  This paper considers inference in a partially identified moment (in)equality
model with many moment inequalities. We propose a novel two-step inference
procedure that combines the methods proposed by Chernozhukov, Chetverikov and
Kato (2018a) (CCK18, hereafter) with a first step moment inequality selection
based on the Lasso. Our method controls asymptotic size uniformly, both in
underlying parameter and data distribution. Also, the power of our method
compares favorably with that of the corresponding two-step method in CCK18 for
large parts of the parameter space, both in theory and in simulations. Finally,
we show that our Lasso-based first step can be implemented by thresholding
standardized sample averages, and so it is straightforward to implement.
