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Econometrics Paper
Likelihood inference on semiparametric models with generated regressors
Yukitoshi Matsushita and Taisuke Otsu
September 2016
Paper No' EM 587:
Full Paper (pdf)

JEL Classification: C12; C14

Tags: generated regressor; empirical likelihood

Hahn and Ridder (2013) formulated influence functions of semiparametric three step estimators where generated regressors are computed in the first step. This class of estimators covers several important examples for empirical analysis, such as production function estimators by Olley and Pakes (1996), and propensity score matching estimators for treatment effects by Heckman, Ichimura and Todd (1998). This paper develops a nonparametric likelihood- based inference method for the parameters in such three step estimation problems. By modifying the moment functions to account for influences from the first and second step estimation, the resulting likelihood ratio statistic becomes asymptotically pivotal not only without estimating the asymptotic variance but also without undersmoothing.