Using panel data techniques captures the relationships between variables over the period of the sample and can control for the possibility that the unobserved effects may be correlated with the regressors.17 The two most commonly employed panel models are the fixed effects model (FEM) and the random effects model (REM). In the FEM, the intercept terms are allowed to vary over the individual units (in this case the importing and exporting country pairs) but are held constant over time. REM assumes that the intercepts of individual units are randomly distributed and independent of the explanatory variables. A priori, the FEM would be expected to be a better fit in the gravity model context as the panel tracks pairs of countries over time and it is not realistic to consider them to be randomly drawn. If this is the case and the unobserved effects are correlated with regressors, the REM estimates will be biased. 18
A shortcoming of the FEM is that variables that do not vary over time (distance or common language for example) cannot be estimated as they are dropped in the fixed effects transformation. Cheng and Wall (2005) solve this problem by estimating an auxiliary equation in the FEM in which the time invariant explanatory variables are
r e g r e s s e d o n t h e e s t i m a t e d c o u n t r y p a i r i n t e r c e p t s α i j f r o m t h e F E M r e g r e s s i o n u s i OLS: n g
i j 1 2 i j 3 i j 4 i j 5 i j i j ˆ = + l n D i s t a n c e + A d j a c e n c y + L a n g u a g e + E U + α β β β β β ν
Both FEM and REM are estimated and their efficiency compared. First, the Breusch- Pagan test is applied to the REM and compared to the pooled OLS estimator. The null hypothesis is rejected, indicating that REM is a better estimator than OLS.19 Second, as noted above it is likely that OLS and REM suffer from heterogeneity bias and endogenous explanatory variables respectively. Table 3 shows that the estimated coefficients using OLS and REM are very close. The Hausman test is applied to REM and FEM. The test statistic of 14.61 is greater than the chi-squared critical value at six degrees of freedom at the 5 percent significance level (12.59), therefore the null hypothesis that the REM is consistent is rejected, the REM is shown to suffer from correlation and generate biased estimates.
As an alternative to both the fixed effects and random effects models, Egger (2002, 2005) proposes using the Hausman and Taylor model (HTM).20 The HTM employs an instrumental variable approach that uses information solely from within the dataset to eliminate the correlation between the explanatory variables and the unobserved individual effects that undermines the appropriateness of the REM in the gravity model
17 Baier and Bergstrand (2005b) provide a detailed discussion of the potential sources of bias in gravity model estimation and the techniques that may be used to overcome this problem.
18 In the gravity model relationship it is more likely than not that the REM will be biased. Egger (2005, p883) cites the example of an observed variable such as GDP being correlated with unobservable determinants of trade such as human capital stock or trade barriers in the importing and exporting countries. The explanatory variables are considered to be endogenous as they are correlated with the error term. See Cheng and Wall (2005) for a more detailed discussion.
19 A test statistic of 2597 is greater than the critical chi-squared value at one degree of freedom at 1% significance level (6.63).
See Hausman and Taylor (1981).