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Re: st: xtreg fe - skewness and kurtosis in independent variables


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtreg fe - skewness and kurtosis in independent variables
Date   Sun, 10 Mar 2013 08:35:11 -0400

Dear Lothar,

In a regression model, the predictor variables (a better choice of
words than "independent variables," because they are seldom
"independent") are not required to follow a normal distribution, or to
follow any distribution at all.  Many models involve dichotomous
predictors ("dummy variables," preferably "indicator variables"),
which take only 0 and 1 as their values.

You should, however, check whether the relation between the dependent
variable and each of the predictor variables is reasonably close to
linear.  As a start, you can look at the corresponding scatterplots,
but the choice should ultimately be made in the context of the full
model.  If those relations are curved, you may be able to straighten
them by transforming the dependent variable or the predictor variables
or both.

David Hoaglin

On Sun, Mar 10, 2013 at 8:02 AM,  <L_4_U@gmx.de> wrote:
> Dear statalist,
>
> I'm using an unbalanced datapanel (financial data) with 576 observations to estimate a fixed effects model with Stata 12.0. Tests indicate first order autocorrelation and heteroscedasticity of the error term, therefore I use robust standard errors. The command
>
> xtreg depv indv1 indv2 indv3 indv4 indv5 indv6 indv7 indv8 indv9 indv10, fe vce (ro)
>
> can be run without problems and delivers satisfactory results without any obvious irregularities.
>
> However, the descriptive statistics show above normal skewness and kurtosis of the independent variables. I. e. the independent variables INDV1 to INDV10 used to estimate the FE model are non-normally distributed:
>
> var     obs     mean    std.-   min     max     skewn.  kurtosis
>                         dev.
> ----------------------------------------------------------------
> depv    576     -0.123  0.279   -0.805  0.815   0.322   3.187
> indv1   576     0.820   0.260   0.171   1.001   -1.261  3.228
> indv2   576     -0.007  0.757   -14.255 5.389   -11.511 229.900
> indv3   576     0.000   0.091   -0.310  0.581   0.790   7.727
> indv4   576     0.669   0.234   0.231   1.100   0.082   1.612
> indv5   576     0.486   0.236   0.000   3.030   2.301   28.001
> indv6   576     0.050   0.989   -2.549  1.492   -0.74   2.671
> indv7   576     0.378   0.621   0.014   7.721   8.651   86.881
> indv8   576     0.024   0.037   0.002   0.250   3.501   16.339
> indv9   576     0.041   0.117   0.001   0.570   3.410   13.440
> indv10  576     2.073   6.638   0.002   63.120  5.555   37.301
>
> Questions:
>
> - Does xtreg estimate the FE-model correctly, despite non-normality of the independent variables?
>
> - If not, will I have to normalize the independent variables before using xtreg?
>
> Any comments are welcome!
>
> Thanks,
> Lothar

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