Stata users:
I'am using the "xtreg" command to run random effects models on panel data (unbalanced panel).
My unit of analysis is Korea government agencies.
My question concerns the "rsquared between" and "rsquared overall".
In model 1, there are no quadratic terms. In model 2, I include 4 quadratic terms.
Though one of these quadratic term is statistically significant, "rsquared between" and "rsquared overall" declines.
As far as I know, rsquared (not adjusted rsquared) is supposed to never decrease when variables are added to a model.
Does this apply differently to panel rsquared?
I know that xtreg, fe calculates rsquared differently from areg. But my model is RE.
I would appreciate any help regarding this issue.
# delimit
xtreg reput c.c_z_coder12_r c.c_z_sv_amb_di_r c.c_z_amb_ev c.c_z_amb_pri
c_sq_age2 c_ln_fi_total c_ln_size_full c_sq_up5_r c_fi_ex_ratio c_factor_cen c_factor_pbase
i.org_type i.year
, re vce(cl org) theta;
# delimit cr
# delimit
xtreg reput c.c_z_coder12_r##c.c_z_coder12_r c.c_z_sv_amb_di_r##c.c_z_sv_amb_di_r c.c_z_amb_ev##c.c_z_amb_ev c.c_z_amb_pri##c.c_z_amb_pri
c_sq_age2 c_ln_fi_total c_ln_size_full c_sq_up5_r c_fi_ex_ratio c_factor_cen c_factor_pbase
i.org_type i.year
, re vce(cl org) theta;
# delimit cr
Randomeffects GLS regression Number of obs = 228
Group variable: org Number of groups = 44
Rsq: Obs per group:
within = 0.0994 min = 1
between = 0.3990 avg = 5.2
overall = 0.3377 max = 7
Wald chi2(19) = 70.29
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
 theta 
min 5% median 95% max
0.3668 0.4993 0.7046 0.7046 0.7046
(Std. Err. adjusted for 44 clusters in org)

 Robust
reput  Coef. Std. Err. z P>z [95% Conf. Interval]
+
c_z_coder12_r  .1582868 .121043 1.31 0.191 .3955268 .0789532
c_z_sv_amb_di_r  .1300482 .0996248 1.31 0.192 .0652129 .3253093
c_z_amb_ev  .2304708 .0934306 2.47 0.014 .0473501 .4135914
c_z_amb_pri  .1374347 .1141718 1.20 0.229 .0863379 .3612073
c_sq_age2  .0527441 .0909437 0.58 0.562 .1255023 .2309906
c_ln_fi_total  .1303679 .0615055 2.12 0.034 .2509165 .0098193
c_ln_size_full  .5278446 .2200759 2.40 0.016 .9591855 .0965037
c_sq_up5_r  .7677916 1.11694 0.69 0.492 2.956955 1.421371
c_fi_ex_ratio  3.959733 5.413107 0.73 0.464 6.649762 14.56923
c_factor_pbase  .2466075 .1336372 1.85 0.065 .0153165 .5085316
c_factor_cen  .1580916 .1283419 1.23 0.218 .4096371 .0934538

org_type 
2  .3448319 .5811616 0.59 0.553 .794224 1.483888
3  .0150424 .4863613 0.03 0.975 .968293 .9382083

year 
2012  .5635269 .2108262 2.67 0.008 .1503152 .9767386
2013  .5536817 .260991 2.12 0.034 .0421486 1.065215
2014  .6628218 .3493855 1.90 0.058 .0219612 1.347605
2015  .7331962 .3281427 2.23 0.025 .0900483 1.376344
2016  .4634112 .3310233 1.40 0.162 .1853825 1.112205
2017  .753503 .2953417 2.55 0.011 .1746438 1.332362

_cons  .4609324 .4146254 1.11 0.266 1.273583 .3517184
+
sigma_u  1.0696963
sigma_e  .8750723
rho  .59908334 (fraction of variance due to u_i)

Randomeffects GLS regression Number of obs = 228
Group variable: org Number of groups = 44
Rsq: Obs per group:
within = 0.1197 min = 1
between = 0.3884 avg = 5.2
overall = 0.3240 max = 7
Wald chi2(23) = 78.44
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
 theta 
min 5% median 95% max
0.3962 0.5278 0.7247 0.7247 0.7247
(Std. Err. adjusted for 44 clusters in org)

 Robust
reput  Coef. Std. Err. z P>z [95% Conf. Interval]
+
c_z_coder12_r  .3011932 .1001225 3.01 0.003 .4974297 .1049568

c.c_z_coder12_r#
c.c_z_coder12_r  .1389741 .0609769 2.28 0.023 .0194616 .2584866

c_z_sv_amb_di_r  .1418791 .1084855 1.31 0.191 .0707486 .3545068

c.c_z_sv_amb_di_r#
c.c_z_sv_amb_di_r  .0106288 .0501871 0.21 0.832 .1089937 .0877362

c_z_amb_ev  .2514924 .1086162 2.32 0.021 .0386086 .4643762

c.c_z_amb_ev#c.c_z_amb_ev  .0153864 .0526041 0.29 0.770 .1184885 .0877157

c_z_amb_pri  .1215835 .1303769 0.93 0.351 .1339506 .3771175

c.c_z_amb_pri#c.c_z_amb_pri  .0300072 .0432316 0.69 0.488 .0547252 .1147395

c_sq_age2  .0359767 .0931003 0.39 0.699 .1464964 .2184499
c_ln_fi_total  .1343288 .0637824 2.11 0.035 .2593401 .0093176
c_ln_size_full  .5118246 .2192068 2.33 0.020 .9414621 .0821871
c_sq_up5_r  .4459308 1.165331 0.38 0.702 2.729937 1.838075
c_fi_ex_ratio  4.136125 5.672302 0.73 0.466 6.981382 15.25363
c_factor_cen  .1714061 .1405665 1.22 0.223 .4469115 .1040992
c_factor_pbase  .2743009 .1450345 1.89 0.059 .0099614 .5585632

org_type 
2  .376366 .5685421 0.66 0.508 .7379561 1.490688
3  .1222509 .4832368 0.25 0.800 .8248757 1.069378

year 
2012  .5509363 .2144268 2.57 0.010 .1306675 .9712051
2013  .6018072 .2458745 2.45 0.014 .119902 1.083712
2014  .7005422 .3292841 2.13 0.033 .0551572 1.345927
2015  .7299815 .2984586 2.45 0.014 .1450134 1.31495
2016  .4727062 .3103182 1.52 0.128 .1355062 1.080919
2017  .8041507 .2874125 2.80 0.005 .2408324 1.367469

_cons  .6848513 .4418399 1.55 0.121 1.550842 .181139
+
sigma_u  1.1598991
sigma_e  .87865805
rho  .63538406 (fraction of variance due to u_i)

I'am using the "xtreg" command to run random effects models on panel data (unbalanced panel).
My unit of analysis is Korea government agencies.
My question concerns the "rsquared between" and "rsquared overall".
In model 1, there are no quadratic terms. In model 2, I include 4 quadratic terms.
Though one of these quadratic term is statistically significant, "rsquared between" and "rsquared overall" declines.
As far as I know, rsquared (not adjusted rsquared) is supposed to never decrease when variables are added to a model.
Does this apply differently to panel rsquared?
I know that xtreg, fe calculates rsquared differently from areg. But my model is RE.
I would appreciate any help regarding this issue.
# delimit
xtreg reput c.c_z_coder12_r c.c_z_sv_amb_di_r c.c_z_amb_ev c.c_z_amb_pri
c_sq_age2 c_ln_fi_total c_ln_size_full c_sq_up5_r c_fi_ex_ratio c_factor_cen c_factor_pbase
i.org_type i.year
, re vce(cl org) theta;
# delimit cr
# delimit
xtreg reput c.c_z_coder12_r##c.c_z_coder12_r c.c_z_sv_amb_di_r##c.c_z_sv_amb_di_r c.c_z_amb_ev##c.c_z_amb_ev c.c_z_amb_pri##c.c_z_amb_pri
c_sq_age2 c_ln_fi_total c_ln_size_full c_sq_up5_r c_fi_ex_ratio c_factor_cen c_factor_pbase
i.org_type i.year
, re vce(cl org) theta;
# delimit cr
Randomeffects GLS regression Number of obs = 228
Group variable: org Number of groups = 44
Rsq: Obs per group:
within = 0.0994 min = 1
between = 0.3990 avg = 5.2
overall = 0.3377 max = 7
Wald chi2(19) = 70.29
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
 theta 
min 5% median 95% max
0.3668 0.4993 0.7046 0.7046 0.7046
(Std. Err. adjusted for 44 clusters in org)

 Robust
reput  Coef. Std. Err. z P>z [95% Conf. Interval]
+
c_z_coder12_r  .1582868 .121043 1.31 0.191 .3955268 .0789532
c_z_sv_amb_di_r  .1300482 .0996248 1.31 0.192 .0652129 .3253093
c_z_amb_ev  .2304708 .0934306 2.47 0.014 .0473501 .4135914
c_z_amb_pri  .1374347 .1141718 1.20 0.229 .0863379 .3612073
c_sq_age2  .0527441 .0909437 0.58 0.562 .1255023 .2309906
c_ln_fi_total  .1303679 .0615055 2.12 0.034 .2509165 .0098193
c_ln_size_full  .5278446 .2200759 2.40 0.016 .9591855 .0965037
c_sq_up5_r  .7677916 1.11694 0.69 0.492 2.956955 1.421371
c_fi_ex_ratio  3.959733 5.413107 0.73 0.464 6.649762 14.56923
c_factor_pbase  .2466075 .1336372 1.85 0.065 .0153165 .5085316
c_factor_cen  .1580916 .1283419 1.23 0.218 .4096371 .0934538

org_type 
2  .3448319 .5811616 0.59 0.553 .794224 1.483888
3  .0150424 .4863613 0.03 0.975 .968293 .9382083

year 
2012  .5635269 .2108262 2.67 0.008 .1503152 .9767386
2013  .5536817 .260991 2.12 0.034 .0421486 1.065215
2014  .6628218 .3493855 1.90 0.058 .0219612 1.347605
2015  .7331962 .3281427 2.23 0.025 .0900483 1.376344
2016  .4634112 .3310233 1.40 0.162 .1853825 1.112205
2017  .753503 .2953417 2.55 0.011 .1746438 1.332362

_cons  .4609324 .4146254 1.11 0.266 1.273583 .3517184
+
sigma_u  1.0696963
sigma_e  .8750723
rho  .59908334 (fraction of variance due to u_i)

Randomeffects GLS regression Number of obs = 228
Group variable: org Number of groups = 44
Rsq: Obs per group:
within = 0.1197 min = 1
between = 0.3884 avg = 5.2
overall = 0.3240 max = 7
Wald chi2(23) = 78.44
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
 theta 
min 5% median 95% max
0.3962 0.5278 0.7247 0.7247 0.7247
(Std. Err. adjusted for 44 clusters in org)

 Robust
reput  Coef. Std. Err. z P>z [95% Conf. Interval]
+
c_z_coder12_r  .3011932 .1001225 3.01 0.003 .4974297 .1049568

c.c_z_coder12_r#
c.c_z_coder12_r  .1389741 .0609769 2.28 0.023 .0194616 .2584866

c_z_sv_amb_di_r  .1418791 .1084855 1.31 0.191 .0707486 .3545068

c.c_z_sv_amb_di_r#
c.c_z_sv_amb_di_r  .0106288 .0501871 0.21 0.832 .1089937 .0877362

c_z_amb_ev  .2514924 .1086162 2.32 0.021 .0386086 .4643762

c.c_z_amb_ev#c.c_z_amb_ev  .0153864 .0526041 0.29 0.770 .1184885 .0877157

c_z_amb_pri  .1215835 .1303769 0.93 0.351 .1339506 .3771175

c.c_z_amb_pri#c.c_z_amb_pri  .0300072 .0432316 0.69 0.488 .0547252 .1147395

c_sq_age2  .0359767 .0931003 0.39 0.699 .1464964 .2184499
c_ln_fi_total  .1343288 .0637824 2.11 0.035 .2593401 .0093176
c_ln_size_full  .5118246 .2192068 2.33 0.020 .9414621 .0821871
c_sq_up5_r  .4459308 1.165331 0.38 0.702 2.729937 1.838075
c_fi_ex_ratio  4.136125 5.672302 0.73 0.466 6.981382 15.25363
c_factor_cen  .1714061 .1405665 1.22 0.223 .4469115 .1040992
c_factor_pbase  .2743009 .1450345 1.89 0.059 .0099614 .5585632

org_type 
2  .376366 .5685421 0.66 0.508 .7379561 1.490688
3  .1222509 .4832368 0.25 0.800 .8248757 1.069378

year 
2012  .5509363 .2144268 2.57 0.010 .1306675 .9712051
2013  .6018072 .2458745 2.45 0.014 .119902 1.083712
2014  .7005422 .3292841 2.13 0.033 .0551572 1.345927
2015  .7299815 .2984586 2.45 0.014 .1450134 1.31495
2016  .4727062 .3103182 1.52 0.128 .1355062 1.080919
2017  .8041507 .2874125 2.80 0.005 .2408324 1.367469

_cons  .6848513 .4418399 1.55 0.121 1.550842 .181139
+
sigma_u  1.1598991
sigma_e  .87865805
rho  .63538406 (fraction of variance due to u_i)

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