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The treatment effect, the cross difference, and the interaction term in nonlinear “difference-in-differences” models

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  • Puhani, Patrick A.

Abstract

In any nonlinear “difference-in-differences” model with strictly monotonic transformation function, the treatment effect is the cross difference of the observed outcome minus the cross difference of the potential non-treatment outcome, which equals the incremental effect of the interaction term coefficient.

Suggested Citation

  • Puhani, Patrick A., 2012. "The treatment effect, the cross difference, and the interaction term in nonlinear “difference-in-differences” models," Economics Letters, Elsevier, vol. 115(1), pages 85-87.
  • Handle: RePEc:eee:ecolet:v:115:y:2012:i:1:p:85-87
    DOI: 10.1016/j.econlet.2011.11.025
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    1. Richard Blundell & Monica Costa Dias, 2009. "Alternative Approaches to Evaluation in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 44(3).
    2. Richard Blundell & Monica Costa Dias, 2002. "Alternative approaches to evaluation in empirical microeconomics," CeMMAP working papers 10/02, Institute for Fiscal Studies.
    3. Richard Blundell & Monica Costa Dias, 2008. "Alternative approaches to evaluation in empirical microeconomics," CeMMAP working papers 26/08, Institute for Fiscal Studies.
    4. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    5. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    6. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
    7. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    8. Meyer, Bruce D, 1995. "Natural and Quasi-experiments in Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 151-161, April.
    9. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    10. Heckman, James J. & Lalonde, Robert J. & Smith, Jeffrey A., 1999. "The economics and econometrics of active labor market programs," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 31, pages 1865-2097, Elsevier.
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    More about this item

    Keywords

    Identification; Potential outcomes; Probit; Logit; Tobit;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • H0 - Public Economics - - General
    • I0 - Health, Education, and Welfare - - General
    • J0 - Labor and Demographic Economics - - General

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