IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v20y2021icp87-108.html
   My bibliography  Save this article

Flexible Mixture Priors for Large Time-varying Parameter Models

Author

Listed:
  • Hauzenberger, Niko

Abstract

Time-varying parameter (TVP) models often assume that the TVPs evolve according to a random walk. This assumption, however, might be questionable since it implies that coefficients change smoothly and in an unbounded manner. This assumption is relaxed by proposing a flexible law of motion for the TVPs in large-scale vector autoregressions (VARs). Instead of imposing a restrictive random walk evolution of the latent states, hierarchical mixture priors on the coefficients in the state equation are carefully designed. These priors effectively allow for discriminating between periods in which coefficients evolve according to a random walk and times where the TVPs are better characterized by a stationary stochastic process. Moreover, this approach is capable of introducing dynamic sparsity by pushing small parameter changes towards zero if necessary. The merits of the model are illustrated by means of two applications. Using synthetic data these flexible modeling techniques yield precise parameter estimates. When applied to US data, the model reveals interesting patterns of low-frequency dynamics in coefficients and forecasts well relative to a wide range of competing models.

Suggested Citation

  • Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
  • Handle: RePEc:eee:ecosta:v:20:y:2021:i:c:p:87-108
    DOI: 10.1016/j.ecosta.2021.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306221000654
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles

    File URL: https://libkey.io/10.1016/j.ecosta.2021.06.001?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    2. Gary M. Koop, 2013. "Forecasting with Medium and Large Bayesian VARS," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 177-203, March.
    3. Martin Kliem & Alexander Kriwoluzky & Samad Sarferaz, 2016. "On the Low‐Frequency Relationship Between Public Deficits and Inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 566-583, April.
    4. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
    5. Marta Bańbura, 2008. "Large Bayesian VARs," 2008 Meeting Papers 334, Society for Economic Dynamics.
    6. 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.
    7. 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.
    8. 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.
    9. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    10. Joshua C.C. Chan & Rodney W. Strachan, 2020. "Bayesian state space models in macroeconometrics," CAMA Working Papers 2020-90, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. Niko Hauzenberger & Florian Huber & Gary Koop, 2020. "Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods," Papers 2005.03906, arXiv.org.
    12. Olivier Coibion & Yuriy Gorodnichenko, 2015. "Is the Phillips Curve Alive and Well after All? Inflation Expectations and the Missing Disinflation," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 197-232, January.
    13. Dimitris Korobilis, 2013. "Assessing the Transmission of Monetary Policy Using Time-varying Parameter Dynamic Factor Models-super-," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(2), pages 157-179, April.
    14. Daniel R. Kowal & David S. Matteson & David Ruppert, 2019. "Dynamic shrinkage processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(4), pages 781-804, September.
    15. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
    16. Laurence Ball & Sandeep Mazumder, 2011. "Inflation Dynamics and the Great Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 42(1 (Spring), pages 337-405.
    17. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    18. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    19. Joshua C.C. Chan, 2019. "Large hybrid time-varying parameter VARs," CAMA Working Papers 2019-77, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    20. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-09 Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 43(1 (Spring), pages 81-156.
    21. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen V.K. Rombouts, 2015. "The Contribution of Structural Break Models to Forecasting Macroeconomic Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 596-620, June.
    22. Gary Koop & Simon M. Potter, 2007. "Estimation and Forecasting in Models with Multiple Breaks," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 763-789.
    23. Giordani, Paolo & Kohn, Robert, 2008. "Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 66-77, January.
    24. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    25. Martin Feldkircher & Florian Huber & Gregor Kastner, 2017. "Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?," Papers 1711.00564, arXiv.org, revised Nov 2017.
    26. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2010. "Inflation-Gap Persistence in the US," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 43-69, January.
    27. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    28. Jan J. J. Groen & Richard Paap & Francesco Ravazzolo, 2013. "Real-Time Inflation Forecasting in a Changing World," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 29-44, January.
    29. Chan, Joshua C.C. & Eisenstat, Eric & Strachan, Rodney W., 2020. "Reducing the state space dimension in a large TVP-VAR," Journal of Econometrics, Elsevier, vol. 218(1), pages 105-118.
    30. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2012. "Time Varying Dimension Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 358-367, January.
    31. Miguel A.G. Belmonte & Gary Koop & Dimitris Korobilis, 2014. "Hierarchical Shrinkage in Time‐Varying Parameter Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 80-94, January.
    32. Thomas J. Sargent & Paolo Surico, 2011. "Two Illustrations of the Quantity Theory of Money: Breakdowns and Revivals," American Economic Review, American Economic Association, vol. 101(1), pages 109-128, February.
    33. Kastner, Gregor, 2016. "Dealing with Stochastic Volatility in Time Series Using the R Package stochvol," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i05).
    34. Serena Ng & Jonathan H. Wright, 2013. "Facts and Challenges from the Great Recession for Forecasting and Macroeconomic Modeling," Journal of Economic Literature, American Economic Association, vol. 51(4), pages 1120-1154, December.
    35. Luc Bauwens & Gary Koop & Dimitris Korobilis & Jeroen V.K. Rombouts, 2015. "The Contribution of Structural Break Models to Forecasting Macroeconomic Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 596-620, June.
    36. Jouchi Nakajima & Mike West, 2013. "Bayesian Analysis of Latent Threshold Dynamic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 151-164, April.
    37. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    38. 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.
    39. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2013. "Macroeconomic forecasting and structural change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 82-101, January.
    40. Florian Huber & Gregor Kastner & Martin Feldkircher, 2016. "Should I stay or should I go? A latent threshold approach to large-scale mixture innovation models," Papers 1607.04532, arXiv.org, revised Jul 2018.
    41. Gary Koop & Dimitris Korobilis, 2018. "Bayesian dynamic variable selection in high dimensions," Papers 1809.03031, arXiv.org, revised May 2020.
    42. 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.
    43. James H. Stock & Mark W. Watson, 2007. "Erratum to “Why Has U.S. Inflation Become Harder to Forecast?”," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    44. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-749, September.
    45. Gregor Kastner & Florian Huber, 2020. "Sparse Bayesian vector autoregressions in huge dimensions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1142-1165, November.
    46. Follett, Lendie & Yu, Cindy, 2019. "Achieving parsimony in Bayesian vector autoregressions with the horseshoe prior," Econometrics and Statistics, Elsevier, vol. 11(C), pages 130-144.
    47. 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.
    48. Pascal Paul, 2020. "The Time-Varying Effect of Monetary Policy on Asset Prices," The Review of Economics and Statistics, MIT Press, vol. 102(4), pages 690-704, October.
    49. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    50. Korobilis, D, 2017. "Forecasting with many predictors using message passing algorithms," Essex Finance Centre Working Papers 19565, University of Essex, Essex Business School.
    51. Kalli, Maria & Griffin, Jim E., 2014. "Time-varying sparsity in dynamic regression models," Journal of Econometrics, Elsevier, vol. 178(2), pages 779-793.
    52. 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.
    53. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    54. 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.
    55. Dimitris Korobilis, 2021. "High-Dimensional Macroeconomic Forecasting Using Message Passing Algorithms," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 493-504, March.
    56. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2009. "On the evolution of the monetary policy transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 997-1017, April.
    57. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    58. 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.
    59. Florian Huber & Martin Feldkircher, 2019. "Adaptive Shrinkage in Bayesian Vector Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 27-39, January.
    60. Czudaj, Robert L., 2019. "Dynamics between trading volume, volatility and open interest in agricultural futures markets: A Bayesian time-varying coefficient approach," Econometrics and Statistics, Elsevier, vol. 12(C), pages 78-145.
    61. Korobilis, Dimitris, 2019. "High-dimensional macroeconomic forecasting using message passing algorithms," MPRA Paper 96079, University Library of Munich, Germany.
    62. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
    63. Chang-Jin Kim & Charles R. Nelson, 1999. "Has The U.S. Economy Become More Stable? A Bayesian Approach Based On A Markov-Switching Model Of The Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 608-616, November.
    64. Florian Huber & Gregor Kastner & Martin Feldkircher, 2019. "Should I stay or should I go? A latent threshold approach to large‐scale mixture innovation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 621-640, August.
    65. Haroon Mumtaz & Konstantinos Theodoridis, 2018. "The Changing Transmission of Uncertainty Shocks in the U.S," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 239-252, April.
    66. Mark W. Watson, 2014. "Inflation Persistence, the NAIRU, and the Great Recession," American Economic Review, American Economic Association, vol. 104(5), pages 31-36, May.
    67. Florian Huber & Gary Koop & Michael Pfarrhofer, 2020. "Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations," Papers 2002.10274, arXiv.org.
    68. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    69. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-09 Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 44(1 (Spring), pages 81-156.
    70. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-2009 Recession," NBER Working Papers 18094, National Bureau of Economic Research, Inc.
    71. Sandra Eickmeier & Wolfgang Lemke & Massimiliano Marcellino, 2015. "Classical time varying factor-augmented vector auto-regressive models—estimation, forecasting and structural analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 493-533, June.
    72. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    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. Niko Hauzenberger & Daniel Kaufmann & Rebecca Stuart & Cédric Tille, 2022. "What Drives Long-Term Interest Rates? Evidence from the Entire Swiss Franc History 1852-2020," IRENE Working Papers 22-03, IRENE Institute of Economic Research.

    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. Niko Hauzenberger, 2020. "Flexible Mixture Priors for Large Time-varying Parameter Models," Papers 2006.10088, arXiv.org, revised Nov 2020.
    2. Nima Nonejad, 2021. "An Overview Of Dynamic Model Averaging Techniques In Time‐Series Econometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 566-614, April.
    3. Joshua C.C. Chan & Rodney W. Strachan, 2020. "Bayesian state space models in macroeconometrics," CAMA Working Papers 2020-90, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    4. Florian Huber & Gary Koop & Michael Pfarrhofer, 2020. "Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations," Papers 2002.10274, arXiv.org.
    5. Gregor Kastner & Florian Huber, 2020. "Sparse Bayesian vector autoregressions in huge dimensions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1142-1165, November.
    6. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    7. Chan, Joshua C.C., 2021. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1212-1226.
    8. 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.
    9. Fischer, Manfred M. & Hauzenberger, Niko & Huber, Florian & Pfarrhofer, Michael, 2022. "General Bayesian time-varying parameter VARs for modeling government bond yields," Working Papers in Regional Science 2021/01, WU Vienna University of Economics and Business.
    10. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    11. 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.
    12. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    13. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    14. Manfred M. Fischer & Niko Hauzenberger & Florian Huber & Michael Pfarrhofer, 2021. "General Bayesian time-varying parameter VARs for predicting government bond yields," Papers 2102.13393, arXiv.org.
    15. Tallman, Ellis W. & Zaman, Saeed, 2020. "Combining survey long-run forecasts and nowcasts with BVAR forecasts using relative entropy," International Journal of Forecasting, Elsevier, vol. 36(2), pages 373-398.
    16. Martin Feldkircher & Nico Hauzenberger, 2019. "How useful are time-varying parameter models for forecasting economic growth in CESEE?," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue Q1/19, pages 29-48.
    17. Kastner, Gregor, 2019. "Sparse Bayesian time-varying covariance estimation in many dimensions," Journal of Econometrics, Elsevier, vol. 210(1), pages 98-115.
    18. Raffaella Giacomini & Barbara Rossi, 2015. "Forecasting in Nonstationary Environments: What Works and What Doesn't in Reduced-Form and Structural Models," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 207-229, August.
    19. Eric Eisenstat & Joshua C. C. Chan & Rodney W. Strachan, 2016. "Stochastic Model Specification Search for Time-Varying Parameter VARs," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1638-1665, December.
    20. Korobilis, Dimitris & Koop, Gary, 2018. "Variational Bayes inference in high-dimensional time-varying parameter models," Essex Finance Centre Working Papers 22665, University of Essex, Essex Business School.

    More about this item

    Keywords

    Time-varying parameter vector autoregressions; hierarchical modeling; clustering; macroeconomic forecasting;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • 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:eee:ecosta:v:20:y:2021:i:c:p:87-108. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.