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Identification Verification for Structural Vector Autoregressions with Sparse Heterogeneous Markov Switching Heteroskedasticity

Fei Shang, Tomasz Woźniak

Abstract

We propose a structural vector autoregressive model with a new and flexible specification of the volatility process which we call Sparse Heterogeneous Markov-Switching Heteroskedasticity. In this model, the conditional variance of each structural shock changes in time according to its own Markov process. Additionally, it features a sparse representation of Markov processes, in which the number of regimes is set to exceed that of the data-generating process, with some regimes allowed to have zero occurrences throughout the sample. We complement these developments with a definition of a new distribution for normalised conditional variances that facilitates Gibbs sampling and identification verification. In effect, our model: (i) normalises the system and estimates the structural parameters more precisely than popular alternatives; (ii) can be used to verify homoskedasticity reliably and, thus, inform identification through heteroskedasticity; and (iii) features excellent forecasting performance comparable with Stochastic Volatility. Finally, revisiting a prominent macro-financial structural system, we provide evidence for the identification of the US monetary policy shock via heteroskedasticity, with estimates consistent with those reported in the literature.

Identification Verification for Structural Vector Autoregressions with Sparse Heterogeneous Markov Switching Heteroskedasticity

Abstract

We propose a structural vector autoregressive model with a new and flexible specification of the volatility process which we call Sparse Heterogeneous Markov-Switching Heteroskedasticity. In this model, the conditional variance of each structural shock changes in time according to its own Markov process. Additionally, it features a sparse representation of Markov processes, in which the number of regimes is set to exceed that of the data-generating process, with some regimes allowed to have zero occurrences throughout the sample. We complement these developments with a definition of a new distribution for normalised conditional variances that facilitates Gibbs sampling and identification verification. In effect, our model: (i) normalises the system and estimates the structural parameters more precisely than popular alternatives; (ii) can be used to verify homoskedasticity reliably and, thus, inform identification through heteroskedasticity; and (iii) features excellent forecasting performance comparable with Stochastic Volatility. Finally, revisiting a prominent macro-financial structural system, we provide evidence for the identification of the US monetary policy shock via heteroskedasticity, with estimates consistent with those reported in the literature.
Paper Structure (15 sections, 18 equations, 3 figures, 6 tables)

This paper contains 15 sections, 18 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The SVAR-HMSH Model
  3. Structural Vector Autoregression
  4. Heterogeneous Markov-Switching Heteroskedasticity
  5. Homoskedasticity Verification Using Bayes Factor
  6. Alternative Volatility Specifications
  7. Normalisation of the Structural Model
  8. Estimation
  9. Two Monte Carlo Experiments
  10. Estimation Efficiency Under Misspecified Heteroskedasticity
  11. Assessing the Verification Procedure for Partial Identification
  12. Forecasting Study
  13. Monetary Policy Shock Identification
  14. Conclusions
  15. Prior Distributions

Figures (3)

  • Figure 1: Estimation results: time-varying conditional standard deviation of the monetary policy shock for SVARs with vaious volatility models.
  • Figure 2: Estimation results: impulse responses of the first five variables to the monetary policy shock identified through heteroskedasticity using SVARs with various volatility specifications.
  • Figure 3: Estimation results: impulse responses of the last five variables to the monetary policy shock identified through heteroskedasticity using SVARs with various volatility specifications.

Theorems & Definitions (1)

  • proof