Aggregation and persistence in a macromodel

This paper shows that the behaviour of an otherwise conventional model of real business cycles (RBCs) in which heterogeneous individual firms are subject to temporary technology shocks will be characterised by long memory and nonlinearity. We start from microfoundations, using a standard RBC model of monopolistic competition. We then derive the fundamental intertemporal equilibrium path of the economy and we study analytically the time series properties of GDP. We show that the resulting stochastic process is radically different from the process followed by the firms' productivities, which are conventional stable loglinear Auto-Regressive (AR) processes. This new process is nonlinear, more persistent than any stable AR and yet is mean-reverting (unlike unit-root processes). In our model, small temporary shocks can lead to large fluctuations and/or persistence at the macro level, without requiring large shocks or unit roots at the microeconomic level. Within our model, common shocks are more potent than idiosyncratic ones. The process is also characterised by long cycles which have random lengths and which are asymmetric. Increased monopoly power will tend to reduce the amplitude and increase the persistence of business cycles.