Pooled OLS, Random Effects and Fixed Effects all giving exact same results!

[Louis James]

Hi there,

I am using a panel data set to investigate the link between inequality and growth.

But I am getting the exact same results for fixed effects, random effects and pooled OLS and have no idea why?! Seems very strange to me.

I have attached photos to show my regression results (for some reason stata was not letting me use ssc install dataex to download example!)

Sigm_u is coming up as zero for random effects (not shown in images). I understand this means there is a negative bias which makes pooled OLS and random effects the same but I would not expect this to make the fixed effects results the same?

Any pointers would be greatly appreciated!

[Carlo Lazzaro]

Louis:
if you have Stata 15, -dataex- comes with it; if you're using an older Stata release, as per FAQ you should tell the list.
That said, what does -hausman- test outcome look like?

[Louis James]

Hi Carlo,

Thanks for your response. I am using stata 15.1.

I have run a Hausman test - results are attached.

Are there any conditions for RE FE and POLS all to give the exact same coefficient estimates?

[Carlo Lazzaro]

Louis:
while is not surprising that OLS with i.panelid gives identical to -xtreg,fe-, a R-sq between in -re- is actually strange.
You may want to test with the user-written command -xtoverid- if the -re- specification fits your data.

[Phil Bromiley]

To add to Carlo's helpful comments, there is something very strange about fe and re giving identical results. It is even stranger since the fe estimate indicates the fixed effects are highly correlated with the regressors, and re imposes the assumption they are not. In addition, the fe indicates the panel effects do matter.

In short, this is not a standard issue of fe-vs-re-vs-pooled choice. There is something screwy with the estimates, and what it is is not clear. As Carlo suggests, it may be worth trying to understand the r-square of 1 for between in the re estimates.

[Louis James]

Thanks for the responses!

When inputting xtoverid into stata I receive the response:

Error - must have ivreg2/ivreg29/ivreg28 version 2.1.15 or greater installed.

Not sure how to amend this?

As this is for my dissertation, the only way I have been able to move forward and present my results in a way I can explain them is by dropping the dummy variable i.countryid. This makes the results all differ in a way I can explain - pooled OLS, fe and re now all yield different results.

Any idea why dropping the country dummy variable causes this?

[Carlo Lazzaro]

Louis:
just install, say, the community-contributed command -ivreg2- (type withinStata -search ivreg2- and install it) before using -xtoverid- and try again.

[Louis James]

Thanks Carlo!

I have tried to input the xtoverid command after installing ivreg2 but now I am getting this response:

"xtoverid not compatible with xtreg model fe"

Any idea why?

[Carlo Lazzaro]

Louis:
the error message is right, in that -xtoverid-, unlike -hausman- can only test whether the -re- specification is right for your data.
Hence, you shoud run -xtreg,re- and then invoke -xtoverid-: if the test outcome does not reach statistical significance, go -re-; otherwise, switch to -fe-.

[Louis James]

I have tried this and got the response:

Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS

How can I interpret this? As the fixed effects results are also identical to POLS does this mean all the results are problematic? Im struggling to see a reason why they are all coming out the same!

[Andrew Musau]

This can happen if you do not have any between variation in your data, which is my guess at what is happening here.

webuse grunfeld, clear
keep if company==1
expand 2
replace company=2 if inrange(_n, 21, 40)
xtreg invest mvalue kstock, fe
xtreg invest mvalue kstock, re
regress invest mvalue kstock

Result:

. xtreg invest mvalue kstock, fe

Fixed-effects (within) regression               Number of obs     =         40
Group variable: company                         Number of groups  =          2

R-sq:                                           Obs per group:
     within  = 0.9214                                         min =         20
     between =      .                                         avg =       20.0
     overall = 0.9214                                         max =         20

                                                F(2,36)           =     210.87
corr(u_i, Xb)  =      .                         Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1192808   .0177528     6.72   0.000     .0832764    .1552852
      kstock |   .3714448   .0254759    14.58   0.000     .3197774    .4231122
       _cons |  -149.7824   72.73303    -2.06   0.047    -297.2918   -2.272972
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  89.195743
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(1, 36) = 0.00                       Prob > F = 1.0000

. xtreg invest mvalue kstock, re

Random-effects GLS regression                   Number of obs     =         40
Group variable: company                         Number of groups  =          2

R-sq:                                           Obs per group:
     within  = 0.0000                                         min =         20
     between = 0.0000                                         avg =       20.0
     overall = 0.9214                                         max =         20

                                                Wald chi2(2)      =     433.46
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1192808   .0175113     6.81   0.000     .0849593    .1536023
      kstock |   .3714448   .0251292    14.78   0.000     .3221924    .4206972
       _cons |  -149.7824   71.74342    -2.09   0.037    -290.3969   -9.167877
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  89.195743
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. regress invest mvalue kstock

      Source |       SS           df       MS      Number of obs   =        40
-------------+----------------------------------   F(2, 37)        =    216.73
       Model |   3355373.3         2  1677686.65   Prob > F        =    0.0000
    Residual |    286411.7        37  7740.85675   R-squared       =    0.9214
-------------+----------------------------------   Adj R-squared   =    0.9171
       Total |     3641785        39  93379.1027   Root MSE        =    87.982

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1192808   .0175113     6.81   0.000     .0837996    .1547621
      kstock |   .3714448   .0251292    14.78   0.000     .3205281    .4223615
       _cons |  -149.7824   71.74342    -2.09   0.044    -295.1484   -4.416419
------------------------------------------------------------------------------

ADDED IN EDIT: I see from your previous posts that you have between R2=1. Same case as above except that your variables across panels are linear combinations of each other. Here is the extension based on my example.

webuse grunfeld, clear
keep if company==1
expand 2
replace company=2 if inrange(_n, 21, 40)
*VARIABLES FOR COMPANY 2 ARE (2*COMPANY 1)
foreach var in invest mvalue kstock{
replace `var'= `var'*2 if inrange(_n, 21, 40)
}
xtreg invest mvalue kstock, re
regress invest mvalue kstock

Result:

. xtreg invest mvalue kstock, re

Random-effects GLS regression                   Number of obs     =         40
Group variable: company                         Number of groups  =          2

R-sq:                                           Obs per group:
     within  = 0.9174                                         min =         20
     between = 1.0000                                         avg =       20.0
     overall = 0.9391                                         max =         20

                                                Wald chi2(2)      =     570.98
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .0930732   .0102064     9.12   0.000     .0730689    .1130775
      kstock |   .3805043   .0256835    14.82   0.000     .3301656     .430843
       _cons |  -63.11561   62.71374    -1.01   0.314    -186.0323    59.80105
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  141.03085
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. regress invest mvalue kstock

      Source |       SS           df       MS      Number of obs   =        40
-------------+----------------------------------   F(2, 37)        =    285.49
       Model |  12022292.4         2  6011146.22   Prob > F        =    0.0000
    Residual |  779053.301        37  21055.4946   R-squared       =    0.9391
-------------+----------------------------------   Adj R-squared   =    0.9359
       Total |  12801345.7        39  328239.635   Root MSE        =    145.11

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .0930732   .0102064     9.12   0.000      .072393    .1137534
      kstock |   .3805043   .0256835    14.82   0.000     .3284647    .4325439
       _cons |  -63.11561   62.71374    -1.01   0.321    -190.1857    63.95449
------------------------------------------------------------------------------

[Karaca ali]

Hi everyone,

I am kind of dealing with same problem and could not solve it. I am working on panel data analysis. However, OLS and random effects coefficients are the same. I know there is a problem but do not know what and how to solve it.

Here are my results for OLS, LSDV (OLS with dummies), fixed effects model, and random effects model;

1-) linear regression (OLS)

. asdoc regress AERY MktRF SMB HML RMW CMA Mom, replace


Source | SS df MS Number of obs = 66
-------------+---------------------------------- F(6, 59) = 5416.37
Model | 29128.9313 6 4854.82188 Prob > F = 0.0000
Residual | 52.8831237 59 .89632413 R-squared = 0.9982
-------------+---------------------------------- Adj R-squared = 0.9980
Total | 29181.8144 65 448.950991 Root MSE = .94674

------------------------------------------------------------------------------
AERY | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
MktRF | 1.001499 .0081823 122.40 0.000 .9851261 1.017872
SMB | .4192452 .0171385 24.46 0.000 .3849511 .4535394
HML | .0470112 .016713 2.81 0.007 .0135686 .0804539
RMW | .0168759 .0247946 0.68 0.499 -.0327379 .0664897
CMA | .0038372 .0201636 0.19 0.850 -.0365101 .0441845
Mom | .0128932 .006925 1.86 0.068 -.0009637 .0267501
_cons | -.1946927 .1818611 -1.07 0.289 -.5585959 .1692106
------------------------------------------------------------------------------

2-) OLS with dummies (LSDV)

. asdoc regress AERY MktRF SMB HML RMW CMA Mom D2 D3 D4 D5 D6, replace

Source | SS df MS Number of obs = 66
-------------+---------------------------------- F(11, 54) = 3139.43
Model | 29136.2543 11 2648.75039 Prob > F = 0.0000
Residual | 45.5600888 54 .843705347 R-squared = 0.9984
-------------+---------------------------------- Adj R-squared = 0.9981
Total | 29181.8144 65 448.950991 Root MSE = .91853

------------------------------------------------------------------------------
AERY | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
MktRF | 1.00382 .0084108 119.35 0.000 .9869576 1.020683
SMB | .4114549 .0188748 21.80 0.000 .3736132 .4492967
HML | .0545304 .0191644 2.85 0.006 .0161082 .0929526
RMW | .014417 .0262901 0.55 0.586 -.0382916 .0671256
CMA | .0029491 .0210127 0.14 0.889 -.039179 .0450771
Mom | .0134288 .0075123 1.79 0.079 -.0016324 .0284901
D2 | -.5252351 .3938701 -1.33 0.188 -1.314897 .264427
D3 | .3736749 .4112653 0.91 0.368 -.4508623 1.198212
D4 | .3567764 .4165184 0.86 0.395 -.4782927 1.191846
D5 | .3522308 .4256779 0.83 0.412 -.5012021 1.205664
D6 | -.2605524 .4363413 -0.60 0.553 -1.135364 .6142594
_cons | -.2455959 .3246247 -0.76 0.453 -.8964293 .4052375
------------------------------------------------------------------------------


3-) Fixed Effects Model

. asdoc xtreg AERY MktRF SMB HML RMW CMA Mom, fe, replace

Fixed-effects (within) regression Number of obs = 66
Group variable: Reg Number of groups = 6

R-sq: Obs per group:
within = 0.9984 min = 11
between = 0.9675 avg = 11.0
overall = 0.9982 max = 11

F(6,54) = 5720.94
corr(u_i, Xb) = -0.0450 Prob > F = 0.0000

------------------------------------------------------------------------------
AERY | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
MktRF | 1.00382 .0084108 119.35 0.000 .9869576 1.020683
SMB | .4114549 .0188748 21.80 0.000 .3736132 .4492967
HML | .0545304 .0191644 2.85 0.006 .0161082 .0929526
RMW | .014417 .0262901 0.55 0.586 -.0382916 .0671256
CMA | .0029491 .0210127 0.14 0.889 -.039179 .0450771
Mom | .0134288 .0075123 1.79 0.079 -.0016324 .0284901
_cons | -.1961135 .1790362 -1.10 0.278 -.5550595 .1628325
-------------+----------------------------------------------------------------
sigma_u | .37948838
sigma_e | .91853435
rho | .14580235 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(5, 54) = 1.74 Prob > F = 0.1421


4-) Random Effects Model

. asdoc xtreg AERY MktRF SMB HML RMW CMA Mom, re, replace

Random-effects GLS regression Number of obs = 66
Group variable: Reg Number of groups = 6

R-sq: Obs per group:
within = 0.9984 min = 11
between = 0.9709 avg = 11.0
overall = 0.9982 max = 11

Wald chi2(6) = 32498.21
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
AERY | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
MktRF | 1.001499 .0081823 122.40 0.000 .9854618 1.017536
SMB | .4192452 .0171385 24.46 0.000 .3856543 .4528361
HML | .0470112 .016713 2.81 0.005 .0142544 .0797681
RMW | .0168759 .0247946 0.68 0.496 -.0317205 .0654723
CMA | .0038372 .0201636 0.19 0.849 -.0356827 .0433572
Mom | .0128932 .006925 1.86 0.063 -.0006795 .0264659
_cons | -.1946927 .1818611 -1.07 0.284 -.5511339 .1617486
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .91853435
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------

Thank you

[Karaca ali]

Numbers are don't look okay. here is the word version


1-) Linear regression

AERY	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
MktRF	1.001		.008	122.40		0	.985		1.018		***
SMB	.419		.017	24.46		0	.385		.454		***
HML	.047		.017	2.81		.007	.014		.08		***
RMW	.017		.025	0.68		.499	-.033		.066
CMA	.004		.02	0.19		.85	-.037		.044
Mom	.013		.007	1.86		.068	-.001		.027		*
Constant	-.195		.182	-1.07		.289	-.559		.169
Mean dependent var		12.480			SD dependent var			21.188
R-squared		0.998			Number of obs			66.000
F-test		5416.369			Prob > F			0.000
Akaike crit. (AIC)		186.676			Bayesian crit. (BIC)			202.004
*** p<.01, ** p<.05, * p<.1
2-) Linear regression (linear square dummy variable) LSDV AERY Coef. St.Err. t-value p-value [95% Conf Interval] Sig MktRF 1.004 .008 119.35 0 .987 1.021 *** SMB .411 .019 21.80 0 .374 .449 *** HML .055 .019 2.85 .006 .016 .093 *** RMW .014 .026 0.55 .586 -.038 .067 CMA .003 .021 0.14 .889 -.039 .045 Mom .013 .008 1.79 .079 -.002 .028 * D2 -.525 .394 -1.33 .188 -1.315 .264 D3 .374 .411 0.91 .368 -.451 1.198 D4 .357 .417 0.86 .395 -.478 1.192 D5 .352 .426 0.83 .412 -.501 1.206 D6 -.261 .436 -0.60 .553 -1.135 .614 Constant -.246 .325 -0.76 .453 -.896 .405 Mean dependent var 12.480 SD dependent var 21.188 R-squared 0.998 Number of obs 66.000 F-test 3139.426 Prob > F 0.000 Akaike crit. (AIC) 186.839 Bayesian crit. (BIC) 213.115 *** p<.01, ** p<.05, * p<.1 3-) Regression results (xtreg, ………………..., fe) Fixed effects Model AERY Coef. St.Err. t-value p-value [95% Conf Interval] Sig MktRF 1.004 .008 119.35 0 .987 1.021 *** SMB .411 .019 21.80 0 .374 .449 *** HML .055 .019 2.85 .006 .016 .093 *** RMW .014 .026 0.55 .586 -.038 .067 CMA .003 .021 0.14 .889 -.039 .045 Mom .013 .008 1.79 .079 -.002 .028 * Constant -.196 .179 -1.10 .278 -.555 .163 Mean dependent var 12.480 SD dependent var 21.188 R-squared 0.998 Number of obs 66.000 F-test 5720.938 Prob > F 0.000 Akaike crit. (AIC) 176.839 Bayesian crit. (BIC) 192.166 *** p<.01, ** p<.05, * p<.1 4-) Regression results (xtreg, ………………..., re) Random effects Model AERY Coef. St.Err. t-value p-value [95% Conf Interval] Sig MktRF 1.001 .008 122.40 0 .985 1.018 *** SMB .419 .017 24.46 0 .386 .453 *** HML .047 .017 2.81 .005 .014 .08 *** RMW .017 .025 0.68 .496 -.032 .065 CMA .004 .02 0.19 .849 -.036 .043 Mom .013 .007 1.86 .063 -.001 .026 * Constant -.195 .182 -1.07 .284 -.551 .162 Mean dependent var 12.480 SD dependent var 21.188 Overall r-squared 0.998 Number of obs 66.000 Chi-square 32498.212 Prob > chi2 0.000 R-squared within 0.998 R-squared between 0.971 *** p<.01, ** p<.05, * p<.1

[Chinmay Korgaonkar]

Hello. I was getting the exact same error. My mistake was that I was using

 xtset Time_variable Panel_variable

instead of

 xtset Panel_variable Time_variable

.