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Bayesian Inference of Local Projections with Roughness Penalty Priors

  • Masahiro TanakaEmail author
Article
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Abstract

A local projection is a statistical framework that accounts for the relationship between an exogenous variable and an endogenous variable, measured at different time points. Local projections are often applied in impulse response analyses and direct forecasting. While local projections are becoming increasingly popular because of their robustness to misspecification and their flexibility, they are less statistically efficient than standard methods, such as vector autoregression. In this study, we seek to improve the statistical efficiency of local projections by developing a fully Bayesian approach that can be used to estimate local projections using roughness penalty priors. By incorporating such prior-induced smoothness, we can use information contained in successive observations to enhance the statistical efficiency of an inference. We apply the proposed approach to an analysis of monetary policy in the United States, showing that the roughness penalty priors successfully estimate the impulse response functions and improve the predictive accuracy of local projections.

Keywords

Local projection Roughness penalty prior Bayesian B-spline Impulse response 

JEL Classification

C11 C14 C51 

Notes

Supplementary material

10614_2019_9905_MOESM1_ESM.pdf (211 kb)
Supplementary material 1 (pdf 210 KB)

References

  1. Aikman, D., Bush, O., & Taylor, A. M. (2016). Monetary versus macroprudential policies: Causal impacts of interest rates and credit controls in the era of the UK radcliffe report. NBER working paper 22380.Google Scholar
  2. Alvarez, I., Niemi, J., & Simpson, M. (2014). Bayesian inference for a covariance matrix. In 26th Annual conference on applied statistics in agriculture.Google Scholar
  3. Auerbach, A. J., & Gorodnichenko, Y. (2013). Fiscal multipliers in recession and expansion. In A. Alesina & F. Giavazzi (Eds.), Fiscal policy after the financial crisis (pp. 63–98). Chicago: University of Chicago Press.CrossRefGoogle Scholar
  4. Barnichon, R., & Matthes, C. (2019). Functional approximations of impulse responses. Journal of Monetary Economics, 99(1), 41–55.Google Scholar
  5. Barnichon, R., & Brownlees, C. (2019). Impulse response estimation by smooth local projections. Review of Economics and Statistics, 101(3), 522–230.CrossRefGoogle Scholar
  6. Byrd, R. H., Peihuang, L., Nocedal, J., & Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, 1190–1208.CrossRefGoogle Scholar
  7. Coibion, O., Gorodnichenko, Y., Kueng, L., & Silvia, J. (2017). Innocent bystanders? Monetary policy and inequality. Journal of Monetary Economics, 88, 70–89.CrossRefGoogle Scholar
  8. De Boor, C. (1978). A practical guide to splines (Vol. 27). New York: Springer.CrossRefGoogle Scholar
  9. Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89–121.CrossRefGoogle Scholar
  10. El-Shagi, M. (2019). A simple estimator for smooth local projections. Applied Economics Letters, 26, 830–834.CrossRefGoogle Scholar
  11. Geweke, J. (2005). Contemporary Bayesian econometrics and statistics (Vol. 537). New York: Wiley.CrossRefGoogle Scholar
  12. Guo, W. (2002). Functional mixed effects models. Biometrics, 58, 121–128.CrossRefGoogle Scholar
  13. Huang, A., & Wand, M. P. (2013). Simple marginally noninformative prior distributions for covariance matrices. Bayesian Analysis, 8, 439–452.CrossRefGoogle Scholar
  14. Hurvich, C. M., Simonoff, J. S., & Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60, 271–293.CrossRefGoogle Scholar
  15. Jordà, Ò. (2005). Estimation and inference of impulse responses local projections. American Economic Review, 95, 161–182.CrossRefGoogle Scholar
  16. Lang, S., & Brezger, A. (2004). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13, 183–212.CrossRefGoogle Scholar
  17. Miranda-Agrippino, S., & Ricco, G. (2017). The transmission of monetary policy shocks. Staff working paper 657, Bank of England.Google Scholar
  18. Morris, J. S., & Carroll, R. J. (2006). Wavelet-based functional mixed models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 179–199.CrossRefGoogle Scholar
  19. Ramey, V. A. (2016). Macroeconomic shocks and their propagation, Chap. 2. In J. B. Taylor & H. Uhlig (Eds.), Handbook of macroeconomics (Vol. 2A, pp. 71–162). Amsterdam: Elsevier.Google Scholar
  20. Ramey, V. A., & Zubuairy, S. (2018). Government spending multipliers in good times and in bad: Evidence from U.S. historical data. Journal of Political Economy, 126(2), 850–901.Google Scholar
  21. Riera-Crichton, D., Vegh, C. A., & Vuletin, G. (2015). Procyclical and countercyclical fiscal multipliers: Evidence from OECD countries. Journal of International Money and Finance, 52, 15–31.CrossRefGoogle Scholar
  22. Romer, C. D., & Romer, D. H. (2004). A new measure of monetary shocks: Derivation and implications. American Economic Review, 94, 1055–1084.CrossRefGoogle Scholar
  23. Rue, H. (2001). Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society, Series B, 63, 325–338.CrossRefGoogle Scholar
  24. Rue, H., & Held, L. (2005). Gaussian Markov random fields: Theory and applications. Boca Raton: CRC Press.CrossRefGoogle Scholar
  25. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B, 64, 583–639.CrossRefGoogle Scholar
  26. Stock, J. H., & Watson, M. W. (2007). Why has US inflation become harder to forecast? Journal of Money, Credit and Banking, 39, 3–33.CrossRefGoogle Scholar
  27. Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11, 3571–3594.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of EconomicsWaseda UniversityTokyoJapan

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