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This is to certify that the

dissertation entitled

ESSAYS ON THE MACROECONOMICS OF THE 19208:
HYPERINFLATION, VOLATILITY AND MONEY DEMAND

presented by

Michael Raymond Redfearn

has been accepted towards fulfillment
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Ph . D . degree in Economic S

 

 

 

 

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_‘—"—'—'—" - ‘I—w

ESSAYS ON THE MACROECONOMICS OF THE 19208: HYPERINFLATION,
VOLATILITY AND MONEY DEMAND

BY
Michael Raymond Redfearn

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1992

ABSTRACT

ESSAYS ON THE MACROECONOMICS OF THE 19208: HYPERINFLATION,
VOLATILITY AND MONEY DEMAND

BY
Michael Raymond Redfearn

This dissertation consists of two essays:

1. "News and the Volatility of Exchange Rates" examines the
time series properties of exchange rates for Belgium, Britain,
France, Germany, Italy, Holland and Switzerland. Tests for
cointegration between spot rates and forward rates are
reported. No evidence is found for the theory that the spot
exchange rates in this era were cointegrated. However,
evidence is found for the stationarity of some forward
premiums. Generalized. .Autoregressive Conditional
Heteroskedastic models are estimated and are found to provide
an adequate description of the first two conditional moments
of the exchange rate data. The analysis then focuses on the
volatility of exchange rates during the 1920s. The
application of robust inferential techniques follows. The
essay concludes by examining whether there exists any
volatility spillovers between the various currencies. While
the Italian.and.Swiss exchange rates show some departures from
weak form efficiency, the 19208 market appears to be
relatively efficient.

2. "Purchasing Power Parity and the Demand for Money in the

19208" reexamines the existence of long-run Purchasing Power

Parity (PPP) in the 19208 for currency combinations between
Belgium, Britain, France, Germany, Holland and the United
States using both wholesale prices and different measures of
retail prices. A maximum likelihood procedure due to Johansen
(1988) is used. Some evidence consistent with purchasing
power parity is found. However, some currency/price
combinations yield more than one cointegrating relationship.
The analysis then proceeds to use the existence of PPP to
propose the forward premium as a proxy for inflationary
expectations during high inflation periods. Demand for money
equations are estimated and the results indicate that the
forward premium is not a statistically significant variable
for explaining the demand for money during high inflation

episodes.

Dedicated to Amber, My Grandmother

ACKNO'LEDGENENTS

I wish to thank my dissertation committee chairman,
Professor Richard T. Baillie, for his comments, advice, and
guidance over the period of this project. It also wish to
thank my other committee members, Professor Rowena A.
Pecchenino and Professor Robert H. Rasche, whose valuable
comments, assistance and advice improved and helped complete
this dissertation.

I would like to thank Margie Tieslau for her help and
support during this undertaking; Dr. Lewis M. Abernathy,
Chairman of the Department of Economics at the University of
North Texas, for his support, advice and encouragement; Kari
Foreback for providing excellent word processing assistance;
and Roger Speas for providing computing assistance.

I also would like to thank my family: my parents,
Patricia and Arnold Redfearn, and my brothers, David, Shawn
and Scott for their support and encouragement of my efforts;

and my grandparents for believing in me.

iv

TABLE 0? CONTENTS

LISTOFTABLES 0.0....00...0.0......00..00.0.00..0000.. Vi

LISTOF FIGURES 000.0.0.00.0...0....0000...0...00.0.000Viii
CHAPTER I: INTRODUCTION ....0.....0000.0...000.00....O 1

CHAPTER II: NEWS AND THE VOLATILITY OF EXCHANGE RATES

1. INTRODUCTION ................................. 3
2. GENERAL TIME SERIES PROPERTIES ............... 6
3. THE BASIC MODEL .............................. 14
4. THE IMPORTANCE OF NEWS AND THE VOLATILITY OF
EXCHANGE RATES ............................... 22
5. VOLATILITY SPILLOVERS BETWEEN CURRENCIES ..... 30
6. CONCLUSIONS .................................. 33

LIST OFREFERENCES 0.......0..000.00.......0.0..00 69

CHAPTER III: PURCHASING POWER PARITY AND THE DEMAND FOR
MONEY IN THE 19208 .

1. INTRODUCTION ................................ 75
2. GENERAL TIME SERIES PROPERTIES AND THE

EXISTENCE OF PURCHASING POWER PARITY ........ 79
3. MONEY DEMAND AND PURCHASING POWER PARITY .... 84
4. CONCLUSIONS ................................. 92

LIST OFREFERENCES .00....0.000.00.0..00.0.0.0000 126

APPENDIXI .0..00.......0000......0.0.0.0.0000... 131
LIST OFREFERENCES .0.00.0....0.00.........000... 153

APPENDIXZ 00......00...0..0. .......... O ....... .0 154
LIST OFREFERENCES 000.....0...0....0.........00. 158

CHAPTER II

Table

Table

Table

Table

Table

Table
Table

Table

Table

Table

Table

Table

Table

Table

1

10

11

12

13

14

LIST OF TABLES

Summary of Unit Root Tests on Exchange

Rates

Phillips-Perron Tests

Kwiatkowski, Phillips, Schmidt and Shin

Tests

Johansen Trace Tests for Cointegration ........

Johansen Trace Tests for Cointegration,
Spot and Forward Rate Combinations ... ........ .

Weekly 30-day Forward Premium .................

Estimation of the Model.......... ..............

Estimation of the Model, t-Distributed

EI‘I‘OI‘S

Estimation of the Model .......................

Estimation and Robust Inference on the
Madel 00000000000000.00000000000 0000000 00000000

Volatility Patterns From Robust GARCH

Estimation

Wald Tests From Robust Estimation with Dummy

Variables

Robust Wald Tests for Causality in the Mean ...

Robust Wald Tests for Causality in Variance ...

CHAPTER III

Table

Table

1

2

Summary of Purchasing Power Parity Results....

Phillips-Perron Tests

36

38

4O

43

44
46

48

49

50

51

52

53
56

58

96

99

Table 3 Kwiatkowski, Phillips, Schmidt and Shin
Tests ........................... ............ . 103

Table 4 Johansen Trace Tests for Cointegration . ...... 109

Table 5 Likelihood Ratio Test of Restriction 1, 1, -1
on Cointegrating Vector ..................... 113

Table 6 Unit Root Tests of Real Exchange Rates ....... 114
Table 7 Phillips-Perron Tests ....................... 119
Table 8 Analysis of the Monthly Forward Premium ...... 121
Table 9 Money Demand Estimation ..................... 122

Table 10 Money Demand Estimation with Correction for
Autocorrelation 0.000000000000000...0.0000000 123

Table 11 Money Demand Estimation with Real Income .... 124

Table 12 Cointegration Tests for German Real Money
Balances ......000000000000000000000000000000 125

vii

CHAPTER II

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

1

10

11

12

13

14

LIST OF FIGURES

Log of the Weekly Belgian Spot Rate
February 1922 - April 1925 ............. ......

Log of the Weekly British Spot Rate
February 1922 - April 1925 ...................

Log of the Weekly French Spot Rate
February 1922 - April 1925 ....... ........... .

Log of the Weekly Dutch Spot Rate
February 1922 - April 1925 ... ............. ...

Log of the Weekly Italian Spot Rate
February 1922 - April 1925 ...... ....... ......

Log of the Weekly Swiss Spot Rate
February 1922 - April 1925 ...................

Belgian Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

British Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

French Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

Dutch Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

Italian Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

Swiss Rate of Return from Weekly Spot Rates,
February 1922 - April 1925 ...................

Log of the Belgian, French and Italian Spot
Rates, February 1922 - April 1925 ............

Log of the Swiss Spot Rate versus the 30-Day
Forward Rate, February 1922 - April 1925 .....

viii

59

59

60

60

61

61

62

62

63

63

64

64

65

65

Figure

Figure

Figure

Figure

Figure

Figure

15

16

17

18

19

20

Belgian Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

British Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

French Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

Dutch Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

Italian Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

Swiss Conditional Variance versus Rate of
Return, February 1922 - April 1925 ...........

66

66

67

67

68

68

I . INTRODUCTION

CHAPTER I

INTRODUCTION

Widespread floating exchange rates in this century
occurred during two periods; first from mid 1919 to 1928, and
secondly from 1973 to the present day. A further period when
some exchange rates floated occurred between 1931 and 1938
when most countries left the Gold Standard. Britain left the
Gold Standard in 1931 and the United States abandoned gold in
1933. France, Belgium, Holland, Italy and Switzerland, the
members of the Gold Bloc, remained on the Gold Standard until
1936 when the last of the remaining members, Holland and
Switzerland, suspended the convertibility of their currencies
and allowed them to freely depreciate in the market. Since
there are approximately only two years when the whole system
of exchange rates could potentially float freely, this period
does not constitute a freely floating regime system. Since
there are only two jperiods of floating exchange rates,
analysis of the 19208 period is potentially useful for our
understanding of exchange rates today.

The 19208 period is useful for examining questions of
market efficiency, the desirability of different exchange rate
Iregimes, the role of speculation in determining the behavior
<Jf exchange rates, the applicability of the purchasing power
parity relationship, the formation of expectations, and the
role of "news" in explaining the behavior of exchange rates.

1

2

The 1920s period is similar to the post 1973 period in
several‘waysw IBoth followed periods in which nominal exchange
rates had been explicitly fixed. This was accomplished by
government decree during the First World War and by the
Bretton Woods Agreement from 1944 - 1971.

The 1920s period is characterized by a wide variety of
monetary and non-monetary events, including German war
reparations between 1921 to mid 1924; the occurrence of the
hyperinflation in Germany; the "bear squeezes" of M. Poincaré
in March of 1924 and July of 1926; and the successful return
of Great Britain to a gold type standard.

The 1920s period is an interim.period of adjustment from
war-enforced exchange rate parities to the pre-war gold or
dollar parities. It was widely, although eventually
erroneously, believed that domestic currencies would
eventually return to their pre-war parity.

Unlike the recent float, the 1920s period had no
intervention corresponding to anything as sophisticated as the
European Monetary System where there are bands within which
exchange rates are allowed to fluctuate. Generally exchange
rates moved freely according to market conditions, although
Belgium, Britain, France and Holland all intervened heavily in
support of their respective currencies. However, there did
not exist a concerted effort to force exchange rates to pre-

war parity levels .

II. NEWS AND THE VOLATILITY OR EXCHANGE RATES

CHAPTER II

NEWS AND THE VOLATILITY OF EXCHANGE RATES

1. INTRODUCTION

As mentioned in Chapter I, the 1920s is one of the two
periods of freely floating exchange rates in this century.
Despite the relative abundance of data in the 1920s,
relatively little research has examined the general time
series properties of this floating regime. The focus of this
essay is to examine the evolution of spot exchange rates; the
volatility of the spot exchange rate; the effect of "news" on
the volatility of exchange rates; and the possible existence
of volatility spillovers between exchange rates.

Mussa (1979) notes that many exchange rates seem to
possess tranquil and also highly volatile periods. Figures 1
through 6 plot the log of the weekly spot exchange rate from
February 1922 throuthApril 1925 for Belgium, Britain, France,
Holland, Italy and Switzerland. IFigures.7 through 12 plot the
rate of return (the first difference of the log of the weekly
spot rates) for the six countries over the same sample period.
These plots confirm Mussa's observation concerning tranquil
and volatile periods. This type of volatility clustering was
first identified by Mandelbrot (1963) and Fama (1965) who
noted this implied that price changes were not independent
over time. This non-independence of price changes means that
higher order' moments of the distribution of prices are

3

4
related. Thus, if both economic and noneconomic events are to
be used to explain volatile periods, the model used must be
able to account for clusters of volatility.

One such class of models is the Autoregressive
Conditional Heteroskedastic (ARCH) model of Engle (1982) and
the Generalized Autoregressive Conditional Heteroskedastic
(GARCH) models of Bollerslev (1986) and Engle and Bollerslev
(1986). The GARCH process specifically models time varying
conditional variances, which are assumed to be influenced by
lagged squared innovations and lagged conditional variances.

The present essay uses GARCH processes to model the
volatility of the of the 19203 spot exchange rates.

Fama (1970, 1976, 1991) proposed three definitions of
market efficiency which differ according to the information
set available. In general, a financial market is efficient if
prices fully and instantaneously reflect »all available
information. More specifically, a financial market is weak-
form efficient if the information in past prices or returns is
not useful in predicting future returns. A market is semi-
strong-form efficient if all publicly available information is
not useful in predicting future returns. Similarly, strong
form efficiency requires both public and private information
to be of no use in predicting future returns. If one exchange
rate is influenced by another exchange rate's lagged
innovation or volatility, then this is a violation of semi-

strong efficiency.

5

There are institutional factors that could negatively
influence the efficiency of the foreign exchange market.
Advanced computer technology did not exist during the time
period and long distance telephone service was unreliable.
Also, Einzig (1962) pointed out that forward markets began to
slowly reappear after 1919 and resulted in forward markets
whose basic set up were not the same across geographical
boundaries. These institutional factors could slow down the
dissemination of information to market participants and hence
lead to a violation of market efficiency.

Many authors have pointed out the importance of "news" on
the behavior of financial markets; for example, Urich (1982),
Roley (1983) , O'Brien (1984) , Hoffman and Schlagenhauf (1985) ,
Hein (1985), Roley (1985), Bailey (1988), Cook and Hahn
(1988), Baxter (1989), and Schirm, Sheehan, and Ferri (1989).
These studies show, with varying degrees of success, that
policy announcements can be very important in describing the
behavior of the conditional mean of an asset's price. Thus,
the identification of important events, both economic and
noneconomic, even ex-post, gives the policy maker valuable
insight into the behavior of past returns. It is, therefore,
important to identify such events and to make allowances for
them in the analysis.

This paper is organized as follows. The next section
contains an analysis of the general time series properties of
both the spot and forward exchange rates, with specific

emphasis being given to the concepts of nonstationarity and

6
cointegration. Section 3 builds the basic model. Section 4
investigates the effects of "news" on the volatility of spot
exchange rates. Section 5 examines the existence of
volatility spillovers, where the volatility of one exchange
rate influences the volatility of another exchange rate.

Section 6 contains a summary of the conclusions.

2. GENERAL TIME SERIES PROPERTIES

This section examines the general time series behavior of
the log of the weekly spot rate, the 30-day forward rate, and
the 90-day forward rate. Although subsequent analysis in this
study only deals with the spot exchange rate, details
concerning the forward rates are included for interest. Unit
root tests are conducted to determine if the spot exchange
rate follows a martingale. Tests for equilibrium
relationships among various groups of exchange rates are also
conducted.

The data used in this analysis are taken from Einzig
(1937), and consist of exchange rates from seven countries:
Belgium, Britain, France, Germany, Holland, Italy, and
Switzerland. The rates quoted come from the Saturday of each
week. ‘When the market was closed on a Saturday, the last open
day before Saturday was used. All the exchange rates were
originally quoted with respect to the pound sterling.
However, triangular arbitrage is used to express all the rates
in terms of a numeraire U.S. dollar. Over the period of

analysis, the 0.8. dollar did not float freely and remained

7
tied to gold until 1933. Since one of the goals of this study
is to analyze the effect of news on the volatility of exchange
rates, a stable numeraire is necessary to ensure that any
movement in the exchange rate is due to movement in the
particular currency under examination. A list of the data is
provided in Appendix one.

The sample period for each of the series is from February
25, 1922 to April 4, 1925 which gives a total of 163
observations. However, the German sample period is truncated
in September 1, 1923, since severe hyperinflation led to the
suspension of the exchange of the Mark.

The existence of a unit root is an important issue to
consider. Fama (1965) showed that successive changes in stock
prices were uncorrelated, which is consistent with the
martingale model. Hence, the current price of an asset
reflects all available information and the expected one period
rate of return to speculation is zero, which is in accord with
weak form efficiency.

There have been many studies that examine the post
Bretton Woods data for unit roots. Table 1 contains a summary
of these results. Meese and Singleton (1982) , Corbae and
Ouliaris (1986) and Kim (1987) using weekly data, Baillie and
Bollerslev (1989a) and Coleman (1990) using daily data and
MacDonald and Taylor (1989) , Baillie and Pecchenino (1991) and
Shephton and Larson (1991) using monthly data show that a unit

root could not be rejected. Therefore, there is evidence that

8
daily and weekly exchange rates in the post Bretton Woods
period contains a unit root.

To test the validity of the conclusion of Meese and
Singleton, tests derived by Phillips and Perron (1988) and
Kwiatkowski, Phillips, Schmidt, and.Shin (1991) are:app1ied.to
all the series. lThe Phillips-Perron tests are used instead of
the Dickey-Fuller tests (Fuller (1976), Dickey and Fuller
(1979), and Dickey and Fuller (1981)), since the Phillips-
Perron tests are robust to many forms of time dependent
heteroskedasticity. This point is important since many
financial market time series exhibit time dependent
heteroskedasticity.

The Phillips-Perron tests involve running the following

three regressions using ordinary least squares:

Yt = a yt-l + “t (1)
* * *

Y1: = 4‘ + a Yt_1 + ut (2)

yt = u + fl (t - T/Z) + aYt_1 + ut (3)

where T is the sample size and at, u: and {it are regression
disturbances. In model (1) the null hypothesis of a unit root

is tested against the stationary alternative, Ho: 3 = 1,

versus Ha: & < 1 by the test statistic Z(t&).

9

{Model (2) provides a test for a unit root with or without
drift, Ho: (1* = 1 and Ho: u* = 0, a* = 1 by the test
statistics Z(ta*) and 2(01), respectively.

Model (3) , which allows for a deterministic trend, yields
the following three null hypotheses: Ho: d'==1, HO: 5= 0, d
a 1, and Ho: fi-== 0, 6 = 0, d = 1. These are tested by the
statistics 2(ta), 2(93), and 2(92), respectively. In all
models, ut is assumed to have limited memory and could be
autocorrelated. The one percent and five percent critical
values of all the above statistics are tabulated in Fu11er
(1976) and Dickey and Fuller (1981).

Table 2 shows the results of the Phillips-Perron tests
for each of the countries. Apart from Germany, a unit root
cannot be rejected for any exchange rate. The results for
Germany indicate the possible existence of an explosive root.
The joint hypothesis of a unit root with no drift is only
rejected for the Italian 90-day forward rate. The inclusion
of a time trend does not change the results. Overall, there
is strong evidence for the presence of a unit root for six of
the seven currencies.

The Kwiatkowski, Phillips, Schmidt, and Shin test
statistics (hereafter' KPSS) are jpartly' motivated. by' the
concern that standard unit root tests, which assume a null
hypothesis of nonstationarity, fail to reject the null
hypothesis too often. The KPSS test is based on a null

hypothesis of stationarity.

10
The KPSS approach assumes a components representation
that specifies the univariate time series as a sum of a
deterministic trend, a random walk and a stationary
disturbance. The test statistic is based on the Lagrange
Multiplier score testing principle. The KPSS test is defined

as:

-2 2 2
n = 'r zst/s (k). (4)
where
t
S = E e.
t i=1 1

is the partial sum of the residual ei, when the series has
been‘regressed on an intercept.and.possibly also a time trend;
T is the sample size. sz(k) is a consistent nonparametric
estimate of the disturbance variance and is computed using a
Bartlett window adjustment based on the first k
autocovariances as suggested by Newey and West (1987). The
test statistic is denoted by a“ when the residuals are
computed from an equation with only an intercept, and by at
‘whenta time trend is included in the regression. The critical

values of :7 and :71 are 0.739 and 0.216 at the 0.01 level and

p
(3.463 and 0.146 at the 0.05 level, respectively.

Table 3 contains the KPSS tests for the spot, 30-day
forward, and 90-day forward rates when the series are

regressed on a constant, and also when they are regressed on

a constant with a time trend for the k=4 and k=8 cases. For

11

the spot rates the hypothesis of trend stationarity can be
rejected at the 5% level in all cases except Germany. The
null hypothesis of level stationarity can be rejected at the
5% level for all countries except Britain and Holland. For
the 30-day and 90-day forward rates the results are similar.
The hypothesis of level stationarity can be rejected in all
cases except for both the 30-day and 90-day forward rates for
Britain and Holland. The null hypothesis of trend
stationarity can be rejected for all cases except for the
Italian series.

The results of the Phillips-Perron tests and KPSS tests
are strongly supportive of a unit root in the series and
suggest that all the series are nonstationary.1 The
Phillips-Perron tests indicate that German spot rate contains
an explosive root, which is intuitively appealing, given the
extreme currency depreciation that Germany experienced. The
only major discrepancy between the two tests is the behavior
of the British and Dutch series. However, given the fact
that, in general, exchange rate series, both in the 1980s and
19208, contain a unit root, analysis will proceed under the
assumption that they contain a unit root.

We now' consider the jpossible existence of long-run

cointegrated relationships among the various spot exchange

 

1 Phillips-Perron tests were performed on the first
differences of all seven series. The null hypothesis of
nonstationarity was rejected at the 1% level in every case.
Thus, there do not appear to be two unit roots in any of the
time series.

Sh
ce1
run
C011

the

12

rate series. Shepherd (1936) noted that the Belgian franc and
the French franc should have similar co-movements due to the
similarity’ of their' economic «conditions. Einzig (1937)
pointed out that the Belgian and French francs tended to move
together due to psychological factors. Aliber (1962) noted
that the Belgian and French francs moved together because
people believed that the French franc and the Belgian franc
would eventually equal each other, as they did in the pre-war
era. Finally, Einzig (1962) noted that the Belgian franc,
French franc, and the Italian lira should have similar
movements. He also stated that the movement of all western
currencies tended to be synchronized. Figure 13 contains
graphs of the log of the weekly Belgian, French, and Italian
spot rates for February 1922 through April 1925 and clearly
shows that there are common movements among the series at
certain times. Formally, this suggests there may be a long-
run relationship between the series which is consistent with
cointegration. Tests for cointegration attempt to identify
the existence of any long-run relationship between the
variables in question. Appendix 2 contains a formal
presentation of the Johansen (1988) and Johansen and.Juselius
(1989) framework for testing for the existence of a long-run
equilibrium relationship.

Table 4 contains the results of the Johansen (1988) trace
tests for cointegration between the six exchange rates and
also between the subsets of Belgium, France, and Italy, and

Belgium and France. The existence of a cointegrating

13

relationship among the variables can be rejected in all cases.
In addition, the residuals from a regression of the Belgium
spot rate on a constant and the French spot rate are
nonstationary, indicating a lack of .long-run equilibrium
relationship. Thus, despite the claims that certain spot
rates during this period should move together, there is no
evidence of a long-run cointegrating relationship.

There are strong theoretical reasons for believing that
forward premia are stationary. This hypothesis could not be
rejected on daily data in the 1980s by Baillie and Bollerslev
(1989). Figure 14 contains graphs of the log of the weekly
Swiss spot and 30-day forward rates for February 1922 through
April 1925. As expected, these two rates have many similar
co-movements. To test this hypothesis, trace tests were
repeated for both the spot rate and the 30-day forward rate
and the spot rate and the 90-day forward rate.‘

Table 5 provides tests for cointegration between the spot
rates and the 30- and 90-day forward rates for Belgium,
France, Italy, and Switzerland. Thus, for these pairs of
exchange rates, there exists a long-run equilibrium
relationship so that the forward premium is integrated of
order zero. Table 5 also contains the likelihood ratio values
for the hypothesis that the value of coefficients in the
cointegrating relationship between the spot rate and the
forward rate is: st = ft + 5t. In no case can this form of

the relationship be rejected. However, Table 5 indicates that

14
a long-run equilibrium relationship does not exist for the
British, Dutch, or German pairs.

Table 6 contains Phillips-Perron tests, KPSS tests, and
the autocorrelation functions for the 30-day forward.premium.
The results indicate that the autocorrelation functions decay
slowly for Britain, Holland and Switzerland; the existence of
a unit root cannot be rejected for these countries using
Phillips-Perron and KPSS tests. The results concerning
Switzerland are in direct contrast to those using the trace
test. Despite the result of the KPSS test the overall
evidence indicates that the German forward premium is
stationary.

Thus, the results from this section indicate that the
series in this study are nonstationary with the German spot
rate exhibiting explosive behavior. When the six spot rates
are considered as a system, the cointegration tests indicate
that there is no long-run equilibrium relationship. However,
the forward premia for Belgium, France, Germany and Italy are
stationary, where as those for Britain, Holland and
Switzerland are nonstationary. These characteristics are used

in the construction of the basic model in section 3.

3. THE BASIC NODEL

Section 2 suggests that the existence of a unit root can
not be rejected by the data. This result implies that it is
appropriate to specify the first difference of the log of the

spot exchange rate as

15

100 (Alog s = b + 6t (5)

t)

n - N(0,u) (6)

‘t' t-1
where st is the spot rate at time t, b is a constant, and 6t
is a random error term with a conditional normal distribution,
with mean zero and variance 0. The random error is
conditioned on n, the information set at time t-1.

Table 7 reports the results for six currencies together
with the Ljung and Box (1978) test statistic Q(k) for kth
order serial correlation in ct.2 The null hypothesis for the
Ljung-Box statistic is that changes in the spot rate are
uncorrelated while under the alternative hypothesis they are
generated by an AR(p) or MA(q) model. The only exchange rate
which appears autocorrelated is Belgium. The statistics m

3

and m are the sample measures of skewness and kurtosis, and

4
are defined as the third and fourth moments around the mean.
If the null hypothesis.of a normal distribution is valid, then
m

is asymptotically distributed as N(0,6/T) and. m as

3 4
N(0,24/T) . There is significant kurtosis present in all seven
series which is in agreement with the results on exchange
rates in the recent float; see Westerfield (1977), McFarland,
Pettit and Sung (1982) and Hsieh (1989), Baillie and

Bollerslev (1989b).

 

2 Since the unit root tests indicate that unit root
hypotheses for Germany may not be appropriate, the German
results are only approximately correct. While the results
appear in the tables, they will not be discussed formally.

16

Table 7 also contains the Ljung-Box test statistic for
serial correlation in the squared residuals. The null
hypothesis of no ARCH effects is rejected at the 5% level for
all the series.

One class of models that is consistent with this type of
behavior is the ARCH models of Engle (1982) and the GARCH
models of Bollerslev (1986b) and Engle and Bollerslev (1986).
GARCH models have been successfully applied to many types of
financial time series. Diebold and Nerlove (1989), Baillie
and. Bollerslev (1989), Lastrapes (1989) and. Baillie and
Bollerslev (1991) apply these models to exchange rates in the

present float. A regression model with GARCH innovations is

given by:
yt = xtb + 6t (7)
2
elnt_1 - N(0,at) (8)
2 __ 2 2
at - "0 + Eaiet_i + zfiiot-i (9)

where xt is a vector of exogenous, or predetermined variables,
it is a random error, and.A(L) and B(L) are polynomials in the
lag operator. Following the results of previous studies, the
GARCH(1,1) specification is imposed in the remainder of this

study; i.e.

100 (A109 st) = b0 + at (10)

con-
rem
for

Peru

17

etlnt-l - N(0,oafl (11)
2 2 2
at = "0 + 06t_1 + Bat_1 (12)

Table 8 contains the results of estimating this model for
all the currencies. The model was estimated using a Maximum
Likelihood procedure which utilizes the Berndt, Hall, Hall,
and Hausman (1974) algorithm. For all the exchange rates, the
likelihood ratio test that both a and 3 are equal to zero is
rejected. All coefficients are significant. There is no
evidence of autocorrelation for any of the series.

The GARCH(1,1) process is stationary if a + B < 1. When
a + 8 = 1 the process is integrated in variance or Integrated
GARCH (IGARCH). In this situation an 5 step ahead forecast of

the conditional variance is equal to the last value of the

2 _ 2
t+s - °t+1°

remains important for forecasts of the conditional variance

conditional variance, i.e. Ea Current information
for all horizons. Thus, a shock to the system today is
permanent.

Table 8 reveals that both the British and Italian series
exhibit a high degree of persistence with the sum of a and 6
being 0.867 and 0.943 respectively. For Belgium, France,
Germany and Holland the sum of the estimates of the a and 8
parameters exceeds unity. A likelihood ratio test that a + 3
= 1 could not be rejected for Belgium, Britain, France,

Germany, Holland and Italy.

of
EXC
est
impj
Valt
the
4.92:

Ital}

18

A feature of all the above models is the existence of
excess kurtosis in the residuals. Baillie and Bollerslev
(1989a) documented this same problem with exchange rate data
in the 1980s and they estimated a GARCH model with t-
distributed errors to daily, weekly, and fortnightly spot
exchange rate data. Table 9 contains the results from
estimation of the GARCH(1,1) model with a conditional Student

t density. The model is

100 Alog st = b + 6t (13)
e In no 02 v) (14)
t t-1 " ' t'

2 __ 2 2

at - u + aet_1 + fiat_1 (15)

where v is the degrees of freedom parameter, t is the Student-
t distribution and all other variables are as defined above.

The substantive conclusions from Table 8 are still valid.
The GARCH(1,1) model appears to be an adequate representation
of the first two conditional moments of the data. However,
excess kurtosis is still apparent for these models. The
estimated value of v, the degrees of freedom parameter,
implies a conditional kurtosis equal to 3(v-2)(v-4)-1. This
value can be compared to m4 in Table 9. The value implied of
the conditional kurtosis is 7.013, 11.915, 32.703, 4.425,
4.927, and 20.241 for Belgium, Britain, France, Holland,

Italy, and Switzerland respectively, which is much larger than

F011
Yt C1
Like;

19
the sample kurtosis as measured by m 4 for all countries except
Holland and Italy. Thus, using a Student-t density does not
fully account for the leptokurtosis in the data.

The presence of excess kurtosis can lead to inappropriate
inference and given the degree of excess kurtosis present in
the exchange rate returns all the estimated models used in
this study apply robust inference methods of weiss (1986),
Wooldridge (1990) and Bollerslev and Wooldridge (1991).

The robust procedure is based on a Quasi Maximum
Likelihood Estimator (QMLE) which uses the standard Gaussian
likelihood and is robust to departures from normality. The

robust procedure can by described by letting
“t(6) = Et-1(Yt)
02(6) = var ( )
t t-1 Yt

denote the conditional mean and the variance for yt as a
function of the px1 vector of unknown parameters 8. The

disturbances are given by
€t(o) . Yt - ut(6)°

Following Bollerslev and Wooldridge (1991), if the model for
yt correctly parameterizes ut(0) and o§(6), the Quasi Maximum
Likelihood Estimator (QMLE) for 6, say 6T , obtained under the

auxiliary assumption of conditional normality, will under

Not
der
Onlj
der j

c0nd

20
fairly general regularity conditions be VT consistent for the
true parameters, 00, and asymptotically normally distributed.
Furthermore, a consistent estimate for the asymptotic

covariance matrix for 6T is readily available, as

VT(AT'1fiT£T'1)’3(6T - 60) Q N(0,I) (16)
where

T
A- _1 A ' A _2A
AT- T £:1[V9"t(eT) vauthwt (9T)

2 . 2 -4 .
+ .5vbat(9T)'vbat(eT)'v at(eT)] (17)
A -1 T A -2 A A
= c
Br T ;:1[Ve“t(em) vact (9T) e(eT)

+ .sv60§(éT)'a;‘(8T)(e§<5T)-ai<5T)>1

v a'2(§T)e(§T) +

(9T). 9 t

Ve“t

.5 v9a§(éT)'a;‘(8T)(ei(§T)—oi(§T))]' (13)

Note, the expressions in (17) and (18) involve first
derivatives of the conditional mean and variance functions
only. This is particularly appealing when numerical
derivatives are being used. Also, when the assumption of
conditional normality is satisfied, the usual equalities hold

A_1A A- A- A..-
true; i.e., E(AT 3T AT = E(AT]) = E(BT]).

0‘

the
par
lik
star

d0 c

an a
meme“
fr”

sectic

e"Mai

rate c

21

While the preceding discussion assumed that the model
correctly parameterizes both the conditional mean and the
conditional variance functions, it is possible to show that
the asymptotic covariance matrix in (16) remains valid under
fairly' general conditions, when ‘the conditional. mean is
correctly specified, but the maintained .assumption of
conditional homoskedasticity, i.e. .02t(9) = w for all t, is
violated. In that situation, the covariance matrix in (16)
reduces to the well known covariance matrix adjustment in
White (1982). Using this estimate of the asymptotic
covariance matrix, Wald tests are conducted to test the
relative importance of news and to test for ‘volatility
overspills.

Table 10 reports estimates of the GARCH(1,1) models using
the robust standard error’ procedure. .As expected, the
parameter estimates and the value of the lmaximized log
likelihoods are very close to the results in Table 8; the
standard errors of the parameter estimates, on the other hand,
do change.

The results indicate that the GARCH(1,1) model provides
an adequate representation of the first two conditional
moments of the exchange rate series. The GARCH(1,1) models
from Table 10 are necessary for inference. In the next two
sections this model will be used to examine whether news
explains volatility and whether volatility of one exchange

rate causes others to be volatile.

Br;
COM
MOM

are

Patt.
Vith

are;

22

4 . THE IMPORTANCE OF NEWS AND THE VOLATILITY OP EXCHANGE
RATES

This section considers the importance of news for
explaining the volatility of the spot.exchange:rates~ Figures
15 through 20 plot the rate of return for each of the six
countries versus the conditional variance generated by the
GARCH(1,1) process from Table 10 for the period February 1922
through April 1925. Each figure indicates that large
fluctuations in the weekly rate of return are associated with
spikes in the conditional variance; these fluctuations in the
rate of return correspond to large innovations which, due to
the GARCH(1,1) specification, increase the conditional
variance. The focus of this section is to match the
innovations with known events.

Table 11 contains the dates on which an innovation was
greater than plus or minus two standard deviations away from
the mean and also the corresponding sign of the innovation.
Table 11 yields some interesting patterns” The only time when
the Holland spot rate has a significant innovation is when
Britain.has one (note the converse is not true); there are six
common movements. Belgium and France also share six common
movements, but unlike the Britain-Holland relationship, there
are three instances when the Belgium rate moves independently.

Further evaluation of Table 11 reveals eight distinct
patterns or "episodes"; an episode is a time period associated
with specific behavior of the innovations. The eight episodes

are: the Italian Episode, October 28, 1922 - November 18,

Vh
Mu
c0}
Wit
Dar
the
the;

The

23

1922; co-movement of the Belgian, French, and Italian spot
rates on November 18, 1922; the Swiss Episode, June 30, 1923 -
July 21, 1923; co-movement of the Belgian, Italian and Swiss
spot rates on July 7, 1923; co-movement of the British and
Dutch spot rates over the period November 10, 1923 - November
24, 1923; co-movement of the Belgian, British, Dutch, Italian,
and Swiss spot rates on NOvember 17, 1923; for France and
Belgium, the Bear Squeeze, March 8, 1924 - March 22, 1924; and
the co-movement.of the British, Dutch, and Swiss spot rates on

August 9, 1924.
The Italian episode covers the period from October 28,
1922 - November 18, 1922. This four week period consisted of
a week of sharp depreciation followed by three weeks of
appreciation. This episode is associated with the uncertainty
surrounding the coming to power of Mussolini's Fascisti Party.
The government of Signor Facta did not have the votes to
survive an election against the Fascisti. A consensus among
ministers was reached on October 16 that the government should
resign. This consensus quickly changed by October 18, 1922
when negotiations began between some of the old government and
Mussolini. The rise to power was not due to armed
confrontation, but from the support of the people. Associated
with the rise of Mussolini is the fall of Signor Facta's
party. This political event creates uncertainty not only from
the change in the type of government, but also from the
uncertainty associated with the policies of the new party.

The new government moved quickly to stabilize public opinion

PC
1a.

Ger
mad
192
Voui
bill

I85;

rePa;

going

24
and instituted policies of new revenue collection, the
elimination of many regional port authorities, and the
simplification of tax laws.

The second episode is the co-movement of the Belgian,
French, and Italian spot rates on November 18, 1922. In this
incident, different factors influenced the Italian lira and
the Belgian and French francs. The continued appreciation of
the Lira was a continuation of the perceived positive
influence of the new Italian government. The appreciation of
the Belgian and French francs was a corrective effort from the
over reaction of the previous week due to news on the
reparations issue.

On June 28, 1919 the Treaty of Versailles was signed
which required Germany to make reparations for all damage
"done to the civilian population of the Allied and associate
powers and their property by the aggression of Germany by
land, by sea and from the air" (Moulton and Pasuolsky 1929
p.10). The treaty did not fix the total amount for which
Germany was liable; the assessment of the total sum was to be
made by May 1, 1921 by a reparation commission. On April 27,
1921 the commission determined the total German liability
would be 132 billion gold marks with 68.64 billion, 13.20
billion and 10.56 billion going to France, Italy and Belgium
respectively.

During the week of November 11, 1922 settlement of the
reparation question (whether Belgium, France, and Italy were

going to receive payments) did not seem probable. The German

 

in
OD]
Swj
eff
Nat
the
For

Svis

Itali
Vbich

eX’Plaj

25

government, under the severe financial restrictions place upon
it by the reparations commission, was near collapse. The
collapse of the government would mean that Belgium and France
would be unable to receive reparation payments. However, at
the end of this week, a report published by a panel of experts
of the reparation committee indicated that Germany should be
able to make its payments given the current state of German
finances. This caused an appreciation of the French and
Belgian currencies.

The third episode, the Swiss episode, was a reaction by
the market to specific activities of the Swiss government.
The first two weeks of this period were marked.by depreciation
of the franc. This depreciation was caused by capital outflow
from Switzerland. This outflow was influenced by a threat of
a capital levy, a lower Swiss capital rate than other
industrialized countries, a scarcity of Swiss investment
opportunities, a high rate of taxation and the conversion of
Swiss francs to German marks by the German government. In an
effort to stop the depreciation of its currency, the Swiss
National Bank announced on July 14, 1923 that it would raise
the official discount rate to 4% and the Lombard rate to 5%.
For the next two‘weeks, there was a marked appreciation in the
Swiss franc.

The next episode is the co-movement of the Belgian,
Italian, and Swiss spot rates on July 7, 1923. The factors
‘which accounted for the depreciation of the Swiss franc are

explained above. The Belgian and Italian rates, along with

C0!

and
1921
Pure
norm
At t)
the 1
Briti
deman‘

affeCt

26

the French rate, were known as the reparation currencies.
These currencies should be effected by adverse news about the
reparations issue. In the week ending July 7, 1923
negotiations aimed at ending the Ruhr occupation had reached
an impasse affecting the Belgian and Italian currencies.

The French currency did not suffer during this time for
two reasons. First, the French government had been
considering a British proposal for a solution to the crisis
for approximately one month. Mbst French investors
anticipated the attitude of the French government (i.e. France
will not leave the Ruhr valley unless Germany agrees to pay).
Second, there was good news for France during this week as the
government passed the budgets for 1923 and 1924. While most
people realized that these budgets were unattainable, given
the protracted French budgetary process, this event was to be
considered a success.

The fifth episode is the exact co-movement of the British
and Dutch spot rates from November 10, 1923 - November 24,
1923. In Britain, there were heavier than usual seasonal
purchases of cotton and grain from abroad. These larger than
normal purchases meant a larger demand for foreign currency.
At the same time, there was.a capital outflow from Europe into
the United States. Much of the funds flowed through the
British currency market which affected the relative supply and
demand for pounds. While this effect was not news, it did

affect the British exchange rate.

th
ab
H01

Kal-

Qde

27

For the Holland currency, the situation is unclear. It
is possible that the Dutch authorities were reacting to what
was happening to the British pound. As mentioned above, there
are six common movements between the British and Dutch
innovations. The pound was the international currency.
Britain was the only European country that took explicit
economic steps to ensure a return to the pre-war parity
levels. The Dutch government may have been adjusting its
exchange rate in order to retain a certain level of purchasing
power between the two currencies. It is possible to test,
using the Johansen (1988) framework, whether there exists a
long-run relationship between these two spot rates. The trace
statistic for s 1 long-run relationship is 8.965 and for no
long-run relationship is 2.146. Both these values are well
below the critical values tabulated in Johansen (1988) . Thus,
there does not appear to be a long-run relationship.

The sixth episode is November 11, 1923, a day on which
the Belgian, British, Dutch, Italian, and Swiss rates all
depreciated. This is explained by the above mentioned
uncertainty in Europe. Investors wanted a safe haven for
their money. In addition, the U.S. interest rate climbed
above the British rate, thus giving investors better returns.
Money flowed out of Europe into the United States.

The seventh episode is the Bear Squeeze, March 8, 1924 -
March 22, 1924. French Premier, Raymond Poincaré, intended to
trap speculators operating on a bear market. On the week

ending March 8, 1924, French and Belgian currencies were under

In

1'!

es;
the
Cha

0f

Varj
hark
EVen;
elithe

°°Cou

28

speculative attack. Investors were liquidating their holdings
of francs. In an effort to punish those who were selling
short, M. Poincare secretly negotiated loans from 0:8. and
British banks. Acting as French agents, the banks started
buying large quantities of francs on March 11, 1924. The
severe depreciation was reversed and for the next two weeks,
both the French and Belgian francs appreciated sharply.

The final episode is August 9, 1924. On this day the
British, Dutch, and Swiss spot rates all appreciated, For the
Swiss rate, the realization by investors that the capital
levy was an unlikely occurrence caused an inflow of funds.
Also, there ‘was an ‘unexpected increase in 'tourism. into
Switzerland which increases the demand for the currency.
Thus, money flowed back into the country.

For the British rate, the unexpected agreement by the
inter-allied conference on the Ruhr occupation and reparation
question led to a strengthening most currencies, but
especially in Britain since Britain was the chief sponsor of
the conference. If changes in the gilder are related to
changes in the pound, Dutch authorities influenced the value
of its currency to reflect changes in the value of the pound.

Hodgson (1972) and Baillie and Bailey (1985) use dummy
variables in ‘their analyses of the 1920s exchange. rate
markets. Hodgson used dummies to proxy the occurrence of
events which might influence the evolution of the spot
exchange rate. Baillie and Bailey use dummy variables to

account for unpredictable periods of volatility. Lamoureux

 

by.
to

Oct
192
and
Rest
Sign
th€s<

Cendi

Varia,

29
and Lastrapes (1990) have shown that large outliers in the
innovation series implied that estimates of the conditional
variance parameters could exhibit extreme persistence.

Table 12 contains the tests that the eight episodes are
important for explaining 'volatile ‘movements in. the spot
exchange rate. For each date tested, a dummy variable is
included in the mean or the variance both individually and as
a group. The GARCH(1,1) model is estimated using the robust
estimation procedure and a wald test is calculated for the
significance of a dummy variable or of a group of dummies.
Under the null hypothesis of zero restriction(s), the Wald
test is distributed chi-squared with m degrees of freedom,
where m is the number of restrictions.

For inferences concerning the conditional mean, the null
hypothesis that the coefficient on the dummy variable is‘equal
to zero is:rejected.except for the following instances: Italy,
October 28, 1922; Switzerland, June 30, 1923 and July 14,
1923; Britain, November 10, 1923; Holland, November 10, 1923
and November 17, 1923; and Belgium and France, March 8, 1924.
Restrictions on a group of dummy variables are all highly
significant. Overall, excluding the above stated instances,
these episodes are significant for explaining movement in the
conditional mean of the spot rates in the GARCH(1,1) model.

The results for inferences about the conditional
variances are less encouraging; .All individual. dummies

associated. 'with. particular economic events are not

re

an
du
Br;
thi
Dut
NOV!
rate

sect

Volat
heat

to be
narke:
C3U595

a”othe

30
significant, while groups of dummies are highly significant
for the mean and variance.

Thus, the following observations can be made. First,
country specific events are important for explaining
volatility. Second, movement in the conditional variance is
only significant when a long episode of volatile movement is

observed.

5. VOLATILITY SPILLOVERS BETWEEN CURRENCIES

Section 4 demonstrated that there were times when certain
rates did react to the same news. For instance, the French
and Belgian rates during the Bear Squeeze, Belgium and Italy
during the reparations controversy, and the co-movement of the
British and Dutch rates. Moreover, a possible explanation of
this co-movement is that the British rate started to move and
Dutch officials intervened to adjust its currency. Thus,
movements in the British rate led to movements in the Dutch
rate. ‘This idea of a volatility spillover is examined in this
section.

Engle, Ito, and Lin (1990) developed two concepts of
volatility spillovers: heat waves and meteor showers. In a
heat wave, a reaction today in the New York market is likely
to be followed tomorrow by a similar reaction in the New York
market. A meteor shower is an occasion when an event that
causes volatility in the New York market is transmitted to

another market location.

at
0t
Co

th.

31

Engle, Ito and Lin (1990) using intra-daily foreign
exchange rate data report evidence in favor of a spillover
effect in volatility between different market locations.
Hamao, Masulis and Ng (1990) examine volatility patterns in
equity markets. Using opening and closing prices they find a
spillover from the New York market to the Tokyo market, but
not the converse. Baillie and Bollerslev (1991) using hourly
data on four' major floating exchange rates examine the
relationship between return and volatility in different
currency markets around the world. They find evidence that is
consistent with the meteor shower hypothesis.

All the above studies use finely sampled data and data
from several different markets. This study uses data from
only one market. Thus, the ideas of heat waves and meteor
showers are not directly applicable. However, the key idea of
seeing' how 'volatility spills over from. one currency’ to
another, either contemporaneously or with a lag, remains the
same.

The innovation, conditional standard deviation and
conditional variance series of the GARCH(1,1) model from Table
10 are used to examine volatility spillovers. The analysis
proceeds in three steps. The conditional mean equation is
augmented to include the estimated lagged innovations from
other countries both individually and as a group. The
conditional standard deviation of one currency is included in

the conditional mean equation for another currency. Hence

In

C4

de

de‘
are
sta
Nei

inf

00nd
CODG
38 a

What

32
volatility on one exchange rate is allowed to influence mean
returns on another.

The significance of any volatility term in explaining
mean returns would imply a rejection of market efficiency.
Thus, there are opportunities for profit exploitation.

Table 13 contains the results for estimation concerning
the conditional mean equation. The null hypothesis is that
the variable has a parameter value of zero. This hypothesis
is tested by a Wald statistic with a chi-squared distribution
with m degrees of freedom, m being the number of restrictions.
No estimated lagged innovation, individually or as a group, is
significant. Thus, despite some very large residuals in some
series, these residuals do not affect the behavior of other
conditional means.

There is some evidence that the conditional standard
deviation is important for explaining the conditional mean.
The:Dutch.conditional.mean is influenced.by the Swiss standard
deviation, but not conversely. The Italian and Swiss means
are affected by both the Belgian and French conditional
standard deviations as well as all five standard deviations.
Neither the Italian nor the Swiss standard deviation
influences either the French or Belgian conditional means.

Table 14 contains the results of inferences in the
conditional variance. Evidence is found that the Belgian
conditional variance and all countries' conditional variances
as a group influence volatility of the pound. This is perhaps

what should be expected. The spot rates come from the London

eX<
the
1m
het
390‘

effe

Sing

33

market. All transactions out of a certain exchange were made
in pounds. Thus, increases in the variability of spot rates
might cause investors to shift out of one currency into
another. The French rate is also affected by the Belgian
conditional variance, but not conversely. Both the Italian
and Swiss variances are affected by the British and Dutch
conditional variances. The Swiss rate is also influenced by
all the conditional variances as a group.

Overall, the market seems to be relatively efficient.
The Italian and Swiss rates seem to be the least efficient
with Belgian and French conditional standard deviations and
British and Dutch conditional variances being useful for
explaining the volatility of these rates. Yet despite the
seemingly primitive conditions of the 1920s foreign exchange

market, the market was relatively efficient.

6. CONCLUSIONS

This study attempts to uncover the behavior of the
exchange rates in the 1920s. Specific emphasis is given to
the ideas of nonstationarity, cointegration, martingale
models, generalized autoregressive conditional
heteroskedasticity, the impact of news on the volatility of
spot exchange rates, and the existence of volatility spillover
effects.

The exchange rates examined in this study all possess a

single unit root and are clearly nonstationary. A.martingale

he
es
ch

30

GA}
est
Sin
Ma
PM

the

par,

34
model was used since higher order moments of successive price
changes were not independent.

There is no long-run relationship between the spot rate
of Belgium, Britain, France, Holland, Italy, and Switzerland.
Thus, during this time, these rates showed.no tendency to move
toward any long-run equilibrium. This is significant since
most people believed that the spot rates would eventually
return to their pre-war parity levels.

There is a cointegrating relationship between the spot
rates and 30- and 90-day forward rates for Belgium, France,
Italy and Switzerland and evidence that the forward premium
are stationary.

The martingale models of section 3 were expanded to allow
for the presence of time dependent conditional
heteroskedasticity. A martingale GARCH(1,1) model was
estimated for the seven exchange rates. The model
characterizes the first two conditional moments of the spot
exchange rates well (with the possible exception of Germany).

There was the presence of excess sample kurtosis in these
GARCH(1,1) models. A conditional t distribution was
estimated, but this did not account for the leptokurtosis.
Since excess kurtosis can invalidate estimation concerning
mean and variance parameters, a robust standard error
procedure was employed. This martingale GARCH(1,1) model is
the one used throughout the remainder of the paper.

Inferences concerning conditional mean and variance

parameters were under taken to determine whether certain

re
re
ir

is

35

events cause increases in volatility. First, each spot rate
is influenced by its own market fundamentals. Second, events,
whether political or economic, affect the conditional mean
more than the conditional variance. Third, the conditional
variance is effected when a long string of events or one
particular event lasts for a long time. Thus, a cumulative
force is necessary for the conditional variance to be
effected. Overall, news affects the behavior of the spot
exchange rate.

The last section examines whether the volatility of one
exchange rate is transmitted to another exchange rate. This
question has direct implications for market efficiency. If
the increase in volatility of one rate causes another rate to
become more volatile, then knowing that the former rate has
jumped is useful information about the behavior of the latter
rate. Apart from some relationship between the Italian spot
rate and the French, Belgian, British and Dutch.rates and some
influence on the Swiss rate, for the most part the conclusion

is that the foreign exchange market is efficient.

36

TABLE 1

Summary of Unit Root Tests on Exchange Rates

Author

Meese &
Singleton
(1982)

Corbae &
Ouliaris
(1986)

Kim
(1987)

Baillie &
Bollerslev
(1989)

MacDonald &
Taylor
(1989)

Coleman
(1990)

Baillie &
Pecchenino
(1991)

Shephton &
Larson
(1991)

*

follows:

Canada,

Countries
Examined

CN, GR, sw

CN, GR, SW
FR, UK, JP

CN, FR, GR
IT, JP, SW
UK

FR:
JP,

IT, GR
SW, UK

as,
FR:
HL,
UK

BL, DN
GR, IT
CN, JP

AU, DN, FN
NZ, NW, sw,
SP, SD

BL,
FR:
JP,
UK

CN,
HR.
sw,

HL,
IT,
GR,

UK

CN, GR,
JP, UK

FR,

l/7/76

Sample

Period Methodology Results
1/7/76* - Dickey Unit

7/8/81w Fuller Roots
1/2/76 - Phillips Unit

1/2/85w Perron Roots
1973.1 - REGF NO Unit
1985.6 ,w,m Roots
3/1/80 — Phillips Unit

2/28/85d Perron Roots
1973.1 - Dickey Unit

1985.12m Fuller Roots
1/2/76 - Dickey Unit

12/30/88d Fuller Roots
6/1/73 - Dickey Unit

12/320/88d Fuller Roots
1973.3 - Phillips Unit

1990.5m Perron & Roots

KPSS
1975.7 - Dickey Unit
1988.12m Fuller Roots

The sample periods for Meese and Singleton (1982) are as
- 6/24/81;

West Germany, 1/7/76 -

7/2/81; and Switzerland, 1/7/76 - 7/8/81.

(grungy):

N

37

TABLE 1 (cont'd)

Key: AS = Australia, AU = Austria, BL = Belgium, CN = Canada,
ON = Denmark, FN = Finland, FR.= France, GR.=‘West Germany, HK
= Hong Kong, HL = Holland, IT = Italy, JP = Japan, NZ = New
Zealand, NW = Norway, SN = Singapore, SP = Spain, SD = Sweden,
SW = Switzerland and UK = United Kingdom.

KPSS = Kwiatkowski, Phillips, Schmidt and Shin tests.

REGF is an F test where the log first difference of the spot
rate is regressed on a constant and past first
differences, and the coefficients on the lagged first
differences are jointly tested for significance.

38

TABLE 2

Phillips-Perron Tests

2(ta) 2(ta*) 2(41) Z(t&) zuz) 2(43)
Belgium
st 1.026 -1.906 2.547 -1.048 1.718 1.850
132° 1.027 -1.910 2.556 -l.048 1.722 1.856
153° 1.029 -1.921 2.577 -1.056 1.734 1.874
Britain
st 0.814 -l.038 0.954 -l.136 0.866 0.890
152° 0.820 -1.015 0.936 -1.126 0.876 0.899
£20 0.828 -0.971 0.898 -l.108 0.894 0.923
France
st 1.121 -l.642 2.212 -1.775 2.103 2.122
£30 1. 118 —1.654 2 .227 -l.764 2 . 094 2. 115
£20 1.115 -1.674 2.253 -l.756 2.088 2.116
Germany
st 2.845 1.964 4.495 0.248 4.947 2.703
£30 2.378 1.678 2.833 -0.361 5.000 3.987
Holland
st -0.581 -1.438 1.231 -1.462 0.880 1.133
£20 -O.578 -l.464 1.266 -1.491 0.903 1.171
£20 -0.561 -1.511 1.326 -1.538 0.941 1.239

39
TABLE 2 (cont'd)

2(t8) Z(ta*) 2(01) Z(ta) 2(42) 2(03)

Italy ‘

st 0.740 -1.894 2.220 -2.558 2.558 3.325
£20 0.727 -1.907 2.241 -2.576 2.590 :3.387
£20 0.028 -11.695 331.837 -31.374 276.380 416.149
Swit

st 0.106 -1.485 1.121 -1.061 1.586 2.369
£29 0.103 -1.504 1.149 -1.148 1.605 2.398
£20 0.082 -1.679 1.686 -1.385 1.829 2.736

Key} The 5% critical values for z(t;), z(ta*) and z(t;) are -
1.95, -2.86, and -3.41 respectively. The 95% significance

level for 2(41), 2(92) and z(¢3) are 4.59, 4.68 and 6.25
respectively.

40

TABLE 3

Kwiatkowski, Phillips, Schmidt and Shin Tests

Spot Rates
No Trend
K=4 =8
Belgium 2.429 1.409
Britain 0.387 0.227
France 2.674 1.561
Germany 1.612 0.972
Holland 0.359 0.210
Italy 1.751 1.075
Switzerland 0.779 0.451
Trend

K= =8
Belgium 0.688 0.417
Britain 0.381 0.222
France 0.524 0.333
Germany 0.181 0.134
Holland 0.384 0.224
Italy 0.098 0.409
Switzerland 0.706 0.222

41

TABLE 3 (cont'd)

30 day forward rates

No Trend

K=4 K=8
Belgium 2.419 1.403
Britain 0.399 0.235
France 2.667 1.556
Germany 1.651 0.987
Holland 0.363 0.213
Italy 1.729 1.065
Switzerland 0.752 0.436

Trend

K= =8

Belgium 0.690 0.418
Britain 0.383 0.223
France 0.530 0.335
Germany 0.167 0.129
Holland 0.385 0.225
Italy 0.100 0.065
Switzerland 0.706 0.410

42

TABLE 3 (cont'd)

90 day forward rates

No Trend

=4
Belgium 2.406
Britain 0.425
France 2.648
Holland 0.374
Italy 0.872
Switzerland 0.728

90-day forward rates

Trend
=4 K=8

Belgium 0.693
Britain 0.387
France 0.541
Holland 0.392
Italy 0.059
Switzerland 0.698

=8
1.395
0.250
1.544
0.220
0.666
0.426

0.419

0.226

0.340
0.229
0.050
0.409

Key: The no trend test statistic corresponds to the partial
sum of the residuals from an OLS regression on a constant.

The trend case includes a time trend and a constant.

the number of lags in the residual series.

K equals

43

Table 4

Trace Tests For Cointegration

Spot Exchange Rates
=0 r51 r52 r53 r54 r55

all spot 66.520 43.517 24.431 12.670 4.780 0.072
rates

BL/FR/IT 16.338 5.871 2.329
spot

BL/FR 6.517 2.670
spot

Key: BL = Belgium, FR = France and IT = Italy. The number of
lags in the vector autoregression, K, to ensure white noise
residuals was set equal to 3. All spot rates refers to the
test of Belgium, Britain, France, Holland, Italy and
Switzerland.

44

Table 5

Trace Tests for Cointegration

Spot and Forward Rate Combinations

BL-30
BL-90

BR-30
BR-90

FR-30
FR-90

GR-30

HL-30
HL-90

IT-30
IT-90

SW-30
SW-90

28.161
21.589

3.716
3.928

32.128
28.460

10.535

15.764
14.698

31.712
46.648

22.311
28.964

IA

4.626
4.154

0.842
0.570

3.972
4.011

0.902

4.223
4.442

5.509
5.823

5.830
2.713

45

TABLE 5 (cont'd)

Likelihood Ratio Tests

3t=ft+5t

Spot - 30 day Spot - 90 day
BL 0.103 0.080
FR 0.150 0.127
IT 0.167 0.174
SW 0.057 0.146

Key : BL = Belgium, BR = Britain, FR = France, GR = Germany,
HL = Holland, IT = Italy and SW = Switzerland. To ensure the
residuals are white noise, K, the number of lags in the vector
autoregression was set at 3 for BL-90, FR30, FR90, BL/FR/IT,
and all spot; K was set equal to 4 for BL30, BR30, BR90, HL30,
HL90, IT30, IT90, SW30, and SW90. K was set at 5 for Germany.

Belgium
Britain

France
Germany
Holland

Italy

Swit

Belgium
Britain
France
Germany
Holland
Italy

Swit

-8.016

-1.308

-3.959

-2.234

-10.439

-1.794

Weekly 30-day Forward Premium

Z(t&)

-2.522

0.155

0.474

0.120

0.143

0.328

0.105

0.247

46

TABLE 6

Phillips-Perron Tests

Z(ta*)

-8.564
-1.559
-2.856
-4.878
-2.242
-12.479

-1.792

Trend

zeol) zeta“) 2042)
181.162 -10.074 160.120
1.234 -2.051 1.664
9.046 -3.244 8.244
59.181 -7.020 70.894
2.645 -2.218 1.766
350.875 -12.921 251.476
1.649 -2.179 1.646
KPSS Tests
No Trend
K=8 K=8 K=4
0.122 1.074 0.764
0.280 1.170 0.679
0.094 0.889 0.643
0.125 0.711 0.544
0.206 0.439 0.273
0.088 0.432 0.349
0.154 1.558 0.920

2(43)

240.315
2.493
12.20
109.737
2.641
377.457

2.646

Table 6 (cont'd)

47

Autocorrelation Functions

0.965

0.938

0.915

0.889

0.852

0.814

0.776

0.744

0.704

0.670

0.633

0.594

0.733

0.523

0.378

0.296

0.210

0.208

0.229

0.339

0.296

0.216

0.180

0.151

0.310

0.376

0.237

0.291

0.104

0.077

0.037

0.032

0.034

0.036

0.029

0.029

Belgium Britain France Germany Holland

0.910

0.823

0.760

0.709

0.631

0.568

0.517

0.466

0.410

0.353

0.317

0.259

Italy
0.098
0.190
0.122
0.079
0.075
0.067
0.070
0.056
0.087
0.043
0.035

0.040

Swit
0.951
0.911
0.875
0.836
0.749
0.794
0.709
0.678
0.632
0.587
0.546

0.519

The 5% critical values for Z(t&) Z(ta*) and Z(ta") are

L49
1 0.267
2 0.221
3 0.217
4 0.200
5 0.191
6 0.169
7 0.186
8 0.171
9 0.175
10 0.112
11 0.101
12 -0.012
Key:
-1.95,

respectively.

-2.86 and -3.41,

respectively.

The 95% significance
levels for 2(91), 2(92), and 2(43) are 4.59, 4.68 and 6.25,
For the KPSS tests, K is the number of lags in
the residual series; the 5% critical values are 0.146 when a
trend term is included in the regression and 0.463 when only
a constant is included in the regression.

48

TABLE 7
Estimation of the Model

100 A log st = b + 6t

et|0t_1-N(0,w)

BL

FR GR HL IT SW
b 0.324 -0.052 0.349 13.498 '0.026 0.129 0.009
(0.292) (0.050) (0.340) (3.167) (0.049) (0.145) (0.051)
0 12.008 0.383 13.883 627.168 0.302 3.353 0.441
(0.752) (0.027) (0.595) (66.878) (0.015) (0.292) (0.030)
Log L -431.23 '151.807 -443.732 '366.631 -133.114 -328.140 -163.23
C(10) 27.951 8.887 15.261 13.658 5.753 10.191 16.001
02(10) 40.043 18.090 18.717 10.130 61.105 75.541 28.073
m3 '0.974 -0.432 72.163 1.804 -0.041 0.162 0.215
m“ 8.229 6.041 18.774 6.605 10.483 4.275 6.572
Key : All countries were estimated for T' = 162 weekly

observations from February 25,

1922 through March 28,

Standard errors are in parentheses below the corresponding
parameter estimates; m3 and 1114 are respectively the sample
skewness and kurtosis coefficients of the standardized

residuals. Under the assumption of normality m3 ~ N(0,6/T)
and m4 ~ N(3, 24/T) asymptotically. Q(10) and 02(10) are the
Ljung Box statistics based on the first 10 lags of

autocorrelation of the standardized residuals, and the squared
residuals respectively.

49

TABLE 8
Estimation of the Model
100 A log st = b + 6t

2
6t|0t_1-N(0,e7t)

2 _ 2 2
at -—eo+a t:_1+fia t—1

BL BR FR GR HL IT SW

b 0.016 '0.060 0.211 4.839 0.004 0.145 0.029
(0.195) (0.039) (0.237) (2.476) (0.025) (0.148) (0.051)

0 0.258 0.075 0.761 31.584 0.014 0.200 0.141
(0.193) (0.034) (0.322) (36.035) (0.006) (0.084) (0.040)
a 0.521 0.387 0.429 0.606 0.490 0.214 0.410
(0.124) (0.142) (0.092) (0.236) (0.114) (0.083) (0.106)
3 0.591 0.480 0.586 0.565 0.533 0.729 0.287
(0.062) (0.123) (0.066) (0.144) (0.082) (0.070) (0.129)
Lo; L -398.98 -l41.482 -404.87 -358.54 -90.14 -310.92 ~146.48
Q(10) 13.12 15.57 7.34 10.90 .16.18 8.21 18.93
02(10) 7.72 10.70 13.40 7.44 7.01 14.29 2.79
ms 0.03 -0.76 0.18 0.46 0.03 0.35 0.06
m‘ 4.12 5.90 4.34 3.77 3.71 3.85 4.66
LR 64.50 20.62 77.72 16.18 41.97 34.44 33.50
Key : All countries were estimated for T = 162 weekly

observations from February 25, 1922 through March 28, 1925.
Standard errors are in parentheses below the corresponding
parameter estimates; m3 and m4 are respectively the sample
skewness and kurtosis coefficients of the standardized
residuals. Under the assumption of normality, 103 ~ N(0,6/T)
and m4 ~ N(3, 24/T) asymptotically. 0(10) and 02(10) are the
Ljung Box statistics based on the first 10 lags of
autocorrelation of the standardized residuals, and the squared
residuals respectively. The likelihood ratio test tests the
null hypothesis that a and fl = 0.

50

TABLE 9

Estimation of the Model

100 A log st = b +'6

t

2
e n ~t O a v
tl t-l ( ' t’ )
2 2
a =m+ae + a
t t-1 ’3 t-l
BL BR FR GR HL IT SW
b 0.103 -0.036 0.260 7.921 0.012 0.159 0.027
(0.173) (0.089) (0.194) (2.439) (0.025) (0.120) (0.041)
0 0.389 0.134 0.787 66.266 0.011 0.283 0.094
(0.338) (0.078) (0.531) (99.940) (0.006) (0.175) (0.055)
a 0.535 0.432 0.421 0.379 0.463 0.322 0.372
(0.196) (0.236) (0.189) (0.296) (0.150) (0.160) (0.183)
6 0.579 0.285 0.621 0.682 0.577 0.620 0.468
(0.053) (0.236) (0.105) (0.234) (0.101) (0.111) (0.192)
1/v 0.182 0.214 0.238 0.235 0.130 0.142 0.230
(0.053) (0.032) (0.039) (0.049) (0.065) (0.047) (0.053)
Log L -395.45 -131.11 -399.43 -355.57 -88.46 -308.64 -l40.62
0(10) 13.249 12.265 7.067 10.520 17.476 8.651 18.594
02(10) 7.568 10.107 15.117 7.424 8.287 17.234 3.950
m3 0.091 -0.893 0.169 0.617 0.069 0.414 0.175
m‘ 4.118 6.773 4.442 4.294 3.797 4.058 4.838
Key: All countries were estimated for T = 162 weekly

observations from February 25, 1922 through March 28, 1925.
Standard errors are in parentheses below the corresponding
parameter estimates; m3 and 1114 are respectively the sample
skewness and kurtosis coefficients of the standardized

residuals. Under the assumption of normality, m3 ~ N(0,6/T)
and m4 ~ N(3, 24/T) asymptotically. Q(10) and 02(10) are the
Ljung Box statistics based on the first 10 lags of

autocorrelation of the standardized residuals, and the squared
residuals respectively.

51

TABLE 1 0

Estimation and Robust Inference on the Model

100 A log s = b +'€

t t

2
6t|flt_1-N(0,Ut)

2 _ 2 2
O t-hH-Qé t_1+pa t‘l

BL BR FR GR HL IT SW

b 0.013 '0.060 0.203 5.247 0.004 0.152 0.031
(0.129) (0.049) (0.143) (1.271) (0.022) (0.083) (0.038)

O 0.268 0.076 0.763 34.701 0.006 0.201 0.140
(0.184) (0.042) (0.462) (24.860) (0.009) (0.193) (0.070)

a 0.517 0.394 0.429 0.581 0.483 0.215 0.410
(0.168) (0.137) (0.191) (0.232) (0.184) (0.087) (0.220)

6 0.591 0.473 0.586 0.571 0.533 0.728 0.290
(0.094) (0.181) (0.117) (0.095) (0.113) (0.124) (0.250)
Log L '398.99 '146.492 '404.87 -358.54 -90.14 '310.92 “146.48
C(10) 12.84 15.22 7.12 10.54 16.04 7.97 18.53

02(10) 6.98 10.52 13.04 7.21 6.73 13.82 2.72

as 0.03 ‘0.77 0.18 0.48 0.03 0.36 0.07

m‘ 4.12 5.92 4.33 3.80 3.71 3.86 4.66

Key: All countries were estimated for T = 162 weekly

obeervations from February 25, 1922 through March 28, 1925.
Standard errors are in parentheses below the corresponding
Parameter estimates; m3 and 1114 are respectively the sample
skewness and kurtosis coefficients of the standardized
residuals. Under the assumption of normality m ~ N(0,6/T)
and m4 ~ N(3, 24/T) asymptotically. Q(10) and 023(10) are the
L3 ‘ung Box statistics based on the first 10 lags of
autocorrelation of the standardized residuals, and the squared
‘35 siduals respectively.

 

52

Table 11

Volatility Patterns From Robust GARCH Estimation

15/24/22 IT:+ 8/11/23 GR,SW:+,-
7/8/22 IT:+ 9/1/23 GR:+
8/26/22 IT:+ 11/10/23 BR,HL:+
10/28/22 IT:+ 11/17/23 BL,BR,HL,IT,SW:+
211/4/22 IT,SW:- 11/24/23 BR,HL:-
11/11/22 IT:- 2/2/24 BR,HL:+
3.1/18/22 BL,FR,IT:- 3/8/24 BL,FR:+
12/16/22 BR:- 3/15/24 BL,FR:-
11120/23 GR:+ 3/22/24 BL,FR:-
2/17/23 GR:- 4/5/24 BL:-
6/30/23 GR,SW:+ 5/10/24 BL,FR:+
7/7/23 BL,IT,SW:+ 7/12/24 SW:-
7/14/23 sw:- 8/9/24 BL,BR,HL,SW:-
'7/21/23 SW:- 8/23/24 BR:+
'7/28/23 GR:+ 9/6/24 BR,HL:+

Key: BL = Belgium, BR = Britain, FR = France, GR = Germany,
fiI; = Holland, IT = Italy and SW = Switzerland. Each date is
associated with a residual value that is greater than plus or
minus two standard deviations away from the mean. The plus
(+) sign indicates depreciation of the currency whereas the
minus (-) sign indicates appreciation.

53

Table 12

Wald Tests From Robust Estimation with Dummy Variables

Mean Variance
Italian Episode
10/28/22 0.877 8.266
11/4/22 4271.380 0.623
11/11/22 4230.935 0.001
11/18/22 3204.054 0.552
10/28/22- 5896.790 7523.930
11/18/22
11/18/22
Belgium 6957.672 0.285
France 359.131 0.463
Italy 3204.054 0.552
Swiss Episode
6/30/23 0.010 3.147
7/7/23 14.955 6.001
7/14/23 0.480 0.396
7/21/23 15.485 0.003
6/30/23 - 298263.000 764.474

7/21/23

54

Table 12 (cont'd)

7/7/23

Belgium 730.781 (1.277

Italy 2444.000 0.655
Switzerland 14.928 0.024
11/10/23 -
11/24/23

Britain

11/10/23 0.071 2.26

11/17/23 137.825 0.647

11/24/23 1122.250 0.977
11/10/23 - 1372.57 170.985
11/24/23

Holland

11/10/23 0.096 3.196

11/17/23 0.528 1.441

11/24/23 6113.549 0.023
11/10/23 - 14998.300 1586.65
11/24/23
11/17/23

Belgium 94.974 0.841

Britain 137.825 0.647

Holland 0.528 1.441

Italy 2017.068 0.655
Switzerland 8.876 3.681

55

Table 12 (cont'd)

3/8/24 -
3/22/24
Belgium
3/8/24 0.029 2.067
3/15/24 1719.03 0.665
3/22/24 5127.127 3.415
3/8/24 - 76.785 816.883
3/22/24
France
3/8/24 0.019 1.056
3/15/24 1145670.501 0.426
3/22/24 8844.471 3.337
3/8/24 - 12409.200 17.337
3/22/24
8/9/24
Britain 25.708 2.985
Holland 7.731 3.651
Switzerland 121.893 1.368

Key: The mean and variance columns represent the Wald test
value when a dummy variable or a series of dummy variables is
placed in the mean or variance respectively. The values have
a 1%“) distribution where m is the number of dummy variables
in the conditional mean or conditional variance equation.

row 0

equat‘

€(BL)t_1

€(BR)t_1

£(FR)t—1

€(HL)t_1

€(IT)t_1

€(SW)t_1
5

2 2

j=1 jt-l

56

Table 13

Robust WALD Tests for Causality in the Mean

2
etlflt_1-N(0,O it)

2 ._ 2 2
a it'”1+°‘i‘ it-1+fli° it-l

Lagged Residual Values

BL BR FR HL IT
1.000 0.074 0.314 0.141 1.586
0.050 0.000 0.880 0.5000 0.00001
0.169 0.250 0.088 0.020 0.911
0.427 0.844 0.017 0.027 0.013
0.391 0.790 0.496 0.128 1.235
0.238 0.629 0.045 1.111 3.104
8.655 3.224 9.341 3.768 3.945

SW

0.132

0.545

0.141

0.0001

0.479

5.219

1.805

Key: All the elements in the first six rows have an asymptotic
112 distribution under the null hypothesis and the elements of

the last

row are asymptotically 152 distributed.

The final

row of the table denotes the Wald test statistic when all five
other lagged conditional residuals are included in the

equation

for mean returns .

included.

Own lagged residuals are not

Key

the
row
0the
the

SIG)“:

3(BL)t

3(BR)t

3(FR)t

3(HL)t

3(IT)t

3(SW)t
5

jilajt

Conditional Standard Deviation

BL

0.898

0.560

0.336

0.699

0.474

4.386

7.487

57

Table 13 (cont'd)

100Asit=bi+eit+yja 312'

BR

1.000

1.054

2.678

2.589

1.214

0.286

10.162

FR

1.128

0.055

2.384

0.007

0.084

0.046

4.302

HL

2.116

0.0001

0.826

0.184

2.028

4.054

6.517

IT

14.916

1.359

13.351

0.498

9.620

3.340

31.935

SW

9.434

0.183

5.556

1.0321

1.588

0.885

15.216

Key: All the elements in the first six rows have an asymptotic
x12 distribution under the null hypothesis and the elements of

the last row are asymptotically x52 distributed.

The final

row of the table denotes the Wald test statistic when all five
other lagged conditional standard deviations are included in
the equation. for' mean. returns.

Own lagged. conditional
standard deviations are not included.

 

 

°the;

58

Table 14
Robust Wald Tests for Causality in Variance

2
‘it'nt-I'N(°'° it)

2 _ 2 2 *2
" it‘”i+°‘i‘ it-1+fii° it-1+6j° jt

BL BR FR HL IT sw
62j(BL) ---- 20.250 4.514 0.563 1.000 0.111
3§(BR) 1.250 ---- 0.142 1.591 8.869 29.566
Ezju'R) 0.0003 1.000 ---- 0.444 4.000 0.442
Ezij) 0.857 1.000 0.028 ---- 9.990 5.760
3§(IT) 1.700 0.640 1.846 0.444 ---- 0.0001
3%(871) 3.642 0.016 0.307 0.009 1.313 ----

5 .
E azjt 4.922 26.542 8.291 3.476 5.838 26.865
i=1

Key: All the elements in the first six rows have an.asymptotic
112 distribution under the null hypothesis and the elements of
the last row are asymptotically x52 distributed. The final
row of the table denotes the Wald test statistic when.all five
other conditional variances are included in the equation for
the conditional variance. Own conditional variances are not
included.

AA
.4

 

59

Figure 1.
Log of the Weekly Belgian Spot Rate
February 1922 - April 1925

 

8.2 7

28—

2 4 lllllllllllll1“lllllllllllPllllllilllll§llllllllllllllrllllllllllllIllllllllllllllyllllHlllllIllllllllllllllyllllllllllllillllllllllll[Illllllllllllqllllllll

0 14 28 42 56 70 84 98 112 126 140 '154

WGGKS

Figure 2
Log of the Weekly British Spot Rate
February 1922 - April 1925

 

 

 

 

I

-1.44

I

-I46

-I48

-1.5~

I

-152

I

-154

I

-156

 

__1 58 IlllllllllllIPIIIHIIHIIIPIIIIlllllllllllllllllllllllllllllllll“1%!llllllllllllgllllllllllllljlllllll111111111111]llIll]lI}!!!lllIlllll[Illllllllllllllllllllll

 

 

O 14 28 42 58 7O 84 98 112 128 140 154

Weeks

-— - -
To
1..

.2...

a Go
a ..c

i...
AC

:18
AVG
AB
A. o

~53

0v
need

30

OJ

INC
3..
2...
m V

6O

Fi re 3
Log of the Week y French S ot Rate
February 192 - April 925

 

8(3—

3.1L

27-

 

 

2 3 lllllllllllllllllIllllllllllllllllllllllIllllllllllllllllllllllIlllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
. T I I I I r I f I I I

O 14 28 42 56 7O 84 98 H2 126 140 154
WOGKS
Fi re 4

Log of the Week y Dutch_Spot Rate
February 1922 - April 1925

 

I

(1995

I

(1975

I

 

(1955

I

(1985

I

(1915

 

 

O 895 lIlllllllllll:lllIlllllllll:llllllllllllllrlllllllllllllglllllllllllllllllllllllllllyIlllllllllll:lllllllllllIqllllllllllllllrlllllllllllllyllllllllllll:lllllllll

O 14 28 42 55 7O 84 98 112 126 140 154

WSSKS

 

 

PA .u
n./.

Q ...

:m.

149

r». u
«(L
Q v

phv
AH.

:9
a:

61

Figure 5
Log of the Weekly Italiah Spot Rate
February 1922 - Apr11 1925

 

 

 

 

815"
22 EB'ES llIllllllllllllllllllllllll:lllllllllllIIIIIlllllllll[III]IIIIIIIIIIIIJIIIIIIIIllll:lllllllllllllilllllllllllllg]llllllllllllIllllIllllllII%jIlllllllllllIlllllllll
. II

0 14 28 42 56 7O 84 98 H2 126 140 154
\Nbeks
F1 re 6

Log of the Week y SwissDSpot Rate
February 1922 - Apr11 1925

 

 

 

174'-
lIIIIlllllllllllllllllllllllllllllllllllIllllllllllllIllllllllllllllllllllllllllIllllllIlllllllllllllllllllllllllIIIIllllllllllllllllllllllllllllllllllllllllllllll
I. 63:22 I I I I I I I I I I I

O 14 28 42 56 7O 84 98 H2 126 140 154

VVBGKS

 

62

Figure 7
Belgian Rate of Return from Weekly Spot Rates
February 1922 - April 1925

 

 

 

 

 

 

 

O1 -
005-
Mn/A A 1.11 AAA
O V11 (1111 U
-005-
—O 1-
-O15—
‘02 I l I I I I I flifir I f
O 14 28 42 56 70 84 98 H2 126 140 154
Weeks
1 re 8
British Rate of Return from Weekly sSpot Rates
February 1922 - April 1925
002—
001-

 

‘001‘

 

~002-

 

 

 

 

‘0 03 I I 1 r 1 I 1 I l 1 I
0 I4 28 42 56 7O 84 98 H2 126 140 154

Weeks

63

 

 

 

 

 

 

 

 

 

 

 

Figure 9
French Rate of Return from Weekly2 Spot Rates
February 1922 - April 125
016
008-
O [AVVAnVMV AAVni/[A WVNwVAV‘WAVAVAVRV MN\ m A-
-008~
-O16-
-O24-
I I I I I I I I I I
O 14 28 42 56 7O 84 98 112 126 140 154
Weeks
Fiw re 10
Dutch Rate of Return from Weekly Spot Rates
February 1922 - April 1925
003
002-
001-
O
-OO1-
-OO2-
‘0 03 I | I I I I I I I I I I
O 14 28 42 56 7O 84 98 112 126 140 154

Weeks

 

64
Figure 11

Italian Rafee of Return from Weekly 5Spot Rates

ebruary 1922 - April 1925

 

 

 

 

 

 

 

 

I I f 1 1 1 I r I 1
I4 28 42 56 7O 84 98 I72 I26 I40
weeks
Fi

gurelz
Swiss Rate of Return from Weekly Spot Rates
Fe ebruary 1922 - April 1925

T
154

 

003

002

001

 

‘001

'C02

 

 

III/III“! MI 1 1111 m I
I W U I

 

I I I I I I I I I I

14 28 42 56 7O 84 98 H2 126 140

‘I‘Jeeks

I

154

 

 

:9

A

L

65

Figure 13 .
Log of the Belgian, French and ltal1an Spot Rates
February 1922 - April 1925

 

35

83*-

 

31 —

29"

 

27"

25*

 

 

 

2.317 I I I I I I I I I I I
O 14 28 42 58 7O 84 98 H2 128 I40 154

Weeks
— Belgian Spot Rate —+- French Spot Rate —I— Italian Spot Rate
Figure 14

Log of the Swiss Spot Rate versus the 30-Day Forward Rate
February 1922 - April 1925

 

 

 

 

1.78

1745

17—

166-

162 I I I I I I I e I I I
o 14 28 42 56 7o 84 98 112 126140154

Weeks

—‘— 8001 Rate — Forward Rate

...

66

. Figure 15
Belgian Conditional Variance versus Rate of Return
February 1922 - April 1925

 

 

 

 

 

 

 

 

 

 

Conditional variance Rate 01 Return
.15
200 - _ 0‘1
III .[ I [III
I50nvnvdlll. I 'I'L ‘ I A“ I LL. ,1
' I [I '1 II'II l N '1'" --w.-'IIO
100 — I — -o.05
— -0 1
50 r
-O 15
0 WW I I I I I I I , I -OI2
O 14 28 42 56 7O 84 98 H2 126 140 154
Weeks
—'— Rate of Return — Conditional Varrance
Figure 16
British Conditional Variance versus Rate of Return
ebruary 1922 - April 1925
Condition Variance Rate 01 Return
003
3 ” - 0102
l “001
2 i I i I
r" '11 I I "‘ ‘ ql r' I "L11 0
I I II 1 I III
1 I. - ‘O-OI
MK/ng %102
O _ I I I I I f I l I I I -003
0 14 28 42 56 7O 84 98 H2 126 140 154
Weeks

—'— Rate of Return — Conditional Variance

 

App

v‘v-

“4 4 ‘Y

W
Fi
French Conditional Var1ance versus Rate
February 1922 - Apr11 1925

Conditional Variance

of Return

Rate of Return

 

 

 

 

 

 

 

 

 

 

400
“01
300- \ PM
R-VARMHKAA‘AX VM l-hlw4flfl IMMV AV. ‘0
WW" I IWI VII
200
--01
100k
Wk - _02
2f\\___,1
0 WW I I I I quuuumutmmu -03
O 14 28 42 56 7O 84 98 H2 126 140 154
Weeks
—°— Rate of Return — Conditional Variance
Figure 18
Dutch Conditional Variance versus Rate of Return
February 1922 - April 1925
Conditional Variance Rate 01 Return
03
6' ~oo2
-001
4
I” “1IHI | I" [III“ I‘l‘l O
WWII!" "'i WNW!”
— ,1
2“ 00
1-002
0 I I I , N ‘—003
O 14 28 42 56 70 84 98 H2 126 140 154
Weeks

—°— Rate of Return —— Condition Variance

‘L

A)

68

Figure 19
Italian Conditional Var1ance versus Rate of Return
February 1922 - April 1925

Conditional Variance Rate oi Return

 

“0(76

 

 

 

 

 

IO
5 Y ~-OO2
- mO4
O ’— I f l l l I 1 l l I I ‘0.06
O 14 28 42 56 7O 84 98 H2 126 140 154
Weeks
—‘— Rate of Return — Conditional Variance

Figure 20
Swiss Conditional Variance versus Rate of Return
February 1922 - April 1925

 

 

 

 

Conditional Variance Rate of Return 0 O4
‘003
4— l
“002
3 ”[1001
2_W1Jiliij"puli IJ Muir.“ .rui,
1” 1“£ -001
1 .—
-002
O I I I I '0 03
O 14 28 42 56 7O 84 98 H2 126 140 154

Weeks

—°-' Rate of Return — Condition Variance

LIST 01' REFERENCES

69
LIST 0! REFERENCES

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Baillie, Richard T. and Ralph Bailey (1985), "International
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Baillie, Richard T. and Tim Bollerslev (1989a), "Common
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Baillie, Richard T. and Tim Bollerslev (1989b), "The Message
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Baillie, Richard T. and Tim Bollerslev (1991), "Intra Day and
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Baillie, Richard T. and Rowena A. Pecchenino (1991), "The
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Baxter, Marianne (1989), "Rational Response to Unprecedented
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(

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Engle, Robert F., Takatoshi Ito and Wen-ling Lin (1990),
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_ - ' K0

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Frenkel, Jacob and Kenneth Clements (1981) , "Exchange Rates in
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E

Hoffma

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m1 6' no. 1, 17-43.

III. PURCHASING POWER PARITY AND THE DEMAND FOR MONEY
IN THE 1920!

 

8)

pr

pos

excl

rel;

made
91>le
899 D

(1982;

CHAPTER III

PURCHASING POWER PARITY AND THE
DEMAND FOR MONEY IN THE 19208
1. INTRODUCTION

Cassel (1916, 1918) focused attention on the Purchasing
Power Parity (PPP) doctrine. Cassel believed monetary factors
to be the most important long-run determinant of the exchange
rate, though tariffs, transport costs, capital flows and
expectations could also be important. In its absolute form,
purchasing power parity states that the spot exchange rate,
defined as the price of domestic currency in terms of foreign
currency, adjusts to the ratio of domestic to foreign prices.
The relative version of PPP equates changes in the spot
exchange rate with changes in the ratio of domestic to foreign
prices.

This concept, in either of its forms, presents two
possible interpretations for PPP. Purchasing power parity can
be thought of as a short-run theory of the determination of
exchange rates, or alternatively as a long-run equilibrium
relationship.

The assumption of purchasing power parity is routinely
made when models of exchange rates are derived (for
applications to sticky prices, monetary, and dynamic models
see Dornbusch (1976), Frenkel and Johnston (1981), and Mussa

(1982) respectively.) Many authors, however, Roll (1979),

75

 

an.
tea:
are
evi

Lub;

Rush
I'Elat

76
Frenkel (1981), Darby (1983), and Hakkio (1984), find evidence
that real exchange rates follow a random walk.

The failure of PPP to exist as a short-run phenomenon
does not preclude its validity as a long-run equilibrium
relationship. When PPP is viewed as a long-run concept,
short-run departures are likely, but over time, these
departures should disappear and the spot exchange rate should
adjust to the ratio of relative prices (assuming PPP in its
absolute form).

Table 1 contains recent empirical results on the
existence of long-run PPP. The following observations can be
made. IKim (1990a, 1990b) and Diebold, Husted, and Rush (1991)
using annual data spanning several years find evidence
favorable to PPP. This long-run relationship is more evident
with wholesale prices than with consumer prices. The majority
of the studies using quarterly or monthly data over the post
1973 float reject the existence of PPP except for McNoun and
Wallace (1989) who analyze high inflation countries and Abuaf
and Jorion (1990) who used multivariate techniques to analyze
ten countries. Finally, the results pertaining to the 19208
are mixed. Frenkel (1980) and Taylor and McMahon (1988) find
evidence favorable to PPP, whereas Enders (1988), Ardeni and
Lubian (1989) and Ahking (1990) find evidence against.

The results from Table 1 are not surprising. Hakkio and
Rush (1991) point out that cointegration tests of equilibrium
relationships require long spans of data (hence the existence

of PPP in long annual data sets and the relative sparsity

 

Ci

15

CO
31‘.
exc
Feb

Pun

77
using quarterly and monthly data). They also point out that
the test results are difficult to interpret due to lack of
power of the tests.

The period.that is analyzed in this chapter is the 19208.
Table 1 indicates there is mixed support for the existence of
PPP during this period. The 19208 is another time in this
century when a whole system of exchange rates floated freely.
It was considered an interim period between a war-enforced
fixed exchange rate system and a proposed post-war fixed
exchange rate system. The behavior of the exchange rates in
the 19208 is very similar to that of the post 1973 system in
that both periods are explained by martingale difference
models, both contain time dependent heteroskedasticity, and
foreign exchange markets appear relatively efficient.

During the 19208, the spot exchange rates series and the
price series are quite variable. In fact, the Belgian and
French spot exchange rates depreciated approximately 80% from
1919 until these currencies were successfully stabilized.
Most price levels, which had moved greatly during the war,
continued to fluctuate after exchange controls were lifted in
1919. During the 19208 Germany experienced a severe
hyperinflation and Shepherd (1936) suggests that economic
conditions in France closely resembled that of hyperinflation,
although the maximum monthly French inflation rate only
exceeded nine percent during two months of this period,
February 1923 and January 1924. Both Britain and Holland

pursued domestic economic policies that were aimed at

 

th
US'
prc

inf

gene
exis
3 th.

analy

78
restoring pre-war convertibility levels of their exchange
rates. The 19208 is a period which experienced many short-
term monetary disturbances.

If purchasing power parity exists, it can be used to
generate testable restrictions that can be imposed on a model.
Consider, for example, the demand for money during high
inflationary periods. Cagan (1956) developed a model in which
theidemand for real money balances are assumed to be inversely
related to the rate of change of prices. Cagan assumed that
agents formed inflationary expectations adaptively implying
that expected inflation is a weighted sum of actual past
prices.

This chapter examines the nature of the purchasing power
parity relationship. The methodology which is employed uses
a Maximum Likelihood technique due to Johansen (1988). This
methodology tests for the number of long—run relationships in
a vector of nonstationary I(1) variables as well as tests for
the parameter values of these relationships. This study also
uses the forward premium to proxy expected inflation; this
proxy variable is used to explain the demand for money in high
inflationary episodes.

The plan of the chapter is as follows. In section 2 the
general time series properties of the data and tests for
existence of purchasing power parity are presented. In section
3 the demand for money during high inflationary periods is

analyzed. Section 4 contains the conclusions.

79

2. GENERAL TIME SERIES PROPERTIES AND THE EXISTENCE OP
PURCHASING POWER PARITY

In this section, the existence of long-run purchasing
power parity is examined for the following countries: Belgium,
Britain, France, Germany, Holland, and the United States over
the period 1921 - 1925.:1 The data on exchange rates comes
from Einzig (1937) and represent the last quoted spot rate for
each month. Price data come from two different sources:
wholesale and retail price data come from Tinbergen (1934).
For four countries, Britain, France, Germany, and the U.S.,
there also exists an additional price series published by the
League of Nations.2'3 Wholesale and retail prices are used
since Table 1 indicates that long—run PPP appears more
consistent with the use of wholesale prices, although there is
some evidence consistent with the use of consumer prices.

The test procedure represents the trace test for the
number of long-run equilibrium relationships from Johansen
(1988) . The test procedure is formally discussed in Appendix
2- A necessary condition for the Johansen procedure is that

the variables be integrated of order one. If a linear

1 The data period for Germany is 1921 - August 1923. The
data set is truncated in August due to the severe
hyperinflation that Germany experienced.

2 Monthly Bulletin of Statistics 1921-1925.

3 The retail price indices from Tinbergen (1934) are not
the Same for all countries. For Belgium and France the index
is a general retail price index. The German index represents
home goods. The British and Dutch indices measure retail food
prices. The United States index measures finished goods
Prices,

 

80
combination of the variables is stationary, then long-run PPP
exists.

Two tests for unit roots are employed. The first one is
the Phillips-Perron tests developed by Phillips (1987) and
Phillips and Perron (1988); the second test is due to
Kwiatkowski, Phillips, Schmidt, and Shin (1991). The tests
are formally described in section 2 of Chapter II.

Tables 2 and 3 contain the Phillips-Perron and
Kwiatkowski, Phillips, Schmidt and Shin (KPSS) tests for
different bilateral exchange rates and price series. There is
strong evidence that the monthly spot exchange rates are
nonstationary. The German series displays some instability
over the estimation period. The behavior of the monthly spot
rates is similar to that of the weekly spot rates which are
analyzed in Chapter II; in both cases the German spot rate
appears explosive and Belgium, Britain, France, and Holland
are nonstationary.

The behavior of the price series are similar. The German
price series appear explosive. The Phillips-Perron and KPSS
tests indicate that the wholesale, retail, and League of
Nations price series are integrated of order one. The only
disagreement between the two tests is the behavior of the U.S.
price series; the KPSS test is unable to reject stationarity.
Since the Phillips-Perron tests allow for more tests to be
conducted and the power of these tests may be influenced by
the small sample size, it is assumed that the U.S. series

contain a unit root.

ra
te

stl

the
bil
the

C0111]

Curr
who}.

Veth

81
Tables 2 and 3 indicate that the monthly spot exchange
rates and price series are integrated of the same order. It
is, therefore, appropriate to use the Johansen methodology to
investigate the existence of long-run purchasing power parity.

The absolute version of PPP is
8t = pt ' P t (3)

where st is the log of the spot exchange rate, pt is the log
of the domestic price level, and p*t is log of the foreign

price level. This relationship can be rewritten as
st - pt + p*t = "t (4)

where the quantity on the left hand side is the real exchange
rate. 'Thus, testing for the existence of PPP is equivalent to
testing that the errors in the real exchange rate equation are
stationary.

Table 4 contains the results from the Johansen trace test
that there exists r cointegrating vectors for all independent
bilateral exchange rate/price series combinations. Since
there are six countries, there are 15 independent
combinations.

There exists at least one relationship between all
currency combinations involving the United States when
wholesale prices are used. There are two cointegrating

vectors for the United States/Germany and United

82

States/Holland price and exchange rate combinations. There is
one relationship between the United States and Britain over
this sample period; this contrasts with Taylor and McMahon
(1988), Ardeni and Lubian (1989) and Ahking (1990) who, using
the Engle-Granger two-step method, are unable to find evidence
of a long-run. equilibrium. relationship over this period
although Taylor and McMahon were able to find one long-run
relationship when the sample period was shortened by twelve
months.

The use of retail prices yields similar results. The
currency combinations involving the United States still
exhibit a long-run relationship, although two relationships
now exist between the United States and Britain. The United
States/Britain relationship is the only one which exists for
currency combinations involving the pound. Also, the
relationships whidh emerge are in some instances different
from those using wholesale prices. For instance, when Belgium
is numeraire there are relationships between Britain, Holland,
and the United States using wholesale prices, but France,
Germany and the United States using retail prices. Foodstuffs
data from the League of Nations yield no long-run equilibrium
relationships.

One possible interpretation of multiple cointegrating
vectors is the existence of an informal monetary system.
Under this possibility, there is a long-run relationship
toward which the system would gravitate on its own; there

exists another long-run relationship which the countries are

83
trying to force the system to attain. In fact, the Genoa
conference in 1922 specified that Europe should return to the
Gold standard as soon as possible at pre-war parity levels.
One further hypothesis can be tested for those countries
that exhibit a single long-run relationship. Equation (4) is

a specific example of the more general specification

st = apt + bp*t + "t (5)

with the values of a and b being 1, -1 respectively. This
often assumed hypothesis implies that if both the domestic and
foreign price levels move by the same percentage amounts, the
spot exchange rate will remain unchanged.

This hypothesis can be tested in two ways. First, the
parameter values of the cointegrating vector can be
constrained to equal the hypothesized values. A likelihood
ratio test statistic is formed which is distributed as x:
where m is the number of restrictions when the number of
cointegrating vectors is one. The second procedure involves
unit root tests on bilateral exchange rate combinations.

Table 5 contains the Likelihood Ratio Statistics for the
hypothesis that when r=1 the coefficient on the spot rate is
1, the coefficient on the domestic price level is 1, and the
coefficient on the foreign price level is -1. In no situation
can the hypothesis be rejected that the coefficients in the

cointegrating vector are 1, 1, -1. Table 6 contains Phillips-

Perron and KPSS tests for the real exchange rates for the

84
fifteen bilateral rate combinations. Both tests indicate that
real exchange rates are nonstationary. Thus, the Johansen
methodology, Phillips-Perron tests and KPSS tests yield
conflicting evidence on the properties. of the purchasing power
parity relationship. The difference is possibly due to the
lower power of these tests when the sample size is small. In

section three, the existence of PPP is assumed.

3. NONE! DEMAND AND PURCHASING POWER PARITY

In this section, the Purchasing Power Parity results from
the previous section are used in the analysis of the demand
for money for the countries previously analyzed. The United
States is chosen as the numeraire since previous results
indicate similar behavior with other currency combinations and
the United States was a relatively stable numeraire. As
previously mentioned, Britain and Holland undertook specific
deflationary policies to force the spot exchange rate to
return to the pre-war convertibility level, while Belgium and
France underwent extreme currency depreciation and experienced
a potential monetary collapse with high rates of inflation,
and Germany endured a severe hyperinflation.

Cagan (1956) estimatedrthe.demand for real.money balances

during hyperinflationary times as

ln(M/P)t = y + anet + ‘t (6)

Va

on

Fri

the
How
has
Gen
1an
infl

85

where IM/P are real. money balances, "e are inflationary
expectations and 6t is a serially uncorrelated error term.
Cagan used a least squares procedure which maximized the total
correlation coefficient and found real money balances to be
inversely related to expected inflation, when measured as a
weighted sum of past inflation rates.

Many authors have extended Cagan's analysis of the German
hyperinflation (see, Sargent and Wallace (1973), Frenkel
(1977), Sargent (1977), Evans (1978), Salemi (1979), Frenkel
(1979), Abel, Dornbusch, Huizinga and Marcus (1979), Salemi
(1980a), Salemi (1980b), Desai and Rail (1986), Burmeister and
Wall (1987) and Christiano (1987)). One theme that
researchers analyze is IhOW' to :measure inflationary
expectations.

Cagan argues for the actual rate of inflation. Abel et
al. (1979) show that the actual rate can be used if it is a
proxy for true expectations but measured with error. Another
variable that Abel et al. suggest is the rate of expected
currency depreciation as measured by the forward premium.
Frenkel (1977,1979) had previously argued for the inclusion of
the forward premium in the German money demand function.
However, Salemi (1980a) showed that inflationary expectations
based solely on the forward premium were not rational in
Germany; by November 1922 the forward premium systematically
ignored information in the past history of the rate of

inflation. Salemi (1980b) showed that expected currency

0r

86
depreciation, measured as the first difference of the spot
exchange rate, did not influence the demand for money during
the German hyperinflation.

Suppose PPP does hold as a long-run relationship. Then

*
In St = 1n Pt - 1n Pt + 6t (7)
where s = the spot exchange rate, P = the domestic price
level, and P* = the foreign price level, and 6t is an

equilibrium error. If it were possible to observe

*

1n Pt+1 (3)

Etln st+1 = E ln Pt+1 - Et

*

° ' |
18 next per1od 8 spot rate and Pt+1 and Pt+1

next period's domestic and foreign price level respectively,

are

where st+1

then
ln st - Etln st+1 = (1n Pt - Etln Pt+1)
- 1 P*-El *
( n t t “ Pt+1) + "t' (9’
or
Et(1n Pt+1 — 1n Pt) = (Etln st+1 - 1n st) + pt + nt(10)
where

t *
"t = (1n Pt - Etln Pt+1) (11)

an

de

191
0f

Yie

87

is the expected inflation in the foreign country and "t is a
serially uncorrelated error term with E(nt) = 0. If inflation
is relatively moderate in the foreign country, then the rate
of domestic inflation is determined by the rate of currency
depreciation.

If the future spot rate equals the forward rate plus a
random error term, then
= f

s (12)

t+1 t + Et+1

where st is the spot rate in time t+1, ft is the forward

+1
rate and Et+1 is a random error term. However, equation (12)
suffers from the Siegal (1972) paradox; for purely
mathematical reasons, if the forward price of foreign currency
in terms of domestic currency equals the expected anticipated
future spot rate, then the forward price of the domestic
currency cannot equal the expected value of the corresponding
anticipated future spot rate. McCulloch (1975) has
demonstrated that this paradox is not relevant in empirical
applications; this study employs a log-linear specification
of equation (12).

Taking expectations and substituting into equation (10)
yields

8. —
fit - 1n ft In St + “t + nt (13)

no

im
Ger
eXC

Var

exp,

88

where n: is expected inflation, 1n ft - ln st is the forward
premium and the other variables are defined as above. The
existence of PPP implies that the forward premium can be a
measure of expected inflation if ~foreign inflation is
relatively stable.

Cagan (1956 p.91) observed that extreme short-term
changes in exchange rates primarily reflect variations in the
real value of the currency. The public might expect the
depreciation of the currency to manifest itself more
accurately in depreciation of exchange rates rather than
changes in prices since exchange rate data are observed more
frequently. But real cash balances would be related to
exchange rate depreciation only as long as it remains an
accurate indicator of price changes. The model for the demand

for real balances is
ln(M/P)t = a + B(ln ft - ln St) + Ct

where ln ft - ln st is the forward premium and Ct is a white
noise error term.

This model should be an adequate description for the high
inflation/hyperinflation countries of Belgium, France, and
Germany since there are extreme movements in their foreign
exchanges. British and Dutch foreign exchanges show less
variability than the other countries and this model should be

expected to perform less satisfactorily.

89

The forward exchange rate data comes from Einzig (1937)
and represents the quotation nearest the end of the month.
The money supply data and the price data come from Tinbergen
(1934) and the Monthly Bulletin of Statistics published by the
League of Nations. The price series are described in section
2 and the money supplies are the sum of currency outstanding
and deposits.

Table 7 contains the Phillips-Perron tests for real money
balances when both wholesale prices and retail prices are
used, the 30-day forward rate, and the forward premium.
British and Dutch real money balances are stationary using
wholesale prices. Germany and Belgium are nonstationary. The
results for France are mixed.4 For real money balances using
retail prices, the results are similar except that Belgian
real money balances behave in a similar manner to the French
balances. The 30-day forward exchange rates are all 1(1).
The forward premium is stationary in all cases except for
Germany.

The behavior of the British, Dutch and German monthly
forward premiums are in contrast to the behavior of the weekly
forward premiums analyzed in Chapter II; the weekly forward

premiums for Britain and Holland were nonstationary, whereas

 

‘ KPSS tests were performed for all series. The KPSS
tests for real money balances using wholesale prices indicate
that Britain, France and Holland are stationary where as
Germany is nonstationary. Also, Belgium appears stationary.
The same conclusions hold for real money balances when retail
prices are used. The forward rates are nonstationary and the
forward premiums are stationary with the exception of Germany
which is nonstationary.

90
Germany was stationary. Table 8 contains KPSS tests and
autocorrelation functions for the monthly forward premiums.
The autocorrelation functions decline rapidly for Britain and
Holland; for Germany the function declines more slowly. The
unit root tests indicate Britain and Holland are stationary,
and Germany is nonstationary.

Table 9 contains the money demand results for Belgium,
Britain, France, and Holland. The coefficients for Belgium
and France both have a negative sign and are significant at
the 5% critical level indicating that a depreciation of the
currency as measured by the forward premium results in a
decrease in the demand for real money balances. These two
countries are the ones that experienced. high levels of
inflation. For both the British and Dutch equations, the
forward premium is not statistically significant and is of the
wrong sign. However, there is evidence of autocorrelation for
Belgium, Britain, and France.

Table 10 contains the results for the money demand
equations when a first order Cochrane-Orcutt correction is
used. The correction for autocorrelation changes the signs on
all the estimated coefficients of the forward premium; the
Belgian and French coefficients are now positive, while the
British coefficient is negative. In no case is the forward
premium statistically significant.

One possible reason for the poor performance of the above
regressions is the absence of real income from the list of

explanatory variables. Actual real income data are scarce,

fc

Br

Co;
the

red

91

but for two countries, Britain and France, a proxy does exist.
The French real income data is the General Index of Industrial
Production from Tinbergen (1934). The British data are taken
from Frenkel and Clements (1981) who generate monthly real
income data by interpolating annual. industrial production
using the monthly unemployment series. Table 11 contains the
results for the inclusion of the log of real income in the
demand for money equation for Britain and France when the
Cochrane-Orcutt correction for autocorrelation is used.

When wholesale prices are used, the forward premium has
a negative sign for France, but a positive sign for Britain.
Neither coefficient is statistically significant.
Interestingly, the income variable takes on a negative sign
for both Britain and France and is statistically significant
in the French equation. This negative coefficient could
indicate that during high inflationary periods, an increase in
real income leads to a decrease in the demand for money and an
increase in the demand for some commodity which is a
relatively stable store of value.

The results for retail prices are similar. The French
income measure is negative and statistically significant. The
forward premium is negative in the French and positive in the
British equations, although neither is significant.

Table 12 contains the Johansen trace test for
cointegration for German real balances. The null hypothesis
‘that there exists a long-run equilibrium relationship between

real balances and the forward premium when both wholesale

PI

1' e.
ana

Pet

92
prices and retail prices are used to determine real balances
can be rejected. Thus, the forward premium does not help

determine the equilibrium level of real balances.

4. CONCLUSIONS

This study attempts to characterize the behavior of the
monthly spot rates and the monthly price indices in the 19208
period, investigates the empirical validity of the Purchasing
Power Parity relationship in its absolute form, and examines
the use of Purchasing Power Parity for generating economic
variables for the demand for money function.

Tests for the existence of PPP are carried out using the
Johansen trace test for all independent bilateral exchange
rate and price combinations for the countries of Belgium,
Britain, France, Germany, Holland, and the United States.
This test allows the number of long-run relationships to be
tested. Using both wholesale prices and retail prices, there
appears to be a long-run relationship between most of the
countries tested. For some countries, there is evidence of
more than one long-run relationship to which the exchange
rate/price combinations can move. There is no evidence of a
long-run relationship from any bilateral test when retail
prices collected by the League of Nations are used.

The results indicate the existence of PPP as a long-run
relationship. Furthermore, for some of the countries
analyzed, it does not matter which price level (wholesale or

retail) is chosen .

CC

f c
Th
C01
0n

Sig
(189‘
to

93

One further test is employed concerning the PPP
relationship. A regularly assumed hypothesis is that the
coefficients on the domestic and foreign price levels are
unity and minus unity respectively. For all bilateral
exchange rate/price combinations which exhibited a single
long-run relationship, the null hypothesis of unity and minus
unity cannot be rejected. Thus an equal percentage movement
in domestic and foreign prices does not lead to a change in
the spot exchange rate. However, tests of real exchange rates
indicate that they are nonstationary. This contradicts the
results from using the Johansen (1988) methodology.

The existence of multiple long-run relationships
complicates the interpretation and the usefulness of the PPP
doctrine as a policy guide. The problem for the policy maker
is not knowing which cointegrating vector the system is
operating under if there is more than one vector.
Nonetheless, the system is moving to some long-run
relationship.

When analyzing the demand for money for high inflation
countries, the imposition of PPP leads to the inclusion of the
forward premium as a measure of inflationary expectations.
The preliminary tests show that for the two high inflation
countries, Belgium and France, the signs on the coefficients
on the forward premium are the negative but not statistically
Significant. However, the results are influenced by a high
degree of autocorrelation. Correction for this problem leads

to the coefficient on the forward premium to enter with a

94
positive and insignificant sign for Belgium and France, and a
negative and insignificant sign for Britain. Further analysis
using income variables for Britain and France shows that the
forward premium has the required sign for France, but is not
statistically significant.

Both German real balances and the forward premium are
integrated of order one. Thus, the possibility exists that
there is a long-run equilibrium relationship between these
variables. A test for this equilibrium relationship fails to
find any evidence. Thus, the forward premium and the level of
real money balances do not seem to move together over time.

This general lack of relationship between the forward
premiums and the levels of real balances.is disappointing, but
perhaps not unexpected for these series. The data series are
very short. The maximum number of useable observations is
fifty-two. This sparsity of data could influence the
estimation of the money demand function.

Also, it.is possible that if the country is attempting to
either fix its exchange rate or force its exchange rate to a
specified level that the money supply process is linked to
exchange rate fluctuations or expectations of exchange rate
fluctuations. In this situation, estimation of the money
demand equation is contaminated by the money supply effect
‘which invalidates the results.

While the data sets are very short for the 19208 period,
there have been recent high inflation episodes. The existence

cut these episodes implies that this idea can be extended in

95
two areas. The first is whether PPP holds for these high
inflation countries. The second is, in the case where PPP
does hold, whether the forward premium provides an adequate

proxy for the level of expected inflation.

96

TABLE 1
Summary of Purchasing Power Parity Results

Author Sample Countries Methodology Results

Period Examined
Frenkel 1921.2; w BR,FR,6R, REGAR PPP
(1980) 1925.5 '
Adler & 1964.15 ** REGF Martingale
Lehman 1981.5
(1983)
1900w-+ BR,CN,FR, Martingale
1972 ' 6R,HL,IT,
JP,SW
Baillie & 1973.1 - EGZ no PPP
Selover 1983.120
(1987)
Rush 8 1954.1 5 BR,CN,FR, LowFreq PPPd
Husted 1982.IV 6R,IT,JP,
(1985) sw
Corbae & 1973'75 BR,CN,6R, E62 no PPP
Ouliaris 1986.9 IT
(1988)
Emders 1960.1; CN,GR,JP, E62 JP/US
(1988) 1971.4
1973.1-w CN/US
1986.11
Taylor 1973.6-m BR,CN,FR, E62 no PPP
(1988) 1985.12 GR,JP
Taylor & 1921.2; w BR,FR,6R, E62 PPP
McMahon 1925.5 ’
(1988)
Ardeni & 1921.2; BR,FR,6R, E62 no PPP
Lubian 1925.5 'w
(1989)
Karfakis & 1975.1; BR,FR,IT, EG2 no PPP
Moschos 1987.I JP,GE,GR

(1989)

97

TABLE 1 (cont'd)

McNoun & 1976.1*;* A6,BZ,CH, E62 PPP"
Wallace 1986.6 IS
(1989)
Abuaf & 1900; BL,BR,CN, DFSURE PPP
Jorion 1972 FR,GR,IT,
(1990) JP,HL,NW,
SW

1973.1-c

1987.12 MPPP
Ahking 1921.2; BR E62 no PPP
(1990) 1925.5
Kim 1900; BR,CN,IT, E62/JJ PPP
(1990a) 1987 JP

1914; no PPP

1987
Kim 1900; BR,CN,IT, E62 PPP
(1990b) 1987 JP

1914; no PPP

1987
Mark 1973.65 BL,BR,CN, E62 no PPP
(1990) 1988.2 FR,GR,JP,

IT

Diebold, 1791;+ BL,BR,FR, ARFIMA PPP
Rusted & 1913 GR,SD
Rush
(1991)
Baillie & 1973.35 BR KPSS/PP/ near unit
Pecchinino 1990.5 ARFIMA root
(1991)
w represents the wholesale price index
c represents the consumer price index
* For Germany, the sample period is 1921.1 - 1923.8.
+ 1915 - 1972 CPI
** There are twenty-two countries examined: AG, AS, BL, BR,

sz, CN, CH, DN, FR, GR, HL, IN, IR, IS, IT, JP, ux, NW, SA,
so, sw and VN.

98
TABLE 1 (cont'd)

d When the U.S. is numeraire, PPP is found to hold for all
bilateral exchange rate combinations. However, when
Britain, France and Germany are used, PPP is rejected for
all independent currency combinatiOns.

m represents manufacturing price index

*** The actual samples are: AR 1976.1 - 1986.6 (CPI), 1976.1 -

1985.3 (WPI); 82 1976.3 - 1986.2 (CPI,WPI),’ CH 1972.8 -
1979.12 (CPI), 1972.1 - 1979.12 (WPI); IS 1976.1 - 1985.12
(CPI,WPI).

++ The actual samples are: BL 1832 - 1913 (WPI), 1835 - 1913

(CPI); FR 1806 - 1913 (WPI), 1840 - 1913 (CPI); GR 1792-
1913 (WPI), 1820 - 1913 (CPI); so 1830_1913 (CPI); BR 1798
- 1913 (WPI); and US 1791 - 1913 (WPI).

Key: All exchange rates are in terms of U.S. dollars. AG
Argentina, BL = Belgium, BR = Britain, 32 = Brazil, CN -
Canada, CH = Chile, DN = Denmark, FR = France, GE = Greece, GR
=== Germany, HL = Holland, IN = Indonesia, IR = Iran, IS =
Israel, IT = Italy, JP = Japan, MX = Mexico, NW = Norway, SA
=== South Africa, SD = Sweden, SW = Switzerland, VN = Venezuela,

and US = United States.

E62 == Engle-Granger two-step method.
DFSURE = Dickey Fuller tests are extended to a system of

univariate autoregressions estimated jointly in a
Seemingly Unrelated Regression framework.

InasFREQ = A decomposition of the data into .a low-frequency

' trend component and a high-frequency noise component.

The trends are used in distributed lag regressions to

test for PPP.
REGF = F tests based on regressions estimating the real

exchange rate.

REGAR = OLS regression with correction for autocorelation.

JJ 8 Johansen-Juselius methodology.

ARFIMA = Autoregressive Fractionally Integrated Moving Average
model.

KPSS = Kwiatkowski, Phillips, Schmidt and Shin tests.

PP == Phillips-Perron tests.

I'owFreq = testing low frequency components.

PPP indicates evidence favorable to Purchasing Power Parity.
DIP-PP indicates marginal evidence.
I. o PPP indicates that the real exchange rate appears

M nonstationary .
a~1'1“i.:ingale refers to the Martingale model.

99

TABLE 2
Phillips-Perron Tests

Monthly Spot Exchange Rates 1921.1-1925.5
Belgium Numeraire

. . *
Br1ta1n France Germany Holland U.S.

z(t&) 1.350 -0.890 3.106 1.149 0.823
2(ta.) -0.768 —1.969 2.485 -0.884 -0.967
2(11) 1.465 2.204 5.642 1.404 1.009
z(ta) -1.622 -0.401 1.361 -1.497 -1.705
2(12) 2.220 1.835 5.581 1.979 1.621
2(13) 1.710 2.686 4.138 1.632 1.786

Britain Numeraire

France Germany Holland U.S.

2(ta) 1.367 2.791 0.920 1.139

z(ta.) -0.159 2.413 -0.975 -1.231
2(11) 1.080 5.295 1.220 1.695
z(ta) -2.525 1.255 -1.574 -1.670
z(12) 4.095 5.371 1.852 1.760

2(13) 4.997 4.031 2.164 1.510

100

TABLE 2 (cont'd)

France Numeraire

U.S.
0.785
-0.608
0.644
-2.295
2.844
3.842

Germany* Holland
3.131 1.206
2.497 -0.314
5.711 1.000
1.393 -2.463
5.654 3.889
4.128 4.976

z(t&)
2(ta*)
z(Il)
z(ta)
2(12)
z(13)

Germany Numeraire*

Holland
2.836
2.408
5.263
1.276
5.243
4.018

France
2.926

2.399
5.230

1.244
5.320
3.993

z(t&)
z(ta.)
2(11)
2(ta)
z(Iz)
z(I3)

Holland Numeraire

 

U.S.
z(ta) -1.081
z(ta¢) -1.514
2(11) 1.787
z(ta) -1.627
2(12) 1.535
2(13) 1.583

.22: (I!

Belgium

U.S.

z(ta) 1.289
*

2(ta ) -1.309

2(0 1.853

1)
2(ta) -1.013
2(42) 1.572

2(0 1.083

3)

Belgium

z(t;) 0.421
.2: (ta*) -o.620

z (0 0.315

1)
z (t;) -3.530

2) 5.141

3) 7.678

101

TABLE 2 (cont'd)

Wholesale Price Index

Britain

-1.592

-5.333

15.419
-4.690
10.763

13.698

Britain

-1.625

-3.547

7.421

-2.916

5.162

6.440

France

0.690
-0.336
0.336
-3.721
5.771

8.546

France

0.036

-1.331

0.905

7.318

10.999

Retail Prices

Germany' Holland
2.573 '1.667 '0.589
3.060 ‘4.344 -3.469
7.908 10.552 7.791
1.846 -4.111 '4.795
7.018 7.695 8.902
6.190 10.469 13.023
Germany’ Holland U.S.
1.356 -1.401 '0.961
0.894 I ‘2.368 '5.052
1.381 3.859 12.584
'0.272 -l.732 '4.457
2.122 2.601 8.820
1.825 2.922 12.493

I.

 

102

TABLE 2 (cont'd)

Retail Prices

League of Nations

Britain France Germany* U.S.
2(ta) -1.724 0.036 2.662 -0.811
2(tat) -3.547 ”1.332 2.899 '4.529
2(11) 7.421 0.906 6.930 10.810
2(t6) '2.916 '4.196 2.207 '4.469
2(12) 5.162 7.820 5.991 8.750
2(13) 6.440 11.756 5.566 12.706

i. 1921.1-1923.8
2‘ 1921.8-1925. 5

Key: The 5% critical values for z(t;) , z(ta*) and z(t;) are -
;JL.95, -2.86, and -3.41 respectively. The 95% significance

j]_evel for 2(91), 2(92) and 2(03) are 4.59, 4.68 and 6.25
r espect ive 1y .

103

TABLE 3

Kwiatkowski, Phillips, Schmidt and Shin Tests

Monthly Spot Rates

Belgium Numeraire

No Trend

k=4 =6
BR 1.045 0.773
FR 0.530 0.411
GR* 0.718 0.561
HL 1.033 0.764
US 0.951 0.706

Trend

=4 k=6
BR 0.174 0.139
FR 0.253 0.202
GR 0.200 0.171
HL 0.176 0.142
US 0.141 0.113

104

TABLE 3 (cont'd)

Britain Numeraire

FR
GR
HL
US

FR
GR
HL
US

No Trend

k=4
1.072
0.715
0.469
0.708

Trend

=4
0.114
0.200
0.068
0.169

0.799
0.558
0.439
0.550

=6
0.101
0.171
0.068
0.136

France Numeraire

GR
HL
US

GR
HL
US

No Trend

k=4
0.719
1.061
0.945

Trend

=4
0.200
0.118
0.135

0.562
0.789
0.707

=6
0.171
0.106
0.113

 

105

TABLE 3 (cont'd)

Germany Numeraire*

HL
US

HL
US

No Trend

k=4 k=6
0.715 0.558
0.712 0.556

Trend

k=4 =6
0.200 0.171
0.200 0.170

Holland Numeraire

US

US

No Trend

k=4 k=6
0.653 0.510

Trend

k=4 k=6
0.171 0.140

106

TABLE 3 (cont'd)

Monthly Wholesale Prices

 

No Trend

K=4 =6
BL; 0.894 0.664
BR 0.530 0.416
FR 0.989 0.737
GR* 0.709 0.551
HL 0.806 0.627
vs 0.182 0.157

Trend
=4 =6
BL 0.164 0.133
BR 0.259 0.202
FR 0.167 0.139
GR* 0.205 0.171
HL 0.265 0.214
us 0.079 0.070

107

TABLE 3 (cont'd)

Monthly Retail Prices

BL
BR
FR
GR
HL
US

BL
BR
FR
GR
HL
US

No Trend

k=4
0.902
0.736
0.681
0.559
0.674
0.274

Trend

=4
0.227
0.245
0.251
0.098
0.257
0.118

0.668
0.576
0.525
0.487
0.523
0.236

0.179
0.196
0.205
0.095
0.204
0.102

 

108

TABLE 3 (cont'd)

Monthly Retail Prices

League of Nations

BR
FR
GR
US

BR
FR
GR
US

5* 1921.1-1923.8
2F 1921.8-1925. 5

Jfitdayw The 5% critical values for the KPSS tests are 0.146 when
:5: ‘trend.term is included in the regression and 0.462 when.only
a constant is included in the regression;

No Trend

k=4
0.736
0.694
0.694
0.200

Trend

k=4
0.245
0.251
0.206
0.193

k=6
0.576
0.533
0.541
0.178

=6
0.196
0.206
0.170
0.171

number of lags in the residual series.

k represents the

109

TABLE 4

Johansen Trace Test for Cointegration

Belgium Numeraire

Wholesale Prices;

r=0 r51 r52
BR 39.466 20.134 5.147
FR 18.795 6.743 1.612
GR --- --- ---
HL 43.029 12.523 2.479
US 49.477 12.309 1.741

Retail Prices

r=0 r31 r52
BR 26.044 12.604 3.408
FR 37.911 19.745 6.894'
GR 39.266 6.152 2.198
HL 27.762 10.305 2.301
US 29.899 12.528 1.767

110

TABLE 4 (cont'd)

Britain Numeraire

Wholesale Prices

r=0 r51 r52
FR 35.210 14.584 4.362
GR 24.837 10.100 2.036
HL 27.745 7.056 1.513
US 31.728 14.853 6.070
Retail Prices
r=0 r51 r52
FR 26.847 11.355 2.445
GR 25.892 4.847 0.131
HL 26.334 12.784 4.644
US 47.698 20.555 8.361

Retail Prices -

League of Nations

r=0 r51 r52
FR 28.191 12.308 2.823
GR 19.385 8.884 2.588
US 27.329 15.446 4.620

GR
HL
US

GR
HL
US

111

TABLE 4 (cont'd)

France Numeraire
Wholesale Prices

r=0 r51 r52
20.528 10.490 4.348
36.304 11.193 1.144
31.443 7.951 0.167

Retail Prices

r=0 r51 r52
39.085 9.164 0.880
28.475 11.082 2.083
29.134 15.154 1.659

Retail Prices - League of Nations

GR
US

HL
US

r=0 r51 r52
25.731 12.740 5.719
25.364 12.148 0.812

Germany Numeraire
Wholesale Prices

r=0 r51 r52
29.079 10.690 4.483
29.104 16.336 6.287

112
TABLE 4 (cont'd)

Retail Prices

r=0 r51 ’ r52
HL 33.262 9.673 0.683
US 37.794 16.876 0.743

Retail Prices - League of Nations
r=0 r51 r52
US 22.635 11.562 5.414

Holland Numeraire
Wholesale Prices

r=0 r51 r52
US 42.443 22.264 3.807

Retail Prices

r=0 r51 r52
US 50.572 22.184 4.631

3 1921.8-1925.5

Key: BL=Belgium, BR=Britain, FR=France, GR=Germany, HL=Ho11and
and US=United States. The number of lags in the vector
autoregression to ensure white noise residuals was set equal

to 3 in all cases.

113

TABLE 5

Likelihood Ratio Test of Restriction 1, 1, -1 on
Cointegrating Vector

*
st=pt7pt+€t

Belgium Numeraire

Wholesale Retail

Germany --- 0.951
Holland 0.646 -—-
U.S. 0.819 0.282

Britain Numeraire

Wholesale
France 0.270
U.S. 0.163

France Numeraire

Wholesale Retail

Germany --- 0.760
Holland 0.464 0.225
U.S. 0.437 0.199

German Numeraire

Wholesale Retail
Holland 0.458 0.518
U.S. --- 0.264

Key: The number of lags in the vector autoregression to ensure
white noise residuals was set equal to 3 in all cases.

114

TABLE 6

Unit Root Tests of Real Exchange Rates

2(ta)
+
Belgium
BR 1.537
FR -0.649
HL 1.278
US 0.905
Britain
FR* 1.802
GR 3.032
HL 0.887
US 1.073
France
GR* 3.260
HL 1.487
US 1.028
*
Germany
HL 3.117
US 2.999
Holland
US -1.400

Phillips-Perron

Wholesale Prices

z(ta*)

-1.863
-1.365
-1.786
-1.200

-0.207
-2.895
-2.325
-1.729

-2.982
-0.215
-0.387

2.907
2.933

-1.378

2(01)

3.244
0.994
2.934
1.356

1.863
7.698
3.347
2.713

8.144
1.370
0.722

7.754
7.835

1.885

z(t;)

-1.232
-0.320
-1.088
-1.270

-2.187
1.664
2.184

-1.609

1.811
-2.265
-2.222

1.679
1.735

-1.485

2(02)

2.657
1.738
2.303
1.265

4.045
7.038
2.310
2.023

7.419
3.470
2.682

7.003
6.984

1.601

2(43)

2.143
2.606
1.896
1.139

3.221
5.505
2.925
1.712

5.917
3.262
3.248

5.579
5.692

1.339

z(ta)
Belgium
BR 1.811
FR* -0.209
GR 2.464
HL 1.340
US 1.091
Britain
FR* 1.752
GR 2.389
HL 0.769
US 1.003
France
GR* 2.486
HL 1.279
US 0.937
*
Germany
HL 2.432
US 2.344
Holland
US -0.982

115

TABLE 6 (cont'd)

Retail Prices

z(ta*)

-0.844
-2.422

2.567
-0.705
-0.805

-0.183
-2.557
-2.464
-1.493

2.537
-0.046
-0.256

2.588
2.596

-1.236

2(01)

2.310
3.267
5.732
1.479
1.105

1.594
5.655
3.709
2.179

5.656
0.927
0.549

5.751
5.781

1.222

'z(t;)

-1.374
-0.188

1.680
-1.603
-1.724

-2.809

1.615
-2.352
-1.629

1.682
-2.758
-2.428

1.643
1.706

-1.559

2(92)

2.881
2.584
6.406
2.125
1.792

5.199
6.164
2.553
1.854

6.418
4.101
3.159

6.131
6.155

1.178

z(03)

1.219
3.763
5.611
1.406
1.600

5.248
5.161
3.339
1.571

5.504
4.895
4.194

5.276
5.449

1.266

BR

HL
US

GR
HL
US

GR
HL
US

116

TABLE 6 (cont'd)

KPSS Tests

Wholesale Prices

Belgium
No Trend
k=4 k=6
0.896 0.668
0.257 0.206
0.886 0.659
0.832 0.616
Britain
No Trend
k=4 k=6
1.110 0.825
0.717 0.558
0.178 0.146
0.666 0.510
France
No Trend
k=4 k=6
0.719 0.560
1.087 0.804
0.992 0.736

Trend

=4

0.218
0.222
0.210
0.161

Trend

0.135
0.202
0.181
0.231

Trend

=4

0.202
0.129
0.155

0.170
0.180
0.164
0.129

0.116
0.171
0.146
0.176

=6

0.171
0.108
0.125

117

TABLE 6 (cont'd)

*
Germany
No Trend ~ Trend
k=4 k=6 k=4 k=6
0.715 0.557 0.202 0.171
0.712 0.555 0.202 0.171
Holland
No Trend Trend
=4 =6 k=4 k=6
0.775 0.588 0.218 0.170

Retail Prices

BR

GR
HL
US

GR
HL
US

Belgium
No Trend Trend
k=4 k=6 =4 k=6
1.099 0.814 0.180 0.146
0.677 0.525 0.249 0.205
0.722 0.576 0.164 0.153
1.056 0.780 0.168 0.135
1.016 0.751 0.136 0.109
Britain
No Trend Trend
k=4 k=6 =4 =6
1.114 0.831 0.101 0.097
0.733 0.575 0.168 0.155
0.297 0.264 0.097 0.088
0.748 0.575 0.218 0.171

118

TABLE 6 (cont'd)

France
No Trend ‘ Trend
k=4 k=6 k=4 =6
GR 0.725 0.577 0.164 0.152
HL 1.066 0.794 0.118 0.104
US 0.963 0.719 0.180 0.147
*
Germany
No Trend Trend
k=4 k=6 =4 =6
HL 0.721 0.573 0.170 0.157
US 0.718 0.572 0.169 0.155
Holland
No Trend Trend
k=4 k=6 =4 ‘ =6
US 0.640 0.490 0.211 0.166

+ 1921.8 - 1925.5
* 1921.1 - 1923.8

Key: The 5% critical values for z(t;), z(ta*) and z(t;) are -
1.95, -2.86, and -3.41 respectiveLy. The 95% significance
level for 2(91), 2(5) and 20%) are 4.59, 4.68 and 6.25
respectively. For the KPSS tests, k is the number of lags in
the residual series; the 5% critical values are 0.146 when a
trend term is included in the regression and 0.463 when only
a constant is included in the regression.

119

TABLE 7

Phillips-Perron Tests

Real Money Balances

Wholesale Prices

Belgium Britain France Germany
2(ta) -1.263 -0.966 -1.695 1.750
2(ta.) -1.537 -3.779 -3.015 -0.877
2(11) 2.084 7.922 4.250 1.823
2(t5) -1.229 -3.554 -3.219 -1.705
z(12) 1.663 5.738 7.823 4.308
z(I3) 1.449 8.154 13.384 3.105

Real Money Balances
Retail Prices

Belgium Britain France Germany
z(t&) -1.290 -1.037 -1.527 -1.342
2(tat) -2.862 -3.168 3.027 -1.232
2(11) 4.441 5.918 3.211 0.895
2(ta) -3.786 -2.616 -3.621 -1.716
2(12) 5.995 3.955 9.840 1.162
2(13) 9.023 5.372 17.541 1.618

Holland
-0.0573
-8.211
133.671
-8.680
102.827
154.876

Holland
-0.042
-7.589
117.949
-8.160
93.228
140.365

120
TABLE 7 (cont'd)

Forward Rates

U.S. Numeraire

Belgium Britain France Germany Holland
z(t&) 0.847 -1.056 0.822 2.803 1.109
2(ta') -0.986 -1.490 -0.590 2.364 -1.222
2(11) 1.055 1.725 0.670 5.070 1.642
2(ta) -1.687 -1.657 -2.288 1.229 -1.698
2(12) 1.633 1.148 2.889 5.094 1.720
2(13) 1.772 1.557 3.874 3.928 1.503

Analysis of the Forward Premium
U.S. Numeraire

Belgium Britain France Germany Holland
2(t5) -7.646 -3.431 -3.002 0.695 -3.394
2(ta') -7.403 -3.447 -2.849 0.519 -3.193
2(11) 86.835 10.308 9.654 1.082 9.362
z(ta) -7.268 -3.449 -3.862 -1.444 -2.975
2(12) 59.217 7.856 13.742 5.108 6.855
2(13) 89.700 11.514 21.993 7.970 10.215

Key: The 5% critical values for z(t;), z(ta*) and z(t;) are -
1.95, -2.86, and -3.41 respectively. The 95% significance
level for 2(0 2(02) and 20%) are 4.59, 4.68 and 6.25
respectively.

1).

 

121

TABLE 8

Analysis of the Monthly Forward Premium

KPSS Tests
No Trend Trend
k=4 k=6 =4 k=6
Belgium 0.055 0.081 0.145+ 0.205
Britain 0.130 0.094 0.357** 0.255**
France 0.085** 0.074** 0.698** 0.515+
Germany 0.192 0.150 0.650 0.439
Holland 0.083 0.071 0.308 0.243
Autocorrelation Function
Monthly Forward Premium
lag Belgium Britain France Germany Holland
1 0.025 0.542 0.556 0.670 0.568
2 0.012 0.386 0.459 0.467 0.383
3 -0.058 0.447 0.434 0.444 0.343
4 -0.203 0.333 0.304 0.376 0.134
5 -0.141 0.291 0.203 0.392 0.164
6 0.009 0.168 0.130 0.394 0.102
7 0.017 0.094 0.086 0.180 0.024
8 0.025 0.037 0.107 0.134 -0.036
9 0.011 -0.046 0.041 0.123 -0.111
10 -0.003 -0.165 -0.085 0.026 -0.192
11 0.019 -0.208 0.095 -0.067 -0.197
12 0.009 -0.242 -0.011 -0.115 -0.298
Key: The 5% critical values for the KPSS tests are 0.146 when

a trend term is included in the regression and 0.463 when only
a constant is included in the regression; k is the number of
lags in the residual series.

122

TABLE 9

Money Demand Estimation

ln(M/P)t = a + B(ln ft - ln st) + 6t

Wholesale Prices

BL BR FR HL
6 16.555 16.377 15.732 15.723
(0.025) (0.011) (0.032) (0.062)
a -38.591 7.439 -27.809 34.181
(14.437) (3.087) (7.152) (33.606)
R2 0.140 0.157 0.229 0.020
D.W. 0.197 0.340 0.356 2.103

Retail Prices

BL BR FR HL
6 16.665 16.308 15.908 , 15.729
(0.014) (0.011) (0.021) (0.063)
p -0.148 11.295 -18.934 30.027
(1.881) (2.557) (4.805) (34.363)
R2 0.001 0.277 0.233 0.015
D.W. 0.050 0.541 0.467 2.012

Key: BL = Belgium, BR = Britain, FR = France and HL =
Holland. All equations are estimated using ordinary least
squares. Standard errors are in parentheses. D.W. is the

Durbin Watson statistic.

123

Table 10

Money Demand Estimation with Correction for Autocorrelation

Wholesale Prices

BL BR FR

a 16.445 16.401 15.417

(0.102) (0.023) (0.270)

0 1.456 1.377 0.211

(4.495) (1.371) (2.891)

R2 0.941 0.782 0.906

D.W. 1.447 2.446 2.539
0.945 0.780 0.958

'3)

Retail Prices

BL BR FR

a 16.568 16.338 15.787
(0.239) (0.031) (0.149)

3 0.027 0.794 -0.357
(0.313) (1.575) (2.733)

R2 0.950 0.791 0.823
D.W. 0.939 2.243 2.400
0.989 0.811 0.929

D)

Key: BL = Belgium, BR = Britain, and FR = France. A11
equations are estimated using ordinary least squares with the
Cochrane-Orcutt autocorrelation transformation. Standard
errors are in parentheses. D.W. is the Durbin Watson
statistic.

124

TABLE 11

Money Demand Estimation with Real Income

1m(M/P)t = a + B(ln ft - In St) + yln(income)t + 6t

Wholesale Prices Retail Prices

BR FR BR FR

a 17.222 19.070 16.559 18.303
(0.793) (0.720) (1.007) (0.535)

6 1.642 -0.886 0.838 -1.325
(1.389) (3.120) (1.609) (2.859)

1 -0.180 -0.761 -0.048 -0.545
(0.174) (0.162) (0.221) (0.120)

R2 0.787 0.910 0.791 0.842
D.W. 2.523 2.094 2.257 2.071
5 0.788 0.761 0.818 0.696

Key: BR Britain and FR = All equations are

estimated using ordinary least squares with the Cochrane-
Orcutt autocorrelation transformation.
parentheses.

Standard errors are in
D.W. is the Durbin Watson statistic.

125

TABLE 12

Cointegration Tests for German Real Money Balances

Wholesale Prices

r=0 r51

6.494 2.206
Retail Prices

r=0 r51
7.584 0.895
Key:

The number of lags in the vector autoregression to
ensure white noise residuals was set equal to 3.

126
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APPENDIX 1

 

131

 

APPENDIX 1

Weekly Spot Exchange Rates

Belgium France Germany Holland .Italy Swit U.S.
2125/22 51.62 49.30 975 11.50 86.88 22.46 4.3975
314122 51.33 48.65 1086 11.53 84.13 22.54 4.3875
3111/22 52.07 48.83 1124 11.52 85.75 22.50 4.3600
3118/22 51.42 48.54 1228 11.56 85.50 22.51 4.4000
3/24/22 52.12 48.50 1400 11.59 85.50 22.56 4.3850
411122 52.12 48.50 1282 11.58 85.00 22.55 4.3775
418/22 51.97 48.10 1330 11.62 82.75 22.62 4.4000
4115/22 51.61 47.56 1277 11.63 81.00 22.69 4.4175
4122/22 51.50 47.40 1185 11.64 81.50 22.71 4.4200
4129/22 52.12 48.27 1206 11.60 84.00 22.77 4.4225
516/22 53.04 48.49 1231 11.57 82.75 23.01 4.4500
5113122 53.55 48.78 1280 11.50 84.75 23.06 4.4750
5120/22 53.55 49.07 1342 11.46 87.25 23.32 4.4475
5127122 52.87 48.87 1305 11.43 85.50 23.29 4.4500
613/22 53.16 49.09 1220 11.48 86.00 23.38 4.4750
6110/22 53.61 49.59 1333 11.50 87.50 23.52 4.4975
6117122 53.87 51.03 1432 11.49 89.50 23.42 4.4500
6124/22 54.82 52.16 1500 11.48 94.00 23.25 4.4025
711/22 55.52 52.64 1733 11.47 94.00 23.27 4.4200
718/22 58.80 56.00 2305 11.47 99.50 23.27 4.4525
7115/22 56.82 53.82 1965 11.46 97.25 23.16 4.4425
7122/22 56.09 53.10 2235 11.45 96.00 23.32 4.4600
7129/22 57.25 54.17 2877 11.48 97.50 23.26 4.4475
815/22 57.54 54.38 3362 11.51 96.25 23.43 4.4550
8112/22 57.57 54.46 3440 11.49 97.00 23.45 4.4625
8119/22 59.12 56.10 5540 11.49 98.50 23.48 4.4800
8126122 62.32 59.40 8500 11.44 103.00 23.46 4.4725
912/22 60.12 57.00 5750 11.45 101.50 23.48 4.4675
919/22 60.90 57.56 6200 11.46 102.50 23.50 4.4550
9116/22 61.72 58.26 6525 11.43 105.25 23.65 4.4300
9123/22 61.55 58.09 6087 11.41 105.00 23.66 4.4150
9130/22 61.56 57.77 7100 11.29 103.25 23.44 4.3700
1017/22 62.27 58.10 9670 11.37 103.00 23.60 4.4175
10114122 62.76 58.52 12070 11.39 104.50 23.96 4.4375
10121122 65.22 60.33 19200 11.40 106.50 24.44 4.4675
10128122 68.05 62.15 17950 11.43 112.50 24.69 4.4625
1114/22 69.97 64.97 26000 11.38 106.50 24.36 4.4675
11111122 74.06 69.52 35500 11.39 101.00 24.36 4.4600
11118122 68.12 63.75 29750 11.40 97.00 24.23 4.4800

11/25/22 67.90 62.97 31500 11.41 94.50 24.15 4.5000

 

1212/22
1219122

12116122
12123122
12130122

116/23

1113/23
1120/23
1/27/23
2/3/23

2110/23
2117/23
2124123
313123

3110/23
3117/23
3124/23
3131123
417/23

4114/23
4121/23
4128/23
5/5/23

5112/23
5119/23
5126/23
612/23

619/23

6116/23
6123/23
6130/23
717/23

7/14/23
7121/23
7128/23
814/23

8111/23
8118/23
8125/23
911/23

9/6/23

9/15/23
9122/23
9129/23
1016/23

10113122

Belgium

69.30
70.52
67.80
68.42
89.25
71.95
73.22
78.00
81.35
83.10
85.47
89.23
88.27
88.40
90.67
87.40
83.65
81.75
82.15
81.02
81.07
79.17
80.25
80.97
80.61
81.45
82.75
83.40
84.97
87.25
88.87
96.52
94.27
93.07
94.95
98.95
102.87
103.62
100.07
98.35
99.35
93.25
89.40
87.25
90.95
87.50

Franco
84.
64.
61.
62.
63.
66.
66.
70.
72.
73.
73.
78.
77.
77.
78.
75.
72.
70.
71.
70.
.07

70

68.
69.
69.
69.
69.
71.
71.
73.
.42
75.
79.
78.
.85
77.
78.
80.

74

77

82

25
70
62
65
57
20
82
70
25
02
35
45
60
45
00
02
17
40
00
05

22
30
95
42
87
25
85
15

62
12
32

90
90
75

.65
80.
80.
81.
77.
76.
74.
77.
74.

35
82
40
37
02
17
02
60

Germany

36000
37000
28700
31000
33200
39630
48500
85000
125000
165000
142000
80000
105000
106000
97000
97000
97000
101000
97500
98000
120000
136000
160000
194000
225000
251000
353000
390000
522000
485000
850000
960000
1075000
1600000
4500000
5200000
15000000
18000000
21000000
45000000

132

Holland
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
ll.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.
11.

41
47
61
67
71
74
80
78
76
87
85
86
89
89
89
89
89
88
88
89
88
86
83
81
81
82
81
76
76
77
68
65
73
71
63
62
60
58
58
55
53
55
56
57
58
55

Italy

93.
91.
91.
90.
91.

'82.

94.
97
97.
96.
96.
98.
97.
97.
98.
97.
96
93.
94.
93.
94
94
94
95.
95.
96.
98.
99.

100.
102.

108.
107.
106.
105.
105.
107.
106.
105.
107.
105.
102.
100.

99.
101
99.

25
00
50
75
50
00
00

.00

00
50
75
00
50
75
50
50

.00

25
00
50

.00
.00
.75

00
00
25
75
00
00
25
.00
50
75
00
00
50
50
25
25
75
00
00
75
25
.25
50

Swit

24.

24

24

24

25

25

12

.25
24.
.50
24.
24.
24.
.04
24.
24.
24.
24.
25.
25.
.20
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
26.
26.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
.25

47

45
55
73

86
85
93
97
04
09

23
37
33
43
57
64
52
62
71
65
66
62
66
67
73
89
68
54
95
66
54
15
20
20
19
19
53
55
45
48

U.S.

.5 . .b b D .9 .0 p o .5 a» a o’.o o .b a. o D b .5 .0 .o .o p a .o .5 by.» a .o .o OI a. D a. a» a. b a .3 .p .b o a

.5275
.5700
.6475
.6500
.6350
.6500
.6750
.6675
.6400
.6725
.6825
.6900
.7150
.7025
.7100
.6925
.6900
.6750
.6675
.6575
.6525
.6350
.6275
.6175
.6250
.6250
.6325
.6125
.6125
.6150
.5725
.5650
.6050
.5950
.5850
.5700
.5700
.5575
.5550
.5450
.5350
.5425
.5450
.5525
.5525
.5375

133

 

Belgium France Germany Holland Italy Swit 0.8.
10120123 87.70 75.85 11.55 100.25 25.27 4.5150
10/27/23 88.05 75.92 11.56 99.50 25.24 4.5000
1113/23 90.60 77.67 11.52 100.50 25.09 4.4550
11/10/23 90.55 78.30 11.55 100.50 24.95 4.3900
11117123 96.00 81.85 11.62 ,102.50 24.88 4.3000
11124123 93.92 80.87 11.46 101.00 24.97 4.3650
1211123 93.50 80.42 11.45 100.25 24.87 4.3400
1218/23 94.80 81.77 11.47 100.50 25.00 4.3600
12/15/23 94.97 82.15 11.45 100.50 25.08 4.3544
12122123 96.82 86.00 11.47 100.75 24.90 4.3425
12129123 96.77 84.82 11.39 100.00 24.77 4.3375
115124 99.87 88.30 11.37 99.88 24.65 4.2900
1112124 100.67 90.47 11.37 97.00 24.59 4.2650
1119/24 101.95 92.87 11.39 97.19 24.50 4.2350
1126/24 104.25 94.25 11.40 97.38 24.50 4.2275
212124 104.25 92.17 11.53 98.88 24.88 4.3450
219124 107.20 94.80 11.50 98.25 24.71 4.3000
2116/24 113.97 97.65 11.48 98.81 24.68 4.2875
2123124 113.75 99.75 11.53 99.25 24.90 4.3125
311/24 118.75 103.4 11.53 99.88 24.81 4.2975
318/24 131.37 117.0 11.54 101.00 24.80 4.2775
3115/24 109.75 89.81 11.55 99.83 24.77 4.2825
3122/24 102.50 81.25 11.63 99.69 24.86 4.2975
3129/24 100.00 78.45 11.64 99.00 24.77 4.3000
4/5/24 89.62 74.97 11.61 99.31 24.78 4.3125
4112124 85.12 72.40 11.63 97.50 24.70 4.3350
4119/24 81.25 69.57 11.70 98.25 24.75 4.3600
4126/24 80.62 68.75 11.77 97.56 24.67 4.3825
513/24 81.69 67.87 11.71 97.81 24.62 4.3875
5110/24 89.00 73.00 11.68 97.75 24.59 4.3700
5117/24 89.75 75.82 11.67 97.75 24.62 4.3675
5124/24 93.63 80.42 11.62 98.38 24.59 4.3450
5131/24 97.25 84.40 11.52 99.00 24.46 4.3050
6/7/24 95.50 84.85 11.52 99.13 24.48 4.3125
6117/24 94.13 80.82 11.55 99.25 24.45 4.3175
6/21/24 92.62 79.84 11.58 100.44 24.32 4.3325
6128/24 93.56 81.80 11.50 100.13 24.33 4.3200
715/24 97.44 86.02 11.47 101.31 24.27 4.3275
7112/24 96.12 85.07 11.56 102.00 23.98 4.3675
7119/24 95.87 85.57 11.53 101.50 23.99 4.3775
7126/24 95.75 86.12 11.51 101.44 23.89 4.4000
812/24 94.62 85.25 11.53 101.57 23.74 4.4200
819/24 90.25 82.15 11.61 100.63 23.85 4.5175
8116/24 86.50 79.40 11.62 100.63 24.08 4.5500
8123/24 90.75 83.45 11.59 101.63 23.97 4.4900
8130/24 89.06 82.12 11.62 101.20 23.88 4.5025

134

Belgium France Germany Holland Italy Swit 0.8.

916124 89.75 84.75 11.60 102.00 23.61 4.4375
9113/24 89.40 83.17 11.63 101.62 23.69 4.4600
9120/24 90.05 84.05 11.60 101.77 23.63 4.4650
9127/24 91.85 84.80 11.57 101.80 23.47 4.4725
1014/24 92.50 84.75 11.52 101.82 23.33 4.4625
10/11/24 93.97 86.57 11.47 I102.90 23.39 4.4900
11118124 93.37 85.82 11.49 102.85 23.38 4.4900
10125124 93.70 86.20 11.44 103.80 23.36 4.4900
1111/24 93.87 86.00 11.48 103.95 23.54 4.5325
1118/24 95.47 87.55 11.49 106.57 23.79 4.5850
11115124 95.80 87.65 11.54 106.95 24.02 4.6325
11122124 95.35 87.35 11.52 106.72 24.01 4.6350
11129124 94.42 85.82 11.46 106.47 23.95 4.6225
12/6/24 94.72 86.70 11.56 107.85 24.17 4.6800
12113124 95.00 87.57 11.63 108.80 24.22 4.6925
12120124 94.62 87.30 11.65 110.07 24.29 4.7075
12127124 94.62 87.27 11.65 109.87 24.24 4.7125
113/25 94.87 87.47 11.71 112.15 24.34 4.7475
1110/25 95.92 89.12 11.79 114.00 24.72 4.7850
1117/25 95.25 88.40 11.83 117.12 24.78 4.7738
1124/25 93.97 88.85 11.89 116.31 24.85 4.8000
1131/25 92.32 88.40 11.90 114.82 24.84 4.795

217/25 93.00 88.67 11.87 115.19 24.75 4.7750
2114/25 95.32 91.85 11.87 116.12 24.77 4.7750
2121/25 94.85 90.87 11.88 116.25 24.77 4.7650
2128/25 94.95 92.57 11.90 117.50 24.77 4.7600
317/25 94.15 91.65 11.93 116.75 24.76 4.7675
3114/25 94.62 92.75 11.97 117.62 24.80 4.7875
3121/25 94.35 92.10 11.98 117.56 24.79 4.7800
3128/25 93.15 90.60 11.98 116.75 24.78 4.7775
414125 94.20 92.32 11.99 116.37 24.78 4.7825

Key: The spot exchange rates come from Einzig ( 1937) and
represent end of the week quotations from the London exchange
market. All rates are quoted vis a vis the pound.

30-Day Forward Rates

Belgium France Germany Holland Italy Swit U.S.
2125/22 51.67 49.31 977 11.50 87.19 22.465 4.3969
314/22 51.38 48.66 1087 11.52 84.45 22.545 4.3863

3111/22 52.14 48.84 1125 11.51 85.92 22.505 4.3594

 

3118/22
3124122
411122
418122
4115/22
4122/22
4129/22
516/22
5/13/22
5120122
5127122
613/22
6110/22
6117/22
6124122
711122
7/8/22
7/15/22
7122122
7129/22
815122
8112/22
8119/22
8126122
912/22
919/22
9/16122
9123/22
9/30/22
1017122
10114122
10121122
10128122
11I4/22
11111122
11118122
11125122
1212122
1219122
12116122
12123122
12130122
116/23
1/13/23
1120/23
1/27/23

Belgian
51.
52.
52.
52.
51.
51.
52.
53.
53.
53.
52.
53.
53.
53.
54.
55.
58.
56.
56.

.27

57.

57.

59.

62.

60.

60.

61.

.62

57

61

61.
62.
62.
65.
68.
69.
74.
68.
67.
69.
70.
67.
68.
69.
71.
.26
78.
81.

73

50
19
19
05
69
57
19
11
61
61
90
19
64
90
85
55
83
86
11

53
58
13
33
18
95
79

63
33
82
26
07
99
60
13
91
31
55
90
46
30
99

04
38

135

France Germany Holland Italy
48.55 1229 11.55 85.68

48.50 1401 11.58 85.75
48.51 1283 11.56 85.17
48.11 1330 11.60 82.90
47.57 1277 11.61. 81.14
47.39 1185 11.62 81.65
48.26 1207 11.58 84.08

48.48 1232 11.55 82.83
48.77 1281 11.48 84.81
49.06 1343 11.45 87.31
48.86 1305 11.41 85.51

49.08 1220 11.46 86.02
49.59 1334 11.48 87.51
51.03 1433 11.47 69.51
52.14 1500 11.47 93.99
52.59 1731 11.46 94.00
55.95 2302 11.46 99.48
53.77 1958 11.45 97.24
53.05 2227 11.43 95.98
54.09 2667 11.46 97.25
54.28 3347 11.49 96.25

54.39 3410 11.47 97.00

56.02 5480 11.47 98.50

59.29 8350 11.42 103.00
56.89 5600 11.43 101.60
57.52 6000 11.45 102.58
58.22 6325 11.42 105.35
58.05 5787 11.40 105.12
57.74 6800 11.28 103.33
58.07 9170 11.35 103.08

58.46 11270 11.37 104.31
60.27 17700 11.39 106.60
62.05 15950 11.42 112.62
64.85 22000 11.37 106.62
69.22 28500 11.38 101.08
63.58 27750 11.39 97.18
62.87 27500 11.40 94.70
64.15 32000 11.40 93.70
64.58 32000 11.46 91.15
61.54 27200 11.60 91.75
62.57 29500 11.66 91.07
63.54 31200 11.70 91.72
66.11 36630 11.73 92.11
66.77 46500 11.79 94.20
70.64 77000 11.77 97.25
72.18 108000 11.75 97.25

SW16

23
23
23

23

24

24

.515
22.
.575
22.
.715
22.
.790
23.
23.
23.
23.
23.
23.
23.
.255
.270
.285
23.
23.
.275
23.
23.
23.
23.
23.
. 23.
23.
23.
23.
23.
23.
24.
24.
24.
24.
.240
24.
24.
.255
24.
24.
24.
24.
24.
24.
24.

575

645

730

030
080
335
300
395
535
435

175
340

445
430
500
480
500
520
675
680
460
620
970
450
690
370
375

160
130

470
510
455
545
730
950
863

a a».e .5 .e e .e .e .e .e e .e e e .o e .0 e .o a .e b».e .e e .e .e .e .e .e .e a» a. a. e .e e~.e .e o e- a».e .0 .e o

U.S.

.4000
.3850
.3772
.3994
.4169
.4200
.4222
.4497
.4469
.4463
.4488
.4738

.4486
.4016
.4194
.4513
.4418
.4582
.4444
.4525
.4600
.4775
.4700
.4644
.4525
.4275
.4113
.3663
.4138
.4338
.4625
.4563
.4625
.4510
.4700

.5175
.5600
.6375
.6375
.6238
.6400
.6650
.6575
.6300

 

135

Belgian France Germany Holland Italy Swit. U . S .
3118122 51.50 48.55 1229 11.55 85.68 22.515 4.4000
3124/22 52.19 48.50 1401 11.58 85.75 22.575 4.3850
411122 52.19 48.51 1283 11.56 85.17 22.575 4.3772
418/22 52.05 48.11 1330 11.60 82.90 22.645 4.3994
4115122 51.69 47.57 1277 11.61 81.14 22.715 4.4169
4122/22 51.57 47.39 1165 11.62 81.65 22.730 4.4200
4129122 52.19 48.26 1207 11.58 84.08 22.790 4.4222
516/22 53.11 48.48 1232 11.55 82.83 23.030 4.4497
5113/22 53.61 48.77 1281 11.48 84.81 23.080 4.4469
5/20/22 53.61 49.06 1343 11.45 87.31 23.335 4.4463
5127122 52.90 48.86 1305 11.41 85.51 23.300 4.4488
613122 53.19 49.08 1220 11.46 86.02 23.395 4.4738
6110/22 53.64 49.59 1334 11.48 87.51 23.535 4.4963
6117/22 53.90 51.03 1433 11.47 89.51 23.435 4.4488
6124/22 54.85 52.14 1500 11.47 93.99 23.255 4.4016
711122 55.55 52.59 1731 11.46 94.00 23.270 4.4194
718122 58.83 55.95 2302 11.46 99.48 23.285 4.4513
7115122 56.86 53.77 1958 11.45 97.24 23.175 4.4419
7122122 56.11 53.05 2227 11.43 95.98 23.340 4.4582
7129/22 57.27 54.09 2667 11.46 97.25 23.275 4.4444
815122 57.53 54.28 3347 11.49 96.25 23.445 4.4525
8112/22 57.58 54.39 3410 11.47 97.00 23.430 4.4600
8119/22 59.13 56.02 5480 11.47 98.50 23.500 4.4775
8/26/22 62.33 59.29 8350 11.42 103.00 23.480 4.4700
912/22 60.18 56.89 5600 11.43 101.60 23.500 4.4644
919/22 60.95 57.52 6000 11.45 102.58 23.520 4.4525
9116/22 61.79 58.22 6325 11.42 105.35 23.675 4.4275
9123/22 61.62 58.05 5787 11.40 105.12 23.680 4.4113
9130122 61.63 57.74 6800 11.28 103.33 23.460 4.3663
1017122 62.33 58.07 9170 11.35 103.08 23.620 4.4138
10114122 62.82 58.46 11270 11.37 104.31 23.970 4.4338
10121122 65.26 60.27 17700 11.39 106.60 24.450 4.4625
10128122 68.07 62.05 15950 11.42 112.62 24.690 4.4563
1114/22 69.99 64.85 22000 11.37 106.62 24.370 4.4625
11111122 74.60 69.22 28500 11.38 101.08 24.375 4.4519
11118122 68.13 63.58 27750 11.39 97.18 24.240 4.4700
11125122 67.91 62.87 27500 11.40 94.70 24.160 4.4900
1212122 69.31 64.15 32000 11.40 93.70 24.130 4.5175
1219/22 70.55 64.58 32000 11.46 91.15 24.255 4.5600
12116122 67.90 61.54 27200 11.60 91.75 24.470 4.6375
12123122 68.46 62.57 29500 11.66 91.07 24.510 4.6375
12130122 69.30 63.54 31200 11.70 91.72 24.455 4.6238
116/23 71.99 66.11 36630 11.73 92.11 24.545 4.6400
1113123 73.26 66.77 46500 11.79 94.20 24.730 4.6650
1120/23 78.04 70.64 77000 11.77 97.25 24.950 4.6575
1127123 81.38 72.18 108000 11.75 97.25 24.863 4.6300

Belsbun

136

213123

2110123
2117123
2124123
313/23

3110/23
3117/23
3124/23
3131123
417/23

4114123
4121123
4128123
515123

5112/23
5119/23
5126123
612/23

619/23

6116/23
6123/23
6130123
717/23

7114/23
7121/23
7128123
814123

83.
85.
89.
88.
88.
90.
.43
83.
81.
82.
81.
81.
79.
.28
81.
80.
.47
82.
83.
84.
.27
88.
96.
.31
93.
95.
98.

87

80

81

87

94

11
47
26
30
43
71

68
78
17
05
10
19

00
63

77
40
97

89
55

13
00
99

8111123
8118/23
8125/23

102.82
103.54
100.01

911/23
918/23
9115123
9122/23
9129123
1016123
10113122
10120123
10127123
1113123
11110123
11117123
11124123
1211123
1218123
12115123

87

90.
87.
87.
88.
90.
90.
95.
93.
.42
94.
.93

93

97

.25
99.
93.
89.
.21

26
15

88
45
65
00
54
49
94
85

74

France Germany Holland Italy
72.87 135000 11.86 96.80
73.23 117000 11.84 97.00
78.33 60000 11.85 98.30
77.50 69000 11.88 97.75
77.34 89000 11.88 97.96
77.91 92000 11.89 98.70
74.94 94000 11.89 97.73
72.09 94000 11.89 96.17
70.31 96000 11.88 93.44
70.95 91500 11.88 94.19
70.01 93000 11.89 93.70
70.03 111000 11.88 94.02
68.19 121000 11.85 94.21
69.26 143000 11.82 94.91
69.91 172000 11.80 95.13
69.39 199000 11.80 95.16
69.84 215000 11.81 96.40
71.21 308000 11.80 98.92
71.80 365000 11.75 99.17
73.10 489000 11.75 100.18
74.37 420000 11.76 102.46
75.56 680000 11.66 104.21
79.07 585000 11.63 108.75
78.30 725000 11.72 108.04
77.82 900000 11.70 106.32
77.86 2.9e+06 11.62 105.30
78.84 200000 11.61 105.79
80.71 9.0e+06 11.60 107.74
82.60 9.00+06 11.58 106.49
80.31 1.4e+10 11.58 105.51
80.77 2.56+10 11.55 107.97
80.37 11.53 105.22
77.32 11.55 102.18
76.00 11.56 100.94
74.14 11.58 94.44
76.94 11.58 101.41
74.57 11.55 99.15
75.82 11.55 100.16
75.88 11.56 99.68
77.60 11.52 100.60
78.21 11.55 100.06
81.74 11.62 102.59
80.77 11.45 101.09
80.36 11.43 100.18
81.71 11.44 100.56
82.10 11.42 100.56

Swit
24.880
24.940
25.000
25.070
25.125
25.220
25.260
25.405
25.370
25.470
25.600
25.690
25.563
25.660
25.750
25.675
25.685
25.635
25.675
25.680
25.750
25.915
26.685
26.520
25.945
25.660
25.510
25.090
25.120
25.140
25.140
25.135
25.515
25.535
25.400
25.450
25.210
25.235
25.205
25.060
24.920
24.845
24.930
24.840
24.975
25.055

U.S.

O .o a .o a a .b .0 o .p .p .5 .5 a- a~ a a 5 r o n b a a e- o a a .1 p .b .b 5 .b at b at a» O .o b' a. a o a» a

.6625
.6725
.6800
.7050
.6913
.7000
.6825
.6800
.6650
.6600
.6488
.8438
.8263
.6182
.6088
.6163
.6163
.6238
.6038
.6063
.6088
.5663
.5613
.6006
.5900
.5813
.5681
.5688
.5550
.5528
.5425
.5306
.5388
.5406
.5488
.5488
.5331
.5106
.4956
.4506
.3825
.2931
.3581
.3375
.3550
.3481

12122123
12129123

115124

1112124
1119/24
1126124
212124

219124

2116/24
2123124
311124

318124

3115124
3122124
3129124
415124

4112124
4119124
4126124
513/24

5110/24
5117/24
5124/24
5131124
617124

6117/24
6121/24
6128124
715124

7112/24
7119124
7126124
812/24

819/24

8116/24
8123/24
8130124
916/24

9113/24
9120/24
9127/24
1014124

10111124
11118124
10125124

1111124

96.
96.
99.
100
101
104
104
107

114.
113.
118.
130.
109.
102.

99.
89.
85.
81.
80.
81.
88.
89.
93.
97.
95.
94.
92.
93.
97.
96.
95.
95.
94.
90.
86.
90.
89.
89.
89.
90.
91.
92.
93.
93.

93.

Belgium

80
75
83
.64
.95
.27
.29
.22
02
55
50
47
20
00
85
57
07
23
60
69
65
65
53
10
38
06
55
49
37
02
86
73
59
25
48
72
02
72
39
05
82
43
92
31

80

France Germany Holland
85.
84.
88.
90.
92.
93.
91.
94.
.22
99.
102.30
113.45
86.
80.
77.
74.
71.
69.
68.
67.
71.
75.
79.
83.
.33

97

84

80.
79.
81.
85.
84.
85.
86.
85.
82.
79.
.39
82.
84.
83.

83

84

85

96
78
22
25
44
98
95
55

17

06
00
33
52
90
37
55
62
60
22
87
70

57
54
50
72
87
42
05
20
07
37

05
71
12

.00
84.
84.
86.

71
67
43

.67
86.
85.

07
84

113'7

11.43
11.34
11.35
11.34
11.36
11.37
11.51
11.48
11.46
11.52
11.52
11.54
11.54
11.63
11.64
11.60
11.62
11.69
11.76
11.69
11.67
11.66
11.62
11.51
11.51
11.54
11.57
11.49
11.46
11.56
11.53
11.52
11.54
11.64
11.64
11.60
11.63
11.60
11.63
11.59
11.56
11.49
11.45
11.47
11.42
11.45

Italy
100.79
100.14
100.58
97.06
97.99
97.49
98.99
98.34
98.92
99.34
99.95
101.08
99.81
99.75
99.07
98.37
97.54
98.24
97.59
97.81
97.88
97.88
98.38
99.00
99.11
99.25
100.44
100.17
101.31
102.07
101.58
101.54
101.64
100.75
100.80
101.83
101.32
102.09
101.74
101.99
101.91
101.91
102.99
102.94
103.86
103.95

Swit
24.870
24.725
24.605
24.565
24.485
24.490
24.870
24.700
24.670
24.675
24.770
24.760
24.730
24.620
24.740
24.740
24.660
24.715
24.640
24.595
24.570
24.600
24.575
24.450
24.460
24.430
24.300
24.300
24.240
23.950
23.940
23.640
23.630
23.730
23.960
23.650
23.770
23.560
23.620
23.580
23.400
23.260
23.340
23.330
23.320
23.520

U.S.

a o .b .5 .5 .3 0’ &* a».b .b .p r b b .b a».& .b u a a b b .b b a .0 o D 3 p tr.» .3 a b a .b .0 .b a a a b a

.3363
.3325
.2831
.2581
.2281
.2213
.3375
.2950
.2844
.3088
.2956
.2763
.2819
.2975
.2994
.3106
.3325
.3575
.3806
.3856
.3681
.3650
.3434
.3038
.3113
.3175
.3325
.3206
.3284
.3700
.3819
.4063
.4238
.5225
.5550
.4956
.5081
.4431
.4644
.4706
.4781
.4669
.4938
.4919
.4931
.5350

 

138

Belgium France Germany Holland Italy Swit U.S.
1118/24 95.37 87.25 11.46 106.57 23.760 4.5844
11115124 95.68 87.37 11.50 106.95 24.010 4.6325
11122124 95.23 87.15 11.47 106.72 23.940 4.6350
11129124 94.34 85.57 11.42 106.47 23.940 4.6228
1216/24 94.64 86.20 11.54 107.85 24.150 4.6797
12113124 94.93 87.19 11.62 108.87 24.200 4.6922
12120124 94.59 86.88 11.64 110.12 24.270 4.7072
12127124 94.58 86.80 11.63 109.92 24.200 4.7122
113/25 94.83 86.97 11.69 112.20 24.310 4.7456
1110125 95.92 88.69 11.79 114.05 24.720 4.7847
1117/25 95.25 88.16 11.83 117.17 24.780 4.7734
1124125 93.97 88.65 11.89 116.36 24.850 4.7997
1131125 92.30 88.12 11.90 114.87 24.840 4.7944
217/25 92.92 88.32 11.87 115.24 24.760 4.7741
2114/25 95.23 91.40 11.87 116.18 24.775 4.7741
2121125 94.78 90.44 11.90 116.32 24.770 4.7644
2128125 94.87 92.09 11.92 117.60 24.780 4.7594
317/25 94.14 91.33 11.95 116.83 24.770 4.7675
3114/25 94.63 92.50 11.99 117.68 24.810 4.7875
3121/25 94.35 91.88 12.00 117.64 24.790 4.7800
3128125 93.18 90.30 12.00 116.83 24.790 4.7781
414/25 94.23 91.75 12.00 116.54 24.790 4.7828

Key: The 30-Day forward rates come from Einzig (1937) and
represent end of the week quotations from the London exchange
market. All rates are quoted vis a vis the pound.

90-Day Forward Rates

Belgium France Holland Italy Swit U.S.
2125/22 51.77 49.32 11.493 87.81 22.48 4.39563
314/22 51.48 48.67 11.493 85.09 22.56 4.38375
3111/22 52.28 48.85 11.490 86.26 22.52 4.35813
3118/22 51.65 48.56 11.530 86.04 22.53 4.40000
3124/22 52.33 48.50 11.545 86.25 22.61 4.38469
411122 52.33 48.52 11.520 85.51 22.63 4.37656
418/22 52.21 48.12 11.560 83.20 22.70 4.39813
4115/22 51.84 47.58 11.555 81.41 22.77 4.41563
4122/22 51.70 47.37 11.580 81.94 22.77 4.41906
4129122 52.33 48.25 11.540 84.24 22.83 4.42156
516/22 53.25 48.46 11.510 82.99 23.07 4.44906
5113/22 53.79 48.75 11.440 84.92 23.12 4.44563
5120/22 53.79 49.04 11.415 87.42 23.37 4.44375
5127122 52.96 48.84 11.363 85.53 23.32 4.44625

 

 

613/22
6110122
6117/22
6124122
711122
718122
7115122
7122122
7129122
815122
8112/22
8119/22
8126122
912122
919/22
9116/22
9123122
9130122
1017122
10114122
10121122
10128122
1114122
11111122
11118122
11125122
1212122
1219122
12116122
12123122
12130122
116123
1113/23
1120123
1127123
213123
2110/23
2117/23
2124123
313123
3110123
3117/23
3124/23
3131123
417123
4114123

Belgium
53.24
53.69
53.95
54.90
55.61
58.89
56.93
56.15
57.30
57.51
57.60
59.15
62.35
60.22
61.05
61.93
61.76
61.77
62.45
62.94
65.34
68.11
70.03
74.64
68.15
67.93
69.33
70.61
68.10
68.54
69.40
72.08
73.34
78.16
81.49
83.13
85.54
89.33
88.36
88.41
90.79
87.45
83.77
81.85
82.25
81.11

France
49.05
49.58
51.02
52.10
52.49
55.85
53.67
52.94
53.93
54.11
54.25
55.86
59.16
56.76
57.47
58.17
58.00
57.68
58.01
58.34
60.15
61.85
64.61
68.82
63.35
62.67
63.95
64.40
61.40
62.50
63.49
66.00
66.67
70.54
72.09
72.72
73.05
78.20
77.35
77.22
77.79
74.82
71.99
70.21
70.88
69.95

1.359

Holland
11.405
11.425
11.415
11.443
11.433
11.425
11.430
11.390
11.420
11.450
11.430
11.430
11.380
11.390
11.430
11.400
11.380
11.260
11.310
11.330
11.370
11.400
11.350
11.360
11.370
11.380
11.380
11.440
11.580
11.640
11.680
11.710
11.770
11.750
11.738
11.840
11.820
11.830
11.865
11.890
11.890
11.890
11.890
11.880
11.880
11.890

Italy
66.06
97.53
69.53
93.97
94.00
99.44
97.21
95.94
97.25
96.25
97.00
96.50
103.00
101.80
102.74
105.55
105.36
103.49
103.24
104.43
106.80
112.66
106.66
101.24
97.54
95.10
93.85
91.45
92.25
91.65
92.16
92.33
94.60
97.40
97.75
97.40
97.50
96.60
98.00
96.32
99.03
96.16
96.45
93.70
94.45
93.95

Swit

23.
23.
23.
.27
23.
23.
.21
.38
23.
23.
23.
23.
23.
23.
23.
23.
23.
23.
23.
23.
24.
24.
24.
24.
.26
24.
24.
.27
24.
24.
24.
24.
.73
24.
24.
24.
24.
25.
25.
25.
25.
25.
25.
25.
25.
25.

23

23
23

24

24

24

43
57
47

32
32

31
48
39
54
52
54
56
73
72
50
66
79
47
72
39
41

18
15

49
53
47
54

97
87
94
96
06
12

26
31
38
44
54
67

.1 . .1.. . .. .. .. .1 .1 . . . . .1.. .1.. .. . . . . .1 . . .1 .1 .1.. .1 . . . .1 . .1 .1 . .. . . . .1 . ..

U.S.

.47125
.49375
.44625
.39969
.41813
.44875
.44063
.45438
.43813
.44750
.45500
.47250
.46500
.45625
.44750
.42250
.40375
.35875
.40625
.42625
.45250
.43750
.44250
.43188
.45000
.47000
.49750
.54000
.61750
.61750
.60500
.62125
.64500
.63750
.61625
.64250
.65250
.66000
.68500
.66875
.67750
.66250
.66000
.64500
.64250
.63000

4121/23
4128123
515/23
5112123
5119123
5126123
612/23
619/23
6116/23
6123/23
6130123
717/23
7114/23
7121/23
7128123
814/23
8111/23
8118/23
8125123
911/23
918/23
9115/23
9122/23
9129/23
1016123
10113122
10120123
10127123
1113123
11110123
11117123
11124123
1211123
1218123
12115123
12122123
12129123
115124
1112124
1119124
1126124
212124
219124
2116/24
2123124
311124

Belgium France
69.
68.
69.
69.
69.
69.
71.
71.
73.
74.
75.
79.
78.
77.
.82
78.
.64
82.
.25

81.17
79.25
80.34
81.06
80.68
81.50
82.81
83.42
84.99
87.29
88.91
96.58
94.40
93.20
95.11
99.07
102.78
103.48
99.93
98.17
99.19
93.06
89.31
87.17
90.82
87.38
87.58
87.95
90.48
90.43
95.86
93.76
93.28
94.62
94.87
96.74
96.69
99.79
100.59
101.95
104.30
104.39
107.27
114.12
113.25
118.00

77

80

80

80.
81.
.27
75.
74.
76.
.52
75.
75.
77.
78.
81.
80.
.25

77

74

80

81.
82.
85.
84.
88.

90

91.
.48
91.
94.
96.
.95
99.

93

97

96
13
20
85
34
79
14
71
00
30
49
00
25
80

80

55

71
33

95
12
89

78
83
50
10
63
57

61
02
89
74
11

.04

67

57

15

40

20

140

Holland
11.880
11.840
11.813
11.780
11.780
11.790
11.780
11.730
11.733
11.738
11.640
11.605
11.700
11.685
11.603
11.603
11.590
11.571
11.575
11.546
11.526
11.546
11.555
11.563
11.573
11.545
11.549
11.562
11.521
11.552
11.598
11.430
11.400
11.425
11.380
11.385
11.290
11.320
11.310
11.310
11.330
11.470
11.450
11.435
11.490
11.500

Italy
94.55
94.55
95.05
95.32
95.40
96.66
99.23
99.45
100.46
102.60
104.56
109.15
106.45
106.63
105.77
106.25
106.13
106.90
105.97
106.35
105.55
102.55
101.20
99.75
101.73
99.93
100.75
99.95
100.80
100.66
102.64
101.32
101.34
100.75
100.76
100.97
100.26
100.08
97.17
98.25
97.70
99.16
98.48
99.14
99.50
100.08

Swit

25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
26.
26.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
25.
24.
24.
24.
24.
25.
25.
24.
24.
24.
24.
24.
24.
24.
24.
24.
24.
24.

76
66
73
81
72
72
65
70
70
78
95
71
49
94
64
46
02
03
08
04
04
43
48
37
40
14
17
14
00
86
78
86
78
93
01
85
68
56
52
46
46
84
67
64
84
71

. . 1. . . . .1 . .1 . . . .. .. .. . . .. . . . . .1 . . .. .. . . .1 . . . . .1 . . 1. 1. .. . . . . .. .

U.S.

.62625
.60750
.60000
.58875
.59750
.60000
.60813
.58625
.59250
.59625
.55500
.55125
.59125
.58125
.57375
.56313
.56375
.55125
.54625
.53750
.52188
.52750
.53000
.54000
.54000
.52313
.50063
.48625
.44000
.36750
.27938
.34375
.32563
.34625
.33938
.32625
.32250
.27250
.24750
.21563
.21063
.32625
.28500
.27625
.30188
.29188

318124
3115/24
3122/24
3129124
415/24
4112124
4119124
4126124
513124
5110/24
5117/24
5124/24
5131124
617/24
6117/24
6121/24
6128124
715/24
7112124
7119124
7126124
812/24
819124
8116/24
8123/24
8130/24
916/24
9113/24
9120/24
9127124
1014124
10111124
11118124
10125124
1111/24
1118124
11115124
11122124
11129124
1216124
12113124
12120124
12127124
113125
1110125
1117125

Belgium France
107.00
80.
78.
75.
73.
70.
69.
68.

128.17
108.15
101.60
99.65
89.42
84.92
81.21
80.60
81.64
88.20
89.48
93.33
96.90
95.18
93.88
92.37
93.36
97.24
95.90
95.83
95.70
94.54
90.25
86.44
90.67
88.93
89.64
89.35
90.05
91.77
92.34
93.84
93.24
93.62
93.75
95.22
95.48
95.15
94.22
94.55
94.83
94.52
94.50
94.75
95.92
95.25

67

74

84

84

83
84

84.
86.
85.
85.
85.
86.
86.
86.
85.
85.
86.
86.
86.
86.
.83
.68

87
87

56
00
45
17
80
02
15

.25
69.
.57
78.
82.
83.
79.
79.
80.
85.

65

92
40
80
97
14
93
27

.49
85.
85.
85.
81.
79.
83.
81.
.60
83.

09
82
05
93
19
19
87

02

.90
.60

56
19
43
81
52
78
88
78
19
25
57
13
07
30

141

Holland
11.525
11.525
11.615
11.628
11.580
11.610
11.678
11.735
11.665
11.648
11.643
11.600
11.500
11.498
11.523
11.553
11.475
11.440
11.555
11.528
11.514
11.538
11.633
11.645
11.605
11.630
11.600
11.620
11.575
11.533
11.455
11.410
11.428
11.378
11.410
11.420
11.458
11.430
11.369
11.495
11.603
11.618
11.620
11.673
11.790
11.830

Italy

101
99.
99.
99.
98.
97.
98.
97.
97.
97.
97.
96.
98.
99.
99.
100
100

101.
102.
101.

101

101.
100.
100.
102.
101.
102.
101.
102.
102.
102.
103.
103.

103.
106.
106.
106.
106.
107.
108.
110.
110.
112.

114

117.

.20
81
81
17
48
67
24
65
86
88
76
38
96
05
17
.36
.25
33
15
67
.64
74
88
98
03
54
30
95
09
12
12
17
13
.08
95
59
97
78
51
89
97
22
02
27
.12
24

Swit

24

24.
24.

24

24.
24.
.65

24

24.
24.
24.
24.
24.
24.
24.
24.
.27
.26
.20
23.
23.
23.
23.

24
24
24

23

23

23
23
23
23

24

24

24

.68

67
76

.68

68
60

59
55
53
57
55
41
43
40

91
84
77
52

.63
23.
23.
.68
23.
23.
23.
23.
.15
.26
.26
.25
23.
23.
23.
23.
23.
.11
24.
.24
24.
.26
27.
24.

88
75

41
52
52
30

46
71
97
96
92

16

18

72
78

. . .. .. .. .. . . .1 . .. .. .1 .1 . . .. .. . . . . .1 . .1 . . .. . . . .1 . .1 .1 . . .. .. . . ..1 . .. .. .

U.S.

.27250
.27875
.29563
.29813
.30500
.32688
.35188
.37375
.37813
.36125
.35938
.33938
.30000
.30875
.31625
.33125
.32125
.32813
.37000
.38375
.41250
.42875
.52625
.55813
.49875
.51125
.44625
.46688
.47375
.48375
.47250
.49875
.49563
.49688
.53813
.58438
.63250
.63500
.62281
.68125
.69438
.70656
.71063
.74375
.78344
.77219

142

Belgium France Holland Italy Swit U.S.
1124/25 93.97 88.30 11.890 116.43 24.85 4.79875
1131/25 92.24 87.77 11.900 114.94 24.84 4.79375
217/25 92.80 87.87 11.870 115.35 24.78 4.77344
2114/25 95.14 90.60 11.870 116.28 24.79 4.77281
2121125 94.68 89.67 11.905 116.42 24.79 4.76313
2128125 94.77 91.37 11.933 117.75 24.80 4.75813
317125 94.08 90.73 11.965 116.98 24.79 4.76750
3114/25 94.64 92.00 12.010 117.85 24.83 4.78750
3121/25 94.35 91.33 12.015 117.79 24.79 4.78000
3128125 93.22 89.80 12.018 116.98 24.80 4.77850
414/25 94.25 91.02 12.005 116.77 24.80 4.78250

Key: The 90-Day forward rates come from Einzig (1937) and
represent end of the week quotations from the London exchange
market. All rates are quoted vis a vis the pound.

Monthly Wholesale Prices

Belgium Britain France Germany Holland U.S.

1129/21 246 415 143900 214 114.0
2126/21 225 385 137600 198 104.9
3126/21 211 367 133800 188 102.4
4130/21 205 354 132600 177 4 98.9
5128/21 202 337 130800 182 96.2
6125/21 198 332 136600 183 93.4
7130/21 194 337 142800 177 93.4
8127/21 347 190 338 191700 180 93.5
9124/21 368 187 351 206700 180 93.4
10129121 372 181 338 246000 170 94.1
11126121 374 173 339 341600 166 94.2
12131121 369 168 333 348700 166 92.9
1128/22 366 164 320 366500 163 91.4
2125/22 356 162 313 410300 165 92.9
3125/22 350 160 314 543300 164 92.8
4129122 344 160 320 635500 163 93.2
5127122 348 160 323 645800 165 96.1
6124/22 356 160 332 703000 165 96.3
7129122 360 160 332 1005900 164 99.4
8126/22 360 156 338 1920000 156 98.6
9130122 364 154 336 2870000 152 99.3
10128122 385 155 344 5660000 155 99.6
11125122 408 157 360 11540000 158 100.5

12130122 407 156 370 14750000 155 100.7

143

Belgium Britain France Germany Holland U.S.

1127123 434 157 395 27650000 157 102.0
2124/23 474 156 431 55650000 155 103.3
3131123 462 160 433 46660000 156 104.5
4126123 480 162 423 52120000 156 103.9
5126/23 474 160 415 61700000 149 101.9
6130/23 464 159 417 1.94e+08 149 100.3
7129123 504 157 415 7.48e+08 145 96.4
6125/23 529 155 420 9.44.+09 142 . 97.6
9129/23 514 156 433 145 99.7
10127123 515 158 429 146 99.4
11124123 531 161 452 153 96.4
12129123 545 163 468 154 96.1
1126/24 560 165 505 156 99.6
2123/24 642 167 555 156 99.7
3129/24 625 165 510 155 96.5
4/26/24 555 165 459 154 97.3
5131/24 557 164 468 153 95.9
6126/24 565 163 475 151 94.9
7126124 566 163 491 151 95.6
6130124 547 165 487 151 97.0
9127/24 550 167 496 158 97.1
10125124 555 170 506 161 98.2
11129124 569 170 514 161 99.1
12127124 566 170 516 160 101.5
1131125 559 171 525 160 102.9
2126/25 551 169 526 159 _ 104.0
3126/25 546 166 524 155 104.2
4125125 536 162 523 151 101.9
5130125 537 159 531 151 101.6

Key: The monthly wholesale prices are the general wholesale
price indices. The data come from Tinbergen (1934).

Monthly Retail Prices

Belgium Britain France Germany Holland U.S.

1129121 450 263 410 182300 205 119.2
2126121 434 249 392 166000 199 111.7
3126121 411 238 358 161500 194 110.1
4130121 399 232 328 156000 185 107.4

5128121 389 218 317 152300 191 103.1

6125121
7130/21
8127/21
9124121

10129121
11126121
12131121

1128122
2125/22
3125122
4129122
5127122
6124122
7129122
8126122
9130122

10128122
11125122
12130122

1127123
2124/23
3131/23
4128/23
5126123
6130123
7128123
8125/23
9129123

10127123
11124123
12129123

1126/24
2123/24
3129124
4126124
5131/24
6128124
7126124
8130/24
9127124

10125124
11129124
12127124

1131125
2128125
3128125

Belgium
384
379
384
386
391
394
393
387
380
371
367
365
366
366
366
371
376
384
384
383
397
408
409
413
419
429
439
453
458
463
470
480
495
510
498
485
492
493
498
503
513
520
521
521
517
511

Britain
220
226
225
210
200
195
185
179
177
173
172
170
180
175
172
172
176
178
175
173
171
168
162
160
162
165
168
172
173
176
175
177

167
163
160
162
164
166
172

180
178
176
176
170

France
312
306
317
329
331
326
323
319
307
294
304
317
307
292
289
291
290
297
305
309
316
321
320
325
331
321
328
339

355
365
376
384
392
380
378

360
366

383
396
404
408
410
415

144

Germany
159500
172100
193500
264300
356500
566200
507100
507500
560000
746300
620300
661700
947900
1365400
324900
431100
903400
214100
243200
475600
679600
661600
746600
1306100
3116600

10024400
1.33e+08

Holland

192
183
192
187
173
168
168
166
169
168
168
168
167
163
151
144
148
154
153
154
151
149
146
138
137
135
132
136
142
148
152
153
158
154
151
150
149
149
151
161
166
166
164
161
159
154

U.S.
100.7
99.
98.
97.
97.
97.
95.
92.
92.
93.
94.
96.
97.
97.
96.
98.
99.
99.
99.
100.1
101.1
102.4
102.4
101.0
99.
98
97.
98.
97.
96.
96.
98.
98.
97
95.
95.
94.
94
95
95.
95.
96.
99
99.
100.4
100.9

CIVJ‘ONCUONQOGDUUQONO

HOGQUUHU‘NG’UGNNUQUNNN

145

Belgian Britain France Germany Holland U . S .
4125125 506 167 409 149 98 . 8
5130/25 502 166 418 148 99 . 6

Key: The data come from Tinbergen (1934). The price indices
for Belgium and France represent general retail prices. The
German index represents home goods. The British and Dutch
indices measure retail food prices. The United States index
measures finished good prices.

Monthly Retail Prices League of Nations

Britain France Germany U . S .
1129/21 263 410 1040 169
2/26/21 249 382 1107 155
3126121 238 358 1137 154
4130/21 232 326 1107 149
5129/21 216 317 1117 142
6125121 220 312 1147 _ 141
7130/21 226 306 1278 145
6127/21 225 317 1324 152
9124121 210 329 1359 150
10129121 200 331 1357 150
11/26/21 195 326 1286 149
12131121 185 323 1198 147
1128122 179 319 1123 139
2125122 177 307 3020 139
3/25/22 173 294 3602 136
4129122 172 304 4356 136
5/27/22 170 317 4680 136
6124122 180 307 5119 138
7129122 175 297 6836 139

8/26/22 172 289 9746 136

146

Britain France Germany U . S .
9130122 172 291 15417 137
10128122 176 290 26623 140
11125122 176 297 .54982 142
12130122 175 305 60702 144
1/27/23 173 309 136606 141
2/24/23 171 316 318300 139
3131123 168 321 332000 139
4128123 162 320 350000 140
5/26/23 160 325 462000 140
6130123 162 331 1935000 141
7/28/23 165 321 4651000 144
8125123 168 328 67049000 143
9129123 172 339 146
10/27/23 173 349 147
11124123 176 355 146
12129123 175 365 147
1126124 177 376 146
2123124 176 364 144
3129124 167 392 141
4/26/24 163 380 138
5131124 160 378 138
6128124 162 370 140
7126124 164 360 141
9130124 166 366 141
9127124 172 374 144
10125124 179 363 146
11/29/24 180 396 147
12127124 178 404 149
1131/25 176 408 151
2126125 176 410 148

3/28/25 170 415 148

147

Britain France Germany U . S .
4125/25 167 409 147
5/30/25 166 418 148

Key: The data come from the Monthly Bulletin of Statistics
from the League of Nations. Each index measures the retail
price of food.

Monthly Money Supply

Belgium Britain France Germany Holland
1129/21 22.71388 21.59623 22.08578 11.2921 20.80715
2126121 22.72407 21.56138 22.04048 11.2820 20.76277
3126/21 22.71196 21.54128 21.98654 11.2923 20.75689
4130/21 22.70330 21.54437 21.95115 11.2999 20.77738
5128/21 22.70399 21.56440 21.97059 11.3081 20.78229
6125/21 22.69651 21.57042 21.89513 11.3302 20.72766
7130121 22.68926 21.57853 22.02754 11.3595 20.75263
8127121 22.69498 21.56095 21.86972 11.3822 20.73687
9124121 22.68575 21.56613 21.79759 11.4278 20.73322
10129121 22.66832 21.57938 21.81418 11.4860 20.75940
11126121 22.66732 21.56224 21.80541 11.5563‘ 20.75515
12131121 22.66014 21.59079 21.88015 11.6606 20.74610
1128122 22.66617 21.58700 21.77304 11.7255 20.75776
2125122 22.67587 21.57427 21.76177 11.7496 20.71301
3125/22 22.68364 21.54040 21.70422 11.8103 20.69394
4129122 22.67445 21.53952 21.75467 11.8882 20.73500
5127122 22.68054 21.54305 21.73268 11.9611 20.75573
6124122 22.68505 21.54084 21.76988 12.0518 20.70092
7129122 22.67445 21.53108 21.75787 12.1636 20.72466
8126/22 22.67288 21.51172 21.67222 12.3314 20.68888
9130122 22.70950 21.49522 21.69367 12.5776 20.69846
10128122 22.71251 21.50671 21.66600 12.9029 20.71614
11125122 22.71004 21.49522 21.66639 13.3224 20.70754
12130122 22.69261 21.50854 21.73632 13.8138 20.70030
1127123 22.68603 21.51626 21.70234 14.2951 20.71473
2124/23 22.68772 21.47892 21.70834 14.7996 20.67145
3131123 22.69901 21.45803 21.64633 15.3070 20.66489
4128123 22.69554 21.46568 21.65700 15.6180 20.68536
5126/23 22.71374 21.46616 21.67647 15.8392 20.66701

6130123 22.69457 21.48173 21.68185 16.3228 20.64617

148

Belgium Britain France Germany Holland
7128/23 22.70164 21.48360 21.64195 17.1346 22.97991
8125123 22.72136 21.47090 21.59121 18.9761 20.85937
9129123 22.74455 21.31216 21.61526 20.69661
10127123 22.74733 21.47232 21.62017 20.73371
11/24/23 22.75115 21.47421 21.69631 20.74140
12129123 22.76306 21.50305 21.76707 20.76143
1126/24 22.78924 21.49615 21.76071 20.75370
2123/24 22.79694 21.47327 21.76000 20.73123
3129/24 22.80620 21.46091 22.03780 20.71604
4126124 22.80670 21.47043 21.79211 20.73104
5131124 22.79857 21.46948 21.71763 20.71876
6128/24 22.79379 21.49799 21.68949 20.69167
7/26/24 22.79051 21.48641 21.69858 20.69641
8130/24 22.79367 21.47657 21.63233 20.68317
9127124 22.79304 21.47090 21.52257 20.69969
10125124 22.78835 21.48267 21.62343 20.69208
11129124 22.79518 21.47421 21.62870 20.68192
12127124 22.80645 21.49430 21.62748 20.66691
1131/25 22.80794 21.49152 21.65700 22.94919
2/28/25 22.78835 21.48314 21.62546 20.62001
3128125 22.78110 21.46330 21.66756 20.62422
4125/25 22.78212 21.46853 21.62058 20.61857
5130/25 22.76799 21.45803 21.62627 20.62201

Key: The data come from Tinbergen (1934) . The money supplies
for Belgium, France, Holland and Britain are the sum of notes
in circulation and private bank deposits. The data are in

logs.
Monthly Spot Exchange Rates

Belgium France Germany Holland U . S .
1129/21 51.83 54.37 221 11.40 3.860
2126121 51.80 54.98 241. 11.35 3.870
3126/21 53.20 56.58 247 11.37 3.920
4130/21 51.22 51.19 262 11.27 3.960
5128121 46.70 46.70 242 11.24 3.895
6125/21 46.86 46.74 271 11.33 3.730

7130121
8127/21
9124121
10129121
11126121
12131121
1129/22
2125/22
3125122
4129122
5127122
6124122
7129122
6126122
9130122
10126/22
11125122
12130122
1127123
2124123
3131/23
4128/23
5126/23
6/30/23
7126123
6125/23
9129123
10127123
11124123
12129123
1126124

Belgium

48.55
49.20
52.80
55.25
61.25
54.50
54.10
51.62
52.12
52.12
52.87
54.82
57.25
62.32
61.56
68.05
67.90
69.25
81.35
88.27
81.75
79.17
81.45
88.87
94.95

100.07

87.25
88.05
93.92
96.77

104.25

France

46.92
47.65
52.35
54.00
57.80
51.88
51.80
49.30
48.50
48.27
48.87
52.16
54.17
59.40
57.77
62.15
62.97
63.57
72.25
77.60
70.40
68.22
69.87
75.62
77.90
80.35
74.17
75.92
80.87
84.82
94.25

149
Germany

290
322
405
690
1175
770
847
975
1400
1206
1305
1500
2677
9500
7100
17950
31500
33200
125000
105000
101000
136000
251000
650000
4500000

21000000

Holland

11.58
11.82
11.76
11.52
11.18
11.40
11.56
11.50
11.59
11.60
11.43
11.48
11.48
11.44
11.29
11.43
11.41
11.71
11.76
11.89
11.88
11.86
11.82
11.68
11.63
11.58
11.57
11.56
11.46
11.38
11.40

3.563
3.688
3.735
3.925
3.985
4.215
4.250
4.398
4.385
4.423
4.450
4.403
4.448
4.473
4.370
4.463
4.500
4.635
4.640
4.715
4.675
4.635
4.625
4.573
4.585
4.555
4.553
4.500
4.365
4.338
4.228

2123124
3129124
4126124
5131124
6/28/24
7126124
6130124
9127124

10125124
11129124
12127124

1131125
2126125
3126125
4125125
5130125

Belgium

113.75
100.00
80.62
97.25
93.56
95.75
89.06
91.85
93.70
94.42
94.62
92.32
94.95
93.15
95.60
99.30

France

99.75
78.45
68.75
84.40
81.80
86.12
82.12
84.80
86.20
85.82
87.27
88.40
92.57
90.60
92.60
96.92

150

Germany Holland

11.53
11.64
11.77
11.52
11.50
11.51
11.62
11.57
11.44
11.46
11.65
11.90
11.90
11.98
12.02
12.10

U.S.

4.313
4.300
4.383
4.305
4.320
4.400
4.503
4.473
4.490
4.623
4.713
4.795
4.760
4.773
4.813
4.860

Key: The data are from Einzig (1937) and represent the weekly
quotation nearest the end of the month from January 1921
through April 4 1925, except in the German case when the data
is truncated in August 1923.

Monthly Forward Rates

Belgium France Germany Holland U . S .
1/29/21 51.48 54.07 219 11.405 3.87750
2/26/21 51.43 54.68 239 11.345 3.88750
3/26/21 52.85 56.31 245 11.365 3.92500
4/30/21 50.99 51.04 260 11.260 3.96188
5/28/21 46.53 46.26 240 11.240 3290375
6/25/21 48.73 46.66 270 11.330 3.73625
7/30/21. 48.50 46.96 289 11.580 3.56750

6127121
9124121
10129121
11/26/21
12131121
1126122
2125122
3125122
4129122
51271222
6/24/22
7129122
8/26/22
9130122
10126122
11125122
12130122
1127123
2124123
3131123
4126123
5/26/23
6/30/23
7126123
6125123
9129123
10127123
11124123
12129123
1/26/24
2123124

Belgium

49.15
52.75
55.15
61.19
54.40
54.02
51.57
52.05
52.05
52.84
54.80
57.24
62.31
61.49
68.03
67.89
69.20
81.32
88.24
81.72
79.15
81.44
88.85
94.90
100.13
87.29
88.10
93.99
96.79
104.23
113.95

France

47.68
52.36
54.03
57.82
51.89
51.79
49.30
48.50
48.28
48.88
52.18
54.25
59.51
57.80
62.25
63.07
63.60
72.32
77.70
70.49
68.25
69.10
75.68
77.94
80.40
74.20
75.97
80.87
84.87
94.52
100.33

151

Germany

320
405
688
1173
768
845
973
1400
1206
1305
1501
2687
8650
7400
19950
35500
35200
142000
141000
106000
151000
287000
1020000
6100000

28000000

Holland

11.820
11.760
11.525
11.185
11.415
11.565
11.503
11.605
11.620
11.453
11.493
11.500
11.460
11.300
11.440
11.420
11.720
11.768
11.898
11.880
11.868
11.830
11.697
11.640
11.581
11.573
11.559
11.470
11.440
11.428
11.543

U.S.

3.69125
3.73625
3.93000
3.98000
4.21688
4.25063
4.39813
4.38500
4.42281
4.45125
4.40344
4.45063
4.47500
4.37375
4.46875
4.51000
4.64625
4.65000
4.72500
4.68500
4.64375
4.63375
4.57875
4.58875
4.57719
4.55625
4.50438
4.37875
4.34250
4.23375
4.31625

152

Belgium France Germany Holland U . S .
3/29/24 100.15 79.57 11.644 4.30063
4126124 60.64 66.95 11.761 4.38438
5/31/24 97.40 85.10 11.530 4.30625
6126124 93.63 62.10 11.510 4.31936
7/26/24 95.77 86.19 11.517 4.39375
8/30/24 89.10 82.19 11.625 4.49688
9/27/24 91.88 84.89 11.585 4.46688
10/25/24 93.74 86.33 11.463 4.48688
11/29/24 94.50 86.07 11.503 4.62219
12/27/24 94.66 87.74 11.668 4.71281
1/31/25 92.34 88.68 11.900 4.79563
2/28/25 95.03 93.05 11.881 4.76063
3/28/25 93.12 90.90 11.963 4.77938
4/25/25 95.56 93.13 12.013 4.80938
5/30/25 99.27 97.47 12.093 4.85625

a...

Key: The data are from Einzig (1937) and represent the weekly
quotation nearest the end of the month from January 1921
through April 4 1925, except in the German case when the data
is truncated in August 1923.

153

LIST 0! REFERENCES

Einzig. Paul (1937). Was. London;
Macmillan and Company.

League Of Nations, WM: 1921-1925-

Tinbergen, J. (1934), International .Abstract. of Economic

Statistics 1919-1930, International Conference of
Economic Time Series, London.

 

APPENDIX 2

 

154

APPENDIX 2

The Johansen Methodology

One method for investigating long-run equilibrium
relationships is to use the concept of cointegration
introduced by Granger ( 1986) and Engle and Granger (1987) .
Two or more variables can be individually nonstationary, but
if a linear combination. exists that is stationary, the
variables are said to be cointegrated. In addition, the
existence of cointegration implies Granger-causality in at
least one direction.

The Engle and Granger (1987) two-step method involves
estimating the "cointegrating" relationship and then
subjecting the residuals from this regression to a test for
unit roots. If the residual series are nonstationary, the
variables in the relationship will have no tendency to move
together. While Stock (1987) shows that the estimate of the
cointegrating value is consistent, there are two potential
problems that exist.

Banerjee et al (1986) point out the possibility of small
sample bias in the cointegrating relationship. This is
particularly relevant for the 1920s since the data sets
analyzed in chapter three contain at most 53 observations.

Another drawback is that this method assumes that there
exists only one cointegrating vector. The possibility
certainly exists for a series of three or more variables to

have more than one long-run equilibrium. The possibility of

 

K

”i

 

 

155

multiple vectors complicates the analysis since economic
theory does not usually provide guidance as to the choice of
the "correct” equilibrium relationship.

The procedure that is utilized in this study is based on
work by Johansen (1988,1989)‘ and Johansen and Juselius (1989) .
This methodology employs full information maximum likelihood
estimation. It allows estimation of multiple cointegrating
vectors as well as allowing tests based on the number of
cointegrating vectors to be carried out. Finally, the tests
have nonstandard limiting distributions that are well defined
and invariant.

Consider the following p dimensional vector xt, xt =
(xlt’ xpt) '. If this vector is generated by a vector

autoregression, then

R .
x=2nx +61: (1)

where "s are matrices of coefficients and 6t is independently
and identically distributed as normal with zero mean and
constant variance (i.e. i.i.d. N(O, 0)).

It is useful to rewrite the model in (1) as

AXt = 2 rsAxt-s - nX

+ 6 (2)
5:1 tpk t

where

156
u = I - fl - o o o - "k
and
P = -I + n + o o o + n (s=1, ... , k-l)

Notice that (2) is the usual VAR in first differences
except that it contains the lagged levels xt-k’ The
coefficient matrix a on xt-k contains information about the
long-run behavior of the system.

1 contains three

The Granger Representation Theorem
possible scenarios concerning the behavior of it. If the
coefficient.matrix has full rank (i.e. rank(n) = p), then each
variable in this vector autoregression is individually
integrated of order zero.2 If 1! has full rank, then the
concept of cointegration loses its meaning.

In the other extreme, if the rank of n is zero, then all
the variables are individually nonstationary and no

cointegration exists. Thus, the system does not have a long-

run relationship.

 

1 R. Engle and C. Granger , "Co-integration and Error
Correction: Representation, Estimation and Testing,"

Econometric; 55 (1987): 255-256.

2 A variable is said to be integrated of order d, I(d),
if this variable attains stationarity after differencing d
times.

157

For cointegration to exist, the rank of u must equal r,
where r is less than p. If this is the case, there exists r
cointegrating vectors. Furthermore, if cointegration exists,
then u = a3' where B is a pxr matrix of cointegrating vectors
and a is a pxr matrix of error-correction terms.

The test that is employed in chapters two and three is
the "trace test" for the number of cointegrating vectors. The
null hypothesis in this test is that there are at most r
cointegrating vectors (the alternative hypothesis is that
there are no cointegrating vectors). The test statistic is
formed by solving an eigenvalue problem developed from three
moment matrices of residuals from two auxiliary VARs that
regress AXt and xt-k on Axt—s (s=1, ... , k-l). The test
statistic

-21n(Q) = -T g 1n(1-i )

s=r+1 S
where is s=r+1, . . ., p are eigenvalues with 11>12> o o o>1p,
has a nonstandard limiting distribution. Critical values for

the test statistic are tabulated in Table 0.2 in Johansen and

Juselius (1989).

158

LIST 0? REFERENCES

Banerjee, A., J. Dolada, D. Hendry and George Smith (1986), ”
Exploring Equilibrium Relationships in Econometrics
Through Static Models: Some Monte Carlo Evidence,"

WWW. 48. 253-277-

Engle, R. and C.W.J. Granger (1987) , "Co-integration and Error
Correction: Representation, Estimation and. Testing,"

Eggngmetriga. 55. 251-276-

Granger, C,W.J. (1986), "Developments in the Study of

Cointegrated Economic Variables," Qxfgrd_fiullg§in_gfi
E9909mics.and.§§atistics. 48. 213-228-

Johansen, S. (1988), "Statistical Analysis of Cointegration

Vectors " I9urn___9f_E29n9mic_Dxnamic__ang_§gnLrgl 12
231- -254.

Johansen, S. (1989) , "Estimation and Testing for Cointegration
Vectors in Gaussian Vector Autoregressive Models,"
Institute of Mathematical Statistics, University of
Copenhagen, Preprint 3.

Johansen, S. and K. Juselius (1989), "The Full Information
Maximum Likelihood Procedure for Inference on
Cointegration - with Applications,” Institute of
Mathematical Statistics, University of Copenhagen,
Preprint 4.

Stock, J.H. (1987), "Asymptotic Properties of Least Squares
Estimates of Cointegration Vectors," Eggngmgtzigg, 55,
1035-1056.

 

"‘1011001?