TY - JOUR
ID - st0369
A1 - Chernozhukov, V.
A1 - Kim, W.
A1 - Lee, S.
A1 - Rosen, A.
TI - Implementing intersection bounds in Stata
JF - Stata Journal
PB - Stata Press
CY - College Station, TX
Y1 - 2015
VL - 15
IS - 1
SP - 21
EP - 44
KW - clrbound
KW - clr2bound
KW - clr3bound
KW - clrtest
KW - intersection bounds
KW - bound analysis
KW - conditional moments
KW - partial identification
KW - infinite dimensional constraints
KW - adaptive moment selection
UR - http://www.stata-journal.com/article.html?article=st0369
L1 - http://www.stata-journal.com/sjpdf.html?article=st0369
AB - We present the clrbound, clr2bound, clr3bound, and clrtest commands
for estimation and inference on intersection bounds as developed by Chernozhukov,
Lee, and Rosen (2013, Econometrica 81: 667-737). The intersection
bounds framework encompasses situations where a population parameter of interest
is partially identified by a collection of consistently estimable upper and lower
bounds. The identified set for the parameter is the intersection of regions defined
by this collection of bounds. More generally, the methodology can be applied
to settings where an estimable function of a vector-valued parameter is bounded
from above and below, as is the case when the identified set is characterized by
conditional moment inequalities.
The commands clrbound, clr2bound, and clr3bound provide bound estimates
that can be used directly for estimation or to construct asymptotically valid
confidence sets. clrtest performs an intersection bound test of the hypothesis
that a collection of lower intersection bounds is no greater than zero. The command
clrbound provides bound estimates for one-sided lower or upper intersection
bounds on a parameter, while clr2bound and clr3bound provide two-sided bound
estimates using both lower and upper intersection bounds. clr2bound uses Bonferroniâ€™s
inequality to construct two-sided bounds that can be used to perform
asymptotically valid inference on the identified set or the parameter of interest,
whereas clr3bound provides a generally tighter confidence interval for the parameter
by inverting the hypothesis test performed by clrtest. More broadly,
inversion of this test can also be used to construct confidence sets based on conditional
moment inequalities as described in Chernozhukov, Lee, and Rosen (2013).
The commands include parametric, series, and local linear estimation procedures.
ER -