A Synthesis of the Grossman and Becker-Murphy Models of Health and Addiction: Theoretical and Empirical Implications

This paper develops and estimates a model that integrates two fundamental theories of individual health behaviour: the Becker-Murphy model of rational addiction and the Grossman model of health investment. We define an individual's lifetime smoking consumption pattern and investments in health capital as simultaneous choices within a single optimization problem allowing for the presence of an addiction stock and investments in preventive medical care. The resulting system of first-order difference equations is reduced to a single fourth-order difference equation defined both for smoking and health and which preserve the dynamic roots of the system. GMM systems estimation using the British Household Panel Survey reveals strong persistence in the evolution of both smoking consumption and health capital with direct effects of past health and smoking observed for up to three and four lagged periods for men and women respectively. Conditional on dynamics there is a limited role for the direct effects of socio-economic status. A convincing understanding of an individual's optimal lifetime health trajectory requires an appreciation of how both investments and accumulated disinvestments in health separately impact on the dynamics of health capital. The integrated approach presented here offers such a framework.