Inference in partially identified models with many moment inequalities using Lasso

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 et al. (2018a) (Chernozhukov et al., 2018a, hereafter) with a first step moment inequality selection based on the Lasso. Our method controls asymptotic size uniformly, both in the underlying parameter and the data distribution. Also, the power of our method compares favorably with that of the corresponding two-step method in Chernozhukov et al. (2018a) 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.