Abstract :
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 bestudied 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 termstructure
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-ofrisk
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.
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