Inverse-probability-of-treatment weighting for endogeneity correction: A hidden Markov model for assessing effects of multiple direct mail campaigns

We extend the hidden Markov model with a novel dynamic version of the inverse- probability-of-treatment weighting methodology for endogeneity correction. The static weighed estimator, as applied in other fields, is less applicable due to the dynamics in firms’ marketing strategies. The method results in an assessment of causal effects by replicating a randomized field experiment setting through weighting. The likelihood function of the model is maximized through the Expectation-Maximization algorithm that is suitably modified to account for the weights. Standard errors of the parameters are provided by a non-parametric bootstrap method. We assess the effects of multiple direct mailings on customers’ financial product portfolio developments at a large European bank. Prospects have been selected by managers based on the assumed probability to respond; hence giving rise to a classical endogeneity issue. We compare the proposal with standard hidden Markov models and we perform a simulation study computing the bias of the proposed approach as the difference between the estimates obtained under a randomized experiment and those obtained by adding covariates as observed confounders.