not significant coefficient

[Amine OL]

Hi,

I am working on an econometric study on the relationship between financial performance and financial structure using panel data from 33 companies over a period of 8 years.

I used stata for regression and the hausman test recommended the fixed effect model. But when I do the regression on the fixed effect model, the coefficients are not significant whereas on a random effect model they are... you can recommend what to do in this case? can I use another method to estimate the fixed effect model apart from the LSDV method or do I have to use the random effect model?

Thank you very much

here are the results obtained

Fixed-effects (within) regression Number of obs = 264
Group variable: i Number of groups = 33

R-sq: within = 0.0176 Obs per group: min = 8
between = 0.0833 avg = 8.0
overall = 0.0525 max = 8

F(4,227) = 1.02
corr(u_i, Xb) = 0.1484 Prob > F = 0.3985

------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .0951219 .1182338 0.80 0.422 -.1378543 .3280981
x2 | 1.165032 1.059505 1.10 0.273 -.9226902 3.252754
x3 | .0734147 .0498684 1.47 0.142 -.0248494 .1716789
x4 | .1073965 .5094289 0.21 0.833 -.8964177 1.111211
_cons | -.0980683 4.659254 -0.02 0.983 -9.278986 9.082849
-------------+----------------------------------------------------------------
sigma_u | .85510437
sigma_e | .583749
rho | .68211419 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(32, 227) = 11.29 Prob > F = 0.0000

Random-effects GLS regression Number of obs = 264
Group variable: i Number of groups = 33

R-sq: within = 0.0096 Obs per group: min = 8
between = 0.2880 avg = 8.0
overall = 0.2019 max = 8

Wald chi2(4) = 13.99
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0073

------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | -.0912966 .107237 -0.85 0.395 -.3014773 .118884
x2 | 2.27522 1.006464 2.26 0.024 .3025879 4.247853
x3 | .0933697 .049818 1.87 0.061 -.0042717 .1910112
x4 | .5357245 .2042515 2.62 0.009 .1353989 .9360501
_cons | -3.997099 1.873139 -2.13 0.033 -7.668385 -.3258139
-------------+----------------------------------------------------------------
sigma_u | .65118255
sigma_e | .583749
rho | .55444276 (fraction of variance due to u_i)
------------------------------------------------------------------------------


. hausman fe re

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
x1 | .0951219 -.0912966 .1864185 .0497943
x2 | 1.165032 2.27522 -1.110188 .3310314
x3 | .0734147 .0933697 -.019955 .0022422
x4 | .1073965 .5357245 -.428328 .4666896
------------------------------------------------------------------------------
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(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 14.82
Prob>chi2 = 0.0051
(V_b-V_B is not positive definite)

[Carlo Lazzaro]

Amine:
welcome to this forum.
The lack of significance is not, per se, a good reason to hunt for significance via another model.
Your concerns should focus on the following issue, rather than the lack of statistical significance of your model (which may well depend on your pretty small sample size): does the right-hand side of your regression model give a fair and true representation of the data generating process? Is there any omitted predictor, according to the literature of your research field? Should any relationship between predictors and dependent variable be,say, quadratic instead of linear? Have you excluded any reverse causation between financial performance and financial structure?
To wrap up: switching to -re- specification would, in all likeliood, give back biased results (even though significant).
As an aside, for the future please use CODE delimiters (see the FAQ on this nad other posting-related topics) to share what you typed nad what Stata gave you back. Thanks.

[Amine OL]

I'm sorry, here I added the code, I hope I did the right thing.

You know, Carlo, your answer made me think a lot. So, in conclusion, to have more significant coefficients in this case I would do better to add other explanatory variables in the model?

[Carlo Lazzaro]

Amin:
sorry but I do not speak French.
Anyway, if I can get the gist of your message right: yes, including more predictors (provided that their inclusion is supported by the literature in your research field, because they're part of the data generating process) could improve your model.
However, please note that a p-value<0.05 is not the right approach for choiosing among different regression models.

[Amine OL]

Thank you very much Carlo.

[Phil Bromiley]

There is another way to think about fixed vs. random effects. Fixed effects look at the influence of x's within panels. Random effects include both within and cross-panel effects. If the cross-panel effects differ from within-panel effects, you'll get a difference between fixed and random effects. There are cases (like plant output) where within effects (variation in output over time given a largely constant physical plant) and cross panel effects (different designs and locations of plants) should have different influences.

You might look at Mundlak, xthtaylor, and similar estimators that separate the two effects. The xtreg documentation also illustrates a way to think about these differences.