GMM estimation for high-dimensional panel data models

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where the factors are unobserved and these factor loadings are nonparametrically unknown smooth functions of individual characteristic variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with the sample size. This is a very general framework and is closely related to many existing linear and nonlinear panel data models. In order to estimate the unknown parameters, factors and factor loadings, we propose a sieve-based generalized method of moments estimation method and we show that under a set of simple identification conditions, all those unknown quantities can be consistently estimated. Further we establish asymptotic distributions of the proposed estimators. In addition, we propose tests for over-identification, specification of factor loading functions, and establish their large sample properties. Moreover, a number of simulation studies are conducted to examine the performance of the proposed estimators and test statistics in finite samples. An empirical example on stock return prediction is studied to demonstrate both the empirical relevance and the applicability of the proposed framework and corresponding estimation and testing methods.