A discrete/continuous choice model on a nonconvex budget set

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.