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 "V-shape"'. 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 "V-shape" relation between the volatility of futures prices and
the slope of the term-structure.