(p.225) Appendix: International Finance Theory and Empirical Reality
(p.225) Appendix: International Finance Theory and Empirical Reality
Abstract and Keywords
The authors of the Representative Agent Intertemporal Optimization Models (RAIOM) argue that this model should supplant the Mundell–Dornbusch–Fleming model as the dominant paradigm in international finance to be used by central banks, finance ministries, and international economic agencies. First, the basic logic of this model as a possible explanation of the current account and real exchange rate is presented. Second, it is shown that the representative agent model as well as the Monetary and Purchasing Power Parity models lack explanatory power and are not consistent with the evidence. These failures induced us to develop the NATREX model, which is consistent with the evidence and has explanatory power.
1. Questions to Be Answered and the Succession of Theories
We have developed the NATREX approach, with all of its difficulties and limitations, because of the serious problems with the contemporary models. An evaluation of these contemporary models provides the justification for taking a different approach. This appendix summarizes the underlying rationale of these models and shows why economists have been so disappointed in their ability to explain the determination of exchange rates and capital flows.
Good economic theory should explain with simplicity and clarity the complex world of experience. Its propositions should be logical and mutually consistent and should imply testable propositions that are consistent with empirical reality. Ultimately, the usefulness of any scientific theory depends on the quality of its answers to important empirical questions. In studying exchange‐rate determination, we would like a theory to answer questions Q1–Q5. The answers one gets to these questions differ depending upon the theory (model) that is used.
(Q1) Have exchange rates been as stable as the macroeconomic fundamentals? What are these fundamentals? If there has been ‘excess volatility’, what has produced it? (Q2) What determines the real exchange rate? (Q3) Has the purchasing‐power‐parity (PPP) theory been valid under floating rates? Do deviations from PPP indicate over‐or under‐valuation of a currency? (Q4) Are variations in real exchange rates caused by changes in the fundamentals or merely by noise? (Q5) Are variations in nominal exchange rates explained primarily by monetary factors that produce changes in relative nominal prices or also by real disturbances that change the equilibrium real exchange rate?
The failure of flexible exchange rates to perform as economists had expected raised a number of important questions about how (p.226) exchange rates actually do behave in the real world, and about the validity of various models. The performance of these theories in explaining exchange rates has not been encouraging, particularly for the period of the 1980s. The failure of the models gave rise to a succession of new models of exchange rate determination. De Grauwe states, in his 1989 study summarizing the developments of exchange‐rate theories and their application to empirical reality, that the current
Meese (1990) has concluded that ‘economists do not yet understand the determinants of short‐to medium‐run movements in exchange rates’. It is our contention that the focus on the short‐run of recent empirical studies of exchange rates is responsible for this state of affairs.models are unable to explain either the long swings in the exchange rate or the systematic bias in the forward rate as a predictor of the future. In the past we economists have tried to explain, and even predict, how particular disturbances in the ‘fundamental’ variables affect exchange rates. We should reduce our ambitions in this field. Movements of the real exchange rates are, within certain bounds, unexplainable. All we can hope to do is to analyse the nature of the variability, without necessarily being able to explain why a particular movement (for example the appreciation of the dollar from 1982 to 1985) occurred. (1989: 179)
In the decade before the move to floating exchange rates in 1973, the Mundell–Fleming model was the standard view of balance‐of‐payments and exchange‐rate determination. The Mundell–Fleming model was the open‐economy version of the Hicks IS–LM model. Because prices were assumed to be fixed during the period of adjustment, changes in nominal and real exchange rates were identical. The Mundell–Fleming models emphasized the role of the goods market and the trade balance in determining the real exchange rate, and gave little attention to modelling the asset markets.
The move to floating exchange rates in the early 1970s and the ensuing growth of international financial markets pointed up the importance of asset markets in determining the nominal exchange rate. Subsequent theoretical developments shifted the emphasis away from the real exchange rate to the nominal exchange rate and to the roles of asset markets and money in its determination. A variety of monetary and asset‐market models have been used in recent years to to try to explain the short‐run determination of nominal exchange rates. The essential feature of all of the contemporary (p.227) monetary models is that the nominal exchange rate depends only on relative prices in the two countries, which in turn depend on relative money stocks per unit of output.
Portfolio models, based on the theory of optimal portfolio selection of Markowitz and Tobin, emphasized the imperfect substitutability among assets, requiring the specification of markets for a number of financial assets, one of them being money. Given the difficulties of estimating a wide array of asset demands, empirical estimates of portfolio models have often been limited to looking for measures of a risk premium to explain deviations from open‐interest rate parity. Whereas portfolio models depict demands for several assets, monetary models focus almost all attention on money. Assumptions of perfect capital mobility and perfect substitutability among assets permit summarizing the non‐money assets with a simple open‐interest‐parity condition. Assumptions guaranteeing neutral money and ignoring real disturbances lead to the assertion of a constant real exchange rate, and that the nominal exchange rate depends upon relative money stocks per unit of output.
The simple monetary models were extended to include exchange‐rate and monetary dynamics with rational expectations, beginning with Dornbusch's 1976 paper. In these models, prices are assumed to be sticky in the short run, so that an increase in the money supply initially depreciates both the nominal and real exchange rates. The real exchange rate is viewed as stationary, however, in the sense that it converges to a constant as prices gradually move to their equilibrium values. The long‐run equilibrium is consistent with the monetary model, but the dynamics of these models offered a rationale for wide fluctuations in exchange rates in markets with rational participants. By 1988 these ‘overshooting’ models dominated explanations of nominal exchange‐rate determination.
Several factors have led more recently to the popularity of intertemporal optimization models of exchange‐rate determination. Among these factors have been the desire to support macroeconomic models with explicit microeconomic foundations based on optimizing behaviour, growing awareness of the importance of intertemporal budget constraints for behaviour over time, and a recognition of the need to include forward‐looking behaviour more explicity. The intertemporal optimization models (IOM) apply well‐known theories and analytical techniques of intertemporal (p.228) pricing of storable commodities to international finance. Yet, in spite of their dynamic optimizing properties, most intertemporal optimization models of exchange‐rate determination are in many ways quite similar to the monetary models. They incorporate assumptions of a stationary real exchange rate and a simple demand for money. Not surprisingly, many also end up claiming that the nominal exchange rate is proportional to relative prices, which, in turn, are proportional to relative supplies of money per unit of output.
Each of these asset and monetary models is logical within its own set of assumptions and constraints and also captures some aspect of exchange‐rate determination that appears to describe the real world. But empirical tests of these models as a means of explaining recent movements of nominal exchange rates have been notably unsuccessful. Neither their structural nor reduced form equations are consistent with the evidence, giving rise to the views expressed by Meese and De Grauwe, cited above. The paradox is that, although the empirical failure of these models and their structural equations is well known (Boughton 1988), they continue to be offered as the dominant explanation of nominal exchange determination. Although most scholars are aware of the deficiencies of these models, the profession continues to use them wholly or partly because they do not have a logically satisfactory substitute.
Given the continuing popularity of these contemporary models of exchange‐rate determination, which are based on monetary dynamics with rational expectations, we summarize first their basic properties in Part 2 and then their failure empirically to explain the movements in nominal exchange rates in Part 3. Part 4 addresses the limitations of the intertemporal optimization models for empirical explanation of exchange rates.
2. The Logic of the State of the Art Theories: The Crucial Role of the Asset Markets, Monetary Dynamics With Rational Expectations
The contemporary models we are evaluating focus on the short‐run determinants of the nominal exchange rate in asset markets dominated by speculative capital flows. In today's international financial markets, with $1,000 billion traded every day in the world's (p.229) foreign‐exchange markets, expectations of future nominal exchange rates dominate the fundamental determinants of the real exchange rate in any short‐run analysis. These expectations are standardly modelled as rational expectations, defined below. The logic of all of these models is that the considerable variations in the nominal exchange rate can be explained by current and rationally expected monetary factors. All of these models contain three crucial equilibrium relationships: (a) Fisher open interest‐rate parity with rational expectations, (b) a stationary real exchange rate, and (c) dependence of relative inflation rates on relative rates of growth of money supplies. Each of these crucial assumptions will be evaluated in this appendix.
We first define the real and nominal exchange rates. The nominal exchange rate N is defined as the foreign‐currency price of domestic currency, so that a rise in N is an appreciation. The real exchange rate R is the product of the nominal exchange rate N and relative prices (p/p′), where p is the domestic GDP deflator, and p′ the foreign GDP deflator. The real exchange rate is simply the ratio of domestic to foreign prices, measured in a common currency, making it an inverse measure of competitiveness.
There are three crucial equations (A.3)–(A.5) underlying the contemporary models. Equation (A.3) is the Fisher Open Rational Expectations (FORE), or uncovered interest‐rate parity–rational expectations equation.^{1} Equation (A.4) is the stationarity of the real exchange rate. Equation (A.5) is the monetary explanation of relative prices.
Fisher open interest‐rate parity states that the subjectively expected (by the market) percentage change in the nominal exchange rate will equal the difference between the foreign and domestic nominal interest rates, implying perfect capital mobility and perfect substitutability between comparable domestic and foreign assets. If, in addition, expectations are assumed to be rational in the sense of Muth (MRE = Muth Rational Expectations), then the difference between the subjectively expected change and the realized change is (p.230) random variable z′ which is iid with a zero expectation. Fisher open interest parity with rational expectations (the FORE hypothesis) can then be expressed in terms of observed changes in the exchange rate, equation (A.3) or the regression equation (A.3a). They state that short‐term capital flows occur to produce equality in the rationally expected rates of return on domestic and foreign assets. The nominal interest rate on the domestic asset is i(t − 1) and on the foreign asset of comparable risk it is i′(t − 1), at time t − 1. The percentage appreciation of the domestic currency from t − 1 to t is log N(t) − log N(t − 1), denoted Dlog N. Thus the rationally expected percentage change in the nominal value of the domestic currency is equal to the foreign less domestic nominal interest rates on comparable assets. In regression (A.3a) coefficient β = 1 and term z′ is an iid term with a zero expectation. Refer to this as the FORE hypothesis.
Equation (A.4) states the hypothesis that the real exchange rate is stationary at a constant value C. At any time, the real exchange rate may not equal the constant C, for example because prices are sticky in the short run, but it will converge to this value. Term z″ is an iid term with a zero expectation, coefficient b is a positive fraction significantly different from zero.
The third assumption is that relative prices are ultimately determined by ratios of money per unit of output m (home country) and m′ (foreign country), equation (A.5), where the P's are functions, which need not be the same in both countries. If the relative money supplies stabilize at m, m′ then relative prices will converge to (P(m)/P(m′))(T) at more distant date T. This terminal date is a transversality condition. (p.231)
The models containing these assumptions continue to be used to ‘explain’ why exchange rates are volatile. The volatility of the current nominal exchange rate N(t) will be produced by rationally expected temporary and permanent changes in relative money supplies during the interval from the present (time t) to the more distant date T. To understand this we must invoke forward‐looking rational expectations over a sufficiently long interval of time from the present time t to the longer‐run equilibrium at time T. This is done as follows.
Sum the rationally expected percentage changes in the real exchange rate in equation (A.3) from time t to later date T, and derive (A.6), which states that the average percentage change in the nominal exchange rate per unit of time from t to T is equal to the average nominal interest rate differential (i′ − i) during that interval.^{3} (The index s goes from t − 1 to T − 1).
The economic content of (A.6) or (A.8) can be expressed in several ways. (a) The percentage difference between the current and equilibrium nominal value of the currency log N(T) − log N(t) is the product of the average nominal interest differential (i′ − i) between these two dates, and the time h = T − t that it takes for the nominal exchange rate to converge to its equilibrium value. (b) The average rate of appreciation, measured as a per cent per annum, [log N(T) − log N(t)]/(T − t) is equal to the average interest‐rate differential (i′ − i) between these two dates, which is the slope of the curve in Figure A1.
The ‘beauty’ of the FORE/PPP model is that it has an explanation of exchange‐rate volatility, which may be independent of anything that is observed at the present. The rational expectations assumption is that at time t < T people know the expectation of log N(T), based upon their knowledge of (a) the stationary real exchange rate C, (b) the rationally expected relative price levels, p′(T)/p(T), (c) how long it will take for N(t) to attain its equilibrium value N(T), and (d) the average nominal interest‐rate differential (i′ − i) during the interval from t to T. The trajectory is from log N(t) to log N(T). The current nominal exchange rate N(t) is obtained by moving backwards from the fixed point N(T). The exchange rate appreciates at rate (i′ − i) to log N(T). Since the exchange rate remains steady at the equilibrium log N(T), then nominal interest rates must be equal from T on.
(p.233) The causes of variations in the nominal exchange rate are easily ‘explained’ in this model. The current exchange rate varies because either the rationally expected fixed point log N(T) = C + log P′(T)/P(T) = C + P(m′(T))/P(m(T)) varies, or because the rationally expected slope, average interest rate differential (i′ − i), varies. A temporary monetary change just changes the slope; and a permanent change in monetary policy changes both the fixed point and the slope. There can be considerable variations in nominal exchange rates even though current policies have not changed, as long as they are rationally expected to change.^{4}
An example of this forward‐looking rational expectations process will prepare the way for an evaluation of empirical testing. Suppose that initially the exchange rate N(t) is equal to its equilibrium value N(T) = a, which requires that the interest‐rate differential equal zero. This is curve aa. Let there be a rationally expected permanent rise in the relative foreign to domestic money supplies, which will occur some time in the future. Consider both the fixed point at time T and the slope, representing the average rationally expected interest‐rate differential during the interval (t, T). The rationally expected change in money stocks is rationally expected to change the relative price levels. Since the real exchange rate is assumed to be stationary, the rationally expected fixed‐point changes from log N(T) = a to log N(T) = d. The rationally expected steady‐state value of the currency will appreciate by ad per cent. This is the intercept effect.
Moreover, the effect of the rationally expected rise in foreign money per unit of output relative to the domestic money is to lower the foreign less domestic interest rate during the period when prices are sticky. Therefore, the rationally expected average foreign less domestic interest rate differential, the average slope, is now negative. Since the rationally expected average domestic interest rate exceeds the foreign rate, there is a capital inflow and the domestic currency immediately appreciates above its steady‐state value. The net effect is to move the trajectory from aa to cd. Both the slope and intercept are changed. This has several important implications.
(1) The nominal exchange rate will appreciate immediately as a result of rationally anticipated changes in relative money stocks (p.234) which will occur sometime in the future. (2) The initial appreciation ac exceeds the steady‐state appreciation ad, because of the temporary decline in the foreign less domestic interest rate (decline in slope) during the period of price stickiness. The inequality ac > ad is called ‘overshooting’. (3) The expected change in relative price levels is produced by rationally expected permanent changes in money per unit of output. Thus nominal exchange‐rate volatility is explained by rationally anticipated monetary policies either now or sometime in the future. (4) A rationally expected temporary change in relative money supplies will not change the steady‐state value N(T) but will change the average interest rates during the interval. This changes the slope of the trajectory. Hence the current value of the nominal exchange rate N(t) will change because there is a rationally expected temporary change in interest rates sometime in the future. That is, the exchange market reacts at present to anticipated changes in monetary policy. (5) The moral of the story, according to the proponents of this theory, is that there can be considerable exchange‐rate volatility even though there are very few current changes in monetary magnitudes, if future policies are rationally expected to be volatile. Therefore, credible stable money‐supply policies in the future will lead to stable nominal exchange rates^{5} in the present. Volatility in nominal exchange rates is attributed to volatility in rationally expected money‐supply policies in the future. Unless this hypothesis is quantified, it can easily become a tautology. The major issue is whether this forward‐looking rational‐expectations monetary view is consistent with the evidence. Does it have any explanatory power?
3. The FORE/PPP Models Are not Consistent With the Evidence
Economists have been disappointed to find that the models based upon equations (A.3)–(A.5) lack explanatory power. Empirical studies have shown that both the structural and reduced‐form equations are inconsistent with the evidence. Section 3.1 shows why we reject the (Purchasing Power Parity) hypothesis that the real (p.235) exchange rate has been stationary during the period 1975.1–1992.2. Section 3.2 explains why the FORE hypothesis (uncovered interest‐rate parity with Rational Expectations) is rejected. Moreover, we show in Section 3.3 the basis for rejecting the portfolio models, which contain an endogenous risk premium based upon relative asset supplies, adjoined to the Rational Expectations hypothesis. That is, one cannot explain the failure of the FORE hypothesis by invoking a risk premium which is a function of the ratio of domestic to foreign assets. The Sections 3.1, 3.2, and 3.3 concern the structural equations. Section 3.4 presents evidence why the reduced‐form equations, relating monetary variables to the nominal exchange rate, lack explanatory power. This corpus of evidence explains the disillusionment of economists with the state of the art theories. Our presentation is consistent with published results, so we may be terse and intuitive.
3.1 The Stationarity of the Real Exchange Rate Is Rejected
In this section we show that one may reject the hypothesis that there has been a fixed steady‐state real exchange rate C to which the actual real exchange rate gravitates as price flexibility increases (equation A.4), during the period 1975.1–1992.2. In so far as R(t) converges on average to the constant C, variations in the equilibrium nominal exchange rate (fixed point in Figure A1) are closely tied to variations in relative prices. The real exchange rate will be stationary if b in equation A.4 is significantly different from unity. If b is not significantly different from unity, then the real exchange rate has a unit root, is integrated of order one I(1), and is not stationary. The non‐stationarity of the real exchange rate rejects the Purchasing Power Parity Hypothesis.
Table A1 presents the adjusted Dickey–Fuller (ADF) statistics for the real effective (trade‐weighted) exchange rate for seven currencies, based upon quarterly data 1975.1–1992.2. The ADF is the t‐statistic for 1 − b. For the seven currencies, 1 − b is not significantly different from zero. Hence b is not significantly different from unity. The real effective exchange rate has a unit root, and we reject the hypothesis that the real exchange rate is stationary. This rejects the PPP hypothesis during the period considered. Although the levels R are not stationary, the first differences (Dlog R) are stationary.
Table A1 Adjusted Dickey–Fuller Statistics: Unit Root Tests for the Stationarity of the Real Effective Exchange Rate UROOT (C,1) Quarterly 1975.2–1992.2
Country 
ADF(C,1) 

United States 
−1.219 
United Kingdom 
−1.6745 
Canada 
−1.6638 
Germany 
−0.7072 
France 
−2.2817 
Japan 
−1.7796 
Italy 
−2.5035 
Data: from data bank of Federal Reserve Bank of St Louis. Significance levels denoted by asterisk (MacKinnon values, 5% = −2.9; 10% =−2.58). ADF (constant, lag)
In the earlier chapters we explained what are the fundamental determinants (vector Z) of the steady‐state real exchange rate, denoted by R(Z). Vector Z consists of the exogenous disturbances: social thrift, the productivity of capital, the terms of trade, and the world real rate of interest, depending upon the size of the economy. The real exchange rate is not stationary because variables in Z are not stationary. We explained the historical evolution of the real exchange rate in terms of the observed values of Z. However, it is impossible to predict the long‐run evolution of Z, which has a unit root, because the variance increases with the length of the forecasting horizon.
3.2 The Fisher Open/rational‐Expectations Hypothesis
Equation (A.3) the uncovered interest‐rate parity with rational expectations (Fisher Open Rational Expectations, FORE) is rejected for every major pair of currencies. The percentage change in the nominal exchange rate from t − 1 to t, Dlog N = log N(t) − log N(t − 1), is unrelated to the nominal interest‐rate differential i′(t − 1) − i(t − 1) at initial time t−1. The interest‐rate differential is (p.237) equal to the forward premium on the domestic currency^{6} at time t − 1. Table A2 presents estimates of β, and the 95 per cent confidence limits for coefficient b, in equation (A.3a) above. This is based upon daily observations at non‐overlapping monthly intervals, during the period 1981.05–1989.09. Figures 2.1 and 2.2 in Chapter 2 plot the actual rate of appreciation of the currency Dlog N on the vertical axis against the forward premium i′(t − 1) − i(t − 1) on the horizontal axis for the the $US–$Canadian and for $US–DM. A regression line is drawn for the reader's convenience. The FORE hypothesis is that the observations lie along a 45‐degree line (β = 1) plus an iid term with a zero expectation. We observe that there is no relation between the two variables. The OLS estimate of β is b in the first column, and the 95 per cent confidence limits in the second column. Table A2 shows that for the major currencies we may reject the FORE hypothesis that the slope is unity and not zero (see column 2). The nominal value of the exchange rate does not appreciate at a rate equal to the foreign less domestic interest rate at time t − 1. The FORE hypothesis is also rejected for the major currencies at horizons of 1, 3, 6, and 12 months (Longworth, Boothe, and Clinton).
3.3 Portfolio Models With Endogenous Risk Premium
Equation A.3 presupposes that there is perfect capital mobility and perfect asset substitutability; hence there is no risk premium. The portfolio‐balance models argue that there is an endogenous risk premium which depends upon the ratio of foreign to domestic assets. In the typical investor's portfolio the greater the fraction of foreign‐currency denominated assets relative to assets denominated in the domestic currency, the greater must be the expected return on foreign relative to domestic assets. Since we are drawing upon a Bank of Canada study, let the two countries be Canada and the US (world). In the FORE context, let B represent Canadian currency outside assets, B′ represents outside assets in US currency, and (p.238)
Table A2 Test of Hypothesis Concerning One‐Month Nominal Exchange‐Rate Changes and Initial One‐Month Nominal Interest‐Rate Differentials 1981.05–1989.08
b(s) 
b± t(.05)s 
adj. R‐square 


Britain 
− 5.43 (1.478) 
[− 2.5, − 8.36] 
0.11 
Canada 
− .2947 (.63) 
[.96, − 1.54] 
− 0.008 
France 
.826 (.58) 
[1.98,−.32] 
0.01 
Japan 
− 2.685 (.938) 
[− .82, − 4.55] 
0.068 
Switz. 
− .678 (1.469) 
[2.24, − 3.59] 
− 0.008 
W. Germany 
− 2.97 (2.43) 
[1.85, − 7.79] 
0.005 
Notes: Column 1 is the estimate b and in parentheses, its standard error. Column 2 is the 95 per cent confidence interval for β. Column 3 shows that the current interest‐rate differential (forward premium or discount) has no informational value concerning the subsequent evolution of the exchange rate
The Canadian–US interest rate (i−i′) differential is measured by the forward premium on the $US. Three measures of the endogenous (p.239) risk premium are used, based upon the portfolio theory. Regression equation (A.9c) is obtained.^{7} B = Canadian federal debt; W = world wealth, in Canadian dollars; Wc = Canadian wealth. The period is 1971.01–1982.11.
The portfolio/MRE hypothesis is that in equation (A.9b) the coefficient of the Canadian–US interest rate differential is unity, and the coefficient of the ratio of Canadian to US denominated assets is positive.^{8}
The results reject the portfolio version of the FORE hypothesis. (i) We may reject the hypothesis that the coefficient of the interest‐rate differential is unity, the foundation of the FORE hypothesis. (ii) We may reject the hypothesis that the ratios of outside assets are significantly positive.
The conclusions are cogently stated by the authors of the Bank of Canada study:
The MRE hypothesis arbitrarily assumes that the market always knows the objective expectation of a distribution, but it contains no theory to explain the speed of convergence. As we have shown, the (p.240) Muth rational expectations hypothesis (MRE), that people know the objective distributions of the stochastic variables, is rejected in markets for foreign‐exchange and financial instruments. This implies that short‐term capital flows are not reflections of rational expectations, but are noise. Figures 2.1 and 2.2 in Chapter 2 show that the difference in interest rates is small, but there are large variations in the exchange rate which are unrelated to the short‐term interest‐rate differentials. In the chapters above, we used the Asymptotically Rational Expectations hypothesis^{9} (ARE), whereby the market uses all available information efficiently, and the speed of convergence to MRE depends upon the nature of the exogenous disturbances. When the latter are not stationary (i.e., have unit roots, see Table A1), the speed of convergence to MRE is slow. If the disturbances are stationary, the limit point of ARE is MRE.Rational expectations models generally do not provide statistically significant evidence that differences in expected rates of return on Canadian and US dollar short‐term instruments are dependent on stocks of Canadian and US government bonds, as they would if such assets were imperfect substitutes. This implies that there is no evidence of a variable risk premium depending on asset stocks. Since recent empirical work has strongly rejected the joint hypothesis of rational expectations and a constant risk premium, our interpretation of the evidence is that there is likely a failure of the rational expectations hypothesis; indeed, it seems that expectations can often be of an adaptive or extrapolative nature. Longworth et al., 1983: 4–5).
The results of this section can be summarized with a quotation from the study by the Reserve Bank of Australia (Blundell‐Wignall et al.) cited in Chapter 3 above.
No economic hypothesis has been rejected more decisively, over more time periods, and for more countries than UIP [uncovered interest‐rate parity with rational expectations] . . . Many researchers interpret rejection of UIP as evidence of a time varying risk premium, while still maintaining the assumption of rational expectations. However, as the risk premium is then typically defined to be the deviation from UIP, this interpretation is merely a tautology.
3.4 Reduced‐Form Equations: Effects of Monetary Policies
We have explained why the structural equations of the class of models discussed in Part 2 are inconsistent with the evidence. We now explain why the implied reduced form of the structural equations is also inconsistent with the evidence.
The crucial variable in explaining the variation in nominal exchange rates is the rationally expected inflation differential. The value of the expected inflation differential is then associated with expected differentials in the growth of money per unit of output: the expected growth of money per unit of output abroad EDlog (p.241) (M′/y′), which determines the foreign rate of inflation, less the expected growth of money per unit of output at home EDlog(M/y), which determines the domestic rate of inflation. The rationally expected inflation differential is equal to E[Dlog(M′/y′) − Dlog(M/y)]. Reduced‐form equation (A.10) is implied by^{10} the structural equations in Part 2.
Variations in the current nominal exchange rate are linked to rationally expected differentials in money growth per unit of output in the future. If these forward‐looking rational expectations hypotheses are to have scientific content (be meaningful propositions), one must give empirical, non‐tautological content to what is meant by rationally expected differentials in money growth per unit of output in the future. Some authors arbitrarily assume that money growth is a martingale such that E(Dlog M(t)) = Dlog M(t − 1). Others assume that expected money growth is a weighted average of past rates of growth $\sum _{0}^{h}\text{}a(t\text{}i)\text{}\text{D}\text{}(\text{log}\text{}M(t\text{}i))$, which contains the martingale as a special case. In Table A.3 below, we consider a general version of equation (A.10), where the regressors are current and lagged values of the growth rate of money at home less that abroad x(t − i), and the growth of real income at home less that abroad w(t). The rationally expected rates of money growth $\text{E}(\text{D}\text{log}\text{}M/M\prime )\text{}=\text{}\sum _{0}^{h}\text{}a(t\text{}i)\text{}x(t\text{}i)$.
This is statistical equation (A.11), which is the implication of theoretical equation (A.10)
(p.242) The statistical hypotheses implied by this set of models are as follows. (1) Coefficients a sum to minus unity. Exchange‐rate depreciation is produced by differential money growth. (2) Coefficient b is positive. Differential real growth appreciates the currency. (3) The ‘overshooting’ hypothesis, discussed in Part 2, is that negative coefficient a(t) is greater than minus one in absolute value, since prices are assumed to be sticky in the short run.
Table A.3, based upon quarterly data, considers several exchange rates. The value of: the Canadian dollar, the DM, the French franc, the pound sterling, the Italian lira, and the Japanese yen, relative to the $US during the period 1973.2–1989.1. Thus the dependent variable is the percentage change in the nominal value of these six currencies relative to the $US. In each cell is the value of the regression coefficient a(t − i) or b, and in parentheses the t‐value. For each country, two regressions were performed. In the first case, just the current rate of relative money growth x(t) was used: the martingale hypothesis. In the second case, current and lagged values of x(t − i) were used. Table A.3 presents estimates^{11} of the coefficients in equation (A.11).
The conclusions drawn from Table A.3 are as follows. (a) The evidence for five out of the six exchange rates (the Canadian dollar, the DM, the French franc, the pound sterling, and the Japanese yen) rejects the monetary hypotheses completely. (1) There is no explanatory power to the monetary models that imply equation (A.11). The adjusted R‐squares are negligible, ranging from 0.000 to 0.24. (2.1) In the martingale case, where the contemporaneous relative money growth is used, there is not only no evidence of overshooting but the relative monetary variable x(0) is not significantly different from zero. (2.2) Where current and lagged relative rates of monetary growth are regressors, one can reject the hypothesis that the sum of the coefficients a(t − i) is minus one (using an F‐test). Moreover, this sum is not significantly different from zero. (2.3) The coefficient for relative real income growth b(t) is not positive, as hypothesized. (b) The evidence for the Italian lira is (1) consistent with the monetary aspect of the hypothesis. Relative money growth depreciates the lira. (2) The relative growth of real income is not a significant variable. (3) The adjusted R‐square is only 0.22.
Table A3 Estimates of the Relation Between the Percentage Appreciation of the Currency and Relative Rates of Money Growth X, and Relative Rate of Real Income Growth W, Sample Period Is 1973.2–1989.1. The T‐Statistic Is in Parentheses
x(0) 
x(1) 
x(2) 
x(3) 
x(4) 
w(0) 
adj‐R ^{2} 


Canada 
− .068 
.322 
.16 

(− .71) 
(.18) 

− .154 
− .178 
.224 
.211 
.172 
− .14 
.24 

(− 1.5) 
(− 1.6) 
(2.1) 
(1.9) 
(1.6) 
(− .8) 

DM 
− .325 
− .227 
.05 

(− .77) 
(− .46) 

− .37 
− .19 
.13 
.16 
.067 
− .25 
.00 

(− .83) 
(− .42) 
(.29) 
(.35) 
(.15) 
(− .49) 

France 
− .24 
− .15 
.18 

(− .9) 
(− .25) 

− .28 
− .04 
− .05 
.069 
− .036 
.187 
.00 

(− .92) 
(− .13) 
(− .17) 
(.22) 
(.12) 
(.66) 

UK 
.256 
− .117 
.008 

(.71) 
(− .32) 

.297 
− .62 
− .037 
.156 
.05 
− .067 
.00 

(.78) 
(− 1.7) 
(− .1) 
(.42) 
(.14) 
(− .18) 

Italy 
− .76 
.42 
.22 

(− 2.6) 
(.88) 

− .79 
− .16 
− .05 
.2 
.22 
.39 
.17 

(− 2.5) 
(.53) 
(− .17) 
(.66) 
(.7) 
(.78) 

Japan 
− .16 
− .55 
.09 

(− .49) 
(.94) 

− .19 
− .47 
− .45 
.18 
− .2 
− .16 
.098 

(− .57) 
(− 1.4) 
(− 1.3) 
(.56) 
(− .65) 
(.27) 
The rejection of both the structural equations (stationarity of the real exchange rate, uncovered interest‐rate parity/Muth Rational Expectations, with or without an endogenous risk premium) and the reduced‐form equation are the reasons why economists who have examined the evidence are disillusioned with the state of the art theories. More complex models which continue to be based upon these structural equations are unlikely to succeed in explaining the empirical phenomena.
(p.244) 4. Intertemporal Optimization Models
The authors of the Representative Agent Intertemporal Optimization Model (RAIOM)^{12} argue that this model, which now dominates the theoretical literature, should supplant the MDF model as the dominant paradigm in international finance to be used by central banks, finance ministries, and international economic agencies. We first present the basic logic of this model as an explanation of the current account and real exchange rate. Second, we show how the RAIOM responds to the questions in Section 1 above. Then we show that this model lacks explanatory power and is not consistent with the evidence. We share the views of Dornbusch and Frankel and Krugman that the RAIOM is not a promising line of approach.
4.1 The Logic of the Model
We present the basic model without the unnecessary complexities so that its strengths and weaknesses are apparent. In the MDF models, the real exchange rate adjusts the current account to independent saving‐less‐investment decisions made by households, government, and firms. The RAIOM rejects this approach. Instead, the RAIOM assumes that there is a representative agent who simultaneously makes the saving–investment decision without a market mechanism to reconcile the different decisions of savers and investors. The agent selects the profile of consumption over time, c(t), to maximize a time‐separable utility function u(c) over an infinite horizon. The discount rate is δ. This is equation (A.12). In the single‐good model, there is an intertemporal budget constraint (IBC) that the present value of the terminal debt be zero. There is no loss of generality if we consider a two‐period model,^{13} the present time t and the future time t + 1. Production or GDP is y, the interest rate is r, and initial net foreign assets is A(t). Insofar as there are no terminal assets or debt, the IBC is equation (A.13).
There is no theoretical reason to select one utility function rather than another. The authors arbitrarily select an isoelastic time‐separable utility function. The authors cannot justify selecting either that function or the degree of relative risk aversion (elasticity of intertemporal substitution).^{14} The logic of the model is clear if we select a logarithmic function u[c(t)] = log c(t).
The implied optimal consumption, c(t), is given by equation (A.14). The present value of life‐time GDP is Y ^{*}(t) in equation (A.14a), and one can call β [Y ^{*}(t) + A(t)] in equation (A.14b) permanent income, Y _{p}(t). Parameter β (defined in equation (A.14c) is positively related to the discount rate.
In the analysis above, consumption, c(t), is social consumption: government consumption, g(t), plus private consumption, c′(t). No distinction is made between the public and private sectors. Often a dichotomy is made between private and public consumption. In that case, the current account equation (A.15) can be written as equation (A.15a).^{15} From the optimization, private consumption, (p.246) c′(t), is equal to permanent income less permanent government consumption, Y _{p}(t) − G _{p}(t).
Unlike the MFD models, there is no real exchange rate in the current account equation. There is no such a thing as a current account deficit owing to an overvalued exchange rate. The reason for this ‘anti‐conventional wisdom’ is that there are no independent saving and investment equations. The nation is just a representative consumer who can borrow and lend at a given world interest rate.
In order to include an exchange rate, it is necessary to introduce two sectors: a tradable and a non‐tradable goods sector. Then, the real exchange rate is positively related to the ratio p(t) of the price of non‐tradable goods, p _{n}(t), to the price of tradable goods, p _{T}(t)—equation (A.16). In this type of model, one can refer to the relative price of non‐tradables as the real exchange rate.^{16}
The representative agent is assumed to have a Cobb–Douglas utility function, so that the optimal pattern of consumption is such that the ratio of expenditures on consumption of tradables, p _{T}(t)c _{T}(t), to non‐tradables, p _{n}(t)c _{n}(t), is constant 1/α based on the utility function. This implies: (p.247)
4.2 The Empirical Measures and Tests of the Predictions of the RAIOM
The RAIOM asserts that agents make their current decisions by looking forward to future developments and have rational expectations. The rational expectations hypothesis is that agents agree what is the correct model^{18} and know the distribution functions of the exogenous variables. This is contrasted invidiously with the (p.248) conventional wisdom, which generally^{19} emphasizes current variables. Hence, the concepts of ‘permanent income’, ‘permanent government spending’, and ‘anticipated productivity growth’ in the tradable sector are the essence of the RAIOM. To avoid tautological statements concerning why the current account changes from surplus to deficit, or why the real value of the currency rises and falls, there must be objective measures of what is ‘permanent’ or ‘anticipated’. We first show how the authors of the RAIOM measure these crucial variables. It will be clear that there is nothing forward‐looking about these measures, and that they are arbitrary methods of extrapolation similar to adaptive expectations. Thus, the empirical implementation of the RAIOM is subjective, and is no more forward‐looking than adaptive expectations.
Obstfeld and Rogoff (1995)^{20} measure permanent income as equation (A.19), which is proportional to the expected present value of the future income stream, where index i goes from the present time, t, to infinity. The expectation of future income is given by equation (A.20), which implies equation (A.20a). The expected growth rate of real income is (ρ − 1). Substitute (A.20a) into (A.19) and derive equation (A.21) as ‘permanent income’, where the interest rate must exceed the growth rate.
(p.249) The current account equation (A.15a), using equation (A.21), becomes:
Therefore, all of the explanation must be in the second term, the difference between government expenditure and its permanent level, g(t) − G _{p}(t). To form an estimate of permanent government spending, Obstfeld and Rogoff use ‘an autoregressive forecasting model of detrended government spending’ (1995: fn. 57 in sect. 4.2.2).
The study by Ahmed (1986)^{21} regressed the trade balance, B(t), on the level of ‘permanent government spending’, G _{p}(t), and the difference between the actual and permanent levels [g(t) − G _{p} (t)]—equation (A.23). The hypothesis is that coefficient a of ‘temporary deviations of government spending’ is negative and coefficient b of permanent government expenditures is zero. This conforms to equation (A.15a).
Ahmed found that he could not reject the null hypothesis. Obstfeld and Rogoff recognize that Ahmed's tests were incorrect and unable to differentiate between the RAIOM and the conventional wisdom. They run the regression of the current account on the deviation [g(t) − G _{p}(t)] and the actual level of government spending, g(t): (p.250)
In his attempt to see if the RAIOM can explain the Japanese real exchange rate, Rogoff^{23} tests the following proposition: ‘whereas perfectly anticipated shocks do not lead to changes in the real exchange rate, unanticipated shocks do.’ This is based upon equations (A.17) and (A.18) above, in the following way. From (A.17) derive (A.25). The consumption of tradables is based upon permanent income in tradables. Its change results from unanticipated changes in the productivity of producing traded goods. The unanticipated component is random. Therefore the first term [log c _{T}(t) − log c _{T}(t − 1)] in equation (A.25) is random.
To separate the unanticipated component from the anticipated component of productivity shocks, he uses a Box–Jenkins analysis. He states that for ‘both oil and manufacturing productivity, a simple (1,1,0) process fits the data fairly well. The residuals from the regression were used to proxy for unanticipated changes in lifetime traded goods income’ (pp. 24–5).
(p.251) How forward‐looking is this procedure such that it is rational rather than adaptive expectations? What is its theoretical justification? Peter Kennedy (1985: p. 205) describes the Box—Jenkins procedure as follows: ‘The main competitor to econometric models for forecasting purposes is time‐series analysis, also known as Box—Jenkins analysis. Rather than making use of explanatory variables to produce forecasts, the key to forecasting with econometric models, time‐series models rely only on the past behaviour of the variable predicted. Thus it is in essence no more than a sophisticated method of extrapolation.’
Given that the measures of anticipation are just extrapolations without theory, what are Rogoff's results? He regresses the change in the real exchange rate on his measures of unanticipated changes in productivity and the price of oil, which should appreciate the currency, and government expenditures, which decrease the consumption of non‐traded goods and should also appreciate the currency. The results (Rogoff 1992: p. 25) are most disappointing. First, Rogoff (1992: fig. 2) finds that a rise in the ratio of Japanese government consumption to GNP does not appreciate the real value of the yen. It seems to depreciate it, contrary to the RAIOM. Second, for the full sample period, ‘The coefficient on the innovation to the world real price of oil is of the correct sign and is highly significant . . . However, neither the productivity differential innovation or government consumption differential . . . appear important.’ For the latter half of the sample period, 1981(1)–1990(3), ‘Despite the apparent high correlation between oil and the real exchange rate . . . the coefficient of the oil shock loses its statistical significance’.
The conclusions so far are the following. First, the measures of anticipated or permanent variables are based upon arbitrary assumptions and are just sophisticated methods of extrapolation from past values of these same variables. Despite the use of the term ‘rational expectations’, no economic theory is used in their construction. They are no different from adaptive expectations. Second, since these measures are arbitrary, it is difficult for independent researchers to apply the RAIOM to the analysis of other bilateral exchange rates, because they are unable to state that the measures used will be the same as those used by the advocates of the RAIOM. Third, even using their own measures of unanticipated variables, the econometric tests reject their hypotheses.
(p.252) 4.3 An Evaluation of the Answers the RAIOM Gives to the Questions
Initially we posed the questions to be answered by a scientific theory. Let us evaluate how the RAIOM answers these questions in a way different from the ‘conventional wisdom’ and the validity of those answers.
The RAIOM cannot explain the trends in either the current account or the real exchange rate, because it claims that both are random walks. The expected change in permanent income is zero, hence the expected change in the real exchange rate is zero.
Suppose that we are given the expected productivity of capital and government expenditures, either at the beginning of the Reagan period for the USA or, in the case of Germany, as the result of unification. What does the RAIOM predict compared with the Mundell—Fleming—Dornbusch (MFD) model?
The MFD model claims that there will be current account deficits and an appreciation of the real exchange rate owing in large measure to government budget deficits. These deficits are not sustainable, and the real exchange rate is overvalued. There is misalignment. The RAIOM denies this and claims that current account deficits are the result of deviations of the current level of government spending from its permanent level. There may have been an unanticipated rise in government expenditures at the beginning of the Reagan period, producing a current account deficit. But since this deviation is noise with a zero expectation, why should it persist? A similar argument applies to the current account resulting from German unification.
According to the RAIOM any fiscal policy is sustainable. It will affect only permanent government expenditures and hence not the current account. There is no such thing as an overvalued real exchange rate that produces an unsustainable current account and growth of the foreign debt. The foreign debt is not a problem, because it is the result of an intertemporal optimization with an intertemporal budget constraint.
The RAIOM cannot answer the questions posed at the beginning of this appendix. It is difficult to give this model empirical content since its key variables are not objectively measurable. When the authors attempt to test the model, it is rejected. The failure of the model stems from its basic theoretical structure. Obstfeld and (p.253) Rogoff derive an equation for the steady‐state debt as a fraction of GDP. Using ‘reasonable’ estimates for the key parameters they conclude (1995: end of sect. 3.1.1) that the steady‐state foreign debt will be 2,000 per cent of GDP and the economy's trade balance will be 80 per cent of GDP. They are aware of the fact that these implications of the model are incredible. This is a devastating result.
The main ‘positive’ contribution of the RAIOM is that they claim that the log of the real exchange rate should follow a random walk. We share the reaction of Dornbusch and Frankel (1988: 162–3): ‘The ultimate extrapolation of the argument occurs when the modern macroeconomist derives pride from his failure to explain any movement . . . in . . . the real exchange rate . . . He then goes on to “test” his theory “empirically” by seeing whether he can statistically reject the hypothesis that the real exchange rate follows a random walk. Rather than being humbled or embarrassed about his statistical failure to explain any movement in the macroeconomic variable that he has been investigating, he proudly proclaims it as confirming his theory on the grounds that the theory did not explain any movement in the variable.’
We have explained why the RAIOM is not a satisfactory approach and cannot be recommended as a substitute for the ‘conventional wisdom’. An alternative approach is called for.
5. Conclusions
First: we posed some of the most important questions that a theory should answer. Second: we examined the logical structure of the contemporary models of international finance. It is well known among the empirical researchers that these models are inconsistent with the evidence. The deficiencies of these models are not easily rectifiable. For example, Meese and Rose (1989) concluded their study as follows:
We have applied a battery of parametric and non‐parametric techniques to five structural exchange rate models in an attempt to account for potentially important sources of non‐linearities in exchange rate models. However, our results are quite negative. There is no evidence that time deformation is responsible for significant non‐linearities in exchange rate models. There is also little evidence that inappropriate transformations of fundamentals are responsible for the poor performance of the models considered. We conclude that accounting for non‐linearities in exchange rate models does not (p.254) appear to be a promising way to improve our ability to explain currency movements between major OECD countries. (1989: 36)
That is why economists who have examined the evidence, such as De Grauwe (quoted at the beginning of the chapter) are unable to accept the state of the art models as scientific explanations. The rejection stems from the facts that: (1) The real exchange rate is not stationary; (2) the monetary explanations of nominal exchange‐rate variation have no explanatory power; (3) the currently popular RAIOM with MRE have yet to demonstrate their improvements over their predecessors as positive economics, i.e., as offering explanations of evidence. The NATREX models continue where De Grauwe stopped and attempt to provide an explanation of the fundamental determinants of real exchange rates.
Notes:
(1) Below, we discuss the portfolio balance theories which imply that assets are not perfect substitutes.
(2) The solution of (A.4) is that the expected value of the deviation [R(t) − C] = [R(0) − C](b)^{t}. It half of the deviation has been reduced at time T, then time T = log 0.5/log b. If b = 1, equation (A.4) has a unit root, the denominator is zero, and convergence never occurs.
(3) Since we are summing the rationally expected percentage changes, the error terms z′ are zero.
(4) This is the so‐called peso problem: the market is reaching rationally to an expected policy change.
(5) A large literature concerning what are credible policies has developed from this approach.
(6) The covered interest‐rate parity always holds for the major currencies. The forward premium on the domestic currency is always equal to the foreign less domestic interest rate in the Euro market. We measure the interest rate differential i′(t − 1) − i(t − 1) as the forward premium on the domestic currency, on a contract at time t − 1 maturing at time t. The model, however, in equation (A.3) concerns the uncovered interest‐rate parity/rational expectations.
(8) The Bank of Canada study used as the exchange rate, the price of foreign exchange S(t) = $C/$US and s=logS. A rise in S is a depreciation of the $C. Their s = log S = − log N in our notation. Hence, we reverse the signs in their regressions.
(9) See Chow 1989 for empirical tests which reject the MRE. See Stein 1992 and Econ. Record 1992 for the development of the ARE, and Harrison 1992 for tests of this hypothesis.
(10) The derivation of (A.10) is obtained in several ways. First: if the real exchange rate is stationary, equation (A.2) states that the nominal exchange rate will move with relative prices. Equation (A.5) states that relative prices depend upon money per unit of output. Second: from (A.6) the average proportionate rate of change of the exchange rate is equal to the average expected nominal interest‐rate differential. The nominal interest rate is equal to a relatively constant real interest rate plus the rationally anticipated rate of inflation. Hence the average proportionate rate of change of the exchange rate is tied to the rationally expected differential in rates of money growth per unit of output.
(11) The data source is the OECD and the table was prepared by Chi‐Young Song.
(12) The basic references are Obstfeld and Rogoff (1995) and Rogoff (1992). I follow these two papers for the exposition of the model and empirical results. My interpretation of their contribution differs from theirs.
(13) A dynamic programming approach has this logic. The use of many periods is an unnecessary complexity.
(14) The degree of relative risk aversion determines whether a rise in the expected return on capital raises or lowers saving (see Merton 1990: 115–16). Hence, the arbitrary choice of the degree of relative risk aversion introduces another arbitrary assumption into their model.
(15) In the budget constraint equation (A.13), social consumption c is private plus government consumption. Hence, private consumption is c − g, and the resources available to the consumer are y − g. Then equation (A.15a) follows from the optimization.
(16) The real exchange rate (a rise is an appreciation) is R = Np/p′, where nominal exchange rate N is foreign currency/domestic currency (a rise is an appreciation), p is the domestic GDP deflator, and p′ is the foreign GDP deflator. Let the deflators be geometric averages of the prices of traded goods (subscript T) and non‐traded goods (subscript n). Then R = N[(p _{T})^{1 − a}(p _{n})^{a}]/[p′_{T})^{1 − a′}(p′_{n})^{a′}]. The weights are a at home and a′ abroad. Let the ratio of the prices of non‐traded to traded goods be p at home and p′ abroad. Then R = (Np _{T}/p′_{T})p ^{a}/p′^{a′}. Using the law of one price for traded goods, the first term is unity and R = p ^{a}/p′^{a′}. This is why the real exchange rate is positively related to the relative price of non‐tradables.
(17) The constraint looks just like equation (A.13) except that it only involves traded goods. Hence, the optimal consumption of traded goods follows the same logic as before.
(18) If the rational expectations hypothesis was correct, why is there such a disagreement concerning the correct model in international finance?
(19) The Dornbusch, but not Mundell/Fleming, model does contain the uncovered interest rate parity/rational expectations equation. Hence it does have anticipations of future monetary policy as a crucial variable. We know that the hypothesis of uncovered interest rate parity/rational expectations is inconsistent with the evidence.
(20) Equations (A.19), (A.20), and (A.21) in the text correspond to Obstfeld and Rogoff (1995) equations (48), (47), and (49), respectively.
(21) I am following the exposition in Obstfeld and Rogoff (1995: sect. 4.2.2). I always follow their exposition faithfully but use a different notation.
(22) Obstfeld and Rogoff (1995: last para. in sect. 4.2.2). In section 4.2.3 they discuss other statistical manipulations and indicate that they end up regressing the current account on its lagged values. To find that the current account is related to its lagged values cannot be construed as evidence in favour of the anti‐conventional wisdom, the RAIOM.