Test for moderation effect in FE panel regression

[zulfiqar ali shah]

Hello Stata experts.
I am beginner to Stata. I need help regarding testing for moderation effect

Size X Returns

in Stata. additionally, I want to test of the coefficient either two interactions coefficients are same or different? The two moderating variables are in the same model.

Small Size X Returns

and

Large Size x Returns

in the below sample models.

Y = B1.Returns + B2.Size+ B3.SizeXReturns, fe vce( cluster panel ID)

Y= B1.Small Size + B2.Large Size + B3.Small Size X Returns + B4.Large Size x Returns, fe vce(cluster ID)

[Carlo Lazzaro]

Zulfiqar:
1) I'm not clear why small and large sizes cannot be gathered together in an unique two-level categorical variable, so that your code becomes more efficient;
2) that said, the following toy-example might be helpful (BTW: whendealing with a real research topic I would plug -i-timevar- in the right-hand side of the -xtreg.fe- equation):

. 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 i.not_smsa##c.tenure, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,093
Group variable: idcode                          Number of groups  =      4,699

R-sq:                                           Obs per group:
     within  = 0.1024                                         min =          1
     between = 0.2507                                         avg =        6.0
     overall = 0.1781                                         max =         15

                                                F(3,4698)         =     440.94
corr(u_i, Xb)  = 0.1891                         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]
------------------+----------------------------------------------------------------
       1.not_smsa |  -.0682325   .0156008    -4.37   0.000    -.0988173   -.0376477
           tenure |   .0373424   .0011226    33.26   0.000     .0351416    .0395432
                  |
not_smsa#c.tenure |
               1  |  -.0108808    .002068    -5.26   0.000    -.0149351   -.0068266
                  |
            _cons |   1.589381   .0052665   301.79   0.000     1.579057    1.599706
------------------+----------------------------------------------------------------
          sigma_u |  .38309987
          sigma_e |  .30274651
              rho |  .61557302   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,6]
              0b.            1.                0b.not_smsa#   1.not_smsa#             
        not_smsa      not_smsa        tenure     co.tenure      c.tenure         _cons
y1             0    -.06823252     .03734239             0    -.01088083     1.5893814

. test 0b.not_smsa#co.tenure=1.not_smsa#co.tenure

 ( 1)  0b.not_smsa#co.tenure - 1.not_smsa#c.tenure = 0

       F(  1,  4698) =   27.68
            Prob > F =    0.0000

.