Is treatment "intensity" associated with healthier lifestyle choices? An application of the dose response function

Healthy lifestyle choices and doctor consultations can be substitutes or complements in the health production function. In this paper we consider the relation between the number of doctor consultations and the frequency of patient physical activity. We use a novel application of the Dose-Response Function model proposed by Hirano and Imbens (2004) to deal with treatment endogeneity under the no unmeasured confounding assumption. Our application takes account of unobserved heterogeneity and uses dynamic non-linear models for the treatment and outcome variables of interest. Using seven waves of the British Household Panel Survey, we find that higher treatment intensity and frequency of physical activity are inversely related. We show that accounting for both treatment selection and unobserved heterogeneity halves the size of this relationship. An additional doctor consultation is associated with a 0.5 percentage point reduction in the probability of undertaking vigorous physical activity. Our results hold for a sub-sample visiting the doctor for health check-ups, and are shown to be robust using instrumental variables.