Testing for equality of coefficients across quantiles with qreg2

[Maria Martins]

Hi,

Is there a way to test for equality of coefficients across quantiles using the qreg2 as we can do with the command test in sqreg?

Thank you.

[Carlo Lazzaro]

Maria:
welcome to this forum.
The community-contributed module (as you're kindly request to mention it, for reasons that are well explained in the FAQ) supports the postestimation command -test-:

. . sysuse auto
(1978 automobile data)

. qreg2 price weight length foreign

Median regression
R-squared = .53467262
Number of obs = 74
Objective function = 735.28776

                     Heteroskedasticity robust standard errors
------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   3.933588    4.41814     0.89   0.376    -4.878115    12.74529
      length |  -41.25191   117.0082    -0.35   0.725    -274.6174    192.1136
     foreign |   3377.771   1338.855     2.52   0.014     707.5096    6048.032
       _cons |   344.6489   9596.801     0.04   0.971    -18795.57    19484.87
------------------------------------------------------------------------------

Machado-Santos Silva test for heteroskedasticity
         Ho: Constant variance
         Variables: Fitted values of price and its squares

         chi2(2)      =  28.806
         Prob > chi2  =   0.000

. test weight=length

 ( 1)  weight - length = 0

       F(  1,    70) =    0.14
            Prob > F =    0.7107

. qreg2 price weight length foreign,quantile(0.25)

.25 Quantile regression
R-squared = .49241394
Number of obs = 74
Objective function = 470.29428

                     Heteroskedasticity robust standard errors
------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   1.831789    1.07567     1.70   0.093    -.3135663    3.977144
      length |    2.84556   25.20125     0.11   0.910    -47.41674    53.10786
     foreign |   2209.925   693.7268     3.19   0.002     826.3309     3593.52
       _cons |  -1879.775   2341.838    -0.80   0.425    -6550.424    2790.875
------------------------------------------------------------------------------

Machado-Santos Silva test for heteroskedasticity
         Ho: Constant variance
         Variables: Fitted values of price and its squares

         chi2(2)      =  27.928
         Prob > chi2  =   0.000

. test weight=length

 ( 1)  weight - length = 0

       F(  1,    70) =    0.00
            Prob > F =    0.9692

. 


.

[Maria Martins]

Thanks for the reply, Carlo. But I was actually looking to test [q25]weight = [q50]weight, i.e., to test the linearity assumption.

[Joao Santos Silva]

Dear Maria Martins,

I am afraid that is not possible because qreg2 does not compute the covariance between the estimates of different quantiles. Note, however, that testing that a variable has the same effect in different quantiles is not a test of linearity. A simple way to test if a variable has different impacts on different quantiles is to test whether there is hetroskedasticity in the model and it depends on that variable.

Best wishes,

Joao