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Frequentist Shrinkage under Inequality Constraints

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Document pages: 28 pages

Abstract: This paper shows how to shrink extremum estimators towards inequalityconstraints motivated by economic theory. We propose an Inequality ConstrainedShrinkage Estimator (ICSE) which takes the form of a weighted average betweenthe unconstrained and inequality constrained estimators with the data dependentweight. The weight drives both the direction and degree of shrinkage. We use alocal asymptotic framework to derive the asymptotic distribution and risk ofthe ICSE. We provide conditions under which the asymptotic risk of the ICSE isstrictly less than that of the unrestricted extremum estimator. The degree ofshrinkage cannot be consistently estimated under the local asymptoticframework. To address this issue, we propose a feasible plug-in estimator andinvestigate its finite sample behavior. We also apply our framework to gasolinedemand estimation under the Slutsky restriction.

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