Estimate whether coefficient of different models are JOINTLY equal to zero

[Stefano Bevilacqua]

Dear network,

I have 10 independent variables (x1, x2, x3, x4, x5, x6, x7, x8, x9, and x10) and five dependent variables (y1, y2, y3, y4, y5). I run the following regressions:

regress y1 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y2 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y3 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y4 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y5 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10

I would like to test whether the coefficient of x1 is JOINTLY equal to 0 across all the five models. Similarly, I want to do it also for the rest of coefficients. This is, I would like to make 10 joint F-tests.

Any suggestion?

Thanks!

[Andrew Musau]

See

help suest

[Stefano Bevilacqua]

Dear Andrew, thank you for your answer. To me it is not clear how to use suest. Can you provide the code for my case? How would you approach it?

[Stefano Bevilacqua]

.

[Andrew Musau]

Have you read the suggested documentation?

sysuse auto, clear
regress mpg weight disp turn 
est sto m1
regress gear weight disp turn
est sto m2
regress price weight disp turn
est sto m3
suest m1 m2 m3
test weight

Res.:

. suest m1 m2 m3

Simultaneous results for m1, m2, m3

                                                Number of obs     =         74

------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
m1_mean      |
      weight |  -.0059274   .0014223    -4.17   0.000    -.0087151   -.0031398
displacement |   .0055957   .0072121     0.78   0.438    -.0085398    .0197312
        turn |  -.1386576   .1465774    -0.95   0.344     -.425944    .1486287
       _cons |   43.58846   3.619669    12.04   0.000     36.49404    50.68288
-------------+----------------------------------------------------------------
m1_lnvar     |
       _cons |   2.485941   .2544152     9.77   0.000     1.987296    2.984586
-------------+----------------------------------------------------------------
m2_mean      |
      weight |  -.0000187   .0001045    -0.18   0.858    -.0002234    .0001861
displacement |  -.0037113    .000557    -6.66   0.000    -.0048029   -.0026197
        turn |  -.0071388   .0140147    -0.51   0.610     -.034607    .0203295
       _cons |   4.086461   .3569343    11.45   0.000     3.386883    4.786039
-------------+----------------------------------------------------------------
m2_lnvar     |
       _cons |  -2.697928   .1164597   -23.17   0.000    -2.926185   -2.469671
-------------+----------------------------------------------------------------
m3_mean      |
      weight |   3.611532   1.274715     2.83   0.005     1.113136    6.109927
displacement |   2.967384   6.711805     0.44   0.658    -10.18751    16.12228
        turn |  -387.5994   174.3707    -2.22   0.026    -729.3597   -45.83917
       _cons |   10042.72   4255.971     2.36   0.018      1701.17    18384.27
-------------+----------------------------------------------------------------
m3_lnvar     |
       _cons |   15.54384   .1724191    90.15   0.000     15.20591    15.88178
------------------------------------------------------------------------------

. 
. test weight

 ( 1)  [m1_mean]weight = 0
 ( 2)  [m2_mean]weight = 0
 ( 3)  [m3_mean]weight = 0

           chi2(  3) =   24.89
         Prob > chi2 =    0.0000

.

[Stefano Bevilacqua]

Thanks. May I ask you why in this case you suggest to use a suest (seemingly unrelated estimation) instead of sureg (seemingly unrelated regression?

[Carlo Lazzaro]

Stefano:
shamelessly elaborating on Andrew's code, in his example you could have used both -sureg- (estimator) and -suest- (postestimation command), with negligible differences:

. regress mpg weight disp turn

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     44.47
       Model |  1602.59024         3  534.196747   Prob > F        =    0.0000
    Residual |  840.869218        70  12.0124174   R-squared       =    0.6559
-------------+----------------------------------   Adj R-squared   =    0.6411
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4659

------------------------------------------------------------------------------
         mpg | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |  -.0059274   .0014326    -4.14   0.000    -.0087847   -.0030701
displacement |   .0055957    .009906     0.56   0.574    -.0141613    .0253527
        turn |  -.1386576   .1793412    -0.77   0.442    -.4963424    .2190272
       _cons |   43.58846   4.964215     8.78   0.000     33.68765    53.48928
------------------------------------------------------------------------------

. est sto m1

. regress gear weight disp turn

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     51.89
       Model |   10.484304         3  3.49476801   Prob > F        =    0.0000
    Residual |  4.71414374        70  .067344911   R-squared       =    0.6898
-------------+----------------------------------   Adj R-squared   =    0.6765
       Total |  15.1984478        73  .208197915   Root MSE        =    .25951

------------------------------------------------------------------------------
  gear_ratio | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |  -.0000187   .0001073    -0.17   0.862    -.0002326    .0001953
displacement |  -.0037113   .0007417    -5.00   0.000    -.0051906    -.002232
        turn |  -.0071388   .0134282    -0.53   0.597    -.0339204    .0196429
       _cons |   4.086461   .3716959    10.99   0.000     3.345137    4.827785
------------------------------------------------------------------------------

. est sto m2

. regress price weight disp turn

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     14.26
       Model |   240877549         3  80292516.4   Prob > F        =    0.0000
    Residual |   394187847        70  5631254.95   R-squared       =    0.3793
-------------+----------------------------------   Adj R-squared   =    0.3527
       Total |   635065396        73  8699525.97   Root MSE        =      2373

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   3.611532   .9808912     3.68   0.000     1.655206    5.567857
displacement |   2.967384   6.782459     0.44   0.663     -10.5598    16.49457
        turn |  -387.5994   122.7913    -3.16   0.002    -632.4989   -142.6999
       _cons |   10042.72   3398.897     2.95   0.004     3263.835    16821.61
------------------------------------------------------------------------------

. est sto m3

. suest m1 m2 m3

Simultaneous results for m1, m2, m3                         Number of obs = 74

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
m1_mean      |
      weight |  -.0059274   .0014223    -4.17   0.000    -.0087151   -.0031398
displacement |   .0055957   .0072121     0.78   0.438    -.0085398    .0197312
        turn |  -.1386576   .1465774    -0.95   0.344     -.425944    .1486287
       _cons |   43.58846   3.619669    12.04   0.000     36.49404    50.68288
-------------+----------------------------------------------------------------
m1_lnvar     |
       _cons |   2.485941   .2544152     9.77   0.000     1.987296    2.984586
-------------+----------------------------------------------------------------
m2_mean      |
      weight |  -.0000187   .0001045    -0.18   0.858    -.0002234    .0001861
displacement |  -.0037113    .000557    -6.66   0.000    -.0048029   -.0026197
        turn |  -.0071388   .0140147    -0.51   0.610     -.034607    .0203295
       _cons |   4.086461   .3569343    11.45   0.000     3.386883    4.786039
-------------+----------------------------------------------------------------
m2_lnvar     |
       _cons |  -2.697928   .1164597   -23.17   0.000    -2.926185   -2.469671
-------------+----------------------------------------------------------------
m3_mean      |
      weight |   3.611532   1.274715     2.83   0.005     1.113136    6.109927
displacement |   2.967384   6.711805     0.44   0.658    -10.18751    16.12228
        turn |  -387.5994   174.3707    -2.22   0.026    -729.3597   -45.83917
       _cons |   10042.72   4255.971     2.36   0.018      1701.17    18384.27
-------------+----------------------------------------------------------------
m3_lnvar     |
       _cons |   15.54384   .1724191    90.15   0.000     15.20591    15.88178
------------------------------------------------------------------------------

. test weight

 ( 1)  [m1_mean]weight = 0
 ( 2)  [m2_mean]weight = 0
 ( 3)  [m3_mean]weight = 0

           chi2(  3) =   24.89
         Prob > chi2 =    0.0000

. sureg (mpg weight disp turn) (gear weight disp turn) (price weight disp turn)

Seemingly unrelated regression
------------------------------------------------------------------------------
Equation             Obs   Params         RMSE  "R-squared"      chi2   P>chi2
------------------------------------------------------------------------------
mpg                   74        3     3.370919      0.6559     141.03   0.0000
gear_ratio            74        3     .2523978      0.6898     164.58   0.0000
price                 74        3         2308      0.3793      45.22   0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
mpg          |
      weight |  -.0059274   .0013934    -4.25   0.000    -.0086584   -.0031965
displacement |   .0055957   .0096346     0.58   0.561    -.0132877    .0244791
        turn |  -.1386576   .1744268    -0.79   0.427     -.480528    .2032127
       _cons |   43.58846   4.828183     9.03   0.000      34.1254    53.05153
-------------+----------------------------------------------------------------
gear_ratio   |
      weight |  -.0000187   .0001043    -0.18   0.858    -.0002231    .0001858
displacement |  -.0037113   .0007214    -5.14   0.000    -.0051252   -.0022974
        turn |  -.0071388   .0130602    -0.55   0.585    -.0327363    .0184588
       _cons |   4.086461   .3615105    11.30   0.000     3.377914    4.795009
-------------+----------------------------------------------------------------
price        |
      weight |   3.611532   .9540123     3.79   0.000     1.741702    5.481361
displacement |   2.967384   6.596602     0.45   0.653    -9.961719    15.89649
        turn |  -387.5994   119.4265    -3.25   0.001    -621.6711   -153.5278
       _cons |   10042.72   3305.759     3.04   0.002     3563.553    16521.89
------------------------------------------------------------------------------

. test weight

 ( 1)  [mpg]weight = 0
 ( 2)  [gear_ratio]weight = 0
 ( 3)  [price]weight = 0

           chi2(  3) =   29.80
         Prob > chi2 =    0.0000

.

That said, there are relevant differences between the two (dealing with nesting design; score option; availabe non-default standard errors, just to mention a few).
The following (old) Stata thread may be enlightening: https://www.stata.com/statalist/arch.../msg01160.html.

.

[Stefano Bevilacqua]

Dear Dr. Carlo, thank you for your answer. In my case I am using this test to inspect whether some macroeconomic variables (1-10) are significantly different from zero across all the equations; in these cases, the 5 dependent variables are some factors that I retrived with a factor analysis (factors explaining the cross-sectional variation of stock returns)

regress y1 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y2 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y3 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y4 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
regress y5 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10

I just tried both methods and I get some differences in the results. May I ask you which test you would recommend to use to understanding which method is more appropriate?

Thank you for your help!

[Carlo Lazzaro]

Stefano:
see Example 2 under -sureg- entry, Stata .pdf manual.
In addition, please call me Carlo, like all on (and many more off) this list do. Thanks.

[Stefano Bevilacqua]

Carlo, thank you for your suggestion. I see that indeed the example 2 is very similar to what I have to do. I will proceed with sureg then. I can specify the degrees of freedom in sureg. For a sample of stock returns (monthy, 180 observations) is it necessary to adjust for small degrees of freedom in your perspective?

[Carlo Lazzaro]

Stefano:
given your sample size, I'd skip the small sample adjustment.