# What Do We Know About the Long-Run Real Exchange Rate?

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Cletus C. Coughtin and Kees Koedjjk Cletus a Coughlin is a research officer at the Federal Reserve Bank of St. Louis. Kees Koedijk is a professor of economics at Erasmus University, Rotteitam, Thomas A. Pollmann provided research assistance, What Do We Know About the Long-Run Real Exchange Rate? REAL EXCHANGE rate is defined as the country is affected adversely by an appreciating foreign currency price of a unit of domestic (depreciating) real exchange rate.’ currency (that is, the nominal exchange rate) multiplied by the ratio of the domestic to the Despite much research, however, there is no foreign price level. The real exchange rate has consensus on which variables cause changes in been at the center of economic policy discus- the real exchange rate. Like any asset price, sions in the 1980s for at least two reasons. real exchange rates are related to the determi- First, this relative price has been more variable nants of the relevant supply and demand curves in the floating-rate period than in the preceding now and in the future.’ With real exchange era of fixed (nominal) exchange rates.’ Second, rates, the relevant determinants are those affec- this price is related to international trade pat- ting the relative supplies and demands for the terns because the competitive position of an in- currencies of two countries. Claims have been dividual exporting (import-competing) firm in a made, however, that the real exchange rates 1 See Frankel and Meese (1987) and Dornbusch (1989) for ogenous rather than endogenous variable, For example, a surveys of this literature. As noted by Dornbusch, the in- standard assertion is that a depreciating dollar boosts U.S. creased variability and lack of knowledge have contributed manufacturing output. A declining dollar is expected to to divergent policy recommendations, which include a raise the dollar prices of U.S. imports and lower the return to some form of a managed exchange-rate system, foreign currency prices of U.S. exports. Consequently, taxes on foreign exchange transactions as well as doing consumption and production of U.S. exports and import- nothing. competing goods would rise, This analysis is faulty ‘The U.S. dollar has been at the center of the controversy, because changes in the value of the dollar are not in- with the dollar allegedly being undervalued in the late dependent of U.S. industrial developments and, in fact, 1970s/early l9BOs and overvalued in the mid-1980s. Dur- can be the direct result of industrial developments. For ex- ing the period of undervaluation, U.S. tradeable goods in- ample, an economic policy that boosts productive capacity dustries were stimulated and induced to overexpand. The can generate a positive relationship between the value of costs of this alleged overexpansion were exacerbated by the dollar and U.S. manufacturing output. Details on this the subsequent overvaluation, which resulted in layoffs, argument can be found in Tatom (1988). plant closings and bankruptcies in these same industries, ‘This elementary principle is ignored when the exchange rate in macroeconomic settings is treated as an ex-

often differ substantially from levels consistent rate, q, is defined as follows: with the underlying economic fundamentals and (1) q = that these differences persist for long periods. where e is the foreign currency price of a unit A primary goal of our research is to provide of domestic currency, p is the domestic price an elementary understanding of the major theo- level as measured by the consumer price index retical approaches to the determination of long- and p~is the similarly measured foreign price run real exchange rates. These approaches iden- level.’ tify numerous variables that have been tested for their relationships to the changing values of Since the advent of flexible exchange rates in the real exchange rate. Empirically, we examine 1973, real exchange rates have been more vari- the six bilateral real exchange rates among the able than they were previously. This point is il- United States, West Germany, Japan and the lustrated in figure 1 over 1957 to 1988 for the United Kingdom.4 Using a data set covering ap- pound/dollar, mark/dollar and yen/dollar real ex- change rates. The increased variability has in- proximately the same time period, we make a duced many researchers to focus on the fun- straightforward comparison of the three pri- damental relationships that determine real ex- mary approaches and present a clear picture of change rates. what can be said about the determinants of real exchange rates. The concept of purchasing power parity has been one of the most important building blocks Research to explain movements in the long- for nominal, as well as real, exchange rate run real exchange rate is unnecessary if pur- modeling during the 1.970s and 1980s. In its chasing power parity (PPP) holds in the long absolute version, PPP states that the equilibrium run. Thus, we begin by reviewing the literature value of the nominal exchange rate between on PPP in the long run. This provides a natural the currencies of two countries will equal the starting point from which to examine the dif- ratio of the countries’ price levels.°Thus, a ferent theoretical approaches to real exchange deviation of the nominal exchange rate from rate determination and the major empirical find- PPP has been viewed as a measure of a curren- ings. Next, we undertake unit root and cointe- cy’s over/undervaluation. In its relative version, gration tests to examine whether long-run rela- PPP states that the equilibrium value of the tionships exist between the real exchange rate nominal exchange rate will change according to and some of its potential determinants. the relative change of the countries’ price levels. A noteworthy implication of both versions of PPP is that the real exchange rate will remain constant over time. Economists have debated whether P1W applies in the short run, long run or neither. By the As a point of departure, it is useful to define end of the 1970s, PPP, at least in the short run, the real exchange as it is used throughout this was i-ejected convincingly by the data.’ Whether paper. A standard representation expresses all PPP in the long run can be rejected is less clear. variables in logarithms, so that a real exchange A standard theoretical argument in support of 4 rate (domestic currency value per unit of foreign currency), Our selection of countries is based on research by Koedijk and Schotman (1989), which indicates that the movements P is an index of domestic prices, P~is an index of foreign of real exchange rates for 15 industrial countries can be prices and K is a scalar, In this view, the PPP hypothesis partitioned into four groups led by the United States, West is a homogeneity postulate of monetary theory rather than Germany, Japan and the United Kingdom. an arbitrage condition, Thus, a monetary disturbance 5 causes an equiproportionate change in money, commodity Wholesale price indexes are also frequently used in the prices and the price of foreign exchange, while relative calculation of real exchange rates. The use of wholesale prices are unchanged. The influence of real factors on the rather than consumer prices can generate different results, relationship between exchange rates and national price For an example, see McNown and Wallace (1989). For a levels is captured by K, which is a function of structural brief discussion of why a broad-based measure of prices factors that can alter the relative prices of goods. such as consumer prices is more appropriate than one of wholesale prices in calculating real exchange rates, see ‘See Adler and Lehmann (1983) for the references underly- Cox (1987). ing this consensus. °Moregenerally, PPP has been stated in Edison and Klovland (1987) as E=K(PIP*), where E is the exchange

Figure 1 Real Bilateral Exchange Rates in the Fixed and Floating Rate Periods 1957 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 1989

PPP is that deviations from parity, assuming cannot be rejected, then the variable is said to zero transportation costs and no trade barriers, follow a random walk. Using data from various indicate profitable opportunities for commodity developed countries, recent studies by Darby arbitrage. Deviations from PPP imply that the (1983), Adler and Lehmann (1983), Huizinga same good, after adjusting for the exchange (1987), Baillie and Selover (1987) and Taylor rate, will sell at different prices in two loca- (1988) could not reject the unit root hypothesis tions. Simultaneously buying the good in the for the real exchange rate in the current float- low-price country and selling the good in the ing rate period and, hence, rejected the notion high-price country will force the nominal ex- of long-run PPP. change rate to PPP and the real exchange rate The issue, nevertheless, remains controversial. to some constant value. One reason is that some researchers have found The chief issue is whether the real exchange evidence to reject the random-walk hypothesis rate returns over time to a fixed value, the in some cases.’ In addition, doubts about the long-run equilibrium real exchange rate, On the power of standard tests to discriminate between other hand, it is possible that the equilibrium true iandom walks and near random walks value of the real exchange rate is not constant have been raised. For example, Hakkio (1986) over time, but instead changes in response to demonstrated that, when the real exchange rate changes in some fundamental economic vari- differs modestly from a random walk, the re- ables, For example, an increase in a country’s sults of standard tests are biased in favor of the real interest rate, ceteris paribus, could cause an random-walk hypothesis. In other words, there appreciation of the country’s real exchange rate. is a high probability of failing to reject the ran- dom-walk hypothesis even if it is false.b0 One conclusion, however, is clear: if the real exchange rate follows a random walk, long-run Another possibility is that the current floating- PPP does not hold. A variable is said to follow a rate period is too brief to assess accurately the validity of PPP. Lothian (1989), using unit root random walk if its value in the next period equals its value in the current period plus a tests and annual data for over 100 years for random error that cannot be forecast using Japan, the United States, the United Kingdom and France, found that real exchange rates available information. If the real exchange rate tended to return to their long-run equilibrium follows a random walk, then it will not return values, but that the period of adjustment was to some average value associated with PPP over quite long. For example, adjustment periods time. In fact, its deviation from the PPP value ranging from three to five years were found. becomes unbounded in the long run. Consequently, the cuirent floating-i-ate period The unit root test is a common procedure to might not be long enough to identify the long- use in determining is’hether a variable follows a run tendency of the real exchange rate to re- random walk.’ If the existence of a unit root turn to an equilibrium. ‘The issue is whether the real exchange rate is stationary. ‘°Thepreceding problem motivated Sims (1988) to develop If the real exchange rate is stationary, then random distur- a new test for discriminating between true and near ran- bances have no permanent effects on this rate. If the real dom walks, Applying this new test, Whitt (1989) was able exchange rate is nonstationary, then there is no tendency to reject the hypothesis that the real exchange rate was a for this rate to return to an “average” value over time. To random walk. A forthcoming issue of the Journal of determine whether the real exchange rate is stationary, a Econometrics, however, concludes that the ap- standard procedure is to use the Dickey-Fuller test for unit propriateness of Bayesian approaches in detecting unit roots. This procedure is described later in the text. roots remains in doubt because many questions, some re- ‘Examples include Cumby and Obstfeld (1984) and Frankel quiring highly technical responses, have not been (1986). Using monthly data between September 1975 and answered, Consequently, we did not use this technique in May 1981, Cumby and Obstfeld rejected the random-walk our analysis. hypothesis for the real exchange rate between the United States and Canada. On the other hand, they were unable to relect the random-walk hypothesis for the real exchange rate when the United States was paired with each of the following countries—United Kingdom, West Germany, Switzerland and Japan. Frankel (1986) rejected the random-walk hypothesis for the real U.S. dollar/British pound exchange rate using annual data between 1869 and 1984, but was not able to reject the hypothesis using data for 1945-1984.

the overall price level, and p~and be the logs of the price levels of traded and non-traded J,~[]~N~’ ff11/V goods; an asterisk denotes the foreign country. The overall price level is related to the prices of Our goal is not to resolve the preceding con- tradeable and non-tradeable goods by troversy about PPP in the long run. Rather, it is (2) p = (1 — a)pT + apNT to examine, as well as extend empirically, the research efforts of those who have provided and models that allow for the long-run real ex- (3) ~ = (1 — j3)p + change rate to vary over time, In other words, our goal is to examine the attempts by resear- where a and J3 denote the shares of the non- chers skeptical about PPP in the long run to ex- tradeable goods sectors in the economies.h1 plain movements in the long-run real exchange Assuming the law of one price for tradeable rate, Two real approaches and a monetary ap- goods, proach to exchange-rate determination have (4) e + p — p; = 0, been used to explain movements in the equilib- 1 rium real exchange rate. The first real approach where e is the log of the nominal exchange is concerned with movements in the real ex- rate, measured as the foreign currency price of change rate that arise from incorporating the a unit of domestic currency.” difference between tradeable and non-tradeable By substituting equations 2, 3 and 4 into equa- goods prices. The other real approach deals tion 1, the real exchange rate, q, can be written with the implications of incorporating a balance as of payments constraint. The monetary ap- (5) n = —aN — n ) + R(n* — proach, in contrast, focuses on the relationship ‘-1 VT t’NT I t’T VNT’ between real exchange rates and real interest Thus, the real exchange rate depends on rela- rates. tive prices between tradeable and non-tradeable ~ AilOfl-1 goods as well as the sizes of the non-tradeable goods sectors in the two countries. Our focus is Absolute PPP implies that the equilibrium restricted to the possibility that persistent dif- value of the nominal exchange rate between the ferences between the price changes of tradeable currencies of two countries would equal the and non-tradeable goods across the two ratio of the countries’ price levels, which is economies can cause real exchange rate commonly measured by the respective consum- movements. er price indexes. Ignoring transportation costs, Two main proxies, one using relative prices, free international trade eliminates the price dif- the other using output measures, have been us- ference between the same good in two coun- ed to measure the tradeables/non-tradeables tries; however, price differences across coun- distinction. As Wolff (1987) has noted, a stan- tries for non-traded goods may persist and may dard empirical proxy in analyzing relative prices change substantially over time. Frequently, this in a world with internationally traded and non- possibility is referred to as PPP holding only for traded goods is the ratio of wholesale prices to internationally traded goods; however, one consumer prices. The reasoning is straightfor- could view this possibility as a substantial modi- ward. Wholesale price indexes generally pertain fication of PPP. To prevent confusion, we do to baskets of goods that contain larger shares of not call this P1W, but rather characterize it as traded goods than consumer price indexes do. the law of one price for traded goods. Consumer price indexes tend to contain relative- A simple model illustrating this approach is ly larger shares of non-traded consumer ser- presented below, Let p be the logarithm (log) of vices. To date, however, empirical evidence on “These indexes suggest that the price level is constructed l2As a check, using wholesale prices for the prices of traded as follows: P = P”~fP;,, where the upper-case Ps repre- goods, we found that e+p,—pwas not stationary. Thus, sent levels. Price indexes are not really constructed this one of the building blocks for this approach does not hold way; however, following Hsieh (1982), this construction was for our data. In addition, even if one were to define the chosen to simplify the derivation, Hsieh has argued that real exchange rate using wholesale rather than consumer his empirical results were not distorted by this assumed prices, PPP would not appear to hold in the long run, construction because he used highly aggregated data.

the importance of relative prices in explaining real exchange rate movements is lacking 2 ~ ~ 2 The other proxy for the tradeables/non- An alternative real approach to analyze move- tradeables distinction was highlighted by Balassa ments in the real exchange rate is to include a (1964). Balassa assumed that the law of one balance-of-payments constraint.” This approach price held for traded goods, that wages in the focuses on the theoretical relationship between tradeable goods sector are linked to productivity changes in the equilibrium real exchange rate and that wages across industries are equal. and changes in the current account, The long- These assumptions cause the price of non-trade- run equilibrium real exchange rate is the rate able goods relative to tradeable goods to in- that equilibrates the current account in the long crease more over time in a country with high run. Recall that balance-of-payments accounting productivity growth in the tradeable goods sec- ensures that the current account is identical to tor than in a country with low productivity the negative of the capital account, which is growth. Such a productivity differential, in con- simply the rate of change of net foreign hold- junction with a general price index that covers ings. Thus, the current account equilibrium in both traded and non-traded goods, will result in the long run is determined by the rate at which a real exchange rate appreciation for fast- foreign and domestic residents wish to change growing countries even with the prices of traded their net foreign asset positions in the long run. goods equalized across countries. Any fundamental economic factor that in- For the empirical application of the productivi- fluences the current account affects the real ex- ty approach, Balassa suggested that there should change rate. Consequently, the long-run equilib- be a positive link between the real exchange rium real exchange rate depends on real fac- rate and real per capita gross national product, tors—whose changes can either be anticipated which assumes that inter-country productivity or unanticipated—that cause shifts in the de- differences are reflected in per capita income mand for and supply of domestic and foreign levels. The effect of shifts in sectoral productivi- goods. The most notable example is the relative ty have been investigated by Hsieh (1982) and output differential. Relatively faster output Edison and Klovland (1987). Hsieh found that growth domestically will induce an appreciation real exchange-rate changes for West Germany of the long-run equilibrium real exchange rate. and Japan could be explained by differences in the relative growth rates of labor productivity A key aspect of this approach focuses on the between traded and non-traded sectors for these possibility that unanticipated changes in the cur- countries and their major trading partners. rent account affect the long-run real exchange rate. Unexpected changes in the current ac- Similarly, Edison and Klovland, using annual count are assumed to reflect changes in under- data, found a long-run equilibrium relation be- lying determinants that, in turn, require offset- tween the pound/Norwegian krone real ex- ting changes in the real exchange rate to ensure change rate and the real output differential and current account equilibrium in the long run. A between the real exchange rate and the com- long-run balance-of-payments constraint sug- modity/service productivity ratio differential. gests that any revisions in expectations about The results of Edison and Klovland raise a the long-run values of variables that affect the number of interesting questions because the balance of payments affect the expected value data cover a period that is both long, 1874-1971, of the long-run real exchange rate. As Isard and does not encompass the current floating- (1983) notes, the substantial changes in the rela- rate period. Consequently, one is left wondering tive price of oil during the 1970s are excellent ex- whether 15 years of data, which require the amples of how unexpected changes in a determi- use of data more frequent than annual observa- nant of the current account caused revised expec- tions, is sufficient to reach strong conclusions tations about the long-run real exchange rate. about the current period and whether Edison and Kiovland’s results would be altered by data An illustration highlighting the importance of from the current period. unanticipated current account changes is pre- 13 Examples may be found in Isard (1983) and Frenkel and Mussa (1985).

sented by Dornbusch and Fischer (1980). In sumption is that the deviations are eliminated at their model, a current account surplus causes a a constant rate. The adjustment process can be rise in wealth through the net inflow of foreign represented as follows: assets. Assuming the rise in wealth is unantici- (6) Ejq,÷. — q,~3 = Qk(q — ii), 0

(10) ~ — q,) = k fi*t — k B,, where the k-period interest rate, k~1’is the dif- ference between the nominal interest rate less the expected rate of change in prices. Substi- tuting equation 10 into equation 8 yields Our empirical analysis proceeds in two steps. First, using unit root tests, we test for the sta- (11) q, = d~R7 ~R,) — + q,. tionarity of the six real exchange iates that result from pairwise combinations of the for- Therefore, the essence of the monetary ap- eign exchange rates of the United States, Japan, proach is that changes in the real exchange rate West Germany and the United Kingdom. The are directly related to changes in the real in- stationarity of five potential determinants for terest differential. As expected real domestic in- these exchange rates is examined as well. De- terest rates rise relative to foreign rates; the tails on the construction of these variables are real exchange rate of the domestic country rises presented in the appendix. Unless noted other- as well. wise, we used monthly data from June 1973 to June 1988 for all variables. Thus, in the first Equation 11 provided the foundation for vari- step, we provide additional evidence on the ex- ous statistical tests by Meese and Rogoff (1988). istence of PPP in the long run. Second, we test As noted in the appendix, the measurement of for cointegration between the real exchange expected real interest rates is problematic. While rates and each of the potential determinants. the sign of the relationship between the long- The goal is to identify which variables, if any, term real interest rate differential and the real from the models that we have reviewed explain exchange rate was consistent with theory, the variations in the real exchange rate over time. relationship was not statistically significant. We used the test developed by Dickey and Fuller (1979) for testing for unit roots.’°In the In summary, the existing literature points to present case, the test consists of regressing the five potential determinants of long-run real ex- first difference of the variable under considera- change rates that we use. The real approach tion on its own lagged level, a constant and, to identifies three possibilities, two based on the control for autocorrelation, an appropriate num- tradeables/non-tradeables distinction and one ber of lagged first differences.” The coefficient based on the balance-of-payments equilibrium. estimate on the lagged level is crucial, because The proxies to measure the tradeables/non- the null hypothesis of a unit root implies that it tradeables distinction have used the ratio of is zero. ‘The test-statistic is simply the estimate wholesale to consumer prices and real per cap- of the coefficient divided by its standard error. ita gross national product differences, while the ‘this test-statistic, which does not have the usual cumulated current account difference is used t-distribution, is then compared with critical for the balance of payments. The other major values tabulated in Fuller (1976). approach, the monetary approach, highlights the role of interest rate differentials, Both short- The results listed in table 1 show that we can- term and long-term interest rate differentials not reject the null hypothesis of a unit root for across countries have been used. any of the bilateral real exchange rates.’8 The “See Trehan (1988) for a basic introduction to the intuition percent. Given the nature of the cointegration tests, this underlying unit roots and cointegration, as well as a prac- caveat applies to these results as well. tical illustration, “If lagged first differences are needed, then the test is an “augmented” Dickey-Fuller test; otherwise, the test is simply a Dickey-Fuller test, The chosen lag length is the smallest lag length for which there is no autocorrelation, “An important caveat concerning the interpretation of unit root tests is the extremely low power of these tests. Given a sample size of approximately 100 observations, the prob- ability of accepting a coefficient of 1.0 on the lagged dependent variable when it is actually 0.95 is roughly 80

r Table 1 Unit Root Tests For Real Exchange Rates and Potential Determinants Countries q PWlPc~PW*/Pc* GNP-GNP’ TB-T8 RS-RS RL-RL’ UKIUS 1 63 031 2.20 1 86 2,96’ 2.77 WOIUS 1 27 013 1.51 272 3 15’ 1,52 JPIUS 088 1,44 —0.47 0.10 3.66’ 1.48 UK’WO 1.56 1 15 2.48 208 204 2.03 JP/WG 0.84 043 0.70 256 2921 2.68 UKIJP 1.27 0 68 0.32 1.91 4 4Ql 2.73 Statistically significant at the 0.05 level, NOTE: The test-statistic reported is minus the regression t-stalistic on u in a regression of the follow- ing general form’ ~x -c -~x ~ZflAx .~E, The lag length n is chosen as the smallest value for which no autocorrelation exists For a sample of 100 observations. tne critical value for a significance level of 5 percent s 2.89 real exchange rate measures are nonstationary since there is no tendency for the real exchange rates to return to an average value over time. Even though the real exchange rate has a unit Thus, consistent with studies cited previously, root, it is possible that there is a long-run rela- we reject long-run PPP. tionship between it and other variables that also contain unit roots. For an equilibrium relation- Table 1 also contains the results of unit root ship to exist between these variables, the distur- tests for the potential determinants of real ex- bances that cause nonstationary behavior in one change rates. Both proxies used to measure the variable must also cause nonstationary behavior tradeables/non-tradeables distinction, the dif- ference between countries of their ratios of in the other variable. wholesale to consumer prices (PW/PC.PW*/PC*) To test whether there is a long-run relation- and real per capita gross national products ship between variables that contain unit roots, (GNP.GNP*), are nonstationary. An identical con- the residuals from an ordinary-least-squares clusion is reached for the cumulated current ac- regression between the variables can be exam- count difference (TB.TB*), the proxy based on ined for stationarity. In other words, a Dickey- the balance-of-payments approach. In every Fuller test is performed on the residuals resul- case, we cannot reject the null hypothesis of a ting from regressing one variable—the real ex- unit root. change rate in our case—on a potential determi- The results for the two proxies based on the nant. The first difference of the residual series monetary approach are mixed. The difference is regressed on its lagged level, a constant and between the short-term interest rates (RS.RS*) an appropriate number of lagged first differ- appears to be stationary in most cases. In only ences. A hypothesis test is performed using the one case, United Kingdom/West Germany, the coefficient estimate on the lagged level. If the null hypothesis of a unit root is accepted. On null hypothesis of a coefficient of zero can be the other hand, the difference between the rejected, then the residuals are stationary. If the long-term interest rates (RL~RL*)appears to be residuals are stationary, then the variables will nonstationary because the null hypothesis of a not drift away from each other, Such variables unit root is accepted in each case. are said to be cointegrated. Since cointegration

Table 2 Cointegration Tests of Real Exchange Rates and Potential Determinants Countries PW/PC-PW’/PC GNP-GNP TB-TB’ RS-RS’ RL-RL UF

r Figure 2 Colntegration of Real Mark/Dollar Exchange Rate and Real Long Interest Rate Differential 4 2 0 —2 —4 —6 —8 —10 1973 74 75 76 77 78 79 80 81 82 83 84 85 86 1987 the real exchange rate and differences in real too brief, especially in view of our statistical per capita gross national product across coun- tools, to draw conclusions about the long-run tries. On the other hand, the monetary ap- behavior of real exchange rates. Assuming no proach seems to have some value in the West change in exchange-rate regime, the passage of German/United States case. An equilibrium rela- time will ultimately rectify this problem. Until tionship appears to exist between the real ex- sufficient time passes, however, it would be pre- change rate and the difference in long-term in- mature to discard the theoretical approaches terest rates. In view of the low power of unit that have been proposed. root tests, this finding is especially noteworthy. A second possibility is that the existing models The fact remains that our knowledge of the are deficient. Our review identified instances in determination of real exchange rates is meager, which the assumptions underlying the models did at best. ‘the logical question is to ask where not hold. In addition, since real exchange rates are research might be directed to expand our asset prices, the role of expectations is an aspect knowledge in this area. Numerous explanations, of the modeling process that deserves additional in addition to measurement problems, can be scrutiny. The failure of existing models might re- offered for the fact that fundamental variables sult fiom the fact that expectations are formed have not yielded good explanations of real ex- differently than our models suggest. Consequently, change rate movements. One possibility is that the development of alternative expectations for- the recent period of floating exchange rates is mation mechanisms might prove productive.

A final possibility is that random shocks of _______- “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials:’ American various origins, such as oil price shocks, have Economic Review (September 1979), pp. 610-22. moved the real exchange rate. While identification Frankel, Jeffrey A., and Richard Meese, “Are Exchange of the real factors that might have affected ex- Rates Excessively Variable?” in National Bureau of change rates is difficult, Meese and Rogoff (1988) Economic Research, Macroeconomics Annual 198% Stanley Fischer, ed, (MIT Press, 1987), pp. 117-53. suggest that further attention should be focused Frenkel, Jacob A., and Michael L. Mussa, “Asset Markets, on the role of real shocks. Thus, models utilizing Exchange Rates and the Balance of Payments:’ in Ronald modern real business-cycle research might W. Jones and Peter B. Kenen, eds., Handbook of Interna- tional Economics (Amsterdam: Elsevier Science Publishers generate some insights. 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r / / / / / / For all variables except interest rates, we use rate on three-month Treasury bills from the monthly data from International Financial Statis- Federal Reserve Board. tics for June 1973 to June 1988. Recall that q is The nominal long-term interest rates and their the log of the real exchange rate with the con- sources are as follows: Japan—average yield to sumer price index of the respective countries as maturity on government bonds with constant the deflator. GNP is the log of real gross na- remaining maturity of nine years from the Bank tional product, where nominal gross national of Japan; United Kingdom—average yield to product is deflated with the gross national pro- maturity on government bonds with remaining duct price deflator. Since gross national product maturity between eight and 12 years from the data are not available monthly, we interpolated Financial Times; West Germany—average yield from quarterly to monthly observations using to maturity on government bonds with remain- industrial production. Note that all the potential ing maturity over eight years from the Frank- determinants are defined as differences, with an furter Ailgemeine .Zeitung; and United States— asterisk indicating the respective value in the yield to maturity of government bonds with re- other country. PWIPC is the log of the whole- maining maturity of 10 years from the Federal sale price index divided by the consumer price Reserve Board. We calculated the real short- index. TB is the cumulated trade balance (that term and long-term interest rates, RS and RL, in is, the sum from January 1972 to time period t the same manner as Meese and Rogoff (1988). of the difference between exports and imports) Thus, actual inflation rates based on the preced- divided by gross national product. ing 12 months as measured by the consumer For the interest rates not involving Japan, the price index are subtracted from the nominal in- time period is June 1973 to June 1987, while terest rates to generate the real rates. As a re- for those involving Japan, the time period is sult, the inflation measure does not correspond July 1977 to June 1987. The nominal short-term to the term of the interest rates. A problem interest rates and their sources are as follows: with this construction, as well as many others, Japan—one-month Gensaki rate from the Bank is that negative real interest rates are computed. of Japan; United Kingdom—one-month interbank For example, the long-term (short-term) real in- deposit rate from the Financial Times; West terest rate is negative for 25 (42) percent of the Germany—one-month interbank rate from the U.S. observations, 38 (30) percent of the British Frankfurter Aligemeine Zeitung; and United observations, 0 (9) percent of the West German States—the yield on one-month ‘Treasury bills observations and 6 (7) percent of the Japanese until April 1984 and, afterward, the interest observations.

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