Bayesian Inference for Sequential Treatments Under Latent Sequential Ignorability

• Activity Number: 155
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Fabrizia Mealli*+ and Alessandra Mattei and Federico Ricciardi
• Companies: University of Florence and University of Florence and University of Florence
• Keywords: Sequential treatments ; Principal stratification ; Latent sequential ignorability ; Rubin Causal Model ; Bayesian Inference ; Program evaluation

Abstract

We focus on the analysis of sequential treatments in observational studies. A questionable assumption usually invoked is Sequential Ignorability (SI). To relax SI, we rely on Principal Stratification, and introduce an assumption called Latent Sequential Ignorability (LSI), where latent? indicates that we condition on latent principal strata. We adopt the Bayesian approach for inference and propose additional Markov type assumptions to face the curse of dimensionality. Simulations are conducted to compare SI and LSI and show that when SI does not hold, inference performed under SI may lead to misleading conclusions. Conversely LSI generally leads to well-shaped posterior distributions centered around the true values irrespective of which assumption holds. Analyses conducted under LSI allow to assess the heterogeneity of effects across sub-groups characterized by different intermediate outcome values. We apply our framework to investigate the effects of interest free loans on firm employment policies: the effects are highly heterogeneous with respect to the intermediate firms' hiring behavior, highlighting some limits of inference drawn under SI for the entire population.