We develop, solve and implement numerically an intertemporal general equilibrium model with overlapping generations subject to endogenous mortality, the latter depending on individual health care and medical technology. In so doing, we explicitly study a three sector model, where a medical sector (e.g. hospitals) and an R&D sector developing medical technology operate beside a production sector.
We derive from individual choice an age-specific demand for health care as well as its underlying value. Aggregating across cohorts, we show how the total demand for health care translates, via the medical sector, into a demand for medical innovation. We assess the efficiency of the allocation and how it depends on the competitive and institutional environment. Specifically, we contrast the decentral allocation against a first-best solution, which we derive using age-structured optimal control techniques.
Calibrating the model to US and European data, we examine numerically how the dynamics are shaped by the nature of medical technology, by population change (e.g. exogenous ageing, baby-boom/bust) and by policy (e.g. health insurance, provider regulation, patent policy). Our numerical model allows us to trace the out-of-steady-state dynamics.
First Results (Status: 10 March 2016)
Initially, we study the impact of an unanticipated exogenous increase in medical knowledge, leading to an increased effectiveness of health care in lowering mortality rates. We consider three scenarios:
Benchmark (blue plot): index of medical knowledge = 1; rate of time preference = 0.02; US mortality schedule (taken from Human Mortality Database); rate of capital depreciation = 0.05. Two sectors: Final goods production with capital and labour; Health care with labour.
General Equilibrium impact of medical shock (green plot): index of medical knowledge = 2 from the point of time at which the focal cohort is aged 50. In this scenario all markets (capital, labour, final goods and health care) are in equilibrium, implying that the price for health care, the wage rate and interest rate adjust to the shock.
Partial equilibrium impact of medical shock (red plot): In this (hypothetical) scenario, we consider the individual life-cycle allocation for a given set of prices. Contrasting it against the general equilibrium result reveals the extent to which movements in prices alter the initial impact of the medical shock on the individual life-cycle allocation.
The medical breakthrough induces the individual to re-allocate individual resources from consumption to health-care and leads to a reduction in the value of life.
The impacts (at t=150) are markedly reduced in the general equilibrium setting. This is because the wage rate and the price for health care are increasing, while the interest rate is decreasing. In this regard the partial equilibrium effects of medical change are over-estimating the true impact.
The price changes are induced by the increased demand for labour within the expanding health care sector. As a consequence the health expenditure share of GDP rises.
In many instances, medical advances are anticipated. In that case, individuals defer consumption and health expenditures to post-innovation times (t > 200). The ensuing increase in savings triggers a temporary economic boom before the innovation.