Nonlinear impact estimation in spatial autoregressive models

This paper extends the literature on the calculation and interpretation of impacts for spatial autoregressive models. Using a Bayesian framework, we show how the individual direct and indirect impacts associated with an exogenous variable introduced in a nonlinear way in such models can be computed, theoretically and empirically. Rather than averaging the individual impacts, we suggest to graphically analyze them along with their confidence intervals calculated from Markov chain Monte Carlo (MCMC). We also explicitly derive the form of the gap between individual impacts in the spatial autoregressive model and the corresponding model without a spatial lag and show, in our application on the Boston dataset, that it is higher for spatially highly connected observations.