Cross-sectional heterogeneity and the persistence of aggregate fluctuations

A well-known fact in the time series of aggregate output is the persistence of shocks. This paper argues that the empirical relation between the expected growth rate of a firm and its size provides a microfoundation of aggregate persistence. In fact, the empirical evidence claims that small firms grow faster than big ones. If this is true, a shock that reallocates units across sizes will be absorbed, yet at very low decreasing rates. Once the shock hits the system, firms are reallocated across sizes. If small firms grow faster than big ones, the shock will then be absorbed. However, fast growing small firms eventually become big and grow as big firms. Thus the number of small firms shrinks over time as well as the rate at which the shock is absorbed. This transmission mechanism matches well the micro evidence with the observed degree of aggregate persistence. It does not require changes in either the number of firms in the market or the rate of technological progress. It is just the result of the cross-sectional heterogeneity that we observe daily in real economies.