RDP 2006-02: Term Structure Rules for Monetary Policy 1. Introduction
April 2006
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The transmission mechanism of monetary policy is traditionally perceived as going from a short-term nominal interest rate to a long-term real interest rate that influences aggregate demand. Recently, there have been proposals involving the use of nominal long-term interest rates for the conduct of monetary policy. On the one hand, as Goodfriend (1993) notes, long-term nominal interest rates may contain information about long-term inflationary expectations, thus making them useful indicators for the central bank. On the other hand, the potential of long-term rates to directly influence economic activity motivates the study of policy rules which incorporate longer-term rates.^{[1]} The goal of this paper is to study monetary policy rules that involve long-term nominal interest rates in these two distinct roles.
1.1 Inflationary Expectations: Type-1 Rules
The Fisher decomposition reveals that two terms are crucial for the equilibrium determination of nominal interest rates: an expected real rate and an expected inflation term. Thus, policy-makers might want to use long-term nominal interest rates to help measure the private sector's long-term inflationary expectations. To the extent that the predominant force moving long-term yields is the expected inflation component, a monetary authority interested in keeping inflation under control might be interested in the use of reaction functions that incorporate long-term yields as arguments. Interestingly, McCallum (1994) has shown that a monetary policy rule that responds to the prevailing level of the spread between a long-term rate and a short-term rate can rationalise an important empirical failure of the expectations hypothesis.^{[2]} However, such behaviour by the central bank raises two important considerations.
First, one can show that the theory of the term structure that emerges from optimising behaviour in a New Keynesian model is the expectations hypothesis. Thus, the market determines nominal long-term interest rates as the average expected level of nominal short-term interest rates over the maturity horizon under consideration. A monetary policy reaction function that includes a long-term rate immediately raises the question of whether or not a unique rational expectations equilibrium (REE) exists in this case. The question is important since the combined power of the expectations hypothesis and the proposed monetary policy rule might give rise to self-fulfilling prophecies in the equilibrium determination of the yield curve.^{[3]} What are the conditions that guarantee uniqueness of the REE when the central bank's actions depend on the level of a long-term interest rate in addition to inflation and the output gap?
Second, assuming that the conditions that ensure a unique REE exist, is it desirable to have the central bank responding to long-term rates in this way? And if so, which is the best maturity length for the monetary authority to react to?
To study these questions I propose a modification of a standard Taylor rule that adds a long-term rate as an additional variable to which the central bank adjusts its short-term rate; hereafter, these are referred to as type-1 rules. In the context of a standard New Keynesian model, I show that there are large and empirically plausible regions of the policy-parameter space where a unique REE exists when the central bank conducts policy in this manner. In addition, I find that reacting to movements in long-term rates does not improve the performance of the central bank relative to the standard Taylor rule, regardless of the maturity length in question.
1.2 Long-term Interest Rates: Type-2 Rules
It has been suggested that long-term rates might be used as instruments of monetary policy in Taylor rules (that is, where the long rate replaces the short rate as the argument of the rule; hereafter referred to as type-2 rules). Various aspects of this proposal have been studied by Kulish (2005) and McGough, Rudebusch and Williams (2005). This does not imply, however, that type-2 rules require monetary authorities to alter their current operating procedures – that is, by switching to a longer-term nominal interest rate as their instrument. Indeed, interest rates of various maturities are linked by the expectations hypothesis in the New Keynesian model so that long-term interest rate rules could alternatively be written as more complicated short-term rate rules.^{[4]}
In this paper I study the determinacy properties of the REE as well as the performance of long-term interest rate rules. This study is interesting in its own right, but it is also of general theoretical importance to monetary economics for the following reason.
One might initially suspect that a unique REE will not arise if the monetary authority decides to use a two-period interest rate rule. The reason is that, in a context in which the expectations hypothesis holds true, there will exist infinite paths for the one-period rate that satisfy the central bank's setting of the two-period rate. Notice that abstracting from a term premium and default risk, the two-period rate is an average of the current one-period rate and the current expectation of the one-period rate in the next period. In other words, if the central bank wishes to set the two-period interest rate at, say, 5 per cent, then in equilibrium the one-period rate could follow any number of paths provided that the average for the one-period rate's path is 5 per cent.
This argument suggests that a unique equilibrium would not exist when the central bank uses a rule for the two-period rate, or its equivalent in terms of the one-period rate. Imagine for a moment that this is indeed the case and recall that almost all of the modern dynamic discrete time models of monetary economics are based on a quarterly frequency. So in theory the operating instrument is usually a 3-month interest rate, whereas the actual operating instrument of monetary policy in most developed economies is an overnight rate. The inability to map the theoretical operating instrument with the actual one would be a damning result. Fortunately, this suspicion turns out to be incorrect. In fact, as shown below, large and empirically plausible regions of the policy-parameter space for long-term interest rate rules yield a unique REE for the economy.^{[5]} Thus, the results of this paper provide a theoretical foundation for the study of monetary models at different frequencies.
These alternative monetary policy rules are studied in the context of a New Keynesian model for the following reasons. First, a standard version of the New Keynesian model embodies the traditional view of the monetary transmission mechanism, in which the central bank controls the short-term nominal interest rate, while the long-term real interest rate determines aggregate demand. Second, as emphasised by Goodfriend and King (1997), the New Keynesian model has achieved a certain consensus in the macroeconomic literature, to the point that the authors refer to it as the New Neoclassical Synthesis. Third, the New Keynesian model is now extensively used for theoretical analysis of monetary policy.^{[6]}
The rest of the paper is organised as follows. Section 2 describes the model. Section 3 discusses determinacy of the REE under term structure rules and their implications for the dynamic behaviour of the economy.^{[7]} Section 4 studies the performance of these alternative term structure rules against two benchmarks: the robust optimal policy rule and the standard Taylor-type rule. Section 5 summarises the main results.
Footnotes
See Bernanke (2002) and Clouse et al (2003). [1]
This failure is related to the magnitude of the slope coefficients in regressions of the short rate on long-short spreads. A partial equilibrium interpretation of the expectations hypothesis implies that the slope coefficient, b, in a regression of the form, ½(R_{1,t} − R_{1,t−1}) = a + b(R_{i,t} − R_{1,t−1}) + shock, should have a probability limit of 1. Many empirical findings in the literature yield a value for b considerably below 1. As shown by McCallum (1994) the expectations hypothesis is consistent with these findings if it is recognised that the term premium follows an exogenous random process and monetary policy involves smoothing of the instrument as well as a response to the level of the spread. [2]
In fact, Bernanke and Woodford (1997) show that a policy rule, in which the short-term rate reacts only to a long-term rate, is unable to yield a unique REE. However, in this paper I consider more general rules that nest Bernanke and Woodford's case as a special one. [3]
In other words, the choice of operating instrument when constrained to a functional form of the policy rule is equivalent to some choice of functional form when constrained to one particular instrument. [4]
This result may also be of practical importance in light of the zero-bound/liquidity trap problem. See Bernanke (2002), Kulish (2005), and McGough et al (2005) for more details on this issue. [5]
See Clarida, Galí and Gertler (1999), Goodfriend and King (1997), Walsh (1998), Woodford (2003) and the references therein. [6]
Elsewhere in the literature, Gallmeyer, Hollifield and Zin (2005) have proposed the term ‘McCallum rules’ to refer to a monetary policy rule in which the instrument is sensitive to the slope of the yield curve. Here, ‘term structure rules’ refer to monetary policy rules that involve long-term rates in a more general way. In my terminology, a McCallum rule is a special case of a term structure rule. [7]