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.

We show that the introduction of a constant tariff or subsidy levied on foreign energy can lead to a rich set of endogenous fluctuations around the unique steady state, including stable 2-, 4-, 8-, and 15-cycles, quasiperiodic orbits, and chaos. This is demonstrated in a standard neoclassical growth model with social increasing returns to scale. Numerical exercises could be viewed from a methodological perspective as illustrating that capital income taxes and tariffs are equivalent in generating endogenous fluctuations because Guo and Lansing [Guo, J.T. and K.J. Lansing (2002) Fiscal policy, increasing returns and endogenous fluctuations. Macroeconomic Dynamics 6, 633–664] show that a constant capital tax or subsidy has the same effect on the model dynamics in a one-sector closed economy.