# Bootstrap inference in a linear equation estimated by instrumental variables

*Russell Davidson* and
*James MacKinnon* ()

*Econometrics Journal*, 2008, vol. 11, issue 3, 443-477

**Abstract:**
We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics--Student's t, Anderson--Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)--as functions of six random quantities leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice. Copyright The Author(s). Journal compilation Royal Economic Society 2008

**Date:** 2008

**References:** Add references at CitEc

**Citations:** View citations in EconPapers (17) Track citations by RSS feed

**Downloads:** (external link)

http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00247.x link to full text (text/html)

Access to full text is restricted to subscribers.

**Related works:**

Working Paper: Bootstrap inference in a linear equation estimated by instrumental variables (2009)

Working Paper: Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables (2008)

Working Paper: BOOTSTRAP INFERENCE IN A LINEAR EQUATION ESTIMATED BY INSTRUMENTAL VARIABLES (2006)

Working Paper: Bootstrap Inference In A Linear Equation Estimated By Instrumental Variables (2006)

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:ect:emjrnl:v:11:y:2008:i:3:p:443-477

**Ordering information:** This journal article can be ordered from

http://www.ectj.org

Access Statistics for this article

Econometrics Journal is currently edited by *Richard J. Smith*, *Oliver Linton*, *Pierre Perron*, *Jaap Abbring* and *Marius Ooms*

More articles in Econometrics Journal from Royal Economic Society Contact information at EDIRC.

Bibliographic data for series maintained by Wiley-Blackwell Digital Licensing ().