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Implementing intersection bounds in Stata

Authors: Victor Chernozhukov , Wooyoung Kim , Sokbae (Simon) Lee and Adam Rosen
Date: 16 March 2015
Type: Journal article, Stata Journal, Vol. 15, No.1, pp. 21-44


We present the clrboundclr2boundclr3bound, 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 clrboundclr2bound, 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 Bonferroni’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.

Accopnaying software is publicly available here and can be installed at the Stata command prompt.

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Victor Chernozhukov, Wooyoung Kim, Sokbae (Simon) Lee and Adam Rosen May 2014, Implementing intersection bounds in Stata, cemmap Working Paper, Institute for Fiscal Studies

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