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

42 Pages Posted: 16 Feb 2009

See all articles by Katelijne A. E. Carbonez

Katelijne A. E. Carbonez

KU Leuven - Faculty of Business and Economics (FEB)

Van Thi Tuong Nguyen

KU Leuven

Piet Sercu

FEB at KU Leuven

Date Written: February 16, 2009


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. In implementing this idea we compare three models for current scarcity, based on inventory levels, the spot price or both. We use 72 years of weekly data from two different periods, 1/1885 to 12/1935 and 1/1985 to 7/2007, and we study contracts for corn, wheat, and oats in the first period; and for corn, wheat and soybeans in the second period.

Our proposed model performs noticeably better than the traditional model that only focuses on the measurement for scarcity and not on the nature of the relation between scarcity, time to maturity and convenience yield. More importantly, though the combination of spot price and inventory is a better proxy for scarcity than either spot price or inventory separately, the new spot price model performs nearly as well as the new model with the combined proxy. In addition, the new spot price model always beats the new inventory model even in periods where inventory is more informative than spot prices in the traditional models used before. This is important because inventory data are typically hard to obtain and noisy. Our model still exhibits a clear "Working curve'', with slopes changing with time to maturity and harvest periods.

In the recent data, the spot price was much more informative than either inventory or inventory and time to maturity. We try out, and reject, four explanations: the unusual peak prices in the early 1990s, an unnecessarily narrow definition of inventories (Chicago v the Great Lakes or the entire U.S.), inadequacies caused by normalization, an possible influx of speculative money, and the lengthening of the contracts between now and then. Thus, the fact that prices used to be less informative remains a bit of a puzzle. However, there is a structural break on convenience yield and spot prices during early 1997, but we cannot identify the cause. The success of the traditional inventory model in the past probably reflects the better relevance of the inventory data: Chicago used to hold a far bigger share of nationwide supplies, and we find no seasonals or other hints that could indicate data inadequacies. This certainly explains the inventory orientation of the early literature studies.

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

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

Suggested Citation

Carbonez, Katelijne A. E. and Nguyen, Van Thi Tuong and Sercu, Piet M. F. A., Remodeling the Working Curve: The Roles of Scarcity, Time to Maturity and Time to Harvest (February 16, 2009). Available at SSRN: or

Katelijne A. E. Carbonez

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000

Van Thi Tuong Nguyen (Contact Author)

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
0032 16 32 64 62 (Phone)

Piet M. F. A. Sercu

FEB at KU Leuven ( email )

Naamsestraat 69
Faculty of Economics and Business
Leuven, 3000
+32 16 32 67 56 (Phone)
+32 16 32 67 32 (Fax)

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