Heteroskedasticity and Multicollinearity

[Mustapha Younis]

When I use the command (estat hettest) after doing the panel regression with re and fe then hausman then hausman, sigmamore I got and error r(321), I don't know why this error, I searched a lot online about it but did not find a solution.

I also want to test for multicollinearity but don't know the command.

Here attached the message I get from stata when I do the hettest.

Thank you.

[Carlo Lazzaro]

Mustapha:
-estat hettest- is not allowed after -xt- suite commands.
Go visual fo a heteroskedasticity test.
For the future, please report between CODE delimiters the error message thrown by Stata; do not attach screenshots. Thanks.

[Mustapha Younis]

Thank you Mr. Carlo,

But actually I don't understand what is the meaning of going visual for a heteroskedasticity test. Sorry, I am new to STATA.

Regards.

[Carlo Lazzaro]

Mustapha:
my bad, probably.
I meant to plot espilon residual distribution vs fitted values via a scatterplot.
If you detect heteroskedastcity and/or autocorrelation, just invoke -robust- or -cluster- options and go on with your panel data regression.
Obviously, Carlo is enough!

[Mustapha Younis]

Thanks Carlo,

I still have a problem. I cannot rvfplot is not working also with me. I get the following error message:

error . . . . . . . . . . . . . . . . . . . . . . . . Return code 301
last estimates not found;
You typed an estimation command, such as regress, without
arguments or attempted to perform a test or typed predict,
but there were no previous estimation results.

Is it a problem with my stata software or these commands don't work with xtreg?

Thanks.

[Carlo Lazzaro]

Mustapha:
-rvfplot- does not work after -xtreg-.
You have to obtain both fitted values and epsilon residuals via -predict- and then create a -scatter- plot with this two variables to investigare potenziali heteroskedasticity..

[Mustapha Younis]

Thanks Carlo.

Also predict is not working, I get a message that it is already defined when I choose a variable.

But I did the scatter plot with fitted values. If you would like to take a look at it and guide me if it will be enough in my case or not I'll be grateful.

Regrads.

[Jacob Sano]

Mustapha,
To clarify, you must create a new variable when using predict (syntax: predict [what value you want to predict] newvariable) where the name of the new variable does not already exist in your dataset. If you use predict more than once, you must choose a different variable name every time or clear your variable previously created through predict.

[Carlo Lazzaro]

Mustapha:
I do hope that the folowing toy-example can be helpful:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age tenure, fe

Fixed-effects (within) regression               Number of obs     =     28,101
Group variable: idcode                          Number of groups  =      4,699

R-sq:                                           Obs per group:
     within  = 0.1296                                         min =          1
     between = 0.1916                                         avg =        6.0
     overall = 0.1456                                         max =         15

                                                F(2,23400)        =    1742.76
corr(u_i, Xb)  = 0.1302                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0121949   .0004131    29.52   0.000     .0113852    .0130045
      tenure |   .0211313   .0008015    26.37   0.000     .0195604    .0227023
       _cons |   1.256467   .0109792   114.44   0.000     1.234947    1.277987
-------------+----------------------------------------------------------------
     sigma_u |  .39034493
     sigma_e |  .29808194
         rho |  .63165531   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4698, 23400) = 8.02                 Prob > F = 0.0000

. predict fitted, xb
(433 missing values generated)

. predict epsilon, e
(433 missing values generated)

. twoway (scatter epsilon fitted)

. xtreg ln_wage age tenure, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,101
Group variable: idcode                          Number of groups  =      4,699

R-sq:                                           Obs per group:
     within  = 0.1296                                         min =          1
     between = 0.1916                                         avg =        6.0
     overall = 0.1456                                         max =         15

                                                F(2,4698)         =     766.79
corr(u_i, Xb)  = 0.1302                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,699 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0121949   .0007414    16.45   0.000     .0107414    .0136483
      tenure |   .0211313   .0012112    17.45   0.000     .0187568    .0235059
       _cons |   1.256467   .0194187    64.70   0.000     1.218397    1.294537
-------------+----------------------------------------------------------------
     sigma_u |  .39034493
     sigma_e |  .29808194
         rho |  .63165531   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

The scatteplot shows heteroskedasticity and the subsequent adoption of cluster-robust standard errors support that evidence, since they are larger that the default ones.

[Mustapha Younis]

Hello Carlo Lazzaro ,

It seems that the analysis has heteroskedasticity as follows:





and concerning the multicollinearity, this the Correlation matrix of coefficients of xtreg model:

      |                                                                              o. 1.OilE~g#          
        e(V) | Manufa~a  Foreig~i  Grosss~S  Inflat~l  Highte~a  Popula~l  School~y  OilExp~g  c.Manu~a     _cons
-------------+----------------------------------------------------------------------------------------------------
Manufactur~a |   1.0000                                                                                          
Foreigndir~i |  -0.1706    1.0000                                                                                
Grosssavin~S |  -0.1738    0.4278    1.0000                                                                      
InflationG~l |   0.1167   -0.1280   -0.2759    1.0000                                                            
Hightechno~a |   0.0703   -0.0183   -0.0214    0.3656    1.0000                                                  
Population~l |  -0.0762    0.0472   -0.0581    0.0007   -0.0359    1.0000                                        
Schoolenro~y |  -0.1090   -0.0086   -0.3732   -0.0842   -0.1214    0.0130    1.0000                              
o.OilExpor~g |        .         .         .         .         .         .         .         .                    
1.OilExpor~g#|                                                                                                    
c.Manufact~a |  -0.5660    0.1188    0.0931   -0.4755   -0.2640   -0.0600    0.0942         .    1.0000          
       _cons |   0.1242   -0.1953    0.1263    0.0018   -0.1958   -0.2031   -0.8862         .    0.0062    1.0000

Does this mean that I have multicollinearity?

And if I have both heteroskedasticity and multicollinearity what should I do in this case?

Thank you for helping out.

Regards.

[Carlo Lazzaro]

Mustapha:
as heteroskedasticity seems apparent, just go -xtreg- with -robust- or -cluster()- standard errors; this way you will take also autocorrelation into account If any).
In addition (as I missed the last part of your query, I'm editing the current reply): multicollinearity is, in general, not an issue, as oftentimes reminded on this forum. That said, a sign of nasty multicollinearity is the evidence of "weird" standard errors.

[Mustapha Younis]

Thank you Carlo,

I just don't know the exact command that I should use and in which step? Is it the final step?

Regards.

[Carlo Lazzaro]

Mustapha:
elaborating on my previous reply:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)

. xtreg ln_wage age tenure, fe vce(cluster idcode)

[Mustapha Younis]

Dear Carlo,

I see that the command contains fe. I just want to elaborate my model here may be you can help because this is my first model ever.

xtreg GDPgrowthannual Manufacturingvalueaddedannua Foreigndirectinvestmentneti GrosssavingscurrentUS InflationGDPdeflatorannual Hightechnologyexportsofma Populationgrowthannual Schoolenrollmentsecondary OilExporting c.Manufacturingvalueaddedannua#OilExporting, re
estimates store random
xtreg GDPgrowthannual Manufacturingvalueaddedannua Foreigndirectinvestmentneti GrosssavingscurrentUS InflationGDPdeflatorannual Hightechnologyexportsofma Populationgrowthannual Schoolenrollmentsecondary OilExporting c.Manufacturingvalueaddedannua# OilExporting, fe
estimates store fixed
hausman fixed random
hausman fixed random, sigmamore
predict fitted, xb
predict epsilon, e
twoway (scatter epsilon fitted)
estat vce, corr

I did a regression with random effect, then a regression with fixed effect, then the hausman test to choose between re or fe and the result is in favor of re.

In the previously mentioned command xtreg ln_wage age tenure, fe vce(cluster idcode) , should I put re instead of fe?

[Carlo Lazzaro]

Mustapha,
yes you can well replace -fe- with -re- specification in your -xtreg- code.
That said, if you want to keep non-default standard errors (eg, due to heteroskedasticity of epsilon distribution), -hausman- won't do and you have to switch to the community-contributed command -xtoverid-, which, being a bit old-fashioned- does not support -fvvarlist-notation. The usual fix then is to prefix your -xtreg- code with -xi:-.
Eventually, -xtoverid- needs only the -re- specification to point you towards -re- (the null hypothesis) or -fe-:

xi: xtreg GDPgrowthannual Manufacturingvalueaddedannua Foreigndirectinvestmentneti GrosssavingscurrentUS InflationGDPdeflatorannual Hightechnologyexportsofma Populationgrowthannual Schoolenrollmentsecondary OilExporting c.Manufacturingvalueaddedannua#OilExporting, re vce (cluster panelid)
xtoverid