We develop and test a model describing the influence of natural gas storage on the electricity forward premium. The model is constructed by linking the effect of gas storage on the higher moments of the distribution of electricity prices to an established model of the effect of those moments on the forward premium. The model predicts a (weakly) positive effect of gas storage on the electricity forward premium when loads are light, but a sharply negative effect when demand for electricity is high and demand for gas is low. The model predicts a daily pattern of stronger effects in the afternoon. Empirical results, based on PJM data, strongly support the model.