A Practitioner's Guide to Bayesian Estimation of Discrete Choice Dynamic Programming Models

Quantitative Marketing and Economics, Forthcoming

62 Pages Posted: 7 May 2009 Last revised: 15 Jan 2012

See all articles by Andrew T. Ching

Andrew T. Ching

Johns Hopkins University - Carey Business School

Susumu Imai

Queen's University - Department of Economics

Masakazu Ishihara

New York University (NYU) - Leonard N. Stern School of Business

Neelam Jain

City University London

Date Written: October 27, 2011

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, Jain and Ching, Econometrica 77:1865-1899, 2009) (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 reward programs. We show that the parameters of this model, including the discount factor, are well-identified. 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, D90, M31

Suggested Citation

Ching, Andrew T. and Imai, Susumu and Ishihara, Masakazu and Jain, Neelam, A Practitioner's Guide to Bayesian Estimation of Discrete Choice Dynamic Programming Models (October 27, 2011). Quantitative Marketing and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1398444 or http://dx.doi.org/10.2139/ssrn.1398444

Andrew T. Ching (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Susumu Imai

Queen's University - Department of Economics ( email )

99 University Avenue
Kingston K7L 3N6, Ontario
Canada

HOME PAGE: http://qed.econ.queensu.ca/pub/faculty/imai/

Masakazu Ishihara

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Neelam Jain

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

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