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Empirical Likelihood‐Based Inference in Conditional Moment Restriction Models
Author(s) -
Kitamura Yuichi,
Tripathi Gautam,
Ahn Hyungtaik
Publication year - 2004
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/j.1468-0262.2004.00550.x
Subject(s) - empirical likelihood , estimator , mathematics , kernel smoother , moment (physics) , efficient estimator , minimum variance unbiased estimator , inference , restricted maximum likelihood , statistic , delta method , statistics , smoothing , econometrics , kernel method , estimation theory , computer science , artificial intelligence , classical mechanics , radial basis function kernel , support vector machine , physics
This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood‐based procedure. This yields a one‐step estimator which avoids estimating optimal instruments. Our likelihood ratio‐type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.