Empirical Likelihood-Based Inference in Conditional Moment Restriction Models

Kitamura, Yuichi; Tripathi, Gautam; Ahn, Hyo Jun

doi:10.1111/j.1468-0262.2004.00550.x

Cited by 149 publications

(169 citation statements)

References 38 publications

Supporting

Mentioning

166

Contrasting

Order By: Relevance

“…Testing is considered in Kitamura (2001) for moments restrictions, and Tripathi and Kitamura (2002) for conditional moment restrictions. Estimation and testing with conditional moment restrictions are studied in Donald, Imbens and Newey (2003) and Kitamura, Tripathi and Ahn (2002). They found that EL posses the attractive features of avoiding estimating optimal instruments and achieving asymptotic pivotalness.…”

Section: Introductionmentioning

confidence: 99%

On the second-order properties of empirical likelihood with moment restrictions

Chen

Cui

2007

Journal of Econometrics

View full text Add to dashboard Cite

This paper considers the second order properties of empirical likelihood for a parameter defined by moment restrictions, which is the framework operated upon by the Generalized Method of Moments. It is shown that the empirical likelihood defined for this general framework still admits the delicate second order property of Bartlett correction, which represents a substantial extension of all the established cases of Bartlett correction for the empirical likelihood. An empirical Bartlett correction is proposed, which is shown to work effectively in improving the coverage accuracy of confidence regions for the parameter. KeywordsBartlett correction, coverage accuracy, empirical likelihood, generalized method of moments Disciplines Statistics and Probability CommentsThis preprint was published as Song Xi Chen and Hengjian Cui, "On the second-order properties of empirical likelihood with moment restrictions", Journal of Econometrics (2007) Abstract. This paper considers the second order properties of empirical likelihood for a parameter defined by moment restrictions, which is the framework operated upon by the Generalized Method of Moments. It is shown that the empirical likelihood defined for this general framework still admits the delicate second order property of Bartlett correction, which represents a substantial extension of all the established cases of Bartlett correction for the empirical likelihood. An empirical Bartlett correction is proposed, which is shown to work effectively in improving the coverage accuracy of confidence regions for the parameter.

show abstract

Section: Introductionmentioning

confidence: 99%

On the second-order properties of empirical likelihood with moment restrictions

Chen

Cui

2007

Journal of Econometrics

View full text Add to dashboard Cite

show abstract

“…When the moment function a is finitely parameterized, the conditional density projections correspond to the population counterpart of the objective function of semiparametric efficient estimator (Kitamura et al, 2004). Having sufficient conditions for the existence of the limit of the objective is the building step to study the properties of these estimators under misspecification.…”

Section: Discussionmentioning

confidence: 99%

Existence and Characterization of Conditional Density Projections

Komunjer

Ragusa

2015

Econom. Theory

View full text Add to dashboard Cite

In this paper we propose primitive conditions under which a projection of a conditional density onto a set defined by conditional moment restrictions exists and is unique. Moreover, we provide an analytic expression of the obtained projection. The range of applications where conditional density projections are used is wide. The derived results are potentially useful in a variety of areas including: semiparametric efficient estimation and optimal testing in (conditional) moment models, Bayesian prior determination and inference in semiparametric models, density forecasting, and simulation-based econometric analysis.Regarding existence, we propose three different combinations of assumptions that are all sufficient to show that the projection exists and is unique. The proposed conditions exhibit a clear trade off between restrictions put on the divergence between the conditional densities and on the moment function which defines the projection set. Depending on the nature of the application, the researcher can pick and choose which set of conditions to use. Our second set of results characterizes the projection. The expression for the projected density is new though not surprising given the previously obtained results for the unconditional case. The projection is characterized by the dual of the original projection problem. In establishing the strong duality, however, we work with a constraint qualification condition that is weaker than that used by Borwein and Lewis (1991a, 1992a in their seminal work concerning the unconditional case.

show abstract

“…Section A.2 contains the consistency proof. By and large, we follow the structure of the proofs in Kitamura, Tripathi, and Ahn (2004) and Newey and Smith (2004), making the necessary adjustments for the presence of the inequality moment conditions. In Section A.3 the quadratic approximation of the objective function is obtained.…”

Section: A Appendix: Proofs and Derivationsmentioning

confidence: 99%