Cruz, Luiz M., and Marcelo J. Moreira. 2005. "On the Validity of Econometric Techniques with Weak Instruments: Inference on Returns to Education Using Compulsory School Attendance Laws." Journal of Human Resources 40(2): 393-410.

We evaluate Angrist and Krueger (1991) and Bound, Jaeger, and Baker (1995) by constructing reliable confidence regions around the 2SLS and LIML estimators for returns-to-schooling regardless of the quality of the instruments. The results indicate that the returns-to-schooling were between 8 and 25 percent in 1970 and between 4 and 14 percent in 1980. Although the estimates are less accurate than previously thought, most specifications by Angrist and Krueger (1991) are informative for returns-to-schooling. In particular, concern about the reliability of the model with 178 instruments is unfounded despite the low first-stage F-statistic. Finally, we briefly discuss bias-adjustment of estimators and pretesting procedures as solutions to the weak-instrument problem.

Luiz Cruz is a Ph.D. student of economics at the University of California at Berkeley. Marcelo Moreira is an assistant professor of economics at Harvard University. This paper was also circulated under the title “Recipes for Applied Researchers: Inference when Instruments May Be Weak.” The authors thank David Jaeger and Douglas Staiger for the data, and Joshua Angrist, Kenneth Chay, Larry Katz, Alan Krueger, David Lee, Thomas Rothenberg, and two referees for helpful comments. The data used in this article may be obtained from the authors between October 2005 and September 2008.