Production chains and aggregate output volatility

A production chain's aggregate output volatility depends upon a number of factors including the number of firms in a chain, the management strategy of the firms, the point at which products are differentiated, lead times, and the persistence of demand shocks. The influence of these factors is quantified here with an N-firm model of the production chain. Under pure production-to-stock (PTS), the firms in the chain respond simultaneously to a demand shock producing a positive covariance across firms that raises aggregate volatility. Under production to order (PTO), the chain's response to a demand shock is staggered but when demand shocks are persistent there is a catch-up effect that raises the volatility of each firm's production above that of a firm that under PTS. Nevertheless, PTO chains typically exhibit less volatility than PTS chains thanks to the covariance effect. Further simulations demonstrate that the production chain stabilizes as the number of production cycles in an observation period increases.