Remodeling the Working-Kaldor Curve: The Roles of Scarcity, Time to Maturity and Time to Harvest

Abstract

This paper proposes that, when modeling for the relation between the convenience yield and current scarcity, time to maturity and time to harvest should interact with current scarcity, i.e. the two should enter multiplicatively. In implementing this idea we also compare three models for current scarcity, based on inventory levels, the spot price or both. We use data for corn, wheat and soybeans, 1/1986 to 7/2007. The multiplicative model performs noticeably better than the traditional version, which only focuses on the measurement for scarcity and not on the nature of the relation between scarcity, time to maturity, harvest and convenience yield. More importantly, though the combination of spot price and inventory provides a better proxy for scarcity than either spot price or inventory separately, the pure spot-price version performs nearly as well as the spot/inventory combination, and much better than the pure inventory version. This is useful because inventory data are typically hard to obtain and increasingly noisy. Our model still exhibits a clear “Working curve”, albeit with slopes changing with time to maturity and harvest periods. We can also show that the multiplicative model still works better than the traditional model even during the government loan program period in the middle 1980’s and that the program seems to have little impact on modeling the convenience yield. Nor did the changing in the delivery system for corn and soybeans, as of 2000, have a big impact.

Keywords: backwardation, convenience yield, theory of storage, scarcity

JEL Classification: G12, G14, G1, N32, N52, Q11