Bartolucci, Francesco and Grilli, Leonardo and Pieroni, Luca (2012): Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator.

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Abstract
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 timevarying 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 (LCIPW), which is based on two steps: first, a finite mixture model is fitted in order to compute latentclassspecific weights; then, these weights are used to fit the Marginal Structural Model of interest. A simulation study shows that the LCIPW 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 LCIPW 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.
Item Type:  MPRA Paper 

Original Title:  Estimating dynamic causal effects with unobserved confounders: a latent class version of the inverse probability weighted estimator 
Language:  English 
Keywords:  Causal inference, Longitudinal design, Mixture model, Potential outcomes, Sequential treatment 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection H  Public Economics > H2  Taxation, Subsidies, and Revenue > H25  Business Taxes and Subsidies C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C33  Panel Data Models ; Spatiotemporal Models 
Item ID:  43430 
Depositing User:  Luca Pieroni 
Date Deposited:  26 Dec 2012 14:55 
Last Modified:  06 Oct 2016 20:45 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43430 