Statistical inference of partially linear time-varying coefficients spatial autoregressive panel data model

TL;DR

This paper develops a novel two-stage least squares method for estimating both constant and time-varying coefficients in a complex spatial autoregressive panel data model, avoiding first differencing and enabling effective inference.

Contribution

It introduces the 2SLS-PLLDV estimator for partially linear spatial panel models with fixed effects and time-varying coefficients, along with a goodness-of-fit test and bootstrap inference.

Findings

Estimator performs well in simulations

Method effectively captures time-varying effects

Application to Chinese carbon data demonstrates practical utility

Abstract

This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares estimation method based on profile local linear dummy variables (2SLS-PLLDV) is proposed to estimate both constant and time-varying coefficients without the need for first differencing. The asymptotic properties of the estimator are derived under certain conditions. Furthermore, a residual-based goodness-of-fit test is constructed for the model, and a residual-based bootstrap method is used to obtain p-values. Simulation studies show the good performance of the proposed method in various scenarios. The Chinese provincial carbon emission data set is analyzed for illustration.