Random Effects & Pooled OLS results the same in panel data analysis

[Andrew Fisher]

Hi,

This is my first post here and I'm relatively new to stata. I'm doing some panel data analysis and my fixed effect, random effects and pooled ols results are all relatively similar (although RE & OLS are identical). Why might this be the case and how can I correct for it?

[Clyde Schechter]

It might just be that there isn't much variation by panel. Or, you might be doing something wrong. Without seeing the actual output, it's really impossible to say. Please show the exact commands you gave and the exact response you got from Stata. To insure readability and fidelity, do this by copying from the Results window or your log file to the clipboard and then paste that into a code block on the Forum. If you don't know how to set up a code block, see FAQ #12, 7th paragraph for instructions. Please do not edit or in any way modify. There are no unimportant details.

[Jeff Wooldridge]

If you have some variables that change over time, and RE and POLS are identical, I suspect it is because there is negative serial correlation in the residuals. For example, maybe the dependent and/or independent variables are differences. In any case, when a negative variance is estimated for the unobserved effect, Stata sets it to zero. Which means RE becomes pooled OLS.

But like Clyde said, seeing the Stata output would help a lot.

[Andrew Fisher]

Apologies for the delay - I did not have access to Stata.

Here's the output:

. xtset countryp year
       panel variable:  countryp (strongly balanced)
        time variable:  year, 1970 to 2005, but with gaps
                delta:  1 unit

. xtreg growth giniincome schoolyrs gdpus2005

Random-effects GLS regression                   Number o
> f obs     =        368
Group variable: countryp                        Number o
> f groups  =         46

R-sq:                                           Obs per 
> group:
     within  = 0.3320                                   
>       min =          8
     between = 0.0211                                   
>       avg =        8.0
     overall = 0.0556                                   
>       max =          8

                                                Wald chi
> 2(3)      =     135.61
corr(u_i, X)   = 0 (assumed)                    Prob > c
> hi2       =     0.0000

--------------------------------------------------------
> ----------------------
      growth |      Coef.   Std. Err.      z    P>|z|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
  giniincome |  -.0119427   .0100119    -1.19   0.233   
>  -.0315658                                            
>               .0076803
   schoolyrs |   .1711932   .0304771     5.62   0.000   
>   .1114592                                            
>               .2309272
   gdpus2005 |  -.0000927   8.20e-06   -11.30   0.000   
>  -.0001088                                            
>              -.0000766
       _cons |   2.668791   .4849675     5.50   0.000   
>   1.718273                                            
>                3.61931
-------------+------------------------------------------
> ----------------------
     sigma_u |  1.1781187
     sigma_e |  .65951429
         rho |  .76139466   (fraction of variance due to
>  u_i)
--------------------------------------------------------
> ----------------------

. xtreg growth giniincome schoolyrs gdpus2005

Random-effects GLS regression                   Number o
> f obs     =        368
Group variable: countryp                        Number o
> f groups  =         46

R-sq:                                           Obs per 
> group:
     within  = 0.3320                                   
>       min =          8
     between = 0.0211                                   
>       avg =        8.0
     overall = 0.0556                                   
>       max =          8

                                                Wald chi
> 2(3)      =     135.61
corr(u_i, X)   = 0 (assumed)                    Prob > c
> hi2       =     0.0000

--------------------------------------------------------
> ----------------------
      growth |      Coef.   Std. Err.      z    P>|z|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
  giniincome |  -.0119427   .0100119    -1.19   0.233   
>  -.0315658                                            
>               .0076803
   schoolyrs |   .1711932   .0304771     5.62   0.000   
>   .1114592                                            
>               .2309272
   gdpus2005 |  -.0000927   8.20e-06   -11.30   0.000   
>  -.0001088                                            
>              -.0000766
       _cons |   2.668791   .4849675     5.50   0.000   
>   1.718273                                            
>                3.61931
-------------+------------------------------------------
> ----------------------
     sigma_u |  1.1781187
     sigma_e |  .65951429
         rho |  .76139466   (fraction of variance due to
>  u_i)
--------------------------------------------------------
> ----------------------

. xtreg growth giniincome schoolyrs gdpus2005, fe

Fixed-effects (within) regression               Number o
> f obs                                                 
>           =                                           
>                    368
Group variable: countryp                        Number o
> f groups                                              
>           =                                           
>                     46

R-sq:                                           Obs per 
> group:
     within  = 0.3341                                   
>       min                                             
>           =                                           
>                      8
     between = 0.0161                                   
>       avg                                             
>           =                                           
>                    8.0
     overall = 0.0488                                   
>       max                                             
>           =                                           
>                      8

                                                F(3,319)
>           =                                           
>                  53.35
corr(u_i, Xb)  = -0.5255                        Prob > F
>           =                                           
>                 0.0000

--------------------------------------------------------
> ----------------------
      growth |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
  giniincome |  -.0130093   .0113308    -1.15   0.252   
>  -.0353018                                            
>               .0092832
   schoolyrs |   .2248358    .032007     7.02   0.000   
>   .1618643                                            
>               .2878073
   gdpus2005 |  -.0001077   8.87e-06   -12.14   0.000   
>  -.0001251                                            
>              -.0000902
       _cons |   2.523526   .4884427     5.17   0.000   
>    1.56255                                            
>               3.484502
-------------+------------------------------------------
> ----------------------
     sigma_u |  1.4849086
     sigma_e |  .65951429
         rho |  .83523732   (fraction of variance due to
>  u_i)
--------------------------------------------------------
> ----------------------
F test that all u_i=0: F(45, 319) = 27.22               
>      Prob > F = 0.0000

. xtreg growth giniincome schoolyrs gdpus2005, re

Random-effects GLS regression                   Number o
> f obs     =        368
Group variable: countryp                        Number o
> f groups  =         46

R-sq:                                           Obs per 
> group:
     within  = 0.3320                                   
>       min =          8
     between = 0.0211                                   
>       avg =        8.0
     overall = 0.0556                                   
>       max =          8

                                                Wald chi
> 2(3)      =     135.61
corr(u_i, X)   = 0 (assumed)                    Prob > c
> hi2       =     0.0000

--------------------------------------------------------
> ----------------------
      growth |      Coef.   Std. Err.      z    P>|z|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
  giniincome |  -.0119427   .0100119    -1.19   0.233   
>  -.0315658                                            
>               .0076803
   schoolyrs |   .1711932   .0304771     5.62   0.000   
>   .1114592                                            
>               .2309272
   gdpus2005 |  -.0000927   8.20e-06   -11.30   0.000   
>  -.0001088                                            
>              -.0000766
       _cons |   2.668791   .4849675     5.50   0.000   
>   1.718273                                            
>                3.61931
-------------+------------------------------------------
> ----------------------
     sigma_u |  1.1781187
     sigma_e |  .65951429
         rho |  .76139466   (fraction of variance due to
>  u_i)
--------------------------------------------------------
> ----------------------

. xtreg growth giniincome schoolyrs gdpus2005, re vce (r
> obust)

Random-effects GLS regression                   Number o
> f obs     =        368
Group variable: countryp                        Number o
> f groups  =         46

R-sq:                                           Obs per 
> group:
     within  = 0.3320                                   
>       min =          8
     between = 0.0211                                   
>       avg =        8.0
     overall = 0.0556                                   
>       max =          8

                                                Wald chi
> 2(3)      =      50.32
corr(u_i, X)   = 0 (assumed)                    Prob > c
> hi2       =     0.0000

                              (Std. Err. adjusted for 46
>  clusters in countryp)
--------------------------------------------------------
> ----------------------
             |               Robust
      growth |      Coef.   Std. Err.      z    P>|z|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
  giniincome |  -.0119427   .0211862    -0.56   0.573   
>  -.0534669                                            
>               .0295815
   schoolyrs |   .1711932    .059544     2.88   0.004   
>    .054489                                            
>               .2878974
   gdpus2005 |  -.0000927   .0000142    -6.51   0.000   
>  -.0001206                                            
>              -.0000648
       _cons |   2.668791   .8338707     3.20   0.001   
>   1.034435                                            
>               4.303148
-------------+------------------------------------------
> ----------------------
     sigma_u |  1.1781187
     sigma_e |  .65951429
         rho |  .76139466   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Clyde Schechter]

Well, thank you for showing us more detail. But what you've posted doesn't correspond to your question in #1. You have shown us the results of the random effects model three times. Stuck in the middle, there are the results for the fixed-effects regression, which are largely similar, as is often the case. Your original question was about the random effects model showing exactly the same results as OLS, but you don't show us the OLS results, so we can't comment on that. Suffice it to say that given the high value of rho, it is highly implausible that an OLS run on this same model will produce the same results that the random effects model did: it suggests you made a mistake of some kind with the OLS, but we can't say more without seeing that.

Finally you show us the results of the random effects model with robust VCE. As expected, this produces exactly the same coefficient estimates as random effects with ordinary VCE, but different standard errors--that's what robust VCE does. But you never even mentioned this analysis in your original question, so I'm wondering why you have posted it here.

[Carlo Lazzaro]

Andew:
I agree with all previos comments.
Just an aside: the significance of the F-test at the foot of the -xtreg,fe- outcome table rules out POLS.

[Stefano Alderighi]

Sorry to reopen this post, but the situation described below by Jeff just happened to me:

If you have some variables that change over time, and RE and POLS are identical, I suspect it is because there is negative serial correlation in the residuals. For example, maybe the dependent and/or independent variables are differences. In any case, when a negative variance is estimated for the unobserved effect, Stata sets it to zero. Which means RE becomes pooled OLS.

That is, when running a pooled and a RE model, the two models give exactly the same results. Sigma_u is indeed set to zero in the RE model.

Is there a way around this? How do I estimate a RE model for this specification? And how do I detect whether it's because of the dependent variable, or whether some regressor is causing it?

I think my question does not require reporting any coding, I am in a typical situation as below:

reg y x1 x2 x3

xtreg y x1 x2 x3, re

But if you need anything more than this, happy to show my stata codes.

Thanks so much.

[Carlo Lazzaro]

Stefano:
as usual, seeing Stata output will help.
That said, I do not think that you should find any work-around: as per your data pooled OLS is one among the possible states of the world.

[Stefano Alderighi]

Here is my output:


. use database, clear
. preserve

.
. replace orderimb = orderimb/10000000
(2,655 real changes made)

.
. reg orderimb ///
> debt_GDP save_GDP export_GDP GDPg real_int sd_erate* ///
> danni* dmesi* ///
> Cap Capsq ForList DomList number_ETFs ETFsq number_DRs ///
> returns volatility ///
> returns_cac40 returns_ftse ///
> returns_dj VIX ///
> returns_MSCI_EM returns_MSCIFrontier ///
> correlation_dj correlation_cac40 correlation_ftse
note: danni13 omitted because of collinearity
note: dmesi9 omitted because of collinearity

Source | SS df MS Number of obs = 2,248
-------------+---------------------------------- F(49, 2198) = 7.46
Model | 2243982.23 49 45795.5558 Prob > F = 0.0000
Residual | 13500041.2 2,198 6141.96595 R-squared = 0.1425
-------------+---------------------------------- Adj R-squared = 0.1234
Total | 15744023.4 2,247 7006.68598 Root MSE = 78.371

--------------------------------------------------------------------------------------
orderimbalance_usd | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
debt_GDP | .222624 .0642685 3.46 0.001 .0965906 .3486574
save_GDP | .5229846 .319304 1.64 0.102 -.1031845 1.149154
export_GDP | -.088665 .1071196 -0.83 0.408 -.2987312 .1214013
GDPgrowth | 30.07946 31.8514 0.94 0.345 -32.38253 92.54145
real_interest | -376.5329 231.9006 -1.62 0.105 -831.3001 78.23434
sd_erate_eur_local | .0544178 .5065307 0.11 0.914 -.9389111 1.047747
sd_erate_gbp_local | -.0504349 .4447534 -0.11 0.910 -.9226158 .821746
sd_erate_usd_local | .1738648 .6477234 0.27 0.788 -1.096349 1.444079
danni1 | 30.80424 15.51111 1.99 0.047 .3862698 61.22222
danni2 | 14.99537 14.80921 1.01 0.311 -14.04614 44.03687
danni3 | 24.6064 15.92751 1.54 0.123 -6.628143 55.84094
danni4 | 14.27155 15.96148 0.89 0.371 -17.02962 45.57271
danni5 | 22.59426 14.50741 1.56 0.120 -5.855409 51.04392
danni6 | .1094486 14.39828 0.01 0.994 -28.12622 28.34511
danni7 | 21.02187 13.86401 1.52 0.130 -6.166061 48.2098
danni8 | 17.50801 13.82934 1.27 0.206 -9.61193 44.62796
danni9 | 21.47281 13.60663 1.58 0.115 -5.210387 48.156
danni10 | 8.387162 13.44896 0.62 0.533 -17.98684 34.76117
danni11 | -.3265862 13.54149 -0.02 0.981 -26.88204 26.22887
danni12 | -5.926994 13.38611 -0.44 0.658 -32.17775 20.32376
danni13 | 0 (omitted)
dmesi1 | 10.54829 8.512255 1.24 0.215 -6.144611 27.2412
dmesi2 | -6.29114 8.223336 -0.77 0.444 -22.41746 9.835182
dmesi3 | 10.62027 8.292123 1.28 0.200 -5.640943 26.88149
dmesi4 | -2.003622 8.457868 -0.24 0.813 -18.58987 14.58263
dmesi5 | -5.771782 8.453353 -0.68 0.495 -22.34918 10.80561
dmesi6 | -9.438484 8.540515 -1.11 0.269 -26.18681 7.309839
dmesi7 | -3.596115 8.519784 -0.42 0.673 -20.30379 13.11156
dmesi8 | -14.13892 8.362565 -1.69 0.091 -30.53828 2.260435
dmesi9 | 0 (omitted)
dmesi10 | -5.762943 8.439636 -0.68 0.495 -22.31344 10.78755
dmesi11 | -9.224132 8.542679 -1.08 0.280 -25.9767 7.528436
dmesi12 | -12.1577 8.496434 -1.43 0.153 -28.81958 4.504178
Cap | 4.30e-12 1.55e-11 0.28 0.782 -2.61e-11 3.47e-11
Capsq | -1.74e-24 8.27e-24 -0.21 0.834 -1.79e-23 1.45e-23
ForList | .2291861 .1490587 1.54 0.124 -.0631246 .5214968
DomList | -.0044051 .0025849 -1.70 0.088 -.0094741 .0006639
number_ETFs | 1.352742 .4235643 3.19 0.001 .5221133 2.18337
ETFsq | -.0217042 .005277 -4.11 0.000 -.0320527 -.0113556
number_DRs | .3473208 .1060765 3.27 0.001 .1393002 .5553414
returns | 234.7997 30.95248 7.59 0.000 174.1006 295.4989
volatility | -365.8186 160.6097 -2.28 0.023 -680.7812 -50.85605
returns_cac40 | -52.65409 70.19708 -0.75 0.453 -190.3136 85.00546
returns_ftse | 180.2156 99.22442 1.82 0.069 -14.36782 374.7991
returns_dj | -68.03225 88.4912 -0.77 0.442 -241.5674 105.5029
VIX | -.0832553 .4268673 -0.20 0.845 -.9203608 .7538501
returns_MSCI_EM | 173.6945 55.08124 3.15 0.002 65.67779 281.7112
returns_MSCIFrontier | 30.19763 58.33422 0.52 0.605 -84.19833 144.5936
correlation_dj | 4.536252 8.351046 0.54 0.587 -11.84052 20.91302
correlation_cac40 | -12.21204 9.574764 -1.28 0.202 -30.98858 6.56449
correlation_ftse | -1.330383 9.528218 -0.14 0.889 -20.01564 17.35487
_cons | -22.71233 17.81487 -1.27 0.202 -57.64808 12.22341
--------------------------------------------------------------------------------------

.
. estimates store pooled

.
.
. xtreg orderimb ///
> debt_GDP save_GDP export_GDP GDPg real_int sd_erate* ///
> danni* dmesi* ///
> Cap Capsq ForList DomList number_ETFs ETFsq number_DRs ///
> returns volatility ///
> returns_cac40 returns_ftse ///
> returns_dj VIX ///
> returns_MSCI_EM returns_MSCIFrontier ///
> correlation_dj correlation_cac40 correlation_ftse ///
> , re
note: danni13 omitted because of collinearity
note: dmesi12 omitted because of collinearity

Random-effects GLS regression Number of obs = 2,248
Group variable: id Number of groups = 20

R-sq: Obs per group:
within = 0.1261 min = 39
between = 0.6157 avg = 112.4
overall = 0.1425 max = 146

Wald chi2(47) = .
corr(u_i, X) = 0 (assumed) Prob > chi2 = .

--------------------------------------------------------------------------------------
orderimbalance_usd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
debt_GDP | .222624 .0642685 3.46 0.001 .09666 .348588
save_GDP | .5229846 .319304 1.64 0.101 -.1028397 1.148809
export_GDP | -.088665 .1071196 -0.83 0.408 -.2986156 .1212856
GDPgrowth | 30.07946 31.8514 0.94 0.345 -32.34813 92.50706
real_interest | -376.5329 231.9006 -1.62 0.104 -831.0497 77.98392
sd_erate_eur_local | .0544178 .5065307 0.11 0.914 -.9383642 1.0472
sd_erate_gbp_local | -.0504349 .4447534 -0.11 0.910 -.9221356 .8212657
sd_erate_usd_local | .1738648 .6477234 0.27 0.788 -1.09565 1.443379
danni1 | 30.80424 15.51111 1.99 0.047 .4030198 61.20547
danni2 | 14.99537 14.80921 1.01 0.311 -14.03014 44.02088
danni3 | 24.6064 15.92751 1.54 0.122 -6.610943 55.82374
danni4 | 14.27155 15.96148 0.89 0.371 -17.01238 45.55547
danni5 | 22.59426 14.50741 1.56 0.119 -5.839743 51.02825
danni6 | .1094486 14.39828 0.01 0.994 -28.11067 28.32956
danni7 | 21.02187 13.86401 1.52 0.129 -6.15109 48.19483
danni8 | 17.50801 13.82934 1.27 0.206 -9.596996 44.61302
danni9 | 21.47281 13.60663 1.58 0.115 -5.195694 48.14131
danni10 | 8.387162 13.44896 0.62 0.533 -17.97232 34.74664
danni11 | -.3265862 13.54149 -0.02 0.981 -26.86742 26.21425
danni12 | -5.926994 13.38611 -0.44 0.658 -32.16329 20.30931
danni13 | 0 (omitted)
dmesi1 | 22.706 8.636455 2.63 0.009 5.778855 39.63314
dmesi2 | 5.866563 8.131505 0.72 0.471 -10.07089 21.80402
dmesi3 | 22.77798 8.495018 2.68 0.007 6.128048 39.42791
dmesi4 | 10.15408 8.431972 1.20 0.228 -6.37228 26.68044
dmesi5 | 6.38592 8.373474 0.76 0.446 -10.02579 22.79763
dmesi6 | 2.719218 8.596298 0.32 0.752 -14.12922 19.56765
dmesi7 | 8.561588 8.308598 1.03 0.303 -7.722965 24.84614
dmesi8 | -1.981219 8.309507 -0.24 0.812 -18.26755 14.30512
dmesi9 | 12.1577 8.496434 1.43 0.152 -4.495003 28.81041
dmesi10 | 6.39476 8.417602 0.76 0.447 -10.10344 22.89296
dmesi11 | 2.933571 8.607229 0.34 0.733 -13.93629 19.80343
dmesi12 | 0 (omitted)
Cap | 4.30e-12 1.55e-11 0.28 0.782 -2.61e-11 3.47e-11
Capsq | -1.74e-24 8.27e-24 -0.21 0.834 -1.79e-23 1.45e-23
ForList | .2291861 .1490587 1.54 0.124 -.0629636 .5213358
DomList | -.0044051 .0025849 -1.70 0.088 -.0094714 .0006611
number_ETFs | 1.352742 .4235643 3.19 0.001 .5225707 2.182912
ETFsq | -.0217042 .005277 -4.11 0.000 -.032047 -.0113613
number_DRs | .3473208 .1060765 3.27 0.001 .1394147 .5552269
returns | 234.7997 30.95248 7.59 0.000 174.134 295.4655
volatility | -365.8186 160.6097 -2.28 0.023 -680.6078 -51.02948
returns_cac40 | -52.65409 70.19708 -0.75 0.453 -190.2378 84.92966
returns_ftse | 180.2156 99.22442 1.82 0.069 -14.26067 374.6919
returns_dj | -68.03225 88.4912 -0.77 0.442 -241.4718 105.4073
VIX | -.0832553 .4268673 -0.20 0.845 -.9198999 .7533892
returns_MSCI_EM | 173.6945 55.08124 3.15 0.002 65.73727 281.6518
returns_MSCIFrontier | 30.19763 58.33422 0.52 0.605 -84.13533 144.5306
correlation_dj | 4.536252 8.351046 0.54 0.587 -11.8315 20.904
correlation_cac40 | -12.21204 9.574764 -1.28 0.202 -30.97824 6.55415
correlation_ftse | -1.330383 9.528218 -0.14 0.889 -20.00535 17.34458
_cons | -34.87004 17.26604 -2.02 0.043 -68.71085 -1.029223
---------------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | 77.481641
rho | 0 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------

. estimates store RE

.
. restore

Carlo: what you're suggesting is that in this case RE is simply reducing to a pooled OLS estimator, therefore there's not anything wrong with that? I understood it was because of Stata somewhat artificially setting sigma_u = 0, while in fact it might be estimated otherwise.

Thanks for your help!

[Carlo Lazzaro]

Stefano:
some comments about your query:
1) please use CODe delimiters to post your Stata outputs (otherwise your results are hardly readable);
2) a pooled OLS needs clustered standard errors (otherwise you pretend you have independent observations whereas it is not the case due to the panel structure of your data). This won't affect coefficients;
3) I'm not clear why you created categorical variables by hand (-danni-[year dummies]; -dmesi-[month dummies]; by the way: why including both of them? how did you -xtset- your data?) instead of relying on the wonderful capabilities of -fvvarlist-. By the way, I'm also not sure that your data are in -lomg-format;
4) you seemingly have 2,248 observations and 20 groups; hence your time variable should be about 2,248/20=112,4 (months?). If that were the case you would deal with a T>N panel dataset; hence, you should switch to -xtgls- (in such a long T panel dataset, autocorrelation surely needs attention).

[Stefano Alderighi]

Thanks Carlo, let me respond to you:

1) Sorry for this, will keep that in mind;

2) Thanks for suggesting; as it does not affect the coefficient, I did not put the clustering in the code I reported; in my analyses I am surely clustering the standard errors!

3) My time variable is monthly as you noted. The monthly dummies you see are January, February etc... that is, they would be equal to 1 for Jan 2006, Jan 2007 etc. I am introducing these variables to capture "monthly regularities", that is to strip out whether the dependent variable regularly behaves in a similar way on depending in the month. As I am studying stock market trading, this might be the case if most markets I am studying have concomitant fiscal-year ends; I am using dummies as I am exporting using esttab, and would like to indicate yes/no in the table without reporting coefficients. Using i.variable on categorical variables creates problems with the subcommand indicate in esttab: any way around it?

4) Interesting. Thanks so much for this. I thought that clustering would be enough, and wasn't aware of this command: let me go and try that out!

Going back to the original question, in a nutshell, should I consider the RE model collapsed on a pooled as valid?

[Carlo Lazzaro]

Stefano:
3) if you plug in monthly and yearly dummies by hand, you should omit one of them to avoid the so called dummy trap; Stata does it by default omitting one dummy for month and for year due to collibneraity. This way, however, you have no control on which dummy to omit. Best off if you rely on the wonderfful capabilities of -fvvarlist-. That said, from a more substantive side, I would test whether you monthly and yearly dummies are jointly significant (see -testparm-).

Going back to the original question: pooled OLS (reminder: with clustered standard errors) is consistent in the RE model (but not in the FE one), as RE requires that both the components of the error terms are uncorrelated with the vector of the regressors (and this is the same prerequisite of OLS, event though focused on idiosincratic error only in this case). However, if RE were the way to go, I would not consider switching to pooled OLS.

[huk hyung jung]

If you have some variables that change over time, and RE and POLS are identical, I suspect it is because there is negative serial correlation in the residuals. For example, maybe the dependent and/or independent variables are differences. In any case, when a negative variance is estimated for the unobserved effect, Stata sets it to zero. Which means RE becomes pooled OLS.

But like Clyde said, seeing the Stata output would help a lot.

Hi Jeff, I am facing this problem in my analysis (negative serial correlation, causing OLS = RE). I read that this problem can be a consequence of relevant variable omission, but if I ignore this my analysis will be prejudiced?

ps: Through the tests, the model chosen was random effect model

Thanks!

[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

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

[Carlo Lazzaro]

Karaca:
are you sure that you have a panel-wise effect?
What does -xttest0- after -xtreg,re- give you back?
That said, please do not urge privately potentially interested listers to reply to your queries : we're all busy persons (like you) and, from time to time, may well have dynamic priorities settings that rank replying to Stata queries in the middle instead of at the top of the list. Thanks.