“What if the Fed increased the weight of the stock price gap in its reaction function?” Katarzyna Romaniuk1

Abstract: The Fed has never admitted targeting stock prices. Yet our empirical analysis, based on a small macroeconometric model of the U.S. economy in the period 1981-2002, shows that the Fed explicitly takes into account stock price variations in its reaction function. Furthermore, our simulation results suggest that increasing the weight attributed to stock price changes could prove advisable, as the stock market wealth effect increases. This measure would help to contain the additional instability brought about by this economic evolution, and confirm the current political trend towards protecting stock owners. JEL classification: E17; E44; E52. Keywords: monetary policy; stock prices; wealth effect; macroeconomic and financial stability.

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University of Paris 1 Panthéon-Sorbonne, PRISM-OSES, 1, rue Victor Cousin, 75005 Paris, France. E-mail address : [email protected].

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1. Introduction In the United States, the goals of monetary policy are defined in the Federal Reserve Act: The Board of Governors and the Federal Open Market Committee seek “to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates.”2 Mathematically, these purposes can be summarized in the objective of minimizing the variance of the deviations of inflation from its desired level, of output from potential, and of the interest rate from its equilibrium value. Although the asset price stabilization does not appear in its stated objectives, many economists have emphasized in the recent years that the Fed should follow an additional goal: targeting the equilibrium asset price level. The reason lies in the emergence of stock market bubbles, whose burst at a late stage can cause important damage to the economy as a whole, as was the case after the 1929 stock market crash for example. The proponents of asset price targeting think that the central bank, by closely observing the evolution of financial markets, and reacting pre-emptively when a stock market bubble appears, can prick a bubble at an early stage, and by so doing prevent a heavy recession. Yet this problem does not appear as a simple one. Other economists see this measure as inadvisable. Their main arguments focus on the fact that asset price targeting does not constitute an objective of the central bank, which should focus exclusively on price stability and macroeconomic growth. Furthermore, the emergence of a bubble is hardly observable, and trying to prick a possible bubble can prove destabilizing for the economic system. The literature often chooses the monetary policy framework first proposed by Taylor (1993) to conduct this debate. This author described a simple and convenient way of summarizing the conduct of monetary policy: The interest rate set by the central bank is defined as a linear, positive function of the deviation of inflation from its desired level and of the deviation of output from its potential. Proponents of asset price targeting think

2

The Federal Reserve Board. The Federal Reserve System: Purposes and Functions. http://www.federalreserve.gov/pf/pf.htm.

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that a third term should complete this formulation: the deviation of the asset price level from its fundamental value. As to the possible incorporation of asset prices in Taylor’s monetary policy rule, no consensus has been reached in the literature: Some authors oppose this solution (Reinhart 1998; Bernanke and Gertler 1999; Bullard and Schaling 2002), while others are favorable to it (Cecchetti et al. 2000; Genberg 2001; Kontonikas and Ioannidis 2005). The Fed’s position as to this debate appears as very clear. The actual monetary policy stance in the United States, relevant to the Alan Greenspan as well as to the Ben S. Bernanke era, is well described by Vice Chairman Roger W. Ferguson Jr in his speech in November 2005: “Without targeting asset prices, we need to be more attentive now to financial markets because asset prices affect spending to a greater degree than before and because asset prices provide us with a greater amount of timely information to guide policy.”3 Translating into Taylor’s framework, this statement means that the Fed does not include asset price variations directly in its reaction function. The United States central bank nonetheless closely observes the evolutions in financial markets, in the purpose of extracting useful information for the respect of its ultimate objectives: stable prices and maximum sustainable growth. Let us now focus on another dimension of this quotation: “We need to be more attentive now to financial markets because asset prices affect spending to a greater degree than before”. Put differently, as the stock market wealth effect increased, stock market fluctuations should be observed more closely by the central bank. What is the precise definition of the wealth effect? It goes back to the works by J.M. Keynes and A.C. Pigou in the 1930s. Classical studies in economics define the wealth effect as the positive link between the price of financial assets and global consumption. The mechanism of the stock market wealth effect is the following: When financial asset prices rise, and if this increase is considered as permanent, then economic agents will take into account this evolution by upgrading their long-run wealth level estimate, and thus increase consumption.

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R.W. Ferguson Jr. Asset Price Levels and Volatility: Causes and Implications. http://www.federalreserve.gov/BoardDocs/speeches/2005/200511152/default.htm.

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In recent years, the stock market wealth effect increased in the United States (Boone et al. 1998; Shirvani and Wilbratte 2002). Stock ownership deepened - people invest a larger part of their wealth in stocks - and widened - a larger part of the population holds stocks. As stock ownership continues to be more and more widespread, one could expect a further increase in the stock market wealth effect. Financial markets being characterized by a high volatility, a growing link between stock prices and macroeconomic outcomes could further destabilize the economic system. The question to address is then the appropriate form of the Fed’s reaction function in the context of an increasing wealth effect. The analysis conducted in this paper has two main purposes: an estimation of the Fed’s monetary policy rule, in order to assess the actual role asset price variations play in the conduct of monetary policy in the United States and an implementation of simulations, with the objective of evaluating the effect of a growing wealth effect on the characteristics of the optimal form of the Fed’s reaction function. The framework chosen is a small macroeconometric model of the United States economy, estimated with quarterly data from 1981 to 2002. The estimation result shows that the Fed actually takes into account stock price changes in its reaction function: An increase by 10 percentage points in the stock price growth rate brings about an increase by 0.6 percentage points in the interest rate in the same period. The simulation results suggest that a relatively high weight should be attributed to stock price variations in the Fed’s reaction function in order to contain macroeconomic and financial instability, and that the optimal weight of stock price fluctuations increases when the stock market wealth effect becomes larger. We therefore recommend the Fed to respond more sharply to stock price variations so as to prevent an increase in macroeconomic instability resulting from a growing stock ownership. This policy would be advantageous to all economic agents as they would benefit from a stabilized economic system and a better predictable future economic evolution. Beyond the macroeconomic stability objective, a strong response to stock price variations is also required to fight financial market instability. The proposed

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measure would then improve the situation of stock owners, and thus confirm the current political trend towards protecting them.4 The paper is organized as follows. Section 2 introduces the model, which is then estimated. Simulation results are provided in section 3. Section 4 concludes the paper. 2. The model of the United States economy The model, whose formulation builds on the contributions by Smets (1997), Reinhart (1998), Rudebusch and Svensson (1998 and 2002), Filardo (2000) and Aksoy et al. (2002), is defined by the four following equations:5

πt

o

= ∑ λ ππn π t − n + λ πy y t −1 + ε πt

(1)

n =1

p

yt = ∑ λ yyn yt −n − λ yr ∆(r t −1) + λ ys st −1 + ε ty

(2)

n =1 q

s st = ∑ λ ssn st −n − λ sr ∆(r t −1) + ε t

(3)

r r t = γ rπ π t + γ ry y t + γ rs st + ε t

(4)

n =1

where π denotes inflation, y the output growth rate, r the interest rate determined by the central bank (the monetary policy instrument), s the stock price growth rate and ∆ the first difference operator. ε correspond to shocks, defined as unanticipated variations of the variables, following a centered normal law and assumed to be mutually uncorrelated. Equation (1), which is a version of the standard Phillips curve, defines inflation as a linear function of past values of inflation and the value of the output growth rate of the preceding period. Equation (2), representing an IS curve, models the positive reaction of investment and consumption to a reduction in the interest rate and the existence of a wealth effect 4

In the recent years, policy makers became increasingly preoccupied with neutralizing all forms of risks connected with stock owners' wealth. For example, the Sarbanes-Oxley Act of 2002, aimed at increasing the accountability of executive officers and board directors and better supervising accounting practices, constitutes a major sign of this preoccupation. 5 Following Bullard and Schaling (2002), the four variables are defined as deviations from the equilibrium value.

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consumption is stimulated by a stock price increase.6 Several lags in output are also considered. Concerning the monetary policy transmission process, a variation in the interest rate first impacts on output. As emphasized by Aksoy et al. (2002), it impacts on inflation in the following period only, via the effect on output. The stock price growth rate, defined in equation (3), reacts positively to a reduction in the interest rate. Past values of the stock price growth rate are also determining for the level of this variable. Equation (4) models the interest rate as a function of inflation, the output growth rate and the stock price growth rate. It forms the reaction function of the central bank, in the lines of Taylor (1993). As other variables than inflation and the output gap determine the level of the interest rate, the policy rule takes the form of a so-called augmented Taylor rule (Fourçans and Vranceanu 2004). Smets (1997) and Clarida et al. (2000) emphasize that the objective of inflation stabilization requires the value of γrπ to be higher than 1 and the one of γry to be positive: The real interest rate then increases when inflation is above its target value and/or the output growth rate above its potential. Furthermore, the following condition must be met: γrs ≥ 0, so as to insure the stock price-stabilizing properties of the monetary policy rule. Let us now proceed to an estimation of the proposed model. We choose the framework of the economic system of the United States to conduct the analysis. Data, taken from Datastream, are quarterly and concern the period 1981.II to 2002.II. The variables are defined as follows: The GDP growth rate represents the output growth rate, the growth rate of the consumption price index – inflation, the growth rate of the S&P 500 index - the stock price growth rate and the Federal funds rate – the interest rate.7,8

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A stock price increase also fosters investment, by reducing the cost of capital. The first three rates are calculated as the variation of the current quarter to the corresponding quarter of the preceding year in percent. The interest rate variable takes the form of an average of the four preceding quarters. 8 The equilibrium value, defined as the mean value of the data (Rudebusch and Svensson 2002; Fair and Howrey 1996), is subtracted from the four rates. 7

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As the model defines a simultaneous equation system9, three-stage least squares are used to estimate the system (Fair and Howrey 1996). The estimation result is the following:

π t = 1.0026 * π t −1 − 0.1515 * π t − 2 + 0.0814 * yt −1 ( −1.65)

(10.04)

(5)

(3.11)

yt = 1.2404 * yt −1 − 0.3264 * yt −2 − 0.5583 * ∆(r t −1) + 0.0147 * st −1

(6)

st = 0.8134 * st −1 − 5.6585 * ∆(r t −1)

(7)

r t = 1.3974 *π t + 0.2683 * yt + 0.0579 * st

(8)

( −3.51)

(14.09)

( 2.76)

( −2.38)

(12.61)

(7.49)

( −2.38)

( 2.74)

( 4.12)

with t-statistics given in brackets.10 The choice of the number of past periods taken into account results from whether coefficients are significant and from the information criteria of Akaike and Schwarz. The adjusted R² are 82.31% for equation (5), 88.86% for (6), 65.28% for (7) and 50.50% for (8). The values of the coefficients, which are all significant and with the expected signs, can be connected with the ones of other authors: Taylor (1993), Bernanke and Gertler (1999), Clarida et al. (2000), Filardo (2000) and Rudebusch and Svensson (2002). Two elements nonetheless differ from the estimates found in the literature. Let us first emphasize the presence of a measurable stock market wealth effect: The estimation result shows that an increase by 10 percentage points in the stock price growth rate deviation leads to an increase in the output growth rate gap by 0.15 percentage points in the next period. Furthermore, contrary to what is officially stated, the Fed responds to stock price variations in its monetary policy rule: An increase by 10 percentage points in the stock price growth rate deviation brings about an increase by 0.6 percentage points in the interest rate deviation in the same period. 9

Endogenous variables appear in the right-hand side of the equation defining the interest rate. Before accepting this estimation result, several tests have been conducted, which allowed to validate the proposed result: a Granger test, in order to confirm the causality relations assumed by the model, reestimations of the model with periods of different lengths and alternative estimation methods and comparison to an unrestricted VAR(4), along the lines of Rudebusch and Svensson (1998), by observing whether the responses of the structural model go beyond the confidence intervals of the VAR model impulse responses. 10

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3. The optimal monetary policy design in the context of an increasing wealth effect: some simulation results

The analysis of the transmission of shocks and their impact on the economic system stability constitutes the purpose of this section. Our objective is to determine the optimal form of the Fed’s reaction function in different economic environments. A definition of the optimal form of the reaction function in our framework is first required. As already said, the goals of the Fed’s monetary policy are maximum employment, stable prices, and moderate long-term interest rates. Mathematically, these purposes can be summarized in the objective of minimizing the variance of the deviations of inflation from its desired level, of output from potential, and of the interest rate from its equilibrium value. The optimal form of the reaction function is the one characteristic of this minimum. In our analysis, we assume that the coefficients of inflation and output stabilization in the Fed’s monetary policy rule remain constant throughout the simulations. We vary the asset price stabilization coefficient only, in order to isolate the impact of a variation in this variable. By so doing, we follow Bullard and Schaling (2002), who emphasize that the debate is made in a framework where responses to deviations in inflation and the output gap are considered as fixed. The important question is the one of a possible improvement by adding a response to variations in stock prices. Historical shocks, defined as the residuals from the model estimation, are used in the simulations. The analysis is conducted in three steps. We first address the question of the best response to stock price changes within the benchmark model, for the estimated wealth effect. Then the impact of a wealth effect increase on the system stability is studied. The third step analyzes once again the question of the optimal response to stock price changes, this time in the case of a wealth effect increase. The benchmark situation

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A modification in the response to stock price changes is represented by a variation in the coefficient γrs (between 0 and 0.2).11 The Fed minimizes the variance of the deviations of inflation, output and the interest rate. The simple curves in the figures 1 to 3 display the variance of the given variable when varying the response to stock price changes, for the estimated (or benchmark) wealth effect. The minimum of the curve corresponds to 0.02 for inflation, 0.12 for output and 0.03 for the interest rate. The optimal value of the coefficient γrs is thus strictly positive for the three variables: A given response to stock price changes is thus advisable when trying to stabilize inflation, output or the interest rate. Yet the optimal level differs for the three variables. As a consequence, the Fed will have to fix its relative preferences for stabilizing inflation, output and the interest rate before determining its response to stock price variations. What is the economic intuition for this stabilizing effect of a response to stock price variations? The reason lies in the existence of the stock price wealth effect. Taking into account stock price variations in the reaction function means that the chosen value of the interest rate will be more stock price-stabilizing. As the stock price impacts output, and also inflation (via the effect on output) because of the wealth effect, a more stable stock price has a stabilizing effect on output and inflation. Finally, let us note that the coefficient γrs should not be too high, because of risks of system destabilization: The model becomes explosive when γrs equals 0.14 approximately. This result can be explained by the high volatility of the stock price, as compared to the ones of the other variables. Taking into account stock price variations when conducting monetary policy can help stabilizing the economic system, yet when the weight attributed to stock price fluctuations is excessive, the much higher volatility of the stock price is passed on to the other variables. To sum up, the simulation results show that a moderate response to stock price variations has a stabilizing effect on inflation, output and the interest rate.

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Following Fair and Howrey (1996), it is assumed that the parameters of the model do not vary when the monetary policy rule changes.

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Figure 1: Wealth effect and optimal response to stock price changes: the case of inflation Wealth effect and optimal response to stock price changes: the case of inflation 0.00015 0.000149

inflation variance

0.000148 0.000147 0.000146 0.000145 0.000144 0.000143 0.000142 0.000141 0.00014 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.11 0.12 0.13 0.14 0.15

response to stock price changes benchmark effect

effect of 0.019

effect of 0.024

effect of 0.029

Figure 2: Wealth effect and optimal response to stock price changes: the case of output Wealth effect and optimal response to stock price changes: the case of output

output growth rate variance

0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.11 0.12 0.13 0.14 0.15

response to stock price changes benchmark effect

effect of 0.019

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effect of 0.024

effect of 0.029

Figure 3: Wealth effect and optimal response to stock price changes: the case of the interest rate Wealth effect and optimal response to stock price changes: the case of the interest rate 0.0008

interest rate variance

0.00075

0.0007

0.00065

0.0006

0.00055 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.11 0.12 0.13 0.14

response to stock price changes benchmark effect

effect of 0.019

effect of 0.024

effect of 0.029

Does instability rise when the wealth effect increases?

An increase in the coefficient λys (between 0 and 0.03) signifies an increase in the wealth effect. When increasing the wealth effect, instability also increases. Figures 4 to 6 show this positive relation between the wealth effect level and the key variable variance. This relation is increasing for output and the interest rate. As to inflation, the relation becomes increasing from a wealth effect increase of 0.004 approximately. This result could be foreseen. Financial markets are characterized by a high volatility. When the link between financial markets and macroeconomic variables becomes more pronounced – in the form of an increased wealth effect -, one could fear an increase in the instability of the economic system.

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The question to address is then the appropriate way to conduct monetary policy in this new, more instable environment. Put differently, the question is the following: Can a modification in the response to stock price changes help to contain this new instability? Figure 4: Impact of a wealth effect increase on inflation stability Impact of a wealth effect increase on inflation stability 0.00016

inflation variance

0.000155

0.00015

0.000145

0.00014

0.000135 0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03

wealth effect increase

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Figure 5: Impact of a wealth effect increase on output growth rate stability Impact of a wealth effect increase on output growth rate stability 0.0009

output growth rate variance

0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0

0.002 0.004 0.006 0.008

0.01

0.012 0.014 0.016 0.018

0.02

0.022 0.024 0.026 0.028

0.03

wealth effect increase

Figure 6: Impact of a wealth effect increase on the interest rate stability Impact of a wealth effect increase on the interest rate stability 0.00067 0.00066

interest rate variance

0.00065 0.00064 0.00063 0.00062 0.00061 0.0006 0.00059 0.00058 0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03

wealth effect increase

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Adapting the monetary policy design to an increasing wealth effect

Let us look once again at figures 1 to 3, which display the variance of the key variables with respect to the level of the coefficient γrs, for different values of the wealth effect. The minimum of the curves moves to the right when the wealth effect increases for all of the three variables, although the movement is more pronounced for inflation than for output and the interest rate. The optimal value of γrs goes approximately from 0.02 to 0.07 for inflation, from 0.12 to 0.14 for output, from 0.03 to 0.04 for the interest rate when the wealth effect doubles. To sum up, an increased wealth effect requires increasing the weight attributed to stock price variations in the Fed’s reaction function, in order to limit the additional instability brought about by this economic evolution. This result appears as predictable. As the impact of stock price variations on output increases because of a stronger wealth effect, increasing the weight of stock price variations in the reaction function leads to an interest rate which is even more stock pricestabilizing. This increased stability of the stock price allows to outweigh the increased link between the financial market and macroeconomic outcomes. What about the financial market stability?

Until now, we focused of the three basic goals of monetary policy, which refer to inflation, output and the interest rate. Let us now get a look on the implications of our policy recommendations on the financial market stability.12 Figures 7 and 8 display the variance of the stock price growth rate with respect to the level of the coefficient γrs and for different values of the wealth effect, and with respect to the wealth effect level respectively.

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In order to take into account the preoccupation of the central bank with financial market stability, Durré (2001) even proposed to include the variance of the stock price deviation in the objective function to minimize.

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Figure 7: Wealth effect and optimal response to stock price changes: the case of the stock price Wealth effect and optimal response to stock price changes: the case of the stock price 0.035

variance of the stock price growth rate

0.033 0.031 0.029 0.027 0.025 0.023 0.021 0.019 0.017 0.015 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.11 0.12 0.13 0.14

response to stock price changes benchmark effect

effect of 0.019

effect of 0.024

effect of 0.029

Figure 8: Impact of a wealth effect increase on the stability of the stock price growth rate Impact of a wealth effect increase on the stability of the stock price growth rate

variance of the stock price growth rate

0.023 0.0228 0.0226 0.0224 0.0222 0.022 0.0218 0.0216 0.0214 0.0212 0.021 0

0.002 0.004 0.006 0.008

0.01

0.012 0.014 0.016 0.018

wealth effect increase

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0.02

0.022 0.024 0.026 0.028

0.03

As to the benchmark wealth effect, the optimal response to stock price changes, when stabilizing the financial market, equals 0.13 (figure 7). A considerable response is thus advisable. This result appears as predictable: An interest rate which heavily takes into account stock price variations reduces the financial market volatility. Concerning the implications of a wealth effect increase, figure 8 provides a rather interesting conclusion: A wealth effect increase stabilizes the financial market. What are the mechanisms leading to this negative relation? Let us consider the case of a stock price increase. When the wealth effect becomes more pronounced, stock price variations impact more on output, and also on inflation – via their impact on output. This means that output and inflation increase more than they would otherwise increase, which in turn impacts on the level of the interest rate, which also increases more heavily than in the standard case. As a consequence, in the next period, the stock price will be stabilized to a greater extent - via the effect of the interest rate - than it would otherwise be. Yet this mechanism does not explain why the stock price volatility decreases, and not the ones of output and inflation, which are also more heavily stabilized. The main reason lies in the much greater volatility of the financial market, as compared to output and inflation. When the wealth effect increases, some proportion of this higher volatility of the stock price is passed on to inflation and output, which leads to the destabilization of these two variables. Figure 7 shows that the optimal response to stock price changes does not vary when the wealth effect increases: It remains at 0.13. To sum up, although a wealth effect increase reduces the financial market volatility and the optimal value of the coefficient γrs remains constant when increasing the wealth effect, one notes that the optimal response to stock price changes is heavy. The financial market stability objective thus requires a strong response to stock price variations.

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4. Conclusion

Officially, asset price targeting is not an objective of the Fed. Yet our estimation result of a United States economy model in the period 1981-2002 leads to an opposite conclusion: The Fed actually takes into account stock price variations in its reaction function. An increase by 10 percentage points in the stock price growth rate brings about an increase by 0.6 percentage points in the interest rate in the same period. Simulations building on the estimated system suggest that a response to stock price fluctuations is advisable, because of its stabilizing effect on the economic system. The reason for this lies in the existence of a measurable stock market wealth effect: The estimation result shows that an increase by 10 percentage points in the stock price growth rate leads to an increase in the output growth rate by 0.15 percentage points in the next period. As stock ownership still widens and deepens, a further increase in the wealth effect seems likely. Some dangerous consequences could result from such an economic evolution: As financial markets are highly volatile, a more pronounced link between stock prices and macroeconomic outcomes could lead to an increase in the instability of the economic system. The simulation results prove the validity of this logic: An increase in the wealth effect destabilizes the key variables - inflation, output and the interest rate. In order to counteract this new instability, an increase in the weight attributed to stock price variations in the Fed’s reaction function appears as a solution: The simulation results show that the optimal response to stock price fluctuations increases when the wealth effect becomes larger. We conclude that a more pronounced response of the Fed to stock price changes helps to contain economic instability, originated in a growing stock ownership. This policy change is therefore beneficial to all economic agents, given the improved predictability of the economic system. Beyond the macroeconomic stability objective, a stronger response to stock price variations is also required to fight financial market instability. The proposed measure will thus have a direct effect on stock owners' wealth. On a different level, it could also enhance the confidence in financial markets, which could in turn contribute to an increase in stock ownership, and thus to an increase in the

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stock market wealth effect. As a consequence, the measure could prove to be selfenforcing. But we do not think that this fact could invalidate it, because the increase in stock ownership appears as a general trend, supported by many economic and social factors, and the consequences of the monetary policy design cannot be seen as the determining ones, even if they can play an enhancing role. This aspect nonetheless proves that the issue is a rather complicated one, and that the Fed should be cautious when determining the scale and the frequency of its policy adjustments, which could be numerous because of the long-lasting feature of the evolution in stock ownership patterns. To illustrate the difficulty underlying this decision, let us note that too sharp responses to stock price changes or too frequent policy adjustments can be destabilizing, and thus lead to a result opposite to the expected one. No automatic response is allowed, and the analysis made in our paper is aimed rather at proposing the general trend to be followed by the Fed than defining the precise form of the central bank reaction function. Acknowledgements

I am very grateful to Radu Vranceanu for extensive discussions. I would like to thank Patrice Poncet for very valuable suggestions. I have also benefited from helpful comments from Damien Besancenot, Jean-François Boulier, Hubert de la Bruslerie, Steven Haberman, Jean-Pierre Indjehagopian, François Mouriaux, François QuittardPinon, Hélène Rainelli, Alexandre Steyer and the participants of the 52nd French Economics Association Annual Meeting in Paris in September 2003 and the 4th International Conference on Money, Investment and Risk in Nottingham in November 2003. I would like to thank four anonymous referees, whose remarks substantially improved the overall quality of the paper. All remaining errors are mine. References

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