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On the Predictive Distributions of Outcome Gains in the Presence of an Unidentified Parameter

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  • Poirier, Dale J
  • Tobias, Justin L

Abstract

In this article we describe methods for obtaining the predictive distributions of outcome gains in the framework of a standard latent variable selection model. Although most previous work has focused on estimation of mean treatment parameters as the method for characterizing outcome gains from program participation, we show how the entire distributions associated with these gains can be obtained in certain situations. Although the out-of-sample outcome gain distributions depend on an unidentified parameter, we use the results of Koop and Poirier to show that learning can take place about this parameter through information contained in the identified parameters via a positive definiteness restriction on the covariance matrix. In cases where this type of learning is not highly informative, the spread of the predictive distributions depends more critically on the prior. We show both theoretically and in extensive generated data experiments how learning occurs, and delineate the sensitivity of our results to the prior specifications. We relate our analysis to three treatment parameters widely used in the evaluation literature--the average treatment effect, the effect of treatment on the treated, and the local average treatment effect--and show how one might approach estimation of the predictive distributions associated with these outcome gains rather than simply the estimation of mean effects. We apply these techniques to predict the effect of literacy on the weekly wages of a sample of New Jersey child laborers in 1903.

Suggested Citation

  • Poirier, Dale J & Tobias, Justin L, 2003. "On the Predictive Distributions of Outcome Gains in the Presence of an Unidentified Parameter," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 258-268, April.
  • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:2:p:258-68
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    1. repec:taf:japsta:v:44:y:2017:i:12:p:2142-2160 is not listed on IDEAS
    2. Giorgio Calzolari & Antonino Di Pino, 2017. "Self-selection and direct estimation of across-regime correlation parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2142-2160, September.
    3. Ariun Ishdorj & Mary Kay Crepinsek & Helen H. Jensen, 2013. "Children's Consumption of Fruits and Vegetables: Do School Environment and Policies Affect Choices at School and Away from School?," Applied Economic Perspectives and Policy, Agricultural and Applied Economics Association, vol. 35(2), pages 341-359.
    4. Munkin, Murat K. & Trivedi, Pravin K., 2008. "Bayesian analysis of the ordered probit model with endogenous selection," Journal of Econometrics, Elsevier, vol. 143(2), pages 334-348, April.
    5. Ishdorj, Ariun & Crepinsek, Mary Kay & Jensen, Helen H., 2012. "Children’s Consumption of Fruits and Vegetables: Do School Environment and Policies Affect Choice in School Meals?," 2012 AAEA/EAAE Food Environment Symposium, May 30-31, Boston, MA 123534, Agricultural and Applied Economics Association.
    6. Shimeles Abebe & Andinet Woldemichael, 2015. "Working Paper 225 - Measuring the Impact of Micro-Health Insurance on Healthcare Utilization: A Bayesian Potential Outcomes Approach," Working Paper Series 2166, African Development Bank.
    7. Muto, Sachio, 2006. "Estimation of the bid rent function with the usage decision model," Journal of Urban Economics, Elsevier, vol. 60(1), pages 33-49, July.
    8. Li, Mingliang & Tobias, Justin L., 2011. "Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling," Journal of Econometrics, Elsevier, vol. 162(2), pages 345-361, June.
    9. Chib, Siddhartha, 2007. "Analysis of treatment response data without the joint distribution of potential outcomes," Journal of Econometrics, Elsevier, vol. 140(2), pages 401-412, October.
    10. Ariun Ishdorj & Helen H. Jensen & Justin Tobias, 2007. "Intra-Household Allocation and Consumption of WIC-Approved Foods: A Bayesian Approach," Center for Agricultural and Rural Development (CARD) Publications 07-wp452, Center for Agricultural and Rural Development (CARD) at Iowa State University.

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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