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Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market

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  • George Hall and John Rust, Yale University

Abstract

This paper studies the econometric problems associated with estimation of a stochastic process that is endogenously sampled. Our interest is to infer the law of motion of a discrete-time stochastic process p_t that is observed only at a subset of times t_1, ...,t_n that depend on the outcome of a probabilistic sampling rule that depends on the history of the p_t process as well as other observed covariates x_t. We focus on a particular example where p_t denotes the daily wholesale price of a standardized steel product. There is no centralized spot market for steel, which is better described as a "telephone market" where individual transactions result from private bilateral negotiations between buyers and sellers. Although there is no central record of daily transactions prices in the steel market, we do observe transaction prices for a particular trader --- an intermediary that purchases steel in the wholesale market for subsequent resale in the retail market. The endogenous sampling problem arises from the fact that we only observe p_t on the days that the trader decides to make purchases. We present a parametric analysis of this problem under the assumption that the timing of steel purchases is part of an optimal trading strategy that maximizes the intermediary's expected discounted trading profits. We derive a parametric partial information maximum likelihood (PIML) estimator that solves the endogenous sampling problem and efficiently estimates the unknown parameters of the Markov law of motion for p_t together with the structural parameters that determine the optimal trading rule. We also introduce an alternative consistent, less efficient, but computationally simpler simulated minimum distance (SMD) estimator that avoids high dimensional numerical integrations required by the PIML estimator. Using the SMD estimator, we provide estimates of a truncated lognormal AR(1) model of the wholesale price processes for particular types of steel plate. We use this to infer the fraction of the intermediary's discounted profits that are due to the markups it charges its retail customers, and what fraction is due to pure commodity price speculation, i.e. its success in timing purchases of steel in order to profit from "buying low and selling high."

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 274.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:274

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Keywords: simulation; speculation; endogenous sampling; (S; s) rule;

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References

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  1. Aguirregabiria, Victor, 1999. "The Dynamics of Markups and Inventories in Retailing Firms," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 275-308, April.
  2. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
  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. Hugo Benitez-Silva & John Rust & Gunter Hitsch & Giorgio Pauletto & George Hall, 2000. "A Comparison Of Discrete And Parametric Methods For Continuous-State Dynamic Programming Problems," Computing in Economics and Finance 2000 24, Society for Computational Economics.
  5. repec:rus:hseeco:72158 is not listed on IDEAS
  6. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
  7. John Rust & Hui Man Chan & George Hall, 2004. "Price Discrimination in the Steel Market," 2004 Meeting Papers 44, Society for Economic Dynamics.
  8. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  9. Williams,Jeffrey C. & Wright,Brian D., 1991. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521326162, October.
  10. Angus Deaton & Guy Laroque, 1990. "On The Behavior of Commodity Prices," NBER Working Papers 3439, National Bureau of Economic Research, Inc.
  11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  12. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  13. George Hall & John Rust, 1999. "An Empirical Model of Inventory Investment by Durable Commodity Intermediaries," Macroeconomics 9904005, EconWPA.
  14. Tülin Erdem & Michael P. Keane, 1996. "Decision-Making Under Uncertainty: Capturing Dynamic Brand Choice Processes in Turbulent Consumer Goods Markets," Marketing Science, INFORMS, vol. 15(1), pages 1-20.
  15. Lee, Bong-Soo & Ingram, Beth Fisher, 1991. "Simulation estimation of time-series models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 197-205, February.
  16. J. Rust & J. F. Traub & H. Wozniakowski, 2002. "Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?," Econometrica, Econometric Society, vol. 70(1), pages 285-329, January.
  17. Kamran Moinzadeh, 1997. "Replenishment and Stocking Policies for Inventory Systems with Random Deal Offerings," Management Science, INFORMS, vol. 43(3), pages 334-342, March.
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