Inference in partially identified models with many moment inequalities using Lasso

This paper considers the problem of inference in a partially identified moment (in)equality model with possibly many moment inequalities. Our contribution is to propose a novel two-step new inference method based on the combination of two ideas. On the one hand, our test statistic and critical values are based on those proposed by Chernozhukov, Chetverikov and Kato (2014) (CCK14, hereafter). On the other hand, we propose a new first step selection procedure based on the Lasso. Some of the advantages of our two-step inference method are that (i) it can be used to conduct hypothesis tests and to construct confidence sets for the true parameter value that is uniformly valid, both in underlying parameter $\theta$ and distribution of the data; (ii) our test is asymptotically optimal in a minimax sense and (iii) our method has better power than CCK14 in large parts of the parameter space, both in theory and in simulations. Finally, we show that the Lasso-based first step can be implemented with a thresholding least squares procedure that makes it extremely simple to compute.