Lawrence Carter

Overview

Lawrence R. Carter is a statistician and demographer best known as co-developer (with Ronald Lee) of the Lee-Carter (LC) model for mortality forecasting, introduced in the 1992 JASA paper "Modeling and Forecasting U.S. Mortality." The LC model became the standard reference model for long-run actuarial mortality projection in the United States and internationally, adopted by SSA, the Census Bureau, and numerous academic researchers. Carter's earlier collaboration with Lee on joint fertility and nuptiality forecasting (1986 JASA) established the "index + fixed schedule" architecture that the LC model later applied to mortality.

Key Contributions / Features

• Joint fertility and nuptiality forecasting (Carter and Lee 1986): Developed the index-based forecasting framework defining scalar marital fertility index g(t) and nuptiality index h(t) convolved with fixed demographic schedules. Compared five Box-Jenkins modeling strategies; univariate ARIMA won for nuptiality, transfer function for fertility. Demonstrated unbounded forecast uncertainty growth (±100% by forecast year 14). This paper established the "scalar index × fixed age schedule" architecture later used in Lee-Carter (1992). See Stochastic Fertility Forecasting.
• Lee-Carter model (Lee and Carter 1992): Co-developed the bilinear log-rate decomposition $\ln m(x,t) = a_x + b_x k_t + \varepsilon$, the SVD estimation procedure on U.S. vital statistics data 1933–1987, and the ARIMA(0,1,0) with drift model for the latent mortality index $k_t$. The resulting central forecast — $e_0 = 86.05$ in 2065 — exceeded SSA's 1989 intermediate projection by 5.6 years, with SSA's figure falling at exactly the lower bound of the LC 95% confidence interval. See Lee-Carter Model.
• b_x instability and extended Lee-Carter (Carter and Prskawetz 2001): Extended the LC model by fitting 30 rolling 24-year submatrices (sliding SVD window) to Austrian mortality data 1947–1999. Found that b_x is NOT stable over time — pre-1970 improvement was concentrated at young/middle ages, post-1970 at old ages (structural shift ~1968). k_t and a_x were relatively stable. Extended LC reduces e_0 fitting error ~0.3 years for females and substantially improves e_60 fit. Base-period choice matters substantially for males (+3.5 years by 2050 using the most-recent 1976–1999 subsample vs. the full series). See Carter and Prskawetz 2001 — Examining Structural Shifts in Mortality Using the Lee-Carter Method and Lee-Carter Model.

Related

• Ronald Lee
• Lee-Carter Model
• Stochastic Fertility Forecasting
• Period Mortality
• SSA Mortality Forecasting

Sources

• Carter and Lee 1986 — Joint Forecasts of US Marital Fertility, Nuptiality, Births, and Marriages
• Lee and Carter 1992 — Modeling and Forecasting U.S. Mortality
• Bell 1997 — Comparing and Assessing Time Series Methods for Forecasting Age-Specific Fertility and Mortality Rates
• Booth Maindonald and Smith 2002 — Age-Time Interactions in Mortality Projections Applying Lee-Carter to Australia
• Carter and Prskawetz 2001 — Examining Structural Shifts in Mortality Using the Lee-Carter Method
• Lee 2000 — The Lee-Carter Method for Forecasting Mortality with Various Extensions and Applications
• Pedroza and King 2002 — Revisiting Demographic Methods
• Tuljapurkar, Li and Boe 2000 — A Universal Pattern of Mortality Decline in the G7 Countries