An integrated life-cycle model of addiction, health capital and smoking: theoretical and empirical implications

This paper develops and estimates a life-cycle model that integrates the human capital model of health investment with the model of rational addiction. This unified framework recognises that smoking behaviour and positive investment in health capital are simultaneous choices of a single optimisation problem. We define an individual’s lifetime smoking consumption pattern through a dynamic optimisation problem where smoking is influenced by a series of interconnected factors: the use of preventive medical care, the evolution of an individual’s health endowment and the accumulation of an addiction stock.

This inter-temporal optimisation framework leads to a system of interrelated first-order difference equations (FODE). These equations can be reduced into single fourth-order difference equations for health and smoking and estimated as dynamic panel data models on data from the British Household Panel Survey (BHPS) employing generalized method of moments (GMM) estimation techniques. An implication of the reduction process is that the roots of the single fourth-order difference equations are the same as the roots of the system of first-order difference equations and accordingly can be used to investigate the dynamics of the system.

Our estimates find strong and statistically significant persistence of both smoking consumption and health capital up until the third lag in our fourth-order difference equations of smoking and health, respectively. We implement a series of specification tests of autocorrelation as well as tests of over-identifying restrictions. Furthermore, we compare our GMM estimates with results obtained from the within estimator and ordinary least squares (OLS) models.  

This paper provides several contributions to the literature. Firstly, this is the first attempt to formally reconcile two important economic theories of individual behaviour: the human capital model of health investment and the model of rational addiction. Secondly, this integrated framework provides a novel interpretation for the underlying mechanisms that lead individuals with heterogeneous health profiles and different preferences on investing in their health capital to different addiction accumulation paths and in turn to alternative lifetime smoking pathways. Finally, we present and discuss an empirical implementation of this framework that preserves the dynamic roots of the system of equations resulting from the dynamic optimisation problem.       

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