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Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator


  • Bartolucci, Francesco
  • Grilli, Leonardo
  • Pieroni, Luca


We consider estimation of the causal effect of a sequential binary treatment (typically corresponding to a policy or a subsidy in the economic context) on a final outcome, when the treatment assignment at a given occasion depends on the sequence of previous assignments as well as on time-varying confounders. In this case, a popular modeling strategy is represented by Marginal Structural Models; within this approach, the causal effect of the treatment is estimated by the Inverse Probability Weighting (IPW) estimator, which is consistent provided that all the confounders are observed (sequential ignorability). To alleviate this serious limitation, we propose a new estimator, called Latent Class Inverse Probability Weighting (LC-IPW), which is based on two steps: first, a finite mixture model is fitted in order to compute latent-class-specific weights; then, these weights are used to fit the Marginal Structural Model of interest. A simulation study shows that the LC-IPW estimator outperforms the IPW estimator for all the considered configurations, even in cases of no unobserved confounding. The proposed approach is applied to the estimation of the causal effect of wage subsidies on employment, using a dataset of Finnish firms observed for eight years. The LC-IPW estimate confirms the existence of a positive effect, but its magnitude is nearly halved with respect to the IPW estimate, pointing out the substantial role of unobserved confounding in this setting.

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  • Bartolucci, Francesco & Grilli, Leonardo & Pieroni, Luca, 2012. "Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator," MPRA Paper 43430, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43430

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    References listed on IDEAS

    1. Aki Kangasharju, 2007. "Do Wage Subsidies Increase Employment in Subsidized Firms?," Economica, London School of Economics and Political Science, vol. 74(293), pages 51-67, February.
    2. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 195-212, September.
    3. Matz Dahlberg & Anders Forslund, 2005. "Direct Displacement Effects of Labour Market Programmes," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(3), pages 475-494, September.
    4. GrĂ¼n, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    5. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    6. van der Wal, Willem M. & Geskus, Ronald B., 2011. "ipw: An R Package for Inverse Probability Weighting," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i13).
    7. Andrea Rotnitzky & Lingling Li & Xiaochun Li, 2010. "A note on overadjustment in inverse probability weighted estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 997-1001.
    8. Lechner, Michael, 2009. "Sequential Causal Models for the Evaluation of Labor Market Programs," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 71-83.
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    More about this item


    Causal inference; Longitudinal design; Mixture model; Potential outcomes; Sequential treatment;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • H25 - Public Economics - - Taxation, Subsidies, and Revenue - - - Business Taxes and Subsidies
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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