Estimation of the Non-Parametric Spatial Dynamic Panel Data Model with Fixed Effects

In this paper, the spatial dynamic panel data (SDPD) model with fixed effects is extended to a non-parametric form by relaxing the linear or nonlinear parameter structure of explanatory variables. The non-parametric spatial dynamic panel data (NSDPD) model with fixed effects not only retains the advantages of the SDPD model which can deal with spatial and/or temporal individual characteristics and spatio-temporal dependencies but also solves the limitation that may lead to specification errors. It also enhances the flexibility and practicability of the spatial econometric model. Since the model to be estimated contains unknown functions, we propose this profile maximum likelihood (PML) method to solve the problem of the incidental parameters in the estimation. Under the assumption that the spatial coefficients are known, we first eliminate the influence of the time effect by substitution and then use the local polynomial estimation to preliminarily estimate the unknown function so as to transform the model into the parametric form for solving. We derive the asymptotic properties of PMLEs and find that under certain regularity conditions, both parametric and non-parametric estimators are consistent. The Monte Carlo results show that the estimators have good finite sample performance. We illustrate the empirical relevance of the model by applying it to examine the impact of tourism dynamics on economic development in the Yangtze River Delta region of China.