Information Dispersion and Equilibrium Multiplicity

This paper studies the implications of correlation of private signals about the liquidation value of a risky asset in a variation of a standard noisy rational expectations model in which traders receive endowment shocks which are private information and have a common component. We …nd that a necessary condition to generate multiple linear partially revealing rational expectations equilibria is the existence of several sources of information dispersion. In this context equilibrium multiplicity tends to occur when information is more dispersed. A necessary condition to have strategic complementarity in information acquisition is to have mul- tiple equilibria. When the equilibrium is unique there is strategic substi- tutability in information acquisition, corroborating the result obtained in Grossman and Stiglitz (1980). JEL Classi…cation: D82, D83, G14 Keywords: Multiplicity of equilibria, strategic complementarity, asym- metric information.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Public and private learning from prices, strategic substitutability and complementarity, and equilibrium multiplicity

We study a general static noisy rational expectations model where investors have private information about asset payoffs, with common and private components, and about their own exposure to an aggregate risk factor, and derive conditions for existence and uniqueness (or multiplicity) of equilibria. We find that a main driver of the characterization of equilibria is whether the actions of investors are strategic substitutes or complements. This latter property in turn is driven by the strength of a private learning channel from prices, arising from the multidimensional sources of asymmetric information, in relation to the usual public learning channel. When the private learning channel is strong (weak) in relation to the public we have strong (weak) strategic complementarity in actions and potentially multiple (unique) equilibria. The results enable a precise characterization of whether information acquisition decisions are strategic substitutes or complements. We find that the strategic substitutability in information acquisition result obtained in Grossman and Stiglitz (1980) is robust. JEL Classification: D82, D83, G14 Keywords: Rational expectations equilibrium, asymmetric information, risk exposure, hedging, supply information, information acquisition.

Simulating the Impact of Sectorial Productivity Gains on Two Regional Economies: Key Sectors from a Supply Side Perspective

In this paper we simulate and analyse the economic impact that sectorial productivity gains have on two regional Spanish economies (Catalonia and Extremadura). In particular we study the quantitative effect that each sector’s productivity gain has on household welfare (real disposable income and equivalent variation), on the consumption price indices and factor relative prices, on real production (GDP) and on the government’s net income (net taxation revenues of social transfers to households). The analytical approach consists of a computable general equilibrium model, in which we assume perfect competition and cleared markets, including factor markets. All the parameters and exogenous variables of the model are calibrated by means of two social accounting matrices, one for each region under study. The results allow us to identify those sectors with the greatest impact on consumer welfare as the key sectors in the regional economies. Keywords: Productivity gains, key sectors, computable general equilibrium

A New open economy macroeconomic model with endogenous portfolio diversification and firms entry

This paper provides a new benchmark for the analysis of the international diversi…cation puzzle in a tractable new open economy macroeconomic model. Building on Cole and Obstfeld (1991) and Heathcote and Perri (2009), this model speci…es an equilibrium model of perfect risk sharing in incomplete markets, with endogenous portfolios and number of varieties. Equity home bias may not be a puzzle but a perfectly optimal allocation for hedging risk. In contrast to previous work, the model shows that: (i) optimal international portfolio diversi…cation is driven by home bias in capital goods, independently of home bias in consumption, and by the share of income accruing to labour. The model explains reasonably well the recent patterns of portfolio allocations in developed economies; and (ii) optimal portfolio shares are independent of market dynamics.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.

Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

Essays in equilibrium asset pricing

This thesis consists of four essays in equilibrium asset pricing. The main topic is investors' heterogeneity: I investigates the equilibrium implications for the financial markets when investors have different attitudes toward risk. The first chapter studies why expected risk and remuneration on the aggregate market are negatively related, even if intuition and standard theory suggest a positive relation. I show that the negative trade-off can obtain in equilibrium if investors' beliefs about economic fundamentals are procyclically biased and the market Sharpe ratio is countercyclical. I verify that such conditions hold in the real markets and I find empirical support for the risk-return dynamics predicted by the model. The second chapter consists of two essays. The first essay studies how het¬erogeneity in risk preferences interacts with other sources of heterogeneity and how this affects asset prices in equilibrium. Using perceived macroeconomic un¬certainty as source of heterogeneity, the model helps to explain some patterns of financial returns, even if heterogeneity is small as suggested by survey data. The second essay determines conditions such that equilibrium prices have analytical solutions when investors have heterogeneous risk attitudes and macroeconomic fundamentals feature latent uncertainty. This approach provides additional in-sights to the previous literature where models require numerical solutions. The third chapter studies why equity claims (i.e. assets paying a single future dividend) feature premia and risk decreasing with the horizon, even if standard models imply the opposite shape. I show that labor relations helps to explain the puzzle. When workers have bargaining power to exploit partial income insurance within the firm, wages are smoother and dividends are riskier than in a standard economy. Distributional risk among workers and shareholders provides a rationale to the equity short-term risk, which leads to downward sloping term structures of premia and risk for equity claim. Résumé Cette thèse se compose de quatre essais dans l'évaluation des actifs d'équilibre. Le sujet principal est l'hétérogénéité des investisseurs: J'étudie les implications d'équilibre pour les marchés financiers où les investisseurs ont des attitudes différentes face au risque. Le première chapitre étudie pourquoi attendus risque et la rémunération sur le marché global sont liées négativement, même si l'intuition et la théorie standard suggèrent une relation positive. Je montre que le compromis négatif peut obtenir en équilibre si les croyances des investisseurs sur les fondamentaux économiques sont procyclique biaisées et le ratio de Sharpe du marché est anticyclique. Je vérifier que ces conditions sont réalisées dans les marchés réels et je trouve un appui empirique à la dynamique risque-rendement prédites par le modèle. Le deuxième chapitre se compose de deux essais. Le première essai étudie com¬ment hétérogénéité dans les préférences de risque inter agit avec d'autres sources d'hétérogénéité et comment cela affecte les prix des actifs en équilibre. Utili¬sation de l'incertitude macroéconomique perù comme source d'hétérogénéité, le modèle permet d'expliquer certaines tendances de rendements financiers, même si l'hétérogénéité est faible comme suggéré par les données d'enquête. Le deuxième essai détermine des conditions telles que les prix d'équilibre disposer de solutions analytiques lorsque les investisseurs ont des attitudes des risques hétérogènes et les fondamentaux macroéconomiques disposent d'incertitude latente. Cette approche fournit un éclairage supplémentaire à la littérature antérieure où les modèles nécessitent des solutions numériques. Le troisième chapitre étudie pourquoi les equity-claims (actifs que paient un seul dividende futur) ont les primes et le risque décroissante avec l'horizon, mme si les modèles standards impliquent la forme opposée. Je montre que les relations de travail contribue à expliquer l'énigme. Lorsque les travailleurs ont le pouvoir de négociation d'exploiter assurance revenu partiel dans l'entreprise, les salaires sont plus lisses et les dividendes sont plus risqués que dans une économie standard. Risque de répartition entre les travailleurs et les actionnaires fournit une justification à le risque à court terme, ce qui conduit à des term-structures en pente descendante des primes et des risques pour les equity-claims.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p.There are many statistical tests being used to check whether empirical marker data obeys theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE)are numerical in nature, requiring the computation of a test statistic and a p-value.There is however, ample space for the use of graphics in HWE tests, in particular for the ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Social capital and the equilibrium number of entrepreneurs

Social capital is viewed either as a proprietary asset that serves private interests, including those of entrepreneurs, or as a collective asset that supports trust-based transactions saving on transaction costs both in markets and within the boundaries of firms, and benefiting society as a whole. This paper explains the relative specialization between entrepreneurs and market-governed exchanges as a result of the interaction between social capital that lowers transaction costs, and the scale economies of ability in managerial jobs (Lucas 1978). The main hypothesis formulated in the paper is that higher social capital will benefit the hierarchy relatively more than the market as a governance mechanism, and therefore in economies with higher social capital, the equilibrium number of entrepreneurs will be lower and their average span of control larger than in economies with lower social capital. The empirical evidence, with data from the Spanish Autonomous Communities, is consistent with this prediction.

Equilibrium of drops on inclined hydrophilic surfaces

Why does not gravity make drops slip down the inclined surfaces, e.g., plant leaves? The current explanation is based on the existence of surface inhomogeneities, which cause a sustaining force that pins the contact line. Following this theory, the drop remains in equilibrium until a critical value of the sustaining force is reached. We propose an alternative analysis, from the point of view of energy balance, for the particular case in which the drop leaves a liquid film behind. The critical angle of the inclined surface at which the drop slips down is predicted. This result does not depend explicitly on surface inhomogeneities, but only on the drop size and surface tensions. There is good agreement with experiments for contact angles below 90° where the formation of the film is expected, whereas for greater contact angles great discrepancies arise

Supply Multipliers in Two Regional Economies

This paper focuses on the analysis of the economic impact that sectorial total factor productivity – or valued added - gains have on two regional Spanish economies (Catalonia and Extremadura). In particular it is studied the quantitative effect that each sector’s valued added injections has on household welfare (real disposable income), on the consumption price indices and factor relative prices, on real production (GDP) and on the government and foreign net income. To do that, we introduce the concept of supply multiplier. The analytical approach consists of a computable general equilibrium model, in which it is assumed perfect competition and cleared markets of goods and factors. All the parameters and exogenous variables of the model are calibrated by means of two social accounting matrices, one for each region under study. The results allow identifying those sectors with the greatest multipliers impact on consumer welfare as the key sectors in the regional economies. Keywords: efficiency gains, supply multipliers, key sectors, computable general equilibrium. JEL Classification: C68, R13.