Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

On the growth rate of minor-closed classes of graphs

"Vegeu el resum a l'inici del document del fitxer adjunt."

Immigration and Firm Growth: Evidence from Spanish cities

This article analyses the effect of immigration flows on the growth and efficiency of manufacturing firms in Spanish cities. To date, most studies have tended to focus on the effect immigrants have on labour markets at an aggregate level. Here, however, we undertake an exhaustive analysis at the firm level and report conclusive empirical findings. Ten years ago, Spain began to register massive immigration flows, concentrated above all on its most dynamic and advanced regions. Here, therefore, rather than focusing on the impact this has had on Spain’s labour market (changes to the skill structure of the workforce, increase in labour supply, the displacement of native workers, etc.), we examine the arrival of immigrants in terms of the changes this has meant to the structure of the country’s cities and their amenities. Thus, we argue that the impact of immigration on firm performance should not only be considered in terms of the labour market, but also in terms of how a city’s amenities can affect the performance of firms. Employing a panel data methodology, we show that the increasing pressure brought to bear by immigrants has a positive effect on the evolution of labour productivity and wages and a negative effect on the job evolution of these manufacturing firms. In addition, both small and new firms are more sensitive to the pressures of such immigrant inflows, while foreign market oriented firms report higher productivity levels and a less marked impact of immigration than their counterparts. In this paper, we also present a set of instruments to correct the endogeneity bias, which confirms the effect of local immigration flows on the performance of manufacturing firms.

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

Productivity growth and competition in Spanish manufacturing firms: What has happened in recent years?

This paper addresses the issue of the relationship between productivity and market competition. In comparison to the economies of other European countries, the Spanish economy has been growing, while productivity growth has stagnated. Here we provide empirical evidence about the relationship between productivity and market competition from Spanish manufacturing firms at firm level between 1994 and 2004. Correcting for selection bias, our study pays special attention to the patterns of productivity growth between openness and non-openness firms. When market competition increases the effect on firms operating in domestic markets is positive but when the level of competition is high incentives to invest in innovation and productivity gains disappear. The empirical relationship between competition and productivity is an inverted U-shape, where productivity growth is highest at intermediate levels of competition. The productivity growth of firms operating in international markets is higher than that of non-openness firms, but when market competition rises they moderate their productivity growth. Our empirical results suggest that the correct competition policy in the Spanish economy should remove the barriers to competition in internal markets in order to increase the incentives for manufacturing firms to invest in innovation and productivity growth.

The international trade as the sole engine of growth for an economy

Can international trade act as the sole engine of growth for an economy? If yes, what are the mechanisms through which trade operates in transmitting permanent growth? This paper answers these questions with two simple two-country models, in which only one country enjoys sustained growth in autarky. The models differ in the assumptions on technical change, which is either labour- or capital-augmenting. In both cases, the stagnant economy imports growth by trading. In the first model, growth is transmitted because of permanent increases in the trade volume. In the alternative framework, the stagnant economy imports sustained growth because its terms of trade permanently improve.

Are the high-growth recovery periods over?

We present evidence about the loss of the so-called "plucking effect", that is, a high-growth phase of the cycle typically observed at the end of recessions. This result matches the popular belief, presented informally by different authors, that the current recession will have permanent effects, or that the current recession will have an L shape versus the old-time recessions that have always had a V shape. Furthermore, we show that the loss of the "plucking effect" can explain part of the Great Moderation. We postulate that these two phenomena may be due to changes in inventory management brought about by improvements in information and communications technologies.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Small firms, growth and financial constraints

This paper analyses the impact of different sources of finance on the growth of firms. Using panel data from Spanish manufacturing firms for the period 2000-2006, we investigate the effects of internal and external finances on firm growth. In particular, we examine three dimensions of these financial sources: a) the performance of the firms’ capital structure in accordance with firm size; b) the effects of internal and external financial sources on growth performance; c) the combined effect of equity, external debt and cash flow on firm growth. We find that low-growth firms are sensitive to cash flow and short-term bank debt, while high-growth firms are more sensitive to long-term debt. Furthermore, equity capital seems to reduce barriers to external finance. Our main conclusion is that during the start-up phase, firms are unable to increase their financial leverage and so their capital structure fails to promote correct investment strategies. However, as their equity capital increases, alternative financial mechanisms, in particular long-term debt, become available, which have a positive impact on firm growth.

Risk Attitude And Wage Growth: Replication And Reconstruction

We replicate Shaw (1996) who found that individual wage growth is higher for individuals with greater preference for risk taking. Expanding her dataset with more American observations and data for Germany, Spain and Italy, we find mixed support for the earlier results. We present and estimate a new model and find that in particular the wage level is sensitive to attitudes towards risk taking. Comments given at the Labour Economics Conference in honour of Niels Westergaard (Nyborg, August 2008) and EALE 2008 (Amsterdam) and at seminars in Maastricht,Reus and Essen (RWI) are gratefully acknowledged. The authors also acknowledge financial support from the Spanish Ministry of Science and Innovation (grant number SEJ2007-66318) and from the Barcelona Economics Program of CREA. JEL code: J24; J30. Key words: wage growth, risk, post-school investment.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.