Stabilizing Structural Change and Cycle: Goodwin Meets Neumann on the Turnpike

This study examines the applicability of the turnpike property in nonlinear optimal control theory to economics. The turnpike property implies that, under certain assumptions, the optimal path, which is the solution to the dynamically optimal control problem, remains for almost all periods close to the Neumann ray (i.e., turnpike), which is the solution to the static optimal control problem, if sufficiently long periods are considered. We consider structural economic dynamics and cycles as examples of applicable fields. Based on Goodwin’s growth cycle, we construct a dynamically nonlinear optimal control model using government cost function. Our numerical analysis demonstrates that the optimal path remains near the turnpike for almost all periods if sufficiently long periods are considered, in contrast to Goodwin’s assertion that the turnpike embedded in the growth cycle model is unstable. Because the essence of the turnpike property is unrelated to the number of sectors, it can be applied to a broader class of models that have rarely been considered in the analysis of the turnpike theorem. We also show the possibility of the government choosing the turnpike (i.e., the ideal trajectory) by determining the parameters and form of the cost function. This study develops on the theoretical implications for Pasinetti’s work on structural economic dynamics to show that institutions matter for stable economic growth.