Simple vs. generalized interest rate and purchasing power parity models of exchange rates

The Quarterly Review of Economics and Finance, Vol. 36, No. 2, Summer, 1996, pages 197-218 Copyright 0 1996 Trustees of the University of Illinois All rights of reproduction in any form reserved ISSN 1062-9769

Simple vs. Generalized Interest Rate and Purchasing Power Parity Models of Exchange Rates

SU ZHOU and SAEID MAHDAVI University

of Texas

at San Antonio

We construct a model in which the real exchange rate is affected by the real interest rate and price differentials as well as real factors that cause shocks to the expected flexible-price equilibrium value of the real exchange rate. The model is then employed to test for the “generalized” uncouered interest rate parity and purchasing power parity relations using the data for eight advanced countries and the cointegration techniqw. Simple versions of the parity conditions are also tested for the purpose of comparisons. We find evidence of cointegration only for the generalized version of the parity relations. Also, out-of-sample forecasts generated from error-cowection models indicate that they are more accurate relative to those obtained from a random walk model for half of the countries in the sample.

Explaining the fluctuations in the (real) exchange rates of major currencies in the “modern floating period” has proved to be an empirically challenging task. The bulk of the evidence accumulated so far does not favor the simple purchasing- ower-parity (PPP) models of the exchange rate behavior even in the long run. 7 Moreover, Meese and Rogoff (1983, 1988) report results suggesting that another class of monetary models, known as “uncovered interest parity” or UIPwhich attributes variations in the real exchange rates to real interest rate differentials- does not yield better out-of-sample predictions than a naive model. A possible explanation for this poor performance according to the authors (1988, p. 943) is that “the disturbances impinging on exchange markets are predominantly real. Thus, models that focus primarily on monetary disturbances should not be expected to explain very much.” (Emphasis added). The potential role of real shocks in causing variations in the long-run “equilibrium” value of the real exchange rate has an important empirical implication. If real shocks are primarily responsible for the (nearly) nonstationary behavior of the real exchange rate over time, and to the extent that real interest rate differentials are affected by shocks of different origins, then the real exchange rate

197

198

QUARTERLY

REVIEW

OF ECONOMICS

AND FINANCE

and the (long-term) real interest rate differentials will not move in tandem as suggested by the UIP model. In fact, the results obtained by Meese and Rogoff (1988)-using bilateral data for the U.S., Germany, Japan, and the U.K.-provide no evidence of cointegration between the two variables. Their results have been confirmed by several other studies many of which have attempted to incorporate the effects of real factors in the dynamic modeling of the real exchange rates. The authors of some of these studies have contended that the exclusion of real factors -which might have independent effects on the real exchange ratesfrom cointegrating regressions could lead to a false conclusion of noncointegration.* Since there is no unique set of determinants of the exchange rate, a reasonable approach is to specify a more general cointegrating equation by including several of its major potential determinants (and build down if necessary) rather than limiting the number of the variables to one or two as in many earlier studies. Recent evidence of the relative success of this approach has been provided by Throop (1993). Within the framework of a “generalized uncovered interest parity” (GUIP) model, Throop specifies cointegrating equations for three key bilateral exchange rates (i.e., DM/$, &/$, Y/$) and the U.S. trade-weighted exchange rate which includes proxies for productivity growth, budget balances, and real price of oil in addition to the real interest rate differential. His results suggest that the exchange rates are cointegrated with these fundamentals and that their inclusions in the cointegration analysis improve the out-of-sample prediction relative to a random walk model.3 This paper builds on the GUIP model developed by Throop and offers sevFirst, within the framework of multivariate eral empirical extensions. cointegrating equations, we examine the existence of a long-run relationship between bilateral (real) exchange rates of the currencies of eight countries (i.e., Austria, Canada, Germany, Italy, Japan, the Netherlands, the United Kingdom, and Switzerland) against the U.S. dollar and a set of factors consisting of measures of the real price of oil, fiscal expansion, as well as differentials in productivity growth rate, cumulated current account balance, interest rate, and price level. Our expanded sample includes at least four countries that have relatively small economies and, thus, exercise less influence on world prices of traded goods, international interest rates, and exchange rates. The inclusion of countries with small and large economies provides an opportunity to assess the differential impacts of variables such as fiscal expansion on the real exchange rates. Second, the specified model may also be considered as a “generalized purchasing power parity model” (GPPP) for it relates the exchange rates to price differential variables while allowing for the effects of several other relevant factors. The model, thus, enables us to test for both interest rate as well as purchasing power parity relations based on the significance of relevant coefficients in cointegrating equations. Third, given the importance of the order of integration of the variables in cointegration tests, we employ both the conventional tests with the null hypothesis of nonstationarity and a more recent test

EXCHANGE

RATES

199

developed by Kwiatkowski, Phillips, Schmidt, and Shin (1992) with the null of stationarity. The rest of this paper is organized as follows. Section I presents a brief outline of the theoretical GUIP (GPPP) model. This is followed by specification of the empirical version of the model in Section II. Also presented in this section are the results of cointegration tests and dynamic out of sample forecasts generated using error-correction models. The final section summarizes the paper’s main findings and draws conclusions based on them.

I.

THE THEORETICAL

FRAMEWORK

For a comparable financial instrument with k periods to maturity issued in home and foreign countries the condition for uncovered interest rate parity (UIP) may be written as follows:

E&+k) - et +

prt = &kit - kit*)

(1)

where: et = natural log of the nominal exchange rate of the home currency (i.e., number of units of home currency per unit of foreign currency; or the U.S. dollar in this case), Q(e,+k) = the expected value at time t of e after K periods, pr, = risk premium, and &* = the home and foreign interest rates, respectively (throughout this section, an * denotes a foreign value). Equation 1 suggests that the excess of the home interest rate over the foreign interest rate, compounded over k periods, is equal to the expected depreciation of the home currency over this period allowing for a risk premium, if any. Otherwise, market arbitrage will change the exchange rate between the home and foreign currencies so that uncovered interest parity holds. Equation 1 can be expressed in terms of the real interest rate kRt = kit - pt (where krrt is the expected rate of inflation over k periods at time t in the home country) and the log of the real exchange rate qt = e, + p,* - p, (where p is the log of home country’s overall price level):

qt = %t+d

- k[(kR, - &*)I + Prt

(2)

The expected value of the real exchange rate in Equation 2 may be replaced by a constant representing the flexible-price equilibrium value of q assuming that PPP holds in the long run. However, as Balassa (1964) has pointed out, since the productivity growth rate is likely to be faster in the traded goods sector of the

200

QUARTERLY

REVIEW

OF ECONOMICS

AND FINANCE

economy relative to the non-traded goods sector, q when expressed in terms of overall price levels can change even when q measured in terms of the price indexes for traded goods is constant at its PPP value. Specifically, q of the home currency in terms of overall prices appreciates if the relative prices of traded goods fall faster at home than abroad. A version of Equation 2 accounting for the impact of productivity growth differentials on q through the relative price of traded goods may be written as follows:

41 =

ao+ E&+d +

a2 [@t, -

pt,*)-

(p, -

p,*)l-

a3

(kRt -kR,*)

(3)

where E,(q&+k) is the expected value at time t of q in terms of price indexes for traded goods k periods later and ptl is the log of price index for traded goods at home.4 Again, the term E,(qtt+k) in Equation 3 can be treated as a constant if PPP in traded goods holds. However, traded goods at the home and foreign countries are not perfect substitutes causing deviations from PPP. In addition, shocks arising from changes in real factors cause the expected value term itself to change, thus, leading to changes in q measured in terms of overall prices. For estimation purposes, Equation 3 may be further specified by making the term E,(qt,+k) a function of some of its potentially important real determinants. In what follows, we shall briefly discuss the set of factors included in our specification of Equation 3. The real price of oil has been identified as a major source of shock to the flexible-price equilibrium value of the real exchange rate (Amano and Van Nor1993). An increase in the real price of oil causes a den, 199313; Throop, deterioration in the trade balance and a reduction in aggregate demand of an oil-importing country. As a result, the real value of the country’s currency is expected to depreciate to restore equilibrium in the goods market, ceteris paribus. However, to the extent that the country is less dependent on oil imports relative to its trading partners, its currency vis-a-vis the currencies of the trading partners is expected to actually appreciate. A second source of variation in the expected value of the real exchange rate is change in domestic absorption resulting from persistent fiscal expansion. In an open economy with no significant capital control and a flexible exchange rate regime, an increase in government spending (deficit) initially leads to higher domestic real interest rates, net inflow of foreign capital and appreciation of the domestic currency in the short to medium term. The trade balance, however, begins to deteriorate as part of the increase in spending falls on foreign products. This tends to dampen the extent of expected appreciation of the real exchange rate over the market’s relevant time horizon. For small economies, however, the portion of the increase in spending which falls on imports is likely to be higher given that these economies generally have a higher degree of openness (i.e., the ratio of exports plus imports to GDP) relative to larger economies.

EXCHANGE

RATES

201

The implication is that the appreciation of the real exchange rate for the small economies resulting from domestic fiscal expansion may not be significant. In the long run, however, the real exchange rate is expected to depreciate to raise net exports in order to make up for earlier trade deficits and to service foreign debt. Stated differently, as the cumulated current account (trade) deficits continue to grow over time the solvency constraint is likely to become more binding. In theory, therefore, the long-run depreciation of the real exchange rate must be large enough to stop the net foreign indebtedness from rising further.” The pressure on q to change in the long run due to persistent fiscal expansion at home and the resultant accumulation of foreign debt may be captured by the differential in the cumulated current account between the home and foreign countries.

II.

THE EMPIRICAL ANALYSIS

Based on the discussion of Equation 3:

in Section

I, we specify the following empirical

1nRER = PO + Bl 1nPoil + p2 1nG + B3 1nUSG + B4 1nPD + p5 CCAD + B6 RD

version

(4)

where: 1nRER = the log of home currency real exchange rate or 1nRER = 1nER + (lnPGUS - 1nPG); 1nER = the log of nominal exchange rate defined as units of domestic currency per U.S. dollar; PG, PGUS = home and U.S. overall price levels, respectively, as measured by GDP (or GNP) price deflators; lnPoi1 = the world real price of oil defined as the log of the crude oil price index of the United Arab Emirates divided by the world non-fuel price index; 1nG and 1nUSG = the logs of the ratios of home and U.S. government spending to GDP (or GNP), respectively;6 1nPD = (1nPT - InPTUS) - (1nPG - lnPGUS); PT, PTus = the price indexes of traded goods for the home country and the U.S., respectively, as proxied by respective wholesale price indexes; CCAD = the differential in the cumulated current account balance to GDP (or GNP) ratios between the home country and the U.S.; RD = the real interest rate differential defined as R - Rus = (i n) - (i”” - F);

202

QUARTERLY

REVIEW

OF ECONOMICS

AND FINANCE

i, ius = home and U.S. yields on the long-term government bonds, respectively; Tc,7cus= home and U.S. expected inflation rates, respectively, where R is proxied by a centered two-year (nine-quarter) moving average of inflation in consumer prices. The sample period for all the countries with the exception of the Netherlands is 1973:QII-1993:QI. For the Netherlands the sample period is 1977:QI1992:QIV.’ Since by definition 1nRER = 1nER + (lnPGUS - 1nPG) there is an automatic correlation between 1nRER and 1nPD in Equation 4. To avoid estimation problems arising from this correlation, Equation 4 may have to be estimated in terms of nominal exchange rates if the variable 1nPD is included in the cointegrating equation. After substituting for 1nRER and simplifying, the following equation for the nominal exchange rate is obtained: 1nER = PO + Bl lnPoi1 + B2 1nG + B3 1nUSG + B4 (1nPT - lnPTuS) + (l-B4)(lnPG - lnPGUS) + p5 CAAD + /36 RD

(5)

For future references, we define the following additional price differentials variables: 1nPTD = (1nPT - lnPTuS) and 1nPGD = (1nPG - lnPGUS). We begin our empirical analysis by determining the order of integration of the variables of the empirical model. To this end, we employ three types of tests: The augmented Dickey-Fuller (ADF) test (Dickey and Fuller, 1979; Said and Dickey, 1984), the Phillips-Perron (PP) test (1988), and a more recent test developed by Kwiatkowski, Phillips, Schmidt and Shin (1992) referred to as KPSS test. The null hypothesis in the ADF and PP tests-which are routinely used in empirical studies-is that the variable in question has a unit root or is nonstationary. The null hypothesis in the KPSS test, on the other hand, is that the variable being examined is stationary. By employing the KPSS test in addition to the ADF and PP tests one can avoid a situation where the “deck is stacked” against the null of stationarity in the testing procedure (Maddala, 1991). If for a process the ADF (PP) test rejects the null of nonstationarity and the KPSS test fails to reject the null of stationarity the evidence that the process is I(0) is said to be “strong.” Similarly, there is strong evidence in favor of an I(1) process if the ADF (PP) test fails to reject the null of nonstationarity and the KPSS test rejects the null of stationarity (Baillie and Pecchenino, 1991). In determining the order of integration, each of the three tests discussed above is performed with and without a time trend variable. The results of the stationarity tests are presented in Table Al in the Appendix section. Several points are worth noting in relation to these results: First, with few exceptions, most variables tested are first-differenced stationary or I(1) processes. Moreover, the evidence supporting the hypothesis that these variables are well described by I(1) processes is strong, for it is based on consistent results of the

EXCHANGE

RATES

203

ADF, PP, and KPSS tests. In this connection, note that the levels of all the eight bilateral real exchange rates over the sample period are nonstationary. This result is of particular interest, for the existence of a unit root in the real exchange rate is often interpreted as evidence against the PPP hypothesis. Unlike many earlier studies, however, this conclusion is not due to simply failing to reject the null hypothesis of nonstationary levels, but also based on rejecting the null of stationarity. Second, there are two variables-i.e., the CCAD variable for Japan and the 1nPTD variable for the Netherlands-for which the three tests do not yield consistent results: The level of CCAD seems to be either I( 1) or I(2) while the level of 1nPTD is either I(0) or I( 1). Third, test results suggest evidence of level stationarity in the case of 1nG in Austria and Germany and RD in the U.K. For the 1nG variable, the values of KPSS statistics are only marginally below the 5% level critical value, but they reject the null of stationarity at the 10% level of significance. Given the low power of the conventional tests, the borderline values of the KPSS test statistics in some cases, and the theoretical relevance of the variables whose degree of integration could not be exactly determined, we lean on the side of keeping these variables for conducting cointegration tests.’ Our cointegration tests are based on the procedure suggested by Johansen (1988) and Johansen and Juselius (1990).’ For each country, the number of cointegrating vectors is se uentially determined using the “maximum eigenvalue” test statistic or A,,,. 9 ’ The top panel of Table 1 presents the results of our cointegration analysis applied to a simple version of PPP according to which the nominal exchange rate between two countries is equal to the differential in their price levels. For none of the countries the null of r = 0 could be rejected at the 5% level of significance. The finding of “noncointegration” tends to reject the simple PPP relation and is consistent with the conclusion drawn based on nonstationarity of the real exchange rates noted earlier. Similarly, as can be seen from the lower panel of Table 1, the simple version of the UIP model does not receive support from the cointegration test results: Only for the U.K. there seems to be a cointegrating relationship between the real exchange rate (RER) and the real interest rate differential(RD). The estimated coefficient of RD (&d) in the cointegrating vector is significantly different from zero, whereas the coefficient of 1nRER is not, according to the x2 test statistic.” These results, however, probably reflect stationarity of RD in the case of the U.K. l2 Cointegration tests for the generalized versions of the two parity conditions are conducted based on Equation 5. Since there are eight variables in the equation, there could be a maximum seven distinct cointegrating vectors for each country. According to the top panel of Table 2, the number of cointegrating vectors for the countries of the sample ranges from 2 to 4. This lends empirical support to the view that lack of cointegrating relations between the variables of the simple versions of PPP and UIP was probably due to omissions of some important variables which might have caused deviations from the parity relations. The remaining part of Table 2 reports the estimated coefficients of the cointegrating vectors for each country. Since the existence of more than one

Table 1.

COINTEGRATION

2.50

r
No&s:

= 2.59

3.22

For Ho: &d = 0, x2(1)

4.63

2.70

4

9.25

3

= 10.31

3.86

15.19*

4

8.18

14.90

8.18

14.90

5% Critical Value

The sample period for the Netherlands is from the first quarter of 1977 to the last quarter of 1992. For all the other countries, the sample period runs from the second quarter of 1973 to the first quarter of 1993. The critical values for the cointegration tests are taken from Osterwald-Lenum (1992). The lag length J is chosen on the basis of the Bay&an Information Criterion (BIG) of Schwartz (1978). r is the hypothesized number of cointegrating vectors. R’s are the parameters of the cointegrating vectors normalized on exchange rates. The 5-percent critical value for the x2( 1) statistic is 3.84. * denotes significantly different from zero at the 5-percent level.

[p,,,, &d] = L-1.00, -0.20’1 = 0, x2(1)

3.40

0.16

3.59

For Ho: p,,,

12.09

9.73

8.61

3

2.80

Statistics

6.91

B. Estimated Cointegrating Vector for the U.K.

8.75

r=O

3 &,,,

4

4

UIP

3

j

H,:

for Simple

3.68

0.30

Testing

14.50

9.58 4.41

4.11 0.54

6.81

3

3.51

4

11.98

3

3.08

PPP

U.K.

8.73

Statistics

3

Switzerland

6.85

a,,

for Simple

Netherlands

10.58

3

Testing

Japan

1.54

4

GelYllaIly

6.98

4

Canada

rll

3

Austria

r=O

H,:

j

country: IdY

TESTS FOR THE SIMPLE PPP AND UIP CONDITIONS

A. Testing for the Number of Cointegrating Vectors

EXCHANGE

RATES

205

cointegrating vector tends to complicate interpretation of the results we need to select one cointegrating vector for each country which reflects the relationship between the exchange rate and other variables. The selection criterion is based on the statistical significance of the x2 statistic for the coefficient of the exchange rate across the estimated cointegrating vectors. l3 The selected cointegrating relation for each country is printed in boldface. In interpreting the estimated coefficients reported in Table 2, it should be born in mind that the coefftcients of all the variables, with the exception of the general price-index variable, are the same as those in the equations for the real and nominal exchange rates (see Equations 4 and 5). The coefftcient of the real price of oil in the selected cointegrating vectors is statistically significant in the cases of Austria, Canada, Japan, and Switzerland and in all of these cases displays the expected positive sign. The elasticities of the nominal exchange rate with respect to changes in the real price of oil are the largest for Switzerland and Japan suggesting that Swiss Franc and yen substantially depreciate when the real price of oil rises. This is expected in view of the fact that these two countries are heavily dependent on oil imports. Domestic fiscal expansion (as proxied by an increases in the output share of government) in Canada, Germany, Japan, and the U.K. shows to be significantly associated with currency appreciations in these countries (depreciation in the case of Italy). However, small-economies’ exchange rates are generally less sensitive to domestic fiscal expansion as one would expect. A rise in the measure of U.S. fiscal expansion, on the other hand, seems to have no significant effect on the exchange rates. Note that for Italy, the coefficient of 1nUSG is significant, but it displays the “wrong” sign. These results, however, need to be interpreted with caution considering the fact that the variables 1nG and 1nUSG are deficient measures of fiscal expansion and that their short term effects on the exchange rates could be reversed in the long run. The variable 1nPTD (i.e., traded-goods price differential) has a relatively large positive elasticity coefftcients and is significantly different from zero for Austria, Canada, Germany, Japan, Switzerland and the U.K. Accordingly, productivity improvements leading to a relative decline in the relative price of tradeables are associated with a fall (appreciation) of the exchange rates of these countries. For example, using the estimated coefficient, a one percent fall in the relative price of tradeables in Japan is associated with roughly 5.3 percent decline in the real Y/$ exchange rate, or alternatively, an appreciation of yen relative to the U.S. dollar by 5.3 percent. The statistical significance of the coefficients of the 1nPTD in the context of multivariate cointegrating relations also supports validity of GPPP when it is expressed in terms of prices of traded goods. It should be pointed out that when GPPP holds in terms of traded goods prices it may not necessarily hold in terms of overall price levels. However, consistent with Equation (5), the coefficient of the variable 1nPGD in the selected cointegrating relations are mostly negative when they are statistically significant.

COINTEGRATION

B.

0.67* (5.81) 0.20 (0.96) 1.74* (7.68)

-1.00 (3.08) -1.00* (6.57) -1.00 (2.47)

1

3

2

2

-4.89* (5.21) -3.36* (6.97) 2.30 (1.56)

-3.16* (19.67) -0.32* (7.60)

0.17 (3.12) 0.12* (7.58)

-1.00 (1.70) -1.00* (7.40)

1

4

3

2

1.02 (1.03) -1.70 (1.02) -4.88 (2.56) -0.64 (1.68)

-0.68* (16.81) -0.68* (12.92) 0.08 (0.12) 0.13* (5.68)

-1.00 (3.20) -1.00 (1.81) -1.00 (0.22) -1.00* (6.32)

1

PP

Ppoil

Per

58.56* 51.34* 42.79; 33.06 24.12 16.15 13.36 4.69

3

Germany

Vector

Vectors

67.55’ 45.55’ 37.83 32.01 21.99 16.00 13.15 0.96

3

4

96.05’ 54.69* 39.45’ 33.62’ 26.81 20.26 13.91 0.01

Canada

Austria

Estimated Cointegrating

I:,: r=O l-2 1 l-12 r13 r<4 I-55 1.56 r<7

Country:

Vectors

68.15’ 53.07’ 37.28 26.86 18.32 15.54 10.96 4.48

Italy 3

-1.63 (1.42) 3.76 (3.40) 4.35 (1.74)

Germany

1.87* (15.66) -0.02 (0.05)

Canada

1.74 (1.36) -6.89* (11.22) 1.41 (0.45) 0.60 (1.03)

Austria

PU%

Pp**

2 66.53’ 45.85* 35.56 28.11 25.07 17.82 8.12 4.19

0.99 (0.10) 5.64’ (3.93) -7.74 (2.67)

3.60* (6.01) 1.66* (7.70)

0.34 (0.02) 11.26* (10.32) -6.45 (2.44) 1.77+ (4.34)

3 h,,, Statlstlcs 92.01’ 44.96* 32.97 31.78 17.04 13.67 5.66 0.09

Netherlands

0.95 (0.17) 4.97 (2.08) 14.47* (6.93)

-2.81 (2.26) -2.26* (6.96)

-0.56 (0.03) -15.73* (9.46) 13.07* (4.38) -0.69 (1.93)

hw’

72.74’ 61.31* 36.36 25.20 24.39 18.03 6.61 0.57

2

Switzerland

PPP AND UIP CONDITIONS

Japan

TESTS FOR THE GENERALIZED

A. Test for the Number of Cointegrating

Table 2.

-1.27 (1.72) -1.45 (1.16) 6.20* (6.38)

-3.30 (14.07) -0.56. (5.93)

-2.33* (27.15) -0.45 (0.91) -2.40* (3.89) -0.25* (6.32)

P ccad

55.89’ 52.05’ 42.61’ 30.34 21.16 15.79 10.69 0.12

4

U.K.

0.06* (6.85) 0.01 (1.39) -0.05 (0.90)

-0.04* (11.47) 0.00 (1.29)

-0.03 (1.10) -0.04 (0.87) -0.01 (0.01) -0.04 (2.76)

P rd

51.07 44.91 39.43 33.32 27.14 21.07 14.90 8.18

5% critical Value

:

E

i

2

R

g

9 F1 Q

%

5

$

$

w

Nok

-1.00 (3.37) -1.00* (8.27)

-1.00 (2.75) -1.00* (9.86)

-1 .oo (2.68) -1.00* (9.44) -1.00 (1.67)

1

1

1

Numbers

3

2

2

2

2

in parentheses

-1.00* (23.10) -1.00 (2.12)

1

2

-1.00* (12.23) -1.00 (2.08)

1

are the x2(1) statistics

(3.30) -0.17 (2.55) -386.7* (17.69)

0.99

-0.51* (4.13) 0.46* (16.21)

0.80* (12.27) 0.11 (0.57)

0.24* (5.13) 1.44* (8.27)

-0.30 (3.63) 2.15* (9.98)

-0.41 (0.14) -0.52 (0.08) -2181.2* (2.25)

U.K.

-4.86* (10.98) -0.59 (2.01)

Switzerland

-3.59 (3.75) -0.52 (0.11)

Netherlands

-1.43 (2.82) 3.34* (5.62)

JaJaJ

Italy -3.50* (11.64) 7.28* (9.95)

for HO: f3, = 0. Also see notes to Table

-2.76 (2.40) -2.32* (4.01) 2803.2* (12.02)

0.22 (0.09) -0.18 (0.10)

6.99* (9.74) -2.46 (2.06)

-2.38* (16.87) -1.85 (1.05)

2.87* (12.37) 4.32* (5.99)

I.

2383.0* (9.70)

3.81

-0.18 (0.01) 4.13* (10.12)

0.33 (0.02) -0.04 (0.00)

5.27* (33.99) -2.35 (1.10)

-0.10 (0.50) -0.82 (1.13)

4.95 (3.71) -1.49* (7.61) -2039.2* (12.12)

3.78 (2.78) -3.84* (10.78)

7.22* (4.15) -3.22 (1.30)

-3.51* (12.45) 7.60* (4.52)

1.14* (4.80) -2.47 (0.87)

1.82 (0.94) 4.28* (5.16) -1391.0 (1.16)

-14.39* (11.43) -0.08 (2.58)

8.07* (7.33) -4.oa* (4.46)

0.48 (1.10) 2.92 (1.64)

2.33 (1.96) 13.23 (2.19)

-0.05* (3.85) 0.01 (0.52) -63.70* (8.26)

0.04* (5.89) 0.02 (2.92)

0.05 (2.45) -0.01 (0.35)

0.00 (0.20) -0.01 (0.03)

-0.10* (15.08) 0.00 (3.10)

5 M

2

E

208

QUARTERLY

REVIEW OF ECONOMICS

AND FINANCE

One may recall that the CCAD variable has been included to capture forward-looking expectations about exchange rates related to sustainability of the balance of payments in the longer run. On this basis, a rise in CCAD should be associated with an appreciation of the home country’s currency because of the favorable net change in cumulated current account balances. The negative sign of the coefftcients of the CCAD variable is consistent with this argument. The real exchange rates of Austria, Canada, the Netherlands and the U.K. appreciate against U.S. dollar as the gap between each country’s cumulated current account to output ratio and the same ratio for the U.S. grows. It is worth noting that the CCAD variable is insignificant in the case of Japan. This result is counter-intuitive given that Japan has been accumulating huge trade surpluses against the U.S. over time and that yen has been appreciating against the U.S. dollar since the mid 1980s. One possible explanation for this result may lie in the fact that the CCAD variable in the case of Japan is probably I(2) and, strictly speaking, cannot be included in the cointegrating equation along with other variables all of which have a lower order of integration. Finally, in most cases the real interest differential variable (RD) has the negative sign as in the theoretical GUIP model (see Equation 3); but, except for Italy, its coefficients in the selected cointegrating equations are not statistically significant. The results, therefore, generally fail to support GUIP. In the final part of our empirical analysis we use error-correction models (ECM) associated with the selected cointegrating equations for generating outof-sample forecasts of the nominal exchange rates. To this end, we split the sample period into two parts. The first period is used for the purpose of estimation. For all countries except the Netherlands the estimation period is 1973:QII1982:QIV (for the Netherlands, the estimation period is 1977:QII-1986:QIV). To save degrees of freedom and to deal with the problem associated with more than one cointegrating vector, a restricted version of the error-correction model is used for each country. Specifically, the number of lags is set equal to one for all the variables and the series for the error-correction term (included to capture the adjustment towards the long-term equilibrium relationship) is obtained using fixed coefficients of the selected cointegrating vectors estimated based on the entire sample. We then generate out-of-sample forecasts over the forecast period of 1983:QI-1993:QI (1987:QI-1992:QIV for the Netherlands) using a rolling regression approach. In this approach, the estimated equation is used to generate one- to several-periods ahead forecasts. After each forecasting round, the equation is re-estimated by adding to the sample one more observation set using actual realized values of the variables. New forecasts are then generated based on the re-estimated equation and so on. The predictive accuracy of the model for each country is then evaluated by computing the root-mean-squareerror (RMSE) statistic over the forecast period. To assess relative forecasting performance of the error-correction models, we also compute RMSE from a random walk model (RWM) of the exchange rate.

EXCHANGE

RATES

209

Out of sample forecasts based on the dynamic approach described above were generated for periods ranging from one quarter to eight quarters ahead. Table 3 reports the results in terms of the RMSE values from the ECM and the RWM of the exchange rate for one and two quarter ahead forecasts. As can be seen from the table, the ECM outperforms the RWM in the case Austria, Canada, Japan, and the Netherlands for the indicated periods. With the exception of Japan, all these countries have relatively small economies. The results for longer forecast horizons (not reported) suggest that the ECM has a superior forecasting performance for all the periods in the cases of Austria and Japan. For Canada and the Netherlands, however, the RWM consistently outperforms the ECM for horizons longer than two quarters. The findings that the ECM can generate more accurate forecasts of the nominal exchange rates of half of the countries of the sample relative to a naive model of no change and then only for short horizons in two cases may be rather disappointing. These findings, however, may be interpreted in a more favorable light considering (a) the low success rates of many of previous studies noted earlier, (b) the limitations imposed by a relatively small sample size on estimation and dynamic forecasting of the exchange rate using error-correction models, and (c) the fact that forecast errors tend to be larger the longer the horizon over which the exchange rate is forecast regardless of the model used.

III.

SUMMARY

AND CONCLUSIONS

In this paper, we constructed an empirical model in which the (real) exchange rate was linked to the real interest rate differential, price level differential, and several other variables which affect the exchange rate through shocks to the expected value of the real exchange rate. Using the data on the bilateral exchange rates of Austria, Canada, Germany, Italy, Japan, the Netherlands, Switzerland and the U.K. against the U.S. dollar over the modern floating period, we tested for existence of cointegrating relations among the variables of the model and generated dynamic out-of-sample forecasts of the exchange rates using error-correction models. The main findings of our empirical analysis are summarized below: 1.

Cointegration tests applied to simple (bivariate) versions of the model did not provide support for the uncovered interest rate parity (UIP) or purchasing power parity (PPP) conditions in almost all the countries of the sample. Lack of support for the simple version of the PPP relation from cointegration test applied to the nominal exchange rate and price level differential was consistent with our earlier finding of “strong” evidence against mean-reverting behavior of the real exchange rates. The latter finding was based on both the conventional tests (with the null hypothesis of nonstationarity) and the KPSS test (with the null of sta-

Model RWM ECM RWM ECM 2.0 1.8 3.0 3.0

Canada 7.1 7.8 10.7 12.2

GXlll~Y

Japan 6.3 6.1 9.6 9.4

IdY RMSE 6.7 7.2 10.6 11.9 7.6 7.0 10.1 9.7

Netherlands

7.6 8.3 11.3 12.8

Switzerland

7.0 7.0 9.9 10.7

U.K.

in percentage terms. The forecasting period for Netherlands is from the first quarter of 1987 to the last quarter of 1992. For all the other countries, the forecasting period runs from the lirst quarter of 1983 to the first quarter of 1993. The error-correction model used in forecasting for each country consists of a restricted error-correction term and lagged first differences of all eight variables included in Equation (5). The restricted error term in each model is equal to I3 xt_l, where X is a vector of eight variables and 5 is the estimated cointegrating vector in which R,,. is found to be statistically signilicant. The lag length of the model is set equal to one for all eight countries.

6.9 6.7 10.6 10.3

Austria

FORECASTING PERFORMANCE COMPARISONS

No~ux These statistics are approximately

2 quarters

Horizon 1 quarter

Country:

Table3.

EXCHANGE

2.

3.

RATES

211

tionarity). We found evidence of one or more cointegrating vector(s) among the variables of the full model. In the context of cointegrating equations, the “generalized” version of UIP did not perform any better than its simple version. The generalized PPP relation expressed in terms of price indexes of traded goods, however, received empirical support in six countries of the sample. Dynamic out-of-sample forecasts generated based on error-correction models were found to be more accurate than those generated by a naive model of no change in four countries over one and two quarter horizons.

Our results provide additional support for the point emphasized by Throop (1993) and others that shocks to the expected equilibrium values of the exchange rates arising from changes in some real factors lead to deviations of the exchange rates from their PPP values and weaken their links with the real interest rate differentials. An implication of these results is a diminished role for the interest rate differentials (and, therefore, for monetary policy) in affecting of the the exchange rates. l4 At a more practical level, the cointegration exchange rates with the aforementioned factors indicates that part of the shortterm changes in the exchange rates reflects an error-correction process. The inclusion of an error-correction term in the (real) exchange rate models is thus expected to improve their forecasting ability. We would like to thank two anonymous referees for helpful comments on an earlier version of this paper. Financial support provided by a summer research grant from the College of Business of the University of Texas at San Antonio is gratefully acknowledged.

Acknowledgment:

APPENDIX

TO FOLLOW

Austria

1nER 1nRER 1nG InPTD 1nPGD CCAD RD

3. Germany

1nER InRER InG 1nPTD 1nPGD CCAD RD

2. Canada

InER InRER 1nG 1nITD InPGD CCAD RD

1.

InPoil 1nUSG

Variable

TableA. 1

APPENDIX

-1.38 -2.19 -3.60* -1.76 -2.11 -2.02 -2.61

-1.57 -1.23 -2.30 -1.51 -2.74 -2.85 -2.26

-1.34 -2.10 -4.80* -1.33 -2.09 -2.15 -2.47

-2.09 -2.62

-2.89

tr.

-2.17 -2.15 -4.09’ -1.71 -0.72 -3.40 -2.86

-1.57 -2.19 -2.70 -1.70 -1.83 -3.32 -2.67

-1.89 -1.87 -3.38’ -2.83 -1.97 0.12 -1.92

-1.59 -1.41 -1.48 -1.03 -2.87 -1.02 -1.46

-1.86 -1.96 -6.68* -1.67 -1.65 -1.41 -1.84

-2.76 -2.40

-1.93 -2.52

-2.17 -2.30 -4.44* -2.44 -1.16 -2.29 -2.50

-2.89

WJ

-3.45

tr

UNIT ROOT TESTS

Level

-2.16 -1.87 -4.39’ -1.78 0.33 -1.33 -2.34

-1.40 -1.89 -2.09 -1.04 -1.98 -0.99 -1.88

-2.17 -2.05 -3.52* -1.79 -1.74 -1.37 -2.01

.748* .469* ,427 1.355’ 1.630* 1.417’ ,529’

1.028’ ,807’ ,600’ 1.480’ 1.071’ .507* .468*

.829’ ,470’ ,450 1.491’ 1.478’ ,483’ ,465’

,489’ ,470’

.463

-3.45 -2.86 -2.41

qP 5% Critical Value

Test Statistics Z&J

.176* .212* .143 .315* ,401’ .357* .198*

,342’ .247* .149* .244* .254* .227” .166*

.213* .319* .408’ .182*

,145

,174’ ,190’

,322’ .150*

.146

IlT

-7.41’ -7.26’ -4.31’ -8.40’ -2.92’ -4.49*

-3.77’ -3.30’ -2.90* -3.96’

-7.16* -5.66* -7.29’ -6.20* -4.93* -3.55* -4.66’

-7.77’ -15.02. -6.611 -7.79’

-8.18; -8.35;

-5.40* -5.79*

First Difference

-2.89

Z&L)

-3.38’ -3.78’;

-3.44* -3.62* -3.59’ -2.92; -3.15; -3.16’ -3.18’

-2.98” -3.03* -2.96; -3.51’

-3.29* -3.56*

-4.33* -4.41*

-2.89

tu.

,456 .434 ,309 ,080

,089

,089

,170 .076 ,081 ,197 .458 ,315 .098

.157 ,158 ,453 ,088

,075 ,088

,284 .073

.463

qP

I(1) I(l) l(l) I(1)

I(1) I(l) I(O)

I(1) l(l) I(l) I(l) l(1) I(l) I(l)

I(l) I(l) I(O) I(l) I(l) I(l) l(1)

I(l) l(l)

Conclusion

InER 1nRER InG InPTD 1nPGD CCAD RD

7. Switzerland

1nER InRER InG 1nPTD InPGD CCAD RD

-2.23 -2.35 -1.87 4.64’ -2.83 -1.98 -2.04

-1.74 -2.21 -0.11 -3.74’ -2.39 -0.81 -2.47

-2.83

RD

6. Netherlands

-0.58 -1.68 -2.48 0.22 -0.04 -0.19

-1.85 -2.09 -0.55 -1.82 -2.34 -2.82 -0.95

lnER InRER 1nG 1nITD 1nPGD CCAD

5. Japan

InER 1nRER InG 1nPTD InPGD CCAD RD

4. Italy

-2.79 -2.51 -2.85 -3.22 -1.40 -1.88* -2.07

-2.15 -2.02 -3.21 -3.68; -2.21 -3.71’ -2.64

-3.07

-3.05 -2.71 -2.34 -3.35 -3.20 -3.08

-2.28 -2.46 -2.49 -3.22 0.29 -3.35 -2.80

-1.77 -1.87 -1.51 -2.86 -2.78 -2.80 -1.65

-1.33 -1.63 -0.25 -2.78 -1.46 -0.78 -1.79

-1.99

-0.59 -1.72 -2.78 0.08 0.45 1.48

-1.49 -1.68 -0.72 -2.87 -2.85 -0.76 -0.91

-2.16 -2.10 -2.24 -1.20 -0.45 -1.93 -2.00

-1.58 -1.54 -3.15 -2.16 -1.82 -2.36 -1.84

-2.14

1.022* .45 1 .982* 1.343: 1.309’ .602* ,547

,441 .284 1.271’ .598* 1.362* 1.321’ .203

.464’

.123 ,177’ ,128 .365* ,401’ ,345‘ ,223’

,246’ .255* .175* ,129 ,148’ .213* .189*

,151’

-3.51* -3.50’ -3.37’ -3.51’ -3.03* -3.15; -3.65’

-3.53’ -3.75’ -4.76; -3.50’ -3.91’ -3.54’ -3.70;

-3.44*

-2.92’

-2.99’ -3.31’ -4.44’ -6.38’ -2.98’ -3.60* -5.16’

(For the second difference of CCAD

.305* ,234’ ,148’ .195* .410* ,232” .149*

-4.04* 417* -3.29* -4.76; -3.39’ -2.89’

1.451* ,865’: ,472‘ 1.784’ 1.617’ 1.571*

1.221’ .801* 1.540* 1.456’ 1.697’ 1.235’ 1.302*

,153’ ,149’ .338* .169* .245* ,422”

-2.24 -2.25 -2.68 -2.58 -2.54 -1.15

-1.60 -2.03 -3.28 -2.53 0.74 -2.54 -2.93

-7.86’ -8.35’ -15.79’ -4.71’ -11.30* -4.41* -4.45*

-6.34’ -6.32’ -l&98* -3.68* -7.20’ -3.73’; 4.35’

,089 ,064 ,143 ,460 ,440 .388 ,122

.lll ,123 ,151 ,128 ,202 ,424 .092

,095)

-9.31’ 4.05’

,066 ,062 .309 .125 ,452 .658*

.142 .069 .I28 .038 .460 ,272 .105

-6.87* -6.75’ -19.86’ 4.20* -3.45* -1.96

-6.06: -6.35; -10.71* -23.98$ -3.58: -3.15’ -6.31*

I(l) I(l) I(1) I(1)

Iili

I(1)

I(1)

I(1) I(1)

I(l)

I(1) I(1) I(l) I(0) or I(1)

I(l)

I( 1) or I(2)

I(l) I(1) I(1) I(l) I(1)

v1

t;

ha

5

Rn

!z

E n

Ndw

1nER 1nRER 1nG 1nPTD InPGD CCAD RD

8. U.K.

-2.10 -2.13 -2.50 -2.78 -2.42 -1.55 -3.16’

-2.89

tP

CONTINUED

-2.41 -2.36 -2.65 -3.28 -1.41 -3.40 -3.68*

-3.45

tr

-1.86 -1.91 -2.41 -1.02 -2.36 0.95 -2.91’

-2.89

Wp)

Level

-2.07 -2.14 -2.38 -1.77 -0.86 -2.00 -3.49’

-3.45

w

,795’ .537* ,482: 1.615’ 1.660’ 1.510’ .235

.463

S 5% Critical Value

Test Statistics

,182’ ,151’ ,195’ ,183’ ,415’ .374* .066

.146

q7

-4.01; -4.17’ -3.40’ -3.08* -3.26* -2.96’

-2.89

b

-6.47’ -6.28’ -11.07’ -4.25’ -4.11* -3.05’

First Difference

-2.89

z&J

.070 ,066 ,103 ,101 ,445 ,452

.463

qcr

I(l) I(l) I(l) I(1) I(1) I(1) I(O)

Conclusion

(I) The sample period for the Netherlands is from the lirst quarter of 1977 to the last quarter of 1992. For all the other countries, the sample period runs from the second quarter of 1973 to the first quarter of 19%. (2) The t and X(t) statistics are for the ADF tests and Phillips-Perron tests, respectively. t,, and Z(F) pre for the model with a constant term but no time trend. h and Z(t,) are for the model with a constant term and a time trend. I&, and qr are the KPSS statlstlcs based on residuals from regressions with a constant term only, and with a constant term and a time trend, respectively. (3) We do not report tr, Z(t,). and qr statistics for the lirst differences because there is no significant time trend in the first differences of the variables. (4) * denotes significance at the .i-percent level.

Variable

TableA I.

EXCHANGE

RATES

215

NOTES *Direct all correspondence to: Su Zhou or Saeid Mahdavi, The University of Texas at San Antonio, Division of Economics and Finance, San Antonio, TX 78249-0633. 1. One test of PPP is whether the real exchange rate is a stationary variable. Another test is based on the existence of cointegrating relationship between the log of nominal exchange rate (or its percentage change) and the price level (or inflation rate) differential. See, for example, MacDonald and Taylor (1992) and Fung and Lo (1992) for a review of the empirical evidence in developed countries and references. Results favoring PPP in some high-inflation developing countries have been reported by Mahdavi and Zhou (1994). 2. Coughlin and Koedijk (1990) g enerally reject the existence of cointegrating relationships in a bivariate setting between the aforementioned exchange rates and differentials in the real interest rates, the ratio of wholesale price to consumer price, real output per capita output, and cumulated current account balance. They point out that their results, among other things, may reflect a sample period (June 1973-June 1988) which is too brief to capture the long-run tendency of the real exchange rate and the possibility that the latter is affected by random real shocks. Similarly, Lim (1992) finds that various models of the real exchange rates between the U.S and other G- 10 countries based on several combinations of measures of thrift, productivity, terms of trade, and real interest rate differentials fail to produce stationary residuals. Edison and Pauls’ (1993) analysis of both the trade-weighted and bilateral values of the U.S. dollar over the period 1974:Q3-1990Q4 indicates that the null hypothesis of noncointegration between the exchange values and real interest rate differentials cannot be rejected even when a measure of cumulated current account balance is included in the cointegrating equations. The authors suspect that their results may be due to omissions of some relevant variables from cointegrating relationships. On the other hand, Amano and Van Norden (1993a, 1993b) presented evidence suggesting that the U.S-Canada real exchange rate is cointegrated with terms-of-trade variables and that the U.S. real effective exchange rate is cointegrated with the price of oil. 3. Throop’s empirical analysis has the advantage of using an error-correction model for the purpose of forecasting. However, he does not test for the statistical significance of the model’s coefficients. Moreover, one cannot infer from his paper whether the coefficients of the cointegrating vector in the dynamic out-of-sample forecasting were restricted or not. The latter, as will be pointed out later, is an important consideration in forecasting based on an error-correction model. 4. In deriving Equation 3 it is assumed that the expected difference between home and foreign countries relative prices is a linear function of the current difference. 5. In terms of Equation 2 this means that the depreciation of the real exchange rate must offset the increase in the risk premium demanded by foreign lenders. 6. Admittedly, the relative share of government spending as a measure of fiscal expansion is not a good substitute for more refined variables such as (high-employment) budget deficits. The choice of the former variable, however, was based on two practical considerations: (a) Budget deficit data are not available for all countries of the sample on a quarterly basis and (b) unit root tests indicate that the U.S. budget deficit is probably stationary; thus it cannot help explain the nonstationary trend movements of the real exchange rates. 7. With the exception of the current account data, all the data were taken from the International Financial Statisticspublished by the International Monetary Fund. The current

216

QUARTERLY

REVIEW OF ECONOMICS

AND FINANCE

account data were collected from the OECD Main Economic Indicators. For Japan, the data on the current account balance in terms of yen were not available. Therefore, we used the trade balance data instead. 8. Two general points to be noted in this connection are that an I(0) variable, in principle, can be included in the cointegrating equation along with I(1) variables. In this case, an additional unit vector, for example (0 0 . . 1 O..O), would result (Johansen and Juselius, 1990, p. 192). Also, as pointed out by Banerjee, Dolado, Gailbraith and Hendry (1993, p.308) the omission of a relevant I( 1) variable from a relationship results in serious biases. 9. Johansen tests of cointegration are conducted through a vector error-correction model of the following form: j-1

AYt =

c i=

IiAYt_i+IIYt_j+a+$ 1

where YLis a n x 1 vector of I(1) variables, rand II are n x n matrices of short and longrun effects, respectively, and & is a vector white noise errors. If the rank of II is r, where r < n - 1, then II can be decomposed into two n x r matrices a and p such that fl =ap’. The matrix p consists of r linear, cointegrating vectors while a can be interpreted as a matrix of vector error-correction parameters. The elements of p are estimated using the maximum likelihood approach. In our cointegration tests, the lag length j in the above model has been chosen on the basis of the Bayesian Information Criterion (BIC) suggested by Schwartz (1978). 10. If based on the value of the statistic the null of r = 0 can be rejected, then the null that there is at most one cointegrating vector (r 5 1) is tested and so on. In an n-variable case 0 < r I n - 1. Johansen (1988) also proposes another likelihood ratio test known as the “trace” test for the determining the number of cointegrating relationships. Of these two tests, however, the maximum eigenvalue test is expected to provide more “clear cut” results than the trace test (Johansen and Juselius, 1990). The statistical package used in cointegration analysis of Tables 1 and 2 is “Microfit 3.0” (Pesaran and Pesaran, 1991). 11. In Tables 1 and 2, we test the “statistical significance” of an individual element of the cointegrating vectors (pi) by testing whether the restriction J$ = 0 imposed on the cointegrating vector can be rejected in favor of pi # 0. The test is a likelihood ratio test constructed from the estimated eigenvalues of the restricted and unrestricted models. In Table 2, figures in parentheses below individual coefficients are individual test statistics values to be compared with the critical value of x2 (1). 12. It is worth noting that Throop (1993, Table 1) finds that the real exchange rate and real long-term interest differential are cointegrated for the U.K. at the 5% level of significance. This casts doubt on the need for his subsequent testing of cointegration in the context of a more general model. Moreover, since Throop does not report either the significance level for the coefficients of the cointegrating vectors or the unit-root test results for variables, it is not possible to assess the validity of this part of his results. 13. This is because a cointegrating vector indicates a long-run relationship between the exchange rate and other variables only if the coefficient of the exchange rate in that vector is significantly different from zero. The value of the test statistic in the case of an individual variable may be interpreted as an indication of its importance in the cointegrating relation (Juselius and Hargreaves, 1992, pp. 269-273).

EXCHANGE

RATES

217

14. This assessment, however, may have to be moderated in view of problems associated with measuring real interest rate (e.g., formulating inflationary expectations), possibility of time-varying risk premium, and phenomena such as speculative bubbles.

REFERENCES Amano, Robert A. and Simon Van Norden. 1993a. Terms of Trade and Real Exchange Rates: The Canadian Evidence. Working paper 93-3, Bank of Canada. 1993b. Oil Prices and the Rise and Fall of the U.S. Real Exchange Rate. Working -. paper 93-15, Bank of Canada. Baillie, Richard T. and Rowena Pecchenino. 1991. “The Search for Equilibrium Relationships in International Finance: The Case of the Monetary Model,“Joumal of International Money and Finance, 10: 582-593. Balassa, Bela. 1964. “The Purchasing Power Parity Doctrine: A Reappraisal,” Journal of Political Economy, 72: 584-596. Banerjee, Anindya, Juan J. Dolado, John W. Galbraith and David F. Hendry (eds.). 1993. Co-Integration, Error Correction, and the Econometric Analysis of Non-stationary Data. New York: Oxford University Press. Coughlin, Cletus C. and Kees Koedijk. 1990. “What Do We Know about the Long-Run Real Exchange Rate?” Federal Reserve Bank of St. Louis Economic Review, (January/February): 36-48. Dickey, David A. and Wayne A. Fuller. 1979. “Distribution of the Estimators for Autoregressive Series with a Unit Root,” Journal of American Statistical Association, 74: 427-43 1. Edison, Hali J. and B. Dianne Pauls. 1993. “A Re-assessment of the Relationship between Real Exchange Rates and Real Interest Rates: 1974- 1990,” Journal of Monetary Economics, 31: 165-187. Fung, Hung-Gay and Wai-Chung Lo. 1992. “Deviations from Purchasing Power Parity,” Financial Review, 27: 553-570. Johansen, Soren. 1988. “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, 12: 231-254. Johansen, S. and Katarina Juselius. 1990. “Maximum Likelihood Estimation and Inference on Cointegration-With Applications to the Demand for Money,” Oxford Bulletin of Economics and Statistics,52: 169-2 10. Juselius, Katarina and Colin P. Hargreaves. 1992. “Long-Run Relations in Australian Monetary Data.” In Macroeconomic Modelling of the Long Run, edited by Colin P. Hargreaves. Edgar Elgar Publishing Limited. Kwiatkowski, Denis, Peter C.B. Phillips, Peter Schmidt and Yongcheol Shin. 1992. “Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?,” Journal of Econometrics, 54: 159- 178. Lim. G.C. 1992. “Testing for the Fundamental Determinants of the Long Run Real Exchange Rate,” Journal of Banking and Finance, 16: 625-642. MacDonald, Ronald and Mark P. Taylor. 1992. “Exchange Rate Economics: A Survey,” IMF Staff Papers, 39: l-57. Maddala, G.S. 1991. Introduction to Econometrics. New York: Macmillan.

218

QUARTERLY REVIEW OF ECONOMICS

AND FINANCE

Mahdavi, Saeid and Su Zhou. 1994. “Purchasing Power Parity in High-Inflation Countries: Further Evidence,” Journal of Macroeconomics, 16: 403-422. Meese, Richard and Kenneth Rogoff. 1983. “Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?,” Journal of International Economics, 23: 324. 1988. “Was It Real? The Exchange Rate-Interest Differential Relation Over the -. Modern Floating-Rate Period,” Journal of Finance, 43: 933-948. Osterwald-Lenum, Michael. 1992. “A Note with Quantiles of the Asymptotic Distribution of the Likelihood Cointegration Rank Test Statistics: Four Cases,” Oxford Bulletin of Economics and Statistics, 54: 461-472. Pesaran, M. Hashem and Bahram Pesaran. 1991. Micro@ 3.0: An Interactive Econometric Software Package. New York: Oxford University Press. Phillips, Peter C.B. and Pierre Perron. 1988. “Testing for a Unit Root in Time Series Regression,” Biometrika, 75: 335346. Said, Said E. and David A. Dickey. 1984. “Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order,” Biometrika, 71: 599-607. Schwartz, William G. 1978. “Estimating the Dimension of a Model.” Annals of Statistics, 6: 45 l-454. Throop, Adrian W. 1993. “A Generalized Uncovered Interest Parity Model of Exchange Rates,” Federal Reserve Bank of San Francisco Economic Review, 2: 3-16.