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Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market


George J. Hall


Department of Economics and International Business School; Brandeis University - Department of Economics

John P. Rust


University of Maryland - Department of Economics; National Bureau of Economic Research (NBER)

July 2002

Cowles Foundation Discussion Paper No. 1376

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 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 p_t 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.

Number of Pages in PDF File: 57

Keywords: Endogenous Sampling, Markov Processes, Maximum Likelihood, Simulation Estimation

JEL Classification: C13-15

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Date posted: August 12, 2002  

Suggested Citation

Hall, George J. and Rust, John P., Econometric Methods for Endogenously Sampled Time Series: The Case of Commodity Price Speculation in the Steel Market (July 2002). Cowles Foundation Discussion Paper No. 1376. Available at SSRN: http://ssrn.com/abstract=322180

Contact Information

George J. Hall (Contact Author)
Department of Economics and International Business School ( email )
Mailstop 32
Waltham, MA 02454-9110
United States
781-736-2242 (Phone)
HOME PAGE: http://people.brandeis.edu/~ghall
Brandeis University - Department of Economics ( email )
Waltham, MA 02454-9110
United States
John P. Rust
University of Maryland - Department of Economics ( email )
4115 Tydings Hall
College Park, MD 20742
United States
301-405-3489 (Phone)
301-405-3542 (Fax)
HOME PAGE: http://gemini.econ.umd.edu/jrust
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
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