Lee-Carter Mortality Model
Also known as: Lee-Carter Method, Log-Bilinear Mortality Model, LC Mortality Forecast, Poisson Lee-Carter Model
The Lee-Carter model is the benchmark method for forecasting human mortality. Introduced by Ronald Lee and Lawrence Carter in 1992 for U.S. data, it captures the entire schedule of age-specific death rates with a remarkably parsimonious structure: the logarithm of the death rate at each age is a fixed average age profile, plus an age-specific sensitivity multiplied by a single time index that summarizes the overall level of mortality in each year. Because mortality has fallen steadily across the twentieth century, this single index trends downward over time, and forecasting it as a simple time-series process, typically a random walk with drift, propagates the historical pace of improvement into the future for every age at once. Brouhns, Denuit, and Vermunt later recast the fitting step as a Poisson regression on observed death counts, giving the model a proper statistical likelihood and more reliable uncertainty, and the approach now anchors official population and pension projections worldwide.
Key highlights
- Reduces a high-dimensional age-by-year forecasting problem to projecting a single time-varying mortality index.
- Parsimonious and transparent, with parameters that have clear demographic interpretations.
- Produces probabilistic forecasts with widening prediction intervals derived from the time-series model of the index.
- Serves as a robust, widely validated benchmark and has spawned a large family of extensions for cohort, multi-population, and Bayesian settings.
Intuition
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How it works
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When to use it
Use the Lee-Carter model when you have a long run of age-specific mortality data, ideally several decades of death rates or counts with exposures across the full age range, and you want coherent probabilistic forecasts of mortality and life expectancy. It is the natural choice for national population projections, pension and annuity valuation, and any setting where a parsimonious, well-understood benchmark is valued and where mortality has improved in a broadly regular fashion. The Poisson variant is preferred when count data are available, especially because of small numbers at advanced ages. The model is less suitable for very short series, for populations with abrupt structural breaks such as wars or epidemics that violate the smooth-trend assumption, for forecasting at single small areas with sparse data without pooling, or when cohort effects are strong, in which case extensions like the age-period-cohort or Cairns-Blake-Dowd families are more appropriate.
Strengths & limitations
- Reduces a high-dimensional age-by-year forecasting problem to projecting a single time-varying mortality index.
- Parsimonious and transparent, with parameters that have clear demographic interpretations.
- Produces probabilistic forecasts with widening prediction intervals derived from the time-series model of the index.
- Serves as a robust, widely validated benchmark and has spawned a large family of extensions for cohort, multi-population, and Bayesian settings.
- Assumes age sensitivities are constant over time, so it cannot capture changes in the age pattern of mortality improvement.
- The original SVD fit assumes homoskedastic log-scale errors, understating noise at older ages where death counts are small.
- A single time index forces all ages to improve together and ignores cohort effects that drive some real mortality patterns.
- Forecasts hinge on extrapolating the historical drift, which can mislead when structural breaks or trend changes occur.
Common pitfalls
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Applications
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Frequently asked
What do the parameters a_x, b_x, and k_t mean?
The term a_x is the average log death rate at age x over the fitting period, so it fixes the typical shape of the mortality curve. The term k_t is the mortality index, a single number per year summarizing the overall level of mortality, which trends downward as mortality falls. The term b_x is the sensitivity of age x to changes in that index: large where mortality at that age has improved a lot, small where it has changed little. Together they reconstruct the log death rate at every age and year, and forecasting reduces to projecting k_t.
Why is the mortality index usually forecast as a random walk with drift?
Empirically the fitted time index in many populations declines in a roughly linear fashion with random year-to-year fluctuations, which is exactly the behavior of a random walk with drift. Lee and Carter found this for U.S. data, and the choice has two virtues: the constant drift carries the historical pace of improvement forward, and the accumulating random shocks generate prediction intervals that widen with the horizon, giving honest uncertainty. Other time-series specifications can be used if diagnostics warrant, but the random walk with drift is the standard default.
What does the Poisson version add over the original SVD fit?
The original singular value decomposition fit assumes errors of constant variance on the log scale, which is unrealistic because death counts at older ages rest on small populations and are far noisier. Brouhns, Denuit, and Vermunt kept the same log-bilinear age-period structure but modeled the actual death counts as Poisson given exposures, fitting by maximum likelihood. This respects the count nature of the data, appropriately downweights unreliable sparse cells, and produces better-calibrated parameter and forecast uncertainty, making it the preferred estimation method when death and exposure counts are available.
Sources
- 1.Lee, R. D., & Carter, L. R. (1992). Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87(419), 659-671.
- 2.Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373-393.
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ScholarGate. (2026, June 23). Lee-Carter Mortality Model. ScholarGate. https://scholargate.app/demography/lee-carter-mortality-model