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An Empirical Model of Inventory Investment by Durable Commodity Intermediaries

This paper introduces a new detailed data set of high-frequency observations on inventory investment by a U.S. steel wholesaler. Our analysis of these data leads to six main conclusions: orders and sales are made infrequently; orders are more volatile than sales; order sizes vary considerably; there is substantial high-frequency variation in the firm's sales prices; inventory/sales ratios are unstable; and there are occasional stockouts. We model the firm generically as a durable commodity intermediary that engages in commodity price speculation. We demonstrate that the firm's inventory investment behavior at the product level is well approximated by an optimal trading strategy from the solution to a nonlinear dynamic programming problem with two continuous state variables and one continuous control variable that is subject to frequently binding inequality constraints. We show that the optimal trading strategy is a generalized (S,s) rule. That is, whenever the firm's inventory level q falls below the order threshold s(p) the firm places an order of size S(p) - q in order to attain a target inventory level S(p) satisfying S(p) >= s(p), where p is the current spot price at which the firm can purchase unlimited amounts of the commodity after incurring a fixed order cost K. We show that the (S,s) bands are decreasing functions of p, capturing the basic intuition of commodity price speculation, namely, that it is optimal for the firm to hold higher inventories when the spot price is low than when it is high in order to profit from "buying low and selling high." We simulate a calibrated version of this model and show that the simulated data exhibit the key features of inventory investment we observe in the data.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1228.

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Length: 45 pages
Date of creation: Jun 1999
Date of revision:
Publication status: Published in Carnegie-Rochester Conference Series on Public Policy, June 2000
Handle: RePEc:cwl:cwldpp:1228
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Yale University, Box 208281, New Haven, CT 06520-8281 USA

Phone: (203) 432-3702
Fax: (203) 432-6167
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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. John Rust, 1997. "A Comparison of Policy Iteration Methods for Solving Continuous-State, Infinite-Horizon Markovian Decision Problems Using Random, Quasi-random, and Deterministic Discretizations," Computational Economics 9704001, EconWPA.
  2. Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-34, April.
  3. Blanchard, Olivier J, 1983. "The Production and Inventory Behavior of the American Automobile Industry," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 365-400, June.
  4. Fisher, J.D.M. & Hornstein, A., 1995. "(S,s)Inventory Policies in General Equilibrium," UWO Department of Economics Working Papers 9514, University of Western Ontario, Department of Economics.
  5. Martin Feldstein & Alan Auerbach, 1976. "Inventory Behavior in Durable-Goods Manufacturing: The Target-Adjustment Model," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 7(2), pages 351-408.
  6. Bils, M. & Kahn, J.A., 1996. "What Inventory Behavior Tells Us About Business Cycles," RCER Working Papers 428, University of Rochester - Center for Economic Research (RCER).
  7. Valerie A. Ramey & Kenneth D. West, 1997. "Inventories," NBER Working Papers 6315, National Bureau of Economic Research, Inc.
    • Ramey, Valerie A. & West, Kenneth D., 1999. "Inventories," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 13, pages 863-923 Elsevier.
  8. James A. Kahn, 1992. "Why is Production More Volatile than Sales? Theory and Evidence on the Stockout-Avoidance Motive for Inventory-Holding," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 481-510.
  9. George J. Hall, 1997. "Non-Convex Costs and Capital Utilization: A Study of Production Scheduling at Automobile Assembly Plants," Cowles Foundation Discussion Papers 1169, Cowles Foundation for Research in Economics, Yale University.
  10. Eichenbaum, Martin, 1989. "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," American Economic Review, American Economic Association, vol. 79(4), pages 853-64, September.
  11. Eichenbaum, Martin S., 1984. "Rational expectations and the smoothing properties of inventories of finished goods," Journal of Monetary Economics, Elsevier, vol. 14(1), pages 71-96, July.
  12. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
  13. Andrew B. Abel, 1985. "Inventories, Stock-Outs and Production Smoothing," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 283-293.
  14. Jeffrey A. Miron & Stephen P. Zeldes, 1987. "Seasonality, Cost Shocks, and the Production Smoothing Model of Inventories," NBER Working Papers 2360, National Bureau of Economic Research, Inc.
  15. Williams,Jeffrey C. & Wright,Brian D., 2005. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521023399, April.
  16. Ray C. Fair, 1989. "The Production Smoothing Model Is Alive and Well," Cowles Foundation Discussion Papers 896, Cowles Foundation for Research in Economics, Yale University.
  17. Jeffrey A. Miron & Stephen P. Zeldes, . "Production, Sales and the Change in Inventories: An Identity that Doesn't Add Up," Rodney L. White Center for Financial Research Working Papers 20-87, Wharton School Rodney L. White Center for Financial Research.
  18. Timothy F. Bresnahan & Valerie A. Ramey, 1994. "Output Fluctuations at the Plant Level," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 593-624.
  19. West, Kenneth D, 1986. "A Variance Bounds Test of the Linear Quadratic Inventory Model," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 374-401, April.
  20. Caplin, Andrew S, 1985. "The Variability of Aggregate Demand with (S, s) Inventory Policies," Econometrica, Econometric Society, vol. 53(6), pages 1395-1409, November.
  21. Blinder, Alan S, 1986. "More on the Speed of Adjustment in Inventory Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 18(3), pages 355-65, August.
  22. John Rust & Department of Economics & University of Wisconsin, 1994. "Using Randomization to Break the Curse of Dimensionality," Computational Economics 9403001, EconWPA, revised 04 Jul 1994.
  23. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-79, September.
  24. John Rust & Joseph Traub & Henryk Wozniakowski, 1999. "No Curse of Dimensionality for Contraction Fixed Points Even in the Worst Case," Computational Economics 9902001, EconWPA.
  25. Alan S. Blinder, 1984. "Can The Production Smoothing Model of Inventory Behavior be Saved?," NBER Working Papers 1257, National Bureau of Economic Research, Inc.
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