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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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    Cited by:

    1. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, 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. Sule Alan, 2012. "Do disaster expectations explain household portfolios?," Quantitative Economics, Econometric Society, vol. 3(1), pages 1-28, March.
    4. Susumu Imai & Kala Krishna & Abhiroop Mukhopadhyay, 2004. "Do security deposit rates matter: Evidence from a secondary market," Discussion Papers 05-02, Indian Statistical Institute, Delhi.
    5. 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.
    6. Oleksiy Kryvtsov & Virgiliu Midrigan, 2013. "Inventories, Markups, and Real Rigidities in Menu Cost Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 249-276.
    7. 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.
    8. Sule Alan & Martin Browning, 2010. "Estimating Intertemporal Allocation Parameters using Synthetic Residual Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1231-1261.
    9. Jeremy Lise, 2006. "On-the-Job Search and Precautionary Savings: Theory and Empirics of Earnings and Wealth Inequality," 2006 Meeting Papers 137, Society for Economic Dynamics.
    10. Mark Coppejans & Donna Gilleskie & Holger Sieg & Koleman Strumpf, 2007. "Consumer Demand under Price Uncertainty: Empirical Evidence from the Market for Cigarettes," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 510-521, August.
    11. Tim Landvoigt, 2010. "Housing Demand during the Boom: The Role of Expectations and Credit Constraints," 2010 Meeting Papers 1022, Society for Economic Dynamics.
    12. 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.
    13. 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.
    14. International Monetary Fund, 2004. "Quota Brokers," IMF Working Papers 2004/179, International Monetary Fund.
    15. Martin Browning & Sule Alan, 2006. "Estimating Intertemporal Allocation Parameters using Simulated Expectation Errors," Economics Series Working Papers 284, University of Oxford, Department of Economics.

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    Keywords

    simulation; speculation; endogenous sampling; (S; s) rule;
    All these keywords.

    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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