Modeling and calculating the effect of treatment at baseline from panel outcomes |
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Authors: | Siddhartha Chib Liana Jacobi |
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Affiliation: | aJohn M. Olin School of Business, Campus Box 1133, Washington University in St. Louis, 1 Brookings Dr., St. Louis, MO 63130, USA;bDepartment of Economics, The University of Melbourne, Victoria 3010, Australia |
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Abstract: | We propose and examine a panel data model for isolating the effect of a treatment, taken once at baseline, from outcomes observed over subsequent time periods. In the model, the treatment intake and outcomes are assumed to be correlated, due to unobserved or unmeasured confounders. Intake is partly determined by a set of instrumental variables and the confounding on unobservables is modeled in a flexible way, varying both by time and treatment state. Covariate effects are assumed to be subject-specific and potentially correlated with other covariates. Estimation and inference is by Bayesian methods that are implemented by tuned Markov chain Monte Carlo methods. Because our analysis is based on the framework developed by Chib [2004. Analysis of treatment response data without the joint distribution of counterfactuals. Journal of Econometrics, in press], the modeling and estimation does not involve either the unknowable joint distribution of the potential outcomes or the missing counterfactuals. The problem of model choice through marginal likelihoods and Bayes factors is also considered. The methods are illustrated in simulation experiments and in an application dealing with the effect of participation in high school athletics on future labor market earnings. |
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Keywords: | Confounding Heterogeneity Instrumental variable Marginal likelihood Markov chain Monte Carlo Metropolis– Hastings algorithm Non-randomly assigned treatment Panel data Potential outcomes Treatment effect |
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