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This paper studies whether monetary policy should respond to changes in monetary aggregates or stock market indices. Based on an empirical model of the US it presents estimates of how the inclusion of monetary aggregates or stock market indices in the central bank’s information set affects the stabilization performance of an optimal monetary policy rule. It is shown that accounting for uncertainty about the structural relationships within the economy leads to a strong deterioration in the stabilization success of monetary policy reaction functions that respond to the growth rates of monetary aggregates or stock market indices. In addition it is analyzed whether money growth or changes in stock market indices help to explain US monetary policy in the recent years.

This paper investigates whether the stabilization performance of interest rate rules can be improved by responding to monetary growth rates or stock market indices. There has been an intense debate whether the central bank should react to these variables and theoretical arguments have been presented both for and against such a proposition. In this paper I present an empirical evaluation of the economic effects that result from including such variables in the monetary policy reaction function. This is achieved by simulating and comparing the stabilization results from alternative optimal interest rate rules that have been derived from an empirical model of the US economy. The simulation pays special attention to the fact that the central bank faces uncertainty about the structure of the economy. The monetary policy reaction function most widely discussed is the Taylor rule (Taylor, 1993) which assumes that the interest rate is set by the central bank in response to current, lagged or forecast values of the inflation rate and the output gap or the deviation of the unemployment rate from its natural level. Additional variables that have been proposed to be included in the monetary policy reaction function are the exchange rate (e.g. Ball, 2000 and Leitemo and Söderström, 2005) and the growth rates of monetary aggregates.1 In the now standard New Keynesian macro model there is no special role for monetary aggregates in the conduct of monetary policy. In such models money only reacts endogenously to the interest rate set by the central bank and it is the interest rate which matters for the effects of monetary policy.2 However, it has been argued that even within this class of models monetary aggregates may contain information useful for monetary policy making.3 An additional set of variables that might be included in the monetary policy reaction function are asset prices, in particular stock prices. The most convincing arguments in favor of monetary policy reacting to changes in stock prices refer to the predictive content of asset prices with respect to future output and inflation. These studies recommend that monetary policy should respond to changes in asset prices to the extent that these changes through their effects on firm’s financing conditions and household consumption signal future deviations of unemployment, output and inflation from their targets (e.g. Bernanke and Gertler, 2000, Bernanke and Gertler, 2001 and Gilchrist and Leahy, 2002). Other authors argue that asset prices should be targeted by monetary policy in their own right because drastic changes in asset prices – in particular stock market or housing market crashes – have strong and persistent negative effects on output and employment (e.g. Cecchetti et al., 2000 and Bordo and Jeanne, 2002). In contrast, other authors warn that including stock market variables in monetary policy reaction functions might at best be irrelevant for the overall economic outcome but might cause considerable harm in the worst case (Bullard and Schaling, 2002).4 Which variables should be included in a monetary policy rule and how the interest rate should be set in response to them can be studied analytically by deriving optimal monetary policy rules. Optimal monetary policy rules are reaction functions that minimize a prespecified central bank loss function (e.g. Ball, 1999, Clarida et al., 2001, Giannoni and Woodford, 2003a, Giannoni and Woodford, 2003b, Schmitt-Grohe and Uribe, 2004 and Svensson, 2003). In these models the optimal reaction function is determined by assumptions about the structural relationships within the economy and by the parameters of the loss function. The central bank reacts to all economic variables relative to their predictive content with respect to future values of the central bank’s goal variables. These theoretically derived optimal policy rules assume that the central bank knows the structural relationships within the economy with certainty. In practice, however, central banks must rely on estimated models of the monetary transmission mechanism and have only a rough understanding of how the economy operates. This leads to an important caveat concerning the practical implementation of optimal monetary policy rules: for many models optimal reaction functions tend to be quite complex and very sensitive to changes in the structural assumptions of the model. This sensitivity of optimal policy rules in combination with uncertainty about the structure of the economy has led to a number of studies on “robust” monetary policy rules. A monetary policy reaction function is robust if its performance as measured by a loss function is not very sensitive to changes in the underlying structural economic model. That is, for a robust model the value of the loss function does not deteriorate dramatically if the structural equations or coefficients of the model are changed. That approach is similar to the one in this paper: the parameters of the reaction function are chosen to minimize the central bank’s loss function under the assumption of a particular structural economic model. Finally, the performance of the optimized simple reaction function is studied for alternative structural models different from the one it was optimized for. This is done by simulating the altered structural model together with the unchanged reaction function and comparing the resulting values of the loss function or the resulting variances of the central bank’s goal variables (e.g. Walsh, 2003). This technique captures the inherent uncertainty of monetary policy makers about the true structure of the economy. While relatively simple monetary policy reaction functions generally perform worse than complex ones in the model they were optimized for, many studies have shown that the performance of simple rules deteriorates less under different economic structures than that of more complex reaction functions (e.g. Levin and Williams, 2003, Levin et al., 1998, Orphanides and Williams, 2002 and Williams, 2003). This leads directly to the question how different policy rules that include different sets of variables can be ranked with respect to their robustness and how the relative performance of these rules changes if central assumptions under which they were derived turn out to be erroneous? This paper’s contributions are twofold: first, the paper investigates whether the inclusion of monetary aggregates or stock market variables in an optimal monetary policy reaction function improves its ability to explain actually observed monetary policy in the US in the recent period. This does not conclude whether the Fed did or did not use these variables in its monetary policy deliberations but it indicates whether the variable in question helps to describe the Fed’s behavior and can be used for forecasting the Federal Funds Rate. For example, monetary aggregates might be correlated with other financial information the Fed actually looks at when deciding about the Federal Funds Rate Target, such as credit volume. Second, the paper compares the robustness of optimal policy rules containing alternative sets of economic variables. This is done by explicitly accounting for uncertainty about the true structural relationships in the economy both in deriving the optimal policy rules and in evaluating their stabilization performance. The empirical analysis proceeds as follows: the starting point is an empirical model suggested by Sack (2000) who shows that US monetary policy can be approximated fairly well by a policy rule derived from an optimal control model in which the structure of the economy is assumed to be given by an estimated vector autoregression (VAR). The dynamic programming problem of the central bank is solved and an optimal monetary policy reaction function is derived. This approach is similar to the literature on optimal policy rules but the structural model imposes only relatively few restrictions on the economy. By including different sets of variables in the model I arrive at alternative optimal monetary policy rules. For these rules I compare how the generated path for the interest rate fits the observed time series of the Federal Funds Rate. If the fit of the policy rule improves by adding a specific economic variable this might indicate that the variable in question represents information that is helpful in explaining how the Fed sets the Federal Funds Rate Target. Next, the robustness of the different policy rules is studied assuming uncertainty about the structure of the economy. Two types of uncertainty are considered: (1) relatively small deviations in the economic structure are introduced by small random variations in the structural coefficients of the VAR model. (2) The predictive power of monetary aggregates and the stock market index for the other economic variables is altered drastically by imposing zero restrictions on some coefficients of the structural model. These experiments indicate how much might be gained for stabilization policy by including money growth or stock market variables in the policy rule. Generally, the results show that the inclusion of monetary aggregates in the policy reaction function improves its fit. However, the resulting policy rules are found to be much more sensitive with respect to uncertainty about the economy’s structure than the simple rule which includes neither money growth nor the stock market index. A related study is Fair (2005) who combines various simple interest rate rules with the large-scale structural multi-country model discussed in Fair (1994). He also simulates a smaller model for the US with a numerically derived optimal monetary policy rule. His study differs in some important respects from the one presented here. First, he accounts for uncertainty only by simulating the structural model with randomly drawn shock series, i.e. treats the structural coefficients as being known with certainty. Second, some of the coefficients in the central bank’s loss function are chosen arbitrarily instead of being estimated, and third, the reaction functions studied differ in the numerical value of their coefficients but not in their structure, i.e. there is no comparison between reaction functions that respond to a specific variable and those that do not. The paper is structured as follows: Section 2.1 presents the empirical model of the US economy and derives the optimal monetary policy rules. In Section 2.2 the free parameters of the model are estimated and different policy rules are compared with respect to their ability to track the actually observed Federal Funds Rate. In Section 3 an approximation technique from Sack (2000) is applied to derive optimal reaction functions assuming that the central bank faces uncertainty about the parameters in the structural economic model. Then, the relative stabilization performance of the different rules is simulated in the presence of random perturbations to the structural economic model. Finally, the monetary policy rules are simulated under modified versions of the structural models in which the information content of monetary aggregates or stock market variables is altered more drastically in order to compare how the various rules perform under strongly adverse conditions.

This paper has shown that the actual time series of Federal Funds Rate can be approximated by an optimal monetary policy reaction function derived from a simple structural model. Having the Federal Funds Rate also respond optimally to the growth rates of M1 or M3 improves the ability of the optimal rule to explain the actual time series of the Federal Funds Rate. In contrast, including a stock market index does not improve the fit of the optimal policy rule. These results show that monetary aggregates contain some information that helps to explain the Fed’s behavior. This does not necessarily imply that the Fed, in fact, reacts to changes in the growth rates of monetary aggregates but that money growth might be correlated with some other variables that the Fed considers in setting interest rates, such as credit growth, and financial market conditions. While the optimal reaction functions reproduce the general path of the Funds Rate quite well, the simulated interest rate is much more volatile than actually observed. Allowing for uncertainty about the true economic structure to enter into the analysis affects the comparisons between different optimal policy rules in various ways. It was shown that the volatility of the optimal Federal Funds Rate declined for almost all the policy rules under consideration. The policy rules that included monetary growth rates still tracked the actually observed Funds Rate more closely than the policy rule without them. Interestingly, all the optimized policy rules were able to explain the large decrease in the Federal Funds Rate in 2001. Even those rules that do not react to changes in stock prices recommended a strong decline in the Federal Funds Rate. A detailed study of the robustness of the different policy rules showed the stabilization performance of the simple rule (not including monetary growth rates or a stock market index) to deteriorate less relative to the other optimal rules if the model under which it was derived was assumed to be wrong. The simple rule is less sensitive to changes in the structure of the economy or to errors in the estimation of the structural relationships. While money growth or stock market data might have some predictive power for the other economic variables, the possible gains for stabilization policy from this, however, are most often compensated by the loss in stabilization performance that results from unstable and weak relationships between these financial variables and the rest of the economic system. Overall, the simulation study presented in this paper shows that assigning a prominent role to monetary aggregates in the formulation of monetary policy might have some benefits but also carries high risks. Such a strategy is only attractive if the policymaker has high confidence in his knowledge of the structural relationships within the economy. The stock market index, however, has such an unreliable relationship to the other economic variables that including it consistently in the policy rule will lead to a severe deterioration of the stabilization performance.