Generalized Maximum Entropy Estimation of Spatial Autoregressive Models

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable and residuals. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators in small and medium sized samples relative to classical estimators. Finally, the estimators are applied to a model allocating agricultural disaster payments across regions. 3 1.0 Introduction In this paper we examine the use of generalized maximum entropy estimators for linear and censored regression models when the data generating process is afflicted by first order spatial autoregression in either the dependent variable or error term. Generalized maximum entropy (GME) estimators of regression models in the presence of spatial autocorrelation are of interest because they 1) offer a systematic way of incorporating prior information on parameters of the model, 2) are straightforwardly applicable to non-normal error distributions, and 3) are robust for ill-posed problems (Golan, Judge, and Miller 1996). Prior information in the form of parameter restrictions arise naturally in the context of spatial models because spatial correlation coefficients are themselves inherently bounded. The development of estimators with finite sample justification across a wide range of sampling distributions and an investigation of their performance relative to established asymptotically justified estimators provides important insight and guidance to applied economists regarding model and estimator choice. 1 Various econometric approaches have been proposed for accommodating spatial autocorrelation in linear regression models and in limited dependent variable models. In the case of the linear regression model, Cliff and Ord (1981) provide a useful introduction to spatial statistics. Anselin (1988) provides foundations for spatial effects