Measuring the natural yield curve

Abstract

We generalize the concept of the natural rate of interest (Laubach and Williams, 2003; Woodford, 2003) by defining and estimating the natural yield curve (NYC) – the term structure of natural interest rates. Our motivation stems i.a. from the observation that at times when central banks attempt to directly affect long-term interest rates (e.g. via quantitative easing) the gap between the short-term real and natural rate is no more a good indicator of the monetary policy stance. We estimate the NYC on US data, document its main properties and show i.a. that in the period 2008 to 2011 the NYC allows to better capture the US monetary policy stance than the short-term natural rate.

Keywords:

• natural rate of interest
• natural yield curve
• unconventional monetary policy
• Kalman filter

JEL Classification:

• C32
• E43
• E52

Acknowledgements

The views expressed herein are ours and not necessarily those of the National Bank of Poland or the Warsaw School of Economics. This research project was conducted under the NBP Economic Research Committee open competition for research projects to be carried out by the NBP staff and economists from outside the NBP and was financed by the National Bank of Poland. We would like to thank Ryszard Kokoszczyski and the participants of the Computing in Economics and Finance conference, Ecomod conference, European Economic Association Meeting and seminars at the National Bank of Poland and Warsaw School of Economics for useful comments and discussions.

Notes

1. ¹Svensson (1994) adds a second curvature factor to improve the goodness of fit and Christensen et al. (2009) incorporate a second slope factor to impose the no-arbitrage restriction.

2. ² We decided not to add a second curvature factor as proposed by Svensson because it helps to fit the longer end of the yield curve while we use maturities up to 10 years only which can be matched by one curvature factor. Moreover, it would be difficult to find a clear economic interpretation for this factor.

3. ³Morales (2010) shows that the difference between the one- and two-step estimation approch is minor in practice.

4. ⁴This follows the observation derived from (1) that .

5. ⁵Sometimes humps on the yield curve may result from the lack of liquidity or inefficiency of the market. This, however, does not seem to be the case for the US T-bonds market.

6. ⁶Pooter (2007) reviews different strategies for estimation of DNS model examining both one-step and two-step approaches.

7. ⁷ The discussion on numerical issues related to the estimation and calibration of the DNS model can be found in Gilli et al. (2010).

8. ⁸ Following the literature (e.g. Diebold and Li, 2002; Diebold et al., 2006) we refer to empirical counterparts of the estimated factors. From (1) we have and .

It follows that the closest empirical counterpart for the level factor is the longest available yield and for the slope factor the difference between the shortest and longest yield. For our estimate of λ = 0.2255 these are: and . The empirical counterpart for the curvature factor is in turn defined as the difference between twice the medium-term yield and the sum of short- and long-term yields. This is .

These relations show that for the finite maturities the estimated slope and curvature factors would have higher amplitudes and variances than their empirical counterparts.