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Inference in Incomplete Models

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  • Alfred Galichon

    ()
    (Harvard University - Department of Economics)

  • Marc Henry

    ()
    (Columbia University - Department of Economics)

Abstract

We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a Kolmogorov-Smirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria.

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Bibliographic Info

Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0506-28.

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Length: 51 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:clu:wpaper:0506-28

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Cited by:
  1. Arie Beresteanu, 2009. "Sharp Identification Regions in Models with Convex Predictions: Games, Individual Choice, and Incomplete Data," Working Papers 428, University of Pittsburgh, Department of Economics, revised Sep 2010.
  2. Komunjer, Ivana, 2007. "Global Identification In Nonlinear Semiparametric Models," University of California at San Diego, Economics Working Paper Series qt8dk0n386, Department of Economics, UC San Diego.
  3. Toru Kitagawa, 2011. "Inference and decision for set identified parameters using posterior lower and upper probabilities," CeMMAP working papers CWP16/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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