Leis de potência em economia e finanças

Nesta dissertação aborda-se a aplicação de Leis de Potência (LPs), também designadas de Leis de Pareto ou Leis de Zipf, a dados económicos. As LPs são distribuições estatísticas amplamente usadas na compreensão de sistemas naturais e artificiais. O aparecimento das LPs deve-se a Vilfredo Pareto que, no século XIX, publicou o manual de economia política,“Cours d’Economie Politique”. Nesse manual refere que grande parte da economia mundial segue uma LP, em que 20% da população reúne 80% da riqueza do país. Esta propriedade carateriza uma variável que segue uma distribuição de Pareto (ou LP). Desde então, as LPs foram aplicadas a outros fenómenos, nomeadamente a ocorrência de palavras em textos, os sobrenomes das pessoas, a variação dos rendimentos pessoais ou de empresas, o número de vítimas de inundações ou tremores de terra, os acessos a sítios da internet, etc. Neste trabalho, é estudado um conjunto de dados relativos às fortunas particulares ou coletivas de pessoas ou organizações. Mais concretamente são analisados dados recolhidos sobre as fortunas das mulheres mais ricas do mundo, dos homens mais ricos no ramo da tecnologia, das famílias mais ricas, das 20 mulheres mais ricas da América, dos 400 homens mais ricos da América, dos homens mais ricos do mundo, dos estabelecimentos mais ricos do mundo, das empresas mais ricas do mundo e dos países mais ricos do mundo, bem como o valor de algumas empresas no mercado de ações. Os resultados obtidos revelam uma boa aproximação de parte desses dados a uma LP simples e uma boa aproximação pelos restantes dados a uma LP dupla. Observa-se, assim, diferenciação na forma de crescimento das fortunas nos diferentes casos estudados. Como trabalho futuro, procurar-se-á analisar estes e outros dados, utilizando outras distribuições estatísticas, como a exponencial ou a lognormal, que possuem comportamentos semelhantes à LP, com o intuito de serem comparados os resultados. Um outro aspeto interessante será o de encontrar a explicação analítica para as vantagens da aproximação de dados económicos por uma LP simples vs por uma LP dupla.

Food consumption, physical activity and socio-economic status related to BMI, waist circumference and waist-to-height ratio in adolescents

Objective: To examine the association between obesity and food group intakes, physical activity and socio-economic status in adolescents. Design: A cross-sectional study was carried out in 2008. Cole’s cut-off points were used to categorize BMI. Abdominal obesity was defined by a waist circumference at or above the 90th percentile, as well as a waist-to-height ratio at or above 0?500. Diet was evaluated using an FFQ, and the food group consumption was categorized using sex-specific tertiles of each food group amount. Physical activity was assessed via a self-report questionnaire. Socio-economic status was assessed referring to parental education and employment status. Data were analysed separately for girls and boys and the associations among food consumption, physical activity, socio-economic status and BMI, waist circumference and waist-to-height ratio were evaluated using logistic regression analysis, adjusting the results for potential confounders. Setting: Public schools in the Azorean Archipelago, Portugal. Subjects: Adolescents (n 1209) aged 15–18 years. Results: After adjustment, in boys, higher intake of ready-to-eat cereals was a negative predictor while vegetables were a positive predictor of overweight/ obesity and abdominal obesity. Active boys had lower odds of abdominal obesity compared with inactive boys. Boys whose mother showed a low education level had higher odds of abdominal obesity compared with boys whose mother presented a high education level. Concerning girls, higher intake of sweets and pastries was a negative predictor of overweight/obesity and abdominal obesity. Girls in tertile 2 of milk intake had lower odds of abdominal obesity than those in tertile 1. Girls whose father had no relationship with employment displayed higher odds of abdominal obesity compared with girls whose father had high employment status. Conclusions: We have found that different measures of obesity have distinct associations with food group intakes, physical activity and socio-economic status.

Age-period-cohort effects in the incidence of hip fractures: political and economic events are coincident with changes in risk

Introduction: Healthcare improvements have allowed prevention but have also increased life expectancy, resulting in more people being at risk. Our aim was to analyse the separate effects of age, period and cohort on incidence rates by sex in Portugal, 2000–2008. Methods: From the National Hospital Discharge Register, we selected admissions (aged ≥49 years) with hip fractures (ICD9-CM, codes 820.x) caused by low/moderate trauma (falls from standing height or less), readmissions and bone cancer cases. We calculated person-years at risk using population data from Statistics Portugal. To identify period and cohort effects for all ages, we used an age–period–cohort model (1-year intervals) followed by generalised additive models with a negative binomial distribution of the observed incidence rates of hip fractures. Results: There were 77,083 hospital admissions (77.4 % women). Incidence rates increased exponentially with age for both sexes (age effect). Incidence rates fell after 2004 for women and were random for men (period effect). There was a general cohort effect similar in both sexes; risk of hip fracture altered from an increasing trend for those born before 1930 to a decreasing trend following that year. Risk alterations (not statistically significant) coincident with major political and economic change in the history of Portugal were observed around birth cohorts 1920 (stable–increasing), 1940 (decreasing–increasing) and 1950 (increasing–decreasing only among women). Conclusions: Hip fracture risk was higher for those born during major economically/politically unstable periods. Although bone quality reflects lifetime exposure, conditions at birth may determine future risk for hip fractures.