GEL-based inference with unconditional moment inequality restrictions

Nicky L. Grant and Richard J. Smith
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Nicky L. Grant: Institute for Fiscal Studies
Richard J. Smith: Institute for Fiscal Studies

No CWP23/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper studies the properties of generalised empirical likelihood (GEL) methods for the estimation of and inference on partially identifi ed parameters in models specifi ed by unconditional moment inequality constraints. The central result is, as in moment equality condition models, a large sample equivalence between the scaled optimised GEL objective function and that for generalised method of moments (GMM) with weight matrix equal to the inverse of the efficient GMM metric for moment equality restrictions. Consequently, the paper provides a generalisation of results in the extant literature for GMM for the non-diagonal GMM weight matrix setting. The paper demonstrates that GMM in such circumstances delivers a consistent estimator of the identi fied set, i.e., those parameter values that satisfy the moment inequalities, and derives the corresponding rate of convergence. Based on these results the consistency of and rate of convergence for the GEL estimator of the identifi ed set are obtained. A number of alternative equivalent GEL criteria are also considered and discussed. The paper proposes simple conservative consistent confi dence regions for the identi fied set and the true parameter vector based on both GMM with a non-diagonal weight matrix and GEL. A simulation study examines the efficacy of the non-diagonal GMM and GEL procedures proposed in the paper and compares them with the standard diagonal GMM method.

Keywords: Moment Inequalities; Generalised Empirical Likelihood; GMM; Set Identification (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 C19 (search for similar items in EconPapers)
Date: 2018-03-28
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