Estimation of partially specified spatial panel data models with random-effects and spatially correlated error components

This paper studies estimation of a partially specified spatial panel data linear regression with random-effects and spatially correlated error components. Under the assumption of exogenous spatial weighting matrix and exogenous regressors, the unknown parameter is estimated by applying the instrumental variable estimation. Under some 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 the parametric and unknown components are provided. The Monte Carlo simulation results suggest that the approach has some practical value.