Bayesian Estimation of Demand Functions under Block Rate Pricing
This article proposes a Bayesian estimation method of demand functions under block rate pricing, focusing on increasing one, where we first considered the separability condition explicitly which has been ignored in the previous literature. 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. Solving this maximization problem leads to a statistical model that includes many inequalities, such as the so-called separability condition. Because of them, it is virtually impractical to numerically maximize the likelihood function. Thus, 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 applied to estimate the Japanese residential water demand function.
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