IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v225y2021i1p27-46.html
   My bibliography  Save this article

Identification of structural vector autoregressions through higher unconditional moments

Author

Listed:
  • Guay, Alain

Abstract

This paper pursues two objectives. First, we determine the sufficient condition for local, statistical identification of SVAR processes through the third and fourth unconditional moments of the reduced-form innovations. Our findings provide novel insights when the entire system is not identified, as they highlight which subset of structural parameters is identified and which is not. Second, we elaborate a tractable testing procedure to verify whether the identification condition holds, prior to the estimation of the structural parameters of the SVAR process. To do so, we design a new bootstrap procedure that improves the small-sample properties of rank tests for the symmetry and kurtosis of the structural shocks.

Suggested Citation

  • Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    • Handle: RePEc:eee:econom:v:225:y:2021:i:1:p:27-46
    DOI: 10.1016/j.jeconom.2020.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620303651
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.10.006?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. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    2. Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
    3. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    4. Andrew Mountford & Harald Uhlig, 2009. "What are the effects of fiscal policy shocks?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 960-992.
    5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    6. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    7. Robert J. Gordon, 1986. "The American Business Cycle: Continuity and Change," NBER Books, National Bureau of Economic Research, Inc, number gord86-1, June.
    8. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    9. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(2), pages 151-175, April.
    10. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    11. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    12. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.
    13. Bernd Funovits, 2019. "Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs," Papers 1910.04087, arXiv.org.
    14. Carlo Favero & Francesco Giavazzi, 2009. "How large are the effects of tax changes?," NBER Working Papers 15303, National Bureau of Economic Research, Inc.
    15. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, November.
    16. Helmut Lütkepohl & Aleksei Netsunajev, 2014. "Structural Vector Autoregressions with Smooth Transition in Variances: The Interaction between U.S. Monetary Policy and the Stock Market," Discussion Papers of DIW Berlin 1388, DIW Berlin, German Institute for Economic Research.
    17. Lütkepohl, Helmut & Schlaak, Thore, 2018. "Choosing Between Different Time-Varying Volatility Models for Structural Vector Autoregressive Analysis," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, issue 4, pages 715-735.
    18. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.
    19. Al-Sadoon, Majid M., 2017. "A unifying theory of tests of rank," Journal of Econometrics, Elsevier, vol. 199(1), pages 49-62.
    20. Horowitz, J., 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    21. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    22. Nikolay Gospodinov & Serena Ng, 2015. "Minimum Distance Estimation of Possibly Noninvertible Moving Average Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 403-417, July.
    23. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    24. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    25. Roberto Perotti, 2005. "Estimating the effects of fiscal policy in OECD countries," Proceedings, Federal Reserve Bank of San Francisco.
    26. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    27. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    28. Mertens, Karel & Ravn, Morten O., 2014. "A reconciliation of SVAR and narrative estimates of tax multipliers," Journal of Monetary Economics, Elsevier, vol. 68(S), pages 1-19.
    29. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    30. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    31. Normandin, Michel & Phaneuf, Louis, 2004. "Monetary policy shocks:: Testing identification conditions under time-varying conditional volatility," Journal of Monetary Economics, Elsevier, vol. 51(6), pages 1217-1243, September.
    32. Bekaert, Geert & Harvey, Campbell R., 1997. "Emerging equity market volatility," Journal of Financial Economics, Elsevier, vol. 43(1), pages 29-77, January.
    33. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    34. Olivier Blanchard & Roberto Perotti, 2002. "An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1329-1368.
    35. Lanne, Markku & Lütkepohl, Helmut & Maciejowska, Katarzyna, 2010. "Structural vector autoregressions with Markov switching," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 121-131, February.
    36. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j01si09a2 is not listed on IDEAS
    37. Lanne, Markku & Lütkepohl, Helmut, 2010. "Structural Vector Autoregressions With Nonnormal Residuals," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 159-168.
    38. Gonzalo Camba-Mendez & George Kapetanios, 2009. "Statistical Tests and Estimators of the Rank of a Matrix and Their Applications in Econometric Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 581-611.
    39. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09j01si09a2 is not listed on IDEAS
    40. Olivier J. Blanchard & Mark W. Watson, 1986. "Are Business Cycles All Alike?," NBER Chapters, in: The American Business Cycle: Continuity and Change, pages 123-180, National Bureau of Economic Research, Inc.
    41. François Portier & Bernard Delyon, 2014. "Bootstrap Testing of the Rank of a Matrix via Least-Squared Constrained Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 160-172, March.
    42. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    43. Boothe, Paul & Glassman, Debra, 1987. "The statistical distribution of exchange rates: Empirical evidence and economic implications," Journal of International Economics, Elsevier, vol. 22(3-4), pages 297-319, May.
    44. Bouakez, Hafedh & Chihi, Foued & Normandin, Michel, 2014. "Measuring the effects of fiscal policy," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 123-151.
    45. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
    46. Portier, Francois & Delyon, Bernard, 2014. "Bootstrap testing of the rank of a matrix via least- squared constrained estimation," LIDAM Reprints ISBA 2014050, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    47. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    48. Alessio Moneta & Doris Entner & Patrik O. Hoyer & Alex Coad, 2013. "Causal Inference by Independent Component Analysis: Theory and Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(5), pages 705-730, 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. Sascha A. Keweloh, 2023. "Uncertain Short-Run Restrictions and Statistically Identified Structural Vector Autoregressions," Papers 2303.13281, arXiv.org, revised Apr 2024.
    2. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    3. Brandts, Jordi & El Baroudi, Sabrine & Huber, Stefanie J. & Rott, Christina, 2021. "Gender differences in private and public goal setting," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 222-247.
    4. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    5. Geert Mesters & Piotr Zwiernik, 2022. "Non-independent components analysis," Economics Working Papers 1845, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Drautzburg, Thorsten & Wright, Jonathan H., 2023. "Refining set-identification in VARs through independence," Journal of Econometrics, Elsevier, vol. 235(2), pages 1827-1847.
    7. Sascha A. Keweloh, 2023. "Structural Vector Autoregressions and Higher Moments: Challenges and Solutions in Small Samples," Papers 2310.08173, arXiv.org.
    8. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.
    9. Cordoni, Francesco & Dorémus, Nicolas & Moneta, Alessio, 2024. "Identification of vector autoregressive models with nonlinear contemporaneous structure," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    10. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Robust inference for non-Gaussian SVAR models," Economics Working Papers 1847, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Lukas Hoesch & Adam Lee & Geert Mesters, 2022. "Locally Robust Inference for Non-Gaussian SVAR Models," Working Papers 1367, Barcelona School of Economics.
    12. Gabriele Fiorentini & Alessio Moneta & Francesca Papagni, 2024. "Identification of one independent shock in structural VARs," LEM Papers Series 2024/28, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    13. Martin Bruns & Sascha A. Keweloh, 2023. "Testing for Strong Exogeneity in Proxy-VARS," University of East Anglia School of Economics Working Paper Series 2023-07, School of Economics, University of East Anglia, Norwich, UK..
    14. Miguel Cabello, 2022. "Robust Estimation of the non-Gaussian Dimension in Structural Linear Models," Papers 2212.07263, arXiv.org, revised Sep 2023.

    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. Alain Guay, 2020. "Identification of Structural Vector Autoregressions Through Higher Unconditional Moments," Working Papers 20-19, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    2. Miguel Cabello, 2022. "Robust Estimation of the non-Gaussian Dimension in Structural Linear Models," Papers 2212.07263, arXiv.org, revised Sep 2023.
    3. Dominik Bertsche & Robin Braun, 2022. "Identification of Structural Vector Autoregressions by Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 328-341, January.
    4. Karamysheva, Madina & Skrobotov, Anton, 2022. "Do we reject restrictions identifying fiscal shocks? identification based on non-Gaussian innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 138(C).
    5. Herwartz, Helmut & Lange, Alexander & Maxand, Simone, 2019. "Statistical identification in SVARs - Monte Carlo experiments and a comparative assessment of the role of economic uncertainties for the US business cycle," University of Göttingen Working Papers in Economics 375, University of Goettingen, Department of Economics.
    6. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    7. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with heteroskedasticity: A review of different volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 2-18.
    8. Herwartz, Helmut & Rohloff, Hannes & Wang, Shu, 2020. "Proxy SVAR identification of monetary policy shocks: MonteCarlo evidence and insights for the US," University of Göttingen Working Papers in Economics 404, University of Goettingen, Department of Economics.
    9. Helmut Herwartz & Alexander Lange & Simone Maxand, 2022. "Data‐driven identification in SVARs—When and how can statistical characteristics be used to unravel causal relationships?," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 668-693, April.
    10. Cordoni, Francesco & Dorémus, Nicolas & Moneta, Alessio, 2024. "Identification of vector autoregressive models with nonlinear contemporaneous structure," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    11. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    12. Braun, Robin, 2021. "The importance of supply and demand for oil prices: evidence from non-Gaussianity," Bank of England working papers 957, Bank of England.
    13. Daniel J Lewis, 2021. "Identifying Shocks via Time-Varying Volatility [First Order Autoregressive Processes and Strong Mixing]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(6), pages 3086-3124.
    14. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Sascha A. Keweloh, 2023. "Uncertain Short-Run Restrictions and Statistically Identified Structural Vector Autoregressions," Papers 2303.13281, arXiv.org, revised Apr 2024.
    16. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    17. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    18. Herwartz, Helmut & Rohloff, Hannes & Wang, Shu, 2022. "Proxy SVAR identification of monetary policy shocks - Monte Carlo evidence and insights for the US," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    19. Fritsche, Jan Philipp & Klein, Mathias & Rieth, Malte, 2021. "Government spending multipliers in (un)certain times," Journal of Public Economics, Elsevier, vol. 203(C).
    20. Dmitry Kulikov & Aleksei Netsunajev, 2016. "Identifying Shocks in Structural VAR models via heteroskedasticity: a Bayesian approach," Bank of Estonia Working Papers wp2015-8, Bank of Estonia, revised 19 Feb 2016.

    More about this item

    Keywords

    Bootstrap procedure; Excess kurtosis; Identification condition; Rank test; Skewness; Structural vector autoregression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    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:econom:v:225:y:2021:i:1:p:27-46. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.