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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