Elia Lapenta (Toulouse School of Economics)

A specification test for semiparametric models with generated covariates

Abstract:  In this paper, I provide a test for a conditional moment restriction which is specified in a semiparametric way, and includes some variables that are not observed but can be estimated by using nonparametric techniques. The methodology I present can be employed in order to check the correct specification of several semiparametric models used in Economics, ranging from discrete-choice models with endogenous regressors, to semiparametric regressions with endogeneity and control functions, semiparametric sample-selection models, and incomplete-information games. Checking the correct specification of these frameworks is relevant from an empirical point of view, as if the model is not specified in a correct way then both the estimates of the effects of a variable and the counterfactual analysis will be wrong. I propose a statistic that contains a bias correction for the nonparametric estimators empolyed, which enables the implementation of the test without undersmoothing. Since the statistic converges to an intricate distribution with unknown quantiles, in order to obtain the critical values I propose a wild-bootstrap procedure which is very easy to implement. I prove its the validity under low-level assumptions. Accordingly, the test can be readily applied by the researcher. Through a Monte-Carlo simulation study, I show that the test has good performance in small samples.