We examine the behavior of trade inventories using both industry-level and high-frequency firm-level data. The cost structure underlying the firm's optimization problem--convex delivery costs vs. fixed costs of ordering--provides the two competing hypotheses. In the presence of fixed costs (S,s) inventory policies are optimal, and steady-state reduced-form predictions regarding the dynamics of inventories and sales can be used to test the model. The alternative of convex delivery costs is provided by structural estimation of a linear-quadratic (L-Q) model. At the industry level, the results are consistent with the reduced-form predictions of the (S,s) model, and structural parameter estimates obtained from Euler equation estimation indicate that the L-Q model does not fit the data. At the firm level, however, estimates of the structural cost parameters are economically plausible, statistically significant, and generate observationally equivalent dynamics of inventories and deliveries as those predicted by the steady-state reduced-form probability relationships derived from the (S,s) model.