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.
Notes
1 Panel data have many advantages over cross-sectional or time series data. More details can be found in Hsiao (Citation2014).
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, in real applications.
3 For simplicity, we use the same bandwidth h for different covariates.