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| An Empirical Model of Inventory Investment |
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| 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.
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