Province and year fixed effects

[Sumaiya Sara]

Hello altruists,
I am new to this forum. I've been working on province and year fixed effects and have to determine the following:

1. Baseline (current regression)
2. Baseline + province FEs
3. Baseline + year FEs
4. Baseline + province and year FEs

While I've been successful to generate all of the above, the problem remains with the regression output of 3. and 4. The regression coefficients are same when I calculate time (year in my case) fixed effects and time+ province fixed effects.

The command I've used for year fixed effect is as follows:
xtreg giniaftertax wage debt edu unempl i.year, fe

The Stata (17) output for time fixed effects:

Fixed-effects (within) regression Number of obs = 290
Group variable: province2 Number of groups = 10

R-squared: Obs per group:
Within = 0.5965 min = 29
Between = 0.2444 avg = 29.0
Overall = 0.1041 max = 29

F(32,248) = 11.46
corr(u_i, Xb) = -0.2288 Prob > F = 0.0000

------------------------------------------------------------------------------
giniaftertax | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
wage | -.015787 .0045584 -3.46 0.001 -.024765 -.0068089
debt | -.0047514 .0024122 -1.97 0.050 -.0095023 -4.69e-07
edu | -.0230065 .015932 -1.44 0.150 -.0543858 .0083727
unempl | -.0003568 .0005727 -0.62 0.534 -.0014848 .0007712
|
year |
1991 | .001659 .0036165 0.46 0.647 -.0054639 .0087819
1992 | .0059149 .0037789 1.57 0.119 -.0015279 .0133576
1993 | -.0047124 .0038415 -1.23 0.221 -.0122785 .0028538
1994 | -.0035752 .0038273 -0.93 0.351 -.0111134 .0039631
1995 | -.0008383 .0037379 -0.22 0.823 -.0082003 .0065237
1996 | .0014287 .0039361 0.36 0.717 -.0063238 .0091811
1997 | .0025584 .0040056 0.64 0.524 -.0053309 .0104478
1998 | .014094 .003906 3.61 0.000 .0064008 .0217872
1999 | .0135665 .0038861 3.49 0.001 .0059125 .0212204
2000 | .019438 .0040101 4.85 0.000 .0115399 .0273361
2001 | .0208594 .003976 5.25 0.000 .0130284 .0286905
2002 | .0250461 .0040201 6.23 0.000 .0171283 .032964
2003 | .0215969 .0040066 5.39 0.000 .0137056 .0294882
2004 | .0244702 .0041125 5.95 0.000 .0163704 .0325699
2005 | .0237914 .0040532 5.87 0.000 .0158083 .0317746
2006 | .0265157 .004132 6.42 0.000 .0183775 .0346539
2007 | .0258257 .0042889 6.02 0.000 .0173784 .0342729
2008 | .0243988 .0042888 5.69 0.000 .0159517 .032846
2009 | .0274427 .0042705 6.43 0.000 .0190316 .0358538
2010 | .0266284 .0043256 6.16 0.000 .0181088 .0351479
2011 | .026752 .0045462 5.88 0.000 .0177979 .035706
2012 | .0274172 .0047169 5.81 0.000 .0181269 .0367075
2013 | .0350216 .0050894 6.88 0.000 .0249976 .0450456
2014 | .0295932 .0052916 5.59 0.000 .0191711 .0400154
2015 | .0344198 .0054243 6.35 0.000 .0237363 .0451034
2016 | .0266727 .0056189 4.75 0.000 .0156058 .0377396
2017 | .0333765 .006044 5.52 0.000 .0214723 .0452807
2018 | .0286212 .0062414 4.59 0.000 .0163283 .0409142
|
_cons | .3445261 .0237769 14.49 0.000 .2976957 .3913565
-------------+----------------------------------------------------------------
sigma_u | .01656777
sigma_e | .00778372
rho | .81918717 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 248) = 62.28 Prob > F = 0.0000


The command I've used for province and year fixed effect is as follows:
xtreg giniaftertax wage debt edu unempl i.year i.province2 , fe

The Stata output for province and year fixed effect:
note: 2.province2 omitted because of collinearity.
note: 3.province2 omitted because of collinearity.
note: 4.province2 omitted because of collinearity.
note: 5.province2 omitted because of collinearity.
note: 6.province2 omitted because of collinearity.
note: 7.province2 omitted because of collinearity.
note: 8.province2 omitted because of collinearity.
note: 9.province2 omitted because of collinearity.
note: 10.province2 omitted because of collinearity.

Fixed-effects (within) regression Number of obs = 290
Group variable: province2 Number of groups = 10

R-squared: Obs per group:
Within = 0.5965 min = 29
Between = 0.2444 avg = 29.0
Overall = 0.1041 max = 29

F(32,248) = 11.46
corr(u_i, Xb) = -0.2288 Prob > F = 0.0000

------------------------------------------------------------------------------
giniaftertax | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
wage | -.015787 .0045584 -3.46 0.001 -.024765 -.0068089
debt | -.0047514 .0024122 -1.97 0.050 -.0095023 -4.69e-07
edu | -.0230065 .015932 -1.44 0.150 -.0543858 .0083727
unempl | -.0003568 .0005727 -0.62 0.534 -.0014848 .0007712
|
year |
1991 | .001659 .0036165 0.46 0.647 -.0054639 .0087819
1992 | .0059149 .0037789 1.57 0.119 -.0015279 .0133576
1993 | -.0047124 .0038415 -1.23 0.221 -.0122785 .0028538
1994 | -.0035752 .0038273 -0.93 0.351 -.0111134 .0039631
1995 | -.0008383 .0037379 -0.22 0.823 -.0082003 .0065237
1996 | .0014287 .0039361 0.36 0.717 -.0063238 .0091811
1997 | .0025584 .0040056 0.64 0.524 -.0053309 .0104478
1998 | .014094 .003906 3.61 0.000 .0064008 .0217872
1999 | .0135665 .0038861 3.49 0.001 .0059125 .0212204
2000 | .019438 .0040101 4.85 0.000 .0115399 .0273361
2001 | .0208594 .003976 5.25 0.000 .0130284 .0286905
2002 | .0250461 .0040201 6.23 0.000 .0171283 .032964
2003 | .0215969 .0040066 5.39 0.000 .0137056 .0294882
2004 | .0244702 .0041125 5.95 0.000 .0163704 .0325699
2005 | .0237914 .0040532 5.87 0.000 .0158083 .0317746
2006 | .0265157 .004132 6.42 0.000 .0183775 .0346539
2007 | .0258257 .0042889 6.02 0.000 .0173784 .0342729
2008 | .0243988 .0042888 5.69 0.000 .0159517 .032846
2009 | .0274427 .0042705 6.43 0.000 .0190316 .0358538
2010 | .0266284 .0043256 6.16 0.000 .0181088 .0351479
2011 | .026752 .0045462 5.88 0.000 .0177979 .035706
2012 | .0274172 .0047169 5.81 0.000 .0181269 .0367075
2013 | .0350216 .0050894 6.88 0.000 .0249976 .0450456
2014 | .0295932 .0052916 5.59 0.000 .0191711 .0400154
2015 | .0344198 .0054243 6.35 0.000 .0237363 .0451034
2016 | .0266727 .0056189 4.75 0.000 .0156058 .0377396
2017 | .0333765 .006044 5.52 0.000 .0214723 .0452807
2018 | .0286212 .0062414 4.59 0.000 .0163283 .0409142
|
province2 |
BC | 0 (omitted)
MB | 0 (omitted)
NB | 0 (omitted)
NL | 0 (omitted)
NS | 0 (omitted)
ON | 0 (omitted)
PEI | 0 (omitted)
QC | 0 (omitted)
SK | 0 (omitted)
|
_cons | .3445261 .0237769 14.49 0.000 .2976957 .3913565
-------------+----------------------------------------------------------------
sigma_u | .01656777
sigma_e | .00778372
rho | .81918717 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 248) = 62.28 Prob > F = 0.0000


Is it normal to have same coefficients for the 'year fixed effects' and 'year + province fixed effects'?
I've been trying to figure out this, but have not found any YouTube video/article discussing specifically about this issue.
Thanks in advance

[Carlo Lazzaro]

Sumaiya:
welcome to this forum.
Since -province2- was omitted from the regression as perfectly collinear with your -panelid-, no wonder that the results are the same.

[Sumaiya Sara]

Hi Carlo,

I appreciate your super prompt response. Can you kindly guide me how to resolve the issue? That being said, how to determine 'year + province fixed effects' in my case? Thank you very much again.

[Carlo Lazzaro]

Sumaya:
there's nothing to fix here; you simpy cannot include -panelid- as a predictor. .
Personally, I would be fine with -year- only and test its joint statistical significance via -testparm-.
In addition, with 290 panels I would consider cluster-robust standard errors (see -vce(cluster panelid) or -robust- options; they do the very same job under -xtreg-).