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

47 Pages Posted: 3 Dec 2018

See all articles by Pennoni Fulvia

Pennoni Fulvia

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

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.

Keywords: Causality, Direct Marketing, Endogeneity, Expectation-Maximization Algorithm

JEL Classification: C10, C13, M30

Suggested Citation

Fulvia, Pennoni 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

Pennoni Fulvia (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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