A spatial autoregressive Poisson gravity model

In this paper, a Poisson gravity model is introduced that incorporates spatial dependence of the explained variable without relying on restrictive distributional assumptions of the underlying data generating process. The model comprises a spatially filtered component - including the origin, destination and origin-destination specific variables - and a spatial residual variable that captures origin- and destination-based spatial autocorrelation. We derive a 2-stage nonlinear least squares estimator that is heteroscedasticity-robust and, thus, controls for the problem of over- or underdispersion that often is present in the empirical analysis of discrete data or, in the case of overdispersion, if spatial autocorrelation is present. This estimator can be shown to have desirable properties for different distributional assumptions, like the observed flows or (spatially) filtered component being either Poisson or Negative Binomial. In our spatial autoregressive model specifcation, the resulting parameter estimates can be interpreted as the implied total impact effects defined as the sum of direct and indirect spatial feedback effects. Monte Carlo results indicate marginal finite sample biases in the mean and standard deviation of the parameter estimates and convergence to the true parameter values as the sample size increases. In addition, the paper illustrates the model by analysing patent citation flows data across European regions.