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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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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 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. However there are no formal exchanges or centralized markets where steel is traded and pt can be observed. Instead nearly all steel transaction prices are a result of private bilateral negotiations between buyers and sellers, typically intermediated by middlemen known as steel service centers. Even though there is no central record of daily transactions prices in the steel market, we do observe transaction prices for a particular firm -- a steel service center that purchases large quantities of steel in the wholesale market for subsequent resale in the retail market. The endogenous sampling problem arises from the fact that the firm only records p_t on the days that it purchases steel. 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 firm'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 a Markov transition probability that determines the law of motion for the underlying {p_t} process. The PIML estimator also yields estimates of 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 share of the middleman's discounted profits that are due to markups paid by its retail customers, and the share due to price speculation. The latter measures the firm's success in forecasting steel prices and in timing its purchases in order to "buy low and sell high'." The more successful the firm is in speculation (i.e., in strategically timing its purchases), the more serious are the potential biases that would result from failing to account for the endogeneity of the sampling process.

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  • 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 for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1376
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    6. 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.
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    12. 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.
    13. 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.
    14. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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 2004/179, International Monetary Fund.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    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.

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    More about this item

    Keywords

    Endogenous sampling; Markov processes; Maximum likelihood; Simulation estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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