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Bayesian Estimation of Demand Functions under Block Rate Pricing

Author

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  • Koji Miyawaki

    (Nihon University, Population Research Institute)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Akira Hibiki

    (Department of Social Engineering, Tokyo Institute of Technology)

Abstract

This article proposes a Bayesian estimation method of demand functions under block rate pricing, focusing on increasing one, where we first considered the separability condition explicitly which has been ignored in the previous literature. Under this pricing structure, price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. Solving this maximization problem leads to a statistical model that includes many inequalities, such as the so-called separability condition. Because of them, it is virtually impractical to numerically maximize the likelihood function. Thus, taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to properly estimate the demand function. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. These proposed methods are applied to estimate the Japanese residential water demand function.

Suggested Citation

  • Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2009. "Bayesian Estimation of Demand Functions under Block Rate Pricing," CIRJE F-Series CIRJE-F-631, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf631
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    References listed on IDEAS

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    1. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649, Elsevier.
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    6. Jasper M. Dalhuisen & Raymond J. G. M. Florax & JHenri L. F. de Groot & Peter Nijkamp, 2003. "Price and Income Elasticities of Residential Water Demand: A Meta-Analysis," Land Economics, University of Wisconsin Press, vol. 79(2), pages 292-308.
    7. Olmstead, Sheila M. & Michael Hanemann, W. & Stavins, Robert N., 2007. "Water demand under alternative price structures," Journal of Environmental Economics and Management, Elsevier, vol. 54(2), pages 181-198, September.
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    Cited by:

    1. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2010. "Discrete/Continuous Choice Model of the Residential Gas Demand on the Nonconvex Budget Set," CIRJE F-Series CIRJE-F-770, CIRJE, Faculty of Economics, University of Tokyo.
    2. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2011. "Panel Data Analysis Of Japanese Residential Water Demand Using A Discrete/Continuous Choice Approach," The Japanese Economic Review, Japanese Economic Association, vol. 62(3), pages 365-386, September.
    3. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2018. "A discrete/continuous choice model on a nonconvex budget set," Econometric Reviews, Taylor & Francis Journals, vol. 37(2), pages 89-113, February.
    4. Kertous, Mourad & Zerzour, Sahad, 2015. "To pay or not to pay? Water bill and delay in payment in Bejaia (Algeria): A duration analysis," MPRA Paper 67801, University Library of Munich, Germany.
    5. Henrique Monteiro, 2010. "Residential Water Demand in Portugal: checking for efficiency-based justifications for increasing block tariffs," Working Papers Series 1 ercwp0110, ISCTE-IUL, Business Research Unit (BRU-IUL).
    6. Koji Miyawaki & Yasuhiro Omori, 2007. "Duality-Based Analysis of Residential Gas Demand under Decreasing Block Rate Pricing," CIRJE F-Series CIRJE-F-506, CIRJE, Faculty of Economics, University of Tokyo.

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