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Bayesian Estimation of Demand Functions under Block Rate Pricing

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Author Info
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)

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Abstract

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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Publisher Info
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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  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 419-30, October.
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  4. John Geweke, 2004. "Getting It Right: Joint Distribution Tests of Posterior Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 799-804, January. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
  8. Olmstead, Sheila & Hanemann, Michael & Stavins, Robert, 2005. "Do Consumers React to the Shape of Supply? Water Demand Under Heterogeneous Price Structures," Working Paper Series rwp05-039, Harvard University, John F. Kennedy School of Government. [Downloadable!]
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  9. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639. [Downloadable!] (restricted)
  10. 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 1103-30, December. [Downloadable!] (restricted)
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  11. Sheila Olmstead & W. Michael Hanemann & Robert N. Stavins, 2007. "Water Demand Under Alternative Price Structures," NBER Working Papers 13573, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Misiolek, Walter S., 1980. "Effluent taxation in monopoly markets," Journal of Environmental Economics and Management, Elsevier, vol. 7(2), pages 103-107, June. [Downloadable!] (restricted)
  13. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99. [Downloadable!] (restricted)
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