Health insurance, endogenous medical progress, health expenditure growth, and welfare

We study the impact of health insurance expansion on medical spending, longevity and welfare in an OLG economy in which individuals purchase health care to lower mortality and medical progress is profit-driven. Three sectors are considered: final goods production; a health care sector, selling medical services to individuals; and an R&D sector, selling increasingly effective medical technology to the health care sector. We calibrate the model to the development of the US economy/health care system from 1965 to 2005 and study numerically the impact of the insurance expansion. We find that more extensive health insurance accounts for a large share of the rise in US health spending but also boosts the rate of medical progress. A welfare analysis shows that while the subsidization of health care through health insurance creates excessive health care spending, the gains in life expectancy brought about by induced medical progress more than compensate for this.

Local environmental quality and heterogeneity in an OLG agent-based model with spatial externalities

Most of the theoretical contributions on the relationship between economy and environment assume the environment as a good distributed homogeneously among agents. The aim of this work is to relax this hypothesis and to consider that the environment can have a local character even if conditioned through externalities by the choices made at the global level. In this article, we adapt the classical framework introduced in John and Pecchenino (Econ J 104(427):1393-1410, 1994) to analyze the dynamic relationship between environment and economic process, and we propose an OLG agent-based model where each agent perceives her own level of environmental quality determined by her own decisions, and by the decisions of those living around her. Despite the attention devoted to local environmental aspects, network externalities (determined through the scheme of Moore neighborhoods) play a fundamental role in defining environmental dynamics and they may induce the emergence of cyclical dynamics. The occurrence of oscillations in the local environmental quality is partially mitigated by the presence of heterogeneity in individuals' preferences. Finally, when a centralized planner is introduced, the dynamics converge to stationary values regardless of the assumption on heterogeneity of agents.

Trade and Resource Sustainability with Asset Markets

Trade changes incentives to protect an open-access natural resource independently of its effect on the resource price. General equilibrium linkages cause resource policy to affect the price of privately owned assets regardless of whether they are used in the resource sector. In the closed economy, the asset market in our overlapping generations setting creates incentives for currently living agents to protect the natural resource. The interplay of the asset market and general equilibrium effects causes trade to reverse these incentives. Trade liberalization and the establishment of formal property rights are policy complements: the former makes the latter more important.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s13235-021-00400-4.

Endogenous longevity and optimal tax progressivity

We study the impact of endogenous longevity on optimal tax progressivity and inequality in an overlapping generations model with skill heterogeneity. Higher tax progressivity decreases both the longevity gap and net income inequality, but at the expense of lower average lifetime and income. We find that the welfare-maximizing income tax is less progressive in our model with endogenous longevity than in our model with exogenous longevity. In a highly stylized calibration of the US economy, we show that optimal tax progressivity is less than what prevails under the current US tax system. Our results are robust to the range of empirical labor supply elasticity and the assumptions of missing annuity markets and stochastic health. Our conclusion for the optimal progressivity of the US tax system can be altered by the adoption of a more egalitarian welfare function or by increases in prevailing levels of wage inequality.

On the Anatomy of Medical Progress Within an Overlapping Generations Economy

We study medical progress within a two-sector economy of overlapping generations subject to endogenous mortality. Individuals demand health care with a view to lowering mortality over their life-cycle. We characterise the individual optimum and the general equilibrium, and study the impact of a major medical innovation leading to an improvement in the effectiveness of health care. We find that general equilibrium effects dampen strongly the increase in health care usage following medical innovation. Moreover, an increase in savings offsets the negative impact on GDP per capita of a decline in the support ratio. Finally, we show that the reallocation of resources between the final goods and health care sector, following the innovation, plays a crucial role in shaping the general equilibrium impact.

Estimation of the variance effective population size in age structured populations

The variance effective population size for age structured populations is generally hard to estimate and the temporal method often gives biased estimates. Here, we give an explicit expression for a correction factor which, combined with estimates from the temporal method, yield approximately unbiased estimates. The calculation of the correction factor requires knowledge of the age specific offspring distribution and survival probabilities as well as possible correlation between survival and reproductive success. In order to relax these requirements, we show that only first order moments of these distributions need to be known if the time between samples is large, or individuals from all age classes which reproduce are sampled. A very explicit approximate expression for the asymptotic coefficient of standard deviation of the estimator is derived, and it can be used to construct confidence intervals and optimal ways of weighting information from different markers. The asymptotic coefficient of standard deviation can also be used to design studies and we show that in order to maximize the precision for a given sample size, individuals from older age classes should be sampled since their expected variance of allele frequency change is higher and easier to estimate. However, for populations with fluctuating age class sizes, the accuracy of the method is reduced when samples are taken from older age classes with high demographic variation. We also present a method for simultaneous estimation of the variance effective and census population size.

Biological fitness and the Price Equation in class-structured populations

Price׳s extended covariance selection mathematics is applied to class-structured populations with additional assumptions, to derive the 'genetic Price Equation with class structure'. Each individual belongs to a class, and there may be overlapping generations; the equation is genetic because the trait is restricted to an arbitrary weighted sum of allele frequencies. Two special cases are then considered, a demography-like case corresponding to Fisher's fundamental theorem of natural selection, and a sex-ratio-like case corresponding to Fisher's sex ratio argument: these differ in whether it is natural to assume that the per-capita or the total reproductive values of each class are maintained from the parental to the descendant population. These cases also match the two existing attempts to eliminate from the effects of natural selection those passive changes in allele frequencies that are caused by the class structure, and suggest improvements in one of them. In each case a more specialised Price Equation, and a 'fundamental theorem of natural selection', are proved, which hold out of class-structure equilibrium, showing that passive changes can be eliminated in more than one way, and hinting at the possibility of a more general formulation. Previous class-structured Price Equations and a 'fundamental theorem' are linked to these results. The power of Price's formal approach is vividly illustrated by this lucid conspectus of otherwise self-standing theories with confusing interconnections.

Total reproductive values for females and for males in sexual diploids are not equal

A very simple mathematical exposition of reproductive value in an age- and sex-structured sexual diploid population employs reproductive value as the probability that a random gene in a distant generation traces its ancestry to a given individual or set of individuals today. Although the total reproductive values of all females and that of all males are not in general equal, but instead proportional to the average age of a new mother and a new father, respectively, Fisher׳s equal-investment conclusion for the sex ratio remains valid because the total reproductive value of age-zero females equals the total reproductive value of age-zero males. However, the conclusion is seen to require an extra assumption, namely stability of the age-distribution.