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

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  • Tobias, Justin

Abstract

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.

Suggested Citation

  • 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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    1. Vijverberg, Wim P. M., 1993. "Measuring the unidentified parameter of the extended Roy model of selectivity," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 69-89.
    2. Heady, Christopher, 2003. "The Effect of Child Labor on Learning Achievement," World Development, Elsevier, vol. 31(2), pages 385-398, February.
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    8. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute of Labor Economics (IZA).
    9. Mingliang Li & Dale J. Poirier & Justin L. Tobias, 2004. "Do dropouts suffer from dropping out? Estimation and prediction of outcome gains in generalized selection models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 203-225.
    10. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
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    14. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    15. James Heckman & Justin L. Tobias & Edward Vytlacil, 2003. "Simple Estimators for Treatment Parameters in a Latent-Variable Framework," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 748-755, August.
    16. Daniel Millimet & John List, 2004. "The Case of the Missing Pollution Haven Hypothesis," Journal of Regulatory Economics, Springer, vol. 26(3), pages 239-262, August.
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    18. James Heckman & Justin L. Tobias & Edward Vytlacil, 2001. "Four Parameters of Interest in the Evaluation of Social Programs," Southern Economic Journal, John Wiley & Sons, vol. 68(2), pages 210-223, October.
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    20. Chib, Siddhartha & Hamilton, Barton H., 2000. "Bayesian analysis of cross-section and clustered data treatment models," Journal of Econometrics, Elsevier, vol. 97(1), pages 25-50, July.
    21. Bjorklund, Anders & Moffitt, Robert, 1987. "The Estimation of Wage Gains and Welfare Gains in Self-selection," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 42-49, February.
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    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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