Endogenous thresholds in energy prices: Modeling and empirical estimation

Spot prices or front-month futures prices for energy commodities can exhibit occasional sharp peaks and drops (even to negative values), accompanied by large backwardations or contangos and unusually low or high levels of working stocks. We present a model of storage arbitrage that rationalizes such episodes, relevant for markets for energy commodities such as petroleum, natural gas, or storable electricity, where free disposal is not available. Based on price data only, we offer an empirical approach to estimate key parameters that determine the dynamics of prices, including endogenous price thresholds that indicate lower and upper bounds on discretionary stocks. Price movements in the regime within these bounds are moderated by responses of speculative storage. In the two regimes where price is respectively above or below threshold prices, sharp price jumps are more likely. We are the first to prove consistency and asymptotic normality of a method of estimating this model on prices with endogenous jumps. We explore the behavior of our estimator for small samples, and illustrate its application using petroleum prices. Although the model structure and the distributions of the disturbances in the Euler equation are quite complex, a nice feature of our estimator is its simplicity; it is straightforward non-linear least squares. Moreover, our estimation approach is robust to the demand functional form and the distribution of the shocks.