Essays On The Competitive Commodity Storage Model
This dissertation consists of three essays on the competitive commodity storage model. This model provides a basis for rationalizing many of the observed qualitative features of the behavior of prices of storable commodities. I attempt to make a contribution to this model in three dimensions: empirical (chapter 1), numerical (chapter 2), and theoretical (chapter 3).
In the first chapter, I analyze the ability of the standard commodity storage model to replicate serial correlation in annual prices. Calendar year averages of prices induce spurious smoothing of price spikes, a fact that has been surprisingly overlooked in several empirical studies of the annual commodity storage model for agricultural commodities. I present an application of a maximum likelihood estimator of the storage model for maize prices, correcting for the spurious smoothing. My results, using this data set, imply serious differences in magnitudes of interest. These differences include the location and skewness of the empirical distribution of prices relative to the cutoff price of zero stocks, the likelihood of stockouts, and the fit to data on stocks-to-use ratios.
In the second chapter, I propose an alternative numerical strategy for solving nonlinear rational expectation models with inequality constraints. It addresses three problems observed in the standard solution method: lack of robustness to scaling transformation of the stationary rational expectation function, errors of approximation due to extrapolation within the ergodic set, and interpolation around the kink implied by the inequality constraint. In comparison with the standard solution method, my findings suggest that the numerical strategy I propose is robust to scaling transformation, removes the approximation errors due to extrapolation, and avoids interpolation above the kink.
Finally in the third chapter, I present a critique of a theoretical version of the competitive commodity storage model that assumes a support for the speculative storage that is bounded from below at zero, and above at a exogenous predetermined maximum capacity. By proposing a counter-example, I show that the fixed point iteration operator proposed by Oglend and Kleppe (2017) to solve this version of the model does not converge in general, as they claim.