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

Effective action in DSR1 quantum field theory

We present the one-loop effective action of a quantum scalar field with DSR1 space-time symmetry as a sum over field modes. The effective action has real and imaginary parts and manifest charge conjugation asymmetry, which provides an alternative theoretical setting to the study of the particle-antiparticle asymmetry in nature.Comment: 8 page

On the dynamics of bubbles in boiling water

We investigate the dynamics of many interacting bubbles in boiling water by using a laser scattering experiment. Specifically, we analyze the temporal variations of a laser intensity signal which passed through a sample of boiling water. Our empirical results indicate that the return interval distribution of the laser signal does not follow an exponential distribution; contrariwise, a heavy-tailed distribution has been found. Additionally, we compare the experimental results with those obtained from a minimalist phenomenological model, finding a good agreement.Comment: Accepted for publication in Chaos, Solitons & Fractal

On the nonlinearity interpretation of q- and f-deformation and some applications

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.Comment: 11 pages Late

Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.Comment: LATEX,21 pages,submitted to Physica Script

Geometry, stochastic calculus and quantum fields in a non-commutative space-time

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space-time, on quantum stochastic calculus and on the construction of quantum fields. Some of these effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur

As redes sociais pessoais das crianças e jovens institucionalizados

A pedagogia da vinculação assenta na ideia generalizada de que o contexto familiar reúne as condições privilegiadas para o desenvolvimento e educação das crianças, enfatizando a díade mãe-filho (Singer, 1993). Esta conceção, largamente partilhada pela cultura do sensocomum e fundamentada na perspetiva psicológica das teorias da vinculação, serve de padrão, com base no qual é aferida a qualidade das relações das crianças/jovens em regime institucional com adultos de referência. Contudo, o caráter necessário da intimidade e da proximidade relacional nas instituições de atendimento à infância não reúne consenso. Ziehe (1989) questiona-o e propõe o conceito de intensidade das relações, traduzido numa rede complexa e densa de pessoas, meios e atividades, que criam uma multiplicidade de oportunidades para as crianças, cabendo às instituições a sua promoção e a criação de condições para a sua ampliação e desenvolvimento sustentado. Nesta linha, Sluzki (1996) propõe o conceito de Rede Social Pessoal (R.S.P.) como o conjunto das relações que o indivíduo percebe como significativas ou diferenciadas em diferentes dimensões da sua vida (família, amigos, escola/trabalho e comunidade). Reconhecida a relevância desenvolvimental das relações pessoais significativas e a sua influência no bem-estar individual, torna-se pertinente estudar o seu papel para as crianças/jovens institucionalizados e o papel desempenhado pelas instituições de acolhimento na sua promoção. Assim, com este estudo, pretende-se: a) caraterizar as R.S.P de crianças/jovens em regime de acolhimento institucional (amplitude, intensidade, significado e funções desempenhadas pelos diferentes elementos da R.S.P.), com recurso ao Inventário de Avaliação de Redes Sociais Pessoais – Revisto (adaptado por Alarcão; Abreu & Sousa, 2003); b) caraterizar o conhecimento das R.S.P. das crianças acolhidas pelas instituições de acolhimento e o seu papel na promoção destas redes; c) caraterizar o papel das redes naturais primárias e, neste âmbito, o papel da família e das fratrias; d) caraterizar o papel das Famílias Amigas e a sua relação com a qualidade de vida destas crianças/jovens

Transition from small to large world in growing networks

We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether the attachment probability decays slower or faster than $(age)^{-1}$. The network becomes one-dimensional when the attachment probability decays faster than $(age)^{-2}$. We describe structural characteristics of these phases and transitions between them.Comment: 5 page