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TESTS OF ALTERNATIVE
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TESTS OF ALTERNATIVE
EXCHANGE RATE HYPOTHESES

BY

Seth Tobin Kaplan

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Economics

1986

4/0 - 66:”:

ABSTRACT

TESTS OF ALTERNATIVE
EXCHANGE RATE HYPOTHESES

By
Seth Tobin Kaplan

The study is an empirical investigation of the monetary and asset
approach to exchange rate determination. A general model which
includes monetary, real and portfolio balance effects is formulated
and estimated. The model includes p0pular continuous equilibrium and
short run disequilibrium exchange rate specifications as restricted
cases.

Tine alternative exchange rate hypotheses are subjected to four
tests. First, the various restrictions imposed on the general model
are tested. Second, the stability of the coefficient estimates are
examined over several time periods. Third, the competing specifi-
cations are subjected to Hausman-wu tests. Fourth, joint tests of
model specification and rational expectations are conducted.

The model is estimated for the mark-U.S. dollar, Canadian
dollar-U.S. dollar, and U.S. dollar-U.K. pound sterling over four
sample periods. Although weak evidence is found supporting portfolio
balance and real interest rate effects, the results are not robust.
Both unrestricted and restricted versions of the general model perform
poorly over most samples. Further, the joint test of model

specification and rational expectations is rejected in all cases.

ACKNOWLEDGEMENTS

I would like to give special thanks to Professor Mordechai
Kreinin, chairman of my dissertation comittee, for his invaluable
comments and suggestions on this dissertation. I would also like to
thank Professor Peter Schmidt for his generous contributions of time
and effort regarding the empirical aspects of the thesis. In
addition, my thanks go to Professors Robert Rasche and Steven Matusz
for also serving on the dissertation committee.

I would like to thank several graduate students and friends for
encouragement and support during the writing of this thesis. They
include Sharon Cisco, Randall Bennett, Rick Rever, Michael Deerfield,
and Jack Sayre. I also gratefully acknowledge the fine job of typing
the manuscript under a time constraint by Ms. Marilyn "Sam" Miller.

Finally, I wish to thank my parents, Leo and Ann Kaplan. Their
love, guidance and encouragement is a constant source of strength in

my life.

ii

TABLE OF CONTENTS

Page
LIST OF TABLES ................................................ v
CHAPTER
I. INTRODUCTION ...... . ..................................... 1
II. AN OVERVIEW OF MONETARY AND ASSET MODELS ................ 5
2.1 Introduction ....................................... 5
2.2 Precursors to the Monetary/Asset Approach .......... 6
2.3 The Early Monetary Approach .... ....... . ............ 13
2.4 Development of the Monetary/Asset Approach ......... 19
2.5 Testing the Theory ................................. 28
2.6 Conclusion ......................................... 30
Footnotes - Chapter II ..... ............................. 35
III. SOME POPULAR MODELS OF EXCHANGE RATE DETERMINATION ...... 38
3.1 Introduction ....................................... 38
3.2 Isard's Formulation ............ . ................... 39
3.3 Some Popular Exchange Rate Models .................. 40
3.4 Estimation ......................................... 46
3.5 Results: Summary of Estimation ..................... 49
3.6 Conclusion: Comparison of Alternative
Exchange Rate Models ...... ....... . ................. 62
Appendix 3.A. Variable Proxies and
Unobservable Variables .................................. 65
Appendix 3.8. Data Sources ............................. 69
Footnotes - Chapter III ..................... . ........... 71

fl

iii

IV.

ESTIMATION OF THE GENERAL MODEL ......................... 73

4.1 Introduction ....................................... 73
4.2 An Econometric Model ............................... 75
4.3 Results: Summary of Estimation 1974:1-1983z3 ....... 80
4.4 Results: Summary of Estimation 1980:2-1984:6 ....... 99
4.5 Summary and Conclusion ............................. 106
Footnotes - Chapter IV .................................. 110
CONCLUSION .............................................. 111

iv

LIST OF TABLES

Tests of the Monetary/Asset Approaches ..... ...........

Regressions of the General and Restricted Models
on the L0 of Mark/U.S. Dollar Exchange Rate,

1974:1- 983:3 coo-eon.ooooeoeoooooooooooooo oooooooooo

Regressions of the General and Restricted Models
on the Log of Mark/U.S. Dollar Exchange Rate,

1974:1 :TT978z3 .......................................

Regressions of the General and Restricted Models
on the L0 of Mark/U.S. Dollar Exchange Rate,

I978:4 - 983:3 ......... . ........... . .................

Regressions of the General and Restricted Models
on the L0 of Canadian Dollar/U.S. Dollar Exchange

Rate,1 :1‘1983:3 0000000000 00.000000000000000 .....

Regressions of the General and Restricted Models
on the L0 of Canadian Dollar/U.S. Dollar Exchange

Rate, 1 :1 - 1978:3 .............. ...... . ............

Regressions of the General and Restricted Models
on the L0 of Canadian Dollar/U.S. Dollar Exchange

Rate, 1 :4 - 1983:3 ... ...... . ................ . ......

Regressions of Exogenous Variables on Their Own

Lagged Values, Germany-U.S., 1974:1 - 1983:3 ..........

Regressions of Exogenous Variables on Their Own

Lagged Values, Germany-U.S., 1974:1 - 1978:3 ..........

Regressions of Exogenous Variables on Their Own

Lagged Values, Germany-U.S., 1978:3 - 1983:3 ..........

Regression of the Unrestricted Reduced Form

Equations, Germany-United States, 1974:1 - 1983:3 .....

Regression of the Unrestricted Reduced Form

Equations, Germany-United States, 1974:1 - 1978:3 .....

Page
31

52

53

54

58

59

60

82

83

84

86

87

4.15

4.16

Regression of the Unrestricted Reduced Form
Equations, Germany-United States, 1978:4 - 1983:3

Tests of Rational Expectations Restrictions
and FIML Estimates of Coefficients ......... . .....

Regressions of Exogenous Variables on Their Own
Lagged Values, Canada-U.S., 1974:1 - 1983:3 ......

Regressions of Exogenous Variables on Their Own
Lagged Values, Canada-U.S., 1974:1 - 1978:3 ......

Regressions of Exogenous Variables on Their Own
Lagged Values, Canada-U.S., 1978:3 — 1983:3 ......

Regression of Unrestricted Reduced Form Equations,
Canada-United States, 1974:1 - 1983:3 ............

Regression of Unrestricted Reduced Form Equations,
Canada-United States, 1974:1 - 1978:3 ............

Regression of the Unrestricted Reduced Form

Equations, Canada-United States, 1978:3 - 1983:3 .

Germany-United States, 1980:6 - 1984:6 ...........

Regression of the Unrestricted Reduced Form
Equations, Germany-United States, 1980:6 - 1984:6

Canada-United States, 1980:6 - 1984:6 ............

Regression of the Unrestricted Reduced Form

Equations, Canada-United States, 1980:6 - 1984:6 .

Regression of Endogenous Variables on Their

Own Lagged Values, U.K./U.S., 1980:6 - 1984:6 ....

Regression of the Unrestricted Reduced Form

Equations, U.K./U.S., 1980:6 - 1984:6 .... ........

vi

....... 88

....... 9O

....... 92

....... 93

....... 94

....... 95

....... 96

....... 97
....... 100

....... 103

....... 104

....... 105

CHAPTER I
INTRODUCTION

The last fifteen years has seen a dual revolution in inter-
national finance. The collapse of the Bretton Woods fixed exchange
rate system in 1973 ushered in an era of floating exchange rates
between major national currencies. Over approximately the same
period, an equally dramatic shift occurred in balance of payments and
exchange rate theory: the monetary/asset approach replaced the
components or “account by account" view as the dominant theoretical
perspective. While the theoretical foundations of the newer approach
appear sound, its empirical validity is an Open question. The purpose
of this study is to examine the explanatory power of the monetary/
asset approach during the floating rate era.

According to the monetary/asset approach to exchange rate
determination, changes in the exchange rate equilibrate the supply and
demand for asset stocks denominated in different national currencies.
Consequently, long term exchange rate trends reflect the relative
growth of asset stocks, in general, and money, in particular. This
long-term relationship is often formulated in terms of price levels.
Given the first degree homogeneity of money and prices, the exchange
rate is expected to reflect the ratio of price levels between
countries. Restated, long-term exchange rate trends should tend

toward purchasing power parity (PPP).

2

The monetary/asset approach also accounts for highly volatile
short-term exchange rate fluctuations. Since most models are
formulated with rational expectations, unanticipated changes in asset
stocks can drastically effect the exchange rate. This is particularly
true of unanticipated permanent changes in asset stock growth rates.
The effect of unanticipated shocks on the volatility of exchange
movements is exacerbated by "sticky" prices in comedity markets, a
common assumption in monetary/asset models.

The purpose of this study is twofold. First,“ the eXplanatory
power of five p0pular monetary/asset exchange rate models is examined.
These include both equilibrium and disequilibrium specifications as
well as "pure" monetary and portfolio balance versions. fSecgndI1the~“
validity of the rational expectations assumptionwis,exam1ned, A joint
test of the models and rational expectations is conducted.

In Chapter II, both the theoretical and empirical literature is
reviewed. The review begins with a discussion of the theoretical
precussors of the monetary/asset approach: purchasing power parity,
interest rate parity and the "Keynesian" flow approach. The
discussion proceeds by examining monetary/asset models of greater and '
greater generality. These include the “pure" monetary models of the
"Chicago" school, disequilibrium models and finally, models which
include terms of trade and portfolio balance effects. The chapter
concludes with a discussion of the empirical literature, both
estimation techniques and results.

In Chapter III, five p0pular monetary/asset models are deveTOped
within a cannon framework, the Isard identity. These include the

models of Bilson (1978), Frenkel (1976), Dornbush (1976), Frankel

3
(1979), and Hooper and Morton (1980). A general specification which
includes the five models as restricted cases, is estimated, using
ordinary least-squares (OLS) and instrumental variable (IV)
techniques.

The U.S. dollar-mark and U.S. dollar-Canadian dollar exchange
rates are examined for the period'1973z6-1983z6. The models are
compared using four criteria: coefficient sign, coefficient
significance, robustness, and model specification. All five models
are found to perform poorly.

\/' In Chapter IV, a simultaneous equation monetary/asset model is
estimated. A, joint “test, of” ”model.--aspec.i..ti.cati.9n“and..."catienaLm
Wgfldugtgd. Unrestricted and restricted full
information maximum likelihood (FIML) estimates of the equation system
form the basis of the tests. The system estimation is preceeded by
tests to determine the lag structure for the exogenous variables as
well as single equation estimates of model. An additional sample
period, 1980:6-1984:6, is included as well as an additional exchange
rate, U.S. dollar-U.K. pound sterling. This period covers the
monotonic appreciation of the dollar. The relatively “clean“ float of
the U.S. dollar-U.K. pound sterling exchange rate precipitated its
inclusion. The results of the estimation were generally poor. The
joint test of rational expectations and the model were rejected in all
cases. 0f the single equation estimates, only the U.S. dollar-mark
rate showed mixed results.

In Chapter V, the conclusions of the study are discussed.

The major contributions of this dissertation lie in its approach

to the issue and its conclusions. The study presents a systematic

4
analysis of papular exchange rate models within the monetary/asset
approach. The estimated models are subjected to tests of coefficient
stability, model specification (Hausman-Nu tests) and joint tests of
model specification and rational expectations. The results of these
tests confirm the general inadequacy of the monetary/asset approach in
providing a robust explanation of exchange rate movements during the

post-Bretton Hoods era.

CHAPTER II
AN OVERVIEW OF MONETARY AND ASSET MODELS

2.1 Introduction

The collapse of the Bretton Hood system in 1973, coupled with
advances in closed economy macroeconomic theory, led to a resurgence
of interest in international finance in general and exchange rate
determination in particular. The new models differed significantly
from the Keynesian approach prevalent during the early post-World War
11 period. Specifically, exchange rate equilibrium is defined in
terms of asset stocks rather than commodity flows. Moreover, general
equilibrium models replace the earlier "account by account" partial
equilibrium analysis.

This chapter traces the development of monetary and asset models
of exchange rate determination during the last fifteen years. The
models will be presented according to criteria of theoretical
similarity and generality with the least general models examined
first.

Section 2.2 examines the precursors to the monetary and asset
models. Recent developments in exchange rate theory can be viewed as
attempts to integrate the early approaches into models predicated on
stock equilibrimm. Three different approaches will be summarized as
each motivated different aspects of the monetary/asset models. First,

the purchasing power parity approach (PPP) will be examined. Many of

6

the floating exchange rate models define PPP as an equilibrium
condition. Second, the interest rate parity condition is defined and
explored. Interest rate parity, sometimes in conjunction with PPP, is
often used to explain equilibrium and disequilibrium adjustment in
monetary/asset floating rate models. Finally, aspects of the
Keynesian flow model will be considered. The emphasis of the current
account in Keynesian models was temporarily abandoned in monetary/
asset exchange rate models. It has, however, been reincorporated into
the stock models as a mechanism to transfer wealth and limit
divergence from equilibrium.

Section 2.3 traces the develOpment of early monetary models.
Special attention will be focused upon the assumptions of the monetary
approach and its divergence from the Keynesian flow model. The
origins of the model will also be explored.

Section 2.4 continues the discussion of the monetary/asset
approach by considering models of greater generality. Five extensions
are discussed: 1) expectations, 2) currency substitution, 3) devia-
tions from equilibrium, 4) real effects, and 5) wealth effects. The
relationship between the newer models and the approaches in Section
2.2 will be examined.

A summary of the empirical literature which examines both
econometric technique and results appears in Section 2.5. Section 2.6

offers a brief conclusion.

2.2 Precursors to the Monetary/Asset Approach

1

A. Purchasing Power Parity. At the core of all purchasing power

 

parity (PPP) variants lies the contention that the exchange rate

between two national currencies reflects the ratio of prices in the

7
countries of denomination. This relationship can be formulated in two
ways: absolute PPP and relative PPP. The former holds that the
exchange rate is equal to the ratio of price levels in the two
countries. The latter postulates that the exchange rate is a constant
multiple of the ratio of price indexes. Due to the dearth of price
level data relative PPP is often the only testable hypothesis.2

PPP is not an economic theory: it offers no explanation of the
relationship it posits. Rather, it is an equilibrium condition
arising from several different theoretical formulations of the
international market mechanism. Each explanation of market behavior
gives rise to a different variant of PPP using different price indexes
to describe equilibrium (see below). Further, each view of market
behavior suggests the possibility of deviation from PPP and the length
of the adjustment process.

The theoretical foundations of PPP can be traced to four
different types of international arbitrage. Each form of arbitrage
yields an apprOpriate price index ratio in which to state PPP equili-
brium while explaining both deviation and adjustment to PPP. The
first form of PPP suggests the use of general price indexes and
contends that commodity arbitrage will ensure one price in
unobstructed international markets. A second version makes the
distinction between tradable and non-tradable goods. PPP is still
formulated with general price indexes when assuming the relative price
of tradables and non-tradables remain constant. However, if this

assumption is drOpped, PPP needs to be reformulated using import/

export price indexes.

8

Another version of PPP is based on the mobility of factors of
production rather than the mobility of commodities. Deviations from
PPP are corrected by the movement of labor and capital in uncontrolled
international markets. PPP is then formulated using cost of produc-
tion indexes.

Finally, PPP can be derived. from the relationship between
exchange rate and price level expectations. It has been argued that
arbitrage in the international asset markets ensures that the eXpected

3 It is

exchange rate equals the ratio of expected price levels.
further claimed that changes in the observed values parallel those of
expected values. Thus, PPP holds as a proximate condition. General
price levels are used in formulating this theoretical construction.

Empirical evidence suggests that PPP does not hold continuously
and, therefore, does not present an adequate explanation of short-run
exchange rate fluctuations.‘4 Clearly, influences other than general
price levels can precipitate short-run exchange rate movements. This
suggests that models which employ PPP are generally in disequilibrium
when estimated in the short run.

The validity of PPP in the long run is open to question. It is
unclear whether portfolio balance and real effects have a systematic
influence on the long run equilibrium exchange rate. During periods
of extreme price instability PPP appears to offer the most adequate

5

explanation of exchange rate movement. It is, however, uncertain

whether this is due to the validity of PPP or the shear magnitude of

the price effect.

6

8. Interest Rate Parity and Interest Rate Arbitrage. Interest

 

rate parity (IRP) is an equilibrium condition which equates the

9
return, expressed in domestic currency, of domestic and foreign

assets.7

Equilibrium is maintained by arbitraguers acting in the
asset and forward exchange markets. As such, IRP provides the
theoretical foundation for the uncovered and covered interest
arbitrage schedules.

The IRP condition connects domestic and foreign asset markets
with spot and forward exchange markets. Consider a two period, two
asset world in which domestic and foreign assets earn rates of
interest r and r*, respectively. The assets mature in period two. A
domestic investor, with endowment A, will receive A(1+r) in period two
by purchasing domestic assets in period one. Alternatively, he can
guarantee his domestic currency return on foreign investment by
simultaneously: 1) converting endowment A into foreign currency at the
spot exchange rate, 5 (expressed as foreign currency per unit of
domestic currency), 2) purchasing A-s worth of foreign assets, and
3) contracting to sell A-s(1+r*) of foreign currency at forward rate,
f. The second period domestic currency accumulation on foreign
investment is Avs(1+r*)/f. Equating the accumulations and rearranging
terms yields the IRP condition: (f-s)/s=r*-r. Deviations from IRP are
corrected by arbitraguers.

The analysis can be expanded by assuming the actions of a

8 The speculator buys or sells forward currency if the

expected future spot rate, se, differs from the forward rate. The

speculator.

difference between the rates is a risk premium attributable to
portfolio balance considerations: f=se-risk (Solnik, 1974; Dornbush,
1980). Substituting the previous expression into the IRP condition

yields (Se-s)/s=r*-r-risk, the covered interest arbitrage schedule. A

10
zero risk premium implies uncovered interest arbitrage. Both
schedules are used extensively in models of exchange rate deter-
mination.

Test of the empirical validity of IRP and interest rate
arbitrage has given rise to an extensive literature. Attention has
focused on three questions: 1) Does IRP hold continuously, 2) Is the
forward rate an unbiased estimate of the future spot rate, and 3) Is
the forward rate an efficient estimate of the future spot rate?

The first question can be answered in the affirmative. The
weight of evidence suggests IRP holds continuously in Eurocurrency

markets.9

Evidence suggesting deviations from IRP use asset markets
that are not fully integrated. This is the case when domestic and
foreign Treasury bond yields are substituted for Eurocurrency rates.
The second and third questions remain unanswered. The forward
rate appears unbiased over periods in which the exchange rate both
appreciates and depreciates. However, the forward rate consistently
underestimates the volitility of the spot rate. The question of
forward market efficiency also remains unanswered. It should be

noted, however, that a non-zero risk premium does not imply bias.

C. The Components Approach. The income/elasticity approach was

 

the dominant view of balance-of-payments and exchange rate determi-
nation during the Bretton Woods era. The approach is a synthesis of
Keynesian Open economy national income determination and devaluation
analysis associated with Marshall, Lerner and others.10

According to the most papular versions of the elasticity
approach, equilibrium is defined as either a zero trade balance or

current account balance. Movements of the current account are

11
considered responses to underlying economic fundamentals while the
capital account plays an accommodating role by financing the decisions
made on the "real" part of the balance-of-payments statement. Thus,
sole emphasis is placed on imports and exports while capital flows are
all but ignored.

The income approach emphasizes the relationship between the
equilibrium level of national income and the balance of trade.
Autonomous increases in expenditures move the trade balance toward
deficit by increasing the flow of imports. The result is due to the
income elasticity of imports or marginal propensity to import
specified in Keynesian type models.

Although both approaches were originally constructed to analyze
fixed and pegged exchange rate regimes, they can be reformulated to
examine the floating rate case. The exchange rate, once exogenous,
becomes endogenous. However, the fundamental results of the models
remain unchanged.

Consider a shift toward current account deficit caused by a
change in preference toward imported goods. The elasticity approach
suggests that equilibrium on the current account is restored by a
change in the relative price (i.e. terms of trade) of imports. This
is accomplished by a depreciation in the exchange rate resulting in a
deterioration in the terms of trade. The value of eXports would

11 The

increase relative to imports and move to restore equilibriwm.
central result of the elasticity approach, given a movement toward

current account deficit, is the ceteris paribus depreciation of the

 

exchange rate.

12

The income approach posits a direct relationship between income
and the exchange rate. An exogenous increase in income raises the
demand for imports via the marginal propensity to import. The
increase in demand for foreign goods is translated into an increased
demand for foreign exchange. This, in turn, depreciates the exchange
rate expressed in terms of domestic currency and dampens or reverses
the process.

A simple merging of the income and elasticity approaches into a
single equation model yields the result most commonly associated with
flow models of the Bretton Woods era: exogenous increases in domestic
income cw" exogenous movements of the current account toward deficit
are associated with depreciation of the exchange rate. An additional
result, the effect of interest rate changes, is develOped from
separate analysis of the capital account. Exogenous increases in the
domestic interest rate lead to increased demand for domestic currency
and, therefore, exchange rate appreciation.

Although the Keynesian flow approach is often characterized by a
single equation model with determinate signs for the exogenous
variables, several qualifications are in order. First, the separate
theoretical relationships of the exchange rate with income, interest
rates and the current account are derived from partial equilibrium
analysis. Second, the exogeneity requirements imposed by a single
equation model violate the clear interaction of the variables. This
is evident when considering the current account and income: increases
in income raise imports and move the current account towards deficit.
The single equation model should not be confused with a general

equilibrium analysis.

13
2.3 The Early Monetary Approach

Advocates of the monetary approach claim the supply and demand of
money stocks are the primary determinates of equilibrium in open
macroeconomic systems. The approach encompasses both balance of
payments analysis under fixed exchange rate regimes and exchange rate
determination in floating rate regimes.

Several characteristics of the monetary approach distinguish it
from other theories. First, monetary models define equilibrium in
stocks rather than flows. Second, the balance-of—payments is analyzed
in tgtgm_rather than account by account. Third, the effects of real
variables are generally transmitted through the arguments of the money
demand equation rather than directly. Fburth, the exchange rate is
considered the relative price of currencies rather than the relative
price of domestic and foreign goods. These characteristics lead to
conclusions radically different than earlier partial equilibrium
approaches.

Elements of the monetary approach appear as early as the
sixteenth century in Sweden where it was argued that increases in the
money stock depreciate the currency.12 This argument was repeated in
the U.K. bullionist controversy. The fixed rate analogy, that
increases in the money supply cause balance-of—payments deficit, was
suggested by several economists including Keynes. Other aspects of
the monetary approach appear throughout the classical literature.13

The modern interpretation and formalization of the monetary

14 For a variety of

approach began at the International Monetary Fund.
practical and theoretical considerations, the monetary approach became

a prime instrument for policy analysis. However, it was not until the

14
late 1960's that the monetary approach entered the academic mainstream
through the work of Mundell and Johnson.15

An analysis of money market adjustment is the central emphasis of
both the fixed and floating exchange rate versions of the monetary
approach. Development of either version begins by specifying a money
demand equation. The specification of choice, Md=Pf(y,r), states the
demand for nominal money balances, Md, equals the product of the price
level, P, with a function (f) of real income, y, and the nominal
interest rate, r. This conventional specification assumes the demand
for money is directly related to real income, inversely related to the
interest rate, homogeneous to degree one with respect to the price
level and relatively stable over time.

The analysis is continued by specifying the supply of money and
clearing the market. The nominal supply of money, MS, equals the
money multiplier, m, times the foreign, R, and domestic, 0, components
of the monetary base: Ms=m(R+D). Setting money supply equal to money
demand yields: m(R+D)=Pf(y,r). This equation is the foundation for
the fixed exchange rate case of the monetary approach.

The model is completed by specifying the price income and
interest rate variables. The global monetarists assume the following:
first, real income is exogenous due to long run full employment and,
second, the price level and interest rate are exogenous due to the law
of one price in both commodity and capital markets. The exogeneity of
prices and interest rates can also be explained by the small country
assumption without reference to the law of one price.

Examination of the fully Specified money market equation shows

that balance of payments disequilibriwm, R, is directly attributable

15
to changes in either the domestic component Of the monetary base or
the demand for MONEY! mAR=AIPf(V.r)]-mAD.16 Balance Of payment flows
continue until adjustment in the money market is complete and stock
equilibrium is restored.

Consider an Open market operation which increases the domestic
component Of the monetary base. This creates an excess stock supply
Of money. The demand side exogeneity assumptions allow only one
channel for adjustment: changes in the foreign component Of the
monetary base. Thus, money market adjustment is associated with
balance Of payments' surplus and deficit.

It follows directly that the stock supply Of money is endogenous
in fixed rate versions Of the monetary approach. Changes in the
domestic component Of the monetary base are met by equal and Opposite
changes in the foreign component. Barring sterilization, government
authorities control the composition Of the money supply, but have no
control over its level.17

The endogeneity Of the money supply is also apparent when changes
in money demand are examined. Increases in either the price level or
real income increase the stock demand for money. Without changes in
domestic credit, the only source Of funds is from abroad. Thus, both
increased price and income levels create a temporary balance Of
payments' surplus as the foreign component Of the monetary base
expands. The process continues until stock equilibrium is restored.

Conversely, an increase in the interest rate creates an excess
supply Of money. Decreases in foreign reserves are necessary to
restore money market equilibrium. Thus, a higher interest rate is

associated with a balance Of payments deficit.

16

Two aspects Of monetary balance Of payments analysis should be
emphasized. First, changes in the demand for money and the domestic
component Of the monetary base create balance Of payments disequi-
librium: the causation is unidirectional. Second, the composition Of
temporary balance Of payment flows is irrelevant: the monetary
approach does not distinguish between the current and capital
accounts.

The second point accounts for the apparent contradiction between
the monetary and component account approaches. Keynesian analysis
predicts a current account deficit following an increase in real
income and a capital account surplus following an increase in the
interest rate. As shown above, the monetary approach predicts a
balance Of payment surplus in the former and a deficit in the latter.

The conflicting results derive from the ceteris paribus assumptions

 

present in a "component account" partial equilibrium analysis.

B. The Floating Rate Case. While the modern revivers Of the

 

monetary approach suggest it is applicable to both fixed and floating
exchange rate regimes, development Of monetary exchange rate models
lagged behind their balance Of payments counterparts. This situation
was remedied by the collapse Of the Bretton Woods system and the
advent Of floating rates. The focus Of theoretical attention shifted
towards models Of exchange rate determination.

The first major difference between floating rate and fixed rate
models stems directly from exchange rate endogeneity. Both moneta-
rists and nonmonetarists would agree that a freely floating exchange
rate clears the foreign exchange market. This implies continuous

balance Of payments equilibrium, or, equivalently, no changes in the

17
foreign component of the monetary base. Consequently, a floating
exchange rate implies nominal money supply exogeneity.

The second major difference between fixed and floating rate
regimes is the method Of adjustment toward equilibrium. In the fixed
rate case, changes in the foreign component of the monetary base act
to equilibrate the money market by changing the nominal money stock.
The exogenous price level assured adjustment between the real money
stock and the demand for real balances. In the floating rate case,
the exogeneity Of the money stock forces adjustment through the price
level and, consequently, the exchange rate.

These and other aspects Of the monetary approach to exchange rate
determination are best examined with reference to a simply specified
model. The money markets Of the two countries can be described by
conventional money demand equations and exogenous money supplies.
Assuming both markets clear:

(1) M = Pf(y,r)
(2) M* = P*f(y*,r*)
where "*" denotes foreign country variables. The model is completed
by assuming PPP (s = P/P*), solving the money markets for prices, and
substituting:
(3) s = Mf(y*,r*)/M*f(y,r)

As iri the fixed rate case, the exchange rate is determined by
money market conditions in the two countries. Changes in income and
interest rates associated with a surplus/deficit in the fixed rate
case are associated with an appreciation/depreciation in the floating
rate case. Consider an exogenous increase in income. This increases

the stock demand for money and creates an incipient balance Of

18

payments surplus. Under fixed rates an actual surplus ensues through
an increase in the foreign component Of the money supply. Under
floating rates a decrease in the price level raises real balances and
restores money market equilibrium. Falling domestic prices
simultaneously appreciate the currency through PPP. Increases in the
money supply or interest rate precipitate a depreciation by effecting
an incipient balance of payments deficit.

The preceding model assumes that PPP holds continuously, and the
exchange rate is determined soley by present values Of arguments in
the money market equations. This implies that equation (3) is:
1) valid as both a short and long run explanation Of exchange rate
determination, and 2) equivalent to a fully specified general
equilibrium model including all aspects of the components approach.18
Excess supply/demand for money is instantaneously balanced by excess
demand/supply Of gOOds and nonmonetary assets.

Several criticisms, however, have been leveled at this specifi-
cation Of the monetary approach. The first criticism cites the lack
Of attention paid to nonmonetary asset markets. The assumption Of
interest rate exogeneity in a ffloating rate world seems very strong

indeed.19

The second criticism is leveled at the PPP assumption.
Critics have cited two different Objections. The first group Of
Observers accepts PPP as a long run condition but rejects instan-
taneous price adjustment. This leads to short run deviations from PPP
in the context Of disequilibrium adjustment. A second group rejects
PPP as a statement describing the exchange rate and general price

levels in both the short and long run. They agree that the relative

price Of tradable goods will reflect the exchange rate, but there is

19
no necessary reason to expect nontraded goods to meet that condition.
If this were the case, the exchange rate will generally ngt_reflect

the ratio of absolute price levels.

2.4 DevelOpment Of the Monetary/Asset Approach

This section reviews the development Of monetary exchange rate
models. The develOpment can be viewed as a process in which the
strict assumptions Of the simple model are relaxed. Although the
exchange rate is always viewed in the context Of stock equilibrium,
its determination is characterized by factors not present in the
simple specification.

The factors which determine the exchange rate are: 1) the money,
asset and goods market specifications, 2) the restrictions imposed on
the models solution, and 3) the mechanism for dynamic adjustment (in
models which allow deviations from equilibrium). The monetary
approach to exchange rate determination has evolved through the
develOpment Of these factors and their determinants.

The discussion will proceed by examining five extensions of the
simple model. While they are Often combined in particular exchange
rate models, each extension creates a new factor which influences the
exchange rate. First, expectations are introduced by examining the
asset market in the context Of continuous PPP. Second, currency
substitution models are developed by allowing residents to demand both
domestic and foreign monies. Third, asset and commodity markets are
examined under conditions of short run disequilibrium. Fourth, the
effects Of relative price changes are explored by the introduction Of
two or more goods. Fifth, portfolio balance models are considered,

and the effects Of wealth shifts and risk are explicitly examined.

20

A. Expectations. While the assumptions Of our simple model

 

assure the equality Of real interest rates, the relationship between
nominal interest rates and the exchange rate is not fully specified.
Two alternative yet complimentary approaches have been used to close
the models: the first introduces IRP, while the second introduces
Fisher equations. Both invoke rational expectations.

According to IRP, the nominal interest rate differential reflects
the lgg_difference between the forward and spot rates. The forward
rate, in turn, can be made endogenous by assuming the uncovered
interest arbitrage condition: the forward rate equals the expected
future spot rate. By performing these substitutions in the simple
model, the exchange rate is seen as a function Of money supplies,
incomes and the expected spot rate. The analysis is completed by
invoking rational expectations and modeling the expected spot rate
using expected future values Of the exogenous variables.20

The exchange rate and interest rates were directly linked using
IRP; Fisher equations link them indirectly through PPP. Since real
interest rates are assumed equal across countries, nominal interest
rate differentials can be attributed to differing levels Of inflation
expectations. The exchange rate, as.a ratio Of two price levels, is
now determined by money supplies, incomes and inflation expectations.
By invoking rational expectations, inflation expectations are shown tO
be determined in the money market according to expected future values
Of the exogenous variables. Thus, the IRP and Fisher equation
approaches are equivalent in the simple model with continuous PPP

equilibrium.21

21

The use of rational expectations changes the character Of the
exchange rate solution. In particular, the exchange rate depends upon
both current and expected future values Of the exogenous variables as
well as the interest elasticity Of the demand for money.22

B. Currency Substitution. Models of currency substitution extend

 

the standard monetary model by allowing residents to hold both
domestic and foreign currencies. The composition Of the currency
portfolio is determined by expected rates Of return. The differential
expected rate Of return equals the rate Of depreciation for
noninterest earning assets.

Two variants Of currency substitution models exist in the
literature. The global monetarist models generally assume integrated

23 A second variant

capital markets, one gOOd, and two countries.
analyzes a small country, twO good model in the absence of capital
flows.24 Changes in the supply Of foreign currency occur through the
current account. Models Of the second variety will be examined at a
later point in the discussion.

Global monetarist currency substitution models define the
exchange rate as a function Of money supplies and relative holding
costs Of domestic and foreign currencies. This is evident when the
money demand specifications are considered. The transaction demand
for domestic money is determined by the sum Of domestic and foreign
income; the same is true for foreign currency.25 Further, real money
stocks are expressed in terms Of domestic prices in both countries tO
avoid the PPP condition. The exchange rate, as a ratio of money

market equations, is determined by relative money supplies and the

interest rate differential.

| 22

Assuming uncovered interest arbitrage, the nominal interest
differential equals the expected rate Of depreciation (i.e. the
expected future rate minus the spot rate). Imposing rational
expectations yields an expression for the exchange rate which includes
current and expected future values Of exogenous variables adjusted by
a parameter which measures the elasticity Of substitution between
currencies.26

The currency substitution model views the exchange rate as an
asset price which equilibrates the holding cost Of currencies. If
currency substitution is not perfect, an interest rate differential or
expected depreciation can exist. However, in the case Of perfect
substitution, interest rates must be equal or one currency will be
driven from circulation: no investor would hold a currency expected to

depreciate (in the absence Of risk).

C. Disequilibrium. Thus far, innovations in exogenous variables

 

led to instantaneous adjustment in both the asset and goods market.
The exchange rate, therefore, is in constant equilibrium. Models Of
exchange rate disequilibrium break from these assumptions. The
exchange rate deviates from its equilibrium level as a consequence Of
slowly adjusting markets. Dynamic models, then, are concerned with
both the equilibrium path and adjustment to that path.

The distinction between the behavior Of asset prices and
commodity prices is central to dynamic disequilibrium models.27 while
asset prices adjust quickly tO information effecting their current and
future value, commodity prices often respond slowly. This results in

exchange market disequilibrium.

23

Consider a simple one gOOd two country monetary model with
rational expectations where the equilibrium exchange rate is defined
by PPP.28 Assume that current or future changes in the exogenous
variables are not expected. Given equilibrium, this implies real
interest rates are equal (in a world Of perfect capital mobility), and
inflation rates are zero.

Consider an unanticipated one time decrease in the domestic money
supply. An immediate appreciation of the equilibrium exchange rate
is needed to restore money market equilibrium. If this is accompanied
by an instantaneous proportional decrease in the domestic price level,
equilibrium PPP would hold continuously. If, however, domestic
commodity prices are slow to adjust, equilibrium PPP is not
immediately restored.

When output prices are sticky, the decrease in real balances
(caused by the decrease in the domestic money supply) raises the
domestic cost Of capital or real interest rate. This implies a real
interest rate differential between home and abroad. The differential,
in turn, creates a forward premium on domestic currency (IRP) equal to
the expected depreciation (rational expectations). As commodity
prices adjust to the new money supply, the exchange rate continues to
depreciate and the interest rate differential narrows. Equilibrium
PPP is restored once prices fully adjust.29

Two aspects Of the preceding analysis should be noted. First,
equilibrimn and disequilibrimm exchange rate paths are determined by
the price adjustment specification. In the above example, the
implicit price mechanism caused the exchange rate to overshoot its

3D

equilibrium level. A general specification describes both the

24

equilibrium and disequilibrium price path. Price adjusts to expected
changes in its equilibrium value and to goods market disequilibrium.31

Second, the disequilibrium model can change the interpretation Of
the nominal interest rate differential. In models Of continuous
equilibrium the differential represents differing inflation (expec-
tations. However, in disequilibrium models, nominal differentials can
be associated with real differentials. The exchange rate depreciates

in the former case but appreciates in the latter.

0. Several Goods. The notion that the terms-Of-trade (TOT)

 

influence the exchange rate has a long history in international
finance. The elasticity approach views the TOT as the central
mechanism in balance-of—payments adjustment. Change in relative
rather than absolute prices play the key role.

The extension Of the monetary approach to two goods Opens new
avenues for exchange rate determination. First, real effects are
allowed channels Of causation other than the income term Of the money
demand equation. Second, the addition Of relative prices allow
deviations from PPP in both equilibrium and disequilibrium
specifications. Third, the current account can play an explicit role
in exchange rate adjustment.

Consider a two country, two good model with complete speciali-
zation in production. The TOT is defined as the relative price Of the
domestic good in terms of the foreign good. Movements in the TOT can
occur through changes in the ratio Of domestic and foreign good prices
and/or the exchange rate. The homogeneity properties Of prices and
the exchange rate with respect to money preclude permanent TOT

Inovements associated with changes in nominal money stocks. However,

25
real changes in the supply and demand for goods will effect the
equilibrium TOT.
Assume an increase in foreign demand for domestic output. This

would, ceteris paribus, increase the ratio Of domestic to foreign

 

prices. It would also increase the demand for domestic currency as
foreigners attempt to substitute goods from abroad for those produced
at home. Thus, an increase in the terms Of trade appreciates the
exchange rate. Further, the appreciation is associated with
deviations from PPP: the exchange rate which equalizes the balance Of
trade increases relative to PPP. Finally, this result Obtains in
conditions Of continuous equilibrium.32

Slowly adjusting prices create another source Of PPP deviatiOns
in two good dynamic models. However, these are disequilibrium
phenomena when the equilibrium TOT is fixed.33

Consider an exogenous shock which increases the equilibrium
general price level while leaving the equilibrium 'TOT unchanged.
Equal increases in the general price level and the exchange rate will
occur in the long run. However, short run disequilibrium will ensue
when the price Of domestic goods are "sticky." The shock creates an
excess supply Of money which drives down the domestic interest rate
(if real balances remain constant). This depreciates the exchange
rate. The TOT deteriorate since the depreciation is not accompanied
by rising domestic good prices. Consequently, general price levels no
longer reflect PPP in the short run.

The adjustment process in a two gOOd model parallels model

adjustment in a one good model with one major difference. Slowly

increasing domestic prices increase the TOT and consequently the

26
general price level. The exchange rate appreciates and the interest
rate increase until equilibrium is restored. The exchange rate and
TOT move together in both equilibrium and disequilibrium adjustment.

According to the income and absorption approaches the current
account plays an important role in equilibrating the exchange rate.
In fact, exchange rate equilibrium is defined as a zero current
account. Some dynamic disequilibrium monetary models have
incorporated the effects Of current account imbalances.34

As in the previous analysis, the asset market determines the
exchange rate. It is the current account, however, that determines
the path. In particular, the income from fOreign assets enters the
money demand function. Moreover, the real value Of external assets
held by residents is a determinate Of domestic wealth. Finally,
wealth and the terms Of trade are arguments in the demand for domestic
goods.

The solution to the model demonstrates that only one level of
wealth will clear the money and good markets given the relationship
between the equilibrium TOT and external assets held by domestic
residents. Below this level Of wealth assets are accumulated creating
a current account surplus. The increase in wealth associated with the
surplus increases the demand for domestic goods and improves the TOT.
With foreign prices fixed, the current account surplus is associated
with an exchange rate appreciation.

E. Portfolio Balance Effects35. Thus far, the forward exchange

 

rate has been identified with the expected future spot rate. Given

IRP, this implies outside bonds denominated in different currencies

27
are perfect substitutes. Further, it implicitly assumes that
bondholders are risk neutral.

Models Of portfolio-balance eliminate these restrictive
assumptions. Investors attempt to maximize the utility from their
portfolio, subject tO their perception Of risk, by equalizing expected
asset yields. Given domestic and foreign interest rates, expected
yields are equalized by the expected rate Of appreciation.

In a risk averse environment, expected yields are effected by the

excess Of supply Of bonds.36

Assume a forward premium on domestic
currency. If the supply Of bonds denominated in domestic currency

increased, ceteris paribus, investors would demand a higher expected

 

rate of return to willingly accept them into their portfolios. At
existing interest rates, a risk premium, above the forward premium, is
needed to clear the asset market. The expected future spot rate would
then exceed the forward rate.

The risk premium is also sensitive to the international
distribution Of wealth if domestic and foreign residents differ in
their perceptions Of risk. A transfer Of wealth from home to abroad
will increase the risk premium if domestic residents have a relative
preference for assets denominated in domestic currency. The excess
supply Of bonds created by the transfer requires an increase in the
expected rate Of appreciation to clear the asset market.

TO sunlnarize, either increases in the relative supply Of bonds
denominated in domestic currency or transfers Of wealth abroad,

ceteris paribus, raise the risk premium on domestic currency. This

 

severs the expected future spot rate - forward rate identity.

28
Finally, the current account has been reestablished as an
important mechanism in achieving exchange rate equilibrium. 'The
wealth effect generated by current account flows influences the
exchange rate in two ways. First, an increase in wealth causes a
relative price effect by raising the demand for domestic output in two
good models. Second, the wealth effect precipitates a rebalancing Of

portfolios.

2.5 Testing The Theory

This section overviews the estimation procedures employed in
testing the monetary/asset approach to exchange rate determination. A
general description Of single equation and systems techniques will be
examined. A discussion Of proxy variables is also included.

One group Of studies uses single equation techniques tO test the
sign and significance Of exogenous variable coefficients. Studies Of
this variety have grown to include all the theoretical effects
described earlier in the chapter; although, many employ only a subset.
As a general specification, the exchange rate is estimated as a func-
tion Of money supplies, incomes, interest rates, expected inflation,
real effects, and risk.

While the proxies for monies, incomes and interest rates have
conventional interpretations, the other variables present modeling
problems since they are unobservable. Because Of this, the expected
inflation rate has been proxied in several different ways. First,
long term interest rate differentials or long term forward rate
premiwms have been substituted for expected inflation differentials.
This will yield unbiased estimates if the Fisher equation is assumed,

real interest rates are equal, and there is coefficient equality

29
across countries. A second alternative employes an adaptive mechanism )///
to predict future inflation. A six or twelve month moving average Of \PTA
past inflation rates is generally used.

The risk term has also found several proxies: the supply Of
government bonds, the supply Of foreign bonds held by residents,
current account statistics, and complete specifications. The first
proxy attempts tO capture changes in risk associated with relative
changes in the supply Of outside assets. The second and third proxies
capture change in risk associated with changes in the residence of
wealth. Finally, the general specifications attempt tO capture both
effects.

Real effects, exchange rate movements due to changes in supply
and demand for domestic and foreign goods, are proxied in two ways.
First, relative import and export price ratios are used. This proxy
attempts tO distinguish between relative and absolute price changes.
Second, either current account or trade statistics are employed in an
attempt to capture supply and demand changes. An extension Of this
technique uses unexpected changes in the current account or trade
balance to model real effects. The expected balance is calculated!
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A second group Of empirical studies explicitly accounts for the

 

rational expectation assumption present in most theoretical models.
V/The stochastic processes Of exogenous variables are eiifl§£_2§§!fl§fl“2£,.
W Estimates Of the general exchange rate model include a

joint test Of the model and the rational expectations assumption.

30

In this type Of procedure, the expectational variables are no
longer proxied. Rather, the solution Of the model determines the
exchange rate as a function Of present, past and expected future
changes in the exogenous variables. Consider, for example, the simple
monetary model. The interest rate differential or expected
depreciation is a function Of past, present, and expected future
values of monies and incomes.

Table 2.1 reviews the empirical exchange rate studies Of the
monetary/asset approach since 1978.37 The studies which employ FIML
or maximum likelihood estimation test for rational expectations as
well as model specification. The conclusions drawn in the "results"
column are my own and may not necessarily agree with the author(s) Of
the study. "Positive" results imply significance Of all exogenous

variables.

2.6 Conclusion

The monetary/asset approach has become the dominant theoretical
explanation Of exchange rate determination. The approach differs from
its immediate predecessors by defining equilibrium in terms of stocks
rather than flows. Further, the approach is a general equilibrium
formulation as Opposed tO earlier account-by-account analysis.

The historical development Of the monetary/asset approach can be
viewed as a series of extensions Of the simple monetary model.
Specifically, general formulations Of the bond and goods markets allow
for stock/flow interaction to determine the exchange rate and its
path. The specification Of various price adjustment mechanisms
determine both the equilibrium and disequilibrium behavior Of the

exchange rate.

31

 

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34
Tests Of the monetary/asset approach are, thus far, inconclusive.
It appears, however, that results are very sensitive to both the
choice Of countries and the time period. This could be the result Of
unstable money demand equations or changing asset preferences. Alter-

nately, the model could be misspecified.

35

FOOTNOTES - CHAPTER II

1For a review Of the PPP literature, see Officer (1976) and
Officer (1984).

2The formulation Of absolute PPP requires weights to constrict
price levels. This poses major difficulties. See Officer (1984).

3This relationship is Often posited in the monetary approach.

4
tests.

5The post World War I German hyperinflation is a case in point.
See Frenkel, 1976.

6For a review of the pre-1970 IRP literature, see Officer and
Willett (1970).

7

See Kreinin and Officer (1978) for references to empirical

The development Of IRP begins with Keynes (1923).
8See, for example, Aliber (1973).

9See Marston (1976) and Herring and Marston (1976).

10Many consider Harberger (1950) as the classic article.
11We assume the Marshall-Lerner conditions tO hold.

12See Myhrman (1976) for a discussion Of the Swedish debate.

13The roots Of the monetary approach are examined in Frenkel
(1976), Frenkel and Johnson (1976) and Kreinin and Officer (1978).

14Studies Of the monetary approach originated at the IMF are
collected in International Monetary Fund (1977).

15The works of Mundell (1968, 1971), Johnson (1972) and Komiya
(1969) are generally credited for introducing the monetary approach to
the academic establishment.

16This assumes the money multiplier, m, is constant.

17Sterlization is generally assumed away in early monetary models.
See, for example, Magee (1976).

36

18This fact is recognized by many authors including Bilson (1979)
and Isard (1978).

19Although real interest may be exogenous, nominal dates are
effected by inflation expections. The exogeneity of inflation
expectations is a contradition in a "rational" model.

20The use Of rational expectations has been common since the
mid-1970's. Some Of the earlier examples include Frenkel (1976b),
Mussa (1976) and Dornbush (1976).

lef PPP or equilibrium PPP were not continuous, the IRP and
Fisher equation interpretations would not be equivalent.

22In some solutions, past, as well as current and future values
describe the exchange rate path.

23Girton and Roper (1976) did the initial study.

24The models Of Kouri (1976) and Calvo and Rodriguez (1977) are
examples Of this formulation.

2SCurrency substitution models Often specify money demand as a
function Of wealth.

26This parameter is dependent upon the interest elasticity Of
money demand.

27The term "commodity" should be considered synonymous with
"output."

28No good dynamic models are discussed in the terms-Of-trade
section.

29

The analysis presented parallels a one good Dornbush (1976)
model or Frankels' (1979) model without “secular" inflation.

30The relationship between overshooting and the price adjustment
mechanism is discussed in Either (1979), Mussa (1982) and others.

31See, for example, Mussa (1981).

32A model Of continuous equilibrium which allows deviations from
PPP is developed by Stockman (1980).

33See Dornbush (1976), Mussa (1982) and references therein.

34See Kouri (1976), Dornbush and Fisher (1980), Rodriguez (1980).

35The portfolio balance model determines the relative level Of
spot and expected future exchange rates. The determination Of
absolute levels require a general specification which includes prices.
Consequently, the portfolio balance effect can be integrated into the
earlier models.

37
36A formal derivation Of risk is presented by Solnik (1974) and
Dornbush (1980). An empirical application is found in Isard (1980).

37See Kreinin and Officer (1978) for earlier references.

CHAPTER III

SOME POPULAR MODELS OF
EXCHANGE RATE DETERMINATION

3.1 - Introduction

The develOpment Of the monetary/asset approach to exchange rate
determination was reviewed in Chapter II. Although each model defined
exchange rate equilibrium in terms Of asset stocks, disparate and
sometimes contradictory specifications were produced. This chapter
develops and estimates five Of the most popular models.

The models represent three distinct views Of exchange rate
determination within the monetary/asset approach. The "pure“ monetary
or continuous equilibrium models Of Bilson (1978) and Frenkel (1976)
are representative Of the "Chicago" school.1 The Dornbush (1976) and
Frankel (1979) specifications are disequilibrium monetary models.2
Finally, the Hooper and Morton (1980) model includes both real

3 and portfolio balance considerations.4

exchange rate effects

The exposition Of the models is twofold. First, the models are
develOped directly from the behavioral assumptions and adjustment
mechanisms suggested by the author. Second, the models are developed
within the Isard identity. This allows for the comparison Of the
models within a common framework.

Section 3.2 introduces the the accounting framework develOped by
Isard (1982) which equates the exchange rate with price differentials,

interest rate chferentials, expected inflation differentials, risk,

38

39
and the expected real exchange rate. Section 3.3 develops the models
Of Bilson (1978), Frenkel (1976), Dornbush (1976), Frankel (1979), and
Hooper and Morton (1982). Section 3.3 is intended to introduce models
Of greater and greater generality within the asset approach. Section
3.4 presents estimable forms of the models and discusses estimation
procedures. Section 3.5 presents and interprets the results Of the
estimation. Section 3.6 Offers a summary and conclusions as to which
hypothesis is supported by the results. Two appendices are also
included. The first discusses modeling Of unobservable variables. The

second cites data sources.

3.2 - Isard's Formulation
An accounting framework develOped by Isard (1982) is a useful
tOOl for develOping behavioral models Of exchange rate determination.
The framework includes monetary, real and portfolio balance effects.
The interest rate parity condition coupled with definitions of

risk and the real exchange rate provide a foundation for analysis.

(1) f = s + r - r* Interest Rate Parity Condition
(2) Etrisk = Ets - f Risk Identity
(3) q = s + p* - p Real Exchange Rate Identity
(3') th = Ets + Etp* - Etp Expected Real EXchange Rate
Identity
where
s, f are the logs Of the spot and forward exchange rates
defined as the price Of foreign currency
risk is the risk premium

p, p* are the logs Of the domestic and foreign price levels

r, r* are domestic and foreign interest rates
q is the lgg_of the real exchange rate
E is the expectations Operator

40
Combining (1) (2) and - (3') yields:

(4) S = Etp - Etp* + r* - r + th - Etrisk

The framework is completed in two steps. First, expected logarithmic

price levels are approximated by:

(5) EtP = P + W
and (5') Etp* = p* + n*
where it and 1r* are domestic and foreign expected inflation rates.

Second, equations (5) and (5') are substituted into equation (4):
(6) s = (p - p*) - (r - r*) + (ii- r*) + th - Etrisk

The exchange rate reflects relative prices, relative interest rates,
relative expected inflation rates, the expected real exchange rate and
expected risk. Note that equation (6) is an accounting identity and
not an equilibrium condition. The addition Of behavioral assumptions

are needed to generate a fully specified model.

3.3 Some Popular Exchange Rate Models

Competing explanations Of exchange rate determination exist
within the monetary/asset approach. This section examines five
popular models and identifies their similarities and differences. The
explication is twofold. First, the models are developed from their
behavioral assumptions, market specifications and adjustment
mechanisms. Second, the models are examined within a cannon frame-
work, the Isard identity. The conceptual perspective forms the

foundation for later empirical analysis.

41

The models develOped and estimated by Bilson (1978) and Frenkel
(1976) are early variants Of the monetary/asset approach. These pure
monetary specifications are representative Of the "Chicago" school.
According to this view, the exchange rate is assumed tO reflect the
ratio Of price levels between countries. Flexible prices ensure that
purchasing power parity (PPP) and, consequently, exchange rate
equilibrium hold continuously. A further assumption, price levels
determined solely in the money markets, accounts for the pure monetary
nature of the models.

The Bilson and Frenkel models are formally derived by substi-
tuting money market specifications into the equilibrium exchange rate
equations. Assuming the equilibrium exchange rate is defined by PPP
gives:

(7) s = p - 6*
where “-" denotes equilibrium value. Bilson models price levels using

conventional money demand equations with identical parameters for both

countries:
(8) m - P = oy - 1r
(9) m* - p* = ¢y* - 1r*
where
m, m* are lgg§_of domestic and foreign money supplies

y, y* are logs Of domestic and foreign real outputs.
Frenkel adapts an alternative specification:
(10) m - p = 6y - An
and

(11) m* - p* = ¢y* - xn*

42

The assumption Of continuous PPP eliminates the distinction between
current and equilibrium values. Substituting equations (8) and (9)
into (7) yields the Bilson model:

(12) s = (m-m*) - ¢(y-y*) + §(r-r*)
Substituting equation (10) and (11) into (7) gives the Frenkel speci-
fication:

(13) s = (In-m) - ¢(y-y*) + Mir-r*)

Coefficient signs Of the independent variables reflect the
monetary nature of exchange rate determination. Increases in the
domestic money supply will depreciate the spot rate by raising
domestic prices. Increases in domestic-income increase demand for
money and appreciate the spot rate. Finally, increases in the
domestic interest rate or expected inflation rate decrease the demand
for domestic money and depreciate the currency.

The similarity Of the Bilson and Frenkel specifications stem from
the assumption Of continuous PPP. An examination Of the models within
the Isard framework (equation 6) reveals three common restrictions.
First, the nominal interest. rate differential equals the) expected
inflation differential. This implies real interest rates are equal
across countries. Second, the log Of the real exchange rate is zero.
Restated, the law Of one price holds in conmodity markets. Third,
expected risk is zero. Consequently, assets are perfect substitutes.
These common restrictions imply theoretical equivalence between the
models.

In contrast to the monetary models of the "Chicago" school,
Dornbush (1976) explicitly allows for short run deviations from

equilibrium PPP. This result stems from a dichotomy in market

43
adjustment mechanisms. Dornbush assumes prices adjust slowly in
commodity markets while asset prices adjust instantaneously.
Consequently, the spot exchange rate can deviate from its equilibrium
value in the short run. Three assumptions in addition to the
previously specified money market and equilibrium exchange rate
equations form the model. First, uncovered interest rate parity holds
continuously: the forward premium or expected rate Of depreciation, d,
equals the nominal interest rate differential.
(14) d = r - r*
Second, the expected rate Of depreciation is a function Of the
difference between the equilibrium and spot exchange rate:
(15) d = 9 (§ - s)

where 9 is a speed Of adjustment coefficients.

Third, the expected inflation differential is zero when the
exchange market is in equilibrium.

The solution Of the model is straightforward. Combining
equations (14) and (15) yields

(16) r — r* = O(§-s)
The disequilibrium nature Of the model is revealed in this equation.
It is evident that the spot rate deviates from equilibrium directly
with interest rate differentials. Substituting equation (13) for 5,
setting (nhn*)=0 and rearranging terms gives6
(17) s = (m-m*) - 6(y-y*) - B(r-r*)

The Dornbush model suggests an alternative explanation for

exchange rate movements. While the signs Of the money supply and

income terms parallel the monetary models Of Frenkel and Bilson, the

interest rate differential has an Opposite effect on the spot rate.

44
This result is directly attributable to deviations from PPP allowed by
equation (16). The existence Of "sticky" prices alters the interpre-
tation Of interest rate movements.

Consider for example a decrease in the domestic money supply
without a proportional decrease in domestic prices. Domestic interest
rates rise to clear the money market. The interest rate differential
creates an inflow Of foreign capital and, consequently, an apprecia-
tion Of the exchange rate. Equilibrium is restored in the exchange
market as prices fall.7

Interpretation Of interest rate movements reflect the
equilibrium/disequilibrium nature Of underlying price changes. In the
Bilson-Frenkel type models, interest rate changes are associated with
changes in inflation expectations. Higher expected price levels,
indicated by increasing interest rates, depreciate the spot rate. In
the Dornbush model, higher interest rates reflect tighter money market
conditions caused by slowly adjusting prices in the goods market. A
real interest rate differential, indicated by a nominal differential,
creates a capital inflow and spot appreciation.

The relationship between the equilibrium and disequilibrium
models is further clarified by the use Of Isard's identity. The
Dornbush model follows from equation (6) by assuming 1) the expected
inflation differential is zero; 2) the real exchange rate is constant;
3) no risk premium exists; and, 4) the equilibrium exchange rate is
defined by PPP. Either specification Of the price level yields
equation (17), the Dornbush specification.

The real interest rate differential implicit in Dornbush is

modelled explicitly by Frankel (1979). Both expected inflation rates

45
and nominal interest rates are included in the exchange rate adjust-
ment condition.
(18) r - r* = e(§-s) + n-n*
This formulation allows for changes in the nominal interest. rate
differential without concurrent exchange market disequilibrium.
Further, deviations from equilibrium are synonymous with [gal_interest
rate differentials. The Frankel model is completed by substituting
equation (9) for E in equation (18) and solving for s:
(19) s = (m-m*) - 6(y-y*) - %(r-r*) + (%+X)(n—n*)

Equation (19) follows directly from Isard's identity, equation
(6), if we assume 1) the real exchange rate is constant; 2) no risk
premium; and, 3) long run PPP with prices modeled by either conven-
tional or Cagen-type money demand functions. This model extends the
monetary/asset approach by differentiating the roles Of interest rates
and expected inflation rates on exchange rate movements.

Thus far, deviations from PPP are considered disequilibrium
phenomena. This result is a consequence Of two assumptions: the law
Of one price in the asset markets and a constant real exchange rate.
The former assumption eliminates exchange rate movements associated
with imperfect asset substitution. The latter removes effects
associated with changes in the real economy. The Hooper and Morton
(1980) model relaxes both restrictions.

Eliminating‘ the assumption Of perfect substitution, between
domestic and fOreign assets introduces exchange risk. Consequently,
the IRP condition (equation (14)) no longer reflects asset market
equilibrium. A risk premium, in addition to the interest rate

differential, is needed to clear the market.

46
(20) d = r-r* + Etrisk
Combining equations (20) and (18) yields
(21) s = ‘s' - %[(r-r*) + n-ir* — Etrisk]

The existence Of risk creates disequilibrium in the exchange market if
real interest rates are equalized.

A general version Of the monetary/asset model is completed by
allowing changes in the real exchange rate. The real economy can now

effect the nominal exchange rate directly. Further, real exchange

rate movements cause equilibrium deviations from PPP.

 

(22) 6 = § + 5* - 5
Combining equations (7), (8) and (22) yields a solution for s.
Substituting this result into equation (21) completes the model.
(23) s = (m-m*) - ¢(y-y*) - %(r-r*) + (%+1)(n-w*) + th - % Etrisk
This result also follows directly from equation (6), Isard's identity,
when assuming the price component is modeled by conventional money

demand equations.

3.4 - Estimation

Rather than estimating each specification individually, a general
model will be estimated which includes each Of the previous specifi-
cations as restricted cases. This will allow comparisons between
models in a unified framework. Tests conducted upon alternative
restrictions will be used to evaluate the empirical viability Of the
competing models.8 The general model is an unrestricted version Of

the Hooper and Morton specification:

(26) s

a1+u2m-a3m*-a4y+osy*-a6r
+97"*+93 ~°9*+91oq+9urisk

47

All of the models presented in Section 3.3 carry two common
restrictions:

l) 012 = 013 = 1
and ii) a4 = OS
The assumption Of unitary elasticity Of prices with respect to money
embodied in standard money demand equations accounts for the first
restriction. The assumption that domestic and foreign money demand
equations have identical coefficients accounts for the second.

The alternative models can now be defined by additional

restrictions:
1. Bilson: ' 0.6 = 417 Mid a8 = 39 = 0.10 3 all = 0
2. Frenkel: a8 = (19 and as = 017 = “10 = 0‘11 = 0

Frankel 1: a6 = a7, a8 = 019 and 0110 =0111 = 0

01-9

Frankel 2: 016 = O7, 018 = 019 and 0:10 = O

6. HOOper and Morton: 016 = 01-, and 018 = 0:9

It should be noted that the interest rate restriction imposed in
the Bilson model reflects the assumption Of identical domestic and
foreign money demand equation. However, the interest rate restriction
in the Dornbush, Frankel 1, Frankel 2, and HOOper and Morton models
follow from assumptions concerning price adjustment rather than money
demand considerations.

Equation (26) will be estimated in unrestricted form and with
money supply coefficients set equal to one. Frankel correctly notes

that this does not impose the restriction of equal money demand

48
elasticities if we believe in the homogeneity of money with respect tO
the exchange rate a_prigri.

The general model will be estimated using the U.S. dollar-mark
and U.S. dollar-Canadian dollar exchange rates. The U.S. dollar-mark
rate was chosen for several reasons. The unexpected volatility Of the
U.S. dollar-mark calls particular attention tO this rate. The large
intra- and intercountry variations in money growth rates, interest
rates, inflation rates, and real growth rates throughout the
post-Bretton Woods period suggest this rate is particularly well
suited for both the equilibrium and disequilibrium models. Further,
the pOpularity Of this exchange rate as expressed in previous
empirical studies allows for comparisons of results.

It should be noted that the Germany participates in a joint float
with other European countries. Consequently, the exchange value of
the mark does not float "cleanly" against the dollar. However, the
mark dominates the other currencies as an international money. Due to
this fact, the D.M. participation in the snake has minimal effects on
the dollar-mark exchange rate.9

The Canadian rate is Of special interest for two reasons. First,
the large volume Of trade flows should shed particular light on real
exchange rate effects. Second, the relative similarity Of inflation
expectations during certain periods will test Frankel's contention
that model performance is related tO variations in expected inflation
differentials.

The sample period consists Of monthly Observations between April,

1973 and March, 1983. The structural stability Of the coefficients

49

are examined by estimation Of the five-year periods preceding and
following March 1978.10

The model is estimated by ordinary least squares and instrumental
variables with interest rates, inflation expectations, the expected
real exchange rate, and expected risk considered endogenous.
Following Frankel (1981), ratios Of outstanding government debt to
monetary base and long term interest rates are used as instruments for
short term interest rates and expected inflation rates, respectively.
Instruments for the expected real exchange rate and expected risk
include cumulative current. account balances and government. budget
deficits. Lagged values Of all endogenous and included exogenous
variables are also included as instruments to remove serial correla-

tion. Complete structural models are estimated in the next chapter.

3.5 - Results: Summary Of Estimation

Comparison Of the different theoretical specifications is based
upon four criteria: tests Of 1) coefficient equality restrictions; 2)
coefficient sign, 3) coefficient significance; and, 4) coefficient
stability. These criteria are examined for the sample period and two
subperiods. Further, they are examined for three different inflation
expectations proxies: adaptive, rational, and survey.

Germany and Canada are analyzed separately before a general
conclusion is drawn. The results are based upon ordinary least
squares and two-stage least squares estimation corrected for serial
correlation. All unrestricted and restricted versions Of the general
model were autocorrelated over the sample and subsamples examined.
One explanation for the existence Of autocorrelation in monthly

Observations is government intervention in the exchange market, an

50
omitted variable in the general model.11 Evidence suggests that over
a quarterly period serial correlation is not present.

A. Germany. Tests Of equality restrictions imposed by assuming

 

identical money demand functions generally failed for money supplies,
interest rates, and inflation rates but held for income. This
suggests that restricted versions Of the general model which do not
have theoretical origins will lead tO biased estimates. Thus, both
the Bilson and Frenkel models must be analyzed using either the
general model or a restricted model with the coefficient on the
difference between the l_09_ Of the money supplies set to one. The
Dornbush, Frankel, and HOOper and Morton models must have inflation
rates unrestricted. Further, if the speed Of adjustment term is
separated into domestic and foreign components, then the interest
rates must be unrestricted.12

The preceding analysis implies four specifications: the general
model and three restricted versions. All restrictions are a_prigri
assumptions imposed by theoretical relationships posited in the

earlier exchange rate models. Therefore, the tables tO follow report

the four specifications:

(27) e = “1c + azm + a3m* + a4y + a5y* + o6r

+ a7r‘k + a8"- + agn" + aloq + allRTSk

(28) e - m + m* = alc + o4y + a5y* + a6r + o7r*

+ can + o9n* + aloq + allRisk

(29) e = alc + o12(m - m*) + a4y + o5y* + a13(r - r*)
+ can + agn* + aloq + allRisk

51
(30) e - m + m* = “1° + day + a5y* = a13(r - r*)
+ C18“ + agTI* + (1qu + allRi 5k

Equation (27) is the general model. Equation (28) sets the coeffi-
cients Of domestic and foreign money supplies to one and negative one,
respectively; Equation (29) restricts the money supply coefficients
and interest rate coefficients to be equal across countries. Equation
(30) sets the money supply coefficient equal to one. Tables 3.1, 3.2,
and 3.3 report OLS and IV estimates Of the four preceding specifi-
cations for the sample period and two subperiods.

Ordinary least squares and instrumental variable (IV) estimates
Of the general model over the sample period yield domestic and foreign
money supply coefficients of the wrong sign. The first subsample from
January 1974 tO March 1978, yielded correct signs. They were,
however, significantly different from the hypothesized values Of one
and negative one. The second subsample estimates, from April, 1978 to
March, 1983, were Of the wrong sign. Constraining the money supply
coefficients tO equal and Opposite signs did not alter the results:
the coefficient was generally Of the wrong sign and always signi-
ficantly different than one.

Estimates Of the domestic and foreign income term were generally
Of the expected sign and were significant in six out Of eight cases
using instrumental variables estimation. Both subsamples.,yielded
similar results with coefficients found highly significant using
ordinary least squares estimation over the first subsample.

'The fhndings pertaining to domestic and foreign interest rates
are particularly important: The expected sign Of interest rates

distinguishes between the alternative theories. It was found that

52

TABLE 3.1

REGRESSIONS OF THE GENERAL AND RESTRICTED MODELS
ON THE LOG OF MARK-U.S. DOLLAR EXCHANGE RATE
’T— 1974:1 - 1983:3

 

 

Variable (1) (2) (3) (4) (5) (6) (7) (8)
c 5.99 4.83 1.95 -.145 7.55 6.92 2.80 3.90
(1.05) (0.96) (1.30) (1.62) (1.71) (1.32) (1.10) (1.60)
m—m* 1.00 t -0.48 1.00 1.00 -0.06 1.00
(cstr) (0.28) (cstr) (cstr) (0.34) (cstr)
m -o.79‘ -0.94
(0.31) (0.92)
m* 0.18 0.20
(0.23) (0.61)
y -0.59b -0.33 -0.20 0.05 -1.23b -1.27b -l.56b -2.08b
(0.22) (0.25) (0.25) (0.24) ((0.37) (0.46) (0.47) (0.70)
y* 0.10 -0.30 -0.03 0.48 0.51 0.20 1.18b 1.55b
(0.19) (0.21) (0.27) (0.32) (0.33) (0.37) (0 32) (0.47)
r-r* -2.96b -2.20‘ 2.90 5.23
(1.11) (1.08) (2.14) (3.05)
r 2.65 8.79d 4.36 14.06d
(2.08) (1.97) (4.87) (3.07)
r* 3.41b 3.25b 2.14 1.87
(1.02) (1.14) (1.77) (2.12)
n 7.12 18.96b 6.72 1.63 1.39 3.31 1.72b 3.11b
(4.14) (4.18) (4.96) (5.23) (1.98) (1.97) (0.47) (0.24)
'n*‘} -15.30b -19.81° -8.52b -4.15 -3.94b -s.14b -o.98b -1.21b
_,/ (1.40) (1.27) 2.34) (3.13) (0.67) (0.34) (0.11) (0.13)
q 0.01 0.01 0.01 0.01 0.02 0.05 0.12 -0.13
(0.01) (0.04) (0.03) (0.03) (0.10) (0.09) (0.11) (0.14)
Risk -1.92a 2.31d 1.16 -O.87 —2.83 2.38d 1.14c 1.23d
(0.98) (0.38) (0.75) (1.41) (2.47) (0.41) (0.37) (0.56)
42 0.85 0.86 0.27 0.09
0.v. 1.99 1.99 2.20 2.24 1.99 1.97 2.00 1.98
8 0.04 0.42 0.08 0.96 0.28 0.32 0.27 0.34

 

Standard errors are in parentheses.

Equations (1) - (4) estimated using Cochrane-Orcutt procedure.

Equations (5) - (8) estimated using Ray Fair's procedure to correct for serial correlation
Of instrumental variable estimates.

significant at .05 level, correct sign
significant at .01 level, correct sign
significant at .05 level, incorrect sign
significant at .01 level, incorrect sign
constrained

”GOOD
IIIII

523

TABLE 3.2

REGRESSIONS OF THE GENERAL AND RESTRICTED MODELS
ON THE L9§_OF MARK-U.S. DOLLAR EXCHANGE RATE

1974:1 - 1978:3

 

 

Variable (l) (2) (3) (4) (5) (6) (7) (8)
c 11.88 0.74 0.67 0.41 5.77 0.89 0.67 0.76
(1.74) (1.64) (1.53) (1.56) (5.16) (2.31) (2.65) (2.64)
m-m* 1.00 t 0.38 1.00 1.00 1.27 1.00
(cstr) (0.38) (cstr) (cstr) (1.05) (cstr)
m 0.55 0.74
(0.37) (0.77)
m* -2.86b -1.85
(0.57) (1.08)
y -O.80b —O.82b -0.88b -O.83b -0.47 0.08 -o.71 -0.74
(0.29) (0.30) (0.29) (0.30) (0.80) (0.88) (1.04) (1.05)
y* 1.30b 0.88b 0.89b 0.96b 0.76 -0.19 1.01 0.99
(0.31) (0.35) (0.29) (0.30) (0.87) (0.63) (0.63) (0.62)
r-r* -1.53 -O.91 3.14 2.62
(1.80) (1.79) (4.32) (4.06)
r -1.02 -O.36 5.65 14.04c
(2.54) (2.78) (6.70) (6.00)
r* -1.72 1.48 -0.95 2.54
(2.30) (2.55) (4.94) (3.97)
n -3.78 1.92 -0.40 0.94 3.78 8.20b 1.50a 1.50a
(5.41) (6.18) (5.80) (5.82) (3.92) (2.26) (0.68) (0 61)
.u4 -1.16 -2.40 -2.41 -2.16 -1.16 -2.13’ -0.33 -0.41
(2.90) (3.49) (3.17) (3.21) (1.18) (1.09) (0.31) (0.28)
q 0.08 0.03 0.02 0.02 0.22 0.28 0.04a 0.04a
(0.06) (0.06) (0.06) (0.06) (0.16) (0.15) (0.01) (0.02)
Risk -1.78 -0.36 -O.56 -0.30 -1.67 -3.17 3.70 3.12
(1.35) (1.39) (1.41) (1.32) (2.53) (3.01) (2.88) (2.17)
R2 0.81 0.26 0.29 0.27
0.v. 1.79 1.88 1.87 1.90 1.77 1.85 1.79 1.80
a 0.42 0.96 0.96 0.97 0.24 0.22 0.25 0.29

 

Standard errors

in parentheses.

Equations (1) - (4) estimated using Cochrane-Orcutt procedure.

Equations (5) - (8) estimated using Ray Fair's procedure to correct for serial correlation

"GOOD

Of instrumental variable estimates.

significant at
significant at
significant at
significant at
constrained

.05 level, correct sign
.01 level, correct sign
.05 level, incorrect sign
.01 level, incorrect sign

54'

TABLE 3.3

REGRESSIONS OF THE GENERAL AND RESTRICTED MODELS
ON THE LOG OF MARK-U.S. DOLLAR EXCHANGE RATE

1978z4 - 1983:3

 

 

Variable (I) (2) (3) (4) (5) (5) (7) (8)
c 0.62 0.75 -2.07 -2.65 2.50 3.25 -2.00 -o.83
(2.61) (2.14) (1.90) (2.32) (4.12) (0.83) (3.16) (3.25)
m—m* 1.00 -0.70 1.00 1.00 -0.52 1.00
(0.35) (0.76)
m -o.21 -0.99
(0.46) (1.36)
m* 0.28 0.40
(0.37) (1.07)
y -0.11 0.05 -0.19 -0.13 -0.35 -0.56 -0.62 -1.05
(0 28) (0.30) (0.29) (0.34) (0.55) (0.57) (0.61) (0.69)
y* 0.21 -0.15 0.51 0.41 0.60 0.26 1.29” 1.45”
(0.37) (0.37) (0.33) (0.41) (0.64) (0.58) (0.44) (0 42)
r-r* -3.46” -3.39‘ 2.71 3.30
(1.14) (1.37) (2.42) (2 54)
r 2.88 7.27“ 5.00 13.58“
(2.94) (2.82) (7.24) (5.11)
r* 3.80” 3.84” -.25 -0.52
(1.13) (1.20) (2.62) (2.58)
n -3.40 1.98 2.83 18.17” 2.62 4.34 1.698 2.31”
(6.08) (7.23) (6.57) (6.88) (3.78) (3.68) (0.82) (0.67)
n* -12.39” -19.58” -11.15” -20.70” -4.48” -5.74” -1.08” -1.49”
(3.05) (2.21) (2.93) (2.61) (1 39) (0.82) (o 34) (0 21)
q -0.01 0.01 -0.01 -0.02 0.11 0.11 0.06 0.08
(0.03) (0.04) (0.03) (0.04) (0.09) (0.10) (0.12) (0.13)
Risk -3.79° -4.82” -4.30‘ -6.63b -0.77 2.12 2.94 -1.31
(1.82) (1.87) (1.81) (2.10) (4.32) (2.97) (3.46) (3.04)
R2 0.79 0.87 0.78 0.80
0.v. 1.86 1.90 1.95 2.07 1.88 1.93 2.00 2.00
6 .60 .57 .58 .61 .44 .35 .39 .26

 

Standard errors

Equations (1) -

Equations (5) - (8) estimated using Ray Fair's procedure to correct for serial correlation

an U9

in parentheses.

(4) estimated using Cochrane-Orcutt procedure.

of instrumental variable estimates.

significant at .05 level, correct sign
significant at .01 level, correct sign
significant at .05 level, incorrect sign
significant at .01 level, incorrect sign

55

both domestic and foreign interest rates were positively correlated
with the exchange rate using both OLS and IV techniques. This result
did not change when the log difference Of money supplies was set to
one, a theoretical restriction present in all exchange rate
determination theories examined. The results also show that fully
half Of the estimates were significant at the one percent level.
Estimates Obtained from the earlier subsample carry negative signs in
OLS estimation and positive correlations using IV techniques. In
either case, the coefficients are insignificant in seven Of eight
cases. The later subsample has results similar to the sample as a
whole.

The estimates obtained when restricting interest rate coeffi-
cients to equal and Opposite signs diverge radically from unrestricted
estimates. Ordinary least squares results find the correlation
negative and significant although both interest rate coefficients were
positive in the unrestricted model. (This result can be explained by
the statistical properties of the restriction. See Haynes and Stone
(1981)). The instrumental variable estimates had positive and
insignificant coefficients on the interest rate differential. These
results are also found in the earlier subsample. While the second
subsample carried the same signs, the estimates were insignificant.
It should also be noted that the correlation coefficient of both the
sample and earlier subsample drOp dramatically when the interest rate
differential is substituted for interest rate levels.

Estimates Of inflation expectations, when proxied by an adaptive
model, were found significant at the one percent level in ten Of

sixteen cases and were always of the expected sign13. Estimates Of

56

the April, 1978 to March, 1983 period mirrored these results with
eleven Of sixteen cases significant. Results from the earlier
subperiod were insignificant using OLS but improved using IV: four Of
eight coefficients were significant and all Of the expected sign.

When IBIIQEIQO-§XQ§Ctat10nS were proxied using an interpolated
OECD survey, the estimates were generally Of the expected sign but
insignificant. The results Of the second subperiod are superior to
the first. There are, however, two reasons to discount these results.
First, the expectations have an eighteen-month horizon, a length
generally acknowledged to be shorter than the "long run.“ Second, the
survey is based partially on Opinion research and partially upon the
OECD model. Improvements in the model can possibly account for the
surveys' increased success in the second subperiod. BisignanO and
Hoover (1980) have found that the Livingston survey yields positive
and significant estimates. However, it also suffers from the first
criticism.

Attempts to estimate the model when inflation expectations were
derived rationally failed to produce significant estimates and, in the

case Of United States inflation rates, failed to produce the correct

sign. The estimation procedure, suggested by McCallum (1976).Usedwm
QQPHQLIVIUIE,__.I-DII9W)" rates while including the variables Of, them
information set in thefllist Of instrumental variables. The time..-

horizon‘was chosen from estimates found in the literature and, this,”

-limited estimation to the first subsample.
Estimates of the real exchange rate generally carried the
correct sign but failed the significance tests. The most encouraging

results were found during the earlier subperiod.

\/

57

' The risk variable showed mixed results for the entire sample
period but significant results for the second subperiod. Previous
evidence suggests the risk premium is time varying. The results
conform tO that conclusion. Since the demand component Of the risk
term is included in the coefficient the results also conform to an
alternative hypothesis: the habitat of OPEC investments has changed
since the second Oil shock.14

The structural stability of the general model is called into
question by comparison Of coefficient estimates Of the two subperiods.
Examination Of the general model coefficients show that money
supplies, interest rates, foreign inflation rates, and real exchange
rates produce significantly different OLS and IV estimates. This
result is confirmed using estimates Obtained in the exchange rate
literature: the general model is sensitive to choice Of sample period,
especially with respect tO money supplies, interest rates and risk.

8. Canada. The Canadian regressions reported in Tables 3.4, 3.5,
and 3.6 show domestic money supply coefficients Of the correct sign
and foreign coefficients of the incorrect sign. _ In general, both
coefficients differ significantly from one. The restricted money
supply estimates are also Of the expected sign and insignificant with
the exception Of IV estimates covering the whole sample period.
However, it is significantly different from one, the theoretical
expectation.

The income terms carry the expected sign in nineteen Of
twenty-four cases and over half Of the coefficients are significant.
The results are especially strong using IV techniques in the entire

sample—period, and second subsample. The incorrect signs are

Regressions Of the General and Restricted Models

523

Table 3-4

on the ng_of Canadian Dollar/U.S. Dollar Exchange Rate
l974:l - 1983:3

 

 

variable (1) (2) (3) (4) (5) (6) (7) (8)
c -l.88 1.65 -O.46 0.86 -2.38 -1.09 1.09 .47
(0.63) (0.98) (0.78) (0.89) (1.71) (0.97) (0.92) (0.98)
m - m* 1.00 0.02 1.00 1.00 0.58” 1.00
(0.11) (0.15)
m 0.08 0.19
(0.10) (0.19)
m* 0.26c 0.30
(0.12) (0 37)
y 0.01 -0.15 0.01 -O.l8 -0.25 -0.76' -0.35 -0.41
(0.12) (0.17) (0.12) (0.18) (0.21) (0.35) (0.26) (0.27)
y* 0.02 0.25 0.12 0.45. 0.30 1.35” 0.38“ 0.69”
(0.14) (0.22) (0.15) (0.20) (0.20) (0.34) (O.l8) (0.25)
r - r* -1.11 0.32 -4.56a 1.72
(0.75) (1.07) (2.08) (2.38)
r 0.89 2.14 -2.65 -3.95
(0.96) (1.47) (1.4)) (2.43)
r* 0.89 -O.38 1.17 -2.21
(0.73) (1.05) (1.22) (2.03)
r -0.91 -O.69 -1.12 -0.45 0.27 0.45 0.14 -0.12
(1.38) (2 12) (1.53) (2.12) (0.68) (0.27) (0.12) (0.26)
4* 0.16 -0.03 0.18 0.12 0.09 -0.11 -0.19° -0.07
(1.17) (1.96) (l.48) (1.88) (0.46) (0.45) (0.08) (0.14)
q -0.01 -0.01 -0.01 -0.01 -0.02 0.01 -0.05 0.01
(0.01) (0.01) (0.01) (0.01) (0.02) (0.03) (0.03) (0.02)
Risk -0.51 -2.57“ -0.53 -2.82 2.49 -7.23” -5.74” -7.29”
(0.82) (l.08) (0.80) (1.06) (3.64) (1.63) (1.29) (1.80)
R2 .48 .11 .50 .06
0.v. 2.36 2.21 2.60 2.23 2.10 2.02 1.99 2.18
o .83 .92 .97 .90 .56 .62 .52 .80

 

Equations (1) -
Equations (5) -
of instrumental
a - significant
b - significant
c - significant
d - significant

(4) estimated using Cochrane-Orcutt procedure.

(8) estimated using Ray Fair's procedure to correct for serial correlation
variable estimates.
at .05 level, correct sign
at .Ol level, correct sign
at .05 level, incorrect sign
at .Ol level, incorrect sign

Regression Of the General and Restricted Models

59

Table 3-5

on the ng_of Canadian Dollar/U.S. Dollar Exchange Rate

1974:1 - 1978:3

 

 

Variable (I) (2) (3) (4) (5) (6) (7) (8)
c -2.63 3.25 0.06 2.75 -1.12 4.18 0.35 4.36
(0.86) (1.49) (0.89) (1.33) (1.60) (2.16) (1.29) (1.76)
m - m* 1.00 0.07 1.00 1.00 0.04 1.00
(0.15) (0.22)
m 0.12 0.16
(0.14) (0.28)
m* 0.58c 0.27
(0.24) (0.44)
y -0.31 -0.23 -0.14 -0.21 -0.31 -0.34 -0.17 -0.41
(0.18) (0.29) (0.17) (0.28) (0.28) (0.36) (0.22) (0.37)
y* 0.07 0.06 0.10 0.13 0.17 -0.02 ' 0.13 0.04
(0.15) (0.29) (0.16) (0.26) (0.23) (0.42) (0.18) (0.33)
r - r* -0.38 -l.46 0.20 4.25
(1.40) (2.37) (2.87) (5.29)
r -2.58 -O.36 -9.13” 3.75
(1.62) (2.90) (2.41) (6.39)
r* 1.75 1.89 5.79a -2.22
(1.39) (2.51) (2.39) (5.06)
. 2.08 -3.35 -0 49 -3.18 0.18 -1.31 0.18 -0.26
(1.59) (3.19) 1.87) (3.16) (0.71) (1.35) (0.22) (0.34)
4* 1.90 4.74 -0.02 4.48 0.11 , 1.22 -0.23 0.28
(2.21) (3.82) (2.32) (3.80) (0.89) (1.58) (0.27) (0.39)
q -0.01 0.01 -0.01 -0.01 0.01 -0.04 -0.02 -0.03
(0.01) (0.02) (0.01) (0.02) (0.03) (0.03) (0.02) (0.03)
Risk -0.46 -O.38 -0.91 -0.41 1.74 2.53 -0.37 -l.87
(1 00) (1.50) (0.89) (1.49) (2.35) (2.51) (1.55) (2.57)
R2 .81 .07 .07 .06
0.v. 1.89 1.93 1.89 1.96 1.70 1.64 1.90 1.91
o .50 .98 0.98 0.97 .36 .97 .92 0.95

 

Equations (1) - (4
Equations (5) - (8

estimated using Cochrane-Orcutt procedure.

estimated using Ray Fair's procedure to correct for serial correlation
Of instrumental variable estimates.
a - significant at .05 level, correct Sign
O - significant at .01 level, correct sign
c - significant at .05 level. incorrect sign
0 - significant at .01 level, incorrect sign

Regressions Of the General and Restricted Models

60

Table 3-6

on the egg of Canadian Dollar/U.S. Dollar Exchange Rate

1978:4 - 1983:3

 

 

Variable (I) (2) (3) (4) (5) (6) (7) (8)
c -O.62 0.75 -0.39 1.41 0.93 2.63 0.18 2.05
(2.62) (2.14) (0.87) (1.03) (1.82) (1.65) (1.17) (1.09)
m - m* 1.00 0.03 1.00 ' 1.00 0.37 1.00
(0.17) (0.27)
m -o.21 0.36
(0.46) (0.21)
m* 0.28 -0.23
(0.39) (0.37)
y -0.11 0.05 -0.11 -0.39 -0.29 -0.87b -O.48 -0.93”
(0.28) (0.30) (0.18) (0.23) (0.20) (0.33) (0.26) (0.31)
y* 0.12 -0.15 0.19 0.58' -o.1s 0.84 0.601' 1.01”
(0.36) (0.37) (0.22) (0.30) (0.28) (0.48) (0.26) (0.35)
r - r* -0.67 1.55 1.28 2.38
(1.00) (1.25) (1.57) (1.81)
r 2.88 7.27“ 3.44“ 3.67
(2.94) (2.82) (1.58) (2.58)
r* 3.80” 3.84” -1.05 -2.78
(1.13) (1.21) (1.08) (1.59)
n -3.40 1.98 -o.97 -2.69 -0.70 -1.04 0.05 -0.18
(6.89) (7.23) (1.20) (1.71) (0.43) (0.82) (0.08) (0.12)
4* -12.39” -19.58” -1.99“ -O.86 -0.30 0.28 -0.143 0.06
(3 05) (2.21) (0.82) (1.09) (0.42) . (0.30) (0.06) (0.08)
q -0.01 0.01 -0.01 -0.01 -0.01 -0.03 -0.02 -0.04
(0.03) (0.04) (0.01) (0.01) (0.02) (0.03) (0.02) (0.04)
Risk -3.79a -4.83” -3.07‘ -1.91 -1.22 1.04 -4.58” 0.43
(1.82) (1.87) (1.09) (1.31) (3.74) (1.93) (1.35) (1.62)
R2 .79 .87 .45 .11
0.9. 1.86 1.90 1.96 1.98 1.99 2.00 1.97 2.00
o .60 .57 .34 .46 .11 .30 .19 .30

 

Equations (l) -
Equations (5) -
of instrumental
8 - significant
b - significant
c - significant
0 - significant

(4) estimated using Cochranc-Orcutt procedure.

(8) estimated using Ray Fair‘s procedure to correct for serial correlation
variable estimates.
.05 level, correct sign
.Ol level, correct sign
.05 level, incorrect sign
.0) level, incorrect sign

at
at
at
at

61
associated with regressions in which the l_O_g_ difference Of money
supplies is constrained to equal one.

Estimates Of domestic and foreign interest rates vary substan-
tially between samples. Results from the first subperiod show the
expected signs and are significant using IV on the general model. The
second subsample shows mixed results: OLS estimates are positive for
both domestic and foreign rates while IV estimates have incorrect
signs. The sample estimates are insignificant with four Of eight
signs correct.

Restricting the interest rate coefficients to equal and Opposite
signs does not improve the results. The sign is wrong in seven of
twelve cases and significant in only one. Further, sign reversals
occur in four estimates suggesting the statistical prOperties Of the
restricted estimation produce spurious correlations. In seven Of the
twelve cases the restricted estimate does not fall within the range Of
unrestricted estimates. ‘

Estimates of inflation expectations (adaptive process) indicate
that during the second subperiod foreign inflation rates contribute to
the explanation Of exchange rate levels. In the first subperiod and
the sample as a whole, however, inflation expectations were not
significant. Further, the signs were correct in only fifty percent Of
the cases. The use Of either rational or survey inflation expectation
proxies did not improve the results.

Although the real exchange rate was not a significant determinant
of nominal exchange rate determination, the risk term proved to be

significant in over half of the sample and second subsample

62
regressions. The risk coefficient was found tO have the correct sign
in six Of the eight earlier subsample estimates.

Tests of structural stability indicate that both interest rates
and the fOreign inflation rate estimates vary significantly between
periods. This lends further credence to the notion that the alter-
native exchange rate models Offer no general explanation of exchange

rate movements .

3.6 - Conclusion: Comparison Of Alternative Exchange Rate Models

The early Optimism Of monetary and asset approaches to exchange
rate determination was in part based upon positive results Obtained
from money supply estimates: coefficients Of the M difference'of
money supplies were significant and near unity. However, the results
Of this and other studies strongly contradict that finding. This
might suggest the‘iejection Of the monetary/asset approach.

This conclusion, however, is overdrawn. The dependent variable
can be changed from the exchange rate to the exchange rate minus the
difference in money supplies. on ‘theoretical grounds: the standard
money demand function imposes this restriction. While the general
model test§_if the money coefficient is equal to one, the restricted
model assumes it. This allows for comparison Of alternative exchange
rate hypothesis without rejection Of the monetary approach.15

The mark-U.S. dollar experience lends support to models which
include inflation expectations as an explanatory variable. When the
second Canadian dollar-U.S. dollar subperiod is also considered,
support is found for Frankel's contention that inflation expectations
are a key exchange rate determinant in periods Of significant

inflation and intercountry inflation differentials. The absence Of

63
significant inflation expectations estimates during the first Canadian
dollar-U.S. dollar subperiod lend further credence to this argument.

The second. subperiod results for: both exchange rates support
portfolio balance approaches as Opposed to models which do not include
risk. The evidence Of a risk premium tends to add credence“ to the
contention that assets denominated in different currencies are not
perfect substitutes and that exchange risk is related to national
debt. When the results from the earlier subperiod and general sample
are also examined several interpretations are possible. The demand
side Of the asset market, which is subsumed in the risk coefficient,
can account for two possibilities: first, wealth transfers between
agents with different asset preferences, and second, changes in the
asset preferences Of agents holding the assets. 80th explanations
could be related to OPEC.

Weak support is found for the real exchange rate variable in the
German case. ‘The Canadian estimates, however, fail to support the
hypothesis. Part of the problem lies in the theoretical underpin-
nings; it is unclear whether bilateral or world trade is the correct
specification. Further, it is difficult to capture changes in world
import and export demand in a bilateral exchange rate model. Finally,
it has been suggested that wealth effects rather than real exchange_
rate ,effectsare. captured. by current. ,accoun.’c_19..84_.-t!ie.99 .§E§$L§HE§:..

As was noted earlier, the expected sign Of the interest rate
differential has been hypothesized tO be positive, negative and zero
by different exchange rate models. Unfortunately, the results do not
indicate a clear pattern. Unrestricted and restricted interest rate

estimates in the first subperiod have signs which support the general

64

or disequilibrium model when estimated by OLS. However, the IV
results produce sign reversals. 17) either: case, the results are
generally insignificant. Estimates from the second subperiod conform
to the Bilson specification when IV techniques are used and show
identical signs with significant coefficients when estimated using
OLS. German results over the sample mirror these OLS finding.
Restricted versions Often have coefficients outside the range Of the
unrestricted estimates.

During the post-Bretton WOOds period increased interest rate
differentials are associated with both appreciation and depreciation
Of the exchange rate. The apparent success of the disequilibrium
models during the early floating rate period found in other studies is
not repeated. One explanation is the use Of monthly averages Of
exchange rates and interest rates in other investigations: this
violates the interest rate parity condition.

The introduction Of the monetary and asset models Of exchange
rate determination have integrated the advances Of monetary theory
into international finance. However, it is unclear which specifi-
cation most adequately represents the post-Bretton Woods experience.
Some have blamed the apparent inadequacy on the money demand equation
upon which all Of the above specifications rely. The simplification
of the theoretical models for convenience Of estimation is an

alternative explanation.

65

APPENDIX 3.A
VARIABLE PROXIES AND MODELING OF UNOBSERVABLE VARIABLES

The interest rate parity condition, fundamental to all the models
presented, imposes strong requirements on the collection Of exchange
rate and interest rate data. 80th from a theoretical and empirical
perspective, slight deviations from interest rate parity are
arbitraged away very quickly. Thus, spot exchange rates and interest
rates must be collected at the same time or constructed to conform to
IRP. In general, averages will fail to meet this condition.

Proxies or models Of long term expected inflation rates pose

substantial difficulties. One Often-used approach proxies expected,

tnflationrate differentials with long term interest rate differen-

tials (bond yields). The logic behind this approach is that interest
_rate differentials equal 'Aexpected inflation differentials in
equilibrium. The use Of Jongwterm interest_rates is premised by the
assumption that adjustment to PPP occurs before the "long-term" is
reached thus assuring real interest rates are equalized. An advantage
to this proxy is that changes in the rates reflect new and up-tO-date
information. This lends support to the rationality Of the proxy.
However, if money demand equations are not assumed identical
across countries then the use Of long-term interest rates to proxy
expected inflation will bias the estimates. Although long-term real

interest rates are equal across countries over time, the real interest

66 /
rate is not necessarily constant over time. Problems of multi-
colinearity may also present themselves when both the short- and
long—term interest rate are right hand side variables.

An alternative for inflation expectations js expectational survey
data. This avoids the error in variables encountered when using
interest rates, while preserving the rationality of the series.
However, the horizon must be "long run" for real rates to be equal
between countries. Estimates suggest that a horizon over two years is
needed.

Finally, the use Of either adaptive or rational models Of
inflationary expectations present a final alternative. ‘Rationalflv
‘9§pectatiQfl$“CStimation, as prOposed by McCallum (1976), useSHQQ£uel_v/l
futurefinflation values while adding variables in the information set
to the list Of instruments. Adaptive processes have precedent 151399
literature although the rationality Of the expectation, is now in
question.

 

 

 

......— -..

relative real changes in both cost and demand structures between
countries. Central to this analysis is the relationship between the
real exchange rate and the balance of trade popularized by the
traditional "flow” ,view of exchange rate determination. The real
exchange rate is expected to equilibrate the balance Of trade and
assure a finite bound on net foreign debt. If this were not the case,
infinite wealth transfers or infinite debt accumulation would be
possible with a steady state real exchange rate, an implausible

result.

67

‘v Both current account and trade balance data have been suggested
as proxies for the real exchange_rate. The use Of bilateral or
"world" positions has not found a general_c0ncensus. In.either_case,g
distinguishing between temporary andpermanent shifts, inunderlying
L9,“) determinantsisa -.difficult_ta§k_. The use of bilateralwtradefl
data, however, does have certain advantages. First, it has a_long A
history Of use in the flow literature which supplies the_tbe9tetiga1-
foundation for real rate. Second, “it does notflinoludefluniglatergajn
transfers which do_not-.refle,ctunderlying real_,_c_h_aoges_. Third, it
highlights_cost changes between differentiated.manufacturednprnducts,.
EEPVIWFCY,CPWP°"°"F Of United States-German and United Stateseganadian

.EC?“e°

 

The existence Of exchange risk can be traced to private
investors} uncertainty about expected spot rates and risk minimization
in the currency composition Of private portfolios (Dornbush, 1980).
The risk premium is affected by changes in the stock Of public debt
denominated in different currencies, the distribution Of financial
wealth, and private investors subjective preference for assets
denominated in different currencies. If, for example, outside assets
denominated in the foreign currency increase, the) immediate spot
depreciation must coincide with an increase in expected appreciation
for investors to accept new foreign debt into their portfolios at
given interest rates. The forward rate falls relative to the expected
spot rate, thereby increasing risk. A similar process occurs if
wealth is transferred from a country with low home currency preference

tO a country with high home currency preference. Finally, preference

68
changes within either country toward the home currency yield the same
result.
Dornbush (1980) has formalized this relationship in a
mean/variance framework in accordance with the theory Of portfolio

selection. Risk can be defined as:

sQ*
”'V'wi

(32) RISK = 1 ‘1' WT;
1 u .TH'

 

where

u, u* are coefficients Of risk aversion that characterize home
and foreign currency preferences

v is the perceived variance Of-Etst+1 - tft+1

WI, W* represent global private wealth and foreigners' private
» wealth, respectively

0, 0* are the total Of outside assets denominated in domestic
and foreign currency, respectively

By subsuming the preference and variance components into the risk
coefficient during estimation, ignoring wealth effects (i.e, u=u*),
and defining global wealth as the sum Of outside assets (W=O+O*) (27)
can be rewritten as:

(33) (Risk - 1)
u . v

= sQ*/(sQ* + 0) = 1/(1 + Q/sQ*)

These rather stringent assumptions are more a result Of the paucity of

wealth data than an algebraic simplification.

69

APPENDIX 3.8
DATA SOURCES

All data is unadjusted and end Of period unless otherwise noted.

EXCHANGE RATES:

MONEY SUPPLIES:

INCOMES:

INTEREST RATES:
Short term:

Long term:

SUPPLY OF
OUTSIDE ASSETS:

Defined as DM/U.S.$, Can S/U.S.$, £/U.S.$ rates.
Reported monthly for the last business day Of the
month. Average Of the bid/asked spread. Financial
Times (London). ““"""

U.S.: M1 in billions Of U.S. dollars, monthly
Germany: M1 in billions Of DM, monthly

Canada: M1 in billions Of Can. dollars, monthly
U.S.: M1 in billions Of pound sterling, monthly
As reported in O.E.C.D. Main Economic Indicators.

 

Index of Industrial Production in each country,
monthly. As reported in O.E.C.D. Main Economic

 

Indicators.

 

Three month Eurocurrency Rates (LIBOR). Collected
monthly on the last business day Of the month.
Quoted at the identical time as the exchange rate
quotations above. Reported in the Financial Times

 

(London).

U.S.: Long term bond yields, monthly. Reported in
the Federal Reserve Bulletin.

 

Germany: Yields on government securities with ten
years tO maturity, monthly. Duetches Bundesbank.

 

Canada: Long term bond yields on government
securities, monthly. Bank of_Canada.

U.K.: Long term bond rates (ten years or more) on
government securities, monthly. Bank of England.

U.S.: Federal debt held by the public, monthly.
Federal Reserve Bulletin.

 

Germany: Federal Government debt, monthly.
Duetches Bundesbank.

 

PRICES:

INFLATION
EXPECTATIONS:

CURRENT ACCOUNTS:

TRADE BALANCES:

BILATERAL
TRADE BALANCES:

70

Canada: Federal government debt, monthly. Bank Of

Canada.

U.K.: Public debt, monthly. Bank of_England.

Consumer Price Indexes, all times, monthly.
Reported in O.E.C.0. Main Economic Indicators.

 

Eighteen month forecasts, bi-annually. O.E.C.D.
Economic Outlook.

 

Each country in its respective currency, quarterly.
O.E.C.D. Main Economic Indicators.

 

Each country, in its respective currency, monthly.
O.E.C.D. Main Economic Indicators.

 

U.S.: In U.S. dollars, monthly. Survey Of Current

 

Business.

Germany: In DM, monthly. Duetches Bundesbank.

 

71

FOOTNOTES - CHAPTER 111

1See Kreinin and Officer [1978] for detailed explanation Of the
monetary approach and extensive references to empirical work.

2Disequilibrium in the context Of the Frenkel and Dornbush
models refer to short run deviations from equilibrium.

3Also, see Mussa [1982] for a non-PPP model including
terms-Of-trade effects.

4An extensive literature exists on the existence of a risk
premium. See references contained in cited papers.

5See the appendix in Frankel (1979) for the derivation.

6The development Of alternative models retains the essential
features Of the original work.

7The adjustment process describes the "overshooting" case i.e.
the exchange rate overshoots its equilibrium level. Conditions for
the overshooting result appear in Glassner (1982).

8See Mizon [1977] for advantages to this technique.

9Germany is now a member Of the European Mogetary System.

10The apprOpriate test statistic isi¢ VBRA+VARB-2'CUVAB where A
and 8 denote estimated coefficients from different sample periods.

11This might also be explained by government action in the money
market: the monetary authority can adjust the money supply to trend
over time once a shock has set it Off trend.

12This specification would model goods market adjustment in each
country separately.

131 adopt the Frankel (1979) process: a six month moving average
Of actual inflation rates.

14See appendix for characterization Of risk.

15The assumption that actual rates are equilibrium rates in the
money market could also be responsible for this result. This
possibility is examined in the next chapter.

72

15Given the enormous wealth transfers to OPEC countries, an
increase in the risk premium is indicated if OPEC countries find third
country bonds relatively less preferable than third country residents.

CHAPTER IV
ESTIMATION OF THE GENERAL MODEL

4.1 Introduction

In Chapter III, five popular money/asset models were tested
using single equation estimation techniques. However, a majority Of
the exchange rate models were originally formulated as simultaneous
systems. A dichotomy is created between. theory and practice when a
simultaneous model is reduced to a single equation for estimation.
The estimated model is not a true test Of its theoretical precussor.
The misspecification results in inconsistent estimates. Consequently,
this chapter reestimates the general model using-systemutechniques.

Several reasons in addition to the aforementioned methodological
and statistical considerations suggest the use Of simultaneous
equation techniques. "first, system estimates allow for the explicit
examination Of the interest rate and price specifications. Since the
behavioral assumptions inherent in the interest rate equation underly
exchange rate determination, it is useful tO examine them directly.
Equilibrium as well as disequilibrium adjustment is defined by the
price equation in monetary models. Direct tests of the price
mechanism also seem warranted.

.§§£98§:~system estimation is necessary to examine the rational

gxpectati ons hypothesiLspec ifiodJn4hetheoret1calJensiQnLnf. the- ._

 

 

 

..999F11" The overidentifying restrictions imposed by a rational

73

74

formulation can be jointly tested with the structural assumptions by

means of a likelihood ratio test Of restrictedand unrestricted

estimates.

“finally, the system estimates allow for an examination Of model
specification and variable endogeneity.- Comparison Of ordinary least
squares, two-stage least squares ”and full information maximum
likelihood (FIML) estimates can be conducted using Hausman-Wu tests.

A simultaneous version Of the restricted model will be examined
in Section 4.2. Driskill and Sheffrin (1981) have estimated the model
without risk under rational expectations assuming the Frankel (1979)
price adjustment mechanism and specific lag structures for the
exogenous variables. Several refinements are considered. A discus-
sion Of the estimation techniques and testing procedures is also
included.

Section 4.3 reports the results Of the estimation for the
mark-U.S. dollar and Canadian dollar-U.S. dollar exchange rates over

the sample period beginning January 1974 and ending March 1983.

IT) Section 4.4, tests of the model are conducted over thgfllgggwmw

through Iggggperiod to see whether the persistent appreciation Of the
U.S. dollar is explained by any Of the alternative specifications.
Claims Of the U.S. dollar's overvaluation by some Observers lend prior
support to the real interest differential models. Others believe that
exchange risk or the "safe haven“ argument Offers an explanation for
the dollar's strength. Estimates Of the U.S. dollar-U.K. pound
sterling exchange rate are included for this sample period.

A sumary is Offered in Section 4.5.

75
4.2 An Econometric Model

The simultaneous model presented in this section is an econo-
metric specification of the single equation restricted model presented
in Chapter II. The relative price level and interest rate
differential are endogenous while specific processes for the exogenous
variables are considered. The stochastic processes of the exogenous
variables place overidentifying restrictions on the model allowing
examination of the rational expectations hypothesis, a hypothesis
assumed in many of the theoretical models.

The covered interest arbitrage condition is assumed to hold:

or (1) rt-rt* = Et St+1 - st + riskt
Risk arises when assets denominated in different currencies are not
considered perfect substitutes. In the absence of risk, open interest
rate arbitrage exists.

Traditional money demand equations are posited with coefficients
on income and interest rates held equal across countries. An error
term is added to the equation.

(2) (m-m*)t - (p-p*)t = ¢Ky<y*)t - Air-r*)t + atl

The price equation allows for both equilibrium and disequilibrium
adjustment:

' (3) (p-p*)t - (p-p*)t_1 = 5(e-p+p*)t_l + A(n-1r*)t_1 + etz
Disequilibrium in the goods market, defined by deviation from PPP,
adjusts toward fquilibrium at rate 6. Changes in the relative
equilibrium price path are synonomous with changes in the relative
equilibrium inflation rate.

The model is completed by Specifying the stochastic processes of

the exogenous variables which include money, income, risk and

76
inflation. Following Driskill and Sheffrin (1981), it is assumed that
relative equilibrium income follows a randomwalk:1
(4) (Y'y*)t : (.Y‘y*)t_1 + V1
_Risk also follows this process:
(5) riSkt = riSkt_1 + V2

The relative equilibrium money supply is specified in several

ways:
(6) (m'm*)t = (M‘m*)t_1 + (W‘fl*)t_l + V3
or
(6') (In—m*)t = (m-m*)t_1 + trend + v4
or

(6") (In-m*)t = a1(m-m*)t_1 + ...+ “n(m’m*)t-n + trend + v5
where
(7) (n- 11*)t = (n- "fit-1 + v6
and v1, v2, v3, v4, v5, v6, v7 are zero mean serially uncorrelated
random errors.

In equations (6) and (6') the equilibrium relative money supply
follows a random walk with drift. The assumption of the stochastic
processes following a random walk place the overidentifying
restrictions imposed by rational expectations on the variables rather
than the variance-covariance matrix of residuals.2

The price equation and inflation equation, e.g. (7), can be
considered econometric rather than economic specifications. Since the
complete model can be solved for equilibrium prices (when s=p-p*), it
follows that the equilibrium relative price path (the expected
equilibrium inflation differential) has a solution. Mussa (1981) has

shown that a rational price adjustment mechanism uses expected future

77

values of income and money supply to form the equilibrium price path
while past values determine disequilibrium adjustment. ‘Equation (3)
with n-n* exogenous has undesirable steady state properties. However,
the limited time horizon for expected future values of income and
money supply suggest that a trend would offer a reasonable
approximation in empirical work. Further, an exogenous expected
inflation differential allows the use of survey data which implicitly
includes information not found in the above specification.

The solution to the nominal exchange rate is preceded by the
solution to its expectation. By positing the expected spot rate as a
function of expectations of the exogenous variables and relative
prices, the alternative stochastic processes can be used to offer
specific solutions. Substitution of a solution into equation (1) in
conjunction with the money demand and price equations yields a
solution to the nominal rate. Right-hand side coefficients are
determined by the various solutions to the expected spot rate.

It should be noted that the interest rate differential is

endogenous in the preceding systems.3

The use of the money demand
equation in solving the expected spot rate in the interest rate
arbitrage condition (equation (1)) introduces an error term correlated
with the interest rate differential. As a result, OLS estimation of
the nominal exchange rate with interest rates as exogenous variables
lead to inconsistent estimates. Either instrumental variable or

system techniques are required.

"Solution of the above system, equations (1)-(7), yields three-..

-essim飧§l§_§jmfllfiéneousmequations:

(8) st = F1 + F2(m-m*)t + F3(p-p*lt + F4(y-y*)t + F5(n-n*)t + 6riskt

78

,(9) r-r* = 61 + sz-ur").c + G3(P-P*)t + 64(y-y*)t
(10) p-p* = H1 + H2 et“1 + H3(p-p*)t_1 + H4(N' W*)t_1

It is also possible to obtain consistent estimates of the exchange
rate equation with the interest rate differential included as a right-
hand side variable using simultaneous techniques:

\/(11) 5t = (21 + w2(m-m*)t + w3(y-y*)t + (mu-r*). + w5(n-n*)t + wsriskt

The specific solution to Equations (8)-(10) depends upon the
processes generating the exogenous variables: each combination of
stochastic processes generates different parameterizations for the
coefficients and, therefore, different. in-equation, cross-equation,
and variance-covariance restrictions implied by rationality.4 Ihu§,m_
.191n1e£§§£§_9£_1h§_mngel and xjgfional.9xpectations are_possible for_
anuuuad_alteggatjve rationality hypothesesa,

For example, Driskill and Sheffrin (1981) estimate the model
using equations (4)-(7) as the exogenous variable paths. The
assumption of random walk processes places six within and cross-
equation constraints. No restrictions on the variance-covariance
matrix are implied. The relaxation of the random walk assumption
would place eight restrictions on the variance-covariance matrix if
the autoregressive process was limited to one period.

The estimation will procede in four steps. First, simple regres-
sions of the exogenous variables on their own past values will be
conducted. This allows for a determination of lag length as well as a
determination of lagged variable coefficients. The possibilitonf a
random walk process can be examined. Lag length will be limited to

four periods in this analysis. Although a process of longer duration

79
is possible in some of the exogenous variables, the resulting number
of restrictions would approach the number of observations.

Second, ordinary least-squares regressions for the exchange rate,
interest rate differential, and price differential equations will be
conducted. This allows for explicit examination of each component of
the theoretical systems. Additional information concerning the
generally poor' performance of the general model in thel preceding
chapter could be gained.

The results of the interest rate equation are of particular
interest. Previous estimates of money demand equations (our equation
is estimated for interest rates instead of real balances) suggest that
the choice of interest rate(s) as well as instruments could greatly
effect the coefficients. The relatively simple econometric specifi-
cation employed in exchange rate studies could be the source of the
poor results obtained in previous work. Likewise, the theoretical
specification could be the source of the problem.

Third, FIML estimates of the unrestricted and restricted versions
of the three equation systems will be calculated.5 This allows for a
joint test of the model and rational expectations: twice the absolute
value of the difference between the log of the likelihood functions is
distributed as a chi-square. Results of the test will offer the most
direct evidence on the theoretical models.

Finally, instrumental variable estimates of the exchange rate
equation with the interest rate included will be conducted. This
avoids the problem of using price data which some authors have

suggested as too "noisy."

80

The results will be examined for (1) coefficient sign, (2)1C0ef7
Jjgjgntflflgfluufljficancerr~43) coeffigignts_§t§bj)lfiyg (4) ,rational_h
expectations,“jun1 (S) specification. mmAlternative inflation proxies
will alsobe tested.

The duetchemark-U.S. dollar and Canadian dollar-U.S. dollar
exchange rates will be examined from January 1974 through March 1983.
Once again, subperiods preceding and anteceding March 1978 will be
considered.

Further, estimates covering the period of the U.S. dollar's
appreciation in the first half of the 1980's will be reported. This
period is of special interest for a variety of reasons. First, it
allows examination of the monetary/asset approach during a period
without extreme fluctuations. Second, it offers a particularly
appropriate period for comparison of the theoretically predicted sign
of the interest rate. Third, the alleged U.S. dollar's overvaluation
relative to PPP can be examined in a framework which explicitly allows
for real interest rate differentials. Equilibrium and disequilibrium

models can be compared.

4.3 Results: Summary of Estimation 1974:1-1983:35

The mark-U.S. dollar and Canadian dollar-U.S. dollar exchange
rates will be examined separately. Particular attention will be
paid to the system estimation and the rationality assumption central
to all of the theoretical constructions. A general conclusion will be
drawn following an analysis of the 1980:6-198&;&_period examined in
the next section.

A. Germany. Tests of the stochastic processes of the exogenous

 

variables suggest that a random walk cannot be rejected for relative

81
money supplies over the sample or either subsample (see Tables 4.1-3).
The use of a random walk on levels with drift in latter estimation
offered no improvement over the simple random walk hypothesis.
Relative income can also be modeled as a simple random walk.

Tests on the lag structure of relative expected inflation rates
(survey proxy) suggest that a one period lag is inappropriate in both
the first subsample and the sample as a whole. Further, coefficients
on the first lag were significantly less than one. This is also the
case when a moving average is used proxy expected inflation differen-
tials.

Risk, a construction of outside assets, was found to follow a
random walk with a significant positive trend. This reflects the
relative growth of debt issued by the United States.

Examination of the exchange rate equation reveals that over the
sample only income, expected inflation, and risk carry the correct
sign. Relative money supplies are significant and of the wrong sign.
After correction for serial correlation, the correlation coefficient
falls substantially.

Estimation of the first subsample shows only relative income as
significant and of the correct sign. Expected inflation is no longer
significant during this period, a finding which does not support the
real interest rate models. After correction for autocorrelation the
correlation coefficient drops dramatically.

The second subsample lends some support to the real interest rate
hypothesis by showing a positive and significant correlation between

the expected inflation differential and the exchange rate. Once

82
TABLE 4.1

REGRESSIONS 0F EXOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

GERMANY-U.S.
1974:1-1983:3

 

 

Variable C Var_1 Var_2 R2 D.M.
m-m* -.01 .98 .97 1.82
(.01) (.02)
m-m* -.01 1.06 -.09 .97 1.99
(.01) (.09) (.09)
y-y* .01 .89 .80 2.07
(.01) (.04)
y-y* .01 .84 .05 .80 1.96
(.01) (.09) (.09)
n-n* .00 .80 .67 2.30
(.01) (.05)
n-n* .00 .64 .19 .68 1.97
(.01) (.06) (.09)
risk .08 .98 .99 2.23
(001) (.01)
risk .01 .86 .12 .99 2.04
(.01) (.09) (.09)

 

Standard errors in parentheses.

83
TABLE 4.2

REGRESSIONS 0F EXOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

GERMANY-U.S.
1974:1-1978:3

 

 

Variable C Var_1 \(ar_2 R2 0.H.
m-m* 0.00 .99 .98 2.12
m-m* 0.00 .93 0.06 .98 2.01
(.00) (.14) (.14)

y-y* .01 .85 ' .65 1.39
(.01) (.08)

y-y* .00 .76 .14 .69 1.96
(.01) (.15) (.15)

n-n* .00 .77 .63 2.38
(.01) (.08)

n-n* .00 .57 .26 .65 1.92
(.01) (.13) (.13)

risk .01 .98 .99 2.19

risk .01 .88 .09 .99 2.06
(.01) (.14) (.14)

 

Standard errors in parentheses.

84
TABLE 4.3

REGRESSIONS 0F EXOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

GERMANY-U.S.
1978:3-1983:3

 

 

Variable C Var__1 Var_2 R o.w.
m-m* -.01 .98 .96 1.80
(.01) (.03)
m-m* -.01 1.08 -.10 .96 1.97
(.02) (.13) (.13)
y-y* .01 .84 .71 2.10
(.01) (.07)
y-y* .01 .76 .12 .71 2.02
(001) (015) (015)
n-fl* .00 .79 .61 2.13
(.01) (.08)
n~fl* .00 .71 .10 .62 1.99
(.01) (.13) (.14)
risk .02 .93 .93 2.31
(.01) (.03)
risk .02 .77 .16 .95 2.03
(001) (013) (013)

 

Standard errors in parentheses.

85
again, however, the money supply differential is of the wrong sign and
is statistically significant.

The interest rate equation is at the heart of all the models.
Estimates suggest that although money supply, price, and income
differentials carry the correct sign, their correlation with the
interest rate differential is low. After correction for autocor-
relation, the sample R2 equaled only .13, a value higher than either
subsample.

One explanation for this result is the lack of a time trend in
the regressions. The significant negative time trend in the United
States money demand equation and the even more puzzling positive time
trend in the German money demand equation call into question the
traditional demand for real balances equation. Some authors have
suggested that the relatively poor out-of-sample performance of the
monetary models rests upon the money demand equation.

The price equation performed very well in the sample. Both the
lagged exchange rate and lagged price differential were significant
and of the correct sign. Inflation expectations, however, were not
significant. In both subsamples the lagged price continued to
perform well although the lagged exchange rate lost its significance.

It is important to note that none of the inflation expectations
proxies--adaptive, rational, or survey--produced significant results
in the price equation. A constant trend was found significant over
the sample.

The results reveal that variable coefficients in the exchange
rate equation were generally not stable between subperiods. Only

relative income and risk were exceptions to the above conclusions.

86

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e.¢ m4m<k

87

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m.¢ u4m<h

88

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o.¢ u4m<h

89
However, the relatively large variance of the risk term and its
insignificance in both subsamples suggest that little weight can be
attached to this result. Especially troubling is the inflation
expectation coefficients: the difference in magnitude and significance
between the subsamples does not lend clear support to any of the
exchange rate hypotheses.

The interest rate equation was stable throughout the sample.
However, the poor correlation and general insignificance of the
coefficients suggest that stability is relatively meaningless in this
context.

The price equation was found stable in lagged prices and lagged
exchange rates although lagged exchange rates were significant in only
one of the subsamples.

Joint tests of the model and rational expectations proved
negative in both sample and subsamples for all stochastic processes
examined. Table 4.7 reports the results for restrictions imposed by
assuming that the exogenous variables follow random walks. The
results are similar to those found by Driskill and Sheffrin (1981):
the sign of A is incorrect in two of the three estimates.

Hausman-Hu specification tests were conducted between the OLS and
IV estimates obtained in Chapter III as well as the IV and FIML
estimates reported above. The former can be considered a structural
test of exogeneity while the latter is a pure specification test. The
estimates were compared for all endogenous variables.

The results show that exogeneity could be rejected for interest
rates, expected inflation, and risk. 'The joint test also rejected

exogeneity. This result held for the sample and subsample periods

9()

TABLE 4.7

TESTS OF RATIONAL EXPECTATIONS RESTRICTIONS
ANO FIML ESTIMATES OF COEFFICIENTS

 

Duetchemark-U.S. Dollar Canadian Dollar-U.S. Dollar
1974:1-1983:3
A -.0008 .05b
(.019) (.01)
a -.3ob .003
(.07) (.099)
n 3.4 -.11
5 .018b .004
(.003) (.006)
. + a.
2 |Lu-Lc| 203.6 591.8
\v// l97?3!:121§2§.
x .074 -.02
(.043) (.04)
I -.12 -.06
(.08) (.04)
n .12 .08
(.29) (.13)
6 .028a .06b
.012 (.02)
. + +
2 |Lu-Lc| 4.71 95.0
V//. l978:4-1983:3
x -.031 .06b
(.027) (.01)
6 -.051b -.10
(.016) (.07)
n 2.97 .42
(.94) (.22)
5 .021b .047b
(.004) .015
. + +
2 |Lu-Lc| 38.1 123.8

+Twice the absolute value of the difference between the lo of the likelihgod
function of the unconstrained and contrained models is stributed as a X .

Standard errors in parentheses.

91
alike. The test between single equation or system specification found

significantly different coefficients. The prior theoretical justi-

 

fication for simultaneous system estimation is maintained by the
econometric results. OLS and IV estimations suffer from specification
bias.

8. Canada. Regressions of exogenous variables on their own

 

lagged values support the assumption of a first order autoregressive
process. Inflation expectations were the exception. In the case of
money supplies and incomes, the hypothesis of a random walk cannot be
rejected. A negative intercept is associated with the relative money
supply regression. (Table 4.8—10)

Both inflation expectations and risk were found to have coeffi-
cients significantly less than one on their first lagged value.
Inflation expectations follow a second order process. This alters the
restrictions imposed by rational expectations, since the solution to
the three equation system depends upon the coefficients of the lagged
values of the exogenous variables.

The exchange-rate equation, corrected for autocorrelation, did
not yield interesting results. Although the relative money supply
coefficient was positive in two of three cases, it was significantly
different from one. Relative income was not significantly different
from zero in the sample or either subsample. Further, in all but the
second subsample inflation expectations were of the wrong sign
although insignificant. Relative prices were insignificant in all
three cases and carried the correct sign only once. (Tables 4.11-13)

The interest rate differential equation produced similar results

once corrected for serial correlation: only the money supply was of

92
TABLE 4.8

REGRESSIONS OF EXOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

CANADA-U.S.
1974:1-1983:3

 

 

Variable C Var_1 Var_2 R D.H.
m-m* -.18 .94 .92 1.82
(.07) (.03)
m-m* -.18 1.02 -.08 .92 1.96
(.07) (.09) (.09)
y-y* .01 .91 .82 1.99
(.01) (.04)
y-y* -.01 .90 .01 .82 1.98
(.01) (.09) (.09)
n-n* .OO .73 .53 2.42
(.01) (.06)
n-n* .00 .52 .30 .57 2.13
(.01) (.04) (.09)
risk .00 .98 .95 2.28
(.01) (.02)
risk .00 .84 .14 .95 2.04
(.01) (.09) (.09)

 

Standard errors in parentheses.

REGRESSIONS OF EXOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

93
TABLE 4.9

CANADA-U.S.

1974:1—1978:3

 

 

Variable C Var_1 Var_2 2 D.H.
m-m* -.14 .95 .95 1.57
(.08) (.28)
m-m* -.14 1.14 -.19 96 1.86
(.08) (.13) (.13)
y-y* .00 .91 .82 1.81
y-y* .00 .79 .11 .84 1.93
(.01) (.11) (.11)
n4n* .00 .62 .39 2.14
n~n* .00 .54 .14 .40 2.00
risk .02 .77 .59 2.11
(.01) (.09)
risk .02 .71 .07 .59 2.00
(.01) (.13) (.13)

 

Standard errors in parentheses.

94
TABLE 4.10

REGRESSIONS OF EXOGENOUS VARIABLES
ON THEIR OHN LAGGED VALUES

CANADA-U.S.
1978:3-1983:3

 

 

Variable C Var__1 Var“2 R2 D.H.
m-m* -.17 .94 .86 1.97
(.14) (.05)
m-m* —.18 .95 .01 .86 1.99
(.14) (.13) (.13)
y-y* -.O3 .68 .45 1.93
y-y* -.02 .69 -.02 .45 1.96
(.01) (.14) (.14)
n-n* .00 .73 .53 2.45
(001)
n-n* .OO .49 .33 .58 2.13
(.01) (.12) (.13)
risk .01 .88 .88 2.23
(.01) (.04)
risk .01 .76 .13 .88 2.06
(.01) (.13) (.13)

 

Standard errors in parentheses.

95

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H-A.e.=e N-,.a-a. a-” u
.mNo.v .oeo.v aNo.v Aeo.v
NN. Nam. 8o. Noo.- coo.- nmo.- No.- «L.2 NNON
AeNo.v ACNo.V Amo.v ANo..
mNo. a mmo. No.- «0.- «2.2 mac
RON. ANN.V NNN.. Amm.v .oN.V ”om.v
NN. oo.N N0. N8. oN.- No. NN.- mo. NN. m Naou
.em.. Am”. .oN.. ANN.V Aoo.v .N~.v
mm. mm. mm.o No. nom.- 4N. awn. Ne. 6 mac
N .=.o NN NNN 48-8 «a-» «8-8 «5-5 u LN> 88:86:
NHNNNN-NH¢NNN
mme<em oNpNz=-<a<z<u

mzo-<=ou zmou amusamx ouboumhmmmza mzh mo zommmumomm

HH.¢ m4m<k

96

zoom uumgcou .~o>mp Ho. no

oooooooooom - o

cm_m pumccou .Pmoop mo. an acoupoocmom . o
.mmmozucocoo co mgogcm ucovcopm

 

 

 

Aooo.. mo. Aooo.o .ooo.o
oH.N oo. ooo. mo. omoo. oooo. to-o moo
HINLFIFV Mafia-A: Him 0
Aooo.o Aooo.o Aooo.o
oo. No.o oo. Nmo. moo. ooo. ta-a omoo
AoNo.o ”Noo.. ANoo.o .oNo.o
ooo. oooo. Noo.- ooo. «L-L moo
.oo.. Aom.. ANNN.. .oo.o .Nmo.o Rom.o
oN.N oo. NN. oN.- Hoo.- No. , NNo.- NN.- m oooo
.No.mo .om.o ANoN.o ANo.o. AoNN.o Aoo..
No. NN. oo.m NN.- moo. ooN.N ooo.- No.- 8 moo
o .:.o No goo .o.: to.» so-o «5.5 o too oooomz
NuoNoN-NHoNoN
mmo<om ouoozo-<o<z<o
zoommooomg

monH<=ou amok amazoum omhuumhmuazz mzh mo

NH.¢ m4m<h

97

zoom uuogeou .pm>up Ho. an acaupovcmom - o
coon uumccou .Fo>op we. we acouowocmvm - a
.mummsucmcoo co mgosgo vgoucapm

 

 

 

.oo.o Amo.o .NNo.. Aooo..
moo. No. ooo. ooo. oNo. Noo.- o-o moo
3-2-e.g. H-z-o-o. o.“ a
AoNo.. Aoo.o “No.. Aoo..
No. oo.N No. Noo. No.- omo.- oo.- 42-2 oNoo
.oo.o Aoo. .oNo.o .oNo.. Aooo.o .No..
oo. «o. oo.N oN. Noo.- Noo. ooo. oo.- ss-L moo
398 3H; A2; EN; EN; Sm;
N¢.N oo. oo.o ooo. NN.- NN. oo. NN. m moo
o .:.o ‘No goo .e-o so-» «o-o as-e o Loo oooooz
ouoooN-ouoooo
moo<om omoozo-<o<z<o
ozooo<ooo zoom oooooNN ooooooomoozo ozo do zoommooooo

mH.e u4m<h

98
the correct sign and significant. Sign reversals occurred in both
prices and incomes when autocorrelation was corrected. These results
are especially disturbing considering (I) the mark-U.S. dollar
interest rate results, and (2) the importance of the money demand
equation to the theoretical models.

The price equation estimates of the sample period found lagged
price differentials, exchange rate, and inflation expectations
significant and of the expected sign. Inflation expectations were
found to be insignificant during the first subsample while the lagged
exchange rate was insignificant during the second.

The stability of coefficients between subperiods is generally a
result of the large variances in relation to the coefficients. With
the exception of the price equation the poor results allowed stability
tests to find little significant coefficient change. As most of the
coefficients were insignificant, however, this result is generally
meaningless. The only conclusion that can be drawn is the inability
any of the models to explain the Canadian dollar-U.S. dollar rate over
either of the subperiods.

The unconstrained and constrained FIML estimates are reported in
Table 4.8. The rational expectations restrictions are soundly
rejected. The coefficients generally have the correct signs but the
magnitudes vary substantially from their theoretical priors. Tests
conducted using more general lag structures for the exogenous
variables produced similar results.

Specification tests comparing OLS and IV estimates find signifi-
cantly different coefficients. This indicates the endogeneity of

certain right hand side variables. Comparison of IV and FIML

99
estimates were also significantly different. This result indicates
the misspecification of the IV model. These results confirm the
theoretical supposition of simultaneity and correlation across

equations.

4.4 Results: Summary of Estimation 1980:6-1984:6

The continuous appreciation of the U.S. dollar during the early
1980's offers a particularly interesting period in which to examine
exchange rate models. First, the United States has not intervened in
the foreign exchange market. Second, Federal Reserve Bank policy has
been relatively consistent. And finally, certain foreign central
banks have abstained from exchange market intervention, i.e. the U.K.

Several explanations have been offered for the dollar apprecia-
tion. The existence of a real interest rate differential is one
explanation. Others have suggested the "safe haven" argument: U.S.
securities offer the least uncertainty in both a political and
economic sense.

-A casual inspection of the mark-U.S. dollar rate suggests that
the real interest rate argument offers an adequate explanation.
Tables 4.15 and 4.17 report the exchange rate equation for the
mark-U.S. dollar and Canadian dollar-U.S. dollar. Both expected
inflation rate and interest rate differentials have the correct sign;
the mark-U.S. dollar coefficients are significant. However, the
complete system must be examined.

Regressions of exogenous variables and lagged values indicate
that with the exception of risk a one-step random walk is appropriate
(Table 4.14). The mark-U.S. dollar exchange rate equation when

corrected for serial correlation gives a positive and significant sign

1(30

TABLE 4.14

GERMANY-UNITED STATES

1980:6-1984:6

 

 

 

 

 

c m-m* y-y* r-r* u-ii* RSK R2 o.w. 8
Germany- b
0.5. .45 -.64 -.2o -3.79° 2.63 .07 .00002 .54 1.96 .67
(.27) (.45) (.18) (1.47) (.79) (.06) (.00004)
GERMANY-U.S.
1980:6 - 1984:6
Variable c Var_l var_2 R2 0.w.
m-m* -.05° .92b .90 1.99
(.02) (.05)
m-m* -.053a .90b .02 90 1.96
(.027) (.15) (.14)
y-y* -.0005 1.06b .80 1.81
(.008) (.08)
y-y* .001 .86b .22 .80 1.58
(.008) (.200 (.21)
n-n* .0004 .95b .98 1.66
(.0007) (.02)
n-n* .0002 1.12b -.16 .98 2.01
(.0007) (.15) (.14)
RSK .27b .09 .07 2.00
(.04) (.14)
RSK .60a -.12 -1.32 .04 2.01
(.27) (.15) (1.11)

 

Standard errors in parentheses.

101
to the expected inflation differential (Table 4.15). Income and price
are both significant and of the correct sign. The money supply, once
again, is of the wrong sign.

The interest rate equation has all variables of the correct sign
with relative money supplies being significant. The price equation,
however, carries the wrong sign on the lagged expected inflation
differential and lagged exchange rate.

FIML estimation produces the wrong sign on X and soundly rejects
the rational expectation restructions. However, 4) and 5 are signi-
ficant.

The Canadian dollar-U.S. dollar results also fail to support the
real interest rate hypothesis. The exchange rate equation produces
the wrong sign for expected inflation, and the money supply
coefficient is significantly below one. The price differential is
also of the wrong sign and significant.

The interest rate equation fares no better. Only the relative
money supply coefficient is significant and of the correct sign. The
price equation, while producing correct signs, shows significance only
for the lagged price term.

Estimates from the restricted FIML estimation produce the wrong
sign for A. The restrictions imposed by rational expectations are
rejected. The inflation expectation coefficient is insignificant.

The U.S. dollar-U.K. pound sterling rate should be particularly
revealing. The general lack of exchange market intervention by both
British and American authorities allows for an analysis of a clean
float. Table 4.18 suggests the random walk hypothesis is apprOpriate

for income and inflation.

2102

TABLE 4.15

REGRESSION OF THE UNRESTRICTED REDUCED FORM EQUATIONS
GERMANY-UNITED STATES

 

 

1980:6-1984:6
Method Var C m-m* p-p* y-y* n-n* RSK R2 D.H. a
015 s -.31 -.50 -3.01b -.45b 1.85b .02 .93 1.25
(.27) (.39) (.70) (.16) (.50) (.07)
cont s -.44 -.35 -4.osb -.31' 1.78b .06 .77 2.01 .48
(.35) (.42) (1.07) (.14) (.61) (.06)
015 (r-r*) -.009 -.11b .25b .03b .28 .83
(.03) (.03) (.08) (.01)
coac (r-r') -.04o ..08b .08 .023 .15 1.89 .56
(.024) (.03) (.10) (.014)
C 5.; (p-p*l-1 (n-n*)_1 22 o.w.
01$ (p-p*) -.o3b -.013 .84b .03 .96 1.40
(.01) (.009) (.06) (.03)
conc (p-p*) -.02b -.014 .56b -.06 .67 1.96 .64
(.01) (.012) (.11) (.05)

TESTS OF RATIONAL EXPECTATIONS
Hark-U.S. Dollar

.043
(.064)

f ..05
(.03)

-.18b
(.04)

5 .026b
(.006)

2 'ILv‘Lcl 74.6

 

Standard errors in parentheses.
a - significant at .05 level, correct sign
b - significant at .01 level, correct sign

103

TABLE 4.16
CANADA-UNITED STATES
1980:6 - 1984:6

 

 

 

 

 

c mom* y-y* r-r* n- n* RSK o R2 0.0.
Canada-
U.S. .50 .11 -.17 -.89 .12 .01 .000005 .22 2.27 .96
(.28) (.100 (.100 (.70) (.26) (.02) 1.000003)
CANADA-UNITED STATES
1980:6 - 1984:6
Variable C Var_1 Var_2 R2 D-H.
m-m* .33 .88b ' .81 1.94
m—m* -.33 .89b -.01 .81 1.96
y-y* -.02‘ .77b .54 2.10
(.01) (.10)
y-y* .70 .70b .09 .55 1.99
(.14) (.14) (.15)
n-nt .004 .88b .94 1.68
(.006) (.033)
n-n* .004 1.03b -.14 .94 1.97
(.006) (.15) (.13)
nsx .10b .002 .01 2.00
(.01) (.1)
RSK -.47 -.06 5.92 .07 2.02
(.32) (.14) (3.25)

 

Standard errors in parentheses.

1(34

TABLE 4.17

REGRESSION OF THE UNRESTRICTED REDUCED FORM EQUATIONS
CANADA-UNITED STATES
1980:6-1984:6

 

 

Method Var c m-m* p-p* y-y* n-n* RSK R2 0.w. a
015 s .67b .19a .50b -.429 .21a .06a .81 1.07
(.23) (.08) (.09) (.12) (.10) (.03)
cone s .618 .15 .60b -.16 -.37 .01 .25 2.28 .80
(.26) (.09) (.20) (.10) (.27) (.02)
015 (r-r*) -.26b -.09b -.09b .001 .39 .66
1 05) (.01) (.02) (.028)
conc (r-r*) -.18b -.07b -.05 .02 .21 1.71 .71
(.05) (.02) (.03) (.02)
015 p-p* .003 .0003 .98b .03 .98 2.15
(.008) (.0424) (.03) (.03)
TESTS or RATIOHAL EXPECTATIONS
Canadian Dollar-U.S. Dollar
1 .016
(.06)
4 -.02
(.03)
n -.05D
(.02)
6 .05
(.03)
2 |Lv-Lcl 220.6

 

Standard errors in parentheses.
a - significant at .05 level, correct sign
b - significant at .01 level, correct sign

REGRESSION OF ENDOGENOUS VARIABLES
ON THEIR OWN LAGGED VALUES

105
TABLE 4.18

U.K./U.S.

1980:6 - 1984:6

 

 

Variable C Var_1 Var“2 R2 D.M.
m-m* .02a .94b .91 1.97
.01) (.07)
m-m* .02a .92b .03 .91 1.93
.01) (.14) (.15)
y-y* .OO .94 .85 1.75
.01) (.09)
y-y* .00 .85b .10 .85 1.66
.01) (.20) (.19)
n-n* .00 .79b .08 .98 1.88
.01) (.08) (.08)
n—n* .00 .79b .08 .98 1.81
.01) (.12) (.12)
Risk .02a .93b .87 1.91
.01) (.09)
Risk .02a .84b .09 .88 1.92
.01) (.20) (.16)

 

Standard errors in parentheses.

106

Estimation of the exchange rate equation (Table 4.19) fail to
support the real interest rate hypothesis. The money and price
coefficients sum to significantly less than one. The interest rate
equation fares no better: only the money supply coefficient is
significant. The price equation performed well because of the lagged
price term. A joint test of the model and rational expectations
hypothesis was rejected.

The system estimation does not verify the real interest rate
hypothesis in either the mark-dollar, Canadian dollar-U.S. dollar or
U.S. dollar-U.K. pound sterling case. However, the expected inflation
differential is of the correct Sign and significant in the German
case. The speed of adjustment term is also Significant in the
mark-dollar case. This, however, should be discounted as the lagged
exchange rate in the price equation is of the wrong Sign.

Neither the Canadian nor the British case lends support to any of
the models. The British case is especially revealing: the lack of
exchange market intervention does not improve the results. Neither
the sticky price or flexible price models explain the appreciation of

the U.S. dollar in the 1980's.

4.5 Summary and Conclusion

This chapter has tested a simultaneous version of monetary and
asset exchange rate models using system estimation techniques. The
movitation was derived from the inconsistent estimates produced by
ordinary least squares estimation and the use of ad hoc instruments in
instrumental variable estimation. Further, the use of system techni-
ques allowed for a more thorough examination of the models structure

including rational expectations.

107

TABLE 4.19

REGRESSION OF THE UNRESTRICTED REDUCED FORM EQUATIONS
U.K./U.S.
1980:6 - 1984:6

 

Method Var C m-m* p-p* y-y* u-n* RSK R2 D.H.

 

015 s 1.21 .26 .31b -.37° .24 .05 .85 1.21
(.71) (.15) (.10) (.18) (.11) (.03)

coac s 1.07 .17 .32a -.34‘ .11 .04 .49 1.81 .85
(.82) (.18) (.16) (.20) (.14) (.03)

OLS r-r* .14b .07a .12a .06 .36 1.25
(.05) (.03) (.05) (.07)

CORC r-r* .12 .06a .09 .05 .22 1.79 .68
(.07) (.03) (.05) (.09)
n C s_1 (p-p*)_l (nan*)_1 R2 D.H.
01$ p-p* .02 .01 .86 .04 .97 1.74

(.03) (.01) (.04) (.03)

 

Tests of Rational Expectations

1 -.02
(.03)
4 -.08°
(.04)

n .27
(.18)

6 .03
(.02)

2 (lLu-Lc D 118.4

 

Standard errors in parentheses.

108

The results suggest that the monetary model examined did not
adequately explain the exchange rate fluctuations in the floating rate
period for the Canadian dollar-U.S. dollar rate. Although several
different Specifications were used to describe the processes of
exogenous variables, all were found lacking.

The estimates of the exchange rate equation were particularly
poor. Once the estimates were corrected for serial correlation the
significance of the coefficients all but disappeared. The relative
inflation differential was significant only during the second
subperiod. Clearly, the Canadian experience does not lend support to
any of the monetary model variants.

The mark-U.S. dollar exchange rate was more adequately described
by the monetary model. Inflation expectations play a significant role
in explaining the fluctuations over the floating rate period.
Surprisingly, the first subperiod failed to support the expected
inflation hypothesis. The lack of significance of the interest rate
differential suggests that a Bilson-type hypothesis most adequately
explains the mark-dollar exchange rate. However, the wrong Sign on
both the money supply and price differentials cautions against too
strong an endorsement.

The failure of the monetary model to explain the U.S. dollar-U.K.
pound sterling rate is particularly disconcerting. The sample period
was particularly well suited for a positive result: a continuously
appreciating dollar in the absence of exchange market intervention.
Only the income term was significant.

The hypothesis of rational expectations using either a random

walk or first order autoregressive process for the exogenous variables

109
failed for all rates during all periods. It Should be noted, however,
that the likelihood ratio test is a joint test of both the model and
rational expectations. The failure might also be explained by the
limited lag structure of the autoregressions: the imposition of
additional restrictions might alter the result.

The use of Simultaneous equation techniques is supported by the
results of structural Specification tests. The joint exogeneity of
the contemporaneous explanatory variables is rejected for the exchange
rate equation. Further, the results also find that system estimates
are significantly different from instrumental variable estimates.
These results mirror the findings of researchers using Granger-Sims
type tests to examine the exogeneity of money supplies, incomes, and
interest rates in exchange rate models.

The monetary-asset approach employed in this chapter failed as a
general description of exchange rate fluctuation. Although it enjoyed
limited success for the mark-U.S. dollar rate, it did not capture
either the Canadian dollar-U.S. dollar' or' U.S. dollar-U.K. pound
sterling movements. All explanatory variables with significant
coefficients were found unstable over the four periods considered.
Estimates were very sensitive to specification as well as sample

period.

110

FOOTNOTES - CHAPTER IV

1The possibility of a first order autoregressive process is
examined later.

2The assumption of a random walk also ensure the "overshooting"
result found in many exchange rate models.

3This has been noted by many authors: See Edison, Driskill and
Sheffrin (1981) and others.

4The relaxation of the random walk assumption turns the model
into a seven equation system. In addition to equations (8)-(10),
equations for the exogenous variables must be jointly estimated:

(y-y*)t = A1(y-y*)t_1 + 21
(Ill-m*)t = A2(m-m*)t-1 + trend + 22
(ii-11*)t = A3in-n*)t_1 + Z3

riskt = A4(risk)t_1 + Z4

5Estimates of the seven equation system did not significantly
change the results of the exchange rate equation nor affect the tests
of rational expectations.

6The results are reported assuming that the "correct" coefficient
signs are those produced by the theoretical monetary/asset models.

CHAPTER V
CONCLUSIONS

This dissertation is an empirical investigation of the monetary
and asset approach to exchange rate determination. Estimates of
alternative exchange rate models within the approach led to these
principle conclusions:

1. The general and restricted versions of the monetary/
asset models examined in the study do not offer a
consistent explanation of exchange rate movements during
the post-Bretton Hoods era.

2. The joint hypothesis of model specification and rational
expectations is rejected given the exogenous variable
processes examined in this study.

3. The single equation empirical versions of simultaneous
equation theoretical exchange rate models are mis-
Specified.

Other findings, of less significance, are also of interest:

4. The modeling of inflation expectations is extremely
sensitive to proxy choice. The use of adaptive,
rational or survey proxies dramatically alter coeffi-
cient estimates.

5. The coefficient sign reversals noted in previous studies
are repeated.

Several aSpects of this study distinguish it from previous work.
First, the use of a ten-year sample with two five-year subsamples
allowed for a systematic examination of the robustness of alternative

exchange rate hypothesis. Second, the use of Hausman-Hu tests was the

111

112

first structural examination of simultaneity in exchange rate models.

 

Third, the study used adaptive, rational, and survey data proxies in
measuring inflation expectations.

while this study does not yield direct policy implications, it
does interject a note of caution into discussions of exchange rate
regimes. The conclusions of this study suggest the difficulty of
explaining exchange rate movements and, consequently, the difficulty
of determining the equilibrium exchange rate. Policy planners wishing
to reestablish a system of fixed exchange rates should bear this in
mind. The adjustment costs associated with establishing a fixed
exchange rate that deviates substantially from the freely floating
equilibrium rate are well known.

The results of the study suggest several areas for future
research. First, the effect of central bank exchange market
intervention in both exchange rates and exchange rate expectations
needs further study. This effect has been dramatically demonstrated
by the recent dollar depreciation following the Group of Five meeting
in November, 1985. Second, an expanded real sector is needed to
adequately explain exchange rate movements. Changes in both
technology and preferences should be integrated into the model.
Third, alternative money market specifications could improve the
model. The inadequacy of the present money market equations is often
blamed for the poor results of monetary/asset models. Finally,
alternative models of expectations could be included. This would
allow the possibility of speculative bubbles and self-fulfilling

expectations.

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