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A Simple Approach to Treatment Effects on Durations When the Treatment Timing is Chosen

Author

Listed:
  • Lee, Myoung-jae

    () (Korea University)

  • Johansson, Per

    () (Uppsala University)

Abstract

When a treatment unambiguously defines the treatment and control groups at a given time point, its effects are usually found by comparing the two groups' mean responses. But there are many cases where the treatment timing is chosen, for which the conventional approach fails. This paper sets up an ideal causal framework for such cases to propose a simple gamma-mixed proportional-hazard approach with three durations: the waiting time until treatment, the untreated duration from the baseline, and the treated duration from the treatment timing. To implement the proposal, we use semiparametric piecewise-constant hazards as well as Weibull hazards with a multiplicative gamma unobserved heterogeneity affecting all three durations. Despite the three durations interwoven in complex ways, surprisingly simple closed-form likelihoods are obtained whose maximization converges well. The estimators are applied to the same data as used by Fredriksson and Johansson (2008) for employment subsidy effects on unemployment duration to find about 11.1 month reduction.

Suggested Citation

  • Lee, Myoung-jae & Johansson, Per, 2013. "A Simple Approach to Treatment Effects on Durations When the Treatment Timing is Chosen," IZA Discussion Papers 7249, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp7249
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    References listed on IDEAS

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    1. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    2. de Luna, Xavier & Johansson, Per, 2009. "Non-Parametric Inference for the Effect of a Treatment on Survival Times with Application in the Health and Social Sciences," IZA Discussion Papers 3966, Institute for the Study of Labor (IZA).
    3. Fredriksson, Peter & Johansson, Per, 2008. "Dynamic Treatment Assignment," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 435-445.
    4. Han, Aaron & Hausman, Jerry A, 1990. "Flexible Parametric Estimation of Duration and Competing Risk Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(1), pages 1-28, January-M.
    5. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    6. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    7. Carling, Kenneth & Richardson, Katarina, 2004. "The relative efficiency of labor market programs: Swedish experience from the 1990s," Labour Economics, Elsevier, vol. 11(3), pages 335-354, June.
    8. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710.
    9. Gaure, Simen & Roed, Knut & Zhang, Tao, 2007. "Time and causality: A Monte Carlo assessment of the timing-of-events approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1159-1195, December.
    10. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
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    More about this item

    Keywords

    treatment effect; duration; treatment timing; proportional hazard; gamma heterogeneity;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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