Generalized Taylor and Generalized Calvo price and wage-setting: micro evidence with macro implications

The Generalized Calvo and the Generalized Taylor model of price and wage-setting are, unlike the standard Calvo and Taylor counterparts, exactly consistent with the distribution of durations observed in the data. Using price and wage micro-data from a major euro-area economy (France), we develop calibrated versions of these models. We assess the consequences for monetary policy transmission by embedding these calibrated models in a standard DSGE model. The Generalized Taylor model is found to help rationalizing the hump-shaped response of inflation, without resorting to the counterfactual assumption of systematic wage and price indexation.Contract length, steady state, hazard rate, Calvo, Taylor, wage-setting, price-setting.

Evaluating Monetary Policy Rules in Estimated Forward-Looking Models: A Comparison of US and German Monetary Policies.

In this paper, we estimate two small, forward-looking, macroeconomic models for the US and Germany and we compare the implied optimal monetary policy rules. Both models have a standard structure: an I-S curve, a Phillips curve, a short term interest-rate rule and a long term interest rate determined by the Expectations Hypothesis. They are intended to fit the data while allowing for some forward-looking behavior. They are estimated from 1968 to 1998, using the full-information maximum-likelihood procedure, so that forward-looking expectations are fully model-consistent. In order to evaluate monetary policy, we compute optimal policy frontiers and we perform some simulations of the model. German optimal monetary policy is found to require a more persistent and slightly stronger response to inflation and output than the US optimal policy.Forward-looking model ; monetary policy rules

ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the New Phillips Curve)

Many macroeconomic models involve hybrid equations, in which some variables are a function of both their lags and their expected future value. The hybrid "New Keynesian" Phillips Curve is a prominent example. Estimates of such hybrid models have produced conflicting empirical results: Studies which use ML estimation tend to find the forward-looking component to be small, while those using GMM have reported the inflation dynamics to be predominantly forward-looking. This paper provides a rationalization for this empirical conflict. Allowing for two alternative and straightforward mis-specifications (measurement error and omitted dynamics) in a hybrid model, we show that the ML estimator tends to undervalue the weight of the forward-looking component, while the GMM estimator tends to overstate it. This result is shown to hold analytically in a simple DGP. Monte-Carlo experiments indicate that it remains valid in a wide range of more plausible DGPs. Simulations also suggest that the gap obtained between the two estimators in the context of the new Phillips curve can more readily be accounted for by mis-specification, than by the finite-sample biases.Rational-expectation model ; GMM estimator ; ML estimator ; Inflation ; New Phillips curve

Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US Data.

The "New Keynesian" Phillips Curve (NKPC) states that inflation has a purely forward-looking dynamics. In this paper, we test whether European and US inflation dynamics can be described by this model. For this purpose, we estimate hybrid Phillips curves, which include both backward and forward-looking components, for major European countries, the euro area, and the US. Estimation is performed using the GMM technique as well as the ML approach. We examine the sensitivity of the results to the choice of output gap or marginal cost as the driving variable, and test the stability of the obtained specifications. Our findings can be summarized as follows. First, in all countries, the NKPC has to be augmented by additional lags and leads of inflation, in contrast to the prediction of the core model. Second, the fraction of backward-looking price setters is large (in most cases, more than 50 percent), suggesting only limited differences between the US and the euro area. Finally, our preferred specification includes marginal cost in the case of the US and the UK, and output gap in the euro area.Forward-looking ; Phillips curve ; euro area ; GMM estimator ; ML estimator.

Inattentive professional forecasters

We use the ECB Survey of Professional Forecasters to characterize the dynamics of expectations at the micro level. We find that forecasters (i) have predictable forecast errors; (ii) disagree; (iii) fail to systematically update their forecasts in the wake of new information; (iv) disagree even when updating; and (v) differ in their frequency of updating and forecast performances. We argue that these micro data facts are qualitatively in line with recent models in which expectations are formed by inattentive agents. However building and estimating an expectation model that features two types of inattention, namely sticky information à la Mankiw-Reis and noisy information à la Sims, we cannot quantitatively generate the error and disagreement that are observed in the SPF data. The rejection is mainly due to the fact that professionals relatively agree on very sluggish forecasts.imperfect information, inattention, forecast errors, disagreement, business cycle.

Quatre indicateurs d'inflation sous-jacente: application et interpretation.

Dans ce papier, nous comparons quatre indicateurs de l'inflation sous-jacente: l'approche par exclusion de postes, les estimateurs "a influence limitee" comme l'inflation mediane, les mesures issues d'un VAR structurel et une mesure tiree d'un modele a composantes inobservables. Ces indicateurs sont discutes du point de vue de leur interpretation et de leur utilisation a des fins conjoncturelles.Econometrie ; Inflation ; Instruments de mesure

Price Stickiness and Sectoral Inflation Persistence: Additional Evidence

In this paper, using US as well as French sectoral data and indicators of price rigidity, we re-examine the (lack of) relation between price stickiness and inflation persistence. This has recently been put forward by Bils and Klenow (2004) as evidence against time-dependent price setting models. We obtain that, when filtering out sector-specific shocks along the lines of Boivin et al. (2009), and allowing for an alternative assumption on the marginal cost process, the case against the time-dependent Calvo model is substantially weakened.Sticky prices, Heterogeneity, Inflation persistence.

Riemannian Gaussian distributions on the space of positive-definite quaternion matrices

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it develops the Riemannian geometry of the space of positive-definite quaternion matrices, which is shown to be a Riemannian symmetric space of non-positive curvature. The paper gives original formulae for the Riemannian metric of this space, its geodesics, and distance function. Then, it develops the theory of Riemannian Gaussian distributions, including the exact expression of their probability density, their sampling algorithm and statistical inference.Comment: 8 pages, submitted to GSI 201

Density estimation on the rotation group using diffusive wavelets

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an existing technique using the De La Vall\'ee Poussin kernel estimator. The heat-kernel wavelet approach appears to offer the best convergence, with faster convergence to the optimal bound and guaranteed positivity of the estimated probability density function

Isotropic Multiple Scattering Processes on Hyperspheres

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres ${\mathbb S}^{p-1}$. It allows one to derive the Fourier expansions on ${\mathbb S}^{p-1}$ of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on ${\mathbb S}^{p-1}$ is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on ${\mathbb S}^{p-1}$ are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on ${\mathbb S}^{p-1}$.Comment: 16 pages, 4 figure