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.
Authors
Northwestern University
Joachim Freyberger
Journal article details
- DOI
- 10.1016/j.jeconom.2015.06.020
- Publisher
- Elsevier
- Issue
- Volume 189, Issue 1, November 2015
Suggested citation
Freyberger, J and Horowitz, J. (2015). 'Identification and shape restrictions in nonparametric instrumental variables estimation' 189(1/2015)
More from IFS
Understand this issue
Empty defence spending promises are a shot in the dark
29 April 2024
Public investment: what you need to know
25 April 2024
The £600 billion problem awaiting the next government
25 April 2024
Policy analysis
Recent trends in and the outlook for health-related benefits
19 April 2024
4.2 million working-age people now claiming health-related benefits, could rise by 30% by the end of the decade
19 April 2024
Progression of nurses within the NHS
12 April 2024
Academic research
The employment and distributional impacts of nationwide minimum wage changes
10 April 2024
Willingness to pay for improved public education and public healthcare systems: the role of income mobility prospects
14 March 2024
Unfunded mandates and taxation
14 March 2024