How to interpret random and fixed effects coefficients

[Karoline Karlsson]

Hi all,

I am running both a random-effects model and a fixed-effect model, to see whether a firm's ESG score has an effect on return.

xtreg Return ESGscore Mktrf SMB HML CMA RMW i.sector i.month, re cluster(firm ID)
xtreg Return ESGscore Mktrf SMB HML CMA RMW i.sector i.month, fe cluster(firm ID)

My question is, how do I interpret the coefficient for the ESG score? I found this explanation for the random effect coefficient "Interpretation of the coefficients is tricky since they include both the within-entity and between-entity effects. In the case of TSCS data represents the average effect of X over Y when X changes across time and between individuals by one unit." If the coefficient is then -0.5, is the interpretation then, that 1-point increase in ESG score is associated with a -0.5% decrease in return on average?

And for the fixed effects I found this "Coefficients of the regressors indicate how much Y changes when X increases by one unit" - So would that be interpreted as a 1-point increase in ESG score is associated with a 0.5% decrease in return?

Thanks,

Karoline

[Carlo Lazzaro]

Karoline:
as per FAQ, could you please post what Stata gave you back, too? Thanks.

[Karoline Karlsson]

Hi Carlo,

[Carlo Lazzaro]

Karoline:
the most striking issue about your -xtreg,re- is the absence of evidence on any panel-wise effect (sigma_u is dramaticlly lower than sigma_e).
What does -xttest0- tell you?
Are you sure that your model is correctly specified?

[Karoline Karlsson]

When testing for RE vs. FE i get the following results:

Comparing Pooled OLS vs. LSDV1
F(359, 36178)	1.74
Prob > F	0.0000
Comparing Pooled OLS vs. LSDV2
F(102, 36435)	3.07
Prob > F	0.0000
Comparing LSDV1 vs. LSDV3
F(102, 36076)	3.12
Prob > F	0.0000
Comparing Pooled OLS vs. Random effects
chibar2(01)	38.90
Prob > chibar2	0.0000
Hausman test for FE vs. RE
chi2(106)	100.06
Prob > chi2	0.6443

Or do you mean to run the following?
xtreg Return ESGscore Mktrf SMB HML CMA RMW i.sector i.month, re cluster(firm ID)
xttest0

Karoline

[Carlo Lazzaro]

Karoline:
please go:

xtreg Return ESGscore Mktrf SMB HML CMA RMW i.sector i.month, re cluster(firm ID)
xttest0

Thanks.

[Karoline Karlsson]

This is the result,

Thanks

[Carlo Lazzaro]

Karoline:
you do not have evidence of a panel-wise effect.
Go pooled OLS.

[Karoline Karlsson]

Hi Carlo,

Thanks for the answers.

Assuming that the above is not a problem, how would I interpret the coefficient in the RE model?

[Carlo Lazzaro]

Karoline:
what above is an issue.
That said, your interpretation reported in your first post is correct, but has short legs, as the coefficient under discussion is not statistically significantly different from zero.

[Pierre Akilimali]

Dear Team
I think that I should to report random effect model because Haussman test gave a p-value of (Prob > chi2 = )0.6285 ( see attached) But I am wondering How I should interpret the Re coefficient

[Pierre Akilimali]

I used ln_MMR ( ln MMR) as dependant avriable, and I am trying to interpret for example for cap: 1000 unit more of cap would result to about 1.5 of MMR! I used xtreg: xtreg ln_MMR cesarrate comdeliv cap anc1 , re


Random-effects GLS regression Number of obs = 269
Group variable: district Number of groups = 58

R-squared: Obs per group:
Within = 0.0554 min = 2
Between = 0.3789 avg = 4.6
Overall = 0.2196 max = 5

Wald chi2(4) = 47.19
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_MMR | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
cesarrate | .0692179 .0166798 4.15 0.000 .036526 .1019097
comdeliv | .0465794 .0097608 4.77 0.000 .0274486 .0657102
cap | -.0000152 5.15e-06 -2.95 0.003 -.0000253 -5.12e-06
anc1 | -.0013694 .0017693 -0.77 0.439 -.0048372 .0020983
_cons | 4.626092 .1797396 25.74 0.000 4.273809 4.978375
-------------+----------------------------------------------------------------
sigma_u | .44555197
sigma_e | .82241569
rho | .22690611 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Pierre:
what does the -xttest0- post estimation command give you back after -xtreg,re-?