Exact Estimation of Demand Functions under Block-Rate Pricing

Koji Miyawaki, Yasuhiro Omori, Akira Hibiki

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This article proposes an exact 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.

Original languageEnglish
Pages (from-to)311-343
Number of pages33
JournalEconometric Reviews
Issue number3
Publication statusPublished - 2016 Mar 15
Externally publishedYes


  • Discrete/continuous choice approach
  • Markov chain Monte Carlo method
  • Piecewise-linear budget constraint
  • Residential water demand
  • Separability condition

ASJC Scopus subject areas

  • Economics and Econometrics


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