New Approach to Estimating Gravity Models with Heteroscedasticity and Zero Trade Values

This paper proposes new estimation techniques for gravity models with zero trade values and heteroscedasticity. We revisit the standard PPML estimator and we propose an improved version. We also propose various Heckman estimators with different distributions of the residuals, nonlinear forms of both selection and measure equations, and various process of the variance. We add to the existent literature alternative estimation methods taking into account the non-linearity of both the variance and the selection equation. Moreover, because of the unavailability of pre-set package in the econometrics software (Stata, Eviews, Matlab, etc.) to perform the estimation of the above-mentioned Heckman versions, we had to code it in Matlab using a combination of fminsearch and fminunc functions. Using numerical gradient matrix G, we report standard errors based on the BHHH technique. The proposed new Heckman version could be used in other applications. Our results suggest that previous empirical studies might be overestimating the contribution of the GDP of both import and export countries in determining the bilateral trade.