Inverse-Probability-of-Treatment Weighting for Endogeneity Correction: A Hidden Markov Model for Assessing Effects of Multiple Direct Mail Campaigns

Abstract

A multivariate hidden Markov model is proposed with a dynamic version of the inverse-probability-of-treatment weighting methodology for endogeneity correction.
The method results in assessing the average treatment effects by replicating a randomized experiment using counterfactual reasoning. The likelihood function of the model is maximized through the Expectation-Maximization algorithm that is suitably modified to account for the estimated time-varying individual weights
related to the probability of
receiving the treatment given pre-treatment covariates. Standard errors of the parameters are provided by applying non-parametric bootstrap. An extensive simulation study is performed to evaluate the finite sample properties of the proposed estimator
and to compare the proposal
with alternative estimators with covariates and without weights.
In the empirical illustration, we assess the effects of multiple direct mailings on customers' financial product portfolios at a large European bank.

Keywords: causality, direct marketing, expectation-maximization algorithm, latent Markov model

JEL Classification: C10, C13, M30