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.

Privatization and social welfare in an international mixed Stackelberg duopoly

Competition between public and private firms exists in a range of industries like telecommunications, electricity, natural gas, airlines industries, as weel as services including hospitals, banking and education. Some authors studied mixed oligopolies under Cournot competition (firms move simultaneously) and some others considered Stackelberg models (firms move sequentially). Tomaru [1] analyzed, in a Cournot model, how decision-making upon cost-reducing R&D investment by a domestic public firm is affected by privatization when competing in the domestic market with a foreign firm. He shows that privatization of the domestic public firm lowers productive efficiency and deteriorates domestic social welfare. In this paper, we examine the same question but in a Stackelberg formulation instead of Cournot. The model is a three-stage game. In the first stage, the domestic firm chooses the amount of cost-reducing R&D investment. Then, the firms compete à la Stackelberg. Two cases are considered: (i) The domestic firm is the leader; (ii) The foreign firm is the leader. We show that the results obtained in [1] for Cournot competition are robust in the sence that they are also true when firms move sequentially.