When operate RIF-QR, does the command 'rifhdreg' contain a Gaussian kernel distribution?

[Kim Myounghwan]

Generally, the Gaussian kernel distribution is recommended for RIF quantile regression.

When I use the 'rifhdreg' command, don't I need to insert a separate option to use the Gaussian kernel distribution?

[FernandoRios]

Hi Kim
Just a few points
1. There is no real recommendations regarding which kernel function is the most adequate. Based on the non-parametric literature, the choice of kernel is of second order importance. However, because gaussian distributions are easier to use (simply using normaldensity), that is the one that is most often used.
2. The are more recommendations regarding the appropriate bandwidth. On that regard, the way i programmed rifhdreg uses the Silverman's Rule of Thumb plug-in bandwidth. This is slightly different from the bandwidth used within the "kdensity" program.
3. The commands rifhdreg, oaxaca_rif and _grifvar all use gaussian kernels with Silverman's Rule of Thumb bandwidths. If you would like to play with different bandwidths or kernel functions, you could do something like this:

webuse nlswork, clear
rifhdreg ln_wage age grade i.race msp , rif(q(25)) robust
est sto m1
rifhdreg ln_wage age grade i.race msp , rif(q(25) kernel(ep)) robust
est sto m2
rifhdreg ln_wage age grade i.race msp , rif(q(25) kernel(biweight)) robust
est sto m3
esttab m1 m2 m3, se nogaps scalar(rifmean)



------------------------------------------------------------
                      (1)             (2)             (3)   
             RIF(ln_wage)    RIF(ln_wage)    RIF(ln_wage)   
------------------------------------------------------------
age               0.00473***      0.00471***      0.00471***
               (0.000449)      (0.000447)      (0.000447)   
grade              0.0593***       0.0590***       0.0590***
                (0.00117)       (0.00116)       (0.00116)   
1.race                  0               0               0   
                      (.)             (.)             (.)   
2.race             -0.109***       -0.109***       -0.109***
                (0.00688)       (0.00685)       (0.00685)   
3.race            -0.0117         -0.0117         -0.0117   
                 (0.0244)        (0.0243)        (0.0243)   
msp              -0.00633        -0.00630        -0.00630   
                (0.00593)       (0.00591)       (0.00591)   
_cons               0.516***        0.520***        0.520***
                 (0.0186)        (0.0185)        (0.0185)   
------------------------------------------------------------
N                   28492           28492           28492   
rifmean             1.362           1.362           1.362   
------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001

Notice that the point estimates vary very little, except, perhaps with the constant. The standard errors are also quite close across different kernels functions.

If you would like to use your own bandwidth (one taken from other strategy) you could use something like:

rifhdreg ln_wage age grade i.race msp , rif(q(25) bw(0.1)) robust
rifhdreg ln_wage age grade i.race msp , rif(q(25) bw(0.15)) robust
rifhdreg ln_wage age grade i.race msp , rif(q(25) bw(0.025)) robust

In these examples, Im assuming Gaussian kernel, with three different Bandwidths.

Hope this helps
Fernando

[Kim Myounghwan]

Dear Fernando.
Thank you for your kind comments.

[yang zx]

hi, I found the results from rifhdreg and results from rifreg are different, and it is due to the difference in the recentered outcome variable
webuse nlswork, clear
rifhdreg ln_wage , rif(q(50)) retain(rif1)
rifreg ln_wage , q(50) retain(rif2)
sum rif*

Variable Obs Mean Std. Dev. Min Max

rif1 28,534 1.640541 .5686096 1.071941 2.209141
rif2 28,534 1.640541 .5661384 1.074413 2.20667

the difference is no much in this data ,but differs a lot in my data
could you please explain the reason ?
Thanks!

[FernandoRios]

Hi Yang,
The reason for that is because of how rifreg sets the bandwidth for the estimation of the density function.
namely, rifreg uses the output from kdensity, whereas rifhdreg uses silverman plugin bw.
if you would like to replicate rifreg results, you would need to obtain the bw from kdensity first. See the code below:

webuse nlswork, clear 
rifreg ln_wage , q(50) retain(rif1)
kdensity ln_wage, nograph
* This replicates rifreg
rifhdreg ln_wage , rif(q(50) bw(`r(bwidth)')) retain(rif2) 
* this uses alternative bandwidth.
rifhdreg ln_wage , rif(q(50)) retain(rif3) 
sum rif1 rif2 rif3

Now, results shouldnt vary much between rifreg and rifhdreg. However, if they do, I would re-examine your dependent variable.
Perhaps there is a spike around the point of interest you are analyzing, or that you need a better method to obtain an estimate for the bandwidth.
You could also use different bandwidths as robustness for your results.
Best
Fernando

[Francisco Callado]

Hi, I have very different results with rifreg and rifhdreg:

rifreg lshoraact, quantile(0.5)

kdensity lshoraact, nograph
rifhdreg lshoraact, rif(q(0.5) bw(`r(bwidth)'))

Coefficients:
With rifreg: 2.50
With rifhdreg=0.586

Why could they be so different?
Thanks

[FernandoRios]

if you are interested in the median you need to use "q(50)" not q(0.50).
It was a programming decision i made that quantiles will be defined between 0 - 100. rather than between 0-1.

[Francisco Callado]

Thank you very much.
i followed the same quantity of rifreg....

[FernandoRios]

Right, but "rifreg" parses what goes in "q()" different from what I do. For RIFREG, q(0.5) is interpreted the same as q(50).

[yang zx]

Hi Yang,
The reason for that is because of how rifreg sets the bandwidth for the estimation of the density function.
namely, rifreg uses the output from kdensity, whereas rifhdreg uses silverman plugin bw.
if you would like to replicate rifreg results, you would need to obtain the bw from kdensity first. See the code below:

webuse nlswork, clear
rifreg ln_wage , q(50) retain(rif1)
kdensity ln_wage, nograph
* This replicates rifreg
rifhdreg ln_wage , rif(q(50) bw(`r(bwidth)')) retain(rif2)
* this uses alternative bandwidth.
rifhdreg ln_wage , rif(q(50)) retain(rif3)
sum rif1 rif2 rif3

Now, results shouldnt vary much between rifreg and rifhdreg. However, if they do, I would re-examine your dependent variable.
Perhaps there is a spike around the point of interest you are analyzing, or that you need a better method to obtain an estimate for the bandwidth.
You could also use different bandwidths as robustness for your results.
Best
Fernando

Thank you so much for your help！