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Locally- but not Globally-identified SVARs

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  • Emanuele Bacchiocchi
  • Toru Kitagawa
Abstract
This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally equivalent under the imposed restrictions. Although the data do not inform us which observationally equivalent point should be selected, the common frequentist practice is to obtain one as a maximum likelihood estimate and perform impulse response analysis accordingly. For Bayesians, the lack of global identification translates to non-vanishing sensitivity of the posterior to the prior, and the multi-modal likelihood gives rise to computational challenges as posterior sampling algorithms can fail to explore all the modes. This paper overcomes these challenges by proposing novel estimation and inference procedures. We characterize a class of identifying restrictions that deliver local but non-global identification, and the resulting number of observationally equivalent parameter values. We propose algorithms to exhaustively compute all admissible structural parameters given reduced-form parameters and utilize them to sample from the multi-modal posterior. In addition, viewing the set of observationally equivalent parameter points as the identified set, we develop Bayesian and frequentist procedures for inference on the corresponding set of impulse responses. An empirical example illustrates our proposal.

Suggested Citation

  • Emanuele Bacchiocchi & Toru Kitagawa, 2022. "Locally- but not Globally-identified SVARs," Working Papers wp1171, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:wp1171
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    1. Karel Mertens & Morten O. Ravn, 2013. "The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States," American Economic Review, American Economic Association, vol. 103(4), pages 1212-1247, June.
    2. 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.
    3. 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.
    4. Drautzburg, Thorsten & Wright, Jonathan H., 2023. "Refining set-identification in VARs through independence," Journal of Econometrics, Elsevier, vol. 235(2), pages 1827-1847.
    5. Giacomini, Raffaella & Kitagawa, Toru & Read, Matthew, 2022. "Robust Bayesian inference in proxy SVARs," Journal of Econometrics, Elsevier, vol. 228(1), pages 107-126.
    6. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    7. Emanuele Bacchiocchi, 2017. "On the Identification of Interdependence and Contagion of Financial Crises," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(6), pages 1148-1175, December.
    8. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    9. A. Norets & X. Tang, 2014. "Semiparametric Inference in Dynamic Binary Choice Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1229-1262.
    10. 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.
    11. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    12. S. Boragan Aruoba & Frank Schorfheide, 2011. "Sticky Prices versus Monetary Frictions: An Estimation of Policy Trade-Offs," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 60-90, January.
    13. Eleonora Granziera & Hyungsik Roger Moon & Frank Schorfheide, 2018. "Inference for VARs identified with sign restrictions," Quantitative Economics, Econometric Society, vol. 9(3), pages 1087-1121, November.
    14. Zhongjun Qu & Denis Tkachenko, 2012. "Identification and frequency domain quasi‐maximum likelihood estimation of linearized dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 3(1), pages 95-132, March.
    15. Majid M. Al-Sadoon & Piotr Zwiernik, 2019. "The Identification Problem for Linear Rational Expectations Models," Working Papers 1114, Barcelona School of Economics.
    16. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    17. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    18. 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.
    19. Ravenna, Federico, 2007. "Vector autoregressions and reduced form representations of DSGE models," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2048-2064, October.
    20. Emanuele Bacchiocchi & Toru Kitagawa, 2021. "A note on global identi?cation in structural vector autoregressions," CeMMAP working papers CWP03/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Emanuele Bacchiocchi & Luca Fanelli, 2015. "Identification in Structural Vector Autoregressive Models with Structural Changes, with an Application to US Monetary Policy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 761-779, December.
    22. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, September.
    23. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    24. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    25. Christiane Baumeister & James D. Hamilton, 2015. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, Econometric Society, vol. 83(5), pages 1963-1999, September.
    26. Andrzej Kocięcki & Marcin Kolasa, 2018. "Global identification of linearized DSGE models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1243-1263, November.
    27. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    28. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    29. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    30. Giovanni Angelini & Luca Fanelli, 2019. "Exogenous uncertainty and the identification of structural vector autoregressions with external instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 951-971, September.
    31. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    32. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106, National Bureau of Economic Research, Inc.
    33. Lucchetti, Riccardo, 2006. "Identification Of Covariance Structures," Econometric Theory, Cambridge University Press, vol. 22(2), pages 235-257, April.
    34. 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.
    35. Emanuele Bacchiocchi & Massimo Florio & Mara Grasseni, 2005. "The missing shock: the macroeconomic impact of British Privatizations," Applied Economics, Taylor & Francis Journals, vol. 37(14), pages 1585-1596.
    36. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
    37. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    38. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    39. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    40. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    41. Markus Brunnermeier & Darius Palia & Karthik A. Sastry & Christopher A. Sims, 2021. "Feedbacks: Financial Markets and Economic Activity," American Economic Review, American Economic Association, vol. 111(6), pages 1845-1879, June.
    42. Kelly, Jerry S, 1975. "Linear Cross-Equation Constraints and the Identification Problem," Econometrica, Econometric Society, vol. 43(1), pages 125-140, January.
    43. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    44. 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.
    45. Gafarov, Bulat & Meier, Matthias & Montiel Olea, José Luis, 2018. "Delta-method inference for a class of set-identified SVARs," Journal of Econometrics, Elsevier, vol. 203(2), pages 316-327.
    46. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    47. 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.
    48. Bernanke, Ben S., 1986. "Alternative explanations of the money-income correlation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 49-99, January.
    49. Canova, Fabio & Nicolo, Gianni De, 2002. "Monetary disturbances matter for business fluctuations in the G-7," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1131-1159, September.
    50. 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.
    51. 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.
    52. Bacchiocchi, Emanuele & Castelnuovo, Efrem & Fanelli, Luca, 2018. "Gimme A Break! Identification And Estimation Of The Macroeconomic Effects Of Monetary Policy Shocks In The United States," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1613-1651, September.
    53. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    54. 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.
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    Cited by:

    1. Drautzburg, Thorsten & Wright, Jonathan H., 2023. "Refining set-identification in VARs through independence," Journal of Econometrics, Elsevier, vol. 235(2), pages 1827-1847.
    2. Emanuele Bacchiocchi & Toru Kitagawa, 2021. "A note on global identification in structural vector autoregressions," Papers 2102.04048, arXiv.org, revised Feb 2021.
    3. Bacchiocchi, Emanuele & Dragomirescu-Gaina, Catalin, 2024. "Uncertainty spill-overs: When policy and financial realms overlap," Journal of International Money and Finance, Elsevier, vol. 143(C).
    4. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Robust Bayesian Analysis for Econometrics," Working Paper Series WP-2021-11, Federal Reserve Bank of Chicago.
    5. Angelini, Giovanni & Cavaliere, Giuseppe & Fanelli, Luca, 2024. "An identification and testing strategy for proxy-SVARs with weak proxies," Journal of Econometrics, Elsevier, vol. 238(2).
    6. 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).
    7. Herwartz, Helmut & Wang, Shu, 2023. "Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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