Identification and shape restrictions in nonparametric instrumental variables estimation

Joachim Freyberger and Joel L. Horowitz ()
Additional contact information
Joachim Freyberger: Institute for Fiscal Studies and University of Bonn
Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University

No CWP15/12, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper is concerned with inference about an unidentified linear functional, L(g), where the function g satisfies the relation Y = g(X) + U; E(U | W) = 0. In this relation, Y is the dependent variable, X is a possibly endogenous explanatory variable, W is an instrument for X, and U is an unobserved random variable. The data are an independent random sample of (Y,X,W). In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, neither g nor L(g) is nonparametrically identified. Indeed, L(g) can have any value in (-8, 8). In applied research, this problem is typically overcome and point identification is achieved by assuming that g is a linear function of X. However, the assumption of linearity is arbitrary. It is untestable if W is binary, as is the case in many applications. This paper explores the use of shape restrictions, such as monotonicity or convexity, for achieving interval identification of L(g). Economic theory often provides such shape restrictions. This paper shows that they restrict L(g) to an interval whose upper and lower bounds can be obtained by solving linear programming problems. Inference about the identified interval and the functional L(g) can be carried out by using by using the bootstrap. An empirical application illustrates the usefulness of shape restrictions for carrying out nonparametric inference about L(g).

Date: 2012-06-27
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.cemmap.ac.uk/wps/cwp151212.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:15/12

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().