Bounds for the probability distribution function of the linear ACD process

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

Bounds on functionals of the distribution treatment effects

Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

A note on learning chaotic sunspot equilibrium

In this paper we prove convergence to chaotic sunspot equilibrium through two learning rules used in the bounded rationality literature. The rst one shows the convergence of the actual dynamics generated by simple adaptive learning rules to a probability distribution that is close to the stationary measure of the sunspot equilibrium; since this stationary measure is absolutely continuous it results in a robust convergence to the stochastic equilibrium. The second one is based on the E-stability criterion for testing stability of rational expectations equilibrium, we show that the conditional probability distribution de ned by the sunspot equilibrium is expectational stable under a reasonable updating rule of this parameter. We also report some numerical simulations of the processes proposed.

Análise e extração das expectativas dos agentes de mercado em torno da data do COPOM

Este trabalho explora um importante conceito desenvolvido por Breeden & Litzenberger para extrair informações contidas nas opções de juros no mercado brasileiro (Opção Sobre IDI), no âmbito da Bolsa de Valores, Mercadorias e Futuros de São Paulo (BM&FBOVESPA) dias antes e após a decisão do COPOM sobre a taxa Selic. O método consiste em determinar a distribuição de probabilidade através dos preços das opções sobre IDI, após o cálculo da superfície de volatilidade implícita, utilizando duas técnicas difundidas no mercado: Interpolação Cúbica (Spline Cubic) e Modelo de Black (1976). Serão analisados os quatro primeiros momentos da distribuição: valor esperado, variância, assimetria e curtose, assim como suas respectivas variações.

Robustness and stabilization properties of monetary policy rules in Brazil

Based on three versions of a small macroeconomic model for Brazil, this paper presents empirical evidence on the effects of parameter uncertainty on monetary policy rules and on the robustness of optimal and simple rules over different model specifications. By comparing the optimal policy rule under parameter uncertainty with the rule calculated under purely additive uncertainty, we find that parameter uncertainty should make policymakers react less aggressively to the economy's state variables, as suggested by Brainard's "conservatism principIe", although this effect seems to be relatively small. We then informally investigate each rule's robustness by analyzing the performance of policy rules derived from each model under each one of the alternative models. We find that optimal rules derived from each model perform very poorly under alternative models, whereas a simple Taylor rule is relatively robusto We also fmd that even within a specific model, the Taylor rule may perform better than the optimal rule under particularly unfavorable realizations from the policymaker' s loss distribution function.

Optimal provision of implicit and explicit incentives in asset management contracts

This paper investigates the importance of the fiow of funds as an implicit incetive provided by investors to portfolio managers in a two-period relationship. We show that the fiow of funds is a powerful incentive in an asset management contract. We build a binomial moral hazard model to explain the main trade-ofIs in the relationship between fiow, fees and performance. The main assumption is that efIort depend" on the combination of implicit and explicit incentives while the probability distrioutioll function of returns depends on efIort. In the case of full commitment, the investor's relevant trade-ofI is to give up expected return in the second period vis-à-vis to induce efIort in the first período The more concerned the investor is with today's payoff. the more willing he will be to give up expected return in the following periods. That is. in the second period, the investor penalizes observed low returns by withdrawing resources from non-performing portfolio managers. Besides, he pays performance fee when the observed excess return is positive. When commitment is not a plausible hypothesis, we consider that the investor also learns some symmetríc and imperfect information about the ability of the manager to generate positive excess returno In this case, observed returns reveal ability as well as efIort choices exerted by the portfolio manager. We show that implicit incentives can explain the fiow-performance relationship and, conversely, endogenous expected return determines incentives provision and define their optimal leveIs. We provide a numerical solution in Matlab that characterize these results.

Extraindo as expectativas de mercado para a taxa de juros no Brasil usando opções sobre IDI

Este trabalho demonstra como podemos usar opções sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI) para extrair a função densidade de probabilidade (FDP) para os próximos passos do Comitê de Política Monetária (COPOM). Como a decisão do COPOM tem uma natureza discreta, podemos estimar a FDP usando Mínimo Quadrados Ordinários (MQO). Esta técnica permite incluir restrições sobre as probabilidades estimadas. As probabilidades calculadas usando opções sobre IDI são então comparadas com as probabilidades encontradas usando o Futuro de DI e as probabilidades calculadas através de pesquisas.

Income inequality in a job-search model with heterogeneous discount factors: (revised version, forthcoming 2006, Revista Economia)

This paper investigates the income inequality generated by a jobsearch process when di§erent cohorts of homogeneous workers are allowed to have di§erent degrees of impatience. Using the fact the average wage under the invariant Markovian distribution is a decreasing function of the discount factor (Cysne (2004, 2006)), I show that the Lorenz curve and the between-cohort Gini coe¢ cient of income inequality can be easily derived in this case. An example with arbitrary measures regarding the wage o§ers and the distribution of time preferences among cohorts provides some insights into how much income inequality can be generated, and into how it varies as a function of the probability of unemployment and of the probability that the worker does not Önd a job o§er each period.

Income inequality: the role of impatience in a job-search process

This paper investigates the income inequality generated by a jobsearch process when di§erent cohorts of homogeneous workers are allowed to have di§erent degrees of impatience. Using the fact the average wage under the invariant Markovian distribution is a decreasing function of the time preference (Cysne (2004)), I show that the Lorenz curve and the between-cohort Gini coe¢ cient of income inequality can be easily derived in this case. An example with arbitrary measures regarding the wage o§ers and the distribution of time preferences among cohorts provides some quantitative insights into how much income inequality can be generated, and into how it varies as a function of the probability of unemployment and of the probability that the worker does not Önd a job o§er each period.

Money distribution with intermediation

This pap er analyzes the distribution of money holdings in a commo dity money search-based mo del with intermediation. Intro ducing heterogeneity of costs to the Kiyotaki e Wright ( 1989 ) mo del, Cavalcanti e Puzzello ( 2010) gives rise to a non-degenerated distribution of money. We extend further this mo del intro ducing intermediation in the trading pro cess. We show that the distribution of money matters for savings decisions. This gives rises to a xed p oint problem for the saving function that di cults nding the optimal solution. Through some examples, we show that this friction shrinks the distribution of money. In contrast to the Cavalcanti e Puzzello ( 2010 ) mo del, the optimal solution may not present the entire surplus going to the consumer. At the end of the pap er, we present a strong result, for a su cient large numb er of intermediaries the distribution of money is degenerated.

Social security effects on income distribution: a counterfactual analysis for Brazil

According to Diamond (1977), one of the reasons for the existence of social security systems is that they function as an income redistribution mechanism. There is an extensive literature that tests whether social security systems produce the desired results in developed countries (mainly for the U.S.A.). Nevertheless, there is not an obvious consensus about this social security property and there is little evidence for developing countries. In this article, we test this property for the Brazilian Social Security System. In addition, we also look at another question which has not been answered yet in the previous literature. Is the trend of social security systems increasingly progressive or regressive? We conclude that the changes in Brazilian Social Security legislation reduced inequality between 1987 and 1996, but only for the elderly. For the other age groups, there is a stable trend. Results for the period between 1996 and 2006 reveal that the Brazilian system is neutral for all cohorts. Therefore, we found out that social security systems are not an effective mechanism for income redistribution, as predicted by previous studies.

Does liquidity constraints matter for Ricardian equivalence?

The paper analysis a general equilibrium model with two periods, several households and a government that has to finance some expenditures in the first period. Households may have some private information either about their type (adverse selection) or about some action levei chosen in the first period that affects the probability of certain states of nature in the second period (moral hazard). Trade of financiai assets are intermediated by a finite collection of banks. Banks objective functions are determined in equilibrium by shareholders. Due to private information it may be optimal for the banks to introduce constraints in the set of available portfolios for each household as wellas household specific asset prices. In particular, households may face distinct interest rates for holding the risk-free asset. The government finances its expenditures either by taxing households in the first period or by issuing bonds in the first period and taxing households in the second period. Taxes may be state-dependent. Suppose government policies are neutml: i) government policies do not affect the distribution of wealth across households; and ii) if the government decides to tax a household in the second period there is a portfolio available for the banks that generates the Mme payoff in each state of nature as the household taxes. Tben, Ricardian equivalence holds if and only if an appropriate boundary condition is satisfied. Moreover, at every free-entry equilibrium the boundary condition is satisfied and thus Ricardian equivalence holds. These results do not require any particular assumption on the banks' objective function. In particular, we do not assume banks to be risk neutral.