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by Ronald Lee and Timothy Miller

The Lee-Carter method for forecasting mortality was published eight years ago, with an application to US mortality data, 1900-1989. The method has been quite well received, but there have also been criticisms. Some have thought that the probability bands are implausibly narrow. Others have argued that many age specific rates are so low that they can't realistically be projected to decline much further. Some argue that it must be sub-optimal to ignore biomedical information that might inform the forecasts, and that forecasts based on expert opinion should be preferred. Some have called for more within sample testing of the methods, and others have questioned whether the ax and bx should be treated as invariant. Bell (1997) noted that the model did not fit the jump off data very well. In this paper we will examine many of these issues.

This paper will assess the performance of the 1992 forecast over the years since 1989. It will also conduct some more demanding tests of its performance within sample for the US as well as for some other countries. It will compare within sample performance to the performance of the projections of the Social Security Administration (SSA) and some other US forecasts. It will consider some extensions and modifications of the original procedure.

Results include:

• The original forecast started with an initial level of e0 that was .6 years higher than the actual for 1989. This error was carried over to all subsequent years of the forecast. Adjusting for this error in data for initial level, the forecast was within 0.2 years of e0 in 1998 and similarly close to the rates of decline of the individual age groups from 1989 to 1997.
• Applying the method retroactively to project to e0 in 1998, using only data available up to each historic start point, the hypothetical forecasts are quite accurate, with forecasts starting in 1946 having errors of two years or less. The 95% probability bounds contained the true value for 1998 85% of the time.
• We analyze 78 hypothetical forecasts with jump-off years from 1920 to 1997 and forecast horizons from 78 years to 1 year. The method tended to under-predict gains in life expectancy in the US, particularly when launched from earlier dates. 91% of errors at 31-40 year horizons were negative (predicted e0 less than actual) and 100% of errors beyond a 50 year horizon were negative. The true e(0) fell within the 95% probability interval for 2,984 out of 3,081 forecasted e(0) values or 97% of the time. The probability bounds appear to be too broad for horizons up to 40 years and too narrow for horizons beyond 50 years.
• The average error and mean squared error for LC forecasts since 1950 are substantially lower than those of SSA since 1950.
• If the method had been used to forecast 1995 e0 for Sweden, starting in 1950, it would have been right on target until 1980, and two years too low in 1995. Results for France and Canada are very similar. For Japan, the data only start in 1950; forecasts from 1975 to 1996 are below the actual value, and one year too low by 1996. Looking at all the forecasts combined, the 95% probability bounds contain the actual e(0) values for 152 out of 162 forecasted values or 94% of the time.
• There have been very significant changes in the relative rates of decline of mortality by age, in the US, Sweden, France, Canada, and Japan, contrary to an assumption of the original method. This requires that the ax and bx coefficients be estimated on data since 1950 or so, not over the whole century.
• Forecasts should use actual last observed death rates as the base for forecasts, as described in the paper. Second stage fitting can be done more easily using actual e0 as the fit criterion in place of matching the total number of deaths.

Paper presented at the 2000 Annual Meetings of the Population Association of America in Los Angeles.

• The original paper is available in pdf format. The latest revision is also available now titled: "Evaluating the Performance of Lee-Carter Mortality Forecasts."