Identification and shape restrictions in nonparametric instrumental variables estimation

Joachim Freyberger, Joel L. Horowitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This paper is concerned with inference about an unidentified linear functional, L(g), where g satisfies Y=g(X)+U; E(U|W)=0. In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, L(g) is not identified nonparametrically and can have any value in (-∞,∞). This paper uses shape restrictions, such as monotonicity or convexity, to achieve interval identification of L(g). The paper shows that under shape restrictions, L(g) is contained in an interval whose bounds can be obtained by solving linear programming problems. Inference about L(g) can be carried out by using the bootstrap. An empirical application illustrates the usefulness of the method.

Original languageEnglish (US)
Pages (from-to)41-53
Number of pages13
JournalJournal of Econometrics
Issue number1
StatePublished - Nov 1 2015


  • Bootstrap
  • Linear programming
  • Partial identification

ASJC Scopus subject areas

  • Economics and Econometrics

Fingerprint Dive into the research topics of 'Identification and shape restrictions in nonparametric instrumental variables estimation'. Together they form a unique fingerprint.

Cite this