IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v213y2019i1p210-234.html
   My bibliography  Save this article

Partial identification of the treatment effect distribution and its functionals

Author

Listed:
  • Firpo, Sergio
  • Ridder, Geert

Abstract

In the treatment effect problem, the available information is on the marginal distributions of potential outcomes, but not on their joint distribution. The only point identified functional of the treatment effect distribution is its average, the average treatment effect (ATE). Quantiles and other functionals of the distribution of treatment effect are only partially identified. Bounds on a single quantile and on the cumulative distribution function (c.d.f.) in a single point are sharp (Makarov bounds). We show that bounds on functionals of the quantile process that use Makarov bounds are not sharp, because the Makarov bounds are pointwise, but not uniformly sharp. This allows us to propose improved bounds on functionals of the c.d.f. As an intermediate result, we find that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in a finite number of points can be improved. We provide numerical illustrations throughout the paper permitting a clear visualization of how the method works.

Suggested Citation

  • Firpo, Sergio & Ridder, Geert, 2019. "Partial identification of the treatment effect distribution and its functionals," Journal of Econometrics, Elsevier, vol. 213(1), pages 210-234.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:1:p:210-234
    DOI: 10.1016/j.jeconom.2019.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407619300673
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2019.04.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    2. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    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. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    5. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    6. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute of Labor Economics (IZA).
    7. Jörg Stoye, 2010. "Partial identification of spread parameters," Quantitative Economics, Econometric Society, vol. 1(2), pages 323-357, November.
    8. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "2001 Lawrence R. Klein Lecture Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 361-422, May.
    9. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.
    10. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70, Elsevier.
    11. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    12. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    13. James J. Heckman & Jeffrey A. Smith, 1998. "Evaluating the Welfare State," NBER Working Papers 6542, National Bureau of Economic Research, Inc.
    14. Yanqin Fan & Jisong Wu, 2010. "Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1002-1041.
    15. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    16. Aakvik, Arild & Heckman, James J. & Vytlacil, Edward J., 2005. "Estimating treatment effects for discrete outcomes when responses to treatment vary: an application to Norwegian vocational rehabilitation programs," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 15-51.
    17. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    18. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    2. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Childhood Intervention," IZA Discussion Papers 13101, Institute of Labor Economics (IZA).
    3. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Child Intervention," CEPR Discussion Papers 14721, C.E.P.R. Discussion Papers.
    4. Vira Semenova, 2023. "Aggregated Intersection Bounds and Aggregated Minimax Values," Papers 2303.00982, arXiv.org, revised Jun 2024.
    5. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    6. Kim, Dongwoo, 2023. "Partially identifying competing risks models: An application to the war on cancer," Journal of Econometrics, Elsevier, vol. 234(2), pages 536-564.
    7. Han, Sukjin & Yang, Shenshen, 2024. "A computational approach to identification of treatment effects for policy evaluation," Journal of Econometrics, Elsevier, vol. 240(1).
    8. Aaron L. Bodoh-Creed & Brent R. Hickman & John A. List & Ian Muir & Gregory K. Sun, 2023. "Stress Testing Structural Models of Unobserved Heterogeneity: Robust Inference on Optimal Nonlinear Pricing," NBER Working Papers 31647, National Bureau of Economic Research, Inc.
    9. Vladislav Morozov, 2022. "Inference on Extreme Quantiles of Unobserved Individual Heterogeneity," Papers 2210.08524, arXiv.org, revised Jun 2023.
    10. 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.
    11. Sungwon Lee, 2021. "Partial Identification and Inference for Conditional Distributions of Treatment Effects," Papers 2108.00723, arXiv.org, revised Nov 2023.
    12. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.

    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. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    2. Yanqin Fan & Sang Soo Park, 2009. "Partial identification of the distribution of treatment effects and its confidence sets," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 3-70, Emerald Group Publishing Limited.
    3. Lee, Ji Hyung & Park, Byoung G., 2023. "Nonparametric identification and estimation of the extended Roy model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1087-1113.
    4. Sergio Firpo & Cristine Pinto, 2016. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 457-486, April.
    5. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    6. Flavio Cunha & James Heckman & Salvador Navarro, 2005. "Separating uncertainty from heterogeneity in life cycle earnings," Oxford Economic Papers, Oxford University Press, vol. 57(2), pages 191-261, April.
    7. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    8. Battistin, Erich & Lamarche, Carlos & Rettore, Enrico, 2020. "Quantiles of the Gain Distribution of an Early Childhood Intervention," IZA Discussion Papers 13101, Institute of Labor Economics (IZA).
    9. Anders Forslund & Oskar Nordström Stans, 2006. "Swedish Youth Labour Market Policies Revisited," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 75(3), pages 168-185.
    10. 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.
    11. Paul. B. Kenfac Dongmezo & P. N. Mwita & I. R. Kamga Tchwaket, 2018. "Distributive and Quantile Treatment Effects: Imputation Based Estimators Approach," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 7(2), pages 1-3.
    12. James J. Heckman, 2008. "Econometric Causality," International Statistical Review, International Statistical Institute, vol. 76(1), pages 1-27, April.
    13. Cunha, Flavio & Heckman, James, 2008. "A New Framework For The Analysis Of Inequality," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S2), pages 315-354, September.
    14. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.
    15. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    16. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    17. Stéphane Bonhomme & Ulrich Sauder, 2009. "Accounting for Unobservables in Comparing Selective and Comprehensive Schooling," Working Papers wp2009_0906, CEMFI.
    18. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    19. Sungwon Lee, 2021. "Partial Identification and Inference for Conditional Distributions of Treatment Effects," Papers 2108.00723, arXiv.org, revised Nov 2023.
    20. Shukla, Sumedha & Arora, Gaurav, 2022. "A rank similarity test for quantile treatment effects in conjunction with propensity score matching: An application to crop yield impacts of agricultural credit," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322569, Agricultural and Applied Economics Association.

    More about this item

    Keywords

    Distribution of treatment effects; Bounds;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

    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:eee:econom:v:213:y:2019:i:1:p:210-234. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.