A causal hidden Markov model for assessing effects of multiple direct mail campaigns

We propose assessing the causal effects of a dynamic treatment in a longitudinal observational study, given observed confounders under suitable assumptions. The causal hidden Markov model is based on potential versions of discrete latent variables, and it accounts for the estimated propensity to be assigned to each treatment level over time using inverse probability weighting. Estimation of the model parameters is carried out through a weighted maximum log-likelihood approach. Standard errors for the parameter estimates are provided by nonparametric bootstrap. The proposal is validated through a simulation study aimed at comparing different model specifications. As an illustrative example, we consider a marketing campaign conducted by a large European bank over time on its customers. Findings provide straightforward managerial implications.