[Ashani Abayasekara]

Thanks Carlo. How exactly would I use -test- and -lincom- in this case?

[Carlo Lazzaro]

Ashani:
I do hope the following toy-example is useful:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage i.race##i.union c.age##c.age, fe vce(cluster idcode)
note: 2.race omitted because of collinearity.
note: 3.race omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =     19,229
Group variable: idcode                          Number of groups  =      4,150

R-squared:                                      Obs per group:
     Within  = 0.0986                                         min =          1
     Between = 0.0451                                         avg =        4.6
     Overall = 0.0576                                         max =         12

                                                F(5, 4149)        =     137.88
corr(u_i, Xb) = 0.0133                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,150 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        race |
      Black  |          0  (omitted)
      Other  |          0  (omitted)
             |
     1.union |   .1103597    .012985     8.50   0.000     .0849021    .1358173
             |
  race#union |
    Black#1  |  -.0073757   .0195842    -0.38   0.706    -.0457713    .0310198
    Other#1  |  -.3047801   .1156961    -2.63   0.008    -.5316064   -.0779537
             |
         age |   .0323436   .0051042     6.34   0.000     .0223367    .0423506
             |
 c.age#c.age |  -.0002734   .0000817    -3.35   0.001    -.0004337   -.0001132
             |
       _cons |   .9950981   .0782405    12.72   0.000     .8417048    1.148492
-------------+----------------------------------------------------------------
     sigma_u |  .42313891
     sigma_e |  .26182965
         rho |  .72312438   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,14]
            1b.         2o.         3o.         0b.          1.    1b.race#    1b.race#    2o.race#     2.race#    3o.race#     3.race#                  c.age#
          race        race        race       union       union    0b.union    1o.union    0b.union     1.union    0b.union     1.union         age       c.age
y1           0           0           0           0   .11035969           0           0           0  -.00737575           0   -.3047801   .03234362  -.00027342

               
         _cons
y1   .99509814

. test 2.race#1.union=3.race#1.union

 ( 1)  2.race#1.union - 3.race#1.union = 0

       F(  1,  4149) =    6.58
            Prob > F =    0.0103

. testparm i.race##i.union

 ( 1)  1.union = 0
 ( 2)  2.race#1.union = 0
 ( 3)  3.race#1.union = 0

       F(  3,  4149) =   41.33
            Prob > F =    0.0000

. help lincom

. lincom 1.union - 0b.union

 ( 1)  - 0b.union + 1.union = 0

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .1103597    .012985     8.50   0.000     .0849021    .1358173
------------------------------------------------------------------------------

.

[Ashani Abayasekara]

Hi Carlo,

Thank you very much for the illustration which is very helpful. In my case, to test for differences in the effect of unemployment and staff firing by mental health status, would the following code work (which indicates that there is a marginally significant difference in terms of the unemployment effect, but not for staff firing)?

xtreg jobsec mh9_q1##( c.unemp c.fire1) i.j1, fe i(id) cluster(id)

Fixed-effects (within) regression               Number of obs     =     48,024
Group variable: id                              Number of groups  =      6,003

R-squared:                                      Obs per group:
     Within  = 0.2570                                         min =          8
     Between = 0.0188                                         avg =        8.0
     Overall = 0.1829                                         max =          8

                                                F(15,6002)        =     576.94
corr(u_i, Xb) = -0.0213                         Prob > F          =     0.0000

                                   (Std. err. adjusted for 6,003 clusters in id)
--------------------------------------------------------------------------------
               |               Robust
        jobsec | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
      1.mh9_q1 |          0  (omitted)
         unemp |  -.1211826    .003892   -31.14   0.000    -.1288124   -.1135529
         fire1 |  -.1585208   .0020321   -78.01   0.000    -.1625044   -.1545372
               |
mh9_q1#c.unemp |
            1  |   .0164109   .0090537     1.81   0.070    -.0013377    .0341594
               |
mh9_q1#c.fire1 |
            1  |   .0064037   .0043519     1.47   0.141    -.0021276     .014935
               |
            j1 |
            2  |  -.0108441   .0408108    -0.27   0.790    -.0908479    .0691598
            3  |  -.0382829    .041024    -0.93   0.351    -.1187047    .0421388
            4  |  -.0483699   .0409416    -1.18   0.237    -.1286301    .0318904
            5  |   .0057767   .0415139     0.14   0.889    -.0756055    .0871589
            6  |  -.0189513   .0409312    -0.46   0.643    -.0991912    .0612887
            7  |   .0492266   .0409829     1.20   0.230    -.0311146    .1295678
            8  |   .0070104   .0408559     0.17   0.864    -.0730819    .0871027
            9  |  -.0415234   .0415246    -1.00   0.317    -.1229267    .0398798
           10  |   .0093576   .0406655     0.23   0.818    -.0703614    .0890765
           11  |   -.025912   .0403782    -0.64   0.521    -.1050678    .0532437
           12  |    -.02021   .0411519    -0.49   0.623    -.1008825    .0604625
               |
         _cons |   6.656268   .0291539   228.32   0.000     6.599116     6.71342
---------------+----------------------------------------------------------------
       sigma_u |  1.2659379
       sigma_e |  1.7768792
           rho |   .3366876   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

test 0b.mh9_q1#co.unemp=1.mh9_q1#c.unemp

 ( 1)  0b.mh9_q1#co.unemp - 1.mh9_q1#c.unemp = 0

       F(  1,  6002) =    3.29
            Prob > F =    0.0699


test 0b.mh9_q1#co.fire1=1.mh9_q1#c.fire1

 ( 1)  0b.mh9_q1#co.fire1 - 1.mh9_q1#c.fire1 = 0

       F(  1,  6002) =    2.17
            Prob > F =    0.1412

I also have a follow-up question. Since the mental health variable does not change across the different evaluations for a given person, it is omitted in the fixed-effects regression. If I remove the fixed-effects specification (and presumably estimate a random-effects model), the mental health indicator variable is retained and the results are somewhat different. How do I decide which model is better?

Thank you very much.

[Ashani Abayasekara]

Alternatively, could I test for the difference as follows?

lincom 0b.mh9_q1#co.unemp-1.mh9_q1#c.unemp

 ( 1)  0b.mh9_q1#co.unemp - 1.mh9_q1#c.unemp = 0

------------------------------------------------------------------------------
      jobsec | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |  -.0164109   .0090537    -1.81   0.070    -.0341594    .0013377
------------------------------------------------------------------------------

[Carlo Lazzaro]

Ashani:
1) choosing which one of the two specifications is -fe- or -re- is better for your research (see Changing effect directions in fixed-effects estimation compared to OLS. - Statalist);
2) if you're interested in the coefficient of a time-invariant predictor you may want to consider Mundlak;
3) yes, you can also go -lincom-.

[Ashani Abayasekara]

Hi all,

Related to #14 above, what I have done so far is to run:

xtreg jobsec mh9_q1##( c.unemp male1 c.age c.tenure contract c.fire1 c.hire1) i.j1, cluster(id)

and then test whether the 'unemp' coefficients for mh9_qn1=0 and mh9_qn1=1 are statistically different, using:

lincom 0b.mh8_qn1#co.unemp_av6-1.mh8_qn1#c.unemp_av6

I now want to conduct a one-tailed test, to specifically test whether the unemp coefficient is significantly more negative for those in good mental health (mh9_qn1=0). How would I do this?

Many thanks in advance.