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Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs

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  • Gonzalez-Casasus, Oriol
  • Schorfheide, Frank

Abstract

VARs are often estimated with Bayesian techniques to cope with model dimensionality. The posterior means define a class of shrinkage estimators, indexed by hyperparameters that determine the relative weight on maximum likelihood estimates and prior means. In a Bayesian setting, it is natural to choose these hyperparameters by maximizing the marginal data density. However, this is undesirable if the VAR is misspecified. In this paper, we derive asymptotically unbiased estimates of the multi-step forecasting risk and the impulse response estimation risk to determine hyperparameters in settings where the VAR is (potentially) misspecified. The proposed criteria can be used to jointly select the optimal shrinkage hyperparameter, VAR lag length, and to choose among different types of multi-step-ahead predictors; or among IRF estimates based on VARs and local projections. The selection approach is illustrated in a Monte Carlo study and an empirical application.

Suggested Citation

  • Gonzalez-Casasus, Oriol & Schorfheide, Frank, 2025. "Misspecification-Robust Shrinkage and Selection for VAR Forecasts and IRFs," CEPR Discussion Papers 19915, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:19915
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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