On the positive correlation between income inequality and unemployment

Several empirical studies in the literature have documented the existence of a positive correlation between income inequalitiy and unemployment. I provide a theoretical framework under which this correlation can be better understood. The analysis is based on a dynamic job search under uncertainty. I start by proving the uniqueness of a stationary distribution of wages in the economy. Drawing upon this distribution, I provide a general expression for the Gini coefficient of income inequality. The expression has the advantage of not requiring a particular specification of the distribution of wage offers. Next, I show how the Gini coefficient varies as a function of the parameters of the model, and how it can be expected to be positively correlated with the rate of unemployment. Two examples are offered. The first, of a technical nature, to show that the convergence of the measures implied by the underlying Markov process can fail in some cases. The second, to provide a quantitative assessment of the model and of the mechanism linking unemployment and inequality.

The impact of price expectations on consumer's behavior in frequently purchased goods markets: empirical evidence and implications

Este trabalho investiga como os padrões de compras de consumidores de bens estocáveis são afetados por suas expectativas de preços. Usando um modelo dinâmico padrão de maximização da utilidade, deriva-se uma expressão analítica para as compras dos consumidores como uma função das suas expectativas em relação aos preços futuros. Em seguida, uma versão mais tratável do modelo é construída, de forma a ilustrar graficamente como os diferentes tipos de expectativas de preços implicam diferentes padrões de compras dos consumidores. Além disso, na aplicação empírica, investigo qual o modelo de expectativas de preços, entre aqueles comumente utilizados na literatura, é consistente com os dados. Por fim, encontra-se suficiente heterogeneidade em expectativa de preços dos consumidores. Mostra-se que famílias de pequeno porte acreditam que os preços seguem um processo de Markov de primeira ordem, enquanto famílias de alta renda são racionais.

Ensaios em gestão de risco e regulação bancária

Esta tese é constituída por três ensaios. O primeiro ensaio analisa a informação pública disponível sobre o risco das carteiras de crédito dos bancos brasileiros, sendo dividido em dois capítulos. O primeiro analisa a limitação da informação pública disponibilizada pelos bancos e pelo Banco Central, quando comparada a informação gerencial disponível internamente pelos bancos. Concluiu-se que existe espaço para o aumento da transparência na divulgação das informações, fato que vem ocorrendo gradativamente no Brasil através de novas normas relacionadas ao Pilar 3 de Basileia II e à divulgação de informações mais detalhas pelo Bacen, como, por exemplo, aquelas do “Top50” . A segunda parte do primeiro ensaio mostra a discrepância entre o índice de inadimplência contábil (NPL) e a probabilidade de inadimplência (PD) e também discute a relação entre provisão e perda esperada. Através da utilização de matrizes de migração e de uma simulação baseada na sobreposição de safras de carteira de crédito de grandes bancos, concluiu-se que o índice de inadimplência subestima a PD e que a provisão constituída pelos bancos é menor que a perda esperada do SFN. O segundo ensaio relaciona a gestão de risco à discriminação de preço. Foi desenvolvido um modelo que consiste em um duopólio de Cournot em um mercado de crédito de varejo, em que os bancos podem realizar discriminação de terceiro grau. Neste modelo, os potenciais tomadores de crédito podem ser de dois tipos, de baixo ou de alto risco, sendo que tomadores de baixo risco possuem demanda mais elástica. Segundo o modelo, se o custo para observar o tipo do cliente for alto, a estratégia dos bancos será não discriminar (pooling equilibrium). Mas, se este custo for suficientemente baixo, será ótimo para os bancos cobrarem taxas diferentes para cada grupo. É argumentado que o Acordo de Basileia II funcionou como um choque exógeno que deslocou o equilíbrio para uma situação com maior discriminação. O terceiro ensaio é divido em dois capítulos. O primeiro discute a aplicação dos conceitos de probabilidade subjetiva e incerteza Knigthiana a modelos de VaR e a importância da avaliação do “risco de modelo”, que compreende os riscos de estimação, especificação e identificação. O ensaio propõe que a metodologia dos “quatro elementos” de risco operacional (dados internos, externos, ambiente de negócios e cenários) seja estendida à mensuração de outros riscos (risco de mercado e risco de crédito). A segunda parte deste último ensaio trata da aplicação do elemento análise de cenários para a mensuração da volatilidade condicional nas datas de divulgação econômica relevante, especificamente nos dias de reuniões do Copom.

The size of excavators within a polymorphic termite species governs tunnel topology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the spectrum of stochastic perturbations of the shift and Julia sets

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelo regional da ionosfera (MOD_ION): implementação em tempo real

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A model of osteoporosis impact in Switzerland 2000-2020

The aim of our study was to develop a modeling framework suitable to quantify the incidence, absolute number and economic impact of osteoporosis-attributable hip, vertebral and distal forearm fractures, with a particular focus on change over time, and with application to the situation in Switzerland from 2000 to 2020. A Markov process model was developed and analyzed by Monte Carlo simulation. A demographic scenario provided by the Swiss Federal Statistical Office and various Swiss and international data sources were used as model inputs. Demographic and epidemiologic input parameters were reproduced correctly, confirming the internal validity of the model. The proportion of the Swiss population aged 50 years or over will rise from 33.3% in 2000 to 41.3% in 2020. At the total population level, osteoporosis-attributable incidence will rise from 1.16 to 1.54 per 1,000 person-years in the case of hip fracture, from 3.28 to 4.18 per 1,000 person-years in the case of radiographic vertebral fracture, and from 0.59 to 0.70 per 1,000 person-years in the case of distal forearm fracture. Osteoporosis-attributable hip fracture numbers will rise from 8,375 to 11,353, vertebral fracture numbers will rise from 23,584 to 30,883, and distal forearm fracture numbers will rise from 4,209 to 5,186. Population-level osteoporosis-related direct medical inpatient costs per year will rise from 713.4 million Swiss francs (CHF) to CHF946.2 million. These figures correspond to 1.6% and 2.2% of Swiss health care expenditures in 2000. The modeling framework described can be applied to a wide variety of settings. It can be used to assess the impact of new prevention, diagnostic and treatment strategies. In Switzerland incidences of osteoporotic hip, vertebral and distal forearm fracture will rise by 33%, 27%, and 19%, respectively, between 2000 and 2020, if current prevention and treatment patterns are maintained. Corresponding absolute fracture numbers will rise by 36%, 31%, and 23%. Related direct medical inpatient costs are predicted to increase by 33%; however, this estimate is subject to uncertainty due to limited availability of input data.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Distribution of quality adjusted life expectancy: A systems approach

Statistical methods are developed which assess survival data for two attributes; (1) prolongation of life, (2) quality of life. Health state transition probabilities correspond to prolongation of life and are modeled as a discrete-time semi-Markov process. Imbedded within the sojourn time of a particular health state are the quality of life transitions. They reflect events which differentiate perceptions of pain and suffering over a fixed time period. Quality of life transition probabilities are derived from the assumptions of a simple Markov process. These probabilities depend on the health state currently occupied and the next health state to which a transition is made. Utilizing the two forms of attributes the model has the capability to estimate the distribution of expected quality adjusted life years (in addition to the distribution of expected survival times). The expected quality of life can also be estimated within the health state sojourn time making more flexible the assessment of utility preferences. The methods are demonstrated on a subset of follow-up data from the Beta Blocker Heart Attack Trial (BHAT). This model contains the structure necessary to make inferences when assessing a general survival problem with a two dimensional outcome. ^

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Modelos baseados em agentes aplicados à dinâmica de preços do mercado imobiliário

Um dos aspectos regulatórios fundamentais para o mercado imobiliário no Brasil são os limites para obtenção de financiamento no Sistema Financeiro de Habitação. Esses limites podem ser definidos de forma a aumentar ou reduzir a oferta de crédito neste mercado, alterando o comportamento dos seus agentes e, com isso, o preço de mercado dos imóveis. Neste trabalho, propomos um modelo de formação de preços no mercado imobiliário brasileiro com base no comportamento dos agentes que o compõem. Os agentes vendedores têm comportamento heterogêneo e são influenciados pela demanda histórica, enquanto que os agentes compradores têm o seu comportamento determinado pela disponibilidade de crédito. Esta disponibilidade de crédito, por sua vez, é definida pelos limites para concessão de financiamento no Sistema Financeiro de Habitação. Verificamos que o processo markoviano que descreve preço de mercado converge para um sistema dinâmico determinístico quando o número de agentes aumenta, e analisamos o comportamento deste sistema dinâmico. Mostramos qual é a família de variáveis aleatórias que representa o comportamento dos agentes vendedores de forma que o sistema apresente um preço de equilíbrio não trivial, condizente com a realidade. Verificamos ainda que o preço de equilíbrio depende não só das regras de concessão de financiamento no Sistema Financeiro de Habitação, como também do preço de reserva dos compradores e da memória e da sensibilidade dos vendedores a alterações na demanda. A memória e a sensibilidade dos vendedores podem levar a oscilações de preços acima ou abaixo do preço de equilíbrio (típicas de processos de formação de bolhas); ou até mesmo a uma bifurcação de Neimark-Sacker, quando o sistema apresenta dinâmica oscilatória estável.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Effect of weather and the hybrid energy storage on the availability of standalone microgrid

This paper presents a model for availability analysis of standalone hybrid microgrid. The microgrid used in the study consists of wind, solar storage and diesel generator. Boolean driven Markov process is used to develop the availability of the system in the proposed method. By modifying the developed model, the relationship between the availability of the system with the fine (normal) weather and disturbed (stormy) weather durations are analyzed. Effects of different converter technologies on the availability of standalone microgrid were investigated and the results have shown that the availability of microgrid increased by 5.80 % when a storage system is added. On the other hand, the availability of standalone microgrid could be overestimated by 3.56 % when weather factor is neglected. In the same way 200, 500 and 1000 hours of disturbed weather durations reduced the availability of the system by 5.36%, 9.73% and 13.05 %, respectively. In addition, the hybrid energy storage cascade topology with a capacitor in the middle maximized the system availability.