The width of resonances for slowly varying perturbations of one-dimensional periodic Schr\"{o}dinger operators

In this talk, we report on results about the width of the resonances for a slowly varying perturbation of a periodic operator. The study takes place in dimension one. The perturbation is assumed to be analytic and local in the sense that it tends to a constant at $+\infty$ and at $-\infty$; these constants may differ. Modulo an assumption on the relative position of the range of the local perturbation with respect to the spectrum of the background periodic operator, we show that the width of the resonances is essentially given by a tunneling effect in a suitable phase space

Solving Rational Expectations Models

In this chapter, we present theoretical foundations of main methods solving rational expectations models with a special focus on perturbation approaches. We restrict our attention to models with a finite number of state variables. We first give some insights on the solution methods for linear models. Second, we show how to use the perturbation approach for solving non-linear models. We then document the limits of this approach. The perturbation approach, while it is the most common solution method in the macroeconomic literature, is inappropriate in a context of large fluctuations (large shocks or regime switching) and of strong non-linearities (e.g. occasionally binding constraints). The former case is then illustrated extensively by studying regime switching models. We also illustrate the latter case by studying existing methods for solving rational expectations models under the Zero Lower Bound constraint, i.e. the condition of non negativity of the nominal interest rate. Finally, we end up with a brief presentation of global methods which are alternatives when the perturbation approach fails in solving models

State-Dependent Probability Distributions in Non Linear Rational Expectations Models

In this paper, we provide solution methods for non-linear rational expectations models in which regime-switching or the shocks themselves may be "endogenous", i.e. follow state-dependent probability distributions. We use the perturbation approach to find determinacy conditions, i.e. conditions for the existence of a unique stable equilibrium. We show that these conditions directly follow from the corresponding conditions in the exogenous regime-switching model. Whereas these conditions are diffcult to check in the general case, we provide for easily verifiable and sufficient determinacy conditions and first-order approximation of the solution for purely forward-looking models. Finally, we illustrate our results with a Fisherian model of inflation determination in which the monetary policy rule may change across regimes according to a state-dependent transition probability matrix.Dans ce papier, nous proposons une méthode de résolution de modèles non linéaires à anticipations rationnelles dans lesquels les changements de régimes ou les chocs eux-même peuvent être "endogènes", c'est-à-dire suivre des distributions de probabilités dépendant de l'état de l'économie. Par une méthode de perturbation, nous trouvons des conditions de détermination, i.e. des conditions d'existence d'un unique équilibre stable. Nous montrons que ces conditions découlent directement des conditions correspondantes dans le modèle à changements de régimes exogènes. Bien que ces conditions soient difficiles à vérifier dans le cas général, nous donnons, dans le cas des modèles à changements de régimes purement tournés vers le futur, des conditions de détermination faciles à calculer et une approximation au premier ordre de la solution. Enfin, nous illustrons nos résultats avec un modèle de Fisher de détermination d'inflation dans lequel la règle de politique monétaire change entre les régimes selon une matrice de transition dépendant de l'état de l'économie

A two-pillar DSGE monetary policy model for the euro area

The current financial crisis has revived the interest for monitoring both monetary and credit developments. Over the past two decades, consistent with the adoption of inflation targeting strategies by a growing number of central banks and the development of New Keynesian models for which monetary aggregates are largely irrelevant, money and credit have been progressively neglected in the conduct of monetary policy. A striking exception has been the Eurosystem, which has implemented a strategy known as the “two-pillar monetary policy strategy” giving a prominent role for money. In this paper, we develop a small optimizing model based on Ireland (2004), estimated on euro area data and featuring this two-pillar strategy. We evaluate an ECB-style cross-checking policy rule in a DSGE model with real balance effects of money. We find some evidence that indeed money plays a non-trivial role in explaining the euro area business cycle. This provides a rationale for the central bank to factor in monetary developments but also raises some issues regarding the reliability of M3 as an appropriate monetary indicator. We find some evidence that the ECB has systematically reacted to a filtered measure of money growth but weak evidence it has reacted more aggressively during excess money growth periods

Trends and Cycles: An Historical Review of the Euro Area

We analyze the euro area business cycle in a medium scale DSGE model where we assume two stochastic trends: one on total factor productivity and one on the inflation target of the central bank. To justify our choice of integrated trends, we test alternative specifications for both of them. We do so, estimating trends together with the model's structural parameters, to prevent estimation biases. In our estimates, business cycle fluctuations are dominated by investment specific shocks and preference shocks of households. Our results cast doubts on the view that cost push shocks dominate economic fluctuations in DSGE models and show that productivity shocks drive fluctuations on a longer term. As a conclusion, we present our estimation's historical reading of the business cycle in the euro area. This estimation gives credible explanations of major economic events since 1985.Nous analysons les fluctuations du cycle économique en Zone Euro dans le cadre d'un modèle DSGE comprenant deux tendances stochastiques, une sur la productivité globale des facteurs et l'autre sur la cible d'inflation. Pour justifier notre choix de tendances intégrées, nous testons des spécifications différentes pour chacune d'elles. Afin d'éviter des biais dans l'estimation, nous estimons conjointement les tendances et les paramètres structurels du modèle. Nos estimations montrent que les fluctuations du cycle économique sont principalement expliquées par des chocs spécifiques d'investissement et des chocs de préférence des ménages. Nos résultats mettent en défaut l'idée que les chocs de mark-up sont les principaux vecteurs des fluctuations économiques dans les modèles DSGE et montrent que les chocs de productivité expliquent les fluctuations de long terme. En conclusion, nous présentons une relecture historique du cycle économique en zone euro à l'aune de notre estimation. Cette estimation donne une explication crédible des événements économiques majeurs depuis 1985

Inflation tolerance ranges in the new keynesian model

Los bancos centrales de varios países avanzados utilizan rangos, o bandas, en torno a su objetivo de inflación para formular su estrategia de política monetaria. La adopción de estos rangos ha sido propuesta por algunos responsables de política monetaria en el contexto de las revisiones de la estrategia de la Fed y del BCE. Utilizando un modelo macroeconómico neokeynesiano estándar, analizamos las consecuencias de las políticas de rangos de tolerancia, caracterizadas por una reacción más fuerte del banco central a la inflación cuando esta se encuentra fuera del rango que cuando está cerca del objetivo, es decir, del valor central de la banda. Demostramos que: i) una banda de tolerancia no debería ser una zona de inacción: la falta de reacción dentro de la banda pone en peligro la estabilidad macroeconómica y conduce a la posibilidad de múltiples equilibrios; ii) el trade-off entre la reacción necesaria fuera de la banda y dentro de ella parece desfavorable: cuando la inflación está lejos del objetivo, se requiere una reacción muy fuerte para compensar una reacción moderadamente menor dentro de la banda de tolerancia, y iii) estos resultados, obtenidos en el marco de un modelo estilizado, son robustos a muchas alteraciones, en particular a la imposición de un límite inferior a los tipos de interés.A number of central banks in advanced countries use ranges, or bands, around their inflation target to formulate their monetary policy strategy. The adoption of such ranges has been proposed by some policymakers in the context of the Fed and the ECB reviews of their strategies. Using a standard New Keynesian macroeconomic model, we analyze the consequences of tolerance range policies, characterized by a stronger reaction of the central bank to inflation when inflation lies outside the range, than when it is close to the target, i.e., the central value of the band. We show that (i) a tolerance band should not be a zone of inaction: the lack of reaction within the band endangers macroeconomic stability and leads to the possibility of multiple equilibria; (ii) the trade-off between the reaction needed outside the range versus inside appears unfavorable: a very strong reaction, when inflation is far from the target, is required to compensate for a moderately lower reaction within tolerance band; (iii) these results, obtained within the framework of a stylized model, are robust to many alterations, in particular allowing for the zero lower bound

On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators

We study spectral properties of a family of quasiperiodic Schrödinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curve has a real branch that is extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent and show that the spectrum is purely singular. This result was conjectured and proved in a particular case by Fedotov and Klopp (2005)

Measurement of open charm production in dd+Au collisions at sNN\sqrt{s_{NN}}=200 GeV

We present the first comprehensive measurement of $D^{0}, D^{+}, D^{*+}$ and their charge conjugate states at mid-rapidity in $d$+Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV using the STAR TPC. The directly measured open charm multiplicity distribution covers a broad transverse momentum region of 0$<p_{T}<11$ GeV/$c$. The measured $dN/dy$ at mid-rapidity for $D^{0}$ is $0.0265\pm 0.0036 (stat.) \pm 0.0071 (syst.)$ and the measured $D^{*+}/D^{0}$ and $D^{+}/D^{0}$ ratios are approximately equal with a magnitude of $0.40\pm 0.09(stat.) \pm 0.13(syst.)$. The total $c\bar{c}$ cross section per nucleon-nucleon collision extracted from this study is $1.18 \pm 0.21(stat.) \pm 0.39(syst.)$mb. The direct measurement of open charm production is consistent with STAR single electron data. This cross section is higher than expectations from PYTHIA and other pQCD calculations. The measured $p_{T}$ distribution is harder than the pQCD prediction using the Peterson fragmentation function.Comment: Quark Matter 2004 Proceeding