Testing a Goodwin's model with capacity utilization to the US economy

We present an extension of the Goodwin growth-cycle model that considers the rate of capacity utilization as a new variable in an adapted Lotka-Volterra system of differential equations. We derive a differential equation for the capacity utilization that is proportional to the difference between the output expansion function and capital accumulation. With this approach, we clarify the connections between demand, labour market, and capital accumulation in a model that generates a cyclical pattern for employment rate, profit share, and capacity utilization. After studying the obtained model from a qualitative viewpoint, we test it by using a vector autoregression (VAR) on the US economy using quarterly data from 1970 to 2019. From generalized impulse-response functions, we conclude that a positive profit share innovation positively affects both the employment rate and the rate of capacity utilization, suggesting a profit-led pattern. These results support the theoretical model presented, especially regarding the profit-squeeze mechanism. In sum, the results support Goodwin’s idea that, in the last decades, cycles have been an inherent characteristic of the growth process for the US economy.