Controlling for Heterogeneity in Gravity Models of Trade

More documents

Recommendations

Info

heterogeneity, and these models can be regarded as restricted forms of the FE model. Usingmany of the same arguments we use to argue for the FE model, Bayoumi and Eichengreen (1997)propose estimating the gravity equation in first differences. This method of handlingheterogeneity is nearly identical to ours, except in the restrictions that it imposes on the effects oftime. An additional difference between their model and our FEa model is that they use theirindependent variables are the products of the GDPs and populations, therefore imposing theadditional restrictions that β1= β2and β3= β4. Because we wish to focus on their treatment ofheterogeneity only, we will not estimate the model under those restrictions. However, as is clearfrom the results, these additional restrictions are easily rejected statistically.Taking the time difference of (5), the model that we will estimate (BEa) is∆ ln Xijt= γ0+ γt+ β1∆lnYit+ β2∆lnYjt+ β3∆lnNit+ β4∆lnNjt+ µijt; (6)where the intercept is as defined in Section 2, γ0+ γt= αt− αt−1. To prevent collinearity, we setthe time dummy for 1992 equal to zero, meaning that other time dummies are measured relativeto it. In terms of the more-general FEa model, this is equivalent to restricting the commoncomponent of the change in the period-specific effects as equal to the difference in the first twoperiod-specific effects, i.e. γ = α − .13 The empirical results are presented in Table 2.0 2α1The results for the FEa and BEa models are very similar in terms of the signs and order ofmagnitude of the coefficients. Also, as illustrated by the lower-left panel of Figure 1, the BEamodel is not subject to the obviously biased residuals of the PCSa model. Nonetheless, the FEa13 The alternative assumption that the sum of the year dummies is zero means that γ0= αT − α1, and yields thesame results except for the time dummies and the constant.18
and BEa results differ enough to reject the restrictions needed to obtain BEa model. This isconfirmed by a likelihood ratio test. Further, in terms of fitting the data, the FEa model ispreferred in terms of the sum of squared residuals, the Akaike Information Criteria, and theAmemiya Probability Criteria. As for the further restrictions in Bayoumi and Eichengreen (1997)that β1= β2and β3= β4, our results indicate that this would clearly have significant effects onthe estimates, and therefore should not be imposed.The other alternative to the FEa model is due to Mátyás (1997), who proposes using thespecificationln Xijt= α0+ αt+ θi+ ωj+ β1lnYit+ β2lnYjt+ β3ln Nit+ β4ln Njt+ εijt; (7)where the effect when a country is an exporter is θi, and when it is an importer isωj. Thismodel is a restricted form of the FEb model in that it imposes arbitrary cross-pair restrictions onthe country-pair effects; α = α − ω + θ .ijikkjThe empirical results, summarized by the last column of Table 2, show that the coefficientsare identical to those from the FEa model, although their standard errors are very large. In fact,they are large enough to reject the statistical significance of all but the coefficient on destinationGDP. The lower-right panel of Figure 1 plots the residuals of this model against the log ofexports, and shows that this model has very peculiar results. The wide dispersion of the residualsalso indicates a very poor fit relative to FEa. Further, a likelihood ratio test easily rejects the nullhypotheses that the cross-pair restrictions do not change the results in a statistically importantway. So, although this model eliminates the bias in the estimates of the coefficients on the19
Page 1 and 2: WORKING PAPER SERIESControlling for
Page 3 and 4: Controlling for Heterogeneity in Gr
Page 5 and 6: simply on the basis of goodness of
Page 8 and 9: independent variables are assumed t
Page 10: GDPs, their populations, and the di
Page 13 and 14: GDP should be associated with a 6.2
Page 15 and 16: that it may be different for each d
Page 17 and 18: cross-section results, the year dum
Page 19: country-pair effects from the FE mo
Page 23 and 24: primary change over the period was
Page 25 and 26: 7. ConclusionsThe objective of this
Page 27 and 28: ReferencesAitken, N. D., 1973, “T
Page 29 and 30: Table 1: Regression results for sin
Page 31 and 32: Table 3: Regression results with in

Controlling for Heterogeneity in Gravity Models of Trade

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?