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This paper considers inference in a partially identified moment (in)equalitymodel with many moment inequalities. We propose a novel two-step inferenceprocedure that combines the methods proposed by Chernozhukov, Chetverikov andKato (2018a) (CCK18, hereafter) with a first step moment inequality selectionbased on the Lasso. Our method controls asymptotic size uniformly, both inunderlying parameter and data distribution. Also, the power of our methodcompares favorably with that of the corresponding two-step method in CCK18 forlarge parts of the parameter space, both in theory and in simulations. Finally,we show that our Lasso-based first step can be implemented by thresholdingstandardized sample averages, and so it is straightforward to implement.

Inference in partially identified models with many moment inequalities using Lasso