Robust estimation and inference of spatial panel data models with fixed effects

It is well established that the quasi maximum likelihood (QML) estimation of the spatial regression models is generally inconsistent under unknown cross-sectional heteroskedasticity (CH) and the CH-robust methods have been developed. The same issue remains for the spatial panel data (SPD) models but the similar studies based on QML approach do not seem to have been carried out. This paper focuses on the SPD model with fixed effects (FE). We argue that under unknown CH the QML estimator for the SPD-FE model is inconsistent in general, but there are ‘special cases’ where it may remain consistent although the exact conditions may not be possible to check, as in practice the type of CH is generally unknown. Thus, we introduce a new set of estimation and inference methods based on the adjusted quasi scores (AQS), which are fully robust against unknown CH. Consistency and asymptotic normality of the proposed AQS estimators are established. Robust standard error estimates are provided and their consistency is proved. To improve the finite sample performance, a set of AQS methods based on concentrated quasi scores is also introduced and its asymptotic properties examined. Extensive Monte Carlo results show that the new estimator outperforms the QML estimator even when the latter seems robust.