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Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information

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  • Christiane Baumeister
  • James D. Hamilton

Abstract

This paper makes the following original contributions to the literature. (1) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions that can be used for models that are overidentified, just-identified, or underidentified. (2) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n-variable VAR is confined to the set of values that orthogonalize the population variance-covariance matrix of OLS residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (3) We provide analytical characterizations of the informative prior distributions for impulse-response functions that are implicit in the traditional sign-restriction approach to VARs, and note, as a special case of result (2), that the influence of these priors does not vanish asymptotically. (4) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just-identified models. (5) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and illustrate how this could be done using a simple model of the U.S. labor market.

Suggested Citation

  • Christiane Baumeister & James D. Hamilton, 2014. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," NBER Working Papers 20741, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:20741
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    1. Eleonora Granziera & Hyungsik Roger Moon & Frank Schorfheide, 2018. "Inference for VARs identified with sign restrictions," Quantitative Economics, Econometric Society, vol. 9(3), pages 1087-1121, November.
    2. Lichter, Andreas & Peichl, Andreas & Siegloch, Sebastian, 2015. "The own-wage elasticity of labor demand: A meta-regression analysis," European Economic Review, Elsevier, vol. 80(C), pages 94-119.
    3. Renée Fry & Adrian Pagan, 2011. "Sign Restrictions in Structural Vector Autoregressions: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 938-960, December.
    4. Jordi Galí & Frank Smets & Rafael Wouters, 2012. "Unemployment in an Estimated New Keynesian Model," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 329-360.
    5. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 665-696.
    6. Raj Chetty & Adam Guren & Day Manoli & Andrea Weber, 2013. "Does Indivisible Labor Explain the Difference between Micro and Macro Elasticities? A Meta-Analysis of Extensive Margin Elasticities," NBER Macroeconomics Annual, University of Chicago Press, vol. 27(1), pages 1-56.
    7. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    8. Matthew Shapiro & Mark Watson, 1988. "Sources of Business Cycles Fluctuations," NBER Chapters, in: NBER Macroeconomics Annual 1988, Volume 3, pages 111-156, National Bureau of Economic Research, Inc.
    9. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599, September.
    10. Lutz Kilian & Daniel P. Murphy, 2012. "Why Agnostic Sign Restrictions Are Not Enough: Understanding The Dynamics Of Oil Market Var Models," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 1166-1188, October.
    11. Felix Reichling & Charles Whalen, 2012. "Review of Estimates of the Frisch Elasticity of Labor Supply: Working Paper 2012-13," Working Papers 43676, Congressional Budget Office.
    12. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
    13. Cho, Jang-Ok & Cooley, Thomas F., 1994. "Employment and hours over the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 18(2), pages 411-432, March.
    14. Canova, Fabio & Nicolo, Gianni De, 2002. "Monetary disturbances matter for business fluctuations in the G-7," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1131-1159, September.
    15. Leamer, Edward E, 1981. "Is It a Demand Curve, or Is It a Supply Curve? Partial Identification through Inequality Constraints," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 319-327, August.
    16. John Haltiwanger & Steven J. Davis, 1999. "On the Driving Forces behind Cyclical Movements in Employment and Job Reallocation," American Economic Review, American Economic Association, vol. 89(5), pages 1234-1258, December.
    17. Faust, Jon & Leeper, Eric M, 1997. "When Do Long-Run Identifying Restrictions Give Reliable Results?," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 345-353, July.
    18. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    19. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    20. Gustafson, Paul, 2009. "What Are the Limits of Posterior Distributions Arising From Nonidentified Models, and Why Should We Care?," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1682-1695.
    21. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    22. Canova, Fabio & Paustian, Matthias, 2011. "Business cycle measurement with some theory," Journal of Monetary Economics, Elsevier, vol. 58(4), pages 345-361.
    23. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(4), pages 483-509, August.
    24. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    25. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity

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