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Confidence intervals for partially identified parameters

  • Guido Imbens

    ()

    (Institute for Fiscal Studies and Stanford Graduate School of Business)

  • Charles F. Manski

    (Institute for Fiscal Studies)

In the last decade a growing body of research has studied inference on partially identified parameters (e.g., Manski, 1990, 2003). In many cases where the parameter of interest is realvalued, the identification region is an interval whose lower and upper bounds may be estimated from sample data. Confidence intervals may be constructed to take account of the sampling variation in estimates of these bounds. Horowitz and Manski (1998, 2000) proposed and applied interval estimates that asymptotically cover the entire identification region with fixed probability. Here we introduce conceptually different interval estimates that asymptotically cover each element in the identification region with fixed probability (but not necessarily every element simultaneously). We show that these two types of interval estimate are different in practice, the latter in general being shorter. The difference in length (in excess of the length of the identification set itself) can be substantial, and in large samples is comparable to the difference of one and twosided confidence intervals. A complication arises from the fact that the simplest version of the proposed interval is discontinuous in the limit case of point identification, leading to coverage rates that are not uniform in important subsets of the parameter space. We develop a modification depending on the width of the identification region that restores uniformity. We show that under some conditions, using the estimated width of the identification region instead of the true width maintains uniformity.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0309.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP09/03.

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Length: 24 pp.
Date of creation: May 2003
Date of revision:
Handle: RePEc:ifs:cemmap:09/03
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  1. 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.
  2. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2006. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CIRJE F-Series CIRJE-F-420, CIRJE, Faculty of Economics, University of Tokyo.
  3. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
  4. Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
  5. 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 322-40, June.
  6. repec:att:wimass:8909 is not listed on IDEAS
  7. 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.
  8. David S. Lee, 2002. "Trimming for Bounds on Treatment Effects with Missing Outcomes," NBER Technical Working Papers 0277, National Bureau of Economic Research, Inc.
  9. 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.
  10. Molinari, Francesca, 2005. "Partial Identification of Probability Distributions with Misclassified Data," Working Papers 05-10, Cornell University, Center for Analytic Economics.
  11. 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.
  12. 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.
  13. 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.
  14. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  15. 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.
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