Precautionary Savings, Health Expenditures and the Demand for Health Insurance

Presenter: Petra Schumacher, Ludwig-Maximilians-University Munich

Abstract

Rationale: Most theoretical papers examine the demand for health insurance in a static setting (see e.g. Cutler and Zeckhauser (2000)) even though the decision for appropriate health insurance in order to cover increasing health expenditures with age can be considered as a lifetime decision. Yet, there are empirical papers that investigate the demand for health insurance in a life-cycle context and, thus, analyse the relation between rising health expenditures and precautionary savings, e.g. Kotlikoff (1988), Hubbard, Skinner and Zeldes (1995) and Palombo (1999). They show that the threat of higher health care costs at older ages induces people to accumulate significant financial reserves.

Objectives: The submitted paper deals with a theoretical investigation of the relation between precautionary savings, health expenditures and health insurance in a life-cycle consumption framework, which has not been provided so far. The demand for health insurance will be analyzed in an expected utility framework with the intention to determine the influence of expected health state in the future on the savings behaviour and on the incentives to insure.

Methodology: As a point of reference for the multi period investigation described later, a single period setting is modelled at first. In this context, it can either be optimal to fully insure or not to be treated at all if the utility reduction when falling ill does not exceed certain values and the health care costs are sufficiently high.
Subsequently, the analysis is extended to a two period model. At t1, individuals decide on their consumption at both points of time and whether or not to insure against health care costs at t2. At t2, the individual will be ill with a probability of p and, in that case, will suffer from a reduction of utility. In this general setting, it still holds true that full-coverage insurance contracts that are priced actuarily fairly are always beneficial compared to privately covering the treatment costs. Yet, the decision not to insure and not to be treated can be rational as well. In particular, this decision depends on the treatment costs and the reduction of utility in case of an illness.

Results: In the two period model, it is shown that an illness probability that increases in age creates incentives to privately accumulate funds if individuals decide against insurance and treatment. The results from the two period model will then be compared with those in one period. It is calculated that the expectation of a rising health risk will decrease incentives to insure as individuals can privately accumulate savings in order to compensate for a utility reduction in case of an illness.

Conclusion:
In summary, the model demonstrates that the probability of a utility reduction in case of an untreated, non-insured illness in the future provides another motive for precautionary savings besides income risk. In particular, this might be relevant as the incentives to insure and to be treated are diminished when observing a lifetime context.