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Unordered Monotonicity

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  • James J. Heckman
  • Rodrigo Pinto

Abstract

This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogenous agents and discrete-valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.

Suggested Citation

  • James J. Heckman & Rodrigo Pinto, 2017. "Unordered Monotonicity," NBER Working Papers 23497, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:23497
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. 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.
    4. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
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    6. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    7. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706.
    8. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
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    More about this item

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • J15 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination

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