Shilnikov chaos, low interest rates, and New Keynesian macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feed- back 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 pa- rameter space where uniqueness of the equilibrium prevails locally. Implications, rang- ing 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 nomi- nal 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 func- tion, in the utility function, or not in the model at all. But our results do depend upon the existence of sticky prices.