APPENDIX

D

The Effect of Projection Error in Life Expectancy

Errors in past mortality projections have generally been modest, and we do not expect future errors to be larger. These errors appear not to affect projected population greatly, being more limited in their impact than fertility or migration error. Could mortality errors nevertheless affect some other projected demographic parameters more severely? We consider this question by simulating projections of two hypothetical countries.

METHOD

The first hypothetical country (A) is assumed to resemble Brazil in 1995, with total fertility of 2.5 births and life expectancy for males and females combined of 70 years. The second hypothetical country (B) is assumed to resemble France, with initial total fertility of about 1.5 births and initial combined life expectancy of 78 years.

We project these hypothetical countries as the U.N. does, along trajectories that lead to life expectancies of 84.9 years after 50 years in country A and of 86.6 years after the same period in country B. Total fertility is assumed to follow trajectories, in each country, similar to those applied by the U.N. We assume that these base scenarios represent the true course of demographic trends.

We also produce “error” scenarios for each country by choosing different long-term life expectancy levels. For country A, the alternative is a life expectancy, after 50 years, of 75.7, or 9.2 years below the value in the



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BEYOND SIX BILLION: Forecasting the World's Population APPENDIX D The Effect of Projection Error in Life Expectancy Errors in past mortality projections have generally been modest, and we do not expect future errors to be larger. These errors appear not to affect projected population greatly, being more limited in their impact than fertility or migration error. Could mortality errors nevertheless affect some other projected demographic parameters more severely? We consider this question by simulating projections of two hypothetical countries. METHOD The first hypothetical country (A) is assumed to resemble Brazil in 1995, with total fertility of 2.5 births and life expectancy for males and females combined of 70 years. The second hypothetical country (B) is assumed to resemble France, with initial total fertility of about 1.5 births and initial combined life expectancy of 78 years. We project these hypothetical countries as the U.N. does, along trajectories that lead to life expectancies of 84.9 years after 50 years in country A and of 86.6 years after the same period in country B. Total fertility is assumed to follow trajectories, in each country, similar to those applied by the U.N. We assume that these base scenarios represent the true course of demographic trends. We also produce “error” scenarios for each country by choosing different long-term life expectancy levels. For country A, the alternative is a life expectancy, after 50 years, of 75.7, or 9.2 years below the value in the

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BEYOND SIX BILLION: Forecasting the World's Population base projection. For country B, the alternative is a life expectancy, after 50 years, of 81.95, or 4.7 years below the value in the base projection. Each error scenario involves underestimating future life expectancy, the most common type of error in past projections. These assumed errors are relatively large but are difficult to compare directly with actual errors in recent projections, which have been evaluated for shorter periods only. In 25-year projections, mean error in life expectancy across countries is only 0.52 years. Actual mean absolute error is larger at 4.3 years, but a large part of this can be attributed to absolute error in the base estimate, which averages 1.8 years (see Appendix Table B-5). RESULTS Table D-1 shows selected projection outcomes, from each of these scenarios, in projections of 30 and 50 years. The table confirms that the effect on population of error in projected life expectancy is small. Given the larger assumed life expectancy error for Country A than for Country B, the resulting error in projected population is somewhat larger in the former case than in the latter. Raw error in projected death rates is understandably greater, in each case, than error in projected birth rates. Proportional error in the projected age structure is estimated not from the percentage distributions but from the projected numbers of people. This error affects the elderly much more than the young. In Country A, the number aged 65 and older is underprojected by 15 percent after 30 years, 33 percent after 50 years. The number aged 75 and older is underprojected by 24 percent after 30 years and 41 percent after 50 years. Similar, though smaller proportional errors appear for Country B. However, the dependency ratio is more affected in Country B, being 10 points too low (per hundred workers) in the most extreme case. The results suggest that, overall, the effects of error in projected life expectancy are generally mild. For particular age groups, however, misspecification can produce larger effects.

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BEYOND SIX BILLION: Forecasting the World's Population TABLE D-1 Selected population outcomes in simulated projections with varying gains in life expectancy   Crude rates (per 1000) Percent of population Country, projection length, and scenario Population (millions) Births Deaths Under 15.0 65 and older 75 and older Dependency ratio Country A after 30 years Base scenario 237.3 14.9 5.4 21.5 12.6 4.6 51.9 Error scenario 229.9 15.3 7.8 21.9 11.1 3.6 49.2 Error a −0.031 0.4 2.4 −0.013 −0.147 −0.242 −2.7 Country A after 50 years Base scenario 273.3 12.6 8.5 19.0 21.0 10.3 66.7 Error scenario 251.3 13.6 11.1 20.1 15.3 6.6 57.9 Error a −0.080 1.0 2.6 −0.027 −0.330 −0.411 −8.8 Country B after 30 years Base scenario 62.3 11.1 9.3 16.8 23.6 11.7 67.8 Error scenario 60.8 11.1 11.3 17.2 22.1 10.5 64.8 Error a −0.024 0.0 2.0 −0.001 −0.086 −0.124 −3.0 Country B after 50 years Base scenario 62.6 10.3 10.7 16.3 28.4 17.1 81.0 Error scenario 58.9 11.3 13.3 17.0 24.5 13.4 71.0 Error a −0.059 1.0 2.6 −0.019 −0.188 −0.263 −10.0 aThe difference between the error scenario and the base scenario is given for crude rates and the dependency ratio. For population, proportional error is shown, as it is for population by age group. For age groups, proportional error is based not on the percentage distribution but on the projected numbers of people.