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Sharp identification regions in models with convex predictions: games, individual choice, and incomplete data

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  • Arie Beresteanu

    (Institute for Fiscal Studies and Duke)

  • Ilya Molchanov
  • Francesca Molinari

    ()
    (Institute for Fiscal Studies and Cornell University)

Abstract

We provide a tractable characterization of the sharp identification region of the parameters θ in a broad class of incomplete econometric models. Models in this class have set-valued predictions that yield a convex set of conditional or unconditional moments for the model variables. In short, we call these models with convex predictions. Examples include static, simultaneous move finite games of complete information in the presence of multiple mixed strategy Nash equilibria; random utility models of multinomial choice in the presence of interval regressors data; and best linear predictors with interval outcome and covariate data. Given a candidate value for θ, we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly defined random set. The sharp identification region of θ, denoted Θ I, can then be obtained as the set of minimizers of the distance from a properly specified vector of moments of random variables to this Aumann expectation. We show that algorithms in convex programming can be exploited to efficiently verify whether a candidate θ is in Θ I. We use examples analyzed in the literature to illustrate the gains in identification and computational tractability afforded by our method. This paper is a revised version of cemmap working paper CWP15/08

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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 CWP27/09.

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Date of creation: Oct 2009
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Handle: RePEc:ifs:cemmap:27/09

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  1. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics.
  2. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
  3. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
  4. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
  5. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  6. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," Econometric Society 2004 North American Winter Meetings 517, Econometric Society.
  7. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  8. 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.
  9. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
  10. Alfred Galichon & Marc Henry, 2006. "Inference in Incomplete Models," Discussion Papers 0506-28, Columbia University, Department of Economics.
  11. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, 09.
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Cited by:
  1. Aureo de Paula, 2012. "Econometric analysis of games with multiple equilibria," CeMMAP working papers CWP29/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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