Implementing intersection bounds in Stata
We present the clrbound, clr2bound, clr3bound, and clrtest commands for estimation and inference on intersection bounds as developed by Chernozhukov et al. (2013). The intersection bounds framework encompasses situations where a population parameter of interest is partially identi?ed by a collection of consistently estimable upper and lower bounds. The identi?ed set for the parameter is the intersection of regions de?ned 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 identi?ed 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 con?dence 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 based on 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 identi?ed set or the parameter of interest, whereas clr3bound provides a generally tighter con?dence interval for the parameter by inverting the hypothesis test performed by clrtest. More broadly, inversion of this test can also be used to construct con?dence sets based on conditional moment inequalities as described in Chernozhukov et al. (2013). The commands include parametric, series, and local linear estimation procedures, and can be installed from within STATA by typing “ssc install clrbound”.
Chernozhukov, V; Kim, W; Lee, SS; Rosen, A