*! version 1.1.1

Title

exquantile -- Executes estimation and inference for (conditional) extremal quantiles.

Syntax

exquantile
depvar
[indepvar]
[if] [in]
[, q(real) k(real) xval(real)]

Description

exquantile estimates (conditional) extremal quantiles based on the nearest neighbor method for Hill's estimator of the tail index in the increasing-k framework, cf. Appendix A.5 of
Sasaki and Wang (2022)
(The fixed-k framework does not provide an estimate or a standard error, and hence it is not implemented in the current Stata command.
Interested researchers can find a MATLAB code
here
for constructing fixed-k confidence intervals.)
If indepvar is absent in the command line, then the unconditional extremal quantile is computed.
If indepvar is present in the command line, then the conditional extremal quantile is computed given the value of indepvar specified by the xval option.
To compute conditional extremal quantiles given a continuous indepvar, the data have to be either panel or repeated cross-sectional data.
For unconditional extremal quantiles (or conditional extremal quantiles given a discrete variable), on the other hand, data can be cross-sectional or repeated cross-sectional.

Options

q(real) sets the quantile value. As an extremal quantile, it is natural to be set either below 0.05 or above 0.95. (A warning message shows up if q is set betwen 0.05 and 0.95.)
The default value is
q(0.99).

k(real) sets the number of tail observations to be used. If this option is not called, then
k
is automatically set to be an integer that is smaller than 5% of the sample size by default.

xval(real) sets the value of
indepvar
x
at which the conditional extremal quantile is estimated. If
indepvar
is included and this option is not called, then
xval
is automatically set to the sample average of
indepvar
by default.

Examples

Estimation of the 0.1-th percentile of the infant birthweight:

. use "natl_random.dta"

. exquantile birwt, q(0.001)

Estimation of the first percentile of the infant birthweight for non-smoking and smoking mothers:

. use "natl_random.dta"

. exquantile birwt if nosmoke, q(0.01)

. exquantile birwt if !nosmoke, q(0.01)

Estimation of the first percentile of the infant birthweight for non-smoking and smoking mothers of age 40:

. use "natl_random.dta"

. xtset id time

. exquantile birwt age if nosmoke, q(0.01) xval(40)

. exquantile birwt age if !nosmoke, q(0.01) xval(40)

Note that conditioning on a continuous variable requires to use either panel or repeated cross-sectional data. The panel or repeated cross-sectional structure can be first set by the xtset command before running exquantile.

Stored results

exquantile stores the following in e():

Scalars

e(N) observations

e(q) quantile value

e(k) tail observations

Macros

e(cmd) exquantile

e(properties) b V

Matrices

e(b) coefficient vector

e(V) variance-covariance matrix of the estimators

Functions

e(sample) marks estimation sample

Reference

Sasaki, Y. and Y. Wang 2022. Fixed-k Inference for Conditional Extremal Quantiles. Journal of Business & Economic Statistics, 40 (2): 829-837.
Link to Paper.

Authors

Yuya Sasaki, Vanderbilt University, Nashville, TN.

Yulong Wang, Syracuse University, Syracuse, NY.