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Hierarchical Bayes Models with Many Instrumental Variables

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  • Gary Chamberlain
  • Guido W. Imbens

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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0204.

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Date of creation: Sep 1996
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Handle: RePEc:nbr:nberte:0204

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  1. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  2. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc.
  3. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  5. Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
  6. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
  7. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800 Elsevier.
  8. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-35, April.
  9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  10. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
  11. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  12. John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
  13. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
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Cited by:
  1. Alan Krueger & Mikael Lindahl, 1998. "Education for Growth in Sweden and the World," Working Papers 790, Princeton University, Department of Economics, Industrial Relations Section..
  2. Rajeev Dehejia, 2000. "Was There a Riverside Miracle? A Framework for Evaluating Multi-Site Programs," NBER Working Papers 7844, National Bureau of Economic Research, Inc.
  3. Daron Acemoglu & Joshua Angrist, 1999. "How Large are the Social Returns to Education? Evidence from Compulsory Schooling Laws," Working papers 99-30, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
  5. Rajeev H. Dehejia, 2002. "Program evaluation as a decision problem," Discussion Papers 0102-23, Columbia University, Department of Economics.
  6. Edward E. Leamer, 2010. "Tantalus on the Road to Asymptopia," Journal of Economic Perspectives, American Economic Association, vol. 24(2), pages 31-46, Spring.
  7. Thomas Knox & James H. Stock & Mark W. Watson, 2000. "Empirical Bayes Forecasts of One Time Series Using Many Predictors," Econometric Society World Congress 2000 Contributed Papers 1421, Econometric Society.
  8. Joshua D. Angrist & Jinyong Hahn, 1999. "When to Control for Covariates? Panel-Asymptotic Results for Estimates of Treatment Effects," NBER Technical Working Papers 0241, National Bureau of Economic Research, Inc.

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