Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may ABSTRACTA parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an illposed inverse problem. Such problems arise in many settings in economics and other fields where the parameter of interest is a function. This paper explains how ill-posedness arises and why it causes problems for estimation. The need to modify or "regularize" the identifying mapping is explained, and methods for regularization and estimation are discussed. Methods for forming confidence intervals and testing hypotheses are summarized. It is shown that a hypothesis test can be more "precise" in a certain sense than an estimator. An empirical example illustrates estimation in an ill-posed setting in economics.

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Posterior Consistency of Nonparametric Conditional Moment Restricted Models

Liao

Jiang²

2010

SSRN Journal

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This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0. We estimate it in a quasi-Bayesian way based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thintail prior (a prior that has very thin tail outside a growing bounded set), and (iii) normal prior with non-shrinking variance. In addition, g0 is allowed to be only partially identified in the frequentist sense, and the parameter space does not need to be compact. The posterior is regularized using a slowly-growing sieve dimension, and it is shown that the posterior converges to any small neighborhood of the identified region. We then apply our results to the nonparametric instrumental regression model. Finally, the posterior consistency using a random sieve dimension parameter is studied.

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Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter

Cited by 5 publications

References 25 publications

Asymptotic Normal Inference in Linear Inverse Problems

Asymptotic Normal Inference in Linear Inverse Problems

Ill-Posed Inverse Problems in Economics

Posterior Consistency of Nonparametric Conditional Moment Restricted Models

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