Convergence of singular integrals with general measures

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.

Global Nash convergence of Foster and Young's regret testing

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about the game. In fact, players' actions are based only on their own past payoffs and, in a variant of the strategy, players need not even know that their payoffs are determined through other players' actions. The procedure works for general finite games and is based on appropriate modifications of a simple stochastic learningrule introduced by Foster and Young.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

Convergence across countries and regions: theory and empirics

This paper surveys the recent literature on convergence across countries and regions. I discuss the main convergence and divergence mechanisms identified in the literature and develop a simple model that illustrates their implications for income dynamics. I then review the existing empirical evidence and discuss its theoretical implications. Early optimism concerning the ability of a human capital-augmented neoclassical model to explain productivity differences across economies has been questioned on the basis of more recent contributions that make use of panel data techniques and obtain theoretically implausible results. Some recent research in this area tries to reconcile these findings with sensible theoretical models by exploring the role of alternative convergence mechanisms and the possible shortcomings of panel data techniques for convergence analysis.

Gerogescu-Roegen versus Solow/Stiglitz and the convergence to the Cobb-Douglas

The value of the elasticity of substitution of capital for resources is a crucial element in the debate over whether continual growth is possible. It is generally held that the elasticity has to be at least one to permit continual growth and that there is no way of estimating this outside the range of the data. This paper presents a model in which the elasticity is determined endogenously and may converge to one. It is concluded that the general opinion is wrong: that the possibility of continual growth does not depend on the exogenously given value of the elasticity and that the value of the elasticity outside the range of the data can be studied by econometric methods.

Polynomial and linearized normal forms for almost periodic differential systems

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Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Price level convergence, purchasing power parity and multiple structural breaks: an application to US cities

This article provides a fresh methodological and empirical approach for assessing price level convergence and its relation to purchasing power parity (PPP) using annual price data for seventeen US cities. We suggest a new procedure that can handle a wide range of PPP concepts in the presence of multiple structural breaks using all possible pairs of real exchange rates. To deal with cross-sectional dependence, we use both cross-sectional demeaned data and a parametric bootstrap approach. In general, we find more evidence for stationarity when the parity restriction is not imposed, while imposing parity restriction provides leads toward the rejection of the panel stationar- ity. Our results can be embedded on the view of the Balassa-Samuelson approach, but where the slope of the time trend is allowed to change in the long-run. The median half-life point estimate are found to be lower than the consensus view regardless of the parity restriction.

Known and new results on absolute convergence of Fourier integrals

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d &= 2.

Human capital spillovers, productivity and regional convergence in Spain

This paper analyses the differential impact of human capital, in terms of different levels of schooling, on regional productivity and convergence. The potential existence of geographical spillovers of human capital is also considered by applying spatial panel data techniques. The empirical analysis of Spanish provinces between 1980 and 2007 confirms the positive impact of human capital on regional productivity and convergence, but reveals no evidence of any positive geographical spillovers of human capital. In fact, in some specifications the spatial lag presented by tertiary studies has a negative effect on the variables under consideration.

Statmedia 3 : activitats on-line individualitzades d'estadística i matemàtiques als ensenyaments de Ciències Experimentals i Socials

El projecte Statmedia 3 ha consolidat definitivament la proposta de les assignatures Bioestadística de Biologia, Anàlisi de dades de Ciències Ambientals i d’Estadística Matemàtica de la Diplomatura renovant una part del material creat amb Statmedia 2. S’han inclòs a més Matemàtiques d’Ambientals i Introducció a la Probabilitat del Grau d’Estadística. L’anterior MQD abastava només pràctiques mentre que aquest projecte permet una oferta diversa d’activitats individualitzades. La individualització consisteix en que cada estudiant rep una proposta de cas personalitzada amb dades diferents. Les activitats poden ser programades presencialment o no, però la clau de l’èxit de l’activitat és que l’alumne obtingui reconeixement del seu treball en l’avaluació continuada. La valoració que fan als alumnes de Statmedia és molt bo, i observem que es produeix una millora en els resultats acadèmics. Statmedia 3 ha implicat un important esforç en la vessant informàtica del projecte, la barreja de tecnologies que utilitzem son punteres: Ajax, servlets i applets Java... Hem posat a punt un assistent on-line per dissenyar documents i planificar activitats que facilita la tasca dels professors. La nostre participació en primera línea del procés de convergència a l’EEES ens ha permès anticipar alguns canvis, i s’ha traduït en que el claustre del Departament d’Estadística assumís que Statmedia és una metodologia essencial dels seus plans docents. El projecte continua en un quart projecte MQD consecutiu, on desplegarem la nova tecnologia implementada. L’objectiu principal serà dotar a les assignatures dels 7 graus on participa el departament d’activitats individualitzades en forma de casos pràctics, problemes i proves diverses. La col·lecció de material emmagatzemada en la nostra biblioteca, forjada després de quasi deu anys de treball continuat, juntament amb l’experiència acumulada de com utilitzar Statmedia de la forma més eficient han començat a ser explotades en els nous graus aquest mateix curs 2009-2010.

Absolute convergence of Fourier integrals

In this survey, results on the representation of a function as an absolutely convergent Fourier integral are collected, classified and discussed. Certain applications are also given.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Two-sided learning in new keynesian models: dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank (two-sided learning) in a New Keynesian framework in which both sides of the economy have asymmetric and imperfect knowledge about the true data generating process. We assume that all agents employ the data that they observe (which may be distinct for different sets of agents) to form beliefs about unknown aspects of the true model of the economy, use their beliefs to decide on actions, and revise these beliefs through a statistical learning algorithm as new information becomes available. We study the short-run dynamics of our model and derive its policy recommendations, particularly with respect to central bank communications. We demonstrate that two-sided learning can generate substantial increases in volatility and persistence, and alter the behavior of the variables in the model in a signifficant way. Our simulations do not converge to a symmetric rational expectations equilibrium and we highlight one source that invalidates the convergence results of Marcet and Sargent (1989). Finally, we identify a novel aspect of central bank communication in models of learning: communication can be harmful if the central bank's model is substantially mis-specified