Endogenous Cycles in Optimal Monetary Policy with a Nonlinear Phillips Curve

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy with sticky prices a la Calvo and forward looking behavior. In this paper we extend this standard model by introducing nonlinearity into the Phillips curve. As the linear Phillips curve may be questioned on theoretical grounds and seems not to be favoured by empirical evidence, a similar procedure has already been undertaken in a series papers over the last few years, e.g., Schaling (1999), Semmler and Zhang (2004), Nobay and Peel (2000), Tambakis (1999), and Dolado et al. (2004). However, these papers were mainly concerned with the analysis of the problem of inflation bias, by deriving an interest rate rule which is nonlinear, leaving the issues of stability and the possible existence of endogenous cycles in such a framework mostly overlooked. Under the specific form of nonlinearity proposed in our paper (which allows for both convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into a fully deterministic structure of the standard model produces significant changes to the major conclusions regarding stability and the efficiency of monetary policy in the standard model. We should emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable and chaotic fixed points (endogenous cycles); (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem interesting. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate may have a lower mean and is certainly less volatile; secondly, for changes in the degree of price stickiness the results are not are clear cut as in the previous case, however, we can also observe that when such stickiness is high the inflation rate tends to display a somewhat larger mean and also higher volatility; and thirdly, it shows that the target values for inflation and the output gap (π^,x^), both crucially affect the dynamics of the economy in terms of average values and volatility of the endogenous variables --- e.g., the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility --- while in the linear case only the π^ does so (obviously, only affecting in this case the level of the endogenous variables). Moreover, the existence of endogenous cycles due to chaotic motion may raise serious questions about whether the old dictum of monetary policy (that the Central Bank should conduct policy with discretion instead of commitment) is not still very much in the business of monetary policy.Optimal monetary policy, Interest Rate Rules, Nonlinear Phillips Curve, Endogenous Fluctuations and Stabilization

Chaotic Dynamics in Optimal Monetary Policy

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King (1997), Clarida et al. (1999), Svensson (1999) and Woodford (2003). In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.Comment: 11 page

Chain reorientation in ß-PVDF films upon transverse mechanical deformation studied by SEM and dielectric relaxation

Chain reorientation may be induced in polyvinylidene fluoride (PVDF) in its ß-phase by applying a deformation perpendicular to the pre-oriented polymeric chains. This reorientation begins right after the yielding point and seems to be completed when the stress-strain curve stabilizes. We have studied the chain reorientation mechanism by scanning electron microscopy (SEM) and dielectric relaxation methods and we have analyzed its influence in the alpha- and ß-relaxations of the polymer. SEM images confirm the existence of a reorientation upon transversal deformation. The decrease of crystallinity with increasing reorientation and the dependence of the dielectric permittivity upon deformation indicate that a model of stress-induced melting followed by an incomplete recrystallization properly describes the reorientation mechanism.Fundação para a Ciência e Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI) - POCTI/CTM/33501/99

Stress induced magnetic anisotropy on BaTiO3-CoFe2O4 nanogranular composite thin films

The influence of stress on the magnetic properties of BaTiO3-CoFe2O4 nanocomposites deposited by laser ablation on platinum covered Si(001) substrates, was characterized. The cobalt ferrite phase was under compressive strain in the growth direction that progressively relaxed as its concentration increased. A stress induced perpendicular magnetic anisotropy was observed, that decreased with increasing CoFe2O4 content, due to the relaxation of stress in the films.This work has been financially supported by the Portuguese Foundation for Science and Technology (FCT) and FEDER, through the projects POCI/CTM/60181/2004, FEDER/POCTI/0155/94, and through the Associated Laboratory-IN

RF CMOS Wireless Implantable Microsystem for Sacral Roots Stimulation with On-Chip Antenna and Far-Field Wireless Powering

The use of heterogeneous integration technologies is the path for the development of further miniaturized, smarter, and energy autonomous microdevices, which are required to tackle the challenge of monitoring and/or control the health condition of everyone, everywhere. The interaction with human body requires the use of flexible materials, while the electronic component are based on rigid materials, like silicon substrates. Also, once inside the human body, it is desirable to have a wireless link for data communication, as well for RF powering, using energy harvesting techniques or dedicated powering RF links. This paper shows the design of an implantable microsystem to be used for functional electrical stimulation of sacral roots. The proposed system includes flexible electrodes, integrated with an RF CMOS chip, which is powered by a wireless link through an efficient on-chip antenna.This work was supported by the Portuguese Foundation for Science and Technology (SFRH/BD/62608/2009), FCT-PTDC/EEI-TEL/2881/2012, Programa Operacional Temático Fatores de Competitividade (COMPETE) and Fundo Comunitário Europeu FEDER.info:eu-repo/semantics/publishedVersio

Structural and dielectric properties of laser ablated BaTiO3 films deposited over electrophoretically dispersed CoFe2O4 grains

Thin film nanocomposites with mixed connectivity, composed by CoFe2O4 grains deposited by electrophoresis on Si|Pt substrates and subsequently covered by a laser ablation deposited BaTiO3 layer were prepared with different cobalt ferrite concentrations. Their structure presented a combination of BaTiO3, with its tetragonal and the orthorhombic phases coexisting at room temperature, and CoFe2O4 with the cubic spinel structure. The cobalt ferrite nanograins were under in-plane tensile stress, while the BaTiO3 phase was under in-plane compressive stress. The dielectric measurements showed that as the barium titanate grain size decreased, its ferroelectric Curie temperature shifted to lower temperatures relative to the bulk. This grain size dependent TC shift was associated and modeled by a core-shell structure of BaTiO3 grains in the films, with a tetragonal core and cubic shell. Additionally a diffuse tetragonal-orthorhombic phase transition was observed and, in agreement with Raman spectroscopy results, associated to the coexistence of barium titanate orthorhombic and tetragonal phases in the room temperature region. This led to the formation of polar nanoclusters with random polarization orientations, which induced a frustrated phase transition between the tetragonal and orthorhombic phases of barium titanate in the films.This work has been supported by Fundacao para a Ciencia e Tecnologia (FCT) and FEDER, through the projects PTDC/CTM/099415/2008 and PTDC/CTM-NAN/115125/2009 and by QREN-ON2-O Novo Norte, through the project Operacao Norte-070124-FEDER-000070. J. G. Barbosa and I. T. Gomes gratefully acknowledge PhD grants from Fundacao para a Ciencia e Tecnologia (SFRH/BD/41913/2007 and SFRH/BD/36348/2007, respectively)