Modeling and calculating the effect of treatment at baseline from panel outcomes

• Published in: Journal of econometrics Vol. 140; no. 2; pp. 781 - 801
• Main Authors: Chib, Siddhartha, Jacobi, Liana
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2007; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Algorithms; Applications; Bayesian analysis; Confounding; Counterfactual thinking; Earnings; Econometrics; Economic models; Exact sciences and technology; Heterogeneity; Impact analysis; Instrumental variable; Insurance, economics, finance; Labor market; Marginal likelihood; Markov analysis; Markov chain Monte Carlo; Markov processes; Markovian processes; Mathematics; Metropolis–Hastings algorithm; Monte Carlo simulation; Non-randomly assigned treatment; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Panel data; Parametric inference; Potential outcomes; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Secondary schools; Simulation; Sports; Statistics; Studies; Treatment effect; Instrumental variable; Heterogeneity; Metropolis–Hastings algorithm; Panel data; Potential outcomes; Markov chain Monte Carlo; Treatment effect; Confounding; Non-randomly assigned treatment; Marginal likelihood; Statistical distribution; Labour market; Metropolis-Hastings algorithm; Covariate; Stochastic method; Economic data; Implementation; Markov chain; Marginal distribution; Distribution function; Approximation theory; Bayes estimation; Economics; Monte Carlo method; Data analysis; Treatment efficiency; Econometric model; Statistical estimation; Joint distribution; Statistical method; Missing data; Numerical analysis; Simulation; Correlation analysis; Econometrics
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2006.07.014

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.