Globally Indeterminate Growth Paths in the Lucas Model of Endogenous Growth

Abstract

This paper shows that global indeterminacy may characterize the three-dimensional vector field implied by the Lucas [(1988) Journal of Monetary Economics 22, 3–42] endogenous growth model. To achieve this result, we demonstrate the emergence of a family of homoclinic orbits connecting the steady state to itself in backward and forward time, when the stable and unstable manifolds are locally governed by real eigenvalues. In this situation, we prove that if the saddle quantity is negative, and other genericity conditions are fulfilled, a stable limit cycle bifurcates from the homoclinic orbit. Orbits originating in a tubular neighborhood of the homoclinic orbit are then bound to converge to this limit cycle, creating the conditions for the onset of global indeterminacy. Some economic intuitions related to this phenomenon are finally explored.

Global Indeterminacy and Invariant Manifolds Near Homoclinic Orbit to a Real Saddle in a Resource Optimal System

“…Any initial condition starting inside this tubular neighborhood gives rise to perfect-foresight equilibrium. Finally, with similar arguments introduced in [9], we are able to show global indeterminacy of the equilibrium for the model, since the result is valid beyond the small neighborhood relevant for the local analysis.…”

Does boundary solutions of the Lucas endogenous growth model explain why some countries are not accumulating human capital?

“…As it appears clear, the general predictions of the Lucas model are roughly satisfied, and the quadratic fitting line reports a R 2 = 0.24, unexpectedly high considering the simplifying assumption adopted and the ill-equipped nature (for our purposes) of the datasets. 5 We observe the following: for observations characterized by Sign(Υ) < 0, there is a steep tendency of human capital to growth; the economy finds it optimal to diverte time from goods producing and convey all the available effort towards the schooling sector. Consistently with the transient dynamics of (an interior solution) the Lucas model, u(t) is decreasing and diverging from the upper limit of its domain of existence.…”

Human Capital, Economic Growth and Poverty Reduction Nexus: Why Investment in Free Compulsory Universal Education Matters for Africa

“…Marginson (2019) acknowledges that certain policy variables, like education subsidies, have a beneficial effect on long-term economic growth. Bella et al (2019) assert that human capital as a factor of production impacts positively on economic growth , while Habib et al (2019) elucidated that making human capital productive requires skills and knowledge that come out of education and training. Human capital encapsulates the acquired skill set, abilities and knowledge possessed by individual workers.…”