Sub-national forecasts (cont.)
Ratio methods (cont.)
The raking procedure is illustrated here for a population divided into two types of area and three broad age groups. Using ratio methods, the urban population is forecast to be one third of the total at the date in question. The national population forecast for the same date is 5 million and this forecast yields a rather different age structure from that obtained by extrapolating using ratio methods.
| Age group |
Urban
population (%) |
Rural
population (%) |
Urban + rural
population (%) |
National
Projection (‘000) |
| 0-14 |
14 |
30 |
44 |
2100 |
| 15-64 |
17 |
33 |
50 |
2400 |
| 65+ |
2.33 |
3.67 |
6 |
500 |
| Total |
33.33 |
66.67 |
100 |
5000 |
Click the bottom below to display each of Step 1 to Step 4 in turn.
Reveal step 1
Step 1: The national forecast for each age group is divided between urban and rural areas in ratio to the forecast of their relative size:
| Age group |
Urban population |
Rural population |
Total population |
| 0-14 |
700 |
1400 |
2100 |
| 15-64 |
800 |
1600 |
2400 |
| 65+ |
167 |
333 |
500 |
| Total |
1667 |
3333 |
5000 |
Reveal step 2
Step 2: The age distributions from each of the two sub-national projections are applied to the adjusted sub-national population totals and the rows are summed to give the total population in each age group.
| Age group |
Urban population |
Rural population |
Total population |
| 0-14 |
700 |
1500 |
2200 |
| 15-64 |
850 |
1650 |
2500 |
| 65+ |
117 |
183 |
300 |
| Total |
1667 |
3333 |
5000 |
Reveal step 3
Step 3: The distribution by area of residence of each age group obtained in Step 2 is applied to the national forecast of the total population in that age group and the columns are summed to give totals for the urban and rural populations
| Age group |
Urban population |
Rural population |
Total population |
| 0-14 |
668 |
1432 |
2100 |
| 15-64 |
816 |
1584 |
2400 |
| 65+ |
194 |
306 |
500 |
| Total |
1679 |
3321 |
5000 |
Reveal step 4
Exercise
Step 4: To complete Step 4, apply the age distributions obtained for each sub-population in Step 3 to the adjusted total sizes of the two sub-national populations and sum each row to get the total population in each age group.
Reval answer
| Age group |
Urban population |
Rural population |
Total population |
| 0-14 |
663 |
1437 |
2100 |
| 15-64 |
810 |
1590 |
2400 |
| 65+ |
193 |
307 |
500 |
| Total |
1667 |
3333 |
5000 |
You can see that, after Step 4, not only the column totals but also the row totals have converged to those established in Step 1. If you were working with exact numbers, not thousands, you would need to repeat Step 3 one more time in order for the cells to sum to 5 million exactly.