IDEAS home Printed from https://ideas.repec.org/a/tpr/restat/v99y2017i2p319-329.html
   My bibliography  Save this article

Granger Causal Priority and Choice of Variables in Vector Autoregressions

Author

Listed:
  • Marek Jarociński

    (European Central Bank)

  • Bartosz Maćkowiak

    (European Central Bank and CEPR)

Abstract

We derive a closed-form expression for the posterior probability of Granger noncausality in a gaussian vector autoregression with a conjugate prior. We also express in closed form the posterior probability of Granger causal priority, a more general relation that accounts for indirect effects between variables and therefore is suitable in a multivariate context. One can use these results to answer the classic question, “Is variable z relevant for variable x?” and to choose variables for a vector autoregression.

Suggested Citation

  • Marek Jarociński & Bartosz Maćkowiak, 2017. "Granger Causal Priority and Choice of Variables in Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 319-329, May.
    • Handle: RePEc:tpr:restat:v:99:y:2017:i:2:p:319-329
    as

    Download full text from publisher

    File URL: http://www.mitpressjournals.org/doi/pdf/10.1162/REST_a_00601
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Lippi, Marco & Reichlin, Lucrezia, 1993. "The Dynamic Effects of Aggregate Demand and Supply Disturbances: Comment," American Economic Review, American Economic Association, vol. 83(3), pages 644-652, June.
    3. Christopher A. Sims, 1993. "A Nine-Variable Probabilistic Macroeconomic Forecasting Model," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 179-212, National Bureau of Economic Research, Inc.
    4. Domenico Giannone & Lucrezia Reichlin, 2006. "Does information help recovering structural shocks from past observations?," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 455-465, 04-05.
    5. James H. Stock & Mark W. Watson, 1993. "Business Cycles, Indicators, and Forecasting," NBER Books, National Bureau of Economic Research, Inc, number stoc93-1.
    6. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
    7. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 665-696.
    8. Angeloni,Ignazio & Kashyap,Anil K. & Mojon,Benoît (ed.), 2003. "Monetary Policy Transmission in the Euro Area," Cambridge Books, Cambridge University Press, number 9780521828642, September.
    9. David Altig & Lawrence Christiano & Martin Eichenbaum & Jesper Linde, 2011. "Firm-Specific Capital, Nominal Rigidities and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 225-247, April.
    10. 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.
    11. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    12. 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.
    13. Forni, Mario & Gambetti, Luca, 2014. "Sufficient information in structural VARs," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 124-136.
    14. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
    15. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    16. Stock, James H. & Watson, Mark W. (ed.), 1993. "Business Cycles, Indicators, and Forecasting," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226774886, September.
    17. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    18. 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.
    19. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    20. 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.
    21. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    22. Jeff Fuhrer & Jane Sneddon Little & Yolanda K. Kodrzycki & Giovanni P. Olivei (ed.), 2009. "Understanding Inflation and the Implications for Monetary Policy: A Phillips Curve Retrospective," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262013630, April.
    23. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    24. 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.
    25. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    26. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    27. Cushman, David O. & Zha, Tao, 1997. "Identifying monetary policy in a small open economy under flexible exchange rates," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 433-448, August.
    28. David Altig & Lawrence Christiano & Martin Eichenbaum & Jesper Linde, 2011. "Firm-Specific Capital, Nominal Rigidities and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 225-247, April.
    29. Peersman, Gert & Smets, Frank, 2001. "The monetary transmission mechanism in the euro area: more evidence from VAR analysis," Working Paper Series 91, European Central Bank.
    30. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    31. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    32. repec:ulb:ulbeco:2013/13388 is not listed on IDEAS
    33. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
    34. Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June.
    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. Woźniak, Tomasz, 2015. "Testing causality between two vectors in multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 876-894.
    2. James Morley & Benjamin Wong, 2020. "Estimating and accounting for the output gap with large Bayesian vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 1-18, January.
    3. Al-Sadoon, Majid M., 2019. "Testing subspace Granger causality," Econometrics and Statistics, Elsevier, vol. 9(C), pages 42-61.
    4. Donal Smith, 2016. "The International Impact of Financial Shocks: A Global VAR and Connectedness Measures Approach," Discussion Papers 16/07, Department of Economics, University of York.
    5. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    6. Morley, James & Rodríguez-Palenzuela, Diego & Sun, Yiqiao & Wong, Benjamin, 2023. "Estimating the euro area output gap using multivariate information and addressing the COVID-19 pandemic," European Economic Review, Elsevier, vol. 153(C).
    7. Iskrev, Nikolay, 2019. "On the sources of information about latent variables in DSGE models," European Economic Review, Elsevier, vol. 119(C), pages 318-332.
    8. Joshua C. C. Chan & Eric Eisenstat & Chenghan Hou & Gary Koop, 2020. "Composite likelihood methods for large Bayesian VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 692-711, September.
    9. Matthieu Droumaguet & Anders Warne & Tomasz Wozniak, 2015. "Granger Causality and Regime Inference in Bayesian Markov-Switching VARs," Department of Economics - Working Papers Series 1191, The University of Melbourne.
    10. Alonso, Pablo, 2018. "Creation and Evolution of Inflation Expectations in Paraguay," IDB Publications (Working Papers) 9027, Inter-American Development Bank.
    11. Zhang, Ailian & Pan, Mengmeng & Liu, Bai & Weng, Yin-Che, 2020. "Systemic risk: The coordination of macroprudential and monetary policies in China," Economic Modelling, Elsevier, vol. 93(C), pages 415-429.
    12. Manfred Kremer, 2016. "Macroeconomic effects of financial stress and the role of monetary policy: a VAR analysis for the euro area," International Economics and Economic Policy, Springer, vol. 13(1), pages 105-138, January.
    13. Dominik Bertsche & Ralf Brüggemann & Christian Kascha, 2023. "Directed graphs and variable selection in large vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 223-246, 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. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    2. Chris Bloor & Troy Matheson, 2010. "Analysing shock transmission in a data-rich environment: a large BVAR for New Zealand," Empirical Economics, Springer, vol. 39(2), pages 537-558, October.
    3. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    4. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    5. repec:spo:wpmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    6. Bańbura, Marta & Giannone, Domenico & Lenza, Michele, 2015. "Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections," International Journal of Forecasting, Elsevier, vol. 31(3), pages 739-756.
    7. Tomasz Wozniak, 2016. "Rare Events and Risk Perception: Evidence from Fukushima Accident," Department of Economics - Working Papers Series 2021, The University of Melbourne.
    8. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    9. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Large Vector Autoregressions with Stochastic Volatility and Flexible Priors," Working Papers (Old Series) 1617, Federal Reserve Bank of Cleveland.
    10. 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.
    11. 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.
    12. 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.
    13. Bloor, Chris & Matheson, Troy, 2011. "Real-time conditional forecasts with Bayesian VARs: An application to New Zealand," The North American Journal of Economics and Finance, Elsevier, vol. 22(1), pages 26-42, January.
    14. Bekiros, Stelios D. & Paccagnini, Alessia, 2014. "Bayesian forecasting with small and medium scale factor-augmented vector autoregressive DSGE models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 298-323.
    15. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    16. Peter McAdam & Anders Warne, 2024. "Density forecast combinations: The real‐time dimension," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1153-1172, August.
    17. Fuentes-Albero, Cristina & Melosi, Leonardo, 2013. "Methods for computing marginal data densities from the Gibbs output," Journal of Econometrics, Elsevier, vol. 175(2), pages 132-141.
    18. Lutz Kilian, 2013. "Structural vector autoregressions," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 22, pages 515-554, Edward Elgar Publishing.
    19. Carlo A. Favero, 2009. "The Econometrics of Monetary Policy: An Overview," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 16, pages 821-850, Palgrave Macmillan.
    20. 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.
    21. 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.
    22. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.

    More about this item

    JEL classification:

    • 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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    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:tpr:restat:v:99:y:2017:i:2:p:319-329. 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: Kelly McDougall (email available below). General contact details of provider: https://direct.mit.edu/journals .

    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.