Real-time pricing of electricity for residential customers: Econometric analysis of an experiment
利用法国国有电力公司的六费率实时电价实验数据，通过估计弗里希需求函数和卡尔曼滤波方法，分析居民对实时电价的响应，发现该定价方案改善了多数参与者的福利。
Under real-time pricing, a network operator sets the price level for a period according to a predefined scheme which depends on the state of demand and costs, and announces this price shortly before the period begins. The French state-owned electric utility experimented with a six-rate real-time tariff, which divides the year into three types of days and each day into two periods. The number of days of each type is known in advance to the consumer, but the type of any particular day is announced only at the end of the preceding day. In order to evaluate the responsiveness of customers to this pricing option, we estimate the Frisch demand functions for daily electricity consumption, derived from a simple dynamic model based on an additively separable intertemporal utility function. As the marginal utility of expenditure which enters the Frisch demands follows a known stochastic process, the econometric model has a state-space representation. We can then apply the Kalman filter to compute the log-likelihood function associated with each consumer's time series of electricity consumption. The main result of the analysis is that the real-time tariff improves the welfare of a majority of consumers participating in the experiment.