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. 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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