LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS
LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS
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DOI：
10.1017/s026646661900029x
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发表时间：
2019-11
影响因子：
0.8
通讯作者：
Yukitoshi Matsushita;Taisuke Otsu
中科院分区：
文献类型：
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作者：
Yukitoshi Matsushita;Taisuke Otsu
Hahn和Ridder（2013，Econometrica 81，315-340）制定了半参数三步估计的影响函数，其中生成的回归量在第一步中计算。这类估计量涵盖了实证分析的几个重要例子，如Olley和Pakes（1996，Econometrica 64，1263-1297）的生产函数估计量，以及Heckman、Ichimura和托德（1998，Review of Economic Studies 65，261-294）的治疗效应的倾向得分匹配估计量。本文研究了这类三步估计问题中参数的非参数似然推断方法。特别是，我们应用Bravo，Escanciano和货车Keilegom（2018，统计年鉴，即将出版）的一般经验似然理论来修改半参数矩函数，以考虑插件估计对上述重要设置的影响，并表明所得的似然比统计量在第一步和第二步非参数估计中变得渐近关键而不欠平滑。
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.