Marriage selection and mortality patterns: Inferences and fallacies

The central refutation is valid. Earlier researchers reasoned "if selection is at work, the mortality gap must shrink after marriage stops; ours didn't; therefore selection isn't the cause." One counterexample defeats that, and the paper supplies several with all settings stated. The refutation of Livi-Bacci 1985 is especially clean: he assumed that equally strong selection everywhere would make the gap larger where fewer people stay single, and the model shows that with selection strength held fixed the relationship can go either way. The strongest move in the paper is a second line of attack: even where selection does produce the expected pattern, theories that marriage protects health (Durkheim 1951, Gove 1973) predict the same pattern, so it cannot discriminate between them.

Two problems substantially undermine the stated conclusions. First, the paper treats an inference as unjustified whenever the pattern does not necessarily follow, but never characterizes how large the region of counterexamples is. The examples that stay flat or keep rising require 15–25% of the population to carry a lifelong 4.5-fold death risk. Whether that is a narrow corner or a broad swath is never addressed, so the paper earns "not necessarily justifiable" rather than "generally not justifiable." Second, the closing move from "these two aggregate patterns fail" to "cross-sectional data is of doubtful use, and longitudinal data may be the only promising approach" eliminates one alternative and offers no positive case for the survivor. The surrounding language ("indefensible," "meaningless") does not hedge.

The core concepts are sharp inside the model. The mortality gap is precisely defined, selection is stipulated cleanly (no health benefit from marriage, healthier people marry faster), and "strength of selection" is defined as the ratio of frail to healthy marriage rates. Three concepts are used more loosely than the analysis supports.

• Plausible--the paper claims its parameter choices are realistic, but the only evidence it gives is that the whole batch of examples produces life expectancies around 55 (from age 20) and marriage rates of 87–98% by age 40. It never shows that any individual example has internally consistent demographics — just that the outputs land in a plausible ballpark when you look at them as a group.
• Meaningless--the paper calls the correlation between share single and the mortality gap "meaningless," which overstates the finding. Its model shows the correlation can't tell you how strong selection is — but its sign (positive or negative) still reveals whether the healthy or the frail group's marriage behavior is what varies across populations.
• Cross-sectional is treated as if it meant only aggregate death-registration data; individual-level surveys with health measures are never considered but fall under the conclusion.

The definition of selection strength also does unflagged work: Livi-Bacci's phrase "screening action with respect to health" could be read as the amount of screening achieved, which depends on absolute marriage rates too, and the paper picks the reading under which he is wrong without considering the other.

The paper plays fair. Opponents are quoted at length and their premises stated precisely before being attacked. Several of the inferences being demolished are the author's own (Kisker and Goldman 1987; Hu and Goldman 1990; Goldman, Lord and Hu 1992). Had the simulations shown selection always produces a post-40 decline, there would be no paper. The period-versus-cohort mismatch in the earlier literature — reasoning about how a birth cohort ages using a single year's snapshot — is acknowledged and adopted rather than exploited.

The weaknesses recur throughout: a deductive standard applied where researchers actually use evidential reasoning; no survey of how much of the plausible parameter space produces counterexamples; a model feature (the frail group dies at a fixed 4.5- to 8-fold multiple of the healthy rate at every age, for life) that keeps the two groups from converging and so produces the flat-and-rising patterns, without the paper identifying it as the thing doing the work; and the longitudinal recommendation reached by elimination with no positive argument. A mechanism central to the mixed-sign results — that raising everyone's marriage rate raises the death rate of the married as well as the single — is credited to "mathematical results not shown." Durkheim's argument was about suicide specifically, and the paper does not address whether a two-type all-cause frailty model transfers to a single behavioral cause of death, though Durkheim is listed among the refuted.

Inside the model, everything can be followed. The appendix gives the equations, each figure lists its settings, and the baseline curves are specified closely enough for anyone with a spreadsheet to redraw the results. The verbal explanation of the key mechanism — faster marriage among the healthy drains healthy people from the single pool and widens the gap; faster marriage among the frail does the opposite; both shrink the single population — is clear. A critical reader can name exactly which assumption to reject. Funding from the National Science Foundation and the Japan Foundation is disclosed; the paper was peer-reviewed in Demography.

The problems are all at the boundary between model and world. Plausibility is asserted for the examples as a set, never checked individually. The constant frailty multiplier is not flagged as essential. The population-size analysis is done at age 40 only, while the studies being criticized used various ages. Two supporting derivations are withheld, and a further claim (that convergence need not begin within a human lifespan) is deferred to a then-forthcoming companion paper. The distinction the paper draws at the start of its results — between claims it will "prove false" and claims it will show are "inconclusive" — is honored in the results section and dropped in the conclusion.

Citations are accurate where they can be checked and fairly represented through direct quotation with page numbers. The one verifiable self-citation (Hu and Goldman 1990) is characterized correctly, though that study correlated the absolute death rate of singles rather than the ratio, which is closer to what the paper later recommends than the main text implies. Livi-Bacci 1985 is summarized as favoring selection when his quoted text is more mixed by sex. Carter and Glick 1970 is cited for "the most educated are least likely to marry" without noting this held for women and reversed for men. The prospective studies cited for a marriage benefit are mostly studies of social ties in general, often in elderly samples, which the paper's own footnote half-concedes. None of this affects the core argument, which rests on the author's simulations rather than on the literature. The larger problem is that key results are deferred to an unpublished companion paper or labeled "not shown," so citation support for the mathematical claims is nearly absent even though citation integrity is sound.

No financial or institutional conflicts. Funding comes from a government science agency and a cultural-exchange body with no stake in whether marriage differences arise from selection or protection. The one structural pressure present — the author's own prior work drew the inferences under attack — is handled by naming that work among the targets alongside Durkheim and Livi-Bacci. The reliance on the author's own group for unshown derivations is a transparency issue, not a conflict.