Board of Governors of the Federal Reserve System

May 21, 2019

Tips from TIPS: Update and Discussions

Don Kim, Cait Walsh (Columbia Business School), and Min Wei¹

1. Introduction

The spread between the yield on a nominal Treasury security and that on a Treasury inflation protected security (TIPS) of comparable maturities—usually called the "breakeven inflation rate" or "inflation compensation"—has been often used as a real-time proxy for market participants' inflation expectations. However, policymakers and market participants are also cognizant that this spread is an imperfect measure, as it contains other components that can drive a wedge between inflation compensation and market participants' true inflation expectations.

In a recently published paper (D'Amico, Kim, and Wei (DKW), 2018), D'Amico and two of us use a no-arbitrage term structure model to decompose TIPS inflation compensation into three components—inflation expectation, inflation risk premium, and TIPS liquidity premium—over the 1990-2013 period. The model is also used to decompose nominal yields or forward rates into four components—expected real short rate, expected inflation, inflation risk premium, and real term premium.

In this Note, we update and extend the estimation to a longer period from 1983 to the present. The additional sample includes the period over which longer-term inflation expectations moved down significantly following the Volcker disinflation, which may help in pinning down the dynamics of the persistent components of inflation and inflation expectations.² After reviewing some basic aspects of the model, we discuss correlations of longer-horizon inflation compensation with risk sentiment proxies and with oil prices, and compare our model implied estimates of longer-run inflation expectations and equilibrium real rate with other estimates in the literature.

2. A brief review of the DKW model

The DKW model is a no-arbitrage term structure model, in which nominal yields, real yields, and inflation expectations are all assumed to be affine (i.e. linear) functions of latent factors that follow normal distributions. The model is specified in a "maximally flexible" way, i.e., the parameterization of the model is of the most general form that can be econometrically identified for the given assumptions. The model allows TIPS yields to deviate from "true" real yields. This differential, which we call "TIPS liquidity premium" as it primarily reflects the lower liquidity of TIPS relative to nominal Treasury securities, is modeled as an affine function of the latent factors that are common to nominal and real yields and an additional latent factor that is independent of the common factors.

By standard economic theory, nominal and real yields can be decomposed as:

nominal yield = real yield + expected inflation + inflation risk premium; (1)

real yield = expected average future real short rate + real term premium, (2)

where the inflation risk premium and the real term premium are extra compensations bond investors demand for bearing inflation risks and real interest rate risks, respectively. Nominal and real forward rates can be decomposed in the same way.

In the model, TIPS yields typically exceed "true" real yields (or real yields that are consistent with nominal yields) due to the TIPS liquidity premium:³

TIPS yield = real yield + TIPS liquidity premium. (3)

As a result, TIPS inflation compensation (IC)—defined as the nominal yield minus the TIPS yield—can be decomposed into three components,

TIPS IC = expected inflation + inflation risk premium – TIPS liquidity premium. (4)

TIPS IC can deviate from expected inflation for two reasons: a non-zero inflation risk premium or a non-zero TIPS liquidity premium. The first term, inflation risk premium, is the extra compensation nominal bond investors demand for bearing inflation risks, and its value depends on the covariance between inflation and real economic activity. This premium is believed to have been positive and sizeable in the 1970s and 1980s, when investors were more worried about stagflation scenarios with higher inflation accompanied by lower growth, but appears to have declined in recent decades to lower or even negative levels, as investors have become more concerned about outcomes where lower inflation is associated with lower growth.⁴

By contrast, TIPS liquidity premium is not connected to inflation risk but rather reflects factors that drive a wedge between TIPS yields and true real yields. This premium was high when TIPS was first launched, as it took some time for TIPS to gain popularity among investors, and again surged during the 2008-2009 Financial Crisis, as investors fled from less liquid or more risky instruments and sought the safety and liquidity of nominal Treasury securities. Apart from lower liquidity of TIPS relative to nominal Treasuries, this premium may also reflect supply-demand imbalance of TIPS versus nominal securities and a greater concentration of buy-and-hold investors in TIPS market compared with the nominal Treasury market.

Following DKW, we estimate the model with weekly data on nominal yields, TIPS yields and monthly data on seasonally-adjusted CPI, supplemented by survey forecasts of inflation and 3-month T-bill yield to address small sample problems associated with persistent time series such as interest rates.^5,6 To extend the estimation, we use nominal Treasury yields and survey forecasts from January 1983 to May 2018.⁷

Figure 1: Decomposition of inflation compensation

The upper and lower panels of Figure 1 show decompositions of 10-year and 5-to-10-year TIPS IC, respectively, into the three components according to Equation (4), based on the updated DKW model. TIPS inflation compensations move around a fair bit, even at the 5-to-10-year horizon where market participants and policymakers often look for signals regarding longer-horizon inflation expectations, and are substantially more volatile than the model-implied inflation expectations. The variations in model-implied inflation risk premium and TIPS liquidity premium follow the patterns outlined in the previous paragraphs.

3. Relationship of longer-horizon IC with sentiment proxies and oil prices

Longer-horizon TIPS IC not only moves around quite a bit, but also tends to co-move with variables that proxy for changing market sentiment. For example, Figure 2 shows a visible negative correlation between the 5-to-10-year IC and the high-yield (HY) corporate bond spread (upper panel) or the VIX (middle panel).⁸ Over the period since 2014, longer-horizon TIPS IC also appears to comove with oil prices, as both IC and oil prices declined notably in 2014H2 and in late 2018.⁹

Figure 2: Comovement between 5-to-10-year TIPS inflation compensation and market sentiment proxies or oil prices

These visual impressions are confirmed by Panel A of Table 1, which shows pairwise correlations between weekly changes in TIPS IC and its model-implied components, on the one hand, and the two sentiment proxies and oil prices, on the other, for the full sample since 1999. Changes in IC covary negatively with those in the HY spread and in VIX, and positively with those in oil prices. The magnitudes of correlations are higher in the post-crisis period (Panel C) and lower in the pre-crisis period (Panel E). The co-movements of IC with HY spread and VIX appear more elevated when there are notable shifts in risk sentiments. As can be seen from Panels B and D, the correlations of VIX and IC in weeks when VIX moves by more than one standard deviation is substantially larger in magnitude than the corresponding unconditional correlations both over the full sample and since the crisis.¹⁰

Table 1: Correlation of 5-to-10-year TIPS IC with sentiment indicators and oil prices

The correlation between risk sentiments indicators and the longer-horizon IC could arise from two channels. First, deteriorating risk sentiment is generally accompanied by, if not triggered by, perception of increased downside risks to growth. As mentioned earlier, in recent decades market participants appear to associate lower inflation with states of the world with lower real economic growth. As a result, perception of increased downside risk would likely push down both the inflation risk premium component and the expected inflation component of TIPS IC. Second, episodes of deteriorating risk sentiments are typically associated with strong safe haven flows into nominal Treasury securities. The increased demand for nominal Treasury securities would push up nominal Treasury prices relative to TIPS, resulting in higher TIPS liquidity premium. The patterns in Table 1 are consistent with both of these effects: Model-implied inflation expectation and inflation risk premium are negatively correlated with, while the TIPS liquidity premium is positively correlated with, the HY spread and the VIX.

The positive correlation between longer-horizon IC and oil prices is more puzzling. Food and energy prices are part of the (total) CPI to which TIPS are indexed, so it is natural to expect some correlation between near-term IC and oil prices, but it is less clear what mechanism underlies the comovement for longer-horizon IC. In 2014H2 and late 2018 when both oil prices and IC declined notably, a substantial fraction of these oil-price declines seemed to be driven by an oversupply of oil.¹¹ But concerns about weaker global demand and deteriorated risk sentiment may also have contributed to oil-price declines. If we compute the correlation of oil prices and longer-horizon IC using only observations when VIX moved more than one standard deviation (i.e., weeks with substantial changes in risk sentiment), the magnitude of oil price and IC correlation almost doubles, as can be seen in Table 1 (e.g., from 0.18 to 0.36 in the 1999-present sample), suggesting that common factors, such as risk sentiment, may have contributed to the variations in both series.

4. Longer-horizon inflation expectations (π*)

Longer-horizon inflation expectations are of considerable interest to investors, policymakers and researchers alike. As discussed above, it is natural to view that bond prices, being set by forward-looking market participants, embed this information, but some modeling is necessary to separate out other components of TIPS IC. The black line in Figure 3 presents the estimate of the 5-to-10-year inflation expectation going back to 1983 based on the updated DKW (2018) model.

Other researchers in the Federal Reserve System, including Abrahams, Adrian, Crump, Moench, and Yu (henceforth AACMY, 2016), Ajello, Benzoni, and Chyruk (henceforth ABC, 2012), Christensen, Lopez, and Rudebusch (henceforth CLR, 2010), and Haubrich, Pennacchi, and Ritchken (henceforth HPR, 2012), also developed term structure models that can be used to generate real-time measures of inflation expectations. Apart from nominal Treasury yields and inflation, the HPR model uses inflation swaps instead of TIPS yields. The AACMY and the CLR models use TIPS yields, where AACMY model the TIPS liquidity premium as a function of observable liquidity metrics while CLR ignore the lower liquidity of TIPS and exclude the earlier sample of TIPS. The ABC model does not use either inflation swap or TIPS in the estimation.^12,13,14,15

Figure 3: Term structure model estimates of 5-to-10-year-ahead inflation expectations

As can be seen from Figure 3, the estimates of longer horizon inflation expectations can vary significantly across models. The AACMY measure was practically immobile during the entire period for which the data were available. The CLR measure is also very stable up to 2011. By contrast, our measure and the ABC and HPR measures show higher variabilities as well as a notable downward trend since early 1980s, consistent with Blue Chip Financial Forecasts (BCFF) survey forecast of inflation 5 to 10 years ahead. Over the past decade the three measures show very similar variations, although the updated DKW and the ABC measure lie somewhat above the HPR measure. The range of these estimates has narrowed over time and currently varies from 2% (AACMY) to 2.4% (updated DKW) for CPI inflation, or roughly 1.7% to 2.1% for PCE inflation after taking into account the level difference between the two inflation measures.

One may view the extreme stability of the AACMY measure as evidence that the market's longer-horizon inflation expectations are very well anchored. However, it seems more likely to us that the apparent stability reflects the small sample problems noted in footnote [6] that standard implementations of term structure models frequently encounter; as a result, the persistence of (expected) inflation in that model were likely underestimated such that inflation expectations revert to its long-run mean in less than 5 years, leaving little variations beyond that horizon.

5. Longer-run equilibrium real rate (r^LR)

Another interesting object the model can shed light on is the expected real short rate 5-to-10-years ahead, which can be viewed as a measure of the equilibrium level of the real federal funds rate in the longer run (r^LR), defined as the rate consistent with the economy operating at its potential once the transitory effects of economic shocks have abated. Figure 4 compares our r^LR estimates with those from the other term structure models discussed above (AACMY, ABC, CLR, and HPR) and a real term structure model developed by Christensen and Rudebusch (CR) (2017) and estimated using TIPS yields only. The range of r^LR estimates across models is quite wide and currently much wider than that seen in Figure 3 for inflation expectations. The AACMY measure hovered near zero for the entire period since the late 1990s, spending nearly half of the time in the negative territory, and lay below all other measures up to the crisis. The CLR measure, on the other hand, provided the upper end of the range over most of its sample since 2003 and is currently at 1.4%. Our measure is closest to the CR measure in terms of level and variabilities.

Figure 4: Estimates of r^LR from term structure models

Estimates of r^LR can also be obtained from macro models, where time-series methods can be used to infer r^LR from the co-movement of macroeconomic series such as inflation, interest rates, and output. Figure 5 plots several such measures constructed by researchers at the Federal Reserve System—Del Negro, Giannone, Gianonni, and Tambalotti (henceforth DNGGT, 2017), Holston, Laubach, and Williams (henceforth HLW, 2017), Johannsen and Mertens (henceforth JM, 2016), Kiley (2015), Lewis and Vazquez-Grande (henceforth LVG, 2017), and Lubik and Matthes (henceforth LM, 2015). With the exception of JM, all models show a pronounced decline in r^LR around the 2008-2009 financial crisis.

Figure 5: Estimates of r^LR from macro models

Figure 6 shows our measure and a survey-based measure, against the backdrop of the range of those macro model-based estimates. Similar to the JM measure in Figure 5, our model indicates a more gradual downward drift in r^LR over the past couple of decades. Our measure has stayed within the range of macro model estimates since the crisis, but lies at or below the bottom of the range for most of the pre-crisis years. Our measure is close to the survey-implied measure in recent years but exhibits somewhat less variability over the longer span of time since mid-1980s.¹⁶

Figure 6: Estimates of r^LR from DKW, macro models, and BCFF survey

All measures in Figures 5 and 6 share the feature that r^LR is currently lower than its average values in 1990s and before the financial crisis, implying that in the current tightening cycle policymakers might not have to raise rates to the same level as they had done in the past tightening episodes. That said, the range of r^LR estimates is currently pretty wide, ranging between 0.5 and 2 percent, which underscores the importance of cautiously evaluating incoming data to assess the stance of monetary policy. In addition, estimates of r^LR appear to vary substantially depending on modeling and implementation choices. While certain choices may arguably be justifiable than others, it is important to keep in mind that expectations and risk attitudes, which ultimately determine market prices of nominal and TIPS securities, are quite complex, and models are only approximate representations of the rich behaviors of the yield curve and the economy. Caution is therefore always warranted in interpreting r^LR estimates or any other outputs from models.

6. Data release

Beginning with the publication of this Note, we will provide monthly updates of model decompositions of the 5-year, 10-year, and 5-to-10-year nominal Treasury yields and inflation compensation up to the last business day of the previous month. In general, we will endeavor to have the updated series posted sometime after 10:00 a.m. on the fourth business day of each month. Because this is a staff research product and not an official statistical release, it is subject to delay, revision, or methodological changes without advance notice.¹⁷

The latest estimates will be posted as a comma-separated values (CSV) file at the URL https://www.federalreserve.gov/econres/notes/feds-notes/DKW-updates.csv. As of this publication, daily data are available for the period from January 3, 1983 to March 28, 2024.

References

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Ajello, A., L. Benzoni, O. Chyruk (2012), "Core and 'Crust': Consumer Prices and the Term Structure of Interest Rates," working paper. (Forthcoming in Review of Financial Studies.)

Campbell J. Y., A. Sunderam, and L. M. Viceira (2017), "Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds," Critical Finance Review, 6, pp. 263-301.

Christensen, J. H.E., J. A. Lopez, and G. D. Rudebusch (2010), "Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, 42(S1), pp. 143-178.

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