New Nonparametric Estimation of the Marginal Effects in Fixed-Effects Panel Models : An Application on the Environmental Kuznets Curve

This paper considers kernel-based nonparametric estimation of panel models using local linear least squares, when both the fixed individual effects and the time effects present. The marginal effect is of the main interest. A within-group type nonparametric estimator is developed, where the within transformation is based on locally weighted average. For nonparametric fixed-effects models, it is shown that conventional within transformation or first difference render panel nonparametric estimators biased and the bias does not degenerate even with large samples. The proposed estimator, on the other hand, not only achieves the degenerating approximated bias of the order h^2 but also has the approximated variance of the order 1/(NT(h^3)). The optimal bandwidth parameter is also obtained to be of the order (NT)^{-1/7}. The new estimation is applied to analyze the nonlinear relationship between emission and income (i.e., the environmental Kuznets curve) using U.S. state-level panel data on nitrogen oxide and sulfur dioxide emissions