Exogeneity and the export-led growth hypothesis: the case of China.
During the past two decades, many empirical studies such as Balassa [3, 4], Emery , Fajana , Feder , Maizels , Rams [22, 23], Tyler , Voivodas , Williamson , and others have found that exports promote economic growth. In all of these studies, a real output growth variable is regressed on either (i) export levels, (ii) export shares or (iii) export growth by using a single-equation model. The statistical significance of the (positive) coefficient of the export variables has then been interpreted as evidence supporting the export-led growth hypothesis.
Chow , Hsiao , and Jung and Marshall  have recently questioned the validity of the above findings. This is because the single-equation (or so called "impact") studies using OLS regression are, from an econometric perspective, mostly inadequate in addressing the issue of causality. If a bidirectional causality between these two variables (exports and output) exists, the estimation and tests used in the impact studies are inconsistent. These concerns have subsequently generated a series of new empirical work aimed directly at resolving the issue of causality between exports and output growth [1; 2; 14; 20]. The Granger  causality tests carried out in these studies have revealed that the causal direction, in general, depends on the country and commodity group under consideration.
Notwithstanding the important contributions of the above mentioned causality studies, there are shortcomings that must be dealt with to permit a better understanding of the subject matter. First, the impact studies presume that the export variable is exogenous. This is a rather restrictive assumption as a feedback from output to exports is very likely [17; 20]. Second, the existing causality studies do not make a clear distinction between "exogeneity" and "causality". As suggested by Engle, Hendry and Richard [10, hereinafter EHR], causality tests, such as the Granger  method, are valid only for testing one component of "strong" exogeneity because they are concerned with sequential marginalizing feedback effects, rather than contemporaneous conditioning upon which (weak) exogeneity is crucially based.(1) Thus, the presence of Granger's causal relationship is neither a necessary nor a sufficient condition for any discussion on export-promotion policies.
In this paper, we argue that these shortcomings should be dealt with by carrying out formal exogeneity tests under a framework proposed by EHR. The three distinct concepts of exogeneity (weak, strong and super) will directly address the issues of (i) validity and efficiency of existing impact studies estimates, (ii) whether export growth helps forecast output growth, and (iii) whether the relationship between export growth and output growth is structurally stable and invariant to policy interventions.
In line with the above, an analysis of exogeneity will be applied to newly released statistics from the People's Republic of China for the period 1952-85. We choose China as the focus of our study because Kwan and Cotsomitis  have recently found that the size of the Chinese export sector Granger causes its economic growth.(2) Since the concepts of "causality" and "exogeneity" are different, it would be of considerable interest to extend their analysis by employing the EHR exogeneity framework. In addition, recent economic data from China indicate that national income and exports rose 11.6 and 30 times respectively during our sample period. In light of the parallel growth in these two variables, it is important to examine the validity of the export-led growth hypothesis in the case of China. In particular, our super exogeneity test results may shed some light on the policy implication of this hypothesis.
The remainder of this paper is organized as follows. Section II presents the econometric methodology, the data used and the model specification. Section III reports our empirical results. Section IV offers some concluding remarks.
II. Econometric Methodology, Data and Model Specification
If the export-led growth hypothesis is to be tested, then there must be a causal relationship posited of the form:
[Mathematical Expression Omitted]
with output growth D[Y.sub.t] and export growth D[X.sub.t].(3,4,5) This specification admits an AR(k) process for DY, current and lagged effects of export growth, as well as other variables [w.sup.t] to enter the relationship. The vector of coefficients is given by [Alpha]; that the subset of coefficients [Mathematical Expression Omitted] whose sum should be positive for export-led growth.
Most empirical studies of the export-led growth hypothesis only explore special cases of (1). The "impact" studies typically ignore the dynamic structure of the variables and focus exclusively on the contemporaneous relationship between DX and DY. The causality studies, on the other hand, pay close attention to dynamic specifications but omit either the potential influence of other variables or the effect of current export growth on output growth.(6) As is well known in econometrics, inadequate exploration of dynamic specification and omitted variables may lead to erroneous inferences. In order to avoid these shortcomings, we adopt a general functional form like (1) which allows not only for current and lagged effects of export growth(7) but also for other variables that are likely to influence output growth.
Including D[X.sub.t] in (1), however, poses a potential problem, namely that the current export growth variable may not be exogeneous. This will be the case if (1) is part of a simultaneous system of structural equations or if the "growth-caused exports"  is indeed the correct hypothesis. In this paper, we argue that a careful analysis of the exogeneity property of D[X.sub.t] in (1) is essential in studying the validity of the export-led growth hypothesis. To do so, the EHR concepts of exogeneity are applied to (1).
Let [Lambda] be the vector of parameters of interest and D[X.sub.t] the variable whose exogeneity properties are under examination.(8) According to EHR, D[X.sub.t] is weakly exogenous for [Lambda] if (i) [Lambda] is a function of [Alpha] alone, and (ii) [Lambda] and the parameters in the marginal distribution of D[X.sub.t] are variation free. If in addition to being weakly exogenous for [Lambda], lagged values of D[Y.sub.t] do not Granger cause D[X.sub.t], then D[X.sub.t] is said to be strongly exogenous. For super exogeneity, we require weak exogeneity and the invariance of [Lambda] to changes in the marginal distribution of D[X.sub.t]. As noted by EHR, the concept of super exogeneity is closely associated with the Lucas  critique.
To test for weak and super exogeneity of D[X.sub.t], we make use of a strategy developed by Engle and Hendry [8, 9, hereinafter EH]. The EH procedure is designed for a linear Gaussian model of the form:
D[Y.sub.t] = [Beta]D[X.sub.t] + [z.sub.t][Gamma] + [[Epsilon].sub.t], (2)
with D[Y.sub.t] and D[X.sub.t] jointly IID normal, conditional on the information set [I.sub.t]. Relating (2) to (1) and the definitions above, this implies that f([center dot], [Alpha]) is linear, [[Epsilon].sub.t] is normal, [Lambda] = [Beta], and [z.sub.t] is a vector consisting of [w.sub.t] and all the lagged DX as well as DY variables. Suppose that there exist a set of instruments [Z.sub.t] [an element of] [I.sub.t], including [z.sub.t], such that the mean of D[X.sub.t] can be estimated as [Mathematical Expression Omitted] from the least-squares regression [Mathematical Expression Omitted].(9) Then if [Epsilon] and [Eta] are jointly homoscedastic (under the null hypothesis of exogeneity), a test for the weak exogeneity of D[X.sub.t] for [Beta] is to augment (2) with [Mathematical Expression Omitted] as an additional regressor and then test for its significance. To test the invariance of [Beta] to the changes in the first moment of DX, which is required for super exogeneity, both [Mathematical Expression Omitted] and [Mathematical Expression Omitted] should be added to (2) and their joint significance tested.(10) In both cases a significant test statistic indicates a rejection of the null hypothesis of D[X.sub.t] being exogeneous for [Beta] in favor of the alternative hypothesis that D[X.sub.t] is not exogeneous for [Beta].
Since the EH procedure presupposes that (2) is the correct specification, careful diagnostics must be carded out to ensure that (2) is a reasonable representation of (1) and that (2) satisfies the required distributional assumptions. This entails, as a first step, the proper specification of the lag structures for DY and DX and the choice of [w.sub.t]. Then standard diagnostic checking should be carried out to detect for possible non-linear functional form, non-normality, serial correlation and (conditional as well as unconditional) heteroscedasticity.
Table I. The FPE values for (k, m) of Equation (1)
Lag FPE(k) FPE([k.sup.*], m)
0 0.0062 1 0.0116 0.0068 2 0.0118 0.0073 3 0.0107 0.0077 ([k.sup.*] = 3) ([k.sup.*] = 3, [m.sup.*] = 0)
To determine the optimal lags for DY and DX, we employ the final prediction error [FPE(k, m)] criterion. The FPE(k, m) is calculated in a 2-step process where m is set conditional to k = [k.sup.*]. First, setting m = 0, k = [k.sup.*] which minimizes FPE(k):
FPE(k) = [(T + P)/(T - P)]/(SSR/T),
where T is the sample size, SSR is sum of squared residuals for (2) in which [w.sub.t] are excluded, and P is the number of parameters to be estimated. Second, having determined k = [k.sup.*], we solve for m = [m.sup.*] so as to minimize FPE([k.sup.*], m). The resulting structure ([k.sup.*], [m.sup.*]) specifies the optimal lags for DX and DY. As for [w.sub.t], we allow the growth rate of labor force (DL) and the ratio of domestic investment to GDP (IY) to enter (2). As is well documented in the economic development literature, these two variables are expected to provide good explanatory power in the standard output growth model.
We calculated the FPE's of DX and DY by varying the values of (k, m) from 0 to 3.(11) The results of the FPE are reported in Table I, and indicate that the optimal values of (k, m) are (3,0). On the basis of this finding, (2) can be written as:
D[Y.sub.t] = [[Alpha].sub.0] + [summation of] [[Alpha].sub.j]D[Y.sub.t-j] where j=1 to 3 + [Beta]D[X.sub.t] + [[Gamma].sub.1]D[L.sub.t] + [[Gamma].sub.2]I[Y.sub.t] + [[Epsilon].sub.t], (3)
where [Epsilon] is a non-autocorrelated error term.(12) In this paper, (3) serves as a benchmark for exogeneity testing.
For strong exogeneity which includes weak exogeneity and Granger non-causality from lagged DY to DX, the Granger causality test is used. In the bivariate case, Granger  proposed the following causal model:
D[Y.sub.t] = [a.sub.0] + [summation of] [a.sub.i]D[Y.sub.t-i] where i=1 to j + [summation of] [b.sub.i]D[X.sub.t-i] where i=1 to k + [[Epsilon].sub.1t], (4)
D[X.sub.t] = [c.sub.0] + [summation of] [c.sub.i]D[X.sub.t-i] where i=1 to l + [summation of] [d.sub.i]D[Y.sub.t-i] where i=1 to m + [[Epsilon].sub.2t], (5)
where D[X.sub.t] and D[Y.sub.t] are stationary time series, the values (j, k, l, m) are optimal lag lengths, and [[Epsilon].sub.1t] and [[Epsilon].sub.2t] are random errors.(13)
As regards the required data, they are obtained from Kwan and Cotsomitis  and the Statistical Yearbook of China . Since the time series of GDP and the labor force are not available in these publications, they are proxied by national income and population, respectively.
III. Empirical Results
Our results for the exogeneity (weak, strong and super) tests are summarized in Tables II to V. Due to data transformation, the effective sample size for the output growth equation is from 1956 to 1985.
An examination of the regression results suggest that current real export growth (D[X.sub.t]), current investment-output ratio (I[Y.sub.t]), and current labor force growth (D[L.sub.t]) have positive coefficients and are significant at least at the 5% level. The results of the diagnostic tests including the Godfrey LM test for first- and second-order serial correlation (Serial  and Serial ), the Engle test for first- and second-order autoregressive conditional heteroscedasticity (ARCH and ARCH), the White test for heteroscedasticity (WHITE), the Bera-Jacque test for normality (B-J), and the Ramsey test for model misspecification (RESET), indicate no obvious model inadequacy.
In order to construct tests for weak and super exogeneity, the mean vector of DX, [Mu], must be quantified. This is done by using an auxiliary export growth equation where D[X.sub.t] is regressed on a set of selected instruments. In an effort to search for the most appropriate export equation, we considered, as instruments, a number of combinations of economic variables.(14) To conserve space, we report only the export growth equation (see Table III) which gives the best results in terms of model diagnostics and economic reasoning.(15)
From the results in Table III, we find that three out of the five regressors (D[Y.sub.t-1], D[L.sub.t] and I[Y.sub.t]) retained from the output equation are significant at least at the 10% level.(16) However, all other instruments considered do not seem to provide good explanatory power in the export growth equation. In order to carry out our super exogeneity analysis, an additional dummy variable (DUM78) is included to incorporate the impact of the "1978 Four Modernizations" which promoted the "outward looking" strategy .(17,18) Since the adoption of the said policy, China's real export growth has risen steadily.(19) Indeed, our results indicate that DUM78 is positive and highly significant, suggesting the existence of a structural break.
[TABULAR DATA FOR TABLE II OMITTED]
[TABULAR DATA FOR TABLE III OMITTED]
In Table IV, we report the results of the EH [8; 9] exogeneity tests. A test for the assumption of weak exogeneity of D[X.sub.t] (for its regression coefficient) is formulated in Test Regression (A) as a test of significance for the coefficient of [Mathematical Expression Omitted]. At the 10% level, we found that the hypothesis of weak exogeneity cannot be rejected.(20,21) In Test Regression (B) the test for super exogeneity of D[X.sub.t] is formulated as the test of joint significance of the regression coefficients for [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. The F-test statistic is 2.179 and does not lead to a rejection of the null hypothesis of super exogeneity at the 10% level. This suggests that the real export growth variable possesses the super exogeneity status; that is, the coefficient of the export growth variable is invariant to policy interventions like the "Four Modernizations" thereby making policy evaluation possible.
Next, the Granger test is conducted to check for the existence (or absence) of a causal relationship between export growth and output growth. The empirical results reported in Table V reveal a unidirectional causality from lagged DX to DY. An inspection of the sign of the causal impact indicates a positive sum of the lagged coefficients of DX, suggesting that a change in [TABULAR DATA FOR TABLE IV OMITTED] [TABULAR DATA FOR TABLE V OMITTED] lagged export growth helps forecast current output growth.(22) Since the hypothesis of Granger non-causality from lagged DY to DX cannot be rejected at the conventional level of significance, we therefore conclude that the export growth variable is strongly exogeneous.
IV. Concluding Remarks
The issue of exogeneity has been one of the important research areas in econometrics for the past few decades. This paper is a first attempt to apply the EHR framework to examine empirically the exogeneity assumptions of the real export growth variable in an output growth equation. Using data on China for the period 1952-85, we have found that while the weak, strong and super exogeneity assumptions appear valid, the current export growth variable has significant and positive coefficient. Our results therefore support the validity of the export-led growth hypothesis. As well, our super exogeneity test results indicate that the coefficient of the current export growth variable is structurally invariant to "1978 Four Modernizations".
As for future research, it would be interesting to extend the present analysis to newly industrializing countries such as the "four little tigers" (Hong Kong, South Korea, Singapore, and Taiwan) which are often used as evidence in support of the export-led growth hypothesis. These test results would be of considerable importance because they will allow us to directly evaluate the validity of many existing studies on the subject.
1. The definition of "strong" exogeneity is given in section II.
2. It must be noted that the empirical results of Kwan and Cotsomitis  are sensitive to the chosen sample period.
3. DY and DX denote the first difference of Y (log of real output) and X (log of real exports), respectively.
4. We assume that (1) is conditional on an information set [I.sub.t].
5. We would like to thank the referee for directing our attention to this framework.
6. Exceptions include Kunst and Marin  who used a four-variable VAR structure, and Chow  who allowed for the influence of D[X.sub.t] in a bivariate causal framework.
7. It is possible to have a situation where the Granger causality test may suggest no causality from lagged export growth to output growth while the two variables are, in fact, contemporaneously correlated (i.e. there is instantaneous causality).
8. Throughout this section, we maintain that all the right-hand-side variables other than D[X.sub.t] are valid conditioning variables and are a part of an information set [I.sub.t], since otherwise those suspected as non-exogeneous would simply be reclassified as part of an extended vector.
9. [Z.sub.t] may contain dummy variables as well.
10. This point is further elaborated by Fischer .
11. Before we calculate the FPEs of DX and DY, we use the Zivot-Andrews  unit root test to examine for the presence of unit roots in X and Y. Our results indicate that while the output variable is stationary, the export variable possesses a unit root. When the Zivot-Andrews test is applied to the export growth series (i.e., first differences of X), the null hypothesis of a unit root can be rejected at the conventional level of significance. Using Box and Jenkins's  terminology, Y and X are said to be integrated of orders zero and one, respectively.
12. Although X and Y do not possess the same degree of integration, it is important to note that both DX and DY (first differences of X and Y) are stationary series. Furthermore, since DX and DY are used in (3), our attention is confined to the impact of real export growth on real output growth.
13. The appropriate lag lengths of the casual model (i.e., equations (4) and (5)) are set according to the FPE criterion. Since the causal inference is sensitive to the presence of serial correlation among residuals, the Godfrey LM test is used here. If the hypothesis of no serial correlation is rejected, a filtering procedure will be employed.
14. The instruments considered are lagged DX, lagged DY, the size of the agricultural sector, the ratio of construction expenditure to national income, the rate of growth of agricultural production, and the U.S. GNP growth.
15. As indicated in Engle and Hendry , the set of instruments whose combination can best approximate [Mu] should result in more powerful tests.
16. Note that the inclusion of these variables are required to ensure the consistency and validity of the subsequent exogeneity tests.
17. [DUM78.sub.t] = 1 for t [greater than or equal to] 1978 and [DUM78.sub.t] = 0 if otherwise.
18. When the dummy (DUM78) is introduced in the output equation to capture the impact of the non-export-related "Modernization", our empirical results indicate that this variable is not significant at the 10% level. This set of regression results is available upon request.
19. The average growth rates of China's real exports for the periods of 1953-77 and 1978-85 are 6.1% and 18.7%, respectively.
20. Note, however, that by including the structural break variable (DUM78) in the export equation, this is essentially a joint test of weak exogeneity and invariance to the structural break of 1978 (while maintaining general invariance of [Beta] to the moments of DX). Had this test led to a rejection, it is not clear whether it would be a rejection of weak exogeneity or invariance to the 1978 shift. Ideally a "pure" test for weak exogeneity can be constructed using either the sub-samples before or after the break, however, our limited sample size prevents us from doing so.
21. Since DX is weakly exogenous in the output growth equation, DY cannot be weakly exogeneous in the export growth equation; see EHR and EH for a detailed discussion on this issue. Our results, therefore, exclude the possibility of growth-caused exports.
22. This result may seem contrary to that of Kwan and Cotsomitis  who found a bidirectional causality between exports and output. It is important to note, however, that the export variables used in their study are defined as export-sector size as well as growth rates of the export sector.
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