Price's Northampton mortality table overestimated mortality, a directional bias good for insurers and adverse to annuity buyers

actuarial-historyinsurancemortality-tableshistorical-demographymechanism-design

Richard Price's Northampton mortality table — the survivorship data behind Observations on Reversionary Payments (1771) and the actuarial standard for roughly a century — is generally described as having overestimated mortality: it implied that people died sooner than they actually did. A table biased toward death is "good for the insurance business, and adverse for those purchasing annuities." The reference that anchored a century of British premium-setting therefore carried a known directional error in the insurer's favour.

The mechanism is one of incidence. If a table overstates mortality, life-assurance premiums computed from it are set conservatively high — the insurer collects more than a true-longevity table would justify — while the same overstatement makes annuities look cheaper to grant than they truly are, so an annuity purchaser (or seller) is disadvantaged when the annuitants live longer than the table predicted. The bias is usually attributed to defects in the underlying Northampton parish data, such as in-migration and baptism records inflating the apparent count of deaths relative to births [unverified-mechanism — this sentence carries no pointer: the cited Wikipedia page says only "It, too, overestimated mortality" (fetched 2026-09-11); covered by the note's flag and routed question, not settled].

This extends the vault's thread on demographic data that is load-bearing yet imperfectly grounded: a mortality dataset read too straight repeats the selection-and-censoring trap catalogued in claim-osteological-paradox-skeletal-statistics-confound-past-health, where a sample of the dead is a distorted window on the living. It also rhymes with the mispricing that ran through early actuarial history before age-rating — the flat-rate annuities that Dodson's age-scaled premiums were built to correct.

The specific direction, magnitude, and incidence of the bias rest only on a Tier 3–4 summary; the claim is flagged [unverified-quant/mechanism] and routed to question-verify-northampton-table-overestimated-mortality-primary.

Addendum (2026-07-25). The first empirical check on Northampton from assured-lives data came in about 1811, when the Amicable Society's registrar compiled its own mortality experience and found it "more favourable than that shown by the Northampton Table" (claim-pensam-1811-amicable-experience-first-assured-lives-mortality-data). Two distinct effects point the same way and should not be collapsed: Northampton's own overestimation bias, described in this note, and the separate fact that an assured population is screened and so dies more slowly than the general population the table described.

Addendum (2026-08-24). An independent corroborating account (Bernstein, Against the Gods, 1996, via a Goodreads-mediated transcription) complicates the "adverse for those purchasing annuities" half of this claim rather than confirming it cleanly. The same passage's next sentence: "the British government, using the same tables to determine annuity payments to its pensioners, lost heavily" — describing the government as annuity seller/grantor losing money because pensioners lived longer than the table predicted, the opposite incidence from "adverse for those purchasing annuities" read as naming the individual annuity buyer. The two readings are not necessarily in conflict (the phrase could mean an institution purchasing annuity liabilities off its own book, i.e. the same institution that grants them), but the ambiguity is itself the finding: this note's own phrasing is not precise enough to say which party it names, and the one concrete episode found points toward the seller/grantor being the loser, not the individual annuitant. Marked [unverified-quant/mechanism — needs primary], resting on the same secondary Bernstein passage as the corroborating claim above, and tracked at question-verify-northampton-table-overestimated-mortality-primary rather than resolved here. The Tier 1–2 primary most likely to settle it — William Sutton's 1874 paper on Price's method — is now identified but access-blocked; see entity-william-sutton.