Self-reported health status and latent health dynamics

Abstract

Many dynamic structural models that include health as a state variable use categorical self-reported health status (SRHS) as their sole empirical measure of health. Commonly, transition probabilities among discrete health states are calculated directly from one-wave-ahead transitions observed in panel data. The predicted dynamics of SRHS generated from these calculations rapidly deviate from empirical transitions more than one wave ahead, as the assumption of a Markovian process is not satisfied. Consequently, models that treat SRHS as a true representation of health are not well calibrated to accurately match the long term dynamics of individual health. This paper specifies a model in which SRHS is a noisy measure of a continuous latent health state. I estimate the model by maximum likelihood on several panel datasets, exploiting long sequences of SRHS rather than simple wave-to-wave transitions. By accounting for transitory reporting error, the latent health model is able to match both short-run and long-run SRHS transitions up to twenty years in the future, as well as other features of empirical SRHS dynamics. Moreover, the measure of latent health is at least as good at predicting other outcomes (including mortality, labor supply, and medical expenses) as SRHS itself. To aid structural modelers in replacing their representation of health, I provide simple software tools for generating a discretized latent health process, and for filtering observed sequences of SRHS into (a distribution of) latent health.