Which model to use, Fixed effects, Random effects or GLS?

[Luc de Ridder]

Hello everyone,

I am pretty new to Stata and I do not exactly know which regressions and especially commands I need to use. Currently I am writing a paper about excess returns of funds. I have strongly balanced panel data (monthly returns) of approximately 1700 actively managed mutual funds. My time period is monthly and goes from 2010 until the end of 2020.

I would like to make a regression with the excess return of the funds as dependent variable and the excess market return and Fama French 5-factor model factors (SMB, HML, RMW and CMA) and Carhart 4 factor model factors (SMB, HML and MOM) as independent variables. When doing the hausman test the outcome was to use fixed effects for the fama French model and to use random effects for the carhart 4 factor model. However, my professor told me a fixed effects model adds an additional (fixed) effect, which may bias the outcome of the regression but he wasnt sure how it exactly worked. Can anyone tell me which model is appropriate to use?

Also the wooldridge test for autocorrelation in panel data showed evidence for autocorrelation.

I would really appreciate it if someone could help me.

Kind regards,

Luc

[Carlo Lazzaro]

Luc:
as far as I know, -fe- estimator:
1) wipes aout time-invariant variables;
2) allows the correlation between panelwise effect and the vector of predictors.

Perhaps your supervisor referred to the incidental parameter problem (see http://www.econ.brown.edu/Faculty/Tony_Lancaster/papers/IncidentalParameters1948.pdf) that, however, does not affect regression with continuous regressand.

Assuming that you're using -xtreg-, both -robust- and -cluster- options deal with heteroskedastcity and/or autocorrelation.

[Joro Kolev]

This is not how the asset pricing exercise works at all.

In these factor models the excess return is explained by the factors times the factor exposure, and the factor exposure is asset specific.

Therefore what you have here are 1700 time series regressions run separately for each asset (mutual fund in your case).

[Sabyasachi Tripathi]

Dear Profossors,
My panel data estimation, the Hausman test suggests considering the FE model. But F stat of the estimated FE model is not significant. Also, in terms of the level of significance and expected signs of the independent variables, RE is preferred. Could you please suggest to me what to do.

With Kind Regards,
Sabyasachi

[Carlo Lazzaro]

Sabyasachi:
as per FAQ please provide what you typed and what Stata gave you back.
That said, if your F-stat it is not significant I would check the predictors in the right hand-side of your regression equation.

[Sabyasachi Tripathi]

Following is my results

Fixed-effects (within) regression Number of obs = 244
Group variable: group Number of groups = 129

R-sq: within = 0.0390 Obs per group: min = 1
between = 0.1654 avg = 1.9
overall = 0.1713 max = 2

F(8,107) = 0.54
corr(u_i, Xb) = -0.6297 Prob > F = 0.8214

------------------------------------------------------------------------------
overall | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mys_f | -.0863394 .0707954 -1.22 0.225 -.226683 .0540043
gnp_f | .0000249 .0000219 1.14 0.259 -.0000186 .0000683
perliament_f | .0040838 .0138565 0.29 0.769 -.0233852 .0315528
lpr_f | -.0075438 .0078917 -0.96 0.341 -.0231881 .0081005
tfr | .0507179 .1745054 0.29 0.772 -.2952187 .3966545
urban | -.0185426 .0433478 -0.43 0.670 -.1044746 .0673894
bank_bran | .0011547 .0109667 0.11 0.916 -.0205855 .0228948
atm | .0002444 .0043872 0.06 0.956 -.0084526 .0089415
_cons | 1.673578 2.702381 0.62 0.537 -3.683577 7.030734
-------------+----------------------------------------------------------------
sigma_u | 1.6447654
sigma_e | .34865253
rho | .95699799 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(128, 107) = 6.31 Prob > F = 0.0000


F(8,107) = 0.54 is not significant... also independent variables are also not significant... but random effect shows better results.


Thanking you,

With Kind Regards,
Sabyasachi

[Carlo Lazzaro]

Sabyasachi:
the issue here is that you apparently have a very small within panel variation for time-varying variables.
This diagnosis is also supported by the very low R-sq: within = 0.0390.
Even though the random effect estimator shows better results, they might be misleading, as the random effect estimator is not efficient if the fixed effect specification is the way to go.