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Counterfactual Worlds

Author

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  • Andrew Chesher
  • Adam M. Rosen

Abstract

We study an extension of a treatment effect model in which an observed discrete classifier indicates which one of a set of counterfactual processes occurs, each of which may result in the realization of several endogenous outcomes. In addition to the classifier indicating which process was realized, other observed outcomes are delivered by the particular counterfactual process. Models of the counterfactual processes can be incomplete in the sense that even with knowledge of the values of observed exogenous and unobserved variables they may not deliver a unique value of the endogenous outcomes. Thus, relative to the usual treatment effect models, counterfactual outcomes are replaced by counterfactual processes. The determination of endogenous variables in these counterfactual processes may be modeled by the researcher, and impacted by observable exogenous variables restricted to be independent of certain unobservable variables as in instrumental variable models. We study the identifying power of models of this sort that incorporate (i) conditional independence restrictions under which unobserved variables and the classifier variable are stochastically independent conditional on some of the observed exogenous variables and (ii) marginal independence restrictions under which unobservable variables and a subset of the exogenous variables are independently distributed. Building on results in Chesher and Rosen (2017), we characterize the identifying power of these models for fundamental structural relationships and probability distributions of unobservable heterogeneity.

Suggested Citation

  • Andrew Chesher & Adam M. Rosen, 2021. "Counterfactual Worlds," Annals of Economics and Statistics, GENES, issue 142, pages 311-335.
  • Handle: RePEc:adr:anecst:y:2021:i:142:p:311-335
    DOI: https://doi.org/10.15609/annaeconstat2009.142.0311
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    References listed on IDEAS

    as
    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2008. "Instrumental Variables in Models with Multiple Outcomes: The General Unordered Case," Annals of Economics and Statistics, GENES, issue 91-92, pages 151-174.
    2. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    3. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    4. Andrew Chesher & Adam Rosen, 2013. "Generalized instrumental variable models," CeMMAP working papers 43/13, Institute for Fiscal Studies.
    5. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1264-1298.
    6. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers 21/12, Institute for Fiscal Studies.
    7. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    8. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
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    11. Heckman, James & Pinto, Rodrigo, 2015. "Causal Analysis After Haavelmo," Econometric Theory, Cambridge University Press, vol. 31(1), pages 115-151, February.
    12. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
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    More about this item

    Keywords

    Conditional Independence; Counterfactual Inference; Endogeneity; Incomplete Models; Instrumental Variables; Partial Identification; Random Sets.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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