Abstract
This paper develops a time-varying coefficient spatial autoregressive panel data model with the individual fixed effects to capture the nonlinear effects of the regressors, which vary over the time. To effectively estimate the model, we propose a method that incorporates the nonparametric local linear method and the concentrated quasi-maximum likelihood estimation method to obtain consistent estimators for the spatial coefficient and the time-varying coefficient function. The asymptotic properties of these estimators are derived as well, showing the regular sqrt(NT)-rate of convergence for the parametric parameters and the common sqrt(NTh)-rate of convergence for the nonparametric component, respectively. Monte Carlo simulations are conducted to illustrate the finite sample performance of our proposed method. Meanwhile, we apply our method to study the Chinese labor productivity to identify the spatial influences and the time-varying spillover effects among 185 Chinese cities with comparison to the results on a subregion East China.
Highlights
Panel data analysis has widely been used in many fields of social sciences as it usually enables strong identification and increases estimation efficiency
Even though some dependence assumptions can be made in the error term, no clear cross-sectional dependence structure can be modelled in pure panel data models
2When time-varying coefficients and trends involved in regressors do not exist, our model reduces to a classical spatial panel data model which is considered in Lee and Yu (2010)
Summary
Panel data analysis has widely been used in many fields of social sciences as it usually enables strong identification and increases estimation efficiency. Even though some dependence assumptions can be made in the error term, no clear cross-sectional dependence structure can be modelled in pure panel data models. Lee and Yu (2010) consider a QML method to estimate spatial autoregressive panel models under a fixed effects setup. In this paper, we propose a time-varying coefficient spatial panel data model with fixed effects. This model allows for regressors to be trending nonstationary so that level data may be used directly without differencing.. To further evaluate the finite–sample performance and empirical relevance, we apply our model and the associated estimation method to the analysis of a Chinese labour productivity dataset, which includes 185 cities over the period of 1995–2009.
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