A Bayesian Spatial Interaction Model Variant of the Poisson Pseudo-Maximum Likelihood Estimator

Gravity or spatial interaction models have a long history in regional science and international trade. In the empirical trade literature, Poisson pseudo-maximum likelihood estimation methods (PPML) have become popular as a way of dealing with several econometric issues that arise when modeling origin-destination flows [e.g., Silva and Tenreyro (2006, 2010, 2011) and Gourieroux, Monfort and Trognon (1984)]. This approach to estimating Poisson models has several econometric advantages which we outline. We extend the PPML to allow for spatial dependence between flows from nearby regions, a phenomena that has been recognized in the spatial econometrics literature. Our (Bayesian) model allows spatial spillovers to arise from changes in the characteristics of a single region i. We provide simulations to show the impact of ignoring spatial spillovers on non-spatial PPML. An application of the proposed spatial model is provided using a dataset for commuting-to-work flows from Toulouse, France. In this setting, an increase in resident population of an origin i will lead to more (commuting) outflows from i, as well as more commuting outflows from regions neighboring i (after conditioning on distance). An increase in jobs of a destination region j will lead to more commuting inflows to region j as well spatial spillovers taking the form of more inflows to regions neighboring j (after conditioning on distance). The non-spatial PPML model assumes that changes in characteristics such as economic size (income) of a region i will only impact flows directly involving region i, and not flows to regions that neighbor i