This paper introduces a new detailed data set 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.
Hall, George J. and Rust, John, "An Empirical Model of Inventory Investment by Durable Commodity Intermediaries" (1999). Cowles Foundation Discussion Papers. 1476.