RDP 2011-01: Estimating Inflation Expectations with a Limited Number of Inflation-indexed Bonds 1. Introduction

Reliable and accurate estimates of inflation expectations are important to central banks given the role of these expectations in influencing inflation and economic activity. Inflation expectations may also indicate over what horizon individuals believe that a central bank will achieve its inflation target, if at all.

The difference between the yields on nominal and inflation-indexed bonds, referred to as the inflation yield or break-even inflation, is often used as a measure of inflation expectations.^[1] Since nominal bonds are not indexed to inflation, investors in these bonds require higher yields, relative to those available on inflation-indexed bonds, as compensation for inflation. The inflation yield may not give an accurate reading of inflation expectations, however. This is because investors in nominal bonds will likely demand a premium, over and above their inflation expectations, for bearing inflation risk. That is, the inflation yield will include a premium that will depend positively on the extent of uncertainty about future inflation. If we wish to estimate inflation expectations we must separate this inflation risk premia from the inflation yield. By treating inflation as a random process, we are able to model expected inflation and the cost of the uncertainty associated with inflation separately.

Inflation expectations and inflation risk premia have been estimated for the United Kingdom and the United States using models similar to the one used in this paper. Beechey (2008) and Joyce, Lildholdt and Sorensen (2010) find that inflation risk premia decreased in the UK, first after the Bank of England adopted an inflation target and then again after it was granted independence. Using US Treasury Inflation-Protected Securities (TIPS) data, Durham (2006) estimates expected inflation and inflation risk premia, although he finds that inflation risk premia are not significantly correlated with measures of the uncertainty of future inflation or monetary policy. Also using TIPS data, D'Amico, Kim and Wei (2008) find inconsistent results due to the decreasing liquidity premia in the US, although their estimates are improved by including survey forecasts and using a sample over which the liquidity premia are constant.

In this paper we estimate a time series for inflation expectations for Australia at various horizons, taking into account inflation risk premia, using a latent factor affine term structure model which is widely used in the literature. Compared to the United Kingdom and the United States, there are a very limited number of inflation-indexed bonds on issue in Australia. This complicates the estimation but also highlights the usefulness of our approach. In particular, the limited number of inflation-indexed bonds means that we cannot reliably estimate a zero-coupon real yield curve and so cannot estimate the model in the standard way. Instead, we develop a novel technique that allows us to estimate the model using the price of coupon-bearing inflation-indexed bonds instead of zero-coupon real yields. The estimation of inflation expectations and risk premia for Australia, as well as the technique we employ to do so, are the chief contributions of this paper to the literature.

To better identify model parameters we also incorporate inflation forecasts from Consensus Economics in the estimation. Inflation forecasts provide shorter maturity information (for example, forecasts exist for inflation next quarter), as well as information on inflation expectations that is separate from risk premia. Theoretically the model is able to estimate inflation expectations and inflation risk premia purely from the nominal and inflation-indexed bond data – inflation risk premia compensate investors for exposure to variation in inflation, which should be captured by the observed variation in prices of bonds at various maturities. This is, however, a lot of information to extract from a limited amount of bond data. Adding forecast data helps to better anchor the model estimates of inflation expectations and so improves model fit.

Inflation expectations as estimated in this paper have a number of advantages over using the inflation yield to measure expectations. For example, 5-year-ahead inflation expectations as estimated in this paper (i) account for risk premia and (ii) can measure expectations of the inflation rate in five years time (as well as the average expectation over the next five years). In contrast, the 5-year inflation yield ignores risk premia and only gives an average of inflation rates over the next five years.^[2] The techniques used in the paper are potentially useful for other countries with a limited number of inflation-indexed bonds on issue, such as Germany or New Zealand.

In Section 2 we outline the model. Section 3 describes the data, estimation of the model parameters and latent factors, and how these are used to extract our estimates of inflation expectations. Results are presented in Section 4 and conclusions are drawn in Section 5.

Footnotes

The income stream from an inflation-indexed bond is adjusted by the rate of inflation and maintains its value in real terms. Terms and conditions of Treasury inflation-indexed bonds are available at http://www.aofm.gov.au/content/borrowing/terms/indexed_bonds.asp. [1]

In addition, due to the lack of zero-coupon real yields in Australia's case, yields-to-maturity of coupon-bearing nominal and inflation-indexed bonds have historically been used when calculating the inflation yield. This restricts the horizon of inflation yields that can be estimated to the maturities of the existing inflation-indexed bonds, and is not a like-for-like comparison due to the differing coupon streams of inflation-indexed and nominal bonds. [2]