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Point Decisions for Interval-Identified Parameters

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Author Info
Kyungchul Song () (Department of Economics, University of Pennsylvania)
Abstract

This paper focuses on a situation where the decision-maker prefers to make a point-decision when the object of interest is interval-identified. Such a situation frequently arises when the interval-identified parameter is closely related to an optimal policy decision. To obtain a reasonable decision, this paper slices asymptotic normal experiments into subclasses corresponding to localized interval lengths, and finds a local asymptotic minimax decision for each subclass. Then, this paper suggests a decision that is based on the subclass minimax decisions, and explains the sense in which the decision is reasonable. One remarkable aspect of this solution is that the optimality of the solution remains intact even when the order of the interval bounds is misspecified. A small sample simulation study illustrates the solution’s usefulness.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-036.

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Length: 36 pages
Date of creation: 08 Sep 2009
Date of revision:
Handle: RePEc:pen:papers:09-036

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Related research
Keywords: Partial Identification; Inequality Restrictions; Local Asymptotic Minimax Estimation; Semiparametric Efficiency;

Find related papers by JEL classification:
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research

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  5. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07. [Downloadable!] (restricted)
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  6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun. [Downloadable!] (restricted)
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  8. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09. [Downloadable!] (restricted)
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  11. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May. [Downloadable!] (restricted)
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  14. Gilstein, C Zachary & Leamer, Edward E, 1983. "Robust Sets of Regression Estimates," Econometrica, Econometric Society, vol. 51(2), pages 321-33, March. [Downloadable!] (restricted)
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