LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS
研究了半参数三步估计中基于非参数似然的推断方法，将经验似然理论应用于修正矩函数，使似然比统计量渐近枢轴，适用于生产函数估计和倾向得分匹配等实证分析。
Hahn and Ridder (2013, Econometrica 81, 315–340) 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, Econometrica 64, 1263–1297) and propensity score matching estimators for treatment effects by Heckman, Ichimura, and Todd (1998, Review of Economic Studies 65, 261–294). The present article studies a nonparametric likelihood-based inference method for the parameters in such three-step estimation problems. In particular, we apply the general empirical likelihood theory of Bravo, Escanciano, and van Keilegom (2018, Annals of Statistics , forthcoming) to modify semiparametric moment functions to account for influences from plug-in estimates into the above important setup, and show that the resulting likelihood ratio statistic becomes asymptotically pivotal without undersmoothing in the first and second step nonparametric estimates.