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

  • Lee, Myoung-jae

    ()

    (Korea University)

  • Johansson, Per

    ()

    (IFAU)

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.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 7249.

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Length: 34 pages
Date of creation: Feb 2013
Date of revision:
Handle: RePEc:iza:izadps:dp7249
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  1. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-56, July.
  2. 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.
  3. Gaure, Simen & Røed, Knut & Zhang, Tao, 2005. "Time and Causality: A Monte Carlo Assessment of the Timing-of-Events Approach," Memorandum 19/2005, Oslo University, Department of Economics.
  4. Wooldridge, Jeffrey M. & Imbens, Guido, 2009. "Recent Developments in the Econometrics of Program Evaluation," Scholarly Articles 3043416, Harvard University Department of Economics.
  5. 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).
  6. Abbring, Jaap H & van den Berg, Gerard J, 2007. "The Unobserved Heterogeneity Distribution in Duration Analysis," CEPR Discussion Papers 6219, C.E.P.R. Discussion Papers.
  7. 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.
  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. 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.
  10. Fredriksson, Peter & Johansson, Per, 2008. "Dynamic Treatment Assignment," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 435-445.
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