Inference in partially identified models with many moment inequalities using Lasso

Federico A. Bugni*, Mehmet Caner, Anders Bredahl Kock, Soumendra Lahiri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)211-248
Number of pages38
JournalJournal of Statistical Planning and Inference
StatePublished - May 2020


  • Empirical bootstrap
  • Inequality selection
  • Lasso
  • Many moment inequalities
  • Multiplier bootstrap
  • Self-normalizing sum

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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