Normalization in panel data

[Pranshu Tripathi]

I have balanced panel data for 1600 companies for 8 years and 6 variables. Do I need to check for normality?
I applied the Hausman test without normalizing it, and it suggested using a fixed-effect model.

[Carlo Lazzaro]

Pranshu:
what follows holds for cross-sectional datasets, too: normality is a (weak) requirement for epsilon (and u, in panel data analysis) only.
Therefore, you do not have to test/adjust for normality and live with your data as they are.
In addition, with 1600 panels, you shoud switch from default to clustered-ribust standard error (just add the -robust- or the -vce(lcuster idcode)-) option; the do the very same job under -xtreg-).
As -hausman- does not allow non-defalut standard errors, you should test the -re- (only) specification via the community-contributed module -xtoverid- (its null is that -re- is the way to go).
Otherwise, having a balanced panel dataset you can test the -fe- vs. the -re- specification via the Mundlak approach (see https://blog.stata.com/2015/10/29/fi...ndlak-approach).

[Pranshu Tripathi]

Thanks, Mr. Lazzaro.
If I am not wrong in interpreting what you have suggested, then you mean that we can not run the Hausman test with the clustered error, so we should go with

xtreg y x1, x2, x3,re vce(cluster id)
xtoverid

OR
bysort id: egen mean_x2 = mean(x2)
bysort id: egen mean_x3 = mean(x3)
quietly xtreg y x1 x2 x3 mean_x2 mean_x3, vce(robust)
estimates store mundlak
test mean_x2 mean_x3
( 1) mean_x2 = 0
( 2) mean_x3 = 0 (credit:https://blog.stata.com/2015/10/29/fi...dlak-approach/)
and they do the same job.

[Carlo Lazzaro]

Pranshu:
correct.
The more efficient code is the one that includes -xtoverid-. Unfortunately, being glorious but a bit old-fashioned, -xtoverid- does not support-fvvarlist- notation. The usual fix is to prefix your -xtreg,re- code with -xi:- for categorical variables and creating interactions by hand.
As an aside, please call me Carlo, as all on (and many more off) this forum do. Thanks.

[Pranshu Tripathi]

Thanks, Carlo.
For clearing my doubts.

[Pranshu Tripathi]

Hey Carlo,
I have a third-order interaction as an explanatory variable.
It has two categorical and one continuous variable.
To find the appropriate model, I am doing as given below

xi:xtreg inv tobq size tang lev cash categoricaldummy1 categoricaldummy2 categoricaldummy1categoricaldummy2 tobqcategoricaldummy1 tobqcategoricaldummy2 tobqcategoricaldummy1categoricaldummy2, re vce(cluster id)

xtoverid

Is this the correct code to select the appropriate model?

And can I do this with clustering by time also?

[Carlo Lazzaro]

Pranshu:
1) -xi:- takes categorical variables only into account;
2) interactions should be created by hand as in the following toy-example:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. g mpg_weight= mpg*weight

. regress price mpg weight mpg_weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     13.11
       Model |   228430463         3  76143487.7   Prob > F        =    0.0000
    Residual |   406634933        70  5809070.47   R-squared       =    0.3597
-------------+----------------------------------   Adj R-squared   =    0.3323
       Total |   635065396        73  8699525.97   Root MSE        =    2410.2

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   396.7844   185.2023     2.14   0.036     27.41003    766.1587
      weight |   5.067008   1.378057     3.68   0.000      2.31856    7.815455
  mpg_weight |  -.1916795   .0711936    -2.69   0.009    -.3336706   -.0496885
       _cons |  -5944.881   4525.706    -1.31   0.193    -14971.12    3081.356
------------------------------------------------------------------------------

that, as expected, give back the very same results as:

. regress price c.mpg##c.weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     13.11
       Model |   228430463         3  76143487.7   Prob > F        =    0.0000
    Residual |   406634933        70  5809070.47   R-squared       =    0.3597
-------------+----------------------------------   Adj R-squared   =    0.3323
       Total |   635065396        73  8699525.97   Root MSE        =    2410.2

--------------------------------------------------------------------------------
         price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
           mpg |   396.7844   185.2023     2.14   0.036     27.41003    766.1587
        weight |   5.067008   1.378057     3.68   0.000      2.31856    7.815455
               |
c.mpg#c.weight |  -.1916795   .0711936    -2.69   0.009    -.3336706   -.0496885
               |
         _cons |  -5944.881   4525.706    -1.31   0.193    -14971.12    3081.356
--------------------------------------------------------------------------------

.

3) n-clustering is not supported by -xtoverid- (and by -xtreg- either). You may want to keep -i.timevar- as a predictor, though.

[Pranshu Tripathi]

Thanks, Carlo for bearing with me.

[Carlo Lazzaro]

Pranshu:
no bearing with you at all; we're simply reharsing together!