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

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. r

Estimating a treatment effect under uncertainty with application to a high‐speed railway system

“…To address such an aspect, the dynamic treatment effect model with panel data is necessary. Chib & Jacobi () proposed a treatment effect model for the panel data and its Bayesian estimation. An extension of their model within our framework is an important future work.…”

Risk-shifting, Regulation and Government Assistance

“…This model offers two salient extensions to the potential outcome framework of Rubin (1978) applied in longitudinal settings Hamilton, 2000, 2002;Chib and Jacobi, 2007). First, the standard joint model of treatment assignment and potential outcomes is extended into a difference-in-difference framework so that the treated and control groups are observed before and after the assignment of a treatment and not solely in the post-treatment period.…”

A Bayesian analysis of payday loans and their regulation

“…As the notation of (13) makes clear, draws from (13) are conditional upon values of the covariates x f . To eliminate this dependence in our results, we follow Chib and Jacobi (2007) and sample values of the covariates that are not involved in the construction of our counterfactual from the empirical distribution of covariates in our sample. We do this for each iteration of the sampler.…”