Estimation, Learning and Parameters of Interest in a Multiple Outcome Selection Model
AbstractWe 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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Bibliographic InfoPaper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 12480.
Date of creation: 01 Jan 2006
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Publication status: Published in Econometric Reviews 2006, vol. 25, pp. 1-40
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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
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- 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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