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On Heckits, LATE, and Numerical Equivalence

Author

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  • Patrick Kline
  • Christopher R. Walters

Abstract

Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman's (1979) two‐step (“Heckit”) control function estimator which, with two‐sided non‐compliance, can be used to compute estimates of a variety of causal parameters. Equivalence with IV is established for a semiparametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises.

Suggested Citation

  • Patrick Kline & Christopher R. Walters, 2019. "On Heckits, LATE, and Numerical Equivalence," Econometrica, Econometric Society, vol. 87(2), pages 677-696, March.
    • Handle: RePEc:wly:emetrp:v:87:y:2019:i:2:p:677-696
    DOI: 10.3982/ECTA15444
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    Cited by:

    1. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    2. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    3. Tymon Sloczynski, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," Working Papers 125, Brandeis University, Department of Economics and International Business School.
    4. Mourifié, Ismael & Wan, Yuanyuan, 2025. "Layered policy analysis in program evaluation using the marginal treatment effect," Journal of Econometrics, Elsevier, vol. 251(C).
    5. 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.
    6. Amanda E Kowalski, 2023. "Behaviour within a Clinical Trial and Implications for Mammography Guidelines," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(1), pages 432-462.
    7. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy," Papers 2005.09130, arXiv.org, revised Jun 2020.
    8. Susan Athey & Raj Chetty & Guido Imbens, 2020. "Using Experiments to Correct for Selection in Observational Studies," Papers 2006.09676, arXiv.org, revised May 2025.
    9. Sebastian Galiani & Juan Pantano, 2021. "Structural Models: Inception and Frontier," NBER Working Papers 28698, National Bureau of Economic Research, Inc.
    10. Nobel Prize Committee, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    11. Ante Sterc, 2022. "Limited Consideration in the Investment Fund Choice," CERGE-EI Working Papers wp729, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    12. Luther Yap, 2022. "Sensitivity of Policy Relevant Treatment Parameters to Violations of Monotonicity," Working Papers 655, Princeton University, Department of Economics, Industrial Relations Section..
    13. Davide Cipullo, 2021. "Gender Gaps in Political Careers: Evidence from Competitive Elections," CESifo Working Paper Series 9075, CESifo.
    14. Valentin Verdier, 2020. "Average treatment effects for stayers with correlated random coefficient models of panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 917-939, November.
    15. Yu‐Chang Chen & Haitian Xie, 2022. "Global Representation of the Conditional LATE Model: A Separability Result," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 789-798, August.
    16. Phillip Heiler & Asbj{o}rn Kaufmann & Bezirgen Veliyev, 2024. "Treatment Evaluation at the Intensive and Extensive Margins," Papers 2412.11179, arXiv.org.
    17. Marx, Philip, 2024. "Sharp bounds in the latent index selection model," Journal of Econometrics, Elsevier, vol. 238(2).
    18. Semenova, Vira, 2025. "Generalized Lee bounds," Journal of Econometrics, Elsevier, vol. 251(C).
    19. Elior Cohen, 2022. "The Effect of Housing First Programs on Future Homelessness and Socioeconomic Outcomes," Research Working Paper RWP 22-03, Federal Reserve Bank of Kansas City.
    20. Opper, Isaac M., 2024. "From LATE to ATE: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 246(1).
    21. Shuxi Zeng & Fan Li & Peng Ding, 2020. "Is being an only child harmful to psychological health?: evidence from an instrumental variable analysis of China's one‐child policy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1615-1635, October.
    22. 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.
    23. Phillip Heiler, 2022. "Efficient Covariate Balancing for the Local Average Treatment Effect," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1569-1582, October.
    24. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2021. "On Estimating Multiple Treatment Effects with Regression," Working Papers 2021-41, Princeton University. Economics Department..

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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