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

Lingling Tian, Chuanhua Wei, Mixia Wu

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.

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

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.

Paper Structure

This paper contains 15 sections, 85 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The 2SLS-PLLDV estimation
  3. Instrumental estimation of the spatial lag term
  4. PLLDV estimation of regression coefficients
  5. Asymptotic properties
  6. Test for time-varying regression coefficients
  7. Construction of the test statistic
  8. Bootstrap method based on residual to calculate p-value
  9. Simulation studies
  10. Simulation of estimation method
  11. Simulation on the proposed test
  12. Empirical sizes of the proposed test
  13. Power of the test
  14. Empirical Application
  15. Conclusion

Figures (3)

  • Figure 1: The average estimates curves and true curves of $\rho(\tau_t)$, $\beta_1(\tau_t)$ and $\beta_2(\tau_t)$
  • Figure 2: The power of the test under the significance level $\alpha =0.05$
  • Figure 3: The fitting curve of the time-varying coefficients in model (20).