```help qreg2                                       also see:  qreg postestimation

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Title

qreg2 -- Quantile regression with robust standard errors

Syntax

qreg2 depvar [indepvars] [if] [in] [weight] [, qreg2_options]

options                    Description
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quantile(#)              estimate # quantile; default is quantile(.5)

norobust                 displays results based on the non-robust
covariance matrix estimator

mss(varlist)             use varlist in the MSS heteroskedasticity test

nomss                    suppresses the computation of the MSS test

wlsiter(#)               attempt # weighted least-squares iterations
before doing linear programming iterations

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qreg2 allows fweights; see weight.
See [R] qreg postestimation for features available after estimation.

Description

qreg2 is a wrapper for [R] qreg which estimates quantile regression and
reports standard errors and t-statistics that are asymptotically valid
under heteroskedasticity and misspecification. The robust covariance
matrix is computed following Chamberlain (1994), Angrist et al. (2006),
and Powell (1984).  The non-robust results can also displayed with the
option norobust. Additionally, qreg2 reports the value of the objective
function, defined as the average of the check function; the R-squared,
defined as the square of the correlation between the fitted values and
the dependent variable (note however that in quantile regressions the
R-squared is even less meaningful than usual); and the result of the
Machado-Santos Silva (2000) test for heteroskedasticity. This test is
valid after quantile regression estimation and by default the test
variables are the fitted values of the dependent variable and its squares
as in the "Special case of the White test"; see Wooldridge (2009, p.
276). Alternative sets of test variables can be specified with
mss(varlist) and the computation of the statistic can be suppressed with
the option nomss.

Options

quantile(#) specifies the quantile to be estimated and should be a number
between 0 and 1, exclusive.  Numbers larger than 1 are interpreted as
percentages.  The default value of 0.5 corresponds to the median.

norobust display results based on the non-robust covariance matrix
estimator.

mss(varlist) specifies the list of variables to be used in the
Machado-Santos Silva (2000) heteroskedasticity test.  By default, the
test is performed using the fitted values of the dependent variable
and its squares.

nomss suppresses the computation of the MSS test.

wlsiter(#) specifies the number of weighted least-squares iterations that
will be attempted before the linear programming iterations are
started.  The default value is 1.  If there are convergence problems,
increasing this number should help.

Remarks

qreg2 was written by J.A.F. Machado and J.M.C. Santos Silva and it is not
jmcss@essex.ac.uk. Please notice that this software is provided as is,
without warranty of any kind, express or implied, including but not
limited to the warranties of merchantability, fitness for a particular
purpose and noninfringement. In no event shall the authors be liable for
any claim, damages or other liability, whether in an action of contract,
tort or otherwise, arising from, out of or in connection with the
software or the use or other dealings in the software.

Examples

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Setup
. sysuse auto

Median regression
. qreg2 price weight length foreign

Median regression with non-robust output
. qreg2 price weight length foreign,nor

Estimate .25 quantile
. qreg2 price weight length foreign, quantile(.25)

Median regression computing the MSS test using the regressors as test
variables
. qreg2 price weight length foreign, mss(weight length foreign)

Median regression suppressing the MSS test
. qreg2 price weight length foreign, nomss

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Saved results

qreg2 saves the following in e():

Scalars
e(N)           number of observations
e(df_m)        model degrees of freedom
e(df_r)        residual degrees of freedom
e(q)           quantile requested
e(q_v)         value of the quantile
e(sum_rdev)    sum of raw deviations
e(obj_func)    mean of the check function
e(f_r)         residual density estimate
e(rank)        rank of the non-robust covariance matrix
e(convcode)    0 if converged; otherwise, return code for why
nonconvergence
e(r2)          R-squared defined as the square of the correlation
between the fitted values and the dependent variable
e(mss_chi2)    MSS test statistic (if computed)
e(mss_df)      degrees of freedom of the MSS test (if computed)
e(mss_p)       p-value of the MSS test (if computed)

Macros
e(cmd)         qreg2
e(cmdline)     command as used in the estimation
e(depvar)      name of dependent variable
e(properties)  b V
e(predict)     program used to implement predict
e(marginsnotok)
predictions disallowed by margins

Matrices
e(b)           coefficient vector
e(V)           variance-covariance matrix

Functions
e(sample)      marks estimation sample

References

Angrist, J.; Chernozhukov, V. and Fernández-Val, I. (2006), Quantile
Regression under Misspecification, with an Application to the U.S.
Wage Structure, Econometrica, 74, 539-563.

Chamberlain, G. (1994), Quantile Regression, Censoring and the Structure
of Wages, in Advances in Econometrics, ed. C. A. Sims, Cambridge
University Press, 171-209.

Machado, J.A.F. and Santos Silva, J.M.C. (2000), Glejser's Test
Revisited, Journal of Econometrics, 97(1), 189-202.

Powell, J. L. (1984), Least Absolute Deviation Estimation for the
Censored Regression Model, Journal of Econometrics, 25, 303-325.

Wooldridge, J.M. (2009), Introductory Econometrics, 4th edition, Mason
(OH): South Western.

Also see

Manual:  [R] qreg

Help:  [R] qreg postestimation;

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