Inventory behavior with permanent sales shocks

Empirically, ADF tests fail to reject the null hypothesis that sales are I(1). We build a model of inventory behavior that incorporates permanent sales shocks. Analytically, the model with I(1) sales implies that the variance ratio (of log production to log sales) is one in the long run, regardless of the strength of production smoothing, stockout avoidance, or cost shocks, but that, at business cycle horizons, the conditional variance ratio (conditional on past production and sales) is greater than one. We explain - analytically, using our model, and intuitively - four traditional inventory puzzles and three puzzles about inventories and monetary policy.