Shadow-rate VAR¶

Motivation¶

A shadow-rate VAR is a VAR framework designed for settings where an observed policy rate is constrained by an effective lower bound (ELB).

The key idea is to distinguish between:

an observed short rate \(i_t\) (censored at the ELB), and
a latent shadow rate \(s_t\) that can move below the ELB.

A common measurement (censoring) relationship is:

\[ i_t = \max\{\mathrm{ELB},\, s_t\}. \]

Block-hybrid intuition (paper background)¶

The paper motivating this toolkit discusses block-hybrid variants in which:

macroeconomic variables respond to lagged observed rates, whilst
financial variables may load on lagged shadow rates.

This is intended to capture a distinction between:

economic agents facing administered rates, and
financial markets pricing off shadow policy expectations.

In this toolkit¶

The Python toolkit implements a practical SRVAR workflow centred on:

reduced-form Bayesian VARs,
ELB/shadow-rate data augmentation (sampling latent values at the bound), and
optional diagonal stochastic volatility.

It does not currently implement the full structural SVAR/block-hybrid state-space system described in the paper. Instead, it provides an ELB-aware VAR likelihood by treating ELB-bound observations as latent and sampling them subject to the constraint.