Inventories, Production Smoothing and the Shape of the Cost Function

In this paper we present estimates of inventory models based on firm level panel data and investigate whether an over-simplified specification of the production technology may account for the failure to find technological incentives to smooth production in the context of the standard linear-quadratic model of inventory behaviour. In particular, we argue that if the role of quasi-fixed factors is not modelled properly, this may lead to inconsistent estimates of marginal costs and, therefore, to erroneous conclusions about the convexity/concavity of the cost function. The model is accordingly extended to allow for a general restricted quadratic cost function, on the assumption that capital is costly to adjust. The evidence obtained by estimating the standard inventory model on a panel of Italian manufacturing firms suggests that marginal costs are decreasing. This result is overturned when one allows for the general quadratic cost function with capital as a quasi-fixed input, however, implying that the firm’s technology provides incentives to smooth production. The conclusion that the cost function is convex in output is robust to allowing for adjustment costs for both capital and labour.