RDP 2006-05: Optimal Monetary Policy with Real-time Signal Extraction from the Bond Market 1. Introduction

Hayek (1945) famously argued that market economies are more efficient than planned economies because of markets' ability to efficiently use information dispersed among market participants. According to Hayek, prices in competitive markets reflect all information that is known to anyone and competitive markets can potentially allocate resources more efficiently. In most western economies there is now little planning and almost all prices are determined by market forces without interference from any central authority. However, there is one important exception: the market for short-term nominal debt where central banks borrow and lend at fixed interest rates. In the presence of nominal frictions in product or wage markets, this practise can improve welfare by reducing the volatility of inflation and output. Hayek's insight, though formulated in a more general setting of a planned economy, was that even a central bank that shares the objective of the representative agent may not be able to implement an optimal stabilising policy due to incomplete information. In this paper, the central bank would implement an optimal stabilising policy if it knew the state of the economy with certainty, and any deviation from optimal policy is due only to information imperfections. Under this assumption this paper demonstrates how the central bank can make use of Hayek's insight and use the market for debt of longer maturities as a source of information that makes a more efficient estimation of the state of the business cycle possible, and thus reduces deviations from optimal policy. That this is close to how some central banks think about and use the term structure is illustrated by a quote by the Chairman (then Governor) of the Federal Reserve Board Ben Bernanke:

To the extent that financial markets serve to aggregate private-sector information about the likely future course of inflation, data on asset prices and yields might be used to validate and perhaps improve the Fed's forecasts. (Bernanke 2004)

The suggestion that the bond market can provide information that is valuable to policy-makers is thus not news to the policy-makers themselves. Rather, the contribution of the present paper is to provide a coherent framework for analysing and estimating the interaction between information contained in the term structure and the monetary policy-making process. In the model presented below, the central bank has to set interest rates in an uncertain environment, where the yield curve is informative about the state of the economy and thus also informative about the desired interest rate. This has the consequence that the macroeconomy is not independent of the term structure. The only direct effect of interest rates on the macroeconomy is from the short rate set by the central bank to aggregate demand, as is standard in the New-Keynesian literature. However, there is also an indirect feedback from rates on longer-maturity bonds to the macroeconomy through the informational content of the term structure. The mechanism is the following. Bonds are traded daily and the affine form of the bond pricing function makes the bond pricing equation with macro factors formally equivalent to a linear measurement of the state of the economy. The term structure can thus be viewed as a more timely measure of the state of the economy than collected aggregate information that is available only with delay and sometimes significant measurement error. A movement in the term structure can then signal a shift in the underlying macro factors that induces the central bank to re-evaluate what the optimal short-term interest rate should be. The shift in the term structure thus feeds into a change in demand through the change in the short-term interest rate.

In the present model the policy-makers exploit the fact that bond market participants' expectations about the future are revealed by the term structure. As pointed out by Bernanke and Woodford (1997), letting monetary policy react mechanically to expectations may lead to a situation where expectations become uninformative about the underlying state and no equilibrium exists. They further argue that ‘targeting expectations’ by policy-makers cannot be a substitute to structural modelling. In the proposed framework below, the information in the term structure is complementary to other information and firmly connected to an underlying structural model. Policy-makers then avoid the potential pitfalls of a pure ‘expectations targeting’ regime.

There is a large literature concerning the information content of the term structure. Mostly, it has focused on whether the term structure, often modelled as the spread between short and long rates, can help predict future outcomes of macro variables.^[1] More recent work by Ang, Piazzesi and Wei (2003) suggests that the best predictor of GDP is the short end of the yield curve. The negative correlation between short interest rates and future output is hardly surprising, given the evidence of the real effects of monetary policy. The conclusion of Ang et al highlights the need to distinguish between information in the term structure that tells us something about the transmission mechanism of monetary policy, and information that can be used by a central bank in the policy process when the transmission mechanism is assumed to be known. This paper is solely concerned with the latter.

There are two other potentially important types of information that could be revealed by the term structure that the present model is silent about. Goodfriend (1998) discusses the Federal Reserve's responses to ‘inflation scares’ in the 1980s, which he defines as increases in the long-term yields. He interprets these as doubts by market participants about the Federal Reserve's commitment to fighting inflation. The present paper does not address questions about central bank credibility, but takes a perfectly credible central bank with a publicly known inflation target as given. The model presented here is also not suited to analysing or interpreting market perceptions of the reasons for a change in the monetary policy stance, as done by Ellingsen and Söderström (2001). The policy-makers' relative preferences for stabilising inflation or the output gap are assumed to be known to bond market participants. In this paper, we restrict our attention to what the term structure can tell us about the state of the business cycle.

The practical relevance of any information contained in the term structure is ultimately an empirical question. When bond markets are noisy, observing the term structure is not very informative. In order to quantify the informational content of the term structure, the variances of the non-fundamental shocks in the term structure are estimated simultaneously with the structural parameters of the macroeconomy. The estimation methodology is similar to recent work by Hördahl, Tristani and Vestin (2006) who estimate the term structure dynamics jointly with a small empirical macro model where the central bank is assumed to be perfectly informed. Hördahl et al impose only a no-arbitrage condition on the pricing of bonds while in this paper the bond pricing function and the dynamics of the macroeconomy are derived from the same underlying utility function. This makes the analysis more stringent, but it comes at the cost of an empirically less flexible bond pricing function.

In the next section a model is presented where the central bank extracts information from the term structure about unobservable shocks while recognising that its own actions influence the term structure itself. In Section 3 the model is estimated to quantify the importance of the yield curve as a source of information. Section 4 concludes.

Footnote

For example, Harvey (1988), Mishkin (1990) and Estrella and Mishkin (1998). [1]