Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

Economic determinants of the nominal treasury yield curve

Macroeconomic shocks account for most of the variability of nominal Treasury yields, inducing parallel shifts in the level of the yield curve. We develop a new approach to identifying macroeconomic shocks that exploits model-based empirical shock measures. Technology shocks shift yields through their effect on expected inflation and the term premium. Shocks to preferences for current consumption affect yields through their impact on real rates and expected inflation. For both shocks, the systematic reaction of monetary policy is an important transmission pathway. We find little evidence that fiscal policy shocks are an important source of interest rate variability.     

New Measures for Inflation Uncertainty and Disagreement from Treasury Auctions: Alternative to Surveys

In this article, we propose a novel methodology to construct new uncertainty and disagreement measures for the long-term inflation rate with the use of micro data of Treasury auctions. We employ individual bids submitted in Treasury auctions for nominal and inflation indexed bonds. We argue that these newly formed indicators do not have the problems associated with the survey and market-based uncertainty and disagreement measures. We also focus on the interactions of our proposed measures for inflation rate by comparing the measures commonly used in the literature. The findings of this article are believed to enhance the effectiveness of policy-making by introducing new proxies for crucial economic variables and also by providing the opportunity for other emerging economies with inadequate surveys to construct historical uncertainty and disagreement measures for inflation rates.     

A Phillips Curve with Anchored Expectations and Short‐Term Unemployment

This paper examines the behavior of U.S. core inflation, as measured by the weighted median of industry price changes. We find that core inflation since 1985 is well‐explained by an expectations‐augmented Phillips curve in which expected inflation is measured with professional forecasts and labor‐market slack is captured by the short‐term unemployment rate. We also find that expected inflation was backward‐looking until the late 1990s, but then became strongly anchored at the Federal Reserve's target. This shift in expectations changed the relationship between inflation and unemployment from an accelerationist Phillips curve to a level‐level Phillips curve. Our specification explains why high unemployment during the Great Recession did not reduce inflation greatly: partly because inflation expectations were anchored, and partly because short‐term unemployment rose less sharply than total unemployment.     

Inflation Dynamics When Inflation Is Near Zero

We discuss the likely evolution of U.S. inflation in the near and medium terms on the basis of (i) past U.S. experience with very low levels of inflation, (ii) the most recent Japanese experience with negative inflation, and (iii) some preliminary U.S. micro evidence on downward nominal wage rigidity. Our findings question the view that stable long‐run inflation expectations and downward nominal wage rigidity will necessarily provide sufficient support to prices to avoid further declines in inflation. We show that an inflation model fitted on Japanese data over the past 20 years, which accounts for both short‐ and long‐run inflation expectations, matches the recent U.S. inflation experience quite well. While the model indicates that U.S. inflation might be subject to a lower bound, it does not rule out a prolonged period of low inflation or even mild deflation going forward. In addition, micro‐level data on wages suggest no obvious downward rigidity in the firm's wage bill, downward rigidity in individual wages notwithstanding. As a consequence, downward nominal wage rigidity may not be enough to offset deflationary pressures in the current situation.     

The term structure of inflation expectations

We use information in the term structure of survey-based forecasts of inflation to estimate a factor hidden in the nominal yield curve. We construct a model that accommodates forecasts over multiple horizons from multiple surveys and Treasury real and nominal yields by allowing for differences between risk-neutral, subjective, and objective probability measures. We establish that model-based inflation expectations are driven by inflation, output, and one latent factor. We find that this factor affects inflation expectations at all horizons but has almost no effect on the nominal yields; that is, the latent factor is hidden. We show that this hidden factor is not related to either current and past inflation or the standard set of macro variables studied in the literature. Consistent with the theoretical property of a hidden factor, our model outperforms a standard macro-finance model in its forecasting of inflation and yields.     

Inflation ambiguity and the term structure of U.S. Government bonds

Variations in trend inflation are the main driver for variations in the nominal yield curve. According to empirical data, investors observe a set of empirical models that could all have generated the time-series for trend inflation. This set has been large and volatile during the 1970s and early 1980s and small during the 1990s. I show that log utility together with Knightian uncertainty about trend inflation can explain the term premium in U.S. Treasury bonds. The equilibrium has two inflation premiums, an inflation risk premium and a Knightian inflation ambiguity premium.     

The high-frequency impact of news on long-term yields and forward rates: Is it real?

Macroeconomic news announcements move yields and forward rates on nominal and index-linked bonds and inflation compensation. This paper estimates the reactions using high-frequency data on nominal and index-linked bond yields, allowing the effects of news announcements on real rates and inflation compensation to be parsed far more precisely than is possible using daily data. Long-term nominal yields and forward rates are very sensitive to macroeconomic news announcements. Inflation compensation is sensitive to announcements about price indices and monetary policy. However, for news announcements about real economic activity, such as nonfarm payrolls, the vast majority of the sensitivity is concentrated in real rates. Accordingly, most of the sizeable impact of news about real economic activity on the nominal term structure of interest rates represents changes in expected future real short-term interest rates and/or real risk premia rather than changes in expected future inflation and/or inflation risk premia. Such sensitivity of real rates to macroeconomics news is hard to rationalize within the framework of existing macroeconomic models.     

Raise Rates to Raise Inflation? Neo‐Fisherianism in the New Keynesian Model

Increasing the inflation target in a New Keynesian (NK) model may require increasing, rather than decreasing, the nominal interest rate in the short run. We refer to this positive short‐run comovement between the nominal rates and inflation conditional on a nominal shock as Neo‐Fisherianism. We show that the NK model is more likely to be Neo‐Fisherian the more persistent is the change in the inflation target and the more flexible are prices. Neo‐Fisherianism is driven by the forward‐looking nature of the model. Modifications that make the framework less forward‐looking make it less likely for the model to exhibit Neo‐Fisherianism.     

Are Indexed Bonds Really Inflation Proof? A Model of Real and Nominal Term Structures when Money has Real Effects

This paper studies the general behavior of the nominal and real term structures of interest rates in a general equilibrium framework. A central bank is introduced in the model as an agent facing a tradeoff between inflation and output and choosing a monetary policy variable. Prices and output are jointly determined in our model endogenously. Two multi-factor nominal and real term structure models are given as examples to illustrate the general model. In our economies, inflation indexed bonds are not completely inflation proof, but are still subject to the influence of inflation uncertainties. The models offer us an empirical framework that can be studied with indexed bond data and nominal bond data together in a single estimation.     

The nominal duration of TIPS bonds

This paper studies the price responsiveness (effective duration) of U.S. government issued inflation-indexed bonds, known by the acronym TIPS (Treasury Inflation-Protected Securities), to changes in nominal interest rates, real interest rates, and expected inflation. Using the TIPS pricing formula derived by Laatsch and Klein [Q. Rev. Econ. Finance 43 (2002) 405], we first confirm that TIPS bonds have zero sensitivity to changes solely in expected inflation. By changes solely in expected inflation, we mean that the real rate remains unchanged and the nominal rate changes in accordance with the established Fisher [Publ. Am. Econ. Assoc. 11 (1896)] effect. We show that the first derivative of the TIPS price is zero whenever the real rate is held constant. Thus, the first partial derivative of the TIPS bond pricing formula with respect to expected inflation is zero and the first partial derivative of the TIPS bond price with respect to nominal rates is also zero, given, in each case, that we hold the real rate constant. We then temporarily shift the analysis to zero-coupon TIPS bonds and zero-coupon ordinary Treasury bonds. We prove that the nominal duration of zero-coupon TIPS bonds equals that of zero-coupon ordinary Treasury bonds when the real rate changes but expected inflation is held constant.However, if expected inflation changes and the change in the nominal rate does not yield a constant real rate, zero-coupon TIPS prices will change and they will change by a smaller percentage than will zero-coupon ordinary Treasury bonds. We analyze TIPS responsiveness to changes in nominal rates under such conditions. We derive an approximation to effective duration that demonstrates that the effective durations of various maturity zero-coupon TIPS bonds are approximately linear functions in time to maturity of the effective duration of the one-year zero-coupon TIPS bond, ceteris paribus.Nominal effective duration of TIPS bonds is certainly of interest to fixed income portfolio managers that might have a desire to include such bonds in their portfolio. After all, the greater portion of a typical fixed income portfolio is in traditional, noninflation protected bonds whose major risk exposure is to changes in nominal rates. To properly assess the role of TIPS bonds in the portfolio, portfolio managers need information as to how TIPS bonds respond to the changes in nominal rates that are driving the price behavior of the bulk of the portfolio's assets. Prior to concluding the paper, we demonstrate how portfolio managers can calculate the nominal durations of coupon TIPS bonds using the zero-coupon duration formula we derive.     

The Term Structure of Real Rates and Expected Inflation

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time‐varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves

This paper analyses the UK interest rate term structure over the period since October 1992, when the United Kingdom adopted an explicit inflation target, using an affine term structure model estimated using both government bond yields and survey data. The model imposes no-arbitrage restrictions across nominal and real yields, which enables interest rates to be decomposed into expected real policy rates, expected inflation, real term premia and inflation risk premia. The model is used to shed light on major developments over the period, including the impact of Bank of England independence and the low real bond yield ‘conundrum’.     

Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using this model, we make clear structural relationships among a term structure of real and nominal interest rates, utility form and underlying economic factors (in particular, inflation expectation). Notably, we show that, if (1) the EIS is less than one, (2) the agent is comparatively more risk-averse relative to time-separable utility, (3) short-term interest rates are pro-cyclical, and (4) the rate of expected inflation is negatively correlated with the rate of real output growth and its expected rate, then a nominal yield curve can have a low instantaneous riskless rate and an upward slope.     

Technology,Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?

We argue that the New Keynesian Phillips Curve literature has failed to deliver a convincing measure of real marginal costs. We start from a careful modeling of optimal price setting allowing for nonunitary factor substitution, nonneutral technical change, and time‐varying factor utilization rates. This ensures the resulting real marginal cost measures match volatility reductions and level changes witnessed in many U.S. time series. The cost measure comprises conventional countercyclical cost elements plus procyclical (and covarying) utilization rates. Although procyclical elements seem to dominate, the components of real marginal cost components are becoming less cyclical over time. Incorporating this richer driving variable produces more plausible price‐stickiness estimates than otherwise and suggests a more balanced weight of backward‐ and forward‐looking inflation expectations than commonly found. Our results challenge existing views of inflation determinants and have important implications for modeling inflation in New Keynesian models.     

Effective Use of Survey Information in Estimating the Evolution of Expected Inflation

The evolution of the term structure of expected U.S. inflation is modeled using survey data to provide timely information on structural change not contained in lagged inflation data. To capture shifts in subjective perceptions, the model is adaptive to long‐horizon survey expectations. However, even short‐horizon survey expectations inform shifting‐endpoint estimates that capture the lag between inflation and the perceived inflation target, which anchors inflation expectations. Results show movements of the perceived target are an important source of inflation persistence and suggest historical U.S. monetary policy was not fully credible for much of the postwar sample.     

Modeling the dynamics of inflation compensation

This paper investigates the relationship between short-term and long-term inflation expectations using daily data on inflation compensation derived from the term structure of real and nominal interest rates. We use a flexible econometric model which allows us to uncover this relationship in a data-based manner. We relate our findings to the issue of whether inflation expectations are anchored, unmoored or contained. Our empirical results indicate no support for either unmoored or firmly anchored inflation expectations. Most evidence indicates that inflation expectations are contained.     

Term Structure of Interest Rates Under Recursive Preferences in Continuous Time

This paper proposes a testable continuous-time term-structure model with recursive utility to investigate structural relationships between the real economy and the term structure of real and nominal interest rates. In a representative-agent model with recursive utility and mean-reverting expectations on real output growth and inflation, this paper shows that, if (1) real short-term interest rates are high during economic booms and (2) the agent is comparatively risk-averse (less risk-averse) relative to time-separable utility, then a real yield curve slopes down (slopes up, respectively). Additionally, for the comparatively risk-averse agent, if (3) expected inflation is negatively correlated with the real output and its expected growth, then a nominal yield curve can slope up, regardless of the slope of the real yield curve.     

Inflation risk premia and the expectations hypothesis

We study the properties of the nominal and real risk premia of the term structure of interest rates. We develop and solve the bond pricing implications of a structural monetary version of a real business cycle model, with taxes and endogenous monetary policy. We show the relation of this model with the class of essentially affine models that incorporate an endogenous state-dependent market price of risk. We characterize and estimate the inflation risk premium and find that over the last 40 years the ten-year inflation risk premium has been has averaged 70 basis points. It is time-varying, ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping. The inflation risk premium explains 23% (42%) of the time variation in the five (ten)-year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates.     

Inflation Expectations,Inflation Target Credibility,and the COVID-19 Pandemic: Evidence from Germany

Using the exact wording of the European Central Bank's definition of price stability, we started a representative online survey of German citizens in January 2019 that is designed to measure long-term inflation expectations and the credibility of the inflation target. Our results indicate that credibility has decreased in our sample period, particularly in the course of the deep recession implied by the Covid-19 pandemic. Interestingly, even though inflation rates in Germany have been clearly below 2% for several years, credibility has declined mainly because Germans increasingly expect that inflation will be much higher than 2% over the medium term. We investigate how inflation expectations and the impact of the pandemic depend on personal characteristics including age, gender, education, and political attitude.