[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2107.08498.html
   My bibliography  Save this paper

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

Author

Listed:
  • David Kohns
  • Tibor Szendrei
Abstract
This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates the choice of penalisation through quantile specific loss-functions that are valid in high dimensions. We show in large scale simulations that our selection procedure decreases bias irrespective of the true underlying degree of sparsity in the data, compared to the un-sparsified regression posterior. We apply our two-step approach to a high dimensional growth-at-risk (GaR) exercise. The prediction accuracy of the un-sparsified posterior is retained while yielding interpretable quantile specific variable selection results. Our procedure can be used to communicate to policymakers which variables drive downside risk to the macro economy.

Suggested Citation

  • David Kohns & Tibor Szendrei, 2021. "Decoupling Shrinkage and Selection for the Bayesian Quantile Regression," Papers 2107.08498, arXiv.org.
    • Handle: RePEc:arx:papers:2107.08498
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2107.08498
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wagner Piazza Gaglianone & Luiz Renato Lima, 2012. "Constructing Density Forecasts from Quantile Regressions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(8), pages 1589-1607, December.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    4. Adams, Patrick A. & Adrian, Tobias & Boyarchenko, Nina & Giannone, Domenico, 2021. "Forecasting macroeconomic risks," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1173-1191.
    5. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    6. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    7. Cross, Jamie L. & Hou, Chenghan & Poon, Aubrey, 2020. "Macroeconomic forecasting with large Bayesian VARs: Global-local priors and the illusion of sparsity," International Journal of Forecasting, Elsevier, vol. 36(3), pages 899-915.
    8. Khare, Kshitij & Hobert, James P., 2012. "Geometric ergodicity of the Gibbs sampler for Bayesian quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 108-116.
    9. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    10. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    11. Lucrezia Reichlin & Giovanni Ricco & Thomas Hasenzagl, 2020. "Financial Variables as Predictors of Real Growth Vulnerability," Documents de Travail de l'OFCE 2020-06, Observatoire Francais des Conjonctures Economiques (OFCE).
    12. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    13. Goodfriend, Marvin & King, Robert G., 2005. "The incredible Volcker disinflation," Journal of Monetary Economics, Elsevier, vol. 52(5), pages 981-1015, July.
    14. Florian Huber & Gary Koop & Luca Onorante, 2021. "Inducing Sparsity and Shrinkage in Time-Varying Parameter Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 669-683, July.
    15. David Kohns & Arnab Bhattacharjee, 2020. "Nowcasting Growth using Google Trends Data: A Bayesian Structural Time Series Model," Papers 2011.00938, arXiv.org, revised May 2022.
    16. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    17. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    18. Tobias Adrian & Nina Boyarchenko & Domenico Giannone, 2019. "Vulnerable Growth," American Economic Review, American Economic Association, vol. 109(4), pages 1263-1289, April.
    19. Figueres, Juan Manuel & Jarociński, Marek, 2020. "Vulnerable growth in the euro area: Measuring the financial conditions," Economics Letters, Elsevier, vol. 191(C).
    20. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    21. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    22. Banerjee, Anindya & Marcellino, Massimiliano, 2006. "Are there any reliable leading indicators for US inflation and GDP growth?," International Journal of Forecasting, Elsevier, vol. 22(1), pages 137-151.
    23. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    24. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    25. P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    26. Andrea Carriero & Todd E. Clark & Marcellino Massimiliano, 2020. "Nowcasting Tail Risks to Economic Activity with Many Indicators," Working Papers 20-13R2, Federal Reserve Bank of Cleveland, revised 22 Sep 2020.
    27. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    28. George, Edward I. & Sun, Dongchu & Ni, Shawn, 2008. "Bayesian stochastic search for VAR model restrictions," Journal of Econometrics, Elsevier, vol. 142(1), pages 553-580, January.
    29. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    30. Hubrich, Kirstin & Tetlow, Robert J., 2015. "Financial stress and economic dynamics: The transmission of crises," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 100-115.
    31. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    32. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    33. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
    34. Rochelle M. Edge & Michael T. Kiley & Jean-Philippe Laforte, 2010. "A comparison of forecast performance between Federal Reserve staff forecasts, simple reduced-form models, and a DSGE model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 720-754.
    35. Korobilis, Dimitris, 2017. "Quantile regression forecasts of inflation under model uncertainty," International Journal of Forecasting, Elsevier, vol. 33(1), pages 11-20.
    36. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    37. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    38. McAlinn, Kenichiro & West, Mike, 2019. "Dynamic Bayesian predictive synthesis in time series forecasting," Journal of Econometrics, Elsevier, vol. 210(1), pages 155-169.
    39. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
    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. Szendrei, Tibor & Varga, Katalin, 2023. "Revisiting vulnerable growth in the Euro Area: Identifying the role of financial conditions in the distribution," Economics Letters, Elsevier, vol. 223(C).
    2. Jan Prüser & Florian Huber, 2024. "Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 269-291, March.

    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. Ferrara, Laurent & Mogliani, Matteo & Sahuc, Jean-Guillaume, 2022. "High-frequency monitoring of growth at risk," International Journal of Forecasting, Elsevier, vol. 38(2), pages 582-595.
    2. James Mitchell & Aubrey Poon & Dan Zhu, 2024. "Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 790-812, August.
    3. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    4. Jan Prüser & Florian Huber, 2024. "Nonlinearities in macroeconomic tail risk through the lens of big data quantile regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 269-291, March.
    5. Kohns, David & Potjagailo, Galina, 2023. "Flexible Bayesian MIDAS: time‑variation, group‑shrinkage and sparsity," Bank of England working papers 1025, Bank of England.
    6. 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.
    7. David Kohns & Tibor Szendrei, 2020. "Horseshoe Prior Bayesian Quantile Regression," Papers 2006.07655, arXiv.org, revised Mar 2021.
    8. Sokol, Andrej, 2021. "Fan charts 2.0: flexible forecast distributions with expert judgement," Working Paper Series 2624, European Central Bank.
    9. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    10. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    11. David Kohns & Arnab Bhattacharjee, 2020. "Nowcasting Growth using Google Trends Data: A Bayesian Structural Time Series Model," Papers 2011.00938, arXiv.org, revised May 2022.
    12. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    13. Luis Gruber & Gregor Kastner, 2022. "Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!," Papers 2206.04902, arXiv.org, revised Nov 2024.
    14. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    15. Korobilis, Dimitris & Landau, Bettina & Musso, Alberto & Phella, Anthoulla, 2021. "The time-varying evolution of inflation risks," Working Paper Series 2600, European Central Bank.
    16. Niko Hauzenberger & Florian Huber & Luca Onorante, 2021. "Combining shrinkage and sparsity in conjugate vector autoregressive models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 304-327, April.
    17. Kohns, David & Bhattacharjee, Arnab, 2023. "Nowcasting growth using Google Trends data: A Bayesian Structural Time Series model," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1384-1412.
    18. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Working Papers 22-25, Federal Reserve Bank of Cleveland.
    19. Todd E. Clark & Florian Huber & Gary Koop & Massimiliano Marcellino & Michael Pfarrhofer, 2024. "Investigating Growth-at-Risk Using a Multicountry Nonparametric Quantile Factor Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1302-1317, October.
    20. Barbara Rossi, 2019. "Forecasting in the presence of instabilities: How do we know whether models predict well and how to improve them," Economics Working Papers 1711, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2021.

    More about this item

    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:arx:papers:2107.08498. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.