Help estimating the mean value of the individual fixed effects within cohort groups

[Nicolai Holm Kjaer]

Hi Statalist. I'm having trouble estimating the mean value of individual fixed effects within cohort groups. I'm trying to replicate a paper by "George J. Borjas - The Impact of Foreign Students on the Earnings of Doctorates (https://scholar.harvard.edu/files/gb...reeman2009.pdf). He uses the following approach two-step approach:

I have the following data available, here is an example:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(l_sal p_weight gender uemp) int HDAY5P float child byte AGEGRP float empus byte(EMSIZE EMSECDT RACETHMP) double WTSURVY float(cohort field)
 7.600903 .0010235414 0 0 2010 1 35 0 7 11 1            39.6161 2 20
10.596635  .001126549 1 1 2010 1 40 0 7 11 1             5.2514 2 14
10.714417  .004780876 1 0 1990 1 50 0 5 11 5            32.4895 3  1
10.714417 .0030316154 1 0 2010 0 30 0 6 11 5                  1 2  1
10.714417 .0007754944 1 1 1985 1 65 0 8 11 4            19.3516 2 10
10.819778 .0016915894 0 0 2005 0 50 1 2 12 5 14.808300000000001 2  4
10.819778 .0011296882 0 1 2005 1 40 1 8 11 5            10.4425 1  4
 11.05089 .0016915894 0 0 2015 0 25 1 8 31 5            22.8776 2  4
 11.05089   .02052861 0 0 2005 1 35 1 8 11 5 14.203000000000001 2 22
11.066638 .0011296882 0 0 2005 0 35 1 8 11 7  8.373700000000001 1  4
11.082143           0 0 0 2000 1 40 1 8 11 5            18.5498 1 13
11.141862   .00122859 0 0 2005 0 40 1 8 12 5             5.8696 3  4
11.170435           0 0 0 2005 0 55 1 8 11 4             2.6871 3 13
11.184422  .001171303 1 0 1980 1 60 1 7 11 1 19.333000000000002 2  2
11.225244           0 0 0 2010 0 60 1 3 23 5 3.2468000000000004 1 14
 11.25156 .0004604052 1 0 2005 0 40 1 4 21 5  89.01830000000001 2  8
 11.25156  .000498008 0 0 2000 0 40 1 8 11 5             8.7528 1  8
11.289782           0 1 0 1985 1 55 0 6 11 4             2.5865 2 21
11.289782 .0016915894 0 0 2005 1 40 1 8 32 5             1.9892 2  4
11.314474           0 1 0 1995 0 55 1 8 11 3 11.378300000000001 2 13
11.385092           0 0 0 2000 1 40 1 5 11 5             3.3952 2 13
11.472103 .0010865629 0 1 2000 0 45 1 8 11 1  6.537800000000001 2 12
11.512925           0 0 0 1990 0 55 1 3 21 5 1.4746000000000001 2  5
11.512925 .0016915894 1 1 2005 0 45 1 8 11 1             3.6417 2  4
11.512925 .0007754944 0 0 2005 1 40 1 8 11 5 14.309800000000001 2 10
11.542484           0 1 1 2010 0 30 1 4 11 5 24.783900000000003 1 10
11.561716  .001549987 0 1 2005 0 35 0 5 11 5            29.1175 1 12
11.561716 .0016915894 0 0 2010 0 65 1 6 12 5            14.8041 2  4
11.617286 .0016915894 0 0 2010 0 35 1 8 21 5            11.6028 2  4
11.652687 .0011296882 1 0 2005 1 35 1 8 21 3            13.7058 1  4
 11.66993 .0014695077 0 0 2010 0 40 1 8 11 5                  1 2 11
11.695247           0 1 0 1970 0 70 1 1 22 5            23.2586 2 13
11.695247           0 1 0 2010 0 35 1 8 21 5 16.909000000000002 3  6
 11.73607 .0006116208 1 0 2010 0 30 1 8 11 5 38.051100000000005 3 21
 11.77529 .0002215821 1 0 1985 1 55 1 5 11 3 1.8376000000000001 1  6
 11.83501           0 1 0 2010 1 30 1 8 11 1 3.3339000000000003 1 10
11.849398           0 1 0 1985 0 55 1 7 21 1             5.4634 2 16
11.849398  .001171303 1 0 1995 1 45 1 8 21 5            68.3165 2  2
11.863583 .0003447087 1 0 1995 1 45 1 8 21 5            10.3222 3  3
 11.88449  .001126549 0 0 2005 0 50 1 8 32 3             1.0359 2 14
 11.91839 .0017346054 1 0 1990 1 50 1 3 21 5 45.647200000000005 3  2
 11.91839           0 1 0 1995 0 45 1 8 11 4             1.0904 1 18
 11.91839 .0006116208 1 0 2010 1 40 1 8 21 5            21.1216 3 21
 11.95118           0 1 0 1975 1 65 1 8 31 1 29.337200000000003 2 16
 12.12269 .0005925926 1 0 1990 0 55 1 8 21 1 5.4815000000000005 2  3
 12.15478           0 1 0 2000 0 55 1 4 21 3             6.0602 2 21
12.180755           0 0 0 1995 0 50 1 8 11 5             2.9581 2  5
 12.18587 .0004604052 1 0 1985 1 55 1 6 23 5             2.7446 2  8
12.254863 .0003447087 1 0 1985 0 60 1 8 11 5            14.3194 3  3
12.429216 .0011296882 1 0 1985 0 55 1 7 23 5            22.1174 1  4
end

To estimate this I have made a fairly over-complicated loop, which i'm not sure is the right approach:

cap gen FE = .

mat BIG_STORE = J(23,3,.)
mat rown BIG_STORE = Fields
mat coln BIG_STORE = Cohort


forvalues f = 1(+1)23 {
    forvalues c = 1(+1)3 {
    display("0")
    qui mean l_sal if field == `f' & cohort == `c'
        mat l_sal_f`f'_c`c'_bar = e(b)
        display("1")
    qui    mean p_weight i.gender i.uemp i.HDAY5P i.child i.AGEGRP i.empus i.EMSIZE i.EMSECDT i.RACETHMP if field == `f' & cohort == `c'
        mat x_f`f'_c`c'_bar = e(b)
        display("2")
    qui reg l_sal  p_weight i.gender i.uemp i.HDAY5P i.child i.AGEGRP i.empus i.EMSIZE i.EMSECDT i.RACETHMP [pweight=WTSURVY] if field == `f' & cohort == `c', robust 
    local newcol = colsof(e(b)) - 1
    
    mat Beta_f`f'_c`c'_bar = J(`newcol',1,.)
        forvalues i = 1(+1)`newcol'{
            mat Beta_f`f'_c`c'_bar[`i',1] = e(b)[1,`i']
        }
    mat store = l_sal_f`f'_c`c'_bar + x_f`f'_c`c'_bar * Beta_f`f'_c`c'_bar
    mat BIG_STORE[`f',`c'] = store[1,1]
    replace FE = store[1,1] if field == `f' & cohort == `c'
    display("f`f'c`c'")
    }
}

So to clarify my question. Does my "spaghetti code" do the trick and give me the right results? And if not how do I estimate this correctly?

NB. I use Stata 17 if this is of relevance.

Thanks,
Nicolai Kjær