Structural change in import demand behavior, the Korean experience: a reexamination

NORTH- HOLLAND

Structural Change in Import Demand Behavior, The Korean Experience: A Reexamination Mohsen Bahmani-Oskooee

University of Wisconsin-Milwaukee H y u n - J a e R h e e , Chong Ju University, Korea In a recent issue of this journal, Mah (1993) examined the structural instability of Korea's import demand function using quarterly data over 1971-88 period. Based on cusum and cusum of squares tests, it was revealed that Korea's import demand suffered from structural instability in the early 1980s. The major shortcoming of Mah's analysis is that he reached his conclusion by using nonstationary data. When data are nonstationary and contain unit roots, the analysis and conclusion suffer from what is known as "spurious regression" problem. The problem is that the standard t-ratios cannot be used to infer any statistical significance. The unit root tests and cointegration analysis try to resolve this problem. Indeed, in discussing alternative tests for parameter stability such as Lagrange multiplier test, Hansen (1992, p. 520) argued that it is necessary to exclude nonstationary regressors. Thus, it is the purpose of this note to reexamine the stability of Korea's import demand model by employing Johansen and Juselius (1990) cointegration analysis. It should be mentioned that similar point has also been raised in the literature of the demand for money. Authors such as Haler and Jansen (1991), Hoffman and Rasche (1991), and McNown and Wallace (1992) have used Johansen-Juselius technique to establish the long-run stability of the demand for money in the United States. The import demand model adopted by Mah and others in the literature took the following form: Address correspondence to Prof. Mohsen Bahmani-Oskooee, Department of Economics, The University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, U.S.A. We would like to thank Jai Sheen Mah, who kindly provided his data set. Received March 1995; final draft accepted September 1995. Journal of Policy Modeling 19(2):187-193 (1997) © Society for Policy Modeling, 1997

0161-8938/97/$17.00 SSDI 0161-8938(95)00146-8

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(1)

where M is the volume of import, Y is the real GNP, P M is the import price index, and PD is the Korean whole sale price index. It is usually expected that estimate of b > 0 and c < 0.1 As a first rejection of Mah's conclusion that Korea's import demand suffered from structural instability, we plot the three variables identified in Equation 1 against time in Figure 1. As can be seen from Figure 1, there is no evidence of a sudden structural change in any of the three series. All three variables continue the same increasing trend in case of import and income, and decreasing trend in case of relative prices before and after early 1980s. If we are to provide evidence of structural break in a time series, we can refer to movement of the U.S. dollar. In the early part of 1980s, the dollar appreciated against major currencies by about 42%. In September 1985, central banks of big five industrial countries intervened in the foreign exchange market and pushed down the value of the dollar. Plot of effective exchange rate 1 For data definition and sources, see Mah (1993).

STRUCTURAL

CHANGE

IN IMPORT

DEMAND

BEHAVIOR

189

T a b l e 1" T h e A D F T e s t A p p l i e d to t h e L e v e l as well as F i r s t D i f f e r e n c e d Variables" Variable

Log M Log Y Log P M / P O

Level

First difference

-2.93141 b -2.27[4] -2.77[2]

-4.48[4] -4.06[3] -3.3611]

Notes: a The MacKinnon (1991) critical value for 72 observations when a trend term is included in the test is -3.47 at the 5% level and -3.16 at the 10% level of significance.

b Number inside the brackets are the number of lags.

of the dollar by Bahmani-Oskooee and Payesteh (1993) provides a nice example of structural break in a time series. The question of whether there is a long-run stable relation between three variables in Equation 1 could be investigated by cointegration analysis. Engle and Granger (1987) have shown that set of nonstationary variables could drift apart in the short-run, but if a linear combination among them turns out to be stationary, then those variables are said to be cointegrated, indicating that there is a stable relation among them. However, Johansen's technique for testing cointegration is said to be superior because it is based on maximum likelihood procedure that provides test statistics to determine the number of cointegrating vectors as well as their estimates. Therefore, we intend to test for cointegration among the three variables using Johansen (1988) and JohansenJuselius (1990) technique. In order to apply the cointegration technique, we first need to determine the degree of integration of each variable involved in our analysis. A common practice followed by many in the literature is to rely upon the Augmented Dickey-Fuller (ADF) test. For a time series Z, the A D F test statistics is usually obtained from estimating the following equation: k

A Z , = a + b t + c Z t _ 1 ~- ~ C i m Z t - I -~ W,

(2)

i=1

The test is whether estimate of c = 0. The A D F test statistic is calculated by dividing the estimate of c by its standard error. 2 The 2 The choice of k is usually dictated by the level of significance of the lagged coefficients on AZ,_i variable using the standard t test. For more on this, see Dickey, Bell, and Miller (1986, p. 19).

M . B a h m a n i - O s k o o e e and H.-J. R h e e

190

Table 2: Johansen's M a x i m u m Likelihood Procedure Results

Null

Alternative

k-max statistic

95% critical value

Trace statistic

95% critical value

Case 1: Non-trended case r = 0 r <= 1

r = 1 r = 2

72.93 11.00

22.00 15.67

89.69 16.77

34.91 19.96

r <=

r = 3

5.77

9.24

5.77

9.24

21.07 14.90 8.17

43.54 8.87 0.35

31.52 17.95 8.17

2

Case 2: Trended case, no trend in D G P r = 0 r <= 1 r <= 2

r = 1 r = 2 r = 3

30.66 8.53 0.35

Case 3: Trended case, with trend in D G P r = 0 r <= r <=

1 2

r = 1

34.66

20.96

43.54

29.68

r = 2 r = 3

8.53 0.35

14.06 3.76

8.87 0.35

15.41 3.76

Note: The critical values are from Johansen and Juselius (1990).

cumulative distribution of the A D F statistic is provided by Fuller (1976, p. 373) for specific sample sizes and by MacKinnon (1991) for any sample sizes. If the calculated A D F statistics is less than its critical value, then Z is said to be stationary or integrated of order zero, that is, Z ~ I(0). Table 1 reports these A D F test results for the level as well as for the first differences of all three variables. As can be seen from Table 1 all three variables do achieve stationarity only after being differenced once. Thus they are all integrated of order 1 or I(1). We are now in a position to apply Johansen-Juselius technique. Their method, which is based on maximum likelihood estimation procedure, introduces two tests

Table 3: Estimates of Cointegrating Vectors Normalized on L o g M Cointegrating vector Variable Log M Log Y

Log PM/PD Maximum eigenvalue

Case 1

Case 2

Case 3

-1.00 1.22 -0.08 0.66

-1.00 1.21 -0.11 0.40

-1.00 1.20 -0.11 0.40

S T R U C T U R A L C H A N G E IN I M P O R T D E M A N D B E H A V I O R

191

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k n o w n as h - m a x and trace tests to d e t e r m i n e the n u m b e r of cointegrating vectors, identified by r. In calculating these statistics one has to decide the n u m b e r of lags employed in the procedure. W h e n quarterly data are used, a c o m m o n practice is to employ four lags. A l t h o u g h we used four lags in the procedure, we m a d e sure that the results are not sensitive to the n u m b e r of lags. It should be indicated that the statistical package employed here (MFIT3.0) offers three alternatives in applying the Johansen's technique: n o n - t r e n d e d case, where data are not detrended; t r e n d e d case, with the assumption that there is no trend in the data-generating process (DGP); and t r e n d e d case, with the assumption that there is a trend in the data-generating process. The results of h - m a x and trace tests for all three cases are reported in Table 2. F r o m Table 2 it is evident that the null hypothesis of no cointegration, that is, r = 0, is rejected in all three cases. This is due to the fact that our calculated h - m a x and trace statistics for the null of r = 0 are greater than their critical values. However, the 'null of at least one cointegrating vector, that is, r < = 1, is accepted in all three cases. Thus, we k n o w that there is at least one cointegrating vector among the three variables. R e p o r t e d in Table 3 are

192

M. Bahmani-Oskooee and H.-J. Rhee

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Besiduals Figure 3. Plot of residuals of cointegrating vector (case 2).

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1

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1"~

S T R U C T U R A L C H A N G E IN I M P O R T D E M A N D B E H A V I O R

193

these cointegrated vectors associated with the maximum eigenvalue of the stochastic matrix for each case. Note that these vectors are normalized on Log M in order to be able to read the elasticities directly. From Table 3 we gather that income elasticity is about 1.2 and price elasticity about -0.10. As a further evidence of cointegration, we ploted the residuals of all three cointegrating vectors in Figures 2-4. As can be seen, no matter which figure we consider, the residuals oscillate around their mean value, indicating that they are on a stationary process. REFERENCES Bahmani-Oskooee, M., and Payesteh, S. (1993) Budget Deficits and the Value of the Dollar: An Application of Cointegration and Error-Correction Modeling, Journal of Macroeconomics 15:661-677. Dickey, D.A., Bell, W.R., and Miller R.B. (1986) Unit Roots in Time-Series Models: Tests and Implications, The American Statistician 40:12-26. Engle, R.F., and Granger, C.W.J. (1987) Co-Integration and Error Correction: Representation, Estimation, and Testing, Econometrica March:251-276. Fuller, W.A. (1976) Introduction to Statistical Time Series. New York: John Wiley. Hansen, B.E. (1992) Testing for Parameter Instability in Linear Models, Journal of Policy Modeling 14:517-533. Haler, R.W., and Jansen, D.W. (1991) The Demand for Money in the United States: Evidence from Cointegration Tests, Journal of Money, Credit, and Banking May: 155-168. Hoffman, D., and Rasche, R.H. (1991) Long-Run Income and Interest Elasticities of Money Demand in the United States, The Review of Economics and Statistics November: 665-674. Johansen, S. (1988) Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control 12:231-254. Johansen, S., and Juselius, K. (1990) Maximum Likelihood Estimation and Inference on Cointegration--with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics 52:169-210. MacKinnon, J.J. (1991) Critical Values for Cointegration Tests. In Long-Run Economic Relationships: Readings in Cointegration (R.F. Engle and C.W. Granger, Ed.). Oxford: Oxford University Press, pp. 267-276. Mah, J.S. (1993) Structural Change in Import Demand Behavior: The Korean Experience, Journal of Policy Modeling 15:223-227. McNown, R., and Wallace, M.S. (1993). Cointegration Tests of a Long-Run Related Between Money Demand and the Effective Exchange Rate, Journal oflnternational Money and Finance, February:107-114.