A Closer Look at the Sensitivity Puzzle: The Sensitivity of Expected Future Short Rates and Term Premia to Macroeconomic News

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. A Closer Look at the Sensitivity Puzzle: The Sensitivity of Expected Future Short Rates and Term Premia to Macroeconomic News Meredith Beechey 2007-06 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

A Closer Look at the Sensitivity Puzzle: The Sensitivity of Expected Future Short Rates and Term Premia to Macroeconomic News Meredith Beechey (cid:3) December 26, 2006 Abstract Nominal forward rates are sensitive at surprisingly long horizons to macroeconomic news and monetary-policy surprises. This paper takes advantage of a¢ ne term-structure modelling to demonstrate that movements in term premia, not expected future short rates, account for most of the reaction of forward rates at long horizons. Speci(cid:133)cally, term premia account for about three quarters of the reaction of nominal forward rates 10 to 15 years hence to the surprise component of numerous macroeconomic newsannouncements. Thishasstrongimplicationsfortheinterpretationof interest-rate sensitivity. Contrary to some recent conjectures, long-horizon expectations of the level of in(cid:135)ation and real rates appear reasonably well anchored in the United States, but the associated term premia are quite variable. DivisionofMonetaryA⁄airs,BoardofGovernorsoftheFederalReserveSystem,Washington (cid:3) DC 20551. Email: meredith.j.beechey@frb.gov. I am grateful to Andrew Levin, Jonathan Wright and workshop participants at the ECB and the Reserve Bank of Australia for helpful discussionsandtoBrianBunkerandKatherineFemiaforresearchassistance. Theviewsinthis paper are solely the responsibility of the author and should not be interpreted as re(cid:135)ecting the viewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociated with the Federal Reserve System. 1

1 Introduction The purpose of this paper is to separate the reaction of U.S. Treasury forward rates to macroeconomic news into components attributable to term premia and expected future short rates. The analysis employs the decomposition of forward rates into expected future short rates and term premia made possible by a standard a¢ ne, no-arbitrage, three-factor model of the term structure. Such modelling permits a closer look at the nature of interest rate sensitivity than recent research whose scope has been con(cid:133)ned to nominal forward rates. I con(cid:133)rm that distant-horizon nominal forward rates are sensitive to current economic news and monetary policy surprises but show that movements in term premia, not expected future short rates, account for most of the reaction. Speci(cid:133)cally, movements in term premia account for about three quarters of the reaction of nominal forward rates 10 to 15 years hence in response to a range of important macroeconomic surprises. This has strong implications for the interpretation of interest-rate sensitivity, namely, that long-horizon expectations of in(cid:135)ation and real rates are reasonably well anchored in the United States, contrary to recent conjecture by G(cid:252)rkaynak, Sack, and Swanson (2005) (GSS). Why term premia exhibit such sensitivity to economic news and monetary policy surprises is not clear-cut. It may represent changing uncertainty (a change in the quantity of risk), a change in the price of risk, or a behavioral overreaction to new information. These (cid:133)ndings are relevant to what is meant by "well-anchored expectations". Are interest-rate expectations well anchored when expectations of future nominal policy rates mean revert at reasonable horizons following the release of new information? Or must uncertainty about long-run interest rate expectations also be fairly insensitive to current macroeconomic surprises? The results shown in this paper suggest that the second condition is not met in U.S. Treasury markets. 2

The paper is structured as follows. Section 2 gives a brief overview of the a¢ ne term-structure model usedtogenerate the decompositions, describes the dataand presents the estimation strategy. Section 3 presents and discusses the results and considers an alternative estimate of the term premium and Section 4 concludes. 2 Model and Estimation Strategy 2.1 Term-structure Model The model of the nominal term structure is the implementation by Kim and Orphanides (2005) of a model proposed by Du¢ e (2002) using three underlying latent factors to describe the time-series behavior of the U.S. yield curve. As is standard in a¢ ne term-structure models, the model hinges on the fundamental asset pricing condition E (M R ) = 1 t t+1 t+1 where R is the gross nominal return on a zero-coupon bond at time t+1 and t+1 M is a stochastic discount factor derived from a standard utility maximization t+1 problem of a representative investor. The simple nature of zero-coupon bonds allows the price of an n period bond to be expressed recursively as P = E ((cid:5)n M ): (1) n;t t j=1 t+j The model assumes that the pricing relationship (1) holds for all bonds and in this sense the framework imposes the no-arbitrage restriction. For the model generating the (cid:133)nancial data for this paper, the stochastic discount factor, M , t+1 isspeci(cid:133)edasana¢ nefunctionofa3 1vectoroflatentfactors, X . Itisassumed t (cid:2) 3

to be conditionally lognormal, as in the following discrete-time speci(cid:133)cation: log(M ) = y (cid:21) " 0:5(cid:21) (cid:21) t+1 (cid:0) 1;t (cid:0) 0t t+1 (cid:0) 0t t where y is the one-period yield, (cid:21) is a 3 1 vector, and y and (cid:21) are a¢ ne 1;t t 1;t t (cid:2) functions of the factors, y = (cid:14) +(cid:14) X 1;t 0 01 t (cid:21) = v +v X : t 0 10 t The coe¢ cient (cid:14) is a scalar, (cid:14) and v are 3 1 vectors, v is a 3 3 matrix and 0 1 0 1 (cid:2) (cid:2) the vector of latent factors evolve as a VAR(1),1 X = (cid:8)X +(cid:6)" t t 1 t (cid:0) with the shock " i.i.d. normal with mean zero and identity variance-covariance t matrix and (cid:6) = diag((cid:27) ;(cid:27) ;(cid:27) ). The vector (cid:21) can be interpreted as the market 1 2 3 t priceofrisk,andthemodelpermitsatime-varyingpriceofrisk,aswellastractable and nonnegative bond prices. Yields, forward rates, expected future short rates and term premia are a¢ ne functions of the latent factors. Speci(cid:133)cally, yields can be calculated as follows: y = a +b X n;t n n t where a and b are functions of the parameters of the model ((cid:14) ; (cid:14) ;v ;v ;(cid:8) and n n 0 1 0 1 (cid:27)2 3 ). The parameters of the model are estimated by maximum likelihood j j=1 u(cid:8)sin(cid:9)g monthly nominal zero-coupon yield data from 1961 and the latent factors, forward rates and term premia are constructed at a daily frequency. Rather than 1Inthecontinuous-timespeci(cid:133)cationofthemodel,thevectoroflatentfactorsactuallyevolve as a continuous-time analogue of the vector autoregression, a multivariate Ornstein-Uhlenbeck process, see Kim and Wright (2005). 4

employ both yield-curve and macroeconomic factors for forecasting in the model, as in Diebold, Rudebusch, and Aruoba (2006) and Rudebusch and Wu (2004), this paper considers whether a¢ ne functions of purely latent yield-curve factors exhibit systematic responses to new macroeconomic information not included in the term-structure model. Figure 1plots the forwardrate nine-to-tenyears hence, as well as the model(cid:146)s decomposition into the expected future short rate and term premium. 2.2 Data The (cid:133)nancial data for the analysis consist of zero-coupon yields and forward rates from an estimated nominal Svensson yield curve for U.S. Treasuries. The zerocoupon yields are used to estimate the parameters of the a¢ ne factor model described above, and once estimated, the model provides decompositions of forward rates into expected future nominal short rates and term premia. Daily changes in the one-year forward rates and their components are then employed as dependent variables in announcement regressions. The macroeconomic data consist of the surprise elements of thirteen major U.S. data releases and a monetary-policy target surprise. The macroeconomic surprises are nearly identical to those of GSS (2005) but the sample end-date has been extended from December 2002 to October 2005 and missing observations replaced.2 Following GSS, the surprise component of a macroeconomic data release is measured as the released value less the market expectation reported the prior Friday by Money Market Services (MMS, provided by Action Economics), and each surprise series is divided by its standard error. To facilitate comparison 2Extending the sample to October 2005 has little material e⁄ect on the nominal forward rate sensitivity coe¢ cients. However, sixteen observations of advance GDP releases have been addedtothedatasetbyreplacingmissingobservationsandextendingthesampleusedbyGSS, who relied on only twelve data points for advance GDP surprises. Other special features of the data set, such as removing FOMC announcements that con(cid:135)ict with employment reports early in the sample and excluding the week around September 11, 2001, have been retained. 5

with earlier results, the macroeconomic variables included in the regressions are the subset of releases deemed by GSS to be signi(cid:133)cant determinants of the oneyear forward rate ending one year hence; namely, capacity utilization, consumer con(cid:133)dence, core CPI, civilian employees(cid:146)employment cost index, advance GDP, initial jobless claims, index of leading indicators, ISM PMI index (NAPM), new home sales, change in nonfarm payrolls, core PPI, retail sales and the unemployment rate.3 The monetary policy surprise is measured as the daily change in the current or next month(cid:146)s futures contract around an FOMC announcement, as recommended by Kuttner (2001). 2.3 Estimation Strategy Daily changes in forward rates, expected nominal short rates and term premia from the a¢ ne factor model are regressed at various horizons on the surprise components of macroeconomic data releases. The equations to be estimated take a simple form: 13 (cid:1)f = af + bf news +cfmps +e (2) j;t j i;j i;t j t f;t i=1 X 13 (cid:1)s = as + bs news +csmps +e (3) j;t j i;j i;t j t s;t i=1 X 13 (cid:1)p = ap + bp news +cpmps +e (4) j;t j i;j i;t j t p;t i=1 X where f denotes the one-yearaheadforwardrate endingj = 1;:::;15 years hence j;t at time t, and s and p denote the expected short rate and term premium j;t j;t at horizon j and the di⁄erence operator indicates daily changes.4 The variable news indexes the i = 1;::;13 macro data releases and mps is the monetary i;t t 3These variables continue to be the signi(cid:133)cant for the longer sample used in this paper. 4Anattractiveextensionistoestimateresponsesovernarrowerwindows,butthiswouldalso require forecasting intraday results from the three-factor model. 6

policy surprise at date t. Newey-West standard errors are estimated to take into account any heteroskedasticity and serial correlation. Two points are worth making here. First, the (cid:133)t of the factor model is su¢ cientlygoodthatcoe¢ cientestimatesfromregressionsusingthe(cid:133)ttedforward rates are indistinguishable from those using the Svensson-curve forward rates. Second, while there may be measurement error present in s and p , as long as j;t j;t this measurement error is uncorrelated with the surprise components of the data releases, it will not bias the coe¢ cient estimates but just sacri(cid:133)ce precision. 3 Estimation results Table 1 presents the estimated coe¢ cients from equation (2) from regressing daily changes in Svensson forward rates and the (cid:133)tted factor-model forward rates on economic news variables for the sample January 1990 to December 2002. The columns marked GSS report the results published in GSS (2005). The coe¢ cients estimated from (cid:133)tted forward rates are very similar to the Svensson forward rates and the standard errors remain small, testimony to the good (cid:133)t of the threefactor model. Only the coe¢ cient on advance GDP di⁄ers noticeably, with the replacement of missing data points lowering the estimated response by one third. Table 2 presents the same regressions updated to include data to end-October 2005, also plotted as the solid black line in Figures 2 to 4 (95 percent con(cid:133)dence intervals are shown as dashed lines). Extending the sample has little e⁄ect on the coe¢ cients or standard errors. Table 3 presents the results of equations (3) and (4) for expected future short rates and term premia. The coe¢ cient estimates are summarized in Figures 2 to 4 along with 95 percent con(cid:133)dence intervals. Several points are worth making. First, as expected, the estimated coe¢ cients on the expected short rate and term 7

premium sum to the coe¢ cient on the nominal forward rate at each maturity. Second, it is immediately clear that the majority of the sensitivity of long-horizon forward rates is due to the response of term premia to macroeconomic surprises. Between 70 and 80 percent of the total response at 10 years can be attributed to movement in term premia. Expected nominal short rates respond strongly to macroeconomic shocks in the near term but the response then declines smoothly over the forecast horizon to a small (but precisely estimated) response 10 years hence. The minimal response of expected future nominal short rates at long horizonssuggeststhatthesumoflong-runin(cid:135)ationexpectationsandtheperceived equilibrium real rate is reasonably well anchored in the United States. 3.1 Reaction to macroeconomic news The term premia response at long horizons dominates the expected short-rate response for all economic news variables used as regressors. Positive in(cid:135)ation surprises and real-side surprises cause expected future short rates to rise in the near term, while term premia dominate in the longer run. Notably, nonfarm payrolls surprises seem to elicit a larger response of expected nominal short rates than other variables, suggesting that this important release prompts the most revision to long-run expectations. Weaker-than-expected in(cid:135)ation and real-side news are associated with lower term premia. One possible reason for this is that investors maydemandlesscompensationforin(cid:135)ationriskwhennewsindicatesthatin(cid:135)ation outcomes are likely to be lower, consistent with the positive correlation between the level and volatility of in(cid:135)ation discussed by Svensson (1997) and Mishkin and Westelius (2006), among others. 8

3.2 Reaction to monetary-policy surprises The reaction of forward rates to a monetary-policy surprise(cid:151)de(cid:133)ned as the unexpected target surprise of an FOMC decision(cid:151)is particularly interesting. Positive policy surprises elicit a small rise in nominal short-rate expectations in the near to medium term, but short rates are then projected to revert slowly to their preshock level within a decade. In contrast, a positive policy surprise is associated with a decline in the term premium at all horizons, su¢ cient to o⁄set the rise in nominal short rate expectations. The connection between tighter monetary policy with a lower market price of risk, or a larger market appetite for assets, could be consistent with monetary-policy tightening lowering market uncertainty, especially the compensation that investors demand for in(cid:135)ation risk. 3.3 An alternative estimate of the term premium Cochrane and Piazzesi (2005) estimate bond term premiums by regressing excess bond returns on the term structure of forward rates, where excess bond returns aremeasuredasthereturnonholdingann-yearbondoverthereturnonholdinga one-year bond for a holding period of one year. Their resulting forecasting factor shares a high correlation (0.71) with the termpremiumon a one-year forward rate 5-years hence estimated by the three-factor model. Thus it comes as no surprise that estimating equation (3) on daily changes in the return forecasting factor reveals signi(cid:133)cant reactions to the same news surprises that move term premia (see Table 4). And because excess returns at di⁄erent horizons are proportional to the return forecasting factor, this implies that the response does not diminish with maturity, the same property seen clearly in Figures 2, 3 and 4 for the a¢ ne factor model(cid:146)s term premia. 9

3.4 Discussion An important question to ask at this point is whether the results are an artifact of the construction of the three-factor model. The factors of the arbitrage-free model are estimated as unobservable, latent factors without macroeconomic data input, and as such the regressions presented here do not exploit pre-constructed relationships between expected interest rates, term premia and economic news. Therefore, the assumption that any measurement error in the term premium and expected future short-term rates estimated by the three-factor model should be uncorrelated with the MMS surprises seems reasonable. Similar results to those presented here are obtained using the forward-rate decomposition from a threefactor model augmented with Blue Chip survey in(cid:135)ation expectations (Kim and Orphanides, 2005). These survey expectations presumably incorporate information about macroeconomic surprises comparable to that in MMS expectations used to derive the surprise regressors and, accordingly, the results di⁄er little. The a¢ ne term-structure model also has the characteristic that its latent factors are stationary. However, the half life of the most persistent factor is over 10 years, so gradual that (cid:133)tted term premia and expected short rates can be far from their means for very long periods. The coe¢ cients, and thus the decomposition of the sensitivity puzzle, are quite insensitive to increasing the persistence of the most persistent factor as done by Wright (2006).(). It is also important to remember that term premiums and expected short rates are (cid:133)tted jointly in the model and as such, both are functions of the same three factors. Freely estimated coe¢ cients determine the a¢ ne combination of factors that represent the best (cid:133)t of the data. 10

4 Conclusion This paper has shown that expectations of the central bank(cid:146)s policy rate account foronlyasmallfractionoftheresponseoflong-horizonforwardratestonews. The (cid:133)nding casts doubt upon explanations of long forward-rate sensitivity that posit that data surprises prompt changes in perceptions of the central bank(cid:146)s in(cid:135)ation target,orperceptionsofequilibriumrealinterestrates.Suchexplanationsoverlook theroleofadjustmentofriskpremiainresponsetonewinformation, whichappear to dominate the response at long horizons. Term premia at all maturities rise in response to stronger-than-expected real and in(cid:135)ation news, and in response to surprise policy easings. This is true of both the term premia estimated by the a¢ ne factor model and Cochrane and Piazzesi(cid:146)s (2005) return forecasting factor. This procyclicality contrasts with the common(cid:133)ndingthat termpremiaaresomewhat countercyclical. Thetwoarenot necessarily at odds, however, as countercyclicality is found at the business-cycle frequencyandneednot re(cid:135)ect the high-frequencyreactionof termpremiainshort windows around macroeconomic news announcements. Indeed, the nature of the term-premium response to news(cid:150)declining with weaker-than-expected macroeconomic data and tighter monetary policy(cid:150)is suggestive of a role for in(cid:135)ation risk premia. Paired with the (cid:133)ndings of G(cid:252)rkaynak, Levin, and Swanson (2005), that long-horizon in(cid:135)ation compensation (comprising expected future in(cid:135)ation and an in(cid:135)ation risk premium) also responds to macroeconomic news, it seems likelythat in(cid:135)ation riskpremiaare variable inthe United States. However, to accurately parse out the e⁄ect of news announcements on in(cid:135)ation risk premia and real risk premia requires term-structure models that can identify both quantities and is the subject of ongoing research. 11

References Cochrane, J., and M. Piazzesi (2005): (cid:147)Bond Risk Premia,(cid:148)American Economic Review, 95, 138(cid:150)160. Diebold, F., G. Rudebusch, and S. B. Aruoba (2006): (cid:147)The Macroeconomy and the Yield Curve: A Dynamic Latent Factor Approach,(cid:148)Journal of Econometrics, 131(1-2), 309(cid:150)338. Duffie, G.(2002): (cid:147)TermPremiaandInterestRateForecastsinA¢ neModels,(cid:148) Journal of Finance, 57, 405(cid:150)443. G(cid:252)rkaynak, R., A. Levin, and E. Swanson (2005): (cid:147)In(cid:135)ation Targeting and the Anchoring of Long-Run In(cid:135)ation Expectations: International Evidence from Daily Bond Yield Data,(cid:148)Unpublished manuscript. G(cid:252)rkaynak, R., B. Sack, and E. Swanson (2005): (cid:147)The Excess Sensitivity of Long Term Interest Rates: Evidence and Implications for Macroeconomic Models,(cid:148)American Economic Review, 95, 425(cid:150)436. Kim, D., and A. Orphanides (2005): (cid:147)Term Structure estimation with survey dataoninterestrateforecasts,(cid:148)FEDSWorkingPaperSeriesNo.2005-48,Board of Governors of the Federal Reserve. Kim, D., and J. Wright (2005): (cid:147)An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and Distant-Horizon Forward Rates,(cid:148)FEDS Working Paper Series No. 2005-33, Board of Governors of the Federal Reserve. Kuttner, K. (2001): (cid:147)Monetary Policy Surprises and Interest Rates: Evidence from the Fed Funds Futures Market,(cid:148)Journal of Monetary Economics, 47(3), 523(cid:150)544. Mishkin, F., and N.Westelius(2006): (cid:147)In(cid:135)ationBandTargetingandOptimal In(cid:135)ation Contracts,(cid:148)NBER Working Paper 12384. Rudebusch, G., and T. Wu (2004): (cid:147)A Macro-Finance Model of the Term Structure, Monetary Policy and the Economy,(cid:148)FRBSF Working Paper 2003- 17. Svensson, L. E. O. (1997): (cid:147)Optimal In(cid:135)ation Targets, "Conservative" Central Banks, and Linear In(cid:135)ation Contracts,(cid:148)American Economic Review, 87, 98(cid:150) 114. Wright, J. (2006): (cid:147)Stationarity, Nonstationarity and Near-nonstationarity in Don Kim(cid:146)s model,(cid:148)unpublished manuscript, Board of Governors of the Federal Reserve, April 2006. 12

Figure 1: Decomposition of the 9 to 10-year nominal forward rate Percent 10 Forward Rate 8 Expected Future Short Rate 6 4 2 Term Premium 0 -2 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 13

Figure 2: Response of One-Year Forward Rates and Components to Macroeconomic Surprises Core CPI Inflation Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Employment Cost Index Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Core PPI Inflation Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 3 3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Note: Dashed lines indicate two-standard deviation confidence bands. 14

Figure 3: Response of One-Year Forward Rates and Components to Macroeconomic Surprises Consumer Confidence Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Retail Sales Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) NAPM Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Note: Dashed lines indicate two-standard deviation confidence bands. 15

Figure 4: Response of One-Year Forward Rates and Components to Macroeconomic Surprises Initial Claims Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 1 1 1 0 0 0 -1 -1 -1 -2 -2 -2 -3 -3 -3 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Nonfarm Payrolls Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 9 9 9 7 7 7 5 5 5 3 3 3 1 1 1 -1 -1 -1 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Monetary Policy Surprise Forward Rate Expected Short Rate Term Premium Basis Points Basis Points Basis Points 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 3 5 7 9 11 13 15 Maturity (years) Maturity (years) Maturity (years) Note: Dashed lines indicate two-standard deviation confidence bands. 16

Table 1: Responses of Nominal Forward Rates to Economic News, Jan 1990 to Dec 2002 Ending 1 year ahead Ending 5 years ahead Ending 10 years ahead Three-factor Three-factor Three-factor GSS GSS GSS model model model Macroeconomic data releases Capacity utilisation 1.36*** 1.42*** 1.26** 1.33** 0.80 0.46 (0.33) (0.32) (0.57) (0.57) (0.61) (0.61) Consumer confidence 2.11*** 2.02*** 2.88*** 2.75*** 1.97*** 2.08*** (0.40) (0.40) (0.56) (0.52) (0.54) (0.51) CPI (core) 1.67*** 1.67*** 1.81*** 1.68*** 1.09* 1.10** (0.42) (0.40) (0.60) (0.54) (0.66) (0.52) Employment cost index 3.43*** 3.65*** 4.42*** 4.46*** 3.73*** 3.65*** (0.89) (0.86) (1.13) (0.98) (0.93) (0.87) GDP (advance) 4.39*** 2.69** 4.12* 2.17 3.76** 1.36 (1.42) (1.24) (2.19) (1.62) (1.82) (1.43) Initial Claims -0.83*** -0.95** -0.79*** -0.93** -0.59** -0.65** (0.24) (0.41) (0.29) (0.41) (0.27) (0.33) Leading Indicators 0.95*** 0.95*** 0.61 0.56 0.55 0.57 (0.34) (0.33) (0.57) (0.53) (0.58) (0.55) NAPM 3.00*** 2.91*** 3.29*** 2.98*** 1.53** 1.76*** (0.51) (0.49) (0.54) (0.53) (0.63) (0.54) New home sales 1.08*** 1.10*** 1.65*** 1.55*** 0.92* 1.31*** (0.39) (0.42) (0.54) (0.56) (0.51) (0.51) Non-farm payrolls 5.10*** 4.91*** 3.48*** 3.33*** 1.88* 1.64* (0.57) (0.56) (0.91) (0.90) (0.97) (0.87) PPI (core) 0.39 0.42 1.22** 1.29** 1.46*** 1.32*** (0.45) (0.43) (0.56) (0.51) (0.50) (0.51) Retail sales 2.97*** 3.05*** 2.62** 2.46*** 1.93** 1.83** (0.72) (0.68) (1.03) (0.90) (0.92) (0.87) Unemployment Rate -1.76*** -1.58*** -0.77 -0.62 0.14 0.03 (0.51) (0.47) (0.73) (0.66) (0.66) (0.63) Monetary Policy Surprises 0.47*** 0.44*** -0.04 -0.03 -0.16** -0.13 (0.10) (0.08) (0.14) (0.10) (0.07) (0.09) Notes: Newey-West standard errors. *** indicates significance at the 1-percent level,** at the 5-percent level and * at the 10-percent level. Coefficients in columns labelled 'GSS' are values reported in GSS (2005). The estimated coefficients represent the basis-point repsonse of the one-yearforward rate per standard deviation of the macroeconomic release surprise and per basis-point surprise in monetary policy announcements. Constant terms not shown. 17

Table 2: Responses of Nominal Forward Rates to Economic News, 1990 to 2002 and 1990 to 2005 Ending 1 year ahead Ending 5 years ahead Ending 10 years ahead Jan 1990 - Jan 1990 - Jan 1990 - Jan 1990 - Jan 1990 - Jan 1990 - Dec 2002 Oct 2005 Dec 2002 Oct 2005 Dec 2002 Oct 2005 Macroeconomic data releases Capacity utilisation 1.42*** 1.17*** 1.33** 1.04** 0.46 0.45 (0.32) (0.29) (0.57) (0.48) (0.61) (0.52) Consumer confidence 2.02*** 1.48*** 2.75*** 2.03*** 2.08*** 1.56*** (0.40) (0.37) (0.52) (0.51) (0.51) (0.48) CPI (core) 1.67*** 1.73*** 1.68*** 1.63*** 1.10** 0.93** (0.40) (0.36) (0.54) (0.48) (0.52) (0.46) Employment cost index 3.65*** 1.91** 4.46*** 2.73*** 3.65*** 2.26*** (0.86) (0.89) (0.98) (1.03) (0.87) (0.83) GDP (advance) 2.69** 2.50** 2.17 2.99** 1.36 2.08 (1.24) (0.98) (1.62) (1.30) (1.43) (1.16) Initial Claims -0.95** -0.91*** -0.93** -1.00*** -0.65** -0.66** (0.41) (0.30) (0.41) (0.32) (0.33) (0.27) Leading Indicators 0.95*** 0.65* 0.56 0.59 0.57 0.72 (0.33) (0.34) (0.53) (0.48) (0.55) (0.50) NAPM 2.91*** 2.72*** 2.98*** 3.22*** 1.76*** 1.97*** (0.49) (0.42) (0.53) (0.50) (0.54) (0.49) New home sales 1.10*** 0.80*** 1.55*** 1.15*** 1.31*** 1.04*** (0.42) (0.31) (0.56) (0.43) (0.51) (0.39) Non-farm payrolls 4.91*** 5.20*** 3.33*** 4.19*** 1.64* 2.11* (0.56) (0.50) (0.90) (0.81) (0.87) (0.75) PPI (core) 0.42 0.27 1.29** 1.00** 1.32*** 1.14*** (0.43) (0.34) (0.51) (0.39) (0.51) (0.40) Retail sales 3.05*** 2.33*** 2.46*** 2.13*** 1.83** 1.58** (0.68) (0.59) (0.90) (0.82) (0.87) (0.73) Unemployment Rate -1.58*** -1.30*** -0.62 -0.04 0.03 0.36 (0.47) (0.45) (0.66) (0.65) (0.63) (0.61) Monetary Policy Surprises 0.44*** 0.45*** -0.03 -0.02 -0.13 -0.13 (0.08) (0.08) (0.10) (0.10) (0.09) (0.09) Notes: Newey-West standard errors. *** indicates significance at the 1-percent level,** at the 5-percent level and * at the 10-percent level. The estimated coefficient indicates the basis-point repsonse of the one-year forward rate per standard deviation of the macroeconomic release surprise and per basis-point surprise in monetary policy announcements. Constant terms not shown. 18

Table 3: Responses of Expected Short Rates and Term Premia to Economic News Ending 1 year ahead Ending 5 years ahead Ending 10 years ahead Term Term Term Short rate Short rate Short rate premium premium premium Macroeconomic data releases Capacity utilisation 1.17*** -- 0.34* 0.70** 0.20** 0.24 (0.29) -- (0.18) (0.35) (0.10) (0.44) Consumer confidence 1.48*** -- 0.73*** 1.31*** 0.27*** 1.29*** (0.37) (0.19) (0.37) (0.09) (0.41) CPI (core) 1.73*** -- 0.69*** 0.94*** 0.25*** 0.68* (0.36) (0.15) (0.36) (0.08) (0.40) Employment cost index 1.91*** -- 0.76* 1.98*** 0.44** 1.82** (0.89) (0.40) (0.71) (0.20) (0.73) GDP (advance) 2.50** -- 0.99** 2.00* 0.60*** 1.48 (0.98) (0.41) (1.05) (0.23) (1.03) Initial Claims -0.91** -- -0.35*** -0.65*** -0.18*** -0.49** (0.30) (0.13) (0.23) (0.06) (0.24) Leading Indicators 0.65*** -- 0.37** 0.22 0.18** 0.54 (0.34) (0.16) (0.38) (0.07) (0.46) NAPM 2.72*** -- 1.12*** 2.10*** 0.46*** 1.51*** (0.42) (0.21) (0.38) (0.10) (0.43) New home sales 0.80*** -- 0.42*** 0.73** 0.21*** 0.83** (0.31) (0.14) (0.33) (0.07) (0.35) Non-farm payrolls 5.20*** -- 1.93*** 2.26*** 0.87*** 1.23* (0.50) (0.24) (0.63) (0.14) (0.65) PPI (core) 0.27 -- 0.23 0.78*** 0.14** 1.00*** (0.34) (0.15) (0.29) (0.07) (0.35) Retail sales 2.33*** -- 1.07*** 1.06** 0.55*** 1.04* (0.59) (0.28) (0.58) (0.15) (0.62) Unemployment Rate -1.29*** -- -0.50** 0.46 -0.19** 0.55** (0.45) (0.22) (0.50) (0.11) (0.54) Monetary Policy Surprises 0.45*** -- 0.20*** -0.21*** 0.07*** -0.20*** (0.08) (0.03) (0.07) (0.02) (0.07) Notes: Newey-West standard errors. *** indicates significance at the 1-percent level,** at the 5-percent level and * at the 10-percent level. The estimated coefficient indicates the basis-point repsonse of the one-year forward rate per standard deviation of the macroeconomic release surprise and per basis-point surprise in monetary policy announcements. Constant terms not shown. 19

Table 4: Response of Bond Excess Return Forecasting Factor to Economic News Macroeconomic data releases Capacity utilisation 3.32*** (1.08) Consumer confidence 3.41*** (1.08) CPI (core) 3.48*** (1.11) Employment cost index 5.91** (2.43) GDP (advance) 2.93 (3.69) Initial Claims -1.26* (0.66) Leading Indicators -0.21 (1.02) NAPM 7.78*** (1.30) New home sales 1.26 (1.06) Non-farm payrolls 10.1*** (1.82) PPI (core) 0.52 (0.99) Retail sales 3.39* (1.79) Unemployment Rate 0.20 (1.27) Monetary Policy Surprises -0.29 (0.23) Notes: Newey-West standard errors. *** indicates significance at the 1-percent level, ** at the 5-percent level and * at the 10-percent level. The estimated coefficient indicates the repsonse of Cochrane and Piazzesi's return forecasting factor per one standard-deviation macroeconomic release surprise and per basis-point surprise in monetary policy announcements. Constant terms not shown.