Estimation of fixed effects semiparametric single-index panel model with spatio-temporal correlated errors

Spatial error parametric panel model is one of the most popularly used analytical tools in spatial econometrics. Although this model takes into account the possible spatial correlation of errors, it ignores the potential serial correlation of errors and commonly existed nonlinearity between variables. These may lead to inefficient estimators and model misspecification. Therefore, this paper establishes a fixed effects semiparametric single-index panel model (SPSIPM) with spatio-temporal correlated errors. Firstly, we apply B-spline to approximate the single-index function and incorporate the information of initial period observations into quasi-likelihood function of the model to construct its profile quasi-maximum likelihood estimators (PQMLEs). Secondly, it is proved that PQMLEs of both parameters and single-index function are consistent and asymptotically normal under some mild conditions. Thirdly, we propose a nonparametric bootstrap test for examining the nonlinearity of model. Fourthly, numerical simulations reveal the estimates and test statistic have good finite sample performance. Finally, the model estimation methodology is employed to analyze the driving factors of Chinese resident real wage level.