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A Nonparametric Finite Mixture Approach to Difference-in-Difference Estimation, with an Application to On-the-job Training and Wages

Author

Listed:
  • Oliver Cassagneau-Francis

    (UCL - University College of London [London])

  • Robert Gary-Bobo

    (UP1 UFR02 - Université Paris 1 Panthéon-Sorbonne - École d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CREST-THEMA - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique - THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université)

  • Julie Pernaudet

    (University of Chicago)

  • Jean-Marc Robin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

We develop a finite-mixture framework for nonparametric difference-indifference analysis with unobserved heterogeneity correlating treatment and outcome. Our framework includes an instrumental variable for the treatment, and we demonstrate that this allows us to relax the common-trend assumption. Outcomes can be modeled as first-order Markovian, provided at least 2 post-treatment observations of the outcome are available. We provide a nonparametric identification proof. We apply our framework to evaluate the effect of on-the-job training on wages, using novel French linked employee-employer data. Estimating our model using an EM-algorithm, we find small ATEs and ATTs on hourly wages, around 1%.

Suggested Citation

  • Oliver Cassagneau-Francis & Robert Gary-Bobo & Julie Pernaudet & Jean-Marc Robin, 2022. "A Nonparametric Finite Mixture Approach to Difference-in-Difference Estimation, with an Application to On-the-job Training and Wages," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03869547, HAL.
    • Handle: RePEc:hal:cesptp:hal-03869547
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03869547
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    More about this item

    Keywords

    Finite Mixtures; Unobserved Heterogeneity; EM Algorithm; Wage Distributions; Training; Matched Employer-Employee Data E24; E32; J63; J64;
    All these keywords.

    JEL classification:

    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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