IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v16y2025i3p795-822.html
   My bibliography  Save this article

Forecasting with shadow rate VARs

Author

Listed:
  • Andrea Carriero
  • Todd E. Clark
  • Massimiliano Marcellino
  • Elmar Mertens

Abstract

Vector autoregressions (VARs) are popular for forecasting, but ill‐suited to handle occasionally binding constraints, like the effective lower bound on nominal interest rates. We examine reduced‐form “shadow rate VARs” that model interest rates as censored observations of a latent shadow rate process and develop an efficient Bayesian estimation algorithm that accommodates large models. When compared to a standard VAR, our better‐performing shadow rate VARs generate superior predictions for interest rates and broadly similar predictions for macroeconomic variables. We obtain this result for shadow rate VARs in which the federal funds rate is the only interest rate and in models including additional interest rates. Our shadow rate VARs also deliver notable gains in forecast accuracy relative to a VAR that omits shorter‐term interest rate data in order to avoid modeling the lower bound.

Suggested Citation

  • Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2025. "Forecasting with shadow rate VARs," Quantitative Economics, Econometric Society, vol. 16(3), pages 795-822, July.
  • Handle: RePEc:wly:quante:v:16:y:2025:i:3:p:795-822
    DOI: 10.3982/QE2547
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE2547
    Download Restriction: no

    File URL: https://libkey.io/10.3982/QE2547?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    2. Marco J. Lombardi & Feng Zhu, 2018. "A Shadow Policy Rate to Calibrate U.S. Monetary Policy at the Zero Lower Bound," International Journal of Central Banking, International Journal of Central Banking, vol. 14(5), pages 305-346, December.
    3. Eric T. Swanson & John C. Williams, 2014. "Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates," American Economic Review, American Economic Association, vol. 104(10), pages 3154-3185, October.
    4. Berg Tim Oliver, 2017. "Forecast accuracy of a BVAR under alternative specifications of the zero lower bound," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-29, April.
    5. Christiano, Lawrence J & Eichenbaum, Martin & Evans, Charles, 1996. "The Effects of Monetary Policy Shocks: Evidence from the Flow of Funds," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 16-34, February.
    6. Ben S. Bernanke & Julio J. Rotemberg, 1997. "NBER Macroeconomics Annual 1997, Volume 12," NBER Books, National Bureau of Economic Research, Inc, number bern97-1, July.
    7. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    8. Roberto M. Billi, 2020. "Output Gaps and Robust Monetary Policy Rules," International Journal of Central Banking, International Journal of Central Banking, vol. 16(2), pages 125-152, March.
    9. Marco Del Negro & Domenico Giannone & Marc P. Giannoni & Andrea Tambalotti, 2017. "Safety, Liquidity, and the Natural Rate of Interest," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 48(1 (Spring), pages 235-316.
    10. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    11. Frank Schorfheide & Dongho Song, 2024. "Real-Time Forecasting with a (Standard) Mixed-Frequency VAR During a Pandemic," International Journal of Central Banking, International Journal of Central Banking, vol. 20(4), pages 275-320, October.
    12. Julio J. Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361, National Bureau of Economic Research, Inc.
    13. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    14. Bernanke, Ben S & Blinder, Alan S, 1992. "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review, American Economic Association, vol. 82(4), pages 901-921, September.
    15. Aruoba, S. Borağan & Mlikota, Marko & Schorfheide, Frank & Villalvazo, Sergio, 2022. "SVARs with occasionally-binding constraints," Journal of Econometrics, Elsevier, vol. 231(2), pages 477-499.
    16. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    17. Ben S. Bernanke & Julio J. Rotemberg (ed.), 1997. "NBER Macroeconomics Annual 1997," MIT Press Books, The MIT Press, edition 1, volume 1, number 026252242x, December.
    18. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    19. Gregor Bäurle & Daniel Kaufmann & Sylvia Kaufmann & Rodney W. Strachan, 2016. "Changing dynamics at the zero lower bound," Working Papers 2016-16, Swiss National Bank.
    20. Nakajima Jouchi, 2011. "Monetary Policy Transmission under Zero Interest Rates: An Extended Time-Varying Parameter Vector Autoregression Approach," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-24, October.
    21. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2024. "Addressing COVID-19 Outliers in BVARs with Stochastic Volatility," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1403-1417, September.
    22. David L. Reifschneider & John C. Williams, 2000. "Three lessons for monetary policy in a low-inflation era," Conference Series ; [Proceedings], Federal Reserve Bank of Boston, pages 936-978.
    23. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    24. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    25. Wu, Jing Cynthia & Zhang, Ji, 2019. "A shadow rate New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    26. Daniel F. Waggoner & Tao Zha, 1999. "Conditional Forecasts In Dynamic Multivariate Models," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 639-651, November.
    27. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    28. Christopher Gust & Edward Herbst & David López-Salido & Matthew E. Smith, 2017. "The Empirical Implications of the Interest-Rate Lower Bound," American Economic Review, American Economic Association, vol. 107(7), pages 1971-2006, July.
    29. Ben S. Bernanke & Julio J. Rotemberg, 1997. "Editorial in "NBER Macroeconomics Annual 1997, Volume 12"," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 1-6, National Bureau of Economic Research, Inc.
    30. Manuel Gonzalez-Astudillo & Jean-Philippe Laforte, 2020. "Estimates of r* Consistent with a Supply-Side Structure and a Monetary Policy Rule for the U.S. Economy," Finance and Economics Discussion Series 2020-085, Board of Governors of the Federal Reserve System (U.S.).
    31. Jens H. E. Christensen & Glenn D. Rudebusch, 2015. "Estimating Shadow-Rate Term Structure Models with Near-Zero Yields," Journal of Financial Econometrics, Oxford University Press, vol. 13(2), pages 226-259.
    32. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    33. Joslin, Scott & Le, Anh & Singleton, Kenneth J., 2013. "Why Gaussian macro-finance term structure models are (nearly) unconstrained factor-VARs," Journal of Financial Economics, Elsevier, vol. 109(3), pages 604-622.
    34. Kim, Don H. & Singleton, Kenneth J., 2012. "Term structure models and the zero bound: An empirical investigation of Japanese yields," Journal of Econometrics, Elsevier, vol. 170(1), pages 32-49.
    35. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    36. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    37. Iwata, Shigeru & Wu, Shu, 2006. "Estimating monetary policy effects when interest rates are close to zero," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1395-1408, October.
    38. Joshua C.C. Chan & Rodney Strachan, 2014. "The Zero Lower Bound: Implications for Modelling the Interest Rate," Working Paper series 42_14, Rimini Centre for Economic Analysis.
    39. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano, 2019. "Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors," Journal of Econometrics, Elsevier, vol. 212(1), pages 137-154.
    40. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    41. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    42. Michael D. Bauer & Glenn D. Rudebusch, 2016. "Monetary Policy Expectations at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(7), pages 1439-1465, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aruoba, S. Borağan & Mlikota, Marko & Schorfheide, Frank & Villalvazo, Sergio, 2022. "SVARs with occasionally-binding constraints," Journal of Econometrics, Elsevier, vol. 231(2), pages 477-499.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano & Mertens, Elmar, 2023. "Shadow-rate VARs," Discussion Papers 14/2023, Deutsche Bundesbank.
    2. Benjamin K. Johannsen & Elmar Mertens, 2021. "A Time‐Series Model of Interest Rates with the Effective Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(5), pages 1005-1046, August.
    3. Aymeric Ortmans, 2020. "Evolving Monetary Policy in the Aftermath of the Great Recession," Documents de recherche 20-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    4. John W. Keating & Logan J. Kelly & A. Lee Smith & Victor J. Valcarcel, 2019. "A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(1), pages 227-259, February.
    5. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino & Elmar Mertens, 2024. "Addressing COVID-19 Outliers in BVARs with Stochastic Volatility," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1403-1417, September.
    6. Michael D. Bauer & Glenn D. Rudebusch, 2016. "Monetary Policy Expectations at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(7), pages 1439-1465, October.
    7. Fabian Krüger & Todd E. Clark & Francesco Ravazzolo, 2017. "Using Entropic Tilting to Combine BVAR Forecasts With External Nowcasts," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 470-485, July.
    8. Michael Paetz, 2007. "Robust Control and Persistence in the New Keynesian Economy," Quantitative Macroeconomics Working Papers 20711, Hamburg University, Department of Economics.
    9. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(4), pages 837-862, October.
    10. Richard K. Crump & Stefano Eusepi & Domenico Giannone & Eric Qian & Argia M. Sbordone, 2021. "A Large Bayesian VAR of the United States Economy," Staff Reports 976, Federal Reserve Bank of New York.
    11. Todd E. Clark & Florian Huber & Gary Koop & Massimiliano Marcellino & Michael Pfarrhofer, 2023. "Tail Forecasting With Multivariate Bayesian Additive Regression Trees," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 979-1022, August.
    12. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    13. Nakajima, Jouchi & Kasuya, Munehisa & Watanabe, Toshiaki, 2011. "Bayesian analysis of time-varying parameter vector autoregressive model for the Japanese economy and monetary policy," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 225-245, September.
    14. Chen, Zhengyang, 2019. "The Long-term Rate and Interest Rate Volatility in Monetary Policy Transmission," MPRA Paper 96339, University Library of Munich, Germany.
    15. Jhonatan Portilla & Gabriel Rodríguez & Paul Castillo B., 2022. "Evolution of Monetary Policy in Peru: An Empirical Application Using a Mixture Innovation TVP-VAR-SV Model [Metas de Inflación en Una Economía Dolarizada: La Experencia Del Perú]," CESifo Economic Studies, CESifo Group, vol. 68(1), pages 98-126.
    16. Hirokuni Iiboshi & Mototsugu Shintani & Kozo Ueda, 2022. "Estimating a Nonlinear New Keynesian Model with the Zero Lower Bound for Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 54(6), pages 1637-1671, September.
    17. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    18. Knut Are Aastveit & Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2017. "Have Standard VARS Remained Stable Since the Crisis?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(5), pages 931-951, August.
    19. Eric M. Leeper & Jennifer E. Roush, 2003. "Putting \\"M\\" back in monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 1217-1264.
    20. Necati Tekatli, 2007. "Understanding Sources of the Change in International Business Cycles," Working Papers 335, Barcelona School of Economics.

    More about this item

    JEL classification:

    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:quante:v:16:y:2025:i:3:p:795-822. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.