Aggregation, persistence and volatility in a macro model

We introduce firm heterogeneity into the standard monopolistically competitive real business cycle (RBC) model. The fundamental equilibrium path is derived and the time-series properties of aggregate GDP are studied analytically. Although firms' productivities are subject to temporary shocks, the aggregate process displays a surprising novel form of nonlinearity and long memory which had not been built into the model at the outset. This aggregate GDP turns out to have very different properties from log-linear time-series models such as auto-regressive (AR) models and their extensions. It displays very strong persistence, which ends abruptly with a sudden change of tendency, giving its autocorrelation function (ACF) an S-shape. Although persistent, it is mean-revening, unlike the everlasting memory of unit-root processes. Its volatility is of a greater order of magnitude than that of any of its components, so small micro-shocks can generate large macro fluctuations. It is also characterized by long, asymmetric cycles of random lengths. Increased monopoly power tends to reduce the amplitude and increase the persistence of business cycles. Strikingly, we find that the empirical ACFs constructed from GDP data for the U.K. and the U.S. display this characteristic S-shape.