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Chaos in the UK New Keynesian Macroeconomy

Barnett, William and Bella, Giovanni and Ghosh, Taniya and Mattana, Paolo and Venturi, Beatrice (2021): Chaos in the UK New Keynesian Macroeconomy.

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Abstract

We study the stability properties and conditions for the onset of Shilnikov chaos in the UK New Keynesian macroeconomy, as well as the shifts in the equilibrium dynamics under various policy regimes. We find that Shilnikov chaos emerges for a restricted part of the free parameters space in the baseline rational expectations UK model with no regime switching. When the UK's central bank showed a weak response to inflation in the high inflation regime, the chaos did not occur at all. But Shilnikov chaos appears easily in the case of the low-inflation regime, which is associated with the Bank of England's use of aggressive monetary policy in recent years. Tightening the monetary policy interest-rate-feedback rule via the Taylor coefficient is one of the policy alternatives proposed by the local analysis for restoring uniqueness. We find that doing so accelerates the emergence of unanticipated phenomena such as Shilnikov's chaotic dynamics. Our results with UK data are thereby consistent with the results with US data by Barnett et al. (2021), who found that the adoption of an active interest rate feedback rule in recent years by the Federal Reserve produces Shilnikov chaos and unintentional downward drift in interest rates towards the lower bound. The source of the chaos and downward drift in interest rates is adoption of a myopic short-run interest-rate feedback rule without a terminal condition as long run anchor. A critical assumption of the results with US and UK data are existence of new Keynesian sticky prices. While the model’s parameters were calibrated with pre-Brexit data, we expect that our results will be highly relevant post-Brexit, as the needed data become available. Changes in the geometry of the Shilnikov fractal attractor set can be expected to be revealing about changes in the level and nature of UK economic risk following Brexit.

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