Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model

In this paper, the spatial dynamic panel data (SDPD) model is extended to single-index (Si-SDPD) by introducing a nonlinear connection function reflect interaction between explanatory variables. The Si-SDPD not only retains advantages of parametric SDPD in dealing with and temporal effects spatio-temporal dependencies, but also solves limitations that may lead missed bias. It reduces dimension non-parametric models enhances practicability power models. Since parts be estimated contain unknown functions, we propose new estimation method, profile maximum likelihood (PML) solve problem incidental parameters estimation. Under assumption coefficients are known, preliminarily estimate carrying out local polynomial estimation, so as transform into form for solving purposes. We then via quasi-maximum (QML) derive asymptotic properties estimators (PMLEs) find that, under certain regularity conditions, both consistent. Monte Carlo results show PMLEs have good finite sample performance.