Hi all,

I'm trying to study whether the decline in birth rates had an impact on GDP on a national level. I have therefore gathered data on birth rates and GDP for 169 countries from 1855 to 2018, with an example below:
Code:
input str34 country int year double gdppc float log_gdp double pop float post_treat
"Afghanistan" 1981      1144 7.042286     13676 0
"Afghanistan" 1982      1270 7.146772     12583 0
"Afghanistan" 1983      1347 7.205635     12439 0
"Afghanistan" 1984      1337 7.198184     12769 0
"Afghanistan" 1985      1304 7.173192     13120 0
"Afghanistan" 1986      1344 7.203405     13126 0
"Afghanistan" 1987      1211 7.099202     13056 0
"Afghanistan" 1988      1101 7.003974     13169 0
"Afghanistan" 1989       999 6.906755     13503 0
"Afghanistan" 1990       963 6.870053     13568 0
"Afghanistan" 1991  881.1704 6.781251     13672 0
"Afghanistan" 1992  843.8753 6.738005     15023 0
"Afghanistan" 1993  578.4027 6.360271     17003 0
"Afghanistan" 1994  428.4246 6.060115     18486 0
"Afghanistan" 1995  632.9404 6.450376     19445 0
"Afghanistan" 1996  600.1753 6.397222     20111 0
"Afghanistan" 1997  570.5981 6.346685     20769 0
"Afghanistan" 1998  545.0388 6.300857     21452 0
"Afghanistan" 1999  518.6579 6.251245     22206 0
"Afghanistan" 2000  502.3727 6.219342     22461 1
"Afghanistan" 2001   489.682 6.193756     22507 1
"Afghanistan" 2002  796.8166 6.680624     23600 1
"Afghanistan" 2003  842.8052 6.736736     25005 1
"Afghanistan" 2004  869.0393 6.767388     25698 1
"Afghanistan" 2005  964.4081 6.871514     26335 1
"Afghanistan" 2006 1057.0966 6.963281     27154 1
"Afghanistan" 2007 1259.9967 7.138865     27387 1
"Afghanistan" 2008 1319.6074  7.18509     27706 1
"Afghanistan" 2009 1557.3206 7.350722     28484 1
"Afghanistan" 2010 1627.6716 7.394906     29121 1
"Afghanistan" 2011      1792 7.491087     29758 1
"Afghanistan" 2012      1945 7.573017     30420 1
"Afghanistan" 2013      2025 7.613325     31108 1P
"Afghanistan" 2014      2022 7.611843     31823 1
"Afghanistan" 2015      1928 7.564239     32564 1
"Afghanistan" 2016      1929 7.564757     33332 1
"Afghanistan" 2017 2014.7453 7.608248 34124.811 1
"Afghanistan" 2018  1934.555 7.567633 34940.837 1
"Angola"      1965      2544 7.841493  5134.818 0
"Angola"      1966      2646 7.880805   5201.25 0
"Angola"      1967      2753 7.920446  5247.469 0
"Angola"      1968      2665 7.887959  5350.384 0
"Angola"      1969      2695 7.899154  5471.641 0
"Angola"      1970      2818 7.943783  5605.626 0
"Angola"      1971      2754  7.92081  5752.957 0
"Angola"      1972      2729 7.911691  5895.212 0
"Angola"      1973      2852 7.955776  6026.363 0
"Angola"      1974      2727 7.910957  5987.492 0
"Angola"      1975      1710 7.444249  5885.455 0
"Angola"      1976      1521 7.327123  5943.466 0
"Angola"      1977      1500 7.313221  6163.714 0
"Angola"      1978      1530 7.333023   6287.18 0
"Angola"      1979      1527  7.33106  6452.546 0
"Angola"      1980      1532 7.334329   6743.08 0
end
I have also formulated a fairly simple binary indicator difference-in-difference model:
log(GDPit)=ai+yeart+B1PTit+B2log(popit)+eit

where a denotes country-fixed effects, year are time-fixed effects, log(pop) is the logarithmic value of the population size, PT is an indicator set to 0 before birth rates decline and then set to 1 the year they start to decline and all following years. I then run a fixed effect model using
Code:
 xtreg log_gdp post_treat log_pop yr_dumm*, fe robust cluster(id_var)
I have posted the results of this procedure below (and removed many of the yearly dummies for the sake of clarity):

Code:
xtreg log_gdp post_treat log_pop yr_dumm*, fe robust cluster(id_var)

Fixed-effects (within) regression               Number of obs     =     14,632
Group variable: id_var                          Number of groups  =        169

R-sq:                                           Obs per group:
     within  = 0.7669                                         min =         31
     between = 0.0006                                         avg =       86.6
     overall = 0.1024                                         max =        164

                                                F(132,168)        =          .
corr(u_i, Xb)  = -0.4907                        Prob > F          =          .

                               (Std. Err. adjusted for 169 clusters in id_var)
------------------------------------------------------------------------------
             |               Robust
     log_gdp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  post_treat |  -.1307779   .0433683    -3.02   0.003     -.216395   -.0451609
     log_pop |  -.2143739   .0591918    -3.62   0.000    -.3312295   -.0975182
    yr_dumm2 |   .0107005   .0207205     0.52   0.606    -.0302057    .0516067
    yr_dumm3 |   .0358843   .0206034     1.74   0.083    -.0047908    .0765593
    yr_dumm4 |   .0410382   .0214505     1.91   0.057    -.0013092    .0833855
   .
   .
   .
  yr_dumm161 |   3.274882   .1349918    24.26   0.000     3.008383    3.541381
  yr_dumm162 |   3.287548   .1358326    24.20   0.000      3.01939    3.555707
  yr_dumm163 |    3.31182    .136246    24.31   0.000     3.042845    3.580795
  yr_dumm164 |   3.332759   .1370114    24.32   0.000     3.062273    3.603245
       _cons |   8.297784   .4531923    18.31   0.000     7.403098    9.192469
-------------+----------------------------------------------------------------
     sigma_u |  1.0692478
     sigma_e |  .33960843
         rho |  .90836515   (fraction of variance due to u_i)
------------------------------------------------------------------------------
The vast majority of the yearly dummies are positive and very significant. The effect of declining birth rates appears to be negative, which is somewhat the opposite of what I expected. My question to you all is therefore: am I doing the right thing in adding all those yearly dummies? Whenever I exclude them, the effect of declining birth rates becomes positive and highly significant. But I assume that I must take the time trend of GDP into account?

As a side note, this is my first post so I would greatly appreciate any helpful comments as to how I should post in the future.

I hope you all have a pleasant day,
Niels