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Comparative Statics for Difference-in-Differences

Author

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  • Finn Christensen

    (Department of Economics, Towson University)

Abstract

The stable unit treatment value assumption (SUTVA) in causal estimation rules out spillover effects, but spillover effects are the hallmark of many economic models. Testing model predictions with techniques that employ SUTVA are thus problematic. To address this issue, we first show that without the no interference component of SUTVA, the population difference-in-difference (DiD) identifies the difference in the average potential outcomes between the treated and untreated. We call this estimand the marginal average treatment effect among the treated with spillovers (MATTS). Then, in the context of a model whose equilibrium is characterized by a system of smooth equations, we provide comparative statics results which restrict the sign of MATTS. Specifically, we show that MATTS is positive for any nontrivial treatment group whenever treatment has a strictly positive direct effect if and only if the inverse of the negated Jacobian is a B0-matrix by columns. We then provide several conditions on the Jacobian such that its negated inverse is a B-matrix by columns. Additional related results are presented. These predictions can be tested directly within the DiD framework even when the SUTVA is violated. Consequently, the results in this paper render economic models rejectable with reduced form DiD methods.

Suggested Citation

  • Finn Christensen, 2023. "Comparative Statics for Difference-in-Differences," Working Papers 2023-08, Towson University, Department of Economics, revised Nov 2023.
  • Handle: RePEc:tow:wpaper:2023-08
    as

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    File URL: http://webapps.towson.edu/cbe/economics/workingpapers/2023-08.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Comparative statics; difference-in-differences; SUTVA; spillovers; profit maximization hypothesis; refutability; B-matrix.;
    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
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L21 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Business Objectives of the Firm

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