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On Heckits, LATE, and Numerical Equivalence

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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 semi-parametric 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, 2017. "On Heckits, LATE, and Numerical Equivalence," Papers 1706.05982, arXiv.org, revised Oct 2018.
  • Handle: RePEc:arx:papers:1706.05982
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    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2017. "Using Instrumental Variables for Inference about Policy Relevant Treatment Effects," NBER Working Papers 23568, National Bureau of Economic Research, Inc.
    3. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    4. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    5. repec:pri:cheawb:deaton%20instruments%20of%20development%20keynes%20lecture%202009 is not listed on IDEAS
    6. 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.
    7. Angus Deaton, 2009. "Instruments of development: Randomization in the tropics, and the search for the elusive keys to economic development," Working Papers 1128, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Health and Wellbeing..
    8. Cornelissen, Thomas & Dustmann, Christian & Raute, Anna & Schönberg, Uta, 2016. "From LATE to MTE: Alternative methods for the evaluation of policy interventions," Labour Economics, Elsevier, vol. 41(C), pages 47-60.
    9. Dubin, Jeffrey A & McFadden, Daniel L, 1984. "An Econometric Analysis of Residential Electric Appliance Holdings and Consumption," Econometrica, Econometric Society, vol. 52(2), pages 345-362, March.
    10. 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.
    11. Amanda Kowalski, 2016. "Doing more when you're running LATE: Applying marginal treatment effect methods to examine treatment effect heterogeneity in experiments," Artefactual Field Experiments 00560, The Field Experiments Website.
    12. Christian N. Brinch & Magne Mogstad & Matthew Wiswall, 2017. "Beyond LATE with a Discrete Instrument," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 985-1039.
    13. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    14. Marinho Bertanha & Guido W. Imbens, 2020. "External Validity in Fuzzy Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 593-612, July.
    15. Olsen, Randall J, 1980. "A Least Squares Correction for Selectivity Bias," Econometrica, Econometric Society, vol. 48(7), pages 1815-1820, November.
    16. Garen, John, 1984. "The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable," Econometrica, Econometric Society, vol. 52(5), pages 1199-1218, September.
    17. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    18. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    19. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    20. Richard Blundell & Rosa L. Matzkin, 2014. "Control functions in nonseparable simultaneous equations models," Quantitative Economics, Econometric Society, vol. 5, pages 271-295, July.
    21. repec:pri:cheawb:deaton%20instruments%20of%20development%20keynes%20lecture%202009.pdf is not listed on IDEAS
    22. Lester G. Telser, 1964. "Advertising and Competition," Journal of Political Economy, University of Chicago Press, vol. 72(6), pages 537-537.
    23. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 355-372.
    24. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    25. Joshua D. Angrist, 2004. "Treatment effect heterogeneity in theory and practice," Economic Journal, Royal Economic Society, vol. 114(494), pages 52-83, March.
    26. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    27. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    28. Battistin, Erich & Rettore, Enrico, 2008. "Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs," Journal of Econometrics, Elsevier, vol. 142(2), pages 715-730, February.
    29. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    30. 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.
    31. 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.
    32. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    33. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    34. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    35. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
    36. Bjorklund, Anders & Moffitt, Robert, 1987. "The Estimation of Wage Gains and Welfare Gains in Self-selection," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 42-49, February.
    37. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    38. repec:pri:rpdevs:instruments_of_development.pdf is not listed on IDEAS
    39. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    3. 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.
    4. Committee, Nobel Prize, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    5. Paul Goldsmith-Pinkham & Peter Hull & Michal Koles'ar, 2021. "Contamination Bias in Linear Regressions," Papers 2106.05024, arXiv.org, revised Jun 2024.
    6. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    7. 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.
    8. Davide Cipullo, 2021. "Gender Gaps in Political Careers: Evidence from Competitive Elections," CESifo Working Paper Series 9075, CESifo.
    9. 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.
    10. Phillip Heiler, 2020. "Efficient Covariate Balancing for the Local Average Treatment Effect," Papers 2007.04346, arXiv.org.
    11. Susan Athey & Raj Chetty & Guido Imbens, 2020. "Combining Experimental and Observational Data to Estimate Treatment Effects on Long Term Outcomes," Papers 2006.09676, arXiv.org.
    12. 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.
    13. 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.
    14. 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.
    15. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2021. "On Estimating Multiple Treatment Effects with Regression," Working Papers 2021-41, Princeton University. Economics Department..
    16. 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.
    17. Luther Yap, 2022. "Sensitivity of Policy Relevant Treatment Parameters to Violations of Monotonicity," Working Papers 655, Princeton University, Department of Economics, Industrial Relations Section..
    18. Marx, Philip, 2024. "Sharp bounds in the latent index selection model," Journal of Econometrics, Elsevier, vol. 238(2).
    19. 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.

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    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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