Stata Command: ecic
Stata Command: ecic.ado
The ecic command estimates quantile treatment effects (QTE) at extreme quantiles via changes in changes (CIC) based on Sasaki and Wang (Forthcoming). The designed setting requires that all the units are untreated in the first period (T=0), all the units in the control group (G=0) remain untreated in the second period (T=1), and all the units in the treatment group (G=1) receive treatments in the second period (T=1). The command assumes repeated cross sections.
To accommodate covariates, one can run preliminary regression of the outcome Y on covariates X. Replace Y by the residuals in the ecic command. This residualized procedure is theoretically supported by Sasaki and Wang (Forthcoming; Sec. 6).
Installation:
. ssc install ecic
Usage:
. gen Y_resid = 0
. foreach g of numlist 0/1 {
. foreach t of numlist 0/1 {
. regress Y X if G==`g' & T==`t'
. predict temp_Y_resid if G==`g' & T==`t', residuals
. replace Y_resid = temp_Y_resid if G==`g' & T==`t'
. drop temp_Y_resid
. }
. }
. predict resid_Y, residuals
. ecic resid_Y G T, q(0.98)
Help:
. help ecic
Reference: Sasaki, Y & Y. Wang (Forthcoming) Extreme Changes in Changes. Journal of Business & Economic Statistics . Paper.
ecic -- Executes estimation and inference for changes in changes at extreme quantiles.
Syntax
ecic Y G T [if] [in] [, q(real)]
Description
ecic estimates quantile treatment effects (QTE) at extreme quantiles via changes in changes (CIC) based on Sasaki and Wang (Forthcoming). The designed setting requires that all the units are untreated in the first period (T=0), all the units in the control group (G=0) remain untreated in the second period (T=1), and all the units in the treatment group (G=1) receive treatments in the second period (T=1). The command assumes repeated cross sections.
To accommodate covariates, one can run preliminary regression of the outcome Y on covariates X. Replace Y by the residuals in the ecic command. This residualized procedure is theoretically supported by Sasaki and Wang (Forthcoming; Sec. 6).
Option
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 between 0.05 and 0.95.) The default value is q(0.99).
Example
CIC estimation of the QTE at the 98th percentile with an outcome Y, a covariate X, control/treatment group indicator G = 0, 1, and time variable T = 0, 1:
. gen Y_resid = 0 . foreach g of numlist 0/1 { . foreach t of numlist 0/1 { . regress Y X if G==`g' & T==`t' . predict temp_Y_resid if G==`g' & T==`t', residuals . replace Y_resid = temp_Y_resid if G==`g' & T==`t' . drop temp_Y_resid . } . } . predict resid_Y, residuals . ecic resid_Y G T, q(0.98)
Stored results
ecic stores the following in e():
Scalars e(N) observations e(n00) observations with G = 0 and T = 0 e(n01) observations with G = 0 and T = 1 e(n10) observations with G = 1 and T = 0 e(n11) observations with G = 1 and T = 1 e(k00) order statistics for G = 0 and T = 0 e(k01) order statistics for G = 0 and T = 1 e(k10) order statistics for G = 1 and T = 0 e(k11) order statistics for G = 1 and T = 1 e(q) quantile value
Macros e(cmd) ecic e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimator
Functions e(sample) marks estimation sample
Reference
Sasaki, Y. and Y. Wang. Extreme Changes in Changes. Journal of Business & Economic Statistics, Forthcoming. Link to Paper.
Authors
Yuya Sasaki, Vanderbilt University, Nashville, TN.
Yulong Wang, Syracuse University, Syracuse, NY.