This project carries out research on the behavior of inventories and unfilled orders. The contributions of this research to this line of work are important because unfilled orders play a very significant role in business cycles and in the overall volatility of national output, yet there is relatively little empirical research on unfilled orders and there is no adequate theoretical explanation of the reasons why unfilled orders and inventories are positively correlated. One would think that increases in inventories would reduce unfilled orders, but that is not what the preliminary evidence shows. The research builds on earlier work on the stockout-avoidance motive for inventories in two main directions: First, it extends the stockout-avoidance model to allow for strictly convex costs of production and inventory holding. Second, it incorporates the joint determination of inventories and unfilled orders. This is useful not only for those industries in which orders data are available. Many industries (most notably the automobile industry) are known to have orders, but data on them are not available. Consequently current sales or shipments partly reflect unmeasured unfilled orders. The model developed will resolve this problem. The project also explores some new evidence of increasing marginal cost and extends the stockout-avoidance model to allow for it. Because the model is not linear-quadratic, and it explicitly incorporates non-negativity constraints on inventories, this extension is non-trivial and leads to the use of some numerical methods that may themselves be of independent interest. Preliminary work focused on evidence related to the slope of marginal cost. The extreme sensitivity of inventory behavior in the model to small departures from zero marginal cost suggests that marginal cost may be very close to flat.
