Still after more than thirty years of free floating exchange rates, large parts of exchange rate dynamics remain a puzzl

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Falkmar Butgereit

Exchange Rate Determination Puzzle

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Long Run Behavior and Short Run Dynamics

Diplomica Verlag

Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics : Long Run Behavior and Short Run Dynamics, Diplomica Verlag, 2010. ProQuest Ebook Central,

Falkmar Butgereit Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics ISBN: 978-3-8366-4543-0 Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010

Copyright © 2010. Diplomica Verlag. All rights reserved.

Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtes. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Die Informationen in diesem Werk wurden mit Sorgfalt erarbeitet. Dennoch können Fehler nicht vollständig ausgeschlossen werden und der Verlag, die Autoren oder Übersetzer übernehmen keine juristische Verantwortung oder irgendeine Haftung für evtl. verbliebene fehlerhafte Angaben und deren Folgen. © Diplomica Verlag GmbH http://www.diplomica-verlag.de, Hamburg 2010

Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics : Long Run Behavior and Short Run Dynamics, Diplomica Verlag, 2010. ProQuest Ebook Central,

Table of Contents 1 Introduction ...................................................................................................... 3 2 Long-Run Exchange Rate Behavior ................................................................. 4 2.1 Purchasing Power Parity ........................................................................... 4 2.2 The Simple Monetary Exchange Rate Model ......................................... 10 2.3 Long-Term Cycles ................................................................................... 13 2.4 The Macroeconomic-Balance Approach ................................................. 17 3 Short-Run Exchange Rate Dynamics ............................................................. 19 3.1 Only Random Dynamics?........................................................................ 19 3.2 Technical Traders and Speculators.......................................................... 26 3.2.1 Evidence of the Role of Chartists and Modeling Their Behavior .... 26 3.2.2 Views of Practitioners ...................................................................... 30 3.2.3 Chart-Technique Predicting Future Movements?............................. 32 3.3 The Impact of News ................................................................................ 36 3.3.1 Immediate Response......................................................................... 36 3.3.2 Delayed Response ............................................................................ 41 3.4 Order Flow and Investor Heterogeneity .................................................. 45 3.4.1 Empirical Evidence .......................................................................... 45 3.4.2 Modeling Order Flow ....................................................................... 51 3.4.3 Uncovered Equity Parity .................................................................. 53 4 Spectral Analysis ............................................................................................ 58 4.1 The Approach and Numerical Analysis .............................................. 58 4.2 Graphical Analysis .............................................................................. 63 5 Conclusion ...................................................................................................... 69 Appendix ........................................................................................................... 72

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References ....................................................................................................... 109

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1 Introduction As the foreign exchange rate market operates twenty-four hours a day and seven days a week it can be described as a global marketplace trading in continuous time. The importance of this market place on weal and woe of economies and agents cannot be overestimated. Long lasting disputes about exchange rate over- and under-evaluation between countries (as most prominently the case between China and the USA) and its implications for international trade, growth rates of economies, unemployment levels, financial money flows, and so forth illustrate this point. As reported by the Bank of International Settlement in its triennial Central Bank Survey 2007, covering 54 countries and jurisdictions, the daily average foreign exchange turnover as of April 2007 has reached a mind-staggering $3.21 trillion. This amount marks an increase of 69 percent compared to the $1.97 trillion three years earlier and highlights the still increasing importance of the exchange rate markets. The U.S. dollar is by far the most important currency as it is involved in 86 percent of all transactions amounting to some $2.7 trillion per day. This is by far bigger than the volume of U.S. international trade in goods and services which for the month April 2007 amounted to (imports + exports) $317.5 billion.1 Indeed, only 17 percent of exchange market turnover has been reported to occur with non-financial customer counterparties, while 43 percent of transactions occur between reporting dealers (i.e. the interbank market) and 40 percent occur between reporting and non-reporting financial institutions (e.g. hedge funds, mutual funds, pension funds, insurance companies). Accordingly, more than

2 3

of the turnover was

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traded as derivatives such as foreign exchange swaps, outright forwards, or options, while only 13 constituted spot rate transactions.

These are important facts to consider when talking about forces of

exchange rate determination. On ground of these figures one may reasonably explain why old-fashion standard models like the monetary model or purchasing power parity may only hold in the very long run and

1

as reported by the U.S. Census Bureau and U.S. Bureau of Economic Analysis.

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exchange rate movements may be much more subject to trades based on heterogeneous expectations incurred by investors, speculators and market makers. Particularly in the short-run, exchange rates exhibit considerably greater volatility than macroeconomic time series leaving an impression of noisy and chaotic behavior. Throughout this work it will become evident that heterogeneous beliefs and actions of market participants are the key to understand shortrun exchange rate dynamics from daily to monthly horizons. Over longer horizons of one month and longer standard fundamentals like money, inflation, productivity, interest rates and output will shimmer through and push the exchange rate towards a fair equilibrium value. This thesis is structured as to firstly looking at exchange rate driving forces over longer periods. Afterwards in chapter 3 it will start by examining the low predictive power of standard macroeconomic exchange rate models and present more recent successes in forecasting and explaining exchange rates. It continues with analyses of charttechnique, impact of news, and order flow which all constitute important building blocks of exchange rate determination and prediction over shorter horizons. Part 4 presents some more evidence on the non-linear behavior of exchange rates and the relationships between today’s exchange rate and its historical movements as well as fundamentals (particularly interest rates) at different frequencies. Chapter 5 concludes.

2 Long-Run Exchange Rate Behavior

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2.1 Purchasing Power Parity The Purchasing Power Parity (PPP) approach relates the foreign exchange rate to the ratio of national price levels. Exchange rate movements are thought to reflect changes in relative prices based on the notion of arbitrage across tradable goods and services leading to the law of one price. In practice, however, the law of one price fails dramatically as a large body of empirical evidence shows. This finding may be attributed to a set of reasons. The first natural suspects for the failure of Page|4

Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics : Long Run Behavior and Short Run Dynamics, Diplomica Verlag, 2010. ProQuest Ebook Central,

PPP are transport cost, tariffs, taxes, noncompetitive market structures, as well as entry- and exit barriers. Also, many personal services can considered to be internationally non-tradable because of the high cost of travel relative to the provided value of the service. This, surely, is an important point to bear in mind considering a 60 percent2 share of services in GDP composition of modern industrial economies. Moreover, even seemingly homogenous highly traded goods, like a tomato, come along with large non-traded inputs like local cost of labor (seeding, harvesting, selling, etc), shipping, and supermarket space. Among other possible factors the mentioned issues may create a band of inaction, in the literature also referred to as the “band of agnosticism”3, in which neither arbitraging traded good prices nor taking any long or short currency position seems to be beneficial. It is, therefore, not surprising that PPP does not hold strictly. It should, however, hold approximately in the longer run. Particularly, if significant departures from PPP outside the transaction-cost bands occur, arbitrage would become profitable enough to bring the real exchange rate (RER) back inside the zone of inaction. Rosenberg (2003) marks this band of inaction as about +/- 20 percent from its equilibrium level. In general, the RER is defined as

= ∗

(1)

where denotes the nominal exchange rate as the price of home

currency in terms of one unit of foreign currency and (∗ ) denotes the

domestic (foreign) price level. With lowercase variables denoting the

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log-form of their uppercase counterparts, the log RER can be written as

= + ∗ −

(2)

and is plotted in Figure 1 in terms of the US-dollar against yen, Deutsche

2 3

Obstfeld and Rogoff (1996), p. 202 De Grauwe (1996)

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Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics : Long Run Behavior and Short Run Dynamics, Diplomica Verlag, 2010. ProQuest Ebook Central,

mark4, and pound sterling from January 1974 until mid of 20085. Clearly visible is the 1984-1985 dollar bubble, followed by a sharp appreciation of the real exchange rate (depreciation of the nominal dollar) until the mid nineties.

Figure 1 - Real Exchange Rate of Selected Industrial Countries

1974 = 100 (Logarithmic scale)

RER USD/JPY

RER USD/DM

180 160 140 120 100 80 60 40 1974 1978 1982 1986 1990 1994 1998 2002 2006 Own Computation, Data Source: IMF, International Financial Statistics

PPP postulates stationarity of the real exchange rate. In order to find out if the depicted time series are I(0) processes I test for the presence of a unit root by running augmented Dickey Fuller tests. For the USD/DM exchange rate two autoregressive lags for the tested difference equation are determined to be optimal according to the Akaike and Copyright © 2010. Diplomica Verlag. All rights reserved.

Schwarz Bayesian Information Criterion. For the USD/JPY and USD/GBP exchange rates the fourth order of the autoregressive augmentation is chosen to be optimal by the Akaike Information Criterion. In particular, we have the regressional form

4 5

Only West-Germany until December 1990 For Deutsche Mark until December 1998; the data are monthly averages.

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q = q +

(3)

with regression coefficients and the number of lags n = 2 for USD/DM

and n=4 for USD/JPY and USD/GBP. We can then subtract from

both sides of equation (3) to obtain

∆q = γq − ∆q +

(4)

where for Deutsche Mark = + − 1 and = 1; and for yen and

pound = + + + − 1 and = 3. On basis of difference

equations (4) we can test for the presence of a unit root (i.e. !" : = 0 vs.

! : < 0).

The results of the individual unit root tests are summarized in

table 1 to 36. As can be seen from the MacKinnon approximate p-values for Z(t), which range from 0.22 to 0.33, we have to concede that we cannot reject the null hypothesis of non-stationarity for any of the three real exchange rates over the considered period. It should, however, be remembered that in finite samples it is statistically difficult to distinguish

between being close but not equal to zero and being zero. Therefore, a

type II error of non-rejection of !" although ! is true seems likely.

Also, Blough (1992) has shown that the power of generic unit-root tests

is limited to the size of the test. In effect, the time span of the data since beginning of the floating regime in 1973 may not be sufficient. Further on, it should be considered that the national consumer price indices are of limited help when testing for PPP since they also include non-tradables Copyright © 2010. Diplomica Verlag. All rights reserved.

and differ in their composition across countries. Lastly, Taylor et al. (2001) show that real dollar exchange rates may indeed possess a strong mean reversion, however, they adjust in a non-linear fashion; i.e. adjustments towards long-run equilibrium conditions derived from the fundamentals seem to accelerate the farther away exchange rates are from equilibrium but tend to behave similar to a unit root process around 6

All tables throughout this work can be found in the appendix.

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equilibrium.7 Standard univariate tests may, therefore, be of limited power. Similar results as in case of the individual unit root tests, can be gleaned from the results of panel unit root test in table 4. Here, I have conducted three different kinds of panel unit root tests on the three above mentioned currency pairs for the time horizon 1973:1 to 1998:12. The Levin-Lin-Chu (LLC) test, as well as the Im-Pesaran-Shin (IPS) test can be computed with different lags across the currencies. Taking the previously determined optimal lags results in p-values of 0.12 and 0.15 for LLC and IPS test, respectively, so that the null of non-stationarity cannot be rejected. As opposed to these two tests, the multivariate augmented Dickey-Fuller panel unit root (MADF) test can only be done with equal lags across sections. Among the tested one to ten lags, the seven-, nine-, and ten-lag regressions are able to reject the null hypothesis. However, this result should be taken with care since a rejection of the null only means that at least one panel (i.e. exchange rate) is stationary and not that each of the series is stationary. The tests themselves differ slightly from each other. For instance, the LLC test differs from the MADF test in that the latter is estimated using the seemingly unrelated regressions (SUR) estimator (meaning one equation for each individual) and is restricted under the constraint of a single autoregressive parameter across individuals. The LLC test is the only test which assumes that all series are stationary under the alternative hypothesis. The IPS test is based on the mean of the individual DickeyFuller t-statistics of each unit in the panel and assumes that only a fraction of the series is stationary when rejecting the null.8 Despite difficulties in empirically confirming the PPP hypothesis Copyright © 2010. Diplomica Verlag. All rights reserved.

we should not abandon the assumption of stationarity of exchange rates. As argued above, there are profound reasons why non-stationarity may statistically be hard to reject.

7

For their results they were using an exponential smooth transition autoregressive (ESTAR) model which is described in more detail in chapter 3.1. 8 Compare Sarno and Taylor (1998) for the MADF test; Levin, Lin, Chu (2002) for the LLC test; and Pesaran and Shin (2003) for the IPS test.

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Generally, academic literature agrees upon the speed of convergence of PPP to be fairly slow9 with a half life of deviations from PPP of about three to five years10. Figure 2 illustrates evidence for PPP, particularly for the medium- and longer-run. The ordinate displays inflation differentials and the abscissa measures exchange rate changes. It can be seen for the period 1974-1998 that the longer the considered time horizon the better data fits with the PPP hypothesis. Whereas only 27 percent of exchange rate movements over the time horizon of one year can be explained by inflation differentials, almost 97 percent is explained in the long run over 24 years.

1,5

% change in relative CPIs

% change in relative CPIs

Figure 2 – The Impact of Relative Inflation Rates on Exchange Rates over Different Time Horizons 1-Year Intervals

1 0,5 R² = 0,271 0

0,5

1

1,5

12-Year Intervals R² = 0,948

1 0,5

0

0,5

1

1,5

% change in exchange rates

1,5

24-Year Intervals

1

R² = 0,968

0,5 0

0

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0,5

-0,5

% change in exchange rates

1,5

0 -0,5

R² = 0,708 1

-0,5

% change in relative CPIs

% change in relative CPIs

-0,5

-0,5

6-Year Intervals

0

0 -0,5

1,5

0,5

1

1,5

% change in exchange rates

-0,5

0 -0,5

0,5

1

1,5

% change in exchange rates

Own Computation (Adapted and Broadened from Isard, et al (2001)); Data Source: IMF, International Financial Statistics. The plots are constructed from annual average data on the nominal dollar exchange rates of 23 industrial countries and respective consumer price indices for the period 1974-1998. The first panel plots 552 one-year changes (24 for each country); the second plots 92 six year changes (at annual rates) corresponding to the periods 1974-80, 1980-86, 1986-92, 1992-98; and so forth.

9

if refraining from possible non-linearities See Rogoff (1996)

10

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2.2 The Simple Monetary Exchange Rate Model Evidently, monetary policy has had large impacts on exchange rates. Most recent examples are expansionary monetary policies by the Bank of Japan from 1995 to 1998 and the Federal Reserve from 2002 to 2004 which both led to profound depreciations of yen and USD in nominal and real terms. Although being a controversial matter, these depreciations indicate a relationship between growth of the monetary base and the value of the currency by means of induced inflation (in line with Milton Friedman’s famous quotation that “inflation is always and everywhere a monetary phenomenon”) and further support the evidence presented in figure 2 that exchange rates are strongly linked to inflation differentials. The simple monetary exchange rate model describes the exchange rate as a function of a set of underlying macroeconomic variables over the medium to longer time horizon. More explicitly, the exchange rate depends on relative money supply growth, relative GDP growth, and relative interest rate differentials. The flexible-price model can be derived from its building blocks, namely the foreign and domestic money demand functions (5) and (6), uncovered interest rate parity (UIP) (7), and PPP (8)

& = − '( + )* ∗ &∗ = ∗ − '( + )*∗ ∗ ( = ( + + , −

= + ∗

(5) (6) (7) (8)

where all variables are in log form, & denotes money demand, the

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domestic price level, ( the nominal interest rate between period - and

- + 1, * the real output, as before for the exchange rate, ' and ) are

semi-elasticities of demand for real balances, denotes expectations,

and stars indicate quantities of foreign variables. Substituting equations

(5), (6), and (7) into (8) and solving the resulting equation forward while imposing the transversality condition (9) ' 1 lim 3 4 1 = 0 1→∞ 1 + '

(9)

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Exchange Rate Determination Puzzle: Long Run Behavior and Short Run Dynamics : Long Run Behavior and Short Run Dynamics, Diplomica Verlag, 2010. ProQuest Ebook Central,

the solution for the exchange rate can be obtained as 1 ' 5 = 3 4 +6 , 1+' 1+' ∞

(10)

5

where 6 = 7&5 − &5∗ 8 − )7*5 − *5∗ 8. Accordingly, the determination of

today’s exchange rate depends on a geometrically declining weighted

average of changes in future expected money supply and output differentials between home and foreign. The qualitative effects on the exchange rate by changes of these variables are equal to their signs. Although this simple model is not micro-founded, it yields important results such as that the exchange rate has to be treated like an asset price. Unfortunately, as PPP, this model does not perform very well in the short-run. However, it comprises valuable insights for hyperinflationary environments and the medium- and long-run. On basis of this simple monetary model, Mark (1995) finds significant evidence on predictable components in longer-horizon

exchange rate changes. He assumes 6 to follow a driftless random walk.

In this case equation (10) results into the exact relation of = 6 . Then, he tests the “k-period-ahead change in the log exchange rate on its

current deviation from the fundamental value”11: 9 − = :9 + ;9 76 − 8 +

(11)

where : and ; are linear least-squares estimators and is the projection

error. The fundamental value 6 is constructed with a constant value of

) = 1. The data consists of quarterly observations for the US, Canada, Copyright © 2010. Diplomica Verlag. All rights reserved.

Japan, Germany, and Switzerland from 1973:II to 1991:IV. His results

are shown in table 5. He finds consistently higher ;-coefficients and < ’s

for DM, JPY, and CHF the longer he chooses the forecast horizon from

one quarter to sixteen quarters. A similar pattern can be seen for the CAD, although, with the highest < being observed at the eight-quarter

horizon. For the DM the one-quarter horizon with ; = .04 and 0

(32)

Normally one would expect no asymmetry in exchange rates P a g e | 38

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responses, as for instance in options pricing, a volatility smile is assumed rather than a skew. However, it turns out that exchange rates react asymmetrically to positive and negative news. The latter often exert a greater impact than the former. The average over all 41 indicators suggest higher asymmetry for DM/USD, GBP/USD, and CHF/USD than for JPY/USD and EUR/USD but the impacts on the respective currency pairs vary considerably across the single indicators. A graphical illustration on chosen indicators can be found in the following figure 5. Figure 5 – Asymmetrical news impact curves

Source: Andersen et al. (2003), p. 56

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The paper argues that the asymmetry might be due to the considered time horizon because the period from 1992 to 1998 has been one long bull market. During times of economic expansions negative news may lead to larger price movements compared to positive ones not only because they come about completely unanticipated but also because uncertainty about the state of economy increases. This rise in uncertainty is indeed reflected in the data as the standard deviation of expectations

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across forecasters’ increases in consequence of the arrival of negative news. .

Dominguez (2003) comes to similar results as Andersen et al. She focuses on the impact of monetary intervention operations between 1987 and 1995 of the Federal Reserve Bank, the Bank of Japan, and the Bundesbank onto the respective exchange rates’ mean and volatility within five-minute frequented data. Her regression is similar to equation (31), however, without the autoregressive part. She only uses those 273 days on which monetary interventions have been exercised by the Fed. On more than 80% of these days, the interventions coincide with BoJ and/or Bundesbank interventions. For her news variable she includes signed open market interventions as dummy variables43, official central bank announcements, and other official macro announcements (as control variables). She finds significantly positive coefficients for central bank open market policy and announcements for both USD/DM and USD/JPY, whereat the Bundesbank interventions are found to have the largest impact. Generally, coordinated G-3 interventions are more effective than unilateral ones. In numbers, a sole Fed intervention of 1 billion dollars cumulates to an exchange rate change of approx. 29 basis points when considering the time from one hour before the release of the Reuters report until 30 minutes thereafter. Also, a mean reversion back to zero can be observed after two hours in case of the USD/DM exchange rate. For the USD/JPY the impact cumulates to 42 basis points after 55 minutes and then declines to about 29 basis points after two hours. The evidence of a significant impact on the exchange rates by central bank intervention even before the release of the Reuters report indicates that some traders know about the intervention earlier than others (e.g. trading Copyright © 2010. Diplomica Verlag. All rights reserved.

desks of those banks the central bank trades with). However, the tendency for mean reversion is a sign for an initial overreaction of the market. Out of the twelve included (control-) macro indicators, four were found to be significant. A further result is that the moments of the exchange rate returns are very different on intervention dates (based on

43

taking the values 1 for purchasing dollars, -1 for selling the dollar, and 0 otherwise

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1.6 million observations) compared to all days over the whole sample (12.5 million observations). On intervention days mean returns are large and positive while they are slightly negative over the full sample. Also, kurtosis is considerably higher and rising along with increasing data frequency over the whole sample compared to a rather constant less pronounced kurtosis on intervention days. Moreover, the effects on the exchange rates differ along with the trading hour. Interventions tend to be most effective during those hours of the day which observe the highest trading volume (i.e. during the intersection of open markets in Europe and the U.S.) and, also, which are within a two hours window of another macro announcement. All results can be found in table 25. Lastly, also analysis is done on volatility. The results are in line with other papers and microstructure theory. Generally, on Fed trading days, volatility is substantially higher than on non-trading days. Volatility peaks between 30 minutes before and after the actual intervention and, during that time, rises by as much as 20 times the level of nonintervention days. After the period of one hour altogether, volatility returns back to its initial level. 3.3.2 Delayed Response The above presented evidence is supportive for the efficient market hypothesis since arising news seem to be incorporated into prices instantly. However, there also exists evidence for considerable price movements without news or at some later stage after news-releases. For instance, Cutler et al. (1989) examine that the majority of the 50 largest daily changes in aggregate stock prices between 1946 and 1987 occurred on days without external fundamentals-based news. Copyright © 2010. Diplomica Verlag. All rights reserved.

Romer (1993) suggests a solution for this, at first sight, seemingly irrational phenomenon: Markets may occasionally process and aggregate information imperfectly because agents possess diverse (i.e. superior or inferior) information about fundamentals. If this is the case, the initial reaction to news does not completely reflect the eventual implication for the underlying asset, and further price adjustments will result from additional trading which only after an extended period of time will have revealed, processed, and incorporated all relevant information into the P a g e | 41

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price. In effect, the presence of uncertainty about the quality of one’s and others’ information can cause investors with the best available information to still attribute some weight to the current market price to estimate the fair price, whereas investors with inferior information may attribute excessive weight on their information. For instance, imagine

three possible kinds of private information S , S , and S about any

considered asset where S describes the most superior piece of

information and S the most inferior. Imagine further that these pieces of information can be distributed in two possible ways, each occurring with

50 percent probability. Either, half of the individuals receive S and the

other half S , or one half receives S and the other S . While every

investor knows the quality of his own information, he does not know about the quality of the information received by others. Particularly, all

investors receiving S do not know if they possess superior or inferior

information. The information asymmetry leads to an imperfectly priced

asset which only over time reveals all information to the market and therefore observes delayed responses to new information. Romer gives a practical example for stock markets as, for instance, traders in London monitor the opening of New York markets closely which would only make sense if New Yorker traders possess superior information that would be partially revealed by their trading activity. As for exchange rates Engle et al. (1990) deliver evidence for the above model in that they find autocorrelation of volatility in intra-day exchange rates across countries. An impact of news in one market therefore also enfolds lagged impacts onto other markets. In effect, private information takes a couple of hours of trading to be fully

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processed. Concretely, they estimate a GARCH (1,1) process on hourly yen-dollar exchange rate data from 1985:10:03 to 1986:09:26, i.e. k

Ik, = :k + ;k

where

∆,

,

∆,

ℎk,

+ k

∆,

ℎk,

|Sk, ~F70, Ik, 8

+ kk Ik,

(33)

Here, ℎk, are the business hours in market ( on date - and Sk, is the

information set for market ( on date - which includes past and current P a g e | 42

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information from market 1 to market ( − 1; :, ;, , are regression coefficients and I is the variance. The results are displayed in table 26.

Significant coefficients raise evidence for spillover effects of intra-day volatility across foreign exchange markets. Concerning the magnitude of the coefficients, it turns out that Japanese news has the greatest impact on the volatility spillovers of the yen-dollar exchange rate. This points to the existence of private information taking time to be interpreted by the market. Similarly, Evans (2002) identifies three different drivers of short run dynamics. He analyzes a unique data set that comprehends information on trading of the DM/USD exchange rate among foreign exchange dealers around the world for a four-month period (between 1st

of May and 31st of August 1996) and therefore delivers indicative prices as opposed to firm prices delivered by information providers such as Reuters. He finds that depending on the state of the market (as measured by transaction intensity), firstly, common-knowledge news, secondly, non-common-knowledge news, and thirdly, a sampling component determine the exchange rate dynamics to varying degrees over time. Common-knowledge news is the usual publicly released information

about

fundamentals

and

indicators

or

political

announcements which transform into price shifts instantly. These shocks account for up to 90 percent of persistent exchange rate movement at times of low trading intensity. However, at times of the day where trading activity is very high, they account for less than 20 percent of the variance. At these times of high trading activity 80 percent of the variance in permanent price shocks can be attributed to non-common-knowledge Copyright © 2010. Diplomica Verlag. All rights reserved.

news. This kind of news may arise if official macroeconomic announcements or other publicly available information is not interpreted homogenously but if there exists no consensus about its implications among dealers. Also, non-common knowledge news may stem from the fact that details about direct interdealer trades and customer-dealer trades are not released to the market (as it would for instance be the case for equity), but are only observed by the counterparties. This results into P a g e | 43

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information asymmetry, particularly if large brokers are present in the market processing great amounts of orders and, therefore, possessing superior information. Such superior information only diffuses slowly across market prices. Chapter 3.4 takes a closer look at the implications of investor heterogeneity and order flow. The third factor, the sampling component, arises from the interesting finding that, rather than by a single price, exchange rates at any point in time are represented by a distribution of equilibrium transaction prices quoted by various dealers as there are as many as 200 transactions per minute. The heterogeneous trading decisions of dealers plus the lack of transparency in exchange rate markets lead to dispersion in the equilibrium distribution. Indeed, under normal market conditions this dispersion is able to explain 80 percent of the variance or noise that usually characterizes short-term, high-frequency data. It considerably loses contribution at times of high trading frequency (17 percent). Besides, Evans finds evidence that the overnight nominal interest differential between Deutsche mark and US dollar possesses significant ability to predict the change in the log spot rate within the 24 hours between 16:00 o’clock on day τ and 16:00 o’clock on day τ+1. The negative coefficient (as shown in table 27) implies a dollar appreciation tomorrow if today the US-overnight interest rate is lower than the German interest rate. Additionally, the change in the nominal interest rate differential, say a decrease of US interest rates and constant German interest rates, leads to a depreciation of the dollar. Although this second finding is not significant it is correctly signed and, thus, both are in line with uncovered interest rate parity (UIP), in that a lower dollar interest rate leads to immediate dollar depreciation in order to make room for the Copyright © 2010. Diplomica Verlag. All rights reserved.

expected appreciation required by UIP. We may conclude this chapter with the words of Romer (1990) as the presented evidence within this chapter shows that, “the market is, in effect, engaged in a many-dimensional and a many-agent inference problem with multiple layers of uncertainty and heterogeneity and with frictions in the trading process” (p.1129). This gives room for the manysided exchange rate phenomena, such as persistent large gaps to implied P a g e | 44

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value of fundamentals, excessive movements relative to macro news, only little or no movement at all when macro news occur but also movement without any news. Latest research on order flow data has helped to gain further insights into these multi-dimensional dynamics and shall be topic of the next chapter.

3.4 Order Flow and Investor Heterogeneity 3.4.1 Empirical Evidence It has become clear in the previous chapter that not all information is publicly available. Apart from the macroeconomic-related news there exists microeconomic-related information only available to some agents. Institutional portfolio rebalancing, hedging and liquidity demands, as well as shifts in risk appetite and expectations are examples and consequences of such private information which leaks out to the market via order flow and can, therefore, only be observed indirectly and delayed by all agents on the market. Generally, order flow is defined as the net difference between

buyer-initiated trades and seller-initiated trades during some interval -

(Evans 2002). Consequently, it can indicate a direction of trade for a currency. In fact, it is not even necessary that private agents possess superior information. If they only trade out of allocational motives like export transactions or earnings repatriation, the resulting cumulated transaction flow will convey information about the economy and cause agents to revise their expectations about fundamentals.

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A survey among professional traders and fund managers conducted by Gehrig and Menkhoff (2002) provides evidence that after technical analysis (attached weight of importance: 40.2%) and fundamental analysis (36.3%), the analysis of order flow (23.5%) is a third type of information widely used. In addition, more than 62 percent of participants believe that order flow delivers useful information for

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exchange rate movement from intraday to a few days only, while 15 percent do so for horizons longer than 2 months. Lately, various order flow data sets have been examined and overwhelmingly contributed to the understanding of short-run exchange rate behavior. For example, Evans and Lyons (2002) analyze a fourmonth sample between May 1st and August 31st, 1996 which covers worldwide direct interdealer trades on Reuters Dealing 2000-1 trading system44 for DM/USD and JPY/USD. For each 24 hours order flow is expressed as a cumulated unit value. For instance, if a purchase (sale) for the DM/USD ask (bid) quote is initiated, then order flow is +1 (-1). Specifically they regress ∆ = ; ∆7( − (∗ 8 + ; ∆ +

(34)

where ∆ is the change of interdealer order flows between yesterday and today. The results can be seen in table 28. Indeed, order flow is able to

explain 64 percent of daily changes in log mark/dollar and 46 percent of

log yen/dollar exchange rate movement. The positive ; indicates that net dollar purchases lead to a higher exchange rate, i.e. a dollar

appreciation. Also ; is significant and positively signed and, therefore, in line with UIP. The magnitude of 2.14 for ; of the DM/USD exchange

rate means that if on any particular day there occur 1,000 more dollar purchases than sales, the dollar will on average appreciate by 2.14 percent. In absolute terms, considering an average trading size of $3.9 million, this means that a $1 billion excess of dollar purchases leads to an

exchange rate appreciation of 0.54 percent (=2.1/3.9). Different versions of equation 34 (as also shown in table 28) show that order flow really is a

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driving force of short run exchange rate dynamics, and that, generally, the absolute nominal interest rate differential (but not its change) turns out to be insignificant. The finding that prices increase with buying pressure is a seemingly natural and causal relationship. However, for exchange rates it 44

about 75 percent of total trading occurs between dealers. Thereof, 60 percent are done via direct trading accounts (as opposed to brokered trading accounts). More than 90 percent of the world’s direct interdealer trades take place on Reuters’ trading system. Thus, the data set covers more than 40 percent of worldwide exchange rate trading.

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has conceptual implications since traditional macro models do not necessarily or sufficiently demand actual trades for exchange rate movement! Evans and Lyons (2005) present research work over an extended period of time and a different data set. It spans from 1993:1 to 1999:6 and comprehends all of Citibank’s end-user order flow, meaning nonfinancial corporations, investors, and leveraged traders (such as hedge funds or proprietary trading desks) in the USD/EUR exchange rate spot and forward market. Citibank’s market share is in the 10-15 percent range. Before attempting to forecast exchange rates over one to twenty trading days based on order flow, Evans and Lyons basically confirm the results of Meese and Rogoff (1983) over their considered time horizon. They find that forecasting with help of the interest rate differential produces larger MSE than the naïve random walk. However, they clearly beat the random walk with help of two different order flow based microstructure models. The first model is based on aggregated order flow from the six end-user segments of U.S. and non-U.S. market transactions by the three end-users mentioned earlier: ∆ = : + ; +

(35)

The second microstructure model is based on disaggregated order flow from each segment :

?

~ ∆ = : + ; , +

(36)

The results, as shown in table 29, show that the aggregated model beats

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the random walk at forecast horizons of 10 trading days or longer at the one percent significance level with a minimum MSE-ratio of 0.90 at 20 days. The disaggregated model even beats the random walk from one day forecast horizon onwards with a minimum MSE-ratio of 0.81 at 20 days. Generally, (as always) the predictability accuracy increases as the horizon rises. At 20 days, the disaggregated model accounts for almost 16 percent of the sample variance.

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Rime et al. (2007) contribute further evidence in line with Evans and Lyons. They analyze a data set which is obtained from the Reuters trading platform (D2000-2) but which covers a whole year from 2004:02:13 to 2005:02:14 for the USD versus the three major currencies EUR, JPY, and GBP during the main trading hours between 07:00 and 17:00 GMT. In a regression equal to equation (34), they find highly significant and positive ; for the contemporaneous order flow of all

currencies, among which the impact is highest for the JPY with a

coefficient of 12.4 and smallest for GBP with a coefficient of 1.36. A detailed overview can be found in table 30. Further on, they show that innovative shocks to fundamentals (as calculated from the Money Market Survey, MMS) have mostly significant (at ten percent) effects on order flow, explaining up to 18 percent of its daily variance. Also, this news has significant effects on the exchange rate itself, confirming earlier presented evidence in chapter 3.3.1. Interestingly, regressing both news and order flow onto the daily change of the exchange rate significantly enhances the explanatory value by up to 7.7 times (as in case of the JPY) as opposed to regressing them individually. Precise results can be found in table 31. Once again, this indicates that macroeconomic news influence exchange rates not only directly but also indirectly because order flow gradually conveys information on heterogeneous beliefs about these fundamentals. Noticeably, order flow and exchange rates also show high crosscorrelation across currencies. As table 32 shows, daily exchange rate returns correlate positively with changes of other currency pairs in a

range between 0.20 (for ∆ ∆ ) and 0.53 (for ∆ ⁄∆ ).

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Partly, of course, this is due to the same denomination in U.S.-dollars.

In further analysis, Rime et al. test if three different micro forecast models can outperform the random walk and if positive out-of-sample returns could have been generated after correcting for transaction cost and risk aversion. The first model relates the exchange rate return to lagged order flow of the respective currency itself as well as of the other considered currencies and to lagged exchange rate changes, i.e.: P a g e | 48

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∆ ∆ ∆ : ∆ = : ¡ + ¢ ∆ + £ ∆ + : ∆ ∆ ∆

(37)

where ¢ and £ are the 3 x 3 matrices of estimated coefficients. The

second and third model are variations of equation (37). The second

model assumes £ = 0 so that future exchange rate changes are only determined by order flow information. The third model assumes that the

off-diagonal elements of ¢ and £ are zero so that future exchange rate movements only depend on currency specific order flow and price history. A fourth model considers the simple interest rate differential framework, i.e. the forward bias trading strategy: ∆ ( ( : ∆ = : ¡ + ¤ ¥( − ( ¦ + : ( ∆ (

(38)

with ¤ being the 3 x 1 vector of coefficients. The interest rates used are

the overnight LIBOR fixings for the respective currencies. Finally, the benchmark model is the simple random walk framework with drift: ∆ : ∆ = : ¡ + : ∆

(39)

The investor, dynamically allocates his wealth among the three risky assets (foreign overnight deposits) and one riskless asset (domestic overnight deposit). The weights are chosen such that expected returns are Copyright © 2010. Diplomica Verlag. All rights reserved.

maximized subject to a target conditional volatility (See endorsement 3 for the detailed model framework). Transaction costs are accounted for as a fixed proportion of the traded amount in the different currencies. The first third of the sample (mid-February 2004 until mid-June 2004) is used as an initialization period to estimate the models. The remaining two thirds are used for dynamic one-day out-of-sample predictions. The

prediction is made at 17:00 o’clock on day - for each hour between 07:00

to 17:00 o’clock of the following trading day - + 1. The investor closes

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his trade on an a priori chosen fixed hour. However, the model parameters are re-estimated for each trading hour to check the robustness of the out-of sample performance during different trading hours of the day and also to account for possible performance differences due to dayvarying liquidity in the market. Table 33 shows that each of the three micro models outperforms the random walk and forward discount model in terms of risk adjusted Sharpe ratios. While the random walk model yields an average Sharpe ratio of -0.71, the best performing second micro model (incorporating cross-currency order flow) yields an average Sharpe ratio of 1.3. This is a considerable magnitude, compared to, for instance, a historical S&P 500 Sharpe ratio of around 0.445. While the third micro model which solely accounts for currency specific order flow also yields a positive Sharpe ratio of 0.26, the first micro model, incorporating order flow and interest differentials, merely generates a Sharpe ratio of -0.27. Albeit, it should be mentioned that risk adjusted returns vary considerably depending on the trading hour on which the portfolio is continuously readjusted. 11:00 o’clock appears to be the most appealing time to close trades. Realistically, an investor released from the forced closing hour could probably achieve even higher returns by placing limit orders46 each hour in combination with stop-loss specifications. Another interesting contribution to the phenomenon of the importance of investor heterogeneity is delivered by Lyons (2001). For the time period from 1993:1 to 1999:6 he finds that specific customer’s foreign exchange orders exert greater influence than others. In particular, hedge funds and non-financial corporations played a relatively important role for the yen exchange rate. This certainly is in line with the prevalent Copyright © 2010. Diplomica Verlag. All rights reserved.

occurrence of carry trades starting in the mid nineties. As for the euro, unleveraged fund managers (identified by real-money accounts) played the dominant role. The exact results can be found in table 34.

45

See e.g. Sharpe (1994) Limit orders are orders that are conditional on public information and the (yet unknown) exchange rate. (see e.g. Bacchetta and van Wincoop 2006, p. 554) 46

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All in all, evidence shows not only a strong contemporaneous relationship between order flow and exchange rate movements but also indicates future explanatory power of order flow. Dispersed information about macroeconomic fundamentals seems to be a characteristic feature among heterogeneous agents and, therefore, these fundamentals are not only realized at the macro level but even more so as aggregations of underlying unobserved micro-level shocks (particularly at the short-run).

3.4.2 Modeling Order Flow Bacchetta and van Wincoop (2006) model order flow within a monetary general equilibrium model with information dispersion. There exist two countries and two goods and each agent ( maximizes k −k l a−j bn

k k k s.t. j = 71 + ( 8}k + 7 − + (∗ − ( 8§¨ − ( & © k + *

(40) (41)

k is his where }k constitutes the agent’s initial wealth endowment, §¨

k investment in foreign bonds, & © k his real money holdings, and * the

production which itself depends on money holdings and an exchange rate exposure ªk of his non-asset income through exports.

The setting is similar to the simple monetary exchange rate model

presented in chapter 2.2, equations (5) to (10), except that a risk premium for non-observable trade is added onto the UIP condition in equation (8), resulting in:

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« + − , = ( − (∗ + I §

(42)

with « being the average rational expectation across all agents, a

measure of risk aversion, I the conditional variance of next period’s

exchange rate, and § the exchange rate exposure. Solving the model

forward the equilibrium exchange rate looks slightly different from equation (10): 1 ' 9 9 = 3 4 « +69 − 'I9 §9 , 1+' 1+' ∞

(43)

9"

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From equation (43) one can solve the exchange rate for the special case of Q = 1 (see endorsement 4) as:

1 ' ; ' = 6 + ¬ + 6 − ¬ I § (44) m 71 1+' + '8 ; +; +; 1+'

Here, ¬ > 1 is a magnification factor, ; , ; m , and ; are measures of

precision (i.e. volatility) of agent (’s private information shock, the

public information shock, and his exchange rate exposure shock, respectively. Generally, agents initiate transactions (and thus create order flow) because they either receive new private information about fundamentals or they need to hedge their time-varying exchange rate exposure which arises from their non-asset income through exports and their investment in foreign bonds. We see in equation (44) that the exchange rate depends on exactly these private signals about future

fundamentals and aggregate hedge trades § . However, due to the lack of transparency in the market these hedge trades cannot be observed as a separate aggregate and may be confused with an improvement of other agents’ private information about future fundamentals. So, the mechanism is as follows: A positive order flow resulting from unobservable additional hedging trades leads to a shift of the exchange rate (see equation (44)). This shift itself causes agents to revise their expectations of fundamentals47 and thereby magnifies the initial shift (via the magnification factor ¬). In effect, the market confusion

causes a relatively large part of exchange rate volatility by a relatively smaller amount of unobservable hedge trades. The confusion only dissipates over multiple periods to make room for an adequate,

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fundamental based exchange rate price. Accordingly, the cumulated

impact of a shock to fundamentals peaks at - = 9, while the shock to hedge trades has died out by then. The explanatory value of observed

fundamentals increases from < = 18% for - = 1 to < = 80% for

- = 20.

47

which can be seen in equation (E24) in endorsement 4

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After further derivation shown in endorsement 4 the exchange rate can be expressed in the following way: =

1 ' 6 + ¬ I ∆ 1+' 1+'

(45)

Here we see, how the exchange rate is related to publicly observable fundamentals and order flow which captures the aggregation of private information. Its impact is magnified again by ¬.

The dynamics of the model show that order flow is closely related to

exchange rate dynamics, starting from < = 84% for - = 1 to < =

95% for - = 20. This high correlation is not inconsistent with the close

long-run relationship between fundamentals and exchange rates, because

private information about changes in the fundamentals is reflected in the market as order flow. Only later when the fundamentals can be observed we can measure their relationship to exchange rates. Therefore, the presented model is widely in line with empirical evidence presented in chapter 3.4.1.

3.4.3 Uncovered Equity Parity Hau and Rey (2005) take a different approach to model the exchange rate determination process. They abstract completely from current account considerations such as the PPP condition but take in an entirely new variable which is equity returns. Although investors are concerned about foreign exchange risk when investing abroad, they do not completely hedge this forex risk that goes along with their equity positions. A survey among institutional investors in the U.S. run by Copyright © 2010. Diplomica Verlag. All rights reserved.

Levich et al. (1999), shows that only 55 percent of investors hedge minor (!) parts of their foreign exchange exposure, while the rest is not allowed to or simply does not hedge any exposure. Calculations (as well as indications from large custodians such as State Street Bank and Citibank) show that less than 10 percent of total foreign equity investment is hedged by U.S. investors. Consequently, investors are concerned about the joint return of foreign equity and currency. Therefore, Hau and Rey argue consistently that if foreign stock market return is different from the P a g e | 53

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home stock market return this automatically changes investors’ forex risk exposure and would induce risk-averse investors to rebalance their portfolio. In turn, this rebalancing creates order flow and leads to exchange rate movements. Relatively higher equity returns abroad will induce portfolio shifts (sale of foreign equity and purchase of home equity) in order to cut back exchange rate risk to its initial optimal level and will thereby translate into purchases of home currency. So will dividend repatriation. The so termed uncovered equity parity (UEP) therefore describes a positive correlation between home currency and foreign equity excess return. And in this setting, order flow arises endogenously through optimal dynamic portfolio rebalancing. Formally, in a symmetric two country and two asset setting, home and foreign investor maximize mean-variance adjusted profits in terms of home currency and choose a portfolio according to: &¯°± ,² ³

&¯°²∗

±∗ , ³

¶

1 ] ´ 7−|7E − -88 3∆µ5 − ∆µ5 4_ 2

(46)

5

¶

1 ] ´ 7−|7E − -88 3∆µ5∗ − ∆µ5∗ 4_ 2

(47)

5

where = a , b is the equity portfolio of the domestic investor m

consisting of home and foreign equity and ∗ = · , ¸ is the m∗

∗

respective portfolio of the foreign investor consisting of foreign and

home equity. Furthermore, ∆µ is the excess profit flow resulting from

the product of the equity portfolio and the excess payoff of equity over

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the local riskless bond in local currency terms ∆|t|

[95% Conf. Intervall]

γ

-0.0144888

0.0068069

-2.13

0.034

-0.0278701 -0.0011074

ρ2

0.3040443

0.0493039

6.17

0.000

0.2071201 0.4009685

ρ3

-0.0807133

0.0515092

-1.57

0.118

-0.1819729 0.0205464

ρ4

0.0841761

0.0495999

1.7

0.090

-0.0133301 0.1816824

_cons

-0.0698056

0.0329803

-2.12

0.035

-0.1346399 -0.0049712

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Source: Own computation, data is taken from IMF, time horizon is 1973:1 to 2008:05, regressional from is ∆q = γq − ∑ ∆q + with = 4.

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Table 4 – Panel unit root tests for DM-, GBP-, and JPY-USD exchange rates from tables 1-3

Number of obs = 936 Multivariate Augmented from 3 cross-sectional units Dickey-Fuller Lags Test statistic Approx 5% critical value 1 9.414 13.284 2 12.992 13.291 3 11.192 13.297 4 12.640 13.304 5 11.918 13.310 6 13.037 13.317 7 13.986 13.324 8 13.322 13.331 9 14.284 13.337 10 15.070 13.344 H0: all 3 time series in the panel are I(1) processes Levin-Lin-Chu test (Pooled ADF test) 923 observations with sectional lags (2, 4, 4) Coeff. t-value t-star p -value -0.0163 -3.591 -1.03339 0.1507 H0: Non-stationarity, I(1) behavior Im-Pesaran-Shin test, cross-sectionally demeaned 923 observations with sectional lags (2, 4, 4) t-bar W[t-bar] 10% cv 5% cv 1% cv -2.091 -1.166 -2.01 -2.15 -2.40 H0: All series are non-stationary

p -value 0.122

Source: Own computation, data is taken from IMF, time horizon is 1973:1 to 1998:12

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Table 5 – OLS Regression Estimates for ÙÚÛ − ÙÚ = ÜÛ + ÝÛ 7ÞÚ − ÙÚ 8 + ßÚ k 1 4 8 12 16

Canadian dollar ;9