Hierarchical Bayes Models with Many Instrumental Variables

28 Pages Posted: 5 Sep 2000 Last revised: 25 Jul 2010

See all articles by Gary Chamberlain

Gary Chamberlain

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Guido W. Imbens

Stanford Graduate School of Business

Date Written: September 1996

Abstract

In this paper, we explore Bayesian inference in models with many instrumental variables that are potentially weakly correlated with the endogenous regressor. The prior distribution has a hierarchical (nested) structure. We apply the methods to the Angrist-Krueger (AK, 1991) analysis of returns to schooling using instrumental variables formed by interacting quarter of birth with state/year dummy variables. Bound, Jaeger, and Baker (1995) show that randomly generated instrumental variables, designed to match the AK data set, give two-stage least squares results that look similar to the results based on the actual instrumental variables. Using a hierarchical model with the AK data, we find a posterior distribution for the parameter of interest that is tight and plausible. Using data with randomly generated instruments, the posterior distribution is diffuse. Most of the information in the AK data can in fact be extracted with quarter of birth as the single instrumental variable. Using artificial data patterned on the AK data, we find that if all the information had been in the interactions between quarter of birth and state/year dummies, then the hierarchical model would still have led to precise inferences, whereas the single instrument model would have suggested that there was no information in the data. We conclude that hierarchical modeling is a conceptually straightforward way of efficiently combining many weak instrumental variables.

Suggested Citation

Chamberlain, Gary and Imbens, Guido W., Hierarchical Bayes Models with Many Instrumental Variables (September 1996). NBER Working Paper No. t0204. Available at SSRN: https://ssrn.com/abstract=226627

Gary Chamberlain (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
Room 123
Cambridge, MA 02138
United States
617-495-1869 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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