"Duality-Based Analysis of Residential Gas Demand under Decreasing Block Rate Pricing"

This paper discusses a novel estimation method for the residential gas demand function in Japan where the price per unit decreases as the demand exceeds certain thresholds. Such a price system is known as decreasing block rate pricing. The demand function under decreasing block rate pricing is derived by using the well-known discrete/continuous choice approach. However, because of the nonconvex budget set, the conventional approach imposes highly nonlinear constraints on the model parameters, thus making the maximization of the likelihood function under such constraints difficult to implement. To overcome this difficulty, we first apply the duality relationship in consumer theory, and approximate the conditional expenditure in order to linearize these nonlinear constraints. Then, we adopt a Bayesian approach with the Markov chain Monte Carlo simulation in order to estimate the model parameters under linear constraints. Our proposed method is illustrated by a numerical example and is adopted to analyze the demand for residential gas in Japan.

"Tobit Model with Covariate Dependent Thresholds"

Tobit models are extended to allow threshold values which depend on individuals' characteristics. In such models, the parameters are subject to as many inequality constraints as the number of observations, and the maximum likelihood estimation which requires the numerical maximisation of the likelihood is often difficult to be implemented. Using a Bayesian approach, a Gibbs sampler algorithm is proposed and, further, the convergence to the posterior distribution is accelerated by introducing an additional scale transformation step. The procedure is illustrated using the simulated data, wage data and prime rate changes data.

"Discrete/Continuous Choice Model of the Residential Gas Demand on the Nonconvex Budget Set"

The discrete/continuous choice approach is often used to analyze the demand for public utility services under block rate pricing, which is a nonlinear price system. Although a consumer's budget set is convex under increasing block rate pricing, a consumer's budget set is nonconvex under decreasing block rate pricing as is the case with the gas supply in Japan and the United Kingdom. The nonlinearity problem, which has not been examined in previous studies, arises under nonconvex budget sets in which the indirect utility function corresponding to the demand function becomes highly nonlinear. To address this problem, this article proposes a feasible, efficient method of demand on the nonconvex budget set and implements a case study using household-level data on Japanese residential gas consumption. The advantages of our method are as follows: (i) the construction of an efficient 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.

"Bayesian Estimation of Demand Functions under Block-Rate Pricing"

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.

"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.

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.Block rate pricing, Bayesian analysis, Panel data, residential water demand

"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 random and fixed individual effects. In both models, the price and income elasticities are estimated to be negative and positive, respectively. Further, the number of members and the number of rooms per household have positive relationship to the residential water demand when we apply the model with random individual effects, while they do not in the model with fixed individual effects.

Research on the Activity of Components in Fundamental System in Iron Blast Furnace Slag. III : Measurement of the Activity of Silica and Alumina in CaO-MgO-SiO_2-Al_2O_3 System

Our previous reports described the determination of activity of SiO_2 and Al_2O_3 in the slag of CaO-SiO_2-Al_2O_3 system by using the e. m. f. method of double cell. The present study investigated the effect of MgO on the activity of SiO_2 and Al_2O_3. From the experimental results it was found that at a constant concentration of Al_2O_3, activity coefficient of SiO_2, γ SiO_2 increased as substitution of MgO for CaO increased. With the addition of MgO, the activity of silica approached Raoult\u27s law. At a constant MgO concentration, the amphoteric nature of Al_2O_3 was clarified as in CaO-SiO_2Al_2O_3 system. Concerning the effect of MgO on the activity of Al_2O_3, an intimate relation exists between αAl_2O_5 and basicity, that is, by chosing the basicity as N_/N_, a relationship could be found between log αAl_2O_3 and basicity which corresponded to the results obtained in the slag of CaO-SiO_2-Al_2O_3 System. The above facts show the behaviour of MgO which acts as a base

Research on the Activity of Components in Fundamental System of Iron Blast Furnace Slag. II : Measurement of the Activity of Alumina in the System CaO-SiO_2-Al_2O_3

The e. m. f. of the following cell Fe-Al-C_ | CaO-SiO_2-Al_2O_3 (I) | C or MgO | CaO-SiO_2-Al_2O_3 (II) | Fe-Al-C_. was measured at 1630℃ with the reference slags CaO 45.2, SiO_2 2.2 and Al_2O_3 53.7 wt % respectively. It was found that the e. m. f. sharply increased with increasing concentration of lime, and then decreased gradually. On the other hand, with constant alumina series, a marked increase of the e. m. f. was observed in the range near the liquidus of 2CaO-SiO_2. Now choosing the standard state as the solid alumina at 1630℃, the activity of alumina. in a given slag was calculated from the e. m. f. by the following equation : E=RT/6Flna_ From the authors\u27 data, the isoactivity lines were drawn on the ternary coordinates of CaO-SiO_2-Al_2O_3. And symmetrical isoactivity lines were obtained about the straight line connecting between 2CaO-SiO_2 at CaO-SiO_2 system and Al_2O_3 coordinate, which may be explained by the change of existing anion species of aluminum in the slag. Finally the most probable anion species and their stabilities were discussed

Early Development of Resident Macrophages in the Mouse Cochlea Depends on Yolk Sac Hematopoiesis

Resident macrophages reside in all tissues throughout the body and play a central role in both tissue homeostasis and inflammation. Although the inner ear was once believed to be “immune-privileged, ” recent studies have shown that macrophages are distributed in the cochlea and may play important roles in the immune system thereof. Resident macrophages have heterogeneous origins among tissues and throughout developmental stages. However, the origins of embryonic cochlear macrophages remain unknown. Here, we show that the early development of resident macrophages in the mouse cochlea depends on yolk sac hematopoiesis. Accordingly, our results found that macrophages emerging around the developing otocyst at E10.5 exhibited dynamic changes in distribution and in situ proliferative capacity during embryonic and neonatal stages. Cochlear examination in Csf1r-null mice revealed a substantial decrease in the number of Iba1-positive macrophages in the spiral ganglion and spiral ligament, whereas they were still observed in the cochlear mesenchyme or on the intraluminal surface of the perilymphatic space. Our results demonstrated that two subtypes of resident macrophages are present in the embryonic cochlea, one being Csf1r-dependent macrophages that originate from the yolk sac and the other being Csf1r-independent macrophages that appear to be derived from the fetal liver via systemic circulation. We consider the present study to be a starting point for elucidating the roles of embryonic cochlear resident macrophages. Furthermore, resident macrophages in the embryonic cochlea could be a novel target for the treatment of various inner ear disorders