The Reproductive Value as Part of the Shadow Price of Population

The reproductive value (see Fisher 1930) arises as part of the shadow price of the population in a large class of age-structured optimal control models.Reproductive value, distributed optimal control theory, McKendrick equation, shadow price, indirect effect.

Externalities in a Life-Cycle Model with Endogenous Survival

We study socially vs. individually optimal lifecycle allocations of consumption and health care, when individual health expenditure curbs own mortality but also has a spillover effect on other persons' survival. Such spillovers arise, for instance, when health care activity at aggregate level triggers improvements in treatment through learningbydoing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an agestructured optimal control model at population level with a conventional lifecycle model to derive the social and private value of life. We then examine how individual incentives deviate from social incentives and how they can be aligned by way of a transfer scheme. The agepatterns of socially and individually optimal health expenditure and the transfer rate are derived. Numerical analysis illustrates the workings of our model.Demand for health, externality, life-cycle-model, optimal control, tax-subsidy, value of life.

The Reproductive Value in Distributed Optimal Control Models

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology.Reproductive value, distributed optimal control theory, McKendrick, shadow price, indirect effect, health economics, epidemiology, population biology.

The reproductive value as part of the shadow price of population

The reproductive value (see Fisher [10]) arises as part of the shadow price of the population in a large class of age-structured optimal control models.life history, reproductive value

Optimal Choice of Health and Retirement in a Life-Cycle Model

We examine within a life-cycle set-up the choice of health and retirement. Health care contributes to a reduction in both mortality, determining the need to accumulate retirement wealth, and in morbidity, determining the disutility of work. The retirement age affects health through the value of survival and the value of morbidity reductions. We compare the allocation for a first-best setting where the individual can transfer wealth freely within a perfect annuity market with a second-best set-up with an incentive incompatible (yet actuarially fair) retirement scheme and an imperfect annuity market and show how the inefficiencies shape the health-retirement nexus

Optimal choice of health and retirement in a life-cycle model

We examine within a life-cycle set-up the simultaneous choice of health care and retirement (together with consumption), when health care contributes to both a reduction in mortality and in morbidity. Health tends to impact on retirement via morbidity, determining the disutility of work, and through longevity, determining the need to accumulate retirement wealth. In contrast, the age of retirement drives health through changes in the value of survival and the value of morbidity reductions. We apply our model to analyse the effects of moral hazard in the annuity market: While moral hazard always induces excessive health investments and an excessive duration of working life it also triggers an excessive level of consumption if the impact of health on the disutility of work is sufficiently large. We examine a transfer scheme and mandatory retirement as policies to curtail moral hazard. Numerical analysis illustrates the working of our model

The reproductive value as part of the shadow price of population

The reproductive value (see Fisher 1930) arises as part of the shadow price of the population in a large class of age-structured optimal control models

Quantifying Economic Dependency

In this paper we compare several types of economic dependency ratios for a selection of European countries. These dependency ratios take into account not only the demographic structure of the population, but also the differences in age-specific economic behaviour such as labour market activity, income and consumption as well as age-specific public transfers. In selected simulations where we combine patterns of age-specific economic behaviour and transfers with population projections, we show that in all countries population ageing would lead to a pronounced increase in dependency ratios if present age-specific patterns were not to change. Our analysis of cross-country differences in economic dependency demonstrates that these differences are driven by both differences in age-specific economic behaviour and in the age composition of the populations. The choice of which dependency ratio to use in a specific policy context is determined by the nature of the question to be answered. The comparison of our various dependency ratios across countries gives insights into which strategies might be effective in mitigating the expected increase in economic dependency due to demographic change

The reproductive value in distributed optimal control models

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for changing vital rates. To motivate and demonstrate the general framework, we provide examples in health economics, epidemiology, and population biology

Development of Harmonized Indicators and Estimation Procedures for Forests with Protective Functions against Natural Hazards in the Alpine Space

The present study was developed in the context of Regulation (EC) 2152/2003 on the monitoring of forest and environmental interactions, the so-called "Forest Focus" Regulation. The specific objective of this study was to explore the possible contribution of the national forest inventories (NFIs) to assess protective functions of for-ests in the alpine space. Key components of protective functions could be determined with the help of on-going national and international studies and processes. In order to grant consistency, definitions of forest area, dam-age potential and hazard potential had to be harmonised. Based on those, a strategy for monitoring and report-ing aspects of protective functions of mountain forests in the alpine space was proposed. Estimation procedures based on existing NFI data and field assessments and their integration in different remote sensing techniques were tested for harmonised monitoring. Final results are presented in this report.JRC.DDG.H.7-Land management and natural hazard