Confidence intervals for gradients in npregress

[Tobias Scheckel]

Dear all,

I'm trying to estimate confidence intervals for my gradients after performing a kernel reegression in STATA. I created a mock dataset:

*create dataset with 1000 obs and 3 variables (random residuals, random regressors,
*non-random dep var; seed 1)
set obs 1000
set seed 1
gen e = rnormal(0,1)
gen x = rnormal(5,8)
gen y = 78 + 7*x^2 + e

and then performed:

npregress kernel y x

which returns me an estimate of the mean function as well as for the gradients of y. I just could not find out if and how I can estimate confidence intervals for the gradients.

Regards,
Tobias

[FernandoRios]

Hi Tobias
To obtain the standard errors, you need to add the option vce(bootstrap) to your command line.

. npregress kernel y x, vce(bootstrap, seed(1))
(running npregress on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50

Bandwidth
------------------------------------
             |      Mean     Effect 
-------------+----------------------
           x |  2.028782   3.058894 
------------------------------------

Local-linear regression                    Number of obs      =          1,000
Kernel   : epanechnikov                    E(Kernel obs)      =          1,000
Bandwidth: cross validation                R-squared          =         0.9991
------------------------------------------------------------------------------
             |   Observed   Bootstrap                          Percentile
           y |   Estimate   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Mean         |
           y |   744.0941   30.83909    24.13   0.000     684.1975    805.6043
-------------+----------------------------------------------------------------
Effect       |
           x |   71.68299   3.951594    18.14   0.000     64.68955    80.09341
------------------------------------------------------------------------------
Note: Effect estimates are averages of derivatives.

Same if you want to estimate the marginal effects at some other point of X (instead of the average).

margins, dydx(x) at(x=5) vce(bootstrap)

HTH
Fernando