Lee-Carter Model
Lee-Carter Mortality Forecasting Model · Also known as: LC Model, Lee-Carter Mortality Model, Singular Value Decomposition Mortality Model, Lee-Carter Ölümlülük Modeli
The Lee-Carter model is a stochastic framework for modeling and forecasting age-specific mortality rates, introduced by Ronald Lee and Lawrence Carter in their landmark 1992 paper. It decomposes the logarithm of age-specific death rates into an age pattern of mortality, a time-varying index of mortality level, and an age-specific sensitivity of that index, then forecasts the time index using ARIMA time-series methods to generate probabilistic mortality projections.
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When to use it
Use the Lee-Carter model when you have a long historical series of age-specific death rates (typically 30 or more years) and need probabilistic projections of mortality for actuarial, pension, or demographic planning purposes. The model assumes that age-specific rates of mortality improvement are proportional over time and that the single index κ(t) captures all systematic temporal variation. It is less suited when mortality improvement rates differ substantially across ages over time, when data are sparse or noisy, or when cause-specific mortality dynamics are needed. Extensions such as the Cairns-Blake-Dowd model or the Lee-Miller variant may be preferred in those cases.
Strengths & limitations
- Provides stochastic, probabilistic forecast intervals rather than deterministic point projections, enabling rigorous uncertainty quantification in pension and insurance liabilities.
- Parsimonious bilinear structure requires estimation of relatively few parameters from historical data, reducing overfitting risk.
- The single time-index framework makes long-range forecasting tractable using well-understood ARIMA methods.
- Has become an international benchmark, enabling direct comparison of mortality projections across countries and research groups.
- Assumes proportionality of age-specific improvement rates, which may break down when cohort effects (e.g., the 1918 influenza birth cohort) dominate temporal patterns.
- The random walk with drift specification for κ(t) implies linearly increasing uncertainty; structural breaks in mortality trends violate this assumption.
- Model fit and forecasts can be sensitive to the choice of historical fitting period, and the model offers no mechanism to incorporate expert judgment about future trends.
- Restricted to a single latent factor, so it cannot capture multi-dimensional variation in mortality dynamics without extension to multi-factor variants.
Frequently asked
How many years of historical data are needed to fit the Lee-Carter model reliably?
Most practitioners recommend at least 30 years of complete, age-disaggregated mortality data. Shorter series produce unstable estimates of the age sensitivity vector b(x) and unreliable drift estimates for the mortality index, leading to wide and poorly calibrated forecast intervals. Human Mortality Database data, available for many countries, commonly spans 50–100 years and is the standard source.
What is the difference between the original Lee-Carter model and the Lee-Miller extension?
Lee and Miller (2001) proposed fitting the model to a recent sub-period (e.g., the last 30 years) rather than the full historical series, and jump-starting κ(t) from a level that matches a reference life table rather than the raw historical endpoint. These modifications reduce the impact of distant historical data and improve short- to medium-term forecast accuracy, particularly for countries with recent structural shifts in mortality improvement.
Can the Lee-Carter model handle cause-of-death data?
The original formulation operates on all-cause death rates. Extensions exist that apply the bilinear structure to cause-specific rates separately, but these face coherence challenges because independently projected cause-specific rates need not sum consistently to all-cause projections. Multi-cause extensions require additional constraints and are an active area of methodological research.
Sources
- Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671. DOI: 10.1080/01621459.1992.10475265 ↗
How to cite this page
ScholarGate. (2026, June 2). Lee-Carter Mortality Forecasting Model. ScholarGate. https://scholargate.app/en/demography/lee-carter-model
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