### Testing the hypothesis that monetary policy responds to stock market movements

Abstract

This paper highlights a problem in using the OLS model of Taylor’s rule, including lagged value of fed funds rate and stock index’s return to address whether the monetary policy should respond to asset prices movement or not. However, to know more exactly about the direct or indirect relationship between stock prices and the monetary rules, the more efficient method of Generalized method of moments (GMM) needs to be carried out based on an instrument list of output gap, growth rate of real GDP and inflation. The combination of two above methods gives reasonable results in our empirical framework. In order to derive accuracy empirical result, two country (US 1990-2009, UK 1990-2009) data would be provided in the paper.

## Introduction

In modern macroeconomics, there is a considerable amount of interest in understanding the question whether the central banks should response or ignore asset price volatility. This question has been a controversial issue since the Federal Reserve Chairman Greenspan sparked it, as one of “irrational exuberance” as early as 1996, then was followed by Bernanke and Gertler (1999), Cecchetti (2000), Adam Posen (2006) and many other authors. No agreement has been reached but what all researchers agree on is the necessity of further research on the nature of asset price movement, how they affect the economy and the effect of money policy on volatilities. This paper attempts to estimate this multilateral relationship based on ongoing researches in this field.

There are several reasons why the correlation between monetary-policy framework and asset bubbles is an important issue. From the perspective of central banks, dependable estimates of the reflection of asset prices to the policy instrument plays an essential role in formulating effective policy decisions. In reality, the effect of the short-term interest rates on asset prices has caused much of transmission of inflation targeting. Moreover, the attention of financial press for the Federal Reserve performance states the significant influence of monetary on financial markets. Hence, a well-performed economy does need to have accurate estimates of the reaction of asset prices to monetary policy.

In order to approach these issues, we develop an OLS estimation using simple regression Taylor Rule (1993) and apply Generalized Method of Moments (GMM) to deal with the relationship between monetary policy and asset price movements.

The paper proceeds as follows. Section 2 presents the theoretical framework, in which empirical debates from recent authors including supporting and rejecting are particularly discussed. Data and Testing Method and Empirical Framework are described in section 3. Section 4, empirical framework, is going to present the descriptive statistics with testing procedures of hypothesises. Results on the responsiveness of stock prices and interest rates to monetary policy coming through all of the actual testing process from data collection are presented in section 5 and section 6.

Theoretical Framework

How a central bank should set short-term interest rates

Taylor (1993)[1] estimated policy reaction functions and found that monetary policy can often be well approximated empirically by a simple instrument rule for interest rate setting. The following is one variant of the Taylor rule:

it = r* + ?* + ?(?t – ?*) + ?(yt – yN)

where ? , ? > 0; r* is the average (long-run) real interest rate.

Taylor (1993) found that ?=1.5 and ?=0.5:

it = r* + ?* + 1.5(?t – ?*) + 0.5(yt – yN)

The Taylor rule is acknowledged by all to be a simple approximation to actual policy behavior. It represents a complex process with a small number of parameters.

### Monetary policy should or should not responds to stock market movements

In recent decades, in line with the development of stock market, which provide information about the current and future course of monetary policy goal variables – inflation, employment, and output, the monetary authority should respond to equity price. A more controversial role of equity prices in the monetary policy process concerns whether the monetary policy should or should not take a direct interest in stock market.

It has attracted many researchers to discuss about the usefulness and test the validity of the hypothesis that monetary policy responds to stock market movements. Those researches have created many different results of both supporting and rejecting the hypothesis.

Supporting the hypothesis

Some of the supporters for the hypothesis that the reaction to misalignments in stock prices would have impact on the monetary policy rules are Cecchetti et al. (2000), and Jeff Fuhrer and Geoff Tootell (2004). Cecchetti used a linear rational expectations model, focusing on the output gap and inflation expectations – some primary elements in the policy rules- to support the hypothesis. Hence, the result showed that if the estimation errors are positively correlated, both inflation and misalignments with a positive coefficient increases the impact on the monetary policy. By contrast, Jeff Fuhrer and Geoff Tootell took the regression from the form of Taylor policy that used correlations among the funds rate and the gap measure, a four-quarter moving average of inflation, the real GDP and the lags of stock prices. After that, they used GMM to estimate the regression. Because the data used are ex-post, the policy actions should be taken to the stock prices movements.

However, there are still some contention is that this counter-argument is not entirely valid and these come from several antagonists like Bernanke and Gertler with their predominant abstractions (1999 and 2001).

Rejecting the hypothesis

There have been a significant number of advocates against the responsiveness of central banks to asset price movement in their policy formulation so far. Two of the most important contributors in this field are Bernanke and Gertler with their two seminal studies (1999 and 2001). On the basis of non-optimizing models of monetary policy, where coefficients of interest rates on GDP and inflation is selected specifically, Bernanke and Gertler generated the result that inflation-targeting policymakers should not take asset prices into account other than changes in expected inflation are foreshadowed. Adam Posen (2006), likewise, has argued that central banks need not target asset prices, but would be well advised to monitor them, when those bubbles get very far out of line. By studying the correlation between periods of monetary easing and property bubbles, he found the hypothesis that quantitative easing would result in asset volatility unsupported.

These results are challenged among other researchers including Roubini Nouriel (2006), Andrew Filardo (2004), especially Stephen Cecchetti (2000). Cecchetti arrived at the different results, even though one portion of the testing method he employed was the same with Bernanke and Gertler (1999).

Data and testing method

U.S. Data selection

The data that being selected reflects the period from Q1/1990 to Q4/2009 in the U.S., including time series of

Inflation: Cpi all Items City Average /Index Number /Base year: 2005 /averages /Cnt: United States /Source: IMF, Wash

Fed Funds Rates: Discount Rate (end of Period) /percent per annum /stocks /Cnt: United States /Source: IMF, Wash

Real GDP: Gdp vol 2005 Ref., Chained /U.s. Dollars ,billions of .. /averages /constant prices (seas. /Cnt: United States /Source: IMF, Wash

S&P500 stock index: Finance.Yahoo.Com, the quarterly close price index.

Stock Index S&P500 is chosen because it is typically weighted averages of the prices of the component stocks. Very often dividends are excluded from the return calculation of the index. The composition of most indices changes occasionally, so that a long time series will not be made up of return from a homogeneous asset.

In this paper, we prefer the continuous compounded definition of using logarithm because multi-period returns are then sums of single-period returns. This could make time series of data more smoothing and increase the exactness of estimation[2].

The regressions take the form of Taylor rule, augmented to allow partial-adjustment or “interest rate smoothing”, or more simply the conclusion of a lagged fed funds rate, as discussed in Clarida, Gali, and Gertler (1998). We begin with the regression, in which the fed funds rate responds to contemporaneous observations on a “gap” measure (either the unemployment rate or a Hodrick-Prescott detrended real GDP gap[3]), a four-quarter moving average of an inflation measure, the growth rate of real GDP, and lags of a variety of stock price measures.

Unit root test for f – log(fed funds rate)

Possibly, there is some omitted variables causing autocorrelation. We need to use unit root tests for random variables.

Null Hypothesis: F has a unit root

Exogenous: Constant

Lag Length: 4 (Automatic – based on SIC, maxlag=11)

t-Statistic

Prob.*

Augmented Dickey-Fuller test statistic-3.380296

0.0148

*MacKinnon (1996) one-sided p-values.

As might be seen from the graph, there is a downward trend of fed funds interest rates. The unit root test gives an idea that there should be an inclusion of a lagged dependent variable

Inflation – 100*(log(CPI)t-log(CPI)t-4)

Delta_Y – 100*(log(real_gdp)t-log(real_gdp)t-1)

GAP – a Hodrick-Prescott detrended real GDP gap

U.K. Data selection

The following covers the period from Q1/1990 to Q4/2009 in U.K, including time series of

Inflation: Cpi all Items City Average /Index Number /Base year: 2005 /averages /Cnt: United States /Source: IMF, Wash

Bank of England Interest Rates: Discount Rate (end of Period) /percent per annum /stocks /Cnt: United States /Source: IMF, Wash

Real GDP: Gdp vol 2005 Ref., Chained /U.s. Dollars ,billions of .. /averages /constant prices (seas. /Cnt: United States /Source: IMF, Wash

FTSE 100 stock index: Finance.Yahoo.Com, the quarterly close price index.

Stock Index FTSE 100 is chosen because it is typically weighted averages of the prices of the component stocks. Very often dividends are excluded from the return calculation of the index. The composition of most indices changes occasionally, so that a long time series will not be made up of return from a homogeneous asset.

In this paper, we prefer the continuous compounded definition of using logarithm because multi-period returns are then sums of single-period returns. This could make time series of data more smoothing and increase the exactness of estimation[4].

The regressions take the form of Taylor rule, augmented to allow partial-adjustment or “interest rate smoothing”, or more simply the conclusion of a lagged fed funds rate, as discussed in Clarida, Gali, and Gertler (1998). We begin with the regression, in which the fed funds rate responds to contemporaneous observations on a “gap” measure (either the unemployment rate or a Hodrick-Prescott detrended real GDP gap[5]), a four-quarter moving average of an inflation measure, the growth rate of real GDP, and lags of a variety of stock price measures.

Unit root test for f – log(fed funds rate)

Possibly, there is some omitted variables causing autocorrelation. We need to use unit root tests for random variables.

Null Hypothesis: I has a unit root

Exogenous: Constant

Lag Length: 1 (Automatic – based on SIC, maxlag=11)

t-StatisticProb.*

Augmented Dickey-Fuller test statistic-1.2811770.6347

As might be seen from the graph, there is a downward trend of fed funds interest rates. The unit root test gives an idea that there should be an inclusion of a lagged dependent variable.

Inflation – 100*(log(CPI)t-log(CPI)t-4)

OUTPUT_GAP – 100*(log(real_gdp)t-log(real_gdp)t-1)

Empirical Framework

U.S. Data test section

Methodology

Following the Taylor’s rule, a regression of the model below is going to be estimated:

It = a + bIt-1 + cGapt + d?yt + z?t + ?ekst-k (1)

In which:

It: the quarterly average of the daily observations on the federal funds rate

Gapt: the Hodrick-Prescott detrended real GDP gap

?t: the four-quarter moving average of the rate of inflation in the consumer price index

?yt: the quarterly percentage change in real GDP

st-k: the quarterly percentage change in a stock price index, lagged as k intervals

We choose this specification to begin with because it represents a simple augmentation of the canonical Taylor rule, without worrying about the potential simultaneity between the current funds rate and the current stock prices[6]. Importantly, (1) differs from (0) since we consider more lagged values of the fed funds rates (It-1) and the asset price movements (?ekst-k).

When we estimate equation (1), we set the following null hypothesi

{

H0: ek = 0

H0: ek # 0

If we accept the above null hypothesis, we may safely claim that monetary policy is not accepted by asset price movements. If we reject the above null hypothesis, we may safely claim that asset price movements play a role in determining monetary policy.

We start estimating equation (1) by using only one lag of st and then we proceed from specific to general to decide the correct number of lags (in other words, we estimate the model again by including more lags until we meet a lagged regressor, which is not significan

Eview results of estimating equation (1) using 1 lagged value of st

Dependent Variable: F

Method: Least Squares

Date: 02/07/11Time: 23:57

Sample (adjusted): 1991Q1 2009Q4

Included observations: 76 after adjustments

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-0.123706

0.082768

-1.494617

0.1395

F(-1)

0.852312

0.051377

16.58952

0.0000

GAP

0.010505

0.028245

0.371928

0.7111

DELTA_Y

0.129730

0.040953

3.167808

0.0023

INFLATION

0.064981

0.026331

2.467884

0.0160

S(-1)

0.010320

0.003063

3.368900

0.0012

R-squared0.918894

Mean dependent var1.194237

Adjusted R-squared0.913101

S.D. dependent var0.658791

S.E. of regression0.194203

Akaike info criterion-0.364172

Sum squared resid2.640028

Schwarz criterion-0.180167

Log likelihood19.83853

Hannan-Quinn criter.-0.290634

F-statistic158.6138

Durbin-Watson stat1.742329

Prob(F-statistic)0.000000

It might be noted that the coefficient to s(-1) of 0.010320 is positive and statistically significant (p-value=0.0012 much lower than ?=0.05).

Eview results of re-estimating equation (1) using 2 lagged value of st

Dependent Variable: F

Method: Least Squares

Date: 02/07/11Time: 23:59

Sample (adjusted): 1991Q1 2009Q4

Included observations: 76 after adjustments

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-0.150214

0.086749

-1.731607

0.0878

F(-1)

0.869165

0.053967

16.10563

0.0000

GAP

0.008441

0.028311

0.298142

0.7665

DELTA_Y

0.148092

0.044741

3.310002

0.0015

INFLATION

0.064308

0.026332

2.442183

0.0172

S(-1)

0.009965

0.003082

3.232900

0.0019

S(-2)

-0.003290

0.003233

-1.017793

0.3123

R-squared0.920094

Mean dependent var1.194237

Adjusted R-squared0.913145

S.D. dependent var0.658791

S.E. of regression0.194153

Akaike info criterion-0.352758

Sum squared resid2.600980

Schwarz criterion-0.138085

Log likelihood20.40479

Hannan-Quinn criter.-0.266964

F-statistic132.4186

Durbin-Watson stat1.789665

Prob(F-statistic)0.000000

We may note that the second lag of s (s(-2) of -0.003290) is not significant (p-value of 0.3123 much higher than ?=0.05) whereas the first lag s(-1) is still positive and significant (p-value=0.0019 lower than ?=0.05). This implies that the correct choice about the number of lags implies that we need to include only the first lagged value of the stock index’s return.

Testing significant coefficients

The statistically significant positive coefficient to s(-1) implies that the asset price goes up Fed should increase interest rate. Inflation and real GDP growth rate are significant (p-values are 0.0023 and 0.0160 less than ?=0.05) whereas gap is insignificant (p-value of 0.7665 much higher than ?=0.05). However, there are some conflicts with the theory if the gap is removed out of the specification. Indeed, R-squared and Adjusted R-squared show that the model explains the dependent variable more than 90%. It is necessary to examine the model by applying GMM (the generalized method of moments).

Testing a good fit

As we can see, R2 of 0.918894 and Adjusted R2 of 0.913101 show that the model explains above 90% changes of fed fund rates. F-statistic also depicts that all regressors are jointly significant. This seems to support the view of Cecchetti et al. (2000).

Testing autocorrelation

Durbin’s h test, with n=76, we have

– d = 1.742329

– h=(1-d/2)v(n/(1-n/error(b))) = 1.2559142007 < z-critical = 1.96

We cannot reject H0 of Durbin’s h test and conclude that this model does not suffer from serial correlation.

Breusch-Godfrey Serial Correlation LM Test:

F-statistic1.001164

Prob. F(4,66)0.4134

Obs*R-squared4.347625

Prob. Chi-Square(4)0.3610

Both the LM statistic and the F statistic are quite low, suggesting that we cannot reject the null of no serial correlation (p-value of 0.3610 is much higher than ?=0.05). Therefore, both Durbin’s h and Breusche-Godfrey test conclude that this model does not suffer from autocorrelation.

The analysis above lets us to give a positive answer to the first question we posed before. The significance of the lagged value of s implies that asset price movement plays a role in refining monetary policy.

Testing heteroskedasticity

Both Breusch-Pagan-Godfrey statistic (16.19839) and F statistic (3.792163) are quite high, suggesting the rejection of the null hypothesis of the heteroskedasticity test (p-values of 0.0063 and 0.0043 are much less than ?=0.05). As can be seen from the test results, coefficients of gap, delta_y, and s(-1) are insignificant. Contrastingly, the inflation might have certain impact on the variance of the error terms.

Heteroskedasticity Test: Breusch-Pagan-Godfrey

F-statistic3.792163

Prob. F(5,70)0.0043

Obs*R-squared16.19839

Prob. Chi-Square(5)0.0063

Scaled explained SS55.18278

Prob. Chi-Square(5)0.0000

With White’s test with no cross products, the p-values of both White’s statistic (0.0895) and F statistic (0.0879) are higher than ?=0.05 and these tests do not conclude a rejection of no heteroskedasticity.

Heteroskedasticity Test: White

F-statistic2.009014

Prob. F(5,70)0.0879

Obs*R-squared9.537445

Prob. Chi-Square(5)0.0895

Scaled explained SS32.49105

Prob. Chi-Square(5)0.0000

In White’s test with cross products, both White’s statistic F statistic with p-values nearly zero illustrate that there is a conclusion of a rejection of no heteroskedasticity. Therefore, there is evidence of heteroskedasticity. Intuitively, delta_y*s(-1) and inflation*s(-1) do not have a significant impact on the variance of error terms (p-values are 0.3398 and 0.2187 much higher than ?=0.05, respectively). This might imply that the relationship between delta_y and inflation with s(-1) should be examined in GMM application.

Heteroskedasticity Test: White F-statistic

7.540388

Prob. F(20,55)

0.0000

Obs*R-squared

55.68978

Prob. Chi-Square(20)

0.0000

Scaled explained SS

189.7174

Prob. Chi-Square(20)

0.0000

The graph of residuals also shows that the model does not fit the data precisely (there are more and more underestimates and overestimates, especially from 2000 to 2009).

Testing heteroskedasticity possibly implies that the traditional view as the equation (1) might be violated by heteroskedasticity of cross products. The co-efficiencies are still unbiased and consistent. This has a wide impact on hypothesis testing neither the t statistics or the F statistics are reliable any more for hypothesis testing because they will lead us to reject the null hypothesis too often. This is possible reason to examine whether the relationship between the stock index’s return and fed funds rate is direct or indirect.

Testing misspecification

In Ramsey RESET test, since the p-values of 0.1056 (Likelihood ratio) and 0.1245 (F-statistic) are both higher than ?=0.05, we cannot reject the null hypothesis of correct specification. Notice, as well, that the coefficient of the squared fitted term is not significant (t-stat = 1.555220).

Ramsey RESET Test

Equation: LAG1_V

Specification: F C F(-1) GAP DELTA_Y INFLATION S(-1)

Omitted Variables: Squares of fitted values

Value

df

Probability

t-statistic 1.555220

69

0.1245

F-statistic 2.418708

(1, 69)

0.1245

Likelihood ratio 2.618454

1

0.1056

Generalized method of moments (GMM)

We will evaluate whether the asset price movement plays a role directly or indirectly through its effects on inflation and output growth. We can do this by using a GMM estimator, which is an instrumental variable approach.

By applying the forward-looking extension for Taylor rule, the instrument list of gap (a Hodrick-Prescott detrended real GDP gap), delta_y (the growth rate of real GDP) and inflation (inflation rate) will be taken to perform GMM.

Dependent Variable: F

Method: Generalized Method of Moments

Date: 02/13/11Time: 14:11

Sample (adjusted): 1991Q1 2009Q1

Included observations: 73 after adjustments

Linear estimation with 1 weight update

Estimation weighting matrix: HAC (Bartlett kernel, Newey-West fixed

bandwidth = 4.0000)

Standard errors & covariance computed using estimation weighting matrix

Instrument specification: GAP(+1) GAP(+2) GAP(+3) DELTA_Y(+1)

DELTA_Y(+2) DELTA_Y(+3) INFLATION(+1) INFLATION(+2)

INFLATION(+3)

Constant added to instrument list

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.111616

0.401825

0.277772

0.7820

F(-1)

0.658808

0.294358

2.238116

0.0285

GAP

0.065476

0.072798

0.899426

0.3716

DELTA_Y

0.169216

0.215013

0.787001

0.4341

INFLATION

0.050838

0.045147

1.126059

0.2642

S(-1)

0.028287

0.029343

0.964010

0.3385

Interpreting results

The relationship between inflation and real GDP with fed funds rate

As OLS’ result, the growth rate of real GDP and inflation affects positively the dependent variable and it is statistically significant, while the gap is not. However, it might be spurious if the gap is removed because the heteroskedasticity testing shows that the OLS model (1) is no longer the most efficient estimator[1].

The relationship between FTSE100 and Bank of England interest rate

As GMM’s result, it is important to pay attention to the coefficient associated to s(-1). As OLS’ result, it is positive and significant but this time it is not statistically significant in GMM’s result. This implies that the asset price movements affect the way in which the monetary policy is set only indirectly and not directly.

Consequently, asset price movements have impact on fed funds rates indirectly.

Conclusion

In conclusion, the results of this project show that the hypothesis that refer to whether the volatility of the stock price would affect the monetary policy, in some mood, is proved to be indirectly impact the policy making.

These results might be caused by the limitation of this project. Compare to Cecchetti et al. (2000) who focused on using some estimation of primary elements in the policy rules, including the output gap and inflation expectations to produce the hypothesis. He supposed that these elements would have to depend on some estimation of the evolution of stock prices providing that the asset prices affect the economy’s path. However, we build up two models to by OLS and GMN to test the hypothesis. For GMM, we compare the data and observe that the co-efficient are insignificant. At this time, we switch to OLS model, surprisingly found that the co-efficient of GAP is insignificant. Moreover, it is still controversial to clear about the strength of the endogeneity test for GMM estimation because we do not have another test to compare with. This is the reason why the instrument list we choose is still controversial.

However, the data we estimate is enough that is perfectly applies to the line with the theory of Taylor rule that is approximately well estimated, significant of R-squared, Durbin-Watson and F-test by the means of OLS and GMM model test. Hence, large amount of surveys indicate that recent researches tend to have similar results. For Example, Two of the most important contributors in this field are Bernanke and Gertler with their two seminal studies (1999 and 2001). On the basis of non-optimizing models of monetary policy, where coefficients of interest rates on GDP and inflation is selected specifically, Bernanke and Gertler generated the result that inflation-targeting policymakers should not take asset prices into account other than changes in expected inflation are foreshadowed. Adam Posen (2006), likewise, has argued that central banks need not target asset prices, but would be well advised to monitor them, when those bubbles get very far out of line. By studying the correlation between periods of monetary easing and property bubbles, he found the hypothesis that quantitative easing would result in asset volatility unsupported. Therefore, the results of this project may reflect the nature.

It is likely that the volatility of stock price would have effect on the monetary policy. In order to meet the needs of inflation targeting which is proved by the classical economy theory that slightly inflation could stimulate the real economy, the central bank authorities do evaluate these two factors when making monetary policy decision to maintain the asset price is neither too high nor too low so does the inflation rate.

References

Jeff Fuhrer and Geoff Tootell. “Eyes on the Prize: How Did the Fed Respond to the Stock Market”. Federal Reserve Bank of Boston, Discussion Papers, April 2004, No. 04-2.

Bernanke, Ben and Gertler, Mark. “Money Policy and Asset Volatility”. Federal Reserve Bank of Kansas City Economic Review, Fourth Quarter 1999, 84(4), pp. 17-52.

Bernanke, Ben and Mark Gertler “Should Central Banks Respond to Movements in Asset Prices” American Economic Review, May 2001.

Posen, Adam S. (2006) “Why Central Banks Should not Burst Bubbles”, Institute for International Economics, Washington, DC, working paper 01/06.

Filardo, Andrew (2004) “Monetary Policy and Asset Price Bubbles: Calibrating the Monetary Policy Trade-Offs,” BIS working paper No.155, Basel.

Roubini, Nouriel, (2006), “Why Central Banks Should Burst Bubbles”. International Finance 9, no.1

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Bernanke, Ben and Mark Gertler “Should Central Banks Respond to Movements in Asset Prices” American Economic Review, May 2001.

Posen, Adam S. (2006) “Why Central Banks Should not Burst Bubbles”, Institute for International Economics, Washington, DC, working paper 01/06.

Filardo, Andrew (2004) “Monetary Policy and Asset Price Bubbles: Calibrating the Monetary Policy Trade-Offs,” BIS working paper No.155, Basel

Roubini, Nouriel, (2006), “Why Central Banks Should Burst Bubbles”. International Finance 9, no.

Cecchetti, Stephen ; Genberg, Hans; Lipsky, Jonhn and Wadhwani, Sushil. “Asset Prices and Central Bank Policy”. LondonInternationalCenter for Monetary and Banking Studies, 2000

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Dimitrios Asteriou and Stephen G.Hall. “Applied Econometrics – A modern approach”, Palgrave Macmillan, revised edition 2006, 2007.

H.Studentmund. “Using Econometrics: A practical Guide”. Pearson 2000, International Edition, 5th edition.