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Bayesian Estimation of Demand Functions under Block Rate Pricing

  • Koji Miyawaki

    (Graduate School of Economics, University of Tokyo)

  • Yasuihro Omori

    (Faculty of Economics, University of Tokyo)

  • Akira Hibiki

    (National Institute for Environmental Studies and Department of Social Engineering, Tokyo Institute of Technology)

This article proposes a Bayesian estimation method of demand functions under block rate pricing, focusing on increasing one. 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. We apply the so-called discrete/continuous choice approach to derive the corresponding demand function. Taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to estimate the demand function. Moreover, a separability condition is explicitly considered to obtain proper estimates. 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. The model is also extended to allow random coefficients for panel data and spatial correlation for spatial data. These proposed methods are applied to estimate the Japanese residential water and electricity demand function.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-568.

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Length: 46 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:tky:fseres:2008cf568
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  1. 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.
  2. 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.
  3. Hanemann, W Michael, 1984. "Discrete-Continuous Models of Consumer Demand," Econometrica, Econometric Society, vol. 52(3), pages 541-61, May.
  4. 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.
  5. G. Burtless & J. A. Hausman, 1977. "The Effect of Taxation on Labor Supply: Evaluating the Gary Negative Income Tax Experiment," Working papers 211, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. 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 419-30, October.
  7. Hausman, Jerry A, 1985. "The Econometrics of Nonlinear Budget Sets," Econometrica, Econometric Society, vol. 53(6), pages 1255-82, November.
  8. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
  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. 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.
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