For my master thesis I am conducting research about the effects of the digital divide on the educational attainment in the European continent. For this research I gathered data of 29 countries over a period of 14 years
My dependent variable is the % of the population that compelted tertiary education( age group 24-34)
Independent are : Population that has acces to broadband internet (in %), gini score(from 0 to 100, lower means better)
Then I looked up for some control variables: Population (total) & mean income , (still thinking about adding unemployment rate as another control var)
Upon using fixed and random effect
Fixed:
Code:
. xtreg educ population gini broadband incomeMean, fe
Fixed-effects (within) regression Number of obs = 398
Group variable: country Number of groups = 29
R-squared: Obs per group:
Within = 0.7214 min = 11
Between = 0.3053 avg = 13.7
Overall = 0.3832 max = 14
F(4,365) = 236.33
corr(u_i, Xb) = -0.3124 Prob > F = 0.0000
------------------------------------------------------------------------------
educ | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
population | -9.70e-08 2.92e-07 -0.33 0.740 -6.71e-07 4.77e-07
gini | -.150809 .1070503 -1.41 0.160 -.3613219 .0597038
broadband | .2142734 .0098261 21.81 0.000 .1949504 .2335963
incomeMean | .0004968 .0000762 6.52 0.000 .000347 .0006467
_cons | 20.37698 5.580489 3.65 0.000 9.403037 31.35093
-------------+----------------------------------------------------------------
sigma_u | 7.6449458
sigma_e | 2.5569006
rho | .89939297 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(28, 365) = 91.84 Prob > F = 0.0000Code:
xtreg educ population gini broadband incomeMean, re
Random-effects GLS regression Number of obs = 398
Group variable: country Number of groups = 29
R-squared: Obs per group:
Within = 0.7206 min = 11
Between = 0.3157 avg = 13.7
Overall = 0.3976 max = 14
Wald chi2(4) = 945.94
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
educ | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
population | -8.62e-08 5.70e-08 -1.51 0.130 -1.98e-07 2.54e-08
gini | -.0609734 .1026333 -0.59 0.552 -.262131 .1401841
broadband | .2166468 .0096297 22.50 0.000 .1977729 .2355207
incomeMean | .0004461 .0000651 6.85 0.000 .0003184 .0005737
_cons | 18.24877 3.490679 5.23 0.000 11.40716 25.09037
-------------+----------------------------------------------------------------
sigma_u | 6.9655036
sigma_e | 2.5569006
rho | .88125285 (fraction of variance due to u_i)
------------------------------------------------------------------------------
.Code:
hausman fixed random
Note: the rank of the differenced variance matrix (3) does not equal the number of coefficients being tested (4); be sure this is what you expect, or there may be problems
computing the test. Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a
similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference Std. err.
-------------+----------------------------------------------------------------
population | -9.70e-08 -8.62e-08 -1.08e-08 2.86e-07
gini | -.150809 -.0609734 -.0898356 .0304333
broadband | .2142734 .2166468 -.0023734 .0019549
incomeMean | .0004968 .0004461 .0000508 .0000395
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 8.95
Prob > chi2 = 0.0299
(V_b-V_B is not positive definite)Code:
. xtreg educ population gini broadband incomeMean, fe robust
Fixed-effects (within) regression Number of obs = 398
Group variable: country Number of groups = 29
R-squared: Obs per group:
Within = 0.7214 min = 11
Between = 0.3053 avg = 13.7
Overall = 0.3832 max = 14
F(4,28) = 35.53
corr(u_i, Xb) = -0.3124 Prob > F = 0.0000
(Std. err. adjusted for 29 clusters in country)
------------------------------------------------------------------------------
| Robust
educ | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
population | -9.70e-08 4.97e-07 -0.20 0.847 -1.12e-06 9.21e-07
gini | -.150809 .1814625 -0.83 0.413 -.5225182 .2209001
broadband | .2142734 .0252991 8.47 0.000 .1624506 .2660962
incomeMean | .0004968 .0001977 2.51 0.018 .000092 .0009017
_cons | 20.37698 9.725685 2.10 0.045 .4548208 40.29915
-------------+----------------------------------------------------------------
sigma_u | 7.6449458
sigma_e | 2.5569006
rho | .89939297 (fraction of variance due to u_i)
------------------------------------------------------------------------------Upon adding i.year in the xtreg code like this:
Code:
. xtreg educ population gini broadband incomeMean i.year, fe robust
Fixed-effects (within) regression Number of obs = 398
Group variable: country Number of groups = 29
R-squared: Obs per group:
Within = 0.7746 min = 11
Between = 0.0199 avg = 13.7
Overall = 0.0545 max = 14
F(17,28) = 24.52
corr(u_i, Xb) = -0.8738 Prob > F = 0.0000
(Std. err. adjusted for 29 clusters in country)
------------------------------------------------------------------------------
| Robust
educ | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
population | -8.02e-07 4.62e-07 -1.73 0.094 -1.75e-06 1.45e-07
gini | -.1726822 .165679 -1.04 0.306 -.5120602 .1666957
broadband | .0004282 .0541787 0.01 0.994 -.1105518 .1114082
incomeMean | -.0000562 .0001719 -0.33 0.746 -.0004084 .000296
|
year |
2008 | 1.393604 .514999 2.71 0.011 .3386763 2.448531
2009 | 2.785943 .9833509 2.83 0.008 .7716395 4.800246
2010 | 3.947826 1.240529 3.18 0.004 1.406718 6.488935
2011 | 4.918202 1.571527 3.13 0.004 1.699074 8.137329
2012 | 6.289633 1.930353 3.26 0.003 2.335484 10.24378
2013 | 7.574748 2.091623 3.62 0.001 3.290252 11.85924
2014 | 9.325942 2.29589 4.06 0.000 4.623026 14.02886
2015 | 9.79276 2.449228 4.00 0.000 4.775744 14.80978
2016 | 10.65857 2.584618 4.12 0.000 5.364219 15.95292
2017 | 11.28827 2.743002 4.12 0.000 5.669486 16.90705
2018 | 12.10324 2.847884 4.25 0.000 6.269612 17.93686
2019 | 12.90674 3.009904 4.29 0.000 6.741226 19.07224
2020 | 13.88196 3.176958 4.37 0.000 7.374253 20.38966
|
_cons | 50.14916 8.640671 5.80 0.000 32.44955 67.84878
-------------+----------------------------------------------------------------
sigma_u | 19.538604
sigma_e | 2.3420248
rho | .98583553 (fraction of variance due to u_i)
----Code:
. testparm i.year
( 1) 2008.year = 0
( 2) 2009.year = 0
( 3) 2010.year = 0
( 4) 2011.year = 0
( 5) 2012.year = 0
( 6) 2013.year = 0
( 7) 2014.year = 0
( 8) 2015.year = 0
( 9) 2016.year = 0
(10) 2017.year = 0
(11) 2018.year = 0
(12) 2019.year = 0
(13) 2020.year = 0
F( 13, 28) = 3.71
Prob > F = 0.0018Now my question is am I doing this right by adding i.year into the regression? Because it seems that my dependent variables that were significant are not anymore. Also R-Squared here changed drastically but the F stat still says it's significant.
How can I fix this? Help or hints would greatly help me and is enormously appreciated.
Thank you and sorry for this very long message, but I tried to be as clear as possible by adding every step I took.
Kind regards,
Karim
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