Speed of convergence of recursive least squares learning with ARMA perceptions

This paper fills a gap in the existing literature on least squareslearning in linear rational expectations models by studying a setup inwhich agents learn by fitting ARMA models to a subset of the statevariables. This is a natural specification in models with privateinformation because in the presence of hidden state variables, agentshave an incentive to condition forecasts on the infinite past recordsof observables. We study a particular setting in which it sufficesfor agents to fit a first order ARMA process, which preserves thetractability of a finite dimensional parameterization, while permittingconditioning on the infinite past record. We describe how previousresults (Marcet and Sargent [1989a, 1989b] can be adapted to handlethe convergence of estimators of an ARMA process in our self--referentialenvironment. We also study ``rates'' of convergence analytically and viacomputer simulation.

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.

It's still 2%: evidence on convergence from 116 years of the US States panel data

A new debate over the speed of convergence in per capita income across economies is going on. Cross sectional estimates support the idea of slow convergence of about two percent per year. Panel data estimates support the idea of fast convergence of five, ten or even twenty percent per year. This paper shows that, if you ``do it right'', even the panel data estimation method yields the result of slow convergence of about two percent per year.

Effect of genetic convergence on phylogenetic inference.

Phylogenetic reconstructions are a major component of many studies in evolutionary biology, but their accuracy can be reduced under certain conditions. Recent studies showed that the convergent evolution of some phenotypes resulted from recurrent amino acid substitutions in genes belonging to distant lineages. It has been suggested that these convergent substitutions could bias phylogenetic reconstruction toward grouping convergent phenotypes together, but such an effect has never been appropriately tested. We used computer simulations to determine the effect of convergent substitutions on the accuracy of phylogenetic inference. We show that, in some realistic conditions, even a relatively small proportion of convergent codons can strongly bias phylogenetic reconstruction, especially when amino acid sequences are used as characters. The strength of this bias does not depend on the reconstruction method but varies as a function of how much divergence had occurred among the lineages prior to any episodes of convergent substitutions. While the occurrence of this bias is difficult to predict, the risk of spurious groupings is strongly decreased by considering only 3rd codon positions, which are less subject to selection, as long as saturation problems are not present. Therefore, we recommend that, whenever possible, topologies obtained with amino acid sequences and 3rd codon positions be compared to identify potential phylogenetic biases and avoid evolutionarily misleading conclusions.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Human capital distribution, growth and convergence

This paper studies the dynamic relationship between distribution and endogenous growth in an overlapping generations model with accumulation of human and physical capital. It is shown how human capital can determine a relationship between per capita growth rates and inequality in the distribution of income. Family background effects and spillovers in the transmission of human capital generate a dynamics in which aggregate variables depend not only on the stock, but also on the distribution of human capital. The evolution of this distribution over time is then characterized under different assumptions on private returns and the form of the externality in the technology for humancapital. Conditions for existence, uniqueness and stability of a constant growth equilibrium with a stationary distribution are derived. Increasing returns, idiosyncratic abilities and the possibility of poverty traps are explicitely characterized in a closed form solution of the equilibrium dynamics, showing the role played by technology and preferences parameters.

The poor stay poor: Non-convergence across countries and regions

We study the issue of income convergence across countries and regions witha Bayesian estimator which allows us to use information in an efficient andflexible way. We argue that the very slow convergence rates to a commonlevel of per-capita income found, e.g., by Barro and Xavier Sala-i-Martin,is due to a 'fixed effect bias' that their cross-sectional analysisintroduces in the results. Our approach permits the estimation of differentconvergence rates to different steady states for each cross sectional unit.When this diversity is allowed, we find that convergence of each unit to(its own) steady state income level is much faster than previously estimatedbut that cross sectional differences persist: inequalities will only bereduced by a small amount by the passage of time. The cross countrydistribution of the steady state is largely explained by the cross countrydistribution of initial conditions.

Tracking the invisible hand: Convergence of double auctions to competitive equilibrium

Economics is the science of want and scarcity. We show that want andscarcity, operating within a simple exchange institution (double auction),are sufficient for an economy consisting of multiple inter--related marketsto attain competitive equilibrium (CE). We generalize Gode and Sunder's(1993a, 1993b) single--market finding to multi--market economies, andexplore the role of the scarcity constraint in convergence of economies to CE.When the scarcity constraint is relaxed by allowing arbitrageurs in multiple markets to enter speculative trades, prices still converge to CE,but allocative efficiency of the economy drops. \\Optimization by individual agents, often used to derive competitive equilibria,are unnecessary for an actual economy to approximately attain such equilibria.From the failure of humans to optimize in complex tasks, one need not concludethat the equilibria derived from the competitive model are descriptivelyirrelevant. We show that even in complex economic systems, such equilibriacan be attained under a range of surprisingly weak assumptions about agentbehavior.

Phylogenetic analyses of C4 photosynthesis evolution in grasses: genetics of convergence and convergence of genes

Summary : During the evolutionary diversification of organisms, similar ecological constraints led to the recurrent appearances of the same traits (phenotypes) in distant lineages, a phenomenon called convergence. In most cases, the genetic origins of the convergent traits remain unknown, but recent studies traced the convergent phenotypes to recurrent alterations of the same gene or, in a few cases, to identical genetic changes. However, these cases remain anecdotal and there is a need for a study system that evolved several times independently and whose genetic determinism is well resolved and straightforward, such as C4 photosynthesis. This adaptation to warm environments, possibly driven by past atmospheric CO2 decreases, consists in a CO2-concentrating pump, created by numerous morphological and biochemical novelties. All genes encoding C4 enzymes already existed in C3 ancestors, and are supposed to have been recruited through gene duplication followed by neo-functionalization, to acquire the cell specific expression pattern and altered kinetic properties that characterize Ca-specific enzymes. These predictions have so far been tested only in species-poor and ecologically marginal C4 dicots. The monocots, and especially the grass family (Poaceae), the most important C4 family in terms of species number, ecological dominance and economical importance, have been largely under-considered as suitable study systems. This thesis aimed at understanding the evolution of the C4 trait in grasses at a molecular level and to use the genetics of C4 photosynthesis to infer the evolutionary history of the C4 phenotype and its driving selective pressures. A molecular phylogeny of grasses and affiliated monocots identified 17 to 18 independent acquisitions of the C4 pathway in the grass family. A relaxed molecular clock was used to date these events and the first C4 evolution was estimated in the Chloridoideae subfamily, between 32-25 million years ago, at a period when atmospheric CO2 abruptly declined. Likelihood models showed that after the COZ decline the probability of evolving the C4 pathway strongly increased, confirming low CO2 as a likely driver of C4 photosynthesis evolution. In order to depict the genetic changes linked to the numerous C4 origins, genes encoding phopshoenolpyruvate carboxylase (PEPC), the key-enzyme responsible for the initial fixation of atmospheric CO2 in the C4 pathway, were isolated from a large sample of C3 and C4 grasses. Phylogenetic analyses were used to reconstruct the evolutionary history of the PEPC multigene family and showed that the evolution of C4-specific PEPC had been driven by positive selection on 21 codons simultaneously in up to eight C4 lineages. These selective pressures led to numerous convergent genetic changes in many different C4 clades, highlighting the repeatability of some evolutionary processes, even at the molecular level. PEPC C4-adaptive changes were traced and used to show multiple appearances of the C, pathway in clades where species tree inferences were unable to differentiate multiple C4 appearances and a single appearance followed by C4 to C3 reversion. Further investigations of genes involved in some of the C4 subtypes only (genes encoding decarboxylating enzymes NADP-malic enzyme and phosphoenolpyruvate carboxykinase) showed that these C4-enzymes also evolved through strong positive selection and underwent parallel genetic changes during the different Ca origins. The adaptive changes on these subtype-specific C4 genes were used to retrace the history of the C4-subtypes phenotypes, which revealed that the evolution of C4-PEPC and C4-decarboxylating enzymes was in several cases disconnected, emphasizing the multiplicity of the C4 trait and the gradual acquisition of the features that create the CO2-pump. Finally, phylogenetic analyses of a gene encoding the Rubisco (the enzyme responsible for the fixation of CO2 into organic compounds in all photosynthetic organisms) showed that C4 evolution switched the selective pressures on this gene. Five codons were recurrently mutated to adapt the enzyme kinetics to the high CO2 concentrations of C4 photosynthetic cells. This knowledge could be used to introgress C4-like Rubisco in C3 crops, which could lead to an increased yield under predicted future high CO2 atmosphere. Globally, the phylogenetic framework adopted during this thesis demonstrated the widespread occurrence of genetic convergence on C4-related enzymes. The genetic traces of C4 photosynthesis evolution allowed reconstructing events that happened during the last 30 million years and proved the usefulness of studying genes directly responsible for phenotype variations when inferring evolutionary history of a given trait. Résumé Durant la diversification évolutive des organismes, des pressions écologiques similaires ont amené à l'apparition récurrente de certains traits (phénotypes) dans des lignées distantes, un phénomène appelé évolution convergente. Dans la plupart des cas, l'origine génétique des traits convergents reste inconnue mais des études récentes ont montré qu'ils étaient dus dans certains cas à des changements répétés du même gène ou, dans de rares cas, à des changements génétiques identiques. Malgré tout, ces cas restent anecdotiques et il y a un réel besoin d'un système d'étude qui ait évolué indépendamment de nombreuses fois et dont le déterminisme génétique soit clairement identifié. La photosynthèse dite en Ça répond à ces critères. Cette adaptation aux environnements chauds, dont l'évolution a pu être encouragé par des baisses passées de la concentration atmosphérique en CO2, est constituée de nombreuses nouveautés morphologiques et biochimiques qui créent une pompe à CO2. La totalité des gènes codant les enzymes Ç4 étaient déjà présents dans les ancêtres C3. Leur recrutement pour la photosynthèse Ç4 est supposé s'être fait par le biais de duplications géniques suivies par une néo-fonctionnalisation pour leur conférer l'expression cellule-spécifique et les propriétés cinétiques qui caractérisent les enzymes C4. Ces prédictions n'ont jusqu'à présent été testées que dans des familles C4 contenant peu d'espèces et ayant un rôle écologique marginal. Les graminées (Poaceae), qui sont la famille C4 la plus importante, tant en termes de nombre d'espèces que de dominance écologique et d'importance économique, ont toujours été considérés comme un système d'étude peu adapté et ont fait le sujet de peu d'investigations évolutives. Le but de cette thèse était de comprendre l'évolution de la photosynthèse en C4 chez les graminées au niveau génétique et d'utiliser les gènes pour inférer l'évolution du phénotype C4 ainsi que les pressions de sélection responsables de son évolution. Une phylogénie moléculaire de la famille des graminées et des monocotylédones apparentés a identifié 17 à 18 acquisitions indépendantes de la photosynthèse chez les graminées. Grâce à une méthode d'horloge moléculaire relâchée, ces évènements ont été datés et la première apparition C4 a été estimée dans la sous-famille des Chloridoideae, il y a 32 à 25 millions d'années, à une période où les concentrations atmosphériques de CO2 ont décliné abruptement. Des modèles de maximum de vraisemblance ont montré qu'à la suite du déclin de CO2, la probabilité d'évoluer la photosynthèse C4 a fortement augmenté, confirmant ainsi qu'une faible concentration de CO2 est une cause potentielle de l'évolution de la photosynthèse C4. Afin d'identifier les mécanismes génétiques responsables des évolutions répétées de la photosynthèse C4, un segment des gènes codant pour la phosphoénolpyruvate carboxylase (PEPC), l'enzyme responsable de la fixation initiale du CO2 atmosphérique chez les plantes C4, ont été séquencés dans une centaine de graminées C3 et C4. Des analyses phylogénétiques ont permis de reconstituer l'histoire évolutive de la famille multigénique des PEPC et ont montré que l'évolution de PEPC spécifiques à la photosynthèse Ça a été causée par de la sélection positive agissant sur 21 codons, et ce simultanément dans huit lignées C4 différentes. Cette sélection positive a conduit à un grand nombre de changements génétiques convergents dans de nombreux clades différents, ce qui illustre la répétabilité de certains phénomènes évolutifs, et ce même au niveau génétique. Les changements sur la PEPC liés au C4 ont été utilisés pour confirmer des évolutions indépendantes du phénotype C4 dans des clades où l'arbre des espèces était incapable de différencier des apparitions indépendantes d'une seule apparition suivie par une réversion de C4 en C3. En considérant des gènes codant des protéines impliquées uniquement dans certains sous-types C4 (deux décarboxylases, l'enzyme malique à NADP et la phosphoénolpyruvate carboxykinase), des études ultérieures ont montré que ces enzymes C4 avaient elles-aussi évolué sous forte sélection positive et subi des changements génétiques parallèles lors des différentes origines de la photosynthèse C4. Les changements adaptatifs sur ces gènes liés seulement à certains sous-types C4 ont été utilisés pour retracer l'histoire des phénotypes de sous-types C4, ce qui a révélé que les caractères formant le trait C4 ont, dans certains cas, évolué de manière déconnectée. Ceci souligne la multiplicité du trait C4 et l'acquisition graduelle de composants participant à la pompe à CO2 qu'est la photosynthèse C4. Finalement, des analyses phylogénétiques des gènes codant pour la Rubisco (l'enzyme responsable de la fixation du CO2 en carbones organiques dans tous les organismes photosynthétiques) ont montré que l'évolution de la photosynthèse Ça a changé les pressions de sélection sur ce gène. Cinq codons ont été mutés de façon répétée afin d'adapter les propriétés cinétiques de la Rubisco aux fortes concentrations de CO2 présentes dans les cellules photosynthétiques des plantes C4. Globalement, l'approche phylogénétique adoptée durant cette thèse de doctorat a permis de démontré des phénomène fréquents de convergence génétique sur les enzymes liées à la photosynthèse C4. Les traces génétiques de l'évolution de la photosynthèse C4 ont permis de reconstituer des évènements qui se sont produits durant les derniers 30 millions d'années et ont prouvé l'utilité d'étudier des gènes directement responsables des variations phénotypiques pour inférer l'histoire évolutive d'un trait donné.