Panel Data Regression Steps

[Hidayat Hadi]

Dear Statalist,

I am new to panel data regression analysis and Stata, so forgive me if my questions are too basic.
Currently i am conducting a research on company profitability with ROA as dependent variable and Liquidity, Log Total Asset, Leverage, and Asset Structure as independent variables. The data has 34 companies across 5 years with 170 total observations.

sum roa liquidity size leverage assetstructure

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         roa |       170    .0177706    .1900833     -1.538       .456
   liquidity |       170    1.910747    1.954133       .011     20.167
        size |       170    12.81888    .6328861      10.76      14.01
    leverage |       170    1.254612    2.414883    -15.817     13.152
assetstruc~e |       170    .6500412    .1825059       .106       .996

First, i conducted Breusch-Pagan test that showed Prob>chibar2 = 0.00 which means that RE is chosen over OLS.

xtreg roa liquidity size leverage assetstructure, re
xttest0

Then I ran Hausman test that returned prob>chibar2 = 0.00 meaning FE is more suitable than RE.

hausman fe re

As for the tests, I checked my data for multicollinearity using vif and it showed that my data doesn't have multicollinearity problems. Then i checked for autocorrelation using xtserial and heteroscedasticity using xttest3 which shows that my data suffers from both problems.

 xtserial roa liquidity size leverage assetstructure

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,      33) =      4.472
           Prob > F =      0.0421

xtreg roa liquidity size leverage assetstructure, fe

Fixed-effects (within) regression               Number of obs      =       170
Group variable: code                            Number of groups   =        34

R-sq:  within  = 0.2890                         Obs per group: min =         5
       between = 0.0425                                        avg =       5.0
       overall = 0.0516                                        max =         5

                                                F(4,132)           =     13.41
corr(u_i, Xb)  = -0.8918                        Prob > F           =    0.0000

--------------------------------------------------------------------------------
           roa |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
     liquidity |   .0184212    .007616     2.42   0.017      .003356    .0334865
          size |   .4378722   .0898747     4.87   0.000     .2600913    .6156532
      leverage |   .0204201   .0049537     4.12   0.000     .0106212     .030219
assetstructure |   .5211536   .1530098     3.41   0.001     .2184851    .8238221
         _cons |  -5.994851   1.186008    -5.05   0.000    -8.340892    -3.64881
---------------+----------------------------------------------------------------
       sigma_u |  .32016264
       sigma_e |  .13284938
           rho |  .85311272   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0:     F(33, 132) =     5.51             Prob > F = 0.0000

. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (34)  =   77949.85
Prob>chi2 =      0.0000

After reading other questions on this site, i found that you can deal with autocorrelation and heteroscedasticity by clustering the standard errors. So i did the fixed effect regression using the cluster commands:

xtreg roa liquidity size leverage assetstructure, fe cluster(code)

Fixed-effects (within) regression               Number of obs      =       170
Group variable: code                            Number of groups   =        34

R-sq:  within  = 0.2890                         Obs per group: min =         5
       between = 0.0425                                        avg =       5.0
       overall = 0.0516                                        max =         5

                                                F(4,33)            =      2.70
corr(u_i, Xb)  = -0.8918                        Prob > F           =    0.0472

                                    (Std. Err. adjusted for 34 clusters in code)
--------------------------------------------------------------------------------
               |               Robust
           roa |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
     liquidity |   .0184212   .0091547     2.01   0.052    -.0002042    .0370467
          size |   .4378722   .1960061     2.23   0.032     .0390949    .8366495
      leverage |   .0204201   .0066806     3.06   0.004     .0068284    .0340118
assetstructure |   .5211536   .3114909     1.67   0.104    -.1125794    1.154887
         _cons |  -5.994851   2.717433    -2.21   0.034    -11.52351   -.4661927
---------------+----------------------------------------------------------------
       sigma_u |  .32016264
       sigma_e |  .13284938
           rho |  .85311272   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
(code)

my questions are:
1. Are my steps correct?
2. Do I need check my data with other tests?

Regards,
Hadi

[Carlo Lazzaro]

Hadi:
welcome to this forum.
the only step I would amend is invoking non-default standard errors after -hausman- test.
Hence, since -hausman- does not support non-default standard errors, you shoud check for the best specification via the community-contributed command -xtoverid- (just type -search xtoverid- to spot and install it).
As the null of -xtoverid- is that -re- is the way to go, there's no need to run and store -xtreg,fe- too, as -xtreg,re- will suffice, as you can see in the following toy-example (please note that I've already installed -xtoverid- so I can skip downloading it):

use "https://www.stata-press.com/data/r16/nlswork.dta"
. xi: xtreg ln_wage i.race grade , vce(cluster idcode)
i.race            _Irace_1-3          (naturally coded; _Irace_1 omitted)

Random-effects GLS regression                   Number of obs     =     28,532
Group variable: idcode                          Number of groups  =      4,709

R-sq:                                           Obs per group:
     within  = 0.0000                                         min =          1
     between = 0.3170                                         avg =        6.1
     overall = 0.1970                                         max =         15

                                                Wald chi2(3)      =    1864.97
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                             (Std. Err. adjusted for 4,709 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _Irace_2 |  -.0459478   .0107442    -4.28   0.000     -.067006   -.0248895
    _Irace_3 |   .1039604   .0511939     2.03   0.042     .0036222    .2042986
       grade |   .0909639   .0021824    41.68   0.000     .0866865    .0952413
       _cons |   .5143082   .0285046    18.04   0.000     .4584403    .5701761
-------------+----------------------------------------------------------------
     sigma_u |  .30393641
     sigma_e |  .32028665
         rho |    .473825   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(idcode)
Sargan-Hansen statistic 1864.974  Chi-sq(3)   P-value = 0.0000

.

Two sidelights as I'm finishing my reply off:
1) as many glorious but a but a bit old-fahioned community-contributed Stata commands, -xtoverid- does not support -fvvarlist- notation; hence, you should prefix the whole code with -xi:- if one or more of your predictors are categorical;
2) the results of -xtoverid- points you toward the -fe- specification.

[Hidayat Hadi]

Carlo:
Thank you for the reply.
So, in this case xtoverid will replace Hausman as FE/RE test, right?
I have one more question if you don't mind. When I use clustered standard errors, Stata does not give me the F test at the bottom of the result like in the regular -xtreg fe- does. Is there something that I missed?

[Carlo Lazzaro]

Hidayat:
1) correct;
2) -xtreg- behaves as expected, as the F-tests statistic is too complex to compute with non-default standard errors (see Example 3. -xtreg- entry, Stata .pdf manual).