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 factors are unobserved and factor loadings are nonparametrically unknown smooth functions of individual characteristics variables. We allow the dimension of parameter vector and the number of moment conditions are diverging with sample size. This is a very general framework and includes many existing linear and nonlinear panel data models as special cases. In order to estimate the unknown parameters, factors and factor loading functions involved in the moment conditions, 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 for the proposed estimators. In addition, we propose test statistics for the issue of 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 sample situation; also, an empirical example on stock return prediction is studied to demonstrate the usefulness of this new framework and corresponding estimation and testing procedures