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Bayesian Estimation of Demand Functions under Block-Rate Pricing


  • Koji, Miyawaki

    (National Institute for Environmental Studies)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Akira Hibiki

    (National Institute for Environmental Studies)


This article proposes a Bayesian estimation of demand functions under block-rate pricing by focusing on increasing block-rate pricing. This is the first study that explicitly considers the separability condition which has been ignored in previous literature. Under this pricing structure, the 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 in which model parameters are strongly restricted by the separability condition. In this article, by 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 then applied to estimate the Japanese residential water demand function.

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  • Koji, Miyawaki & Yasuhiro Omori & Akira Hibiki, 2010. "Bayesian Estimation of Demand Functions under Block-Rate Pricing," CIRJE F-Series CIRJE-F-712, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2010cf712

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    References listed on IDEAS

    1. Hanemann, W Michael, 1984. "Discrete-Continuous Models of Consumer Demand," Econometrica, Econometric Society, vol. 52(3), pages 541-561, May.
    2. Herriges, Joseph A & King, Kathleen Kuester, 1994. "Residential Demand for Electricity under Inverted Block Rates: Evidence from a Controlled Experiment," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 419-430, October.
    3. 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.
    4. Hausman, Jerry A, 1985. "The Econometrics of Nonlinear Budget Sets," Econometrica, Econometric Society, vol. 53(6), pages 1255-1282, November.
    5. Burtless, Gary & Hausman, Jerry A, 1978. "The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiments," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 1103-1130, December.
    6. Julie A. Hewitt & W. Michael Hanemann, 1995. "A Discrete/Continuous Choice Approach to Residential Water Demand under Block Rate Pricing," Land Economics, University of Wisconsin Press, vol. 71(2), pages 173-192.
    7. Kunitomo, Naoto & Sato, Seisho, 1996. "Asymmetry in economic time series and the simultaneous switching autoregressive model," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 1-34, March.
    8. De Jong, G. C., 1990. "An indirect utility model of car ownership and private car use," European Economic Review, Elsevier, vol. 34(5), pages 971-985, July.
    9. Peter C. Reiss & Matthew W. White, 2005. "Household Electricity Demand, Revisited," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 853-883.
    10. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2013. "A Discrete/Continuous Choice Model on the Nonconvex Budget Set," CIRJE F-Series CIRJE-F-881, CIRJE, Faculty of Economics, University of Tokyo.
    6. Yuta Kurose & Yasuhiro Omori & Akira Hibiki, 2014. "A Discrete/Continuous Choice Model on a Nonconvex Budget Set," CIRJE F-Series CIRJE-F-942, CIRJE, Faculty of Economics, University of Tokyo.

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