This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.

This paper develops a unified framework for fixed and random effects estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroskedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both a random effects and a fixed effects spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroskedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman-test of the spatial random against the spatial fixed effects model. (authors' abstract) / Series: Department of Economics Working Paper Series