Modelling time of day substitution using the second moments of demand

Time of day (TOD) rates are a commonly used method for peak load pricing of many services. Such services as; electricity, communications, transportation, shared computer facilities, and computer networks (i.e. the Internet), either use, or will use, some form of TOD pricing. However, TOD rates do not ensure a movement towards economic efficiency unless the patterns of TOD substitution are known. The model presented here provedes a method for estimating TOD substitution without the need for rate experiments that have proven to be both costly and limited by sample selection bias problems. This model employs the estimated second moment of demand to estimate a matrix of relative own- and cross-price elasticities and it can estimate elasticities even when there is no apparent TOD price variation. The low level of computations required for the estimates allows the application of a bootstrap procedure to estimate the covariance matrix of the elasticities. Two applications of this model are presented: a case of aggregate demand for computer services and a case of an individual household's electricity demand.