*! version 1.1.1

Title

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 within each (G,T) pair.
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.