*! version 1.0.1 14april2020

Title

qrprocess postestimation -- Postestimation tools for qrprocess

Description

All postestimation commands available after qreg are also available after qrprocess.
In addition, qrprocess predict provides two additional options.

For more detailed information on postestimation options offered by qrprocess, please refer to Chernozhukov, Fernández-Val and Melly (2020).

Command Description

predict predictions, residuals, influence statistics, and other diagnostic measures

Syntax for predict

predict [type] newvar [if] [in]
[, statistic equation(eqno)]

statistic

Usual options
xb linear prediction; the default

stdp standard error of the linear prediction

stddp standard error of the difference in linear predictions

residuals residuals

Specific options
rearranged(numlist) calculates the conditional quantile(s) obtain by rearrangement

cdf(numlist) calculates the conditional cumulative distribution function

Options for predict

Usual options

xb, the default, calculates the linear prediction.

stdp calculates the standard error of the linear prediction.

stddp calculates the standard error of the difference in linear predictions between equations 1 and 2.

residuals calculates the residuals.

Specific options

rearranged(numlist) calculates the conditional quantile(s) obtain by rearrangement as defined in Chernozhukov et al. (2010).
This monotone quantile function can be seen as a sorting or monotone rearrangement of the original function.
The estimated monotone quantile function is numerically equal to the original one if the original curve is increasing in the quantile, but differs from the original function otherwise.
Chernozhukov et al. (2010)
have shown that the rearranged function is asymptotically equivalent with the original one but is closer to the true functions in finite samples.
The numlist specifies the quantile(s) to be calculated. Note that all estimated quantile regressions are used to calculate each conditional quantile.
For instance, the calculated conditional median may not be the same after the estimation of 3 quantile regressions or after 100 quantile regressions.
It is recommended to estimate a large number of quantile regressions to better approximate the conditional distribution.

cdf(numlist)calculates the conditional CDF as defined in Chernozhukov et al. (2010).
The numlist specifies the values at which the CDF will be calculated.
The remarks made in the description of rearranged(numlist) about the number of quantile regressions also apply to this statistic.

Multiple equations

equation(eqno[,eqno]) specifies the equation to which the calculation should be made.
This option matters only for xb, stdp, stddp, and residuals.
For rearranged(numlist) and cdf(numlist) the user must supply the quantiles and y-values directly in parentheses after the option and not through equation.

Examples

Setup - median regression

. sysuse auto

. qrprocess price weight length foreign

Obtain predicted values

. predict hat

Obtain residuals

. predict r, resid

Setup - regression of a large number of quantiles

. qrprocess price weight length foreign, q(0.01(0.01)0.99) noprint

Obtain conditional CDF

. predict cdf, cdf(4000(1000)8000)

References

Chernozhukov, V., I. Fernández-Val, and A. Galichon. 2010. Quantile and probability curves without crossing. Econometrica 78(3): 1093-1125.

Chernozhukov, V., I. Fernández-Val, and B. Melly. 2020b. Quantile and distribution regression in Stata: algorithms, pointwise and functional inference. Working paper.