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Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy

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  • Laurent Callot

    () (VU University Amsterdam, the Tinbergen Institute and CREATES)

  • Johannes Tang Kristensen

    () (University of Southern Denmark and CREATES)

Abstract

This paper studies vector autoregressive models with parsimoniously time-varying parameters. The parameters are assumed to follow parsimonious random walks, where parsimony stems from the assumption that increments to the parameters have a non-zero probability of being exactly equal to zero.We estimate the sparse and high-dimensional vector of changes to the parameters with the Lasso and the adaptive Lasso. The parsimonious random walk allows the parameters to be modelled non parametrically, so that our model can accommodate constant parameters, an unknown number of structural breaks, or parameters varying randomly.We characterize the finite sample properties of the Lasso by deriving upper bounds on the estimation and prediction errors that are valid with high probability, and provide asymptotic conditions under which these bounds tend to zero with probability tending to one.We also provide conditions under which the adaptive Lasso is able to achieve perfectmodel selection. We investigate by simulations the pproperties of the Lasso and the adaptive Lasso in settings where the parameters are stable, experience structural breaks, or follow a parsimonious randomwalk.We use our model to investigate the monetary policy response to inflation and business cycle fluctuations in the US by estimating a parsimoniously time varying parameter Taylor rule.We document substantial changes in the policy response of the Fed in the 1970s and 1980s, and since 2007, but also document the stability of this response in the rest of the sample.

Suggested Citation

  • Laurent Callot & Johannes Tang Kristensen, 2014. "Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy," CREATES Research Papers 2014-41, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2014-41
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    References listed on IDEAS

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    Cited by:

    1. repec:eme:aecozz:s0731-905320150000035011 is not listed on IDEAS
    2. Laurent Callot & Johannes Tang Kristensen, 2016. "Regularized Estimation of Structural Instability in Factor Models: The US Macroeconomy and the Great Moderation," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 437-479 Emerald Publishing Ltd.

    More about this item

    Keywords

    Parsimony; time varying parameters; VAR; structural break; Lasso;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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