Semiparametric Model Selection in Panel Data Models with Deterministic Trends and Cross-Sectional Dependence

In this paper, we consider a model selection issue in semiparametric panel data models with fixed effects. The modelling framework under investigation can accommodate both nonlinear deterministic trends and cross-sectional dependence. And we consider the so-called "large panels" where both the time series and cross sectional sizes are very large. A penalised profile least squares method with first-stage local linear smoothing is developed to select the significant covariates and estimate the regression coefficients simultaneously. The convergence rate and the oracle property of the resulting semiparametric estimator are established by the joint limit approach. The developed semiparametric model selection methodology is illustrated by two Monte-Carlo simulation studies, where we compare the performance in model selection and estimation of three penalties, i.e., the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD), and the minimax concave penalty (MCP).