Panel data: Test between RE and FE

[Massimo Cecchi]

first of all congratulations and thanks for all your valuable suggestions that I found on Statalist.
Following them, I was left with only one doubt about the choice test ta RE and FE. Hope you can help me.

1,810 Companies 9 Years N>T
(11148 obs)
Panel variable: Company (unbalanced)
Time variable: Year, 2011 to 2019, but with gaps
Delta: 1 unit

Variables:
TbQ = Tobin’Q market value index of a company (0 +∞)
LnTA = LnTotal Assets), (0 +∞)
TAE = ratio between Total Assets (TA) and Equity (E) (0 + ∞)
ROE = profitability index (0-+∞)
HDV = efficiency index (0 +∞)
TCV = efficiency index (0 +∞)

xtreg TbQt LnTA TAE ROE HCV TCV, re
Regression results

TbQt	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
LnTA	.032		.002	21.13		0	.029		.035		***
TAE	.004		0	27.27		0	.004		.005		***
ROE	0		0	-19.67		0	0		0		***
HCV	.031		.003	10.95		0	.026		.037		***
TCV	.004		0	7.91		0	.003		.005		***
Constant	.079		.022	3.65		0	.036		.121		***
Mean dependent var		0.547			SD dependent var			0.192
Overall r-squared		0.192			Number of obs			11142
Chi-square		1760.363			Prob > chi2			0.000
R-squared within		0.124			R-squared between			0.200
*** p<.01, ** p<.05, * p<.1

xttest0
Breusch and Pagan Lagrangian multiplier test for random effects
Test: Var(u) = 0
chibar2(01) = 19724.01
Prob > chibar2 = 0.0000

Thus Heterostaticity

So, we need to move on to robust regressions:

xtreg TbQt LnTA TAE ROE HCV TCV, fe vce (cluster Company)
est store fe1
Regression results

TbQt	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
LnTA	.037		.006	6.01		0	.025		.049		***
TAE	.004		.001	3.52		0	.002		.006		***
ROE	0		0	-6.92		0	0		0		***
HCV	.031		.007	4.12		0	.016		.046		***
TCV	.004		.002	2.61		.009	.001		.007		***
Constant	.016		.083	0.19		.851	-.148		.179
Mean dependent var		0.547			SD dependent var			0.192
R-squared		0.125			Number of obs			11142
F-test		27.641			Prob > F			0.000
Akaike crit. (AIC)		-27486.363			Bayesian crit. (BIC)			-27449.771
*** p<.01, ** p<.05, * p<.1

xtreg TbQt LnTA TAE ROE HCV TCV, re vce (cluster Company)
est store re1
Regression results

TbQt	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
LnTA	.032		.003	11.98		0	.027		.038		***
TAE	.004		.001	3.63		0	.002		.007		***
ROE	0		0	-6.69		0	0		0		***
HCV	.031		.006	5.62		0	.02		.042		***
TCV	.004		.001	2.61		.009	.001		.007		***
Constant	.079		.037	2.10		.035	.005		.152		**
Mean dependent var		0.547			SD dependent var			0.192
Overall r-squared		0.192			Number of obs			11142
Chi-square		254.551			Prob > chi2			0.000
R-squared within		0.124			R-squared between			0.200
*** p<.01, ** p<.05, * p<.1

But which of the two tests is appropriate?

rhausman fe1 re1, cluster reps(1000)
Cluster-Robust Hausman Test
(based on 1000 bootstrap repetitions)
b1: obtained from xtreg TbQt LnTA TAE ROE HCV TCV , fe vce (cluster Company)
b2: obtained from xtreg TbQt LnTA TAE ROE HCV TCV, re vce (cluster Company)
Test: Ho: difference in coefficients not systematic
chi2(5) = (b1-b2)' * [V_bootstrapped(b1-b2)]^(-1) * (b1-b2) = 7.26
Prob>chi2 = 0.2019

xtreg TbQt LnTA TAE ROE HCV TCV, fe vce (cluster Company)
xtreg TbQt LnTA TAE ROE HCV TCV, re vce (cluster Company)
xtoverid
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(Company)
Sargan-Hansen statistic 10.451 Chi-sq(5) P-value = 0.0634

[Carlo Lazzaro]

Massimo:
both test outcomes point you to -xtreg,re- (as the null is not rejected).
I personally prefer the communiuty-contributed module -xtoverid-, mostly because I'm more familiar with it than with the other one.
As an aside, you switched to -xtreg,re- with non-default stndard errors, which differs from -rreg-.

[Massimo Cecchi]

Thanks for your answer Carlo.
But I didn't understand your comment: "As an aside," you switched to -xtreg, re- with non-default stndard errors, which differs from -rreg- ":
is there an error in my procedure?

[Carlo Lazzaro]

Massimo:
you made no mistakes,
It simply a matter of technical terms: a regression with a cluster-robust standard errors (as you correctly coded) differs from a robust regression (see -help rreg-).

[Massimo Cecchi]

Thank you for your quick answer :-)