Health, Survival and Consumption Over the Life Cycle: Individual Vs. Social Optimum
Posted: 28 Jun 2007
In recent years most industrialized countries have allocated increasing shares of their GDP to health care while at the same time life-expectancy has continued to increase. Against this background a debate continues on whether too much is spent on health care.
This begs two questions: What motivates individuals to expend resources on the reduction in mortality and to what effect? Do they get it right from a social welfare point of view? We seek to provide an answer to these questions by combining two models:
(i) an age-structured optimal control model, where a social planner maximizes welfare (i.e. individual utilities aggregated over time and age-groups). This model determines the socially optimal pattern of consumption and health care spending.
(ii) a life-cycle model, where an individual maximizes life-time utility. This model determines the individual pattern of consumption and health care expenditure.
In both models health investments lower the force of mortality. This means for model (i) at population level that at each time t a greater number of people within each age group survive to time t+1. Within the individual life-cycle model (ii), health care spending contributes towards greater longevity in a stochastic way.
Whereas model (ii) follows closely the extensive literature on individual health investments in a life-cycle framework (e.g. Grossman 1972, Ehrlich and Chuma 1990, Ehrlich 2000), we are unaware of any previous work seeking - as we do in (i) - to determine the social optimum as the outcome of the maximisation of a welfare function by a social planner. While for an individual age and time are equivalent, a planner faces an age-structured population at each point in time. By introducing age as a second dynamic variable in addition to time, we are able to study the socially optimal age patterns of health investments and consumption as endogenously determined by the population structure and age specific productivity.
Solving and simulating models (i) and (ii) and comparing the respective patterns of consumption and health investment we can deduce conclusions about the inefficiencies in individual behavior and where they arise. Applying the concept of the willingness to pay for mortality reductions, we also derive the social versus private value of life.
We apply the model to two potential inefficiencies in the life-cycle allocation of health care spending. Firstly, we consider an imperfect market of life insurance, where the insurer can observe the average mortality for an age-group but not individual mortality. We illustrate in which way the resulting moral hazard leads to inefficient spending patterns. Secondly, we consider spill-over effects, where individual mortality is not only determined by individual health care expenditure but also affected by per-capita spending at population levels. Spillovers may be positive, e.g. due to learning-by-doing in the provision of care, or negative, due to congestion effects resulting in waiting times or patient dumping. In either case, they imply socially inefficient patterns of health investment over the life-cycle. Again, we illustrate the implications of spillover-effects and how they can be corrected by appropriate taxation.
Keywords: age-structured optimal control, health care spending, life-cycle model
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