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

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

        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

   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
                    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-

  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

                Table 1
                Unit Root Tests For Real Exchange Rates and Potential
                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
               Countries          PW/PC-PW’/PC                 GNP-GNP        TB-TB’       RS-RS’      RL-RL

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







            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. All of these “mights” serve                 By., 1985), pp. 679-747.
as a final reminder of how little we know.                        Fuller, Wayne A. Introduction to Statistical Time Series
                                                                    (Wiley, 1976).
                                                                  Hakkio, Craig S. “Does the Exchange Rate Follow a Ran-
                                                                    dom Walk? A Monte Carlo Study of Four Tests for a Ran-
                                                                    dom Walk’ Journal of International Money and Finance
                                                                    (June 1986), pp. 221-29.
1.4                                                               Hooper, Peter, and John Morton, “Fluctuations in the Dollar:
                                                                    A Model of Nominal and Real Exchange Rate Determina-
Adler, Michael, and Bruce Lehmann, “Deviations from Pur-            tion:’ Journal of International Money and Finance (April
  chasing Power Parity in the Long Run,” Journal of Finance         1982), pp. 39-56.
  (December 1983), pp. 1471-87,
                                                                  Hsieh, David A. “The Determination of the Real Exchange
Baillie, Richard T., and Patrick C. McMahon, The Foreign            Rate:’ Journal of International Economics (May 1982), pp.
  Exchange Market: Theory and Econometric Evidence (Cam-            355-62.
  bridge University Press, 1989).
Baillie, Richard T., and David D. Selover. “Cointegration and     Huizinga, John. “An Empirical Investigation of the Long-Run
  Models of Exchange Rate Determination:’ International            Behavior of Real Exchange Rates:’ Carnegie-Rochester
  Journal of Forecasting (1987:1), pp. 43-51.                      Conference Series on Public Policy (Autumn 1987), pp.
Balassa, Bela, “The Purchasing-Power Parity Doctrine: A
   Reappraisal’ Journal of Political Economy (December            Isard, Peter. “An Accounting Framework and Some Issues
   1964), pp. 584-96.                                               for Modeling How Exchange Rates Respond to the News:’
                                                                    in Jacob A. Frenkel, ed., Exchange Rates and International
Campbell, John Y., and Richard H. Clarida, “The Dollar and          Macroeconomics (University of Chicago Press, 1983), pp.
   Real Interest Rates:’ Carnegie-Rochester Conference Series        19-56.
  on Public Policy (Autumn 1987), pp. 103-40.
Cox, W. Michael. “A Comprehensive New Real Dollar Ex-             Koedijk, Kees, and Peter Schotman. “Dominant Real Ex-
  change Rate lndex’ Federal Reserve Bank of Dallas                 change Rate Movements:’ Journal of International Money
  Economic Review (March 1987), pp. 1-14.                           and Finance (December 1989), pp. 517-31,
Cumby, Robert E., and Maurice Obstfeld, “International In-        Lothian, James R. “A Century Plus of Yen Exchange Rate
  terest Rate and Price Level Linkages under Flexible Ex-           Behavior:’ mimeo, New York University.
  change Rates: A Review of Recent Evidence:’ in John EQ.         McNown, Robert, and Myles S. Wallace, “National Price
   Bilson and Richard C. Marston, eds., Exchange Rate
   Theory and Practice (University of Chicago Press, 1984),         Levels, Purchasing Power Parity, and Cointegration: A Test
   pp. 121-51.                                                     of Four High Inflation Economies:’ Journal of International
                                                                   Money and Finance (December 1989), pp. 533-45.
Darby, Michael R. “Movements in Purchasing Power Parity:
  The Short and Long Runs:’ in Michael A. Darby and               Meese, Richard, and Kenneth Rogotf. “Was It Real? The Ex-
  James R. Lothian, eds. The International Transmission of In-     change Rate-Interest Differential Relation over the Modern
  flation (University of Chicago Press, 1983), pp. 462-77.          Floating-Rate Period7 Journal of Finance (September
                                                                    1988), pp. 933-4&
Dickey, David A., and Wayne A. Fuller. ‘Distribution of the
   Estimators for Autoregressive Time Series With a Unit          Sims, Christopher A. “Bayesian Skepticism on Unit Root
   Root:’ Journal of the American Statistical Association (June     Econometrics:’ Discussion Paper 3, Institute for Empirical
   1979), pp. 427-31.                                               Macroeconomics, Federal Reserve Bank of Minneapolis
Dornbusch, Rudiger. “Real Exchange Rates and Macro-                 and University of Minnesota, May 1988.
   economics: A Selective Survey,” Scandinavian Journal of        Tatom, John A. “The Link Between the Value of the Dollar,
   Economics (1989:2), pp. 401-32.                                  U.S. Trade and Manufacturing Output: Some Recent
_______-    “Expectations and Exchange Rate Dynamics:’              Evidence:’ this Review (NovemberlDecember 1988), pp.
  Journal of Political Economy (December 1976), pp. 1161-76.        24-37.
Dornbusch, Rudiger, and Stanley Fischer, “Exchange Rates          Taylor, Mark P. “An Empirical Examination of Long-Run Pur-
   and the Current Account:’ American Economic Review               chasing Power Parity Using Cointegration Techniques,” Ap-
   (December 1980), pp. 960-71.                                     plied Economics (October 1988), pp. 1369-81.
Dornbusch, Rudiger, and Paul Krugman. “Flexible Exchange          Trehan, Bharat. “The Practice of Monetary Targeting: A
   Rates in the Short Run:’ Brookings Papers on Economic            Case Study of the West German Experience:’ Federal
  Activity (1976:3), pp. 537-75.                                     Reserve Bank of San Francisco Economic Review (Spring
Edison, Hali J., and Jan Tore Klovland, “A Quantitative              1988), pp. 30-44.
   Reassessment of the Purchasing Power Parity Hypothesis:
   Evidence from Norway and the United Kingdom$ Journal           Whiff, Joseph A. Jr. “Purchasing-Power Parity and Exchange
  of Applied Econometrics (October 1987), pp. 309-33.              Rates in the Long Run:’ Federal Reserve Bank of Atlanta
                                                                   Economic Review (JulylAugust 1989), pp. 18-32.
Frankel, Jeffrey A. “International Capital Mobility and
  Crowding-out in the U.S. Economy: Imperfect Integration of      Wolff, Christian CR “Time-Varying Parameters and the Out-
   Financial Markets or of Goods Markets?” in R.W. Hafer,            of-Sample Forecasting Performance of Structural Exchange
  ed,, How Open Is the US. Economy? (D.C. Heath and Com-             Rate Models:’ Journal of Business & Economic Statistics
   pany, 1986), pp. 33-67.                                           (January 1987), pp. 87-97.

           /                 /       /    /                    /                      /

       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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