Decision making under uncertainty: state-dependent utility functions and applications on health outcomes

According to several authors (e.g. Zeckhauser 1970, Arrow 1974), the dependence of the shape of the utility function on health conditions has relevant effects on a wide set of economic behaviors. For example, if marginal utility of consumption increases or decreases as a consequence of illness, this is likely to have an impact on the demand for health insurance (Gyrd Hansen, 2016) or on the optimal level of life-cycle savings (Kools and Knoef, 2017) or on optimal setting of social security systems (Viscusi and Evans, 1990, Finkelstein 2013). According to Finkelstein (2013), we develop an empirical model to estimate how the marginal utility of consumption varies with health. Our purpose is to investigate how possible shocks in the health status may lead to a change in an individual’s preferences and decision making approach. Under the theoretical framework of the state dependent utility function, we developed an empirical model in which the impact of health on the marginal utility of consumption can be estimated from data on permanent income, health and utility proxies. We tested the model on two different dataset. First, we used a sample drawn from retired people living in a subset of European countries, by means of data from the Survey of Health, Ageing and Retirement in Europe (SHARE). Second, we used data drawn from the ‘English Longitudinal Study on Ageing’ (ELSA) dataset. We wanted to check if testing the model on a sample of individuals with different features, values and beliefs, and living in a country with dissimilar social and cultural environment and institutional framework can influence our results, thus leading on different evidence compared to what we obtain on a sample drawn from continental Europe. Our evidences, obtained testing the model on the two different dataset, points to the same direction. In fact, our results, stable in the two different datasets and robust under different specifications of the model, suggest the existence of positive state dependency of the utility function. What we observed is that the marginal utility of consumption tends to increase as a consequence of a health shock. In detail, our evidence related to the sign of the parameter assessing the state dependency of the utility function points in a positive direction, suggesting an increase in marginal utility associated to consumption when moving to an unhealthy state.