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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."

Suggested Citation

  • 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.
  • Handle: RePEc:sce:scecf1:274
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    References listed on IDEAS

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    1. 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.
    2. Victor Aguirregabiria, 1999. "The Dynamics of Markups and Inventories in Retailing Firms," Review of Economic Studies, Oxford University Press, vol. 66(2), pages 275-308.
    3. Williams,Jeffrey C. & Wright,Brian D., 2005. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521023399, December.
    4. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
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    6. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
    7. 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.
    8. 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.
    9. repec:rus:hseeco:72158 is not listed on IDEAS
    10. 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.
    11. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    13. Nicholas Kaldor, 1939. "Speculation and Economic Stability," Review of Economic Studies, Oxford University Press, vol. 7(1), pages 1-27.
    14. Hall, George & Rust, John, 2000. "An empirical model of inventory investment by durable commodity intermediaries," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 52(1), pages 171-214, June.
    15. 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.
    16. 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.
    17. John Rust & Hui Man Chan & George Hall, 2004. "Price Discrimination in the Steel Market," Econometric Society 2004 North American Summer Meetings 245, Econometric Society.
    18. 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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    Cited by:

    1. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1353-1381.
    2. George Alessandria & Joseph P. Kaboski & Virgiliu Midrigan, 2010. "Inventories, Lumpy Trade, and Large Devaluations," American Economic Review, American Economic Association, vol. 100(5), pages 2304-2339, December.
    3. Santos, Manuel S., 2004. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 465-491, June.
    4. Oleksiy Kryvtsov & Virgiliu Midrigan, 2013. "Inventories, Markups, and Real Rigidities in Menu Cost Models," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 249-276.
    5. 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.
    6. International Monetary Fund, 2004. "Quota Brokers," IMF Working Papers 04/179, International Monetary Fund.
    7. Sule Alan & Martin Browning, 2010. "Estimating Intertemporal Allocation Parameters using Synthetic Residual Estimation," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1231-1261.
    8. Mark Coppejans & Donna Gilleskie & Holger Sieg & Koleman Strumpf, "undated". "Consumer Demand under Price Uncertainty: Empirical Evidence from the Market for Cigarettes," GSIA Working Papers 2006-E43, Carnegie Mellon University, Tepper School of Business.
    9. Tim Landvoigt, 2010. "Housing Demand during the Boom: The Role of Expectations and Credit Constraints," 2010 Meeting Papers 1022, Society for Economic Dynamics.
    10. Sule Alan, 2006. "Entry Costs and Stock Market Participation over the Life Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(4), pages 588-611, October.
    11. Santos, Manuel S., 2003. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," UC3M Working papers. Economics we034716, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Martin Browning & Sule Alan, 2006. "Estimating Intertemporal Allocation Parameters using Simulated Expectation Errors," Economics Series Working Papers 284, University of Oxford, Department of Economics.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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