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Confidence Intervals for Partially Identified Parameters

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  • Guido W. Imbens
  • Charles F. Manski

Abstract

Recently a growing body of research has studied inference in settings where parameters of interest are partially identified. In many cases the parameter is real-valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data. For this case confidence intervals (CIs) have been proposed that cover the entire identification region with fixed probability. Here, we introduce a conceptually different type of confidence interval. Rather than cover the entire identification region with fixed probability, we propose CIs that asymptotically cover the true value of the parameter with this probability. However, the exact coverage probabilities of the simplest version of our new CIs do not converge to their nominal values uniformly across different values for the width of the identification region. To avoid the problems associated with this, we modify the proposed CI to ensure that its exact coverage probabilities do converge uniformly to their nominal values. We motivate this modified CI through exact results for the Gaussian case. Copyright The Econometric Society 2004.

Suggested Citation

  • Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:6:p:1845-1857
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00555.x
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    References listed on IDEAS

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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Horowitz, Joel & Manski, Charles, 1997. "Nonparametric Analysis of Randomized Experiments With Missing Covariate and Outcome Data," Working Papers 97-16, University of Iowa, Department of Economics.
    3. Meyer, Bruce D & Viscusi, W Kip & Durbin, David L, 1995. "Workers' Compensation and Injury Duration: Evidence from a Natural Experiment," American Economic Review, American Economic Association, vol. 85(3), pages 322-340, June.
    4. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    5. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    6. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    7. David S. Lee, 2002. "Trimming for Bounds on Treatment Effects with Missing Outcomes," NBER Technical Working Papers 0277, National Bureau of Economic Research, Inc.
    8. E. Tamer & V. Chernozhukov & H. Hong, 2004. "Parameter Set Inference in a Class of Econometric Models," Econometric Society 2004 North American Winter Meetings 382, Econometric Society.
    9. Horowitz, Joel L. & Manski, Charles F., 1998. "Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations," Journal of Econometrics, Elsevier, vol. 84(1), pages 37-58, May.
    10. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    11. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    12. Manski, C.F. & Sandefur, G.D. & Mclanahan, S. & Powers, D., 1990. "Alternative Estimates Of The Effect Of Family Stucture During Adolescence On Hight School Graduation," Working papers 90-31, Wisconsin Madison - Social Systems.
    13. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    14. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
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