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Difference-in-Differences via Common Correlated Effects

Author

Listed:
  • Nicholas Brown

    (Queen's University)

  • Kyle Butts

    (University of Colorado Boulder, Economics Department)

  • Joakim Westerlund

    (Lund University and Deakin University)

Abstract

We study the effect of treatment on an outcome when parallel trends hold conditional on an interactive fixed effects structure. In contrast to the majority of the literature, we propose identification using time-varying covariates. We assume the untreated outcomes and covariates follow a common correlated effects (CCE) model, where the covariates are linear in the same common time effects. We then demonstrate consistent estimation of the treatment effect coefficients by imputing the untreated potential outcomes in post-treatment time periods. Our method accounts for treatment affecting the distribution of the control variables and is valid when the number of pre-treatment time periods is small. We also decompose the overall treatment effect into estimable direct and mediated components.

Suggested Citation

  • Nicholas Brown & Kyle Butts & Joakim Westerlund, 2023. "Difference-in-Differences via Common Correlated Effects," Working Paper 1496, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1496
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1496.pdf
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    More about this item

    Keywords

    difference-in-differences; interactive fixed effects; fixed-T; imputation;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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