On the interpretation of cointegration in the linear–quadratic inventory model

Abstract

The traditional formulation of the linear–quadratic inventory model with unit roots predicts cointegration between inventories and sales. That formulation implies that marginal production costs and the marginal benefits of inventories are both tending to ∞, and the cointegrating coefficient reflects the optimal trade-off between these competing factors. This paper suggests a reformulation of the problem in which marginal production costs and marginal inventory benefits are both stationary and in which the cointegrating coefficient is the same as the value that characterizes the target inventory level in the cost function.