Imports and exports in 50 countries

International Review of Economics and Finance 11 (2002) 101 – 115 Imports and exports in 50 countries Tests of cointegration and structural breaks Augustine C. Arize* College of Business and Technology, Texas A&M University-Commerce, Commerce, TX 75429, USA Received 14 February 2000; received in revised form 18 October 2000; accepted 9 February 2001 Abstract This paper provides new evidence on the long-run convergence between imports and exports in 50 countries over the quarterly period 1973:2 to 1998:1. Cointegration analyses are based on the Johansen [Johansen, S. (1995). Likelihood-based inference in cointegrating vector autoregressive models. New York: Oxford University Press.] and the Stock and Watson [J. Am. Stat. Assoc. 83 (1988) 1097.] system approaches. Evidence of stability of the cointegration space is examined using the SupF test developed by Hansen [J. Bus. Econ. Stat. 10 (1992) 321]. Based on the Johansen technique, we find evidence in favor of cointegration in 35 of the 50 countries. In addition, cointegration is confirmed for all countries (except Mexico) using the Stock and Watson test. This finding indicates that macroeconomic policies have been effective in the long-run and suggests that these countries are largely not in violation of their international budget constraint. We find evidence that in most of the countries where the slope coefficient on the export variable is positive, the cointegrating coefficient is also unity. The cointegration space appears stable for most of the countries. Nonetheless, the results suggest that countries in the regions of the Middle East, Latin America, and Europe have cointegrating relations that are more unstable than those in other regions. D 2002 Published by Elsevier Science Inc. JEL classification: F14; F35 Keywords: Imports; Exports; Cointegration; Structural instability * Tel.: +1-903-886-5691; fax: +1-903-886-5691. E-mail address: chuck _ [email protected] (A.C. Arize). 1059-0560/02/$ – see front matter D 2002 Published by Elsevier Science Inc. PII: S 1 0 5 9 - 0 5 6 0 ( 0 1 ) 0 0 1 0 1 - 0 102 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 1. Introduction In the area of international trade, the long-run equilibrium relationship between imports and exports has received some attention; see, for example, Fountas and Wu (1999), Granger (1986), Gould and Ruffin (1996), and Husted (1992) among others. Most of these inquiries have been conducted using data from the US economy, so that more empirical work that analyzes data from other countries is needed.1 Furthermore, these previous inquiries have yielded conflicting empirical evidence about the relationship between imports and exports. Some studies, such as Husted (1992), which use US quarterly data for the period 1967– 1989, have shown that there is a long-run relationship between imports and exports and that the sign on the estimated cointegrating coefficient is positive. Such a finding is consistent with the view that the US trade deficit is a short-run phenomenon during which its imports and exports may drift apart and converge toward an equilibrium in the long run; see, for example, Gould and Ruffin (1996). It also implies that the trade deficits are sustainable, perhaps by the means of current macropolicies. Put differently, it is an indication that the country’s imports and exports have been brought into a long-run equilibrium through the combined effects of all macroeconomic policies on the trade balance.2 Fountas and Wu (1999), on the other hand, using US quarterly data for the 1967–1994 period and cointegration techniques, have shown that the hypothesis of no long-run relationship between imports and exports cannot be rejected and conclude that the US trade deficits are not sustainable.3 The contribution of this study to the literature is the extension of the analysis to 50 countries, including the United States, using recent advances in time series econometrics. The evidence presented will add an extra dimension to this literature. In recent years, policymakers in many countries have been forced to take renewed interest in the evaluation of the combined effects of all macroeconomic policies, such as exchange rate, fiscal and monetary, on the trade balance—witness the current discussions of Asian financial turmoil. Knowledge of whether imports and exports are cointegrated is essential for the design and evaluation of current and future macropolicies aimed at achieving the trade balance. Another contribution of this study relates to the stability of the cointegrating relationship. In general, previous studies have presumed (either explicitly or implicitly) that the relationship is stable. It is possible that this may not be the case. There is no reason to believe a priori that the relative importance of factors influencing the relationship between imports and exports has remained unchanged. We believe that credible evidence of such a relationship should be ascertained, not only by testing for statistical cointegration, but also by investigating whether the cointegrating relationship has been structurally stable over the sample period. 1 See Bahmani-OsKooee (1994) and Bodman (1997) for a study of Australia and Bahmani-Oskooee and Hyun-Rhee (1997) for a study of Korea. See also McGregor and Swales (1985, p. 18). 2 See Arslan and Wijnbergen (1993) for a discussion of the effects of macroeconomic policies on export growth in the case of Turkey. See also Arize, Bonitsis, Kallianiotis, Kasibhatla, and Malindretos (2000). 3 Note that Granger (1986, p. 213) suggests that one could use the cointegration technique to examine the long-run relation between imports and exports. A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 103 Therefore, the second objective of this study is to provide new evidence on the stability of the cointegrating relationship between imports and exports. For this purpose, we employ the SupF test for parameter instability proposed by Hansen (1992). The analysis in this paper differs from previous studies in five novel aspects. First, we avoid using pooled data of both the fixed and the flexible exchange rate periods, since there is no justification for the relations being symmetrical during the periods. We use the quarterly period 1973:2–1998:1, and the sample includes OECD and developing economies. This diversity makes the sample reasonably representative, and the results of the study can at least be suggestive of some general conclusions regarding other countries that have largely been ignored in the literature and provide a basis to which future studies can be compared. The results may also provide a valid comparison to the single-country studies, such as Fountas and Wu (1999) and Husted (1992). Second, unlike previous studies, we employ more than one pretest. Further, we test for cointegration by using multivariate cointegration techniques developed by Johansen (1995) and Stock and Watson (1988). Both techniques are Full Information Maximum Likelihood (FIML) estimators. The choice of these two estimators follows from the Monte Carlo study by Haug (1996), which shows that the Johansen estimator has the least size distortion, whereas the Stock and Watson estimator has the largest power.4 Therefore, our approach offers deeper insights and a more balanced view. Mention should be made that, while most of the advantages of the system-based approaches are primarily realized in multivariate models, Arize and Darrat (1994) and Enders (1995, 1996) present arguments favoring the system-based techniques over the Engle and Granger (E–G) (1987) procedure, even in bivariate models.5 Third, we add to this literature by checking whether or not the estimated coefficient on the exports variable is statistically equal to unity (i.e., Ho: C1 = 1). In this test, the null hypothesis is that the coefficient on imports is equal to the coefficient on the exports. While the validity of the relationship between imports and exports hinges, not only on their being cointegrated and structurally stable, a test of the proportionality restriction could throw further light on the long-run relationship between imports and exports. It is worth pointing out that the test is conducted only if the Johansen estimator confirms cointegration and that the E–G method is incapable of testing the Ho: C1 = 1 because of inappropriate standard errors. This may partly explain why previous studies have paid relatively little attention to this hypothesis.6 4 Monte Carlo evidence by Gregory (1996) suggests that instances of conflicting test results are likely to occur in cointegration analyses because of sharp power differences that occur as empirical conditions such as sample size, lag orders, and number of regressors differ. In light of this, Gregory notes that it is of considerable practical importance to calculate and report several tests for cointegration in applied studies. 5 The Johansen procedure for a bivariate system is already formulated in Agenor and Taylor (1993, p. 258 – 259) and does not need to be repeated here. 6 Husted (1992) used West’s (1988) ‘‘corrected’’ standard errors for the coefficients in a cointegrating regression, which are asymptotically normal. However, West’s results are based on a two-variable model where the variables are I(1)with drift. It is not clear if his result holds in more general cases such as the final relation in Husted, which includes more than two variables (see Cuthbertson & Barlow, 1991; Pagan & Wickens, 1989); therefore, ‘‘West-corrected standard errors,’’ as used in Husted, must be interpreted with caution. 104 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 Fourth, conditional on the presence of cointegration, we estimate and test coefficients of the cointegrating relations using the FIML estimator of Johansen (1995) and two robust singleequation estimators: the fully modified ordinary least squares (FMOLS) estimator of Phillips and Hansen (1990) and the dynamic ordinary least squares (DOLS) estimator of Stock and Watson (1993). These single-equation estimators have not been employed in any of the previous studies examining the relationship between imports and exports. A number of authors (e.g., Haug, 1996; Stock & Watson, 1993) give reasons for considering possibly more robust singleequation estimation methods. Therefore, by supplementing the FIML estimates with the estimates from these single-equation estimators, we get a feeling for the robustness of the results. Finally, unlike all other studies in this literature, the present one represents the first application of a test for the stability of the cointegration space or the constancy of the longrun parameters in this literature and should improve our understanding of the relationship between imports and exports. The rest of the paper is as follows: Section 2 provides a brief theoretical background. Section 3 provides a brief description of the methodology and estimation results, and the concluding remarks are given in Section 4. 2. Theoretical considerations Husted (1992) presents a simple analysis that implies a long-run equilibrium between imports and exports. The analysis assumes that there is a representative consumer who resides in a small open economy with no government control, and the economy produces and exports a single composite good. The market participant is assumed to use one-period financial instruments to borrow and lend in international markets. It is also assumed that the agent faces a given world rate of interest and wants to maximize lifetime utility subject to budget constraints. Further, the consumer’s resources, which are used for savings and consumption, are composed of endowments of output and redistributed profits from firms. This representative consumer’s current-period budget constraint is C0 ¼ Y0 þ B0  I0  ðI þ r0 ÞB1 ð1Þ where C0 is the current consumption, Y0 is the output, I0 is the investment, r is the one-period world interest rate, B0 is the magnitude of the international borrowing available to the consumer, which could be positive or negative, and (1 + r)B  1 is the initial debt size. Eq. (1) holds for each period so that the economy’s intertemporal budget constraints are formed by combining these period-by-period budget constraints. Then, in order to derive a testable equation, Husted (1992) makes several assumptions, including that imports and exports are assumed to follow a random walk with drifts and that the world interest rate is stationary with mean r. The testable equation is given by IMt ¼ C0 þ C1 EXt þ et ð2Þ where IM is imports of goods and services and EX is exports of goods and services. For the economy to satisfy its intertemporal budget constraint, C1 should be equal to 1, and et should A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 105 be stationary. However, if C1 is less than 1, the economy will fail to satisfy its budget constraint if trade flows are expressed relative to GNP (Hakkio & Rush, 1991; Husted, 1992). In Eq. (2), C0 and C1 might vary over time due to structural changes in the cointegrating vector. This appears more likely to occur when the data cover a long time span. The current study examines whether changes in C0 and C1 have resulted in the instability of the cointegrating relation. 3. Methodology and estimation results To establish whether there is a long-run equilibrium relationship between the variables in Eq. (2), we must employ the concept of cointegration developed by E–G (1987). Cointegration is a statistical concept used in the analysis of the relationship between nonstationary time series. In particular, it is a search for linear combinations of individually nonstationary time series that themselves are stationary. Therefore, stationarity implies that probability laws controlling a process are stable over time; that is, in statistical equilibrium (Vandaele,1983). Series that are nonstationary in levels have a unit root (stochastic trend). Shocks to a time series that has a unit root are, in part, permanent; they change the long-run level of the series permanently. Thus, if Eq. (2) describes a stationary long-run equilibrium relationship, this can be interpreted to mean that the stochastic trend in imports is related to the stochastic trend in exports. In other words, even though deviations from the equilibrium should occur, they are mean reverting. 3.1. The data and the unit root tests The data for our investigation come from the International Monetary Fund (IMF)’s International Financial Statistics (IFS) CD-ROM (June 1998). The data for Nigeria, Greece, Papua New Guinea, and Iran were updated using various issues of IFS Supplements on Trade. All data are quarterly, and, in general, they cover the period 1973:2–1998:1. As noted earlier, countries were chosen to obtain a sample that was representative of various types of industrial and developing economies. The sample consists of 50 countries.7 Out of the 50 countries, 13 are in Asia, 5 are in the Middle East, 9 are in Africa, 7 are in Europe, 12 are in Latin America, and 4 countries are included in a section referred to as ‘‘the Pacific, USA, and Canada section.’’ For our purpose, 7 The sample period is 1973:2 – 1998:1 for Bolivia, Canada, Chile, Costa Rica, the Dominican Republic, Ecuador, El Salvador, Guatemala, Hong Kong, Kenya, Malaysia, Morocco, Tunisia, and the United States; 1973:2 – 1997:4 for Cyprus, India, Israel, Japan, Korea, Myanmar, the Netherlands, Pakistan, Singapore, and Sri Lanka; 1973:2 – 1997:3 for Austria, Fiji, Indonesia, Jordan, Kuwait, Portugal, South Africa, Thailand, and Venezuela; 1973:2 – 1997:2 for Australia and Mexico; 1973:2 – 1997:1 for Burundi, Colombia, Egypt, Haiti, Hungary, Mauritius, New Zealand, and Sweden; 1973:2 – 1996:3 for Zambia; 1973:2 – 1994:1 for Greece; 1973:2 – 1985:4 for Iran; 1973:2 – 1996:2 for Paraguay; 1973:2 – 1996:1 for Ethiopia; 1973:2 – 1995:1 for Nigeria; and 1973:2 – 1994:1 for Papua New Guinea. 106 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 imports in domestic currency are scaled by the nominal gross domestic product (GDP) and are henceforth referred to as IMGt. Exports in domestic currency are scaled by nominal GDP and are henceforth referred to as EXGt. The IFS CD-ROM line numbers for our data are GDP (99b.c), exchange rate (rf), imports (71..d) and exports (70..d). A prerequisite in applying the cointegration procedure is to test the unit root properties of the series. To this end, we use two sets of statistics: (i) the Augmented Dickey–Fuller (ADF) t statistics and (ii) Johansen’s (1995, p. 74) test statistic. For space considerations, the empirical results are not presented here, but they suggest that the null hypothesis of a unit root (i.e., nonstationarity) is accepted when the variables are in levels, but it is rejected when the series are in first differences.8 3.2. Cointegration The Johansen procedure employs two likelihood ratio (LR) test statistics, the maximal eigenvalue (l-max), and trace (Tr) to test the presence or absence of long-run equilibria between the variables in Eq. (2). Note that our l-max and Tr test statistics have been corrected for sample size by multiplying the test statistic by (T  number of estimated parameters)/T, as discussed by Cheung and Lai (1993) and Reinsel and Ahn (1992). For lmax and Tr statistics, the hypotheses are Ho: rk(P) = r against H1: rk(P) = r + 1 and Ho: rk(P) = r against H1: rk(P)  r + 1, respectively. Note that rk is rank, P is a matrix of long-run responses, and the matrix P has rank r, rk(P) = r. If the data cointegrate, P must be of reduced rank, r < N, where N is the number of variables. Before implementing this technique, it is necessary to establish the order of VAR to be applied in each cointegration test. The number of lags applied in each cointegration test is based on information provided by the Akaike Information Criterion, the Sims LR test, and the vector autocorrelation test (Arize et al., 2000). After preliminary testing of the joint hypothesis of both the rank order and the deterministic components, based on the Pantula Principle as described in Harris (1995, pp. 96–97) and Johansen (1995, p. 98), our vector error-correction model (VECM) was allowed to assume linear deterministic trend in the data.9 Table 1 reports the results from the cointegration analyses. Focusing first on the Johansen test results, the first row corresponding to each country’s name reports the results from our preferred VAR order. Starting with the l-max test results in Table 1, the null hypothesis of r = 0 (no cointegration) is rejected in favor of r = 1 (cointegration) in 35 out of 50 countries. The exceptions are Hong Kong, Papua New Guinea, Sri Lanka, Jordan, Burundi, Ethiopia, Morocco, Cyprus, Hungary, the Netherlands, Portugal, the Dominican Republic, Guatemala, Haiti, and Paraguay. For the 35 countries where cointegration exists, the calculated test statistics range from a low of 13.0 in Canada to a high of 27.85 in Myanmar. The critical 8 Throughout this paper, the computations were done with EVIEWS, GAUSS, MICROFIT, and PcGIVE computer packages. See Agenor and Taylor (1993) and Arize (1996) for an overview of the cointegration procedures. 9 It is important to note that, in a few cases, an impulse dummy was included where appropriate in order to exclude outliers from the analysis. For more on this, see Doornik, Hendry, and Nielsen (1998). A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 107 value is 12.98 at the 10% level for all countries except Japan, Malaysia, Singapore, Israel, and Costa Rica, where it is 17.18 for the 10% level.10 Johansen and Juselius (1990, p. 192) point out that ‘‘it seems reasonable . . . to follow a test procedure, which rejects for a higher P value than the usual 5%.’’ Further, the null hypothesis of at most one cointegrating vector (Ho: r  1) is in no case rejected. For the Tr test results, we obtain similar conclusions for these countries when (Ho: r = 0) is tested against the alternative hypothesis of r  1; i.e., Ha: r  1. The calculated Tr statistics range from a low of 16.03 in Iran to a high of 34.5 in Pakistan. These results indicate the presence of one cointegrating relationship for each of the 35 countries, and they imply that the intertemporal budget constraint is not being violated. In the 15 countries where the null hypothesis of no cointegration is accepted, the results imply that the growth in international indebtedness may not be sustainable and over time, the discrepancy between imports and exports as a share of economic activity would grow without bounds. In sum, these findings suggest that there is a long-run equilibrium relationship between imports and exports. To provide complementary evidence and to check the robustness of the Johansen results, we compute Stock and Watson’s cointegration test. The QtF statistics that are reported in Table 1 (see the column labeled Stock and Watson) are consistent with those of the Johansen techniques with respect to the relationship between imports and exports. As seen in Table 1, QtF statistic ranges from  152.23 in Hungary to  19.8 in Iran, whereas the critical value is  19.21 at the 10% level. The exception is Mexico (  17.32). All in all, it is encouraging that the conclusions are not particularly affected by the method of estimation. 3.3. Long-run equilibrium estimates The column referred to as the ‘‘normalized vector’’ in Table 1 also provides parameter estimates that represent the slope coefficient. The estimated slope coefficient for each of the 40 countries is obtained by setting the estimated coefficient on IMGt, equal to  1 and dividing the cointegrating vector by the negative of the estimated IMGt coefficient. The results of this normalization are presented in Table 1, as the normalized vector, C1. An interesting aspect of the results is that C1 has a positive sign in 31 out of 35 countries, and the parameter estimates range from a low of 0.24 in South Africa to a high of 1.85 in Egypt for these 31 countries. The 31 countries are Fiji, India, Japan, Korea, Malaysia, Myanmar, Pakistan, Singapore, Thailand, Egypt, Iran, Israel, Kenya, Mauritius, Nigeria, South Africa, Tunisia, Zambia, Austria, Greece, Sweden, Australia, Canada, New Zealand, the United States, Chile, Costa Rica, Ecuador, El Salvador, Mexico, and Venezuela. The remaining four countries that have negative signs on C1 are Indonesia, Kuwait, Bolivia, and Colombia. Another encouraging aspect of our work is the results obtained from testing the null hypothesis that the estimated slope coefficient on EXGt is zero (i.e., Ho: C1 = 0). These test results are reported in Table 1 (see the column labeled LR test) for each of the 35 countries where cointegration was found by the Johansen estimator. The LR test for the exclusion of a 10 Johansen and Juselius (1990:192) point out that ‘‘it seems reasonable ... to follow a test procedure which rejects for a p-value than the usual 5 percent.’’ 108 Table 1 Cointegration tests and estimates Johansen l-Max test Phillips – Hansen Stock and Watson Hansen Stability test* (SupF [P value]) Tr test r1 r=2 r=0 r=1 r1 r=2 Normalized vector (C1) LR test (Ho: C1 = 0/C1 = 1) FMOLS vector (C1 [t value]) Cointegration test ( QtF) DOLS vector (C1 [t value]) 17.04 12.52 16.26 24.32 19.22B 19.64 16.45B 27.85 26.40 12.12 5.34 2.94 0.60 3.58 7.80 4.10 5.32 0.24 8.13 6.10 22.38 15.46 16.85 27.90 27.02 23.73 21.77 28.10 34.53 18.21 5.34 2.94 0.60 3.58 7.80 4.10 5.32 0.24 8.13 6.10 0.85 0.97 0.71  0.83 0.92 0.66 1.47 0.80 0.92  1.78 (4) (6) (4) (6) (6) (5) (5) (3) (3) (4) 8.67/0.45* – 12.3/2.67* 16.2/3.17* 8.72/0.14* 8.45/1.77* 10.4/2.65* 27.0/7.33 7.86/5.96 – 0.37 0.96 0.61 0.01 1.25 0.42 1.24 0.76 0.26  0.32 [3.49] [21.6] [4.92] [0.52] [8.09] [2.29] [14.1] [12.6] [2.18] [2.19]  85.64  64.49  42.53  58.49  20.14  114.09  26.43  57.84  75.44  64.86 0.36 0.95 0.54 0.12 1.20 0.70 1.31 0.82 0.30  0.20 17.60B 12.91 14.67 3.78 2.74 0.06 21.37 15.65 14.73 3.78 2.74 0.06 1.14 (5) 1.59 (6) 1.20 (4) 15.5/2.56* – 15.1/3.35* 0.81 [4.52] 1.51 [8.50] 1.17 [15.4] Middle East Egypt Iran Israel Jordan Kuwait 19.17 13.27 22.85B 8.24 16.75 4.13 2.76 5.70 1.48 4.10 23.30 16.03 28.55 9.71 20.84 4.13 2.76 5.70 1.48 4.10 1.85 0.99 0.76  0.03  0.17 (5) (4) (5) (4) (6) 13.4/6.12 12.4/0.01* 3.31/1.82* – 1.51/8.17* 1.46 0.40 1.36 0.29 0.34 Africa Burundi Ethiopia Kenya Mauritius Morocco Nigeria South Africa 8.11 9.50 15.36 20.00 12.82 16.95 23.10 3.13 2.94 2.26 3.22 3.93 3.71 5.13 11.24 12.43 17.62 23.22 16.74 20.66 28.20 3.13 2.94 2.26 3.22 3.93 3.71 5.13 1.78 0.62 1.02 0.98 0.98 0.66 0.24 (4) (4) (4) (6) (4) (4) (4) – – 11.9/0.01* 17.7/0.01* – 10.8/1.66* 0.16/19.0 1.23 0.17 0.85 0.18 0.44 0.34 1.01 Asia Fiji Hong Kong India Indonesia Japan Korea Malaysia Myanmar Pakistan Papua New Guinea Singapore Sri Lanka Thailand [5.57] [21.9] [7.13] [1.18] [12.5] [5.55] [16.5] [16.2] [3.48] [2.15] 6.12 [0.20] 12.9 [0.11] 12.0 [0.08] 12.6 [0.13] 8.16 [0.20] 11.2 [0.08] 5.78 [0.20] 5.93 [0.20] 5.34 [0.20] 3.68 [0.20]  24.79  59.51  44.33 0.84 [9.14] 1.47 [10.0] 1.14 [22.2] 6.20 [0.20] 9.37 [0.16] 2.66 [0.20] [5.11] [3.18] [7.39] [0.91] [6.52]  21.49  19.80  55.73  49.87  49.11 0.24 0.67 1.46 1.91 0.17 [0.72] [4.92] [12.9] [3.46] [1.52] 4.89 [0.20] 70.3 [0.01] 18.2 [0.01] 0.68 [0.82] 1.74 [0.01] [6.00] [0.73] [6.32] [1.46] [22.9] [3.13] [22.3]  97.62  45.08  73.78  100.86  59.01  29.14  45.16 0.15 0.62 0.63 0.94 0.65 0.33 0.94 [2.06] [4.49] [7.29] [1.15] [4.40] [4.44] [11.9] 56.5 [0.01] 10.8 [0.09] 5.58 [0.20] 2.52 [0.20] 3.29 [0.20] 5.87 [0.20] 279.9 [0.01] A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 Ho: r = 0 Ha: r = 1 Country 14.21 24.42 2.94 7.03 17.15 31.45 2.94 7.03 Europe Austria Cyprus Greece Hungary Netherlands Portugal Sweden 15.67 11.36 13.72 8.26 7.14 7.08 25.98 3.21 2.92 2.70 2.10 1.44 4.36 5.62 19.89 14.28 16.40 10.31 8.58 11.44 31.61 3.21 2.92 2.70 2.10 1.44 4.36 5.62 0.62 1.08 1.26 0.75 0.73  0.23 0.74 2.40 1.56 1.11 1.59 17.59 14.56 17.33 15.22 2.40 1.56 1.11 1.59 1.30 0.95 0.55 1.37 27.32 20.33 29.31 24.10 8.50 27.34 21.60 10.88 8.67 30.91 10.18 20.56 15.75 Pacific, USA, and Canada Australia 15.20 Canada 13.00 New Zealand 16.22 United States 13.63 Latin America Bolivia Chile Colombia Costa Rica Dominican Ecuador El Salvador Guatemala Haiti Mexico Paraguay Venezuela Ca = 0.10 and the Caribbean 21.48 5.84 14.37 5.96 22.36 6.95 17.34B 6.71 6.55 1.90 23.65 3.70 20.03 1.57 6.14 4.74 7.60B 1.10 25.70 5.25 8.41 1.77 17.39 3.17 12.98 6.50 0.97 (4) 1.42 (4) 9.21/0.02* 16.5/1.13* 0.96 [8.05] 0.52 [3.58] (1) (7) (5) (5) (4) (6) (1) 5.30/3.07* – 8.71/1.14* – – – 15.8/4.90 0.64 1.04 1.37 0.77 0.79 0.63 0.47 [4.89] [8.98] [9.83] [6.57] [31.7] [3.41] [4.99] (4) (4) (6) (4) 10.4/1.29* 10.2/0.67* 5.02/2.91* 13.8/9.31 0.94 0.90 0.92 1.32 5.84  2.50 (4) 5.96 0.47 (4) 6.95  0.08 (3) 6.71 0.62 (3) 1.90  0.34 (6) 3.70 1.57 (4) 1.57 0.47 (5) 4.74 0.16 (3) 1.10 0.62 (4) 5.25 1.63 (5) 1.77 3.87 (4) 3.17 1.27 (6) 6.50** 12.1/16.1 3.42/2.83* 13.3/7.51 3.86/1.97* – 21.7/4.58 20.5/14.6 – – 22.2/12.1 – 11.3/0.27* 0.68 1.15 1.34 0.68 0.24 0.64 0.39 0.43 0.57 1.09 0.47 0.05  91.57  57.03 0.94 [5.84] 0.66 [3.57] 4.68 [0.20] 12.1 [0.16]  42.42  67.02  109.05  152.23  46.38  67.51  57.63 0.70 0.93 1.32 0.93 0.80 0.79 0.56 [8.16] [7.75] [4.62] [8.64] [42.7] [6.99] [7.71] 6.04 [0.20] 49.2 [0.01] 24.0 [0.01] 4.96 [0.20] 9.46 [0.15] 8.43 [0.20] 7.79 [0.20] [4.15] [47.8] [30.4] [16.6]  41.81  29.89  77.01  23.56 1.18 0.88 0.91 1.16 [4.25] [44.8] [38.7] [55.8] [5.37] [36.8] [26.8] [5.72] [2.03] [5.18] [9.11] [2.49] [2.70] [24.1] [1.96] [0.34]  98.41  82.89  38.45  59.81  48.62  44.21  62.93  71.09  40.03  17.32  66.59  56.06 0.75 0.47 0.01 0.63 0.21 0.49 0.33 0.50 0.53 1.02 0.25 0.04 [10.8] [6.00] [2.75] [6.54] [2.27] [4.31] [13.0] [4.30] [3.29] [24.6] [2.41] [0.37] 6.69 6.04 6.35 7.18 [0.20] [0.20] [0.20] [0.20] 74.7 [0.01] 14.8 [0.02] 10.9 [0.20] 7.88 [0.20] 7.42 [0.20] 4.11 [0.20] 228.8 [0.01] 14.8 [0.02] 2.97 [0.20] 93.2 [0.01] 9.55 [0.20] 3.38 [0.20] 109 r denotes the number of cointegrating vectors. The critical values (Ca) are from Osterwald-Lenum (1992). For countries with B, the Ca = 0.10 for the l-max is (17.18, 10.55), and for the Tr, it is (23.08, 10.55). The numbers in parentheses beside C are the VAR lag lengths. For Ho: C1 = 0, and C1 = 1, the critical value is c2(1) = 3.84 at the 5% level. Based on QtF results, we have reported single-equation estimates for each country. The t values have a critical value of 1.64 at the 5% level. For Stock and Watson cointegration test, the critical value at the 5% level is  22.87, and at the 10% level, it is  19.21. * Implies that C1 = 1 is insignificant. A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 Tunisia Zambia 110 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 variable from the cointegration space is performed as suggested by Johansen and Juselius (1990, p. 194). Given that we have a single cointegrating vector, the c2(1) critical value is 2.71 at the 10% level. For the 31 countries mentioned above, the calculated LR statistics range from a low of 0.16 in South Africa to a high of 22.2 in Mexico. Except for South Africa, the LR statistics are significantly different from zero in each of the 31 countries. For the remaining four countries with negative slope coefficients, only Kuwait’s LR statistic is nonsignificant at the 10% level. An appealing aspect of our work is the results obtained from testing the null hypothesis that the estimated coefficient on EXGt is unity (i.e., Ho: C1 = 1). The LR statistic for the null hypothesis that C1 = 1 was constructed as in Johansen (1995) and is chi-squared distributed with one degree of freedom under the null hypothesis. Focusing on the test results (see the LR test column of Table 1) for the 30 countries where the estimated slope coefficient on EXGt is positive and statistically significant, we find that the null hypothesis of C1 = 1 is not rejected in 22 out of 30 countries, namely Fiji, India, Japan, Korea, Malaysia, Singapore, Thailand, Iran, Israel, Kenya, Mauritius, Nigeria, Tunisia, Zambia, Austria, Greece, Australia, Canada, New Zealand, Chile, Costa Rica, and Venezuela. These countries constitute over 73% of that sample. For a country such as Japan, this test result indicates that in the long-run, one yen of imports is balanced by one yen of exports and vice versa, resulting in a long-run trade balance. Nevertheless, short-run imbalances do occur, because exports and imports may drift apart in the short run.11 As further confirmation of our results, we report in the middle part of Table 1 the results obtained from two single-equation estimators, namely FMOLS and DOLS. These estimators impose different assumptions regarding endogeneity, and they differ in how they correct for autocorrelation. Nevertheless, the two estimators possess the same limiting distribution as the FIML estimator and, hence, are asymptotically optimal. Table 1 presents the parameter estimates obtained from the estimators. Overall, the results are encouraging. We find parameter estimates from these estimators to be generally close to those obtained using the Johansen method. 3.4. Structural stability of the cointegration space Having examined the empirical results obtained from these cointegration estimators, it seems prudent to examine whether a one-time structural break occurred in the cointegration space of each country. To test for structural stability, we use a SupF test for I(1) processes proposed by Hansen (1992). The test is based on a sequential search over a trimmed region (0.15T, 0.85T), where the symbol T in the trimming region represents the sample size. The null hypothesis is that there is no structural change, whereas the alternative hypothesis is that there is a sharp or sudden shift in regime that occurred at an unknown point in time. Unlike the stability tests often used in empirical studies that assume stationary forcing variables, this 11 It is worth stressing that a necessary condition for an economy to obey its intertemporal budget constraint is not that C1 be unity but that a cointegration exists between imports and exports. See footnote 2 in Husted (1992). A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 111 test procedure treats the break point as unknown. It is well known that an ad hoc choice of the break point may adversely affect the power of the test; see Hansen (1992) for a detailed discussion. However, note that the size of the test will be incorrect, even in large samples, if a break point is chosen through inspection of the data. The SupF test results are reported in the last column of Table 1. A low P value, below .05 (say), for the test statistic is interpreted as the instability of the parameters of the cointegrating vector; that is, the null hypothesis is rejected against the alternative hypothesis. Two important conclusions emerge from these results. First, according to the SupF test results, the P values of 38 countries are above the .05 required to reject the null hypothesis of parameter stability. Therefore, relying on the evidence for cointegration generated by the Stock and Watson estimator, one could conclude that there is overwhelming evidence in support of the constancy of the cointegration space. Second, if one relies on the evidence for cointegration in 35 countries from the l-max test statistic of the Johansen estimator, the SupF test statistic supports parameter constancy of the cointegration space in the 26 countries, namely, Fiji, India, Indonesia, Japan, Korea, Malaysia, Myanmar, Pakistan, Singapore, Thailand, Egypt, Kenya, Mauritius, Nigeria, Tunisia, Zambia, Austria, Sweden, Australia Canada, New Zealand, the United States, Colombia, Costa Rica, Ecuador, and Venezuela. In the remaining nine countries — Iran, Israel, Kuwait, Bolivia, South Africa, Chile, El Salvador, Mexico and Greece — there is evidence of parameter nonconstancy. Taken together, these results are reassuring, as they imply that our long-run parameter estimates are generally stable. However, to put these results in the proper perspective, we explore this issue of parameter stability further by relating it to the five regions mentioned earlier. Recall that the results in Table 1 are arranged by regions. 3.5. Regional differences Some further insights regarding the relationship among parameter stability, the hypothesis of C1 = 0 and the division of countries by region can be gleaned from Table 1. We highlight three key points. First, for a majority of the countries in Asia, Africa, and the Pacific–USA– Canada region, both the hypothesis of C1 = 0 and parameter stability are supported. Contrary to the common perception, the United States is not among the countries where the hypothesis of C1 = 0 was not rejected. Second, for countries in the Middle East and European regions, the evidence in support of the hypothesis of C1 = 0 and the hypothesis of parameter instability is generally weak. In the case of the Middle East region, the hypothesis of C1 = 0 is supported in three out of the four countries that showed evidence of cointegration. However, parameter stability is rejected in all four cases, except Egypt. For European countries, cointegration is found in three out of eight cases; the hypothesis of C1 = 0 is accepted in these three countries; however, parameter stability is supported in only two of the three countries. Finally, applying the same criteria to Latin American economies, we found only a weak support for the hypotheses of C1 = 0 and parameter stability. Although 8 out of 12 countries exhibited cointegration, with an estimated coefficient that cannot be replaced by zero, 112 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 according to the Johansen test statistics, the SupF test confirms stability in only four of the eight countries. In sum, the analysis suggests that countries in the Middle East, Europe, and Latin America have relations that have exhibited more coefficient instability over time than countries in other regions. 3.6. Income differences To explore this issue of cointegration and parameter stability further, we attempt a brief interpretation of these results, using the World Bank classification of economies by income levels (see World Bank, 1994). For the 14 low-income countries in our sample (Ethiopia, Bolivia, Burundi, Kenya, Myanmar, Pakistan, Sri Lanka, India, Zambia, Papua New Guinea, Haiti, Guatemala, Indonesia, and Egypt), the results of eight countries confirm the presence of cointegration (based on the Johansen estimator) between imports and exports. Parameter stability is confirmed for seven out of the eight countries, the exception being Bolivia. In the case of high-income countries (Singapore, Hong Kong, Japan, Australia, Canada, the United States, the Netherlands, Sweden, Austria, New Zealand, Israel, and Kuwait), the results of 10 countries show evidence in favor of cointegration; however, 2 out of these 10 countries have long-run equilibrium relations that are unstable. There are 24 middle-income countries in our sample;12 the results from 17 countries provide evidence in support of cointegration, whereas the results of 11 countries favor stable long-run relations over time. In sum, the overall evidence indicates that the long-run relationship between imports and exports is fairly stable. 4. Summary and conclusion This paper investigates the long-run convergence between imports and exports in 50 countries over the quarterly period 1973– 1998 and examines the constancy of this relationship. As far as we know, there is no such study in the literature for a diverse sample of developed and developing countries. Past studies have focused largely on the United States. This empirical analysis was characterized by four important elements. First, because the unit root properties of the data play a key role in the analysis, we used both the ADF and the Johansen unit root tests. Second, based on the Monte Carlo study by Haug (1996), we employed a two-system approach, namely the Johansen (1995) and the Stock and Watson (1988), to examine the presence or absence of cointegration. Third, following the Monte Carlo studies of Gregory (1996) and Stock and Watson (1993) among others, we obtained estimates of the cointegrating relations using Johansen’s FIML approach, as well as the Stock 12 The middle-income countries are Chile, Costa Rica, the Dominican Republic, Ecuador, El Salvador, Malaysia, Morocco, Tunisia, Cyprus, Korea, Fiji, Jordan, South Africa, Thailand, Venezuela, Mexico, Colombia, Hungary, Mauritius, Greece, Iran, Paraguay, Portugal, and Nigeria. A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 113 and Watson DOLS procedure and the Phillips and Hansen (1990) FMOLS approach. Fourth, we tested two important hypotheses, namely whether exports can be excluded from the cointegration space and whether the estimated cointegrating coefficient is unity. Finally, we employed Hansen’s (1992) SupF test for I(1) processes to examine the constancy of the cointegration space of each country. The estimation results lead us to some tentative conclusions. First, for the overwhelming majority of the countries, we find evidence of a long-run relationship between imports and exports. In the case of the United States, the results lend support to the findings of Husted (1992) regarding cointegration between imports and exports. The results also lend further support to his findings regarding the sign of the estimated slope coefficient. These results are in conflict with the findings in Fountas and Wu (1999). However, contrary to Husted’s, our results indicate that the cointegrating coefficient, although positive, may be significantly different from unity. This could be due to the exclusion of services from our data for the United States or the use of GDP, since it excludes factor payments abroad. Second, based on Johansen’s exclusion test results, we find evidence that the estimated cointegrating coefficient is positive and significantly different from zero in 86% of the sample; that is, 30 out of 35 countries. In a similar fashion, it appears that the estimated slope coefficient does not differ significantly from unity in most cases. Third, the evidence suggests that the cointegration space is fairly stable over time. Nevertheless, parameter stability does not appear uniformly to all regions. Countries in the Middle East, Europe, and Latin America appear to exhibit more parameter instability than do those in Asia, Africa, and the Pacific– USA–Canada region. Finally, the evidence suggests that imports and exports are cointegrated, not just in lowincome countries but in middle-income and high-income countries as well. Our results concerning constancy of the cointegrating space are robust to income classification. For lowincome countries, over 57% of the countries have stable cointegration space; for the middleincome countries, it is 58%; and for the high-income countries, it is 75%. Broadly speaking, the results have been good in the sense that common equations were able to explain imports and exports of a group of diverse countries. It is conceivable that the results could be improved if the observed instability in some of the countries or if other special features of the countries are incorporated into the estimation. Without attempting to resolve all problematic results here, we have shown that most of the countries are not in violation of their intertemporal budget constraint; that trade deficits in most of these countries are a short-run phenomenon and in the long-run, they are sustainable; and that macroeconomic policies have indeed been effective in making exports and imports converge toward an equilibrium in the long run. Acknowledgments The author would like to thank the Editor and two anonymous referees for helpful comments on an earlier draft. Special thanks to Kathleen Smith and Prarinya Lousudhi for excellent research assistance. 114 A.C. Arize / International Review of Economics and Finance 11 (2002) 101–115 References Agenor, P.-R., & Taylor, M. (1993). The causality between official and parallel exchange rates in developing countries. Applied Financial Economics, 3, 255 – 266. Arize, A. C. (1996). 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