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Priors about observables in vector autoregressions

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  • Jarociński, Marek
  • Marcet, Albert

Abstract

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how to translate the prior on observables into a prior on parameters using strict probability theory principles, a posterior can then be formed with standard procedures. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations. We prove equivalence to a fixed point formulation and a convergence theorem for the algorithm. We use this framework in two well known applications in the VAR literature, we show how priors on observables can address some weaknesses of standard priors, serving as a cross check and an alternative formulation.

Suggested Citation

  • Jarociński, Marek & Marcet, Albert, 2019. "Priors about observables in vector autoregressions," Journal of Econometrics, Elsevier, vol. 209(2), pages 238-255.
  • Handle: RePEc:eee:econom:v:209:y:2019:i:2:p:238-255
    DOI: 10.1016/j.jeconom.2018.12.023
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    Cited by:

    1. Weale, Martin & Wieladek, Tomasz, 2016. "What are the macroeconomic effects of asset purchases?," Journal of Monetary Economics, Elsevier, vol. 79(C), pages 81-93.

    More about this item

    Keywords

    Bayesian estimation; Prior elicitation; Inverse problem; Structural vector autoregression;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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