Semiparametric inferences for panel data models with fixed effects via nearest neighbor difference transformation

Abstract

In this paper, we propose a simple method to estimate a partially varying-coefficient panel data model with fixed effects. By taking difference upon the nearest neighbor of the smoothing variables to remove the fixed effects, we employ the profile least squares method and local linear fitting to estimate the parametric and nonparametric parts, respectively. Moreover, a functional form specification test and a nonparametric Hausman type test are constructed and their asymptotic properties are derived. Monte Carlo simulations are conducted to examine the finite sample performance of our estimators and test statistics.

Keywords:

• Fixed effects
• Hausman-type test
• panel data
• specification test
• varying coefficients

JEL Classification:

• C12
• C13
• C14
• C23

Notes

1 Panel data have many advantages over cross-sectional or time series data. More details can be found in Hsiao (2014).

2 For ease of notation, we only consider the case d = 1. Extension to the case d > 1 involves no fundamentally new ideas. Also, note that models with large d are not practically useful due to the so-called “curse of dimensionality.” Usually, $d\le 3$ in real applications.

3 For simplicity, we use the same bandwidth h for different covariates.

4 Recall that data deletion is required to obtain a nonsingular variance–covariance matrix of errors in (2.3).

Additional information

Funding

This research was partially supported from the National Science Fund of China (NSFC) for Distinguished Scholars (71625001), the NSFC key projects with grant numbers 71631004 and 71131008, and the Basic Scientific Center Project of NSFC (71988101).