Modeling tails of aggregate economic processes in a stochastic growth model

An annual sequence of wages in England starting in 1245 is used. It is shown that a standard AK-type growth model with capital externality and stochastic productivity shocks is unable to explain important features of the data. Random returns to scale are then considered. Moderate episodes of increasing returns to scale and growth are shown to be compatible with convergence of wage’s process towards a unique stationary distribution. This holds true for other relevant values such as GDP and/or capital stock. Furthermore, random returns to scale generate heteroskedasticity, a feature common to macroeconomic time series. Finally, the limit distribution of real wages displays fat tails if returns to scale are episodically increasing. Several inference results supporting randomness of returns to scale are provided.