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Partial Identification of Population Average and Quantile Treatment Effects in Observational Data under Sample Selection

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  • Christelis, Dimitris
  • Messina, Julián

Abstract

We partially identify population treatment effects in observational data under sample selection, without the benefit of random treatment assignment. We provide bounds both for the average and the quantile population treatment effects, combining assumptions for the selected and the non-selected subsamples. We show how different assumptions help narrow identification regions, and illustrate our methods by partially identifying the effect of maternal education on the 2015 PISA math test scores in Brazil. We find that while sample selection increases considerably the uncertainty around the effect of maternal education, it is still possible to calculate informative identification regions.

Suggested Citation

  • Christelis, Dimitris & Messina, Julián, 2019. "Partial Identification of Population Average and Quantile Treatment Effects in Observational Data under Sample Selection," IDB Publications (Working Papers) 9520, Inter-American Development Bank.
  • Handle: RePEc:idb:brikps:9520
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    References listed on IDEAS

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    1. Pamela Giustinelli, 2011. "Non‐parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 783-824, August.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
    3. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
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    6. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    7. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1071-1102.
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    12. Reuben Gronau, 1974. "The Effect of Children on the Housewife's Value of Time," NBER Chapters,in: Economics of the Family: Marriage, Children, and Human Capital, pages 457-490 National Bureau of Economic Research, Inc.
    13. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
    14. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 355-372.
    15. Marina Bassi & Matias Busso & Juan Sebastian Muñoz, 2015. "Enrollment, Graduation, and Dropout Rates in Latin America: Is the Glass Half Empty or Half Full?," Economía Journal, The Latin American and Caribbean Economic Association - LACEA, vol. 0(Fall 2015), pages 113-156, October.
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    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • I2 - Health, Education, and Welfare - - Education

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