Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model

Sanying Feng, Tiejun Tong, Sung Nok Chiu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


This paper studies the estimation and inference of a partially linear varying coefficient spatial autoregressive panel data model with fixed effects. By means of the basis function approximations and the instrumental variable methods, we propose a two-stage least squares estimation procedure to estimate the unknown parametric and nonparametric components, and meanwhile study the asymptotic properties of the proposed estimators. Together with an empirical log-likelihood ratio function for the regression parameters, which follows an asymptotic chi-square distribution under some regularity conditions, we can further construct accurate confidence regions for the unknown parameters. Simulation studies show that the finite sample performance of the proposed methods are satisfactory in a wide range of settings. Lastly, when applied to the public capital data, our proposed model can also better reflect the changing characteristics of the US economy compared to the parametric panel data models.

Original languageEnglish
Article number4606
Number of pages19
Issue number22
Early online date10 Nov 2023
Publication statusPublished - 22 Nov 2023

Scopus Subject Areas

  • Computer Science (miscellaneous)
  • Mathematics(all)
  • Engineering (miscellaneous)

User-Defined Keywords

  • empirical likelihood
  • instrumental variable
  • panel data
  • partially linear varying coefficient model
  • spatial autoregressive model
  • two-stage least squares
  • coefficient model


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