Futures Prices in a Production Economy with Investment Constraints

We document a new stylized fact regarding the term-structure of futures volatility. We show that the relation between the volatility of futures prices and the slope of the term structure of prices is non-monotone and has a %u201CV-shape%u201D'. This aspect of the data cannot be generated by basic models that emphasize storage while this fact is consistent with models that emphasize investment constraints or, more generally, time-varying supply-elasticity. We develop an equilibrium model in which futures prices are determined endogenously in a production economy in which investment is both irreversible and is capacity constrained. Investment constraints affect firms' investment decisions, which in turn determine the dynamic properties of their output and consequently imply that the supply-elasticity of the commodity changes over time. Since demand shocks must be absorbed either by changes in prices, or by changes in supply, time-varying supply-elasticity results in time-varying volatility of futures prices. Calibrating this model, we show it is quantitatively consistent with the aforementioned %u201CV-shape%u201D relation between the volatility of futures prices and the slope of the term-structure.