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

Sanying Feng, Tiejun Tong and Sung Nok Chiu ()
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Sanying Feng: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Tiejun Tong: Department of Mathematics, Hong Kong Baptist University, Hong Kong
Sung Nok Chiu: Department of Mathematics, Hong Kong Baptist University, Hong Kong

Mathematics, 2023, vol. 11, issue 22, 1-19

Abstract: 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.

Keywords: partially linear varying coefficient model; panel data; spatial autoregressive model; instrumental variable; two-stage least squares; empirical likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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