Abstract
The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent, inflation rates have declined to current low levels, such that the real rate of interest may be below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Our results are robust to whether money is in the production function, in the utility function, or not in the model at all. But our results do depend upon the existence of sticky prices.
Highlights
Since the data were not produced from a controlled experiment and the tests did not condition on an economic model, the tests had no way to impute the source of the chaos to the nonlinear dynamics of the economy
We find potentially high relevance of Shilnikov chaos to current problems in the world’s macroeconomies, when active Taylor rule monetary feedback policy is adjoined to a New Keynesian (NK) dynamic macroeconomic model
We offer an alternative explanation, based on the long-run peculiarities of a chaotic attractor and the evolution of the dynamics within that attractor set, such that the economy drifts into the liquidity trap without any policy intent
Summary
The earliest literature used tests developed by physicists for detecting chaos in data produced from controlled experiments Those tests focused primarily on measuring the Hausdorf dimension of the attractor set and testing for positive dominant Liapunov exponent.. The likelihood function can have singularities as it passes over the null hypothesis set.7 Faced with such statistical inference problems, research turned to exploration of the theoretical properties of macroeconomic models. The number of various models from hydrodynamics, optics, chemical kinetics, biology etc., which demonstrated the numerically or experimentally strange attractors with the characteristic spiral structure suggesting the occurrence of a saddle focus homoclinic loop, was overwhelming This scenario has turned out to be typical for a variety of systems and models of very diverse origins.”. We find potentially high relevance of Shilnikov chaos to current problems in the world’s macroeconomies, when active Taylor rule monetary feedback policy is adjoined to a NK dynamic macroeconomic model
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