Panel Data with heteroskedastic - How to procede?

[Jessica Sardinha]

Hello!

I have a unbalanced panel data with 123 cross sections and 247,904 observations . The observations are daily.

After running a Hausman test, I found that a FE is better to used than RE. Next I tested for heteroskedasticity with the Modifiel Wald test and the result indicates that i have to reject H0. So I have heteroskedasticity.

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

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

chi2 (123) = 2.3e+10
Prob>chi2 = 0.0000


After I tested autocorrelation with the Wooldridge test. The result indicates that i can not reject H0. So I don't have autocorrelation.

H0: no first-order autocorrelation
F( 1, 122) = 3.294
Prob > F = 0.0720


So, I want to know if I can correct the heteroskedasticity with the command xtgls?
The other question is if I use the xtgls I have to use igls too?

In other words I have to use the command 1 or 2 above:

1- xtgls dep indep, igls panels (heteroskedastic) force
2- xtgls dep indep, panels (heteroskedastic) force


Sorry my bad English.

Thanks a lot for the help!!!

[Jessica Sardinha]

I read the examples (1 and 3 in the xtgls manual) and the Greene (2012). I understand that the igls is for estimations with MLE and that MLE has no advantages over FGLS in its asymptotic properties. So I think that I don't need to use the igls. I am right?

Thanks a lot for the help!!!

[Carlo Lazzaro]

Jessica:
thanks for reposting on the General Forum.
Yes, you are right.

[Jessica Sardinha]

Once again Thanks a lot!

One thing that worry myselft, is that my Std. Err. are high (the Std. Err. are high in all estimations mentioned below) . Did I do the right steps for the etimation in panel data? The steps that I did:

1- Estimation pooled
2- Chow Test in the estimation FE - With this test I verified that EF is better than pooled
3- Estimation with RE
4- Breusch Pagan Test - With this test I verified that RE is better than pooled
5- Hausman Test - With this test I verified that FE is better than RE
6- Wooldrigde Test for autocorrelation in panel data - The result indicates that i can not reject H0. So I don't have autocorrelation.
7- Modified Wald test for groupwise heteroskedasticity - The result indicates that i have to reject H0. So I have heteroskedasticity.
8 – The last step was the estimation with xtgls with the option panels (heteroskedastic) force. Like below

. xtgls CaptaçãoLíquida Retornomensal Retornoanual TaxaAdministração logIdadedofundo log
> PL, panels (heteroskedastic) force

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: no autocorrelation

Estimated covariances = 123 Number of obs = 246,667
Estimated autocorrelations = 0 Number of groups = 123
Estimated coefficients = 6 Obs per group:
min = 37
avg = 2,005.42
max = 3,012
Wald chi2(5) = 535.99
Prob > chi2 = 0.0000

----------------------------------------------------------------------------------------
CaptaçãoLíquida | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
Retornomensal | 5772.33 2600.166 2.22 0.026 676.0996 10868.56
Retornoanual12meses | 5733.595 680.268 8.43 0.000 4400.294 7066.896
TaxaAdministraçãomáx~a | 70741.21 20093.77 3.52 0.000 31358.14 110124.3
logIdadedofundoemdias | -153.7323 472.171 -0.33 0.745 -1079.171 771.7059
logPL | -6487.57 305.3667 -21.25 0.000 -7086.078 -5889.063
_cons | 38147.88 2082.14 18.32 0.000 34066.96 42228.8
----------------------------------------------------------------------------------------


I think that is importante to talk about my data....
My data is about 126 brasilian’s open end funds in the period of 01/02/2005 until 31/12/2017.
With this data I want to understand the relation between net funding (application - redemption) and profitability.

[Carlo Lazzaro]

Jessica:
please use CODE delimiters to post what you typed and what Stays gave you back. Thanks.
The unit you used to express your data is not clear and may well explain your seemingly high standard errors.

[Jessica Sardinha]

Ok Carlo.

Thanks a lot!!

[Jessica Sardinha]

Hello!

I have more one doubt. In my regressions (pooled, fixed effects and random effects) the coefficient of two variables was negative. But in the estimation with xtgls with the option panels (heteroskedastic) force the coefficient of this two variables are positive. But it makes more sense the coefficient to be negative
What could be wrong?

Thanks

[Carlo Lazzaro]

Jessica:
if you have T>N panel dataset (as it seems from your previous posts), I would stick with -xtgls-.
As an aside, it's virtually impossible to give specific advice without seeing what you typed and what Stata gave you back .

[Jessica Sardinha]

Hello Carlo!
I used xtgls. May I put here the code? I think that will be large...

[Carlo Lazzaro]

Jessica:
yes, please. Just use CODE delimiters.

[Jessica Sardinha]

Dear Carlo,

The Code is:

Pooled Regress (the coefficients TaxaAdministraçãomáxima and logIdadedofundoemdias are negative)

. regress CaptaçãoLíquida Retornomensal Retornoanual TaxaAdministração logIdadedofundo logPL

      Source |       SS           df       MS      Number of obs   =   247,904
-------------+----------------------------------   F(5, 247898)    =     93.06
       Model |  4.4753e+14         5  8.9506e+13   Prob > F        =    0.0000
    Residual |  2.3842e+17   247,898  9.6178e+11   R-squared       =    0.0019
-------------+----------------------------------   Adj R-squared   =    0.0019
       Total |  2.3887e+17   247,903  9.6357e+11   Root MSE        =    9.8e+05

-----------------------------------------------------------------------------------------
        CaptaçãoLíquida |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
          Retornomensal |   71276.54   27456.69     2.60   0.009     17462.16    125090.9
    Retornoanual12meses |   126826.7   6974.834    18.18   0.000     113156.2    140497.2
TaxaAdministraçãomáxima |   -24815.9   164152.9    -0.15   0.880    -346551.3    296919.5
  logIdadedofundoemdias |  -37818.45   5405.091    -7.00   0.000    -48412.28   -27224.61
                  logPL |  -10270.21   2905.327    -3.53   0.000    -15964.57   -4575.841
                  _cons |   183613.6    24376.3     7.53   0.000     135836.7    231390.5
-----------------------------------------------------------------------------------------

Chow Test and Fixed Effects (the coefficients TaxaAdministraçãomáxima and logIdadedofundoemdias are negative)

. xtreg CaptaçãoLíquida Retornomensal Retornoanual TaxaAdministração logIdadedofundo logPL, fe

Fixed-effects (within) regression               Number of obs     =    247,904
Group variable: ID                              Number of groups  =        123

R-sq:                                           Obs per group:
     within  = 0.0019                                         min =         37
     between = 0.0396                                         avg =    2,015.5
     overall = 0.0014                                         max =      3,012

                                                F(5,247776)       =      95.93
corr(u_i, Xb)  = -0.5359                        Prob > F          =     0.0000

-----------------------------------------------------------------------------------------
        CaptaçãoLíquida |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
          Retornomensal |    76228.4   27468.03     2.78   0.006     22391.79      130065
    Retornoanual12meses |   118814.1   7246.879    16.40   0.000     104610.4    133017.7
TaxaAdministraçãomáxima |   -1093949   442198.4    -2.47   0.013     -1960646   -227251.4
  logIdadedofundoemdias |  -111621.2   11936.55    -9.35   0.000    -135016.5   -88225.89
                  logPL |  -13624.51       7005    -1.94   0.052    -27354.12    105.1099
                  _cons |   488539.9   75837.43     6.44   0.000     339900.6    637179.3
------------------------+----------------------------------------------------------------
                sigma_u |  54069.087
                sigma_e |  980261.69
                    rho |  .00303316   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------
F test that all u_i=0: F(122, 247776) = 2.84                 Prob > F = 0.0000

Random Effects (the coefficients TaxaAdministraçãomáxima and logIdadedofundoemdias are negative)

. xtreg CaptaçãoLíquida Retornomensal Retornoanual TaxaAdministração logIdadedofundo logPL,re

Random-effects GLS regression                   Number of obs     =    247,904
Group variable: ID                              Number of groups  =        123

R-sq:                                           Obs per group:
     within  = 0.0018                                         min =         37
     between = 0.0874                                         avg =    2,015.5
     overall = 0.0019                                         max =      3,012

                                                Wald chi2(5)      =     465.31
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
        CaptaçãoLíquida |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
          Retornomensal |   71276.54   27456.69     2.60   0.009     17462.42    125090.7
    Retornoanual12meses |   126826.7   6974.834    18.18   0.000     113156.3    140497.2
TaxaAdministraçãomáxima |   -24815.9   164152.9    -0.15   0.880    -346549.7    296917.9
  logIdadedofundoemdias |  -37818.45   5405.091    -7.00   0.000    -48412.23   -27224.66
                  logPL |  -10270.21   2905.327    -3.53   0.000    -15964.54   -4575.869
                  _cons |   183613.6    24376.3     7.53   0.000       135837    231390.3
------------------------+----------------------------------------------------------------
                sigma_u |          0
                sigma_e |  980261.69
                    rho |          0   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------

Hausman Test (Fixed Effects better than Random Effects)

    Test:  Ho:  difference in coefficients not systematic

                  chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       75.72
                Prob>chi2 =      0.0000

Wooldridge Test for autocorrelation (Don't reject the null hypothesis, so I don't have autocorrelation)

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,     122) =      3.294
           Prob > F =      0.0720

Modified Wald test for groupwise heteroskedasticity (There is heteroskedasticity)

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

chi2 (123)  =   1.6e+10
Prob>chi2 =      0.0000

And then xtgls with the correction for heteroskedasticity (the coefficients TaxaAdministraçãomáxima and logIdadedofundoemdias become positive - It's the question, why? The coefficients was negative in the others estimations)

. xtgls CaptaçãoLíquida Retornomensal Retornoanual TaxaAdministração logIdadedofundo logPL, panels (heteroskedastic) force

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   no autocorrelation

Estimated covariances      =       123          Number of obs     =    247,904
Estimated autocorrelations =         0          Number of groups  =        123
Estimated coefficients     =         6          Obs per group:
                                                              min =         37
                                                              avg =   2,015.48
                                                              max =      3,012
                                                Wald chi2(5)      =     587.51
                                                Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
        CaptaçãoLíquida |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
          Retornomensal |   5823.643   2616.724     2.23   0.026     694.9589    10952.33
    Retornoanual12meses |   5473.559   682.1071     8.02   0.000     4136.654    6810.465
TaxaAdministraçãomáxima |   70031.95   14105.97     4.96   0.000     42384.75    97679.15
  logIdadedofundoemdias |   1065.651   435.9954     2.44   0.015     211.1153    1920.186
                  logPL |  -7155.085   310.4778   -23.05   0.000     -7763.61    -6546.56
                  _cons |   38363.57   2050.466    18.71   0.000     34344.73    42382.41
-----------------------------------------------------------------------------------------

Thanks so much for the help!!

[Carlo Lazzaro]

Jessica:
thanks for providing your resulst via CODE delimiters.
It's actually strange that you do not have autocorrrelation in a T>N panel dataset.
Anyway, as per your panel data structure, I would trust -xtgls- resulst.

[Jessica Sardinha]

Thank you so much!!

[Jessica Sardinha]

Hello again!!

I have other doubt...
If my Chow Test indicates pooled and my Breusch Pagan Test indicates pooled too, and my T>N. Can I use xtgls? I think yes... But Can I use the command "xtserial dep var indep var, output" for test the autocorrelation? And How can I test the heteroskedasticity? Can I use command "hettest" - Breusch-Pagan / Cook-Weisberg test for heteroskedasticity?

For example: Chow Test indicates pooled

. xtreg CaptaçãoLíquida Retornomensal Retornoanual logPL, fe

Fixed-effects (within) regression               Number of obs     =    132,501
Group variable: ID                              Number of groups  =         79

R-sq:                                           Obs per group:
     within  = 0.0004                                         min =         37
     between = 0.0126                                         avg =    1,677.2
     overall = 0.0001                                         max =      3,012

                                                F(3,132419)       =      15.65
corr(u_i, Xb)  = -0.6965                        Prob > F          =     0.0000

-------------------------------------------------------------------------------------
    CaptaçãoLíquida |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
      Retornomensal |  -.0000837   .0001607    -0.52   0.602    -.0003986    .0002312
Retornoanual12meses |   .0002127   .0000424     5.02   0.000     .0001297    .0002957
              logPL |  -.0002023   .0000368    -5.50   0.000    -.0002745   -.0001302
              _cons |   .0014363   .0002631     5.46   0.000     .0009206     .001952
--------------------+----------------------------------------------------------------
            sigma_u |  .00016144
            sigma_e |  .00434129
                rho |   .0013809   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
F test that all u_i=0: F(78, 132419) = 1.10                  Prob > F = 0.2568

Breusch Pagan indicates pooled too:

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        CaptaçãoLíquida[ID,t] = Xb + u[ID] + e[ID,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
               Captaç~da |   .0000189       .0043417
                       e |   .0000188       .0043413
                       u |          0              0

        Test:   Var(u) = 0
                             chibar2(01) =     0.00
                          Prob > chibar2 =   1.0000

This autocorrelation test is right?

 quietly regress CaptaçãoLíquida Retornomensal Retornoanual logPL

. xtserial CaptaçãoLíquida Retornomensal Retornoanual logPL,output

Linear regression                               Number of obs     =    102,655
                                                F(3, 78)          =       0.80
                                                Prob > F          =     0.4951
                                                R-squared         =     0.2403
                                                Root MSE          =     .00435

                                           (Std. Err. adjusted for 79 clusters in ID)
-------------------------------------------------------------------------------------
                    |               Robust
  D.CaptaçãoLíquida |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
      Retornomensal |
                D1. |   -.000602    .000745    -0.81   0.422    -.0020853    .0008813
                    |
Retornoanual12meses |
                D1. |   .0000427   .0002607     0.16   0.870    -.0004764    .0005617
                    |
              logPL |
                D1. |  -.1724137   .1130696    -1.52   0.131    -.3975179    .0526905
-------------------------------------------------------------------------------------

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,      78) =    786.251
           Prob > F =      0.0000

can I use the test below for heteroskedasticity ?

. quietly regress CaptaçãoLíquida Retornomensal Retornoanual logPL

. hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of CaptaçãoLíquida

         chi2(1)      =111673.15
         Prob > chi2  =   0.0000

The last, May I estimate with xtgls like below?

. xtgls CaptaçãoLíquida Retornomensal Retornoanual logPL, panels (heteroskedastic) corr(
> ar1) force

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   common AR(1) coefficient for all panels  (0.1107)

Estimated covariances      =        79          Number of obs     =    132,501
Estimated autocorrelations =         1          Number of groups  =         79
Estimated coefficients     =         4          Obs per group:
                                                              min =         37
                                                              avg =   1,677.23
                                                              max =      3,012
                                                Wald chi2(3)      =     145.25
                                                Prob > chi2       =     0.0000

-------------------------------------------------------------------------------------
    CaptaçãoLíquida |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
      Retornomensal |   5.95e-06   7.63e-06     0.78   0.436    -9.01e-06    .0000209
Retornoanual12meses |   .0000247   2.29e-06    10.80   0.000     .0000202    .0000292
              logPL |  -7.68e-08   8.55e-07    -0.09   0.928    -1.75e-06    1.60e-06
              _cons |  -8.04e-06   5.97e-06    -1.35   0.178    -.0000197    3.65e-06
-------------------------------------------------------------------------------------

Once again so many thanks!!

[Carlo Lazzaro]

Jessica:
since you have a T>N panel dataset, -xtreg- is not the way to go, wheras -xtgls- is what you need.
See also: https://www.stata.com/support/faqs/s...tocorrelation/