Estimation of Semi-parametric Functional-coefficient Panel Data Models with Fixed Effects

Abstract

We consider the problem of estimating a semiparametric varying coefficient panel data model where the unobserved individual effects are correlated with explanatory variables in an unknown arbitrary way using a local linear regression approach. We present a new technique to estimate this model whereby, we locally approximate the fixed-effects-free transformed equation around two different points. Using Monte Carlo simulations, we study potential gains in the finite sample performance and/or the computational time of the proposed estimation procedure over available alternatives under different scenarios. We also consider a conceptually different approach to controlling for unobserved fixed effects in which the fixed effect is modelled as an unknown function of an unordered factor variable indexing individuals. The existing semiparametric estimators for varying-coefficient fixed-effects models exclusively assume one-way fixed effects, typically in the dimension of cross-sectional units. However, more often than not applied researchers wish to control for both the individual and time fixed effects in their panel regressions, with the latter included to account for common unobservable factors correlated with regressors. While rather trivial in a linear model, con- trolling for time effects by explicitly including time-period dummies as additional regressors does not provide a straight-forward estimation procedure in the case of a semiparametric model. We provide an alternative by extending the Sun et al. (2009) smoothed least-squares dummy variable (LSDV) estimator to the case of a functional-coefficient model with two- way fixed effects whereby we allow for unobservable heterogeneity in both dimensions of the data: cross-section and time. Both fixed effects are concentrated out of the model via locally smoothed two-dimensional within transformation. Simulations show that the estimator performs well in finite samples. We showcase its practical usefulness in two different scenarios.