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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

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

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods

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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. 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. [Downloadable!]
  2. Angus Deaton & Guy Laroque, 1990. "On The Behavior of Commodity Prices," NBER Working Papers 3439, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. John Rust & Hui Man Chan & George Hall, 2004. "Price Discrimination in the Steel Market," 2004 Meeting Papers 44, Society for Economic Dynamics.
    Other versions:
  5. 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. [Downloadable!] (restricted)
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  6. Aguirregabiria, Victor, 1999. "The Dynamics of Markups and Inventories in Retailing Firms," Review of Economic Studies, Blackwell Publishing, vol. 66(2), pages 275-308, April. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  9. repec:rus:hseeco:72158 is not listed on IDEAS
  10. Alastair R. Hall & Atsushi Inoue, 2005. "The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models," Econometrics 0505002, EconWPA. [Downloadable!]
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  11. George J. Hall & John Rust, 1999. "An Empirical Model of Inventory Investment by Durable Commodity Intermediaries," Cowles Foundation Discussion Papers 1228, Cowles Foundation, Yale University. [Downloadable!]
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  12. 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. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. repec:cup:cbooks:9780521326162 is not listed on IDEAS
  15. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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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!]
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  2. Martin Browning & Mette Ejrnaes & Javaier Alvarez, 2006. "Modelling income processes with lots of heterogeneity," Economics Series Working Papers 285, University of Oxford, Department of Economics. [Downloadable!]
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  3. Sule Alan & Martin Browning, 2003. "Estimating Intertemporal Allocation Parameters using Simulated Residual Estimation," CAM Working Papers 2003-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics. [Downloadable!]
  4. Manuel S. Santos, 2003. "Simulation-Based Estimation Of Dynamic Models With Continuous Equilibrium Solutions," Economics Working Papers we034716, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  5. Mark Coppejans & Donna Gilleskie & Holger Sieg & Koleman Strumpf, 2006. "Consumer Demand under Price Uncertainty: Empirical Evidence from the Market for Cigarettes," NBER Working Papers 12156, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Kala Krishna & Susumu Imai & Abhiroop Mukhopadhyay & Ling Hui Tan, 2004. "Quota Brokers," IMF Working Papers 04/179, International Monetary Fund. [Downloadable!]
  7. Sule Alan & Martin Browning, 2006. "Estimating Intertemporal Allocation Parameters using Simulated Expectation Errors," Economics Series Working Papers 284, University of Oxford, Department of Economics. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
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  9. 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:
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