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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
  • John Rust

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 {pt} that is observed only at a subset of times {t1,..., tn} that depend on the outcome of a probabilistic sampling rule that depends on the history of the process as well as other observed covariates xt . We focus on a particular example where pt 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 pt 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 {pt} 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," NBER Technical Working Papers 0278, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0278
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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. 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. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
    9. International Monetary Fund, 2004. "Quota Brokers," IMF Working Papers 2004/179, International Monetary Fund.
    10. Martin Browning & Sule Alan, 2006. "Estimating Intertemporal Allocation Parameters using Simulated Expectation Errors," Economics Series Working Papers 284, University of Oxford, Department of Economics.
    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. Tim Landvoigt, 2010. "Housing Demand during the Boom: The Role of Expectations and Credit Constraints," 2010 Meeting Papers 1022, Society for Economic Dynamics.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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