A note on Taylor rules and the term structure

Abstract

This article augments the well-known dynamic macro-economic model of Svensson (1997) to include the term structure of interest rates, in order to support the empirical findings of Fendel and Frenkel (2005) on the information content of the term structure of interest rates for monetary policy published in Applied Economics Letters. The derived Taylor-type rule is an implicit rule that cannot be used mechanically, because it contains an additional forward-looking argument. Only under special conditions of a stable and flat yield curve and/or an aggregate demand specification that only depends on the short-term interest rate this augmented rule collapses to the class of well-known Taylor-type rules.

Notes

¹ For example, in the UK, unlike in the US, expenditure is more sensitive to short-term than to long-term interest rates, owing to the prevalence of floating-rate debt instruments (Batini and Haldane, 1999, p. 164). In our model, the US economy would then be characterized be a higher value of ρ compared to the UK. Differences in this structural feature of economies could also be modelled by choosing differing values of n, since the chosen value need not be identical with the longest maturity available in the economy. Instead, the choice should be driven by considerations about the transmission process.

² For pure convenience, this expression abstracts from the presence of a liquidity premium term. Under the assumption that such a premium would be a stable function of the maturities of the contracts, its inclusion would not alter our main results.

³ The formal derivation is available from the author upon request.

⁴ Again, the formal algebra is available from the author upon request.

⁵ See Equations 6.11 and 6.12 in Svensson (1997, p. 1133).

⁶ Such a case would be graphically represented by a parallel shift in the yield curve without any change in its slope.

⁷ Note that this reasoning differs from the explanation of Rotemberg and Woodford (1997) and Woodford (1999) for optimal interest rate smoothing that is based on the leverage that a smooth adjustment rule may provide the central bank over the longer term interest rates. In their analysis the main idea is that lagged dependence of the short rate permits the central bank to manipulate long-term rates.

⁸ When the expectations term is broad to the left-hand side of the rule, one could alternatively think of expression (14) as a policy rule that sets the path of (expected) short-term interest rates in accordance with the cyclical state of the economy. Since the last term also stands for the longer-term interest rates, the resulting left-hand side can be interpreted as the desired monetary conditions given the state of the economy.