Below the Zero Lower Bound: A Shadow-Rate Term Structure Model for the Euro Area

50 Pages Posted: 5 Oct 2016

See all articles by Wolfgang Lemke

Wolfgang Lemke

European Central Bank

Andreea Vladu

Deutsche Bundesbank

Multiple version iconThere are 2 versions of this paper

Date Written: 2016


We propose an arbitrage-free shadow-rate term structure model to analyze the euro-area yield curve from 1999 to mid-2015, when bond yields turned negative at various maturities. In the model the 'shadow rate' can reach any positive or negative level, while the actual one-month rate cannot fall below some lower bound perceived by market participants. This bound is estimated to have first ranged marginally above zero, before falling to -11 bps in September 2014. We show analytically that the lower bound itself can be interpreted as a 'policy parameter' and interpret the September 2014 ECB rate cut from this perspective. Our model improves upon a standard Gaussian affine model by providing a better match with survey forecasts of short-term rates during the low-rate period and by capturing the decline in yield volatility. The model implies that since mid-2012, the median horizon after which future short rates are expected to return to 25 bps has ranged between 18 and 62 months. However, the liftoff timing, as well as the quantification of forward premia, is highly sensitive to the level of the lower bound.

Keywords: term structure of interest rates, lower bound, nonlinear state-space model, monetary policy expectations

JEL Classification: C32, E43, E52

Suggested Citation

Lemke, Wolfgang and Vladu, Andreea, Below the Zero Lower Bound: A Shadow-Rate Term Structure Model for the Euro Area (2016). Bundesbank Discussion Paper No. 32/2016. Available at SSRN:

Wolfgang Lemke (Contact Author)

European Central Bank ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314

Andreea Vladu

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431

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