IDEAS home Printed from https://ideas.repec.org/p/pen/papers/25-003.html
   My bibliography  Save this paper

Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs

Author

Listed:
  • Oriol Gonzalez-Casasus

    (University of Pennsylvania)

  • Frank Schorfheide

    (University of Pennsylvania CEPR, PIER, NBER)

Abstract

VARs are often estimated with Bayesian techniques to cope with model dimensionality. The posterior means define a class of shrinkage estimators, indexed by hyperparameters that determine the relative weight on maximum likelihood estimates and prior means. In a Bayesian setting, it is natural to choose these hyperparameters by maximizing the marginal data density. However, this is undesirable if the VAR is misspecified. In this paper, we derive asymptotically unbiased estimates of the multi-step forecasting risk and the impulse response estimation risk to determine hyperparameters in settings where the VAR is (potentially) misspecified. The proposed criteria can be used to jointly select the optimal shrinkage hyperparameter, VAR lag length, and to choose among different types of multi-step-ahead predictors; or among IRF estimates based on VARs and local projections. The selection approach is illustrated in a Monte Carlo study and an empirical application.

Suggested Citation

  • Oriol Gonzalez-Casasus & Frank Schorfheide, 2025. "Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs," PIER Working Paper Archive 25-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:25-003
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/system/files/working-papers/25-003%20PIER%20Paper%20Submission.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. T. Speed & Bin Yu, 1993. "Model selection and prediction: Normal regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(1), pages 35-54, March.
    2. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    3. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Bayesian VARs: Specification Choices and Forecast Accuracy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 46-73, January.
    4. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(2), pages 254-279, April.
    5. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, May.
    6. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    7. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
    8. José Luis Montiel Olea & Mikkel Plagborg-Møller & Eric Qian & Christian K. Wolf, 2024. "Double Robustness of Local Projections and Some Unpleasant VARithmetic," NBER Working Papers 32495, National Bureau of Economic Research, Inc.
    9. Dake Li & Mikkel Plagborg-Møller & Christian K. Wolf, 2021. "Local Projections vs. VARs: Lessons From Thousands of DGPs," Working Papers 2021-55, Princeton University. Economics Department..
    10. 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.
    11. James D. Hamilton, 2018. "Why You Should Never Use the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 831-843, December.
    12. Richard A. Lewis & Gregory C. Reinsel, 1988. "Prediction Error Of Multivariate Time Series With Mis‐Specified Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(1), pages 43-57, January.
    13. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, November.
    14. Li, Dake & Plagborg-Møller, Mikkel & Wolf, Christian K., 2024. "Local projections vs. VARs: Lessons from thousands of DGPs," Journal of Econometrics, Elsevier, vol. 244(2).
    15. Mikkel Plagborg‐Møller & Christian K. Wolf, 2021. "Local Projections and VARs Estimate the Same Impulse Responses," Econometrica, Econometric Society, vol. 89(2), pages 955-980, March.
    16. Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
    17. Jos'e Luis Montiel Olea & Mikkel Plagborg-M{o}ller & Eric Qian & Christian K. Wolf, 2024. "Double Robustness of Local Projections and Some Unpleasant VARithmetic," Papers 2405.09509, arXiv.org, revised Aug 2024.
    18. Soonwoo Kwon, 2023. "Optimal Shrinkage Estimation of Fixed Effects in Linear Panel Data Models," Papers 2308.12485, arXiv.org, revised Oct 2023.
    19. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    20. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    21. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March.
    22. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    Full references (including those not matched with items on IDEAS)

    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. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    2. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "Bayesian local projections," Working Papers hal-03373574, HAL.
    3. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    4. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    5. Lucas Ordóñez, 2025. "The Transmission of Supply Shocks to Inflation: the Case of Argentina (2004-2022)," Working Papers 351, Red Nacional de Investigadores en Economía (RedNIE).
    6. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    7. Ordoñez Lucas Sebastián, 2024. "The transmission of Supply Shocks to inflation: The case of Argentina (2004-2023)," Asociación Argentina de Economía Política: Working Papers 4750, Asociación Argentina de Economía Política.
    8. Ho, Paul & Lubik, Thomas A. & Matthes, Christian, 2024. "Averaging impulse responses using prediction pools," Journal of Monetary Economics, Elsevier, vol. 146(C).
    9. Greenaway-McGrevy, Ryan, 2015. "Evaluating panel data forecasts under independent realization," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 108-125.
    10. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "The Transmission of Monetary Policy Shocks," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 74-107, July.
    11. Alfred A. Haug & Christie Smith, 2012. "Local Linear Impulse Responses for a Small Open Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(3), pages 470-492, June.
    12. Lof, Matthijs & Nyberg, Henri, 2024. "Discount rates and cash flows: A local projection approach," Journal of Banking & Finance, Elsevier, vol. 162(C).
    13. Jari Hännikäinen, 2014. "Multi-step forecasting in the presence of breaks," Working Papers 1494, Tampere University, Faculty of Management and Business, Economics.
    14. Eliana González Molano & Luis Fernando Melo Velnadia & Anderson Grajales Olarte, 2007. "Pronósticos directos de la inflación colombiana," Borradores de Economia 4247, Banco de la Republica.
    15. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.
    16. Hitesh Doshi & Kris Jacobs & Rui Liu, 2021. "Information in the Term Structure: A Forecasting Perspective," Management Science, INFORMS, vol. 67(8), pages 5255-5277, August.
    17. Tomasz Woźniak, 2016. "Bayesian Vector Autoregressions," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 49(3), pages 365-380, September.
    18. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    19. Michael W. McCracken & Joseph T. McGillicuddy, 2019. "An empirical investigation of direct and iterated multistep conditional forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 181-204, March.
    20. Michael D. Bauer & Eric T. Swanson, 2023. "A Reassessment of Monetary Policy Surprises and High-Frequency Identification," NBER Macroeconomics Annual, University of Chicago Press, vol. 37(1), pages 87-155.

    More about this item

    Keywords

    Forecasting; Hyperparameter Selection; Local Projections; Misspecification; Multi-step Estimation; Shrinkage Estimators; Vector Autoregressions;
    All these keywords.

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pen:papers:25-003. 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: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.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.