# A practitioner’s guide to Bayesian estimation of discrete choice dynamic programming models

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## Abstract

This paper provides a step-by-step guide to estimating infinite horizon discrete choice dynamic programming (DDP) models using a new Bayesian estimation algorithm (Imai et al., Econometrica 77:1865–1899, 2009a) (IJC). In the conventional nested fixed point algorithm, most of the information obtained in the past iterations remains unused in the current iteration. In contrast, the IJC algorithm extensively uses the computational results obtained from the past iterations to help solve the DDP model at the current iterated parameter values. Consequently, it has the potential to significantly alleviate the computational burden of estimating DDP models. To illustrate this new estimation method, we use a simple dynamic store choice model where stores offer “frequent-buyer” type rewards programs. Our Monte Carlo results demonstrate that the IJC method is able to recover the true parameter values of this model quite precisely. We also show that the IJC method could reduce the estimation time significantly when estimating DDP models with unobserved heterogeneity, especially when the discount factor is close to 1.

### Keywords

Bayesian estimation Dynamic programming Discrete choice models Rewards programs### JEL Classification

C11 C35 C61 D91 M31## Notes

### Acknowledgements

We thank Martin Burda, Monica Meireles, Matthew Osborne, Peter Rossi, Andrei Strijnev, K. Sudhir, S. Siddarth and two anonymous referees for their helpful comments. We also thank the participants of the UCLA Marketing Camp, SBIES conference, Marketing Science Conference, Marketing Dynamics Conference, UTD-FORMS Conference, Canadian Economic Association Meeting, Econometric Society Meeting and Ph.D. seminars at OSU’s Fisher College of Business, Yale School of Management, University of Groningen, University of Zurich and University of Southern California for their useful feedback. Hyunwoo Lim provided excellent research assistance. All remaining errors are ours. Andrew Ching and Susumu Imai acknowledge the financial support from SSHRC.

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