Hierarchical Bayes Models with Many Instrumental Variables

Gary Chamberlain, Guido W. Imbens

NBER Technical Working Paper No. 204
Issued in September 1996
NBER Program(s):Labor Studies

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.

download in pdf format
   (679 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0204

Users who downloaded this paper also downloaded* these:
Chamberlain and Imbens t0200 Nonparametric Applications of Bayesian Inference
Chamberlain w0913 Panel Data
Boskin and Hurd w0204 The Effect of Social Security on Early Retirement
Stock and Wright t0198 Asymptotics for GMM Estimators with Weak Instruments
Chamberlain w0325 Analysis of Covariance With Qualitative Data
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us