Hi

I am running af 2sls model with panel data where I on average have 6 observation for each individual. In that regard I am construction an instrument set, but I am not sure I om doing it in the correct way. I run two regressions only on the initial period for each individual as the information for my instruments only is available for the first observation of each individual. The residuals from these regressions then becomes my instrumental variables. The problem is then I only have instrumental variables for first observations for each individual and I need for every observation. As you can see in the data I have attached what I am doing know is taking the first regression residuals and using for all observations. Is this legal? and do anyone know what the correct approach is to this problem?

Thank you very much in advance

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input double(Prob_work_past_62 Prob_work_past_65) float(Mother_age_at_death Dad_age_at_death resid resid1 under_age_62 age_62_65 resid_times_under_age_62 resid_times_between_age_62_65)
100 100 75 80   52.21634   73.19397 1 0   52.21634          0
  0   0  .  .   52.21634   73.19397 1 0   52.21634          0
100 100  .  .   52.21634   73.19397 1 0   52.21634          0
 90  70  .  .   52.21634   73.19397 0 1          0   73.19397
  .   .  .  .   52.21634   73.19397 0 1          0   73.19397
  .   .  .  .   52.21634   73.19397 0 0          0          0
  .   .  .  .   52.21634   73.19397 0 0          0          0
  .   .  .  .   52.21634   73.19397 0 0          0          0
  .   .  .  .   52.21634   73.19397 0 0          0          0
  .   .  .  .   52.21634   73.19397 0 0          0          0
100 100 69 53   42.85693   67.67946 1 0   42.85693          0
100 100  .  .   42.85693   67.67946 1 0   42.85693          0
100 100  .  .   42.85693   67.67946 1 0   42.85693          0
  .   .  .  .   42.85693   67.67946 0 1          0   67.67946
  .   .  .  .   42.85693   67.67946 0 1          0   67.67946
  .   .  .  .   42.85693   67.67946 0 1          0   67.67946
  .   .  .  .   42.85693   67.67946 0 0          0          0
  .   .  .  .   42.85693   67.67946 0 0          0          0
  .   .  .  .   42.85693   67.67946 0 0          0          0
100  80 50 66   44.70567   49.12651 1 0   44.70567          0
 95  85  .  .   44.70567   49.12651 1 0   44.70567          0
100  80  .  .   44.70567   49.12651 1 0   44.70567          0
  .   .  .  .   44.70567   49.12651 0 1          0   49.12651
  .   .  .  .   44.70567   49.12651 0 1          0   49.12651
  .   .  .  .   44.70567   49.12651 0 0          0          0
  .   .  .  .   44.70567   49.12651 0 0          0          0
  .   .  .  .   44.70567   49.12651 0 0          0          0
  .   .  .  .   44.70567   49.12651 0 0          0          0
 90  50  0 74   43.94625  22.839033 1 0   43.94625          0
100  50  .  .   43.94625  22.839033 1 0   43.94625          0
 80  70  .  .   43.94625  22.839033 1 0   43.94625          0
 90  90  .  .   43.94625  22.839033 1 0   43.94625          0
 80  80  .  .   43.94625  22.839033 1 0   43.94625          0
  . 100  .  .   43.94625  22.839033 0 1          0  22.839033
  . 100  .  .   43.94625  22.839033 0 1          0  22.839033
  .   .  .  .   43.94625  22.839033 0 0          0          0
  .   .  .  .   43.94625  22.839033 0 0          0          0
 40   0 82 45 -17.016924  -32.73683 1 0 -17.016924          0
  .   .  .  . -17.016924  -32.73683 1 0 -17.016924          0
  .   .  .  . -17.016924  -32.73683 1 0 -17.016924          0
  .   .  .  . -17.016924  -32.73683 0 1          0  -32.73683
  .   .  .  . -17.016924  -32.73683 0 0          0          0
  .   .  .  . -17.016924  -32.73683 0 0          0          0
  .   .  .  . -17.016924  -32.73683 0 0          0          0
  .   .  .  . -17.016924  -32.73683 0 0          0          0
  .   .  .  . -17.016924  -32.73683 0 0          0          0
 80  20  0  0   22.37574  -16.85536 1 0   22.37574          0
 85  20  .  .   22.37574  -16.85536 1 0   22.37574          0
  0   0  .  .   22.37574  -16.85536 1 0   22.37574          0
  0   0  .  .   22.37574  -16.85536 0 1          0  -16.85536
  .   .  .  .   22.37574  -16.85536 0 1          0  -16.85536
  .   .  .  .   22.37574  -16.85536 0 1          0  -16.85536
  .   .  .  .   22.37574  -16.85536 0 0          0          0
  .   .  .  .   22.37574  -16.85536 0 0          0          0
 20   0  0 52 -28.805786 -30.038923 1 0 -28.805786          0
  0   0  .  . -28.805786 -30.038923 1 0 -28.805786          0
  0   0  .  . -28.805786 -30.038923 1 0 -28.805786          0
  0   0  .  . -28.805786 -30.038923 1 0 -28.805786          0
  .   .  .  . -28.805786 -30.038923 0 1          0 -30.038923
 10   0 71 73  -41.62628 -26.359983 1 0  -41.62628          0
  2   0  .  .  -41.62628 -26.359983 1 0  -41.62628          0
  .   .  .  .  -41.62628 -26.359983 0 1          0 -26.359983
  .   .  .  .  -41.62628 -26.359983 0 1          0 -26.359983
  .   .  .  .  -41.62628 -26.359983 0 0          0          0
  .   .  .  .  -41.62628 -26.359983 0 0          0          0
  .   .  .  .  -41.62628 -26.359983 0 0          0          0
  .   .  .  .  -41.62628 -26.359983 0 0          0          0
  .   .  .  .  -41.62628 -26.359983 0 0          0          0
 10   0  0 70  -37.60967 -25.504025 1 0  -37.60967          0
  0   0  .  .  -37.60967 -25.504025 1 0  -37.60967          0
  0   0  .  .  -37.60967 -25.504025 1 0  -37.60967          0
  .   .  .  .  -37.60967 -25.504025 0 1          0 -25.504025
  .   .  .  .  -37.60967 -25.504025 0 1          0 -25.504025
100  90  0 66   50.56738   60.01219 1 0   50.56738          0
100  95  .  .   50.56738   60.01219 1 0   50.56738          0
 95  85  .  .   50.56738   60.01219 1 0   50.56738          0
100  85  .  .   50.56738   60.01219 1 0   50.56738          0
  .  95  .  .   50.56738   60.01219 0 1          0   60.01219
  .   .  .  .   50.56738   60.01219 0 1          0   60.01219
  .   .  .  .   50.56738   60.01219 0 0          0          0
  .   .  .  .   50.56738   60.01219 0 0          0          0
 50  50  0 70  -3.319559  17.950354 1 0  -3.319559          0
  .   .  .  .  -3.319559  17.950354 1 0  -3.319559          0
  .   .  .  .  -3.319559  17.950354 1 0  -3.319559          0
  .   .  .  .  -3.319559  17.950354 0 1          0  17.950354
  .   .  .  .  -3.319559  17.950354 0 1          0  17.950354
  .   .  .  .  -3.319559  17.950354 0 0          0          0
  .   .  .  .  -3.319559  17.950354 0 0          0          0
  .   .  .  .  -3.319559  17.950354 0 0          0          0
 70  10  0 83   19.40187 -18.756739 1 0   19.40187          0
  .   .  .  .   19.40187 -18.756739 1 0   19.40187          0
  .   .  .  .   19.40187 -18.756739 1 0   19.40187          0
  .   .  .  .   19.40187 -18.756739 1 0   19.40187          0
  .   .  .  .   19.40187 -18.756739 0 0          0          0
  .   .  .  .   19.40187 -18.756739 0 0          0          0
  .   .  .  .   19.40187 -18.756739 0 0          0          0
  .   .  .  .   19.40187 -18.756739 0 0          0          0
 20  20  0  0  -31.20806 -11.840034 1 0  -31.20806          0
 20  20  .  .  -31.20806 -11.840034 1 0  -31.20806          0
 75  50  .  .  -31.20806 -11.840034 1 0  -31.20806          0
end