Inventory investment and aggregate fluctuations with idiosyncratic shocks

We develop a DSGE model to explain salient empirical regularities regarding fluctuations in aggregate inventory accumulation over the business cycle while simultaneously explaining a distinct set of observations on the behavior of this series at higher frequencies. We begin with a generalized (S,s) model of inventory investment wherein firms fixed costs of ordering inputs that lead them to economize on the frequency of their orders by accumulating inventories. To this environment, we add idiosyncratic shocks to firms’ total factor productivities. We discipline order costs using average aggregate inventory data, and firm productivity differences using observed sales and output growth volatility in firm-level data. As only a fraction of firms place orders in any period, our model yields a nontrivial distribution of firms over productivity and inventory levels. When a firm chooses not to place an order, its existing inventory determines the level of inputs available for its production. This prompts firms to raise their average stocks in times of persistently high aggregate productivity. A second set of factors influencing firms’ sales and inventory decisions are the risks associated with the potential for high fixed order costs in future, alongside the possibility of sharp changes in relative productivity. We find that these idiosyncratic risks can alter firms’ decisions sufficiently to yield important changes in aggregate dynamics. Our micro-founded inventory model succeeds in reproducing important empirical regularities involving inventory investment and the business cycle. In the model, as in the data, inventory investment is procyclical and positively correlated with final sales, and GDP is more variable than sales. Furthermore the inventory-to-sales ratio is countercyclical. Across a variety of cases, we find that the model explains between 40 and 60 percent of the measured volatility in inventory investment. While these cyclical successes are qualitatively robust across cases, we show that changes in micro-level parameters affecting the shape of the order cost distribution and the degree of firm-level productivity risk imply quantitative changes to this set of aggregate results. We show that an aggregate shock to total factor productivity increases total production and final sales, as well as both the number of firms placing orders and the average size of their orders. Because the gradual accumulation of capital slows the rise in intermediate goods supply, however, there is a trade-off between firms’ increased inventory accumulation and their increased production of final goods. Each activity comes at some expense to the other, so the rise in final sales is dampened by, and dampens, the rise in inventory investment. In this sense, the frictions that induce inventories also offset much of the volatility in GDP that might otherwise arise from procyclical fluctuations in inventory investment. An important insight of our analysis is that changes in the persistence and variability of idiosyncratic order costs and productivities alter the distribution of firms over inventory levels. This, in turn, affects the extent and speed of firms’ responses to aggregate shocks, and thus the model’s ability to reproduce high-frequency aspects of the aggregate data. When firms have greater certainty about their order costs, and when shifts in their relative productivities are transitory, they adjust their average inventory holdings faster following an aggregate shock. In such cases, the model succeeds not only with respect to the business cycle facts mentioned above, but also in reproducing two essential high-frequency observations, the negative correlation between sales and inventory investment and the greater volatility in sales relative to production.