Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

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 is 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. Policy options to eliminate or control the chaotic dynamics are developed

Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

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 is 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. Policy options to eliminate or control the chaotic dynamics are developed

Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model

This paper shows that the dynamics of the Lucas (J Monet Econ, 22:3–42, 1988) endogenous growth model with flow externalities may give rise to a 2-torus, a compact three-dimensional manifold enclosed by a two-dimensional surface. The implications of this result are relevant for many fields of economic theory. It is first of all clear that if we choose to initialize the dynamics in the basin of attraction of this trapping region, a continuum of perfect foresight solutions may be observed. A simple econometric exercise, linking the physical-to-human capital ratio (state variable) to the 5-years forward variance of the growth rate of an unbalanced sample of 183 countries, seems to provide empirical backing for the phenomenon. Other important consequences, relevant from the point of view of endogenous cycles theory, are also scrutinized in the paper

The impact of immigration on output and its components: A sectoral analysis for Italy at regional level

This paper studies how immigrants impact on Italian economy. The issue is addressed following the channel output decomposition approach by means of which the effect of immigration is measured with respect to per capita value added and its components. The investigation is carried out at sector level during the 2008–2011 time period. The results show that the main channel through which migration impacts on value added varies on sectoral basis. While at aggregate level, in Manufacturing and in Other Services the impact goes mainly through capital intensity, in the Construction and in the Commerce sectors the principal channel is via total factor productivity

Improvement of antiamoebic activity of Rokitamycin loaded in chitosan microspheres

Rokitamycin is a new macrolide containing 16 carbon atoms, strongly inhibitory for Acanthamoeba castellanii, an opportunistic protozoa of humans which cause primarily amoebic keratitis and chronic, but fatal, amoebic granulomatous meningoencephalitis. Chitosan microspheres were prepared as carriers to obtain a controlled release of rokitamycin, able to improve the antiamoebic activity of this drug. The microparticles were in vitro characterised and the efficacy of rokitamycin alone and encapsulated into microspheres on the growth rate of Acanthamoeba castellani was evaluated. The results obtained suggest that spray-drying is a good technique for the preparation of microspheres loaded with rokitamycin. The loading of the drug into the polymeric network leads to an increase in the dissolution rate compared to drug raw material and improves and prolongs the in vitro antiamoebic activity of the drug. Thus, microspheres based on rokitamycin could be used in the therapy of systemic and topical infections caused by Acanthamoeba

Chaos in the UK New Keynesian Macroeconomy

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

Seasonal drought in Mediterranean soils mainly changes microbial C and N contents whereas chronic drought mainly impairs the capacity of microbes to retain P

Altres ajuts: Acord transformatiu CRUE-CSICIntensification of droughts may aggravate the generally low capacity of Mediterranean soils to store C and nutrients and induce soil C:N:P stoichiometric imbalances through its impact on soil microbial biomass and activity. Soil microbes may nonetheless have different responses to seasonal and chronic drought, but very few studies investigate long-term drought periods under field conditions. This study compares the effects of seasonal drought versus the impacts of 16 years of chronic experimental drought on microbial biomass and nutrients and assess the implications for soil nutrient availability and biogeochemical functioning in a Mediterranean forest. The chronic drought treatment reduced substantially and persistently microbial biomass C, N and particularly P, probably due to P-sparing community shifts or microbial adaptations. The smaller microbial N pool and lower mineralization activity contributed to the accumulation of C- and N-rich organic compounds in the soil and to a lower availability of mineralized forms of N during the vegetation growing season. As a result, chronic drought conditions may increase the risks of N losses from the plant-soil system in Mediterranean ecosystems. Microbial C:N ratios remained unaltered under chronic drought compared to control, likely associated with the equivalent accumulation of C- and N-rich osmolytes by microbial communities. In contrast, microbial biomass increased its C content relative to N content in response to seasonal drought, but also reduced considerably its N and P pool. Therefore, while microbial P was more sensitive to chronic water stress, microbial N and C were more closely coupled to the seasonal fluctuations of water availability

Controlling Chaos in New Keynesian Macroeconomics

In a New Keynesian model, it is believed that combining active monetary policy using a Taylor rule with a passive fiscal rule can achieve local equilibrium determinacy. However, even with such policies, indeterminacy can occur from the emergence of a Shilnikov chaotic attractor in the region of the feasible parameter space. That result, shown by Barnett et al. (2021), implies that the presence of the Shilnikov chaotic attractor can cause the economy to drift towards and finally become stuck in the vicinity of lower-than-targeted inflation and nominal interest rates. The result can become the source of a liquidity trap phenomenon. We propose policy options for eliminating or controlling Shilnikov chaotic dynamics to help the economy escape from the liquidity trap or avoid drifting into it in the first place. We consider ways to eliminate or control the chaos by replacing the usual Taylor rule by an alternative policy design without interest rate feedback, such as a Taylor rule with monetary quantity feedback, an active fiscal policy rule with passive monetary rule, or an open loop policy without feedback. We also consider approaches that retain the Taylor rule with interest rate feedback and the associated Shilnikov chaos, while controlling the chaos through a well-known engineering algorithm using a second policy instrument. We find that a second instrument is needed to incorporate a long-run terminal condition missing from the usual myopic Taylor rule

On the evolution of the Gamma- and X-ray luminosities of Pulsar Wind Nebulae

Pulsar wind nebulae are a prominent class of very high energy (E > 0.1 TeV) Galactic sources. Their Gamma-ray spectra are interpreted as due to inverse Compton scattering of ultrarelativistic electrons on the ambient photons, whereas the X-ray spectra are due to synchrotron emission. We investigate the relation between the Gamma- and-X-ray emission and the pulsars' spin-down luminosity and characteristic age. We find that the distance-independent Gamma- to X-ray flux ratio of the nebulae is inversely proportional to the spin-down luminosity, (\propto \dot{E}^-1.9), while it appears proportional to the characteristic age, (\propto tau_c^2.2), of the parent pulsar. We interpret these results as due to the evolution of the electron energy distribution and the nebular dynamics, supporting the idea of so-called relic pulsar wind nebulae. These empirical relations provide a new tool to classify unidentified diffuse Gamma-ray sources and to estimate the spin-down luminosity and characteristic age of rotation powered pulsars with no detected pulsation from the X- and Gamma-ray properties of the associated pulsar wind nebulae. We apply these relations to predict the spin-down luminosity and characteristic age of four (so far unpulsing) candidate pulsars associated to wind nebulae.Comment: Accepted for publication in ApJ (6 pages, 2 figures