Inventory Behavior with Permanent Sales Shocks

Empirically, sales are I(1). Starting from this fact, we derive three startling results. First, the variance of production is equal to the variance of sales in the long run. Second, this result holds regardless of the strength of production smoothing, stockout avoidance, or cost shocks. Third, at business cycle horizons, the conditional variance of production is greater than that of sales. We explain -- analytically and intuitively -- four traditional inventory puzzles and three puzzles about inventories and monetary policy.