Random Effects versus OLS Prob > chibar2 = 1.0000

[amira elshal]

Dear Sirs,

To test for random effects, I ran the Breusch and Pagan Lagrangian multiplier test for random effects. I got the results below although I did not difference my data. Prob > chibar2 = 1.0000 because u = 0. Please advise on how I shall proceed.

Breusch and Pagan Lagrangian multiplier test for random effects

childmort[id,t] = Xb + u[id] + e[id,t]

Estimated results:
Var sd = sqrt(Var)
---------+-----------------------------
childmort 17.83105 4.222683
e 17.64855 4.201018
u 0 0

Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000

Thank you.

Kind regards,
Amira

[Carlo Lazzaro]

Amira:
failing to reject the null of xttest0- means that you should go OLS (please, see http://www.stata.com/statalist/archi.../msg00011.html).

[Salem Abdussalam]

I quote from Carlo's above link ".......The null for xttest0 is var(u) = 0. If that was the case then there are no random effects. A significant result rejects var(u)=0 in favor of var(u) > 0, in which case the pooled OLS model that assumes that the error process has vce = \sigma^2 I_{NT} is not the appropriate model. So a rejection (significant test result) implies that you should NOT use OLS."

The question is; since the OLS estimation (as mentioned in the answer above) is NOT the appropriate estimator according to the BP test, and the Fixed Effects model is preferred over the Random Effects model according to the HAUSMAN test, DOES this mean that the Fixed Effects model is the most appropriate model over both the Random Effects and OLS estimations?

[Carlo Lazzaro]

Salem:
yes, in that instance the -fe- specification outperforms both -re- specification and (pooled) OLS.

[Karim Syed]

Dear Carlo

I am encountering the same problem as mentioned by Amera in #1 above. SO I chose OLS over RE. But, when I run the hausman test to select between RE and FE models, the results shows :

Test: Ho: difference in coefficients not systematic
chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -2.18 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test.

How should I proceed?

Thanks.

PS. Technically, if the RE model is already rejected in xttest0, why should we still apply hausman to choose between RE and FE? Shouldn't we apply some test to choose beltween pooled OLS and FE?

[Jeff Wooldridge]

I'm suspicious of the original outcome, as it means you had such strong negative serial correlation in the residuals that the estimated variance component was negative. This can happen, but usually only after the data have already been differenced.

I disagree with Carlo about the interpretation of the xttest0. The test is practically useless, and I'm not sure how it ever got used for choosing between OLS and RE. The Breusch-Pagan statistic tests for the presence of positive serial correlation in the composite error term. That's all it does. It can reject for, say, AR(1) serial correlation. It could fail to reject if u(i) is present but e(i,t) has strong negative serial correlation. Importantly, it is never a test of whether OLS is consistent because the presence of u(i) does not cause inconsistency in OLS unless it is correlated with the x(i,t). The BP test is silent on that.

If you show your full set of results I might be able to help. For the RE versus FE problem, use the -sigmamore- option. If you'd shown us your output I could see exactly what you did. Please do so in the future, as is suggested in the site guidelines.

[Carlo Lazzaro]

Jeff.
thanks for correcting me.

[Karim Syed]

Thank you Dear Sir Jeff and Carlo for your feedback.

Here are the details about my econometric model which I am running.

Dit - Dit-1=Bo + B1pos_devit + B2neg_devit

Where
Dit = dividend per share for firm i in year t

pos_dev = Dit*-Dit-1 (i.e. the difference between the desired dividend (Dit*), and the actual dividend paid in last period (Dit-1)). pos_dev is equal to Dit*-Dit-1 if difference is positive, and 0 otherwise.

neg_dev = Dit*-Dit-1 (i.e. the difference between the desired dividend (Dit*), and the actual dividend paid in last period (Dit-1)). neg_dev is equal to Dit*-Dit-1 if difference is negative, and 0 otherwise.

Sorry for delayed response.
Thanks
Karim

[Jeff Wooldridge]

Yes, so as I suspected, you're applying RE to a differenced dependent variable. RE often is inappropriate here because the differences often have negative serial correlation, which can cause problems. You estimated the variance to be zero. Did you notice your OLS and RE estimates were identical?

I would just use pooled OLS. I'm not even sure using firm fixed effects makes sense here. Besides, the strict exogeneity assumption used for FE is almost certainly violated.

[Karim Syed]

Thanks dear Prof. for the feedback. True, my RE and OLS estimates are perfectly identical. So, I go ahead with using the pooled OLS.

For my reading and deeper understanding, may I ask you for a book or article (yours or anyone else's) discussing the above issue directly in detail?

Thanks and regards
Karim

[Nikki Sehmi]

Dear Sirs,

I am encountering the same problem as mentioned by Amira in #1 above. I have performed the Hausman test and it is insignificant. Please see the file attached ( reg.txt ) and advise me on which model I should use i.e. RE model or OLS Pooled model.
Your help is appreciated.

Kind regards
Nikki

[Khaled Ali]

Hell Every one

I run my analysis and the results as follow: But i dint know which model should i use???? i asking for help

regress ChangeDti Eti EtiMAN EtiINS PeviousDti size lev logmtbv logfcf

Source | SS df MS Number of obs = 136
-------------+------------------------------ F( 8, 127) = 3.17
Model | .618809308 8 .077351163 Prob > F = 0.0026
Residual | 3.0942177 127 .024363919 R-squared = 0.1667
-------------+------------------------------ Adj R-squared = 0.1142
Total | 3.713027 135 .027503904 Root MSE = .15609

------------------------------------------------------------------------------
ChangeDti | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Eti | .3737799 .2065007 1.81 0.073 -.0348477 .7824075
EtiMAN | -.0524488 .1444275 -0.36 0.717 -.3382447 .2333471
EtiINS | -.130822 .210914 -0.62 0.536 -.5481828 .2865388
PeviousDti | .2007018 .1805979 1.11 0.269 -.1566687 .5580724
size | .026784 .0289639 0.92 0.357 -.0305304 .0840983
lev | .0016954 .0176075 0.10 0.923 -.0331466 .0365375
logmtbv | .0134619 .0201648 0.67 0.506 -.0264406 .0533643
logfcf | -.0173324 .0244344 -0.71 0.479 -.0656836 .0310189
_cons | -.249956 .2594098 -0.96 0.337 -.7632812 .2633691
------------------------------------------------------------------------------

. xtset code year
panel variable: code (strongly balanced)
time variable: year, 2011 to 2017
delta: 1 unit

.
. xtreg ChangeDti Eti EtiMAN EtiINS PeviousDti size lev logmtbv logfcf, fe

Fixed-effects (within) regression Number of obs = 136
Group variable: code Number of groups = 32

R-sq: within = 0.0718 Obs per group: min = 1
between = 0.6002 avg = 4.3
overall = 0.1209 max = 7

F(8,96) = 0.93
corr(u_i, Xb) = -0.7317 Prob > F = 0.4975

------------------------------------------------------------------------------
ChangeDti | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Eti | .3530723 .3475552 1.02 0.312 -.3368193 1.042964
EtiMAN | -.0115504 .262677 -0.04 0.965 -.5329601 .5098592
EtiINS | -.0814929 .3794769 -0.21 0.830 -.8347486 .6717628
PeviousDti | .2600728 .2732491 0.95 0.344 -.2823225 .802468
size | .0521376 .0883208 0.59 0.556 -.1231778 .227453
lev | .0085421 .0248351 0.34 0.732 -.0407553 .0578394
logmtbv | .0125207 .0335897 0.37 0.710 -.0541543 .0791957
logfcf | .0122173 .0442946 0.28 0.783 -.0757069 .1001415
_cons | -1.127436 1.462421 -0.77 0.443 -4.030319 1.775446
-------------+----------------------------------------------------------------
sigma_u | .09705118
sigma_e | .17055108
rho | .24460561 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(31, 96) = 0.33 Prob > F = 0.9995

. estimates store Fixed

. xtreg ChangeDti Eti EtiMAN EtiINS PeviousDti size lev logmtbv logfcf, re

Random-effects GLS regression Number of obs = 136
Group variable: code Number of groups = 32

R-sq: within = 0.0591 Obs per group: min = 1
between = 0.8094 avg = 4.3
overall = 0.1667 max = 7

Wald chi2(8) = 25.40
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0013

------------------------------------------------------------------------------
ChangeDti | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Eti | .3737799 .2065007 1.81 0.070 -.030954 .7785139
EtiMAN | -.0524488 .1444275 -0.36 0.716 -.3355214 .2306238
EtiINS | -.130822 .210914 -0.62 0.535 -.5442059 .2825619
PeviousDti | .2007018 .1805979 1.11 0.266 -.1532635 .5546671
size | .026784 .0289639 0.92 0.355 -.0299843 .0835522
lev | .0016954 .0176075 0.10 0.923 -.0328146 .0362055
logmtbv | .0134619 .0201648 0.67 0.504 -.0260604 .0529841
logfcf | -.0173324 .0244344 -0.71 0.478 -.0652229 .0305582
_cons | -.249956 .2594098 -0.96 0.335 -.7583898 .2584778
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .17055108
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store Random

. hausman Fixed .

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| Fixed Random Difference S.E.
-------------+----------------------------------------------------------------
Eti | .3530723 .3737799 -.0207076 .2795569
EtiMAN | -.0115504 -.0524488 .0408984 .219408
EtiINS | -.0814929 -.130822 .0493291 .3154647
PeviousDti | .2600728 .2007018 .059371 .2050598
size | .0521376 .026784 .0253536 .0834365
lev | .0085421 .0016954 .0068467 .0175146
logmtbv | .0125207 .0134619 -.0009412 .0268635
logfcf | .0122173 -.0173324 .0295497 .0369456
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.74
Prob>chi2 = 0.9494

. xtreg ChangeDti Eti EtiMAN EtiINS PeviousDti size lev logmtbv logfcf, re

Random-effects GLS regression Number of obs = 136
Group variable: code Number of groups = 32

R-sq: within = 0.0591 Obs per group: min = 1
between = 0.8094 avg = 4.3
overall = 0.1667 max = 7

Wald chi2(8) = 25.40
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0013

------------------------------------------------------------------------------
ChangeDti | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Eti | .3737799 .2065007 1.81 0.070 -.030954 .7785139
EtiMAN | -.0524488 .1444275 -0.36 0.716 -.3355214 .2306238
EtiINS | -.130822 .210914 -0.62 0.535 -.5442059 .2825619
PeviousDti | .2007018 .1805979 1.11 0.266 -.1532635 .5546671
size | .026784 .0289639 0.92 0.355 -.0299843 .0835522
lev | .0016954 .0176075 0.10 0.923 -.0328146 .0362055
logmtbv | .0134619 .0201648 0.67 0.504 -.0260604 .0529841
logfcf | -.0173324 .0244344 -0.71 0.478 -.0652229 .0305582
_cons | -.249956 .2594098 -0.96 0.335 -.7583898 .2584778
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .17055108
rho | 0 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

ChangeDti[code,t] = Xb + u[code] + e[code,t]

Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
ChangeDti | .0275039 .165843
e | .0290877 .1705511
u | 0 0

Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000

[Carlo Lazzaro]

Khaled:
welcome to this forum.
As per

F test that all u_i=0: F(31, 96) = 0.33 Prob > F = 0.9995

you should go pooled OLS.

That said, for the future please start a new thread. Thanks.

[Khaled Ali]

Dear Mr Carlo Lazzaro

Thank you very much for your help. I so sorry for inconvenience place regarding my post and i will next times.

Best Regards
Khaled ALi

[Carlo Lazzaro]

Khaled:
my pleasure.
As an aside, Carlo is by far enough.