# RDP 2011-01: Estimating Inflation Expectations with a Limited Number of Inflation-indexed Bonds 4. Results

## 4.1 Model Parameters and Fit to Data

We estimate the model over the period 31 July 1992 to 15 December 2010 using a number of different specifications. First we estimate both two- and three-factor versions of our model. Using a likelihood-ratio test we reject the hypothesis that there is no improvement of model fit between the two-factor model and three-factor model and so use the three-factor model. (Three factors are usually considered sufficient in the literature, with, for example, the overwhelming majority of variation in yields captured by the first three principal components.)

We also consider the three-factor model both with and without forecast data. Both models are able to fit the inflation yield data well; the model without forecast data, however, gives unrealistic estimates of inflation expectations and inflation risk premia. The 10-year-ahead inflation expectations are implausibly volatile and can be as high as 8 per cent and as low as −1 per cent, which is not consistent with economists' forecasts. These findings are consistent with those of Kim and Orphanides (2005), where the use of forecast data is advocated as a means of separating expectations from risk premia. Note, however, that estimates from the model with forecast data are not solely determined by the forecasts; the model estimates of expected future inflation only roughly match the forecast data and on occasion deviate significantly from them, as seen in Figure 1.

Our preferred model is thus the three-factor model estimated using forecast data. Likelihood ratio tests indicate that two parameters of that model (Λ11 and Λ21) are statistically insignificant and so they are excluded. Our final preferred model has 20 freely estimated parameters which are given in Table 2. We note that the estimate of ρ0, the steady-state inflation rate in our model, is 2.6 per cent, which is within the inflation target range. The persistence of inflation is essentially determined by the diagonal entries of the K matrix, which drives the inflation law of motion as defined by Equations (2) to (4). The first diagonal entry of K is 0.19, which in a single-factor model would imply a half-life of the first latent factor (being the time taken for the latent factor, and so inflation, to revert halfway back to its mean value after experiencing a shock) of around 3½ years. The half-lives of the other two latent factors would be 5 and 10 months.

Index number Parameter 1 (i) 2.64 (0.26) na na 0.19 (0.02) 0 0 −2.88 (0.05) 1.75 (0.05) 0 1.11 (0.05) 1.74 (0.05) 0.80 (0.01) 0.11 (0.02) 1.51 (0.10) 0.96 (0.02) 0.12 (0.01) 0.10 (0.01) −0.01 (0.00) 0 55.44 (0.32) 15.31 (0.06) 0 −107.80 (0.26) −8.91 (0.06) −12.38 (0.08) −144.22 (0.45) −73.07 (0.20) Notes: ρ0 and (Σ)ii are given in percentage points. Standard errors are shown in parentheses.

## 4.2 Qualitative Discussion of Results

### 4.2.1 Inflation expectations

Our estimated expected future inflation rates at horizons of 1, 5 and 10 years are shown in Figure 2. Two points stand out immediately: 1-year-ahead inflation expectations are much more volatile than 5- and 10-year-ahead expectations and, as may be expected, are strongly influenced by current inflation (not shown); and longer-term inflation expectations appear to be well anchored within the 2 to 3 per cent target range.

We see that there is a general decline in inflation expectations from the beginning of the sample until around 1999, the year before the introduction of the Goods and Services Tax (GST). The estimates suggest that the introduction of the GST on 1 July 2000 resulted in a large one-off increase in short-term inflation expectations. This is reflected in the run-up in 1-year-ahead inflation expectations over calendar year 1999, although the peak in the estimated expectations is below the actual peak in year-ended CPI growth of 6.1 per cent.[12] Of particular interest, however, is the non-responsiveness of 5- and 10-year-ahead expectations, which should be the case if the inflation target is seen as credible.

Long-term expectations increased somewhat between mid 2000 and mid 2001, perhaps prompted by easier monetary conditions globally as well as relatively high inflation in Australia. Interestingly, there appears to have been a sustained general rise in inflation expectations between 2004 and 2008 at all horizons. Again this was a time of rising domestic inflation, strong world growth, a boom in the terms of trade and rising asset prices.

In late 2008 the inflation outlook changed and short-term inflation expectations fell dramatically, likely in response to expectations of very weak global demand caused by the financial crisis. Longer-term expectations also fell, before rising over the early part of 2009 as authorities responded to the crisis. The subsequent moderation of longer-term expectations, as well as the relative stabilisation of short-term expectations, over 2010 suggests that financial market participants considered the economic outlook and Australian authorities' response to the crisis sufficient to maintain inflation within the target range.

The latest data, corresponding to December 2010, show 1-year-ahead inflation expectations reaching 3 per cent, close to the Reserve Bank of Australia forecast for inflation of 2¾ over the year to December 2011 given in the November 2010 Statement on Monetary Policy. Longer-term model-implied inflation expectations as at December 2010 are for inflation close to the middle of the 2 to 3 per cent target range.

### 4.2.2 Inflation risk premia

Although more volatile than our long-term inflation expectation estimates, long-term inflation risk premia broadly followed the same pattern – declining over the first third of the sample, gradually increasing between 2004 and 2008 before falling sharply with the onset of the global financial crisis, then rising again as markets reassessed the likelihood of a severe downturn in Australia (Figure 3). The main qualitative point of difference between the two series is in their reaction to the GST. As discussed earlier, the estimates of long-term inflation expectations remained well-anchored during the GST period, whereas as we can see from Figure 3, the estimates of long-term risk premia rose sharply. As the terminology suggests, inflation expectations represent investors' central forecast for inflation, while risk premia can be thought of as representing second-order information – essentially how uncertain investors are about their central forecasts and how much they dislike this uncertainty. So while longer-dated expectations of inflation did not change around the introduction of the GST, the rise in risk premia indicates a more variable and uncertain inflation outlook.

Although our estimates show periods of negative inflation risk premia, indicating that investors were happy to be exposed to inflation risk, this is probably not the case in reality. In our model, inflation risk premia are given by forward rates of inflation (as implied by the inflation yield curve) less inflation expectations. The inflation yield curve is given as the difference between nominal and real yields. Hence if real yields contain a liquidity premium, they will be higher, shifting the inflation yield curve down and reducing the estimated inflation risk premia to below their true level. The inflation-indexed bond market is known to be relatively illiquid in comparison to the nominal bond market and this provides a plausible explanation for our negative estimates. Note, however, that if the illiquidity in the inflation-indexed bond market is constant through time, then the level of the our estimated risk premia will be biased but changes in the risk premia should be accurately estimated. Market liaison suggests that an assumption of relatively constant liquidity is not an unreasonable one; as noted earlier for example, bid-ask spreads have stayed relatively constant over most of the period under consideration.

### 4.2.3 Inflation forward rates

The inflation forward rate reflects the relative prices of traded nominal and inflation-indexed bonds and is given by the sum of inflation expectations and inflation risk premia. As estimates of longer-term inflation expectations are relatively stable, movements in the 5- and 10-year inflation forward rates tend to be driven by changes in estimated risk premia. The inflation forward rate, as shown in Figure 4, generally falls during the first third of the sample, rises around the time of the GST, and rises between 2004 and 2008, before falling sharply with the onset of the financial crisis then rising again.[13]

One notable feature of Figure 4 are the negative inflation forward rates recorded in late 2008. This phenomenon is essentially due to very low break-even inflation rates embodied in the bond price data (2-year-ahead nominal less real yields were only around 90 basis points at this time), together with high realised inflation over 2008 – as break-even inflation rates reflect around five months of historical inflation, a low 2-year break-even inflation rate and high historical inflation necessarily implies a very low or even negative inflation forward rate in the near future. The low break-even inflation rates in turn are due to the yields on inflation-indexed bonds rising relative to the yields on nominal bonds. While it is possible that inflation forward rates were negative at this time, reflecting concern about the economic outlook, an alternative interpretation is that liquidity premia for inflation-indexed bonds increased (in line with increases in liquidity premia for most assets beyond highly rated and highly liquid government securities at this time). This would contradict our assumption of constant liquidity premia, and would result in indexed bond yields rising relative to (more liquid) nominal bond yields, and so in low inflation forward rates.

### 4.2.4 Comparisons with other studies

We compare our estimates of inflation expectations and inflation risk premia with those derived for UK data by Joyce et al (2010). In Figure 5, the 1-year-ahead inflation expectations in the United Kingdom and Australia are seen to display very similar trends. Interestingly, UK inflation expectations also increased over 1999, suggesting the spike in Australia may have been influenced by some global factors in addition to the introduction of the GST. At longer horizons there is greater difference between UK and Australian inflation expectations, with the United Kingdom in particular experiencing a large drop in 10-year-ahead expectations around 1997, the year that the Bank of England was granted independence. The magnitude of the changes in inflation risk premia are a little larger in Australia but the trends are broadly consistent in both countries (here UK inflation risk premia include the ‘residual term’ estimated by Joyce et al (2010), so that inflation expectations plus inflation risk premia equal the inflation forward rate, as is the case in our study).

## Footnotes

The legislation introducing the GST was passed through Federal Parliament in June 1999. [12]

Note that studies using US and UK data essentially start with the inflation forward rate, which they decompose into inflation expectations and inflation risk premia. Due to a lack of data we cannot do this and instead estimate inflation forward rates as part of our model. [13]