Joint Hypothesis Testing

[Nuno Goncalves]

Hi everyone,

My objetive is to test if two joint variables are less than zero ( one sided test - dividing the p-value by two). To this end after estimating the model (panel GMM) I run two codes:

 test _b[x1] + _b[x2]=0

and

 test x1 x2

the results are different, what test should I use?

[Carlo Lazzaro]

Nuno:
I would probably consider -lincom- that, in the following toy-example, overlaps with -test-:

. use "C:\Program Files\Stata18\ado\base\a\auto.dta"
(1978 automobile data)

. regress price i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(4, 64)        =      0.24
       Model |  8360542.63         4  2090135.66   Prob > F        =    0.9174
    Residual |   568436416        64     8881819   R-squared       =    0.0145
-------------+----------------------------------   Adj R-squared   =   -0.0471
       Total |   576796959        68  8482308.22   Root MSE        =    2980.2

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       rep78 |
          2  |   1403.125   2356.085     0.60   0.554    -3303.696    6109.946
          3  |   1864.733   2176.458     0.86   0.395    -2483.242    6212.708
          4  |       1507   2221.338     0.68   0.500    -2930.633    5944.633
          5  |     1348.5   2290.927     0.59   0.558    -3228.153    5925.153
             |
       _cons |     4564.5   2107.347     2.17   0.034     354.5913    8774.409
------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,6]
           1b.         2.         3.         4.         5.           
        rep78      rep78      rep78      rep78      rep78      _cons
y1          0   1403.125  1864.7333       1507     1348.5     4564.5


. test 1b.rep78 2.rep78

 ( 1)  1b.rep78 = 0
 ( 2)  2.rep78 = 0
       Constraint 1 dropped

       F(  1,    64) =    0.35
            Prob > F =    0.5536


. lincom 1b.rep78 + 2.rep78

 ( 1)  1b.rep78 + 2.rep78 = 0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   1403.125   2356.085     0.60   0.554    -3303.696    6109.946
------------------------------------------------------------------------------

. test 1b.rep78 2.rep78

 ( 1)  1b.rep78 = 0
 ( 2)  2.rep78 = 0
       Constraint 1 dropped

       F(  1,    64) =    0.35
            Prob > F =    0.5536

.