Taylor rules, McCallum rules and the term structure of interest rates

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi [2002. The Fed and interest rates—a high-frequency identification. American Economic Review 92, 90-95.]. The result echoes the policy rule used by McCallum [1994a. Monetary policy and the term structure of interest rates. NBER Working Paper No. 4938.] to rationalize the empirical failure of the ‘expectations hypothesis’ applied to the term structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. McCallum showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. “yield-curve smoothing”), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss [1987. The information in long-maturity forward rates. The American Economic Review 77, 680-392.]. McCallum also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor [1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195-214.] Rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term-structure models studied in Duffie and Kan [1996. A yield-factor model of interest rates. Mathematical Finance 57, 405-443.]: a stochastic volatility model and a stochastic price-of-risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by McCallum (i.e., the “McCallum Rule”). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzessi [2003. A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables. Journal of Monetary Economics 50, 745-787.]). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and McCallum Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.     

Using a long-term interest rate as the monetary policy instrument

Using a short-term interest rate as the monetary policy instrument can be problematic near its zero bound constraint. An alternative strategy is to use a long-term interest rate as the policy instrument. We find when Taylor-type policy rules are used by the central bank to set the long rate in a standard New Keynesian model, indeterminacy—that is, multiple rational expectations equilibria—may often result. However, a policy rule with a long-rate policy instrument that responds in a “forward-looking” fashion to inflation expectations can avoid the problem of indeterminacy.     

Trend Inflation, Taylor Principle, and Indeterminacy

Positive trend inflation shrinks the determinacy region of a basic New Keynesian dynamic stochastic general equilibrium model when monetary policy is conducted by a contemporaneous interest rate rule. Neither the Taylor principle, which requires the inflation coefficient to be greater than one, nor the generalized Taylor principle, which requires that the nominal interest rate to be raised by more than the increase in inflation in the long run, is a sufficient condition for local determinacy of equilibrium. This finding holds for different types of Taylor rules, inertial policy rules, and price indexation schemes. Therefore, regardless of the theoretical setup, the monetary literature on interest rate rules cannot disregard average inflation in both theoretical and empirical analyses.     

The expectations theory works for monetary policy shocks

In practice, the expectations theory of the term structure is employed extensively in monetary policy analysis despite its empirical failure. This paper performs a conditional test of the theory that is directly relevant to monetary theory and policy. It finds that the theory holds quite well conditional on identified monetary policy shocks, but fails conditional on aggregate supply shocks that prompt an immediate jump in prices. It also finds that policy responses to movements in the term structure play an important role in uncovering evidence for the theory as predicted by McCallum [1994. Monetary policy and the term structure of interest rates. NBER Working Paper Series, no. 4938].     

Further analysis of the expectations hypothesis using very short-term rates

Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the expectations hypothesis. Journal of Financial Economics 58, 397–415] finds support for the expectations hypothesis at the very short end of the repurchase agreement (repo) term structure while other studies find calendar-time-based regularities cause rejection of the expectations hypothesis. Using Longstaff’s methods on a sample of repo rates that pre-dates Longstaff’s sample, we reject the expectations hypothesis for every maturity. The pre-Longstaff-sample repo data comes from a time period where the behavior of short-term interest rates is similar to the long-run average behavior of short-term interest rates. Our results imply that expectations hold when rates are less volatile and/or that we may be entering a period of lower volatility.     

On money and output: Is money redundant?

There is an emerging consensus that money can be largely ignored in making monetary policy decisions. Rudebusch and Svensson [1999, Policy Rules and Inflation Targeting. In Taylor, J.B. (Ed.), Monetary Policy Rules. University of Chicago Press, Chicago, 203-246; 2002, Eurosystem Monetary Targeting: Lessons from US Data. European Economic Review 46, 417-442] provide some empirical support for this view. We reconsider the role of money and find that money is not redundant. More specifically, there is a significant statistical relationship between lagged values of money and the output gap, even when lagged values of real interest rates and lagged values of the output gap are accounted for. We also find that inside and outside money provide significant information in predicting movements in the output gap.     

Learnability and monetary policy: A global perspective

The recent literature on monetary policy design has emphasized the importance of equilibrium determinacy and learnability in the choice of policy rules. This paper contains an analysis of the learnability of the equilibrium in a class of simple, micro-founded models in which the policy authority uses a Taylor-type monetary policy rule. Unlike previous analyses, the model economy is not linearized about a steady state—instead, a global perspective is adopted. Globally, the nonlinear model economy can possess rational expectations equilibria other than the steady state consistent with the inflation target of the monetary authorities. These include a second, low inflation ‘liquidity trap’ steady state, periodic equilibria, and sunspot equilibria. The main results in the paper characterize the conditions under which these alternative equilibria maybe stable under adaptive learning, even when the policy rule obeys the Taylor principle. The stability of multiple equilibria is associated with policy rules which are forecast-based. An important finding is that backward-looking Taylor-type policy rules can guarantee that the unique learnable equilibrium is the steady state associated with the inflation target of the monetary authority.     

Rational expectations,changing monetary policy rules,and real exchange rate dynamics

This paper reexamines the explanatory power of Taylor rule fundamentals for real exchange rate determination. We assume the agents know the time-varying parameters in central bank policy rules. The empirical results suggest that a monetary policy rule with regime switching is better able to explain the real Deutschemark/dollar exchange rate from 1976 to 1998 compared with a fixed-regime monetary policy rule. The findings show the importance of accounting for the expectation formation effect in changing policy rules as emphasized by the Lucas critique. Ignoring these effects can undermine the value of the rational expectations models.     

The Taylor Principle and Monetary Policy Approaching a Zero Bound on Nominal Rates: Quantile Regression Results for the United States and Japan

This paper offers a new approach that estimates the response of interest rates to inflation and the output gap at various points (quantiles) on the conditional distribution of interest rates. This offers an improvement on empirical estimates conducted only at the mean and also allows us to test the propositions that policy shows greater aggression to inflation in the reaction function in terms of a greater response coefficient as interest rates reach low levels, and increasing aggression as the lower bound is approached. We find support for the Taylor principle, a more aggressive response to inflation than under a Taylor rule, but no detectable evidence of increasing aggression as the zero lower bound is approached in the US and Japan.     

Interest rate pass-through,monetary policy rules and macroeconomic stability

In this paper we analyze equilibrium determinacy in a sticky price model in which the pass-through from policy rates to retail interest rates is sluggish and potentially incomplete. In addition, we empirically characterize and compare the interest rate pass-through process in the euro area and the U.S. We find that if the pass-through is incomplete in the long run, the standard Taylor principle is insufficient to guarantee equilibrium determinacy. Our empirical analysis indicates that this result might be particularly relevant for bank-based financial systems as for instance that in the euro area.     

Inflation targeting,credibility, and non-linear Taylor rules

In this paper we systematically evaluate how central banks respond to deviations from the inflation target. We present a stylized New Keynesian model in which agents' inflation expectations are sensitive to deviations from the inflation target. To (re-) establish credibility, monetary policy under discretion sets higher interest rates today if average inflation exceeded the target in the past. Moreover, the central bank responds non-linearly to past inflation gaps. This is reflected in an additional term in the central bank's instrument rule, which we refer to as the ”credibility loss.” Augmenting a standard Taylor (1993) rule with the latter term, we provide empirical evidence for the interest rate response for a sample of five inflation targeting (IT) economies. We find, first, that past deviations from IT feed back into the reaction function and that this influence is economically meaningful. Deterioration in credibility (ceteris paribus) forces central bankers to undertake larger interest rate steps. Second, we detect an asymmetric reaction to positive and negative credibility losses, with the latter dominating the former.     

Monetary policy when potential output is uncertain: Understanding the growth gamble of the 1990s

The Fed kept interest rates low and essentially unchanged during the late 1990s despite a booming economy and record-low unemployment. These interest rates were accommodative by historical standards. Nonetheless, inflation remained low. How did the Fed succeed in sustaining rapid economic growth without fueling inflation and inflationary expectations? In retrospect, it is evident that the productive capacity of the economy increased. Yet as events unfolded, there was uncertainty about the expansion of the capacity of the economy and therefore about the sustainability of the Fed's policy.This paper provides an explanation for the success of the Fed in accommodating growth with stable inflation in the late 1990s. It shows that if the central bank is committed to reverse policy errors it makes because of unwarranted optimism, inflation can remain in check even if the central bank keeps interest rates low because of this optimism. In particular, a price level target—which is a simple way to model a commitment to offset errors—can serve to anchor inflation even if the public does not share the central bank's optimism about shifts in potential output. The paper shows that price level targeting is superior to inflation targeting in a wide range of situations. The paper also provides econometric evidence that, in contrast to earlier periods, the Fed has recently put substantial weight on the price level in setting interest rates. Moreover, it shows that CPI announcement surprises lead to reversion in the price level. Finally, it provides textual evidence that Alan Greenspan puts relatively more weight on the price level than inflation.     

The information content of Eonia swap rates before and during the financial crisis

Before August 2007, implied forward rates in the overnight interest swap rates closely reflected market expectations about the future path of the Eonia, and therefore, about the future course of the ECB’s monetary policy stance. Nevertheless, this link was weakened considerably during the most acute episode of the financial crisis. Using the expectations hypothesis of the term structure as a benchmark model for the determination of the overnight interest swap rates, we find that after May 2010 the monetary transmission mechanism was partially restored when the ECB implemented various ‘unconventional measures’ in response to the financial crisis. On the contrary, liquidity and credit risks are still present in unsecured deposit markets, distorting the pricing and transmission of the ECB monetary policy stance along the Euribor rates. These results should be of interest for regulators, financial institutions, and researchers in European money markets.     

Instrument instability and short-term monetary control

The literature on instrument instability tends support to a policy of smoothing interest rates: it contends that rigid adherence to a monetary rule would bring about explosive interest-rate movements. This contention is examined using a simple model which incorporates rational expectations; the results suggest that instrument instability is associated with interest-rate smoothing rather than with short-term control of the money supply. Furthermore, policy that attempts to stabilize interest rates may itself account for empirical findings which have hitherto been viewed as evidence that instrument instability would occur if the money supply were closely controlled.     

Monetary Policy and Short-term Interest Rates: An Efficient Markets-Rational Expectations Approach

This paper is an application of efficient markets-rationael xpectations theory to analyze empirically the relationship of money supply growth and short-term interest rates, a hotly debated issue in the literature. This approach has the advantage over earlier research on this subject in that it imposes a theoretical structure that allows easier interpretation of the empirical results as well as more powerful statistical tests. The empirical results uniformly do not support the proposition that increases in money growth are correlated with declines in short rates.     

The Value of Interest Rate Stabilization Policies When Agents Are Learning

We examine the expectational stability (E-stability) of rational expectations equilibrium in the "New Keynesian" model where monetary policy is optimally derived and interest rate stabilization is added to the central bank's traditional objectives of inflation and output stabilization. We consider both the case where the central bank lacks a commitment technology and the case of full commitment. We show that for both cases, optimal policy rules yield rational expectations equilibria that are E-stable for a wide range of empirically plausible parameter values. These findings stand in contrast to Evans and Honkapohja's findings for optimal monetary policy rules in environments where interest rate stabilization is not a central bank objective.     

Changing Monetary Policy Rules, Learning, and Real Exchange Rate Dynamics

When the exchange rate is priced by uncovered interest parity and central banks set nominal interest rates according to a reaction function such as the Taylor rule, the real exchange rate will be determined by expected inflation and the output gap or the unemployment gap of the home and foreign countries. This paper examines the implications of these Taylor rule fundamentals for real exchange rate determination. Because the true parameters in central bank policy rules are unknown to the public and change over time, the model is presented in the context of a least squares learning environment. This simple learning model captures the volatility and the major swings in the real deutschemark/euro–dollar exchange rate from 1976 to 2007.     

Money,Asset Prices,and the Liquidity Premium

This paper examines the effect of monetary policy on the market value of the liquidity services that financial assets provide, known as the liquidity premium. The theory predicts that money supply and nominal interest rates have positive effects on the liquidity premium, but asset supply has a negative effect. The empirical analysis with U.S. data confirms the theoretical predictions. The theory also proposes that the liquidity properties of assets can cause negative nominal yields when the money holding cost is low and liquid assets are scarce. The suggestive empirical findings in Switzerland to support this theoretical result are presented.