SeaTE: Subjective ex ante Treatment Effect of Health on Retirement
AbstractHow does a treatment, such as poor health, affect a behavior, such as retirement? In behavioral data, by which we mean realized outcomes or decisions of economic agents, the econometrician observes only the behavior conditional on the treatment, but not the counterfactual behavior absent the treatment. When there is unobserved heterogeneity across individuals, this inherent feature of behavioral data makes difficult inferences about causal effects. Rather than relying on behavioral data, the paper uses subjective expectations of a behavior or outcomes conditional on values of the treatment to elicit ex ante treatment effects. This strategy allows each individual to be both treatment and control, thereby obviating the unobserved counterfactual problem and allowing for unrestricted heterogeneity across individuals. This approach yields an individual-level estimate of the treatment effect that we call the Subjective ex ante Treatment Effect, or SeaTE for short. Thus, this paper provides a strategy for quantifying person-specific treatment effects and for characterizing the distribution of causal effects across the population.
We implement our approach by asking older workers participating in the Vanguard Research Initiative (VRI) to report the conditional likelihood, on a 0-100 percent chance scale that they will be working to specified horizons under alternative health scenarios. They also report their unconditional likelihoods of working to those horizons and of experiencing those health states. Using these data we generate individual and aggregate level estimates of the Subjective ex ante Treatment Effect (SeaTE) of health on retirement age, given by the difference between respondents’ likelihoods of working in low versus high health. We interpret that the SeaTE in a dynamic programming framework, and estimate a simple structural econometric model of health and retirement combining the conditional probability measures with this theoretical framework.
The Subjective ex ante Treatment Effect (SeaTE) of health on retirement is zero for almost 30% of working respondents aged 57 and higher at both 2 and 4 year horizons. The remaining 70% reports have a strictly negative SeaTE (median of -40% and standard deviation of 24% percent for the 2-year horizon; median of -30% and standard deviation of 25% percent for the 4-year horizon). The structural model implies that moving from high to low health has a large, negative effect on the mean value of continued work, but the within-person correlation of this value is high.