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Inference in Incomplete Models

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  • Alfred Galichon
  • Marc Henry

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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  • Alfred Galichon & Marc Henry, 2021. "Inference in Incomplete Models," Papers 2102.12257, arXiv.org.
    • Handle: RePEc:arx:papers:2102.12257
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    References listed on IDEAS

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    1. Gabriella Salinetti & Roger J.-B. Wets, 1986. "On the Convergence in Distribution of Measurable Multifunctions (Random Sets) Normal Integrands, Stochastic Processes and Stochastic Infima," Mathematics of Operations Research, INFORMS, vol. 11(3), pages 385-419, August.
    2. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-1437, November.
    3. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    4. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    5. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
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