Output volatility and savings in a stochastic Goodwin economy

Both the public and the academic discourse of the post-crisis era have produced most controversial views concerning adequate national savings rates. We add to this discussion by analyzing the role of the savings rate for the dynamics of an economy embedded in a turbulent environment. To this end we study the dynamics of a stochastic Goodwin-type business cycle model using a mix of analytical- and simulation techniques. Focussing on a region of the parameter space that exhibits multi-stability, we apply the stochastic sensitivity function technique and Lyapunov exponents to scrutinize the dynamics of the stochastic economic system. We find that the savings rate affects the sensitivity of the economic system, as well as the distribution of economic states. The sensitivity of the system is inversely related to the level of the savings rate. Specifically, we demonstrate that high volatility phases of the cycle vary as the savings rate is changed. For low (high) levels of the savings rate the stochastic Goodwin economy will remain relatively often in sensitive (robust) states. Our theoretical investigation suggests that strategies involving reasonably high national savings rates might help to avoid the negative welfare implications of sensitive and even chaotic income dynamics along the cycle.