Avoiding Invalid Instruments and Coping with Weak Instruments

Useful advice for when trying to implement IV.

Avoiding Invalid Instruments and Coping with Weak Instruments
Michael P. Murray
Journal of Economic Perspectives—Volume 20, Number 4—Fall 2006—Pages 111–132

Archimedes said, “Give me the place to stand, and a lever long enough, and I will move the Earth” (Hirsch, Kett, and Trefil, 2002, p. 476). Economists have their own powerful lever: the instrumental variable estimator. The instrumental variable estimator can avoid the bias that ordinary least squares suffers when an explanatory variable in a regression is correlated with the regression’s disturbance term. But, like Archimedes’ lever, instrumental variable estimation requires both a valid instrument on which to stand and an instrument that isn’t too short (or “too weak”). This paper briefly reviews instrumental variable estimation, discusses classic strategies for avoiding invalid instruments (instruments themselves correlated with the regression’s disturbances), and describes recently developed strategies for coping with weak instruments (instruments only weakly correlated with the offending explanator).

http://www.eui.eu/Personal/Guiso/Courses/Econometrics/Murray_IV_jep_06.pdf

Identifying Peer Effects Through Variance Restrictions

Kevin’s post on peer effects mentioned the problem of identification, an example of a less standard approach to this issue is the paper by Graham (IDENTIFYING SOCIAL INTERACTIONS THROUGH CONDITIONAL VARIANCE RESTRICTIONS, BRYAN S. GRAHAM, Econometrica, Vol.76, No. 3 (May, 2008), 643–660), which uses variance restrictions to argue that peer effects were important for participants in the Tennessee STAR class size experiment. The intuition is described below (from p.4):

“The application examines the effect of peer quality on kindergarten achievement using data from the Tennessee class size reduction experiment Project STAR. Classrooms of two sizes are observed in the data set: small and large. Students and teachers within participating schools were randomly assigned to one of the two types of classrooms. In large classrooms, clusters of talented students are typically offset by corresponding clusters of below average students, resulting in little variation in mean student ability. In small classrooms, however, groups composed of mostly above or below average students are more frequently observed, generating greater variation in mean ability. As a result, the variance of peer quality (as measured by average student ability in a classroom) is greater across the set of small than it is across the set of large classrooms. In contrast to peer quality, random assignment ensures that the distribution of teacher characteristics is similar across the two types of classrooms. Under some additional restrictions on the educational production function, discussed in detail below, class type provides a plausible source of exogenous variation in the variance of peer quality”.