I(0) In, integration and cointegration out: Time series properties of endogenous growth models

To complement empirical growth studies applying unit root and cointegration methods, this paper shows that integration and cointegration properties arise intrinsically in stochastic endogenous growth models under fairly general conditions. It shows that a unit root has to be present in the autoregressive polynomial of the variables generated by an endogenous growth model, so as to produce steady-state growth in the absence of exogenous growth-generating element. This endogenous-growth-generating mechanism induces difference stationarity of the variables even though the external impulses are stationary, and it leads to the phenomenon of cointegration if the variables satisfy a state space representation. The 'unit root propagation mechanism' is the time series analogue of the 'constant returns' (to reproducible inputs) condition in the theoretical endogenous growth literature. The time series properties of endogenous growth models, when combined with their counterparts for exogenous growth models, lead to testable implications for distinguishing between these two classes of models.