quantile regression VS OLS

[hunter shi]

Hi folks,

I am pretty new to quantile regression. So, I want to learn it by comparing it with the OLS regression. Basically, for the LHS variable, if the mean equals the median, should the quantile regression at the median generate the same coefficients as the OLS regression? To test this, I need to generate a LHS variable with the same mean and median. Is there such a code like this? Say gen y=rnormal(0,1), median==0? Thank you very much for your help!

Ruyi.

[Maarten Buis]

clear all
set seed 516247

program sim, rclass
    drop _all
    set obs 2000
    gen x1 = runiform() < .5
    gen x2 = rnormal()
    gen y = -2 + 0.5*x2 - .5*x1 + 2*rnormal()
    reg y i.x1 x2
    return scalar rb0 = _b[_cons]
    return scalar rse0 = _se[_cons]
    return scalar rb1 = _b[1.x1]
    return scalar rse1 = _se[1.x1]
    return scalar rb2 = _b[x2]
    return scalar rse2 = _se[x2]

    qreg y i.x1 x2
    return scalar qb0 = _b[_cons]
    return scalar qse0 = _se[_cons]
    return scalar qb1 = _b[1.x1]
    return scalar qse1 = _se[1.x1]
    return scalar qb2 = _b[x2]
    return scalar qse2 = _se[x2]
end

simulate rb0=r(rb0) rse0=r(rse0) ///
         rb1=r(rb1) rse1=r(rse1) ///  
         rb2=r(rb2) rse2=r(rse2) ///
         qb0=r(qb0) qse0=r(qse0) ///
         qb1=r(qb1) qse1=r(qse1) ///  
         qb2=r(qb2) qse2=r(qse2) ///
         , reps(2000) : sim

ssc install simsum
simsum rb1 qb1, se(rse1 qse1) true(.5)

[hunter shi]

clear all
set seed 516247

program sim, rclass
drop _all
set obs 2000
gen x1 = runiform() < .5
gen x2 = rnormal()
gen y = -2 + 0.5*x2 - .5*x1 + 2*rnormal()
reg y i.x1 x2
return scalar rb0 = _b[_cons]
return scalar rse0 = _se[_cons]
return scalar rb1 = _b[1.x1]
return scalar rse1 = _se[1.x1]
return scalar rb2 = _b[x2]
return scalar rse2 = _se[x2]

qreg y i.x1 x2
return scalar qb0 = _b[_cons]
return scalar qse0 = _se[_cons]
return scalar qb1 = _b[1.x1]
return scalar qse1 = _se[1.x1]
return scalar qb2 = _b[x2]
return scalar qse2 = _se[x2]
end

simulate rb0=r(rb0) rse0=r(rse0) ///
rb1=r(rb1) rse1=r(rse1) ///
rb2=r(rb2) rse2=r(rse2) ///
qb0=r(qb0) qse0=r(qse0) ///
qb1=r(qb1) qse1=r(qse1) ///
qb2=r(qb2) qse2=r(qse2) ///
, reps(2000) : sim

ssc install simsum
simsum rb1 qb1, se(rse1 qse1) true(.5)

Hi Maarten,

Thanks a lot! That works!

Cheers,
Ruyi.