A note on the theory and empirics of the Goodwin model

I discuss some theoretical and empirical points about the Goodwin model. First, I offer a simple proof that solution trajectories around the stable critical point in the Goodwin model are closed orbits but not limit cycles. Moreover, in a neighborhood of the stable critical point, the closed orbits are ellipses. Second, I compare the predictions of the Goodwin model with patterns observed in actual annual data for the U.S. economy for the period 1950-2019. I find that the predictions of the model regarding three key aspects of cycles-the amplitude, time period and the direction of motion-are fully or partially at variance with observed data.