Cointegration test of a long-run relation between the trade balance and the terms of trade in sixteen countries

Cointegration Test of a Long-Run Relation Between the Trade Balance and the Terms of Trade in Sixteen Countries A. C. ARIZE

ABSTRACT This paper examines the impact of the terms of trade on the trade balance in 16 countries over the present flexible rate period, 1973:2 through 1992:4. The cointegration tests employed are those suggested by Stock and Watson (1993); Johansen and Juselius (1990) and Engle and Granger (1987). The results indicate that, for a majority of the countries, there exists a positive and significant long-run “statistical equilibrium” between the trade balance and the terms of trade. The approach adopted in this study is found to be an acceptable substitute for testing the Marshall-Lerner condition of stability.

I. INTRODUCTION The effects of currency depreciation or devaluation

on a country’s trade balance are usually examined by the Marshall-Lemer (M-L) condition of stability. This condition requires the estimation of both export and import demand models. Estimating such models can be tedious and often requires proxying world income, world export prices, effective exchange rates, and identifying trading partners, etc. However, for many countries, data for constructing such variables are not readily available. Nonetheless, some studies (e.g., Arize 1990; Goldstein and Khan 1978; Houthakker and Magee 1969; Warner and Kreinin 1983) have employed this approach. The consensus is that the M-L condition is easily satisfied because the demand price elasticities have been found to be quite large in these studies.t Other studies (Arize and Ndubizu 1990; Felmingham 1988; Haynes and Stone 1982; McPheters and Stronge 1979), rather than estimating export and import demand models, have attempted to establish a direct link between the trade balance and the terms of trade.’ That is, by employing an unconstrained distributed lag model and looking at the sum of the estimated coefficients of terms of trade, inference about the Marshall-Lemer condition is made. As Haynes and Stone (1982:704) pointed out, “If deterioration in the terms of trade does not ultimately improve the trade balance, the sum is nonpositive.” A common feature of a majority of these previous studies is that they have generally employed log-level, reduced-form models. Recent contributions in the econometric literature have suggested cointegration analysis as a means of determining whether there is a long-run relationship between variables that contain unit roots. Cointegration provides a useful way of identifying a long-run structural representation from a reduced-form representation.4 A. C. Arize . Professor

of Economics

and Statistics,

College

of Business

and Technology,

Texas A&M

University-Commerce, TX 75429, USA. North American Journal of Economics & Finance 7(Z): 203-2 15 Copyright 0 1996 by JAI Press Inc. ISSN 1062-9408 All rights of reproduction in any form reserved

204

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The aim of this paper is to determine whether a long-run relation exists between the trade balance and the terms of trade. This paper extends previous papers in this area in several ways. First, the previous studies mentioned above have not given any attention to the stochastic properties of the relevant time series. The level specification used in previous studies has been the subject of much recent work, the bulk of which suggests that it fails on theoretical and econometric grounds. If the time series follow a unit-root process, the regression equations that relate such variables could be subject to the “spurious regression phenomenon” first described in Granger and Newbold (1974).5 This study focuses upon the appropriate representation of the nature of nonstationarities apparent in the relevant time series. Second, unlike previous studies, the null hypothesis of no cointegration (against the alternative of cointegration) is tested using the Engle and Granger (1987) procedure, the Stock and Watson (1993) dynamic OLS (DOLS) procedure and the method of maximum likelihood estimation of cointegrated systems suggested by Johansen (1988, 1991) and Johansen and Juselius (1990). As part of Johansen’s approach to cointegration, we also perform tests for the number of cointegrating vectors and a direct test of the null hypothesis that the estimated coefficient of the terms-of-trade variable is zero. Finally, previous studies of the relationship between the trade balance and the terms of trade have been based on limited data sets. Haynes and Stone (1982) used data for the United States; Felmingham (1988) examined data for Australia; and Arize and Ndubizu (1990) studied Malaysia. It appears useful to take a comprehensive sample in order to draw conclusions that have wide applicability. This paper uses available quarterly data for a sample of 16 countries over the 1973:2 through 1992:4 period.6 The G-7 countries-Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States-as well as Denmark, Finland, the Netherlands and Switzerland are included in the sample. Also included in our sample are five newly-industrializing economies (NIEs)-India, Korea, Malaysia, Mexico, and Sri Lanka. The remaining part of this paper is organized as follows. Section 2 describes the theory and model specification. Section 3 represents and discusses the empirical results, and the main conclusions are summarized in Section 4.

II. THEORETICAL

CONSIDERATIONS

AND MODEL SPECIFICATION

The importance of employing a policy of currency depreciation or devaluation to manipulate the terms of trade can be found in any standard textbook in international finance. In general, such a policy is assumed to reduce large external imbalances, increase intemational competitiveness, promote export growth, and correct perceived “overvaluation,” thus improving the trade balance. The 40% devaluation in late 1994 by Mexico, the 50% devaluation in early 1994 by CFA franc zone countries, and the depreciation of the U.S. dollar since the first quarter of 1985 are recent examples of such a policy. Nevertheless, a nominal devaluation can achieve these tasks only if it translates into a real depreciation. A currency depreciation or devaluation works through two channels to affect the trade balance. First, the increased price of foreign currency makes foreign goods more expensive and reduces import spending. Second, the reduction in the price of domestic goods in foreign markets increases demand abroad for the country’s goods and hence raises export revenue. Depending on the size of the demand price elasticities for the country’s exports and imports, the trade balance may improve, worsen, or remain unchanged in response to a

205

Cointegration Test

devaluation. A general rule that determines the actual outcome of a devaluation is referred to as the Marshall-Lemer condition of stability. This condition suggests that (a) if the sum of the absolute values of export and import demand price elasticities is greater than unity, devaluation will improve the trade balance; (b) if the sum of the absolute values of export and import demand price elasticities is less than unity, devaluation will worsen the trade balance; and (c) if the sum of the absolute values of export and import demand price elasticities is equal to unity, de’valuation will not affect the trade balance. The Marshall-Lemer condition of stability, as McPheters and Stronge (1979:451) pointed out “is based on a number of simplifying ceteris paribus assumptions, including infinitely elastic supplies of exports and imports, initial balanced trade, competitive markets, zero cross elasticity of demand for exports and imports, and no allowance for monetary and income or absorption effects.” However, Lindert and Kindleberger (1982:293) have noted that, “when we cannot lean on these assumptions, the condition is a rougher guide to the likelihood of the stabilizing result, since it reminds us of the overall pattern that higher demand elasticities give more stable results.” Given that the Marshall-Lemer condition is a long-run analysis, an alternative approach is the cointegration analysis. Therefore, following existing empirical literature, the longrun equilibrium (cointegrating) relationship between the trade balance and the terms of trade may take the following form (see Haynes and Stone 1982): lnTB, = A + yI InTOT, + E,

(1)

where TB is a measure of the trade balance and is represented by the ratio of exports (X) to imports (I). There are two advantages of using the ratio format. First, it is not sensitive to units of measurement of exports and imports. Second, the ratio is also not sensitive to whether exports and imports are measured in nominal or real terms.’ TOT is a measure of terms of trade and is defined as the ratio of the prices of a country’s imports relative to its exports, both measured in domestic currency;’ E, is an error term; and In is a natural logarithm (A = In v~).~ An increase in the terms of trade due to a decrease in the price of exports relative to the price of imports is expected to increase TB. This is because lower prices of exports imply an increase in export revenues. As exports are encouraged and imports are discouraged (if the Marshall-Lemer elasticity condition operates), it is expected that w1 > 0. Conversely, a decrease in the terms of trade due to an increase in the price of exports relative to the price of imports is expected to decrease TB. That is w1 < 0.

III. ESTIMATION

AND COINTEGRATION

RESULTS

Given the time-series nature of the data, a useful first diagnostic is to test for unit roots in the variables. The cointegration test requires that the series be integrated of the same order. For example, the data should be stationary in their first-differences, but not in levels.” To determine the order of integration, we apply the augmented Dickey-Fuller (ADF) test suggested by Dickey and Fuller (198 1) to the levels as well as the first differences of each series used in the study. To cross-check the ADF results, we also computed the Johansen (1988) unit root test statistic (JJ) using the lag length of four chosen for the ADF statistic.’ ’ Table 1 reports the results.

206

ARIZE

TABLE 1.

Unit-Root Tests

Trade Balance Country Canada

France

Germany

Italy

Japan

UK

USA

Terms of Trade

Statistics

Level

First Difference

Level

First Difference

ADF

-2.33

-4.78*

-1.95

3.97*

~(24)

15.57 (.903)

12.99 (.966)

25.40 (.384)

23.89 (.468)

WX*)

6.40

5.96

6.15

3.87

H2(x2) JJ

1.48

2.56

0.03

0.06

3.62

19.16*

4.47

19.86*

ADF

-3.36

-6.12*

-1.75

-5.65*

~(24)

21.11 (.632)

31.39 (.143)

21.99 (.580)

Hl(x*)

8.16

2.52

24.38 (.440) 8.36

H2(x2) JJ

0.03

0.76

0.07

0.16

7.12

22.44*

2.24

24.44*

ADF

-2.53

-3.11*

-1.64

-4.48*

~(24)

22.94 (S24)

24.02 (.461)

28.23 (.250)

25.69 (.369)

Hl(x2)

9.12

2.74

9.99

4.59

H2(x2) JJ

1.95

3.01

0.30

0.01

5.22

11.21*

2.46

16.58*

ADF

-3.13

-4.47*

-1.35

-4.93*

Q(24)

21.63 (.601)

25.22 (.394)

24.44 (.437)

17.93 (.806)

Hl(x*)

4.03

4.53

3.63

2.87

H2(x2)

1.90

0.01

2.31

2.36

JJ

7.95

19.45*

1.55

27.78*

ADF

-2.15

-4.08*

-2.44

-3.96*

~(24)

26.30 (.201)

28.66 (.233)

13.29 (.961)

16.36 (.874)

Hl(x2)

3.82

3.88

3.10

1.92

H2(x2)

0.05

0.06

1.21

0.49

JJ

5.87

16.19*

2.79

13.26

ADF

-3.08

-4.76*

-2.72

-6.15*

~(24)

26.00 (.353)

26.62 (.322)

26.95 (.307)

28.5 1 (.239)

H1(x2)

3.22

2.39

4.36

2.62

H2(x2)

0.00

1.49

0.94

0.48

JJ

5.89

19.97*

6.12

40.49*

ADF

-1.96

-3.79*

-2.08

-5.03*

~(24)

29.27 (210) 8.68

31.64 (. 136)

11.99 (.980)

11.17 (.988)

10.51

10.2

11.04

0.39

2.43

0.18

0.004

3.41

10.98

7.32

24.51*

Hl(x2) H2(x2) JJ

-

1.79

(continued)

Cointegration

Test

207

TABLE 1

(continued)

Trade Balance Country Finland

Switzerland

Denmark

Netherlands

India

Korea

Malaysia

Terms of Trade

Statistics

Level

First Difference

Level

First Difference

ADF

-2.44

-3.50*

-1.33

-3.83*

Q(24)

19.17 (.743)

7.72 (1 .OO)

16.80 (.857)

15.93 (.891)

Hl(x2)

11.43

4.48

4.75

2.42

H2(x2) JJ

0.35

0.27

1.34

1.58

3.14

23.66*

2.63

20.60*

ADF

-2.02

-3.50*

-2.52

-4.20*

4(24)

21.13 (.631)

31.10 (.151)

20.53 (.667)

Hl(x2)

10.16

10.42

6.15

22.25 (.564) 5.83

H2(x2) JJ

2.36

1.89

0.03

0.09

5.33

10.03*

3.34

20.15*

ADF

-3.10

-5.35*

-1.51

-3.69*

~(24)

18.04 (.799)

15.75 (.897)

23.03 (.518)

24.01 (.461)

Wx2) H2(x2)

6.47

3.80

2.60

1.58

1.11

0.004

0.84

0.66

JJ

4.41

21.80*

3.13

23.50*

ADF

-1.96

-4.44*

-1.76

-8.84

~(24)

15.56 (.903)

15.47 (.906)

17.37 (.832)

14.90 (.924)

Hl(x2)

12.03

9.24

9.25

7.31

H2(x2) JJ

2.15

3.01

0.03

2.16

2.46

29.08*

2.19

11.72

ADF

-1.52

-4.27*

-2.93

-4.36*

4(24)

26.23 (.342)

26.34 (.336)

17.52 (.825)

17.58 (.823)

Hl(x2)

7.97

3.71

9.02

10.58

H2(x2) JJ

1.79

1.41

3.38

0.08

3.19

27.99*

8.17

26.69*

ADF

-2.7

-4.20*

-3.26

-3.94*

4(24)

20.49 (.668)

21.95 (.583)

18.16 (.795)

16.48 (.870)

Hl(x2)

9.87

5.38

9.14

5.74

H2(x2) JJ

0.01

0.00

3.55

3.78

3.60

18.79*

8.42

16.87*

ADF

-2.58

-3.83*

-2.31

-4.46*

cx24)

17.69 (.818)

22.49 (.550)

20.47 (.554)

16.16 (.761) 4.76

Hl(x2)

1.45

1.76

5.88

H2(x2) JJ

3.44

0.41

1.65

1.19

6.59

10.85*

7.14

14.05* (continued)

208

ARIZE

TABLE 1

(continued)

Trade Balance Country Mexico

Sri Lanka

Notes:

The ADF

crnical

for JJ-\lati\tic ti\tlc

Level

First Difference

Level

First Difference

ADF

-1.52

-4.75*

-1.44

-4.18*

Q(24)

7.91 (.753)

7.82 (.716)

3.73 (.957)

2.96 (.914) 3.81

HlQ2)

3.68

2.75

4.86

H2Q2)

1.64

1.23

1.47

1.06

JJ ADF Q(24)

3.00 -2.37 12.29 (.976)

JJl(x’) H2(?) JJ

4.69 1.69 5.31

32.11* -3.54* 13.81 (.951) 5.89 1.12 22.37*

1.87 -2.91 17.50 (.784) 6.84 3.06 7.09

18.49* -3.78* 16.79 (.819) 2.25 2.16 19.69*

bzrlue at the 5% level for tcsling H,,:X,

is 9.243

Q(24)

for helemskedaalicicy.

Engle ARCH

Terms of Trade

Statistics

statistic-the

i\ Ljung-Box

Statistic-the

For the Icvel, the critical crilical

- I( I) ih -3.4704 critical

[MacKinnon

value is 36.41.

HI

19911. The 5% rcjcction

region

i\ the Brcuxh-Pagan-Godfrey

\[a-

value is 12.6. whcrcas for the t.ir\t-dlt?bxces.

I[ is 11.07. Hz IS the

value i\ 3.X4 iit the 556 Icvcl.

As can be seen, the evidence suggests that the trade balance and the terms of trade for each of the 16 countries are integrated of order one, I( 1). That is, the null hypothesis of a single unit root is accepted in favor of stationarity for the first-differenced series. Note that none of our diagnostic tests are significant at the conventional level of 5%. Since all series appear to contain a stochastic trend, the next step is to test for the presence of a common stochastic trend between the trade balance and the terms of trade. A. Testing for Cointegration Cointegration tests proposed by Engle and Cranger (1987), Stock and Watson (1993), and Johansen (1988) are used to test the hypothesis that Equation (1) is a long-run equilibrium relationship. A detailed analysis of the concept of cointegration is provided in Engle and Granger (1987). Briefly, the basic idea of cointegration is that two or more nonstationary variables may be regarded as defining a long-run equilibrium relationship if they move close together in the long-run, even though they may drift apart in the short-run. This longrun is referred to as a cointegrating vector. Because there is a long-run relationship between the variables, a regression containing all the variables of a cointegrating vector will have a stationary error term, even if none of the variables taken alone is stationary.‘* Engle and Granger (1987) suggest three steps to test for cointegration. First, establish that each series is integrated of the same order. Second, if the series are of the same order, regress lnTB, on a constant and InTUT, by OLS. Third, test that the errors are I(0) by using the augmented Dickey-Fuller (ADF) test and the critical values in MacKinnon (199 1). They show that, for a sufficiently large sample, wI in Equation 1 will provide a good estimate of the cointegrating vector. This is so because, if it exists, it is unique and therefore any other constant will provide a residual series with a very large variance. As OLS will choose wI such that the variance oft is minimized, this will provide a good estimate of VI in large samples.

Cu~ntegretjon Test

209

The Stock and Watson (1993) dynamic OLS procedure (DOLS), in which OLS is applied to the model augmented with current and two leads and lagged differences of the regressor, was also employed.13 The standard errors for the t-statistic for the DOLS were calculated using a Newey-West correction procedure. A Barlett lag window of five was chosen to eliminate problems of serial correlation and heteroskedasticity. Another method of conducting cointegration tests is the Johansen approach. As Dickey, Jansen, and Thornton (1991) pointed out, the Johansen approach is particularly promising because it is based on the well-established likelihood ratio principle and avoids some of the drawbacks of the single-equation cointegration procedures. Monte Carlo evidence reported by Gonzalo (1994) supports the relative power of Johansen’s methodology over other alternative (single and multiv~ate) techniques. Furthermore, the Johansen approach offers a test statistic for the number of cointegrating vectors and allows direct hypothesis tests of the coefficients entering the cointegrating vector (Arize and Darrat 1994). A brief exposition of the Johansen technique is as follows.‘4 Let X, (TB,, TOT,)’ = I(l), and then the Johansen tests are on the rank of the long-run impact matrix II in the following vector error-correction model (VECM):

AX, = r, AX,_1+ ... + I-,., AXt_k+, + II X,_k + p*+ vt_ where Tr, . ... rk_[ and FI are coefficient matrices, vt is a vector of Gaussian error-terms and p* is a vector of constant terms. If TB and TOT are cointegrated, then the long-run impact matrix can be factored as II = ap’, where a and p are 01 x r} matrices, with p being the number of variables, and Ythe number of cointegrating relations. I-I will have rank, c such that 0 c r < p.15 The procedure provides two likelihood ratio (LR) statistics for the rank of II: the trace and the maximum eigenvalue (h-max) statistics. Table 2 contains estimates obtained from the three approaches, namely the Johansen,” the Engle-Granger and the Stock and Watson. For h-max and trace statistics, the null hypothesis is that there are, at most, r cointegating vectors, whereas the alternative hypotheses are r + 1 and at least r + I for the h-max and trace statistics, respectively.17 Starting with the 3t-max test results, the null hypothesis r = 0 (no cointegration) is rejected in favor of r = I in each country except Fintand and Denmark. The calculated test statistics range from a low of 4.5 in Denmark to a high of 38.4 in the NetherIands. The critical value at the 10% level from Oste~ald-Lenum (1992467) cannot be rejected in favor of r = 2.” These results indicate the presence of one cointegrating relationship for 14 out of 16 countries. For the trace test results, we obtain similar conclusions for the 14 countries when the null hypothesis of r = 0 is tested against the alternative hypothesis of r 2 1. In sum, these findings suggest that there is a long-run equilibrium relationship between the trade balance and the terms of trade in all countries except Denmark and Finland.” The presence of a unique cointegrating relationship enables us to make inferences concerning the long-run terms-of-trade elasticities. Therefore, to give an economic meaning to the estimated cointegrating vectors, they are normalized on trade balance. That is, the normalized equations are obtained by setting the estimated coefficient on TB,, equal to - 1 and dividing the cointegrating vector by the negative of the estimated TB, coefficient. The resuits of this no~alization, which are also presented in Tabie 2, yield estimates of the long-run terms-of-trade elasticity for each country. An appealing aspect of the results is that the terms-of-trade elasticities have positive signs in 14 countries where there is evidence of cointegration. A positive sign on our

210

ARIZE

TABLE 2.

Cointegration

Tests and Estimates

Johansen

P h-max Test

Country

Trace Test

H,:r=O

r
r=O

r
H,:r=l

r=2

r21

p=2

Engle-Granger

Stock- Watson

Normalized

LR

OLS

Residual

DOLS

Vector

Test

Vector

Statistic

Vector

ADF

ye, [t-value]

WI

15.1*

1.71

16.81*

1.71

WI 0.23 (I)

Ho:w~=o

Canada

2.83* (0.09)

0.21

-3.96 (0) -0.28 [2.80]*

France

22.7*

2.69

25.3*

2.69

0.38 (1)

5.99* (0.01)

0.45

-4.31 (2) 0.34 [2.67]*

Germany

16.1*

3.45

19.9*

3.45

0.88 (1)

10.49* (0.001)

0.66

-3.10 (0) 0.57 [2.95]*

Italy

33.6*

3.54

37.2*

3.54

0.47 (1)

7.04* (0.008)

0.40

-4.29 (1) 0.30 [3.47]*

Japan

21.5*

6.26

27.8*

6.26

0.43 (1)

3.01* (0.08)

0.41

-3.10 (4) 0.42 [2.50]*

UK

26.5*

4.01

32.4*

5.84

0.54 (1)

3.29* (0.07)

0.53

-5.11 (1) 0.32 [1.81]*

USA

21.5*

8.01

29.5*

8.01

0.30 (1)

0.217 (0.642)

0.46

-1.54 (1)

6.4

2.60

9.04

2.60

-0.07 (2)

0.007 (0.93)

-0.05

-1.74 (2) -0.13 [0.52]

20.3*

2.03

22.35*

2.03

0.15 (1)

1.06 (0.30)

0.18

-3.72 (4)

4.5

2.18

6.71

2.18

I .88 (3)

0.60 (0.44)

0.12

-0.47 (2) -0.24 [0.72]

Netherlands

38.4*

1.21

39.6*

1.21

0.19 (1)

20.01* (0.00)

0.18

-4.99 (1) 0.18 [10.79]*

India

19.1*

6.82

25.9*

6.82

2.48 (2)

12.2* (0.00)

0.97

-4.74 (0) 1.44 [5.27]*

Korea

20.9*

4.84

25.8*

4.84

0.93 (1)

3.51* (0.05)

0.41

-3.62 (1) 0.47 [2.15]*

Malaysia

20.3*

12.79

34.3*

14.07

0.53 (4)

0.29 (0.59)

0.21

-2.89 (4)

Mexico

32.8*

6.25

43.0*

10.2

1.06 (2)

0.27 (0.60)

0.24

-3.48 (1) 0.17 [1.67]*

Sri Lanka

25.8*

6.55

32.3*

6.55

0.83 (1)

9.15* (0.002)

0.55

-5.3 (1)

Finland Switzerland Denmark

Ca=o.os

15.6

9.2

19.96

17.9

Ccl=O.IO

13.7

7.5

9.24

7.5

Nota:

r denotes the number of wintergrating Malaysia.

and Mexico,

the C,=o,os

vectors. The critical are 22.0,

value CC,) arc from Octerwald-Lenum

15.67, 34.9 and 19.96, whereas C,,

,. are 19.76,

respectively.

The numbers III parenthcaeh beside B+J are the Var lag length. For the Ht,:

are marginal

Ggnificance

levels of LR statistic. The numbers in parenthevs

ical values are from MacKinnon cance at IO% level.

(I991

1. The critical

be\ide

v , = 0.the

the ADF

vale iit 10% is -3.1. and at S’S i\ -3.42.

0.22 [0.27]

0.06 [0.49]

0.01 [0.31]

0.80 [5.07]*

(lYY2:467).

For UK.

13.7. 32.0 and 17.85. figures in parentheses

are the lag lengths. The critAn a\teri\k

denote\

slgnifi-

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terms-of-trade measure implies that a currency depreciation (that is, an increase in terms of trade) leads to an improvement in the trade balance. Therefore, a policy of currency depreciation or devaluation will be effective in these countries. A test of the null hypothesis that the terms-of-trade elasticity is zero (i.e., H, : v, = 0) is reported in Table 2. For countries where there is evidence of cointegration and the terms-of-trade elasticity also has a positive sign, the computed value of the LR statistic is greater than the critical value of 2.71 at the 10% level in 10 out of 14 countries. 2o The countries are Canada, France, Germany, Italy, Japan, the United Kingdom, the Netherlands, India, Korea, and Sri Lanka. For the United States, Switzerland, Malaysia and Mexico, cointegration is supported, and the sign of the terms-of-trade elasticity is a positive sign, but H, : ~1 = 0 is not rejected.*l What remain to be examined are the results of applying the single-equation techniques. The last two sections of Table 2, labeled “Engle-Granger” and “Stock and Watson,” report these results. Except for the ADF results for the United States, Finland, Denmark, and Malaysia, the Engle and Granger procedure yields cointegration evidence that is consistent with those from Johansen’s technique. The Stock-Watson test also reinforces the above conclusion because the r-value beside the estimated coefficient is significant at the 10% level. Like some of the simulations performed by Stock and Watson, there is no proximity of DOLS and Johansen’s coefficient estimates. All in all, the results obtained from these three alternative techniques provide support for an empirical relationship between the trade balance and the terms of trade.

IV. CONCLUSION The present paper has applied recent developments in the theory of nonstationary variables to analyze the long-run relationship between the trade balance and the terms of trade. In particular, the time-series properties of the data for each of the 16 countries over a floating exchange-rate period were analyzed, then this information was utilized to estimate models and test various null hypotheses. Tests for unit root suggest that each of the series considered in the study are nonstationary integrated variables-a result consistent with Nelson and Plosser (1982). The major finding, based on Johansen’s approach to cointegration test, suggests that, for a majority of the countries, the trade balance and the terms of trade are cointegrated. This implies that, in the long-run, devaluation improves the trade balance. Therefore, cointegration analysis offers an alternative method for establishing the Marshall-Lemer condition of stability. Also, according to the Granger representation theorem (Engle and Granger 1987:255), an error-correction representation relating the changes in the variables to lagged changes and lagged combination of levels exists. In sum, from a methodological point of view, the general methodology of this paper, which is based on the seminal work of Haynes and Stone (1982) and the cointegration literature, is an attractive practical procedure because of its computational simplicity.

Acknowledgments:

The author would like to thank the editor and referees, Ed Manton, Keith McFarland, and Trezzie Pressley for helpful comments on an earlier draft. Special thanks to Kathleen Smith for excellent research assistance. This research is funded by a GSRF-TAMU-C grant.

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NOTES 1. Arize (1994) has shown that there is a long-run relation between the trade balance and the real effective exchange rate, using data for nine Asian developing economies. 2. Note that McPheters and Stronge (1979) used cross-spectra1 analysis and showed that the M-L condition is satisfied if the “gain” statistic exceeds one in algebraic value. Haynes and Stone (1982) offer a regression approach. 3. See Haynes and Stone (1982) for the advantages of the direct test over the traditional approach based on elasticities or M-L condition. It should be pointed out that the Haynes and Stone approach is more a presumptive test than a confirmatory procedure. The existence of a long-run solution from an unrestricted distributed lag model does not ensure cointegration between the variables involved. 4. Testing for cointegration between the trade balance and the terms of trade is consistent with examining “the statistical links between the two series,” as suggested by Haynes and Stone (1982:704). In addition, the cointegration approach can be considered as an alternative to testing the M-L condition because both the cointegration approach and the M-L are indeed long-run analyses. Furthermore, cointegration links the economic notion of a long-run relationship between economic variables to a statistical model of those variables. As Griffiths et al. (1993:700-701) suggest, the concept of cointegration relates to, or in a sense mimics, the concept of long-run equilibrium in which economic variables take the same values from period to period, so Z, = Z,., = Zt_2 = .. Z, until the system is disturbed. 5. In fact, Phillips (1986) formally proves that a regression involving integrated variables is spurious in the absence of cointegration. 6. Even though our sample is quarterly, simulations performed by Hakkio and Rush (1991) suggest that, if we are interested in finding long-run relationships among a set of variables, there is not much difference between the information contained in quarterly data and that contained in monthly data (if available). Data for each country are taken from International Financial Statistics Tape. Data for Mexico for the period 1973-1991 was provided by Carmen Reinhart of IMF research department. 7. A point worth mentioning is that ignoring the logarithm in Equation 1 and defining the regressand (TB) in the following alternative forms (X-I)/CPI; (X-I)/1 and (X-I) yield a positive sign on the coefficient of TOT (if the M-L condition holds). Dividing (X-I) by X, as in Khan and Knight (1983), also yields a positive sign. 8. Following Dombusch and Fischer (1984:665), Katseli (1984), Blundell-Wignall and Gregory (1990) Gruen and Wilkinson (1994:204), and Amano and Norden (1995:83), we assume that changes in the terms of trade reflect the changes in a country’s real exchange rate. Therefore, for the generalized floating era, the terms of trade are proxied by price of imports (effective exchange rate multiplied by foreign price level) scaled by price of exports (domestic price level). 9. The double-log specification in Equation 1 has the added advantage that w, is the elasticity and it is unit-free; that is, it is independent of the units in which the variables are measured. See Pindyck and Rubinfeld (198 1) and Baumol and Blinder (1982) for more on this. 10. A time-series random variable is said to be stationary if its distribution does not depend on time. A variable that is integrated is said to have a unit root in its autoregressive representation. Thus, the statements “X, has a unit root” and “X, is integrated of order one” are equivalent. Furthermore, the degree of integration of each time series is the number of times that it should be differenced to make it stationary. A variable requiring first-order differencing to achieve stationarity is said to be I( 1). A variable is integrated of order zero I(0) when it is stationary in its level. 1 I. There is now a growing consensus that the Dickey-Fuller class of statistics has better smallsample properties than the Phillips and Perron ( 1988) statistic (see Campbell and Perron 1991). A similar observation was made by Schwert ( 1987), who noted that the Phillips and Perron test rejects the null hypothesis of a unit root too often in the presence of a first-order moving average process. 12. Engle and Granger (1987:252-254) define a nonstationary time series y, to be integrated of order d, denoted by y, - r(6), if it becomes stationary after being differenced d times. Suppose yr and

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n, are a pair of variables, each of which is integrated of order d. The linear combination z, = y, - 0:X, will generally be 1(d). However, if there is a nonzero a such that z, is Z(d-b), where b > 0, they, and xt are said to be cointegrated, and the vector [l, -a] is called the cointegrating vector. If zy is I(O), then the relation yI = OLY~ may be considered as the long-run equilibrium relation. 13. The Stock and Watson procedure allows for the possibility that the variables identified by the ADF as possibly integrated of order one may actually be stationary. Stock (1992) shows that the ADF tests may tend to overpredict the presence of unit roots. A second advantage is that the estimates behave well in small samples. 14. For a more complete exposition, see Enders (1995). Computations were made using RATS 4.0 (see Doan 1992). 15. The number of nonzero columns in fl indicates the rank of II. If this matrix is full rank, the vector system is stationary. If it is of rank zero, equation 2 reduces to a standard VAR in first differences, and there is no cointegrating relationship between the variables. 16. The lag length was chosen using the likelihood-ratio test described in Sims (1980). Specifically, we included an intercept term, then we tested down from a general 6-lag system until reducing the order of the VAR by l-lag could be rejected using the likelihood test. That is, the lag length finally selected is the one where the restricted model is rejected. Furthermore, the Ljung-Box statistic supports the white-noise properties of the system. 17. For the United States, seasonal dummies were included; for Malaysia, a dummy variable coded one for the year 1982 and zero otherwise to capture the enormous trade and current account deficits of 1982 (see Arize and Ndubizu 1990); for the United Kingdom, a dummy variable coded one for 1979: 1 through 1985:3 and zero otherwise to capture the structural break discussed in Landesmann and Snell(l989); and, for Mexico, a dummy coded one in 1982: 1 through 1983: 1 and zero otherwise to capture the devaluation of 1982. 18. Johansen and Juselius (1990: 192) pointed out that “it seems reasonable in certain cases to follow a test procedure which rejects for higherp-value than the usual 5%.” 19. According to Engle and Granger (1987), a single cointegrating vector has a straightforward economic interpretation as a unique long-run “equilibrium” relationship, whereas the presence of multiple cointegrating vectors implies that, although the system is stable, it is difficult to identify and interpret such relationships. 20. These results are robust to different assumptions about the drift parameter. However, a test of the null hypothesis of an intercept in the cointegrating vectors against the alternative that there is the linear trend in the variables using LR test is reported here. The computed X2 values are 1.6, 0.008,0.15,0.11,0.78, 0.004,0.68,0.21,0.74, 3.3.0.01,0.29,0.32, 0.51.0.13 and0.25forCanada, France, Germany, Italy, Japan, UK, USA, Finland, Switzerland, Denmark, the Netherlands, India, Korea, Malaysia, Mexico, and Sri Lanka, respectively. The critical value is 3.84 at the 5% level. These results imply that the null hypothesis is accepted, and so no trend was assumed in the process. 21. The relevant point here is that there is some evidence of cointegration. It is well-known that exclusion restriction tests (like the cointegration test) may lack power in a manner similar to situations where unit root tests lack power. Furthermore, skyrocketing budget deficits and domestic price of imports in these countries (especially the USA and Mexico) might help explain our failure to reject the null hypothesis. As is well known, since the September 1985 exchange-rate conference of the Group of Five (G-5) countries in New York’s Plaza Hotel, the depreciation of the U.S. dollar has not yielded any meaningful improvement in the US. trade balance.

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