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Horowitz-Manski-Lee Bounds With Multilayered Sample Selection

Author

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  • Kory Kroft
  • Ismael Mourifié
  • Atom Vayalinkal

Abstract

This paper investigates the causal effect of job training on wage rates in the presence of firm heterogeneity. When training affects the sorting of workers to firms, sample selection is no longer binary but is “multilayered”. This paper extends the canonical Heckman (1979) sample selection model – which assumes selection is binary – to a setting where it is multilayered. In this setting Lee bounds set identifies a total effect that combines a weighted-average of the causal effect of job training on wage rates across firms with a weighted-average of the contrast in wages between different firms for a fixed level of training. Thus, Lee bounds set identifies a policy-relevant estimand only when firms pay homogeneous wages and/or when job training does not affect worker sorting across firms. We derive analytic expressions for sharp bounds for the causal effect of job training on wage rates at each firm that leverage information on firm-specific wages. We illustrate our partial identification approach with two empirical applications to job training experiments. Our estimates demonstrate that even when conventional Lee bounds are strictly positive, our within-firm bounds can be tight around 0, showing that the canonical Lee bounds may capture only a pure sorting effect of job training.

Suggested Citation

  • Kory Kroft & Ismael Mourifié & Atom Vayalinkal, 2024. "Horowitz-Manski-Lee Bounds With Multilayered Sample Selection," NBER Working Papers 32952, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:32952
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    References listed on IDEAS

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    1. Martin Huber & Lukas Laffers & Giovanni Mellace, 2017. "Sharp IV Bounds on Average Treatment Effects on the Treated and Other Populations Under Endogeneity and Noncompliance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 56-79, January.
    2. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    3. François Gerard & Lorenzo Lagos & Edson Severnini & David Card, 2021. "Assortative Matching or Exclusionary Hiring? The Impact of Employment and Pay Policies on Racial Wage Differences in Brazil," American Economic Review, American Economic Association, vol. 111(10), pages 3418-3457, October.
    4. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
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    Cited by:

    1. Ying-Ying Lee & Chu-An Liu, 2024. "Lee Bounds with a Continuous Treatment in Sample Selection," Papers 2411.04312, arXiv.org, revised Feb 2025.

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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • H0 - Public Economics - - General
    • H50 - Public Economics - - National Government Expenditures and Related Policies - - - General
    • J0 - Labor and Demographic Economics - - General
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • J32 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Nonwage Labor Costs and Benefits; Retirement Plans; Private Pensions

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