The Potential Role of Manufacturers' Orders in the Linear-Quadratic Flexible Accelerator Model

Abstract

The linear-quadratic flexible accelerator model has been a staple for empirical analysis within the inventories literature. A key assumption of the model is that sales are a proxy for demand, thus inventories are generated in instances where production does not equilibrate with demand. We seek to improve upon the benchmark linear-quadratic model by introducing firm orders, thus allowing for differentiation between realized and expected demand. Estimation results suggest that the omission of orders heavily biases the coefficient sign and magnitude associated with sales. Furthermore, the estimated adjustment speed of orders is both larger in magnitude and statistical significance than for sales. The disparity in the rates of adjustment between expected and realized demand provides a new contribution towards understanding the adjustment speed puzzles pervasive in the literature. Finally, the addition of orders provides stronger evidence of a cointegrating relationship in a trivariate system of equations versus a standard bivariate system containing strictly inventories and sales. However, exogenous order shocks do not seem to meaningfully impact inventory investment, nor sales. Furthermore, forecast error variance for sales, and inventories are not well explained by orders. These results suggest that orders are important in explaining the underlying data generating processes for sales, and inventories, as well as the long-run relationship between inventory, and sales, but offer little in forecasting potential.