Incentive regulation and efficiency analysis of network utilities often need to take the effect of important external factors, such as the weather conditions, into account. This paper presents a method for estimating the effect of weather conditions on the costs of electricity distribution networks using parametric techniques. It examines whether the use of popular statistical variable reduction techniques is conceptually and econometrically sound for analyzing the effect of weather on the network costs. In this paper we estimate cost functions with the whole set of weather variables, identifying, when necessary, a subset of variables that can accurately reflect the effects of weather conditions. We show that weather conditions significantly affect distribution costs and the absence of weather variables has a downward biased impact on the effect of quality on costs. Also, the performance of statistical weather composites to capture this effect is poor. Finally, we show that there is a distinction between the effects of persistent and time varying weather conditions