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Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities

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Author Info
Adam Rosen () (Institute for Fiscal Studies and University College London)

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Abstract

This paper proposes a new way to construct confidence sets for a parameter of interest in models comprised of finitely many moment inequalities. Building on results from the literature on multivariate one-sided tests, I show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities. The associated test statistic has an asymptotic chi-bar-square distribution, and can be inverted to construct an asymptotic confidence set for the parameter of interest, even if that parameter is only partially identified. The confidence sets are easily computed, and Monte Carlo simulations demonstrate good finite sample performance.

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Publisher Info
Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP25/06.

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Length: 39 pp.
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:ifs:cemmap:25/06

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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Related research
Keywords: Partial identification; inference; moment inequalities;

Other versions of this item:

Find related papers by JEL classification:
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hotz, V Joseph & Mullin, Charles H & Sanders, Seth G, 1997. "Bounding Causal Effects Using Data from a Contaminated Natural Experiment: Analysing the Effects of Teenage Childbearing," Review of Economic Studies, Blackwell Publishing, vol. 64(4), pages 575-603, October. [Downloadable!] (restricted)
  2. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January. [Downloadable!] (restricted)
  3. Manski, C.F., 1990. "The Selection Problem," Working papers 90-12, Wisconsin Madison - Social Systems.
  4. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics. [Downloadable!]
    Other versions:
  5. 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.
  6. 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.
  7. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September. [Downloadable!] (restricted)
  8. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January. [Downloadable!] (restricted)
  9. Moon, Hyungsik Roger & Schorfheide, Frank, 2006. "Boosting Your Instruments: Estimation with Overidentifying Inequality Moment Conditions," CEPR Discussion Papers 5605, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  10. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    Other versions:
  11. 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. [Downloadable!] (restricted)
  12. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    Other versions:
  13. Katherine Ho, 2005. "Insurer-Provider Networks in the Medical Care Market," NBER Working Papers 11822, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  14. Molinari, Francesca, 2005. "Missing Treatments," Working Papers 05-11, Cornell University, Center for Analytic Economics. [Downloadable!]
  15. repec:att:wimass:199526r is not listed on IDEAS
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2008. "Sharp identification regions in games," CeMMAP working papers CWP15/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  3. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation, Yale University. [Downloadable!]
  4. Patrick Bajari & Jeremy Fox & Stephen Ryan, 2008. "Evaluating wireless carrier consolidation using semiparametric demand estimation," Quantitative Marketing and Economics, Springer, vol. 6(4), pages 299-338, December. [Downloadable!] (restricted)
    Other versions:
  5. Guido W. Imbens & Whitney Newey & Geert Ridder, 2006. "Mean-squared-error Calculations for Average Treatment Effects," IEPR Working Papers 06.57, Institute of Economic Policy Research (IEPR). [Downloadable!]
  6. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics. [Downloadable!]
    Other versions:
  7. Adam Rosen, 2007. "Identification and estimation of firms' marginal cost functions with incomplete knowledge of strategic behavior," CeMMAP working papers CWP03/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  8. Patrik Guggenberger, . "Specification Testing under Moment Inequalities (joint with J. Hahn and K. Kim), 2006, revised April 2007," UCLA Economics Online Papers 381, UCLA Department of Economics. [Downloadable!]
  9. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2009. "Intersection Bounds: estimation and inference," CeMMAP working papers CWP19/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  10. Hyungsik Roger Moon & Frank Schorfheide, 2006. "Boosting Your Instruments: Estimation with Overidentifying Inequality Moment Conditions," IEPR Working Papers 06.56, Institute of Economic Policy Research (IEPR). [Downloadable!]
    Other versions:
  11. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  12. Andrew Chesher, 2008. "Instrumental variable models for discrete outcomes," CeMMAP working papers CWP30/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  13. Patrik Guggenberger, 2006. "The limit of finite sample size and a problem with subsampling (joint with D.W.K. Andrews), June 2005, this version March 2007," UCLA Economics Online Papers 372, UCLA Department of Economics. [Downloadable!]
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