RDP 2018-02: Affine Endeavour: Estimating a Joint Model of the Nominal and Real Term Structures of Interest Rates in Australia 1. Introduction

Expectations of future nominal and real interest rates and inflation are crucial economic quantities. Expectations of nominal interest rates provide information about the expected path of monetary policy. Expectations for real interest rates, particularly a long way into the future, provide information about the economy's expected potential growth rate and the neutral real interest rate: the real rate that is expected to prevail in the medium term once all transitory shocks have dissipated.[1] In many economic models, monetary policy is deemed expansionary if current real rates are below this neutral rate, and contractionary if above. Finally, inflation expectations influence price- and wage-setting behaviour, and so affect observed inflation and economic outcomes more generally. Measures of expected inflation may also indicate if, and over what horizon, individuals believe that the central bank will meet its inflation target.

Nominal and inflation-indexed bond yields contain information about market participants' expectations for expected nominal and real rates, respectively. The difference between these two yields, referred to as break-even inflation, contains information about expected inflation. However, these yields also incorporate risk premia, which compensate investors for the various risks that they take on in buying a bond rather than investing in cash. This makes interpretation more difficult, as changes in yields could reflect changes in expectations or premia (or both).

One way to separate these premia from the ‘pure’ expectations component is to use an affine term structure model (ATSM). These models are widely used by policymakers and academics, and have been estimated for a broad range of countries for each of the above variables separately as well as jointly. Some key papers in the literature include: Duffie and Kan (1996), Dai and Singleton (2000) and Duffee (2002) who introduce and popularise the class of ATSMs that we work with; Kim and Orphanides (2012) who argue for the inclusion of survey data to increase the robustness of estimation, as well as Kim and Wright (2005) and Chernov and Mueller (2012) who also work with survey data; Joslin, Singleton and Zhu ((2011); hereafter referred to as JSZ), Hamilton and Wu (2012) and Adrian, Crump and Moench (2013) who introduce efficient estimation methods for these models; and Krippner (2013, 2015) who introduces a tractable framework for enforcing the zero lower bound on interest rates, which is particularly important to account for when the short-term nominal interest rate is near the lower bound, as has been the case in the United States, euro area and Japan recently (although not Australia).

In this paper we estimate a joint model of the term structures of nominal and real yields, which allows us to extract information on expected future short-term nominal and real interest rates, as well as inflation. The model is intended to be a ‘workhorse’ model that can be used for ongoing analysis. We take this into account in our modelling choices, and try to ensure that the model is parsimonious and relatively easy to update.

The results suggest that medium- to long-term expectations for the future short-term real interest rates, which some use as a measure of the neutral real interest rate, have declined somewhat over recent years. Meanwhile longer-term inflation expectations, having fallen over the 1990s as the Reserve Bank's inflation-targeting framework gained credibility, have been reasonably stable more recently, particularly compared with what is implied by break-even inflation rates. The results also suggest that a large portion of the decline in yields on Australian government securities (AGS) since the global financial crisis has reflected lower real term premia – the risk premium associated with variation in real interest rates – rather than declines in inflation expectations or inflation risk premia – premia associated with variation in inflation. The decline has mirrored that in US term premia, suggesting that it reflects some global factor such as foreign central banks' quantitative easing programs and the associated portfolio rebalancing flows.

As well as the Australia-specific contribution, our paper also contributes to the broader literature on ATSMs. Most notably, we extend the technique JSZ use to estimate a nominal ATSM so that we can estimate a joint model of nominal and real yields.[2] We also document how casting the model in terms of a Kalman filter and allowing the survey data to be fully exploited appears to aid estimation. This finding is somewhat counter to JSZ and Guimarães (2016), who find that filtering does not substantially change results. The difference likely reflects the fact that our zero-coupon real yield data contain a moderate amount of measurement error, given Australia has relatively few inflation-indexed bonds on issue, which makes filtering out the noise more important in our case. As such, the finding may be relevant for other countries with a limited number of inflation-indexed bonds, such as Germany and New Zealand. Finally, we also add to the literature by applying these ATSM techniques to an advanced economy that has not been subject to the effective lower bound for interest rates, unlike the United States, United Kingdom or euro area, which are more commonly examined in the literature.


For a further discussion in the Australian context, see McCririck and Rees (2017). See also Vlieghe (2017) for an excellent discussion of the determinants of real interest rates from a macrofinance perspective. [1]