Lawrence R. Carter’s research while affiliated with University of Oregon and other places

This article compares two methodologies for modeling and forecasting statistical time series models of demographic processes: Box-Jenkins ARIMA and structural time series analysis. The Lee-Carter method is used to construct nonlinear demographic models of U.S. mortality rates for the total population, gender, and race and gender combined. Single time varying parameters of k, the index of mortality, are derived from these model and fitted and forecasted using the two methodologies. Forecasts of life expectancy at birth, e0, are generated from these indexes of k. Results show marginal differences in fit and forecasts between the two statistical approaches with a slight advantage to structural models. Stability across models for both methodologies offers support for the robustness of this approach to demographic forecasting.

This article compares two methodologies for modeling and forecasting statistical time series models of demographic processes: Box-Jenkins ARIMA and structural time series analysis. The Lee-Carter method is used to construct nonlinear demographic models of U.S. mortality rates for the total population, gender, and race and gender combined. Single time varying parameters of k, the index of mortality, are derived from these model and fitted and forecasted using the two methodologies. Forecasts of life expectancy at birth, e0, are generated from these indexes of k. Results show marginal differences in fit and forecasts between the two statistical approaches with a slight advantage to structural models. Stability across models for both methodologies offers support for the robustness of this approach to demographic forecasting.

"We have described a method for reducing the dimensionality of the forecasting problem by parsimoniously modeling the evolution over time of the age schedules of vital rates. This method steers a middle course between forecasting aggregates and forecasting individual age specific rates: we reduce the problem to forecasting a single parameter for fertility and another one for mortality. We have described a number of refinements and extensions of those basic methods, which preserve their underlying structure and simplicity. In particular, we show how one can fit the model more simply, incorporate lower bounds to the forecasts of rates, disaggregate by sex or race, and prepare integrated forecasts of rates for a collection of regions. We also discuss alternate approaches to forecasting the estimated indices of fertility and mortality, including state-space methods. These many versions of the basic method have yielded remarkably similar results." (SUMMARY IN FRE)

This paper examines forecasted differentials in age-sex-specific mortality in the United States, 1990-2065. A non-linear model, m(x,t) = exp(a(x) + b(x)k(t) + e(x,t)), is fitted for each sex to a matrix of age-specific US death rates, 1933-1988, using SVD to derive a single time-varying index of mortality, k(t). Box-Jenkins techniques are used to estimate and forecast k(t). These forecasts are used to generate age-specific mortality rates and life expectancies to 2065. Independent forecasts of male and female e0's are 82.0 and 90.4, respectively, for 2065, a difference of 8.4 years. These forecasts are substantially higher with narrower confidence intervals than those prepared regularly by the Actuary of the Social Security Administration [Wade (1989)]. These k(t) generated forecasts of e0 appear more plausible than direct forecasts of e0 Life expectancies derived from jointly estimated and forecasted k(t) are competitive with the independent sex forecasts, but have some problems. Joint forecasts of k(t) are juxtaposed to co-integration speculatively as a direction for future research into linkages between male and female mortality.

Time series methods are used to make long-run forecasts, with confidence intervals, of age-specific mortality in the United States from 1990 to 2065. First, the logs of the age-specific death rates are modeled as a linear function of an unobserved period-specific intensity index, with parameters depending on age. This model is fit to the matrix of U.S. death rates, 1933 to 1987, using the singular value decomposition (SVD) method; it accounts for almost all the variance over time in age-specific death rates as a group. Whereas e0 has risen at a decreasing rate over the century and has decreasing variability, k(t) declines at a roughly constant rate and has roughly constant variability, facilitating forecasting. k(t), which indexes the intensity of mortality, is next modeled as a time series (specifically, a random walk with drift) and forecast. The method performs very well on within-sample forecasts, and the forecasts are insensitive to reductions in the length of the base period from 90 to 30 years; some instability appears for base periods of 10 or 20 years, however. Forecasts of age-specific rates are derived from the forecasts of k, and other life table variables are derived and presented. These imply an increase of 10.5 years in life expectancy to 86.05 in 2065 (sexes combined), with a confidence band of plus 3.9 or minus 5.6 years, including uncertainty concerning the estimated trend. Whereas 46% now survive to age 80, by 2065 46% will survive to age 90. Of the gains forecast for person-years lived over the life cycle from now until 2065, 74% will occur at age 65 and over. These life expectancy forecasts are substantially lower than direct time series forecasts of e0, and have far narrower confidence bands; however, they are substantially higher than the forecasts of the Social Security Administration's Office of the Actuary.

This article presents a new approach to forecasting U.S. marital fertility, nuptiality, births, and marriages. The analysis represents a wedding of demographic and statistical time series in models amenable to Box-Jenkins techniques of model identification, estimation, diagnosis, and forecasting. The models demonstrate the advantages in this approach in forecasting both rates and events as opposed to the common practice of simply forecasting events. Using the best models of indexes of fertility and nuptiality, forecasts of births and first marriages are made for the U.S. for the years 1983–2000. Analyses of these forecasts are made with discussions of their demographic realism in terms of their forecast confidence intervals.

This article presents a new approach to forecasting U.S. marital fertility, nuptiality, births, and marriages. The analysis represents a wedding of demographic and statistical time series in models amenable to Box-Jenkins techniques of model identification, estimation, diagnosis, and forecasting. The models demonstrate the advantages in this approach in forecasting both rates and events as opposed to the common practice of simply forecasting events. Using the best models of indexes of fertility and nuptiality, forecasts of births and first marriages are made for the U.S. for the years 1983-2000. Analyses of these forecasts are made with discussions of their demographic realism in terms of their forecast confidence intervals.