San José State University
Department of Economics 

appletmagic.com Thayer Watkins Silicon Valley & Tornado Alley USA 


The Cohort Survival Projection Method is a simple method for forecasting what the future population will be based upon the survival of the existing population and the births that will occur. This method can be applied for any period of time but it typically it involves fiveyear steps. Applied once it would give the population five years ahead; applied twice it would give the population ten year ahead. For five year projection the base year population must be given by five year age groups.
The key bits of information, besides the base year population, is the five year survival rates and the fertility rates for females by five year age groups. Estimates of these items of information are shown before for the San Jose Standard Metropolitan Statistical Area (SMSA) for 19701975. These are from the California Economic Practices Manual.
CohortSurvival Projection for the San Jose SMSA, 19701975 


Age Group  Male Survival Rate  Female Survival Rate  Female Fertility Rate 
04  .996  .997  .000 
59  .998  .999  .000 
1014  .995  .998  .001 
1519  .990  .997  .056 
2024  .989  .996  .115 
2529  .990  .995  .110 
3034  .987  .993  .053 
3539  .981  .989  .019 
4044  .971  .983  .005 
4549  .955  .975  .000 
5054  .931  .965  .000 
5559  .893  .949  .000 
6064  .844  .921  .000 
6569  .779  .879  .000 
7074  .711  .798  .000 
7579  .595  .677  .000 
8084  .450  .513  .000 
85+  .257  .275  .000 
As can be seen from the above table the female survival rates are different from the male survival rates. For every age group the female survival rates are greater. This leads to there being significantly more females than males in the higher ages groups. For this reason and others the projection must be carried out separately for the two sexes. The method can also be extended to take into account different population groups for which there are differences in survival rates and/or fertility rates. Here however only the two genders will be considered.
Because the analysis must predict births and these are dependent upon the age distribution of the female population the female population must be projected first. The general scheme of the method is shown in the following table.
Cohort Survival Projection of Population  

Age Group  Base Year Population  Survival Rate  Future Popultion 
04  P_{0}  S_{0}  
59  P_{1}  S_{1}  P_{0}S_{0} 
1014  P_{2}  S_{2}  P_{1}S_{1} 
1519  P_{3}  S_{3}  P_{2}S_{2} 
…  …  …  … 
8084  P_{16}  S_{16}  P_{15}S_{15} 
85+  P_{17}  S_{17}  P_{16}S_{16}+P_{17}S_{17} 
As illustrated in the table, the base year population of an age group is multiplied by the survival rate for that age group and the result entered into the table one row down. For the last age group, the 85+ cohort, people in that age group five year ahead can arrive in that category either by surviving from the 8084 cohort or from the 85+ cohort in the base year.
The number of children in the 04 cohort are forecast on a different basis than the future populations of the other cohorts. They are the result of births over the five year period. The fertility rates are the ratio of the number of births in one year for females in each age category. For the prepuberty and postmenopausal age categories they are zero. Number of births in a year is the sum of the products of the female population times the fertility rates; i.e.,
To get the number of births over the five year period some other computations must be performed. The simplest procedure would be to simply multiply the annual births by five. A better procedure is to take into account the possible changes in the age distribution of the female population by using the projected populations as well as the base year population. Let B_{0} be the annual births computed from the base year population and B_{1} the births based upon the projected population. These are roughly the births in the first and last years of the projection period.
With no other information available the average number of births per year in the projection period is the average of B_{0} and B_{1}. The number of births over the five year period would then be 5(B_{0}+B_{1})/2.
This figure is the total births and these must be apportioned to the two sexes. Surprisingly the number of male births is not equal to the number of female births. The ratio, called the sex ratio, is 1.05 male births to 1.00 female births. For an explanation of why this is a biological constant see Explanation of Sex Ratio. With a sex ratio of 1.05 the proportion of male births to total births is then 1.05/(1+1.05)=1.05/2.05=0.5122, or about 51.2 percent. The proportion of female births is then 48.8 percent.
These proportions are then applied to the estimate of the total number of births over the five year period to get the future populations in the 04 years of age cohort. The estimating method for the number of births can be refined to take into account the survival rate of infants. The period of survival for the infants would be, on average, about half of the five year period. The survival rates for male and female infants could be slightly different.
After the female population is projected then the survival of the male populations is projected by the same method as for the female cohorts but the 04 male population is already computed from the projection of births.
There are numerous refinements of the method which can be made. For instance, the fertility rates can be specified by marital status. This would require a separate projection for married and unmarried females. The method as given presumes no net migration from the population area. The migration could be added to the projected population. The method can be used to estimate the net migration that has taken place by deducting the surviving popuation from the actual population based upon a census.
(To be continued.)
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