Heterogeneous dynamics, aggregation and the persistence of economic shocks

It has been recently emphasized that, if individuals have heterogeneous dynamics, estimates of shock persistence based on aggregate data are significatively higher than those derived from its disaggregate counterpart. However, a careful examination of the implications of this statement on the various tools routinely employed to measure persistence is missing in the literature. This paper formally examines this issue. We consider a disaggregate linear model with heterogeneous dynamics and compare the values of several measures of persistence across aggregation levels. Interestingly, we show that the average persistence of aggregate shocks, as measured by the impulse response function (IRF) of the aggregate model or by the average of the individual IRFs, is identical on all horizons. This result remains true even in situations where the units are (short-memory) stationary but the aggregate process is long-memory or even nonstationary. In contrast, other popular persistence measures, such as the sum of the autoregressive coefficients or the largest autoregressive root, tend to be higher the higher the aggregation level. We argue, however, that this should be seen more as an undesirable property of these measures than as evidence of different average persistence across aggregation levels. The results are illustrated in an application using U.S. inflation data.