William Makeham & the Gompertz–Makeham Law (1860)

Event Date: 1860 Category: Actuarial Science — Mortality Refinement / Hazard Modeling

Summary

William Makeham (1826–1891) refined Gompertz’s model by adding an age‑independent component to mortality. The resulting Gompertz–Makeham Law became the dominant mortality model of the late 19th and early 20th centuries. It allowed actuaries to account for background hazards—accidents, epidemics, environmental risks—that affect all ages.

Background / Context

By mid‑century:

• Gompertz’s model worked well for adult mortality
• but it failed to capture age‑independent risks
• insurers needed a more flexible model

Makeham provided the missing piece.

What Happened

⭐ 1. Makeham’s Modification (1860)

Makeham proposed:

μ(x) = A + Be^{Cx} (mortality = age‑independent risk + age‑dependent exponential risk)

This allowed actuaries to model:

• accidents
• epidemics
• environmental hazards
• baseline mortality

⭐ Sidebar: Why Makeham’s Addition Mattered

The first model to separate background risk from aging

Makeham’s insight:

• mortality has two components
  • one that increases with age
  • one that does not

This made mortality modeling more realistic and more useful for insurers.

Impact

• Improved pricing accuracy
• Better fit to observed mortality
• Dominant model for decades
• Foundation for 20th‑century actuarial science

Why It Mattered (Plain English)

Makeham made Gompertz’s model practical in the real world, where people die from more than just aging.

Related Entries

• 1780s–1815 — The Carlisle Mortality Tables — empirical mortality foundations that Gompertz and Makeham later refined
• 1825 — Benjamin Gompertz & the Gompertz Mortality Curve — the original exponential mortality model that Makeham extended
• 1775–1776 — William Morgan & the First Actuarial Valuation (forthcoming) — early valuation methodology that relied on pre‑Gompertz mortality assumptions
• 1848 — Founding of the Institute of Actuaries — the professional body that formalized mortality modeling, including Gompertz–Makeham
• 1870s–1890s — The American Adoption of Actuarial Science — U.S. insurers’ adoption of British mortality models, including Gompertz–Makeham
• 1890s — Punch Cards for Mortality Tables — early mechanical computation that enabled large‑scale application of Gompertz–Makeham
• 1930s–1950s — IBM Punch‑Card Computing & the Rise of Actuarial Automation — mechanized mortality modeling built on Gompertz–Makeham foundations
• 1980s — The Birth of Catastrophe Modeling (AIR, RMS, EQE) — modern hazard‑modeling frameworks that descend from 19th‑century mortality‑hazard models
• 1990s — Predictive Analytics Emerges in Insurance — multivariate modeling and early machine‑learning techniques extending the lineage of hazard‑based modeling
• 21st Century — Predictive Analytics & Machine Learning (forthcoming) — modern data‑science techniques that represent the full maturation of hazard‑based actuarial modeling