Sieve maximum likelihood estimation of the spatial autoregressive Tobit model

Abstract

This paper extends the ML estimation of a spatial autoregressive Tobit model under normal disturbances in Xu and Lee (2015b, Journal of Econometrics) to distribution-free estimation. We examine the sieve MLE of the model, where the disturbances are i.i.d.with an unknown distribution. We show that the spatial autoregressive process with Tobit censoring and related variables are spatial near-epoch dependent (NED). A related contribution is that we develop some exponential inequalities for spatial NED random fields. With these inequalities, we establish the consistency of the estimator. Asymptotic distributions of structural parameters of the model are derived from a functional central limit theorem and projection.Simulations show that the sieve MLE can improve the finite sample performance upon misspecified normal MLEs. As an empirical application, we examine the school district income surtax rates in Iowa. Our results show that the spatial spillover effects are significant, but they may be overestimated if disturbances are restricted to be normally distributed.