Nonseparable Panel Models with Index Structure and Correlated Random Effects

To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in the context of panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution are established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation study to assess finite-sample performance of the proposed estimator and provide an application demonstrating the use of the proposed methodology.