Koji Miyawaki

Panel Data Analysis of Japanese Residential Water Demand Using a Discrete/Continuous Choice Approach

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing in addition to its best-known application in public utility services. Under block rate pricing, consumers face piecewise-linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise-linear budget constraints for demand and price endogeneity. A recent study proposed a methodology to incorporate a separability condition that previous studies ignore, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes a Bayesian hierarchical model incorporating the individual effect. The random coefficients model result shows that the price and income elasticities are estimated to be negative and positive, respectively, and the coefficients of the number of members and the number of rooms per household are estimated to be positive. Furthermore, the AR(1) error component model suggests that the Japanese residential water demand does not have serial correlation.

Panel Data Analysis Of Japanese Residential Water Demand Using A Discrete/Continuous Choice Approach

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing in addition to its best-known application in public utility services. Under block rate pricing, consumers face piecewise-linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise-linear budget constraints for demand and price endogeneity. A recent study proposed a methodology to incorporate a separability condition that previous studies ignore, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes a Bayesian hierarchical model incorporating the individual effect. The random coefficients model result shows that the price and income elasticities are estimated to be negative and positive, respectively, and the coefficients of the number of members and the number of rooms per household are estimated to be positive. Furthermore, the AR(1) error component model suggests that the Japanese residential water demand does not have serial correlation.

Exact Estimation of Demand Functions under Block-Rate Pricing

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.

A discrete/continuous choice model on a nonconvex budget set

ABSTRACT Decreasing block rate pricing is a nonlinear price system often used for public utility services. Residential gas services in Japan and the United Kingdom are provided under this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which has not been examined in previous studies, arises because a consumer’s budget set (a set of affordable consumption amounts) is nonconvex, and hence, the resulting model includes highly nonlinear functions. To address this problem, we propose a feasible, efficient method of demand estimation on the nonconvex budget. The advantages of our method are as follows: (i) the construction of an Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite–Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.

PANEL DATA ANALYSIS OF JAPANESE RESIDENTIAL WATER DEMAND USING A DISCRETE/CONTINUOUS CHOICE APPROACH*: K. Miyawaki, Y. Omori, A. Hibiki: Panel Data Analysis

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing in addition to its best-known application in public utility services. Under block rate pricing, consumers face piecewise-linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise-linear budget constraints for demand and price endogeneity. A recent study proposed a methodology to incorporate a separability condition that previous studies ignore, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes a Bayesian hierarchical model incorporating the individual effect. The random coefficients model result shows that the price and income elasticities are estimated to be negative and positive, respectively, and the coefficients of the number of members and the number of rooms per household are estimated to be positive. Furthermore, the AR(1) error component model suggests that the Japanese residential water demand does not have serial correlation.