Extremal behavior of aggregated economic processes in a structural growth model

This paper proposes a structural approach to growth modeling relying on random return scale. An RBC-like model in which return to scale may be strictly increasing or decreasing depending on shocks is explicitly derived. We show that relevant component of usual macroeconomic models (including capital, growth, various relative prices) are all related to a Random Autoregressive Coefficient model. Recent works on extreme behavior on dependent process emphasize some properties of this model that are worth from the economic viewpoint. First, this model typically displays fat tail behavior event if the shocks do not. Second, records (both historically high and low points) are less frequent than in the usual stationary case but tend to appear in cluster. We show that both fat tails and clustering of extreme values are consistent with arbitrarily small variations of the autoregressive coefficient around the usual unit-root case. As such, distinguishing RCA from a more usual constant autoregressive model from available macro data may then be difficult and typically require very long data set. To this end, we propose a direct test based on the annual sequence of real wages in England recorded since the XIII-th century onwards. The test clearly reject the constant AR model and supports the Random coefficient hypothesis.