UNIFORM INFERENCE FOR NONPARAMETRIC PANEL MODELS WITH FIXED EFFECTS

Abstract

This article studies uniform inference on a function $g(\cdot )$ and its functionals in a nonparametric panel data model with fixed effects. The nonparametric panel model relaxes restrictions on time-series behavior by allowing for arbitrary types of stationary or nonstationary dependence (e.g., stationary mixingale, mildly stationary, or local-to-unity process). After removing the fixed effects via transformations, a sieve estimator is proposed, accompanied by Yurinskii’s coupling principle of Gaussian processes and uniform confidence bands (UCBs) that rely on the sieve score bootstrap method to test for linear functionals of $g(\cdot )$ . Under the asymptotic framework of an increasing cross-sectional dimension and either a fixed or diverging time dimension, we prove that the bootstrapping Kolmogorov–Smirnov (sup-type) test has asymptotic uniform size controls. This article shows that our uniform inference procedure can be extended to the two-way fixed-effects nonparametric panel model with stationary mixingale regressors. Extensive simulations confirm that our sieve estimators and their UCBs work well in finite samples. The present article further applies the above methods to empirical settings and finds some interesting results in nonlinear patterns of consumption concerning income shocks and asset holdings.