IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v242y2024i1s0304407624001313.html
   My bibliography  Save this article

2SLS with multiple treatments

Author

Listed:
  • Bhuller, Manudeep
  • Sigstad, Henrik

Abstract

We study what two-stage least squares (2SLS) identifies in models with multiple treatments under treatment effect heterogeneity. Two conditions are shown to be necessary and sufficient for the 2SLS to identify positively weighted sums of agent-specific effects of each treatment: average conditional monotonicity and no cross effects. Our identification analysis allows for any number of treatments, any number of continuous or discrete instruments, and the inclusion of covariates. We provide testable implications and present characterizations of choice behavior implied by our identification conditions.

Suggested Citation

  • Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    • Handle: RePEc:eee:econom:v:242:y:2024:i:1:s0304407624001313
    DOI: 10.1016/j.jeconom.2024.105785
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407624001313
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2024.105785?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bolhaar, Jonneke & Ketel, Nadine & van der Klaauw, Bas, 2020. "Caseworker's discretion and the effectiveness of welfare-to-work programs," Journal of Public Economics, Elsevier, vol. 183(C).
    2. Amelie Schiprowski, 2020. "The Role of Caseworkers in Unemployment Insurance: Evidence from Unplanned Absences," Journal of Labor Economics, University of Chicago Press, vol. 38(4), pages 1189-1225.
    3. Manudeep Bhuller & Gordon B. Dahl & Katrine V. Løken & Magne Mogstad, 2020. "Incarceration, Recidivism, and Employment," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1269-1324.
    4. Luc Behaghel & Bruno Crépon & Marc Gurgand, 2013. "Robustness of the encouragement design in a two-treatment randomized control trial," Working Papers halshs-00834169, HAL.
    5. Stephen Machin & Kjell G. Salvanes & Panu Pelkonen, 2012. "Education And Mobility," Journal of the European Economic Association, European Economic Association, vol. 10(2), pages 417-450, April.
    6. Stuhler, Jan & Jaeger, David & Ruist, Joakim, 2018. "Shift-Share Instruments and the Impact of Immigration," CEPR Discussion Papers 12701, C.E.P.R. Discussion Papers.
    7. Schmieder, Johannes F & Trenkle, Simon, 2020. "Disincentive effects of unemployment benefits and the role of caseworkers," Journal of Public Economics, Elsevier, vol. 182(C).
    8. Gaurab Aryal & Manudeep Bhuller & Fabian Lange, 2022. "Signaling and Employer Learning with Instruments," American Economic Review, American Economic Association, vol. 112(5), pages 1669-1702, May.
    9. Brigham Frandsen & Lars Lefgren & Emily Leslie, 2023. "Judging Judge Fixed Effects," American Economic Review, American Economic Association, vol. 113(1), pages 253-277, January.
    10. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 71, Elsevier.
    11. Samuel Norris & Matthew Pecenco & Jeffrey Weaver, 2021. "The Effects of Parental and Sibling Incarceration: Evidence from Ohio," American Economic Review, American Economic Association, vol. 111(9), pages 2926-2963, September.
    12. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    13. Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    14. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    15. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    16. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification And Economic Content Of Ordered Choice Models With Stochastic Thresholds," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1273-1309, November.
    17. Aakvik, Arild & Salvanes, Kjell G. & Vaage, Kjell, 2010. "Measuring heterogeneity in the returns to education using an education reform," European Economic Review, Elsevier, vol. 54(4), pages 483-500, May.
    18. 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.
    19. Jack Mountjoy, 2022. "Community Colleges and Upward Mobility," American Economic Review, American Economic Association, vol. 112(8), pages 2580-2630, August.
    20. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    21. Will Dobbie & Jacob Goldin & Crystal S. Yang, 2018. "The Effects of Pretrial Detention on Conviction, Future Crime, and Employment: Evidence from Randomly Assigned Judges," American Economic Review, American Economic Association, vol. 108(2), pages 201-240, February.
    22. Adam Altmejd & Andrés Barrios-Fernández & Marin Drlje & Joshua Goodman & Michael Hurwitz & Dejan Kovac & Christine Mulhern & Christopher Neilson & Jonathan Smith, 2021. "O Brother, Where Start Thou? Sibling Spillovers on College and Major Choice in Four Countries," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1831-1886.
    23. Helmut Farbmacher & Raphael Guber & Sven Klaassen, 2022. "Instrument Validity Tests With Causal Forests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 605-614, April.
    24. Patrick Kline & Christopher R. Walters, 2016. "Evaluating Public Programs with Close Substitutes: The Case of HeadStart," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1795-1848.
    25. 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).
    26. Manudeep Bhuller & Philipp Eisenhauer & Moritz Mendel, 2022. "Sequential Choices, Option Values, and the Returns to Education," Papers 2205.05444, arXiv.org, revised Jul 2024.
    27. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    28. Philip Oreopoulos & Daniel Lang & Joshua Angrist, 2009. "Incentives and Services for College Achievement: Evidence from a Randomized Trial," American Economic Journal: Applied Economics, American Economic Association, vol. 1(1), pages 136-163, January.
    29. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    30. Joshua Angrist & Peter Hull & Christopher R. Walters, 2022. "Methods for Measuring School Effectiveness," NBER Working Papers 30803, National Bureau of Economic Research, Inc.
    31. O. Ashenfelter & D. Card (ed.), 1999. "Handbook of Labor Economics," Handbook of Labor Economics, Elsevier, edition 1, volume 3, number 3.
    32. Mogstad, Magne & Torgovitsky, Alexander & Walters, Christopher R., 2024. "Policy evaluation with multiple instrumental variables," Journal of Econometrics, Elsevier, vol. 243(1).
    33. Manudeep Bhuller & Magne Mogstad & Kjell G. Salvanes, 2017. "Life-Cycle Earnings, Education Premiums, and Internal Rates of Return," Journal of Labor Economics, University of Chicago Press, vol. 35(4), pages 993-1030.
    34. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    35. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2005. "Why the Apple Doesn't Fall Far: Understanding Intergenerational Transmission of Human Capital," American Economic Review, American Economic Association, vol. 95(1), pages 437-449, March.
    36. Heckman, James J. & Lochner, Lance J. & Todd, Petra E., 2006. "Earnings Functions, Rates of Return and Treatment Effects: The Mincer Equation and Beyond," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 1, chapter 7, pages 307-458, Elsevier.
    37. Goff, Leonard, 2024. "A vector monotonicity assumption for multiple instruments," Journal of Econometrics, Elsevier, vol. 241(1).
    38. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
    39. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    40. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    41. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    42. 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.
    43. Altonji, Joseph G, 1993. "The Demand for and Return to Education When Education Outcomes Are Uncertain," Journal of Labor Economics, University of Chicago Press, vol. 11(1), pages 48-83, January.
    44. Karin Monstad & Carol Propper & Kjell G. Salvanes, 2008. "Education and Fertility: Evidence from a Natural Experiment," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(4), pages 827-852, December.
    45. Daron Acemoglu & Simon Johnson, 2005. "Unbundling Institutions," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 949-995, October.
    46. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    47. 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.
    48. Chris Rohlfs, 2006. "The Government's Valuation of Military Life-Saving in War: A Cost Minimization Approach," American Economic Review, American Economic Association, vol. 96(2), pages 39-44, May.
    49. Kevin Lang & David Kropp, 1986. "Human Capital Versus Sorting: The Effects of Compulsory Attendance Laws," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(3), pages 609-624.
    50. Bombardini, Matilde & Li, Bingjing, 2020. "Trade, pollution and mortality in China," Journal of International Economics, Elsevier, vol. 125(C).
    51. Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
    52. Evan K. Rose & Yotam Shem-Tov, 2021. "How Does Incarceration Affect Reoffending? Estimating the Dose-Response Function," Journal of Political Economy, University of Chicago Press, vol. 129(12), pages 3302-3356.
    53. Leonard Goff, 2020. "A Vector Monotonicity Assumption for Multiple Instruments," Papers 2009.00553, arXiv.org, revised Mar 2024.
    54. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    55. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification & Economic Content of Ordered Choice Models with Stochastic Thresholds," Working Papers 200726, Geary Institute, University College Dublin.
    56. Torsten Persson & Guido Tabellini, 2004. "Constitutional Rules and Fiscal Policy Outcomes," American Economic Review, American Economic Association, vol. 94(1), pages 25-45, March.
    57. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    58. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    59. Christine Blandhol & John Bonney & Magne Mogstad & Alexander Torgovitsky, 2022. "When is TSLS Actually LATE?," NBER Working Papers 29709, National Bureau of Economic Research, Inc.
    60. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2021. "On Estimating Multiple Treatment Effects with Regression," Working Papers 2021-41, Princeton University. Economics Department..
    61. repec:adr:anecst:y:2008:i:91-92:p:08 is not listed on IDEAS
    62. Nibbering, Didier & Oosterveen, Matthijs & Silva, Pedro Luís, 2022. "Clustered Local Average Treatment Effects: Fields of Study and Academic Student Progress," IZA Discussion Papers 15159, Institute of Labor Economics (IZA).
    63. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    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. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2023. "Design-Based Identification with Formula Instruments: A Review," NBER Working Papers 31393, National Bureau of Economic Research, Inc.

    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. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    2. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    3. 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.
    4. Manudeep Bhuller & Philipp Eisenhauer & Moritz Mendel, 2022. "Sequential Choices, Option Values, and the Returns to Education," Papers 2205.05444, arXiv.org, revised Jul 2024.
    5. Thomas Carr & Toru Kitagawa, 2021. "Testing Instrument Validity with Covariates," Papers 2112.08092, arXiv.org, revised Sep 2023.
    6. Heckman, James J. & Pinto, Rodrigo, 2022. "Causality and Econometrics," IZA Discussion Papers 15081, Institute of Labor Economics (IZA).
    7. Vishal Kamat & Samuel Norris & Matthew Pecenco, 2023. "Identification in Multiple Treatment Models under Discrete Variation," Papers 2307.06174, arXiv.org.
    8. Binelli, Chiara & Menezes-Filho, Naercio, 2019. "Why Brazil fell behind in college education?," Economics of Education Review, Elsevier, vol. 72(C), pages 80-106.
    9. Belzil, Christian, 2007. "The return to schooling in structural dynamic models: a survey," European Economic Review, Elsevier, vol. 51(5), pages 1059-1105, July.
    10. Heckman, James J. & Urzúa, Sergio, 2010. "Comparing IV with structural models: What simple IV can and cannot identify," Journal of Econometrics, Elsevier, vol. 156(1), pages 27-37, May.
    11. Gaurab Aryal & Manudeep Bhuller & Fabian Lange, 2022. "Signaling and Employer Learning with Instruments," American Economic Review, American Economic Association, vol. 112(5), pages 1669-1702, May.
    12. Manudeep Bhuller & Magne Mogstad & Kjell G. Salvanes, 2017. "Life-Cycle Earnings, Education Premiums, and Internal Rates of Return," Journal of Labor Economics, University of Chicago Press, vol. 35(4), pages 993-1030.
    13. Heckman, James & Pinto, Rodrigo, 2024. "Econometric causality: The central role of thought experiments," Journal of Econometrics, Elsevier, vol. 243(1).
    14. 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.
    15. Leonard Goff, 2024. "When does IV identification not restrict outcomes?," Papers 2406.02835, arXiv.org, revised Sep 2024.
    16. Nadja van 't Hoff, 2023. "Identifying Causal Effects of Discrete, Ordered and ContinuousTreatments using Multiple Instrumental Variables," Papers 2311.17575, arXiv.org, revised Oct 2024.
    17. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    18. Sokbae Lee & Bernard Salani'e, 2020. "Treatment Effects with Targeting Instruments," Papers 2007.10432, arXiv.org, revised Dec 2024.
    19. Carolina Arteaga, 2021. "Parental Incarceration and Children's Educational Attainment," Working Papers tecipa-703, University of Toronto, Department of Economics.
    20. Lars Kirkebøen & Edwin Leuven & Magne Mogstad, 2014. "Field of Study, Earnings, and Self-Selection," NBER Working Papers 20816, National Bureau of Economic Research, Inc.

    More about this item

    Keywords

    Multiple treatments; Monotonicity; Instrumental variables; Two-stage least squares;
    All these keywords.

    JEL classification:

    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

    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:242:y:2024:i:1:s0304407624001313. 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.