A Smooth Shadow-Rate Dynamic Nelson-Siegel Model for Yields at the Zero Lower Bound

Tinbergen Institute Discussion Paper 2022-011/III

56 Pages Posted: 19 Mar 2022 Last revised: 12 Apr 2024

See all articles by Daan Opschoor

Daan Opschoor

Erasmus University Rotterdam (EUR) - Department of Econometrics; Tinbergen Institute

Michel van der Wel

Erasmus University Rotterdam

Date Written: March 24, 2023

Abstract

We propose a smooth shadow-rate version of the dynamic Nelson-Siegel (DNS) model to analyze the term structure of interest rates during a zero lower bound (ZLB) period. By relaxing the no-arbitrage restriction, our shadow-rate model becomes highly tractable with a closed-form yield curve expression. This permits the implementation of readily available DNS extensions such as allowing for time-varying parameters and the integration of macroeconomic variables. Using U.S. Treasury data, we provide clear evidence of a smooth transition of the yields entering and leaving the ZLB state. Moreover, we show that the smooth shadow-rate DNS model dominates the baseline DNS model and (shadow-rate) affine term structure models in terms of fitting and forecasting the yield curve, while it also produces plausible policy insights at the ZLB.

Keywords: Yield curve, zero lower bound, shadow-rate model, Nelson–Siegel model

JEL Classification: E43, E47, C53, C58, G12

Suggested Citation

Opschoor, Daan and van der Wel, Michel, A Smooth Shadow-Rate Dynamic Nelson-Siegel Model for Yields at the Zero Lower Bound (March 24, 2023). Tinbergen Institute Discussion Paper 2022-011/III, Available at SSRN: https://ssrn.com/abstract=4025299 or http://dx.doi.org/10.1080/07350015.2024.2365779

Daan Opschoor

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Michel Van der Wel (Contact Author)

Erasmus University Rotterdam ( email )

Burg. Oudlaan 50
Rotterdam, NL 3062 PA
Netherlands

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