Cletus C. Coughtin and Kees Koedjjk

Cletus a Coughlin is a research officer at the Federal ReserveBank of St. Louis. Kees Koedijk is a professor of economics atErasmus University, Rotteitam, Thomas A. Pollmann providedresearch assistance,

What Do We Know About theLong-Run Real ExchangeRate?

REAL EXCHANGE rate is defined as theforeign currency price of a unit of domesticcurrency (that is, the nominal exchange rate)multiplied by the ratio of the domestic to theforeign price level. The real exchange rate hasbeen at the center of economic policy discus-sions in the 1980s for at least two reasons.First, this relative price has been more variablein the floating-rate period than in the precedingera of fixed (nominal) exchange rates.’ Second,this price is related to international trade pat-terns because the competitive position of an in-dividual exporting (import-competing) firm in a

country is affected adversely by an appreciating(depreciating) real exchange rate.’

Despite much research, however, there is noconsensus on which variables cause changes inthe real exchange rate. Like any asset price,real exchange rates are related to the determi-nants of the relevant supply and demand curvesnow and in the future.’ With real exchangerates, the relevant determinants are those affec-ting the relative supplies and demands for thecurrencies of two countries. Claims have beenmade, however, that the real exchange rates

1See Frankel and Meese (1987) and Dornbusch (1989) forsurveys of this literature. As noted by Dornbusch, the in-creased variability and lack of knowledge have contributedto divergent policy recommendations, which include areturn to some form of a managed exchange-rate system,taxes on foreign exchange transactions as well as doingnothing.

‘The U.S. dollar has been at the center of the controversy,with the dollar allegedly being undervalued in the late1970s/early l9BOs and overvalued in the mid-1980s. Dur-ing the period of undervaluation, U.S. tradeable goods in-dustries were stimulated and induced to overexpand. Thecosts of this alleged overexpansion were exacerbated bythe subsequent overvaluation, which resulted in layoffs,plant closings and bankruptcies in these same industries,

‘This elementary principle is ignored when the exchangerate in macroeconomic settings is treated as an ex-

ogenous rather than endogenous variable, For example, astandard assertion is that a depreciating dollar boosts U.S.manufacturing output. A declining dollar is expected toraise the dollar prices of U.S. imports and lower theforeign currency prices of U.S. exports. Consequently,consumption and production of U.S. exports and import-competing goods would rise, This analysis is faultybecause changes in the value of the dollar are not in-dependent of U.S. industrial developments and, in fact,can be the direct result of industrial developments. For ex-ample, an economic policy that boosts productive capacitycan generate a positive relationship between the value ofthe dollar and U.S. manufacturing output. Details on thisargument can be found in Tatom (1988).

often differ substantially from levels consistentwith the underlying economic fundamentals andthat these differences persist for long periods.

A primary goal of our research is to providean elementary understanding of the major theo-retical approaches to the determination of long-run real exchange rates. These approaches iden-tify numerous variables that have been testedfor their relationships to the changing values ofthe real exchange rate. Empirically, we examinethe six bilateral real exchange rates among theUnited States, West Germany, Japan and theUnited Kingdom.4 Using a data set covering ap-proximately the same time period, we make astraightforward comparison of the three pri-mary approaches and present a clear picture ofwhat can be said about the determinants of realexchange rates.

Research to explain movements in the long-run real exchange rate is unnecessary if pur-chasing power parity (PPP) holds in the longrun. Thus, we begin by reviewing the literatureon PPP in the long run. This provides a naturalstarting point from which to examine the dif-ferent theoretical approaches to real exchangerate determination and the major empirical find-ings. Next, we undertake unit root and cointe-gration tests to examine whether long-run rela-tionships exist between the real exchange rateand some of its potential determinants.

As a point of departure, it is useful to definethe real exchange as it is used throughout thispaper. A standard representation expresses allvariables in logarithms, so that a real exchange

rate, q, is defined as follows:

(1) q =

where e is the foreign currency price of a unitof domestic currency, p is the domestic pricelevel as measured by the consumer price indexand p~is the similarly measured foreign pricelevel.’

Since the advent of flexible exchange rates in1973, real exchange rates have been more vari-able than they were previously. This point is il-lustrated in figure 1 over 1957 to 1988 for thepound/dollar, mark/dollar and yen/dollar real ex-change rates. The increased variability has in-duced many researchers to focus on the fun-damental relationships that determine real ex-change rates.

The concept of purchasing power parity hasbeen one of the most important building blocksfor nominal, as well as real, exchange ratemodeling during the 1.970s and 1980s. In itsabsolute version, PPP states that the equilibriumvalue of the nominal exchange rate betweenthe currencies of two countries will equal theratio of the countries’ price levels.°Thus, adeviation of the nominal exchange rate fromPPP has been viewed as a measure of a curren-cy’s over/undervaluation. In its relative version,PPP states that the equilibrium value of thenominal exchange rate will change according tothe relative change of the countries’ price levels.A noteworthy implication of both versions ofPPP is that the real exchange rate will remainconstant over time.

Economists have debated whether P1W appliesin the short run, long run or neither. By theend of the 1970s, PPP, at least in the short run,was i-ejected convincingly by the data.’ WhetherPPP in the long run can be rejected is less clear.A standard theoretical argument in support of

4Our selection of countries is based on research by Koedijkand Schotman (1989), which indicates that the movementsof real exchange rates for 15 industrial countries can bepartitioned into four groups led by the United States, WestGermany, Japan and the United Kingdom.

5Wholesale price indexes are also frequently used in thecalculation of real exchange rates. The use of wholesalerather than consumer prices can generate different results,For an example, see McNown and Wallace (1989). For abrief discussion of why a broad-based measure of pricessuch as consumer prices is more appropriate than one ofwholesale prices in calculating real exchange rates, seeCox (1987).

°Moregenerally, PPP has been stated in Edison andKlovland (1987) as E=K(PIP*), where E is the exchange

rate (domestic currency value per unit of foreign currency),P is an index of domestic prices, P~is an index of foreignprices and K is a scalar, In this view, the PPP hypothesisis a homogeneity postulate of monetary theory rather thanan arbitrage condition, Thus, a monetary disturbancecauses an equiproportionate change in money, commodityprices and the price of foreign exchange, while relativeprices are unchanged. The influence of real factors on therelationship between exchange rates and national pricelevels is captured by K, which is a function of structuralfactors that can alter the relative prices of goods.‘See Adler and Lehmann (1983) for the references underly-ing this consensus.

Figure 1Real Bilateral Exchange Rates in the Fixed and FloatingRate Periods

1957 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 1989

PPP is that deviations from parity, assumingzero transportation costs and no trade barriers,indicate profitable opportunities for commodityarbitrage. Deviations from PPP imply that thesame good, after adjusting for the exchangerate, will sell at different prices in two loca-tions. Simultaneously buying the good in thelow-price country and selling the good in thehigh-price country will force the nominal ex-change rate to PPP and the real exchange rateto some constant value.

The chief issue is whether the real exchangerate returns over time to a fixed value, thelong-run equilibrium real exchange rate, On theother hand, it is possible that the equilibriumvalue of the real exchange rate is not constantover time, but instead changes in response tochanges in some fundamental economic vari-ables, For example, an increase in a country’sreal interest rate, ceteris paribus, could cause anappreciation of the country’s real exchange rate.

One conclusion, however, is clear: if the realexchange rate follows a random walk, long-runPPP does not hold. A variable is said to follow arandom walk if its value in the next periodequals its value in the current period plus arandom error that cannot be forecast usingavailable information. If the real exchange ratefollows a random walk, then it will not returnto some average value associated with PPP overtime. In fact, its deviation from the PPP valuebecomes unbounded in the long run.

The unit root test is a common procedure touse in determining is’hether a variable follows arandom walk.’ If the existence of a unit root

cannot be rejected, then the variable is said tofollow a random walk. Using data from variousdeveloped countries, recent studies by Darby(1983), Adler and Lehmann (1983), Huizinga(1987), Baillie and Selover (1987) and Taylor(1988) could not reject the unit root hypothesisfor the real exchange rate in the current float-ing rate period and, hence, rejected the notionof long-run PPP.

The issue, nevertheless, remains controversial.

One reason is that some researchers have foundevidence to reject the random-walk hypothesisin some cases.’ In addition, doubts about thepower of standard tests to discriminate betweentrue iandom walks and near random walkshave been raised. For example, Hakkio (1986)demonstrated that, when the real exchange ratediffers modestly from a random walk, the re-sults of standard tests are biased in favor of therandom-walk hypothesis. In other words, thereis a high probability of failing to reject the ran-dom-walk hypothesis even if it is false.b0

Another possibility is that the current floating-rate period is too brief to assess accurately thevalidity of PPP. Lothian (1989), using unit roottests and annual data for over 100 years forJapan, the United States, the United Kingdomand France, found that real exchange ratestended to return to their long-run equilibriumvalues, but that the period of adjustment wasquite long. For example, adjustment periodsranging from three to five years were found.Consequently, the cuirent floating-i-ate periodmight not be long enough to identify the long-run tendency of the real exchange rate to re-turn to an equilibrium.

‘The issue is whether the real exchange rate is stationary.If the real exchange rate is stationary, then random distur-bances have no permanent effects on this rate. If the realexchange rate is nonstationary, then there is no tendencyfor this rate to return to an “average” value over time. Todetermine whether the real exchange rate is stationary, astandard procedure is to use the Dickey-Fuller test for unitroots. This procedure is described later in the text.

‘Examples include Cumby and Obstfeld (1984) and Frankel(1986). Using monthly data between September 1975 andMay 1981, Cumby and Obstfeld rejected the random-walkhypothesis for the real exchange rate between the UnitedStates and Canada. On the other hand, they were unableto relect the random-walk hypothesis for the real exchangerate when the United States was paired with each of thefollowing countries—United Kingdom, West Germany,Switzerland and Japan. Frankel (1986) rejected therandom-walk hypothesis for the real U.S. dollar/Britishpound exchange rate using annual data between 1869 and1984, but was not able to reject the hypothesis using datafor 1945-1984.

‘°Thepreceding problem motivated Sims (1988) to developa new test for discriminating between true and near ran-dom walks, Applying this new test, Whitt (1989) was ableto reject the hypothesis that the real exchange rate was arandom walk. A forthcoming issue of the Journal ofEconometrics, however, concludes that the ap-propriateness of Bayesian approaches in detecting unitroots remains in doubt because many questions, some re-quiring highly technical responses, have not beenanswered, Consequently, we did not use this technique inour analysis.

J,~[]~N~’ff11/V

Our goal is not to resolve the preceding con-troversy about PPP in the long run. Rather, it isto examine, as well as extend empirically, theresearch efforts of those who have providedmodels that allow for the long-run real ex-change rate to vary over time, In other words,our goal is to examine the attempts by resear-chers skeptical about PPP in the long run to ex-plain movements in the long-run real exchangerate, Two real approaches and a monetary ap-proach to exchange-rate determination havebeen used to explain movements in the equilib-rium real exchange rate. The first real approachis concerned with movements in the real ex-change rate that arise from incorporating thedifference between tradeable and non-tradeablegoods prices. The other real approach dealswith the implications of incorporating a balanceof payments constraint. The monetary ap-proach, in contrast, focuses on the relationshipbetween real exchange rates and real interestrates.

~ AilOfl-1

Absolute PPP implies that the equilibriumvalue of the nominal exchange rate between thecurrencies of two countries would equal theratio of the countries’ price levels, which iscommonly measured by the respective consum-er price indexes. Ignoring transportation costs,free international trade eliminates the price dif-ference between the same good in two coun-tries; however, price differences across coun-tries for non-traded goods may persist and maychange substantially over time. Frequently, thispossibility is referred to as PPP holding only forinternationally traded goods; however, onecould view this possibility as a substantial modi-fication of PPP. To prevent confusion, we donot call this P1W, but rather characterize it asthe law of one price for traded goods.

A simple model illustrating this approach ispresented below, Let p be the logarithm (log) of

the overall price level, and p~and be thelogs of the price levels of traded and non-tradedgoods; an asterisk denotes the foreign country.The overall price level is related to the prices oftradeable and non-tradeable goods by

(2) p = (1 — a)pT + apNT

and

(3) ~ = (1 — j3)p +

where a and J3 denote the shares of the non-tradeable goods sectors in the economies.h1

Assuming the law of one price for tradeablegoods,

(4) e + p1 — p; = 0,

where e is the log of the nominal exchangerate, measured as the foreign currency price ofa unit of domestic currency.”

By substituting equations 2, 3 and 4 into equa-

tion 1, the real exchange rate, q, can be writtenas(5) n = —aN — n ) + R(n* —

‘-1 VT t’NT I t’T VNT’

Thus, the real exchange rate depends on rela-tive prices between tradeable and non-tradeablegoods as well as the sizes of the non-tradeablegoods sectors in the two countries. Our focus isrestricted to the possibility that persistent dif-ferences between the price changes of tradeableand non-tradeable goods across the twoeconomies can cause real exchange ratemovements.

Two main proxies, one using relative prices,the other using output measures, have been us-ed to measure the tradeables/non-tradeablesdistinction. As Wolff (1987) has noted, a stan-dard empirical proxy in analyzing relative pricesin a world with internationally traded and non-traded goods is the ratio of wholesale prices toconsumer prices. The reasoning is straightfor-ward. Wholesale price indexes generally pertainto baskets of goods that contain larger shares oftraded goods than consumer price indexes do.Consumer price indexes tend to contain relative-ly larger shares of non-traded consumer ser-vices. To date, however, empirical evidence on

“These indexes suggest that the price level is constructedas follows: P = P”~fP;,, where the upper-case Ps repre-sent levels. Price indexes are not really constructed thisway; however, following Hsieh (1982), this construction waschosen to simplify the derivation, Hsieh has argued thathis empirical results were not distorted by this assumedconstruction because he used highly aggregated data.

l2As a check, using wholesale prices for the prices of tradedgoods, we found that e+p,—pwas not stationary. Thus,one of the building blocks for this approach does not holdfor our data. In addition, even if one were to define thereal exchange rate using wholesale rather than consumerprices, PPP would not appear to hold in the long run,

the importance of relative prices in explainingreal exchange rate movements is lacking

The other proxy for the tradeables/non-tradeables distinction was highlighted by Balassa(1964). Balassa assumed that the law of oneprice held for traded goods, that wages in thetradeable goods sector are linked to productivityand that wages across industries are equal.These assumptions cause the price of non-trade-able goods relative to tradeable goods to in-crease more over time in a country with highproductivity growth in the tradeable goods sec-tor than in a country with low productivitygrowth. Such a productivity differential, in con-junction with a general price index that coversboth traded and non-traded goods, will result ina real exchange rate appreciation for fast-growing countries even with the prices of tradedgoods equalized across countries.

For the empirical application of the productivi-ty approach, Balassa suggested that there shouldbe a positive link between the real exchangerate and real per capita gross national product,which assumes that inter-country productivitydifferences are reflected in per capita incomelevels. The effect of shifts in sectoral productivi-ty have been investigated by Hsieh (1982) andEdison and Klovland (1987). Hsieh found thatreal exchange-rate changes for West Germanyand Japan could be explained by differences inthe relative growth rates of labor productivitybetween traded and non-traded sectors for thesecountries and their major trading partners.

Similarly, Edison and Klovland, using annualdata, found a long-run equilibrium relation be-tween the pound/Norwegian krone real ex-change rate and the real output differential andbetween the real exchange rate and the com-modity/service productivity ratio differential.The results of Edison and Klovland raise anumber of interesting questions because thedata cover a period that is both long, 1874-1971,and does not encompass the current floating-rate period. Consequently, one is left wonderingwhether 15 years of data, which require theuse of data more frequent than annual observa-tions, is sufficient to reach strong conclusionsabout the current period and whether Edisonand Kiovland’s results would be altered by datafrom the current period.

2 ~ ~ 2

An alternative real approach to analyze move-ments in the real exchange rate is to include abalance-of-payments constraint.” This approachfocuses on the theoretical relationship betweenchanges in the equilibrium real exchange rateand changes in the current account, The long-run equilibrium real exchange rate is the ratethat equilibrates the current account in the longrun. Recall that balance-of-payments accountingensures that the current account is identical tothe negative of the capital account, which issimply the rate of change of net foreign hold-ings. Thus, the current account equilibrium inthe long run is determined by the rate at whichforeign and domestic residents wish to changetheir net foreign asset positions in the long run.

Any fundamental economic factor that in-fluences the current account affects the real ex-change rate. Consequently, the long-run equilib-rium real exchange rate depends on real fac-tors—whose changes can either be anticipatedor unanticipated—that cause shifts in the de-mand for and supply of domestic and foreigngoods. The most notable example is the relativeoutput differential. Relatively faster outputgrowth domestically will induce an appreciationof the long-run equilibrium real exchange rate.

A key aspect of this approach focuses on thepossibility that unanticipated changes in the cur-rent account affect the long-run real exchangerate. Unexpected changes in the current ac-count are assumed to reflect changes in under-lying determinants that, in turn, require offset-ting changes in the real exchange rate to ensurecurrent account equilibrium in the long run. Along-run balance-of-payments constraint sug-gests that any revisions in expectations aboutthe long-run values of variables that affect thebalance of payments affect the expected valueof the long-run real exchange rate. As Isard(1983) notes, the substantial changes in the rela-tive price of oil during the 1970s are excellent ex-amples of how unexpected changes in a determi-nant of the current account caused revised expec-tations about the long-run real exchange rate.

An illustration highlighting the importance ofunanticipated current account changes is pre-

13Examples may be found in Isard (1983) and Frenkel andMussa (1985).

sented by Dornbusch and Fischer (1980). Intheir model, a current account surplus causes arise in wealth through the net inflow of foreignassets. Assuming the rise in wealth is unantici-pated, excess demand in the domestic goodsmarket occurs. In turn, an increase in the realexchange rate is required for the new goodsmarket equilibrium. This increase induces thenecessary shift from domestic to foreign goodsby domestic and foreign consumers to eliminatethe excess demand.

[looper and Morton (1982) use this frameworkto relate changes in the real exchange rate toeconomic fundamentals. They use the cumu-lated current account as a determinant of thelong-run equilibrium real exchange rate. In theirmodel, unanticipated changes in the current ac-count are assumed to provide information aboutshifts in the underlying determinants that ne-cessitate offsetting shifts in the real exchangerate to maintain current account equilibrium inthe long run. Consistent with this balance-of-payments approach, their results indicate that,between 1973 and 1978, movements in the cur-rent account have been a significant determi-nant of movements in the real exchange ratefor the U.S. dollar, predominantly throughchanges in expectations.

~t~JI~ OF

As mentioned previously, the monetary ap-proach focuses on the relationship betweenreal exchange rates and real interest rates. Astraightforward exposition of this approach,which can be found in Meese and Rogoff (1988),is based on models developed by Dornbusch(1976), Frankel (1979) and Hooper and Morton(1982). These models are sticky-price” versionsof the monetary model of exchange rates; theyassume that prices of all goods adjust slowly inresponse to disturbances. Thus, temporary devi-ations in the real exchange rate from its long-run equilibrium value (that is, purchasingpower parity) are possible.

These temporary deviations necessitate anexchange-rate adjustment mechanism to restorethe long-run equilibrium value. A standard as-

sumption is that the deviations are eliminated ata constant rate. The adjustment process can berepresented as follows:

(6) Ejq,÷. — q,~3= Qk(q — ii), 0<0<1,

where E is an expectations operator, the sub-scripts designate the time period, q is the loga-rithm of the real exchange rate, the bars in-dicate values that would prevail if all priceswere fully flexible instantaneously and U is thespeed-of-adjustment parameter. Consequently,there is a monotonic adjustment of the real ex-change rate to the long-run equilibrium, ~,, overtime with lower values of U indicating a quickeradjustment process.14

The long-run equilibrium value changes withrandom real shocks; however, assuming all realshocks follow random-walk processes, theseshocks do not affect the expected long-run equi-librium exchange rate. Consequently,

(7) E,~, =

Substituting equation 7 into equation 6 yields

(8) q, = d(E,q,~~- q,) +

where d = i/(Ok — 1) <—1. The observed realexchange rate is its temporary deviation fromits long-run equilibrium value plus its long-runequilibrium value.

To complete the model, uncovered interestparity is assumed.15 This assumption is express-ed as follows:

(9) E,e,1~— e, = kr — kr,

where e is the logarithm of the nominal ex-change rate (foteign currency per domestic cur-rency unit), kr, is the k-period nominal interestrate at time t and the asterisk denotes a foreignvalue. In other words, changes in the nominalexchange rate are directly related to nominal in-terest rate differentials. As domestic nominal in-terest rates rise relative to foreign rates, thenominal exchange rate of the domestic countryis expected to depreciate.

Equation 9 implies that the expected changein the real exchange rate reflects the expectedreal interest rate differential. In symbols,

14For example, a comparison of 0= .6 with 0= .4 after twoperiods reveals that, in the former case, the expected dif-ference between the actual and long-run equilibrium is .36of the difference in the current period, while in the lattercase the expected difference is .16 of the difference in thecurrent period.

“The appropriateness of this assumption can be ques-tioned. The uncovered interest parity assumption requiresthat the forward rate be an unbiased and efficient predic-tor of the future spot rate; however, the empirical resultssummarized by Baillie and McMahon (1989) suggestotherwise.

(10) ~ — q,) = fi* — B,,k t k

where the k-period interest rate, k~1’is the dif-

ference between the nominal interest rate lessthe expected rate of change in prices. Substi-tuting equation 10 into equation 8 yields

(11) q, = d~R7— ~R,) + q,.

Therefore, the essence of the monetary ap-proach is that changes in the real exchange rateare directly related to changes in the real in-terest differential. As expected real domestic in-terest rates rise relative to foreign rates; thereal exchange rate of the domestic country risesas well.

Equation 11 provided the foundation for vari-ous statistical tests by Meese and Rogoff (1988).As noted in the appendix, the measurement ofexpected real interest rates is problematic. Whilethe sign of the relationship between the long-term real interest rate differential and the realexchange rate was consistent with theory, therelationship was not statistically significant.

In summary, the existing literature points tofive potential determinants of long-run real ex-change rates that we use. The real approachidentifies three possibilities, two based on thetradeables/non-tradeables distinction and onebased on the balance-of-payments equilibrium.The proxies to measure the tradeables/non-tradeables distinction have used the ratio ofwholesale to consumer prices and real per cap-ita gross national product differences, while thecumulated current account difference is usedfor the balance of payments. The other majorapproach, the monetary approach, highlightsthe role of interest rate differentials, Both short-term and long-term interest rate differentialsacross countries have been used.

Our empirical analysis proceeds in two steps.First, using unit root tests, we test for the sta-tionarity of the six real exchange iates thatresult from pairwise combinations of the for-eign exchange rates of the United States, Japan,West Germany and the United Kingdom. Thestationarity of five potential determinants forthese exchange rates is examined as well. De-tails on the construction of these variables arepresented in the appendix. Unless noted other-wise, we used monthly data from June 1973 toJune 1988 for all variables. Thus, in the firststep, we provide additional evidence on the ex-istence of PPP in the long run. Second, we testfor cointegration between the real exchangerates and each of the potential determinants.The goal is to identify which variables, if any,from the models that we have reviewed explainvariations in the real exchange rate over time.

We used the test developed by Dickey andFuller (1979) for testing for unit roots.’°In thepresent case, the test consists of regressing thefirst difference of the variable under considera-tion on its own lagged level, a constant and, tocontrol for autocorrelation, an appropriate num-ber of lagged first differences.” The coefficientestimate on the lagged level is crucial, becausethe null hypothesis of a unit root implies that itis zero. ‘The test-statistic is simply the estimateof the coefficient divided by its standard error.‘this test-statistic, which does not have the usualt-distribution, is then compared with criticalvalues tabulated in Fuller (1976).

The results listed in table 1 show that we can-not reject the null hypothesis of a unit root forany of the bilateral real exchange rates.’8 The

“See Trehan (1988) for a basic introduction to the intuitionunderlying unit roots and cointegration, as well as a prac-tical illustration,

“If lagged first differences are needed, then the test is an“augmented” Dickey-Fuller test; otherwise, the test issimply a Dickey-Fuller test, The chosen lag length is thesmallest lag length for which there is no autocorrelation,

“An important caveat concerning the interpretation of unitroot tests is the extremely low power of these tests. Givena sample size of approximately 100 observations, the prob-ability of accepting a coefficient of 1.0 on the laggeddependent variable when it is actually 0.95 is roughly 80

percent. Given the nature of the cointegration tests, thiscaveat applies to these results as well.

r

Table 1Unit Root Tests For Real Exchange Rates and PotentialDeterminantsCountries 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 asample of 100 observations. tne critical value for a significance level of 5 percent s 2.89

real exchange rate measures are nonstationarysince there is no tendency for the real exchangerates to return to an average value over time.Thus, consistent with studies cited previously,we reject long-run PPP.

Table 1 also contains the results of unit roottests for the potential determinants of real ex-change rates. Both proxies used to measure thetradeables/non-tradeables distinction, the dif-ference between countries of their ratios ofwholesale to consumer prices (PW/PC.PW*/PC*)and real per capita gross national products(GNP.GNP*), are nonstationary. An identical con-clusion is reached for the cumulated current ac-count difference (TB.TB*), the proxy based onthe balance-of-payments approach. In everycase, we cannot reject the null hypothesis of aunit root.

The results for the two proxies based on themonetary approach are mixed. The differencebetween the short-term interest rates (RS.RS*)appears to be stationary in most cases. In onlyone case, United Kingdom/West Germany, thenull hypothesis of a unit root is accepted. Onthe other hand, the difference between thelong-term interest rates (RL~RL*)appears to benonstationary because the null hypothesis of aunit root is accepted in each case.

Even though the real exchange rate has a unitroot, it is possible that there is a long-run rela-tionship between it and other variables that alsocontain unit roots. For an equilibrium relation-ship to exist between these variables, the distur-bances that cause nonstationary behavior in onevariable must also cause nonstationary behaviorin the other variable.

To test whether there is a long-run relation-ship between variables that contain unit roots,the residuals from an ordinary-least-squaresregression between the variables can be exam-ined for stationarity. In other words, a Dickey-Fuller test is performed on the residuals resul-ting from regressing one variable—the real ex-change rate in our case—on a potential determi-nant. The first difference of the residual seriesis regressed on its lagged level, a constant andan appropriate number of lagged first differ-ences. A hypothesis test is performed using thecoefficient estimate on the lagged level. If thenull hypothesis of a coefficient of zero can berejected, then the residuals are stationary. If theresiduals are stationary, then the variables willnot drift away from each other, Such variablesare said to be cointegrated. Since cointegration

Table 2Cointegration Tests of Real Exchange Rates and PotentialDeterminantsCountries PW/PC-PW’/PC GNP-GNP TB-TB’ RS-RS’ RL-RL

UF<JUS 1.62 164 1.57 1 83 1 71

WG/US I 49 1 53 1 64 2.45 3.12

JP/US 1.90 1 07 107 1.21 1.23UK/WG 276 2.11 229 2.11 237

JP/WG 263 3501 2.06 139 133

UK/JP 241 149 132 151 1.80

Statistically significant at the 0 05 level

tests are oriented toward rejecting any long.runrelationship, finding cointegration suggests theexistence of a significant statistical link betweenthe variables,

Table 2 shows the results of such cointegra-tion tests. Overall, there is little evidence to in~dicate that the examined variables explain varia-tions in the real exchange rate over time. Realexchange rates and the differences betweenratios of wholesale to consumer prices acrosscountries do not appear to be cointegrated.Despite augmented Dickey-Fuller statistics thatapproach the critical value in two cases, UnitedKingdom/West Germany and West Germany/Japan,the residuals are nonstationary in each case.The real exchange rate and the difference be-tween the real per capita gross national pro-ducts are cointegrated only for West Germanyand Japan. The cointegration tests also revealthat the residuals are nonstationary for both thecumulated trade balance and short-term interestrate differences.

One interesting result is the significant rela-tionship between the real exchange rate and thelong-term real interest differential for theUnited States and West Germany. l’his result

‘9The sample used by Meese and Rogoff (1988), as statedin their table V, terminated in December 1985, while oursample using long-term interest differentials between WestGermany and the United States terminated in June 1987.When we delete these 18 months of observations, theregression t-statistic is 2.77 rather than the 3,12 reportedin our table 2. Like Meese and Rogoff, we would fail tofind cointegration.

contrasts with Campbell and Clarida (1987) andMeese and Rogoff (1988) who fail to find cointe-gration between these variables. Since our pro-xy for the long-term real interest differential isexactly the same as that used by Meese andRogoff, the additional 18 more recent months ofdata seem to account for the different result.”

In figure 2, we have plotted the long-term realinterest differential between the United Statesand Germany and the real mark/dollar exchangerate. As is apparent from the figure, there is astrong link between these variables: a higherlong-term real interest rate in the United Statesrelative to Germany means a stronger dollar,

Unfortunately, as our review of a host ofstudies reveals, little is known about the deter-minants of real exchange rates in the long run.Our systematic survey of five potential explana-tory variables suggests that no approach to thisissue is satisfactory. For example, for certain ex-change rates, the real approach based on thetradeables/non-tradeables distinction yieldsevidence of an equilibrium relationship between

r

Figure 2Colntegration of Real Mark/Dollar Exchange Rateand Real Long Interest Rate Differential

4

2

0

—2

—4

—6

—8

—10

the real exchange rate and differences in realper capita gross national product across coun-tries. On the other hand, the monetary ap-proach seems to have some value in the WestGerman/United States case. An equilibrium rela-tionship appears to exist between the real ex-change rate and the difference in long-term in-terest rates. In view of the low power of unitroot tests, this finding is especially noteworthy.

The fact remains that our knowledge of thedetermination of real exchange rates is meager,at best. ‘the logical question is to ask whereresearch might be directed to expand ourknowledge in this area. Numerous explanations,in addition to measurement problems, can beoffered for the fact that fundamental variableshave not yielded good explanations of real ex-change rate movements. One possibility is thatthe recent period of floating exchange rates is

too brief, especially in view of our statisticaltools, to draw conclusions about the long-runbehavior of real exchange rates. Assuming nochange in exchange-rate regime, the passage oftime will ultimately rectify this problem. Untilsufficient time passes, however, it would be pre-mature to discard the theoretical approachesthat have been proposed.

A second possibility is that the existing modelsare deficient. Our review identified instances inwhich the assumptions underlying the models didnot hold. In addition, since real exchange rates areasset prices, the role of expectations is an aspectof the modeling process that deserves additionalscrutiny. The failure of existing models might re-sult fiom the fact that expectations are formeddifferently than our models suggest. Consequently,the development of alternative expectations for-mation mechanisms might prove productive.

1973 74 75 76 77 78 79 80 81 82 83 84 85 86 1987

A final possibility is that random shocks ofvarious origins, such as oil price shocks, havemoved the real exchange rate. While identificationof the real factors that might have affected ex-change rates is difficult, Meese and Rogoff (1988)suggest that further attention should be focusedon the role of real shocks. Thus, models utilizingmodern real business-cycle research mightgenerate some insights. All of these “mights” serveas a final reminder of how little we know.

1.4

Adler, Michael, and Bruce Lehmann, “Deviations from Pur-chasing Power Parity in the Long Run,” Journal of Finance(December 1983), pp. 1471-87,

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Campbell, John Y., and Richard H. Clarida, “The Dollar andReal Interest Rates:’ Carnegie-Rochester Conference Serieson Public Policy (Autumn 1987), pp. 103-40.

Cox, W. Michael. “A Comprehensive New Real Dollar Ex-change Rate lndex’ Federal Reserve Bank of DallasEconomic Review (March 1987), pp. 1-14.

Cumby, Robert E., and Maurice Obstfeld, “International In-terest Rate and Price Level Linkages under Flexible Ex-change Rates: A Review of Recent Evidence:’ in John EQ.Bilson and Richard C. Marston, eds., Exchange RateTheory and Practice (University of Chicago Press, 1984),pp. 121-51.

Darby, Michael R. “Movements in Purchasing Power Parity:The Short and Long Runs:’ in Michael A. Darby andJames R. Lothian, eds. The International Transmission of In-flation (University of Chicago Press, 1983), pp. 462-77.

Dickey, David A., and Wayne A. Fuller. ‘Distribution of theEstimators for Autoregressive Time Series With a UnitRoot:’ Journal of the American Statistical Association (June1979), pp. 427-31.

Dornbusch, Rudiger. “Real Exchange Rates and Macro-economics: A Selective Survey,” Scandinavian Journal ofEconomics (1989:2), pp. 401-32.

_______- “Expectations and Exchange Rate Dynamics:’Journal of Political Economy (December 1976), pp. 1161-76.

Dornbusch, Rudiger, and Stanley Fischer, “Exchange Ratesand the Current Account:’ American Economic Review(December 1980), pp. 960-71.

Dornbusch, Rudiger, and Paul Krugman. “Flexible ExchangeRates in the Short Run:’ Brookings Papers on EconomicActivity (1976:3), pp. 537-75.

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r

/ / / / / /

For all variables except interest rates, we usemonthly data from International Financial Statis-tics for June 1973 to June 1988. Recall that q isthe log of the real exchange rate with the con-sumer price index of the respective countries asthe deflator. GNP is the log of real gross na-tional product, where nominal gross nationalproduct is deflated with the gross national pro-duct price deflator. Since gross national productdata are not available monthly, we interpolatedfrom quarterly to monthly observations usingindustrial production. Note that all the potentialdeterminants are defined as differences, with anasterisk indicating the respective value in theother country. PWIPC is the log of the whole-sale price index divided by the consumer priceindex. TB is the cumulated trade balance (thatis, the sum from January 1972 to time period tof the difference between exports and imports)divided by gross national product.

For the interest rates not involving Japan, thetime period is June 1973 to June 1987, whilefor those involving Japan, the time period isJuly 1977 to June 1987. The nominal short-terminterest rates and their sources are as follows:Japan—one-month Gensaki rate from the Bankof Japan; United Kingdom—one-month interbankdeposit rate from the Financial Times; WestGermany—one-month interbank rate from theFrankfurter Aligemeine Zeitung; and UnitedStates—the yield on one-month ‘Treasury billsuntil April 1984 and, afterward, the interest

rate on three-month Treasury bills from theFederal Reserve Board.

The nominal long-term interest rates and theirsources are as follows: Japan—average yield tomaturity on government bonds with constantremaining maturity of nine years from the Bankof Japan; United Kingdom—average yield tomaturity on government bonds with remainingmaturity between eight and 12 years from theFinancial Times; West Germany—average yieldto maturity on government bonds with remain-ing maturity over eight years from the Frank-furter Ailgemeine .Zeitung; and United States—yield to maturity of government bonds with re-maining maturity of 10 years from the FederalReserve Board. We calculated the real short-term and long-term interest rates, RS and RL, inthe same manner as Meese and Rogoff (1988).Thus, actual inflation rates based on the preced-ing 12 months as measured by the consumerprice index are subtracted from the nominal in-terest rates to generate the real rates. As a re-sult, the inflation measure does not correspondto the term of the interest rates. A problemwith this construction, as well as many others,is that negative real interest rates are computed.For example, the long-term (short-term) real in-terest rate is negative for 25 (42) percent of theU.S. observations, 38 (30) percent of the Britishobservations, 0 (9) percent of the West Germanobservations and 6 (7) percent of the Japaneseobservations.