Standard errors change when setting a different confidence level with qreg command

[Maria Martins]

Hello to all,

I am using STATA 16 and when running the command qreg with a different confidence level of the default (95), I get different standard errors for the coefficients.
Can you explain the rationale?

Thank you.

An example,

. qreg fips ln_eat
Iteration 1: WLS sum of weighted deviations = 60878960

Iteration 1: sum of abs. weighted deviations = 61014080
Iteration 2: sum of abs. weighted deviations = 60591692

Median regression Number of obs = 898
Raw sum of deviations 6.12e+07 (about 252770)
Min sum of deviations 6.06e+07 Pseudo R2 = 0.0092

------------------------------------------------------------------------------
fips | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ln_eat | -76162.7 18659.58 -4.08 0.000 -112784.3 -39541.14
_cons | 159102.5 21368.75 7.45 0.000 117163.9 201041.1
------------------------------------------------------------------------------

. qreg fips ln_eat, level(68)
Iteration 1: WLS sum of weighted deviations = 60878960

Iteration 1: sum of abs. weighted deviations = 61014080
Iteration 2: sum of abs. weighted deviations = 60591692

Median regression Number of obs = 898
Raw sum of deviations 6.12e+07 (about 252770)
Min sum of deviations 6.06e+07 Pseudo R2 = 0.0092

------------------------------------------------------------------------------
fips | Coef. Std. Err. t P>|t| [68% Conf. Interval]
-------------+----------------------------------------------------------------
ln_eat | -76162.7 20017.61 -3.80 0.000 -96080.42 -56244.98
_cons | 159102.5 22923.95 6.94 0.000 136293 181912.1
------------------------------------------------------------------------------

[Joao Santos Silva]

Dear Maria Martins,

That is because the default bandwith parameter depends on the chosen significance level. If that is inconvenient, you can use Bofinger's bandwidth; please check the help file and the PDF documentation.

Best wishes,

Joao

[Maria Martins]

Thank you for the reply, Joao Santos Silva .
Now, concerning the qreg2 package, the standard errors follow a Chamberlain’s bandwidth?

[Joao Santos Silva]

Dear Maria Martins,

We use the Hall and Sheather's bandwidth assuming a 5% level, as documented in

Parente, P.M.D.C. and Santos Silva, J.M.C. (2016), Quantile Regression with Clustered Data, Journal of Econometric Methods, 5(1), pp. 1-15.

Best wishes,

Joao

[Maria Martins]

Once again, many thanks for the reply, Joao Santos Silva.

If I want a confidence level of 68% with the qreg2 command, would this amendment to the code be sufficient?

qui local _hs=(invnormal(0.84)^(2/3))*(((1.5*((normalden(invnormal(`_eta')))^2))/(2*((invnormal(`_eta'))^2) + 1))^(1/3))

[Joao Santos Silva]

That is correct, Maria Martins.

Best wishes,

Joao