Booth Tickle and Smith 2005 — Evaluation of the Variants of the Lee-Carter Method of Forecasting Mortality A Multi-Country Comparison

Summary

Booth, Tickle, and Smith evaluate three variants of the Lee-Carter model — LC (original), LM (Lee-Miller), and BMS (Booth-Maindonald-Smith) — across ten developed countries using data through 1980 as the fitting base and 1981–1985 as the jump-off period, with 1986–1996 as the out-of-sample forecast window. They decompose forecast error into a jump-off component and a model component, finding that jump-off bias is the dominant failure mode for LC: it accounts for $57\%$ of female and $42\%$ of male total LC error. Both LM and BMS substantially correct for jump-off bias by initializing from observed rather than fitted rates, and BMS is marginally superior to LM in forecast accuracy in a majority of countries.

Key Claims

• LM and BMS are superior to LC in both forecast accuracy and prediction interval width across the 10-country sample (Australia, Canada, Denmark, England & Wales, Finland, France, Italy, Norway, Sweden, Switzerland).
• Jump-off bias accounts for $57\%$ (female) and $42\%$ (male) of LC's total forecast error; for BMS the corresponding shares are only $11\%$ and $4\%$.
• Jump-off bias arises because LC initializes forecasts from fitted (smoothed) rates at the jump-off year rather than observed rates; LM and BMS both initialize from observed rates, eliminating the dominant error source.
• The three variants differ in $k(t)$ adjustment: LC adjusts to total deaths $D_t$; LM adjusts to life expectancy $e_0$; BMS adjusts to the age distribution of deaths $D(x,t)$ via Poisson deviance criterion.
• BMS is marginally superior to LM in forecast accuracy in a majority of countries ($8/10$ for females, $6/10$ for males, measured by root mean squared error (RMSE) of $e_0$).
• LC prediction intervals are too narrow for females in Norway, Sweden, and Switzerland (1986–1990). For males, LC intervals generally contain actual life expectancy (LE) while LM and BMS intervals fail in later years — due to unprecedented rapid male mortality decline during the forecast period, a structural failure common to all three variants.
• Forecast accuracy is highly period-dependent (Keyfitz 1991; Murphy 1995); generalizability of these results beyond the 1986–1996 window is uncertain.

Concepts Introduced or Extended

• Lee-Carter Model

Entities Mentioned

• Heather Booth
• Leonie Tickle
• Len Smith
• Ronald Lee
• Timothy Miller

Quotes

"It has been shown that the LM and BMS variants are superior to LC in both forecast accuracy and width of prediction interval."

"The decomposition of error has demonstrated that jump-off bias is a significant source of error for LC. These results confirm the findings of Lee and Miller (2001)."

"The accuracy of different forecasting methods is highly dependent on the particular period (Keyfitz 1991, Murphy 1995)."

My Take

The jump-off bias decomposition is the paper's core contribution: by separating initialization error from model trend error, it shows that most of LC's inferiority is a fixable artifact — using observed rather than fitted rates at jump-off — not a fundamental failure of the trend structure. The marginal superiority of BMS over LM is real but modest; the fitting-period selection criterion (the distinguishing BMS feature) contributes less here than the jump-off fix that both LM and BMS share. The honest caveat about period dependence is important: the 1986–1996 forecast window featured unusually rapid male mortality decline that none of the three variants could anticipate, and Keyfitz (1991) and Murphy (1995) had already shown that comparative accuracy rankings are sensitive to which period is studied.