The stock market and the Fed

Preliminary and incomplete Do not quote without permission

The stock market and the Fed

by

Leonardo Becchetti

Università di Roma “ Tor Vergata” Departmento di Economia e Istituzioni

Via di Tor Vergata snc, 00133 Roma. E-Mail : becchetti@economia.uniroma2.it

and

Fabrizio Mattesini

Università di Roma “ Tor Vergata” Departmento di Economia e Istituzioni

Via di Tor Vergata snc, 00133 Roma. E-Mail: mattesini@economia.uniroma2.it

Abstract

The paper investigates the relationship between the stock market and the monetary policy of the Federal Reserve in the last twenty years. To this purpose weconstruct an Index of Stock Price Misalignment in which the fundamental value of the stocks is computed on the basis of the discounted cash flow approach and we then include this index, among the regressors, into a forward looking Taylor rule. Our findings show that the Fed reacts to deviations from fundamental values on the stock exchange by raising the Fed Funds rate.

Introduction

Central Bankers have always been aware of the potential threat to macroeconomic stability caused by speculation in the stock market. If we consider the 1920s, for example, we find widespread consensus among economic historians that the need to curb speculation in the stock market was a major determinant of the restrictive monetary policy adopted by the Federal Reserve at the eve of the Great Depression. The debate on the appropriate response to the fast increase in stock prices gave rise to bitter contention between the Federal Reserve Bank of New York which urged quantitative measures of higher discount rates and open market sales, and the Federal Reserve Board, which urged instead direct pressure on banks making securities loans. In the words of Friedman and Schwartz (1963), “the conflict was resolved in 1928 and 1929 by adoption of a monetary policy not restrictive enough to halt the bull market and yet too restrictive to foster vigorous business expansion”.

In more recent times it is quite clear, from looking at the A. Greenspan’s interventions, that the Fed has been highly concerned over the continuing increase in stock prices during the 1990’s, and that the situation of the stock market is an important factor in shaping monetary policy decisions. In the transcripts of the FOMC meeting of April 18, 1994, for example, we find the following words by Governor Greenspan: “ the sharp declines in both stock and bond prices since our last meeting, I think, have defused a significant part of the bubble which had been previously built up […] If we were to get a major contraction or implosion of the financial markets, I suspect that the economic effect s would be quite evident. Consequently, since I think there is a lesser danger in financial markets, although they are still precarious, this enables us to move somewhat faster than our previous planning presupposed.[…] Accordingly, it's my view that we should adjust the funds rate by 25 basis points today and reassess any additional moves at the May meeting.” Again, at the FOMC meeting of December 19, 1995 Governor Greenspan is reported to have said: “I am not worried about product price inflation if for no other reason than I think that the longer term is helpful. […] The real danger is that we are at the edge of a bond and stock bubble […] That is why, if we are perceived to be easing policy, it is conceivable that we could foster further problems in that regard.”

As stock prices continued their increase, Greenspan started voicing his concern in public interventions. In December 1996 he described the situation as a consequence of “irrational exuberance”. In October 1997 he said to the House of Representatives Commettee

on the Budget that stock values had reached a level “not often observed at this stage of economic expansion [...] It would clearly be unrealistic to look for a continuation of stock market gains of anything like the magnitude of those recorded in the past couple of years” and, in the following years, until prices started decreasing again, the evolution of stock prices and the effects on wealth and investment became a central theme of Greenspan’s public speeches.

The reason why policy makers are concerned about non-fundamental fluctuations in stock prices is that they may have important effects on the real economy. Although it is quite difficult to detect the direction of causality in the relationship between stock market fluctuations and business cycles, there is evidence, from the Great Depression to more recent episodes, that booms or busts in the stock market can significantly influence the level of economic activity mainly through three channels: a wealth effect on households’ consumption, a direct effect on investment and a ”balance sheet channel” (Bernanke-Gertler, 1989). According to this last channel, a decrease in asset prices reduces the net worth of firms and households and, in a world of asymmetric information, severely limits the ability to obtain credit.

Since both anecdotic evidence and economic rationale indicate that the Fed monitors very closely stock price fluctuations, an interesting question is whether it also uses monetary policy to deliberately affect them, i.e. whether interest rates are set also in response to misalignments in stock prices. One possible way to analyze this issue, that we follow in this paper, is to use a recent successful description of the Fed’s reaction function, the Taylor rule, and to include in the Fed’s policy rule also some measure of nonfundamental movements in stock prices.

The problem of measuring the reaction of the Fed to stock prices has been recently analyzed by Bernanke and Gertler (1999) and Rigobon and Sack (2001). Bernanke and Gertler estimate a forward looking Taylor rule as in Clarida, Galì and Gertler (2000) and add to the regressors (expected inflation and the output gap) the contemporaneous change in stock prices. They find that the reaction of monetary policy to changes in stock prices is negative and insignificant indicating that, in a forward looking rule, the impact of stock prices is already incorporated in the forecasts of output and inflation.

Rigobon and Sack concentrate on the identification problem that arises when one tries to measure the reaction of monetary policy to the stock market which depends on the fact that

the stock market endogenously responds to monetary policy decisions at the same time that policy is reacting to the stock market. Criticizing the standard procedure used by Bernanke Gertler, which consists of instrumenting for the change in stock prices with lags of macroeconomic variables and stock returns, they propose a simple two variable VAR model and use the heteroschedasticity of stock market returns to identify the reaction of monetary policy to the stock market. Through their model, Rigobon and Sack find that the Fed reacts significantly to stock market movements, with a 5% rise in the S&P 500 index increasing the likelihood of a 25 basis point tightening by about a half.

One common feature of both the Bernanke-Gertler and the Rigobon-Sack papers is that the stock market variable included in the Fed’s reaction function is simply the change in stock prices. Indeed, if changes in stock prices reflect changes in the underlying economic fundamentals, the Fed would have no reason to be concerned with stock price volatility per se. In this case, asset prices would be of interest only as indicators of the state of the economy. If instead asset prices are driven by nonfundamental factors, such as irrational behavior of investors (herd behavior, excessive optimism or short-termism) then they can become a source of aggregate instability and the Central Bank may want to react with appropriate monetary policy measures. Therefore, a correctly specified monetary policy rule implying that the Fed is concerned about the macroeconomic consequences of stock price movements must include some measure of the gap between actual stock prices and fundamental values.

In this paper we try to provide a more adequate specification of the Fed’s reaction function by including, among the regressors, an Index of Stock Price Misalignment, i.e. a measure of the deviation of stock prices from fundamental values. Obviously, estimating stock price misalignments is quite difficult and carries some degree of arbitrariness and indeed many economists and central bankers have questioned the ability of central banks to obtain useful estimates of fundamental values. However, we think that includingestimates of the gap between actual prices and fundamental values in the Fed’s reaction function is a useful exercise for a series of reasons. First, it is evident from the statements of Governor Greenspan that the Fed has clear opinions about stock price misalignments at it is quite plausible that these opinions are supported by empirical evaluations. Second, as we will show in the following pages, there is an interesting literature on the estimation of the fundamental value of stocks and therefore estimates of the degree of misalignment in stock prices can be

easily be obtained. As Cecchetti et al. (2000) claim, this empirical exercise is not more difficult and arbitrary than estimating the NAIRU or preparing inflation forecasts. Third, it is always important to keep in mind that a monetary policy rule is a very synthetic description of a complex decision process and that the measures we provide of the gap may actually capture a series of evaluations made by central bankers in setting monetary policy.

The paper is divided into four sections. In Section 1 we describe the methodology used to construct the Index of Stock Price Misalignment, in Section 2 we describe the properties of this Index, in Section 3 we discuss the specification of our augmented Taylo r’s rule and in Section 4 we report the main findings of our econometric analysis.

1. Measures of misalignment in stock prices

The accounting and economic literature adopt three main approaches to calculate the fundamental value of a stock: i) the comparison of balance sheet multiples (EBITDA, EBIT) for firms in the same sector; ii) the residual income method; iii) the discounted cash flow method (DCF).

The first approach has two types of problems. The first problem is due to the fact that usually market agents have non- homogeneous information sets or adopt different trading strategies, and therefore the benchmark used for comparison may be overvalued or undervalued. In this case, in the presence of a stock market bubble, the value of a stock would be assessed with respect to the overvalued or undervalued average of its sector peers. The second problem with this method is that, as far as firms diversify their activities and develop new products or services which cannot be easily classified into traditional taxonomies, industry or sector classifications become always more tricky. Industrial diversification makes it hard to assume that two firms classified into the same industry may have an identical risk profile and that their multiples may be effectively comparable (Kaplan-Roeback, 1995).

The problem with the second approach (residual income method), which is largely used in the literature (Lee-Myers- Swaminathan, 1999; Frankel- Lee, 1998), is that the formula for evaluating the fundamental value of a stock uses a balance sheet measure whose accuracy and capacity of incorporating changes in the stock fundamental value is limited.1 As shown by Lee-Myers- Swaminathan (1999), for example, the price to book ratio for the Dow Jones

1

The residual income method consists of revaluating the current book value at the discounted excess return of equity (firm expected return of equity minus the discount rate or the equityholder rate of return). By comparing

Industrial Average has risen three times between 1981 and 1996, showing a marked uptrend. This might be the consequence of the fact that accounting methodologies lag behind in adjusting to changes in investors' market value assessments of firms whose share of intangible assets made by human capital and real options is rising over time. 2

The DCF approach that we consider here following Kaplan-Roeback (1995), is based on I/B/E/S forecasts and has therefore the advantage of using only current net earnings as accounting variable. This variable is relatively less prone to measurement errors as it abstracts from the necessity to include the book value of firm assets and liabilities in our evaluation. According to the DCF model - and under the assumption that the discounted cash flow to the firm is equal to net earnings -, the "fundamental price-earning" ratio of the stock may in fact be written as: (1)

∑

[ ]

∞ = + + = 0(1 ) ) 1 ( t CAPM t t t r g E X MV

where MV is the equity market value, X is the current cash flow to the firm,3 E[gt] is the

yearly expected rate of growth of earnings4, rCAPM= R_f +βE[R_m] is the discount rate adopted

by equity investors or the expected return from an investment of comparable risk, Rf

represents the risk free rate, E[R m] the expected stock market premium, β is exposure to

systematic nondiversifiable risk. To calculate the fundamental price-earning ratio we consider the following "two stage growth” approximation of (1)

(2)

∑

= − + + + + + + = 5 1 6 ) ( 6 ) 1 )( ( ]) [ 1 ( ) 1 ( ]) [ 1 ( t CAPM TV CAPM U t CAPM t U r gn r g E X r g E X X MVE the two approaches it is evident that they are equivalent would the current book value be equal to the sum of the normal expected discounted cash flow (or the cash flow growing exactly at a rate equal to the discount rate).

2

The reason for such discrepancy between book value and market value assessment lies probably on the practice

of reporting capital losses at their hystorical value and capital gains at the market value

3

In the well known debate on the relevance/irrelevance of dividends we consider, as large part of the literature, that, under perfect information and no transaction costs, the dividend policy does not affect the value of stocks as non distributed dividends become capital gains (Miller-Modigliani, 1961). The value of equity may be equally calculated as the discounted sum of future expected dividends or as the discounted sum of future expected cash flow to the firm.

4

Actually, when estimating the model we should use the expected rate of growth of cash flow to the firm instead of the expected rate of growth of earnings. Even though earnings are obviously different from cash flow to the firm, our measure is not biased under the assumption that the expected rate of growth of earnings is not different from the expected rate of growth of cash flow to the firm.

where MVE is the "two stage growth" equity market value, E[gU] is the expected yearly rate

of growth of earnings according to the Consensus of stock analysts. 5 According to this formula the stock is assumed to exhibit excess growth in the first stage of growth and to behave like the rest of the economy in the second stage. The second stage contribution to MVE is calculated as a terminal value in the second addend of (2) where rCAPM(TV)=

] [ m

f E R

R + and gn is the perpetual nominal rate of growth of the economy.

The analytical definition of the DCF model imposes some crucial choices on at least five parameters: the risk free rate, the risk premium, the beta, the length of the first stage growth and the rate of growth in the terminal period.

For the risk free rate we use the yield on the three months US Treasury Bill.6 For the risk premium we consider that our measure should be somewhere between the historical difference in the rates of return of stocks and T-bills (between 6 and 9 percent) and the implied premium7 for US equity markets at the end of the sample period which is extremely low and around 2 percent. Both of these two extremes might be incorrect estimates of the risk premium. The former because it assumes that the long-term historical premium is equal to the current premium neglecting fundamental institutional and political changes occurred in the last decades.8 The latter because it assumes that financial markets are correct in evaluating stocks (this is not the case in presence of a bubble or of a nonzero share of noise or liquidity traders trading with arbitrageurs of limited patience).9 The recent literature proposes several alternative sophisticated measures of time varying risk premia (Jagannathan-Wang, 1996).

5

We use 1-year and 2-year ahead average earnin gs forecasts for the first two years and the long term average earning forecasts from the third to the sixth year. The use of the median estimate alternatively to the mean estimate does not change significantly our results as already found by Frankel and Lee (1998).

6

We choose a short term risk free rate to match its time lenght with the average time length of portfolio strategies which will be illustrated in sections 4 and 5. Results obtained when adopting a long term risk free rate (ten year yield on Treasury Bill) are not substantially different from those presented in this paper and are omitted for reasons of space.

7 _{To calculate the current implied premium we use the Gordon et al. (1956) formula in which value is equal to:}

expected dividends next year/(required return on stocks - expected growth rate) where the required return on stocks is the sum of the riskfree rate and the risk premium. In the light of this formula, the extremely low implicit risk premium in the sample period may be interpreted as the availability to pay higher prices for a given expected growth rate even in presence of a low dividend payout.

8

The fact that the implied risk premium is lower today than in periods (such as the sixties) with similar growth and inflation rates may depend for instance on political factors such as the end of the “cold war” which may make investors’ expectations more optimistic over long time horizons therefore reducing the risk of holding the stock.

9

If we just adopt the implied risk premium without weighting it for the historical risk premium, we would implicitly assume that no fundamental value exists or that the fundamental is just what investors believe in that period. In this way changes in the implied risk premium constantly update the fundamental value and the latter becomes just what investors are willing to pay for the stock.

These measures are extremely volatile and this is why we follow the approach of most authors using ranges of historical time invariant risk premia coupled by sensitivity analysis to discount firm fundamental values (Lee-Myers-Swaminathan, 1999; Fama-French,1997, Frankel- Lee, 1998).

The third critical factor in the "two-stage" DCF formula is the terminal value of the stock. We arbitrarily fix at the sixth year the shift from the high growth period to the stable growth period. Sensitivity analysis on this threshold shows nonetheless that this choice is not so crucial for the determination of the value of the stock.10 gn is calculated in a range between 2 and 5 percent which is consistent with values adopted in the literature.11

Finally, the literature generally proposes three alternatives for the choice of beta: the estimation of time varying firm specific or industry specific betas and a fixed unit beta.12 We adopt the first option (estimation of time varying beta in a five year window of monthly observations) which is consistent with the criterion adopted by most financial analysts. 13

2. The Index of Stock Price Misalignment

Using the approach described in (1) and (2) we have constructed the aggregate DCF fundamental of the S&P index computed as an unweighted average of the 309 stocks which remained in the S&P500 during the overall observation period (January 1980 to December 2000). The list of these stocks is provided in the Appendix A.

Figure 1 shows our index of stock price misalignment (ISPM) computed as the ratio between the observed 500S&P index and the aggregate DCF fundamental calculated by setting the risk premium at 8 percent14 and the nominal growth rate of GDP in the terminal period at 3 percent.

10

We must in fact consider that the positive impact on value of an additional year of high growth must be traded off with a heavier discount of the terminal value which represents a significant part of the final value. Information on this sensitivity analysis is available from the authors upon request.

11 _{In the terminal value it is assumed that the stock cannot grow more and cannot be riskier than the rest of the}

economy.

12

Here again we have a vaste literature on sophisticated methods for estimating time varying beta (Harvey-Siddique, 2000; Jagannathan-Wang, 1996)

13

The choice is reasonable given the size and the representativeness of Dow components and given the several potential biases arising in beta estimates (noise, dependence from time varying leverage, product mix and business cycle conditions). The choice is nonetheless confronted with that of an estimated beta in our simulations (see sections 3-5).

14

Damodaran (), for example estimates that the risk premium for the period 1926 -99 is 9.41% or 8.14% if we take respectively arithmetic averages or geometric averages of the stocks -Tbill spread. The 8 percent risk premium is broadly consistent with estimates from Kaplan and Roeback (1995) indicating a value of 7.78 percent and Ibbotson and Associates (1996) reporting a similar value for the arithmetic average of historical risk premium.

As we can see, the fundamental/observed 500S&P ratio has mean 1, is normally distributed, and exhibits a few sharp changes corresponding to:

a) the continuation of the effects of the 1979 oil shock (January -June 1980);

b) the crisis of the International Bank which manifests the weakness of the U.S. banking systems and preludes to the crisis of the S&L. At the same time there is an important change in the Fed’s operating procedures (February 1982-August 1982); c) the stock market crash of October 19, 1987, when the Dow Jones Index dropped

by 22 percent in one day;

d) the effects of the international currency crisis leading to the devaluation of the Italian Lira and of the British pound (March 1992-October 1992);

e) the Russian financial crisis (August 1998-October 1998);

f) the end of the long boom in stock prices linked to the boom of the new economy.

3.1 Specification of the model and econometric issues.

We follow Clarida Galì e Gertler (2000) by estimating an augmented forward looking Taylor rule where the Fed is assumed to react systematically to future values of the output

Index of Stock Price Misalignement

mar-99 ott-98 ott-92 mar-92 dic-87 ott-87 feb-82 ago-82 giu-80 gen-80 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 gen-80 gen-8 1 gen-82 gen-83 gen-8 4 gen-85 gen-8 6 gen-8 7 gen-88 gen-8 9 gen-90 gen-91 gen-9 2 gen-93 gen-9 4 gen-9 5 gen-96 gen-9 7 gen-98 gen-99 gen-0 0 Tempo P/F

gap, the deviation of expected inflation from its target value and our index of stock price misalignment. This rule can be expressed as

(3) r_t* =r*+β(E[π_t,kΩ_t]−π*)+γ(Ey_t,q Ω_t)+δ(P−E[P_t+1Ω_t])+ε_t

where r* is the target rate for the Federal funds’ rate in period t, πt,k denotes the percent

change in the price level between periods t and t+k, π* is the target rate of inflation, yt,q is the

average output gap between t and t+q, defined as the percent deviation between actual GDP and the corresponding target, and Pt,s is the difference between the observed and the

fundamental “average” stock market price between t and t+s. E is the expectation operator and Ωt is the information set at the time the the Federal Funds rate is set.

Defining [ , ] * * t k t t rr E

rr = − π Ω and rr* =r* −π*, equation (3) can be expressed in the terms of the real rate *

t

rr , so that

(4) rr_t* =rr* +(β −1)(E[π_t,k Ω_t]−π*)+γ(Ey_t,qΩ_t)+δ(P−E[P_t+1Ω_t])+ε_t

Let us now assume that the long run rate is constant and independent of nonmonetary factors and that the Fed Funds rate adjusts only partially to the target rate r_t*, i.e.

(5) rt =ρrt−1+(1−ρ)rt*.

In this case the forward looking Taylor rule can be rewritten as

(6) * 1 , , 1 (1 )[ ( 1) *] (1 ) ( ) (1 ) ( ) (1 ) ( ( )) . t t t q t t q t t t t r r rr E E y P E P ρ ρ β π ρ β π ρ γ ρ δ ε − + = + − − − + − Ω + − Ω + − − Ω +

As in Clarida-Gali and Gertler (2000) we replace the expectations of variables in equation (6) with actual realized values of the variables and then we use an instrumental variable technique, i.e. the Generalized Method of Moments, with an optimal weighting matrix that accounts for possible serial correlation. If we assume rational expectations, errors

will not be correlated with the instruments and we can obtain consistent estimates of the parameters of the monetary policy rule.

We use quarterly data for the period 1980:1-2000:4. The interest rate we use is the average Federal Funds rate (FEDF) in the first quarter of each month, expressed in annual rates. The baseline inflation rate is the annualized rate of change of the GDP deflator (INFDEF), but we also use an alternative measure, i.e. a rate of inflation obtained using the Consumer Price Index (INFCPI). The output gap (GDPGAP) is obtained by detrending GDP with the Hodrick-Prescott filter and computing the logarithmic differential between actual and detrended GDP. In the estimates we also use the gap between the actual and detrended unenployment rate (UGAP). The variable expressing the difference between stock market prices and stock market fundamentals is given by the Index of Stock Price Misalignment (ISPM) described above.

Equation (6) is estimated by assuming that the Federal Reserve forms its rational expectations on the output gap, inflation, and the index of stock price misalignment by using a set of indicators which include lagged values of the regressors, the Dow Jones Commodity index (DJCOMM), the difference between long term and short term interest rates (DTASSI), the rate of growth of M2 (M2GROWTH) and the lagged values of two series obtained from the NAPM surveys on new orders (NAPMORD) and on employment decisions (NAPMEMP)15. These last two instruments are introduced to widen the information set that we assume is available to the monetary authorities. The NAPM surveys, in fact, are a very early indicator of the situation of the real economy and therefore are widely used by financial market analysts and policymakers in formulating their expectations.

3.2 The evidence

Tables 1 and 2 present descriptive statistics and correlations among the variables selected for this study. Looking at table 1 we immediately notice that the mean of our Index of Stock Price Misalignment is close to 1. The correlation matrix reported in table 2 indicates that output, inflation and stock market misalignment regressors are not highly correlated among themselves and that there is not a significant multicollinearity problem among the

15

The NAPM survey is based on a sample of over 250 purchasing executives from 21 manufacturing industries, weighted according to each indstry’s contirbution to national income and diversified geographically according to vale added by the state (Dasgupta-Lahiri, 1992). The Survey indicates the shares of executives reporting an increase, decrease or stability of orders. Our index is a weighted average of these shares and, specifically, the difference betweeen the percentage of those reporting an increase minus those reporting a decrease (Theil, 1952).

regressors. The correlation between ISPM and the output gap (GDPGAP) is quite high (0.469) but not high enough to create serious problems to the estimates.

In table 3 we report the estimates of our augmented Taylor rule. In the first column we report our baseline regression, which is a simple a Taylor rule as in CGG. The only difference between this equation and the one estimated by CGG is the inclusion, among the instruments, of NAPMORD and NAPMEMP. As we can see comparing the first column to the second column of table 3 where we report a Taylor rule without these two instruments, including these two instruments improves the specification of the model raising the p value of the Sargan test from 0.97 to 0.99. In line with the literature, the response of the Federal Funds rate to inflation is greater than one, while the response to the output gap is less than one, indicating that the Fed, under the Volcker-Greenspan tenure, was willing to raise real rates in order to stabilize inflation.

In column 3 of table 3 we include, among the regressors of our baseline estimate, our Index of Stock Price Misalignment, using the same set of instruments, plus four lags of ISPM. As we can see, the variable enters significantly in the regression and has a positive sign, indicating that the Fed reacts to an increase in the stock market index relative to its fundamental by raising the Fed Funds rate. It is important to notice that the introduction of the ISPM does not alter the nature of the Taylor rule. The coefficient of the rate of inflation, although smaller, remains significantly greater than one and the coefficient of the output gap remains smaller than one. The introduction of the ISPM also raises the R2 of the regression from 0.91 to 0.94.

In columns 4, 5, 6 and 7 we perform some robustness analysis, by changing some of the variables of the model. In column 4 we keep all the variables of the baseline estimate but we include an alternative measure of inflation, i.e. one based on the Consumer Price Index (INFCPI). In column 5, instead of the output gap, we consider the unemployment gap (UGAP) while the inflation measure is the one based on the GDP deflator. In column 6 we report an estimate where both INFCPI and UGAP are included among the regressors. Finally, in column 7 we include, in our baseline regression, a different measure of the gap, which was obtained by setting the risk premium at 6 percent and the nominal growth rate of GDP in the terminal period at 5.

As we can see, in all these regressions the Index of Stock Price Misalignment enters positively and significantly among the explanatory variables. In all these augmented Taylor

rules the coefficient of inflation is greater than one, while the coefficient of the output or employment gap are less than one. It is important to notice that all the estimates presented in Table 3 pass the Sargan test for overidentifying restrictions that can be applied in a GMM estimate when the number of instruments is higher than the number of regressors. It is also important to notice that, by defining the long run real rate as the average real interest rate over the period, we are also able to compute, as in Clarida, Gertler and Gilichrist (2000) the target rate of inflation π*

which, for almost all regressions lies into reasonable ranges.

In this work, the way we deal with endogeneity of the ISPM is to instrument the Fed Funds rate in order to remove the possible correlation between the Fed Funds rate and our Index of Stock price Misalignment. Since, as argued by Rigobon and Sack (2001), there might be doubts about the effectiveness of this procedure, we performed some Granger causality tests to check for strong exogeneity. As expected, these tests show that the ISPM could be considered exogenous with respect to the Fed Funds rate.16 This is not surprising if we consider that, while there are good reasons to believe that asset prices incorporate expectations about the interest rates set by the monetary authority, it is less clear whether the gap between stock prices and fundamental values is dependent on the Fed Funds rate.

Conclusions

The increasing awareness of the links between the stock exchange and real economy has led many pratictioners, academicians and commentators to argue that the under/overevaluation of the stock market, with its effects on consumers’ confidence and inflation is a concern for the Federal reserve in addition to inflation and output stabilization. So far, this proposition has been tested empirically simply by augmenting a Taylor rule with changes in stock prices.

In this paper we argue that this variable is not the right one, if we want to analyze the Fed’s reaction to the stock market and we propose an interpretation of the Fed’s monetary policy for the period 1980 to the end of 2000, by estimating an augmented Taylor rule where the Fed is assumed to react not only to inflation and deviations of output from the long run trend, but also to deviations of stock market prices from their long run value as indicated by an Index of Stock Price Misalignment constructed on the basis of the S&P500 Index. The

fundamental value of the stocks was computed with the discounted cash flow method applied to the I/B/E/S forecasts.

In accordance with descriptive evidence, which shows the Fed’s Chairman has been particularly concerned over the developments of the stock market, the estimates we obtain suggest that the Federal Reserve, in the period analyzed, has changed the Fed Funds rate also in response to deviations of stock prices from their fundamental values.

This finding raises interesting questions, which however have not been addressed in this paper, over the appropriate response of monetary policy to asset price fluctuations, especially when they are not justified by movements in the underlying fundamental. We indeed believe that our finding should lead to a deeper investigation and understanding of the relationships between business cycle predictors, stock market misalignment and the business cycle itself which may be particularly useful in measuring and evaluating the complex interaction between financial markets and the economy.

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Table 1 Descriptive statistics on variables used in the econometric analysis FEDF GDPGAP INFDEF1 GAPSP INFCPI UGAP

Mean 7.388 -0.131 3.359 _1.057 4.202 0.691 Median 6.430 0.013 2.871 1.066 3.349 1.855 Maximum 17.780 2.216 11.054 _1.322 14.406 20.023 Minimum 2.990 -4.803 0.977 _0.654 1.284 -23.548 Std. Dev. 3.401 1.326 2.173 _0.127 2.801 8.606 Skewness 1.275 -1.283 1.842 _-0.330 2.181 -0.626 Kurtosis 4.362 5.494 6.204 _3.082 7.388 3.237 Jarque -Bera 30.30306 45.89129 85.4007 _4.652 138.7652 5.818632 Probability 0 0 0 _0.098 0 0.054513 Observations 87 86 86 _252.000 87 86 NAPMEM PL NAPMOR D M2GROW TH DJCOMM DTASSI Mean -7.024 7.443 1.480 131.679 1.822 Median -5.500 8.000 1.384 128.080 1.930 Maximum 13.000 40.000 4.869 209.510 4.250 Minimum -40.000 -53.000 -0.544 105.940 -2.360 Std. Dev. 11.909 17.134 0.888 16.876 1.420 Skewness -0.829 -0.640 0.491 1.646 -0.986 Kurtosis 3.233 3.701 4.311 7.650 4.365 Jarque -Bera 9.809265 7.446619 9.608452 117.644 19.65929 Probability 0.007412 0.024154 0.008195 0 0.000054 Observations 84 84 86 87 82

Variable legend: FEDF: federal fund rate; GAPSP: gap between the observed and fundamental S&P500 index (risk premium 8 percent and rate of growth in the terminal period 3 percent); INFDEF1: GDP deflator; UGAP: difference between US rate of unemployment and its Hodrick-Prescott trend; GDPGAP difference between US GDP and its linear time trend; NAPMEMPL: NAPM manufacturers survey results - employment; NAPMORD: NAPM manufacturers survey results – orders; INFCPI: rate of change of the Consumer Price Index .

Table 2 Correlation matrix for variables used in the econometric analysis

FEDF GAPSPPC GDPGAP INFDEF INFCPI UGAP DJCOMM DTASSI NAPMEMPL NAPMORD M2GROWTH

FEDF 1 -0.016 0.059 0.827 0.803 0.310 0.478 -0.703 -0.233 -0.374 0.461 ISPM -0.016 1 0.469 -0.130 -0.113 0.462 0.081 -0.453 0.406 0.144 -0.106 GDPGAP 0.059 0.469 1 0.042 0.081 0.859 0.178 -0.288 0.380 0.024 -0.216 INFDEF 0.827 -0.130 0.042 1 0.936 0.239 0.557 -0.599 -0.234 -0.322 0.257 INFCPI 0.803 -0.113 0.081 0.936 1 0.293 0.600 -0.620 -0.294 -0.444 0.211 UGAP 0.310 0.462 0.859 0.239 0.293 1 0.396 -0.525 0.269 -0.156 -0.067 DJCOMM 0.478 0.081 0.178 0.557 0.600 0.396 1 -0.590 0.162 -0.103 0.084 DTASSI -0.703 -0.453 -0.288 -0.599 -0.620 -0.525 -0.590 1 0.034 0.393 -0.308 NAPMEMP -0.233 0.406 0.380 -0.234 -0.294 0.269 0.162 0.034 1 0.729 -0.174 NAPMORD -0.374 0.144 0.024 -0.322 -0.444 -0.156 -0.103 0.393 0.729 1 -0.134 M2GROWTH 0.461 -0.106 -0.216 0.257 0.211 -0.067 0.084 -0.308 -0.174 -0.134 1

Table 3. Augmented Taylor’s rule estimate. (GMM estimates, quarterly data from January 1980 to December 2000, t values in parethesis)

(1) (2) (3) (4) (5) (6) (7) C 0,63 0,80 0,61 0,21 0,89 0,02 0,61 (10.24) (7.00) (8.91) (4.23) (12.13) (0.53) (8.91) FEDF(-1) 0,72 0,70 0,77 0,84 0,67 0,80 0,77 (54.18) (28.13) (47.63) (61.36) (40.14) (75.58) (47.63) GDPGAP 0,66 0,62 0,42 1,23 0,42 (6.64) (5.08) (4.06) (11.15) (4.06) UGAP 0,003 0,12 (0,04) 6,20 INFDEF 1,57 1.50 1.33 1,35 1,33 (18.62) (13.14) (13.40) (23.10) (13.40) INFCPI 1,35 1,44 (11.15) (23.26) ISPM 0,06 0,08 0,04 0,09 (6.05) (7.51) (5.00) (8.73) ISPM65 0,06 (6.05) INDSP π∗ 2,72 4,26 3,83 1,62 3,26 0,11 3,83 Sargan p-test 0,99 0,97 0,99 0,99 0,99 0,99 0,99 R^2 0,91 0,91 0,94 0,95 0,93 0,94 0,94 Instruments FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFDEF(-1 TO -4) C GDPGAP(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 TO -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFDEF(-1 TO -4) C GDPGAP(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFDEF(-1 TO -4) C GDPGAP(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 to -4) ISPM(-1 to -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFCPI(-1 TO -4) C GDPGAP(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) ISPM(-1 to -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 TO -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFDEF(-1 TO -4) C UGAP(-1 TO -4) ISPM(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 TO -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFCPI(-1 TO -4) C UGAP(-1 TO -4) ISPM(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 TO -4) FEDF(-1 TO -4) DJCOMM(-1 TO -4) INFDEF(-1 TO -4) C GDPGAP(-1 TO -4) ISPM65(-1 TO -4) DTASSI(-1 TO -4) M2GROW TH(1 TO -4) NAPMOR D(-1 TO -4) NAPMEMP (-1 TO -4) N° obs 79 79 79 79 79 79 79