Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technologies

We model the properties of equilibrium spot and futures oil prices in a general equilibrium production economy with two goods. In our model production of the consumption good requires two inputs: the consumption good and a Oil. Oil is produced by wells whose flow rate is costly to adjust. Investment in new Oil wells is costly and irreversible. As a result in equilibrium, investment in Oil wells is infrequent and lumpy. Equilibrium spot price behavior is determined as the shadow value of oil. The resulting equilibrium oil price exhibits mean-reversion and heteroscedasticity. Further, even though the state of the economy is fully described by a one-factor Markov process, the spot oil price is not Markov (in itself). Rather it is best described as a regime-switching process, the regime being an investment `proximity' indicator. Further, our model captures many of the stylized facts of oil futures prices. The futures curve exhibits backwardation as a result of a convenience yield, which arises endogenously due to the productive value of oil as an input for production. This convenience yield is decreasing in the amount of oil available in the economy. We calibrate our model with economic aggregate data and crude oil futures prices. The models does a good job in matching the first two moments of the futures curves and the average consumption of oil-output and output-consumption of capital ratios from the macroeconomic data. The calibration results suggest the presence of convex adjustment costs for the investment in new oil wells. We also test a linear approximation of the equilibrium regime-shifting dynamics implied by our model. Our empirical specification successfully captures spot and futures data. Finally, the specific empirical implementation we use is designed to easily facilitate commodity derivative pricing that is common in two-factor reduced form pricing models.