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Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model


  • Tobias, Justin


We describe estimation, learning and prediction in a treatment-response model with two outcomes. The introduction of potential outcomes in this model introduces four cross-regime correlation parameters that are not contained in the likelihood for the observed data and thus are not identified. Despite this inescapable identification problem, we build upon the results of Koop and Poirier (1997) to describe how learning takes place about the four non-identified correlations through the imposed positive definiteness of the covariance matrix. We then derive bivariate distributions associated with commonly estimated ``treatment parameters'' (including the Average Treatment Effect and effect of Treatment on the Treated), and use the learning that takes place about the non-identified correlations to calculate these densities. We illustrate our points in several generated data experiments and apply our methods to estimate the joint impact of child labor on achievement scores in language and mathematics.

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  • Tobias, Justin, 2006. "Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model," Staff General Research Papers Archive 12480, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:12480

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    References listed on IDEAS

    1. Beghin, John C & Sumner, Daniel A, 1992. "Domestic Content Requirements with Bilateral Monopoly," Oxford Economic Papers, Oxford University Press, vol. 44(2), pages 306-316, April.
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    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    7. André Sapir, 1991. "Le commerce international des services audiovisuels: une source de conflits entre la Communauté Européenne et les Etats-Unis," ULB Institutional Repository 2013/8218, ULB -- Universite Libre de Bruxelles.
    8. Hollander, Abraham, 1987. "Content protection and transnational monopoly," Journal of International Economics, Elsevier, vol. 23(3-4), pages 283-297, November.
    9. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    10. Kala Krishna & Motoshige Itoh, 1988. "Content Protection and Oligopolistic Interactions," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 107-125.
    11. Gene M. Grossman, 1981. "The Theory of Domestic Content Protection and Content Preference," The Quarterly Journal of Economics, Oxford University Press, vol. 96(4), pages 583-603.
    12. Francois, Patrick & van Ypersele, Tanguy, 2002. "On the protection of cultural goods," Journal of International Economics, Elsevier, vol. 56(2), pages 359-369, March.
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    Cited by:

    1. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.

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