Heiss 2011 — Dynamics of Self-Rated Health and Selective Mortality

Summary

Heiss (2011) analyzes the first seven waves of the Health and Retirement Study (HRS; 29,113 individuals, 123,867 observations, 6,921 deaths) to document two fundamental facts about self-rated health status (SRHS): all available lags (up to lag 6) retain significant but geometrically decreasing predictive power for current SRHS, and SRHS strongly predicts future mortality, creating survivorship bias in panel models restricted to living respondents. The paper proposes and estimates a parsimonious joint model — a latent first-order autoregressive (AR(1)) health process shared across both the SRHS and mortality equations — that outperforms independent, random-effects (RE), state-dependence, and combined state-dependence+RE models on fit and parsimony. Simulations show the model reproduces observed SRHS dynamics and survivorship patterns strikingly well. The survivorship decomposition is the paper's most policy-relevant output: at ages 80–89, the direct aging effect on poor/fair SRHS is +13.95 percentage points (pp) but survivorship selection is −12.28 pp, yielding a cross-sectional increase of only +1.67 pp.

Key Claims

• Long memory of SRHS: Even with six prior lags controlled simultaneously, each lag retains significant predictive power for current SRHS. A pure state-dependence model (only lag 1 matters) and a constant-RE model (all lags equally informative) both fail to fit this pattern; only a latent AR(1) process can explain geometrically decreasing lag coefficients.
• AR(1) autocorrelation: Estimated $\rho = 0.941$ (females) / $0.946$ (males) — significantly less than 1 (RE model rejected by likelihood-ratio (LR) statistics of 949.8 and 779.8 for females and males). Latent health is highly persistent but not constant.
• Latent health dominates noise: $\sigma_a \approx 2.9$–$3.0$ vs. independent and identically distributed (i.i.d.) logistic error $\sigma = \pi/\sqrt{3} \approx 1.8$. Unobserved idiosyncratic health is the dominant source of variation in SRHS.
• 10× inter-wave mortality differential: A respondent reporting poor SRHS faces 10× the mortality risk before the next wave compared to one reporting excellent SRHS.
• Long-run cumulative mortality by initial SRHS: Among original HRS cohort with complete 7-wave mortality data (n = 11,624): 43.65% of those with poor SRHS in wave 1 died by wave 7 vs. 6.75% with excellent SRHS; the lines diverge throughout, never converging.
• Survivorship bias decomposition (Table 8, average partial effects on poor/fair SRHS, pp):

Age group	Direct aging effect	Survivorship selection	Net cross-sectional
50–59	+1.98	−0.79	+1.18
60–69	+2.91	−2.28	+0.63
70–79	+7.94	−5.87	+2.07
80–89	+13.95	−12.28	+1.67
90+	+24.55	−28.43	−3.87

At ages 90+, survivorship selection is so powerful that cross-sectional health appears to improve even as the true aging effect is +24.55 pp.

• Female-male SRHS paradox: Women have better latent health (direct effect −2.64 pp vs. men), but their lower mortality means more unhealthy women survive to be observed (+2.55 pp selection effect). In the surviving sample, the female health advantage is nearly invisible (net −0.08 pp). Studies restricted to survivors will dramatically understate the female health advantage.
• Education-health gradient attenuation: Low-education individuals have worse SRHS (direct +15.49 pp) and higher mortality (selection −1.82 pp), so the education-health gradient is understated by ~12% in survivor-restricted analyses.
• Joint SRHS-mortality model parameters (Table 7): latent health loading on mortality: $\sigma^d \approx 0.929$ (males) / $0.942$ (females), both highly significant. Same latent health process drives both SRHS levels and mortality risk via shared frailty. $\rho \approx 0.944$–$0.949$ in joint model.
• Selection on unobservables: Unlike inverse-probability-weighting (IPW) corrections (Contoyannis et al. 2004a; Jones et al. 2006), the joint model allows the same unobserved frailty to drive both SRHS and mortality — a stronger correction that does not require the selection-on-observables assumption.
• Initial conditions problem: Individuals entering the HRS at older ages are positively selected survivors of prior mortality. The likelihood is conditioned on survival to initial sampling, analogous to Heckman's (1981) initial conditions problem.

Concepts Introduced or Extended

• Selective Mortality
• Morbidity-Mortality Distinction

Entities Mentioned

• Florian Heiss
• Health and Retirement Study

Quotes

"SRHS is a frequently used measure of individual health in survey data. Despite its subjectiveness, it has considerable real content. For example, it is a strong predictor of mortality. This leads to a potential survivorship bias—effects of all kinds of determinants of health are confounded by their effect on selective mortality."

"The strongest survivorship bias is found for the age profile, but also the SRHS differences by gender and education are attenuated by selective mortality."

My Take

This is the published journal version of the methodology underlying Heiss et al. (2007) — stripped to a single health dimension (SRH only, no work disability) and focused squarely on the model-comparison argument and survivorship decomposition. The AR(1) model is cleaner than the Contoyannis et al. (2004a) preferred model (state dep + RE) on both parsimony and fit grounds.

The survivorship bias decomposition (Table 8) is the paper's most policy-useful output: it demonstrates that observing only the living understates health deterioration at old age by an order of magnitude (direct effect 10–25 pp, net effect 1–4 pp). For disability insurance (DI) research, this implies that beneficiary panels will mechanically show spuriously improving average health over time through selective exit of the sickest via death — the exact mechanism quantified in DI Beneficiary Mortality and Morbidity-Mortality Distinction.

Limitations: single health dimension only (no work disability); constant $\rho$ and $\sigma_a$ (not age-varying); no reporting style heterogeneity; the paper itself notes two-process models (lethal vs. non-lethal health) might fit better. The Stata code was available from the author but likely not publicly archived.

Relationship to Heiss et al. (2007): The 2007 paper used two health dimensions (SRH + work disability), all four HRS cohorts, and focused on trajectory prediction and work disability → mortality odds ratio (OR). This 2011 paper provides the standalone econometric proof that the AR(1) latent health model dominates standard approaches and provides the detailed survivorship decomposition the 2007 paper did not.