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Bayesian estimation of a simultaneous probit model using error augmentation: An application to multi-buying and churning behavior

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  • Subramanian Balachander

    ()

  • Bikram Ghosh

    ()

Abstract

Researchers in marketing are often interested in analyzing how an agent’s discrete choice decision affects a subsequent or concurrent discrete choice decision by the same or different agent. This analysis may necessitate the use of a simultaneous equations model with discrete and continuous endogenous variables as explanatory variables. In this paper, we offer an error augmentation approach to Hierarchical Bayesian estimation of a simultaneous bivariate probit model containing both discrete and continuous endogenous variables. We accomplish the error augmentation in our MCMC algorithm using a Metropolis-Hastings step that generates the error components of the latent variables in our model. Using simulated data, we demonstrate that our error augmentation algorithm recovers closely the true parameters of the simultaneous bivariate probit model. We then apply our algorithm to customer churn data from a wireless service provider. We formulate a simultaneous bivariate probit model to study the impact of a customer’s multiple product relationships with a firm (multi-buying) on the likelihood of churn by that customer. The empirical results show that the act of multi-buying significantly reduces churn even though the customers who are more predisposed to multi-buy have an inherently higher predisposition to churn. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Subramanian Balachander & Bikram Ghosh, 2013. "Bayesian estimation of a simultaneous probit model using error augmentation: An application to multi-buying and churning behavior," Quantitative Marketing and Economics (QME), Springer, vol. 11(4), pages 437-458, December.
  • Handle: RePEc:kap:qmktec:v:11:y:2013:i:4:p:437-458
    DOI: 10.1007/s11129-013-9137-z
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    References listed on IDEAS

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    1. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
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    8. Sanjog Misra, 2013. "Markov chain Monte Carlo for incomplete information discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 117-153, March.
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    More about this item

    Keywords

    Simultaneous probit model; Error augmentation; Hierarchical Bayesian estimation; Monte Carlo Markov Chain Algorithm; Customer retention; Customer churn; Customer relationship management; C11; C35; M31;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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