High dimensional semiparametric moment restriction models

We consider nonlinear moment restriction semiparametric models where both the dimension of parameter vector and number restrictions are divergent with sample size an unknown smooth function is involved. propose estimation method based on sieve generalized moments (sieve-GMM). establish consistency asymptotic normality for estimated quantities when parameters increases modestly size. also case potential parameters/covariates very large, i.e., rapidly size, but true model exhibits sparsity. use a penalized GMM approach to select relevant variables, oracle property our in this case. provide new results inference. several test statistics over-identification their large properties. simulation study application data from NLSY79 used by Carneiro et al. (2011).