Estimating the Gravity Model When Zero Trade Flows are Frequent and Economically Determined - Martin, Will (World Bank, Washington, DC, 2015)
This paper evaluates the performance of alternative estimators of the gravity equation when zero trade flows result from economically-based data-generating processes with heteroscedastic residuals and potentially-omitted variables. In a standard Monte Carlo analysis, the paper finds that this combination can create seriously biased estimates in gravity models with frequencies of zero frequently observed in real-world data, and that Poisson Pseudo-Maximum-Likelihood models can be important in solving this problem. Standard threshold–Tobit estimators perform well in a Tobit-based data-generating process only if the analysis deals with the heteroscedasticity problem. When the data are generated by a Heckman sample selection model, the Zero-Inflated Poisson model appears to have the lowest bias. When the data are generated by a Helpman, Melitz, and Rubinstein-type model with heterogeneous firms, a Zero-Inflated Poisson estimator including firm numbers appears to provide the best results. Testing on real-world data for total trade throws up additional puzzles with truncated Poisson Pseudo-Maximum-Likelihood and Poisson Pseudo-Maximum-Likelihood estimators being very similar, and Zero-Inflated Poisson and truncated Poisson Pseudo-Maximum-Likelihood identical. Repeating the Monte Carlo analysis taking into account the high frequency of very small predicted trade flows in real-world data reconciles these findings and leads to specific recommendations for estimators.