The Term Structure of Real Rates andexpectedinßation

Transcription

1 Discussion of The Term Structure of Real Rates andexpectedinßation by Andrew Ang and Geert Bekaert Martin Evans Georgetown University, NBER and I.E.S. Fellow, Princeton University

2 Overview The paper presents a No Arbitrage model of nominal interest rates that incorporates regime switching. Model estimates allow us to decompose movements in the nominal term structure into variations in (i) real yields, (ii) expected inßation, and (iii) (inßation) risk premia. The model estimates imply: the real term structure is fairly ßat ~1.4%, real rates are negatively correlated with inßation (expected and unexpected), the inßation risk premium rises with maturity, expected inßation and inßation risk account for ~80% of the variation in nominal rates. Main Comment: This is a nice paper with a clear and important goal.

3 A Nominal Yield Decomposition where y k t = E t π t+k,k +ŷ k t + 1 k E t Nominal Term Premia: Real Term Premia: Inßation Risk Premia: Xk 1 i=0 n θ k i t+i ˆθ k i t+i + ϕ t+i o θ k t E t p k 1 t+1 pk t y1 k 1 ˆθk t E t ˆp t+1 ˆpk t ŷ1 ϕ t yt 1 ŷt 1 E t π t+1,1 Observations: The absence of arbitrage opportunities only places weak restrictions on θ k t, ˆθ k t, and ϕ t. Decomposing movements in y k t will depend critically on how E tπ t+k,k, ŷ k t and the risk premia are identiþed. Previous work on the nominal term structure suggests that θ k t is time-varying.

4 Alternative IdentiÞcation/Estimation Strategies Regression Method (Mishkin 1990): Assume θt+i k i k i ˆθ t+i + ϕ t+i constant, and π t+k,k = E t π t+k,k + η t+k,k where η t+k,k is a RE forecast error. Estimates of ŷt k (and E tπ t+k,k ) are obtained from projecting yt k π t+k,k on variables that span the time t information set. Model-Based 1 (Evans 2003) Identify θt+i k i k i, ˆθ t+i and ϕ t+i via No Arbitrage + other assumptions. Use UK data on yt k and ŷk t to estimate E tπ t+k,k. Model-Based 2 (A&B): Identify θt+i k i k i, ˆθ t+i and ϕ t+i via No Arbitrage + other assumptions. Use US data on yt k and π t+k,k +REtoestimateE t π t+k,k and ŷt k.

5 A&B s Model 1= E t exp ( ˆmt+1 ) R i t+1 ˆm t+1 = δ 0 δ 0 1X t λ 0 t+1λ t+1 λ 0 t+1ε t+1 δ 0 1 = 11δ π λ 0 t+1 = h ³ γ 1 q t λ f s f t+1 0 i X t+1 = µ(s t+1 )+ΦX t + Σ(s t+1 ) 1/2 ε t+1 X 0 t+1 = q t+1 f t+1 π t+1 µ(st+1 ) 0 = 00µ π (s π t+1) diag [Σ(s t+1 )] 0 = h σ 2 q σ 2 f (sf t+1 ) σ2 π(s π t+1) i s i t+1 = {1, 2}, Independent, Markov Chains

6 Observation 1: The model restricts the inßation risk premium. In particular Cov t [exp ( ˆm t+1 ), exp (π t+1,1 )] = 0, so ϕ t = ln [E t exp ( π t+1,1 )] E t π t+1,1 0. Observation 2: The real and nominal term premia can vary within a regime. For example, suppose there is no switching. Then. ˆθ 2,t = Cov t (ˆm t+1,r t+1 ) 1 2 Var t (r t+1 ), = λ f σ f + λ 1 σ q q t 1 2 δ0 1Σδ 1. A&B s estimates q t is very persistent. (NB λ t+1 is not the price of risk when switching is present).

7 Observation 3: The model ignores reporting lags in the CPI. There is variable reporting lag in the CPI of approximately 2 weeks, which might be economically signiþcant when inßation is high and variable. Observation 4: across regimes: Nominal Yields and Inßation display the same persistence y k t = 1 k (A k(s t )+B k X t ) π t,1 = 001 X t X t+1 = µ(s t+1 )+ΦX t + Σ(s t+1 ) 1/2 ε t+1 Evidence on state-dependent mean-reversion in short rates is reported by Gray (1996), Bekaert et al (2001) and Ang and Bekaert (2002). Evidence on state-dependent mean-reversion in inßation is reported in Evans and Wachtel (1993), and Evans and Lewis (1995).

8 Comment 1: Consider a representative consumer model with CRRA utility. With conditional log normality and no switching ψ t = Cov t (m t+1,π t+1,1 ) 1 2 Var t (π t+1,1 ) = γcov t ( c t+1,π t+1,1 ) 1 2 Var t (π t+1,1 ) How big is Cov t ( c t+1,π t+1,1 )? We can estimate Cov ( c t+1,π t+1,1 Ω t ) where Ω t denotes the information set available to the researcher, but Cov ( c t+1,π t+1,1 Ω t )=E [Cov t ( c t+1,π t+1,1 ) Ω t ] Cov ( c t+1,π t+1,1 Ω t ) may be biased. +Cov [E t c t+1,e t π t+1,1 Ω t ]

9 Comment 2: The introduction of switching has more potential than the model allows. For example, we could have X t+1 = µ(s t )+Φ(s t )X t + Σ(s t ) 1/2 ε t+1 A&B chose not to go this route because no closed form solution for yields is available with λ t+1 a function of q t. However, if we eliminated q t from λ t+1 so that ˆm t+1 = δ 0 δ 0 1X t λ(s t )λ t (s t ) λ t (s t )ε t+1 we could solve for yields.

10 Comment 3: Switching makes choosing the right speciþcation tricky. A&B favor version IV of their model because the inßation forecast errors are not serially correlated. This is certainly a large sample property of the model. But :3 1982:3 1983:3 1984:3 1985:3 1986:3 1987:3 1988:3 1989:3 1990:3 1991:3 1992:3 1993:3 1994:3 1995:3 1996:3 1997:3 1998:3 1999:3 SURVEY OF PROFESSIONAL FORECASTERS ACTUAL linflation Clearly the these forecast errors are serially correlated (beyond the forecast horizon).

11 Are the forecasters irrational, or was there a peso/learning problem? The answer matters: Consider the alternative estimates of one-year real yields :3 1982:3 1983:3 1984:3 1985:3 1986:3 1987:3 1988:3 1989:3 1990:3 1991:3 1992:3 1993:3 1994:3 1995:3 1996:3 1997:3 1998:3 1999:3-2 SURVEY REAL YIELD EX POST REAL YIELD

12 Summary Making inferences about the source of nominal term structure movements is HARD. The No Arbitrage model helps, but does not make up for the lack of data on real yields/inßation expectations/an economic model. Introducing regime-switching is a good idea because it has the potential to deliver a good deal of model ßexibility (c.f. changing monetary policy as in Cogley and Sargent 2002). My preference would be to drop within-regime variation in the risk premia, and allow for state-dependent mean reversion (as in Evans 2003). Whatever the approach, relying on just nominal yields and realized inßation is not enough to establish stylized facts. We need: to account for the data on inßation expectations, and/or, a GOOD model for the discount factor ˆm t+1.