LIKELIHOOD INFERENCE on SEMIPARAMETRIC MODELS with GENERATED REGRESSORS

Yukitoshi Matsushita, Taisuke Otsu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)626-657
Number of pages32
JournalEconometric Theory
Volume36
Issue number4
DOIs
Publication statusPublished - 2020 Aug 1
Externally publishedYes

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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