Linear Estimation of Effects for Dynamic, Nonseparable Panel Data

This paper develops linear estimators for structural and causal parameters in dynamic, nonparametric, nonseparable models using panel data. These models incorporate unobserved, time-varying, individual heterogeneity, which may be correlated with the regressors. Estimation is based on an approximation of the nonseparable model by a linear sieve specification with individual-specific parameters. Effects of interest are estimated by a bias corrected average of individual ridge regressions, where the bias correction accounts for dynamics as well as ridge regularization. We demonstrate how this approach can be applied to estimate causal effects and counterfactual consumer welfare and averages of individual taxable income elasticities. We formulate Large-T asymptotic theory for these estimators.