Modelling Tails of Aggregated Economic Processes in a Stochastic Growth Model

We present an annual sequence of wages in England starting in 1245. We show that a standard AK-type growth model with capital externality and stochastic productivity shocks is unable to explain important features of the data. We then consider random returns to scale. Moderate episodes of increasing returns to scale and growth are shown to be compatible with stationarity. Further, random returns to scale generate heteroskedasticity, a feature common to macroeconomic time series. Third, stationary distributions display fat tails if returns to scale are episodically increasing. We provide several inference results to support randomness of returns to scale.