Concepts

Shadow rates

A shadow rate is a latent policy-rate concept used when observed policy rates are constrained by an effective lower bound (ELB).

ELB (shadow-rate) data augmentation

When ELB constraints are enabled, the model treats ELB-constrained observations as latent and samples shadow values subject to the bound.

Stochastic volatility (SVRW)

When volatility is enabled, the toolkit supports diagonal stochastic volatility with random-walk or AR(1) log-variance dynamics, plus triangular and factor covariance variants on the supported sampler paths.

Minnesota prior modes

The toolkit now distinguishes three Minnesota-style shrinkage paths:

• niw_minnesota_legacy: the historical compatibility path and default reproducibility baseline

• niw_minnesota_canonical: the explicit equation-wise canonical path where supported

• niw_minnesota_tempered: an experimental diagonal-SV-only bridge between the legacy and canonical variance maps

Background

This toolkit is inspired by the SRVAR methodology in Grammatikopoulos (2025). For the original MATLAB replication code, see: https://github.com/MichaelGrammmatikopoulos/MLSRVARs