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Study On Monetary Policy And Stock Market

This paper critically analyzes the relationship between monetary policy and the stock market. It looks into the existing literature on the subject and tries to investigate the various issues raised. The issues analyzed and investigated in this paper include: the effect of stock price volatility on monetary policy decisions, the effect of monetary policy decisions on stock price volatility and the direction of causality between the two. We look into both components of monetary policy: Federal funds rate and Money supply and their individual relationships with monetary policy. We use the augmented Taylor rule, Generalized Method of Moments test, simple OLS regression and the pairwise Granger causality test.

INTRODUCTION

Monetary policy is the regulation of the interest rate and money supply of a country by its Central Bank or Federal Reserve in order to achieve the major economic goals which include price stability, full employment, economic growth etc. The stock market on the other hand is often considered a primary indicator of a country’s economic strength and development. History has shown that the economy of any country reacts strongly to movements in stock prices. Recent happenings even confirm this as the latest economic recession was preceded by a crash in the stock market.

As a result of the relationship between the stock market and the economy, it is very important to the Central bank that the stock market performs well as bad performance can seriously disrupt the economy. This is because the stock market serves as a primary source of income and retirement savings to many and movements in the stock can have a major effect on the economy as it influences real activities such as consumption, investments, savings etc The monetary authorities closely monitor the stock market and make monetary policy decisions based on stock market volatility in order to maintain macroeconomic balance. This paper studies the relationship between both components of monetary policy and stock market volatility using an augmented Taylor rule and simple OLS regressions.

The main aim of this paper is to find out if Central banks react directly to asset prices or if they react to asset prices only when they help target inflation. Although most economist believe that policy makers react to stock prices when making decisions concerning the federal funds rates, some other economists argue that stock prices also react to monetary policy decisions. To this effect, we also test for reverse causality between both components of monetary policy and stock market volatility.

In section II, a thorough review of the relevant literature of the topic is carried out. In the next section, we described the variables and data set used in the study. The research methodology is developed in the next section with the models and statistical hypotheses stated. Analysis and interpretation of data is carried out in the next section. We conclude the paper in section V, suggestions for further studies are pointed out and policy implications are also considered.

2. REVIEW OF RELEVANT LITERATURE

Monetary policy is one of the most effective tools a Central Bank has at its disposal (Maskay, 2007) and is used to achieve the macroeconomic goals set by the government. This is done by regulating the two components of monetary policy which are interest rates and money supply to maintain balance in the economy. The stock market is an important indicator of the wellbeing of the economy as stock prices reflect whether the economy is doing well or not. Movements in stock prices have a significant impact on macroeconomics and are therefore likely to be an important factor in the determination of monetary policy (Rigobon and Sack, 2001). The relationship between monetary policy and the stock market is best analyzed by studying the effects of stock market volatility on both interest rates and money supply.

The Effect of Stock Price Volatility on Monetary Policy Decisions.

Some economists( e.g Bernanke and Gertler (2001), Gilchrist and Leahy (2002), Gertler (2008) Cogley (2009) etc) believe that the Central Bank should be mainly concerned about maintaining price stability and that there is no point responding to stock market volatility if they don’t help target inflation. Most of their arguments are based on high stock price volatility; almost unidentifiable misalignments of stock prices and destabilizing effects of systemically reacting to stock prices. One of the reasons for Bernanke and Gertler’s argument was that asset prices are too volatile and when used in determining monetary policy can cause unpredictable effects on market psychology and macroeconomic instability. They also argued that “aggressive inflation-targeting rule stabilizes output and inflation when asset prices are volatile irrespective of the cause of volatility; and that there is no significant extra benefit to responding to asset prices.” Bernanke and Gertler (2001) also argue that all macroeconomic shocks are not as a result of stock market volatility, therefore there is no reason why the stock market should be singled out in making monetary policy decisions. They also argued that although stock volatility might play a role in shock transmission, the advantage of using stock volatility in making monetary policy decisions is quite insignificant. They also believed that bubbles usually amplify inflation and output; central bank policies that aim to stabilize prices and output may have an indirect stabilizing effect on stock prices and inflation and output can therefore stand in for stock prices. This further supports Gertler (2008). Another economist who was in support of this argument was Cogley (2009). He believed it is very difficult to detect asset price misalignments and that any mistake made in this regard may add distort the output. In their study, Gilchrist and Leahy (2002) came to the conclusion that although there are a few good hypothetical reasons for including stock prices in monetary policy decisions, in practice its effect in stabilizing output and inflation is minute. Furher and Moore (1992), Woodford (1994) and Smets(1997) are also in support of the inflation targeting monetary policy rules.

On the other hand, Cecchetti et al ( 2000) argue that “a central bank concerned in stabilizing inflation about a specific target level is likely to achieve superior performance by adjusting its policy instruments not only in response to its forecast of future inflation and the output gap, but to asset prices as well”. They believed that reacting to stock price misalignments in the normal course of policy making will reduce the possibility of stock price occurrence in the first place as this would have been prevented by monetary policy rules. Cecchetti et al (2000) claim the difference between their findings and that of Bernanke and Gertler (1999) is because they (Cechetti et al) investigate a wider range of possible policies. They also proposed that if Central Banks react to stock volatility in a symmetric and transparent manner, it might help to reduce market perceptions of irregularities and that neglect of stock prices by the central bank might destabilize the economy. They do not however propose that Central banks should attempt to burst already existing bubbles as this can lead to economic recession as seen in the case of Japan in the 1980’s but Central banks should aim to prevent bubbles and this can only be done by including stock prices in the monetary policy rule.

Alchian and Klein (1973) argued that the Central bank should be mainly concerned with maintaining the purchasing power of money which includes both current and future consumption.According to Cecchetti et al (2000), “since stock prices refer to future consumption, they should be included alongside the consumer price index as the target variable of the Central Bank”. Cecchetti et al (2000) buttress their point that the central banks should and can react to stock market volatility without targeting inflation with the notion that equity prices contain too much noise to be useful in inflation measurement. There is therefore no point in reacting to stock prices based on their effect on the central banks effect on inflation. They also carry out an out-of-sample forecast using the Goodhart-Hofmann (2000) data and they find that stock prices provide valuable information about future inflation in a number of countries and time periods. Based on these findings, Cecchetti et al (2000) assert that Central banks have an incentive to forecast asset prices on their own and that macroeconomic performance can be enhanced by the reaction of the Central banks to stock prices over and above their reaction to inflation forecasts and output gaps.

Lansing (2003) also opposes the advocates of inflation-targeting. He argued that bubbles alter economic and financial decisions and can be have a very costly effect on the economy. A good example is the purchase of expensive high technology IT services at the expense of other items during the boom of which more than half are currently either under utilized or not in use at all as a result of the economic recession. It could take years to dispel these expensive imbalances. Bubbles also affect employment as was very evident in the last stock market bubble. Firms hired employees in large numbers to satisfy the unsustainable demand growth at the time. When the bubble burst, there was a drop in the demand growth and a lot of people lost their jobs. Bubbles also affect the foreign exchange markets (Lansing, 2003) as the enthusiasm of foreign investors to participate in booming stock exchanges of developing countries hiked the value of foreign currencies contributing to an increase in the account deficits of most developed countries.

The Effect of Monetary Policy on the Stock Market.

According to some other economists (Jensen, Mercer and Johnson (1996), Thorbecke (1997), Jensen and Mercer (2002) and Rigobon and Sack (2002)), stock prices react to monetary policy decisions. This has led the researcher to question the direction of causality between monetary policy and the stock market. There is a large strand of literature puzzling on the reaction of stock prices to monetary policy and also on the direction of causality.

Stocks are claims on real assets and researchers have found considerable evidence that monetary policy can affect real stock prices in the short run (e.g. Bernanke and Kuttner, 2005). According to Bjornland and Leitemo (2009), “since stock prices are determined in a forward-looking manner, monetary policy, and in particular surprise policy moves, is likely to influence stock prices through the interest rate (discount) channel and indirectly through its influence on the determinants of dividends and the stock return premium by influencing the degree of uncertainty faced by agents”. The central bank regulates the economy by either increasing or decreasing the federal fund rates for contractionary and expansionary purposes respectively.

In the study of the relationship between monetary policy and the stock market, it is very important to understand the monetary policy transmission mechanism. This mechanism is the process through which monetary policy decisions flows into the economy and the individual links through which these decisions flow are called transmission channels. The four main transmissions channels are: interest rate, credit, exchange rate and wealth. Changes in monetary policy are transmitted through the stock market via changes in the values of private portfolios (wealth effect) and changes in the cost of capital (Bernanke and Kuttner,2005). Erhmann and Fratzscher (2004) laid emphasis on the credit channel of monetary policy transmission. They believed that when a credit channel is at work for firms that are quoted on stock markets, their stock prices respond heterogeneously to monetary policy as prices of firms that are subject to relatively larger informational asymmetries would react more strongly. For instance, when there is a tightening of monetary policy they will find it harder to access funds therefore their expected future earnings is affected more than firms that are less subject to information asymmetries. A tightening of monetary policy also has a stronger impact on firms that depend highly on bank loans for financing as banks reduce their overall supply of credit (Binder, 1992 and Kashyap, Stein and Wilcox, 1993). Also, banks tend to reduce credit lines first to the customers whom they have the least information about thereby making it more difficult for these firms with little or no publicly available information to access bank loans (Gertler and Hubbard 1988, Gertler and Glichrist 1994). Deteriorating credit market conditions also affect firms by weakening their balance sheets as the present value of collateral falls with rising interest rates ( and Gertler 1989, Kiyotaki and Moore 1997). Some studies e.g. Thorbecke (1997) and Perez-Quiros and Timmerman (2000) have shown that the response of stock returns to monetary policy is smaller for larger firms.

The fact that the market responds to unanticipated policy actions and not anticipated ones makes the study of the effect of monetary policy actions on equity prices more complicated (Bernanke and Kuttner, 2005). To solve this problem, Kuttner (2001) came up with a technique that uses federal funds futures data to measure surprises in interest rate changes. This technique achieves the aim of distinguishing between expected and unexpected monetary policy decisions in order to discern their effects. In their work, Jensen, Mercer and Johnson ( 1996), Thorbecke (1997), Jensen and Mercer ( 2002) and Rigobon and Sack ( 2002) also looked at the effect of monetary policy on the stock market using futures data using Vector Auto Regressions (VAR). Results have also shown that positive surprises tend to have a larger effect on volatility of stock prices than negative surprises (Bomfin, 2000) therefore when interest rates are lower than expected, there will be a higher percentage increase in stock prices than the percentage decrease in asset prices as a result of higher than expected interest rates. This is also in line with research on leverage-feedback hypothesis by Black (1976) and volatility-feedback hypothesis by French, Schwert and Stanbaugh (1987).

Money supply and the Stock Market.

Here we look at the existing literature on money supply and the stock market. Maskay (2007) analyzes the relationship between money supply and stock prices. His findings support that of the real activity theorists who believe that there is a positive relationship between money supply and stock prices and dispute that of the Keynesian activists who argue otherwise. He also separates money supply into anticipated and unanticipated components and adds consumer confidence, real GDP and unemployment rate as control variables. The result from his analysis shows that there is a positive relationship between changes in the money supply and the stock prices thereby supporting the real activity the theorists who argued that a change in money supply provides information on money demand, which is caused by future output expectations. An increase in money supply shows that there has been an increase in the demand for money and this in effect indicates an increase in economic activity. Selin (2001) argued that higher cash flows are the result of increased economic activity which subsequently leads to a rise in stock prices. The result from his analysis on the effect of anticipated and unanticipated change in the money supply on stock market prices shows that anticipated changes in money supply matters more than unanticipated changes. This supports the critics of the efficient market hypothesis. Economists argue that based on the efficient market hypothesis, popularly known as Random Walk Theory, anticipated changes in money supply would not affect stock prices and only the unanticipated component of a change in money supply would affect the stock market prices. Opponents of efficient market hypothesis on the other hand argue that the stock prices do not reflect all the available information and hence stock prices can also be affected by anticipated changes in money supply (Corrado and Jordan, 2005).

Some economists, (Sprinkle (1964), Homa and Jaffee (1971), Hamburger and Kochin (1972)) in the early 1970,s alleged that past data on money supply could be used to predict future stock returns. These finding where not in line with the efficient market hypothesis (Fama, 1970) meaning that anticipated information should not have any effect on current stock prices. While advocates of the efficient market hypothesis (Benanke and Kuttner (2005) etc) hold that all available information is included in the price of a stock, the opponents argue otherwise and that stock prices can also be affected by unanticipated changes in money (Hussain and Mahmood (1999), Corrado and Jordan (2005) etc). The effect of anticipated and unanticipated changes in money supply on stock prices was also analyzed by Sorensen (1982) who found out that unanticipated changes in money supply have a larger impact on the stock market than anticipated changes. Bernanke and Kuttner (2005) on the other hand analyze the impact of announced and unannounced changes in the federal funds rate and find that the stock market reacts more to unannounced changes than to announced changes in the federal funds rate which is also in line with the efficient market hypothesis. Studies by Husain and Mahmood (1999) have opposing results. They analyze the relationship between the money supply and changes in stock market prices and find that changes in money supply causes changes in stock prices both in the short run and long run implying that the efficient market hypothesis does not always hold.

In summary, we have seen from the extensive literature review that there is indeed a relationship between both components of monetary policy and the stock market. We notice however that while some economists argue that monetary policy rules should target only inflation, some others argue that they should target stock prices over and above inflation. We also notice that some economists believe the direction of causality goes from stock prices to monetary while some other economists believe it’s the other way round. All these issues will be analyzed using simple OLS methods and the Pairwise Granger Causality test.

RESEARCH QUESTIONS

Following from the theory and review of relevant literature, this paper is aimed at answering the following questions;

Does stock market volatility affect the federal funds rate component of monetary policy?

Does stock market volatility affect the money supply component of monetary policy?

Is the direction of causality between stock market volatility and monetary policy correct?

RESEARCH METHODOLOGY

The Taylor Rule.

In this section, we test for the relationship between monetary policy and stock prices using the Taylor rule.Ir stipulates how much the Central Bank should change the nominal interest rate in response to the divergence of actual inflation rates from target inflation rates and of actual GDP from potential GDP.

The rule is written as;

Ffrt = r*t + β (π t– π*t) +γ (yt – ŷt) + εt……………………………… (1)

Where it is the target short-term nominal interest rate, r*t is the assumed real equilibrium interest rate, πt is the observed rate of inflation, π*t is the desired rate of inflation, yt is the logarithm of real GDP, ŷt is potential output and εt is the error term. If β is statistically significant it means that inflation has an effect on the federal funds rate and vice versa

As suggested by Taylor (1993), a good conduct of monetary policy should have both β = 0.5 and α=0.5.This will be tested using the Wald-coefficient restrictions test. .

However, to track how monetary policy behaved the following regression equation is estimated;

Ffrt = α + βEt(π t+i– π*t+i) +γEt (yt+i -ŷt+i)+εt ………………………(2)

Where Et(π t+i– π*t+i) is the expected Inflation , Et (yt+i - ŷt+i) is the expected gap and Et is the expected value conditional to information available at the time. If β is statistically significant, we also accept that expected inflation has an effect on the federal funds rate.

The Augmented Taylor Rule;

To test if the monetary authorities react to stock market volatility, we use the following equation where we add lagged values of stock prices (Ѕt-k) to the Taylor rule, augmented to allow for partial adjustment (Clarida et al, 1998);

Ffrt = α + βEt(π t+i– π*t+i) +γEt (yt+i - ŷt+i)+∑δkЅt-k + εt …………………(3)

We test the following hypothesis:

H0: δ = 0

H1: δ ≠ 0

Generalized Method of Moments (GMM) Estimation.

We carry out this test as we would like to find out if stock price volatility has a direct impact on monetary policy or if stock price volatility only affects the decision of monetary authorities only when they help forecast target variables like the output gap and inflation. We do this by estimating the augmented Taylor rule by GMM equation using instrumental variables.

Model:

Ffrt = α + βEt(π t+i– π*t+i) +γEt(yt+i - ŷt+i)+∑δkЅt-k + εt …………………(3i)

Statistical Hypothesis:

H0: δ = 0

H1: Not H0

If δ = 0 (statistically), it means that the stock market indirectly affects monetary policy decisions but if it not, it means it has a direct effect on monetary policy.

The effect of money supply on stock market prices.

In this section, we analyze the relationship between money supply and the stock market by testing if monetary authorities react to stock price volatility by adjusting quantity of money supplied. We use the M2 component of money supply for this purpose because it is a broad classification of money which economists use to quantify the amount of money in circulation and to explain different monetary condition.

The equation is written as:

M2 = α + β*S1 +γ*RGDP + δ*U + εt ………………………………… (4)

Where S is the change in asset prices, α is the intercept, M2 is the percentage change in money supply, G is real GDP and U is the percentage rate of change of money supply.

Statistical Hypothesis:

H0: Stock market volatility does not affect change in money supply.

β = 0

H1: Not H0.

β ≠ 0

The Real GDP and the yearly percentage change in the rate of unemployment are added as control variables.

We add the Real GDP because it is an important determinant of the stock prices as most industries react to changes in the economy and perform well when the economy is doing well and vice versa. Unemployment rate is added to the model because it is one of the major factors that determine the demand for stocks. High unemployment rates lead to lower demand for stocks and vice versa.

Pairwise Granger Causality Test.

Granger Causality measures whether A happens before B and helps predict B (Lion, 2005). In our analysis, we test for reverse causality between monetary policy and the stock market using interest rate (Ffr01) and change in money supply (M2) to represent monetary policy, and S&P500 (St-k) to represent the stock market. This is done using the pairwise granger causality test. We add lags to the two different models until they become significant.

Granger Model 1;

Ffrt = a+ bS1………………………………………………… (5)

S1 = c+ dFfr01 …………………………………………… (6)

Statistical Hypothesis;

H0: S1 does not granger cause Ffr01.

H1: not H0.

2.) H0: Ffr01 does not granger cause S1.

H1: not H0.

Granger Model 2;

M2 = a + bS1

S1 = c + dM2

Statistical Hypothesis;

H0: S1 does not granger cause M2.

H1: not H0.

H0: M2 does not granger cause S1.

H1: not H0.

DATA DESCRIPTION

In this section, we define and describe the various data used in this study. We used quarterly data from 1990 to 2009. The variables used in this analysis include;

The Federal Funds Rate;

It is a monetary policy tool used by Central Banks reserve of the country to regulate the economy. It is increased when there is too much money in circulation and this causes a downward movement in stock prices and vice versa.

The mean and median values of the distribution are very close with the median higher which shows that more than half the values of our data are higher than average. The difference between the maximum and minimum values is quite large hence the large standard deviation from the mean. The skewness statistic which is less than 1 show that the distribution is non-symmetric and is negative because the lower tail of the distribution is thicker than the upper tail. The kurtosis statistic is less than 3(normal distribution of K) implying that the tails of the distribution are not as thick as the normal. All these are pointers that the data is normally distributed and the Jarque-Bera statistic which is less than the critical value of the χ2 distribution (5.99) at the 5% level leads us to accept that the data distribution is normal.

The Consumer Price Index;

A consumer price index (CPI) is an index that estimates the average price of consumer goods and services purchased by households. It is used in our study to calculate inflation and has an inverse relationship with monetary policy.

We can see from the table below that the data is quite normal as the mean and median are very close. The median is less than the mean implying half the values are less than average. The difference between the maximum and minimum is quite wide hence the large standard deviation from the mean. The skewness statistic which is less than 1 show that the data is non-symmetric and is positive because the upper tail of the distribution is thicker than the lower tail. The kurtosis statistic shows that the tails are not as thick as normal. We accept that the data is normally distributed because the Jarque-Bera statistic is less than the critical value of the χ2 distribution (5.99) at the 5% level.

Real GDP:

This reflects the value of all goods and services produced in a given year, expressed in base year prices.

The mean and median values of the data are very close with the median larger than the mean which implies that half the values are higher than the average real gdp. The large difference between the maximum and minimum values of real gdp accounts for the large standard deviation from the mean. The skewness statistic which is less than 1 shows that the data for real GDP is non-symmetric and it is negative because the lower tail is thicker than the upper tail of the distribution. The kurtosis statistic which is less than the normal shows that the tails are not as thick as normal. We reject the null hypothesis that the distribution is normal because the Jarque-Bera statistic is above the critical value of the χ2 distribution (5.99) at the 5% level of significance.

S&P 500;

It is a capital weighted index of the prices of 500 large-cap common stocks actively traded in the United States. It has an inverse relationship with monetary policy as an expansionary (interest rate reduction) monetary policy leads to an upward movement of the s&p500 index.

The mean and median for the data on S&P500 are quite close with the median higher than the mean. This shows that more than half of the values of the data are above the average value. There is a very wide difference between the maximum and minimum values which accounts for the large standard deviation from the mean. The sleekness statistic of the S&P500 is less than 1 which signifies that the distribution is non-symmetric and is negative because the lower tail is thicker than the upper tail. The kurtosis statistic implies that the tails of the distribution are not as thick as the normal. The Jarque-Bera statistic which is greater than the critical value of the χ2 distribution (5.99) at the 5% level of significance leads us to reject that the distribution is normal.

Unemployment Rate;

We use this as a control variable because lower the unemployment rate, the higher the aggregate demand for stock thereby pushing up stock prices. We got the quarterly data by finding quarterly averages from the monthly data provided.

The mean and median of the data on unemployment rate are very close but the median is less than the mean which shows that half of the values are less than the average. The difference between the maximum and the minimum values accounts for the large standard deviation around the mean. The skewness statistic is slightly above 1 implying the data is almost symmetrical and it is positive because the upper tail of the distribution is thicker than the lower tail. The kurtosis statistic (above 3) implies that the tails are thicker than normal. We reject that this distribution is normal because the Jarque-Bera statistic is larger than the critical value of the χ2 distribution at both the 5% and 10% levels of significance.

Money Supply represented by M2;

We use the M2 component of money supply because it is a broader classification of money than M1 and most economists use it when looking to quantify the amount of money in circulation and in trying to explain different economic monetary conditions.

The mean and median for the data on change in money supply (M2) are quite close with the median greater than the mean. This shows that half of the distribution is greater than the average value . There is a big difference between the maximum and minimum values which explains the large standard deviation of the values from the mean. The skewness statistic which is less than 1 implies that the distribution is not symmetric and the negative value implies that the lower tail is thicker than the upper tail of the distribution. The kurtosis statistic is less than 3 which implies that the tails are not as thick as normal. The Jarque-Bera statistic is less than the critical value of the χ2 distribution (5.99) at the 5% level of significance so we accept that the data is normal.

DATA ANALYSIS AND INTERPRETATION

We start our data analysis by estimating the first equation under the Taylor rule;

Ffrt = r*t + β (π t– π*t) +γ (yt – ŷt) + εt……….. (1)

Dependent Variable: FFR01 Method: Least Sqares

Included observations: 76 (after adjustments) R 2 : 0.371356

Variable

Coefficient

Standard Error

T statistic

Probability

C

2.871601

0.455967

6.297821

0.0000

Inflation

0.399264

0.161730

2.468702

0.0159

Gap

0.684359

0.167876

4.076580

0.0001

Table 1.

From the results in table 1 above, we see that the intercept which is the estimated stabilizing rate of interest and the coefficients associated to both inflation and output gap are all positive and statistically significant at the 5% significance level. We therefore accept that Inflation has an effect on monetary policy. An R2 of 0.37 means that we are only able to explain about 37% if the variability in the federal funds rate.

We also run the Wald-coefficient restriction test to determine if β=γ=0.5 and from the results on table 2 below, we see that the p-values are statistically insignificant therefore we accept that β=γ=0.5.

F. Statistic

Chi Square

Values

0.60739

1.214759

Probability

0.547506

0.544777

Table 2.

To analyze the behavior of monetary policy, we go on to estimate the second equation of model 1;

ffrt = α + βEt(π t+i– π*t+i) +γEt (yt+i – ŷt+i)+εt

The results are as follows;

Dependent Variable: FFR01 Method: Least Sqares

Included observations: 74(after adjustments) R 2 : 0.395169

Variable

Coefficient

Standard Error

T statistic

Probability

C

3.161365

0.470575

6.718087

0.0000

EXPINFLATION

0.294358

0.178154

1.652263

0.1029

EXPGAP

0.882778

0.198817

4.440160

0.0000

Table 3.

The intercept which is the stabilizing rate of interest is positive and is statistically significant at the 5% level of significance. The coefficient associated with expected inflation is positive and statistically insignificant at the 5% and 10% levels of significance while the coefficient associated with the expected output gap is positive and statistically significant at the 5% level of significance. An R2 of 0.40 means that we are only able to explain 40% of the variability in the federal funds rate. Here we also accept that expected inflation has an effect on monetary policy.

We also run a Wald-coefficient restriction test and we accept that β=γ=0.5 because the p-values from the results below are greater than 0.05.

F. Statistic

Chi Square

Stat

1.854706

3.709412

Probability

0.164001

0.156499

Table 4.

Next, we estimate the augmented Taylor rule using stock prices to determine if they have a direct or indirect impact on monetary policy;

ffrt = α + βEt(π t+i– π*t+i) +γEt (yt+i+ ŷt+i)+δkЅt-k + εt

Here we add the variable S1 to represent change in asset prices and the coefficient should be significant, we add lags until the coefficient, δ, becomes statistically insignificant.

One Lag;

Dependent Variable: FFR01 Method: Least Sqares

Included observations: 74(after adjustments) R 2 : 0.582783 Durbin Watson Stat: 0.42281

Variable

Coefficient

Standard Error

T statistic

Probability

C

2.958203

0.395279

7.483843

0.0000

EXPINFLATION

0.245547

0.149273

1.644958

0.1045

EXPGAP

0.635961

0.172022

3.696972

0.0004

S1(-1)

0.041905

0.007469

5.610484

0.0000

Table 5.

Figure 1.

The intercept which is the stabilizing rate of interest is positive and statistically significant at the 5% level of significance. The coefficient associated with expected inflation is positive and statistically insignificant while that associated to both expected output and the change in stock prices (with 1 lag) are both positive and statistically significant. The R2 of 0.58 means that we are able to explain 58% of the variability in the federal funds rate. We reject the null hypothesis that δ = 0 at the 5% level of significance.

with two lags;

Dependent Variable: FFR01 Method: Least Sqares

Included observations: 74(after adjustments) R 2 : 0.582783

Durbin Watson Stat:

Variable

Coefficient

Standard Error

T statistic

Probability

C

2.958132

0.399841

7.398267

0.0000

EXPINFLATION

0.245605

0.153317

1.601945

0.1137

EXPGAP

0.636070

0.182139

3.492224

0.0008

S1(-1)

0.041926

0.013413

3.125805

0.0026

S1(-2)

-2.89E-05

0.014968

-0.001932

0.9985

Table 6.

Figure 2.

We stop at two lags because at this point, the p-value of the change in asset prices is statistically insignificant and the null hypothesis that β = 0 cannot be rejected. The intercept is positive and statistically significant at the 5% level of significance. The coefficient associated with expected inflation is positive and statistically insignificant while the coefficients associated with expected output gap and change in asset prices with one lag are both positive and statistically significant. The coefficient associated with change in asset prices with two lags is positive and statistically significant meaning that monetary policy reacts to change in asset prices with just one lag. We are also able to explain 58% of the variability of the federal funds rate as the R2 implies. We reject the null hypothesis that δ = 0 at the 5% level of significance.

5.1. Diagnostic Tests:

We run some tests on the augmented Taylor model to ensure that under the assumptions of the multiple regression models, we have the best linear unbiased estimators (BLUE) of the estimates of our model in accordance with the Gauss-Markov theorem.

1. Jarque-Bera Normality test: This is carried out on the residuals to find out if they are normally distributed.

The p-value of 0.24 shows that the null hypothesis cannot be rejected so we conclude that our residuals are normally distributed and therefore consistent.

2. White Heteroskedasticiy Test: We carry out this test to find out if the error terms are homoskedastic hence efficient.

F-statistic: 2.277949 Probability: 0.027667

Obs*R-squared: 17.95368 Probability: 0.035715

Newey-West HAC Standard Errors & Covariance (lag truncation=3) R2: 0.242517

Variable

Coefficient

Standard Error

T statistic

Probability

C

-0.858670

1.394876

-0.615589

0.5403

EXPINFLATION

0.842139

0.926609

0.908839

0.3668

EXPINFLATION^2

-0.019314

0.177025

-0.109105

0.9135

EXPINFLATION*EXPGAP

0.647504

0.379657

1.705499

0.0930

EXPINFLATION*S1(-1)

-0.033698

0.014899

-2.261784

0.0271

EXPGAP

-1.756175

1.081203

-1.624279

0.1092

EXPGAP^2

-0.229243

0.168575

-1.359893

0.1786

EXPGAP*S1(-1)

0.005279

0.013839

0.381459

0.7041

S1(-1)

0.078170

0.047342

1.651162

0.1036

S1(-1)^2

0.000198

0.000615

0.321209

0.7491

Table 7.

The results show that the p-values of both the f-statistic and R2 are less than 0.05. We therefore reject the hypothesis of no heteroskedasticity. This means that the OLS is not BLUE and we need to rectify this. This is taken care of using the Newey-West test which will be carried out after the test for autocorrelation below.

3. Breusch-Godfret LM test for serial correlation: We use this to test if the residuals are autocorrelated. The results are as follows;

F-statistic: 117.3219 Probability: 0.00000

Obs*R-squared: 46.59581 Probability: 0.00000

Durbin Watson Stat: 1.467334 R2: 0.242517

Variable

Coefficient

Standard Error

T statistic

Probability

C

-0.100760

0.242460

-0.415574

0.6790

EXPINFLATION

0.068881

0.091716

0.751029

0.4552

EXPGAP

-0.043377

0.105515

-0.411101

0.6823

S1(-1)

-0.010105

0.004672

-2.162864

0.0340

RESID(-1)

0.813358

0.075092

10.83152

0.0000

Table 8.

The Durbin Watson statistic is not just less than 1, it is less than 1.5. This indicates strong first-order serial correlation as there are more than 50 observations in the sample. We therefore reject the null hypothesis of serial correlation.

Since we noticed the presence of both heteroskedasticity and serial correlation, it means that our OLS regression model is not BLUE under the necessary assumptions. In order to account for this, we therefore re-estimate the regression model by OLS, computing the covariances differently using the Newey-West option built in eviews. The results are as follows;

Dependent Variable: FFR01 Method: Least Sqares

Included observations: 74(after adjustments) R 2 : 0.582783

Newey-West HAC Standard Errors & Covariance (lag truncation=3) Durbin Watson Stat: 0.422811

Variable

Coefficient

Standard Error

T statistic

Probability

C

2.958203

0.427551

6.918943

0.0000

EXPINFLATION

0.245547

0.197332

1.244332

0.2175

EXPGAP

0.635961

0.204554

3.109020

0.0027

S1(-1)

0.041905

0.012597

3.326511

0.0014

The table shows the result of the Newey-west test and they are not really different from the unadjusted augmented Taylor model. We notice however that the standard errors are larger and the t-statistics have reduced hence larger p-values as a result of the corrections by the test.

As a result of the crash in the stock market in the third quarter of 2007, we suspect the parameters of our model may be unstable. We run the following tests with respect to this:

1. Chow’s breakpoint test:

Breakpoint: 2007:3

F. Statistic

Chi Square

Stat

9.806010

0.000003

Probability

34.51635

0.000001

Eviews results indicate a break in the sample; we therefore accept that the parameters are unstable.

2. Recursive Least Squares:

We can see that there is evidence of instability as the residuals are not always inside the standard error bands.

3. Cumulative Sum (CUSUM) Test:

CUSUM test results show that the parameters are stable as the CUSUM line is always inside the 95% confidence bands although we notice a difference (dip below zero) towards the end of 2007.

Model 2: This is the GMM model and we estimate the following equation in order to find out if stock prices have a direct or indirect effect on monetary policy.

Ffrt = α + βEt(π t+i– π*t+i) +γEt(yt+i - ŷt+i)+∑δkЅt-k + εt …………………(3i)

Dependent Variable: FFR01 Method: GMM

Included observations: 72(after adjustments) R 2 : 0.428409

Durbin Watson Stat: 0.261857 J-statistic: 0.017910

Variable

Coefficient

Standard Error

T statistic

Probability

C

3.131304

0.607318

5.155957

0.0000

EXPINFLATION

0.301272

0.307192

0.980730

0.3302

EXPGAP

0.894450

0.306744

2.915953

0.0048

S1

0.002354

0.025020

0.094087

0.9253

Table 9.

The intercept which is the stabilizing rate of interest is positive and statistically significant at the 5% level of significance. The coefficient associated with expected inflation is positive and statistically insignificant. The coefficient associated with expected output gap is positive and can be said to be statistically insignificant and the coefficient associated with change in asset prices is positive and statistically insignificant. The R2 of 0.43 means that with the GMM estimation we are only able to estimate 43% of the variability of the federal funds rate. We reject the null hypothesis that δ = 0 at the 5% level of significance. This is a pointer that the Central Banks can react to monetary policy without targeting inflation.

Model 3;

M2= α + βSI+γRGDP + δU + εt

Dependent Variable: M2 Method: Least Squares

Included observations: 76(after adjustments) R 2 : 0.443379 Durbin Watson Stat: 0.256571

Variable

Coefficient

Standard Error

T statistic

Probability

S1

-0.027523

0.011276

-2.440828

0.0171

RGDP01

0.000691

6.46E-05

10.69761

0.0000

U

-0.370076

0.122595

-3.018695

0.0035

Table 10.

The intercept which is the stabilizing rate of interest is negative and statistically insignificant at the 5% level of significance. The coefficients associated with real gdp and unemployment rate are both statistically significant and positive and negative respectively (as expected). The coefficient associated with S1 is positive and statistically significant so we reject the null hypothesis that β = 0. The R2 of 0.44 means that we are only able to explain 44% of the variability in stock prices. As we can see from this, stock price volatility has an effect on the M2 component of money supply.

Model 4: Pairwise Granger Causality Test.

1. Test for the direction of causality between S1 and M2.

The following table shows the results of the test;

Null Hypothesis

Obs

F-statistic

Probability

S1 does not Granger Cause FFR01

72

2.64892

0.04135

FFR01 does not Granger Cause S1

1.96834

0.11020

Table 11.

The p-value of 0.04 shows that the first hypothesis is statistically significant and that we reject the null hypothesis that S1 = 0 and does not granger cause FFR01 while the second hypothesis is significant and we cannot reject the null hypothesis that FFR01 = 0 and does not granger cause S1. Therefore, there is no reverse causality between S1 and FFR01; S1 leads FFR01.

2. The direction of causality between M2 and S1.

Null Hypothesis

Obs

F-statistic

Probability

M2 does not Granger Cause S1

73

0.56352

0.64

S1 does not Granger Cause M2

2.96204

0.03845

Table 12.

From the results of this test, the p-value of 0.6 shows that the first hypothesis is statistically insignificant at the 5% and 10% levels and as a result, we accept the null hypothesis that M2 = 0 and does not granger cause S1 while the second hypothesis is significant with a p-value of 0.04, so we reject the null hypothesis that S1 = 0 and does not granger cause M2. There is therefore no reverse causality between S1 and M2; we conclude that S1 leads M2.

From the results of the pairwise granger causality test, the researchers conclude that causality is only in one direction between the stock market and monetary policy and that the stock market volatility leads monetary policy.

6. CONCLUSION AND POLICY RECOMMENDATIONS.

This paper has analyzed the relationship between the money supply and federal funds rate components of monetary policy and the stock market in the period between 1990 and 2009. In particular, the paper focused on three major areas concerning this relationship: The relationship (direct or indirect?) between the federal funds rate and stock prices, the relationship between money supply and the stock market and the direction of causality between both components of monetary policy and the stock market.

The result of this study suggest that federal funds rate reacts directly to stock price volatility (GMM results) although from both the augmented Taylor rule and GMM we notice that the coefficients of change in stock prices though positive are rather small. This implies that change in stock prices holding other variables constant are only able to explain a small percentage of the variability in federal funds rate. However, it is still the only fully statistically significant variable and as such in line with the argument by Cecchetti et al (2000) that monetary policy can and should react to stock prices without targeting inflation.

Our results also show that changes in money supply have an effect on stock prices as is seen although it does not granger cause it (Pairwise Granger Causality Test Results). This simply means that change in money supply does not cause stock price volatility but can be used to prevent and control excessive movements in stock prices. This is also in line with suggestions of Cecchetti et al (2000) to include asset prices in monetary policy decisions in order to prevent misalignments.

Regarding the direction of causality, our results show that there is no bidirectional causality between monetary policy and the stock market as stock price volatility granger causes monetary policy.

As a result of our analysis, we therefore recommend that Central banks should include stock prices in monetary policy rules strictly for the purpose of preventing bubbles and macroeconomic instability.

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