Exchange Rate Determination Puzzle - Long Run Behavior and Short Run Dynamics

Butgereit, Falkmar

Exchange Rate Determination Puzzle - Long Run Behavior and Short Run Dynamics

Zusammenfassung

Inhaltsangabe: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 traded as derivatives such as foreign exchange swaps, outright forwards, or options, while only 1/3 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 exchange rate movements may be much more subject to trades based on heterogeneous expectations incurred by investors, speculators and market makers. Particularly at 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 […]

Leseprobe

Inhaltsverzeichnis

Falkmar Butgereit

Exchange Rate Determination Puzzle - Long Run Behavior and Short Run Dynamics

ISBN: 978-3-8366-3218-8

Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010

Zugl. Johann Wolfgang Goethe-Universität Frankfurt am Main, Frankfurt am Main,

Deutschland, Diplomarbeit, 2009

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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 ... 9

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 ... 73

References ... 110

Auxiliary Means and Declaration of Honor ... 115

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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.

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

of the turnover was

traded as derivatives such as foreign exchange swaps, outright forwards,

or options, while only

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

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

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model or purchasing power parity may only hold in the very long run and

exchange rate movements may be much more subject to trades based on

heterogeneous expectations incurred by investors, speculators and market

makers. Particularly at 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 short-

run 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 chart-

technique, 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 todays

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

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

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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

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 percent

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"

, 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

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

Obstfeld and Rogoff (1996), p. 202

De Grauwe (1996)

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mark

, and pound sterling from January 1974 until mid of 2008

. 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.

100

120

140

160

180

1974

1978

1982

1986

1990

1994

1998

2002

2006

Own Computation, Data Source: IMF, International Financial Statistics

Figure 1 - Real Exchange Rate of Selected Industrial Countries

RER USD/JPY

RER USD/DM

RER USD/GBP

1974 = 100

(Logarithmic scale)

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

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

t-i

i=1

(3)

with regression coefficients

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

Only West-Germany until December 1990

For Deutsche Mark until December 1998; the data are monthly averages.

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

-1

from

both sides of equation (3) to obtain

= q

i+1

t-i

i=1

(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 3

. 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

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

equilibrium.

Standard univariate tests may, therefore, be of limited

power.

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

For their results they were using an exponential smooth transition autoregressive

(ESTAR) model which is described in more detail in chapter 3.1.

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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 Dickey-

Fuller t-statistics of each unit in the panel and assumes that only a

fraction of the series is stationary when rejecting the null.

Despite difficulties in empirically confirming the PPP hypothesis

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.

Generally, academic literature agrees upon the speed of

convergence of PPP to be fairly slow

with a half life of deviations from

PPP of about three to five years

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.

if refraining from possible non-linearities

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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.

Figure 2 The Impact of Relative Inflation Rates on Exchange Rates

over Different Time Horizons

R² = 0,271

-0,5

0,5

1,5

-0,5

0,5

1,5

ati

% change in exchange rates

1-Year Intervals

R² = 0,708

-0,5

0,5

1,5

-0,5

0,5

1,5

% change in exchange rates

6-Year Intervals

R² = 0,948

-0,5

0,5

1,5

-0,5

0,5

1,5

ati

% change in exchange rates

12-Year Intervals

R² = 0,968

-0,5

0,5

1,5

-0,5

0,5

1,5

% change in exchange rates

24-Year Intervals

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.

2.2 The Simple Monetary Exchange Rate Model

Evidently, monetary policy has had large impacts on exchange

See Rogoff (1996)

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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 Friedmans 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

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)

lim

1 +

= 0

(9)

the solution for the exchange rate can be obtained as

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1 +

{

}

(10)

where

- (

). Accordingly, the determination of

todays 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

to follow a driftless random walk.

In this case equation (10) results into the exact relation of

. Then,

he tests the "k-period-ahead change in the log exchange rate on its

current deviation from the fundamental value"

(11)

where

and are linear least-squares estimators and

is the projection

error. The fundamental value

is constructed with a constant value of

= 1. The data consists of quarterly observations for the US, Canada,

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

are shown in table 5. He finds consistently higher

-coefficients and

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

= .02

opposes the sixteen-quarter horizon with

= 1.32 and

= .76

which implies a depreciation of approx. 13% p.a. of the USD over the

Mark (1995), p. 204

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next four years if the dollar was overvalued by 40% today. A

substantially increasing

across all currencies impressively supports

the long-run dependency of the exchange rate on relative money supply

and output growth.

The forecasting abilities of the model are also impressive. Mark

divides the sample into the periods 1973-1981 for an in-sample

estimation of equation (11) and 1981-1991 for an out-of-sample

prediction. The results can be found in table 6. Over the 16 quarter

horizon the out-of-sample root-mean-squared errors (RMSE) exceed the

in-sample RMSE by only 20% for CHF and DM and by about 60% for

the JPY and 110% for the CAD. Particularly interesting is the

comparison to a driftless random walk bootstrap distribution generated

by a vector autoregression with the underlying assumption of

unpredictability of

. Measured again by the relative RMSE, the model

outperforms the random walk over every horizon for the Swiss franc and

yen (by as much as 60 percent and 40 percent respectively for the sixteen

quarter interval) and at twelve and sixteen quarters for the DM (by 20

and 50 percent). The CAD, however, only outperforms at the one quarter

horizon.

Clearly, Mark proves the importance of fundamentals on

exchange rates by showing that they inherit predictable components for

future exchange rate movements, particularly over the medium- and

long-run.

In a milestone paper, MacDonald and Taylor (1993) also find

evidence for the validity of the relationship of the flexible-price monetary

equation, which, analogous to Mark above, results from equation (10) if

all shocks to the fundamentals are assumed to be permanent:

(12)

All notations are as before and

describes the long-run interest rate.

MacDonald and Taylor analyze the monthly pound sterling/US-dollar

exchange rate between 1976:1 and 1990:12 and find that they cannot

reject that every single underlying fundamental follows an I(1) process

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based on Dickey Fuller and Phillips-Perron tests

. Therefore, equation

(12) is only a valid long-run relationship if there exists cointegration

between the exchange rate and the fundamentals. Using an extended

methodology of Johansens (1988) multivariate maximum likelihood

technique of cointegration

they are indeed able to find up to three

cointegrating vectors. However, by additionally testing and rejecting

seven popular monetary restrictions on the model which are listed in

table 8, they show that despite of this long-run evidence the relationship

might not be as simple as equation (12) suggests.

2.3 Long-Term Cycles

Since the end of Bretton Woods and the beginning of free floating

exchange rates in 1973 the dollar and other currencies have evidently

experienced persistent deviations from PPP and longer periods of

consistent upward and downward movements. In recent history these

trends lasted up to 10 years and longer. For example, this was the case

for the DM/USD downtrend from 1985 to 1995. Reasons given for such

trends are numerous and diverse. Business cycles may explain part of the

swings; however, they are usually shorter-lived. A large and permanent

current account surplus for example may explain the yen uptrend from

1983 to 1995. On the other hand, a current account deficit due to the

investment boom in conjunction with the "New Economy" in the US may

explain the dollar upswing from 1995 to 2002.

Figure 3 supplies some evidence of this upswing. Each of the four

panels shows one economic variable versus the USD/SDR exchange rate;

where SDR is an IMF basket of currencies consisting of the euro, yen,

sterling, and dollar. The influences of the economic variables on the

dollar are obvious but seem to vary over time.

The first panel shows the median expected annual U.S.

productivity growth over the next ten years from annual surveys of

See table 7

As opposed to the widely used standard vector cointegration tests using the two-step

cointegration methodology of Engle and Granger (1986).

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Figure 3 USD versus chosen economic variables

0,6

0,65

0,7

0,75

0,8

0,5

1,0

1,5

2,0

2,5

1995 1996 1997 1998 1999 2000 2001 2002 2003

l E

Expected 10Y U.S. Productivity Growth Rate

expec. Productivity Growth

SDR/USD

0,6

0,65

0,7

0,75

0,8

1,0

1,2

1,4

1,6

1,8

1995 19961997 1998 1999 20002001 2002 2003

l E

U.S. Gross Domestic Investment

Gross Domestic Investment

SDR/USD

0,6

0,65

0,7

0,75

0,8

1995 1996 1997 1998 1999 2000 2001 2002 2003

l E

1Y Lagged Federal Funds Rate

1Y Lagged Federal Funds Rate

SDR/USD

0,6

0,65

0,7

0,75

0,8

0,5

1,5

2,5

3,5

199519961997199819992000200120022003

l E

Expected 10Y U.S. Real GDP Growth

expec. GDP growth

SDR/USD

Own computation; data sources: 10Y-Expectation of U.S. Productivity and Real GDP

Growth from Federal Reserve Bank of Philadelphia, Survey of Professional Forecasters;

U.S. Gross Domestic Investment and Federal Funds Target Rate from U.S. Federal

Reserve Bank; USD/SDR exchange rate from IMF International Financial Statistics

professional forecasters

. From 1995 to 1999 the expectations of

long-term productivity growth were averaging out at about 1.5 percent

p.a. Remarkably, these expectations did not adjust gradually but changed

with a tremendous jump to 2.4 percent in 2000 and 2.5 percent in 2001;

alongside the USD appreciated by about 15%. Indeed, as a study of the

Federal Reserve Bank of New York (2001)

finds out, a systematic

increase in the sectoral productivity gap (between traded- and non-traded

goods) in the US compared to a decreasing gap in Japan and a constant

gap in Europe may explain up to 79 percent of USD/JPY and 61 percent

of USD/EUR real exchange rate movement between 1990 and 1999.

The upper right panel of figure 3 shows a similar pattern for the

ten year expected growth in GDP. The remarkable jump in growth

expectations from 2.5 to 3.1 percent occurred simultaneously to the leap

Surveyed by the Federal Reserve Bank of Philadelphia; including more than 30

professional forecasters.

by Tille, Stoffels, Gorbachev (2001)

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in productivity expectations in 2000 and went hand in hand with the

dollar appreciation.

The lower left panel of Figure 3 shows the U.S. investment

boom. The U.S. gross domestic investments were steadily rising from

$1.3 trillion (1995) to more than $1.6 trillion (2000) and in conjunction

the dollar appreciated significantly. Vice versa, as investment decreased

again to $1.5 trillion (2003) the dollar depreciated as well.

Finally, the lower right panel shows the relatively tight monetary

policy of the Federal Reserve which also has seemed to influence the

dollar. Due to a forward looking communication of the Fed with the

market, changes in the federal funds rate are often widely anticipated.

Therefore, in figure 3 the one year lagged federal funds rate is shown

alongside the USD. The correlation coefficient between the two is .26

over the considered period.

Interestingly, Engel and Hamilton (1990) have provided evidence

on the dollar performing long swings. They rejected the null hypothesis

of a random walk behavior in favor of their stochastic model of

segmented time trends. They decomposed the three (non-stationary)

quarterly USD exchange rate series from 1973:III to 1988:I over

Deutsche mark, French franc, and British pound into a sequence of

stochastic, segmented time trends by labeling every quarters change as

one out of two possible states; i.e. state

= 1 if the exchange rate is

presumably drawn from a

(

) distribution and state

= 2 if the

exchange rate is distributed

(

). Since the evolution of

unobserved they put forward the following Markov chain:

= 1

-1

= 1 =

(13)

= 2

-1

= 1 = 1 -

(14)

= 1

-1

= 2 = 1 -

(15)

= 2

-1

= 2 =

(16)

where

denotes probabilities and state

-1

, per definition, captures all

information influencing state

. It turns out that the theory of long

swings, i.e. large values for

and

and opposite signs for

and

dramatically outperforms the random walk, which would be

= 1 -

. Table 9 shows the results of the maximum likelihood estimations.

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For example,

and

of the pound sterling are significant at the 1%

level and amount to 2.6 and -3.8, respectively. The probabilities of

remaining in state one

and in state two

are both 0.9. The

downside volatility amounts to 20 percent and is, therefore, somewhat

higher than the upside volatility of about 17 percent. Similar results are

found for the other considered currencies with the exception of

of the

DM which is not significant. The null hypothesis of a random walk

= 1 -

is strongly rejected for all currencies when applying a

Wald test. The same holds for the null hypothesis of

. In

terms of forecasting, the model also performs well. The in-sample

forecasts for dates

= 1973: IV + to 1988: II, where is the one to

four quarters forecast horizon, outperforms the random walk in terms of

lower mean squared errors by 4 to 14 percent. Also, the post-sample

forecasts for dates

= 1984: I to 1988: I show clear outperformance of

up to 17 percent (for the one quarter pound sterling forecast). The only

two cases where the random walk performs slightly better (by one

percent) is the 4 quarter forecast horizon for DM and franc. The complete

overview of the results can be found in table 10.

A further important variable for exchange rate movement is

government spending. In his paper, Wu (1994) specifies a model

which

shows very similar autocorrelation coefficients of changes in the RER as

well as for the first two moments. The model incorporates a usual

consumption optimization problem subject to the market clearing

condition and includes government spending and technology as

exogenous-forcing variables following a stationary autoregressive

process. The RER, then, results from the consumption decisions and

subsequent price levels. He finds that mean, standard deviation, and

autocorrelation coefficients of actual and model generated data are not

significantly different at the 5% level and consequently concludes that

"disturbances of government spending are important in explaining

movements of real exchange rates"

. The transitional dynamics in the

For a detailed description of the model see endorsement 1 in the appendix

Wu (1994), p.50

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model are as follows: An increase (decrease) in domestic government

spending creates excess demand (supply) in the domestic goods market.

In order to clear markets between home and foreign, the relative price of

domestic goods must increase (decrease) so that foreign consumes less

(more) domestic goods. This implies depreciation (appreciation) of the

real exchange rate. Once government spending is cut back to its initial

value the RER returns to its equilibrium value. However, deviations from

the steady state are found to be very persistent.

All in all, it can be concluded that the dollar observes persistent

long-term cycles. Plenty of possible explanations for this phenomenon

have been put forward. Among them are relative productivity growth

differentials (Harrod-Balassa-Samuelson effect), large current account

imbalances, interest rate differentials, differences in output growth,

shocks to government spending, as well as speculative bubbles and

"irrational" chartists (at which we will look at in chapter 3.2). Also we

have seen that anticipated future events and expectations about economic

fundamentals seem to play an important role.

2.4 The Macroeconomic-Balance Approach

The macroeconomic-balance approach is used to determine a

currencys long-run equilibrium level. Thereby, the equilibrium rate

aligns the countrys current account balance (CA) with the excess of

domestic saving over domestic investment (S-I). As for the CA we have a

positive relationship with the real exchange rate (RER). Although the

effects take some time to unfold and materialize the RER affects the CA

via the volumes and prices of exports and imports, that is, for example,

with constant prices and depreciating nominal dollar (appreciating RER)

domestic American goods become more competitive. As a result

American exports increase, imports decrease and the overall CA

improves.

The savings-investment gap, on the other hand, moves inversely

with the RER. Although aggregate national savings can reasonably

assumed to be widely independent from the exchange rate, investment

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spending tends to move in line with the RER. This relationship stems

from the effect that an appreciating home currency (with constant prices,

i.e. a decreasing RER) lowers profitability for exporting firms via

decreasing their competitiveness and lowering possible mark-ups. As a

result S-I rises.

The exchange rates long run equilibrium can now be found at the

point where a countrys savings-investment imbalance just matches its

current account imbalance. As described by Isard et al (2001), the IMF

usually approaches the long-run exchange rate determination by a three-

step procedure.

Firstly, the IMF calculates a countries underlying account either

via a trading model or uses generated projections by the IMFs country

experts in connection with the World Economic Outlook. The relevant

underlying current account estimate arises from the CA with the

assumption that all countries produce at their potential output levels and

that lagged exchange rate effects have been fully realized.

Secondly, the sustainable medium-run savings-investment

imbalance is calculated by a national income model. It relates (S-I) to

structural fiscal positions (relative to industrial country average) and

cyclically adjusted levels of per capita incomes (relative to the US) and

some country specific constant terms. All terms are ratios to GDP and it

is also assumed that output gaps are zero, or in other words, vanish in the

long-run. Country specific interest rates, however, are not included since

they are not significant. The general objective, here, is to determine how

much foreign capital can be attracted on a sustainable level to finance an

excess investment over domestic savings.

Finally, the equilibrium exchange rate is estimated from the

previous estimates in order to match the two imbalances. An OECD

survey by Koen et al. (2001) of several econometric studies (summarized

in table 11) shows that the dollar was significantly overvalued by up to

40% in 2001. However, the estimates of the equilibrium exchange rate

differ widely, depending on the underlying assumptions in the macro-

econometric model. Yet, all studies agree on the overvaluation of the

dollar over the euro in late 1999 and throughout 2000 where the euro cost

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between $1 and $0.85. The survey estimates for the equilibrium

exchange rate tend to scatter around 1.10 to 1.25 USD/EUR. And indeed,

by the end of 2003 the euro had appreciated up to 1.26 USD/EUR.

Further down the road, until 2007 and 2008, the continued depreciation

of the dollar seemed to have given rise to a laterally reverse

overvaluation of the euro. Figure 4 illustrates the movements.

Source: Own computation; exchange rate data taken from www.oanda.com (daily

averages), the average equilibrium exchange rate spread is calculated from the summary

of several surveys by Koen et al 2001 (see table 11)

It can be outlined that structural changes on a countries internal-

(i.e. its S-I balance) and external balance (i.e. its CA) can affect the RER

significantly. So it happened during the U.S. investment boom and

productivity improvements in the mid and late 1990s, which certainly

were main contributors to the dollar appreciation.

3 Short-Run Exchange Rate Dynamics

3.1 Only Random Dynamics?

As we have seen fundamental factors which influence the

exchange rate are numerous and diverse and often need time to pass

0,80

0,90

1,00

1,10

1,20

1,30

1,40

1,50

1,60

01/01/99

01/01/00

01/01/01

01/01/02

01/01/03

01/01/04

01/01/05

01/01/06

01/01/07

01/01/08

01/01/09

USD per Euro

Figure 4 - USD/EUR Nominal Exchange Rate

USD/EUR Exchange Rate

Average Equilibrium Exchange Rate Spread of 12 Different Studies from 99/00

P a g e

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through. But what can we say about the short-run driving forces of

exchange rate determination? Probably the most recognized paper in the

1980s about exchange rates is written by Meese and Rogoff (1983). They

examine out-of-sample forecasting performance of standard exchange

rate models as well as simple univariate and vector autoregressions and

find that in terms of root mean squared error (RMSE), i.e. the mean

squared deviation between predicted and actual exchange rate, no model

performs significantly better than a plain random walk model over a

one-, six-, and twelve month horizon. They consider the dollar exchange

rate versus pound, mark, yen, and a trade-weighted currency basket

between 1973:03 and 1981:06, using the period until 1976:11 for an

initial estimation of the model coefficients and the first forecast.

Afterwards, parameters are re-estimated including the most recent data

for next periods forecast, i.e. they use rolling regressions. As structural

models they, firstly, test the flexible-price monetary model of Frenkel-

Bilson; secondly, the sticky-price monetary model of Dornbusch-

Frankel; and thirdly, the sticky-price asset model of Hooper-Morton. All

models are in accordance with the derived simple monetary exchange

rate model of equation (10) in chapter 2.2. However, their assumption

that all shocks to money supply or its growth rate are permanent enables

them to express the exchange rate solely in terms of current

fundamentals. Explicitly, these special cases of equation (10) are

(17)

for the Frenkel-Bilson model, which is a amended version of the typical

flexible-price model we have seen in equation (12) and where the last

term in brackets refers to the short-term interest rate differential;

{

} +

(18)

for the Dornbusch-Frankel model allowing for slow domestic

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adjustments via the expected long-run inflation differential

represented

by the last term in brackets; and

(19)

for the Hooper-Morton model, allowing for shocks in the cumulated

foreign trade balance (

As for the univariate time series model, an AR(N) model is used

with N being determined by a function of sample size (M):

log

. Lastly, the multivariate time series model is a VAR(N) with

lagged values of the exchange rate itself and the six explanatory variables

from equation (19), where N is determined by Parzens (1975) lag length

selection criterion

. As for the random model, the current spot rate

simply serves as next periods predictor.

As mentioned earlier, all out-of-sample estimates are compared in

terms of RMSE and can be found in table 12. The USD/DM exchange

rate predictions over the one month horizon by all models but the vector

autoregression model are the only ones which seem to have about the

same accuracy as the random walk forecast. Over all other horizons and

for all other currencies, the RMSE of the models are consistently higher

than the RMSE of the random walk model. This seems to be even more

surprising as actual (at time

unknown) future values were allowed in

the dynamic forecasts. This way of modeling expectations of explanatory

variables, however, remains questionable.

Meese and Rogoff suggest a number of reasons for the poor

performance of the models; amongst them stochastic movements in the

underlying parameters, small sample bias, and possible non-linearities.

As they partly rule out the first suggestion by accounting for potential

parameter instability

possibly caused by oil price shocks and regime

which will be approximated by the long term interest rate differential

which turns out to be 4 for dollar/yen, and 2 for all other exchange rates.

by using Kalman filtering which imposes geometrically declining weights on the time

series.

P a g e

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changes, the other two proposals remain problematic. Another valid

problem are misspecifications about omitted variables and underlying

building blocks of the models such as uncovered interest rate parity

which, empirically, is strongly challenged.

Non-linearities, however, seem to play a valid role as Taylor et al.

(2001) find evidence for the presence of non-linearities in the data.

Consequently, any linear forecast model of exchange rates that does not

account for such might be doomed to failure. In 2003, Kilian and Taylor

use a specific (non-linear) exponential smooth transition autoregression

(ESTAR) model to run in- and out-of-sample forecasts with quarterly data

covering 1978 to 1998. Generating critical values via bootstrapping, they

beat the random walk model in-sample for six out of seven currencies at

the 10% significance level over two and three year forecast horizons but

failed to do so over shorter horizons. Also, the model cannot beat the

random walk out-of-sample except for U.K. and Switzerland at the three

years horizon. They attribute this failure of the out-of-sample forecast to

the small sample which only allowed for an initial estimation period of

eight years for the mean reversion parameter and might thus not be

sufficient to capture unusually large deviations from fundamentals that

are necessary to reveal the presence of a non-linear mean reversion.

Furthermore, they hold the small number of recursive forecast errors in

the sample responsible for a significant loss in explanatory power.

Regarding the failure to forecast more precisely than the random walk,

even in-sample over shorter horizons of one quarter to one year, they

argue that near long-run equilibrium fundamentals as well as exchange

rates are well approximated by a random walk. This would particularly

apply at short horizons. Generally, this effect can be well illustrated by

means of their ESTAR model which they estimate for every country:

= exp

-1

+ 1 -

-2

(20)

where the real exchange rate

(as defined in equation (2)) is demeaned

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and the first term in large brackets on the right hand side of equation (20)

describes the specific exponential transition function with the dimension

set to 5 and each element thereof equal to the same scalar

This scalar

is expected to be smaller than zero if the degree of mean reversion

increases as deviations from equilibrium widen.

Indeed, significant

negativity of

is found for all considered exchange rates

. Also all other

parameters are significant at the ten percent level. Equation (20) also

implies that if the real exchange rate

has been equal to its

equilibrium level

in all

(or if the nominal exchange rate has been

equal to the fundamental equilibrium level

), the

exchange rate will follow a unit root process:

-1

+ 1 -

-2

(21)

A consolidated view of the evidence brought up by Taylor et al.

indicates that non-linearities indeed may be an issue within exchange rate

time series over longer horizons but that these cannot explain short run

dynamics apart from special cases in which exchange rates may be

seemingly well approximated by a random walk as shown in equation

(21).

Other reasons of why exchange rates may be hard to predict in the

short run are brought up by Engel and West (2005). They model

exchange rates in a conventional rational present-value asset-pricing

model, equal to the monetary model in chapter 2.2, equation (10), and

argue that random walk behavior will arise if

is close to zero, i.e. the

discount factor is close to unity. In this case relatively more weight is put

on fundamentals far in the future and, thereby, the importance of current

movements in the fundamentals is reduced significantly. This, of course,

remains theoretically possible.

They find the optimal number of lags of the exchange rate influencing the transition

function, in terms of goodness of fit, equal to 5 for each country.

where, due to the nature of the ESTAR model, they assume a constant long-run

equilibrium level and, therefore, abstract from effects such as the Harrod-Balassa-

Samuelson effect. This assumption may be justifiable considering the relatively short

post-Bretton Woods period they use.

which are dollar exchange rates for Canada, France, Germany, Italy, Japan,

Switzerland, and UK.

P a g e

| 24

As a further suggestion they bring up again that exchange rate

movements will follow a random walk if the underlying fundamentals

inherit a unit autoregressive root. This may be the case for the observable

fundamentals (i.e. money supply, income, prices, and interest rates) for

each of which they fail to reject the null of a unit root

and generally fail

to find cointegration with the US exchange rate of six countries for

quarterly data from 1974:I to 2001:III.

Just as well, the noisy behavior

could arise from unobservable shocks such as shocks to money demand,

productivity, prices, and risk premiums.

However, as can be seen in table 13, Engel and West also provide

evidence on exchange rates possessing some predictive power for

fundamentals, as one would expect if the forward looking present value

model was accurate. They conduct separate Granger causality tests of

each underlying fundamental variable (including a constant and four

lags) on every one of the six currencies. It turns that in nine cases the

null of

failing to Granger-cause respective fundamentals can be

rejected at the five percent level and in three more cases at the ten

percent level. Only

consistently fails to provide evidence on

Granger-causing

. This could be attributed to financial innovations

which may have made standard income measures poor proxies for the

number of transactions. Also for the Canadian dollar and the pound

sterling evidence on causality could not be found. After all, 13 out of 36

tests have been found to significantly reject the null of no Granger-

causality. As one could argue that these results may as well be spurious,

this result opposes to only 2 out of 36 significant rejections if the null is

reversed, i.e. if one tests if

is Granger-causing

The strongest evidence against random dynamics in the short run

comes yet from another two researchers. As mentioned earlier in chapter

2.2 MacDonald and Taylor (1993) find evidence of a multivariate

cointegration in the underlying flexible-price monetary equation (12).

using Dickey-Fuller tests

They conduct five cointegration tests between

and each measure of fundamentals,

, and

for six currencies

(CAD, franc, DM, lira, yen, pound sterling) versus the USD and reject the null of no

cointegration at the five percent level in only five instances.

Details

Seiten
Erscheinungsform: Originalausgabe
Jahr: 2009
ISBN (eBook): 9783836632188
DOI: 10.3239/9783836632188
Dateigröße: 2.2 MB
Sprache: Englisch
Institution / Hochschule: Johann Wolfgang Goethe-Universität Frankfurt am Main – Wirtschaftswissenschaften, Studiengang Volkswirtschaftslehre
Erscheinungsdatum: 2009 (Juli)
Note: 1,3
Schlagworte: monetary exchange rate model order flow long behavior short dynamics uncovered equity parity

Autor

Falkmar Butgereit (Autor:in)

Exchange Rate Determination Puzzle - Long Run Behavior and Short Run Dynamics

Zusammenfassung

Leseprobe

Inhaltsverzeichnis

Details

Autor

Falkmar Butgereit (Autor:in)