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.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

The structural approach of a natrex model on equilibrium exchange rates

Following a general macroeconomic approach, this paper sets a closed micro-founded structural model to determine the long run real exchange rate of a developed economy. In particular, the analysis follows the structure of a Natrex model. The main contribution of this research paper is the development of a solid theoretical framework that analyse in depth the basis of the real exchange rate and the details of the equilibrium dynamics after any shock influencing the steady state. In our case, the intertemporal factors derived from the stock-flow relationship will be particularly determinant. The main results of the paper can be summarised as follows. In first place, a complete well-integrated structural model for long-run real exchange rate determination is developed from first principles. Moreover, within the concrete dynamics of the model, it is found that some convergence restrictions will be necessary. On one hand, for the medium run convergence the sensitivity of the trade balance to changes in real exchange rate should be higher that the correspondent one to the investment decisions. On the other hand, and regarding long-run convergence, it is also necessary both that there exists a negative relationship between investment and capital stock accumulation and that the global saving of the economy depends positively on net foreign debt accumulation. In addition, there are also interesting conclusions about the effects that certain shocks over the exogenous variables of the model have on real exchange rates.

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.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Oscillations in a molecular structured cell population model

We consider a nonlinear cyclin content structured model of a cell population divided into proliferative and quiescent cells. We show, for particular values of the parameters, existence of solutions that do not depend on the cyclin content. We make numerical simulations for the general case obtaining, for some values of the parameters convergence to the steady state but also oscillations of the population for others.

A decision-making Fokker-Planck model in computational neuroscience

Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.

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

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 economyhave asymmetric and imperfect knowledge about the true data generating process. Weassume that all agents employ the data that they observe (which may be distinct fordifferent sets of agents) to form beliefs about unknown aspects of the true model ofthe economy, use their beliefs to decide on actions, and revise these beliefs througha statistical learning algorithm as new information becomes available. We study theshort-run dynamics of our model and derive its policy recommendations, particularlywith respect to central bank communications. We demonstrate that two-sided learningcan generate substantial increases in volatility and persistence, and alter the behaviorof the variables in the model in a significant way. Our simulations do not convergeto a symmetric rational expectations equilibrium and we highlight one source thatinvalidates the convergence results of Marcet and Sargent (1989). Finally, we identifya novel aspect of central bank communication in models of learning: communicationcan be harmful if the central bank's model is substantially mis-specified.

Testing for convergence clubs in income per-capita: A predictive density approach

The paper proposes a technique to jointly test for groupings of unknown size in the cross sectional dimension of a panel and estimates the parameters of each group, and applies it to identifying convergence clubs in income per-capita. The approach uses the predictive density of the data, conditional on the parameters of the model. The steady state distribution of European regional data clusters around four poles of attraction with different economic features. The distribution of incomeper-capita of OECD countries has two poles of attraction and each grouphas clearly identifiable economic characteristics.

Similarities and convergence in G-7 cycles

This paper examines the properties of G-7 cycles using a multicountry Bayesian panelVAR model with time variations, unit specific dynamics and cross country interdependences.We demonstrate the presence of a significant world cycle and show that country specificindicators play a much smaller role. We detect differences across business cycle phasesbut, apart from an increase in synchronicity in the late 1990s, find little evidence of major structural changes. We also find no evidence of the existence of an Euro area specific cycle or of its emergence in the 1990s.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.