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An Empirical Model of Inventory Investment by Durable Commodity Intermediaries

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Author Info
George J. Hall (Cowles Foundation, Yale University)
John Rust (Cowles Foundation, Yale University)

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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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Publisher Info
Paper provided by Cowles Foundation, 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:
Handle: RePEc:cwl:cwldpp:1228

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Commodities; inventories; dynamic programming;

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Find related papers by JEL classification:
D21 - Microeconomics - - Production and Organizations - - - Firm Behavior
E22 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. 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. [Downloadable!] (restricted)
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  2. Angus Deaton & Guy Laroque, 1990. "On The Behavior of Commodity Prices," NBER Working Papers 3439, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Fair, Ray C., 1989. "The production-smoothing model is alive and well," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 353-370, November. [Downloadable!] (restricted)
    Other versions:
  4. 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).
    Other versions:
  5. Andrew B. Abel, 1985. "Inventories, Stock-Outs, and Production Smoothing," NBER Working Papers 1563, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. John Rust & Joseph Traub & Henryk Wozniakowski, 1999. "No Curse of Dimensionality for Contraction Fixed Points Even in the Worst Case," Computational Economics 9902001, EconWPA. [Downloadable!]
  7. 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(1976-2), pages 351-408. [Downloadable!]
  8. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
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  9. 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. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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  11. Valerie A. Ramey & Kenneth D. West, 1997. "Inventories," NBER Working Papers 6315, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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    • 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. [Downloadable!] (restricted)
  12. 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. [Downloadable!]
  13. 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. [Downloadable!] (restricted)
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  14. Jonas D.M. Fisher & Andreas Hornstein, 1998. "(S,s) Inventory policies in general equilibrium," Working Paper 97-07, Federal Reserve Bank of Richmond. [Downloadable!]
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  15. Miron, Jeffrey A. & Zeldes, Stephen P., 1989. "Production, sales, and the change in inventories : An identity that doesn't add up," Journal of Monetary Economics, Elsevier, vol. 24(1), pages 31-51, July. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
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  17. 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. [Downloadable!] (restricted)
  18. 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, Yale University. [Downloadable!]
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  19. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-79, September. [Downloadable!] (restricted)
  20. Blinder, Alan S, 1986. "Can the Production Smoothing Model of Inventory Behavior Be Saved?," The Quarterly Journal of Economics, MIT Press, vol. 101(3), pages 431-53, August. [Downloadable!] (restricted)
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  21. 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. [Downloadable!] (restricted)
  22. 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. [Downloadable!] (restricted)
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  23. repec:cup:cbooks:9780521326162 is not listed on IDEAS
  24. 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. [Downloadable!] (restricted)
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  25. Caplin, Andrew S, 1985. "The Variability of Aggregate Demand with (S, s) Inventory Policies," Econometrica, Econometric Society, vol. 53(6), pages 1395-1409, November. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. George Alessandria & Joseph Kaboski & Virgiliu Midrigan, 2008. "Inventories, lumpy trade, and large devaluations," Working Paper Series WP-08-07, Federal Reserve Bank of Chicago. [Downloadable!]
    Other versions:
  2. George Hall & John Rust, 2002. "Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market," Cowles Foundation Discussion Papers 1376, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. John Rust & George Hall, 2001. "Middle Men Versus Market Makers: A Theory of Competitive Exchange," Cowles Foundation Discussion Papers 1299, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Aubhik Khan & Julia Thomas, 2003. "Inventories and the Business Cycle: An Equilibrium Analysis of (S,s) Policies," NBER Working Papers 10078, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Jia Yan & John Liu, 2008. "Instability of Dynamic Inventory Systems," Working Papers 2008-23, School of Economic Sciences, Washington State University. [Downloadable!]
  7. Joao Miguel Ejarque, 2008. "Evaluating the Economic Cost of Strategic Storage of Natural Gas," Economics Discussion Papers 658, University of Essex, Department of Economics. [Downloadable!]
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