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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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Suggested Citation

  • Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Harvard Institute of Economic Research Working Papers 1781, Harvard - Institute of Economic Research.
    • Handle: RePEc:fth:harver:1781
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    1. John Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
    2. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
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    8. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    9. 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.
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    13. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
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    Cited by:

    1. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    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. Mikael Lindahl & Alan B. Krueger, 2001. "Education for Growth: Why and for Whom?," Journal of Economic Literature, American Economic Association, vol. 39(4), pages 1101-1136, December.
    4. Piero Stanig, 2015. "Regulation of Speech and Media Coverage of Corruption: An Empirical Analysis of the Mexican Press," American Journal of Political Science, John Wiley & Sons, vol. 59(1), pages 175-193, January.
    5. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    6. Daron Acemoglu & Joshua Angrist, 1999. "How Large are the Social Returns to Education? Evidence from Compulsory Schooling Laws," NBER Working Papers 7444, National Bureau of Economic Research, Inc.
    7. Pedro Saramago & Karl Claxton & Nicky J. Welton & Marta Soares, 2020. "Bayesian econometric modelling of observational data for cost‐effectiveness analysis: establishing the value of negative pressure wound therapy in the healing of open surgical wounds," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1575-1593, October.
    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.
    9. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    10. Edward E. Leamer, 2010. "Tantalus on the Road to Asymptopia," Journal of Economic Perspectives, American Economic Association, vol. 24(2), pages 31-46, Spring.
    11. 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.
    12. 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..
    13. Alan B. Krueger & Mikael Lindahl, 1998. "Education for Growth in Sweden and the World," Working Papers 790, Princeton University, Department of Economics, Industrial Relations Section..

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