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Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments

Author

Listed:
  • Xavier D'Haultfoeuille

    (CREST)

  • Stefan Hoderlein

    (Boston College)

  • Yuya Sasaki

    (Johns Hopkins University)

Abstract
This paper studies the identification of nonseparable models with continuous, endogenous regressors, also called treatments, using repeated cross sections. We show that several treatment effect parameters are identified under two assumptions on the effect of time, namely a weak stationarity condition on the distribution of unobservables, and time variation in the distribution of endogenous regressors. Other treatment effect parameters are set identified under curvature conditions, but without any functional form restrictions. This result is related to the difference-in-differences idea, but does neither impose additive time effects nor exogenously defined control groups. Furthermore, we investigate two extrapolation strategies that allow us to point identify the entire model: using monotonicity of the error term, or imposing a linear correlated random coefficient structure. Finally, we illustrate our results by studying the effect of mother's age on infants' birth weight.

Suggested Citation

  • Xavier D'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments," Boston College Working Papers in Economics 839, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:839
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    Cited by:

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    2. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers 31/17, Institute for Fiscal Studies.
    3. Carolina Caetano & Juan Carlos Escaniano, 2015. "Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity," CAEPR Working Papers 2015-009, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    4. Tuliakova Irina R., 2016. "Assessment Of Competitiveness Of Shipbuilding Industry In Russia," Annals of marketing-mba, Department of Marketing, Marketing MBA (RSconsult), vol. 2, August.
    5. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    6. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    7. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    8. Dengov, V. & Melnikova, E., 2013. "Adverse selection in various insurance markets and the ways to deal with it (the experience of practical research)," Annals of marketing-mba, Department of Marketing, Marketing MBA (RSconsult), vol. 2, July.
    9. Alejo, Javier & Galvao, Antonio F. & Montes-Rojas, Gabriel, 2018. "Quantile continuous treatment effects," Econometrics and Statistics, Elsevier, vol. 8(C), pages 13-36.
    10. Michela Maria Tincani, 2017. "Heterogeneous Peer Effects and Rank Concerns: Theory and Evidence," CESifo Working Paper Series 6331, CESifo.
    11. Ishihara, Takuya, 2020. "Identification and estimation of time-varying nonseparable panel data models without stayers," Journal of Econometrics, Elsevier, vol. 215(1), pages 184-208.
    12. Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
    13. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    14. Michela Tincani, 2017. "Heterogeneous Peer Effects and Rank Concerns: Theory and Evidence," Working Papers 2017-006, Human Capital and Economic Opportunity Working Group.
    15. Takuya Ishihara, 2020. "Panel Data Quantile Regression for Treatment Effect Models," Papers 2001.04324, arXiv.org, revised Nov 2021.

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    More about this item

    Keywords

    identification; repeated cross sections; nonlinear models; continuous treatment; random coefficients; endogeneity; difference-in-differences.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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