ Model 21:471–508 Madsen B, Jensen-Butler C (2005) Spatial accounting methods and the construction of spatial social accounting matrices. Econ Syst Res 17:187–210 Miller RE, Blair PD (2009) Input-output analysis: foundations and extensions, 2nd edn. Cambridge University Press, Cambridge Miernyk WH, Bonner ER, Chapman JH, Shellhammer K (1967) Impact of the space program on a local economy: an input-output analysis. West Virginia University Library, Morgantown Miyazawa K (1976) Input-output analysis and the structure of the income distribution. Springer, Berlin Miyazawa K, Masegi S (1963) Interindustry analysis and the structure of income distribution. Metroecon 15:89–103 Oosterhaven J (1981) Interregional input-output analysis and Dutch regional policy problems. Gower Publishing, Aldershot-Hampshire Oosterhaven J (2000) Lessons from the debate on Cole’s model closure. Pap Reg Sci 79:233–242 Oosterhaven J (2007) The net multiplier is a new key sector indicator: reply to De Mesnard’s comment. Ann Reg Sci 41:249–271 Oosterhaven J, Dewhurst JHL (1990) A prototype demo-economic model with an application to Queensland. Int Reg Sci Rev 13:51–64 Oosterhaven J, Folmer H (1985) An interregional labour market model incorporating vacancy chains and social security. Pap Reg Sci Assoc 58:141–155 Oosterhaven J, Stelder TM (2002) Net multipliers avoid exaggerating impacts: with a bi-regional illustration for the Dutch transportation sector. J Reg Sci 42:533–543 Oosterhaven J, van der Knijff EC, Eding GJ (2003) Estimating interregional economic impacts: an evaluation of nonsurvey, semisurvey, and full survey methods. Environ Plan A 35:5–18

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Oosterhaven J, Polenske KR, Hewings GJD (2019) Modern regional input–output and impact analysis. In: Capello R, Nijkamp P (eds) Handbook of regional growth and development theories: revised and extended, 2nd edn. Edward Elgar, Cheltenham Pyatt G (2001) Some early multiplier models and the relationship between income distribution and production structure. Econ Syst Res 13:139–163 Pyatt G, Round JI (1977) Social accounting matrices for development planning. Rev Income Wealth 23:339–364 Pyatt G, Thorbecke E (1976) Planning techniques for a better future. International Labour Office, Geneva Sonis M, Hewings GJD (1999) Miyazawa’s contributions to understanding economic structure: interpretation, evaluation and extensions. In: Hewings GJD, Sonis M, Madden M, Kimura Y (eds) Understanding and interpreting economic structure. Springer, Berlin Tiebout CM (1969) An empirical regional input-output projection model: the State of Washington 1980. Rev Econ Stat 51:334–340 van Dijk J, Oosterhaven J (1986) Regional impacts of migrants’ expenditures: an inputoutput/vacancy-chain approach. In: Batey PWJ, Madden M (eds) Integrated analysis of regional systems (London Pap Reg Sci 15). Pion, London van Dijk J, Folmer H, Oosterhaven J (2019) Regional policy: rationale, foundations and measurement of its effects. In: Capello R, Nijkamp P (eds) Handbook of regional growth and development theories: revised and extended, 2nd edn. Edward Elgar, Cheltenham

Chapter 5

Cost-Push IO Price Models and Their Relation with Quantities

Keywords Cost-push price model · Cost shares · Price multipliers · Price/wage/price inflation processes · Consumption/output ratios · LINE model Chapter 4 ended with the conclusion that it may be more useful to add prices and the supply side to a Type IV interregional IO model, instead of further endogenizing final demand. In this chapter, we investigate of how prices figure in IO models. First, we discuss the basic IO price model, then its interregional extension with endogenous consumption expenditures, and then how it may be used together with its accompanying quantity model.

5.1 Forward Causality of the Single-Region IO Price Model The demand-driven IO quantity models of Chaps. 2, 3 and 4 all have accompanying, dual cost-push price models. In the quantity models, prices are entirely passive, whereas quantities are entirely passive in the price models. Figure 5.1 shows the causal structure of the basic IO price model. It is almost equal to Fig. 2.2, which

Primary input prices

C

I

Total output prices

I

Final output prices

A

Intermediate output prices Fig. 5.1 Causal structure of the basic IO price model. Legend c pj ∈ C = primary input cost shares of type p for industry j, ai j ∈ A = intermediate input cost shares of product i for industry j © The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_5

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shows the causal structure of the corresponding quantity model. Besides prices that replace quantities, the only difference is the direction of causality that is completely reversed, which is why the position of the boxes with final output and primary input has been switched in Fig. 5.1 compared to Fig. 2.2. In the quantity model, the causality runs backward from exogenous final demand ⇒ total output ⇒ intermediate demand, back ⇒ total output, and finally ⇒ primary inputs. In the IO price model, the causality of runs in the opposite, forward direction (see Fig. 5.1). The I prices of the single homogeneous output of each industry i, pi ∈ p , are assumed to be endogenous and uniform along the corresponding rows of the first quadrant and second quadrant of the IOT in Fig. 2.1. The P prices of the single homogeneous primary input of type p, p p ∈ pv (i.e. capital, labour and import prices), on the other hand, are assumed to be exogenous and uniform along the corresponding rows of the third and fourth quadrant of the IOT, as shown in Fig. 5.1 where no arrows are entering the box with primary input prices. Any change in one of the P primary input prices is fully passed on to the I output prices. The size of the subsequent change in output prices is, of course, determined by the size of the primary input cost shares in total output, c pj ∈ C, as indicated by the arrow accompanied by the matrix C. This direct effect on the price of total output, pv C, is fully passed on to all intermediate users (i.e. firms) along the rows of the first quadrant of the IOT and to all final users along the rows of its second quadrant, as indicated by the two arrows with the matrix I. Industries that use these more expensive intermediate outputs, in turn, pass these cost increases fully on to their clients. The size of these first-order indirect effects on the I output prices is, of course, determined by the intermediate input cost shares in total output, ai j ∈ A. These effects thus equal the direct impact pv C times A. These first-order indirect price changes pv CA are again fully passed on, which results in second-order indirect price effects pv CA2 , and so on. The final users are subject to the same price changes of total output by industry, but in the basic model, they do not pass them on any further, as indicated by the absence of arrows leaving the box with final output prices. The cumulative effect of any change in primary input prices on total output prices therefore equals the outcome of the Taylor expansion pv (C + CA + CA2 + CA3 + · · · ) = pv C (I − A)−1 = p . This total effect consists of the direct effect C and the indirect effect, the size of which is determined by the size of the Leontief-inverse (I − A)−1 . Note that the sum of both effects equals unity, i.e. i C (I − A)−1 = i , as follows from the sum of the cost shares that equals unity, i A + i C = i . The mathematics of this basic IO price model (Leontief 1951; Chenery and Clark 1959) formalizes the above explanation of its causality. Its accounting identities are based on the cell values of the columns of the IOT and distinguish quantities from prices, whereas those of the quantity model are based on the rows of the IOT and do not distinguish prices, because the quantity model assumes all prices constant and equal to one (Schuman 1968). The accounting identities for the values of the cells of each column j of the IOT are equal to:

5.1 Forward Causality of the Single-Region IO Price Model

pjxj =

 i

pi z i j +

 p

p p v pj , or in matrix algebra: p xˆ = p Z + pv V

59

(5.1)

Second, just like the quantity model, the price model assumes that intermediate and primary input coefficients are fixed, and co-determine the size of Z and V, as explained in Sect. 2: Z = Aˆx and V = Cˆx

(5.2)

Substitution of both parts of (5.2) in (5.1) and post-multiplication with xˆ −1 shows that the prices of total output equal the sum of the prices for intermediate and primary inputs, weighted by their respective cost shares: p = p A + pv C

(5.3)

Finally, adding the assumption that, under full competition, all price changes are fully passed on to all users delivers the solution of the basic (also called Type I) IO price model. The solution shows how the endogenous prices for total output are determined by the exogenous prices of the primary inputs and both sets of cost shares: p = pv C(I − A)−1 = pv CL

(5.4)

Note that the  aggregate Type I final output price multipliers of exogenous primary input prices, i c pi li j ∈ C(I − A)−1 , equal the aggregate Type I primary input quantity multipliers of exogenous final output from Sect. 2.2. In case of the price model, they represent the total of the direct and indirect weight of the primary input prices in the final output prices, which equals one. In the quantity model, they equal the direct and indirect quantity of primary inputs embodied in final output, which also equals one, as all quantities are measured in base year prices set equal to one. This primal-dual relationship between the IO quantity and price model may be further illustrated by post-multiplying (5.4) with final demand y, which gives: p y = pv C(I − A)−1 y = pv v

(5.5)

This confirms that the value of total final output p y equals the value of total primary input pv v, which also follows from the macroeconomic identity C + I + G + E = Y + M in Fig. 2.1. Second, and more importantly, (5.5) shows the independency (or better duality) of the price and quantity model. Although their solutions are linked by means of (5.5), their variables move independently: with exogenous final demand quantities backwardly determining primary input quantities and exogenous primary input prices forwardly determining final output prices. Obviously, the IO price model is suited to model the impact of any primary input price change (i.e. a change in product tax and subsidy rates, in wage rates, in capital return rates or in import prices) on consumption, investment and export prices by delivering industry. This is why this model is also known as the cost-push

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IO price model. Early applications of this model show the price effects of pollution abatement policies (Evans 1973; Giarratani 1974), and the price effects of energy price increase in a single-region IO model (Miernyk 1976) and in a multi-regional IO model (Polenske 1979). A recent application uses the cost-push price model to chart the vulnerability of US industries to reaching peak oil production rates by simulating a 100% oil price hike (Kerscher et al. 2013).1

5.2 Type II Interregional Price and Quantity Models Combined: Lower Multipliers Naturally, both the Type I multi-regional and interregional extension of the basic IO quantity model, from Sect. 2.3, have an accompanying (dual) cost-push price model. The mathematics and the economics of these two price models are straightforward. The dual of the Type II interregional IO quantity model of Sect. 4.2 is less straightforward, while it is more interesting economically. The bottom part of Fig. 5.2 shows that it models the following causal chain: exogenous non-wage primary input prices (mainly capital and external import prices) ⇒ total output prices ⇒ intermediate input prices and consumption expenditure prices (⇒ wage rates), back ⇒ total output prices, finally ⇒ remaining final output prices. The Type II interregional price model thus allows for an interregional analysis of cost-push price/wage/price inflationary processes, which makes it worth spelling out. To discuss this price model properly, we first need to complete the Type II interregional IO quantity model. The causal structure of this model, shown in Fig. 4.1 in detail for two regions, is summarized in the upper part of Fig. 5.2. Its mathematics consists of four equations: three old ones and a new one that is needed to specify the price model. First, the accounting identities for the rows of an IRIOT (see Fig. 2.3) express that total output/supply, xir ∈ x, follows the sum of intermediate demand Zi, endogenous consumption demand Hi and exogenous final demand f ex , without any change in prices: x = Zi + Hi + f ex

(5.6)

Next, fixed intermediate input coefficients, airjs ∈ A, and fixed average consumption/output ratios, qirjs ∈ Qa , explain intermediate demand and endogenous consumption demand as a function of the output of industry j in region s: Zi = Ax, Hi = Qa x 1 In

(5.7)

(5.1) and (5.10), to keep the mathematics simple, it is assumed that the P exogenous primary input prices are equal for all purchasing industries in all regions. In practical applications, one may, more realistically, equally well assume that these exogenous prices behave differently for each industry.

5.2 Type II Interregional Price and Quantity Models Combined …

Exogenous in the quantity model

Zi

Hi

Qa

I

61

I

A

x I

C

Demand-driven quantity model Cost-push price model I

Crem

p Qa

I I

A

Exogenous in the price model

Fig. 5.2 Interacting Type II interregional IO price and quantity models. Legend pz , ph and pex = vectors with IR identical prices for, respectively, intermediate output Zi, endogenous consumption output Hi and exogenous final output f ex . pr em = vector with P prices of remaining primary inputs. Cr em = matrix with cost shares of the remaining primary inputs in total output. edp = vector with IR price elasticities of exogenous final demand. esp = vector with P price elasticities of exogenous supply of remaining primary inputs

Finally, a new, third behavioural equation with fixed primary input coefficients, cspj ∈ Cr em , is needed to explain the remaining primary inputs of industry j in region s, v spj ∈ Vr em : Vr em = Cr em xˆ , with i C

r em

xˆ = i Cˆx − i Q xˆ and i A + i Q + i C a

a

r em

= i (5.8)

Note that the remaining primary inputs do not have a feedback effect on industry output in the quantity model (see the lacking outgoing arrows within the upper part of Fig. 5.2). The middle  part of (5.8) clarifies that the remaining primary inputs per regional industry, p cspj x sj ∈ i Cr em xˆ , equal the difference between total primary inputs, i Cˆx, and endogenous consumption of local households that is paid from their labour incomes by regional industry, i Qa xˆ , as explained in Sect. 4. In the Type II quantity model, the latter wage-related part of total primary inputs does have a feedback on total output by regional industry, as shown by the arrow with Qa in Fig. 5.2. The solution of the Type II quantity model for the remaining primary inputs and for any other impact variable, such as employment or CO2 emissions, is derived by

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substituting (5.7) into (5.6), moving the terms with endogenous total output from its RHS to its LHS, pre-multiplying the result with the Type II interregional Leontiefinverse L∗∗ = (I − A − Qa )−1 and substituting the result into the first term of (5.8). This gives: x = (I − A − Qa )−1 f ex = L∗∗ f ex and Vr em = Cr em L∗∗ fˆ ex

(5.9)

An overview of the type of regional and interregional impact studies that may be done with (5.9) is given in Oosterhaven et al. (2019). The price dual of the Type II quantity model (5.6)–(5.8) is relatively complex (Oosterhaven 1981). Here, without altering the economic mechanisms of the model, the mathematical presentation is simplified by ignoring the endogenous character of the taxes and savings from endogenous wage income specified in Eq. (4.6). This, especially, simplifies the presentation of accounting identities of the Type II interregional IO price model along the columns of the IRIOT (see Fig. 2.3). They now define the total value of the inputs of industry i in region r as: pir xir ∈ p xˆ = p Z + p H + pr em Vr em

(5.10)

All but one term of (5.10) already appeared in (5.1), but now they are defined for multiple regions instead  of a single region. New is the term ri pir h ri js ∈ p H. It defines the total value of the endogenous consumption expenditures of households paid for by their labour incomes earned in industry j in region s. Note that wages are not explicitly defined in (5.10), but appear implicitly as the weighted average of the prices of the endogenous consumption expenditures. This means that the impact of increasing consumption prices on wages is also modelled implicitly. Finally, note that the precise definition of the last term of (5.10) is given in the middle term of (5.8) (see Footnote 1). Substitution of (5.7) and (5.8) into (5.10) and post-multiplication with xˆ −1 shows that the prices of total output by regional industry equal the sum of the prices for intermediate inputs, endogenous consumption expenditures and remaining primary inputs, weighted by their respective cost shares in regional industry output: p = p A + p Q + pr em Cr em a

(5.11)

Note that wages implicitly have an impact on total cost and thus on output prices through the prices for endogenous consumption expenditures in the term p Qa . Again assuming full competition, any change in one of them will be fully passed on forwardly. The solution of the Type II interregional IO price model is obtained by moving the terms with p from the RHS to the LHS of (5.11), and post-multiplying the result with the Type II interregional Leontief-inverse L∗∗ . This gives: p = pr em Cr em (I − A − Qa )−1 = pr em Cr em L∗∗

(5.12)

5.2 Type II Interregional Price and Quantity Models Combined …

63

Similar to the solution of the single-region Type I price model (5.4), the solution of the interregional Type II price model (5.12) also delivers  final output price multipliers of the P exogenous primary input prices pr em , i.e. ri crpi lirjs ∈ Cr em L∗∗ . They equal the corresponding primary input quantity multipliers of exogenous final demand of the Type II quantity model. Both sets of multipliers again sum to one, now because of the last part of (5.8). In case of the price model, these multipliers represent the direct, indirect and consumption-induced weight of the remaining exogenous primary input prices (mainly tax and subsidy rates, capital return rates and external import prices) in the prices of final output. The similar “equality to one” in both price models, in fact, hides two opposing changes. The exogenous part of the primary input prices has become smaller, because interregional intermediate import prices and wage rates have both become endogenous (see Eq. 5.10), whereas the column sums of the dimensionally larger Leontief-inverse have become larger. The latter even holds for the intra-regional part of the Type II interregional Leontief-inverse. In case of the price model, this is for two reasons. First, the interregional price multipliers will be larger because the following interregional feedback effect has been added: output prices home region = export prices home region = import prices other regions ⇒ output prices of other regions = export prices other regions = import prices home region ⇒ output prices home region and so on. Second, the Type II price multipliers will be larger because the following price/wage/price feedback effect has been added: output prices home region = consumption prices home region and other regions = (implicit) wage rates home region and other regions ⇒ output prices home region and so on. Finally, note that there is an important difference in the use of price multipliers versus quantity multipliers in impact studies. In the quantity model, all quantities are measured in base year index prices that are all equal to one (Schuman 1968). A change in the quantity of exogenous final demand thus represents an absolute change, i.e. if exogenous final demand of an industry is 50 million euro and it goes up with 10%,  f ind = 5 million euro. A change in an exogenous primary input price, however, represents a relative change in its base year value of one, i.e. if the foreign import price goes up with 10%, p f or = 0.10. Taking this into account, the Type II interregional IO price model enables comparable types of cost-push price simulations as the Type I single-region model, but now including the price/wage/price causality chain in an interregional setting. The first application of the above Type II price model may be found in Oosterhaven (1981), who uses it to simulate the regionally different consumer price impacts of the increases in the international oil prices in the 1970s, in case of the Netherlands. More recent applications of the cost-push price model relate to the cost of the Kyoto protocol for consumers across different countries with an interregional Type I price model (Dietzenbacher and Serrano 2012), while the model may equally well be used to simulate the impact of the increasing US import tariffs on Chinese products, in the late 2010s, on US consumer prices and further forwards on the prices of US exports to the RoW, including China.

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Still, no interaction between prices and quantities appears in any of the applications of the IO quantity and price models of whatever Type, with, as far as we know, with one major exception. Madsen and Jensen-Butler (2004, see also Madsen 2008, chap. 6) show how the empirical richness of very detailed, interregional social accounting models may be maintained while introducing various price–quantity interactions, which is usually only achieved for all prices in much smaller, but highly nonlinear computable general equilibrium (CGE) models (see Bröcker 1998; Shoven and Whalley 1992) or more partially, for restricted sets of prices, in larger econometric IO models (see Kratena 2017). The quantity version of the LINE model of Madsen and Jensen-Butler (2004) is akin to the Type IV demo-economic model with endogenous unemployment discussed in Sect. 4.2. It has 12 industries, 20 products, 14 age/gender groups, 5 education levels, 4 household types, 13 public consumption types and 10 capital/investment types, all for 277 Danish municipalities. The price version of the LINE model is the mirror image of its quantity version. The combination of both models is solved by iteratively switching from the quantity model to the price model and back. This iterative method of model solution is summarized in Fig. 5.2, where the Type II interregional IO price and quantity model are linked by means of two sets of price elasticities. An impact study with the combined model may start with either an exogenous primary input price change or an exogenous final demand quantity change. Without loss of generality, let us start with a quantity increase of exogenous final demand f ex in the upper left part of Fig. 5.2. After the quantity model is run for the first time, the required increase in the supply of remaining primary inputs Vr em is then supposed to lead to an increase in the corresponding primary input prices. The size of these primary input price increases is determined by the inverse of the corresponding P primary supply price elasticities (ˆesp )−1 . With the thus estimated increases in remaining primary input prices pr em , the Type II interregional price model is run, starting at the bottom right part of Fig. 5.2. The resulting increase in the prices of exogenous final output pex is next assumed to lead to an opposite change in their quantity. The size of the quantity decreases of exogenous final demand f ex is determined by the corresponding IR final demand price elasticities, eˆ dp , and is fed back into a second run of the quantity model, and so on. When, in absolute terms, this second round quantity decrease is smaller than the first round increase, the iterative solution will converge with ever smaller oscillations to a quantity increase that is considerably smaller than the one that would have been predicted with only a single run of only the IO quantity model. This result, i.e. lower quantity multipliers, is more realistic than the high multipliers that are usually obtained with a regular Type II quantity model that ignores the price effects (see Sect. 4.2 for other reasons why Type II quantity multipliers are too high). The same multiplier size conclusion holds, mutatis mutandis, when the first iteration would start with an exogenous primary input price increase in the bottom right part of Fig. 5.2. In the first round, this will lead to higher final output prices, which lead to lower final demand quantities, lower total output and primary input quantities,

5.2 Type II Interregional Price and Quantity Models Combined …

65

and end up with increases in the price of the primary inputs that are smaller than those obtained with a single run of only the Type II price model. A simple application of the basic idea of Fig. 5.2 would be do just one iteration, starting with the solution of a single-region Type I price model via demand price elasticities back to the solution of the single-region Type I quantity model, as done in Choi et al. (2010) for an analysis of the impacts of a carbon tax on output, resource use and CO2 emissions by US industries. Their interpretation that such an analysis produces the short-run impacts of a carbon tax, whereas doing more iterations would give an indication of the longer run impacts is false, as the length of the market equilibrium process has no relation with the length of iterative solution of the combined model. In fact, Fig. 5.2 still represents a comparative static model. The duration of the market equilibrium process may be quick if people and firms have perfect expectations about future price and quantity changes. It may also take a long time with temporary adaptations in various levels of stocks when information about future changes is not perfect (Romanoff and Levine 1986). Finally, note that notwithstanding the presence of two price/quantity interfaces between the Type II interregional price and quantity models in Fig. 5.2, the combined model still does not serve to simulate the impact of supply-side quantity shocks on the interregional economy, such as those caused by natural or man-made disasters. It only serves to simulate the interregional, interindustry price and quantity impacts of supply-side price shocks, such as international oil price hikes, the introduction of carbon taxes and the imposition of import tariffs.

References Bröcker J (1998) Operational spatial computable general equilibrium modelling. An Reg Sci 32:367–387 Chenery HB, Clark PG (1959) Interindustry economics. Wiley, New York Choi J-K, Bakshi BR, Haab T (2010) Effects of a carbon price in the U.S. on economic sectors, resource use, and emissions: an input-output approach. Energy Pol 38:3527–3536 Dietzenbacher E, Serrano M (2012) How much would the Kyoto Protocol cost to consumers? In: Paper final WIOD conference, Groningen, 24–26 Apr 2012. http://www.wiod.org/conferences/ groningen/Paper_Dietzenbacher_Serrano.pdf. Accessed 26 Aug 2019 Evans MK (1973) A forecasting model applied to pollution control cost. Pap Proc Eighty-fifth Annu Meet Am Econ Assoc 63:244–252 Giarratani F (1974) The effect on relative prices of air pollution abatement: a regional input-output simulation. Model Simul 5:165–170 Kerscher K, Prell C, Feng K, Hubacek K (2013) Economic vulnerability to peak Oil. Global Environ Change 23:1424–1433 Kratena K (2017) General equilibrium analysis. In: ten Raa T (ed) Handbook of input-output analysis. Edward Elgar, Cheltenham Leontief WW (1951) The structure of the American economy: 1919–1939, 2nd edn. Oxford University Press, New York Madsen B (2008) Regional economic development from a local economic perspective—a general accounting and modelling approach. Habilitation thesis, University of Copenhagen

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Madsen B, Jensen-Butler C (2004) Theoretical and operational issues in sub-regional economic modelling, illustrated through the development and application of the LINE model. Econ Model 21:471–508 Miernyk WH (1976) Some regional impacts of the rising costs of energy. Pap Reg Sc Assoc 37:213– 227 Oosterhaven J (1981) Export stagnation and import price inflation in an interregional input-output model. In: Buhr W, Friedrich P (eds) Regional development under stagnation. Nomos-Verlag, Baden-Baden Oosterhaven J, Polenske KR, Hewings GJD (2019) Modern regional input-output and impact analysis. In: Capello R, Nijkamp P (eds) Handbook of regional growth and development theories: revised and extended, 2nd edn. Edward Elgar, Cheltenham Polenske KR (1979) Energy analyses and the determination of multiregional prices. Pap Reg Sci Assoc 43:83–97 Romanoff E, Levine SH (1986) Capacity limitations, inventory, and time-phased production in the sequential interindustry model. Pap Reg Sci Assoc 59:73–91 Schuman J (1968) Input-output analyse. Springer, Berlin Shoven JB, Whalley J (1992) Applying general equilibrium. Cambridge University Press, New York

Chapter 6

Supply-Driven IO Quantity Model and Its Dual, Price Model

Keywords Supply-driven IO quantity model · Ghosh model · Allocation coefficients · Ghosh-inverse · Processing coefficients · Revenue-pull IO price model · Revenue shares · Price multipliers · CGE models Chapter 4 ended with the conclusion that it may be more useful to add prices and the supply side to a Type IV interregional IO model, instead of further endogenizing final demand. Chapter 5 dealt with the role of prices in IO models. Here we continue with the role of the supply side in IO models.

6.1 Plausibility of the Supply-Driven Input-Output Model In the 1970s and 1980s, it was thought that the supply-driven IO model (Ghosh 1958) would be suited to simulate the impacts quantity shocks to the supply side of the economy.

6.1.1 Basic Supply-Driven IO Model: How Factories May Work Without Labour The core assumption of the basic (Type I) supply-driven IO quantity model is that the intermediate and final output ratios (also called allocation coefficients) are fixed along the rows of the IOT and determine the size of the supply of intermediate and final outputs by industry:

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_6

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z i j = xi bi j ∈ Z = xˆ B and yiq = xi diq ∈ Y = xˆ D

(6.1)

When only one single IOT is available, point estimates of the output ratios are calculated along the rows of the IOT by means of B = xˆ −1 Z and D = xˆ −1 Y. Note that (6.1) represents the exact opposite of the assumption of fixed intermediate and primary input ratios of the demand-driven IO model (see Eq. 2.3), which in that model determines the size of the demand for intermediate and primary inputs by industry. The other assumption of the demand-driven model, namely that total output/production follows the demand for outputs along the rows of the IOT, also has its exact opposite in the supply-driven IO model (SDIOM), namely that total input/production follows the supply of primary and intermediate inputs along the columns of the IOT:   zi j + v pj ∈ x = i Z + i V = i Z + v (6.2) xj = i

p

Hence, instead of final demand, the SDIOM has the supply of primary inputs as its exogenous driving force. This is illustrated in Fig. 6.1, with the causal structure of the SDIOM, where no arrows are entering the box with primary inputs. Any increase in exogenous primary inputs leads to an equally large increase in total input, indicated by the outgoing arrow with the matrix I. The equal increase in total output is then distributed among intermediate and final users, in accordance with the fixed intermediate and final output ratios, as indicated by the arrows with the B matrix and the D matrix, respectively. Hence, the direct supply effect of a unit increase in primary inputs equals I, the first round indirect supply effect equals IB, the second round indirect supply effect equals IB2 , and so on. Like in the demand-driven model, the cumulative supply effect of a unit increase in exogenous primary inputs thus equals the outcome of a Taylor expansion, namely I + B + B2 + B3 + … = (I − B)−1 = G, i.e. the Ghosh-inverse. A sufficient condition for this Taylor expansion to converge is that the row sums of the output ratios are all smaller than one, i.e. B i < i (Miller and Blair 2009, p. 33). This will almost always be the case, because B i + D i = i, while the final output is almost always be positive. Another interesting property of Fig. 6.1 is that it is almost equal to the (also forward or downstream) casual structure of the cost-push IO price model shown in

Primary input

I

D

Total output

B

Final output

I

Intermediate output Fig. 6.1 Causal structure of the supply-driven IO quantity model. Legend bi j ∈ B = intermediate output coefficients, indicating the allocation of output of industry i to industry j per unit of output of i, diq ∈ D = comparable final output coefficients

6.1 Plausibility of the Supply-Driven Input-Output Model

69

Fig. 5.1. The causality of both models runs in the same way: exogenous primary input ⇒ total input/output ⇒ intermediate outputs, back ⇒ total input/output, finally ⇒ final output. The only difference is in the content of the effects. This similarity is employed by Dietzenbacher (1997), who mathematically proves that the SDIOM may also be interpreted as the cost-push IO price model expressed in nominal/value terms. In this interpretation, final output price impacts of exogenous primary input price changes are evaluated in terms of changes in values, with constant quantities, instead of in terms of changes in prices, as in (5.1)–(5.2). Thanks to this interpretation, the row sums of the Ghosh-inverse (I − B)−1 may be used to indicate the size of an industry´s forward linkages, just as the column sums of the Leontief-inverse (I − A)−1 are used as a measure of the size of the backward linkages of an industry (for a further discussion, see Sect. 8.1). The economics of the SDIOM may be complex; its mathematical solution is simple. It follows from substituting the first part of (6.1) into (6.2), moving the result to the LHS of (6.2), and instead of pre-multiplication with the Leontief-inverse, the result now has to be post-multiplied with the Ghosh-inverse G = (I − B)−1 . This gives the following solution for total input: x = v (I − B)−1 = v G

(6.3)

Additionally, instead of the endogenous intermediate and primary inputs of the demand-driven model, the SDIOM has endogenous intermediate and final outputs. Their solution follows from substituting (6.3) into (6.1), which gives: Z = vˆ G B and Y = vˆ G D

(6.4)

 In (6.4), j gi j d jq ∈ G D represent the final output (i.e. consumption, investments, government expenditures and exports) quantity multipliers of the exogenous primary input of industry i. Originally, Ghosh (1958) formulated his model for the—then—rather centrally planned Indian economy, which suffered from excess demand and multiple shortages. Distributing the scarce supply of state-controlled industries according to historical allocations seemed a wise first approach to planning the economy. On second thought, however, the consequences of applying the SDIOM in centrally planned economies may be severe, as this model ignores the complementarities of inputs along the columns of the IOT, which may easily lead to the combination of both stocks of redundant supplies and shortages of other products (see Oosterhaven 1988). Early on, the SDIOM also became regarded as a serious alternative for the demanddriven IO model in case of market economies, as Ehret (1970) for Germany, and Giarratani (1981) and Bon (1986) for the USA, reported a similar temporal stability of input and output coefficients. Helmstädter and Richtering (1982), for Germany, for 1960–75, even found output coefficients to be significantly more stable and reported smaller prediction errors for the SDIOM than for the demand-driven IO model. These, hardly discriminating empirical findings are not surprising in view of the following close relationship between the two sets of coefficients:

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

B = xˆ −1 Z = xˆ −1 Aˆx and A = Zˆx−1 = xˆ Bˆx−1

(6.5)

Hence, only under conditions of uneven growth by industry one may expect a significant difference in stability of the two sets, as follows directly from the specification of the temporal change in one set of coefficients if the other set is assumed to be stable (Chen and Rose 1986): Bt+1 = gˆ −1 At gˆ for a stable A matrix, and At+1 = gˆ Bt gˆ −1 for a stable B matrix (6.6) where gˆ = xˆ t+1 xˆ t−1 = a diagonal matrix with the growth rates of total output by industry. Note that (6.6) will, especially, be discriminating if only one or a few industries receive a supply or demand shock, as will typically be relevant in case of impact studies and not in case of projections of an entire economy. Early applications of the SDIOM were done by Augustinovics (1970) and Giarratani (1976). Augustinovics inventively used modifications of Eqs. 2.5 and 6.4 for international and intertemporal comparisons of economic structure, while Giarratani  used the total supply multipliers j gi j ∈ G i to indicate the potential, economywide forward or downstream impact of changing the supply of energy-producing industries i. Later on, the model became used to simulate the impacts of specific product shortages and supply disruptions (Davis and Salkin 1984; Chen and Rose 1986), such despite early warnings about the plausibility of the model (Giarratani 1980; Oosterhaven 1981, 140–41).1 This led to a sharp debate (Oosterhaven 1988; Gruver 1989; Rose et al. 1989; Oosterhaven 1989) leading to the conclusion that the SDIOM is unsuited to do impact studies of quantity shocks to the supply side of the economy. Why? Consider a sudden drop in the production of aluminium of say 50%. Before using the SDIOM, this drop first needs to be translated into an equivalent drop in the primary input of the aluminium industry, as production is endogenous and only primary input is exogenous in the SDIOM. However, what is “equivalent” is not evident. The most plausible drop in primary inputs would be a corresponding 50%. What would common economic sense predict regarding the impact of a sharp drop of 50% in the supply of primary inputs? The direct effect would, of course, be an absolutely much larger drop in total output, about equal to the inverse of the primary input coefficient (also called processing coefficient or working-up ratio, Oosterhaven 1988). Besides, one would expect a drop of about 50% in all other inputs of the aluminium industry, as these are no longer needed. Neither of these two direct effects will be predicted by the SDIOM, which only predicts an output effect that will be much too low, as it is wrongly assumed to be equal to the exogenous primary input effect (see Fig. 6.1).

1 Note

that Chen and Rose (1986) do report “counter-intuitive results” and talk about “absurd machinations of the supply model” in case of a 50% reduction of aluminium production in Taiwan. However, at that time, they did not conclude that the model could not be used for impact studies of such type of events.

6.1 Plausibility of the Supply-Driven Input-Output Model

71

Next, consider the first round indirect effects. Aluminium using industries will be confronted with a reduction of their supply and will look for substitutes, either spatially (imports) or technically (other products). However, these two logical behavioural reactions are not predicted by the SDIOM. Imports cannot change, as they are exogenous in the SDIOM, whereas local industries that are able to produce technical substitutes are predicted by the SDIOM to decrease their output, instead of to increase it. Moreover, cumulatively, all other industries will decrease their production, either directly as aluminium users or indirectly as users of users, but they will not proportionally decrease their value added nor increase their imports of aluminium substitutes, as these are exogenous in the SDIOM (see again Fig. 6.1). The reasons for these false predictions of the SDIOM are found in its theoretical assumptions. The micro-economic foundation of the demand-driven IO model started in Sect. 2.2 with simplifying the most general production function, by assuming a single homogeneous output and multiple heterogenous inputs. The comparable foundation the SDIOM starts with the opposite simplification of assuming a single homogeneous input and multiple heterogeneous outputs that are produced according to the following production function, which is the opposite of Eq. 2.7: 2 xi = max (z i j /bi j , ∀ j; yiq /diq , ∀q)

(6.7)

   under full competiWith (6.7) maximizing profits z p + y p − x p i j j iq q i i j q tion (i.e. at given market prices) comes down to maximizing revenues and producing the heterogenous outputs in fixed proportions according to (6.1). Under full competition, industry i will thus have a perfectly elastic demand for its single homogenous input (it buys everything that is supplied to it at the going price) and will have a perfectly inelastic supply of its multiple intermediate and final outputs (Oosterhaven 1996). The assumption of a production process with a single homogeneous input is ludicrous, as it implies that all inputs are perfect substitutes for each other, i.e. factories may run without labour, cars may drive without gasoline, and so on. This alone should be sufficient reason to not use this model at all. The perfect jointness of all intermediate and final outputs is another extreme assumption.3 Technically, it may apply to some parts of some industries, such as the chemical industry. Economically, 2 An

alternative interpretation in which the Ghosh model is not the exact opposite of the Leontief model is presented by de Mesnard (2009). His point of departure is a physical IO table that has homogenous outputs along its rows and heterogeneous inputs along its columns. With this asymmetric base assumption naturally only asymmetric results can be derived. In reality, however, even tons of steel have different qualities and different prices and cannot be simply added in physical units. In reality, any IOT will have heterogeneous outputs along its rows as well as heterogenous inputs along its columns. This more realistic situation is our point of departure. This is also the reason why do not discuss IO models based on physical data (Miller and Blair 2009, ch. 2), as such data do not exist. 3 The equivalent of this assumption in case of a supply-driven supply-use model consists of the product of two separate assumptions (de Mesnard 2004): (1) the fixed product mix assumption that applies to the rows of the supply table and (2) the fixed (intermediate and final) product sales

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

it may apply to industries that want to keep all their customers equally supplied regardless of their willingness to use/purchase (Giarratani 1981). In fact, only by intelligently combining processing coefficients (i.e. inverse primary input ratios) with intermediate output coefficients, while adapting regional purchase coefficients to accommodate for import and export substitution, one may still use the basic forward linkages causality of the SDIOM (see Oosterhaven 1988, for the theory, Oosterhaven 1981, for a land reclamation application, Cartwright et al. 1982, for a nuclear disaster application and more recently Rose and Wei 2013, for a port shutdown application).

6.1.2 Type II Supply-Driven IO Model: How More Private Cars May Run with Less Gasoline The economic causality and the mathematics of the interregional extension of the single-region or single-nation SDIOM are straightforward. The multi-regional extension is mathematically somewhat more complicated (Bon 1988), but is not of much interest, as most MRIOTs have been subject to RAS procedures, which is why they are usually published and used as IRIOTs (see further Sect. 3.3). The Type II extension of the single-region SDIOM (Davis and Salkin 1984) is more complicated and more interesting, particularly since Guerra and Sancho (2011) claim that this extension makes the SDIOM more plausible in case of centrally planned economies. Oosterhaven (1988, 2012), however, argues that the Type II SDIOM is even more implausible for market economies than the Type I SDIOM, while it becomes even more problematic as a guide for centrally planned economies. Why? The causality of the Type II Ghosh model runs in the same forward direction as that of the extended cost-push price model shown in bottom part of Fig. 5.2. Therefore, its basic accounting identity is very similar to that of (5.10). It expresses that total input/production is determined column-wise, by the exogenous supply of the remaining (non-labour) primary inputs, vr em = i Vr em , the endogenous supply of intermediate inputs, i Z, and endogenous supply of consumption good to workers, i H: x = vr em + i Z + i H

(6.8)

This, additional to the implications of the basic SDIOM, further implies that any increase in household consumption of workers (i.e. in their wage sums) leads to an absolutely equally large direct increase in total input of firms, without the direct need of any other intermediate or primary inputs, as all inputs are perfect substitutes for one another.

ratios assumption that applies to the rows of the use table (see Fig. 3.2). Assumption (1) seems less implausible than the comparable SDIOM assumption, but assumption (2) is equally implausible.

6.1 Plausibility of the Supply-Driven Input-Output Model

73

Table 6.1 Output, value-added and consumption impacts of two* scenarios, with two models** Type II demand-driven Leontief model with a shift in government expenditures

Type II supply-driven Ghosh model with a shift in product taxes and subsidies

Scenario +5 in i1 & −5 in i3

+5 in i2 & −5 in i3

+5 in i1 & −5 in i3

+5 in i2 & −5 in i3

Industry xi

vi

xi

xi

h i

xi

i1

+4.7

+0.9 −0.8 −2.4 −0.5 −1.4

+2.9

+0.6 −0.2

+0.2

i2

−1.6 −0.2 −0.1

+0.1

+4.8 −0.1

+0.2

i3

−5.8 −2.3 −0.7 −6.4 −2.5 −1.2 −2.4 +1.3

−0.7 −3.5 −0.3 −1.1

−2.7 −1.5 −1.5 −6.8 −2.8 −2.8

+2.2

Total***

h i

+2.0

vi

h i

+0.2 −0.2

vi

+8.2 +0.6 +1.7 +0.3 +7.5 +2.2

vi

h i

+1.9 −0.6 −0.6

* The results for a third scenario of “+5 in i1 & −5 in i2” may easily be derived by deducting the results of the first scenario from those of the second scenario. ** All coefficients and values used are derived from Table 2a in Guerra and Sancho (2011). *** Due to individual rounding, the numbers do not necessarily add up to the rounded totals. Source Oosterhaven (2012)

The Type II model, furthermore, requires a split up of the endogenous final output part of (6.1) into H and Yrem , and the subsequent use of now three sets of fixed output ratios: Z = xˆ B, h i j = xi dihj ∈ H = xˆ Dh and Yr em = xˆ Dr em

(6.9)

The new, middle term expresses that any increase in the total supply of industry i leads to a percentage-wise equally large increase in the consumption of i, without the need of any other consumption goods and services. This implies that now consumers may, just like firms in the Type I model, also drive their cars without gasoline as well as run their kitchen appliances without electricity.4 Up till now the Type II Ghosh model has only been used in some numerical exercises that discuss its plausibility (Guerra and Sancho 2011; Oosterhaven 2012; Manresa and Sancho 2013). The additional assumptions of the supply-driven consumption function are shown above to be as implausible as those of the supply-driven intermediate output function. Whether or not the combination of both sets of assumptions makes the Type II model more or less implausible than the Type I model is not directly clear. The impacts of four hypothetical exogenous impulses (scenarios), shown in Table 6.1, answer this question. The impacts shown are calculated by applying the Type II Leontief model to two exogenous final demand scenarios and by applying the Type II Ghosh model to two corresponding exogenous primary input scenarios. The first, upper left number in Table 6.1 (+4.7) indicates that the Type II Leontief model predicts that total output in industry i1 increases with 4.7, say billion dollar, if the government shifts 5 billion dollar of its expenditures from industry i3 to industry i1. 4 The

solution of the Type II Ghosh model is derived in the same way as that of the Type I Ghosh model, now with the Type II Ghosh-inverse G∗ = (I − B − Dh )−1 , i.e. x = (vr em ) G∗ and Yr em = vˆ r em G∗ Dr em .

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

Note that the changes in output xi and the changes in value added vi , for all three industries in both scenarios, move in the same direction when the Type II Leontief model is used. In case of the Type II Ghosh model, however, they move in opposite directions in three of the six cases, which is definitely worse than the already implausible “no change in value added” of the Type I Ghosh model.5 The pattern of the changes in the household consumption h i in the two models leads to a similarly strong conclusion. In the Type II Leontief model, all changes have the same sign, whereas in the Type II Ghosh model, the changes in i3 have a sign that is opposite to the changes in i1 and i2. This means that more cars in the Type II Ghosh model may actually require less gasoline to run, while additional kitchen appliances may actually require less electricity, which also is an outcome that is worse than the “zero change” of the Type I model. Finally, have a look at the totals of the three impact variables shown in Table 6.1. First, note that the changes in the totals for value added and for household consumption are exactly equal in both models, regardless of their opposite role in the causal chain. In the Type II Leontief model, it is total value added that drives the column with consumption expenditures, whereas in the Type II Ghosh model, it is total consumption that drives the row with value added by industry, leading to the same total impact. So, we only need to compare the totals for production and value added to get one more impression of the comparative plausibility of the two extensions. In case of the extended Leontief model, both totals move in the same direction, as they almost always do in real life. In the case of the extended Ghosh model, they move in the opposite direction in one of the two scenarios, which is highly unlikely. That is enough on the implausibility of the SDIOM. What about the plausibility of its dual, price model?

6.2 Revenue-Pull IO Price Model = Plausible Dual of the Ghosh Quantity Model Literally, in the footnotes of the debate on the plausibility of the supply-driven IO model, the question was raised (Oosterhaven 1988) and answered positively (Oosterhaven 1989) whether or not the supply-driven IO quantity model also has a dual, price model. Davar (1989) presented the dual model in detail, but did not discuss the plausibility of the underlying economic assumptions nor their implications. Interestingly, the dual of the Ghosh quantity model has not been used for price impact studies 5 Manresa

and Sancho (2013) rightfully point out, partly in reaction to Oosterhaven (2012), that the mathematical symmetry between the Ghosh and Leontief models regards all outcomes. They, subsequently, suggest that it is equally problematic when production and consumption move in a different direction in case of the Type II Leontief model, as they do in Table 5.1 in two out of four cases, whereas they always move in the same direction in case of the Type II Ghosh model. I disagree. Mathematical symmetry does not imply symmetry in economic plausibility. There is no reason why moving in a different direction should be implausible in case of production and consumption, definitely not by industry and not even at the aggregate level.

6.2 Revenue-Pull IO Price Model = Plausible Dual of the Ghosh Quantity Model Final demand prices

D

Total input prices

I

I

75

Primary input prices

B

Intermediate input prices r s ∈ D= IRFig. 6.2 Causal structure of the interregional revenue-pull IO price model. Legend diq by-IQ matrix indicating the share of final demand type q in region s in the total revenues of industry i in region r, and birjs ∈ B = IR-by-IR matrix with indicating the share of the industry j in region s in the total revenues of i in r

yet, even though this is clearly possible, as follows from both its behavioural assumptions and its solution. Here, we skip the single-region price model (see Oosterhaven 1996) and directly present its interregional extension. Figure 6.2 shows the causal structure of the dual of the interregional Ghosh model. The IQ prices of the single homogeneous input per final demand column q in region s represent the exogenous variables of this model. The direct effect of an increase in these prices of pqs ∈ p y  will be an increase the total revenue of all industries in all regions that supply to final demand type q in s. The size of these revenue increases, of course, equals p y  times the final revenue shares of q in s in the total sales of rs ∈ D. Since quantities, being determined by the quantity each industry i in r, diq model, are constant in the price model, the assumption of full competition ensures that these revenue increases will entirely be passed on backwardly in the price of the single homogeneous input of each i in r. These direct price effects thus equal rs pqs ∈ D p y  , as indicated by the arrow with the matrix D in Fig. 6.2. diq These direct price effects, under full competition, apply to all suppliers of primary and intermediate inputs, as indicated by the two arrows with the matrix I in Fig. 6.2. For the suppliers of primary inputs, this will not lead to any further causal effects, indicated by the absence of outgoing arrows in Fig. 6.2. For the intermediate input suppliers j in region s, however, these price increases represent revenue increases, which equal the direct price increase Dp y  times the intermediate revenue shares of the sales of j in s to i in r, bsrji ∈ B, as indicated by the arrow with the matrix B in Fig. 6.2. These revenue increases, under full competition, are again fully passed on in the prices of the homogenous inputs of the suppliers j in s. The corresponding first round indirect price effects thus equal BDp y  , which are again fully passed on, leading to second round indirect price effects of B2 Dp y  , and so on. The cumulative price effect for the single homogeneous input by regional industry, consequently, equals (I + B + B2 + B3 + · · · )Dp y  = (I − B)−1 Dp y  = G∗∗ Dp y  = p, in which G** = interregional Ghosh-inverse. This description of the causality of this price model clarifies why it may best be labelled as the revenue-pull IO price model, which more accurately summarized its nature than the “demand-pull” label used by Oosterhaven (1996).6 6 Note that the causality of the Ghosh price model in Fig. 6.2 runs in the same, backward way as that

of the Leontief quantity model in Fig. 2.2. This implies that the Leontief quantity model may also

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

The mathematics of the interregional revenue-pull price model starts, not with the column-wise identities for total cost, as in the cost-push price model (5.1), but with the row-wise identities for total revenue: xir

pir

=

s  j

z ri js p sj

+

s 

rs s yiq pq , or

q

in matrix algebra: xˆ p = Zp + Yp y  , with y = i Y

(6.10)

In (6.10), the QR prices for each column with homogeneous final inputs ( pqs ∈ p y  ) are exogenous,7 whereas the IR prices for each column with homogeneous industry inputs ( p sj ∈ p) are endogenous. Note the difference with the cost-push price model. There we had prices for single homogeneous outputs. Here we have prices for single homogeneous inputs. However, in both price models quantities do not change. The quantities of the intermediate and final outputs in (6.10) are determined by the fixed output ratios of the interregional Ghosh quantity model. Substitution of (6.1) in (6.10) and pre-multiplication with xˆ −1 shows that, in case of the revenue-pull price model, total output prices equal the sum of all column-wise uniform intermediate and final input prices, weighed along the rows of the IRIOT with their respective intermediate and final revenue shares (i.e. allocation coefficients): p = B p + D py

(6.11)

Note that the interregional intermediate and final revenue shares add to unity, as the accounting identities (6.10) are measured in base year prices equal to one, i.e. B i + D i = i. The solution of the interregional revenue-pull price model is obtained by moving the endogenous total input prices from the RHS to the LHS of (6.11), and premultiplying the result with the interregional Ghosh-inverse G∗∗ : p = (I − B)−1 D p y  = G∗∗ D p y 

(6.12)

 In (6.12), tj girjt d tsjq ∈ G∗∗ D gives the primary input price multipliers of industry i in r with respect to the exogenous price of final demand q in s. They represent the opposite of the final output price multipliers of exogenous primary input prices in the solution of the cost-push price model in (5.4). Moreover, they equal the final output quantity multipliers of exogenous primary input of the Ghosh quantity model in (6.4). be interpreted as the Ghosh price model expressed in values, instead of in prices, just like the Ghosh quantity model could be interpreted as the Leontief price model expressed in values (Dietzenbacher 1997). 7 This is the basic assumption. In case of revenue-pull price impact studies it may equally well be assumed that say the foreign exports of different products from different regions have different price changes. See the first footnote of Chap. 5 for a comparable qualification in case of cost-push, price impact studies.

6.2 Revenue-Pull IO Price Model = Plausible Dual of the Ghosh Quantity Model

77

Comparable to the primal-dual relationship between the Leontief quantity and price model of (5.5), the primal-dual relationship between the Ghosh quantity and price model may be further illustrated by pre-multiplying (6.13) with total primary input v, which gives: v p = v (I − B)−1 D p y  = x D p y  = y p y 

(6.13)

Obviously, in the Ghosh models, the equality between the value of total primary input v p and the value of total final output y p y  is preserved, just as in the Leontief models. More importantly, Eq. 6.13 shows the independence (or better duality) of the two Ghosh models. Although their solutions are linked by means of (6.13), their variables move independently, with exogenous primary input quantities forwardly determining final output quantities in the Ghosh quantity model, and exogenous final output prices backwardly determining primary input prices in the Ghosh price model. In view of the implausibility of the SDIOM, one would expect a comparable implausibility of its dual, revenue-pull price model. However, this is not the case. In the revenue-pull price model, quantities are assumed to be constant and revenue gains pull the prices backwardly up, just as cost increases forwardly push prices up in the cost-push price model. The major difference between the two price models is the assumption about what may change exogenously, final output prices or primary input prices. After that, the forward or backward nature of the causality chain more or less logically follows from that starting assumption. To our knowledge, the revenue-pull IO price model has not been applied yet. Single-country or single-region applications, however, would be straightforward and could simulate the backward industry output price, wage rates and import price impacts, under full competition, of, e.g. exogenous world market increases of specific export prices. Interregional Type II applications could expand such simulations to the interregional or international price/wage/price backward impacts of specific external export price changes on the prices of industry outputs, wages rates and tax revenues of a series of internal regions or countries.

6.3 Markets: Why All Four IO Models Overestimate Their Typical Impacts After having specified and discussed the fourth and last basic IO model, it is time to take stock of the economics and the applicability of all four IO models. Table 6.2 collects all assumptions that have been made previously. First, note that both sets of models may be derived as special cases/simplifications of a general equilibrium interindustry model, for a regional or national economy, with profit-maximizing firms, operating under full competition, subject to the most general production function with heterogeneous inputs and heterogenous outputs, as measured by either an IOT, a SUT or a SAM (ten Raa 2004; Kratena 2017).

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

Table 6.2 Assumptions and solutions of the four basic input–output models Demand-driven quantity & cost-push price model:

Supply-driven quantity & revenue-pull price model:

For the individual firm – given demand for its single homogeneous output, i.e. perfect substitution among all outputs – full complementarity of all inputs (fixed input ratios) – cost minimization at given input prices – derived demand for inputs (backward linkages) – full competition, i.e. forward passing on of all input price changes into the single output price

– given supply of its single homogeneous input, i.e. perfect substitution among all inputs – perfect jointness of all outputs (fixed output ratios) – revenue maximization at given output prices – derived supply of outputs (forward linkages) – full competition, i.e. backward passing on of all output price changes into the single input price

For the economy as a whole – exogenous demand for final outputs per industry – endogenous demand for all inputs per industry – perfectly elastic supply of all primary inputs, i.e. exogenous primary input prices – endogenous total output prices and quantities

– exogenous supply of primary inputs per industry – endogenous supply of all outputs per industry – perfectly elastic demand for all final outputs, i.e. exogenous final output prices – endogenous total input prices and quantities

Solution of the two Leontief models

Solution of the two Ghosh models

– v = C (I−A)−1 y, with y = Y i and v = V i

– y = v (I − B)−1 D, with y = i Y and v = i V

– p y = p = p v C (I − A)−1

– pv  = p = (I − B)−1 D p y 

Source Extension of Nieuwenhuis (1981) and Oosterhaven (1989, 2012)

The most important simplification appears in the first line of Table 6.2. It, alternatively, assumes either a single homogeneous output (Leontief) or a single homogeneous input (Ghosh). Assuming a single homogeneous output implies the perfect substitution among all outputs in case of the Leontief model, which clearly represents a simplification, but a minor one, whereas assuming perfect substitution among all inputs in case of the Ghosh model represents a major simplification, namely one that allows factories to run without labour and cars to drive without gas. Note that this simplification only makes the Ghosh quantity model implausible, but not its dual, price model, as all quantities are constant in both price models. The next simplifying assumption is fixing the ratios on the other side of the general production function. In case of the Leontief model, this implies assuming full complementarity of all inputs, and in case of the Ghosh model, this implies assuming full jointness of all outputs. Both assumptions are serious simplifications of reality, and one might argue that Leontief’s simplification might be more severe than that of Ghosh, but that very much depends on which variables change exogenously in the application of either model.

6.3 Markets: Why All Four IO Models Overestimate Their …

79

In case of a quantity shock to the demand-side of the economy, assuming fixed input ratios in the Leontief model does not seem problematic, but assuming Ghoshian fixed output ratios in that case implies that all sales in a row of the IOT are assumed to change proportionally to the exogenous shock, which is highly implausible in case of a specific demand shock. In case of a quantity shock to the supply side of the economy, assuming fixed input ratios is very implausible as firms will directly look for substitutes (see further Sect. 7.1), whereas assuming fixed output ratios in case of a supply shock is less of a problem. Note again, that either simplification does not influence the relative plausibility of the two price models, as they both assume all quantities to remain constant in face of a price change. The non-interaction between prices and quantities in both sets of models is illustrated in Fig. 6.3. In the Leontief quantity model, the perfectly inelastic demand for the single homogeneous output of industry i shifts (either exogenously or endogenously) to the left and right along a perfectly elastic supply curve, not causing any price reaction (Fig. 6.3a). In the Leontief price model, the opposite happens. The price of output i (i.e. its supply curve, either exogenously or endogenously) shifts up and down along a perfectly inelastic demand curve, without any impact on the quantity demanded. The same holds for the demand and supply of primary inputs of type p (not shown in Fig. 6.3a). In case of an underutilization of production capacities and factor supplies, i.e. around the bottom of the business cycle, these assumptions are more or less reasonable, but at the top of the business cycle, the Leontief models will overestimate the quantity impacts of both positive and negative demand shocks. In the Ghosh models, opposite assumptions are made. In the Ghosh quantity model, the perfectly inelastic supply of the single homogeneous input of industry j, shifts (either exogenously or endogenously) to the left and right along a perfectly

Fig. 6.3 Functioning of product markets in the four basic input–output models

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6 Supply-Driven IO Quantity Model and Its Dual, Price Model

elastic demand curve, not causing any price reaction (Fig. 6.3b) (i.e. consumers consume whatever is supplied at the going price). This was more or less what happened under the old EU agricultural policy with its fixed product prices and its fluctuating milk lakes and butter mountains. Independently, in the revenue-pull price model, the demand curve (i.e. the price the single homogeneous input of industry j) shifts up and down along a perfectly inelastic supply curve, not causing any quantity reaction of the supply of input j. In this case, the same holds for the supply and demand of final outputs of type q (not shown in Fig. 6.3b). The fact that the two IO quantity models both overestimate the quantity impacts of exogenous changes may also be shown in an informal way. Every economist knows the standard diagonal market equilibrium cross with an upward sloping supply curve and a downward-sloping demand curve. A horizontal quantity shift of one of the two diagonal curves always produces an equilibrium quantity impact that is smaller than the horizontal shift of the curve, because a price reaction will dampen the quantity impact of the shift (see also McGregor et al. 1999). The same holds for the two IO price models. A vertical shift of one of the two diagonal curves always produces an equilibrium price impact that is smaller than the shift of the curve, because a quantity reaction will dampen the price impact. So, both price models overestimate the price impacts of their exogenous changes. From this summary evaluation of the four basic IO models, it is clear that, especially, the Leontief quantity model is far more plausible than its Ghoshian opposite, but it is also clear that both sets of IO models represent extreme cases of a general equilibrium model. Clearly, implementing a CGE model at the combined interindustry and interregional level is more complicated and far more data demanding than a comparable IO model (see Bröcker et al. 2004). For this reason, most developments in IO analysis seek to modify the basic Leontief model by introducing more flexible (e.g. translog) production functions for capital, labour and intermediate inputs (e.g. KLEM) and by introducing econometrically estimated consumption, investment and export functions, while sticking to the Leontief specification for the matrix of intermediate demand only (see Almon 1991; Kratena 2005).

References Almon C (1991) The INFORUM approach to interindustry modeling. Econ Syst Res 3:1–7 Augustinovics M (1970) Methods of international and intertemporal comparison of structure. In: Carter A, Bródy A (eds) Contributions to input-output analysis. North-Holland, Amsterdam Bon R (1986) Comparative stability analysis of demand-side and supply-side input-output models. Int J Forecast 2:231–235 Bon R (1988) Supply-side multiregional input-output models. J Reg Sci 28:41–50 Bröcker J, Meyer R, Schneekloth N, Schürmann C, Spierkemann K, Wegener M (2004) Modelling the socio-economic and spatial impacts of EU transport policy. IASON deliverable 6. ChristianAlbrechts-Universität Kiel/Universität Dortmund

References

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Cartwright JV, Beemiller RM, Trott EA, Younger JM (1982) Estimating the potential impacts of a nuclear reactor accident. Bureau of Economic Analysis, Washington, DC Chen CY, Rose A (1986) The joint stability of input-output production and allocation coefficients. Model Simul 17:251–255 Davar E (1989) Input-output and general equilibrium. Econ Syst Res 1:331–344 Davis HC, Salkin EL (1984) Alternative approaches to the estimation on economic impacts resulting from supply constraints. Ann Reg Sci 18:25–34 de Mesnard L (2004) understanding the shortcomings of commodity-based technology in inputoutput models: an economic-circuit approach. J Reg Sci 44:125–141 de Mesnard L (2009) Is the Ghosh model interesting? J Reg Sci 49:361–372 Dietzenbacher E (1997) In vindication of the Ghosh model: a reinterpretation as a price model. J Reg Sci 37:629–651 Ehret H (1970) Die Anwendbarkeit von input-output Modellen als prognose Instrument. Dunkler & Humbolt, Berlin Ghosh A (1958) Input-output approach in an allocation system. Economica 25:58–64 Giarratani F (1976) Application of an interindustry supply model to energy issues. Environ Plan A 8:44754 Giarratani F (1980) The scientific basis for explanation in regional analysis. Pap Reg Sci Assoc 45:185–196 Giarratani F (1981) A supply-constrained interindustry model: forecasting performance and an evaluation. In: Burh W, Friedrich P (eds) Regional development under stagnation. Nomos Verlag, Baden-Baden Gruver GW (1989) On the plausibility of the supply-driven input-output model: a theoretical basis for input-coefficient change. J Reg Sci 29:441–450 Guerra AI, Sancho F (2011) Revisiting the original Ghosh model: can it be made more plausible? Econ Syst Res 23:319–328 Helmstädter E, Richtering J (1982) Input coefficients and output coefficients types models and empirical findings. In: Proceedings of the Hungarian conference on input-output techniques, Statistical Publishing House, Budapest Kratena K (2005) Prices and factor demand in an endogenized input-output model. Econ Syst Res 17:47–56 Kratena K (2017) General equilibrium analysis. In: ten Raa T (ed) Handbook of input-output analysis. Edward Elgar, Cheltenham Manresa A, Sancho F (2013) Supply and demand biases in linear interindustry models. Econ Model 33:94–100 McGregor P, Swales JK, Yin YP (1999) Spillover and feedback effects in general equilibrium models of the national economy: a requiem for interregional input-output? In: Hewings GJD, Sonis M, Madden M, Kimura Y (eds) Understanding and interpreting economic structure. Springer, Berlin Miller RE, Blair PD (2009) Input-output analysis: foundations and extensions, 2nd edn. Cambridge University Press, Cambridge Nieuwenhuis A (1981) Vraag, aanbod en input-output tabellen. Centraal Planbureau, Notitie nr. 8, The Hague Oosterhaven J (1981) Interregional input-output analysis and Dutch regional policy problems. Gower Publishing, Aldershot-Hampshire Oosterhaven J (1988) On the plausibility of the supply-driven input-output model. J Reg Sci 28:203– 217 Oosterhaven J (1989) The supply-driven input-output model: a new interpretation but still implausible. J Reg Sci 29:459–465 Oosterhaven J (1996) Leontief versus Ghoshian price and quantity models. South Econ J 62:750– 759 Oosterhaven J (2012) Adding supply-driven consumption makes the Ghosh model even more implausible. Econ Syst Res 24:101–111

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Rose A, Allision T, Gruver GW (1989) On the plausibility of the supply-driven input-output model: empirical evidence on joint stability. J Reg Sci 29:451–458 Rose A, Wei D (2013) Estimating the economic consequences of a port shutdown: the special role of resilience. Econ Syst Res 25:212–232 ten Raa T (2004) A neoclassical analysis of total factor productivity using input-output prices. In: Dietzenbacher E, Lahr ML (eds) Wassily Leontief and input-output economics. Cambridge University Press, Cambridge

Chapter 7

Negative IO Supply Shock Analyses: A Disaster and a Solution

Keywords Supply shocks · Terrorist attacks · Disaster impact analysis · Inoperability input–output model · Hypothetical extraction method · CGE models · Nonlinear programming models · Danube and Elbe floods Chapter 6 concluded, among others, that the supply-driven IO quantity model may not be used to simulate the impacts of shocks to the supply side of the economy. This raises the question of what alternative approaches are suitable to estimate the interindustry and interregional impacts of supply shocks, of which natural or manmade disasters are about the most impressive examples.

7.1 Limited Usability of the IO Model in Case of Supply Shocks Over the past two decades, the use of IO models to estimate the indirect economic losses of disasters gained increasing popularity, as evidenced by two special issues of Economic Systems Research (2007/2 and 2014/1) and two edited volumes (Okuyama and Chang 2004; Okuyama and Rose 2019). Of the IO applications, the inoperability IO model (IIM, Santos and Haimes 2004) constitutes the single most used model.1

1 On

26 August 2019, “inoperability input–output model” scored 836 hits on Google Scholar.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_7

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7 Negative IO Supply Shock Analyses: A Disaster and a Solution

To calculate the absolute loss of output by industry, the IIM follows the standard IO literature: x = A x + y ⇒ x = (I − A)−1 y

(7.1)

To this, the IIM adds the normalization of (7.1) by the lagged level of output xˆ −1 , to obtain the relative loss of output by industry q = (ˆx−1 )−1 x and innovatively labels this the inoperability by industry:2 q = (ˆx−1 )−1 A xˆ −1 q + (ˆx−1 )−1 y ⇒ q = (I − (ˆx−1 )−1 A xˆ −1 )−1 (ˆx−1 )−1 y = (I − B)−1 y∗

(7.2)

wherein (I − B)−1 = Ghosh-inverse from Eq. (6.5). With the last part of (7.2), the IIM literature incorrectly suggests that the IIM is a new model with supply-side relations. Instead, it is just a demand-driven IO quantity model “with a small tweak” (Dietzenbacher and Miller 2015). The direct losses in the case of a natural disaster, essentially, represent the destruction of stocks of capital, labour and infrastructure, whereas the wider, indirect effects, essentially, represent the subsequent changes in the flows of production and consumption (Okuyama and Santos 2014). The latter may be negative as well as positive, may occur in the short run and in the longer run and may be due to both supply and demand effects. In the specific case of terrorist attacks, the direct destruction of capital and labour, and the related direct loss of demand and supply are mostly minimal. The main impact is psychological. Its subsequent economic impact will be a—mainly spatial— redistribution of mainly private consumption (travel) demand (Galea et al. 2002). The IIM, as any IO model, is well suited to estimate the further positive and negative backward impacts of such redistribution, especially, when the economy is operating below capacity. Note that not only in the case of disasters, but also in the case of all other impact studies, the honest analyst should try to make an estimate of the net impacts of the event or industry at hand, i.e. an estimate of the difference between the positive and negative impacts (cf. Oosterhaven et al. 2003). In the more general case of natural disasters, the destruction of stocks will cause an almost direct loss of both intermediate and final demand in the disaster region. The short run backward impacts of the direct reduction in final demand may be modelled by means of the IIM without any problem. Estimating the backward impact of the direct reduction of intermediate demand by means of the IIM is problematic, as it requires the analyst to translate the exogenous shock to intermediate demand, which is endogenous in the IIM, into an exogenous shock to final demand that, with the IIM, exactly reproduces the exogenous shock to intermediate demand (see Rose 2004, 2 Dietzenbacher and Miller (2015) show that it is far simpler to do the normalization at the beginning

of (7.1) instead of integrating it in its separate terms as done in the IMM literature. This far more elegantly results in: q = (ˆx−1 )−1 (I − A)−1 y.

7.1 Limited Usability of the IO Model in Case of Supply Shocks

85

on avoiding double counting exogenous and endogenous impacts, and Oosterhaven 2017, about what went wrong in practice). The destruction of stocks will also cause an almost direct loss in the supply of both intermediate and final outputs from the disaster region. Estimating the short run forward impacts of this shock by means of the IIM or any other IO or SU model is impossible for several reasons. First and foremost, firms and households will not react to a negative supply shock by proportionally reducing all their other purchases, as it is implied by the fixed ratio assumptions of, respectively, Type I and Type II IO and SU models. Instead, they will look for substitutes. Three broad types of replacements are possible: 1. Firms and households may look for different firms in the same region that produce the same product. This may lead to changes of the industry market shares in the supply of the product at hand. The assumption that these shares are fixed is hidden in the construction of most symmetric IO tables, but is explicit in the SU model (see Sect. 3.2). 2. Firms and households may look for suppliers from different regions. This may lead to changes in the self-sufficiency and imports ratios for the product at hand, i.e. in changes in the trade origin ratios. The assumption that these ratios are fixed is mostly made implicitly, but is well recognized in the IO and SU literature (see Sects. 2.3 and 4.1). 3. Firms and households may look for different products that perform the same function, e.g. plastic parts instead of metal parts. This implies a change in real technical coefficients for firms and real preference coefficients for households. Especially, in the case of firms, such changes represent the least likely reaction in the short run, as it implies changing the production process.3 In all three cases, the substitution of the lacking inputs by firms and households will lead to positive instead of negative impacts elsewhere in the economy; impacts cannot be estimated by the IIM nor by any other IO or SU model. Only if an input is truly irreplaceable, the lack of its supply may force purchasing firms to shut down their production when the stocks of this input are depleted. The reduction in the supply of the intermediate input at hand, in that case, needs to be multiplied with processing coefficients (i.e. reciprocal real technical coefficients, see Oosterhaven 1988). If the shock relates to the supply of an economically insignificant but crucial input, such as a rare metal, the reduction in the output of the purchasing firm at hand may very well be many, many times larger than the value of the drop in the crucial input! Aside from the above impacts of the destruction of stocks of capital, labour and infrastructure, there will also be short and longer run impacts of private and public aid and reconstruction activities. The positive backward impacts of these activities may well be estimated by means of interregional or, need be, international IO models. 3 Kujawski’s

early (2006) critique of the IIM only related to this assumption of fixed technical coefficients and excess supply in all industries, which did not have an impact on the proliferation of the IIM.

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7 Negative IO Supply Shock Analyses: A Disaster and a Solution

These backward impacts will be spatially concentrated in case of the reconstruction of buildings and infrastructure, but will be spatially spread in case of the reconstruction of the capital stock. In conjunction, financing these activities requires higher insurance premiums and higher taxes, which will lead to longer run negative forward macro-economic impacts, which will be spatially spread, and which cannot be estimated by any IO or SU model. Obviously, since the IIM is able to estimate only part of only the demand-side impacts of a disaster, Eqs. (7.1) and (7.2) may not be used as a risk-management instrument to prioritize the public support for industry resilience programmes as advocated by Santos and Haimes (2004, also Anderson et al. 2007; Barker and Santos 2010). In fact, the results from all kind of IIM applications show total simulated indirect losses of economic activity that are far larger than the direct losses. Santos and Haimes (2004), for example, report ratios of total to direct losses due to terrorist attacks that vary between 2.5 and 3.6. Santos (2006) reports a disaster multiplier of about 2.0 for 9/11, while Anderson et al. (2007) find a disaster multiplier of about 2.2 in case of the 2003 blackout in the northwest of the USA. Such large multipliers are highly implausible, as the IIM completely ignores the positive impacts of a disaster on the supply side of the economy. If IO and SU models are unsuited to estimate most of the indirect impacts of a disaster, what alternative modelling approaches are available? Up till now, the positive substitution effects could only be estimated by means of spatial computable general equilibrium (CGE) models (Tsuchiya et al. 2007; Kajitani and Tatano 2018). In fact, different versions of such a model are needed to model the short run as opposed to the longer run impacts, because short run substitution elasticities are much closer to zero than their longer run equivalents (Rose and Guha 2004). Moreover, in longer run simulations, more variables need to be modelled endogenously. Consequently, CGE models are difficult and rather costly to estimate, even if the necessary data, such as interregional social accounting matrices (SAMs) and all kind of elasticities, are available (see Albala-Bertrand 2013, for a further critique). The hypothetical extraction (HE) method (see Sect. 8.1, for details) is tested by Muldrow and Robinson (2014) and advocated by Dietzenbacher and Miller (2015) as an alternative to the IIM. The HE approach does circumvent the problem of assuming fixed trade origin ratios, as the HE method (implicitly) assume that the lost sales of the extracted industry are compensated by an increase of imports from external regions. However, contrary to what was originally suggested (Paelinck et al. 1965; Strassert 1968), the complete or partial extraction of a row from an IOT does not simulate the forward, supply effects of that HE on its customers. Instead, it measures the backward, demand effects of a drop (or complete disappearance) of the supply of intermediate outputs of the extracted industry. Moreover, HE does not estimate the above discussed three types of positive forward impacts either. The supply-driven IO quantity model also does not constitute a plausible model for studying the forward impacts of disasters (see Sects. 6.1 and 6.3). This negative verdict, of course, also holds for the supply-driven version of the IIM as applied in Crowther and Haimes (2005).

7.1 Limited Usability of the IO Model in Case of Supply Shocks

87

Without a spatial CGE, a more or less plausible estimation of the impacts of an exogenous negative supply shock requires arbitrary rationing schemes and ad hoc assumptions regarding the adaptation behaviour of upstream and downstream industries, as indicated by Oosterhaven (1988) and implemented by Hallegate (2008) and Rose and Wei (2013). The only other alternative to building a spatial CGE is the nonlinear programming approach of Oosterhaven and Bouwmeester (2016), which according to the authors “combines the simplicity of the IRIO model with the plausibility of the CGE approach” (p. 585).

7.2 Nonlinear SU Programming Alternative: Much Smaller Disaster Multipliers The basic idea of this alternative is that firms, households and governments, in the short run after a disruptive event, as much as possible, try to return to their old levels of sales and purchases. This basic idea is made operational by minimizing the weighted total distance between the cells of a simulated post-disaster interregional IO table and an actual pre-disaster IRIOT. The distance between the two IRIOTs may best be measured by means of the information gain measure of Kullback (1959) and Theil (1967). Here, we show how the model may be specified for a use-regionalized interregional SUT (see Fig. 3.3c), as that type of IRSUT represents a more detailed and a more frequently used accounting scheme than an IRIOT. The objective function of the nonlinear interregional SU model equals: Minimize

r 

r,ex r,ex r sic ln sic /sic +

ic

+

r  c

ecr,ex ln ecr /ecr,ex +

rs 

u rcis,ex ln u rcis /u rcis,ex +

ci s 

v·is,ex ln v·is /v·is,ex

rs 

r s,ex r s r s,ex yc· ln yc· /yc·

c

(7.3)

i

The five separate terms of (7.3) specify the information gain of, sequentially: (1) the regional supply tables, (2) the doubly regionalized intermediate use tables, (3) the doubly regionalized total domestic final use columns, (4) the regional external export columns and (5) the regional total value added rows. The symbols of (7.3) are defined in Fig. 3.2 and Fig. 3.3c. The superscript ex, additionally, indicates the exogenous values of cells of the pre-disaster IRSUT, whereas the transactions without an ex define the endogenous values of the cells of the post-disaster IRSUT. The further idea of this approach is to only add the minimally necessary behavioural restrictions to (7.3). The first of these requires that all economic transactions are non-negative. This implies that the ultra-short run depletion of available stocks to cope with supply shortages cannot be part of the objection function (7.3). Adding this adaptation possibility, as in Hallegate (2008) and in Mackenzie et al.

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7 Negative IO Supply Shock Analyses: A Disaster and a Solution

(2012), requires very hard to obtain data on the pre-disaster level of stocks. IOTs and SUTs, for example, only contain information on historic changes in stocks, but never on their actual levels. If data on actual stock levels are available, the values of the stocks may be added as a constant to the RHS of the next equation. Second, and foremost, it is assumed that prices change in such a fashion that the economy remains in short run equilibrium, i.e. it is assumed that demand equals supply, per product, per region: s 

u rcis +

s 

yc·r s + ecr =

i



r sic , ∀c, r

(7.4)

i

A great advantage of this simple specification is that there is no need to specify the underlying supply and demand elasticities or the corresponding price changes. Instead, it is possible to concentrate on modelling the volume changes. Consequently, all variables in this model are measured in base year prices that all equal unity. Third, we assume cost minimization under a Walras–Leontief production function, per industry, per region, which results in (see Sect. 2.2): r 

·s u rcjs = acj



s sjc and v·sj = c·sj

c



s sjc , ∀ j, sa

(7.5)

c

·s wherein acj and c·sj denote fixed technical coefficients that specify the use of inputs regardless of their spatial origin. Thesecoefficients are calculated from the columns ·s +c.sj = 1, ∀ j, s. Note that this “adding of the pre-disaster use table and satisfy c acj to unity” restriction elegantly and automatically also secures that total output equals  total input, per industry, per region, i.e. c s sjc = rc u rcjs + v·sj , ∀ j, s. Fourth, the same cost minimization assumption may also be used for final demand: r 

yc·r s = f c··s

r 

yc·r s , ∀c, s

(7.6)

c

wherein f c··s denote fixed preference coefficients that specify the per unit use of products regardless of their spatial origin. These coefficients are also calculated from the  columns of the pre-disaster use table and satisfy c f c··s = 1, ∀s. The first test that any programming model of this type has to satisfy is that it reproduces the pre-disaster IRIOT or IRSUT from which its ex values and its fixed coefficients are derived. After satisfying that test, additional disaster-specific restrictions have to be added. Oosterhaven and Bouwmeester (2016) did that with a two-region (core/periphery) and a two industry (goods/services) hypothetical IRIOT, which was small enough to inspect all cell-by-cell changes that were simulated for two types of disasters, namely the total shut down of the production of a single region and the total shut down of all transport in a single interregional direction. Both the signs of—and the largest differences in—the impacts of the four disasters could be explained by

7.2 Nonlinear SU Programming Alternative: Much Smaller …

89

Table 7.1 Comparison of indirect disaster estimates in % of the direct impacts Assumptions:

Bayern

Sachsen

Thüringen

Germany

Base model (fixed technology)

13.9

4.1

4.6

11.0

31 // +220

8 // +200

5.7 // +24

19 // +180

+ fixed trade origin shares*

21 // +150

18 // +430

13 // +270

33 // +300

+ both shares fixed*

59 // +420

83 // +2030

42 // +910

97 // +880

+ fixed industry market

shares*

*

The second figure behind // gives the percentage increase in the base estimate of the indirect impacts. Source Adapted from Oosterhaven and Többen (2017)

the economic differences between the two regions and the not explicitly modelled, corresponding changes in prices due to each disaster. Next, Bouwmeester and Oosterhaven (2017) used the same nonlinear IRIO model, calibrated it on the EXIOPOL international IOT (Tukker et al. 2013), and added onesided trade capacity restrictions with which they simulated the possible impacts of four Russian natural gas export boycotts of—parts of—the European Union. The simulations showed considerable effects at lower levels of aggregation, but negligible aggregate economic impacts for the EU and only a little larger than negligible aggregate economic impacts for Russia. The IRSU model of (7.3)–(7.6), calibrated on the IRSUT for Germany of Többen (2017, Chap. 5), with one-sided production capacity restrictions added to it, was used by Oosterhaven and Többen (2017) to simulate the interregional impacts of the 2013 massive floods of the Elbe and the Danube rivers. They find regional and national disaster multipliers that are all smaller than 1.14 (see the first row of Table 7.1). Moreover, they examined the sensitivity of their outcomes to varying economic environments. These sensitivity analyses show that central government support of regional final demand (i.e. disaster aid) substantially reduces the already small indirect losses, whereas being at the top of the business cycle considerably increases them. Their most interesting sensitivity analysis, however, regards the implications of imposing the two remaining fixed ratio assumptions of the standard demand-driven IO or SU model, namely the fixed industry market share assumption and the fixed trade origin ratio assumption. Investigating the impacts of adding these two assumptions enables, first, to examine the size of the indirect economic losses that are avoided because of the ability of industries and final consumers to find alternative suppliers when faced with a negative supply shock. Secondly, it enables an assessment of the overestimation of the indirect disaster impacts when IO and SU models are used that do not allow for these substitution possibilities. The first assumption added to the basic nonlinear model of (7.3)–(7.6) is that the industry market shares in regional product supply are fixed: r r = ric sic

 i

r sic , ∀i, c, r

(7.7)

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7 Negative IO Supply Shock Analyses: A Disaster and a Solution

r wherein ric denote the fixed industry market shares, which are calculated from the columns of the pre-disaster supply table. This fixed ratio assumption is explicitly made in standard SU models and is mostly implicitly made when deriving a symmetric IOT from a standard rectangular SUT (see Sect. 3.2). Adding this assumption is more or less sensible in case of a negative demand shock, but it is highly implausible in case of a negative supply shock. This can easily be shown with an example. Assume the extreme case where a certain product is produced by two industries only. The first provides 90% of the total supply, whereas the second provides the remaining 10%. If this second industry shuts down because of a disaster, assuming fixed industry market shares implies that the first industry will also shut down its 90% share. In the German flooding case, adding this assumption inflates the indirect disaster impact estimates with as much as 180–220% (see the second row of Table 7.1). The second additional assumption is that the trade origin ratios are fixed:

u rcis = m rcis

 r

u rcis , ∀c, i, r, s and yc·r s = m rcsf



yc·r s , ∀c, r, s

(7.8)

r

wherein m rcis and m rcsf denote the fixed trade origin ratios for intermediate and final demand, respectively. These ratios are calculated from the columns of pre-disaster use table. The assumption of fixed trade origin ratios extends the fixed technology assumption (7.5) to the geographical origin of intermediate and final inputs. In the context of a negative demand shock, it is more or less plausible to assume that firms proportionally purchase less inputs from all their suppliers. In the case of a negative supply shock, however, firms will immediately search for different sources for their inputs. In an extreme case, assuming fixed origin trade ratios implies that firms have to shut down all of their production if only one of their suppliers from a specific region is not able to deliver the required inputs. Hence, this fixed ratio assumption also leads to overstating the indirect impacts of disasters. In the case of a demand shock to household income, assuming fixed preference coefficients (7.6) is already a bit problematic, let alone assuming fixed trade origin ratios, as households will not proportionally reduce all their expenditures. Instead, they will maintain their consumption of basic needs and reduce their other consumption. In the case of a negative supply shock, however, households will look for substitutes as much as firms and will show even more flexibility in changing, first, their trade origin ratios (7.8) and, second, their preference coefficients (7.6). In the German flooding case, adding (7.8) for both firms and households inflates the indirect impact estimates with as much as 150–430% (see the third row of Table 7.1). When both ratios are fixed in combination, as in the extended IIM and all other extended IO and SU models, the indirect German flooding loss estimates were amplified with as much as 420–2030% (see the last row of Table 7.1). Disregarding the precise size of the percentage, this clearly shows that almost all disaster multipliers are overestimated heavily. This has an important policy implication, namely that the

7.2 Nonlinear SU Programming Alternative: Much Smaller …

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IIM literature emphasis on stimulating the resilience of the economic system as a whole is not justified. Instead, much more attention needs to be paid to preventing and mitigating the direct cost of natural and man-made disasters.

References Albala-Bertrand JM (2013) Disasters and the networked economy. Routledge, Oxon Anderson CW, Santos JR, Haimes YY (2007) A risk-based input-output methodology for measuring the effects of the August 2003 Northeast blackout. Econ Syst Res 19:183–204 Barker K, Santos JR (2010) Measuring the efficacy of inventory with a dynamic input-output model. Int J Product Econ 126:130–143 Bouwmeester MC, Oosterhaven J (2017) Economic impacts of natural gas flow disruptions between Russia and the EU. Energy Pol 106:288–297 Crowther KG, Haimes YY (2005) Application of the inoperability input-output model (IIM) for systemic risk assessment and management of interdependent infrastructures. Syst Eng 8:323–341 Dietzenbacher E, Miller RE (2015) Reflections on the inoperability input-output model. Econ Syst Res 27:478–486 Galea SJ, Ahern J, Resnick H, Kilpatrick D, Ducuvalas M, Gold J, Vlahov D (2002) Psychological sequelae of the September 11 terrorist attacks in New York city. New Engl J Med 346:982–987 Hallegate S (2008) An adaptive regional input-output model and its application to the assessment of the economic cost of Katrina. Risk An 28:779–799 Kajitani Y, Tatano H (2018) Applicability of a spatial computable general equilibrium model to assess the short-term economic impact of natural disasters. Econ Syst Res 30:289–312 Kujawski E (2006) Multi-period model for disruptive events in interdependent systems. Syst Eng 9:281–295 Kullback S (1959) Information theory and statistics. Wiley, New York MacKenzie CA, Santos JR, Barker K (2012) Measuring changes in international production from a disruption: case study of the Japanese earthquake and tsunami. Int J Prod Econ 138:293–302 Muldrow M, Robinson DP (2014) Three models of structural vulnerability: methods, Issues and empirical comparisons. Paper presented at the annual meeting of the Southern Regional Science Association, San Antonio, Texas Okuyama Y, Chang SE (eds) (2004) Modelling spatial and economic impacts of disasters. Springer, New York Okuyama Y, Rose A (eds) (2019) Modelling spatial and economic impacts of disasters. Springer, New York (to appear) Okuyama Y, Santos JR (2014) Disaster impact and input-output analysis. Econ Syst Res 26:1–12 Oosterhaven J (1988) On the plausibility of the supply-driven input-output model. J Reg Sci 28:203– 217 Oosterhaven J (2017) On the limited usability of the Inoperability IO model. Econ Syst Res 29:452– 461 Oosterhaven J, Bouwmeester MC (2016) A new approach to modelling the impact of disruptive events. J Reg Sci 56:583–595 Oosterhaven J, Többen J (2017) Regional economic impacts of heavy flooding in Germany: a non-linear programming approach. Spat Econ An 12:404–428 Oosterhaven J, van der Knijff EC, Eding GJ (2003) Estimating interregional economic impacts: an evaluation of nonsurvey, semisurvey, and fullsurvey methods. Environ Plan A 35:5–18 According to the SpringerBrief guidlines, this reference needs to be put behind Oosterhaven and Tobben (2017)

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Paelinck J, De Caevel J, Degueldre DJ (1965) Analyse quantitative de certaines phénomènes du développement régional polarisé: Essai de simulation statique d’itérarires de propogation. In: No. 7, Problémes de Conversion Économique: Analyses Théoretiques et Études Appliquées. M.-Th. Génin, Paris Rose A (2004) Economic principles, issues and research priorities in hazard loss estimation. In: Okuyama Y, Chang SE (eds) Modelling spatial and economic impacts of disaster. Springer, Berlin Rose A, Guha GS (2004) Computable general equilibrium modelling of electric utility lifeline losses from earthquakes. In: Okuyama Y, Chang SE (eds) Modelling spatial and economic impacts of disaster. Springer, Berlin Rose A, Wei D (2013) Estimating the economic consequences of a port shutdown: the special role of resilience. Econ Syst Res 25:212–232 Santos JR (2006) Inoperability input-output modelling of disruptions to interdependent economic systems. Syst Eng 9:20–34 Santos JR, Haimes YY (2004) Modeling the demand reduction input-output (I-O) inoperability due to terrorism of connected infrastructures. Risk An 24:1437–1451 Strassert G (1968) Zur bestimmung strategischer sektoren mit hilfe von input-output modellen. Jahrb Nationalök Stat 182:211–215 Theil H (1967) Economics and information theory. North-Holland, Amsterdam Többen J (2017) Effects of energy and climate policy in Germany: a multiregional analysis. Ph.D., Faculty of Economics and Business, University of Groningen Tsuchiya S, Tatana H, Okada N (2007) Economic loss assessment due to railroad and highway disruptions. Econ Syst Res 19:147–162 Tukker A, De Koning A, Wood R, Hawkins T, Lutter S, Acosta J, Rueda-Cantuche JM, Bouwmeester MC, Oosterhaven J, Drosdowski T, Kuenen J (2013) Exiopol—development and illustrative analyses of a detailed global MR EE SUT/IOT. Econ Syst Res 25:50–70

Chapter 8

Other IO Applications with Complications

Keywords Forward and backward linkages · Key sector analysis · Dutch mainport regions · Net multipliers · Shift and share analysis · Structural decomposition analysis · Processing exports · Growth accounting In Chap. 6, it was concluded that, although the demand-driven IO model is far more plausible than the supply-driven model, all four IO models need to be applied with great care to prevent wrong policy advice or to suggest too large quantity and price impacts of, respectively, exogenous quantity and price shocks. In this chapter, we will observe that this advice is more easily given than followed up.

8.1 Key Sector and Linkage Analyses: A Half-Truth The formulation and empirical calculation of linkage measures represent one of the earliest applications of IO analysis (Rasmussen 1956; Chenery and Watanabe 1958). Hundreds of such studies have been done since,1 mostly with the aim to identify so-called key sectors—usually defined as sectors with a high potential of spreading their own growth to the whole of the economy (see Hirschman 1958, for the original formulation, and Perroux 1961, for the first spatial interpretation). The basic idea is that sectors with relatively large intermediate purchases (i.e. backward linkages) and relatively large intermediate sales (i.e. forward linkages) do so most effectively.

1 On

26 August 2019, “forward linkages” and “backward linkages” combined scored about 12,300 hits with Google Scholar, and “key sector analysis” about 520 hits.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_8

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8.1.1 Analytical and Empirical Comparison of Key Sector Measures Temurshoev and Oosterhaven (2014) give an extensive overview of the different forward and backward linkages proposed in the literature and conclude that this delivers nine sensibly different measures. The first eight of them (in the first eight rows of Table 8.1) try to capture the same basic concept, namely the one-sided dependence of the whole of the economy (WoE) on the sector at hand. The only exception is the net backward linkage interpretation (Oosterhaven 2004) of the net multiplier concept (Oosterhaven and Stelder 2002). The reason for this exception is that net linkages intend to capture the two-sided nature of sectoral dependence, as they equal the ratio of the dependence of the WoE on the sector at hand to the dependence of the sector at hand on the WoE (Dietzenbacher 2005). To complete the list, Oosterhaven (2008) defined a tenth measure: the net forward linkage equivalent of the net backward linkage (see the last two rows of Table 8.1 for both). Most linkage measures use output as the impact variable. Hazari (1970), however, already early advocated weighing (or better rescaling) the Rasmussen (1956) linkages with the planner’s preference function, which he operationalized as each sector’s share in total final demand. Whereupon Loviscek (1982) much later reacted with the proposal to weigh the forward linkages with each sector’s share in total primary inputs, instead of its share in final demand. In fact, to be really relevant for policy formulation, linkage measures should not reflect the impacts on total output, whether weighed or unweighted, but the impacts on the policy goal at hand, such as income generation, job creation or CO2 emission reduction (see Oosterhaven 1981; Diamond 1985, for early examples of employment linkages). This requires that linkage measures should be multiplied with the relevant impact variable per unit of output. If this ci in Table 8.1 is replaced by 1.0, the traditional output-based linkage measure Table 8.1 Ten normalized and generalized key sector measures Name of measure

Explanation with jobs as impact variable

Total forward linkage

Linkage formula  i ci ai j /c j  d f i = j bi j c j /ci  tb j = i ci li j /c j  t f i = j gi j c j /ci

Complete HE backward linkage

cb j = tb j / l j j

Extraction of complete j from Leontief model

Complete HE forward linkage

c f i = t f i /gii

Extraction of complete i from Ghosh model

Partial HE backward linkage

pb j = (tb j − 1)/ l j j

Extraction of input column j from Leontief m.

Partial HE forward linkage

p f i = (t f i − 1)/ gii

Extraction of output row i from Ghosh model

Net backward linkage

nb j = tb j (y j / x j )

Total backward linkage × final output ratio j

Net forward linkage

n f i = t f i (vi / xi )

Total forward linkage × primary input ratio i

Direct backward linkage Direct forward linkage Total backward linkage

db j =

Direct jobs with suppliers to j per job in j Direct jobs with buyers from i per job in i Direct+indirect jobs with suppliers to j per … Direct+indirect jobs with buyers from i per …

Legend HE = hypothetical extraction, aij = intermediate input coefficient, bij = intermediate output coefficient, ci = impact variable per unit of output, l ij = cell from Leontief-inverse and gij = cell from Ghosh-inverse Source Adaptation of Temurshoev and Oosterhaven (2014)

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results, which is why the ten linkages of Table 8.1 are labelled generalized linkages. They are also labelled normalized linkages, as they are all made independent of the size of the sector at hand.  Table 8.1 does not include the row sums of the Leontief-inverse, j li j ∈ L i = (I − A)−1 i, as a forward linkage measure (Rasmussen 1956), as these row sums measure the backward impact of a meaningless unit vector of exogenous final demand. Instead, following the subsequent literature, the list uses the row sums of the Ghosh inverse, j gi j ∈ G i = (I − B)−1 i, as first proposed by Beyers (1976) and Jones (1976). This sensible choice, however, implies that the forward linkage measures should not be interpreted as representing the WoE’s total output impact of a primary supply quantity shock to the sector at hand, as the quantity interpretation of Ghosh multipliers has been shown to be highly implausible (see Sect. 6.1). Instead, these measures should be interpreted as the impact on the value of the WoE’s total output due to the complete passing on of a primary supply price shock to the sector at hand (see Sect. 5.1). Table 8.1 also does not include the output-to-output multiplier (Miller and Blair 2009, p. 328) as that multiplier equals the total flow multiplier (Szymer 1984), which on its turn is not included as it equals the earlier hypothetical extraction (HE) of complete sectors (Paelinck et al. 1965; Strassert 1968; Schultz 1977), as first indicated by Szyrmer (1992), and recently proven by Gallego and Lenzen (2005). The hypothetical extraction method is included, because it offers much more flexibility, as it allows for the extraction of any subset of transactions from an IOT. However, all HE variants suggested in the literature (see Miller and Lahr 2001, for an overview) require a cumbersome three-step calculation process and all result in linkage measures that primarily tell the analyst that deleting monetary large parts of an IOT has large impacts. For this reason, HE outcomes always need to be rescaled (normalized) with the size of the industry at hand. Including this normalization, the following generalized three-step HE procedure results: 1. Define A−s as the matrix with intermediate input coefficients with the selected cells equal to zero, c−s as the vector with the impact variable per unit of output with the selected cells equal to zero, and y−s as the vector with exogenous final demand with the selected cells equal to zero. 2. Calculate the impact vector v, without and with the selected cells equal to zero, as vi = j ci li j y j ∈ v = cˆ (I − A)−1 y and vi−s ∈ v−s = cˆ −s (I − A−s )−1 y−s , respectively. 3. Calculate the normalized and generalized HE backward linkages of the selected IO transactions for industry i as H E ib,v,s = (vi − vi−s )/vi . The corresponding HE forward linkages are calculated analogously, but with the Ghosh model. Fortunately, the two most obvious HE key sector measures both have an analytical solution that makes their calculation and comparison with the non-HE measures far more easy. These two HE measures result from, respectively, the complete HE of

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an individual sector, and a column-only or row-only partial HE of an individual sector for the partial HE backward and forward linkages, respectively (see Table 8.1 for the two analytical solutions, and Temurshoev and Oosterhaven 2014, for the mathematical proofs). Temurshoev and Oosterhaven, furthermore, prove that the diagonals of the Leontief-inverse and the Ghosh-inverse are equal (lii = gii , ∀i) and show that the values of the diagonal cells vary empirically between about 1.01 and 1.20. This means that the corresponding HE and total linkages will be very strongly correlated, as these diagonal elements constitute the only difference between them (see the formulas in Table 8.1). They, furthermore, show that the final output ratios of the net backward linkages vary between about 0.35 and 0.85, whereas the primary input ratios of the net forward linkages vary less between about 0.50 and 0.70. Consequently, after inspection of the formulas of Table 8.1, one may predict that the net backward linkages will show a larger deviation from their corresponding total linkages than the net forward linkages from their total linkages. Temurshoev and Oosterhaven (2014) analyse the sector-by-sector similarities of income, employment, and CO2 backward and forward linkages for 34 sectors in 33 countries. In general, the rank order of sectors per country is very dissimilar between the group of backward linkages, on the one hand, and the group of forward linkages, on the other hand, which is not too surprising as these two sets of linkages measure causally fundamentally different impact mechanisms. Within each of these two groups, the rank orders of the 34 sectors in case of the total linkage and the two HE linkages are very similar for almost every country, while the direct linkages are similar to these three linkages, but a little less so. Within the group of forward linkages, the net forward linkages are only weakly correlated with the other (gross) forward linkages, while the net backward linkages within their group are even weaker correlated with the other (gross) backward linkages. The different outcomes for the two net linkages are not too surprising either, as they represent the only measures that try to capture both sides of sectoral dependence.

8.1.2 Cluster and Linkage Analysis for Three Dutch Spatial Policy Regions A typical example of a key sector analysis is the cluster and linkage analysis for three Dutch spatial policy regions by Oosterhaven et al. (2001). It was an investigation commissioned by the Dutch Ministry of Economic Affairs, among others, responsible for Dutch regional policy. At that time, Dutch infrastructure policy and Dutch regional policy were based on strongly held beliefs about the supposedly large national economic importance of the transport and distribution sectors in the two so-called mainport regions—the greater Rotterdam Harbour area and greater Amsterdam Airport/Harbour area. The peripheral and more rural Northern Netherlands, on the other hand, was viewed as a weak region in need of regional policy help,

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with never mentioned, and thus implicitly believed little importance for the national economy. The outcomes of the study, however, did not confirm these beliefs, which is why the Ministry initially refused to publish the report. Thanks to a well-informed journalist who threatened to go to court, the study was published with a few months delay (see Oosterhaven et al. 1999, for a conclusion of the fierce, subsequent Dutch policy debate). The cluster analysis of this study is based on the absolutely and relatively largest direct linkages of the 48 sectors distinguished in each of the three bi-regional IOTs used (RUG/CBS 1999). Clusters are defined as groups of interdependent sectors with linkages in both directions. Against popular belief, the study shows that the transport and distribution sectors of the two mainport regions do not constitute the core of an important cluster of sectors. Instead, the core of the strongest cluster in the greater Amsterdam region consists of printing and publishing, business services and trade services, whereas the core of the strongest cluster in the greater Rotterdam region consists of the chemical sector. Both clusters also have strong direct linkages with comparable sectors in the rest of the country. Against popular belief, this is also the case for the strongest cluster in the Northern Netherlands with agriculture and food processing as its core industries. The second strongest cluster in all three regions has construction as its core sector, but in that case, the relation with comparable sectors in the rest of the country is different. The construction cluster in the two much smaller, but much more densely populated mainport regions is strongly tied to comparable sectors in the rest of the country. The construction cluster in the Northern Netherlands, however, only has strong direct linkages within its own region. The overall totals of the direct linkages of these three regions, i.e. the direct spatial linkages, are summarized in Table 8.2. As expected, the rural North has the strongest intra-regional direct linkages, but those of the two mainport regions are surprisingly strong too. Besides, Greater Amsterdam has the strongest direct linkages with the Rest of the Country, whereas greater Rotterdam has the strongest direct ties with the Rest of the World.2 Table 8.2 Overall trade relations, i.e. direct spatial linkages per region Northern Netherlands

Greater Amsterdam

Greater Rotterdam

Origin of purchases in % // Destination of sales in % Own region

56 // 51

46 // 44

41 // 39

Rest of the Country

20 // 25

29 // 33

25 // 27

Rest of the World

24 // 24

25 // 23

34 // 34

Source RUG/CBS (1999)

2 The

own region origin percentages and the Rest of the Country origin percentages in Table 8.2 represent weighted alternatives for the two unweighted direct backward spatial linkages in Miller and Blair (2009, p. 563), whereas the corresponding destination percentages represent weighted alternatives for the two unweighted direct forward spatial linkages in Miller and Blair.

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Table 8.3 Weighted average total spatial linkages per region, times 100 Northern Netherlands

Greater Amsterdam

Greater Rotterdam

Total backward linkage // Total forward linkage Intra-regional linkages

26 // 24

16 // 16

19 // 19

Bi-regional spillovers

21 // 29

25 // 24

26 // 25

Total: national linkagesa

47 // 53

41 // 40

45 // 44

a The

total forward and the total backward linkage of the weighted average national sector times 100 both equal 50 (see Oosterhaven et al. 2001, footnote 6, for the proof of the equality) Source RUG/TNO (1999)

It is interesting to compare the implicitly weighted direct spatial linkages of Table 8.2 with the explicitly weighted total spatial linkages of Table 8.3. In case of the backward linkages, the weighing is done by means of the share of each regional sector in regional exogenous final demand in the bi-regional Leontief model, yi·r · /i yr · , while the weighing in case of the forward linkages is done by each sector’s share in regional exogenous primary input in the bi-regional Ghosh model, v·ir /(vr ) i. This gives the following formulas for the weighted intra-regional total backward and total forward linkages, respectively:3 i (Lrr − I) yr · /i yr · and (vr ) (Grr − I) i /(vr ) i

(8.1)

Note that both intra-regional linkages are exclusive of the meaningless direct impact I, whose removal is necessary to be able to compare them with the weighted biregional total backward and total forward spillovers, which are calculated likewise: r·

i Lsr yr · /i y and (vr ) Gr s i/(vr ) i

(8.2)

Note that the backward spatial spillover relates to imports, whereas the forward spillover relates to exports.4 As one may expect from inspecting the direct spatial linkages in Table 8.2, the total intra-regional linkages of the Northern Netherlands in Table 8.3 are significantly larger than those of the two mainport regions. The mutual rank order of the two mainport regions, however, reverses. Inspecting only the direct linkages disregards the larger strength of the clusters of the greater Rotterdam area. To a lesser extent, the same holds for the spillovers of the Rotterdam clusters to the Rest of the Country. The direct spillovers in Table 8.2 are clearly smaller than those of Greater Amsterdam, but the total spatial spillovers in Table 8.3 are a little larger. 3 Note that this weighing serves to aggregate the individual sector linkages to a weighted total spatial linkage. It should, therefore, not be confused with the rescaling of individual sector’s total linkages to better represent the planner’s preference as advocated by Hazari (1970) and Loviscek (1982). 4 The two intra-regional total linkages and two bi-regional total spillovers in Table 8.3 represent weighted alternatives for the two sets of two unweighted total spatial linkages in Miller and Blair (2009, p. 563).

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Consequently, the total national linkages in Table 8.3, being the total of the intraregional linkages and the bi-regional spillovers, are also larger for Greater Rotterdam than for Greater Amsterdam, such despite the clearly larger foreign import and foreign export leakages of Greater Rotterdam in Table 8.2. Obviously, only looking at direct linkages may lead to wrong conclusions, despite their positive correlation with the total linkages for practically all countries, as observed by Temurshoev and Oosterhaven (2014). The large size of the total national forward and backward linkages of the Northern Netherlands represented the most shocking outcome of Oosterhaven et al. (2001), as all national policy makers were convinced that those of the two mainport regions would be significantly larger than those of the peripheral North.5

8.1.3 The Other, Cost Side of the Coin The core question, however, is the relevance of the above type of research in selecting sectors that will stimulate regional or national economic growth most. Schaffer (1973) already early points to the rather big gap between key sector analysis and the simultaneous problem of choosing which instruments to use to stimulate which sectors. The problem of bridging the gap with policy-making, to a large extent, depends on which linkages are largest. If a sector is selected because of its large forward linkages, the causality of the cost-push IO price model (see Sect. 5.1), which underlies these linkages, suggests that the appropriate instruments should operate on the primary cost side of that sector; making its outputs cheaper such that its processing sectors are stimulated too. However, if both this sector and its processing sectors completely pass these price reductions on to their customers, as is assumed in the model that underlies the forward linkages, the whole primary cost decrease will end up in lower final output prices. To still get a positive total output effect that is as large as the value decrease of final demand, i.e. as large as the forward linkage, one needs to assume that all final demand elasticities equal minus one, which runs against one of the very assumptions on which the underlying model is based (see Table 6.2). Nevertheless, this “minus one” assumption is more plausible than the “infinite demand elasticity” assumption of the underlying model. It, however, requires that the estimation of the impacts subsequently goes through the circular process described in Fig. 5.2. And this results in ex post forward linkages that are considerably smaller than the ones on which the selection of this sector was based! 5 An interesting side-result is the rather strong relation found

between the relative size of a regional sector, as measured by means of its location quotient (LQ), and the relative size of its total linkages. A clear specialization bonus seems to be present: regional sectors with large LQs systematically have larger total linkages than the corresponding sector in other regions, as first noted in Oosterhaven (1981).

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8 Other IO Applications with Complications

The opposite case is the selection of a sector because of its large backward linkages. Then, the causality of the underlying IO model suggests the use of instruments that increase the volume of that sector’s final demand to stimulate its supplying sectors. There are, however, many ways to do so, each with quite different policy cost. And, again the question is how the stimulated sector and its supplying sectors will react. If the stimulated sector is subject to supply restrictions, it most likely will raise its prices and hardly raise its output, whereupon imports will have to increase to satisfy the larger final demand, implying ex post backward linkages that are smaller than the ones on which this sector was selected! The same reaction may occur with the supplying sectors, also leading to smaller ex post backward linkages. McGilvray (1977) emphasizes that Hirschman (1958), in fact, was looking for potentially growing sectors that could play a leading role in creating disequilibrium, which would induce investment, especially, in supplying sectors that have a minimum operating capacity that is small compared to the additional demand of the stimulated key sector, which implies that the standard total backward linkage measure needs to be rescaled with this ratio in order to be able to select the right key sectors. Both he and Bulmer-Thomas (1978), furthermore, argue that the difference between the total backward linkages based on technical coefficients and those based on intra-regional input coefficients, i.e. i (I − A·r )−1 − i (I − Arr )−1 , should be used to indicate the potential backward impacts of stimulating the sector at hand, as Hirschman’s disequilibrium approach is based on import substitution as a development strategy. As a complement, one may advocate to add a development strategy that is based on substituting exports by domestic processing, which would imply selecting sectors with the largest difference between the total forward linkages measured by what one might call technical output coefficients and those measured with the standard intra-regional output coefficients, i.e. by (I − Br · )−1 i − (I − Brr )−1 i. Hewings (1982) comments that measures of import substitution potential, especially for smaller developing countries and for most regions, should include the potential of import substitution of consumer goods, and not only that of intermediate goods. The same comment may be made for the above-suggested measure of the potential impacts of export substitution. Both comments may easily be accommodated by using the Type II Leontief-inverse and the Type II Ghosh-inverse, respectively, instead of the above two Type I inverses. industryanalysisHowever, the likelihood of actually achieving the thus estimated impacts of import and export substitution strongly depends on the possibilities to increase the comparative advantage of the region or country at hand in, respectively, the domestic production of the targeted imports and the domestic processing of the targeted exports. Obviously, this requires more serious research, than only calculating the above two formulas, i.e. research such as that advocated for a target industry analysis (McLean 2018). Finally, let us assume that all the above qualifications are solved and that total backward and total forward linkages are formulated that correctly predict the benefits in terms of the chosen goal variable per unit of the exogenous impulse that belongs to the linkage at hand. Does that then deliver the key sectors that stimulate the growth of the chosen goal variable most effectively? The answer to this rhetorical question

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is of course NO: but why? Well simply because not one of the gross linkages (see the first eight lines of Table 8.1) tells the user anything about the policy cost of creating one additional unit of the presumed exogenous impulse. Take the case of the key sectors found for the Northern Netherlands. Agriculture has, especially, large forward linkages. Creating a new polder would increase the quantity of its primary inputs and would lead to large positive impacts on its processing sectors, but at large financial and environmental cost (see Oosterhaven 1983). Stimulating agriculture by directly subsidizing its primary inputs is forbidden by the EU, but doing that indirectly by training of labour or stimulating agricultural research is allowed, but involves different cost and different production effects for each measure. The second key sector (food processing) has, especially, large backward linkages. Directly stimulating the size of its final demand is only possible and only allowed by the EU by means of lowering, for instance, the value-added tax on food products. Doing that offers follow-up opportunities, such as stimulating the development of new food products, but each policy option will have different policy cost and different effectiveness in terms of its impact on final demand. Oosterhaven (2017) suggested that using net linkages (see the last two lines of Table 8.1) might solve the problem of specifying the policy cost of stimulating a key sector with one unit, as having a relatively large final demand offers more opportunities for stimulating backward linkages, while having relatively large primary costs makes stimulating forward linkages easier. This claim, however, needs to be rejected as the relative size of final demand or primary cost has no bearing on the policy cost of creating an additional unit of it. In all, the above discussion makes one thing very clear: developing yet another new backward or new forward linkage measure, e.g. by means of using qualitative IO analysis or neural network analysis or graph theory, is completely pointless. Instead, key sector analysis needs to be based on interindustry models with price–quantity interaction, as well as a consideration of both the benefits and the costs of using different policy measures. Calculating linkages only shows one side of the coin.

8.2 Structural Decomposition Analyses: Another Half-Truth The decomposition of output growth into the growth of final demand and changes of the Leontief-inverse is another important field of IO applications dating back to Leontief (1941) himself. Since then, thousands of such structural decomposition analyses (SDAs) have been done (see Miller and Blair 2009, ch. 13, for a recent overview).6 Skolka (1989) explicitly explores the identity splitting options for the basic IO growth equation. In their extensive overview, Rose and Cassler (1996) emphasize the similarities between SDA, shift and share analysis and growth accounting. The communality is that all three approaches decompose a growth equation into its constituent parts. 6 On

26 August 2019 “structural decomposition analysis” and “input–output” combined scored about 3710 hits on Google Scholar.

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8 Other IO Applications with Complications

Here, we emphasize the clarifying, fundamental differences between these three decomposition approaches.

8.2.1 Shift and Share Analysis of Regional Growth We start with the decomposition technique that has no theoretical foundation, except for the notion that the mix of industries is important in explaining the difference between a region and the nation or the world with which one intends to compare that region. Hence, we start with shift and share analysis (SSA, see Perlof et al. 1960, ch. 5, for a first account). Its most general specification decomposes the following identity: vr − v n =

 i

sir vir −

 i

sin vin , with

 i

sir =



sn i i

=1

(8.3)

where v = variable of interest (e.g. total GDP growth, total job growth, average wage level, total energy use or total CO2 emission level) for some unit r (e.g. region) that is to be compared with some norm n (e.g. nation), and that is aggregated over an index i (e.g. industry), with sir = vir / i vir = share of i in r for variable v.7 From (8.3), it follows that SSA may be used to analyse a multitude of problems. Here, we only discuss its oldest and most frequently used application to regional economic growth. Table 8.4 shows the five ways in which Eq. 8.3 may be decomposed. You can easily Table 8.4 Possible shift and share decompositions of Eq. (8.3) No.

Structural component, with:

Growth component, with:

Regional growth rates

National growth rates

Regional industry shares







i

1.

i

(sir − sin ) vin

r r i si (vi

+

2. 3.a

½

4.

+

5.

(sir − sin ) vir

− vin )

National industry shares  r i si (vir − vin )

Combined differences (specialization) component  r n i (si − si ) n r (vi − vi )

+ +

+

½

½

½

+ +

– +

+

a This decomposition results from taking the average of decomposition 1 and 2 as well as that of 4 and 5

Source Oosterhaven and van Loon (1979) 7 Note

that the definition of the share may need to be adapted to the definition of the variable, as in case of labour productivity growth (see Oosterhaven and Broersma 2007). In international economics, when v = export growth, r = some country, n = all of the world and i = products, shift and share analysis is known as constant market share analysis (see Jepma 1986, for an overview and several applications).

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verify that all five decompositions have the desired property of its components being (1) mutually exclusive and (2) completely exhaustive. The first decomposition shows its share in national growth vn , plus a the classical SSA of regional growth vr into  regional shiftdue to a different industry mix i (sir − sin ) vir , plus a residual growth component i sin (vir − vin ). The latter measures whether the nationally weighted, average regional industry grows faster or slower than its national counterpart (the italics indicate the origin of the term “shift and share” analysis). The structural (shift) component and the (residual) growth component may both be measured/weighted differently, as shown in the second decomposition in Table 8.4. Taking the average of the first two decompositions delivers the third decomposition. Taking the simple average is the typical solution of SDA to the problem of choosing between components measured in base year terms and those measured in end year terms (Skolka 1989). In SSA this is not the preferred choice. When the research interest is in comparing different regions, each component needs to be measured/weighted in the same way. This argument makes the first three, and especially the fourth decomposition inacceptable for interregional comparisons. Luckily, there is a fifth decomposition that measures the structural component as well as the growth component in the same way. To reach this result, a third combined differences component needs to be added (see Table 8.4). This third component is theoretically interesting on its own account, as it measures whether the industries in which the region is specialized have a higher or lower score on the variable of interest, i.e. it measures socalled localization economies (see Oosterhaven and Broersma 2008). Hence, this fifth component measures the impact of regional specialization. For this additional reason, the fifth decomposition should even be considered to represent the preferred decomposition when the research interest only regards a single region! In the case of regional wage differences (Oosterhaven and van Loon 1979) and in the case of regional labour productivity differences (Oosterhaven and Broersma 2007), specialization clearly pays off, in the sense that the industries in which a region is specialized have higher levels of labour productivity and pay higher wages than their national counterparts, indicating positive localization economies. In the case of labour volume growth and value-added growth, however, the third, specialization component proved to be negative for all Dutch regions, which was interpreted as representing diminishing returns to these positive localization economies (Oosterhaven and Broersma 2007). The same result was found for earlier periods, for different regions and different industry classifications (Oosterhaven and Pellenbarg 1994); a result that may also be interpreted as indicating a convergence of regional sector structures to the national sector structure. The most mentioned objections against SSA are (1) its lack of a theoretical foundation and (2) the impossibility to determine the statistical significance of its components (Chalmers and Beckhelm 1976; Richardson 1978). The lack of a theoretical foundation, however, may be turned into an advantage when, the structural and the specialization component are used as regular, composite explanatory variables in an econometric estimation of the LHS of (8.3). This, in fact, simultaneously solves the second objection, as it provides a measure of the statistical significance of these

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two components in explaining the LHS of (8.3) (see Graham and Spence 1998, and Broersma and Oosterhaven 2009, for applications of this principle).

8.2.2 Structural Decomposition Analyses of National and Interregional Growth Next, consider the oldest and most simple input–output structural decomposition analysis (SDA), which splits up output growth by industry, xi ∈ x: x = x1 − x0 = (I − A1 )−1 y1 − (I − A0 )−1 y0 = L1 y1 − L0 y0

(8.4)

An SDA of Eq. 8.4 represents a comparative static analysis that sequentially looks at the impact on the variable of interest of changes in each set of parameters, holding the other parameters constant. Note that SDA may be used to decompose any firstorder difference in a matrix equation (such as the difference between national and regional embodied CO2 emissions or the growth of energy use, see Rose and Chen 1991, for an extensive SDA of the latter). However, here, we only discuss its most common application, namely, to economic growth. Just like the decomposition of (8.3), there are also five comparable decompositions of (8.4) (see Table 8.5). Again their components are (1) mutually exclusive and (2) completely exhaustive. Skolka (1989) presents four of them, while No. 4 is presented by Oosterhaven and van der Linden (1997). In choosing between the first two decompositions, Skolka (1989) refers to the circularity principle (UN 1975), which leads to a preference for combining Laspeyres volume indexes with Paasche price indices. Skolka nor Miller and Blair (2009), however, see any such preference in case of SDA, which is why they prefer the third decomposition. This choice neglects the interaction component L y. This is, however, not a real loss, as (1) the interaction component is empirically found to be rather small (Uno 1989), while Table 8.5 Possible structural decompositions of industry output growth x No.

1.

Leontief-inverse change, with:

Final demand change, with:

Base year y

End year y

Base year L

End year L

Interaction component

L y0

L y1

L0 y

L1 y

L y

+

+

½

½

+

2. 3.a

½

4. 5.

+

+ +

½ +

+

– +

a This decomposition results from taking the average of decomposition 1 and 2 as well as of 4 and 5

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(2) it is theoretically considered to have no clear economic interpretation (Miller and Blair 2009). Here, SDA clearly deviates from SSA.8 Departing from the most simple IO model used in (8.4), many, more sophisticated variants with an increasing number of components have been developed (see Rose and Casler 1996, and Miller and Blair 2009, for overviews). Here, we showcase the decomposition of value-added growth in the EU by Oosterhaven and van der Linden (1997), as it includes most of the individual components proposed in the literature. They use the interregional IO model of Sect. 2.3, with each of the intermediate input rs ∈ B (often called coefficients airjs and each of the final demand input coefficients biq bridge coefficients) split up into: (1) a technical or preference coefficient and (2) a trade origin ratio: v = cˆ L B y = cˆ (I − Ma ⊗ A)−1 (M f ⊗ F) y

(8.5)

In (8.5), ⊗ = Hadamar product (i.e. cell-by-cell matrix multiplication), and going backwards along the causal chain, y = QR column with macroeconomic levels of final demand of type q in country s, f iq·s ∈ F = R mutually identical I x QR matrices with final demand preference coefficients, indicating the total use of product i per unit of final demand, m riqs ∈ M f = IR × IQ matrix with cell-specific trade origin ratios, indicating which fraction of that total originates from region r, ai·sj ∈ A = matrix with R mutually identical I × IR matrices with technical coefficients, indicating the total use of product i per unit of output of industry j in s, m ri js ∈ Ma = IR × IR matrix with cell-specific trade origin ratios, indicating which fraction of that total originates from country r, cˆ = IR diagonal matrix with gross value-added coefficients and v = IR column with gross value added. The comparative static decomposition of the change in (8.5) is laborious, but straightforward, except for the decomposition of the change in the intercountry Leontief-inverse L into its constituent parts: L = L1 (Ma ⊗ A)L0 = 0.5 L1 (M0a + M1a ) ⊗ AL0 + 0.5 L1 Ma ⊗ (A0 + A1 )L0

(8.6)

The first equality of (8.6) can be proven by pre-multiplication and post-multiplication of the first two terms of (8.6) with (I − A1 ) and (I − A0 ), respectively. The last term of (8.6) gives the decomposition of the change in the Leontief-inverse without an interaction term. Using (8.6), the laborious overall decomposition of (8.5) may be done in three steps:

8 Elements of SSA may be integrated into an SDA, as suggested by Lahr and Dietzenbacher (2017).

They show that in case of a regional SDA—with the added data from two national IOTs—both y and L may be split up further into changes in the levels and structures of the regional and national y and L. Such a further split up of the decompositions of Table 8.5, however, does not change their demand-driven nature nor their other properties to be discussed next.

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1. The standard decomposition is applied to the four terms of the first part of (8.5). That is done in such a way that the variable with the  moves from the left to the right for the first decomposition, whereas it moves from the right to the left for the second decomposition, after which the average of these two, so-called polar decompositions is taken. This delivers the component for ˆc in (8.7a) and that for y in (8.7f), where each of the two sets of weights nicely shows the polar nature of the two decompositions that are averaged. 2. Eq. 8.6 is substituted into 0.50 (ˆc0 L B1 y1 + cˆ 1 L B0 y0 ), i.e. the component for the change in the Leontief-inverse. This gives the component for Ma in (8.7b) and that for A in (8.7c). 3. The component for the change in the matrix with final demand input or bridge coefficients, i.e. These three operations result in the following decomposition of (8.5): v = 0.50 ˆc (L0 B0 y0 + L1 B1 y1 )

(8.7a)

  +0.25 cˆ 0 L1 Ma ⊗ (A0 + A1 )L0 B1 y1 + cˆ 1 L1 Ma ⊗ (A0 + A1 )L0 B0 y0 (8.7b)   +0.25 cˆ 0 L1 (M0a + M1a ) ⊗ A L0 B1 y1 + cˆ 1 L1 (M0a + M1a ) ⊗ A L0 B0 y0 (8.7c)

  +0.25 cˆ 0 L0 M f ⊗ (F0 + F1 )y1 + cˆ 1 L1 M f ⊗ (F0 + F1 )y0

(8.7d)

  f f f f +0.25 cˆ 0 L0 (M0 + M1 ) ⊗ F y1 + cˆ 1 L1 (M0 + M1 ) ⊗ F y0

(8.7e)

+0.50 (ˆc 0 L0 B0 + cˆ 1 L1 B1 ) y

(8.7f)

The above average of two polar decompositions, however, represents only one of many possible decompositions. Dietzenbacher and Los (1998), also ignoring interaction components, show that the number of possible basic decompositions equals the faculty of the number of components (n). They, luckily, also show that decompositions like that of (8.7a–8.7e), being the average of two polar decompositions, have outcomes that are very close to the average of all n! possible basic decompositions. When used to analyse economic growth, SDA is usually applied to longer time periods, and most often it reports that changes in the level of final demand constitute by far the most important component. Feldman et al. (1987), e.g. following the seminal study of Anne Carter (1970) with more recent and more detailed IO data, analyse a decomposition of the growth of x = LB y for the USA over the period 1963– 1978. They find that changes in y are far more important than changes in either L or B, for some 80% of the 400 American industries distinguished. Coefficient changes were only important in case of the fastest and the slowest growing industries (see Fujimagari 1989, for very comparable results for Canada). From those outcomes, they conclude that the best growth policy is a good macroeconomic policy.

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Applying (8.7a–8.7f) to their EU IRIOTs for 1975–1985, Oosterhaven and van der Linden (1997) also report final demand growth, especially of household consumption expenditures, to be by far the most important component for all eight countries and for almost all of the 25 industries distinguished. The combined effect of the five types of coefficient changes in (8.7a–8.7e) is rather small and predominantly negative, which is mainly caused by a systematic decline in value-added coefficients, indicating more roundabout production processes with longer supply chains with more non-EU value added. At the industry level for individual countries, however, they do find larger impacts of different types of coefficient changes, which lead them to conclude that sector policies may be more important than indicated by Feldman et al. (1978), also because the economically much more open individual EU member states have less scope for macro policies than the USA. Finally, it is interesting to also look at SDA results for the third large international trading unit, i.e. China. Like for the USA and the EU, Andreosso-O’Callaghan and Yue (2002) also find for China that total final demand, and specifically the exports of “high-tech” industries, constitutes the largest contribution to its output growth for 1987–1997. They, however, do not make a distinction between ordinary exports and processing exports that add only limited amounts of domestic value added to mainly imported materials. This distinction is important since processing exports, in contrast to ordinary exports, hardly have any indirect impacts on domestic value added. Pei et al. (2012), using Chinese IOTs with both kinds of exports separated for 2002–2007, conclude that the contribution of exports to domestic value added is overestimated with 32% if the two types of exports are aggregated, while the contribution of exports to the value added of the “high-tech” telecommunication industry is even overestimated with 63%. Still, they too report that domestic final demand “explains” 70% of Chinese GDP growth, whereas changes in coefficients “explain” only minus 5%. The remainder of almost 35% is “explained” by the growth of both types of exports. In the above paragraph, the word explained has been put between quotation marks. As opposed to SSA, SDA is hardly criticized. The main critique (Rose and Casler 1996; Dietzenbacher and Los 1998; Miller and Blair 2009) regards the nonuniqueness of each decomposition and the weak theoretical foundation for taking averages. However, just like SSA, SDA also needs to be criticized because of the impossibility to determine the statistical significance of its components. As opposed to SSA, SDA does have a theoretical foundation, namely the demand-driven IO model. In the case of SSA, the lack of a theoretical foundation and the related presence of a residual component could be turned into an advantage that simultaneously solved the problem of establishing the statistical significance of its non-residual components (Broersma and Oosterhaven 2009). In contrast, having a theoretical foundation may easily be considered to represent the weakest aspect of SDA, for two reasons. (1) As opposed to SSA, and precisely because of its theoretical foundation, SDA does not have a residual component that, by dropping it in an econometric estimation, may be used to establish the statistical significance of the other components. (2) Depending upon the type of application, the assumptions of the underlying demand-driven IO quantity model may represent

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a major problem. This is at least the case in the largest area of SDA applications, i.e. the decomposition of industry output growth and GDP growth. In case of short run, year-to-year changes, especially when the economy operates below full capacity, the Leontief model adequately captures the, in the short run rather important demand-side causes of economic growth and decline.

8.2.3 The Other, Supply Side of the Coin: Growth Accounting In case of the longer run of say five-year and more, SDA unjustly ignores the impact of changes on the supply side of the economy, such as the growth of labour supply, the growth of the capital stock and factor productivity growth. In this context, growth accounting (see Kendrick 1961, for a first account) represents the almost complete opposite of SDA, in that it ignores the demand side and decomposes the growth of industry output and GDP exclusively into contributions of supply-side components. Growth accounting may be founded in production theory (Diewert 1976; Caves et al. 1982). Using a translog production function and assuming full input utilization and constant returns to scale, the relative growth of multi-factor productivity of industry j ( ln A j ) may be defined as the residual of the relative growth of the total output of industry j ( ln x j ) and the sum of the weighted relative growth of its use of capital (k j ), labour (l j ) and intermediate inputs (z j ) (Timmer et al. 2010): (8.8a)  ln A j =  ln x j − wk j  ln k j − wl j  ln l j − wz j  ln z j    with: wk j = pk j k j p j x j , wl j = pl j l j p j x j , wz j = pz j z j p j x j and wk j + wl j + wz j = 1

(8.8b)

wherein: A = level of multi-factor productivity, w = respective weights and p = respective prices. In empirical applications, the capital, labour and total intermediate inputs are often split up further, mostly by means of IOT or SUT data, while the weights are mostly calculated as the average of the begin year weight and the end year weight, as in the well-known and often used EU KLEMS database (see Timmer et al. 2010, ch. 3). Note that (8.8a, 8.8b) may also be calculated with two IOTs or two SUTs, in which case the weights will equal average of the primary and intermediate input coefficients of the begin year and the end year of the analysis. A comparison with SDA and SSA further clarifies the nature of growth accounting. With SDA it has in common that it has a theoretical foundation, be it an entirely contradictory one. With SSA it has in common that it contains a residual growth component ( ln A j ). Comparable to SSA, dropping the residual component allows for an econometric estimation of  ln x j . This, subsequently, delivers an estimate of the statistical significance of the, in that case estimated, weights of the remaining

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components, along with an estimate the real importance of demand-side factors in explaining longer run economic growth, i.e. if such factors are added as explanatory variables. The primary field of application of growth accounting is not the analysis of industry output and GDP growth, but that of productivity growth. Comparing the USA and Europe, van Ark et al. (2008, see also Timmer et al. 2010) show that Europe was catching up in labour productivity until about 1995, after which it experienced a slowdown, whereas the USA significantly accelerated its productivity growth, at least until 2006. At the detailed industry level, traditional manufacturing no longer acted as the productivity engine of Europe, probably due to exhausted catching-up possibilities, while Europe’s industries lagged in participating in the new knowledge economy, lagged in investing in information and communication technology, and lagged in keeping up their multi-factor productivity growth. These differences, especially, led to an increasing gap in the productivity of European trade and business services, of course, with variations from industry to industry and from country to country. Also, in the case of China, growth accounting tells a story that is completely different from that of SDA, where growth of final demand is the dominant explanation of longer-run industry output and GDP growth. Wu (2016) decomposes China’s 9.16% annual GDP growth over the period 1980–2000 into 6.61% due to the growth of capital, 1.32% due to the growth of labour and 1.24% due to total factor productivity (TFP) growth. Of the 1.32% due to labour growth, 75% is attributed to quality improvement and 25% to the growth of hours worked. Of the 1.24% due to TFP growth, 70% is attributed to TFP growth at the industry level and 30% to the reallocation of capital and labour between industries. Differences in the contribution of the individual industries to these aggregate results are mainly explained by industry differences in market structures and policy interventions, running from being essentially centrally planned to being open to world competition. By definition, demand does not play a role in the above growth accounting decomposition analyses. The supply-side arguments dominate the story, as they naturally would when longer-run growth is to be explained. It is the side of the coin that is ignored by SDA.

References Andreosso-O’Callaghan B, Yue G (2002) Sources of output growth in China: 1987–1997: application of a structural decomposition approach. Appl Econ 34:2227–2237 Beyers WB (1976) Empirical identification of key sectors: some further evidence. Environ Plan A 8:231–236 Broersma L, Oosterhaven J (2009) Regional labour productivity in The Netherlands, evidence of agglomeration and congestion. J Reg Sci 49:483–511 Bulmer-Thomas V (1978) Trade, structure and linkages in costa rica: an input-output approach. J Dev Econ 5:73–86

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Carter A (1970) Structural change in the American economy. Harvard University Press, Cambridge MA Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output, and productivity. Econ Soc 50:1393–1414 Chalmers JA, Beckhelm TL (1976) Shift and share and the theory of industrial location. Reg Stud 10:15–23 Chenery HB, Watanabe T (1958) International comparisons of the structure of production. Econom 26:487–521 Diamond J (1985) Interindustry indicators of employment potential. Appl Econ 7:265–273 Dietzenbacher E (2005) More on multipliers. J Reg Sci 45:421–426 Dietzenbacher E, Los B (1998) Structural decomposition techniques: sense and sensitivity. Econ Syst Res 10:307–323 Diewert WE (1976) Exact and superlative index numbers. J Econom 4:115–145 Feldman S, McClain D, Palmer K (1987) Sources of structural change in the United States, 1963– 1978: an input-output perspective. Rev Econ Stat 69:503–510 Fujimagari D (1989) The sources of change in Canadian industry output. Econ Syst Res 1:187–201 Gallego B, Lenzen M (2005) A consistent input-output formulation of shared producer and consumer responsibility. Econ Syst Res 17:365–391 Graham DJ, Spence N (1998) A productivity growth interpretation of the labour demand shift-share model. Reg Stud 32:515–525 Hazari BR (1970) Empirical identification of key sectors in the Indian economy. Rev Econ Stat 52:301–305 Hewings GDD (1982) The empirical identification of key sectors in an economy: a regional perspective. Dev Econ 20:173–195 Hirschman A (1958) The Strategy of Economic Development. Yale University Press, New Haven Jepma CJ (1986) Extensions and Application Possibilities of the Constant Market Share Analysis: The Case of the Developing Countries Exports. PhD, Faculty of Economics, University of Groningen Jones LP (1976) The measurement of Hirschmanian linkages. Q J Econ 90:323–333 Kendrick JW (1961) Productivity Trends in the United States. National Bureau of Economic Research, Cambridge, MA Lahr ML, Dietzenbacher E (2017) Structural decomposition and shift-share analyses: let the parallels converge. In: Jackson R, Schaeffer P (eds) Regional Research Frontiers, vol 2. Springer, Heidelberg Leontief W (1941) The Structure of the American Economy. Oxford University Press, New York Loviscek AL (1982) Industrial analysis: Backward and forward linkages. An Reg Sci 16:36–47 McGilvray JW (1977) Linkages, Key Sectors and Development Theory. In: Leontief WW (ed) Structure, System and Economic Policy. Cambridge University Press, Cambridge McLean M (2018) Understanding Your Economy: Using Analysis to Guide Local Strategic Planning. Routledge, New York Miller RE, Blair PD (2009) Input-output analysis: foundations and extensions, 2nd edn. Cambridge University Press, Cambridge Miller RE, Lahr ML (2001) A taxonomy of extractions. In: Lahr ML, Miller RE (eds) Regional Science Perspectives in Economics: A Festschrift in Memory of Benjamin H. Stevens. Elsevier Science, Amsterdam Oosterhaven J (1981) Interregional Input-Output Analysis and Dutch Regional Policy Problems. Gower Publishing, Aldershot-Hampshire Oosterhaven J (1983) Evaluating land-reclamation plans for northern friesland: an interregional cost-benefit and input-output analysis. Pap Reg Sci Assoc 52:125–137 Oosterhaven J (2017) Key sector analysis: a note on the other side of the coin. SOM Report 2017015-GEM, University of Groningen Oosterhaven J (2004) On the Definition of Key Sectors and the Stability of Net Versus Gross Multipliers. SOM Report 04C01, Faculty of Economics and Business, University of Groningen

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Oosterhaven J, Broersma L (2007) Sector structure and cluster economies: a decomposition of regional labour productivity. Reg Stud 41:639–659 Oosterhaven J, Pellenbarg PH (1994) Regionale spreiding van economische activiteiten en bedrijfsmobiliteit. Maandschr Econ 58:388–404 Oosterhaven J, van der Linden JA (1997) European technology, trade and income changes for 1975–85: an intercountry input-output decomposition. Econ Syst Res 9:393–411 Oosterhaven J, Stelder D (2002) Net multipliers avoid exaggerating impacts: with a bi-regional illustration for the Dutch transportation sector. J Reg Sci 42:533–543 Oosterhaven J (2008) A new approach to the selection of key sectors: Net forward and net backward linkages. International IO Meeting on Managing the Environment, Seville, July 2008 Oosterhaven J, Broersma L (2008) Measuring revealed localisation economies. Lett Spat Res Sc 1:55–60 Oosterhaven J, van Loon J (1979) Sectoral structure and regional wage differentials: a shift and share analysis on 40 Dutch regions for 1973. Tijdschr Econ Soc Geogr 70:3–16 Oosterhaven J, Eding GJ, Stelder D (1999) Over mainports en de rest van het land. Econ-Stat Ber 84:666–668 Oosterhaven J, Eding GJ, Stelder D (2001) Clusters, linkages and interregional spillovers: methodology and policy implications for the two Dutch mainports and the rural North. Reg Stud 35:809–822 Paelinck J, de Caevel J, Degueldre DJ (1965) Analyse quantitative de certaines phénomènes du développement régional polarisé: Essai de simulation statique d’itérarires de propogation. In: No. 7, Problémes de Conversion Économique: Analyses Théoretiques et Études Appliquées, M.-Th. Génin, Paris Pei J, Oosterhaven J, Dietzenbacher E (2012) How much do exports contribute to China’s income growth? Econ Syst Res 24:275–297 Perlof HS, Dunn ES, Lampard EE, Muth RF (1960) Regions, resources, and economic growth. John Hopkins Press, Baltimore Perroux F (1961) La firme motrice dans la région et la région motrice. In: No. 1, Théorie et Politique de l’Expansion Régionale: Actes du Colloque International de l’Institute de Science Économique de l’Université de Liège, Libraire encyclopedique, Brussels Rasmussen PN (1956) Studies in Inter-Sectoral Relations. North-Holland, Amsterdam Richardson HW (1978) Regional and Urban Economics. Penguin, Harmondsworth Rose A, Casler S (1996) Input-output structural decomposition analysis: a critical appraisal. Econ Syst Res 8:33–62 Rose A, Chen CY (1991) Sources of change in energy use in the U.S. economy, 1972–1982. Resour Ener 13:1–21 RUG/CBS (1999) Regionale Samenhang in Nederland. REG-publicatie 20, Stichting Ruimtelijke Economie Groningen, University of Groningen RUG/TNO (1999) Clusters en Linkages in Beeld. REG-publicatie 19, Stichting Ruimtelijke Economie Groningen, University of Groningen Schaffer WA (1973) Determination of key sectors in a regional economy through input-output analysis: comment. Rev Reg Stud 3:33–34 Schultz S (1977) Approaches to identifying key sectors empirically by means of input-output analysis. J Dev Stud 14:77–96 Skolka J (1989) Input-output structural decomposition analysis for Austria. J Pol Mod 11:45–66 Strassert G (1968) Zur bestimmung strategischer sektoren mit hilfe von von input-output modellen. Jahrb Nationalök Stat 182:211–215 Szyrmer JM (1984) Total flow in input-output models. Ph.D. School of Arts and Sciences. University of Pennsylvania, PA Szyrmer JM (1992) Input-output coefficients and multipliers from a total-flow perspective. Environ Plan A 24:921–937 Temurshoev U, Oosterhaven J (2014) Analytical and empirical comparison of policy-relevant key sector measures. Spat Econ Anal 9:284–308

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Timmer MP, Inklaar RC, O’Mahony M, van Ark B (2010) Economic growth in Europe: a comparative industry perspective. Cambridge University Press, Cambridge UN.: A System of Quantity and Price Statistics. United Nations, New York (1975) Uno K (1989) Measurement of Services in An Input-output Framework. North-Holland, Amsterdam van Ark B, O’Mahony M, Timmer MP (2008) The productivity gap between Europe and the United States: tends and causes. J Econ Perspect 22:25–44 Wu HX (2016) On China’s strategic move for a new stage of development—a productivity perspective. In: Jorgenson DW, Fukao K, Timmer MP (eds) The world economy: growth of stagnation?. Cambridge University Press, Cambridge, UK

Chapter 9

Future: What to Forget, to Maintain and to Extend

Keywords Input–output models · Price models · Descriptive statistics · Consumer responsibility · Trade in value added · Social accounting matrices This book has shown that the interpretation of input–output (IO) as a causal model of the working of an economy is best forgotten, not literally of course, but in the sense that it may only be used as a predictive model with the utmost care, and in many cases not at all. This holds, in the extreme, for the supply-driven IO quantity model (Ghosh 1958), which cannot be used to predict the forward impacts of quantity shocks to the primary supply side of the economy. But, it also holds for the demand-driven IO quantity model (Leontief 1941), be it to a much lesser extent. The Leontief model may be used to estimate the backward impacts of quantity shocks to the final demand side of the economy when the economy is functioning below full capacity. Nevertheless, the absence of price reactions, even in that case, leads to a overestimation of the backward impacts of such shocks. This will, especially, be the case when the Leontief model is extended into a Type II demand-driven IO model with endogenous consumption expenditures. The two accompanying price models do something comparable. They systematically overestimate the price impacts of their exogenous price shocks, as they do not take the quantity reactions to these price shocks into account. Nevertheless, both models could, in fact, be used much more. The cost-push IO price model (Leontief 1951) simulates how primary input (capital, labour, import) price shocks, under full competition, will be fully passed on forwardly to end up in final output prices. Hence, this model may well be used to simulate, e.g. the maximum consumer price increases that may result from the increases in tariffs between the USA and China in the late 2010s, while international versions of this price model may be used to simulate the further forward impacts of the indirect increase of export prices on the consumer and investment prices of other countries.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 J. Oosterhaven, Rethinking Input-Output Analysis, SpringerBriefs in Regional Science, https://doi.org/10.1007/978-3-030-33447-5_9

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The revenue-pull IO price model (Davar 1989; Oosterhaven 1989), in turn, may be used to simulate how final output (consumption, investment, export) price shocks, under full competition, may be fully passed on backwardly to end up in primary input prices. Hence, this as yet unused model may well be used to simulate, e.g. the maximum wage increases that may result from the backward passing on of exogenous increases in export prices, such as that of oil and ITC-services, while international versions of this price model may be used to simulate the further backward impact of the indirect increase in import prices on the wages and capital incomes of other countries. Interestingly, in the case of the revenue-pull price model it is precisely the absence of the ludicrous quantity effects predicted by its accompanying supply-driven quantity model that saves this price model from becoming implausible itself. Moreover, especially, the basic demand-driven IO model offers much more than only a one-sided causal interpretation of the working of the economy. It may also, and very fruitfully, be used as a descriptive device. Over the last two to three decades, possibly a majority of the applications of IO analysis regard all kind of calculations of the direct and indirect use of natural resources embodied per unit of final demand, as evidenced by the special issues of Economic Systems Research of 2005/4, 2009/3, 2011/4 and 2016/2. These calculations of consumer responsibility for environmental problems may be as detailed as the direct and indirect CO2 emissions by specific Japanese industries embodied per unit of the consumption of specific goods by EU consumers. More recently, over the last decade or more, the basic interregional IO model has become comparably popular as a descriptive device in the area of international trade, where it is used to quantify such concepts as vertical specialization (Hummels et al. 2001), trade in value added (Johnson and Noguera 2012) and global value chain income (Timmer et al. 2013) (see Koopman et al. 2014, for an integration of some of these concepts). However, all these descriptive applications need to be done very carefully too, as shown by Bouwmeester and Oosterhaven (2013) who report serious sectoral and spatial aggregation errors when such calculations are made with too aggregate international IO models. They also report serious specification errors when worldwide CO2 or value-added footprints are calculated with national IO coefficients instead of with the appropriate international ones. More specifically, there is still much scope for structural decomposition analyses (SDA), not of industry and GDP growth, but of such questions as why do some countries use far less fossil fuels or why do they emit far more CO2 than others. Is it because they have a different composition of demand? Is it because they outsource more of their polluting activities to other countries? Is it because they use cleaner technologies? To analyse longer run industry and GDP growth, instead of SDA, econometric estimates of growth accounting equations with panels of IOTs or supplyuse tables (SUTs), such as WIOD (Dietzenbacher et al. 2013), offer much more analytic opportunities than used hitherto. Finally, IOTs, or better SUTs, of even better social accounting matrices (SAMs), constitute the indispensable databases that are needed to configure realistic interregional interindustry models, i.e. models with price–quantity interactions and spatial

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and technical substitution. The most simple and straightforward of these models combines an interregional SAM quantity model with its companion SAM price model, and solves this combination iteratively (i.e. switching back and forth between the quantity and the price model) using final demand price elasticities and primary supply price elasticities as links between the two models (Madsen 2008). An older tradition (Almon 1991) extends the basic IO model with econometrically estimated functions for final demand (consumption, investments, exports) and ditto for primary inputs (capital, labour, imports). It is especially suited to generate interindustry projections of regional and national economic growth. This tradition continues until today (e.g. Kratena 2005) and will definitely flourish further into the future. A second older tradition (Shoven and Whalley 1992; Bröcker 1998), which will definitively also continue to strive, calibrates computable general equilibrium (CGE) models, with profit maximizing representative firms and utility maximizing representative households, on (inter)regional and (inter)national SAMs, often using behavioural coefficients from different studies. This approach is, especially, suited to simulate the impacts of all kinds of policy measures, as it mostly contains some kind of social welfare measure. A nice example is provided by the evaluation of transport infrastructure projects by means of New Economic Geography (NEG, Fujita et al. 2001) models. In NEG models, different regions sell varieties of the output of each industry on monopolistically competitive regional markets linked by transport cost. CES aggregates of these varieties are combined in Cobb–Douglas consumption and production functions. As freight and passenger transport cost reductions impact different industries differently, detailed interregional SUTs are needed to calibrate them. In NEG models, transport cost reductions (i.e. positive supply shocks) increase each region’s exports (demand) as well as imports (supply). The net economic impact may well be negative for some industries in some regions, while causing the agglomeration of industries in other regions (see Venables and Gasiorek 1998; Knaap and Oosterhaven 2011, for seminal applications). In all, there is plenty of future for IO-based and SAM-based analyses of environmental consumer responsibility, trade in value added, projections of future developments of the economy, and all kinds of regional, interregional, national and international policy simulations.

References Almon C (1991) The INFORUM approach to interindustry modeling. Econ Syst Res 3:1–7 Bouwmeester MC, Oosterhaven J (2013) Specification and aggregation errors in environmentallyextended input-output models. Environ Resour Econ 56:307–335 Bröcker J (1998) Operational spatial computable general equilibrium modelling. An Reg Sci 32(3):367–387 Davar E (1989) Input-output and general equilibrium. Econ Syst Res 1:331–344

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Dietzenbacher E, Los B, Stehrer R, Timmer M, de Vries G (2013) The construction of world input-output tables in the WIOD project. Econ Syst Res 25:71–98 Fujita M, Krugman P, Venables AJ (2001) The spatial economy: cities, regions, and international trade. The MIT Press, Cambridge Ghosh A (1958) Input-output approach in an allocation system. Economica 25:58–64 Hummels D, Ishii J, Yi K-M (2001) The nature and growth of vertical specialization in world trade. J Int Econ 54:75–96 Johnson RC, Noguera G (2012) Accounting for intermediates: production sharing and trade in value added. J Int Econ 86:224–236 Knaap T, Oosterhaven J (2011) Measuring the welfare effects of infrastructure: a simple spatial equilibrium evaluation of Dutch railway proposals. Res Transp Econ 31:19–28 Koopman R, Wang Z, Wei S-J (2014) Tracing value-added and double counting in gross exports. Am Econ Rev 104:459–494 Kratena K (2005) Prices and factor demand in an endogenized input-output model. Econ Syst Res 17:47–56 Leontief WW (1951) The structure of the American economy: 1919–1939, 2nd edn. Oxford University Press, New York Leontief WW (1941) The structure of the American economy, 1919–1929: an empirical application of equilibrium analysis. Cambridge University Press, Cambridge Madsen B (2008) Regional economic development from a local economic perspective – A general accounting and modelling approach. Habilitation Thesis, University of Copenhagen Oosterhaven J (1989) The supply-driven input-output model: a new interpretation but still implausible. J Reg Sci 29:459–465 Shoven JB, Whalley J (1992) Applying general equilibrium. Cambridge University Press, New York Timmer MP, Los B, Stehrer R, De Vries GJ (2013) Fragmentation, incomes and jobs: an analysis of European competitiveness. Econ Pol 28:613–661 Venables AJ, Gasiorek M (1998) The welfare implications of transport improvements in the presence of market failure. Reports to SACTRA, Department of Environment, Transport and Regions, London