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Estimating the structure and efficiency of the Canadian foreign exchange market : 1971-1978 Boothe, Paul Michael 1981

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ESTIMATING THE STRUCTURE AND EFFICIENCY OF THE CANADIAN FOREIGN EXCHANGE MARKET: 1971-1978. by PAUL MICHAEL BOOTHE B.A.(Hon.), The University of Western Ontario, 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Economics) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1981 © Paul Michael Boothe, 1981 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f ECONOMICS The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 D a t e June 4, 1981 DE-6 (2/79) i i Abstract After eight years under the Bretton Woods system, Canada returned to a regime of f l e x i b l e exchange rates in May 1970. Over the remainder of the decade many other countries joined Canada in adopting f l e x i b l e rates, and this movement has opened up a f e r t i l e new area for study by economists. This d i s s e r t a t i o n examines the Canadian foreign exchange market from several d i f f e r e n t points of view. It begins by comparing a number of t h e o r e t i c a l models currently found in the l i t e r a t u r e , showing the common theoreti c a l core from which the models are derived, as well as the differences among them. The models are then estimated using Canadian and U.S. quarterly data over the period 1971-78, and compared to one another on the basis of f i t . The d i s s e r t a t i o n then turns to the question of prediction. Using the models discussed above, and time-series forecasts of the explanatory variables, monthly forecasts of three-month-ahead exchange rates are constructed for the period 1974-78. Care i s taken to ensure that a l l forecasts are based only on information availahle to the market at the time the forecast was to have been made. The forecasts of the three-month-ahead exchange rate are compared to one another and also to the three-month forward rate, which i s taken to be the market's forecast of the future value of the exchange rate. It is shown that the models' forecasts and the forward rate each contain separate information valuable in forecasting the future spot rate. The models and the forward rate are combined to produce a set of ' o p t i m a l ' f o r e c a s t s . The f i n a l c h a p t e r o f t h e d i s s e r t a t i o n f o c u s s e s on s p e c u l a t i o n and m a r k e t e f f i c i e n c y . I t i s shown t h a t t h e f o r e c a s t s c a n be c o m b i n e d w i t h a c r u d e b e t t i n g s t r a t e g y t o p r o d u c e s p e c u l a t i v e p r o f i t s o v e r t h e s i x t y p e r i o d s f r o m 1 9 7 4 - 7 8 . No c o n v e n t i o n a l m e a s u r e o f r i s k c a n be c o n s t r u c t e d , b u t i t i s shown t h a t t h e p r o b a b i l i t y o f mean r e t u r n s b e i n g n e g a t i v e a f t e r s i x t y b e t s i s l e s s t h a n one p e r c e n t . When t r a n s a c t i o n c o s t s a r e t a k e n i n t o a c c o u n t , s p e c u l a t i v e r e t u r n s a r e r e d u c e d , b u t t h e p r o b a b i l i t y o f a v e r a g e r e t u r n s b e i n g n e g a t i v e a f t e r s i x t y b e t s r e m a i n s l e s s t h a n one p e r c e n t . Thus a l l of t h e e s t i m a t e d m o d e l s a p p e a r t o c o n t a i n i n f o r m a t i o n t h a t was n o t e f f i c i e n t l y u s e d by p a r t i c i p a n t s i n t h e f o r e i g n e x c h a n g e m a r k e t b e t w e e n 1974 and 1978. S u b s e q u e n t r e s e a r c h w i l l be r e q u i r e d t o t e l l w h e t h e r t h i s r e p r e s e n t s a l e a r n i n g p e r i o d f o r m a r k e t p a r t i c i p a n t s , o r w h e t h e r e x c h a n g e m a r k e t p a r t i c i p a n t s w i l l c o n t i n u e t o u n d e r v a l u e a v a i l a b l e i n f o r m a t i o n . iv Table of Contents Abstract i i L i s t Of Tables v i L i s t Of Figures v i i i Acknowledgement ' ix Chapter 1 1 1.0 Introduction 1 1.1 Exchange Rate Shocks In The 1970's 3 1.2 Dissertation Outline 4 Chapter 2: Formulating Alternative Models Of Exchange Rate Determination 6 2.0 Introduction 6 2.1 Purchasing-Power-Parity 6 2.2 Real-Interest- And Interest-Parity 10 2.3 Monetary Approach 13 2.4 A Structural Model 19 2.5 Conclusions 23 Notes To Chapter 2: Model Equations 25 Chapter 3: Explaining Movements In The Exchange Rate 28 3.0 Introduction 28 3.1 Purchasing-Power-Parity 28 3.2 Real-Interest- And Interest-Parity 31 3.3 The Monetary Approach 33 3.4 The Structural Approach 34 3.5 Ranking The Models By F i t 36 3.6 Informational Content Of The Models 37 V 3.7 Conclusions 38 Notes To Chapter 3: Data Sources 49 Chapter 4: Comparing Alternative Exchange Rate Forecasts ..51 4.0 Introduction 51 4.1 Constructing Model Forecasts .' 51 4.2 Comparing Model Forecasts 53 4.3 Informational Content Of Alternative Forecasts 55 4.4 Constructing Optimal Forecasts 59 4.5 Conclusions 60 Notes To Chapter 4: Time Series Analysis And Forecasting Exogenous Variables 69 Chapter 5: Speculative P r o f i t s And Market E f f i c i e n c y 84 5.0 Introduction 84 5.1 The E f f i c i e n c y Literature 84 5.2 Constructing A Test Of E f f i c i e n c y 88 5.3 Speculative Returns 89 5.4 Conclusions 95 Chapter 6 102 6.0 Introduction 102 6.1 Summary Of Findings 102 6.2 Conclusions And Directions For Further Research ....106 Bibliography 108 L i s t o f T a b l e s T a b l e 3.1: PPP E s t i m a t e s U s i n g OLS 41 T a b l e 3.2: PPP E s t i m a t e s U s i n g CORC 42 T a b l e 3.3: PPP+M, R I P And I P E s t i m a t e s U s i n g OLS 43 T a b l e 3.4: PPP+M, R I P And I P E s t i m a t e s U s i n g CORC 44 T a b l e 3.5: M o n e t a r y A p p r o a c h E s t i m a t e s U s i n g OLS 45 T a b l e 3.6: M o n e t a r y A p p r o a c h E s t i m a t e s U s i n g CORC 46 T a b l e 3.7: S t r u c t u r a l A p p r o a c h E s t i m a t e s U s i n g OLS And CORC 47 T a b l e 3.8: C o m p a r i n g S e l e c t e d M o d e l s By F i t 47 T a b l e 3.9: F - T e s t Of M o d e l s ' C o n t r i b u t i o n O v e r P F X ( - l ) And P F X F ( - l ) 48 T a b l e 4.1: M o d e l s ' F o r e c a s t s : 1974-78 62 T a b l e 4.2: F - T e s t Of M o d e l s ' C o n t r i b u t i o n Over PFXF 64 T a b l e 4.3: F - T e s t Of P F X F ' s C o n t r i b u t i o n O v e r M o d e l s ' F o r e c a s t s 64 T a b l e 4.4: E s t i m a t e s U s i n g F o r e c a s t s P l u s NEWS 65 T a b l e 4.5: O p t i m a l F o r e c a s t s : 1974-78 67 T a b l e 4.6: V a r i a b l e : P 73 T a b l e 4.7: V a r i a b l e : P* 74 T a b l e 4.8: V a r i a b l e : Y 75 T a b l e 4.9: V a r i a b l e : Y* 76 T a b l e 4.10: V a r i a b l e : R 77 T a b l e 4.11: V a r i a b l e : R* 78 T a b l e 4.12: V a r i a b l e : DP ' 79 T a b l e 4.13: V a r i a b l e : DP* ' 80 Table 4.14: Variable: M 81 Table 4.15: Variable: M* 82 Table 4.16: Variable: L 83 Table 5.1: P-values (p=#correct/n) 97 Table 5.2: Speculation Using Models' Forecasts 98 Table 5.3: Speculation Using Optimal Forecasts 98 Table 5.4: P r o b a b i l i t i e s Of Betting P r o f i t s Using Models' Forecasts 99 Table 5.5: P r o b a b i l i t i e s Of Betting P r o f i t s Using Optimal Forecasts 99 Table 5.6: Speculation Using Models' Forecasts (with Transaction Costs) 100 Table 5.7: Speculation Using Optimal Forecasts (with Transaction Costs) 100 Table 5.8: P r o b a b i l i t i e s Of Betting P r o f i t s After Transaction Costs Using Models' Forecasts 101 Table 5.9: P r o b a b i l i t i e s Of Betting P r o f i t s After Transaction Costs Using Optimal Forecasts 101 v i i i L i s t of Figures Figure 1 27 ix Acknowledgement Every diss e r t a t i o n i s completed with the help of many people, and i t is a pleasure to acknowledge the debts I have aquired in writing mine. My f i r s t debt is to my supervisor, John H e l l i w e l l , without whose instruction, advice and encouragement I could have never finished my thesis. Russ Uhler helped me with every aspect of my di s s e r t a t i o n , and was never too busy to l i s t e n to my "many problems. Eduardo Schwartz lent his expertise in solving several key problems I encountered. My departmental examining committee provided many helpful comments. Frank Flynn was invaluable in helping to overcome my numerous computing problems and Leigh Mazany and Dave Moloney acted as t a c t f u l but determined editors on various chapters. Through Tom Maxwell and later David Longworth, the Bank of Canada provided me with important unpublished data. MacRenzie and MacMillan fellowships provided generous f i n a n c i a l assistance. My f i n a l debt is to my wife Pat, whose love and support sustained me throughout my career as a graduate student. It i s to her that t h i s d i s s e r t a t i o n i s dedicated. T=0.584 DR=2 $5.37, $5.46T $SIGNOFF 1 Chapter 1 1.0 Introduction 1 On May 31, 1970, Canada returned to a f l e x i b l e exchange rate. This lead was followed in the 1970's by many of Canada's major trading partners, so that by the end of the decade much of the western world was on f l e x i b l e rates. One of the most puzzling features of the return to a f l e x i b l e rate regime has been the substantial increase in the v a r i a b i l i t y of exchange rates over the decade. For example, in 1971 the average absolute weekly change in the exchange rate was less than $0,002 Canadian. In 1978 the average absolute change was over $0,005 Canadian 2. How can thi s increased v a r i a b l i l i t y be explained? Some economists have developed 'overshooting' models 3, where the i n i t i a l over- or under-valuation of the exchange rate is b u i l t into the dynamics of adjustment. Others have been led to study the 'ef f i c i e n c y ' of the foreign exchange market. In these studies, investigators have attempted to determine i f market participants make optimal or ' e f f i c i e n t ' use of available information in setting the price of foreign exchange. If markets are e f f i c i e n t and i f prices are set making optimal use of xMuch of what is written in thi s chapter about recent Canadian exchange rate events i s drawn from Freedman and Longworth (1980), Courchene (1976, 1976a, 1977) and from the Bank of Canada Annual Report for various years. 2More examples and a discussion of thi s phenomenon can be found in Artus and Young (1979). 3See Dornbusch (1976) and McKinnon (1976). 2 available information, then remaining v a r i a b i l i t y must be the result of unpredictable events. Current research on the e f f i c i e n c y of the foreign exchange market is i n c o n c l u s i v e 4 . In an attempt to address questions of market e f f i c i e n c y , and other questions as well, t h i s d i s s e r t a t i o n considers a number of a l t e r n a t i v e models of exchange rate determination. These models are compared on a t h e o r e t i c a l basis, estimated, and used to forecast the exchange rate up u n t i l the end of 1978. The d i s s e r t a t i o n t r i e s to answer the following questions: 1) What are the important determinants of the exchange rate and which models do a good job of explaining i t s movements since the beginning of the most recent f l e x i b l e regime period? 2) How well could these alternative models have forecasted the exchange rate over t h i s period r e l a t i v e to the market's forecast which i s embodied in the forward rate? 3) Is the market setting the exchange rate making e f f i c i e n t use of a l l available information, or can the forecasts be used to p r o f i t a b l y speculate in the foreign exchange market? This d i s s e r t a t i o n makes several contributions to current knowledge of the foreign exchange market over th i s period. It i s the f i r s t time a broad spectrum of alternative models has been empirically estimated over a consistent data set. It considers the notion of model 'popularity' and shows the r e l a t i o n s h i p between the market's and the models' information regarding the future value of the exchange rate. F i n a l l y , i t demonstrates that the market was not setting the value of the exchange rate *This issue is examined in d e t a i l in Chapter 5. 3 e f f i c i e n t l y over the period examined and market participants could not have been forming expectations in a 'rational' manner. 1.1 Exchange Rate Shocks in the 1970's The variety of shocks to the exchange market, especially over the period 1970-76, makes thi s period a very interesting one to study. The Canadian do l l a r had been fixed at $0,925 U.S. since June of 1962, and reserves over t h i s period had, with a few exceptions, held f a i r l y constant. The decade began with very tight credit conditions being the order of the day in Canada. Speculative c a p i t a l inflows and f a l l i n g imports were putting upward pressure on the Canadian d o l l a r , and the inflows were being s t e r i l i z e d by the Bank of Canada (hereafter the 'Bank') to avoid an expansion of the money supply. Foreign exchange reserves were growing rapidly. Rather than l e t the money supply expand as they continued to defend -the d o l l a r , authorities opted for a f l e x i b l e exchange rate in June 1970. The early 1970's marked the beginning of a sharp r i s e in the price of raw materials, improving Canada's terms of trade. Partly as a result of this improvement, the economy was protected from the f u l l force of the recession of 1974 in the United States. Another ef f e c t of the improvement was continued upward pressure on the Canadian d o l l a r , which was resisted by authorities at the cost of large increases in the money supply. As Courchene (1976) has argued, i t seems that after forsaking the fixed rate regime in order to tighten c r e d i t conditions r e l a t i v e to the U.S., the Bank immediately abandoned tight money in favour of preventing the d o l l a r form appreciating too 4 rapidly. This had some impact also on the i n f l a t i o n rate, which rose from 2.8% to 10.9% between 1971 and 1974. In September 1975, the Governor of the Bank announced a new dir e c t i o n for monetary po l i c y . In essence the Bank was abandoning the 'appropriate cre d i t conditions' target and turning to a new 'monetarist' objective. Henceforth the Bank would attempt to control the growth of currency and demand deposits, commonly known as Ml. With tight monetary policy r a i s i n g the long-term interest d i f f e r e n t i a l in Canada's favour, large long-term c a p i t a l inflows put added upward pressure on the Canadian d o l l a r . In 1976 the d o l l a r was overvalued by 20% according to some purchasing power parity measures 5. Late in 1976 the Parti Quebecois came to power in Quebec with the stated goal of separation from Canada. The Canadian dol l a r began a steady decline in U.S. terms which by the end of 1978 had reached 21%. 1.2 Dissertation Outline The purpose of Chapter 2 is to compare on a theoret i c a l basis a spectrum of alternative models of exchange rate determination found in the l i t e r a t u r e . These models can be divided into four main groups: Purchasing-Power-Parity (PPP) models, Interest-Parity (IP) models, Monetary Approach models and a Structural model. The chapter i d e n t i f i e s how each successively more sophisticated model r e l i e s on the concepts 5See Freedman and Longworth (1980) p.12. embodied in the simple models. In Chapter 3, the models from Chapter 2 are estimated using quarterly data from Canada and the U.S. over the period 1971-78. Each model i s ranked on the basis of f i t . The models are further examined to see i f they contribute beyond the lagged spot and forward rates to explaining movements of the exchange rate. Chapter 4 takes the models which survive the empirical scrutiny of the previous chapter and uses them to form genuine three-month-ahead forecasts, monthly for the period 1974-78. These forecasts are compared to one another and to the forward rate, and tested to see i f they contain unpopular but v a l i d information, that i s , information useful for explaining the future spot rate but not included in the current forward rate. The forecasts are combined with the forward rate to produce a set of 'optimal' forecasts. F i n a l l y , in Chapter 5 the forecasts are combined with a simple betting strategy to speculate in the forward market over the period 1974-78. The returns from speculation are examined and conclusions are drawn about the e f f i c i e n c y of the market in setting the exchange rate over t h i s period. The d i s s e r t a t i o n jJoncllides with a summary of findings. 6 Chapter 2 Formulating Alternative Models of Exchange Rate Determination 2.0 Introduction The purpose of t h i s chapter i s to develop and to compare on a theoretical basis several alternative models of exchange rate determination under a f l e x i b l e rate regime. The models w i l l be presented in four groups: Purchasing-Power-Parity, (PPP), Real-Interest-Parity, (RIP), the Monetary Approach and the Structural Approach. Each group w i l l be presented in turn, from the simplest, PPP, to the most complex, the Structural Approach. As each group is presented, i t s links with the previous models w i l l be recognized and discussed. F i n a l l y , each model w i l l be expressed in a form amenable to empirical estimation, the results of which w i l l be presented in Chapter 3. 2.1 Purchasing-Power-Parity Attributed o r i g i n a l l y to Wheatley and Ricardo by Frenkel (1976) and Cassels by Isard (1978), the PPP theory of exchange rate determination comes in many forms. Surveys of the di f f e r e n t views can be found in Of f i c e r (1976) and the 1978 Journal of International Economics Symposium on PPP. The theory behind PPP is as follows: " i f goods and services do not s e l l at the same prices in a l l countries, then either actual or incipient movements of products or factors w i l l bring prices back to 7 e q u a l i t y a f t e r a l l o w i n g f o r c o s t s o f t r a n s a c t i o n s , t a r i f f s a n d t r a n s p o r t a t i o n . " 6 The more e a s i l y g o o d s f l o w b e t w e e n e c o n o m i e s , t h e more s t r o n g l y we e x p e c t PPP t o be a c h a r a c t e r i s t i c o f e x c h a n g e m a r k e t e q u i l i b r i u m . The f i r s t d i s t i n c t i o n t o be made i s b e t w e e n ' a b s o l u t e ' a n d ' r e l a t i v e ' PPP. I n i t s a b s o l u t e f o r m , u n d e r a f l o a t i n g r a t e r e g i m e , t h e p r i c e o f one c u r r e n c y i n t e r m s o f a n o t h e r d e p e n d s on t h e r e l a t i v e p r i c e s p r e v a i l i n g i n t h e two e c o n o m i e s : ( 2 . 1 . 1 ) P F X ( t ) = P ( t ) / P * ( t ) , where P F X ( t ) r e p r e s e n t s t h e c u r r e n t ' d o m e s t i c p r i c e o f one u n i t o f f o r e i g n c u r r e n c y , P ( t ) r e p r e s e n t s c u r r e n t d o m e s t i c p r i c e s a n d P * ( t ) r e p r e s e n t s c u r r e n t f o r e i g n p r i c e s . Of c o u r s e , e x c e p t a t a v e r y d i s a g g r e g a t e d l e v e l , p r i c e d a t a a r e r e p o r t e d a s i n d i c e s r a t h e r t h a n a c t u a l p r i c e s . T h i s o b s t a c l e i s o v e r c o m e i n t h e r e l a t i v e v e r s i o n o f PPP w h i c h i s s u m m a r i z e d i n t h e f o l l o w i n g e q u a t i o n : ( 2 . 1 . 2 ) P F X ( t ) / P F X ( 0 ) = { P ( t ) / P ( 0 ) } / [ P * ( t ) / P * ( 0 ) ] , where ' t ' d e n o t e s t h e c u r r e n t p e r i o d a n d '0' d e n o t e s some b a s e p e r i o d c o n s t a n t . when t h e m a r k e t was assumed t o be i n e q u i l i b r i u m . What p r i c e s s h o u l d be c h o s e n a s d e t e r m i n i n g PPP? D i f f e r e n t p o i n t s o f v i e w e x i s t on t h i s i s s u e . N a r r o w v e r s i o n s o f PPP u s e e i t h e r d i s a g g r e g a t e d p r i c e s o r p r i c e s o f t r a d e d g o o d s . H e r e t h e p r o b l e m o f r e v e r s e c a u s a l i t y i s e n c o u n t e r e d , s i n c e t h e e x c h a n g e r a t e i s d e t e r m i n e d by a b r o a d r a n g e o f p r i c e s " w h i l e t h e n a t i o n a l p r i c e s o f t r a d e d g o o d s a r e d e t e r m i n e d by t h e l a n d e d • H e l l i w e l l ( 1 9 7 9 ) , p.426. 8 price of their close s u b s t i t u t e s " 7 . At the disaggregated l e v e l , causality tends to run from the exchange rate to the domestic price, rather than in the opposite d i r e c t i o n . Broad versions of PPP, employing aggregate price measures, are used in an attempt to avoid the problem of reverse ca u s a l i t y . The use of aggregate prices i s j u s t i f i e d either by arguing that factors of production are i n t e r n a t i o n a l l y mobile (so that even non-traded goods have an effect on the exchange rate), or by taking a monetarist view that national currencies are assets, the values • of which are determined by their general purchasing power. It must be recognized that the use of broad measures of prices also presents problems. Changes in other factors (for instance product mix or t a r i f f s ) that a f f e c t price indices besides prices themselves, w i l l weaken PPP predictions unless these changes occur i d e n t i c a l l y in domestic and foreign economies. Thus, t h i s form of PPP should be expected to explain movements in the exchange rate only when the shocks to the economy are monetary in nature. Another form of PPP explains changes in national prices and therefore the exchange rate, using national demand for money functions: (2.1.3) m(t)-p(t)=a+by(t) , m*(t)-p*(t)=a+bY*(t), 8 where 'm' i s the logarithm of money demand and 'y' is the 7 H e l l i w e l l (1979), p.427. "For analytic convenience, c o e f f i c i e n t s and e l a s t i c i t i e s of money demand are assumed equal across countries. Lower case l e t t e r s denote logarithms. Unless otherwise stated, variables always represent the current period. 9 logarithm of real national income. Combining (2.1.3) with PPP (Equation (2.1.1) in logarithmic form) gives: (2.1.4) pfx(t)={m(t)-m*(t)}-b[y(t)-y*(t)]. This model uses the basic PPP equation, but does not take prices to be exogenous. Prices are determined by national money demand functions, so that changes in the exchange rate can be related to changes in the r e l a t i v e growths of national money supplies and/or national incomes. Authors adopting t h i s formulation are actually j o i n t l y testing two separate hypotheses; one concerned with the determination of the exchange rate, and another regarding the form and s t a b i l i t y of money demand functions. Over what time horizon should PPP be expected to be valid? Those who expect i t to be true at every point in time have great f a i t h in immediate and complete commodity arbitrage or factor mobility between countries. The empirical evidence does not support this view. As the time horizon is lengthened i t would seem increasingly l i k e l y that the exchange rate w i l l come into l i n e with PPP predictions. Divergent prices between economies act as an incentive to trade which in the long-run must contribute s i g n i f i c a n t l y to determining the rate of exchange. C r i t i c s who dismiss PPP because of i t s i n a b i l i t y to perform well as a short-run model of exchange rate determination often seem to ignore i t s value as an explanation for longer term exchange rate changes.' F i n a l l y , notwithstanding i t s value as a short-run 'For an an empirical evaluation of PPP's long term performance, see O f f i c e r (1980). 1 0 e x p l a n a t i o n o f e x c h a n g e r a t e s , PPP p l a y s an i m p o r t a n t p a r t i n a l l o f t h e more s o p h i s t i c a t e d e x c h a n g e r a t e m o d e l s , w i t h i t s r o l e b e i n g t o d e t e r m i n e t h e l o n g - r u n e x p e c t e d v a l u e o f t h e e x c h a n g e r a t e . T h i s w i l l become e v i d e n t a s e a c h o f t h e o t h e r m o d e l s a r e d i s c u s s e d . 2.2 R e a l - I n t e r e s t - a n d I n t e r e s t - P a r i t y A l t h o u g h e c o n o m i s t s i n t h e 1 9 t h c e n t u r y had some n o t i o n o f t h e e f f e c t o f i n t e r e s t r a t e s on c a p i t a l f l o w s , K e y n e s ( 1 9 2 3 ) i s c r e d i t e d w i t h e x p o u n d i n g t h e i n t e r e s t - p a r i t y o r f o r w a r d e x c h a n g e t h e o r y i n i t s p r e s e n t f o r m . T h i s t h e o r y r e c e i v e s a c o m p r e h e n s i v e t r e a t m e n t i n G r u b e l ( 1 9 6 6 ) . E s s e n t i a l l y t h e t h e o r y p o s t u l a t e s t h a t t h r o u g h t h e use o f t h e f o r w a r d e x c h a n g e m a r k e t , i n v e s t o r s c a n c h o o s e r i s k l e s s l y t o i n v e s t f u n d s a t home o r a b r o a d , i n s e a r c h o f t h e h i g h e s t r e t u r n . I f i n t e r e s t r a t e s a r e s i g n i f i c a n t l y h i g h e r a b r o a d , i n v e s t o r s w i l l move f u n d s o u t o f t h e d o m e s t i c economy u n t i l t h e gap b e t w e e n t h e f o r w a r d a n d s p o t r a t e no l o n g e r p r e s e n t s t h e o p p o r t u n i t y f o r p r o f i t a b l e a r b i t r a g e . T h i s n o t i o n c a n be e x p r e s s e d i n t h e f o l l o w i n g e q u a t i o n : ( 2 . 2 . 1 ) (1+R)=(1+R*)PFXF/PFX , where R a n d R* r e p r e s e n t d o m e s t i c a n d f o r e i g n i n t e r e s t r a t e s a n d PFXF r e p r e s e n t s t h e d o m e s t i c p r i c e o f one u n i t o f f o r e i g n c u r r e n c y t o be d e l i v e r e d one p e r i o d f o r w a r d . The i n v e s t o r h a s t h e c h o i c e ( a b s t r a c t i n g f r o m t r a n s a c t i o n c o s t s ) o f i n v e s t i n g a t home and r e c e i v i n g (1+R) a t t h e end o f t h e p e r i o d , o r c o n v e r t i n g t o f o r e i g n f u n d s , i n v e s t i n g a b r o a d t o r e c e i v e ( 1 + R * ) , a nd c o n v e r t i n g t h e p r o c e e d s i n a f o r w a r d c o n t r a c t a t PF X F . E q u a t i o n 11 ( 2 . 2 . 1 ) . i s known a s t h e c o v e r e d - i n t e r e s t - p a r i t y c o n d i t i o n . 1 0 t h i s e q u a t i o n c a n be r e - a r r a n g e d t o show t h e r e l a t i o n s h i p b e t w e e n t h e f o r w a r d premium o r d i s c o u n t and t h e i n t e r e s t r a t e d i f f e r e n t i a l : ( 2 . 2 . 2 ) P F X F / P F X = ( 1 + R ) / ( 1 + R * ) . I t i s i m p o r t a n t t o r e c o g n i z e t h a t t h e c o v e r e d - i n t e r e s t - p a r i t y c o n d i t i o n d e t e r m i n e s t h e r a t i o o f t h e s p o t a n d f o r w a r d r a t e o f e x c h a n g e , b u t d e t e r m i n e s t h e l e v e l o f n e i t h e r . I n t e r e s t - p a r i t y must be c o m b i n e d w i t h o t h e r a s s u m p t i o n s o r t h e o r i e s s u c h a s PPP i n o r d e r t o be c o n s i d e r e d a c o m p l e t e t h e o r y o f e x c h a n g e r a t e d e t e r m i n a t i o n . C o n s i d e r t h e f o l l o w i n g R e a l - I n t e r e s t - P a r i t y ( R I P ) p l u s PPP m o d e l : ( 2 . 2 . 3 ) d = r - r * , where d i s t h e e x p e c t e d r a t e o f e x c h a n g e d e p r e c i a t i o n , r i s t h e l o g a r i t h m o f one p l u s t h e d o m e s t i c i n t e r e s t r a t e a n d r * i s t h e l o g a r i t h m o f one p l u s t h e f o r e i g n i n t e r e s t r a t e . A l t h o u g h t h i s i s s i m i l a r t o e q u a t i o n ( 2 . 2 . 2 ) ( t r a n s f o r m e d by l o g a r i t h m s ) , i t i s a c t u a l l y t h e s t r o n g e r u n c o v e r e d - i n t e r e s t - p a r i t y c o n d i t i o n . I m p l i c i t i n t h i s e q u a t i o n i s t h e a s s u m p t i o n t h a t t h e f o r w a r d r a t e i s an a c c u r a t e m e asure o f t h e m a r k e t ' s e x p e c t a t i o n o f t h e f u t u r e v a l u e o f t h e e x c h a n g e r a t e . ' ~ ° ~ ~ The e x p e c t e d r a t e o f e x c h a n g e r a t e d e p r e c i a t i o n c a n a l s o be d i r e c t l y s p e c i f i e d a s an e q u a t i o n o f e x p e c t a t i o n f o r m a t i o n : 1 0 0 f c o u r s e , t h i s i g n o r e s t h e f a c t t h a t i n v e s t o r s a l s o h ave e x p e c t a t i o n s a b o u t t h e f u t u r e v a l u e o f t h e e x c h a n g e r a t e . W i t h t h i s t a k e n i n t o a c c o u n t t h e r e i s no r e a s o n t o e x p e c t an e x a c t c o v e r e d - i n t e r e s t - p a r i t y r e l a t i o n s h i p b e t w e e n s p o t a nd f o r w a r d r a t e s . 12 ( 2 . 2 . 4 ) d = - c ( p f x - p f x ) + D P -DP*. H e r e t h e e x p e c t e d r a t e o f e x c h a n g e d e p r e c i a t i o n i s a f u n c t i o n o f d i f f e r e n c e b e t w e e n t h e l o g a r i t h m o f t h e s p o t r a t e , p f x , and t h e l o g a r i t h m o f t h e e q u i l i b r i u m r a t e , p f x , and t h e e x p e c t e d r a t e s o f i n f l a t i o n a t home a n d a b r o a d , DP and D P * . 1 1 The s p e e d o f a d j u s t m e n t o f t h e e x c h a n g e r a t e t o i t s e q u i l i b r i u m v a l u e i s r e p r e s e n t e d by ' c ' . When p f x = p f x , i t i s e x p e c t e d t h a t t h e e x c h a n g e r a t e w i l l c h a n g e by DP-DP* i n t h e a b s e n c e o f o t h e r c h a n g e s . E q u a t i n g ( 2 . 2 . 3 ) a n d ( 2 . 2 . 4 ) g i v e s : ( 2 . 2 . 5 ) p f x - p f x = - ( l / c ) [ ( r - D P ) - ( r * - D P * ) ] . I n t h i s e q u a t i o n , when p f x = p f x , r-r*=DP-DP*. I n o t h e r w o r d s , i t i s assumed t h a t i n t h e l o n g - r u n , r e a l i n t e r e s t r a t e s a r e e q u a l a c r o s s e c o n o m i e s . I n o r d e r t o d e t e r m i n e t h e e q u l i b r i u m e x c h a n g e r a t e a PPP c o n d i t i o n i s i m p o s e d : ( 2 . 2 . 6 ) p _ f x = p - p * 1 2 , where p a n d p* a r e t h e l o g a r i t h m s o f t h e p r i c e s i n t h e d o m e s t i c and f o r e i g n e c o n o m i e s . S u b s t i t u t i n g ( 2 . 2 . 6 ) i n t o ( 2 . 2 . 5 ) g i v e s t h e e q u a t i o n o f e x c h a n g e r a t e d e t e r m i n a t i o n : ( 2 . 2 . 7 ) p f x = ( p - p * ) - ( l / c ) [ ( r - D P ) - ( r * - D P * ) ] . The e x c h a n g e r a t e i s e x p r e s s e d a s a f u n c t i o n o f p r i c e s a n d r e a l i n t e r e s t r a t e s . R i s e s i n d o m e s t i c r e a l i n t e r e s t r a t e s , o t h e r t h i n g s b e i n g e q u a l , c a u s e t h e d o m e s t i c c u r r e n c y t o a p p r e c i a t e . R i s e s i n e x p e c t e d d o m e s t i c i n f l a t i o n work i n t h e o p p o s i t e l x T h i s v a r i a b l e i s an e x p e c t e d r a t e o f c h a n g e , a nd i s n o t i n l o g a r i t h m i c f o r m . 1 2 T h i s i s t h e l o g a r i t h m i c t r a n f o r m o f e q u a t i o n ( 2 . 1 . 1 ) 13 d i r e c t i o n . I f e x p e c t a t i o n s do n o t d e p e n d on e x p e c t e d f u t u r e i n f l a t i o n , e q u a t i o n ( 2 . 2 . 7 ) may be m o d i f i e d t o a s i m p l e r , ' I n t e r e s t - P a r i t y ' m o d e l : ( 2 . 2 . 8 ) p f x = ( p - p * ) - ( l / c ) ( r - r * ) . I n c o n t r a s t t o PPP, R I P s h o u l d p e r f o r m much b e t t e r u s i n g w e e k l y d a t a t o e x p l a i n t h e e x c h a n g e r a t e . W h i l e t h e c o m m o d i t y a r b i t r a g e i m p l i e d by PPP i s l i k e l y t o be s l o w a nd i m p e r f e c t , f i n a n c i a l a r b i t r a g e i n t h e h i g h l y d e v e l o p e d c a p i t a l m a r k e t s o f t h e w e s t e r n c o u n t r i e s may be a l m o s t i n s t a n t a n e o u s . As shown i n t h i s s e c t i o n , t h e R I P model h a s an i m p o r t a n t d e b t t o PPP i n t r a n s f o r m i n g i t f r o m a t h e o r y w h i c h e x p l a i n s t h e l i n k b e t w e e n t h e s p o t a n d f o r w a r d r a t e t o a t h e o r y o f t h e e x c h a n g e r a t e l e v e l . As t h i s c h a p t e r p r o g r e s s e s , i t w i l l become o b v i o u s t h a t R I P a l s o makes i m p o r t a n t c o n t r i b u t i o n s t o t h e more c o m p l e x m o d e l s . 2.3 M o n e t a r y A p p r o a c h 1 3 The b a l a n c e - o f - p a y m e n t s t h e o r y t h a t h a s come t o be known a s t h e ' M o n e t a r y A p p r o a c h ' i s a t t r i b u t e d o r i g i n a l l y t o P o l l a k ( 1 9 5 7 ) a nd d e v e l o p e d by M u n d e l l ( 1 9 6 8 ) a nd J o h n s o n ( 1 9 7 2 ) . A s u r v e y o f t h e M o n e t a r y A p p r o a c h l i t e r a t u r e c a n be f o u n d i n K r e i n i n a n d O f f i c e r ( 1 9 7 8 ) . I n t h i s a p p r o a c h , money i s t r e a t e d a s an a s s e t , t h e d e s i r e d s t o c k o f w h i c h d e p e n d s on i t s r e t u r n , r i s k , a n d t h e r i s k s and r e t u r n s o f o t h e r a s s e t s b o t h c u r r e n t a nd 1 3 A s i n t h e p r e v i o u s s e c t i o n , m o d e l s p r e s e n t e d h e r e f o l l o w c l o s e l y F r a n k e l ( 1 9 7 9 ) . 14 expected. A p r i n c i p a l tenet of the Monetary Approach i s that BOP flows are not an equilibrium phenomenon, rather they are a result of changing desires on the part of asset holders regarding the stocks of d i f f e r e n t currencies they wish to hold. This i s in marked contrast to the previous models where no mention was made of stock demands and the exchange rate was determined by trade or f i n a n c i a l flows. The Monetary Approach was o r g i n a l l y developed for use in fixed exchange rate regime situations. It has been adapted to f l e x i b l e rate situations by (among others) Mussa (1976), Dornbusch (1976) and Frenkel (1976). Three variations of the Monetary Approach as applied to f l e x i b l e exchange rates are presented. The f i r s t model, by Dornbusch, assumes prices are sticky and can be treated as pre-determined in the short-run. A r i s e in domestic interest rates, other things being equal, comes from a contraction in the domestic money supply. Since real domestic rates r i s e (prices are constant), actual or incipient money flows to the domestic economy cause the home currency to appreciate. The second v a r i a t i o n , by Frenkel, assumes that prices are completely f l e x i b l e . Rises in domestic interest rates are caused by increased expected future i n f l a t i o n . In t h i s case real rates need not change as money • flows out of the economy and the domestic currency depreciates. Frankel's contribution i s a synthesis of these models in which the domestic currency can be affected both by changes in real interest rates and by changes in expected long-run i n f l a t i o n . The Dornbusch model i s examined f i r s t (nomenclature follows 15 the RIP model of the last section). The model begins with an approximation of the i n t e r e s t - p a r i t y condition r e l a t i n g the expected rate of exchange depreciation, 'd', to the difference of logarithms of one plus the domestic and foreign 'rates of interest: (2.3.1) d=r-r*. 1 4 The second equation, following the RIP model, postulates an expectation formation mechanism for 'd' based on the deviation of the exchange rate from i t s equilibrium value, but assuming constant prices: (2.3.2) d=-c(pfx-pfx). Equations (2.3.1) and (2.3.2) are equated to give: (2.3.3) pfx-pfx=-(l/c)(r-r*), so that the deviation of the exchange rate from i t s equilibrium is a function of the difference between the domestic and foreign interest rates. Next, i t is assumed that the equilibrium rate i s determined by PPP: Up u n t i l this point, Dornbusch's formulation d i f f e r s very l i t t l e from the RIP model. Money demand equations are added for each country: (2.3.5) m=p+by-ir, m*=p*+by*-ir*, where 'm' is the logarithm of money demand and 'y' i s the logarithm of real income. Foreign money demand is subtracted from domestic demand to y i e l d : (2.3.4) pfx=p-p*. 1 4A number of equations in t h i s section correspond exactly to equations, in the previous section. Where necessary, they are reproduced here for completeness. 16 (2.3.6) m-m*=p-p*+b(y-y*)-i(r-r*). In equilibrium, r=r* (from (2.3.3)). Combining th i s with (2.3.4) gives: (2.3.7) pfx=p-p*=(m-m*)-b(y-y*). The equilibrium exchange rate i s determined by r e l a t i v e money supplies and real incomes. Substituting equation (2.3.7) into (2.3.3) gives the f i n a l equation: (2.3.8) pfx=(m-m*)-b(y-y*)-(l/c)(r-r*). In this model a domestic monetary contraction works through the f i r s t and t h i r d term of equation (2.3.8) to cause the domestic currency to appreciate. No attention i s paid to possible differences between nominal and real interest rates. The Frenkel model begins with money demand equations which depend on i n f l a t i o n rather than nominal interest rates: (2.3.9) m-p=by-vDP, m*-p*=by*-vDP*. PPP i s assumed always to hold: (2.3.10) pfx=p-p*. Subtracting foreign from domestic money demand and substituting the result into (2.3.10) gives: (2.3.11) pfx=(m-m*)-b(y-y*)+v(DP-DP*). The exchange rate is a function of r e l a t i v e money supplies, real incomes and i n f l a t i o n . rates. The differences between the Dornbusch and Frenkel models now become cle a r . In the Dornbusch model a r i s e in the nominal interest d i f f e r e n t i a l causes the domestic currency to , appreciate, since the real interest d i f f e r e n t i a l i s changed. In the Frenkel model, a r i s e in the expected i n f l a t i o n d i f f e r e n t i a l (assumed to be a proxy for the nominal interest d i f f e r e n t i a l since prices are f l e x i b l e and 17 a d j u s t f u l l y t o m o n e t a r y c h a n g e s ) c a u s e s t h e d o m e s t i c c u r r e n c y t o d e p r e c i a t e . I n h i s 1979 p a p e r , F r a n k e l a t t e m p t s t o s y n t h e s i z e t h e D o r n b u s c h a n d F r e n k e l m o d e l s . I n a d d i t i o n t o e q u a t i o n s ( 2 . 2 . 3 ) t o ( 2 . 2 . 6 ) f r o m t h e R I P m o d e l , he a d d s D o r n b u s c h ' s money demand e q u a t i o n s ( 2 . 3 . 5 ) and ( 2 . 3 . 6 ) : ( 2 . 3 . 6 ) m - m * = p - p * + b ( y - y * ) - i ( r - r * ) . A t t h i s p o i n t he n o t e s t h a t i n e q u i l i b r i u m , p f x = p f x ( f r o m e q u a t i o n ( 2 . 2 . 5 ) ) , w h i c h i m p l i e s r-r*=DP-DP* o r e q u a l i t y o f r e a l i n t e r e s t r a t e s . T h i s , a l o n g w i t h a PPP c o n d i t i o n a l l o w s h i m t o w r i t e : ( 2 . 3 . 1 2 ) p f x = ( p - p * ) = ( m - m * ) - b ( y - y * ) + i ( D P - D P * ) , so t h a t i n e q u i l i b r i u m , t h e e x c h a n g e r a t e i s d e t e r m i n e d by r e l a t i v e money s u p p l i e s , r e a l i n c o m e s and i n f l a t i o n r a t e s . I t o n l y r e m a i n s t o s u b s t i t u t e ( 2 . 3 . 1 2 ) i n t o ( 2 . 3 . 3 ) t o g i v e : ( 2 . 3 . 1 3 ) p f x = ( m - m * ) - b ( y - y * ) - ( l / c ) ( r - r * ) + ( 1 / c + i ) ( D P - D P * ) . As s e e n f r o m e q u a t i o n ( 2 . 3 . 1 3 ) , t h e d o m e s t i c c u r r e n c y a p p r e c i a t e s i n r e s p o n s e t o i n c r e a s e s i n r e a l i n t e r e s t d i f f e r e n t i a l s a n d d e p r e c i a t e s i n r e s p o n s e t o i n c r e a s e s i n r e l a t i v e i n f l a t i o n . S u m m a r i z i n g t h e m o d e l s , D o r n b u s c h b e g i n s w i t h t h e i n t e r e s t -p a r i t y c o n d i t i o n a n d s e t s i t e q u a l t o an e x c h a n g e r a t e a d j u s t m e n t e q u a t i o n . The l e v e l o f t h e e q u i l i b r i u m . e x c h a n g e r a t e i s s e t by i n v o k i n g PPP. Up u n t i l t h i s p o i n t " , he d i f f e r s f r o m t h e R I P m o d e l o n l y i n n o t i n c l u d i n g a r e l a t i v e i n f l a t i o n t e r m i n h i s e x c h a n g e r a t e a d j u s t m e n t e q u a t i o n . W i t h o u t t h i s t e r m , he i s f r e e f r o m t h e a s s u m p t i o n t h a t l o n g - r u n r e a l r a t e s o f r e t u r n a r e e q u a l a c r o s s c o u n t r i e s ( a l t h o u g h s h o r t - r u n n o m i n a l r a t e s a r e assumed 18 e q u a l i n e q u i l i b r i u m ) . He t h e n p r o c e e d s one s t e p f u r t h e r , f o l l o w i n g t h e s t r a t e g y o f t h e PPP p l u s Money m o d e l by r e l a t i n g t h e p r i c e s w h i c h d e t e r m i n e t h e e q u i l i b r i u m e x c h a n g e r a t e t o n a t i o n a l money demand f u n c t i o n s . T h e s e demand f u n c t i o n s a r e e x p a n d e d t o i n c l u d e i n t e r e s t r a t e s . D o r n b u s c h ' s m odel i s b a s e d on t h e PPP, t h e PPP p l u s Money , an d t h e R I P m o d e l s . F o r p r a c t i c a l p u r p o s e s he h a s c o n s t r u c t e d a m o d e l i d e n t i c a l t o t h e PPP p l u s Money m o d e l , w i t h an a d d i t i o n a l • e x p l a n a t o r y v a r i a b l e , t h e n o m i n a l i n t e r e s t d i f f e r e n t i a l , i n c l u d e d . F r e n k e l , on t h e o t h e r h a n d , owes n o t h i n g t o R I P i n t h e d e v e l o p m e n t o f h i s m o d e l . F r e n k e l assumes PPP a l w a y s h o l d s . He t h e n t a k e s t h e PPP p l u s Money r o u t e o f r e l a t i n g t h e p r i c e s t o n a t i o n a l money demands. T h e s e demands a r e d e t e r m i n e d by o u t p u t s , p r i c e s a n d i n f l a t i o n r a t e s . He d e v e l o p s a model i d e n t i c a l t o t h e PPP p l u s Money model w i t h an a d d i t i o n a l e x p l a n a t o r y v a r i a b l e , t h e e x p e c t e d i n f l a t i o n d i f f e r e n t i a l , i n c l u d e d . J e f f r e y F r a n k e l s y n t h e s i z e s t h e m o d e l s o f D o r n b u s c h a nd F r e n k e l i n t h e f o l l o w i n g way. F r a n k e l b e g i n s by e q u a t i n g t h e i n t e r e s t - p a r i t y c o n d i t i o n w i t h an e x c h a n g e r a t e a d j u s t m e n t e q u a t i o n . I n t h i s he f o l l o w s t h e R I P model more c l o s e l y t h a n lDor5Es_cKZlJby— i n c l u d i n g r e l a t i v e i n f l a t i o n r a t e s i n t h e a d j u s t m e n t e q u a t i o n . He u s e s t h e PPP c o n d i t i o n t o d e t e r m i n e t h e e q u i l i b r i u m e x c h a n g e r a t e and f o l l o w s t h e PPP p l u s Money s t r a t e g y o f u s i n g n a t i o n a l money demand f u n c t i o n s t o r e l a t e p r i c e s t o money s u p p l i e s , o u t p u t s a n d i n t e r e s t r a t e s . H i s f i n a l e q u a t i o n i s t h e same a s - t h e PPP p l u s Money m o d e l w i t h t h e a d d i t i o n o f b o t h t h e n o m i n a l i n t e r e s t d i f f e r e n t i a l o f t h e 19 Dornbusch model and the r e l a t i v e i n f l a t i o n rates of the Frenkel model. The Dornbusch and Frankel models are based on both the PPP plus Money model and the RIP model. Frenkel r e l i e s on the PPP plus Money model without using RIP. Given the explanatory variables included in the models, the Dornbusch and Frankel models should have an advantage over the model developed by Frenkel, in that they are based in part on nominal interest rates which adjust quickly and are widely and accurately known by the market. If i t i s assumed that changes in money supplies or in f l a t i o n a r y expectations are known or developed more slowly and with more error, the Frenkel model would be at a r e l a t i v e disadvantage explaining the exchange rate in the short-run. It might however, surpass the Dornbusch model over the longer term, where i n f l a t i o n a r y expectations have a more important role to play. 2.4 A Structural Model Structural or BOP models are b u i l t in an attempt to recognize the interdependence of the rate of exchange and i t s determinants. Examples of thi s approach can be seen in the Canadian quarterly model, RDX2 (see H e l l i w e l l and Maxwell (1972)), the Japanese model, FLEX1 (see Amano (1979)), and in a very simple form in Stein (1980). Starting with the BOP identity, each of the arguments of thi s equation, exports, imports and c a p i t a l flows are examined. The exchange rate, (upon which each of the arguments p a r t i a l l y depend) i s determined as that price which equates the supply and demand for foreign exchange. This is c a l l e d the "market cl e a r i n g " method by Amano 20 (1979). In most cases when the market clearing method is used, the BOP is examined at a f a i r l y disaggregated l e v e l and a large number of equations are involved. In simplifying these models for the purpose of analysis, the problem i s to treat some variables as exogenous (in a sense cutting the l i n k of causality running from PFX to the variable) while choosing to leave other variables endogenous in order to focus on th e i r simultaneous determination with the exchange rate. The model presented in this section follows Stein (1980). It attempts to combine the real-side effects of commodity flows and the f i n a n c i a l side effects which are a result of domestic residents adjusting to reach f i n a n c i a l stock equilibrium. The model begins with a stock demand for net claims against foreigners denoted by L*, where the demand i s normalized by nominal GNP. L* may be greater than zero, in which case domestic residents are net lenders, or less than zero, in which case they are net borrowers: (2.4.1) L*=a 1[PFX-PFXe]+a 2[R-R*], a l < 0 , a2<0. Nomenclature follows the RIP section. R and R* are the three month domestic and foreign interest rates and PFXe i s the spot rate expected by the market to pre v a i l three months in the future. The expected future value of the spot rate depends on the current spot rate and i t s deviation from the long-run equilibrium exchange rate,denoted by PFX: (2.4.2) PFXe=d1PFX+d2[PFX-PFX], d*>0 d2<0. 21 In every period, the desired stock, L*, must be made equal to the actual stock, L, i n h e i r i t e d from l a s t period: (2.4.3) L=L*(PFX,...). To f u l f i l l t his market clearing condition, the exchange rate adjusts so that domestic residents are happy to hold the actual stock, L. Substituting Equations (2.4.1) and (2.4.2) into Equation (2.4.3) and re-arranging gives: (2.4.4) PFX=(a 2/k)(R-R*)-(l/k)L+(a 1d 2/k)PFX, k=-(a 1-a 1d 1-a 1d 2). This equation determines the short-run value of the exchange rate. If l-d 2>d 1, then k>0, and the c o e f f i c i e n t s of (R-R*) and L are negative. The exchange market w i l l not be in long-run equilibrium unless two conditions are s a t i s f i e d . F i r s t the condition of short-run equilibrium outlined above must hold. Second, the exchange rate must be such that the trade account minus net long term c a p i t a l flows cause the stock of net claims against foreigners to change at the same rate as nominal GNP. This is because the actual stock of assets next period i s equal to the current stock of assets plus c a p i t a l flows. Capital flows are in turn related to the balance of trade through the balance of payments id e n t i t y . This process can be expressed in the following three equations: (2.4.5) X-I-F=0. (2.4.6) X-I=b(PFX-PFX), b>0. (2.4.7) L=L(-1)+F. Equation (2.4.5) i s the balance of payments identity for 22 f l o a t i n g exchange rates: Exports minus Imports (using Current Account d e f i n i t i o n s ) minus Capital inflows must equal zero. The trade account, (X-I) in Equation (2.4.6), is a positive function of the gap between the current exchange rate, determined in Equation (2.4.4), and the long-run equilibrium exchange rate. F i n a l l y , the mechanism which drives the current exchange rate toward i t s long-run equilibrium value i s given by Equation (2.4.7). The dynamics of this process are i l l u s t r a t e d in Figure 1. Consider an economy i n i t i a l l y in long-run equilibrium at point A. The trade account i s zero and desired and actual stocks of foreign assets are equal. Suppose there i s an exogenous increase in domestic interest rates which causes L* to s h i f t leftward. The price of foreign exchange immediately f a l l s to induce domestic residents to hold the current stock of foreign assets, L. The new short-run equilibrium i s found at point B. At th i s new, lower exchange rate however, the trade balance i s now in d e f i c i t . This results in c a p i t a l outflows, so that in the next period the stock of assets begins to move back toward the new long-run equilibrium at point C. This model attempts to integrate the short-run need for f i n a n c i a l equilibrium addressed in the RIP model, with the longer run requirement of trade flow equilibrium that i s the concern of the PPP models. In every period the exchange rate adjusts so that the actual and desired f i n a n c i a l stocks are equated. If the short-run PFX determined by this process i s not such that balance of trade i s achieved, then c a p i t a l flows responding to the trade imbalance cause actual f i n a n c i a l stocks 23 to adjust toward the l e v e l where long-run equilibrium i s maintained. 2.5 Conclusions In t h i s chapter, four separate groups of models of exchange rate determination have been presented. The groups are PPP, RIP, the Monetary Approach and the Structural Approach. In each case, one or more s p e c i f i c models have been presented, explained and their links to other models discussed. PPP models focus on commodity arbitrage between countries as the main determinant of the exchange rate. The PPP plus Money model goes one step further by allowing the r e l a t i v e prices which determine the exchange rate to be in turn determined by national money demand functions. The RIP model focusses on f i n a n c i a l arbitrage, combining the in t e r e s t - p a r i t y condition with an equation of exchange rate expectation formation. This model (as do a l l others) r e l i e s on PPP to set the equilibrium value of the exchange rate. Two of the Monetary Approach models begin very much l i k e the RIP model. Both Dornbusch and Frankel proceed by using the PPP plus Money strategy of expressing the r e l a t i v e prices in terms of national money demand functions. The Frenkel model i s derived in exactly the same fashion as the PPP plus Money model without resort to RIP. The only difference is a more detailed s p e c i f i c a t i o n of the money demand fuction. The Structural model recognizes that neither commodity arbitrage or f i n a n c i a l forces are by themselves s u f f i c i e n t to explain movements of the exchange rate. This approach includes 24 both these influences as well as the notion of f i n a n c i a l stock equilibrium from the Monetary Approach. The model imposes 'structure' on the determinants of the exchange rate by recognizing the constraints placed in adjustments to equilibrium by the balance of payments id e n t i t y . A summary of the equations which describe each model can be found in the notes following t h i s chapter. Now that a number of alternative models have been specified and discussed, they must be compared empirically in terms of their r e l a t i v e explanatory power at d i f f e r e n t l e v e l s of time aggregation. They must also be ranked on the basis of their a b i l i t y to forecast the future value of the exchange rate using 'currently' available information. It i s to these tasks that Chapter 3 and Chapter 4 are devoted. N o t e s t o C h a p t e r 2 M o d e l E q u a t i o n s P u r c h a s i n g - P o w e r - P a r i t y ( 2 . 1 . 1 ) P F X ( t ) = P ( t ) / P * ( t ) ( 2 . 1 . 2 ) P F X ( t ) / P F X ( 0 ) = { P ( t ) / P ( 0 ) } / [ P * ( t ) / P * ( 0 ) ] P u r c h a s i n g - P o w e r - P a r i t y p l u s money ( 2 . 1 . 3 ) m ( t ) - p ( t ) = a + b y ( t ) , m ( t ) - p * ( t ) = a + b y * ( t ) ( 2 . 1 . 4 ) p f x ( t ) = ( m ( t ) - m * ( t ) ) - b ( y * ( t ) - y ( t ) ) R e a l - I n t e r e s t - a n d I n t e r e s t - P a r i t y ( 2 . 2 . 1 ) (1+R)=(1+R*)PFXF/PFX ( 2 . 2 . 2 ) PFXF/PFX=(1+R)/(1+R*) ( 2 . 2 . 3 ) d = r - r * ( 2 . 2 . 4 ) d = - c ( p f x - p f x ) + D P - D P * ( 2 . 2 . 5 ) p f x - p f x = - ( l / c ) [ ( r - D P ) - ( r * - D P * ) ] ( 2 . 2 . 6 ) p f x = p - p * ( 2 . 2 . 7 ) p f x = ( p - p * ) - ( l / c ) [ ( r - D P ) - ( r * - D P * ) ] ( 2 . 2 . 8 ) p f x = ( p - p * ) - ( l / c ) ( r - r * ) M o n e t a r y A p p r o a c h ( D o r n b u s c h ) ( 2 . 3 . 1 ) d = r - r * ( 2 . 3 . 2 ) d = - c ( p f x - p f x ) ( 2 . 3 . 3 ) p f x - p f x = - ( l / c ) ( r - r * ) , ( 2 . 3 . 4 ) p_fx=p-p* ( 2 . 3 . 5 ) m=p+by-ir, m*=p*+by*-ir* ( 2 . 3 . 6 ) m - m * = p - p * + b ( y - y * ) - i ( r - r * ) 26 ( 2 . 3 . 7 ) pfx=p-p*=(m-m*)-b(y-y*) ( 2 . 3 . 8 ) p f x = ( m - m * ) - b ( y - y * ) - ( l / c ) ( r - r * ) M o n e t a r y A p p r o a c h ( F r e n k e l ) ( 2 . 3 . 9 ) m-p=by-vDP, m*-p*=by*-vDP* ( 2 . 3 . 1 0 ) p f x = p - p * ( 2 . 3 . 1 1 ) p f x = ( m - m * ) - b ( y - y * ) + v ( D P - D P * ) M o n e t a r y A p p r o a c h ( F r a n k e l ) ( 2 . 3 . 6 ) m - m * = p - p * + b ( y - y * ) - i ( r - r * ) ( 2 . 3 . 1 2 ) p_fx= ( p - p * ) = (m-m* )-b( y - y * ) + i (DP-DP*) ( 2 . 3 . 1 3 ) p f x = ( m - m * ) - b ( y - y * ) - ( l / c ) ( r - r * ) + ( 1 / c + i ) ( D P - D P * ) S t r u c t u r a l M o d e l ( 2 . 4 . 1 ) L * = a 1 [ P F X - P F X e ] + a 2 [ R - R * ] ( 2 . 4 . 2 ) P F X e = d 1 P F X + d 2 [ P F X - P F X ] ( 2 . 4 . 3 ) L = L * ( P F X , . . . ) ( 2 . 4 . 4 ) P F X = ( a 2 / z ) ( R - R * ) - ( 2 / z ) L + ( a 1 d 2 / z ) P F X ( 2 . 4 . 5 ) X-I-F=0 ( 2 . 4 . 6 ) X - I = b ( P F X - P F X ) ( 2 . 4 . 7 ) L = L ( - 1 ) + F 28 Chapter 3 Explaining Movements in the Exchange Rate 3.0 Introduction In t h i s chapter, the models formulated in Chapter 2 are compared to one another on the basis of their a b i l i t y to explain the movements in the exchange rate. A l l models are estimated using quarterly data over the period 1971-78. The estimates are presented in turn accompanied by a short discussion of the steps necessary to make the model operational. Next, the models are ranked on the basis of f i t . F i n a l l y , the models are further examined to determine whether they contain information s i g n i f i c a n t l y different from that summarized in the lagged spot and lagged forward rate. A detailed l i s t of data sources can be found in the notes following t h i s chapter. 3.1 Purchasing-Power-Parity Without data on actual p r i c e s , i t is not possible to estimate an absolute version of the PPP model. In thi s chapter, a modified form of Equation (2.1.2) is estimated. In order to make the results comparable to those of the other models, both sides of the equation were mult i p l i e d by PFX(O). The equation estimated i s of the form: (3.1.1) PFX=b°+b 1PPP+e, b°=0 b* = l where PPP={[P(t)/P(0)]/[P*(t)/P*(0)]}PFX(0). If PPP holds exactly, i t . i s expected that b°=0 and b ^ l . One of the most d i f f i c u l t problems faced by investigators trying to 29 empirically test PPP i s the determination of an appropriate base period denoted in Equation (3.1.1) as period 0. In theory, the base period i s chosen to be some past period in which the foreign exchange market is known to have been in PPP equilibrium. The problem i s that there seems to be l i t t l e agreement on a s p e c i f i c date or period over which PPP was v a l i d . In the absence of any concensus on t h i s issue, four separate moving averages were t r i e d as base periods. These were ten, f i v e , two and one year moving averages of annual data. For example, when a two year moving average was employed, data for a given year were normalized by their average value over the previous two years. The next issue is the choice of prices determining PPP. A broad version of PPP, avoiding problems of reverse causality discussed in Chapter 2, was preferred. Three possible choices were the Wholesale Price Index, the Consumer Price Index and the Gross Domestic Product (GDP) d e f l a t o r 1 5 . With one of the goals of t h i s research being the prediction of the exchange rate on a monthly basis (see Chapter 4), i t was necessary to choose an index which was reported more frequently than at quarterly i n t e r v a l s . For th i s reason the GDP deflator was rejected. The Consumer price index was chosen over the Wholesale price index because of the l a t t e r ' s large traded goods component which would presumably bias the results in favour of PPP. Weekly and monthly data series were aggregated by using the mean value over the 1 5 T h i s is the price measure judged most suitable in O f f i c e r (1978). 30 period. Table 3.1 presents OLSQ estimates of the four d i f f e r e n t base period PPP models. As is evident from the Durbin-Watson s t a t i s t i c s , a high degree of autocorrelation i s present in a l l error terms. This may lead to i n e f f i c i e n t estimates of the parameters, with standard errors of parameter estimates being seriously understated. To correct for the autocorrelation, the Cochrane-Orcutt (CORC) procedure was also used to estimate the models 1 6. The results of thi s estimation are presented in Table 3.2. Comparing the res u l t s using the two techniques, large changes in the parameter estimates are evident. The sign of the one year moving average model i s now negative, but in a l l cases the PPP c o e f f i c i e n t cannot be s t a t i s t i c a l l y distinguished from zero. The magnitude of the s e r i a l c o r r e l a t i o n problem i s evident from the size of the Durbin-Watson s t a t i s t i c presented with the OLSQ estimates, and i s not suprising given that the explanatory variable is normalized by a moving average of i t s past values and past values of the dependent variable. When an attempt i s made to correct for the s e r i a l c o r r e l a t i o n , the models seem to contribute l i t t l e in the way of explanatory power beyond the constant term. This i s not suprising given the findings of Freedman and Longworth (1980) which suggest that PFX was as much as 20% greater than i t s PPP equilibrium value in 1976. The PPP plus money model uses national money demand functions to determine prices, which in turn determine the 1'Another alternative would be to use to 'Fair' technique discussed in Frankel (1979). This technique attempts to correct for problems of both autocorrelation and simultaneity. 31 exchange rate. The equation was estimated in the form: (3.1.2) pfx=b°+b 1(m-m*)+b 2(y-y*)+e, b^O, b 2 < 0 . As in Chapter 2, lower case l e t t e r s denote natural logarithms of the variable in question. M2, a broadly defined monetary aggregate available on a weekly basis, was chosen to represent m and m*. Monthly indexes of i n d u s t r i a l production were chosen to represent y and y* since these were the most frequently reported measure of output. The estimates of this equation are presented in table 3.3 and 3.4. The CORC procedure i s again used to correct for autocorrelation. A l l c o e f f i c i e n t s are of the expected sign, regardless of the estimation procedure used. In the CORC estimates however, standard errors r i s e dramatically r e l a t i v e to the size of the c o e f f i c i e n t s , so that none of the co e f f i c i e n t s can be s t a t i s t i c a l l y distinguished from zero. 3.2 Real-Interest- and Interest-Parity The RIP model uses the condition for covered interest arbitrage and an equation for the expected future depreciation of PFX to express the exchange rate in terms of r e l a t i v e prices and real interest d i f f e r e n t i a l s . This expression can be estimated by one of the following two equations: (3.2.1) pfx=b°+b 1(p-p*)+b 2[(r-DP)-(r*-DP*)]+e, bL>0, b 2<0, or by (3.2.2) pfx=b°+b 1(p-p*)+b 2(r-r*)+e, b l > 0 , b 2 < 0 . These equations follow d i r e c t l y from Section 2.2 of Chapter 2. 32 The second equation is modified so that expectations are based only on the deviation of the exchange rate from PPP equilibrium, and not from the expected i n f l a t i o n d i f f e r e n t i a l . Logarithms of Consumer price indices were used for p and p*. Ninety day finance company paper y i e l d s were chosen as the representative short term interest r a t e s 1 7 . The rates of return on long term (over ten years) government bonds were used as proxies for the expected future rates of i n f l a t i o n . These are denoted by DP and DP*. Estimates using OLSQ are presented in Table 3.3. CORC estimates are reported in Table 3.4. As with the PPP plus money model, the CORC procedure causes the standard errors to r i s e r e l a t i v e to the size of the c o e f f i c i e n t s , with the price d i f f e r e n t i a l c o e f f i c i e n t now being p a r t i c u l a r l y weak, but a l l c o e f f i c i e n t s are of the t h e o r e t i c a l l y expected sign. The co e f f i c i e n t s of re l a t i v e prices and interest rates can be interpreted as e l a s t i c i t i e s because of the log-linear form of the equations. The re l a t i v e interest rate c o e f f i c i e n t should be divided by four i f one wishes to consider the effect of a percentage increase in the annualized interest rate. Estimates (the results of which are not reported here) of this model with nominal interest and expected i n f l a t i o n d i f f ere hi: Ta 1s entered as separate explanatory variables, showed a negative c o e f f i c i e n t associated with the expected i n f l a t i o n d i f f e r e n t i a l . This is at odds with both the theory and with most 1 7These yields (reported in annual terms) were divided by 400 to scale -them c o r r e c t l y as ninety day rates of return. The logarithm of one plus the scaled rate is represented by r. Inf l a t i o n rates are likewise appropriately scaled. 33 i n t u i t i v e notions of how increased i n f l a t i o n a f f e c t s the exchange r a t e 1 8 . The high degree of c o l l i n e a r i t y between the interest and i n f l a t i o n rate variables could be a contributing factor to t h i s result, but the underlying cause i s probably the high degree of c a p i t a l market integration between the U.S. and Canada. 3.3 The Monetary Approach The Monetary Approach models combine the short term interest rate effects of the RIP models with the notion that foreign exchange flows are a result of the desires of economic agents to a t t a i n f i n a n c i a l stock or p o r t f o l i o equilibrium. The three v a r i a t i o n s 1 9 to be tested can be summarized by the following three equations: (3.3.1) pfx=b°+b 1 (m-m*)+b2 (r-r*)+b 3 (y-y*)+e,' b*>0, b2<0, b3<0. (3.3.2) pfx=b°+b 1(m-m*)+b 2(DP-DP*)+b 3(y-y*)+e, b ^ O , b2>0, b3<0. (3.3.3) pfx=b°+b 1(m-m*)+b 2(r-r*)+b 3(DP-DP*)+b 4(y-y*)+e, b^O, b2<0, b3>0, b4<0. Equation (3.3.1) corresponds to the Dornbusch fixed price model described in Chapter 2. Frenkel replaces nominal interest 1 8 I t may be that the sign of thi s c o e f f i c i e n t i s suprising because the long term government bond y i e l d d i f f e r e n t i a l i s inappropriate as a proxy for the expected i n f l a t i o n d i f f e r e n t i a l . This i s however, the proxy used by Frankel (1979) in his Germany-USA exchange rate study which reported exactly opposite r e s u l t s . 1"Following Frankel (1979). 34 d i f f e r e n t i a l s with expected i n f l a t i o n d i f f e r e n t i a l s to obtain Equation (3.3.2). Frankel's synthesis of these two models i s represented by Equation (3.3.3). A l l variables have been introduced in the PPP and RIP sections above. The estimates of these models using the OLSQ and CORC procedures are presented in Tables 3.5 and 3.6. In keeping with the re s u l t s presented e a r l i e r , standard errors rise r e l a t i v e to the size of the c o e f f i c i e n t s when the CORC procedure is used. The estimated rho indicates a high degree of s e r i a l c o r r e l a t i o n i s present. The c o e f f i c i e n t of the expected i n f l a t i o n d i f f e r e n t i a l is signed contrary to the theory's prediction in both of the models in which i t i t s included. Without the expected i n f l a t i o n term, Frankel's synthesis is reduced to the'Dornbusch model, which remains as the sole representative of the Monetary Approach. The sign of a l l other c o e f f i c i e n t s correspond to the i r predicted values. 3.4 The Structural Approach The Structural model uses the balance of payments i d e n t i t y to combine the effects of commodity flows with the desire of economic agents to attain f i n a n c i a l stock equilibrium. Operationally, this model combines a variable used in previous models, r e l a t i v e interest rates, with a new variable, the normalized stock of claims against foreigners, L, to explain the exchange rate. The partially-reduced-form equation to be estimated i s : (3.4.1) PFX=b°+b 1(R-R*)+b 2(PFX)+b 3L+e bx<0, b2>0, b3<0. 35 The symbols R and R* denote domestic and foreign short term interest rates r e s p e c t i v e l y 2 0 . The construction of the net stock of claims against foreigners variable is outlined in the notes following t h i s chapter. The d i f f i c u l t y in estimating t h i s model was that no suitable proxy was found for the expected long run equilibrium exchange rate. A number of alternatives were t r i e d , including the r a t i o of prices, the actual two year future exchange rate (a "perfect foresight" assumption), and even the predictions of a model of the current account with two year ahead forecasts of the explanatory variables. None of these proxies contributed s i g n i f i c a n t l y or c o r r e c t l y (according to the predictions of the theory) to the model. The i n a b i l i t y to find an appropriate proxy for the expected long run equilibrium exchange rate points to a need for further modelling in t h i s area. The estimates of Equation (3.4.1) using the OLSQ and CORC procedures are summarized in Table 3.5. Although t h i s model seems to have somewhat less s e r i a l c o r relation than previous models, standard errors s t i l l r i s e markedly r e l a t i v e to the size of the c o e f f i c i e n t s when the CORC procedure i s used. Two points are worth mentioning regarding the c o e f f i c i e n t s associated with the nominal interest d i f f e r e n t i a l . In a l l models, when the CORC procedure is used to correct for s e r i a l c o r r e l a t i o n , the c o e f f i c i e n t becomes between .5 and .3 times i t s estimated size using the OLSQ procedure. It i s also interesting 2"Again, these rates are scaled to the quarterly time horizon of t h i s study. 36 to note the s t a b i l i t y across models of the estimate of thi s c o e f f i c i e n t using the CORC procedure. Expressed in annual interest rate e l a s t i c i t y terms, the c o e f f i c i e n t ranges in size from about -1.06 in the case of the RIP model to -1.63 in the case of the Dornbusch Monetary Approach model. 3.5 Ranking the Models by F i t The models presented in thi s chapter have used either the logarithm of the exchange rate or the exchange rate i t s e l f as their dependent variable. While individual models can be compared to other models i f the dependent variable i s the same, predicted values from models which are in logarithm form cannot be d i r e c t l y compared to those which are not. In thi s section, predicted values from logarithm form models are converted so that a l l models may be compared on the basis of f i t . Table 3.8 presents three summary s t a t i s t i c s on the prediction errors of five of the models examined above. The Frenkel and Frankel Monetary Approach models are omitted because of the t h e o r e t i c a l l y incorrect sign of the c o e f f i c i e n t of the expected i n f l a t i o n d i f f e r e n t i a l . The PPP models are omitted because of their low explanatory power independent of the CORC procedure. Here the effect of the CORC procedure becomes clear. Since CORC estimates the models in f i r s t difference form, the lagged dependent variable is now added to the equation. This adds more explanatory power to models which previously did a r e l a t i v e l y poor job of explaining PFX, and less to the models which did a r e l a t i v e l y good job. Thus, when CORC estimation i s used, a l l 37 models appear to have roughly the same explanatory power. Three s t a t i s t i c s are calculated to measure the f i t of the models: the Root Mean Squared Error (RMSE), the Mean Absolute Error (MAE) and the Mean Error. Regardless of the s t a t i s t i c used, the Structural model does the best job of explaining the exchange rate over the sample period. It i s followed by the Dornbusch model, the RIP models and the PPP plus money model. The MAE range from about 1.3 cents to 1.0 cents, while the RMSE ranges from about 1.6 cents to 1.3 cents. The difference between the two measures indicates a certain amount of v a r i a b i l i t y in prediction errors common to a l l models. 2 1 3.6 Informational Content of the Models In order to determine whether the explanatory variables of the theoretical models contribute s i g n i f i c a n t l y to explaining movements in the exchange rate, the following test was used. F i r s t the exchange rate was regressed against i t s own value lagged one period using the CORC procedure. This model was then re-estimated with the explanatory variables of the t h e o r e t i c a l models' included. An F - t e s t 2 2 was used to test whether the inclusion of the theoretical models' explanatory variables s i g n i f i c a n t l y improved the f i t of the equation. The results of th i s test are summarized in Table 3.9. Of the fiv e models considered, in the case of every model 2 1These measures of prediction (and forecast) errors are discussed more f u l l y in Chapter 4. 2 2See Kmenta (1971) p.370 for an example of t h i s t e s t . 38 except PPP plus money, the hypothesis that the theoreti c a l models' explanatory variables do not improve the equation's f i t is rejected at the 5% l e v e l . With the RIP models, i t i s possible to reject the n u l l hypothesis at the 5% l e v e l . With the Dornbusch and Structural models, i t is possible to reject the n u l l hypothesis at the 1% l e v e l . This test was repeated substituting the lagged forward rate for the lagged spot rate, in order to see whether the explanatory variables of the the o r e t i c a l models' contain information not included in the lagged forward rate. The results confirmed those found using the lagged spot rate reported above. It i s clear from these results that not a l l of the information about the future value of the exchange rate i s summarized in i t s current value.. Additional information i s included in the future and current values of the the o r e t i c a l models' explanatory variables. This evidence however, i s not s u f f i c i e n t to make inferences about market e f f i c i e n c y , since the certain knowledge (ignoring measurement error) of the future values of the theoretical models' explanatory variables i s included in the f u l l equation, but not included in the regression of the exchange rate on i t s lagged value or the lagged forward rate. Tests of market e f f i c i e n c y are performed Tn~ Chapters 4 and 5. 3.7 Conclusions In t h i s chapter, OLS and CORC estimates of each of the models formulated in Chapter 2 were presented and discussed. The sign of most c o e f f i c i e n t s corresponded to the predictions of the 39 theory, although the c o e f f i c i e n t of the expected i n f l a t i o n d i f f e r e n t i a l in the RIP and Monetary Approach models are an exception. The variables that were estimated most robustly were re l a t i v e interest rates, money supplies and the stock of net claims against foreigners, with r e l a t i v e real-incomes somewhat less strongly represented. Thus models including some of these variables such as the Monetary Approach model of Dornbusch and the Structural Approach model, seem f a i r l y well supported by the estimates. Relative interest rates continued to be strong in the Real-Interest- and Interest-Parity models, but not suprisingly, r e l a t i v e price effects do not seem to have been s i g n i f i c a n t over the sample period. The PPP plus Money model appears to have derived much of i t s explanatory power from the lagged-dependent variable included in using the CORC procedure. The simple PPP models performed even more poorly, with some of the explanatory variables being incorrectly signed. The high l e v e l of autocorrelation in the errors of a l l the OLS estimates strongly suggests that important determinants of the exchange rate have been omitted or mis-specified. Thus none of the models presented here can be singled out as the 'correct' model of market behavior over t h i s period. Selected models were tested to determine whether they contained information which contributed s i g n i f i c a n t l y to explaining the exchange rate beyond the lagged spot and forward rate. This was found to be the case for a l l but one of the models tested. This chapter has compared the alternative models' a b i l i t y to explain movements in the exchange rate. Next, the models must 40 be compared on the basis of their a b i l i t y to predict PFX. It i s to t h i s task that Chapter 4 is devoted. 41 Table 3.1 Purchasing-Power-Parity Models Dependent Variable: PFX(10 year MA) Procedure: OLSQ variable coef f i c ient standard error Constant PPP n = 32 •1.604 2.485 R2=.3375 SER=.0444 0.672 0.635 D.W.=.3202 Dependent Variable: PFX(5 year MA) Procedure: OLSQ var iable c o e f f i c i e n t standard error Constant PPP n=32 •1.171 2.117 R2=.1151 SER=.0514 1.110 1.071 D.W.=.1743 Dependent Variable: PFX(2 year MA) Procedure: OLSQ var iable coef f ic ient standard error Constant PPP n=32 •0.931 1.911 R2=.2968 SER=.0458 0.549 0.537 D.W.=.2356 Dependent Variable: PFX(1 year MA) Procedure: OLSQ variable coeff i c i e n t standard error Constant PPP -0.211 1.216 0.302 0.296 n = 32 R2=.3598 SER=.0437 D.W.=.4404 42 Table 3.2 Purchasing-Power-Parity Models Dependent Variable: PFX(10 year MA) Procedure: CORC variable coef f ic ient standard error Constant PPP n = 31 1.305 0.151 R2=.9284 SER=.0163 Dependent Variable: PFX(5 year MA) 0.637 0.504 rho=.989 Procedure: CORC variable coef f ic ient standard error Constant PPP n = 31 0.850 0.121 R2=.9283 SER=.0148 0.371 0.359 rho=1.13 Dependent Variable: PFX(2 year MA) Procedure: CORC var iable coef f ic ient standard error Constant PPP n=31 1.631 0.125 R2=.9275 SER=.0162 0.555 0.361 rho=.993 Dependent Variable: PFX(1 year MA) Procedure: CORC variable coef f ic ient standard error Constant PPP 1.253 -0.273 0.141 0.139 n = 31 R2=.9365 SER=.0139 rho=1.14 43 Table 3.3 Purchasing-Power-Parity plus money Model Dependent Variable: pfx Procedure: OLSQ variable coef f ic ient standard error Constant m-m* y-y* n = 32 0.855 0.307 0.708 R2=.4948 SER=.0372 0.163 0.061 0.227 D.W.=.3298 Real-Interest-Parity Model Dependent Variable: pfx Procedure: OLSQ variable coef f ic ient standard error Constant p-p* (r-dp)-(r*-dp*) n=32 •0.032 1.829 •9.944 R2=.7101 SER=.0282 0.008 0.217 2.175 D.W.=.5146 Interest-Parity Model Dependent Variable: pfx Procedure: OLSQ variable c o e f f i c i e n t standard error Constant p-p* r - r * 0.004 1.875 -8.781 0.006 0.184 1.440 n = 32 R2=.7814 SER=.0245 D.W.=.6042 4 4 T a b l e 3 . 4 P u r c h a s i n g - P o w e r - P a r i t y p l u s M o n e y M o d e l D e p e n d e n t V a r i a b l e : p f x P r o c e d u r e : C O R C v a r i a b l e c o e f f i c i e n t s t a n d a r d e r r o r C o n s t a n t m - m * y - y * n = 3 1 0 . 5 3 1 0 . 1 2 6 - 0 . 0 1 3 R 2 = . 9 2 2 5 S E R = . 0 1 6 1 0 . 6 2 8 0 . 2 8 6 0 . 1 5 1 r h o = . 9 8 4 R e a l - I n t e r e s t - P a r i t y M o d e l D e p e n d e n t V a r i a b l e : p f x P r o c e d u r e : C O R C v a r i a b l e c o e f f i c i e n t s t a n d a r d e r r o r C o n s t a n t P - P * ( r - D P ) - ( r * - D P * ) n = 3 1 0 . 2 3 5 0 . 5 1 3 • 3 . 0 7 0 R2=.9365 S E R = . 0 1 4 9 0 . 2 1 2 0 . 6 8 8 1 . 5 9 6 r h o = . 9 8 6 I n t e r e s t - P a r i t y M o d e l D e p e n d e n t V a r i a b l e : p f x P r o c e d u r e : C O R C v a r i a b l e c o e f f i c i e n t s t a n d a r d e r r o r C o n s t a n t P - P * r - r * 0 . 1 9 4 0 . 6 3 7 - 3 . 1 7 9 0 . 1 7 1 0 . 6 7 0 1 . 3 9 2 n = 3 1 R 2 = . 9 3 9 5 S E R = . 0 1 4 5 r h o = . 9 8 4 45 Table 3.5 Monetary Approach Models Dependent Variable: pfx (Dornbusch model) variable c o e f f i c i e n t Procedure: OLSQ standard error Constant m-m* r - r * y-y* n = 32 1.487 0.536 -11.094 -0.654 R2=.8403 SER=.0213 0.123 0.045 1.424 0.130 D.W.=.7675 Dependent Variable: pfx (Frenkel model) variable c o e f f i c i e n t Procedure: OLSQ standard error Constant m-m* dp-dp* y-y* n = 32 1.266 0.423 -28.331 -0.442 .7735 SER=.0253 0.131 0.046 4.824 0.162 D.W.=.7338 Dependent Variable: pfx (Frankel model) Procedure: OLSQ variable coef f ic ient standard error Constant m-m* r - r * dp-dp* y-y* L.A8J5_ 0.522 -8.188 -11.279 -0.562 0.117 0.044 1.989 5.655 0.132 n=32 R 2 = . 8 6 0 8 SER=.0202 D.W.=.7567 46 Table 3.6 Monetary Approach Models Dependent Variable: pfx (Dornbusch model) variable c o e f f i c i e n t Procedure: CORC standard error Constant —m* m-m r - r * y-y* n=31 1.480 0.547 -4.893 -0.287 R2=.9440 SER=.0145 0, 0, 1, 513 203 601 0.157 rho=.920 Dependent Variable: pfx (Frenkel model) variable c o e f f i c i e n t Procedure: CORC standard error Constant m-m* dp-dp* y-y* n = 31 R2=.9275 0.982 0.321 -7.014 -0.158 SER=.0158 0.687 0.299 4.563 0.179 rho=.979 Dependent Variable: pfx (Frankel model) Procedure: CORC variable c o e f f i c i e n t standard error Constant m-m* r - r * dp-dp* y-y* 1.602 0.586 -4.350 -5.009 -0.345 0.504 0.198 1.667 4.294 0.165 n=31 R2=.9446 SER=.0144 rho=.913 47 Table 3.7 Structural Approach Model Dependent Variable: PFX variable c o e f f i c i e n t Procedure: OLSQ standard error Constant R-R* L n = 32 0.872 •9.904 •0.885 R2=.8791 SER=.0193 0.011 1.116 0.061 D.W.=.9941 Dependent Variable: PFX variable Constant R-R* L coef f ic ient 0.806 -3.586 -1.052 Procedure: CORC standard error 0.062 1.370 0.232 n = 31 R2=.9408 SER=.0141 rho=.875 Table 3.8 Comparing Selected Models by F i t Model PPP+Money RIP IP Mon. Approach (Dornbusch) Structural RMSE .01588 .01475 .01451 .01403 .01346 MAE .01275 .01149 .01148 .01052 .01042 Mean Error .00128 .00114 .00122 .00038 -.00002 48 T a b l e 3.9 F - T e s t o f M o d e l s ' C o n t r i b u t i o n o v e r P F X ( - l ) a n d P F X F ( - l ) C r i t i c a l V a l u e s : F ( 2 , 2 6 ) = 3 . 3 7 ( 5 % ) 5.53 ( 1 % ) F ( 3 , 2 5 ) = 2 . 7 6 ( 5 % ) 4.18 ( 1 % ) PPP p l u s M o n e y : F ( 2 , 2 6 ) P F X ( - l ) v e r s u s m o d e l p l u s P F X ( - l ) : . F=1.84 P F X F ( - l ) v e r s u s m o d el p l u s P F X F ( - l ) : F=0.88 R I P : F ( 2 , 2 6 ) P F X ( - l ) v e r s u s m o d el p l u s P F X ( - l ) : F=4.98 P F X F ( - l ) v e r s u s m o d el p l u s P F X F ( - l ) : F=4.14 I P : F ( 2 , 2 6 ) P F X ( - l ) v e r s u s m o d el p l u s P F X ( - l ) : F=5.07 P F X F ( - l ) v e r s u s m o d el p l u s P F X F ( - l ) : F=4.42 M o n e t a r y ( D o r n b u s c h ) : F ( 3 , 2 5 ) P F X ( - l ) v e r s u s m o d e l p l u s P F X ( - l ) : F=5.38 P F X F ( - l ) v e r s u s m o d el p l u s P F X F ( - l ) : F=5.57 S t r u c t u r a l : F ( 2 , 2 6 ) P F X ( - l ) v e r s u s m o d e l p l u s P F X ( - l ) : P F X F ( - l ) v e r s u s m o d e l p l u s P F X F ( - l ) : F=6.35 F=5.56 49 Notes to Chapter 3 Data Sources PFX: Wednesday closing Canada-U.S. exchange rates quoted in European terms. Data reported weekly from 1971 to 1978. Source: Bank of Canada Review. R-R*: Nominal interest d i f f e r e n t i a l . Represented by Canadian and U.S. 90 day finance company paper y i e l d s . Data are reported weekly from 1971 to 1978. Canadian data are actual rates, U.S. Data are averages of weeks ending Wednesday. Rates are expressed in annual percentage terms and are divided by 400. Source: Bank of Canada (unpublished) and Federal Reserve B u l l e t i n . DP-DP*: Expected long-run i n f l a t i o n d i f f e r e n t i a l s . Proxied by Canadian and U.S. long term (over 10 years) government bond y i e l d s . Canadian data are actual rates, U.S. Data are averages of weeks ending Wednesday. Rates are expressed in annual percentage terms and are divided by 400. Source: Bank of Canada (unpublished) and Federal Reserve B u l l e t i n . M-M*: Monetary aggregate d i f f e r e n t i a l . Canadian and U.S. M2. Data are reported weekly (Wednesday end) from 1971 to 1978. 50 Source: Bank of Canada (unpublished) and Federal Reserve Bank of San Francisco (unpublished). Real income d i f f e r e n t i a l . Canadian and U.S. seasonally adjusted index of i n d u s t r i a l production. Data reported monthly from 1971 to 1978. 1970=100. Source: IMF International Financial S t a t i s t i c s Price d i f f e r e n t i a l . Canadian and U.S. seasonally adjusted consumer price indices ( a l l items). Data reported monthly from 1971 to 1978. 1970=100. Source: IMF International Financial S t a t i s t i c s Net claims against foreigners. This series was constructed with the 1968 Canadian balance of international indebtedness, and cumulating forward net c a p i t a l flows. An estimate was also made of corporate retained earnings owed to foreigners. This series i s normalized by Canadian nominal GNE (seasonally adjusted). Data reported from 1971 to 1978. Source: Components from Statcan# 13-001 and 67-001. 51 Chapter 4 Comparing Alternative Exchange Rate Forecasts 4.0 Introduction In t h i s chapter models presented in Chapter 2 and estimated in Chapter 3 are used to forecast the Canadian-US exchange rate over the period 1974-78. The models are compared to one another on the basis of their forecasting power. In addition, an attempt is made to determine what information embodied in the models' forecasts of the exchange rate is also included in the,forecasts of the market participants expressed by the forward rate. To deal with t h i s question, the notion of model 'popularity' i s developed. The chapter begins with an outline of the procedure used in constructing each model's forecast. Next, the properties of the forecasts are compared to one another and the forward rate. F i n a l l y , an attempt i s made to develop a set of 'optimal' forecasts which embody the information of the models and of the forward rate. 4.1 Constructing Model Forecasts In order to forecast an economic variable using a theoretical model two things are required: parameter estimates and forecasts of the explanatory variables. If the forecasting is being done ex post, then for the forecasts to be 'genuine', they must be based only on information available at the time the 52 f o r e c a s t was t o have been made. P a r a m e t e r e s t i m a t e s f r o m C h a p t e r 3 were u n s u i t a b l e f o r u s e i n f o r e c a s t i n g f o r two r e a s o n s . F i r s t , f o r e c a s t i n g i n t h i s c h a p t e r i s done u s i n g m o n t h l y r a t h e r t h a n q u a r t e r l y d a t a a s was u s e d i n C h a p t e r 3. More i m p o r t a n t l y , t h e p a r a m e t e r e s t i m a t e s i n C h a p t e r 3 a r e b a s e d on t h e w h o l e s a m p l e p e r i o d f o r m 1971-78 and t h e r e f o r e c o n t a i n i n f o r m a t i o n o r e x p e r i e n c e n o t a v a i l a b l e f o r m a k i n g g e n u i n e f o r e c a s t s w i t h i n t h a t p e r i o d . I n o r d e r t o o b t a i n p a r a m e t e r e s t i m a t e s a p p r o p r i a t e f o r f o r e c a s t i n g , t h e f o l l o w i n g p r o c e d u r e was u s e d . M o d e l s were i n i t i a l l y e s t i m a t e d u s i n g m o n t h l y d a t a o v e r t h e p e r i o d 1 9 7 1 - 7 3 . T h e s e e s t i m a t e s were u s e d t o f o r e c a s t t h e e x c h a n g e r a t e o v e r t h e p e r i o d 1974-78 w i t h m o d e l p a r a m e t e r s b e i n g r e - e s t i m a t e d e v e r y t h r e e months a s more d a t a became a v a i l a b l e . S i n c e t h e f o r e c a s t i n g h o r i z o n was t h r e e m o n t h s , a t a n y g i v e n t i m e f o r e c a s t s were b a s e d o n l y on i n f o r m a t i o n t h a t was known a t l e a s t t h r e e months p r e v i o u s t o t h e f o r e c a s t i n g t a r g e t . F o r e c a s t s o f t h e e x p l a n a t o r y v a r i a b l e s were o b t a i n e d u s i n g a u t o r e g r e s s i v e m o d e l s o f e a c h v a r i a b l e ' s movement t h r o u g h t i m e . The p a r a m e t e r e s t i m a t e s o f t h e s e t i m e s e r i e s m o d e l s were u p d a t e d a t r e g u l a r i n t e r v a l s a s more i n f o r m a t i o n became a v a i l a b l e . D a t a a r e a v a i l a b l e w i t h d i f f e r i n g f r e q u e n c i e s and r e l e a s e d w i t h d i f f e r i n g t i m e l a g s . C a r e was t a k e n s o t h a t f o r e c a s t s o f e x p l a n a t o r y v a r i a b l e s f o r a g i v e n d a t e were b a s e d o n l y on i n f o r m a t i o n known t h r e e months p r e v i o u s t o t h e f o r e c a s t i n g t a r g e t . F u r t h e r d e t a i l s on f o r e c a s t i n g t h e e x p l a n a t o r y v a r i a b l e s a r e g i v e n i n t h e n o t e s f o l l o w i n g t h i s c h a p t e r . 53 4.2 Comparing Model Forecasts Errors in forecasting the future value of the exchange rate can come from three sources: model mis-specification, errors in the forecasted explanatory variables and random behavior of the forecasted variable. A model may be mis-specified i f important variables are omitted or an inappropriate functional form i s used in estimation. Even i f the model is c o r r e c t l y s p e c i f i e d with a l l important variables included, an i n a b i l i t y to forecast the future values of the explanatory variables may lead to errors in forecasting the target variable. In order to identify the contributions of these sources of errors to the t o t a l forecasting error, 'conditional' forecasts were made. These are forecasts which use the same parameter estimates used in forming genuine forecasts, but combine them with the actual future values of the explanatory variables. In this way the second source of error i s eliminated and a l l of the error can be attributed to model mis-specification and random movement of the target variable. Table 4.1 presents six series of monthly forecasts of PFX over a three month horizon for the period 1974-78. Five of the forecasts are based on the models estimated in Chapter 3; the sixth i s the three month forward rate. If there i s no risk premium 2 3 then the forward rate may be taken as the market's expectation of the future value of the spot exchange rate. In any case, i t i s the bench-mark against which the models' 2 3See Levich (1978), Cornell (1977) and Frankel (1980) regarding this view. 54 forecasts should be compared, since i t i s c o s t l e s s l y available to everyone and requires no special interpretation. An alternative bench-mark against which the model's forecasts could be compared, i s a simple autoregressive model of the exchange rate. When t h i s model was estimated and forecasts were generated (using the same procedure as was used to forecast the explanatory var i a b l e s ) , the forecasts were found to have even greater errors than the forward rate. Five summary s t a t i s t i c s are presented for each forecast in Table 4.1. Forecasting error i s defined as the difference between the actual and the forecasted value of the exchange rate. The f i r s t two s t a t i s t i c s are the Root Mean Squared Error (RMSE), which gives greater weight to larger errors, and the Mean Absolute Error (MAE). The f i n a l three s t a t i s t i c s divide the error between Bias, Coefficient and Residual error. If the forecasted series i s regressed against the actual series, then Bias error comes from the intercept term d i f f e r i n g from zero. Coefficient error comes from the slope c o e f f i c i e n t d i f f e r i n g from one and residual error i s the remaining, non-systematic error. Looking at Table 4.1, i t can be seen that a l l the models' genuine forecasts have a lower RMSE than the forward rate, with the Structural model having the lowest at 1.80%. It i s followed c l o s e l y by the Interest-Parity and Real-Interest-Parity models. It i s interesting to note that the ordering of the forecasts i s very d i f f e r e n t from the ranking of models by f i t presented in Chapter 3. The results presented in Table 3.8 of that chapter rank the models estimated using quarterly data over the period 55 1971-78. Only the Structural model's ranking remains unchanged. A l l models show a sizeable difference between MAE and RMSE indicating a wide dispersion of errors. F i n a l l y , when comparing the errors of conditional and genuine forecasts, three of the models show the expected increase in accuracy when the actual future values of the explanatory variables are used. In the case of the IP and RIP forecasts however, t h i s i s not the case. Here genuine forecasts have smaller errors than conditional forecasts. Clearly mis-specification errors and explanatory variable forecast errors are cancelling out one another. Perhaps thi s means that expected (or lagged) values of interest rates have a more important role in forecasting PFX. 4.3 Informational Content of Alternative Forecasts When the market's forecast of the future value of the exchange rate, expressed in the forward rate, is s i g n i f i c a n t l y d i f f e r e n t from the forecast of a theoreti c a l model, that model i s said to be 'unpopular'. Of course i f a model is unpopular and inaccurate, i t s unpopularity is not very i n t e r e s t i n g . If however, a model i s unpopular and contributes beyond the market's.forecast to predicting the future value of the exchange rate, this 'unpopular information' i s valuable to the exchange rate forecaster. The purpose of this section i s to determine i f the theoretical models contain unpopular information. More generally, i t i s useful to examine how the forward rate and the models' forecasts are related and to see i f one can determine which model best describes the market's expectation formation. In order to test for unpopular information in the models' 56 forecasts, the Cochrane-Orcutt technique was used to regress the forward rate against the actual spot rate three months in the future. Next the same regression was run except that in addition to the forward rate, a model's forecast was also included to explain the future spot rate. These regressions were run for each model over the forecasting period 1974-78. An F - t e s t 2 4 was used to determine whether the forecast added s i g n i f i c a n t l y to the forward rate in explaining the future spot rate. A s i g n i f i c a n t contribution i s evidence that the model contains a s i g n i f i c a n t amount of unpopular, but useful, information. It i s clear from Table 4.2 that a l l of the fiv e models' forecasts contribute s i g n i f i c a n t l y to the forward rate in explaining the future spot rate. It i s interesting to note that the Interest-Parity model regression has the highest F-s t a t i s t i c , suggesting that that model contains the most of the unpopular information. The differences between the F - s t a t i s t i c s however, i s probably too small to make any d e f i n i t i v e statement about the r e l a t i v e unpopularity of the models. This test may be modified to examine whether the information contained in the forward rate i s completely contained in any of the models' forecasts. Comparing the regressions run in the previous test to Cochrane-Orcutt regressions of the models' forecasts on the future spot rate, another set of F-tests can be constructed. This F-test shows whether the forward rate contributes s i g n i f i c a n t l y beyond the models' forecasts to explaining the future spot rate. A 2 4 T h i s i s the same as the F-test used in Chapter 3. 57 s i g n i f i c a n t contribution i s evidence that not a l l the information contained in the forward rate i s contained in the models' forecasts. The results are presented in Table 4.3. Although the F - s t a t i s t i c s are smaller than those presented in Table 4.2, the hypothesis that the forward rate does not contribute to the models' forecasts of the future spot rate can be rejected at the 99% l e v e l in every case. From the results presented in Tables 4.2 and 4.3 i t seems that the models' forecasts and the forward rate share some information about the future spot rate. Further, these results show that the models' forecasts and the forward rate each contain some information not found in the other. One way to get access to the information in the forward rate not contained in the models' forecasts, i s to construct a new variable c a l l e d NEWS. Very simply, NEWS i s the difference between the the forward rate and a model's forecast. Regressions explaining the future spot rate using a model's forecast and the NEWS variable were run for each model. The results are presented in Table 4.4. Of course these regressions w i l l explain the future spot rate no better those used to construct the F-tests for Tables 4.2 and 4.3, since they include exactly the same information. Also these predicted values cannot be thought of as forecasts, since information from the whole sample period was used to fin d the optimal combinations of the models' forecasts and NEWS. Section 4.4 combines the models and the forward rate in order to get improved forecasts of the future spot rate. What these regressions do show is the best way, on average, to combine the models' forecasts and NEWS to explain the 58 exchange rate. A l l signs are positive and s t a t i s t i c a l l y s i g n i f i c a n t . The c o e f f i c i e n t of NEWS i s always less than 0.5 as one would expect. This i s because by themselves, the models' forecasts consistently had smaller errors than the forward rate and therefore one would expect the actual exchange rate to be closer to the models' forecasts than the forward rate. This i s v e r i f i e d by the c o e f f i c i e n t of the difference between the models' forecasts and the forward rate always being less than 0.5. The sign of the c o e f f i c i e n t of news is interesting from a market e f f i c i e n c y standpoint. Given the po s i t i v e sign of NEWS i t appears that on average the actual future spot rate f a l l s between the models' forecasts and the forward rate. Since to make p r o f i t a b l e bets in the forward market i t i s necessary to know the dire c t i o n of forward rate error, t h i s may be a clue to potential betting p r o f i t s from forward speculation. Of course i f the sign of NEWS were negative, a betting rule would s t i l l be possible. The strategy would have to be to bet the opposite of what the model predicted about the re l a t i o n between the forward and the future spot rate. The question of market e f f i c i e n c y w i l l be considered in d e t a i l in Chapter 5. 59 4.4 Constructing Optimal F o r e c a s t s 2 5 It is clear from the results presented in the l a s t section that a combination of the models' forecasts and the forward rate can do a better job of predicting the future value of the exchange rate than either can do alone. In this section the models' forecasts and the forward rate are combined to produce a set of 'optimal' forecasts, and the properties of these forecasts are examined. The optimal forecasts were constructed exactly as described in- section 4.1 except that the forward rate was added to each model equation. This is a s l i g h t l y d i f f e r e n t procedure than the one employed in Section 4.3 for two reasons. F i r s t , i t was not the purpose of that section to produce forecasts, so the c o e f f i c i e n t s could be estimated over the whole sample period. With the optimal forecasts, the models were estimated over the period 1971-73 to get an i n i t i a l set of parameters and then re-estimated every three months as new data became av a i l a b l e . This procedure produced genuine forecasts as described in Section 4.1. The second difference i s that in Section 4.3, the models' forecasts and the forward rate were combined d i r e c t l y , so that the c o e f f i c i e n t s of the determinants of the models' forecasts were not allowed to vary when the forward rate was added. In constructing the optimal forecast for each model, the forward 2 5More rigorous procedures for constructing optimal forecasts are available. Those procedures however, are probably not ones which could be considered to have been generally available to market participants acting over th i s period. The author i s grateful to David Rose for pointing this out. 6 0 rate was included in the equation determining the model's forecast so that the c o e f f i c i e n t s of the other determinants were allowed to vary freely when the forward rate was added. The properties of these optimal forecasts are examined in Table 4.5. If these results are compared to those in Table 4.1, i t can be seen that every forecast i s improved by the addition of the forward rate. It i s interesting to note that the IP model now has the lowest RMSE, although as in Table 4.1, the difference between i t and the Structural model i s very small. With the addition of the forward rate the Structural model joins the IP and the RIP models in having i t s genuine forecast error smaller than i t s conditional forecast error. It would seem that for these models, certain knowledge of the future values of the explanatory variables would not improve the forecasts. Comparing the change in the percentage RMSE for the genuine forecasts before and after the forward rate was added shows the IP model forecast improving the most (by . 0 9 % ) and the PPP plus money model forecast improving the least (by.0 3 % ) . This i s another indication that the IP model forecast is the forecast that contains information most complementary to the forward rate. 4.5 Conclusions In t h i s chapter, three month forecasts of the exchange rate were constructed using t h e o r e t i c a l models discussed in Chapters 2 and 3 . The properties of the forecasts were examined and compared to the three month forward rate which was taken to be the market's forecast of the future spot rate. A l l of the models' forecasts considered did a better job predicting the 61 future spot rate than the forward rate. Next, the notion of unpopular information was introduced. It was found that both the models' forecasts and the forward rate each contained information not contained in the other. F i n a l l y , the forward rate and the models were combined to produce a set of optimal forecasts whose properties were examined. In every case, the models' forecasts improved when the forward rate was added. The IP model's forecast improved the most, indicating that this model contained the information most complementary to the forward rate. 62 Table 4.1 Models' Forecasts: 1974-78 Forward Rate RMSE: $0.02372(2.28%) MAE: $0.01980 Bias:6.86% Coefficient:5.90% Residual:87.33% PPP plus Money Model Conditional Forecast RMSE: $0.01904(1.83%) MAE: $0.01520 Bias:15.98% .Coefficient:7.31% Residual:76.11% Genuine Forecast RMSE: $0.02032(1.95%) MAE: $0.01622 Bias:17.48% Coefficient:6.77% Residual:75.45% Real-Interest-Parity Model Conditional Forecast RMSE: $0.01933(1.86%) MAE: $0.01547 Bias:15.80% Coefficient:11.32% Residual:72.92% Genuine Forecast RMSE: $0.01893(1.82%) MAE: $0.01516 Bias:16.34% Coefficient:10.33% Residual:73.24% Interest-Parity Model Conditional Forecast RMSE: $0.01936(1.86%) MAE: $0.01551 Bias:16.72% Coefficient:11.48% Residual:72.22% Genuine Forecast RMSE: $0.01879(1.81%) MAE: $0.01500 Bias:15.83% Coefficient:10.40% Residual:73.56% 6 3 Table 4.1 continued Monetary Approach (Dornbusch) Model Conditional Forecast RMSE: $0.01912(1.84%) MAE: $0.01524 Bias:15.75% Coefficient:8.63% Residual:74.88% Genuine Forecast RMSE: $0.02048(1.97%) MAE: $0.01630 Bias:17.12% Coefficient:7.50% Residual:75.06% Structural Model Conditional Forecast RMSE: $0.01845(1.77%) - MAE: $0.01466 Bias:7.76% Coefficient:4.48% Residual:87.73% Genuine Forecast RMSE: $0.01877(1.80%) MAE: $0.01468 Bias:4.88% Coefficient:2.62% Residual:92.34% Table 4.2 F-Test of Models' Contribution over PFXF C r i t i c a l Value: F(l,55)=7.12 (1%) PPP plus money model: PFXF versus model's forecast plus PFXF: F=23.26 Real-Interest-Parity model: PFXF versus model's forecast plus PFXF: F=27.03 Interest-Parity model: PFXF versus model's forecast plus PFXF: F=27.41 Monetary Approach (Dornbusch) model: PFXF versus model's forecast plus PFXF: F=22.41 Structural model: PFXF versus model's forecast plus PFXF: F=25.37 Table 4.3 F-Test of PFXF's Contribution over models' forecasts C r i t i c a l Value: F(l,55)=7.12 (1%) PPP plus money model: Model's forecast versus model's forecast plus PFXF: F=10.71 Real-Interest-Parity model: Model's forecast versus model's forecast plus PFXF: F=8.79 Interest-Parity model: Model's forecast versus model's forecast plus PFXF: F=8.71 Monetary Approach (Dornbusch) model: Model's forecast versus model's forecast plus PFXF: F=11.93 Structural model: Model's forecast versus model's forecast plus PFXF: F=14.87 65 Table 4.4 Purchasing-Power-Parity plus money model Dependent Variable: pfx Procedure: CORC var iable c o e f f i c i e n t standard error Forecast NEWS n = 59 1.008 0.420 R2=.9532 SER=.0140 0.005 0.121 rho=.685 Real-Interest-Parity Model Dependent Variable: pfx Procedure: CORC variable c o e f f i c i e n t standard error Forecast NEWS n = 59 1.007 0.389 R2=.9553 SER=.0137 0.005 0.118 rho=.668 Interest-Parity Model Dependent Variable: pfx Procedure: CORC variable c o e f f i c i e n t standard error Forecast NEWS n = 59 1.007 0.387 R 2 = . 9 5 5 5 SER=.0137 0.005 0.118 rho=.667 66 Table 4.4 continued Monetary Approach (Dornbusch) Model Dependent Variable: pfx Procedure: CORC var iable coeff ic ient standard error Forecast NEWS n = 59 1.008 0.438 R2=.9527 SER=.0141 0.005 0.120 rho=.685 Structural Model Dependent Variable: pfx Procedure: CORC variable coef f ic ient standard error Forecast NEWS n = 59 1.005 0.454 R2=.9544 SER=.0138 0.005 0.109 rho=.705 67 Table 4.5 Optimal Forecasts: 1974-78 Forward Rate RMSE: $0.02372(2.28%) MAE: $0.01980 Bias:6.86% Coefficient:5.90% Residual:87.33% PPP plus money model Conditional Forecast RMSE: $0.01849(1.78%) MAE: $0.01497 Bias:13.04% Coefficient:5.93% Residual:80.84% Genuine Forecast RMSE: $0.01994(1.92%) MAE: $0.01590 Bias:14.25% Coefficient:4.80% Residual:80.85% Real-Interest-Parity model Conditional Forecast RMSE: $0.01850(1.78%) MAE: $0.01480 Bias:12.59% Coefficient:9.43% Residual:77.49% Genuine Forecast RMSE: $0.01807(1.74%) MAE: $0.01437 Bias:13.18% Coefficient:8.47% Residual:78.26% Interest-Parity Conditional Forecast RMSE: $0.01854(1.78%) MAE: $0.01486 Bias:13.04% Coefficient:9.40% Residual:77.20% Genuine Forecast RMSE: $0.01791(1.72%) MAE: $0.01420 Bias:12.77% Coefficient:8.32% Residual:83.22% 68 Table 4.5 continued Monetary Approach (Dornbusch) model Conditional Forecast RMSE: $0.01831(1.76%) MAE: $0.01477 Bias:12.62% Coefficient:6.94% Residual:79.77% Genuine Forecast RMSE: $0.01990(1.91%) MAE: $0.01571 Bias:13.66% Coefficient:4.47% Residual:81.75% Structural model Conditional Forecast RMSE: $0.01820(1.75%) MAE: $0.01456 Bias:8.48% Coefficient:4.18% Residual:87.34% Genuine Forecast RMSE: $0.01803(1.73%) MAE: $0.01444 Bias:6.50%. Coefficient:2.69% Residual:90.62% 69 Notes to Chapter 4 Time Series Analysis and Forecasting Exogenous Variables The purpose of these notes i s to outline the methodology used in the construction of time series forecasts of the various exogenous variables employed in the alternative models of exchange rate determination. The notes begins with a discussion of the forecasting requirements p a r t i c u l a r to t h i s project. It proceeds' to outline the process involved in the i d e n t i f i c a t i o n and estimation of the time series models and ends with a number of tables which summarize the model parameters used to construct the forecasts. Forecasting Requirements Data necessary for the estimation of the alternative exchange rate models are available at one of two le v e l s of time aggregation: weekly or monthly. Weekly data to be analyzed included monetary .aggregates and interest rates for s e c u r i t i e s of d i f f e r e n t maturities. Monthly data included prices and outputs. As the forecasting target was ninety days ahead of the 'current' period, i t was necessary, given the lags with which some weekly data is released, to forecast as much as f i f t e e n weeks ahead of the last known data point. In the case of the monthly data, i t was necessary (again due to lags in the release of the data) to forecast four months ahead. The Time Series Analysis Procedure Descriptions of the general procedure for the i d e n t i f i c a t i o n and estimation of times series models can be 70 found in Box and Jenkins (1970) and Nelson (1973). Time series analysis being as much an art as a science, the purpose of this section i s to make clear what judgements were made when alternatives presented themselves. F i r s t , the procedure for analyzing weekly data w i l l be described, followed by a description of the methodology used to analyze monthly data. Genuine forecasts are forecasts which are based solely on information available on the date the forecast was made. The date the forecast i s made w i l l be c a l l e d the 'current' period. In t h i s study, forecasts are made every Wednesday with the forecast target being the Wednesday thirteen weeks hence. As interest rates are available (for p r a c t i c a l purposes) instantaneously, a genuine forecast of future rates can be made using a model estimated over a l l past data including the current interest rate. The current interest rate, because i t is 'known' currently, can also act as the 'starting point' from which, along with the estimated parameters of the time series model, forecasts of the future are made. Monetary aggregates are not available currently, but rather, with what amounts to a two week lag. This i s because the monetary figures r e l a t i n g to a given week are released on the Thursday of the following week. Hence they are not incorporated into the forecasting procedure for two weeks. If one were tr u l y forecasting into the future, one might well re-estimate the parameters of the time series model as each new data point became av a i l a b l e . In the case of t h i s study, the cost and time required for such a procedure would be p r o h i b i t i v e . It was decided that each series would be divided 71 into annual sub-periods and the parameters of the time series model would be re-estimated annually. Thus a given year's forecasts are based on the most recently available data and parameters from a time series model estimated over the previous year. New data are available each week to act as the s t a r t i n g point for the current forecast, but the parameters of the time series model are constant for a year at a time. Given t h i s yearly re-estimation, eight time series models were i d e n t i f i e d and estimated for each data series. The methodology used to identi f y and estimate time series models for the monthly data was the same as described above with two important exceptions. In order to get enough observations to provide s t a t i s t i c a l l y meaningful estimates, and at the same time not be too strongly influenced by the less recent (and presumably less important) past, the time series parameters used to forecast a given year are from models estimated using observations from the previous three years. Each monthly observation was a r b i t r a r i l y assigned to the 'middle' Wednesday of the month, that is the f i r s t Wednesday after the fourteenth of the month. This is because the data are customarily released on the f i f t e e n t h of each month with a one month lag. Estimated Model Parameters This section contains a number of tables which summarize the nine time series models used to forecast each data series over the eight yearly sub-periods from 1971-78. Models were chosen over competing alternatives on the basis of minimizing the standard error of the estimate residuals and on the basis of 72 the model's success in reducing i t ' s residuals to 'white noise' as measured by the ' Q ' - s t a t i s t i c . Periods 1 through 8 correspond to the yearly sub-periods from 1971-78, with Period 1 denoting the time series model used to forecast the variable in question for the year 1971. 73 Table 4.6 Variable: P Period 1: ARI(0,1) AR Parameters l r s t : .0 Constant .2828 Period 2: ARI(5,1) AR Parameters 3rd: .286 5th:-.3875 Constant .2754 Period 3: ARI(0,1) AR Parameters l r s t : .0 Constant .3171 Period 4: ARI(1,1) AR Parameters l r s t : .2268 Constant .4468 Period 5: ARI(1,1) AR Parameters l r s t : .4488 Constant .4666 Period 6: ARI(1,1) AR Parameters l r s t : .2714 Constant .789 Period 7: ARI(1,1) AR Parameters l r s t : .3209 Constant .6947 Period 8: ARI(1,1) AR Parameters l r s t : Constant .7501 .2573 74 T a b l e 4.7 V a r i a b l e : P* P e r i o d 1: ART. ( 1 , 1 ) AR P a r a m e t e r s l r s t : .1246 C o n s t a n t .3635 P e r i o d 2: A R I ( 1 , 1 ) AR P a r a m e t e r s l r s t : .3197 C o n s t a n t .2711 P e r i o d 3: A R I ( 6 , 1 ) AR P a r a m e t e r s l r s t : .31 2nd: .34 4 t h : - . 4 7 6 t h : .52 C o n s t a n t .09 P e r i o d 4: A R I ( 2 , 1 ) AR P a r a m e t e r s l r s t : .08 2nd: .46 C o n s t a n t .232 P e r i o d 5: A R I ( 3 , 1 ) AR P a r a m e t e r s l r s t : .035 2nd: .397 3 r d : .36 C o n s t a n t .208 P e r i o d 6: A R I ( 0 , 1 ) AR P a r a m e t e r s l r s t : .0 C o n s t a n t .94 P e r i o d 7: A R I ( 1 , 1 ) AR P a r a m e t e r s l r s t : .5068 C o n s t a n t .4212 P e r i o d 8: A R I ( 1 , 1 ) AR P a r a m e t e r s l r s t : .2703 C o n s t a n t .5329 75 Table 4.8 Variable: Y Period 1: ARI(0,1) AR Parameters l r s t : .0 Constant .3085 Period 2: ARI(0,1) AR Parameters l r s t : .0 Constant .3457 Period 3: ARI(5,1) AR Parameters 3rd: .347 4th:-.2963 5th: .0894 Constant .5142 Period 4: ARI(2,1) AR Parameters lrst:-.268 2nd:-.2839 Constant 1.12 Period 5: ARI(3,1) AR Parameters 3rd: .267 Constant .333 Period 6: ARI(0,1) AR Parameters l r s t : .0 Constant .1285 Period 7: ARI(3,1) AR Parameters 3rd:-.297 Constant .003 Period 8: ARI(1,1) AR Parameters lrst:-.048 Constant .218 Table 4.9 Variable: Y* Period 1: ARI(2,1) AR Parameters l r s t : .277 2nd: .306 Constant -.0263 Period 2: ARI(1,1) AR Parameters l r s t : .2382 Constant .05 Period 3: ARI(1,1) AR Parameters l r s t : .4162 Constant .21 Period 4: ARI(0,1) AR Parameters l r s t : .0 Constant .6485 Period 5: ARI(1,1) AR Parameters l r s t : .9197 Constant -.109 Period 6: ARI(2,1) AR Parameters l r s t : 1.033 2nd:-.2623 Constant .0073 Period 7: ARI(2,1) AR Parameters l r s t : 1.054 2nd:-.2974 Constant .0672 Period 8: ARI(1,1) AR Parameters l r s t : .5921 Constant .32 77 Table 4.10 Variable: R Period 1: ARI(1,1) AR Parameters l r s t : .1578 Constant -.0542 Period 2: ARI(1,1) AR Parameters l r s t : .4634 Constant .0177 Period 3: ARI(1,1) AR Parameters l r s t : .3346 Constant .0167 Period 4: ARI(1,1) AR Parameters l r s t : .1702 Constant .0078 Period 5: ARI(1,1) AR Parameters l r s t : .215 Constant .0112 Period 6: ARI(1,1) AR Parameters l r s t : .4688 Constant .0072 Period 7: ARI(0,1) AR Parameters l r s t : .0 Constant -.0152 Period 8: ARI(4,1) AR Parameters 4th: -.2804 Constant -.0248 78 Table 4.11 Variable: R* Period 1: ARI(1,1) AR Parameters l r s t : .4116 Constant -.0313 Period 2: ARI(1,1) AR Parameters l r s t : .6303 Constant -.0063 Period 3: ARI(2,1) AR Parameters l r s t : .4149 2nd: .1834 Constant .0277 Period 4: ARI(1,1) AR Parameters l r s t : .5444 Constant .0277 Period 5: ARI(1,1) AR Parameters l r s t : .2833 Constant .0069 Period 6: ARI(1,1) AR Parameters l r s t : .5432 Constant -.0238 Period 7: ARI(1,1) AR Parameters l r s t : .3536 Constant .0167 Period 8: ARI(1,1) ,AR_Parameters l r s t : Constant .0207 .3961 79 Table 4.12 Variable: DP Period 1: ARI(1,1) AR Parameters l r s t : .2994 Constant -.0228 Period 2: ARI(8,1) AR Parameters l r s t : .2105 8th: .2307 Constant -.0053 Period 3: ARI(7,1) AR Parameters 2nd: .2879 7th: .3337 Constant -.0017 Period 4: ARI(0,1) AR Parameters l r s t .0 Constant .0217 Period 5: ARI(8,1) AR Parameters l r s t .3217 2nd: .2231 8th: .3121 Constant -.0047 Period 6: ARI(1,1) AR Parameters l r s t .277 Constant .0143 Period 7: ARI(5,1) AR Parameters 4th .3452 5th:-.2823 Constant -.0073 Period 8: ARI(0,1) AR Parameters l r s t .0 Constant .0062 80 Table 4.13 Variable: DP* Period 1: ARI(2,1) AR Parameters l r s t .5652 2nd-.234 Constant -.0117 Period 2: ARI(0,1) AR Parameters l r s t .0 Constant -.006 Period 3: ARI(1,1) AR Parameters l r s t .396 Constant -.0004 Period 4: ARI(1,1) AR Parameters l r s t .4395 Constant .0071 Period 5: ARI(1,1) AR Parameters l r s t .2939 Constant .0077 Period 6: ARI(1,1) AR Parameters l r s t .2182 Constant .005 Period 7: ARI(1,1) AR Parameters l r s t .3613 Constant -.0012 Period 8: ARI(1,1) AR Parameters l r s t .4351 Constant .0091 T a b l e 4.14 V a r i a b l e : M Period 1: A R I ( 0 , 1 ) AR Parameters l r s t : .0 Constant 70.076 Period 2: ARI(9,1) AR Parameters lrst:-.5087 3rd:-.2608 9th: .3807 Constant 80.651 P e r i o d 3: A R I ( 9 , 1 ) AR P a r a m e t e r s l r s t : - . 7 3 2 9 2nd:-.3231 3 r d : - . 2 7 9 4 9 t h : .2983 C o n s t a n t 148.43 Period 4: ARI(8,1) AR Parameters lrst:-.5438 3rd: .2734 4th: .3941 8th:-.2203 Constant 136.3 Period 5: ARI(6,1) AR Parameters lrst:-.1795 6th:-.1748 Constant 166.38 Period 6: ARI(10,1) AR Parameters lrst:-.8689 2nd:-.5056 3rd:-.4142 5th: .2528 7th:-.1514 10th:-.2599 Constant 342.99 Period 7: ARI(9,1) AR Parameters lrst:-.5738 9th: .3427 Constant 223.85 Period 8: A R I ( 3 , 1 ) AR Parameters l r s t : - . 7 8 0 9 Constant 3 6 9 . 9 8 2nd:-.5452 3rd:-.5248 82 Table 4.15 Variable: M* Period 1: ARI(3,1) AR Parameters l r s t : .0379 2nd: .167 3rd: .3847 Constant 3.2 Period 2: ARI(2,1) AR Parameters l r s t : .1504 2nd: .4924 Constant 3.323 Period 3: ARI(5,1) AR Parameters l r s t : .3048 2nd: .0991 4th: .2703 5th:-.297 Constant 6.282 Period 4: ARI(2,1) AR Parameters 2nd: .2246 Constant 6.75 Period 5: ARI(0,1) AR Parameters l r s t : .0 Constant 7.58 Period 6: ARI(7,1) AR Parameters l r s t : .2823 2nd: .265 4th:-.2842 6th:-.1177 7th:-.1032 Constant 10.212 Period 7: ARI(0,1) AR Parameters l r s t : .0 Constant 14.62 Period 8: ARI(3,1) AR Parameters 2nd: .1391 Constant 14.3 3rd:-.2202 83 Table 4.16 Variable: L Period 1: ARI(1,1) AR Parameters l r s t : .7161 Constant -.0025 Period 2: ARI(1,1) AR Parameters l r s t : .8076 Constant -.0016 Period 3: ARI(1,1) AR Parameters l r s t : .6448 Constant -.0008 Period 4: ARI(1,1) AR Parameters l r s t : .4606 Constant -.0012 Period 5: ARI(1,1) AR Parameters l r s t : .3712 Constant -.0014 Period 6: ARI(2,1) AR Parameters l r s t : .5113 2nd: .4043 Constant -.0034 Period 7: ARI(2,1) AR Parameters l r s t : .6268 2nd: .2245 Constant -.0021 Period 8: ARI(1,1) AR Parameters l r s t : .7012 Constant -.0032 84 Chapter 5 Speculative P r o f i t s and Market E f f i c i e n c y 5.0 Introduction Chapter 4 used alternative models to forecast PFX over the period 1974-78. These forecasts were compared with each other and the forward rate, and each model's forecast was shown to add s i g n i f i c a n t l y to the forward rate in predicting the future value of PFX. This chapter uses the models' and optimal forecasts constructed in Chapter 4 to perform a semi-strong test of market e f f i c i e n c y . The forecasts,, in conjunction with a simple betting rule, are combined to make speculative bets in the forward market and the resulting p r o f i t s are examined. The chapter begins with a brief discussion of the l i t e r a t u r e regarding foreign exchange market e f f i c i e n c y . It then proceeds to a description of the test performed and concludes with a presentation and discussion of the returns generated using the betting strategy. 5.1 The E f f i c i e n c y L i t e r a t u r e 2 6 Given that the exchange rafe:'~ Ts vlewed as. anZImpprtant 'summary' price embodying a good deal of information about the r e l a t i v e strengths of two economies, i t is no surprise that as techniques were developed to test e f f i c i e n c y in other markets, 2'This section follows reviews by Fama (1970) and Levich (1978). Another comprehensive review i s found in Kohlhagen (1978). 8 5 some investigators turned these techniques to examining the question of exchange market e f f i c i e n c y . It i s f i r s t important to agree on a d e f i n i t i o n of market e f f i c i e n c y . In Fama's (1970) words: "A market in which prices always ' f u l l y r e f l e c t ' available information i s c a l l e d ' e f f i c i e n t ' " . What i s contained in 'available information' ? Three types of information have been considered in * the l i t e r a t u r e . 'Weak form' tests of e f f i c i e n c y are tests where only h i s t o r i c a l prices are included . In 'semi-strong form' tests, h i s t o r i c a l prices are augmented with announcements and other p u b l i c a l l y available information. F i n a l l y , when the information set includes information known exclusively to groups of agents within the market, 'strong form' market e f f i c i e n c y i s tested. This chapter is primarily concerned with 'semi-strong form' e f f i c i e n c y . One of the well known properties of an e f f i c i e n t market i s that speculators cannot make super-normal p r o f i t s on the basis of available information, 'super-normal' p r o f i t s are defined as p r o f i t s above the normal return on alternative investments of comparable r i s k . How can thi s proposition be made operational? Bachelier (1900) stated that speculation in e f f i c i e n t markets should be a ' f a i r game' so that the expected p r o f i t s in excess of normal rates of return are zero. A process involving a sequence of these f a i r games i s referred to as a 'martingale'. Given the general ' f a i r game' model, investigators began studies based on the premise that market e f f i c i e n c y implied that prices followed a random walk. A random walk i s a special case of the general f a i r game model, which assumes, in addition to 86 the expected change in returns being zero, that successive returns are i d e n t i c a l l y d i s t r i b u t e d and independent of previous changes. Poole (1967), Pippenger (1973) and others have produced c o n f l i c t i n g evidence using the random walk c r i t e r i o n . Levich (1977) and Stein (1980) point out, however, that a random walk price movement i s neither necessary or s u f f i c i e n t for market e f f i c i e n c y . If prices move randomly around a stable equilibrium, then the expected value of price changes w i l l be zero, and actual changes w i l l be uncorrelated from period to period. If the equilibrium changes s i g n i f i c a n t l y through time, especially i f i t follows a non-linear path, prices may s t i l l move randomly around the equilibrium. The f i r s t case s a t i s f i e s the random walk c r i t e r i o n , the second does not. Yet both markets are e f f i c i e n t . Fama (1970) has argued that the assumptions necessary for the random walk test may not be too r e s t r i c t i v e for stock market studies. In a stock market study assumptions might include: (1) Returns are positive in every period, (2) Expected returns are constant over the differencing i n t e r v a l , and (3) Expected returns are generated by a generally accepted c a p i t a l asset p r i c i n g model. While these assumptions may be plausible for asset markets, they do not provide a useful description of the market for foreign exchange. For t h i s , random walk studies seem inappropriate, with more general ' f a i r game' tests such as that of Cornell and D i e t r i c h (1978) being more suitable. Another approach to testing market e f f i c i e n c y i s the ' f i l t e r rule' test f i r s t used by Alexander (1961) and more recently by Poole (1967), Praetz (1976) and Cornell and D i e t r i c h 87 (1978). Based on the premise that e f f i c i e n t markets preclude returns in excess of normal rates, f i l t e r tests attempt to discover whether excess returns were possible given a trading strategy dictated by a f i l t e r rule. F i l t e r tests operate in the following manner. When a foreign currency appreciates a given percentage above a previous low, the currency should be bought. When the currency depreciates a given percentage below a previous high, the currency should be sold. F i l t e r s (the percentages mentioned above) may be any size and need not be equal on buying and s e l l i n g sides of a transaction. Similar tests can be constructed using moving averages instead of previous highs and lows. These tests are motivated by possible bandwagon effects in the foreign exchange market. More recently i t has been argued by Levich (1978,1978b), Harris and Purvis (1978) and Stein (1980) that the tests discussed above a l l share a common, c r u c i a l fault when applied to the foreign exchange market. These papers contend that any test of market e f f i c i e n c y in the foreign exchange market in fact includes the following two separate hypotheses: (1) Model A i s the true model underlying the foreign exchange market and generating the equilibrium prices and, (2) Given model A, economic agents make best use of available information and therefore set prices ' e f f i c i e n t l y ' . Given these 'nested' hypotheses, i t is clear that random walks cannot give a reasonable test of market e f f i c i e n c y unless the agreed-upon 'true' equilibrium model predicts stable prices or returns. Since there is no general agreement on the content of model A, any f a i l u r e to discover e f f i c i e n c y could be dismissed by means 88 of the argument that the 'wrong' underlying model was used to generate the equilibrium predictions. In the case of f i l t e r and other mechanical rules, any indication of excess returns can be explained by the statement that given a set of data and enough time, eventually some mechanical rule can be found to make a p r o f i t . Mechanical rules have no the o r e t i c a l content. 5.2 Constructing a Test of E f f i c i e n c y To deal with the problem of the 'nested hypotheses', the following approach i s adopted. F i r s t , the same c r i t e r i o n of ef f i c i e n c y i s used, namely that in an e f f i c i e n t market, opportunities for abnormal speculative p r o f i t s should not be present. In other words, risk-adjusted returns to speculation should be a f a i r game. Second, since there is l i t t l e agreement over the structure of the 'true' model underlying the market, a range of alternative models are used to generate forecasts, attempting to take into account the d i f f e r e n t forces that are believed to affect the exchange rate. In this approach, agents are assumed to be forming expectations ' r a t i o n a l l y ' . That i s , expectations of the future value of the exchange rate are formed based on knowledge of the 'true' model which underlies the market. In thi s sense, the rejection of market e f f i c i e n c y i s also a rejection of rational expectations in the foreign exchange market, since e f f i c i e n c y must be a necessary condition for r a t i o n a l expectation formation. In order to make thi s approach operational, the forecasts generated by the alternative models and presented in Chapter 4 are combined with a simple betting strategy to speculate in the 89 forward exchange market. To make a speculative bet in the forward market i t is necessary to have an expectation of the direction of forward rate error. For instance, i f a speculator expects the future spot rate (PFX(t+3)) to be greater than the current forward r a t e 2 7 (PFXF(t)) for that maturity, he w i l l buy foreign exchange forward in ant i c i p a t i o n of being able to s e l l in the spot market for a p r o f i t at the time of maturity. If the speculator believes the market overvalues foreign exchange forward, he w i l l s e l l foreign exchange forward (go short) in antic i p a t i o n of being able to f u l f i l l his contract at maturity at a lower pri c e . Given t h i s strategy, i t i s not necessary to have a 'better' (in the sense of lower RMSE) forecast of the exchange rate than the market 2 8. It is only necessary to predict the d i r e c t i o n of forward rate error. A l l models' and optimal forecasts of the exchange rate presented in Chapter 4 do have smaller errors than the forward rate, and the results presented in Table 4.4 using the NEWS variable suggest that on average the models' forecasts do co r r e c t l y predict the di r e c t i o n of forward rate error. Whether this information would allow a speculator to earn abnormal p r o f i t s remains to be shown. 5.3 Speculative Returns A test suggested by Levich (1980), which he c a l l s a test of 2 7 I n the case of forward rate and forecasts, the period found in parentheses denotes the target date for that variable. 2"This i s the d i s t i n c t i o n between accurate and p r o f i t a b l e forecasts discussed in Levich (1980) and Shapiro (1981). 90 forecasting 'expertise', is performed f i r s t . Levich looks at a number of speculative bets' based on forecasting services' predictions of the d i r e c t i o n of forward rate error. If he can reject the hypothesis that the forecasting service c o r r e c t l y predicts the d i r e c t i o n of forward rate error only randomly, then he argues the sevice possesses forecasting 'expertise'. The test was performed here comparing the models' and optimal forecasts to the forward rate and then to the future spot rate to see i f they correctly predicted the d i r e c t i o n of forward rate error. The test was performed using three month forecasts monthly over the period 1974-78 ( 6 0 months). A s t a t i s t i c 'p' was calculated as the number of correct forecasts over the t o t a l number. The s t a t i s t i c was assumed to have a binomial d i s t r i b u t i o n , and using the normal approximation, the c r i t i c a l value for rejecting the n u l l hypothesis that p < 0.5 was p=0.61 at the 95% l e v e l . The results of t h i s test are presented in Table 5.1. It is clear from Table 5.1 that the hypothesis of no forecasting expertise can be rejected in the case of every forecast at the 95% l e v e l 2 ' . The next test examined the returns to speculative bets made on the basis of the models' and optimal forecasts. If the ior^dalsItZIprfiiiicted a future spot rate greater than the forward rate, $1.00 of foreign exchange was bought forward. If the 2'An important caveat to this result i s that i t assumes each t r i a l i s independent. Given these are overlapping bets, t h i s condition may not be s a t i s f i e d . If the t r i a l s are dependent, the estimates are unbiased,but is impossible to determine a p r i o r i i f the variances are under- or over-stated. More w i l l be said about independence when the d i s t r i b u t i o n s of actual returns are discussed. 91 forecast predicted a future spot rate lower than the forward rate, then $1.00 of foreign exchange was sold forward. Returns on bets were calculated as follows: (5.1) P r o f i t = 1.0(PFX(t)-PFXF(t)) for foreign exchange bought. (5.2) P r o f i t =-1.0(PFX(t)-PFXF(t)) for foreign exchange sold. No transaction costs were taken into account in t h i s c a l c u l a t i o n . A problem here is that returns must be expressed as actual amounts per dollar bet. E s s e n t i a l l y this i s because no c a p i t a l is required to bet in the forward market 3 0. Data on returns generated using the forecasts and betting strategy described above for sixty monthly bets over the period 1974-78 are presented in Tables 5.2 and 5.3. These tables show the mean and standard deviation of returns as well as the minimum and maximum values over sixty bets. In the case of both the models' and the optimal forecasts, a l l mean returns are p o s i t i v e and in the order of $0.01 per d o l l a r bet for a three month period. It i s important to remember that this cannot be converted to a rate of return. In both tables, the Monetary Approach forecasts have the highest average 3 0 I f one were to bet in the Chicago currency futures market (although t h i s data does not apply to that market), an amount equal to about 5% of the value of the contract would have to be kept in a margin account, but t h i s account could contain interest-bearing government s e c u r i t i e s . The only cost of c a p i t a l i s the premium being paid for . holding r e l a t i v e l y l i q u i d s e c u r i t i e s in the margin account and in having the l i q u i d i t y to meet possible margin c a l l s . In the forward market there are no formal rules regarding security for forward contracts of customers, but i t is probably safe to say a bank would require some compensating balances which again could be interest-bearing. It i s interesting to note that this is the same kind of bet that firms or individuals take everytime they decide to leave future foreign exchange payments or receipts uncovered. 92 return. It is also interesting to note the deviation of returns is always in the neighbourhood of $0.02, or roughly twice the mean. Optimal forecasts show s l i g h t l y higher means and lower deviations of returns than the models' forecasts. Since p r o f i t s from the betting strategy described above cannot be expressed in the usual r i s k - r a t e of return framework, i t was necessary another method to put the returns in the proper perspective in terms of r i s k . Two sets of p r o b a b i l i t i e s were calculated in an e f f o r t to do t h i s . F i r s t , i f the returns from each set of bets are assumed to be- normally d i s t r i b u t e d with population parameters given by the estimated mean and standard deviation, what is the pr o b a b i l i t y that any given bet w i l l y i e l d negative returns? Second, given population parameters estimated by the sample mean and standard deviation, what i s the probability that after sixty bets the mean return w i l l be negative? Of course the c a l c u l a t i o n of both these p r o b a b i l i t i e s require that the returns be independent 3 1. The results of these calculations for the models' and optimal forecasts are presented in Tables 5.4 and 5.5. As can be seen from these tables, the probability of any given bet y i e l d i n g negative returns i s about 0.33, with the optimal forecasts having a s l i g h t l y greater chance of p r o f i t . If one were to make sixty bets however, the 3 1Given the importance of these re s u l t s , an e f f o r t was made to calculate the degree of dependence among returns due to the overlapping nature of the bets. To measure t h i s , current returns were regressed on their previous value. In most cases the c o e f f i c i e n t of past returns was small and s t a t i s t i c a l l y i n s i g n i f i c a n t . In the few cases the c o e f f i c i e n t was s t a t i s t i c a l l y s i g n i f i c a n t , i t was never greater than 0.26. Thus the assumption that successive returns are independent does not seem unjustifed. 93 pr o b a b i l i t y of a negative mean return is always less than 0.01. Thus for sixty bets, the p r o b a b i l i t y of a negative mean return is very small 3 2. Although these findings are s t r i k i n g , and are not in agreement with the findings of some investigators discussed above 3 3, they do not provide s u f f i c i e n t evidence for the market to be judged i n e f f i c i e n t over the sample period. It i s necessary to determine i f the above strategy could be used to generate po s i t i v e returns after accounting for transaction costs. The problem is that in the forward market, no e x p l i c i t transaction costs are charged. Costs of transactions (as well as the risk premium, i f i t exists) are accounted for in the spread between buying and s e l l i n g rates. Exchange rate data used in t h i s study are midpoint closing rates, which represent a rate mid-way between the buying and s e l l i n g rates at the close of trading. No data on spreads were available over th i s period. To account for transaction costs, one must charge one 'round t r i p ' for the 3 2 0 f course this a very crude strategy, e s p e c i a l l y since the speculator is required to hold the contract u n t i l maturity regardless of whether the rate i s moving against him. A s l i g h t l y more sophisticated strategy (not reported here) where the size of the bet was proportional to th.e ex ante expected p r o f i t was also tested. In t h i s case, the returns for some forecasts doubled, but the relationship between the means and deviations generally remained the same. The crude betting strategy reported here should be thought of as generating a minimum set of returns, which could be improved upon with the use of more sophisticated strategies. 3 3Longworth (1981), has found that the lagged spot rate is a better forecast of the current spot rate than the lagged one month forward rate for the period July 1970 to December 1976. He concludes the market i s i n e f f i c i e n t over t h i s period. This finding i s supported in part by Cornell (1977) and Levich (1978). 94 entire transaction, which i s twice the difference between the quoted midpoint rate and the buying or s e l l i n g rate. This spread was judged to be about 20 points ($0,002) per d o l l a r on a representative transaction of one m i l l i o n d o l l a r s . The betting strategy and the p r o f i t c alculation were both modified to take into account t h i s estimate of transaction costs. F i r s t , no bet was made unless ex-ante expected returns were greater than 20 points per do l l a r bet. Second, whenever bets were made, 20 points was subtracted from the gross p r o f i t . With these modifications, exactly the same procedure as described above was followed. The results of the bets using the models' and optimal forecasts and accounting for transaction costs are presented in Tables 5.6 and 5.7. Comparing the results in these tables to those in Tables 5.2 and 5.3, i t can be seen, as one would expect, that when transaction costs are taken into account returns decline, although generally by less than 20 points (the exception being the optimal Monetary Approach forecast). The deviation of returns remains p r a c t i c a l l y unchanged. The pr o b a b i l i t y of a single bet yi e l d i n g negative returns, and the pr o b a b i l i t y of of a negative mean return after sixty bets were again calculated. These, calculations are presented in Tables 5.8 and 5.9. The proba b i l i t y of a single bet y i e l d i n g a loss remains about 0.33 for a l l forecasts. In every case one can reject at the 99% le v e l the hypothesis that sixty bets w i l l y i e l d a negative mean return. This i s strong evidence that after sixty bets the mean return w i l l be pos i t i v e , even accounting for transaction costs. 95 5.4 Conclusions In this chapter, the genuine forecasts generated in Chapter 4 were used to perform Levich's test of forecasting expertise, and combined with a simple betting strategy to make bets in the forward exchange market. In the absence of measurable c a p i t a l requirements, p r o f i t s from speculation could only be expressed as actual rather than rates of return. The forecasts were found to possess forecasting expertise according to the Levich c r i t e r i o n . Speculative returns over the sixty month sample were on average in the range of $0.01 per doll a r bet, with deviations of returns being about $0.02. It was shown that the pr o b a b i l i t y of any single bet y i e l d i n g a loss was about 0.33, arid the probability of a negative mean return a f t e r sixty bets was less than 0.01. Transaction costs were estimated to be about 20 points ($0,002) per bet and when these costs were taken into account, mean returns f e l l , but generally by less than 20 points. The probability of any given bet yi e l d i n g a loss was again calculated to be about 0.33, while the prob a b i l i t y of a negative mean return after sixty bets was calculated to be less than 0.01. Given that these bets were made on the basis of genuine forecasts using only information available to the market at the time the bet was to have been made, i t would seem that these opportunities were not f u l l y exploited by the market, and thus agents were not setting the price of foreign exchange e f f i c i e n t l y . Further, i t seems hard to believe that over th i s period market participants were forming their expectations in a 9 6 r a t i o n a l manner, given the existence of these unexploited p r o f i t opportunities. Table 5.1 p-values (p=#correct/n) Ho: p=.5 (Reject Ho at 95%: p=.61) Model Model Forecast Optimal Forecast PPP plus money: .63 .63 Interest-Parity: .67 .70 Real-Interest-Parity: .68 • .72 Monetary Approach: .67 .65 Structural: .67 .68 98 Table 5.2 Speculation using Models' Forecasts Dollar Returns on Monthly $1.00 forward bets: 1974-78 min max mean std. dev. PPP plus money -.0312 0598 Interest-Parity -.0402 .0598 Rea1-1nterest-Par i t y -.0402 .0598 Monetary Approach -.0312 .0598 Structural -.0354 .0598 .0096 .0080 .0089 .0107 .0097 .0218 .0225 .0221 .0213 .0218 Table 5.3 Speculation using Optimal Forecasts Dollar Returns on Monthly $1.00 forward bets: 1974-78 min max PPP plus money -.0312 .0598 Interest-Parity -.0312 .0598 Real-Interest-Parity -.0312 .0598 Monetary Approach -.0312 .0598 Structural -.0354 .0598 mean .0095 .0112 .0116 .0153 .0099 std. dev. .0218 .0210 .0208 .0214 .0217 99 Table 5.4 Pr o b a b i l i t i e s of Betting P r o f i t s Using Models' Forecasts Model z-score Prob. of single bet loss PPP plus money: -3.41 33% Interest-Parity: -2.74 36% Real-Interest-Parity: -3.11 34% Monetary Approach: -3.89 31% Struc t u r a l : -3.44 33% C r i t i c a l z(reject Ho:loss over 60 bets at 99%)=-2.57 Table 5.5 Pr o b a b i l i t i e s of Betting P r o f i t s Using Optimal Forecasts Model z-score Prob. of single bet loss PPP plus money': -3.37 33% Interest-Parity: -4.13 30% Real-Interest-Parity: -4.31 29% Monetary Approach: -5.53 24% Struc t u r a l : -3.53 33% C r i t i c a l z(reject Ho:loss over 60 bets at 99%)=-2.57 100 Table 5.6 Speculation using Models' Forecasts (with transaction costs) Dollar Returns on Monthly $1.00 forward bets: 1974-78 mm max PPP plus money (51 bets) -.0332 .0578 Interest-Parity (51 bets) -.0332 .0578 Real-Interest-Parity (50 bets) -.0332 .0578 Monetary Approach (52 bets) -.0332 .0578 Structural (52 bets) -.0374 .0578 mean .0086 .0099 .0101 .0099 .0087 std. dev. . 0218 .0210 .0212 .0212 .0229 Table 5.7 Speculation using Optimal Forecasts (with transaction costs) Dollar Returns on Monthly $1.00 forward bets: 1974-78 min max PPP plus money (54 bets) -.0332 .0578 Interest-Parity (53 bets) -.0332 .0578 Real-Interest-Parity (54 bets) -.0332 .0578 Monetary Approach (56 bets) -.0332 .0578 Structural (52 bets) -.0374 .0578 mean .0090 .0097 .0097 .0095 .0084 std. dev, .0219 .0,208 .0210 .0210 .0229 101 Table 5.8 Pr o b a b i l i t i e s of Betting P r o f i t s After Transaction Costs Using Models' Forecasts Model z-score Prob. of single bet loss PPP plus money: -3.05 35% Interest-Parity: -3.65 32% Real-Interest-Parity: -3.69 32% Monetary Approach: -3.61 32% Structural: -2.94 35% C r i t i c a l z(reject Ho:loss over 60 bets at 99%)=-2.57 Table 5.9 Pr o b a b i l i t i e s of Betting P r o f i t s after Transaction Costs Using Optimal Forecasts Model z-score Prob. of single bet loss PPP plus money: -3.18 34% Interest-Parity: -3.61 32% Real-Interest-Parity: -3.50 33% Monetary Approach: -3.58 32% Struc t u r a l : -2.84 36% C r i t i c a l z(reject Ho:loss over 60 bets at 99%)=-2.57 102 Chapter 6 6.0 Introduction This f i n a l chapter has two goals. In the f i r s t section, the results of each chapter are summarized and put in context with the findings of the previous chapters. The second section draws some general conclusions and points to areas where further research seems warranted. 6.1 Summary of Findings In Chapter 1 the stage i s set with a description of the economic conditions which prevailed at the time Canada returned to a f l e x i b l e exchange rate regime. It continues by outlining some of the shocks the economy was subjected to during the period under study: 1971-78. In early 1970, the monetary authorities were presented with a choice. In the face of large c a p i t a l inflows and mounting reserves, they could either abandon the r e s t r i c t i v e monetary policy they were currently persuing or allow the Canadian d o l l a r to appreciate above $0,925 U.S., the value at which i t had been fixed for the previous eight years. The authorities chose to return to a f l e x i b l e exchange rate. For a number of reasons, the Canadian do l l a r became increasingly over-valued u n t i l in 1976 i t was approximately 20% above i t s PPP value. After the election of the Pa r t i Quebecois in October 1976, the widely held view that the Canadian do l l a r was s i g n i f i c a n t l y over-valued was translated into.action. The d o l l a r began a depreciation which by the end of 103 1978 exceeded 20%. In the second chapter, a number of alternative t h e o r e t i c a l models are considered in an attempt to understand the movements of the Canada-U.S. exchange rate over the period 1971-78. Four groups of models are considered, each in turn more complex and b u i l t on the foundations of the simpler models. In the f i r s t group, PPP models focus on commodity arbitrage through trade flows as the basic determinant of the exchange rate. The second group, Interest-Parity models, combine exchange rate determination by PPP with short-run movements explained by c a p i t a l flows responding to covered interest d i f f e r e n t i a l s . Monetary Approach models make up the t h i r d group. These models treat national currencies as assets, the r e l a t i v e price of which depends upon their r e l a t i v e quantities, returns and r i s k s . The f i n a l group, which contains the Structural Approach, has the short-run exchange rate determined by p o r t f o l i o balance considerations, and the long-run equilibrium attained when the exchange rate i s at a l e v e l which promotes equilibrium trade and c a p i t a l flows. Notes following Chapter 2 summarize the equations which describe each model. Chapter 3 takes the models described in Chapter 2 and estimat es~" "them us7iTLgZq.uarter 1 y data for Canada and the United States over the period 1971-78. In the f i r s t instance, the models were estimated using OLSQ. Using this technique, large differences in explanatory power were found among the models. Durbin-Watson s t a t i s t i c s were uniformly low, indicating that errors were s e r i a l l y correlated. When this problem was corrected using the CORC estimation technique, the information contained 104 in the lagged errors contributed more to the explanatory models which had previously f i t poorly than to the other models, so that only small differences in f i t remained. Several models were rejected because the signs of some of the estimated c o e f f i c i e n t s were in conflic't with the predictions of the theory. These included a l l of the simple PPP models as well as the two Monetary Approach models which contained the expected i n f l a t i o n d i f f e r e n t i a l as an explanatory variable. The Structural model was found to have the lowest RMSE when the models were compared and ranked by f i t . The models were also tested to see i f they possessed explanatory power beyond the lagged spot and forward rates. In every case except one, the hypothesis that the models contained no extra explanatory power was rejected at the 5% l e v e l . The data used to estimate the models are described in notes following this chapter. The models which survived the estimation using quarterly data in Chapter 3 were then estimated using monthly data and used to forecast the exchange rate in Chapter 4. Forecasts were constructed for the period 1974-78. Care was taken to be cert a i n that forecasts were based only on information available to the market at the time the forecast was to have been made, and in that sense the forecasts are genuine. The models were estimated i n i t i a l l y over the period 1971-73 and estimates were updated quarterly as new information became available. These parameter estimates were combined with simple time-series forecasts of the explanatory variables, which were also updated at regular i n t e r v a l s . Notes to t h i s chapter describe the time-series models used to generate the forecasts of the explanatory variables. 105 The forecasts generated using the models were compared to one another and to the forward rate. Every model was found to have a smaller (RMSE) forecast error than the forward rate, with the Structural model's error being the smallest. Tests were performed which showed that the forward rate and the models' forecasts each contained some measure of separate information about the future value of the exchange rate. Thus the models were judged to contain 'unpopular' information. F i n a l l y , in order to incorporate the extra information contained in the forward rate into the models' forecasts, a set of optimal forecasts were generated. These forecasts generally had smaller forecast errors than the models' forecasts. The IP model now had the smallest forecast error, although as in the case of the models' forecasts, the difference between i t and the Structural model was very small. In the f i n a l chapter, the forecasts generated in Chapter 4 were combined with a simple betting strategy to speculate in the forward market over the period 1974-78. The chapter begins with a short review of the exchange market e f f i c i e n c y l i t e r a t u r e . Next a test of forecasting 'expertise' proposed by L'evich (1980) was performed, with each model being found to possess 'expertise' forecasting over t h i s period. A simple 'bet-$1.00-forward' rule was devised and implemented based on the forecasts' predictions of forward rate error. Due to the d i f f i c u l t y of establishing a sensible 'cost of c a p i t a l ' , speculative p r o f i t s were expressed as returns-per-dollar-bet rather than as rates of return. A l l models' and optimal forecasts generated positive mean' returns in the order of $0.01, 106 with the deviation of returns being about twice the mean. It was calculated that the pr o b a b i l i t y of any single bet y i e l d i n g a loss was about .33, while the prob a b i l i t y of sixty bets y i e l d i n g a negative mean return was less than .01. Given that data on bid-ask spreads were unavailable, i t was impossible to d i r e c t l y measure transaction costs. These costs were estimated at twenty points ($0,002) per dollar and when they were taken into account, mean returns f e l l (by less than twenty points) and the deviation of returns remained roughly the same. The pr o b a b i l i t y of a single bet yie l d i n g a loss was again calculated to be in the order of .33, with the prob a b i l i t y of a negative mean return after sixty bets s t i l l less than .01. 6.2 Conclusions and Directions for Further Research In Chapter 3 i t was seen that the f i t of every model improved when estimated with the lagged error term using the CORC technique. Given this fact, i t i s clear that none of the models estimated here can be put forward as a candidate for the 'true' model underlying the foreign exchange market. It may be useful to those interested in better modelling exchange rate determination to try to ide n t i f y the source of the extra information shown to be contained in the lagged error term'and the lagged forward rate. This might provide a clue about what i s missing in the current s p e c i f i c a t i o n of the models. When one turns to forecasting, i t is interesting to note that the models' forecasts and the forward rate each contain separate information about the future spot rate. This was an early indication that the market may have been setting the price 107 i n e f f i c i e n t l y , since not a l l available information was being used. The presence of persistent speculative p r o f i t s after transaction costs i s clear evidence that the s t r i c t requirements of market e f f i c i e n c y were not met over the period studied. Two groups may be interested in this r e s u l t . Advocates of t r u l y f l o a t i n g exchange rates, those who believe that the market knows best the le v e l at which to set the exchange rate, seem deprived of an important foundation to th e i r argument. 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