Abstract
In macroeconomics, the short-term interest rate is usually modeled as a monetary-policy reaction function to a set of macroeconomic variables. A deliberately simple functional form is the Taylor rule; it is the answer to a perennial question in monetary economics of how the monetary authority should implement policy in a systematic manner. Taylor (1993, 214) developed a “hypothetical but representative” rule by using the gap concept of inflation and output. The Taylor rate is 1.5 times inflation plus 0.5 times the output gap, plus 1. For the period between 1982 and 1992, the rule was successful in capturing the actual behavior of the US federal funds rate. As this period is widely regarded as a shift from a “passive” to an “active” stabilizing monetary policy regime, the rule has been used ever since to ask where monetary policy should head in response to fluctuations in inflation and real activity.
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Notes
- 1.
Sargent et al. (2009) and DiCecio and Nelson (2009).
- 2.
Clarida et al. (2000), Rudebusch (2002, 2009), Gerlach and Schnabel (2000), Gerlach-Kristen (2003), Sauer and Sturm (2003), Orphanides (2003) and Fernandez et al. (2008).
- 3.
Clarida et al. (2000), Lubik and Schorfheide (2004), Cogley and Sargent (2005), Boivin (2006), Kim and Nelson (2006) and Castelnuovo et al. (2008).
- 4.
An alternative view of the Great Moderation is taken by Sims and Zha (2006). They identify the reduced volatility of less frequent and lower shocks to inflation and output as the main driver of smoothed macro dynamics during the relevant period beginning in the mid 1980s. To them, reduced inflation persistence was a matter of “good luck” rather than sound monetary policy.
- 5.
See Chap. 3.5.2 for a detailed treatment on affine term structure models.
- 6.
The inflation equation can be derived from a modified version of Svensson (1997) where output is replaced by the lagged real interest rate which monetary policy can affect through its policy rule.
- 7.
Ang and Piazzesi (2003) and the estimation results of Chap. 4.2.1 estimate risk prices to be negative for most sample periods.
- 8.
A general equilibrium approach with imperfect asset substitution has been analyzed by Andres et al. (2004), Marzo et al. (2008) and Zagaglia (2009).
- 9.
The role of term spreads, financial intermediation, financial stability and implications for the conduct of monetary policy is discussed in Chap. 7.4.2. Here, the focus is on bond rate transmission in the presence of the traditional expectations channel of monetary policy.
- 10.
See Taylor and Wieland (2009) or Taylor and Williams (2009a). An excellent classification of monetary policy rules is provided by Fendel (2004).
- 11.
See Chap. 3.4.2 for the empirical rejection of the Expectations Hypothesis as well as Kugler (1997) and Romhányi (2002) for an application to the n-period case.
- 12.
Mehra (2001), Cochrane and Piazzesi (2002), Gerlach-Kristen (2003), Fendel and Frenkel (2005) and Vázquez (2009).
- 13.
See Gallmeyer et al. (2005), McGough et al. (2005), Kulish (2006) or Fendel (2007).
- 14.
Goodfriend (1998, 16) remarks that “there is evidence that the long-term nominal bond rate moves primarily as a result of inflation expectations. Sharp bond rate movements ought to be taken as evidence of worsening or improving credibility on inflation, as the case may be, and taken into account in making decisions on short-term policy.”
- 15.
To be sure, such actions can be supported by active engagements in bond markets through open-market operations but it does not mean that a long rate might be used as instrument of policy as that term is generally understood.
- 16.
The asset pricing relation can be derived by the pure form of the local return hypothesis according to which \(n{i}_{n,t} - (n - 1){E}_{t}{i}_{n-1,t+1} = {i}_{1,t} + (n - 1){\nu }_{{i}_{n},t}\). The left-hand side of this equation is the one-period return which should equal the short-term interest rate plus the risk premium which arises due to the uncertainty about the one-period interest rate. In the simple two-period case, the local hypothesis becomes \(2{i}_{t} - {E}_{t}{i}_{1,t+1} = {i}_{1,t} + {\nu }_{{i}_{n},t}\). The n-period case is thereby derived by recursion. For reasons of computational tractability, in the numerical simulations, in − 1, t + 1 is approximated by in, t + 1 in above model set-up (see also McCallum (2005) and Romhányi (2002) for this modeling strategy).
- 17.
Moreover, in the 2-period case, shock processes are set equal to zero in order to clarify results for determinacy.
- 18.
See Sect. 6.1 for the affine term structure of policy responses.
- 19.
The system being analyzed is said to be determinate if the rational expectations solution is unique and dynamically stable. It is indeterminate in the case of more than one possible stable solution and explosive if none of the solutions are stable (McCallum, 2009).
- 20.
With a n-period bond, the policy rule would include either the expected path of short rates or the expected long-term interest rate. If the Expectations Hypothesis holds, the relevant expected spot rate could be substituted by the implied forward rate.
- 21.
Cited from Eijffinger et al. (2006, 10).
- 22.
This statement should not be taken literally. It rather signifies that the necessary condition of the ex-ante real rate to change more than one-by-one can be assured by a combination of the coefficients α and γ.
- 23.
In the limit (not reported here), with a 40-period bond as relevant variable, it has been also checked for determinacy of the system. It is found that a small positive value of γ with α < 1 still yields a unique RE equilibrium.
- 24.
See for similar results in a different setup Kulish (2006) and Vázquez et al. (2009).
- 25.
For the sake of completeness, the reaction to the output gap in the rule would result in a slightly higher slope of the upward-sloping part of the uniqueness region. Since responding to in, t implicitly means that monetary policy reacts negatively to current output, a higher value of the output coefficient allows for a higher value of γ since the latter is partly compensated by the positive output coefficient in the reaction function.
- 26.
See Giannoni and Woodford (2003a,b,c).
- 27.
See Clarida et al. (1999) or Woodford (2003).
- 28.
For that purpose, the OSR routine of DYNARE is applied but the procedure is modified in the following way; numerical optimization may be sensitive to the initial condition of the optimization routine. Therefore, a grid search over the parameter region is applied in the first place. Then, the optimized coefficients are used as starting values for the OSR routine. Finally, it is checked whether the generated loss can be further improved by using the OSR command.
- 29.
For the sake of completeness, the term-structure rules can be augmented by an output coefficient. However, the losses remain basically unchanged compared to rule (III) and (IV).
- 30.
This finding is also obtained for optimal simple rules based on an estimated euro area model (Stracca, 2006).
- 31.
Following Amato and Laubach (1999), such smoothing can be categorized as seasonal smoothing, event smoothing or day-to-day smoothing. It supports the elimination of calender effects, the erratic behavior of the overnight rate in times of sudden events and it tries to keep the average level of the policy instrument as close as possible to the target level of the central bank.
- 32.
For the US, the effective federal funds rate is the policy rate and for the euro area it is the main refinancing rate. Data are taken from Datastream.
- 33.
This view can be justified by the presence of an inflation bias on part of a central bank’s loss function (Cukierman and Gerlach, 2003); for a central banker’s perspective see Bini-Smaghi (2009). However, there is also evidence that the FED has exhibited such asymmetric preference only until the pre-Volcker area (Surico, 2007).
- 34.
See for instance Clarida et al. (2000), Rudebusch (2002), Sauer and Sturm (2003) or Castelnuovo (2007).
- 35.
See Orphanides (2003) or Bernanke (2007). It should be noted that the gradualistic approach may not always be a valid advice under uncertainty, in particular when there is uncertainty surrounding the structure of the economy. Robust control methods rather advocate a more aggressive response, for example if the structural degree of the inflation process is not known (Söderström, 2002).
- 36.
The R2 measures the forecastability of future interest rate changes; it reports the ratio of the explained variation to total variation.
- 37.
Further evidence on interest-rate forecastability from survey data or from Taylor-augmented interest rate rules with serial correlated shocks largely seem to confirm the view that policy persistence may not (solely) originate from inertia (Söderlind et al., 2005; Gerlach-Kristen, 2003; Castelnuovo et al., 2003; Castelnuovo, 2007; Consolo and Favero, 2009). Based on a simple analysis of a Taylor rule with a serially correlated disturbance term and the Fisher relation, Cochrane (2010) finds that a typical Taylor-rule regression of the policy rate on the inflation rate estimates the disturbance serial correlation parameter rather than the smoothing parameter.
- 38.
An excellent confrontation from a policy perspective can be found in Goodfriend (1986) who makes the case in favor of maintaining secrecy and Poole (2005) who outlines the benefits of increased transparency for the predictability of monetary policy.
- 39.
See Goodhart (2001) for an extensive discussion and critique of the constant-rate approach.
- 40.
Another pitfall is grounded in the information content of asset prices. Too much communication might distort the use of asset prices for the purpose of extracting market expectations if, as a results of public information, not enough private information is priced into asset prices. On account of this “a central bank may face a trade-off between managing market expectations and learning from them” (ECB (2007, 65); Morris and Shin (2002)).
- 41.
The finding is also supported by the analysis of survey expectations (Geiger and Sauter, 2009).
- 42.
See also Sect. 6.4 on the nominal yield curve decomposition.
- 43.
See for instance Ehrmann and Fratzscher (2005), Andersson et al. (2006), Siklos and Bohl (2007). Recent research highlights the interaction of public and private information and its flows over time on money markets. Ehrmann and Sondermann (2009, 1) find that “due to the quarterly frequency at which the Bank of England releases its [inflation report, the reaction to news] can become stable over time. In the course of this process, financial market participants need to rely more on private information. The more time has elapsed since the latest release of an inflation report, market volatility increases, the price response to macroeconomic announcements is more pronounced, and macroeconomic announcements play a more important role in aligning agents’ information set, thus leading to a stronger volatility reduction.”
- 44.
An excellent review about the development of indexed-bond markets is Garcia and van Rixtel (2007). They document an extensive economic literature dating back to W. S. Jevons, I. Fisher, J. M. Keynes, R. Musgrave and M. Fiedman who all favored indexing debt in general, and public debt in particular. For a discussion on the costs and benefits of indexation for macroeconomic stability, the reader is referred to Humphrey (1974).
- 45.
For example, the ECB’s Monthly Bulletin regularly reports 5-year forward break-even inflation rates five years ahead to check whether medium-term inflation expectations are at a level consistent with the central bank’s inflation objective; see for instance the December Monthly Bulletin 2009a.
- 46.
The equation also ignores the implications of Jensen’s inequality terms.
- 47.
Data for the US are taken from the research database of the Federal Reserve System. The daily nominal and real term structure is calculated according to the Nelson-Siegel-Svensson method and both curves are converted to end-of-month data. Gürkaynak et al. (2006b) and Gürkaynak et al. (2008) are the respective research papers explaining the fitting techniques in detail. Monthly nominal and real interest rates for the UK are available directly from the database of the Bank of England. They are calculated using a cubic spline method.
- 48.
The arbitrage-free environment refers to the elimination of all risk-free opportunities between the nominal and real term structure and along the respective term structures with different maturities.
- 49.
It is possible to jointly estimate the real and nominal yield curve without any reference to observable indexed bond prices. By applying the inflation rate in the estimation, real bond yields can be computed entirely consistent with the no-arbitrage model setup. For selected studies with varying model specifications see Buraschi and Jiltsov (2005), Durham (2006), Garcia and van Rixtel (2007), Ang et al. (2008), Chernov and Mueller (2008), D’Amico et al. (2008b), Christensen et al. (2008), Adrian and Wu (2009) or Joyce et al. (2009a).
- 50.
The macroeconomy is assumed to follow the hybrid New-Keynesian view with an empirically justifiable leads and lags structure. I am indebted to Oreste Tristani (ECB) for sharing 10-year estimated risk premia with me.
- 51.
I deeply thank Mike Joyce (BoE) for providing the estimated times series on forward risk premia.
- 52.
The findings are robust to different models and sample periods (D’Amico et al., 2008b).
- 53.
Besides the role of the independence of the BoE, Joyce et al. (2009a) explain the large fall in the level of real term premia by an increased pension-fund demand for inflation-indexed securities against the background of the 1995 Pensions Act which became effective in 1997.
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Geiger, F. (2011). Monetary Policy in the Presence of Term Structure Effects. In: The Yield Curve and Financial Risk Premia. Lecture Notes in Economics and Mathematical Systems, vol 654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21575-9_6
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