Fixed-Effect Regression Interpretation

[Sally Silk]

Dear Community,

I am currently running a fixed-effect regression with time and country-fixed effects. I have a couple of questions regarding my output and would appreciate any help! Just for some background my outcome variable of interest is GDP growth, with my main covariates of interest being economic policy uncertainty and democracy/polyarchy (ranges from 0.000 to 1.000).

Here is my output

xtreg gdpg epu polyarchy polyarchy2 polyepu eys mys trade gcf mort infl leab i.year, fe

Fixed-effects (within) regression Number of obs = 504
Group variable: country Number of groups = 24

R-squared: Obs per group:
Within = 0.6513 min = 21
Between = 0.0901 avg = 21.0
Overall = 0.2108 max = 21

F(31,449) = 27.05
corr(u_i, Xb) = -0.8331 Prob > F = 0.0000

------------------------------------------------------------------------------
gdpg | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
epu | -.026194 .0059042 -4.44 0.000 -.0377972 -.0145907
polyarchy | 47.10087 13.77964 3.42 0.001 20.02027 74.18147
polyarchy2 | -36.38016 9.615551 -3.78 0.000 -55.27723 -17.48309
polyepu | .0303808 .0073758 4.12 0.000 .0158855 .0448761
eys | -.2563044 .164398 -1.56 0.120 -.5793896 .0667807
mys | -1.684913 .3283187 -5.13 0.000 -2.330145 -1.039681
trade | .0418149 .0071237 5.87 0.000 .0278151 .0558148
gcf | .1956006 .0315612 6.20 0.000 .1335746 .2576266
mort | -.0979374 .0458212 -2.14 0.033 -.187988 -.0078869
infl | -.2217516 .0573018 -3.87 0.000 -.3343646 -.1091385
leab | .0571427 .1547104 0.37 0.712 -.2469037 .3611891
|
year |
2001 | -2.1258 .5398174 -3.94 0.000 -3.186682 -1.064917
2002 | -1.777253 .5485515 -3.24 0.001 -2.855301 -.6992063
2003 | -1.374254 .5614857 -2.45 0.015 -2.47772 -.270788
2004 | -.0329219 .5844018 -0.06 0.955 -1.181424 1.11558
2005 | -.8107316 .6042395 -1.34 0.180 -1.99822 .376757
2006 | -.230025 .6345811 -0.36 0.717 -1.477143 1.017093
2007 | -.4702987 .6545978 -0.72 0.473 -1.756755 .8161572
2008 | -2.868747 .6801661 -4.22 0.000 -4.205451 -1.532043
2009 | -6.338044 .7005902 -9.05 0.000 -7.714887 -4.961201
2010 | -.3762288 .7260767 -0.52 0.605 -1.803159 1.050702
2011 | -1.41363 .7656697 -1.85 0.066 -2.918371 .0911115
2012 | -2.461866 .786467 -3.13 0.002 -4.007479 -.9162523
2013 | -2.027235 .8212383 -2.47 0.014 -3.641183 -.4132871
2014 | -1.025382 .8505386 -1.21 0.229 -2.696912 .6461492
2015 | -.4443696 .8643188 -0.51 0.607 -2.142982 1.254243
2016 | -1.216199 .8902149 -1.37 0.173 -2.965704 .5333063
2017 | -.3554842 .912558 -0.39 0.697 -2.148899 1.437931
2018 | -.6058677 .9358398 -0.65 0.518 -2.445038 1.233302
2019 | -1.353752 .9688951 -1.40 0.163 -3.257884 .5503803
2020 | -7.227344 .9229527 -7.83 0.000 -9.041187 -5.4135
|
_cons | 2.170436 13.9184 0.16 0.876 -25.18286 29.52373
-------------+----------------------------------------------------------------
sigma_u | 4.3451978
sigma_e | 1.8559754
rho | .84570729 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(23, 449) = 6.23 Prob > F = 0.0000

My questions are as follows:
1. Are the standard errors reported just robust standard errors?
2. I would like to include the significance/insignificance (level) of my time and country-fixed effects in my analysis, but I am unsure where in the output I can interpret this from.
3. Finally, I have written a rough interpretation of my results, but I am unsure if it is correct.
Economic policy uncertainty (EPU): a one-unit increase in EPU leads to a decrease in GDP growth by -.026194 percentage points.
Polyarchy/democracy: a one-unit increase in the level of democracy leads to an increase in GDP growth by 47.10 units.

Thank you very much!


Sally Silk

[Carlo Lazzaro]

Sally:
1) you reported (without using CODE delimiters, though. Please see the FAQ. Thanks.) default standard errors. Just invoke -robust- or -vce(cluster clusterid)- options to obtain, in both cases, cluster-robust standard errors;
2) see -testparm-;
3) your interpretations sound correct. I would add "when adjusted for the other predictors...".

[Sally Silk]

Thank you very much Carlo!

I had a further question, I excluded one country from my analysis due to it having exceptionally high growth in 2015 (Ireland). The overall magnitude of my results do not change significantly, however the goodness of fit does improve. I am unsure whether I should include Ireland in my main results or not and would appreciate any insight/tips to decide.

Below are the regression results when I exclude Ireland:


Fixed-effects (within) regression Number of obs = 483
Group variable: country Number of groups = 23

R-squared: Obs per group:
Within = 0.7319 min = 21
Between = 0.0520 avg = 21.0
Overall = 0.2350 max = 21

F(30,430) = 39.12
corr(u_i, Xb) = -0.8027 Prob > F = 0.0000

------------------------------------------------------------------------------
gdpg | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
epu | -.0307707 .0049932 -6.16 0.000 -.0405848 -.0209566
polyarchy | 39.64149 11.32283 3.50 0.001 17.38651 61.89647
polyarchy2 | -32.73989 7.885378 -4.15 0.000 -48.23857 -17.24121
polyepu | .0366357 .0062496 5.86 0.000 .0243521 .0489192
mys | -1.269145 .2792629 -4.54 0.000 -1.818035 -.7202543
trade | .0401466 .0064003 6.27 0.000 .0275669 .0527263
gcf | .2858517 .0342597 8.34 0.000 .2185144 .3531891
mort | -.0452997 .0374664 -1.21 0.227 -.1189397 .0283403
leab | .1247299 .1304966 0.96 0.340 -.1317606 .3812204
infl | -.2616434 .0508794 -5.14 0.000 -.3616467 -.1616402
|
year |
2001 | -2.12449 .4511919 -4.71 0.000 -3.011306 -1.237674
2002 | -1.884474 .4572039 -4.12 0.000 -2.783107 -.9858417
2003 | -1.443713 .4651806 -3.10 0.002 -2.358023 -.5294021
2004 | -.3189466 .486407 -0.66 0.512 -1.274978 .6370846
2005 | -1.154159 .5012053 -2.30 0.022 -2.139276 -.1690416
2006 | -.6453212 .5315365 -1.21 0.225 -1.690054 .3994118
2007 | -1.088674 .548479 -1.98 0.048 -2.166707 -.0106404
2008 | -3.208265 .5638559 -5.69 0.000 -4.316522 -2.100008
2009 | -6.591254 .5734179 -11.49 0.000 -7.718304 -5.464203
2010 | -.8198329 .5960959 -1.38 0.170 -1.991457 .3517914
2011 | -1.974402 .6308297 -3.13 0.002 -3.214296 -.734509
2012 | -3.034213 .6503482 -4.67 0.000 -4.312469 -1.755956
2013 | -2.707786 .6702728 -4.04 0.000 -4.025204 -1.390367
2014 | -2.012491 .6921942 -2.91 0.004 -3.372996 -.6519859
2015 | -2.106171 .699332 -3.01 0.003 -3.480705 -.7316366
2016 | -1.828581 .7178592 -2.55 0.011 -3.239531 -.4176319
2017 | -1.343117 .7400911 -1.81 0.070 -2.797763 .1115292
2018 | -1.73197 .7645173 -2.27 0.024 -3.234625 -.2293138
2019 | -2.130107 .7865325 -2.71 0.007 -3.676034 -.5841805
2020 | -8.396218 .7391284 -11.36 0.000 -9.848972 -6.943464
|
_cons | -9.908789 11.65566 -0.85 0.396 -32.81794 13.00036
-------------+----------------------------------------------------------------
sigma_u | 3.9138822
sigma_e | 1.5212943
rho | .86874829 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(22, 430) = 8.32 Prob > F = 0.0000

Thank you!

Sally

[Andrew Musau]

With only 23 countries in the sample, you'd want to avoid further reducing the sample size. I recall a thread on Statalist in which I participated, suggesting a method to correct the high growth rate in Ireland in 2015. You can find it at https://www.statalist.org/forums/for...om-growth-rate, particularly #3 and #4. You may want to consider this adjustment.

[Sally Silk]

Dear Andrew,

Thank you very much. I have read the forum you referred to. Based on your suggestion would you adjust the GDP for Ireland for 2015 as: GDP growth in 2014 and multiply by (1+average growth rate for 2013 and 2014). Following that, would you proceed using the actual GDP growth from 2016 onward?

Thanks!

Sally

[Andrew Musau]

Correct. It's not my suggestion. The OP from the linked thread does not specify the AEJ Macro article that recommends this. You could send her an email and ask.

[Sally Silk]

Thanks Andrew, that is all clear.