An Affine Macro-Factor Model of the UK Yield Curve

Abstract

This paper estimates yield curve models for the UK, where the underlying determinants have a macroeconomic interpretation. The first factor is an unobserved inflation target, the second factor is annual inflation, and the third factor is a 'Taylor rule residual', which, among other things, captures the effects of the output gap and monetary policy surprises in the Taylor rule. We find that the long end of the yield curve is primarily driven by changes in the unobserved inflation target. At shorter maturities, yield curve movements reflect short-run inflation and the Taylor rule residual. For holding periods of one month, our preferred model implies that agents require compensation for risks associated with cyclical and inflation shocks but do not require compensation for shocks to the inflation target. For holding periods beyond one month, agents require compensation for all three sources of risks. Time series of risk premia on long forward rates from the preferred yield curve model have declined since the 1970s, which is consistent with perceptions of declining macroeconomic uncertainty or perhaps more efficient macroeconomic stabilisation policies. Model-implied risk premia at short maturities match up reasonably well with survey-based risk premia, which indicates that the model could be useful for the purpose of extracting market-based interest rate expectations.