Test equality of coefficients across quantiles by manually

[wanhaiyou]

Hi, dear statalists,
First I estimate the quantile regression model and I want to test the equality of coefficients across
quantiles. One way we can implement it as following

sysuse auto,clear
sqreg price weight length foreign, quantile(.25 .5 .75) reps(100)
test [q25]weight - [q25]length=[q50]weight - [q50]length

The wald test be used to test the equality of coefficients across quantiles using the above
codes. However, how could I implement this test manually (step by step)?

Best Regards,
wanhaiyou

[Carlo Lazzaro]

Wanhaijou may want to take a look at -test- entry in Stata 13.1 .pdf manual (pages 2357).

[wanhaiyou]

Thanks very much for your help Carlo. I am reading the related document and then give you the feedback.

Best regards,
wanhaiyou

[wanhaiyou]

Wanhaijou may want to take a look at -test- entry in Stata 13.1 .pdf manual (pages 2357).

Dear Carlo, thanks for your help.Following your suggestions, I have computed the statistical step by step and the result is similar with one using 'test' routine.

sysuse auto,clear
sqreg price weight length foreign, quantile(.25 .5 .75) reps(100)
matrix b = e(b)'
matrix V = e(V)
mat list b
mat list V


***Method 1: Using 'test' command
test [q25]weight - [q25]length=[q50]weight - [q50]length

*** Method 2: step by step
matrix R = (1,-1,0,0,-1,1,0,0,0,0,0,0)  
matrix r = 0
scalar q = rowsof(R)
matrix W = (R*b-r)'*syminv(R*V*R')*(R*b-r)/q
scalar Wald = W[1,1]
scalar k = colsof(R)
display "Wald test statistic: " Wald "  with p-value: " Ftail(q,_N-k,Wald)

Thanks again for your help.

Best regards,
wanhaiyou

[Carlo Lazzaro]

wanhaiyou:
thanks for closing ou this thread positively.

[usef mohammad]

dear @Carlo Lazzaro
Sorry
How to test the equality of coefficients in panel quantile the xtqreg or qregpd ?

test [q25]weight - [q25]length=[q50]weight - [q50]length This command does not work and gives the following error
equation [q25] not found

How is the bootstrap test?

Thank you for your guidance

[Carlo Lazzaro]

Usef:
I do not know whether the community-contributed module -xtqreg- has an option similar to -iqreg-.
Let's hope that Joao Santos Silva chimes in and provides guidance on this interesting topic.

[FernandoRios]

-xtqreg- identifies variation across quantiles based on the Scale component.
for example

sysuse auto, clear
xtqreg price mpg, i(foreign) ls
. xtqreg price mpg, i(foreign) ls



                              MM-QR regression results
Number of obs = 74

                                                           Location parameters
                                (Std. err. adjusted for 2 clusters in foreign)
------------------------------------------------------------------------------
             |               Robust
       price | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   39.22634    -7.50   0.084    -792.6134    204.2223
       _cons |   12430.83    835.415    14.88   0.043     1815.873    23045.78
------------------------------------------------------------------------------
                                                              Scale parameters
                                (Std. err. adjusted for 2 clusters in foreign)
------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -86.66115   60.70132    -1.43   0.389    -857.9445    684.6222
       _cons |   3733.451   1292.774     2.89   0.212     -12692.8     20159.7
------------------------------------------------------------------------------

.5 Quantile regression
------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -258.4703    49.2663    -5.25   0.000    -355.0304   -161.9101
------------------------------------------------------------------------------

The Scale parameter shows MPG has no effect on the conditional heteroskedasticity, thus, quantile coefficients across MPG are all statistically the same