Year fixed effect on Pooled OLS - missing one year period

[Shofia Mumtaza]

Hello Statalist,

I'm about to replicate this Pooled OLS estimation from World Happiness Report (Table 8, page 18): https://happiness-report.s3.amazonaw...l_Appendix.pdf

I believe I used the same data, however my estimation result kind of different from the orginal work and (I think) that's because my estimation missed one year fixed effect. The time fixed effect should be from 2005-2022 but mine was 2006-2022. The data is from 1990-2022 so it actually included 2005 data as well but with many missing data. And I'm struggle to include the 2005 data so it can appear on the estimation. Here's the data example:

* Example generated by -dataex-. For more info, type help dataex
clear
input int Year long country1 double(happiness_score log_GDP_per_capita life_expectancy social_support freedom generosity perceptions_corruption)
1990 1                  .                  .                  .                  .                  .                     .                 .
1991 1                  .                  .                  .                  .                  .                     .                 .
1992 1                  .                  .                  .                  .                  .                     .                 .
1993 1                  .                  .                  .                  .                  .                     .                 .
1994 1                  .                  .                  .                  .                  .                     .                 .
1995 1                  .                  .                  .                  .                  .                     .                 .
1996 1                  .                  .                  .                  .                  .                     .                 .
1997 1                  .                  .                  .                  .                  .                     .                 .
1998 1                  .                  .                  .                  .                  .                     .                 .
1999 1                  .                  .                  .                  .                  .                     .                 .
2000 1                  .                  .                  .                  .                  .                     .                 .
2001 1                  .                  .                  .                  .                  .                     .                 .
2002 1                  .                  .                  .                  .                  .                     .                 .
2003 1                  .                  .                  .                  .                  .                     .                 .
2004 1                  .                  .                  .                  .                  .                     .                 .
2005 1                  .                  .                  .                  .                  .                     .                 .
2006 1                  .                  .                  .                  .                  .                     .                 .
2007 1                  .                  .                  .                  .                  .                     .                 .
2008 1 3.7235898971557617   7.35041618347168               50.5  .4506623148918152  .7181143164634705     .1676524579524994 .8816863298416138
2009 1  4.401778221130371  7.508646011352539  50.79999923706055  .5523084402084351  .6788963675498962    .19080880284309387 .8500354290008545
2010 1  4.758380889892578 7.6138997077941895 51.099998474121094  .5390751957893372  .6001272201538086    .12131604552268982 .7067660689353943
2011 1  3.831719160079956  7.581258773803711 51.400001525878906    .52110356092453  .4959014058113098    .16357149183750153  .731108546257019
2012 1  3.782937526702881  7.660505771636963  51.70000076293945  .5206367373466492  .5309350490570068     .2375875860452652 .7756198048591614
2013 1 3.5721004009246826  7.680333137512207                 52 .48355185985565186  .5779553651809692    .06266622245311737 .8232041001319885
2014 1 3.1308956146240234  7.670638084411621  52.29999923706055   .525568425655365  .5085140466690063    .10575488209724426 .8712419867515564
2015 1 3.9828546047210693  7.653833389282227 52.599998474121094  .5285972356796265  .3889275789260864    .08165227621793747 .8806383013725281
2016 1  4.220168590545654  7.650369644165039  52.92499923706055  .5590717792510986  .5225661993026733   .043916016817092896 .7932455539703369
2017 1 2.6617181301116943  7.647830486297607              53.25  .4908800721168518  .4270108640193939   -.11941047012805939 .9543925523757935
2018 1  2.694303274154663  7.630800724029541  53.57500076293945  .5075158476829529 .37353554368019104   -.09110598266124725 .9276056885719299
2019 1  2.375091791152954  7.640085697174072 53.900001525878906 .41997286677360535  .3936561644077301   -.10601644963026047 .9238491058349609
2020 1                  .                  .                  .                  .                  .                     .                 .
2021 1 2.4360344409942627  7.324032306671143  54.54999923706055  .4541746973991394   .394305944442749   -.08101112395524979 .9462993741035461
2022 1 1.2812711000442505                  .             54.875  .2282172292470932   .368377149105072                     . .7331978678703308
1990 2                  .                  .                  .                  .                  .                     .                 .
1991 2                  .                  .                  .                  .                  .                     .                 .
1992 2                  .                  .                  .                  .                  .                     .                 .
1993 2                  .                  .                  .                  .                  .                     .                 .
1994 2                  .                  .                  .                  .                  .                     .                 .
1995 2                  .                  .                  .                  .                  .                     .                 .
1996 2                  .                  .                  .                  .                  .                     .                 .
1997 2                  .                  .                  .                  .                  .                     .                 .
1998 2                  .                  .                  .                  .                  .                     .                 .
1999 2                  .                  .                  .                  .                  .                     .                 .
2000 2                  .                  .                  .                  .                  .                     .                 .
2001 2                  .                  .                  .                  .                  .                     .                 .
2002 2                  .                  .                  .                  .                  .                     .                 .
2003 2                  .                  .                  .                  .                  .                     .                 .
2004 2                  .                  .                  .                  .                  .                     .                 .
2005 2                  .                  .                  .                  .                  .                     .                 .
2006 2                  .                  .                  .                  .                  .                     .                 .
2007 2  4.634251594543457    9.1217041015625  66.76000213623047  .8213716149330139  .5286047458648682  -.010428507812321186 .8746995329856873
2008 2                  .                  .                  .                  .                  .                     .                 .
2009 2  5.485469818115234  9.241429328918457  67.31999969482422  .8330466151237488  .5252232551574707    -.1592588573694229 .8636654019355774
2010 2  5.268936634063721  9.282793045043945   67.5999984741211  .7331522703170776  .5689584016799927    -.1736752837896347 .7262616753578186
2011 2  5.867421627044678  9.310619354248047  67.87999725341797  .7594338059425354  .4874962568283081   -.20618607103824615 .8770025968551636
2012 2  5.510124206542969  9.326343536376953  68.16000366210938  .7845017910003662  .6015121340751648   -.17046748101711273 .8476752042770386
2013 2  4.550647735595703  9.338146209716797  68.44000244140625  .7594767212867737  .6318302750587463    -.1288250982761383  .862904965877533
2014 2   4.81376314163208  9.357805252075195  68.72000122070313  .6255869269371033  .7346484065055847  -.026297539472579956 .8827044367790222
2015 2 4.6066508293151855  9.382661819458008                 69  .6393561363220215  .7038506865501404   -.08249161392450333 .8847930431365967
2016 2  4.511100769042969   9.41687297821045   69.0250015258789  .6384114623069763  .7298189401626587  -.018664082512259483  .901070773601532
2017 2  4.639548301696777  9.455109596252441  69.05000305175781  .6376982927322388  .7496110200881958  -.030505668371915817 .8761346340179443
2018 2 5.0044026374816895  9.496984481811523  69.07499694824219  .6835916638374329  .8242123126983643   .007197479251772165 .8991293907165527
2019 2 4.9953179359436035  9.521909713745117   69.0999984741211  .6863648891448975   .777351438999176    -.1009097695350647 .9142842888832092
2020 2  5.364909648895264  9.492215156555176             69.125  .7101150155067444  .7536710500717163   .004123116377741098 .8913589715957642
2021 2  5.255481719970703  9.583207130432129   69.1500015258789  .7018827795982361  .8274527192115784    .04137755185365677 .8961266279220581
2022 2  5.212213039398193  9.626482963562012  69.17500305175781  .7240896224975586  .8022497892379761   -.06598725914955139 .8455019593238831
1990 3                  .                  .                  .                  .                  .                     .                 .
1991 3                  .                  .                  .                  .                  .                     .                 .
1992 3                  .                  .                  .                  .                  .                     .                 .
1993 3                  .                  .                  .                  .                  .                     .                 .
1994 3                  .                  .                  .                  .                  .                     .                 .
1995 3                  .                  .                  .                  .                  .                     .                 .
1996 3                  .                  .                  .                  .                  .                     .                 .
1997 3                  .                  .                  .                  .                  .                     .                 .
1998 3                  .                  .                  .                  .                  .                     .                 .
1999 3                  .                  .                  .                  .                  .                     .                 .
2000 3                  .                  .                  .                  .                  .                     .                 .
2001 3                  .                  .                  .                  .                  .                     .                 .
2002 3                  .                  .                  .                  .                  .                     .                 .
2003 3                  .                  .                  .                  .                  .                     .                 .
2004 3                  .                  .                  .                  .                  .                     .                 .
2005 3                  .                  .                  .                  .                  .                     .                 .
2006 3                  .                  .                  .                  .                  .                     .                 .
2007 3                  .                  .                  .                  .                  .                     .                 .
2008 3                  .                  .                  .                  .                  .                     .                 .
2009 3                  .                  .                  .                  .                  .                     .                 .
2010 3  5.463566780090332  9.306354522705078               65.5                  .  .5926958322525024   -.20975297689437866 .6180378794670105
2011 3   5.31719446182251  9.315958023071289   65.5999984741211  .8102344870567322  .5295612812042236   -.18508440256118774  .637981653213501
2012 3   5.60459566116333  9.329961776733398  65.69999694824219  .8393968939781189  .5866634845733643   -.17657119035720825 .6901163458824158
2013 3                  .                  .                  .                  .                  .                     .                 .
2014 3  6.354898452758789  9.355415344238281   65.9000015258789  .8181894421577454                  .                     .                 .
2015 3                  .                  .                  .                  .                  .                     .                 .
2016 3  5.340853691101074  9.383312225341797   66.0999984741211  .7485882639884949                  .                     .                 .
2017 3  5.248912334442139   9.37665843963623  66.19999694824219  .8067538738250732  .4366704821586609    -.1714705228805542 .6997742056846619
2018 3  5.043086051940918  9.369553565979004  66.30000305175781  .7986513376235962  .5833805799484253   -.15055912733078003 .7587041258811951
2019 3  4.744627475738525  9.361109733581543   66.4000015258789  .8032586574554443  .3850834369659424 .00026843760861083865  .740609347820282
2020 3  5.437755107879639  9.291438102722168               66.5  .8676488995552063  .5738906860351563   -.12114762514829636 .7242636680603027
2021 3  5.217017650604248    9.3092622756958   66.5999984741211  .8407102823257446  .5584869384765625   -.11348341405391693 .7119000554084778
2022 3                  .                  .                  .                  .                  .                     .                 .
1990 4                  .                  .                  .                  .                  .                     .                 .
end
label values country1 country1
label def country1 1 "Afghanistan", modify
label def country1 2 "Albania", modify
label def country1 3 "Algeria", modify
label def country1 4 "Angola", modify

Here's the command I used:

xtset country1 Year

reg happiness_score log_GDP_per_capita social_support life_expectancy freedom generosity perceptions_corruption i.Year, vce (cluster Country)

and the result:

Linear regression                               Number of obs     =      1,903
                                                F(22, 147)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.7629
                                                Root MSE          =     .56118

                               (Std. err. adjusted for 148 clusters in Country)
-------------------------------------------------------------------------------
              |               Robust
happiness_s~e | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
log_GDP_per~a |   .3675455   .0686916     5.35   0.000     .2317949    .5032961
social_supp~t |   2.512036   .3649847     6.88   0.000     1.790741    3.233331
life_expect~y |   .0279644    .010497     2.66   0.009     .0072198     .048709
      freedom |   1.262733   .3080191     4.10   0.000     .6540158    1.871451
   generosity |   .5726625   .2571264     2.23   0.027     .0645207    1.080804
perceptions~n |  -.7058856   .2648248    -2.67   0.009    -1.229241     -.18253
              |
         Year |
        2006  |  -.4057297   .0850824    -4.77   0.000    -.5738724   -.2375871
        2007  |   -.160866   .0880224    -1.83   0.070    -.3348189    .0130868
        2008  |  -.0279241     .08615    -0.32   0.746    -.1981765    .1423283
        2009  |  -.1571314   .0961686    -1.63   0.104     -.347183    .0329201
        2010  |   -.238375   .0876574    -2.72   0.007    -.4116065   -.0651435
        2011  |  -.2236417   .0856636    -2.61   0.010     -.392933   -.0543504
        2012  |  -.2462114   .0853725    -2.88   0.005    -.4149274   -.0774955
        2013  |  -.3449375   .0909533    -3.79   0.000    -.5246823   -.1651926
        2014  |   -.388323   .0838999    -4.63   0.000    -.5541289   -.2225172
        2015  |  -.3748464   .0815806    -4.59   0.000    -.5360688    -.213624
        2016  |  -.4021505   .0812837    -4.95   0.000     -.562786    -.241515
        2017  |  -.3293431   .0799498    -4.12   0.000    -.4873425   -.1713437
        2018  |  -.3179049   .0802556    -3.96   0.000    -.4765086   -.1593012
        2019  |  -.3137922   .0798687    -3.93   0.000    -.4716313   -.1559531
        2020  |  -.3063681   .0772614    -3.97   0.000    -.4590547   -.1536815
        2021  |  -.3471287   .0742407    -4.68   0.000    -.4938458   -.2004117
        2022  |  -.3425818   .0729706    -4.69   0.000    -.4867887   -.1983749
              |
        _cons |  -1.900342   .5420774    -3.51   0.001    -2.971613   -.8290705
-------------------------------------------------------------------------------

Please I need any advice on how to include the 2005 year fixed effects and if anything I do was wrong at the beginning. Thank you in advance

[Clyde Schechter]

Well, in your example data, all of the regression variables hav nothing but missing values through 2006. So the data really begins at 2007, from which point on there is no missing data at all through 2022. So, treating this as a dataset running from 2007 through 2022 (which, for present purposes, it is) you should expect to see an output for every year between 2007 through 2022 with the exception of one year omitted as the reference year. As your code does not specify which year you want to be the reference year, by default, Stata chooses 2007 for that role. Consequently the output shows a row for every year from 2008 through 2022. This is exactly what should be expected.

So I don't think there's anything wrong with your code as written (well, except that you say -vce(cluster Country)- when there is no variable named Country, but substituting country1 seems to do something sensible). Either the vast amount of missing data in your data set represents errors in the data management that created it, or, your expectation of seeing output from every year starting with 2005 is in error.

Now, probably your full data set has some data for years earlier than 2007. But I will bet that it does not have any data prior to 2005, and if 2005 is, in fact, the earliest year for which there really is data is 2005. And if that's right, then you should expect to see output only for 2006 through 2022. You can verify what years are actually included in the analysis after you run the regression by running

tab Year if e(sample)

This list will be the same as the list of Years in the regression table, except that the first one will not appear in the regression table. The reference category is always missing.

The reason for this omission, of course, is colinearity. If you prefer, you can overcome the colinearity in a different way: specify the -nocons- option on your regression command. That way you will see the full list of Years that have data in the regression output, no omissions, but there will be no constant term. The results for those Years, by the way, will be rather different from what you have gotten with your present aproach--that is normal. Those Year outputs are meaningless in any case: only differences between years are meaningful. And if you take the trouble to calculate a few to convince yourself, you will see that, except perhaps for minor rounding errors, the differences between corresponding years are the same both ways.

By the way, is there a reason you chose not to include an i.country1 term in your regression? Your model includes Year fixed effects, but not country fixed-effects.