It is well known from time series analysis that shocks to aggregate output have very persistent effects. This paper argues that the relation between the expected growth rate of a firm and its size\ provides a microfoundation for such aggregate persistence. The empirical evidence indicates 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 grows 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 reconciles the micro evidence with the observed degree of aggregate persistence. It requires changes in neither the number of firms in the market nor the rate of technological progress. It is merely the result of the cross-sectional heterogeneity that we observe in real economies.