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An Empirical Model of Inventory Investment by Durable Commodity Intermediaries

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Abstract

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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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1228.pdf
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Bibliographic Info

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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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Commodities; inventories; dynamic programming;

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References

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  1. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
  2. Ray C. Fair, 1990. "The Production Smoothing Model is Alive and Well," NBER Working Papers 2877, National Bureau of Economic Research, Inc.
  3. 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.
  4. Jeffrey A. Miron & Stephen P. Zeldes, 1989. "Production, Sales, and the Change in Inventories: An Identity That Doesn`t Add Up," NBER Working Papers 2765, National Bureau of Economic Research, Inc.
  5. 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.
  6. Bresnahan, Timothy F & Ramey, Valerie A, 1994. "Output Fluctuations at the Plant Level," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages 593-624, August.
  7. 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. Kahn, James A, 1992. "Why Is Production More Volatile Than Sales? Theory and Evidence on the Stockout-Avoidance Motive for Inventory-Holding," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 481-510, May.
  9. Miron, Jeffrey A & Zeldes, Stephen P, 1988. "Seasonality, Cost Shocks, and the Production Smoothing Models of Inventories," Econometrica, Econometric Society, vol. 56(4), pages 877-908, July.
  10. Jonas D.M. Fisher & Andreas Hornstein, 1998. "(S,s) Inventory policies in general equilibrium," Working Paper 97-07, Federal Reserve Bank of Richmond.
  11. Williams,Jeffrey C. & Wright,Brian D., 1991. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521326162, October.
  12. James A. Kahn & Mark Bils, 2000. "What Inventory Behavior Tells Us about Business Cycles," American Economic Review, American Economic Association, vol. 90(3), pages 458-481, June.
  13. 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.
  14. 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.
  15. Deaton, A. & Laroque, G., 1989. "On The Behavior Of Commodity Prices," Papers 145, Princeton, Woodrow Wilson School - Public and International Affairs.
  16. Alan S. Blinder, 1984. "Can The Production Smoothing Model of Inventory Behavior be Saved?," NBER Working Papers 1257, National Bureau of Economic Research, Inc.
  17. Martin S. Eichenbaum, 1990. "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," NBER Working Papers 2523, National Bureau of Economic Research, Inc.
  18. Kenneth D. West, 1985. "A Variance Bounds Test of the Linear Quardractic Inventory Model," NBER Working Papers 1581, National Bureau of Economic Research, Inc.
  19. John Rust & Joseph Traub & Henryk Wozniakowski, 1999. "No Curse of Dimensionality for Contraction Fixed Points Even in the Worst Case," Computational Economics 9902001, EconWPA.
  20. 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.
  21. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-79, September.
  22. Abel, Andrew B, 1985. "Inventories, Stock-Outs and Production Smoothing," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 283-93, April.
  23. Caplin, Andrew S, 1985. "The Variability of Aggregate Demand with (S, s) Inventory Policies," Econometrica, Econometric Society, vol. 53(6), pages 1395-1409, November.
  24. 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.
  25. 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.
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Citations

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Cited by:
  1. Aubhik Khan & Julia K. Thomas, 2004. "Inventories and the business cycle: an equilibrium analysis of (S,s) policies," Working Papers 04-11, Federal Reserve Bank of Philadelphia.
  2. Virgiliu Midrigan & Oleksiy Kryvtsov, 2008. "Inventories, Markups, and Real Rigidities in Menu Cost Models," 2008 Meeting Papers 487, Society for Economic Dynamics.
  3. John Rust & George Hall, 2003. "Middlemen versus Market Makers: A Theory of Competitive Exchange," Journal of Political Economy, University of Chicago Press, vol. 111(2), pages 353-403, April.
  4. Ejarque, João Miguel, 2011. "Evaluating the economic cost of natural gas strategic storage restrictions," Energy Economics, Elsevier, vol. 33(1), pages 44-55, January.
  5. George Alessandria & Joseph P. Kaboski & Virgiliu Midrigan, 2010. "Inventories, Lumpy Trade, and Large Devaluations," American Economic Review, American Economic Association, vol. 100(5), pages 2304-39, December.
  6. George Hall and John Rust, Yale University, 2001. "Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market," Computing in Economics and Finance 2001 274, Society for Computational Economics.
  7. Blume, Lawrence E. & Easley, David & Kleinberg, Jon & Tardos, Éva, 2009. "Trading networks with price-setting agents," Games and Economic Behavior, Elsevier, vol. 67(1), pages 36-50, September.
  8. Joao Miguel Ejarque, 2008. "Evaluating the Economic Cost of Strategic Storage of Natural Gas," Economics Discussion Papers 658, University of Essex, Department of Economics.
  9. Jia Yan & John Liu, 2008. "Instability of Dynamic Inventory Systems," Working Papers 2008-23, School of Economic Sciences, Washington State University.
  10. Florian Zettelmeyer & Fiona Scott Morton & Jorge Silva-Risso, 2006. "Scarcity Rents in Car Retailing: Evidence from Inventory Fluctuations at Dealerships," NBER Working Papers 12177, National Bureau of Economic Research, Inc.

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