In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known
nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The
model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the
capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original
model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of
the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant
modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a
newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the
years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The
comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative
agreement with the growth cycle empirical data.
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