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# Study On Monetary Policy And The Stock Market

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.Â Â The stock market on the other hand is often considered a primary indicator of a countryâ€™s economic strength and development as it is a major source of savings and income for most individuals. History has shown that the economy of any country reacts strongly to movements in stock prices and is replete with examples in which large swings in stock, housing and exchange rate markets coincided with prolonged booms and busts (Cecchetti, Genberg, Lipsky and Wadhwani, 2000). 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 stock prices can have a major effect on the economy as it influences real activities such as consumption, investments, savings etc

While some economists say that monetary policy decisions depend on stock price movements, some others believe that stock price movements depend on monetary policy decisions. In this paper, we analyze both sides of the coin by looking at how stock markets react to monetary policy and how monetary policy reacts to movements in stock markets. This research work is aimed at finding out which granger causes which using the Granger Causality test. We will also analyze the relationship between both interest rates and monetary policy and that between money supply and monetary policy.

In section II, a thorough review of the relevant literature of the topic is carried out as we try to understand more about the relationship between monetary policy and the stock market and the effects of both components (money supply and interest rates) of monetary policy 0n the stock market. In the next section, we describe 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 the macroeconomy 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. Although 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 implies that monetary policy should not affect real stock prices in the long run (Bordo, Dueker and Wheelock, 2007).

To understand the relationship between monetary policy and the stock market, we must first understand what monetary policy is. 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. This measure of monetary policy, however, coincides with changes in business cycle conditions and other relevant economic variables. 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 has shown that the response of US stocks returns to monetary policy shocks based on federal fun 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). Monetary policy shocks that are extracted from structural VAR models or from changes in interest rates using monthly or quarterly data are likely to subject to the endogeneity problem i.e they are unlikely to be purely exogenous ( Ehrmann and Fratzscher, 2004). Another VAR-based method was used by Goto ad Valkanov (2000) to focus on the covariance between inflation and stock returns while Boyd, Jagan and Hu (2001) considered the linkages between policy and stock prices. Their analysis did not focus directly on monetary policy; rather it focused on marketâ€™s response to employment news (Bernanke and Kuttner, 2005).

In their own research paper, Ehrmann and Fratzscher (2004) find that S&P 500 shows a strong effect of monetary policy on equity returns, that the effect of monetary policy is stronger in an environment of increased market uncertainty, that that negative surprises ( i.e monetary policy has tightened less and loosened more than expected) has larger effects on the stock market than positive surprises, that small firms are react more to policy shocks than large firms, that firms with low cash flows are affected more by US monetary shocks and that firms with poor ratings are more prone to monetary policy shocks than those with good ratings. They find that firms react more strongly when no change had been expected, when there is a directional change in the monetary policy stance and during periods of high market uncertainty.

There has also been cross-sectional dimensions of the effect of monetary policy on the stock markets in literature though few. 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 (Ehrmann and Fratzscher, 2004).

According to Bernanke and Kuttner (2005), changes in monetary policy are transmitted through the stock market via changes in the values of private portfolios (â€œwealth effectâ€?), changes in the cost of capital and by other mechanisms. In their paper, they analyzed the stock markets response to policy actions both in the aggregate and at the level of industryâ€™s portfolios and they also tried to understand the reasons for the stock markets response. Their findings show that monetary policy is, for the most part, not directly attributable to policyâ€™s effects on the real interest rate instead it seems to come either through its effects on expected future excess returns or expected future dividends.

While 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 ( Durham, 2000).

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 (Durham, 2000).

Tobins q is the equity market value of a firm divided by its book value. It can also be defined as the ratio of the market value of a firmâ€™s existing shares to the replacement cost of the firmâ€™s physical assets. Higher stock prices reduce the yield on stocks and reduce the cost of financing investment spending through equity issuance (Bosworth, 1975). Tobins q explains on e of the mechanisms through which movements in stock prices can affect the economy: the wealth channel. The other channels of monetary policy transmission include; the interest rate channel and the exchange rate channel. The wealth channel has the investment effect, wealth effects and balance sheet effects (www.oenb.at/en). Bernanke and Blinder (1992) and Kashyap, Stein and Wilcox (1993) show that a tightening of monetary policy has a very strong impact on firms that highly depend on banks loans to financing their investments as banks reduce their overall supply of credit. Deteriorating market conditions affect firms by also weakening their balance sheets as the present value of collateral falls with rising interest rates and that this effect can be stronger for some firms than for others (Bernanke and Gertler 1989, Kiyotaki and Moore 1997). These two arguments are based on information asymmetries as firms for which more information is publicly available may find it easier to collect loans when credit conditions become tighter (Gertler and Hubbard 1988, Gertler and Gilchrist 1994).Stock returns of small firms generally respond more to monetary policy than those of large firms ( Thorbecke 1997, Perez-Quiros and Timmermmann 2000).

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).

The Keynesian economists argue that there is a negative relationship between stock prices and money supply whereas real activity theorists argue that the relationship between the two variables is positive (Sellin, 2001). The Keynesian economists believe that a change in money supply or interest rates will affect stock prices only if the change in the money supply alters expectations about future monetary policy while the real activity economists argue that increase in money supply means that money demand is increasing in anticipation of increase in economic activity (Maskay, 2007). Another factor discussed by Sellin (2001) is the risk premium hypothesis proposed by Cornell i.e higher money supply indicates higher money demand and higher money demand suggests increased risk which leads investors to demand higher risk premiums for holding stocks making them less attractive. The real activity and risk premium hypothesis is combined by Bernanke and Kuttner (2005) who argue that the price of a stock is a function of the present value of future returns and the perceived risk in holding the stock.

While advocates of the efficient market hypothesis 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 (Corrado and Jordan, 2005). 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.

Maskay(2007) analyzes the relationship between money supply and stock prices. He also seperates 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. 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.

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 â€œbubble shocksâ€? 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.

This study will analyze both exogenous and endogenous components of the relationship between monetary policy and the stock market i.e the effect of monetary policy on the stock market and the the effect if any of the stock market on monetary policy decisions. This particular analysis will be done using the federal funds rate as a representative of monetary policy. We also follow the methodology used by Maskay (2007) closely as we try to find the effect of money supply on the stock market. Although Maskay used M2 as a measure of money supply, this study will separate money supply into M1 and M2 and analyze their relationship with the stock prices.

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

How do movements in the stock market affect monetary policy decisions on federal funds rates?

How does monetary policy affect stock market prices?

Do stock market prices react differently to the M1 and M2 components of money supply?

## RESEARCH METHODOLOGY

## The effect of stock market prices on monetary policy.

In this section, I 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 would or 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;

## it = r*t + Î² (Ï€ tâ€“ Ï€*t) +Î³ (yt - Å·t)â€¦â€¦â€¦.. (1)

Where; it = target short-term nominal interest rate.

r*t = assumed equilibrium real interest rate.

Ï€t = the observed rate of inflation.

Ï€*t = the desired rate of inflation.

yt = the logarithm of real GDP.

Å·t = the potential output.

But, to analyze the behavior of monetary policy, the following regression equation is estimated;

## it = Î± + Î²Et(Ï€ t+iâ€“ Ï€*t+i) +Î³Et (yt+i+ Å·t+i)+Îµt â€¦â€¦â€¦..(2)

Where:

Et = the expected value conditional to information available at the time.

A good conduct of monetary policy should have Î² and Î± each equal to 0.5 as suggested by John Taylor.

To conduct our study, we use the following equation;

## it = Î± + Î²Et(Ï€ t+iâ€“ Ï€*t+i) +Î³Et (yt+i+ Å·t+i)+âˆ‘Î´k Ð…t-k + Îµt ..(3)

Because the monetary authorities target variables other than inflation and output deviations from the target (asset prices in this case) thereby making equation (2) mis-specified. A standard Taylor rule is well specified when the monetary authorities target only inflation and output deviations from the target. The addition to this variable is the lagged change in asset prices which is added in order to determine the relationship between monetary policy and stock prices.

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.

## The effect of monetary policy on stock market prices.

In this section, we test whether movements in stock prices are sometimes dependent on monetary policy. This test is carried out by regressing the actual change in federal funds rates upon the S&P 500 index. We us the following simple model for this purpose:

## S&P500 = Î²1 + Î²2*actual change in federal funs rate + Î²3*real GDP + Î²4* unemployment rate.

Real GDP and Unemployment rate are added as control variables. The data for real GDP is obtained from IMF, Washington while the data for unemployment rates in obtained from www.federalreserves.gov.

We add GDP because it is an important determinant of the stock prices as most industries react to changes in the economy and do well as the economy does well and vice versa i.e they are procyclical in nature. When the GDP is low, the stock prices generally tend to be low, as the companyâ€™s performance would be worse than before. A direct, positive relationship is expected between stock prices and the GDP.

Unemployment rate is also used as a control variable in this model because it is one of the major factors that determines the demand for stocks thereby either driving the stock prices up or down. When the unemployment rate is high, demand for stock reduces as less people can afford to buy them and this subsequently drives down stock prices and vice versa. The unemployment rate is also a proxy for for overall aggregate demand in the economy ( Maskay, 2007) and when it is low, aggregate demand is high. We expect an inverse relationship between the unemployment rates and stock prices.

## The effect of M1 and M2 components of money supply on stock prices.

In this section, we test the relationship between monetary policy and stock prices from the money supply angle of monetary policy. We use the M1 and M2 components of money supply for this analysis. This is done by first testing the relationship between the percentage change in M1 and the stock prices and then testing the relationship between M2 and the stock market.

The simple empirical model used for this test is;

## S&P500 = Î²1 + Î²2*%âˆ†M1 + Î²3*Real GDP + Î²4*Unemployment rateâ€¦â€¦â€¦â€¦.. (1)

## S&P500 = Î² 1+ Î²2*%âˆ†M2 + Î²*3Real GDP + Î²4*Unemployment rateâ€¦â€¦â€¦â€¦.. (2)

Unemployment rate and real GDP are also used here as control variables for the same reasons given above. The data on percentage change in M1 and M2 were obtained from Federal Reserve Economic Data from the website of the Federal Reserve Bank of St. Louis. We were able to get the monthly data of M1 and M2 and then got the quarterly averages to produce the quarterly data.

## 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;

The federal funds rate is a monetary policy tool used by the Central Bank/Federal reserve of the country to regulate the economy. Economists believe it has an inverse relationship with stock prices as because when there is an upward movement in stock prices above the desirable level, the federal reserve increases (contractionary) the federal funds rate . This leads to a decrease in the amount of money demanded by individuals thereby causing a lower demand for stocks and pushing down stock prices. We obtained data on the federal funds rate from the website of the federal reserve bank of Louisiana.

## 2. 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. We do this using the eviews software (100 Ã— (cpi â€“ cpi ( -4)). We obtained the quarterly data on CPI from the website of the International Monetary fund in washington. The CPI has an inverse relationship with monetary policy actions.

## 3. Real Gross Domestic Product (Real GDP);

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. Real GDP provides a more accurate figure as it accounts for changes in the price level. The quarterly data on Real GDP is obtained from the website of the International Monetary Fund, Washington.

## 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 quarterly data for the s&p500 is obtained from the federal reserve bank of Louisiana.

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. The quarterly data on unemployment rate is obtained from the website of the Federal Reserve Bank of Louisiana. We get the quarterly data by finding quarterly averages from the monthly data provided.

6. Monetary aggregates â€“ M1 and M2;

M1 is a monetary aggregate and it includes the transaction deposits of banks and cash in circulation and all other money equivalents that are easily convertible into cash while includes M1 plus short-term deposits in banks and 24-hour money market funds. Money supply has a positive relationship with stock prices because the higher the money supply, the higher the demand for stock which eventually increases stock prices. We split money supply into M1 and M2 to find out if they have the same relationship with stock prices. The quarterly data on percentage change in monetary aggregates is obtained from the website of the federal reserve bank of Louisiana. We also had to calculate the quarterly averages of the monthly data given.

## DATA ANALYSIS

Model 1: The Taylor rule

## it = r*t + Î² (Ï€ tâ€“ Ï€*t) +Î³ (yt â€“ Å·t)+ Îµt

Dependent Variable: FED_FUNDS_RATE

Method: Least Squares

Date: 07/05/10 Time: 20:19

Sample(adjusted): 1991:1 2009:4

Included observations: 76 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

3.615513

1.220783

2.961634

0.0041

INFLATION

0.684264

0.156212

4.380348

0.0000

OUTPUT_GAP

-1.42E-06

9.83E-07

-1.442803

0.1534

R-squared

0.249642

Mean dependent var

3.860658

Adjusted R-squared

0.229085

S.D. dependent var

1.686064

S.E. of regression

1.480394

Akaike info criterion

3.661167

Sum squared resid

159.9844

Schwarz criterion

3.753170

Log likelihood

-136.1244

F-statistic

12.14348

Durbin-Watson stat

0.181830

Prob(F-statistic)

0.000028

The estimation results are;

## it =3.62 + 0.68(Ï€ tâ€“ Ï€*t) â€“ 1.42 (yt â€“ Å·t)

The coefficient associated to inflation is positive, 0.68, but is statistically significant with a p-value of 0.00. The coefficient associated with the output gap is negative (-1.42) and statistically significant. The estimated stabilizing rate of interest (c) is positive (3.61) and statistically significant. An R-squared of 0.25 means that we are only able to explain about 25% of the variability in the interest rate.

The augmented taylor rule model:

it = Î± + Î²Et(Ï€ t+iâ€“ Ï€*t+i) +Î³Et (yt+i+ Å·t+i)+âˆ‘Î´1 Ð…t-1 + Îµt ...one lag

Dependent Variable: FED_FUNDS_RATE

Method: Least Squares

Date: 07/05/10 Time: 21:30

Sample(adjusted): 1991:3 2009:4

Included observations: 74 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

8.298961

1.280893

6.479044

0.0000

INFLATION_F

0.548999

0.181198

3.029825

0.0034

OUTPUT_GAP_F

-9.10E-06

1.51E-06

-6.041926

0.0000

S(-1)

4.24E-05

7.35E-06

5.775767

0.0000

R-squared

0.442430

Mean dependent var

3.809595

Adjusted R-squared

0.418534

S.D. dependent var

1.678852

S.E. of regression

1.280190

Akaike info criterion

3.384432

Sum squared resid

114.7220

Schwarz criterion

3.508976

Log likelihood

-121.2240

F-statistic

18.51494

Durbin-Watson stat

0.214690

Prob(F-statistic)

0.000000

Interpretation:

The estimated regression is;

it = 8.30 + 0.55Et(Ï€ t+iâ€“ Ï€*t+i) -9.10Et (yt+i+ Å·t+i)+4.24âˆ‘Ð…t-k

The coefficient associated to expected inflation is positive (0.55) but is statistically significant because it has a p-value of 0f 0.003, the coefficient associated with expected output gap is negative (-9.10) and is statistically significant (p-value = 0.000). The coefficient associated with the change in asset prices (lagged by 1 for better estimation) which is denoted by S (-1) is negative and it is statistically significant therefore we reject the null hypothesis. The measure of goodness of fit (R-square) is 0.44 meaning that we are able to explain about 44% of the variability in the interest rate

Our model consistently overestimates the actual interest rate and the residuals do not seem to be independently and identically distributed. We therefore conduct some tests which include:

1. The Jacque-Bera test: This is a statistic that measures the difference of the skewness and kurtosis of the series with those from a normal distribution.

By simply looking at the histogram, we can see that the distribution is roughly normal and the jarque-bera statistic of 0.58 shows that it is not statistically significant and we should accept the null hypothesis.

The white test: This is used to test whether the errors are heteroskedastic or not. In the presence of heteroskedasticity, OLS estimates are consistent but efficient.

White Heteroskedasticity Test:

F-statistic

3.846209

Probability

0.000621

Obs*R-squared

25.97528

Probability

0.002062

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 07/06/10 Time: 00:41

Sample: 1991:3 2009:4

Included observations: 74

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-35.28961

24.46199

-1.442630

0.1540

INFLATION_F

-5.419657

3.008210

-1.801622

0.0763

INFLATION_F^2

0.307231

0.200286

1.533961

0.1300

INFLATION_F*OUTPUT_GAP_F

5.95E-06

2.83E-06

2.105586

0.0392

INFLATION_F*S(-1)

-2.78E-05

1.73E-05

-1.603361

0.1138

OUTPUT_GAP_F

9.90E-05

5.34E-05

1.852558

0.0686

OUTPUT_GAP_F^2

-6.19E-11

2.74E-11

-2.257288

0.0274

OUTPUT_GAP_F*S(-1)

3.35E-10

1.43E-10

2.337290

0.0226

S(-1)

-0.000309

0.000140

-2.205282

0.0310

S(-1)^2

-7.97E-11

5.33E-10

-0.149679

0.8815

R-squared

0.351017

Mean dependent var

1.550298

Adjusted R-squared

0.259754

S.D. dependent var

1.968439

S.E. of regression

1.693596

Akaike info criterion

4.016674

Sum squared resid

183.5692

Schwarz criterion

4.328034

Log likelihood

-138.6169

F-statistic

3.846209

Durbin-Watson stat

0.580160

Prob(F-statistic)

0.000621

According to the two test statistics involved in the regression result, we can say that the distribution is statistically significant so we can reject null hypothesis.

The Durbin-Watson test: This is used to test for serial correlation. Autocorrelated residuals means that OLS is no longer best, linear, unbiased estimators and that the standard errors computed using the OLS formula are not correct. The Durbin-Watson statistic of 0.214690 shows that there is positive serial correlation as DW< 2 and since there are more than 50 observations in the sample (74), this also indicates strong first-order serial correlation.

## Model 2:

## S&P500 = Î²1 + Î²2 federal funds rate + Î²3real GDP + Î²4unemployment rate.

The aim of this model is to determine if the federal funds rate has any impact on the stock market. Real GDP and unemployment rate are used as control variables for reasons given in the research methodology.

Dependent Variable: SP500

Method: Least Squares

Date: 07/06/10 Time: 01:38

Sample: 1990:1 2009:4

Included observations: 80

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-115.7008

222.2313

-0.520632

0.6041

FED_FUNDS_RATE

0.990301

12.96436

0.076386

0.9393

REAL_GDP01

0.159538

0.010327

15.44916

0.0000

UNEMPLOYMENT_RATE

-119.5674

17.42177

-6.863101

0.0000

R-squared

0.872734

Mean dependent var

924.0339

Adjusted R-squared

0.867710

S.D. dependent var

378.2205

S.E. of regression

137.5651

Akaike info criterion

12.73478

Sum squared resid

1438237.

Schwarz criterion

12.85388

Log likelihood

-505.3912

F-statistic

173.7244

Durbin-Watson stat

0.350064

Prob(F-statistic)

0.000000

Interpretation:

The estimated regression is:

## s&p500 =-115.78 + 0.99*actual change in federal funds rate + 0.16*real GDP â€“ 119.57* unemployment rate.

The coefficient associated with the federal funds rate is negative and is not statistically significant. The coefficient associated with the real GDP is positive and is statistically significant while the coefficient associated with the employment is negative but statistically significant. An R-square of 0.87 shows that we are able to explain about 87% of the variability in the s&p500.

## Model 3:

S&P500 = Î²1 + Î²2*%âˆ†M1 + Î²3*Real GDP + Î²4*Unemployment rate

Dependent Variable: SP500

Method: Least Squares

Date: 07/06/10 Time: 02:20

Sample: 1990:1 2009:4

Included observations: 80

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

46.44939

148.8335

0.312090

0.7558

M1

9.337596

5.174957

1.804382

0.0751

REAL_GDP01

0.157616

0.008466

18.61858

0.0000

UNEMPLOYMENT_RATE

-150.2864

20.48732

-7.335580

0.0000

R-squared

0.877952

Mean dependent var

924.0339

Adjusted R-squared

0.873135

S.D. dependent var

378.2205

S.E. of regression

134.7151

Akaike info criterion

12.69291

Sum squared resid

1379261.

Schwarz criterion

12.81201

Log likelihood

-503.7163

F-statistic

182.2360

Durbin-Watson stat

0.378905

Prob(F-statistic)

0.000000

The estimated regression is:

## S&P500 = 46.45 + 9.34%âˆ†M1 + 0.16Real GDP â€“ 150.29Unemployment rate

Interpretation:

The coefficient associated with the %âˆ†M1 is positive and it is not statistically significant. The coefficient associated with real GDP is positive and it is statistically independent while the coefficient associated with the unemployment rate is negative and it is statistically significant. The R-square shows that we are able to explain 87% of the variability of the s&p500.

Although the actual and fitted line moves at almost the same frequency, the residual line is independently and identically distributed. This shows that their might be a misspecification in the model.

The histogram shows that it is not very normal and the jarque-bera statistic shows that we cannot reject the null hypothesis.

White Heteroskedasticity Test:

F-statistic

15.31572

Probability

0.000000

Obs*R-squared

53.05639

Probability

0.000000

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 07/06/10 Time: 02:46

Sample: 1990:1 2009:4

Included observations: 80

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

970357.2

210038.1

4.619911

0.0000

M1

29162.57

7778.598

3.749077

0.0004

M1^2

75.30446

198.5262

0.379317

0.7056

M1*REAL_GDP01

-0.795715

0.540692

-1.471661

0.1456

M1*UNEMPLOYMENT_RATE

-3397.373

1332.934

-2.548792

0.0130

REAL_GDP01

-68.28240

28.44182

-2.400775

0.0190

REAL_GDP01^2

0.001171

0.001082

1.082364

0.2828

REAL_GDP01*UNEMPLOYMENT_RATE

7.582585

2.401815

3.157023

0.0024

UNEMPLOYMENT_RATE

-211388.2

28973.71

-7.295863

0.0000

UNEMPLOYMENT_RATE^2

11536.47

2587.237

4.458994

0.0000

R-squared

0.663205

Mean dependent var

17240.76

Adjusted R-squared

0.619903

S.D. dependent var

26363.86

S.E. of regression

16253.85

Akaike info criterion

22.34652

Sum squared resid

1.85E+10

Schwarz criterion

22.64427

Log likelihood

-883.8607

F-statistic

15.31572

Durbin-Watson stat

1.553060

Prob(F-statistic)

0.000000

The two statistics in the white test show that evidence of no heteroskedasticity exists.

S&P500 = Î² 1+ Î²2*%âˆ†M2 + Î²*3Real GDP + Î²4*Unemployment rate

Dependent Variable: SP500

Method: Least Squares

Date: 07/06/10 Time: 02:25

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

REAL_GDP01

0.149376

0.010252

14.56981

0.0000

UNEMPLOYMENT_RATE

-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 estimated regression is:

S&P500 = -87.43 + 13.44%âˆ†M2 + 0.15Real GDP â€“ 117.00Unemployment rate

Interpretation:

The coefficients of M2 and real GDP are both positive while that of the unemployment rate is negative while the p-values show that real GDP and unemployment rate are statistically significant while M2 is not. The R-squared shows that we are able to explain the variability of the S&P500 by 87%.

This diagram shows that the actual and fitted lines do not move at exactly the same frequency but are close enough while the residual line is better than that of the M2 showing that it is not quite independently and identically distributed.

From the histogram, we can see that the distribution is roughly distributed and the jarque-bera shows that the null hypothesis cannot be rejected.

White Heteroskedasticity Test:

F-statistic

4.750272

Probability

0.000061

Obs*R-squared

30.33367

Probability

0.000385

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 07/06/10 Time: 02:49

Sample: 1990:1 2009:4

Included observations: 80

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

746131.3

254782.4

2.928504

0.0046

M2

10672.81

13299.74

0.802483

0.4250

M2^2

-504.8870

659.6998

-0.765328

0.4466

M2*REAL_GDP01

1.417689

1.591493

0.890792

0.3761

M2*UNEMPLOYMENT_RATE

-3338.505

1401.946

-2.381336

0.0200

REAL_GDP01

-85.91669

37.86747

-2.268879

0.0264

REAL_GDP01^2

0.001707

0.001357

1.257810

0.2126

REAL_GDP01*UNEMPLOYMENT_RATE

7.019909

2.298457

3.054183

0.0032

UNEMPLOYMENT_RATE

-97773.44

21069.03

-4.640624

0.0000

UNEMPLOYMENT_RATE^2

2824.279

1386.827

2.036504

0.0455

R-squared

0.379171

Mean dependent var

17339.39

Adjusted R-squared

0.299350

S.D. dependent var

25364.16

S.E. of regression

21231.03

Akaike info criterion

22.88078

Sum squared resid

3.16E+10

Schwarz criterion

23.17854

Log likelihood

-905.2313

F-statistic

4.750272

Durbin-Watson stat

1.045072

Prob(F-statistic)

0.000061

The relevant statistics in this test show that the residuals are heteroskedastic.

## CONCLUSION AND RECOMMENDATIONS

The result of this study shows that there is a negative relationship between changes in asset prices and federal funds rates confirming that changes an increase in asset prices leads to a decrease in the federal funds rates ( i.e expansionary monetary policy). This is in line with the arguments of most of the economists who have carried out research on this topic.

Model 2 provides results which show that there is a negative relationship between the federal funds rate even when the s&p500 is used as the dependent variable and that the relationship is statistically insignificant which shows that the federal funds rate does not have much of an impact on the s&p500.

The third model which studies the relationship between money supply and asset prices shows that while there is a positive relationship between money supply and asset prices, both regressions (involving M1 and M2) are not statistically significant.

I would recommend that the central bank continues to closely monitor the stock market in order to make the necessary adjustments to the economy when necessary. It is also important that the federal government does not try to regulate stock market prices using federal fund rates because there is very little impact of federal funds rates on the stock market. Finally, I recommend that although money supply is positively related to the stock market, it does not matter if a particular monetary aggregate is used. The FOMC should focus on ensuring that the money supply is moderate and does not lead to inflation and increase in price levels in the economy