Population Projections
This unit illustrate sthe use of the cohort component method of population projections, with all calculations done in Stata. (An alternate version using Mata is available here. The Mata version includes an eigenanalysis of the Leslie matrix, which we can't do here.)
Reading the Data
We read the data from the datasets section. The file has four columns, the starting age for each group, the population counts for 1993, the person-years 'big-L' column from the life table --which we divide by 100,000-- and the fertility rates.. set type double . infile age p93 L f using /// > http://data.princeton.edu/eco572/datasets/sweden93.dat, clear (18 observations read) . replace L=L/100000 (18 real changes made)
Projections for 5 and 10 years
The first task is to compute the survival ratios used to project people alive at the start of the projection (the sub-diagonal of the Leslie matrix). We store the probability of surviving to an age group, set the last entry to the ratio of time lived at 85+ to 80+. To project we need to multiply these ratios by the population in the previous age group. The last age group is singled-out for special treatment. We try this part of the projection straight away to make sure its OK.
. gen surv = L/L[_n-1]
(1 missing value generated)
. replace surv = L[_N]/(L[_N] + L[_N-1]) in -1
(1 real change made)
. gen p98 = surv * p93[_n-1]
(1 missing value generated)
. replace p98 = p98 + surv*p93 in -1
(1 real change made)
. list age p93 p98
+--------------------------+
| age p93 p98 |
|--------------------------|
1. | 0 293395 . |
2. | 5 248369 293189.18 |
3. | 10 240012 248250.6 |
4. | 15 261346 239833.28 |
5. | 20 285209 261014.93 |
|--------------------------|
6. | 25 314388 284786.85 |
7. | 30 281290 313781.66 |
8. | 35 286923 280463 |
9. | 40 304108 285576.19 |
10. | 45 324946 301730.68 |
|--------------------------|
11. | 50 247613 320974.1 |
12. | 55 211351 243039.01 |
13. | 60 215140 205108.84 |
14. | 65 221764 204943.86 |
15. | 70 223506 204792.8 |
|--------------------------|
16. | 75 183654 194419.01 |
17. | 80 141990 142323.75 |
18. | 85 112424 131768.18 |
+--------------------------+
The results agree with the textbook. Next we need to do the births during the projection period to replace the missing entry in the first age group. We start by computing the average fertility rate for each age group, and then multiply by the number of women and sum.
. gen m = f/2.05
. replace m = L[1]*(m + m[_n+1]*surv[_n+1])/2
(9 real changes made, 1 to missing)
. gen b = p93 * m
(1 missing value generated)
. quietly summarize b
. list b
+-----------+
| b |
|-----------|
1. | 0 |
2. | 0 |
3. | 3492.1153 |
4. | 32562.717 |
5. | 83221.72 |
|-----------|
6. | 100015.75 |
7. | 53405.282 |
8. | 17917.502 |
9. | 2840.4304 |
10. | 118.28518 |
|-----------|
11. | 0 |
12. | 0 |
13. | 0 |
14. | 0 |
15. | 0 |
|-----------|
16. | 0 |
17. | 0 |
18. | . |
+-----------+
. replace p98 = r(sum) in 1
(1 real change made)
The procedure is easily applied for the next five years starting with the last projection:
. gen p03 = surv * p98[_n-1]
(1 missing value generated)
. replace p03 = p03 + surv*p98 in -1
(1 real change made)
. qui replace b = p98 * m
. qui sum b
. replace p03 = r(sum) in 1
(1 real change made)
. format p93 p98 p03 %7.0fc
. list age p93 p98 p03
+-----------------------------------+
| age p93 p98 p03 |
|-----------------------------------|
1. | 0 293,395 293,574 280,121 |
2. | 5 248,369 293,189 293,368 |
3. | 10 240,012 248,251 293,049 |
4. | 15 261,346 239,833 248,066 |
5. | 20 285,209 261,015 239,529 |
|-----------------------------------|
6. | 25 314,388 284,787 260,629 |
7. | 30 281,290 313,782 284,238 |
8. | 35 286,923 280,463 312,859 |
9. | 40 304,108 285,576 279,147 |
10. | 45 324,946 301,731 283,344 |
|-----------------------------------|
11. | 50 247,613 320,974 298,043 |
12. | 55 211,351 243,039 315,045 |
13. | 60 215,140 205,109 235,861 |
14. | 65 221,764 204,944 195,388 |
15. | 70 223,506 204,793 189,260 |
|-----------------------------------|
16. | 75 183,654 194,419 178,141 |
17. | 80 141,990 142,324 150,666 |
18. | 85 112,424 131,768 141,960 |
+-----------------------------------+
. tabstat p93 p98 p03, stat(sum)
stats | p93 p98 p03
---------+------------------------------
sum | 4397428 4449570 4478712
----------------------------------------
The results agree with the textbook.
The Stable Equivalent
We can't calculate the stable equivalent population from an eigen-analysis without Mata, but you could project the population for a long time and see what you get. If the time is long enough you should come really close to the results of the eigenanalysis here.
In the next handout we apply methods based on the continuous time model.