Estimation and Inference in Functional-Coefficient Spatial Autoregressive Panel Data Models with Fixed Effects

Abstract

This paper develops an innovative way of estimating a functional-coefficient spatial autoregressive panel data model with unobserved individual effects which can accommodate (multiple) time-invariant regressors in the model with a large number of cross-sectional units and a fixed number of time periods. The methodology we propose removes unobserved fixed effects from the model by transforming the latter into a semiparametric additive model, the estimation of which however does not require the use of backfitting or marginal integration techniques. We derive the consistency and asymptotic normality results for the proposed kernel and sieve estimators. We also construct a consistent nonparametric test to test for spatial endogeneity in the data. A small Monte Carlo study shows that our proposed estimators and the test statistic exhibit good finite-sample performance.

Keywords: First Difference, Fixed Effects, Hypothesis Testing, Local Linear Regression, Nonparametric GMM, Sieve Estimator, Spatial Autoregressive, Varying Coefficient

JEL Classification: C12, C13, C14, C23