# Monetary Policies at Central Banks

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Monetary policy is the regulation of the interest rate and money supply of a country by its Central Bank or Federal Reserve in other 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.

It is generally assumed that policy makers react to stock prices when making decisions concerning the federal funds rates but some economists argue that stock prices also react to monetary policy decisions. it is the other way round ie tha stock markets react to monetary policy decisions.

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 and the empirical model is developed. Results are presented and discussed in the next section. We conclude the paper in section V and suggestions for further studies are pointed out and policy implications are considered.

## 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 stock market is a financial market where equities are bought and sold either as an IPO (Initial Public Offer) in the primary market or exchange of existing shares between interested parties in the secondary market. 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). Monetary neutrality also implies that monetary policy should not affect real stock prices in the long run (Bordo, Dueker and Wheelock, 2007).

The relationship between monetary policy and the stock market is best analyzed by looking at the effect of both money supply and interest rates on the stock market. 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”. Interest rate can simply be defined as the cost of capital. The central bank regulates the economy by either increasing (contractionary) 0r decreasing (expansionary) the federal fund rates which is the rate at which banks borrow from federal reserves and the discount rates which is the rate at which banks borrow from each other. An increase in the federal funds rate for example will make it more expensive for banks to borrow from the Federal Reserve and they will in turn increase the interest rate thereby making it more expensive for individuals to borrow from banks. While some economists ( Smets (1997), Bernanke and Kuttner (2003) ) argue that the central bank should only respond to unexpected changes in asset prices when the changes affect inflation, some other economists ( Cecchetti, Genberg, Lipsky and Wadhwani , 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”.

Thorbecke (1997) used various approaches to examine the relationship between monetary policy and equity prices. In his first approach, he used Vector Auto Regression (VAR) using the stock market index and ten size-ranked portfolios. Results from this approach showed that monetary tightening has the most negative and the strongest effect on the equity prices of small firms and this is consistent with hypothesis by Gertler and Gilchrist (1993) that an important channel of monetary policy is that it affects the borrowing ability of small firms. Thorbecke (1997) , also used the index of monetary policy as used by Boschen and Mills (1995) to identify shocks and from this, he learned that expansionary monetary policy exerts a large and statistically positive effect on monthly stock returns regardless of whether it was measured by innovations in the federal funds rate and non borrowed reserves or by narrative indicators. In the same year moreover, Thorbecke (1997), carried out an event study with main focus on periods when the federal funds rate was targeted. He used Cook and Hahn's ((1989) federal funds data ( 1974 – 1979 ) and added a similarly constructed series for the period August 1987 to December 1994 and found a significant negative effect on the percentage change in the Dow Jones Industrial Average from policy-induced changes in the federal funds rate.

An understanding of the monetary policy transmission mechanism is very important in the study of the relationship between monetary policy and the stock market. 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 ratel and the wealth . Bernanke and Kuttner (2005) argued that changes in monetary policy are transmitted through the stock market via changes in the values of private portfolios (i.e. the wealth effect), changes in the cost of capital (i.e. the interest rate channel). Erhmann and Fratzscher (2004) laid emphasis on the credit channel of monetary policy transmission. They argued 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. This is because when there is a tightening of monetary policy for instance, 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 those customers whom they have the least information about thereby making it more difficult for firms with little or no publicly available information to access bank loans (Gertler and Hubbard 1988, Gertler and Glichrist 1994). Worsening credit market conditions also affect firms by weakening their balance sheets as the present value of collateral falls with rising interest rates and this effect is stronger for some firms than for others ( and Gertler 1989, Kiyotaki and Moore 1997). Other studies e.g. Thorbecke (1997) and Perez-Quiros and Timmerman (2000) have also 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). This means that lower than expected interest rates leads to a higher percentage increase in asset prices than the percentage decrease in asset prices as a result of higher than expected interest rates. This is also consistent with the research on leverage-feedback hypothesis by Black (1976) and volatility-feedback hypothesis by French, Schwert and Stanbaugh (1987).

Lamont, Polk and Saa-Requejo (2001), Perez-Quiros and Timmerman (2000) among others use change in market interest rates or official rates as their measures of monetary policy. Christiano, Eichenbaum and Evans (1994) extracted monetary policy as the orthogonalized innovations from VAR models proposed by Campbell (1991) and Campbell and Ammer (1993). Research methodology based on this shows that the response of US stocks returns to monetary policy shocks based on federal fund rates show that returns of large firms react less strongly than those of small firms (Thorbecke, 1997), that the overall policy for stock returns is quite low (Patelis, 1997) and that international stock markets react to both to changes in their local monetary policies and that of the United states (Conover, Jensen and Johnson, 1999).

In their study, Ehrmann and Fratzscher (2004) analyzed the effect of monetary policy on equity markets by looking at the returns of the S&P500 index on days of monetary policy decisions of the Federal Reserve since the change of its disclosure practices in 1994 and until 2003. They found that US monetary policy shocks had a strong effect on equity returns and that an unexpected tightening of monetary policy by 50 basis points decreases US equity returns by about 3% on the day of the monetary policy decision while Bernanke and Kuttner (2005) found that on average, an unanticipated 25 basis point cut in the Federal funds rate target is associated with about 1% increase in broad stock indexes. Ehrmann and Fratzscher (2004) also found that equity returns react more strongly to monetary policy shocks when FOMC changes are unexpected, when the change in the monetary policy stance of the Fed is directional and during periods of high equity market volatility. Ehrmann and Fratzscher (2004) came to the following conclusions in their study: S&P 500 shows a strong effect of monetary policy on equity returns; the effect of monetary policy is stronger in an environment of increased market uncertainty; negative surprises ( i.e monetary policy has tightened less and loosened more than expected) have larger effects on the stock market than positive surprises; firms with low cash flows are affected more by US monetary shocks and firms with poor ratings are more prone to monetary policy shocks than those with good ratings.

There have also been a few cross-sectional dimensions of the effect of monetary policy on the stock markets in literature. Hayo and Uhlenbruck (2000), Dedola and Lippi (2000), Peersman and Smets ( 2002), Ganley and Salmon (1997) etc are some economists who have analyzed this and overall, their findings show that the stock prices of firms in cyclical industries, capital-intensive industries and industries that are relatively open to trade are affected more strongly by monetary policy shocks.

While monetary economists commonly associate restrictive/expansive monetary policy with higher/lower levels of economic activity, financial economists discuss various reasons why changes in the discount rate affect stock returns (Durham, 2000). Changes in the discount rate affect the expectations of corporate profitability (Waud, 1970) and discrete policy rate changes influence forecasts of market determined interest rates and the equity cost of capital. Modigliani (1971) suggests that a decrease in interest rates boosts stock prices and therefore financial wealth and lifetime resources, which in turn raises consumption through the welfare effect. Mishkin (1977) on the other hand suggests that lower interest rates increase stock prices and therefore decrease the likelihood of financial distress, leading to increased consumer durable expenditure as consumer liquidity concerns abate.

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 their has been an increase in the demand for money and this in effect, signals an increase in economic activity. Selin (2001) argued that higher cash flows is as a result of higher economic activities and it leads to a rise in stock prices. The opposite is the case when money supply is reduced. 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 ( defined as the proposition that current stock prices fully reflect available information about the value of the firm and there is no way to earn excess profits by using this information), 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 ( Clarke, Jandik and Mandelker, not found). 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 which states that all available information should be reflected in current prices (Fama, 1970) meaning that anticipated information should not have any effect on current stock prices. Most economists believe that stock prices react differently to the anticipated and unanticipated effects of monetary policy (Maskay, 2007). 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 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 (long run and short run) 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.

According to Cecchetti, et al. (2000), macroeconomic performance can be improved if the central bank increases the short-term nominal interest rate in response to temporary “bubble shocks” that raise the stock price index above the value implied by economic fundamentals. On the other hand, Bernanke and Gertler (2001) assumed in their research that the Central Bank cannot tell whether an increase in stock prices is driven by a bubble shock or a fundamental shock.

In 1974, Rozeff tested the efficient market hypothesis against a model he named “predictive monetary portfolio model”. His study showed that lagged money supply data do not predict future stock returns and that returns are related to contemporaneous and future changes in the money supply. This study was further improved by Rogalski and Vinso (1977) who synchronized the data so that the money supply data were generated at intervals that were the same as those for the stock return data and also by taking proper account of the autocorrelation in the time series. They concluded that causality appears to go from stock prices to money supply and not from money supply to stock prices as is generally assumed. The result of a study by Darrat (1990) on the effects of monetary and fiscal policy on the returns on the Toronto Stock Exchange 300 Index showed that monetary policy does not Granger cause stock returns. Bjornland and Leitemo (2009), in their study recognized the fact that the reverse causation from the stock market to monetary policy has been either ignored or not addressed enough. Bhattacharya and Mukherjee ( ……..) investigated the nature of causal relationship between stock prices ( represented by the Bombay Stock Exchange (BSE) Sensitivity Index) and macroeconomic aggregates ( money supply, interest rates etc) in India and their results showed that there is no causal link between stock prices and monetary policy ( money supply and interest rates). Results from early econometric research by Homa and Jaffee (1971), Keran (1971), Reilly and Lewis (1971), Hamburger and Kochin (1972), Malkiel and Quant (1972) and Meigs (1972) showed a strong link between money

Supply and stock prices and also argued that stock prices lag monetary changes.

So far, we have seen that there is indeed a relationship between monetary policy and the stock market. While some economists argue that the relationship is positive, some others argue that a negative relationship exists. The researcher intends to analyze the relationship between monetary policy and the stock market using the Taylor rule. The relationship between money supply and asset prices will also be analyzed in the course of this study. Analysis will also be carried out to find out if stock prices lead or lag monetary policy and this will be carried out with the Granger reverse causality test to test for reverse causality between both money supply and stock prices and interest rates and stock prices.

I understood the meaning of your review, however I have some concerns. If I am correct, what you want to do is:

To analyze whether movements in the stock price impact the monetary policy decisions;

To understand whether the direction of causality goes from monetary policy to stock market or the reverse.

However, your literature review is almost on the second point. You present in few lines the literature on the first point. Given the kind of analysis you are conducing, my feeling is that you should reserve more space to the review of the literature concerning point 1). After that, you can say: ok according to some gays, like Cecchetti et al., and in opposition to the view of Bernanke and Gertler, movements in the stock market should affect monetary policy decision. However, are we sure that the direction of causality is correct? There is a large strand of literature puzzling on the direction of causality. At this point, you may review the most relevant papers on this issue. But, as I said earlier, more space should be reserved to the issue in point 1) above.

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 monetary policy?

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

## RESEARCH METHODOLOGY

## The effect of interest rates and stock market prices.

In this section, we test for the relationship between monetary policy and stock prices using the Taylor rule. The Taylor rule is a monetary policy rule that 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 – Å·t) + 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, Å·t is potential output and εt is the error term.

As suggested by Taylor (1993), a good conduct of monetary policy should have both β = 0.5 and α=0.5. We therefore test our hypothesis as follows:

## H0: Monetary Policy does not react to stock market volatility.

## β = 0.5, γ = 0.5

## H1: Monetary Policy reacts to stock market volatility.

## H1 is not H0

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 -Å·t+i)+εt ………………………(2)

Where Et(π t+i– π*t+i) is the expected Inflation, Et (yt+i - Å·t+i) is the xpected gap and Et is the expected value conditional to information available at the time.

Here we also test the same hypothesis:

## H0; β = γ = 0.5

## H1; not H0

To test if the monetary authorities react to stock market volatility, we use the following equation where we add lagged values of stock prices (represented by the S&P 500) to the Taylor rule;

## Ffrt = α + βEt(π t+i– π*t+i) +γEt (yt+i - Å·t+i)+∑δkÐ…t-k + εt …………………(3)

Where the new variable Ð…t-k is the lagged change in stock prices. This is known as the augmented Taylor rule.

The standard Taylor rule is well specified (ie α and β are estimated correctly) if monetary authorities target only the inflation and output deviations from the target.

If on the other hand monetary authorities react to stock market volatility, our second equation would be misspecified and the coefficient of the lagged asset prices (δ) should be significant. Equation 3 is aimed at finding out if monetary authorities actually react to stock price volatility.

We test the following hypothesis:

## H0: δ = 0

## H1: δ ≠ 0

## Generalized Method of Moments (GMM) Estimation.

GMM is a statistical method for obtaining estimates of parameters of statistical models. It is important 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 - Å·t+i)+∑δkÐ…t-k + εt …………………(3i)

## Instruments:

## Et-1(π t+i– π*t+i), Et-2(π t+i– π*t+i), Et-1 (yt+i - Å·t+i), Et-2(yt+i - Å·t+i)

Statistical Hypothesis:

## H0: β= 0, γ = 0

## H1: Not H0

We use four instruments in accordance to the rule that the number of instruments must be at least equal to the number of parameters to be estimated (α, β, γ and δ) and also because our regression analysis using the augmented Taylor rule became insignificant after two lags of stock prices.

## 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*G + 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: Stock market volatility has an effect on money supply.

## 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. A direct, positive relationship is expected between stock prices and the GDP. Unemployment rate is added to the model because it is one of the major factors that determines the demand for stocks. High unemployment rates lead to lower demand for stocks and vice versa. We expect an inverse relationship between the unemployment rates and stock prices.

## 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 built in eviews. We add lags to the two different models until they become significant.

Granger Model 1;

## Ffrt = α + βS1………………………………………………… (5)

## S1 = α + βFfr01 …………………………………………… (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 = α + βS1

## S1 = α + βM2

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;

General Hypothesis;

## H0: The data on each variable is normally distributed.

## H1: not Ho

## The Federal Funds Rate;

The federal funds rate 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. We obtained quarterly data on the federal funds rate from the website of IMF Washington from the periods 1990 to 2009.

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 shows that the distribution is non symmetric and is negative as a result of the lower tail of the distribution being 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 of significance shows that we cannot reject the null hypothesis that the data 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. The CPI has an inverse relationship with monetary policy actions.

From the descriptive statistics, we can see 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 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 the null hypothesis 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 of significance.

## 4). Real Gross Deposit Product:

This can be defined as a measure which adjusts for inflation and 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. There is a large difference between the maximum and minimum values of real gdp which 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 the negative value of the skewness statistic shows 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.

## 4. 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 is believed to have 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 skewness statistic of the S&P500 is less than 1 which signifies that the distribution is not symmetric and the negative value implies that 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 the null hypothesis that the distribution is normal.

## 5. Unemployment Rate;

The unemployment rate is used as one of the control variables. It is an important indicator of the wellbeing of an economy. The lower the unemployment rate, the higher the aggregate demand for stock thereby pushing up stock prices. We get 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. There is a big difference between the maximum and the minimum values which accounts for the large standard deviation around the mean. The skewness statistic which is above 1 but very close to 1 shows that the data is almost symmetrical and this statistic is positive because the upper tail of the distribution is thicker than the lower tail. The kurtosis statistic which is above 3 implies that the tails are thicker than normal. We reject the null hypothesis 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.

## 6. Money Supply represented by M2;

Money supply is a component of monetary policy used by Central Banks to regulate the economy.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 (I.e. the mean). 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 of 1.9 which is less than the critical value of the χ2 distribution (5.99) at the 5% level of significance shows that we cannot reject the null hypothesis that the data is normal.

## DATA SOURCE;

The data for the CPI (Consumer Price Index), real GDP (Gross Domestic Product) and the federal funds rate are obtained from the IMF Washington website while the data for S&P 500 Index are obtained from the Federal Reserve Economic Data (FRED) of the Federal Reserve Bank of St Louis website; www.federalreserve.gov.

## DATA ANALYSIS

## Model 1 (i): The Taylor rule.

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

H0: β = γ = 0.5

H1: not H0

Dependent Variable: FFR01

Method: Least Squares

Date: 08/22/10 Time: 14:45

Sample(adjusted): 1991:1 2009:4

Included observations: 76 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

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

R-squared

0.371356

Mean dependent var

3.860658

Adjusted R-squared

0.354133

S.D. dependent var

1.686064

S.E. of regression

1.355019

Akaike info criterion

3.484182

Sum squared resid

134.0337

Schwarz criterion

3.576185

Log likelihood

-129.3989

F-statistic

21.56151

Durbin-Watson stat

0.222722

Prob(F-statistic)

0.000000

## The fitted line is;

FFR= 2.87 + 0.40INFLATION + 0.68GAP

## Interpretation;

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 with p-values which are less than 0.05. An R-square of 0.37 means that we are only able to explain about 37% if the variability in the federal funds rate. We reject the null hypothesis that β and γ are each equal to 0.5 as suggested by Taylor (2003).

2. Model I (ii): To analyze the behavior of monetary policy.

it = α + βEt(π t+i– π*t+i) +γEt (yt+i – Å·t+i)+εt

H0; β = γ = 0.5

H1; not H0

Dependent Variable: FFR01

Method: Least Squares

Date: 08/22/10 Time: 15:39

Sample(adjusted): 1991:3 2009:4

Included observations: 74 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

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

R-squared

0.395169

Mean dependent var

3.809595

Adjusted R-squared

0.378132

S.D. dependent var

1.678852

S.E. of regression

1.323920

Akaike info criterion

3.438766

Sum squared resid

124.4462

Schwarz criterion

3.532174

Log likelihood

-124.2344

F-statistic

23.19409

Durbin-Watson stat

0.249315

Prob(F-statistic)

0.000000

## The fitted line is;

FFR01 = 3.16 + 0.29EXPINFLATION + 0.88EXPGAP

## Interpretation;

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 10% and 5% levels of significance while the coefficient associated with the expected output gap is positive and statistically significant at the 5% level of significance. An R-squared of 0.40 means that we are only able to explain 40% of the variability in the federal funds rate. It is safe to reject the null hypothesis that β = γ = 0.5 because the coefficient associated with expected inflation is negligibly insignificant while that associated with the expected output gap is statistically significant.

## Model 1 (iii). The Augmented Taylor Rule;

it = α + βEt(π t+i– π*t+i) +γEt (yt+i+ Å·t+i)+δkÐ…t-k + εt

Ho: δ = 0

H1: δ ≠ 0

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.

1. One Lag;

Dependent Variable: FFR01

Method: Least Squares

Date: 08/22/10 Time: 15:50

Sample(adjusted): 1991:3 2009:4

Included observations: 74 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

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

R-squared

0.582783

Mean dependent var

3.809595

Adjusted R-squared

0.564902

S.D. dependent var

1.678852

S.E. of regression

1.107403

Akaike info criterion

3.094451

Sum squared resid

85.84396

Schwarz criterion

3.218995

Log likelihood

-110.4947

F-statistic

32.59278

Durbin-Watson stat

0.422811

Prob(F-statistic)

0.000000

## The fitted line is;

FFR01= 2.96 + 0.25EXPINFLATION + 0.64EXPGAP + 0.04S1 (-1)

## Interpretation:

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 R-squared 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 Squares

Date: 08/22/10 Time: 15:51

Sample(adjusted): 1991:3 2009:4

Included observations: 74 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

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

R-squared

0.582783

Mean dependent var

3.809595

Adjusted R-squared

0.558596

S.D. dependent var

1.678852

S.E. of regression

1.115399

Akaike info criterion

3.121478

Sum squared resid

85.84396

Schwarz criterion

3.277158

Log likelihood

-110.4947

F-statistic

24.09538

Durbin-Watson stat

0.422945

Prob(F-statistic)

0.000000

## The fitted line is;

FFR01 = 2.96 + 0.25EXPINFLATION + 0.64EXPGAP + 0.042S1 (-1) – 2.89117992e-05*S1 (-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.

## Interpretation:

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 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 and. 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.

## Model 2: GMM Estimation.

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

H0: β= 0, γ = 0

H1: Not H0

Dependent Variable: FFR01

Method: Generalized Method of Moments

Date: 08/25/10 Time: 13:21

Sample(adjusted): 1992:1 2009:4

Included observations: 72 after adjusting endpoints

No prewhitening

Bandwidth: Fixed (3)

Kernel: Bartlett

Convergence achieved after: 8 weight matrices, 9 total coef iterations

Instrument list: EXPINFLATION(-1)EXPINFLATION(-2)EXPGAP(

-1)EXPGAP(-2)

Variable

Coefficient

Std. Error

t-Statistic

Prob.

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

R-squared

0.428409

Mean dependent var

3.786111

Adjusted R-squared

0.403192

S.D. dependent var

1.693777

S.E. of regression

1.308500

Sum squared resid

116.4277

Durbin-Watson stat

0.261857

J-statistic

0.017910

## The fitted line is;

FFR01 = 3.13 + 0.30EXPINFLATION + 0.89EXPGAP + 0.0024S1

## Interpretation;

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 statistically significant and the coefficient associated with change in asset prices is positive and statistically insignificant. The R-sqared 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.

## Model 3;

S = α + βM2 +γG + δU + εt

## H0: β = 0

## H1: β ≠ 0

Dependent Variable: S

Method: Least Squares

Date: 08/25/10 Time: 16:01

Sample: 1990:1 2009:4

Included observations: 80

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-87.42922

124.7649

-0.700752

0.4856

M2

13.44679

8.028875

1.674804

0.0981

RGDP01

0.149376

0.010252

14.56981

0.0000

U

-117.0021

12.34845

-9.475044

0.0000

R-squared

0.877254

Mean dependent var

924.0339

Adjusted R-squared

0.872409

S.D. dependent var

378.2205

S.E. of regression

135.0999

Akaike info criterion

12.69861

Sum squared resid

1387151.

Schwarz criterion

12.81771

Log likelihood

-503.9445

F-statistic

181.0553

Durbin-Watson stat

0.372533

Prob(F-statistic)

0.000000

## The fitted line is:

S = -87.43 + 13.45M2 + 0.15RGDP01 – 117.002U

## Interpretation:

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 expected change in money supply (M2) is positive and statistically insignificant so we accept the null hypothesis that β = 0. The R2 of 0.88 means that we are able to explain 88% of the variability in stock prices.

## Model 4: Pairwise Granger Causality Test.

Pairwise Granger Causality Tests

Date: 08/28/10 Time: 17:45

Sample: 1990:1 2009:4

Lags: 4

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

Pairwise Granger Causality Tests

Date: 08/28/10 Time: 17:46

Sample: 1990:1 2009:4

Lags: 3

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

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