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Bank of England Staff Working Paper No CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF PRACTICE 2007 CODE OF 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PRACTICE 2007 Staff Working Paper No. 756 Bayesian vector autoregressions Silvia Miranda-Agrippino and Giovanni Ricco September 2018 Staff Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. Any views expressed are solely those of the author(s) and so cannot be taken to represent those of the Bank of England or to state Bank of England policy. This paper should therefore not be reported as representing the views of the Bank of England or members of the Monetary Policy Committee, Financial Policy Committee or Prudential Regulation Committee. Staff Working Paper No. 756 Bayesian vector autoregressions Silvia Miranda-Agrippino(1) and Giovanni Ricco(2) Abstract This article reviews Bayesian inference methods for vector autoregression models, commonly used priors for economic and financial variables, and applications to structural analysis and forecasting. Key words: Monetary policy, local projections, VARs, expectations, information rigidity, survey forecasts, external instruments. JEL classification: C30, C32. (1) Bank of England and CFM. Email: [email protected] (2) University of Warwick and OFCE - Science Po. Email: [email protected] This is a draft of an article that has been accepted for publication by Oxford University Press in the forthcoming Economics and Finance Oxford Research Encyclopedia edited by Jonathan Hamilton, and due for publication in 2018. We thank the Editor of the Oxford Research Encyclopedia and an anonymous referee for useful comments and suggestions. We are also grateful to Fabio Canova, Andrea Carriero, Matteo Ciccarelli, Domenico Giannone, Marek Jarociński, Marco del Negro, Massimiliano Marcellino, Giorgio Primiceri, Lucrezia Reichlin, and Frank Shorfheide for helpful comments and discussions. The views expressed are those of the authors and do not reflect those of the Bank of England or any of its Committees. The Bank’s working paper series can be found at www.bankofengland.co.uk/working-paper/staff-working-papers Publications and Design Team, Bank of England, Threadneedle Street, London, EC2R 8AH Telephone +44 (0)20 7601 4030 email [email protected] © Bank of England 2018 ISSN 1749-9135 (on-line) Non-Technical Summary Vector Autoregressions (VARs) are linear multivariate time-series models able to capture the joint dynamics of multiple time series. Bayesian inference treats the VAR parameters as random variables, and it provides a framework to estim- ate `posterior' probability distribution of the location of the model parameters by combining information provided by a sample of observed data and prior inform- ation derived from a variety of sources, such as other macro o micro datasets, theoretical models, other macroeconomic phenomena, or introspection. In empirical work in Economics and Finance, informative prior probability distributions are often adopted. These are intended to summarise stylised repres- entations of the data generating process. For example, `Minnesota' priors, one of the most commonly adopted macroeconomic priors for the VAR coefficients, ex- press the belief that an independent random-walk model for each variable in the system is a reasonable `centre' for the beliefs about their time series behaviour. Other commonly adopted priors, the `single-unit-root' and the `sum-of-coefficients' priors are used to enforce beliefs about relations among the VAR coefficients, such as for example the existence of co-integrating relationships among variables, or of independent unit-roots.
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