Optical/Multiwavelength Observations of GRB Afterglows

I review gamma-ray burst optical/multiwavelength afterglow observations since 1997, when the first counterparts to GRBs were discovered. I discuss what we have learned from multiwavelength observations of GRB afterglows in relation to the `standard' fireball plus relativistic blast-wave models. To first order the `standard' model describes the afterglow observations well, but a wealth of information can be gathered from the deviations of GRB afterglow observations from this `standard' model. These deviations provide information on the nature of the progenitor and on the physics of GRB production. In particular I focus on the possible connection of GRBs to supernovae, on jet and circumstellar wind models, on the early-time afterglow, and on the emission from the reverse shock.Comment: 10 pages, 4 figures; invited review for the 5th Huntsville Gamma-Ray Burst Workshop, eds. M. Kippen, R. Mallozzi, and G. Fishma

Discovery of a tight correlation between pulse lag/luminosity and jet-break times: a connection between gamma-ray burst and afterglow properties

A correlation is presented between the pulse lag and the jet-break time for seven BATSE gamma-ray bursts with known redshifts. This is, to our best knowledge, the first known direct tight correlation between a property of the gamma-ray burst phase (the pulse lag) and the afterglow phase (the jet-break time). As pulse lag and luminosity have been found to be correlated this also represents a correlation between peak luminosity and jet-break time. Observed timescales (variability or spectral lags) as well as peak luminosity naturally have a strong dependence on the Lorentz factor of the outflow and so we propose that much of the variety among GRBs has a purely kinematic origin (the speed or direction of the outflow). We explore a model in which the variation among GRBs is due to a variation in jet-opening angles, and find that the narrowest jets have the fastest outflows. We also explore models in which the jets have similar morphology and size, and the variation among bursts is caused by variation in viewing angle and/or due to a velocity profile. The relations between luminosity, variability, spectral lag and jet-break time can be qualitatively understood from models in which the Lorentz factor decreases as a function of angle from the jet axis. One expects to see high luminosities, short pulse lags and high variability as well as an early jet-break time for bursts viewed on axis, while higher viewing inclinations will yield lower luminosities, longer pulse lags, smoother bursts and later jet-break times.Comment: 10 pages, 3 figures, accepted to ApJ (new version contains minor changes

Grossman’s Missing Health Threshold

We present a generalized solution to Grossman’s model of health capital (1972), relaxing the widely used assumption that individuals can adjust their health stock instantaneously to an “optimal” level without adjustment costs. The Grossman model then predicts the existence of a health threshold above which individuals do not demand medical care. Our generalized solution addresses a significant criticism: the model’s prediction that health and medical care are positively related is consistently rejected by the data. We suggest structural and reduced form equations to test our generalized solution and contrast the predictions of the model with the empirical literature.health, demand for health, health capital, medical care, labor

On The Rise of Health Spending and Longevity

We use a calibrated stochastic life-cycle model of endogenous health spending, asset accumulation and retirement to investigate the causes behind the increase in health spending and life expectancy over the period 1965-2005. We estimate that technological change along with the increase in the generosity of health insurance may explain independently 53% of the rise in health spending (insurance 29% and technology 24%) while income less than 10%. By simultaneously occurring over this period, these changes may have lead to a "synergy" or interaction effect which helps explain an additional 37% increase in health spending. We estimate that technological change, taking the form of increased productivity at an annual rate of 1.8%, explains 59% of the rise in life expectancy at age 50 over this period while insurance and income explain less than 10%.demand for health, health spending, insurance, technological change, longevity

Why the Rich drink More but smoke Less: The Impact of Wealth on Health Behaviors

Wealthier individuals engage in healthier behavior. This paper seeks to explain this phenomenon by developing a theory of health behavior, and exploiting both lottery winnings and inheritances to test the theory. We distinguish between the direct monetary cost and the indirect health cost (value of health lost) of unhealthy consumption. The health cost increases with wealth and the degree of unhealthiness, leading wealthier individuals to consume more healthy and moderately unhealthy, but fewer severely unhealthy goods. The empirical evidence presented suggests that differences in health costs may indeed provide an explanation for behavioral differences, and ultimately health outcomes

A Theory of Education and Health

__Abstract__ This paper presents a unified theory of human capital with both health capital and, what we term, skill capital endogenously determined within the model. By considering joint investment in health capital and in skill capital, the model highlights similarities and differences in these two important components of human capital. Health is distinct from skill: health is important to longevity, provides direct utility, provides time that can be devoted to work or other uses, is valued later in life, and eventually declines, no matter how much one invests in it (a dismal fact of life). Lifetime earnings are strongly multiplicative in skill and health, so that investment in skill capital raises the return to investment in health capital, and vice versa. The theory provides a conceptual framework for empirical and theoretical studies aimed at understanding the complex relati onship between education and health, and generates several new testable predictions

Health Inequalities through the Lens of Health Capital Theory: Issues, Solutions, and Future Directions

We explore what health-capital theory has to offer in terms of informing and directing research into health inequality. We argue that economic theory can help in identifying mechanisms through which specific socioeconomic indicators and health interact. Our reading of the literature, and our own work, leads us to conclude that non-degenerate versions of the Grossman model (1972a;b) and its extensions can explain many salient stylized facts on health inequalities. Yet, further development is required in at least two directions. First, a childhood phase needs to be incorporated, in recognition of the importance of childhood endowments and investments in the determination of later-life socioeconomic and health outcomes. Second, a unified theory of joint investment in skill (or human) capital and in health capital could provide a basis for a theory of the relationship between education and health

Accounting for the Rise of Health Spending and Longevity

We estimate a stochastic life-cycle model of endogenous health spending, asset accumulation and retirement to investigate the causes behind the increase in health spending and longevity in the U.S. over the period 1965-2005. We estimate that technological change and the increase in the generosity of health insurance on their own may explain 36% of the rise in health spending (technology 30% and insurance 6%), while income explains only 4% and other health trends 0.5%. By simultaneously occurring over this period, these changes may have led to complementarity effects which we find to explain an additional 57% increase in health spending. The estimates suggest that the elasticity of health spending with respect to changes in both income and insurance is larger with co-occurring improvements in technology. Technological change, taking the form of increased health care productivity at an annual rate of 1.3%, explains almost all of the rise in life expectancy at age 25 over this period, while changes in insurance and income together explain less than 10%. Welfare gains are substantial and most of the gain appears to be due to technological change

Interactions between financial incentives and health in the early retirement decision

We present a theory of the relation between health and retirement that generates testable predictions regarding the interaction of health, wealth and financial incentives in retirement decisions. The theory predicts (i) that wealthier individuals (compared to poorer individuals) are more likely to retire for health reasons (affordability proposition), and (ii) that health problems make older workers more responsive to financial incentives encouraging retirement (reinforcement proposition). We test these predictions using administrative data on older employees in the Dutch healthcare sector for whom we link adverse health events, proxied by unanticipated hospitalizations, to information on retirement decisions and actual incentives from administrative records of the pension funds. Exploiting unexpected health shocks and quasi-exogenous variation in financial incentives for retirement due to reforms, we account for the endogeneity of health and financial incentives. Making use of the actual individual pension rights diminishes downward bias in estimates of the effect of pension incentives. We find support for our affordability and reinforcement propositions. Both propositions require the benefits function to be convex, as in our data. Our theory and empirical findings highlight the importance of assessing financial incentives for their potential reinforcement of health shocks and point to the possibility that differences in responses to financial incentives and health shocks across countries may relate to whether the benefit function is concave or convex