On natural slow time rhythms in economic growth

This paper is a study of fluctuations in the U.S. gross domestic product (GDP) around locally defined balanced growth paths. In an uncertain environment, we extend the Solow model of economic growth to allow for capital dependent saving, and time delay between output and planned capital investment. Modeling saving rate as a sigmoid function of capital in effect inserts a positive feedback loop into the dynamics. As a consequence, time periods of positive and negative fluctuations about balanced growth paths are prolonged compared to corresponding fluctuations that would occur in the absence of the feedback loop. We first formulate and analyze the model in continuous time and then follow up with a discrete time approximation. Using data derived from the GDP, we estimate parameters by minimizing one-step-ahead prediction error while simultaneously matching second order statistics of the approximation to second order statistics of the data. In the model’s dynamic stationary state, business cycles occur naturally as excursions of bounded random walks from balanced growth paths where the random walks themselves consist of sums of correlated random variables. Linearization of the model about a balanced growth path yields a method for representing fluctuations in growth data as a superposition of three processes that evolve on different time scales—slow, intermediate, and fast. The resulting frequency based decomposition reveals a natural, slow time ebb and flow in output that can be used to predict future growth trends in the economy.