What is the right method of testing hypotheses in panel data regression?

[amalie thomsen]

What is the right method of testing hypotheses in a random effect panel data regression model?

I want to test if the coefficient to the independent variable is higher than 0, i.e. if the independent variable has a positive influence on the dependent variable.
How should these hypotheses look? Is a T-test or a F-test applicable to test these hypotheses? if so, which one should be adopted?

[Carlo Lazzaro]

Amalie:
welcome to this forum.
If the outcome table of, say, -xtreg- does not give you what you want, you can see -test-, as per the following toy-example:

use "http://www.stata-press.com/data/r15/nlswork.dta"
. xtreg ln_wage age, fe rob

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1026                                         min =          1
     between = 0.0877                                         avg =        6.1
     overall = 0.0774                                         max =         15

                                                F(1,4709)         =     884.05
corr(u_i, Xb)  = 0.0314                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0181349   .0006099    29.73   0.000     .0169392    .0193306
       _cons |   1.148214   .0177153    64.81   0.000     1.113483    1.182944
-------------+----------------------------------------------------------------
     sigma_u |  .40635023
     sigma_e |  .30349389
         rho |  .64192015   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test age

 ( 1)  age = 0

       F(  1,  4709) =  884.05
            Prob > F =    0.0000

[amalie thomsen]

Hi Carlo,

Thanks for the reply. I have tried this, but my results appear to look different. See below:

( 1) LognumberofCVC = 0

chi2( 1) = 6.29
Prob > chi2 = 0.0121

Are you perhaps able to explain why it is different?

[Carlo Lazzaro]

Amalie:
I would say first that they differ because -test- was run on two different regression models.
That said, from the outcome you provide, you can say that -LognumberofCVC- is significantly different from 0.

[amalie thomsen]

Dear Carlo,

Okay, thank you, nice to get that confirmed.

The above being a two-sided T-test, I would also like to conduct a one-sided T-test. I have been following this recommended approach: https://www.stata.com/support/faqs/s...-coefficients/

Yet, due to my different results (I don't see either F or degrees of freedom in my test cf the above) I am not able to run the subsequent commands to do the one-sided test.

Can you help me on this?

[Carlo Lazzaro]

Amalie:
just type

return list

after -test- and you'll get all the details you need to run the subsequent commands.

[amalie thomsen]

Okay, when i do this i get the following reuslts :

return list
scalars:
r(drop) = 0
r(chi2) = 3.398229583286582
r(df) = 1
r(p) = .0652664345916576

display "Ho: coef <= 0 p-value = " ttail(r(df),`sign_CVC'*sqrt(r(p)))
Ho: coef <= 0 p-value = .42038337

display "Ho: coef >= 0 p-value = " 1-ttail(r(df),`sign_CVC'*sqrt(r(p)))
Ho: coef >= 0 p-value = .57961663

Is this correct? to me, it doesn't seem like this corresponds to the previous result of -LognumberofCVC- being significantly different from 0. based on this, it doesn't appear that anything can be concluded.

Hope you can help clear this up. Your help is much appreciated

[amalie thomsen]

or is there a mistake in the formula, caused by the different scalars?

[Carlo Lazzaro]

Amalie:
it should be:

ttail(r(df_r),`sign_wgt'*sqrt(r(F)))

not

ttail(r(df_r),`sign_wgt'*sqrt(r(p)))

[amalie thomsen]

Dear Carlo,

I believe that my issues are founded in my initial regression code. My regression code is robust error panel data regression xtreg Y LognumberofCVC, re. This appears to be the reason it is not working for me. I tried it on an ordinary regress, and the code worked perfectly.

Is there an alternative way to do this type of test on a xtreg Y X1 X2, re command?

Best Amalie