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Nonlinear difference-in-differences in repeated cross sections with continuous treatments

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  • Xavier D'Haultfoeuille
  • Stefan Hoderlein

    ()
    (Institute for Fiscal Studies and Boston College)

  • Yuya Sasaki

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 function form restrictions. This result is related to the difference-in-differences idea, but imposes neither 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.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP40/13.

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Date of creation: Aug 2013
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Handle: RePEc:ifs:cemmap:40/13

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Keywords: Identification; repeated cross sections; nonlinear models; continuous treatment; random coefficients; endogeneity; difference-in-differences;

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