Stata Command: exquantile
Stata Command: exquantile.ado
Estimation and inference for (conditional) extremal quantiles based on the nearest neighbor method for the Hill's estimator of the tail index in the increasing-k framework, cf. Appendix A.5 of Sasaki and Wang (2021) (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.) Use it when you want to compute (conditional) extremal quantiles, such as the (conditional) 0.1-th percentile or the (conditional) 99.9-th percentile, which cannot be estimated well by the standard quantile methods. For instance, the following Stata output displays show the 1st (top) and 0.1th (bottom) conditional quantiles of the birth weight in grams for smoking mothers at age 40.
Installation:
. ssc install exquantile
Usage:
. use "natl_random.dta"
. xtset id time
. exquantile birwt age if !nosmoke, q(0.01) xval(40)
Help:
. help exquantile
Reference: Sasaki, Y & Y. Wang (2022) Fixed-k Inference for Conditional Extremal Quantiles. Journal of Business & Economic Statistics , 40 (2), pp. 829-837. Paper.
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 the Hill's estimator of the tail index in the increasing-k framework, cf. Appendix A.5 of Sasaki and Wang (2021) (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.