Statistical inference of partially specified spatial autoregressive model

This paper studies estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, the unknown parameter is estimated by applying the instrumental variable estimation. Under certain sufficient conditions, the proposed estimator for the finite dimensional parameters is shown to be root-n consistent and asymptotically normally distributed; The proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-n. Consistent estimators for the asymptotic variance-covariance matrices of both estimators are provided. Monte Carlo simulations suggest that the proposed procedure has some practical value.