An empirical model of inventory investment by durable commodity intermediaries

Abstract

This paper introduces a new detailed dataset of high-frequency observations on inventory investment by a U.S. steel wholesaler. Our analysis of these data leads to six main conclusions: orders and sales are made infrequently; orders are more volatile than sales; order sizes vary considerably; there is substantial high-frequency variation in the firm's sales prices; inventory/sales ratios are unstable; and there are occasional stockouts. We model the firm generically as a durable commodity intermediary that engages in commodity price speculation. We demonstrate that the firm's inventory investment behavior at the product level is well-approximated by an optimal trading strategy from the solution to a nonlinear dynamic programming problem with two continuous state variables and one continuous control variable that is subject to frequently binding inequality constraints. We show that the optimal trading strategy is a generalized (S, s) rule. That is, whenever the firm's inventory level q falls below the order threshold s(p), the firm places an order of size S(p) − q in order to attain a target inventory level S(p) satisfying S(p) ≥ s(p), where p is the current spot price at which the firm can purchase unlimited amounts of the commodity after incurring a fixed order cost K. We show that the (S, s) bands are decreasing functions of p, capturing the basic intuition of commodity price speculation, namely, that it is optimal for the firm to hold higher inventories when the spot price is low than when it is high in order to profit from “buying low and selling high.” We simulate a calibrated version of this model and show that the simulated data exhibit the key features of inventory investment we observe in the data.