IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/23497.html
   My bibliography  Save this paper

Unordered Monotonicity

Author

Listed:
  • 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
    Note: ED TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w23497.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    3. repec:adr:anecst:y:2008:i:91-92:p:02 is not listed on IDEAS
    4. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706, September.
    5. 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.
    6. 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.
    7. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    8. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    9. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    10. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    11. Jason R. Blevins, 2014. "Nonparametric identification of dynamic decision processes with discrete and continuous choices," Quantitative Economics, Econometric Society, vol. 5(3), pages 531-554, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heckman, James J. & Pinto, Rodrigo, 2022. "Causality and Econometrics," IZA Discussion Papers 15081, Institute of Labor Economics (IZA).
    2. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    3. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    4. Robert A. Moffitt & Matthew V. Zahn, 2019. "The Marginal Labor Supply Disincentives of Welfare: Evidence from Administrative Barriers to Participation," NBER Working Papers 26028, National Bureau of Economic Research, Inc.
    5. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    6. Heckman, James J. & Schmierer, Daniel & Urzua, Sergio, 2010. "Testing the correlated random coefficient model," Journal of Econometrics, Elsevier, vol. 158(2), pages 177-203, October.
    7. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    8. Harry Patrinos & Chris Sakellariou, 2005. "Schooling and Labor Market Impacts of a Natural Policy Experiment," LABOUR, CEIS, vol. 19(4), pages 705-719, December.
    9. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    10. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    11. Heckman, James & Pinto, Rodrigo, 2015. "Causal Analysis After Haavelmo," Econometric Theory, Cambridge University Press, vol. 31(1), pages 115-151, February.
    12. Heckman, James J. & Schmierer, Daniel, 2010. "Tests of hypotheses arising in the correlated random coefficient model," Economic Modelling, Elsevier, vol. 27(6), pages 1355-1367, November.
    13. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    14. Gold, Robert & Dippel, Christian & Heblich, Stephan & Pinto, Rodrigo, 2017. "Instrumental Variables and Causal Mechanisms: Unpacking the Effect of Trade on Workers and Voters," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168152, Verein für Socialpolitik / German Economic Association.
    15. Heckman, James & Pinto, Rodrigo, 2024. "Econometric causality: The central role of thought experiments," Journal of Econometrics, Elsevier, vol. 243(1).
    16. Bartalotti, Otávio & Kédagni, Désiré & Possebom, Vitor, 2023. "Identifying marginal treatment effects in the presence of sample selection," Journal of Econometrics, Elsevier, vol. 234(2), pages 565-584.
    17. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    18. James J. Heckman, 2005. "Micro Data, Heterogeneity and the Evaluation of Public Policy Part 2," The American Economist, Sage Publications, vol. 49(1), pages 16-44, March.
    19. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    20. Marx, Philip, 2024. "Sharp bounds in the latent index selection model," Journal of Econometrics, Elsevier, vol. 238(2).

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:23497. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.