Contemporaneous aggregation of linear dynamic models in large economies

In this paper we provide a formal analysis of the effect of linear contemporaneous aggregation, in the sense of averaging, of ARMA processes driven by a common and an idiosyncratic shock, with random coefficients, as the number of microunits goes to infinity. Heterogeneity of the coefficients is described by means of a mild semiparametric specification of their probability distribution. The possibility of long memory and non-stationarity is fully characterized. The different implications, for aggregate behaviour, of the common and idiosyncratic shocks are presented in details. We propose an empirical application where we estimate the cross-sectional distribution of the parameters governing heterogeneous first-order autoregressive processes, based on a real data set.