...of two key state variables, price inflation and the output gap. considerable and influential research effort has been directed at establishing to what extent this kind of rule can explain the dynamics of policy rates in major industrialized countries (Clarida, Gali, and Gertler, 1998, 2000, and the references therein). The main virtue of this "Taylor" rule is its simplicity, but therein lies a vice, as there is controversy as to whether such a rule can be an adequate representation of a process as complex as that of monetary policy.

Accordingly, an important issue for central banks in recent years, for example, has been what weight to place on asset prices in setting interest rates (Greenspan, 1999; Batini and Nelson, 2000; Goodhart, 2001; Bordo and Jeanne, 2002). In periods of growing optimism, which may be associated with extended periods of economic expansion, asset prices may climb to unsustainable levels even if the path of likely returns (from, say, productivity gains or earnings growth) is unchanged (Shiller, 2000). The possibility of a sharp correction in asset prices may then leave the real economy unduly fragile, and this vulnerability may become an issue for monetary policymakers. Furthermore, macroeconomic imbalances may be exacerbated by the possibility that monetary policymakers may explicitly target asset prices. A useful dichotomy is whether asset price movements are a concern for central banks only because they contain information about future inflation--they are used as information variables--or whether they should be seen as variables to which central banks should react in addition to expected inflation and possibly the output gap. While some authors claim that including stock prices in the central bank's policy rule may be optimal (Cecchetti and others, 2000; Bordo and Jeanne, 2002) and that central banks react significantly to stock market movements by changing the short-term interest rate (Rigobon and Sack, 2003), other studies argue that central banks should not respond directly to asset prices (Bernanke and Gertler, 1999, 2001). (1)

Furthermore, in an open economy, the exchange rate is both a source of extraneous shocks and a mechanism for adjusting to fundamentals' shocks, and thus monetary policy choices are not independent of exchange rate dynamics. Some recent contributions argue that central banks may respond to the exchange rate, and this is particularly relevant in the case of small open economies (Obstfeld and Rogoff, 1995; Taylor, 2001). At the empirical level, some researchers provide evidence that exchange rates are statistically significant in interest rate rules depicting the reaction functions of several major central banks (Clarida, Gali, and Gertler, 1998).

In this paper we extend this analysis to consider jointly the role of asset prices and exchange rates in the interest rate rule to assess whether three major central banks--the U.S. Federal Reserve Bank, the Bank of England, and the Bank of Japan--have responded to asset prices and exchange rates during the last couple of decades or so, or whether they have used asset prices and exchange rates only as information variables that can help predict future inflation or output. In our study we allow asset prices and exchange rates to act both as information variables and as monetary policy targets, which enables us to investigate in an augmented interest rate rule whether and how central banks react to asset price and exchange rate disequilibria.

A subsidiary issue is the extent to which the output gap is correctly measured. In the empirical literature on central banks' reaction functions, the output gap has generally been measured by detrending output using deterministic trends (Taylor, 1993; Clarida, Gali, and Gertler, 1998, 2000) or smoothed trends representing the equilibrium level of output consistent with perfectly flexible prices (Kozicki, 1999, and the references therein). In practice, however, the efficient level of output may behave quite differently in response to real shocks such that potential output may not follow a smooth trend. As a result the output-gap measure that is relevant for monetary policy purposes may be different from the one captured by detrended output (Woodford, 2001). Recently, several contributions (Gali and Gertler, 1999; Gali, Gertler, and Lopez-Salido, 2001) have shown that, under certain restrictions on technology and labor market structure within a local neighborhood of the steady state, real marginal costs are directly related to the output gap.

In this paper we tie together these different, albeit related, strands of the literature in that we investigate a very general monetary policy rule comprising inflation and the output gap as well as asset prices and exchange rates in a unified framework, while examining the role of alternative measures of real marginal costs and the output gap. Using quarterly data since 1979 for the United States, United Kingdom, and Japan we confirm the main results of the empirical literature on forward-looking monetary policy rules. However, we also show that our baseline estimation including asset prices, exchange rates, and an adjusted labor share as the appropriate proxy for the output gap yields significant parameter estimates for all the arguments in the interest rate rule of the United States and United Kingdom, and for all the arguments except asset prices in the case of Japan. These results are open to several alternative interpretations, which we discuss below.

1. Monetary Policy Rule Specification

In this section we briefly review the standard framework of analysis of forward-looking interest rate (or Taylor) rules, which we then generalize to an interest rate rule that explicitly allows for asset prices and exchange rates to act both as information variables and monetary policy targets. Finally, we also discuss a subsidiary issue relating to the calculation of the proxy of the output gap used in interest rate rules.

Forward-Looking Taylor Rules

Following Clarida, Gali, and Gertler (1998, 1999, 2000), assume that within each operating period the central bank has a target for the nominal short-term interest rate [r*.sub.t], which is a function of the state of the economy represented by the gaps between expected inflation and output from their respective targets:

[r*.sub.t] = r* + [beta][E([[pi].sub.t+[k.sub.[pi]]]|[[OMEGA].sub.t]) - [pi]*] + [gamma][E([x.sub.t+[k.sub.y]]|[[OMEGA].sub.t])], (1)

where r* is the desired nominal interest rate when both inflation and output are at their target levels; E([[pi].sub.t+[k.sub.[pi]]]|[[OMEGA].sub.t]) and E([x.sub.t+[k.sub.y]]|[[OMEGA].sub.t]) denote the expectations of inflation at time t + [k.sub.[pi]] and the output gap at time t + [k.sub.y]; [pi]* is the level of inflation (implicitly or explicitly) targeted by the central bank; the output gap [x.sub.t+[k.sub.y]][equivalent to][y.sub.t+[k.sub.y]]-[y*.sub.t+[k.sub.y]], where y is output and y* is the efficient level of output. (2)

Consider the implied target for the ex ante real interest rate. (3) Central banks will pursue monetary policy aimed at stabilizing inflation if the parameter [beta] > 1, while rules characterized by [beta] [less than or equal to] 1 will tend to be destabilizing. Clearly, the parameter [gamma] is consistent with stabilizing output directly only if [gamma] > (Clarida, Gali, and Gertler, 2000).

Equation (1) may be, however, too restrictive to describe the behavior of short-term rates. As documented in earlier contributions (Goodfriend, 1987), central banks may operate smoothing changes in interest rates for different reasons (e.g., effects on capital markets, loss of reputation, private consensus building). To account for this behavior we can specify equation (1) assuming that the current short-term interest rate [r.sub.t] adjusts to the target rate [r*.sub.t] according to a partial adjustment mechanism of the form [r.sub.t] = [1 - [rho](1)][r*.sub.t] + [rho](L) [r.sub.t-1] + [v.sub.t], where [rho](L) is an n - lag polynomial, L is the lag operator, and [v.sub.t] is a zero-mean exogenous interest rate shock. Allowing for smoothing in the above fashion in equation (1) results in an interest rate rule where in each period central banks act on the short-term interest rate, reducing the gap between the current target rate and its past value:

[r.sub.t] = [alpha] + [lambda][[pi].sub.t+[k.sub.[pi]]] + [[thetav]][x.sub.t+[k.sub.y]] + [rho](L)[r.sub.t-1] + [[epsilon].sub.t], (2)

where we have eliminated the unobserved conditional expectations by rewriting equation (1) in terms of realized variables; [alpha] = [1 - [rho](1)](r* - [beta][pi]*); [lambda] = [1 - [rho](1)][beta]; [thetav] = [1 - [rho](1)][gamma]; and the error term [[epsilon].sub.t] = [v.sub.t] - [1 - [rho](1)]{[beta][[[pi].sub.t+[k.sub.[pi]]] - E([[pi].sub.t+[k.sub.[pi]]]|[[OMEGA].sub.t])] + [gamma][[x.sub.t+[k.sub.y]] - E([x.sub.t+[k.sub.y]]|[[OMEGA].sub.t])]} is the sum of a zero-mean exogenous shock and a linear combination of forecast errors that are orthogonal to the variables considered in the information set [[OMEGA].sub.t]. Given estimates of the parameters in the forward-looking Taylor rule given in equation (2), one can therefore recover the implied estimates of [beta] and [gamma].

Augmenting Forward-Looking Taylor Rules with Asset Prices and Exchange Rates

Equation (2) does not explicitly consider the role of asset prices and exchange rates as monetary policy targets (or instruments). It is under debate whether and how asset prices and exchange rates should be taken into account in formulating monetary policy (Taylor, 2001; Clarida, 2001). While asset prices may be used as indicator variables, in the last decade or so several major central banks have started taking into consideration the apparent increase in financial instability, of which...

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