E¢ cient Estimation of the Semiparametric Spatial Autoregressive Model

E¢ cient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest. These estimates are as e¢ cient as ones based on a correct form, in particular they are more e¢ cient than pseudo-Gaussian maximum likelihood estimates at non-Gaussian distributions. Two di¤erent adaptive estimates are considered. One entails a stringent condition on the spatial weight matrix, and is suitable only when observations have substantially many "neighbours". The other adaptive estimate relaxes this requirement, at the expense of alternative conditions and possible computational expense. A Monte Carlo study of …nite sample performance is included. JEL Classi…cations: C13; C14; C21