Estimation of partially specified spatial panel data models with fixed-effects

ABSTRACT

This article extends the spatial panel data regression with fixed-effects to the case where the regression function is partially linear and some regressors may be endogenous or predetermined. Under the assumption that the spatial weighting matrix is strictly exogenous, we propose a sieve two stage least squares (S2SLS) regression. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and that the proposed estimator for the unknown function is consistent and also asymptotically normally distributed but at a rate slower than root-N. Consistent estimators for the asymptotic variances of the proposed estimators are provided. A small scale simulation study is conducted, and the simulation results show that the proposed procedure has good finite sample performance.

KEYWORDS:

• Asymptotic theory
• panel data
• partially linear
• spatial

JEL CLASSIFICATION:

• C14
• C22

Acknowledgments

We appreciate the Editor, a guest editor and three anonymous reviewers for helpful comments. This work is partially supported by the National Natural Science Foundation through grants (71371118, 71401108, 71331006, 71471117, 71573178), Humanities and Social Sciences Foundation of the Ministry of Education (15YJC790150), and Science and Technology Research Project of Shanghai Normal University (SK201507).