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

44 Pages Posted: 3 Dec 2018 Last revised: 1 Nov 2021

See all articles by Fulvia Pennoni

Fulvia Pennoni

Department of Statistics and Quantitative Methods University of Milano-Bicocca

Leo Paas

Massey University - School of Communication, Journalism and Marketing

Francesco Bartolucci

Università di Perugia - Finanza e Statistica - Dipartimento di Economia

Date Written: November 8, 2018

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

Suggested Citation

Pennoni, Fulvia and Paas, Leo and Bartolucci, Francesco, Inverse-Probability-of-Treatment Weighting for Endogeneity Correction: A Hidden Markov Model for Assessing Effects of Multiple Direct Mail Campaigns (November 8, 2018). Available at SSRN: https://ssrn.com/abstract=3281156 or http://dx.doi.org/10.2139/ssrn.3281156

Fulvia Pennoni (Contact Author)

Department of Statistics and Quantitative Methods University of Milano-Bicocca ( email )

Piazza dell’Ateneo Nuovo 1, 20126 Milano
Milano, 20126
Italy

Leo Paas

Massey University - School of Communication, Journalism and Marketing

United States

Francesco Bartolucci

Università di Perugia - Finanza e Statistica - Dipartimento di Economia ( email )

06123

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