THE RELATIONSHIP BETWEEN MONEY SUPPLY AND THE GDP OF UNITED STATES

THE RELATIONSHIP BETWEEN MONEY SUPPLY AND THE GDP OF UNITED STATES BY LIANG, Fang 08050597 Applied Economics & HUANG, Weiya 08050872 Applied Economics An Honors Degree Project Submitted to the School of Business in Partial Fulfillment of the Graduation Requirement for the Degree of Bachelor of Business Administration (Honors) Hong Kong Baptist University Hong Kong April 2011

Acknowledgement We would like to express our deepest gratitude to Professor Wing-Keung Wong for all the encouragement, guidance and support to us in this project, furthermore, whose dedication and enthusiasm in the economic studies motivate us to always be curious and eager to learn while exploring the world of economics. Also, we are greatly grateful to our families and friends who grant us generous care and support which make the completion of this paper a possible. i

Abstract Among the monetary policies that the Fed adopts in intervening the US economy, Open Market Operation is the one which is most frequently used due to its easily observable effect and relatively low cost during operation. Via buying and selling US Treasuries the Fed adjusts the money supply in the market and manipulates the economy. In recent years, a modern practice of this policy is used by the Fed which targets the federal funds rate to control the money supply. Following a brief introduction on the Federal Reserve and its monetary policy making mechanism this paper studies the relationship between money supply and the economic output from theoretical and statistical perspectives. An equation indicating this relationship, focusing on d(gdp) and d(m2), is estimated by OLS by SAS in statistical analysis section. Based on the research, we conclude that lagged changes in GDP play a significant role in estimating the change in M2, and we also predict the estimated change of M2 in 2011Q1 and the corresponding M2 at the end of the first quarter of 2011 through the estimated equation. ii

Table of Contents Acknowledgement... i Abstract... ii 1 Introduction... 1 2 Literature Review... 1 3 Theoretical analysis... 3 3.1 AD-AD, IS-LM Model... 3 3.2 The mechanism of M2... 4 3.3 Presumptions... 6 4 Statistical Analysis... 8 4.1 Research Objective... 8 4.2 Data Collection... 9 4.3 Vector Autoregressive Model... 9 4.3.1 Unit Root Test: Variable Selection... 10 4.3.2 Granger Causality... 11 4.3.3 OLS: Equation Estimation... 13 4.4 Interpretation... 16 5 Prediction... 17 6 Conclusion and limitations... 18 6.1 Conclusion... 18 6.2 Limitations... 20 References... 22 Appendix I... 24 Appendix II... 31 Appendix III... 38 1

THE RELATIONSHIP BETWEEN MONEY SUPPLY AND THE GDP OF UNITED STATES 1 Introduction Since the Federal Reserve has been playing an essential role in affecting or even controlling the US economy system through implementing monetary policies and targeting a stabilized economy system, attention of economists is attracted to follow the fed s policy behavior and implication behind. The three main tools of the Fed in influencing the market are open market operations, discount rate and reserve requirement. The importance of the function of Fed cannot be overemphasized because of its irreplaceable responsibility for the management of aggregate demand via total spending as well as inflation. Several researches have attempted to figure out the rules of policy choices made by the Federal Reserve that influenced interest rates and other economic indicators (Feldstein&Stoc, 1994). Inspired by them, this study mainly focuses on the relationship between M2 and GDP of the United States, as well as a brief prediction of future US economic tendency based on the current policy tendency from the Federal Reserve. 2 Literature Review A substantial number of empirical researches have examined the mechanism of how the Fed operates as an independent private organization. These days, the Federal funds rate, which has gained growing focus from the Federal Reserve, is acting as the primary indicator of the tendency of monetary policy. The federal funds rate target is publicized at every FOMC meeting since more than a decade ago. The federal funds rate can be influenced by the changes in the three monetary policy tools open market operations, reserve requirement, and discount rate. Despite the latter two, which are determined by the board of governors, it is the FOMC that directs the open market operations of buying and selling US government 1

securities to control the federal funds rate targeting the two key objectives of the US monetary policy: price stability and maximum sustainable economic growth. The observation of the decision changes determined by FOMC has strategic meaning as an operational indicator of how the direction of monetary policy has impact on the economic system in a macro aspect. At the meeting itself, staff officers present oral reports on the current and prospective business situation, on conditions in financial markets, and on international financial developments. In its discussions, the Committee considers factors such as trends in prices and wages, employment and production, consumer income and spending, residential and commercial construction, business investment and inventories, foreign exchange markets, interest rates, money and credit aggregates, and fiscal policy. (Anon., 2011) Feldstein and Stock (1994) studied the possibility of using M2 to target the quarterly rate of growth of nominal GDP in their paper in 1994. The study evidenced that the Federal Reserve could probably make use of M2 that reduces both the long-term average inflation rate and the variance of annual GDP growth rate. Similarly, our project would examine the potentially existing relationship of how the monetary directions eventually affect the output by applying econometrical models. The research from Bernanke in 1990 stated that federal funds rate was a good indicator of monetary policy. A tight monetary policy would result in a short-run sell off of banks security holdings, as well as the impact of tautened bank loans that would depress the economy. In addition, the response of unemployment and loans in respect of monetary policy changes are more or less similar in time manner. Lang and Lansing (2010) stated that the economy recession ended in June 2009 since when the U.S. economy has recorded four consecutive quarters of positive real GDP growth. By reducing interest rate to zero and buying bad assets, the Fed has implemented a series of accommodative monetary policy to stabilize asset price and the whole economy. Regardless of the controversy aroused by spending tax revenue to save FannieMae and Freddie Mac, the reaction of the Fed during this unique period and its impact was not to be ignored. Indication 2

from this would be the consideration of policy behavior differences before, during and after the recession. One study of Fed s policy behavior by Fair (2001) estimated the implicit rules relating to interest rate and a set of economic variables, and pointed out that there was a structural change of policy behavior of Fed between 1979 and 1982. By including the structural change factor, the author was able to carry out stable coefficient estimates. The rules derived from the regression interpreted interest rate into a disciplinary changing indicator influenced by other major economic factors. 3 Theoretical analysis Open Market Operations - the most frequently used instrument of monetary policy works with the idea that by adjusting the money supply in the market, the economic output will consequently alter toward particular directions. In this section, the influence to the economy triggered by the change in money supply will be analyzed by adopting the IS-LM curve and AD-AS curve from the aspect of macroeconomics. Then, two approaches of the transmission of monetary policy s impact on output will be explained. Thereafter, the modern view of its monetary policy of Fed and its tight and loose practices of the implementation will be introduced. Finally, based on the observation on the economic environment of recent years and the actions that the Fed has taken in fighting against recession and pulling back the economy from decreasing, we would suggest the Fed continuing implementing the loose monetary policy. The possible aftermath will be concluded based on the theoretical conclusion. 3.1 AD-AD, IS-LM Model According to Keynesian structural model approach, in the money market, when there is an increase in money supply from MS 1 to MS 2 with a constant price level P 1 which leads to a drop in interest rate from r 1 to r 2, LM curve shifts downward from LM 1 to LM 2. In IS-LM model, the downward-shifted LM curve intersects with IS curve at equilibrium with an increased output, 3

Y 2. In AD-AS model, the new output level shifts AD curve up from AD 1 to AD 2. In short run, as we assume that the price is sticky, the upward-shifted AD curve intersects SRAS at a new equilibrium at the higher output level Y 2. In the long term, since the price is flexible and the output will ultimately return to the assumed-full-employment level Y 1, the upward-shifted AD curve will intersect with LRAS curve at Y 1, but at a higher price level P 2. Due to the return in the output, and the rise in price, LM curve will then shift back to the initial position LM 1, and the interest rate reduces back to the original level r 1. In summary, the increase in money supply will decrease the interest rate and increase output in short run. In the long run it has no effect on the interest rate or output, but results in inflations. On the other hand, the influence of the economy from decreasing money supply is the opposite, which will increase the short run interest rate, decrease the output, but lower the price in the long term. Figure 1 illustrates the shifts of AD and LM curve 3.2 The mechanism of M2 According to Frederic S (2007, p.603-607), the traditional Keynesian structural model exams the channels of interest rate effects through which the monetary policy eventually has impact 4

on aggregate demand. After Keynesian, researchers attempt to pursue a much more detailed structural model approach by viewing the monetary transmission mechanism through various channels (Appendix I, figure 2). Other than the traditional interest-rate monetary transmission mechanisms, those channels are separate into two basic categories: operating through asymmetric information effects on credit markets and operating through asset prices. Examples of each are provided as follow. For credit view transmissions, we use the cash flow channel to elaborate the mechanism of expansionary monetary policy. The increased money supply results in lowered nominal interest rate. This leads to an improvement of firms balance sheet since the rising liquidity enables investors to gain confidence of the firms pay back ability. The consequences lessthe moral hazard and adverse selection, and therefore, enhance the economic activities as well as the output. The schematic for the transmission through cash flow channel is: M => i => cash flow => adverse selection => moral hazard, => lending => I => Y For asset prices transmissions, one of the examples is the channel of wealth effects, through which the changes in consumers balance sheets might affect their spending decisions. As money supply is increased, the rise in stock price indicates a boost in financial wealth as consumers lifetime resources. Consequently, the consumption, which stands for the spending by consumers on nondurable goods and services, should increase and eventually cause the output expansion. Schematically, the monetary policy effect is: M => Ps => wealth => consumption => Y Hence, to simplify all the monetary transmissions, a behavioral equation provides the description of the structural approach: M α β µ Y The rectangular represents the structural model evidence of monetary influence from money supply to output. The structural approach emphasizes the procedure of operation in 5

different sectors in the economy. It has the advantage of a better understanding of how the economy works, and enables more precise prediction according to monetary or fiscal policy change. Besides, as opposite to structural model, the other direction of research moves towarda more sophisticated monetarist reduced-form model to examine the substance of money supply to the economic system. Instead of studying the reaction of separated economic sectors, the reduced-form approach directly views the impact of money supply on the output. Monetarists regard the economic activities as a black box between money supply and output in which the behaviors are invisible. M? Y It is believed that the channels through which the monetary policy affects output are continually changing. And it might be too complex to identify all the transmissions of mechanisms in the economic system. In addition, the model avoids the potential missed out of any transmission channels. Therefore, to make this research simple and clear, this approach will be adopted in the statistical analysis. 3.3 Presumptions In the economic markets, the federal funds rate has the essence of being an indicator of monetary policy. As the most important control method of federal funds rate, money supply can directly influence the behavior of federal funds rate. It is the equilibrium of demand and supply for reserves that determines the federal funds rate, which will decrease due to the increase of money supply, or say, open market purchase (figure 3). Nevertheless, when intervenes the market, instead of targeting money supply to boost the output, the Fed targets the ffr or the interest rate to a particular amount while conducting its monetary policy. With an interest rate target, the Fed then acts in the market by buying and selling certain amount of government securities, such as Treasuries, to achieve this target, and 6

Figure 3 illustrates shift of money supply curve to reach the objective of increasing output. When the Fed applies its Open Market Operations in buying and selling government securities, two practices are usually involved - tight monetary policy and loose monetary policy. Theses monetary policies represent different dimensions of the Fed in achieving the ffr target and interest rate target. While conducting the loose monetary policy, in the short run, the Fed increases money supply by purchasing Treasuries to inject money to the market. This increase in money supply decreases the ffr and consequently lowers the short run interest rate. Since the price of borrowing declines, more consumer and business are willing to borrow money from commercial banks, and it will result in an increase in investment, GDP and employment, however, an inevitably permanent increase in price level. The tight monetary policy, on the other hand, decreases the money supply by selling Treasuries, and withdraws the money from the market. With a declined money supply, there is an upward pressure on the ffr as well as the short run interest rate. As it becomes more expensive to borrow money, less consumers and businesses will borrow money form the commercial banks, and it will lead to a decrease in GDP and an increase in unemployment. 7

After the Fed has maintained the ffr at nearly to zero for two years to fight against the economic recession began in 2008, the GDP growth started picking up from negative in late 2009, and the US GDP maintained a positive growth during 2010. Albeit the economy starts to grow and the unemployment has begun to drop, the current unemployment is still dramatically higher than the normal rate. To draw the unemployment down to the safe range, more jobs need to be created, and consumers and businesses should continue being encouraged to borrow money and to increase the output. Therefore at the early stage of economic recovering, the loose monetary dimension should continue being the preferred direction to the tight monetary dimension at the FOMC meetings when monetary policies are made. Based on the analysis above, by implementing the loose monetary policy and remaining the ffr at the 0-.25%, the unemployment will continue declining, GDP growth will remain at a positive and stable rate, and the economy will keep recovering steadily. 4 Statistical Analysis In section 3 we have theoretically analyzed the mechanism of how monetary policies have impacts on the US economy. To generate a more precise relationship between money supply and the reaction of the economy, an empirical study of the presumed reasoning becomes a necessity. In this section, we conduct a quantitative research based on the real time data from the Federal Reserve Banks. We divide this statistical analysis section into two main segments. In part one, we first introduce the research objective, data collection. Then, statistical models are adopted to test the econometrical attributes of the data. We estimate a simple VAR model which involves M2 measuring the money supply, and GDP presenting the economic output. Afterward, we conduct the OLS and estimate the coefficient of each variable. Based on the result of OLS, unit root test, Granger Causality test and variance inflation factor test are conducted. In the second part, we interpret the results and probabilities, as well as provide further explanation of the method behind. 8

4.1 Research Objective In section 3, all the theories evidence that it is the money supply that eventually causes GDP to increase or decrease through a variety of transmission channels, so we focus the study of the economic output on GDP. To measure the money supply in the market, Norman Frumkin (1990, p.179) introduces four measures M1, M2, M3 and L, with a declining liquidity in assets involved. Abel, Bernanke, and Croushore mentioned in Macroeconomics that the two monetary aggregates used to measure the US currency circulation now are M1 and M2. Furthermore, because of the broader definition of M2 which includes components of M1, saving deposits, small-denomination time deposits, and MMMFs, it is usually used to quantify the money supply in the economy. Therefore, we include M2 as the variable reflecting money supply in the model. Hence, based on the theoretical analysis, our primary research objective is to examine the statistical relationship between M2 and GDP. 4.2 Data Collection Based on the research objective, the suitable data set chosen consists of quarterly time series of M2 and nominal GDP of the US over the sample period from quarter one in 2000 to quarter four in 2010. To clarify each variable, here M2 represents the sum of notes and coins (currency) in circulation, traveler's checks of non-bank issuers, demand deposits, other checkable deposits, savings deposits, and time deposits less than $100,000 and money-market deposit accounts for individuals. GDP refers to the market value of all final goods and services produced within a country in a given period in the US. There are 40 observations for each time series. 4.3 Vector Autoregressive Model Inspired by the paper of Feldstein and Stock (1994) which indicated that an optimal M2 rule 9

generated from a simple Vector Autoregressive Model (VAR) reduced GDP variance by 20%, we structure our model by adopting VAR. [ Y ] ] ' t = [ A][ Y ] t 1 +... + [ A ][ Y ] y k + [ e t.(model 1) Where k is the number of lag terms, ' variables, and the [A], and [ A ] are the [ Y ] t, [ Y ] t 1, [ Y ] t k are the 1 p vector of p p matrices of coefficients to be estimated, [ e] t is a 1 p vector of innovations that may be contemporaneously correlated but are unrelated with their own lagged values and uncorrelated with all of the right-hand side variables. 4.3.1 Unit Root Test: Variable Selection While determining the format of variables included, we generate a Unit root test by using EViews, and the results are in the appendix I (table 1). The first column includes time series of GDP and M2 in the form of GDP, M2, log(gdp), log(m2), d(gdp) and d(m2). The column 2, 3 and 4 include t-statistics of these series critical values of 1% level, 5% level and 10% level. The 6 th column consists the probability to reject the null hypothesis of time series not having a unit root. After examining the result, we find that the time series of GDP, M2, log(gdp) and log(m2) all have unit roots, which makes the forecasting result of using GDP and M2 in these forms less significant. However, the probability to reject the null hypothesis of d(m2) is 0, which indicates co-integration exists in series in difference-form, which ensures that difference-formed variables are more suitable in forecasting. Therefore, we consider d(gdp) and d(m2) as the best set of regressors than GDP and M2 and log(gdp) and log(m2), and include them as variables in the VAR model. The model is now specified as, d ) ( GDP t = 1 C + m a d( GDP) i= 1 n b d( M 2) + + 1 i t i 1 i t i t i= 1 e 1 (eq 1) d ) ( M 2 t = 2 C + p a d( M 2) i = 1 q b d( GDP) + + 2 i t i 2 i t i t i= 1 e 2 (eq 2) 10

Where a ij, b ij and error terms. ci are the parameters to be estimated, and e ij s are the stochastic We then conduct VAR test through EViews individually with lag = 1, 2, 3 and 4. The result is in appendix I (table 2). Columns 2 and 3 include dependent variable d(gdp) and d(m2), and independent variables of lagged d(gdp) and d(m2) respectively. The 5 th and 6 th columns indicate the R-square and Adjusted R-square of each lag term. By comparing the values of R-square and Adjusted R-square, we determine that the optimal lag length is 4 due to its largest R-square and Adjusted R-square values. After observing the 8 th column which consists of t-value regarding every independent variable, we find that all t-statistics of lagged d(m2) which are independent variables of d(gdp) are smaller than the critical t-value of 2. That means lagged d(m2) s arestatistically insignificant as independent variables of d(gdp). However, on the other hand, some t-statistics of lagged d(gdp) which are independent variables of d(m2) are larger than 2. That means some lagged d(gdp) s arestatistically significant as independent variables of d(gdp). Based on this analysis, we guess that the equation with d(gdp)as dependent variable is statistically insignificant. 4.3.2 Granger Causality To further test this guess, we apply Granger Causality test to examine the Granger Causality between d(gdp) and d(m2). Before conducting the Granger Causality test, we first need to test whether there exists unit root in each term. The Augmented Dickey-Fuller test result below (table 3) shows that d(gdp) has a unit root, because the probability not to reject the null hypothesis is 0.0193 which is larger than 10%. However, no unit root exists in d(m2) and d(resid), for the probabilities not to reject the null hypotheses are 0. Therefore, the time series of d(gdp) is not stationary, and time d(m2)and the residualare stationary. Detailed test result is in appendix I (table 4). 11

Augmented Dickey-Fuller Test Augmented Dickey-Fuller test statistic t-statistic Test critical values 1% level 5% level 10% level Prob.* d(gdp) 1-3.337624-3.596616-2.933158-2.604867 0.0193 d(m2) 2-6.382221-3.600987-2.935001-2.605836 0 d(resid) 3-11.23685-3.605593-2.936942-2.606857 0 1. Null Hypothesis: d(m2) has a unit root. 2. Null Hypothesis: d(gdp) has a unit root. 3. Null Hypothesis: d(resid) has a unit root. Table 3 Having obtained that result that the residual does not have a unit root, we then apply Granger Causality test to examine the causality between d(gdp) and d(m2). The results indicate that d(m2) does not Granger Cause d(gdp), and d(gdp)granger Causes d(m2). The following table shows the Granger Causality result (table 5). lag=4 Pairwise Granger Causality Tests Sample: 2000Q1 2010Q4 Lags: 4 Null Hypothesis: Obs F-Statistic Prob. D_M2 does not Granger Cause D_GDP 39 0.5557 0.6964 D_GDP does not Granger Cause D_M2 2.57393 0.0578 Table 5 12

The probability of not to reject H 0 : d(m2) does not Granger Cause d(gdp) is 0.6964 which is larger than confidence interval 0.1, so we do not reject H 0, and d(m2) does not Granger Cause d(gdp); The probability of not to reject H 0 : d(gdp) does not Granger Cause d(m2) is 0.0578 which is smaller than confidence interval 0.1, so we reject H 0, and d(gdp) Granger Causes d(m2). Based on the Granger Causality results that d(m2) does not Granger Cause d(gdp), and d(gdp) Granger Causes d(m2), we modify the original model to a new model as, k ( M 2 t = C + aid( M 2) t i i= 1 d ) l + bid ( GDP) t i i= 1 + e t (model 2) and bi 0. 4.3.3 OLS: Equation Estimation Then, we conduct OLS by using SAS to estimate the equation. The results are in appendix II. While inputting data to SAS, we select d(m2) and d(gdp) with lag terms equal to 1, 2, 3 and 4 (i = 1, 2, 3, and 4), which means, for instance, the d(m2) of 2010Q4 might be influenced by d(m2) of 2010Q3, 2010Q2, 2010Q1 and 2009Q4, and d(gdp) of 2010Q3, 2010Q2, 2010Q1 and 2009Q4. With the selecting criteria of C(p), SAS then generates one best model including d(m2) t as independent variable, d(gdp) t-1, d(gdp) t-3, d(m2) t-2, d(m2) t-3 and d(m2) t-4 as independent variables. In the result, R-square is 0.4199. The t-statistics of d(gdp) t-1, d(gdp) t-3 and d(m2) t-2 are -2.60, 2.96 and -2.06 which indicate that the estimated parameters of these variables are statistically significant. However, the coefficients of d(m2) t-3 and d(m2) t-4 with t-statistics of 1.57 and 1.62 are slightly statistically insignificant. After examining the VIF of each variable, we discovered that the multicollinearity is not significant in the model. The estimated equation is 13

d ) ( M 2 t = 62.77548-0.34105 ( M 2) t 2 d + 0.26681d ( M 2) t 3 + 0.26794d ( M 2) t 4 (1.30) (-2.06) (1.57) (1.62) - 0.30798 ( GDP) t 1 (-2.60) (2.96) *() t-value, critical t value = 2.0 d + 0.42308d ( GDP) t 3 (eq 3) In order to find the optimal equation, we also estimate an alternative equation by adapting variables in the format indicating the percentage change of M2 and GDP, which is denoted as, d[log(m2)] being the depend variable, and lagged d[log(m2)] s and d[log(gdp)] s being independent variables. We then estimate the equation in SAS. (Detailed SAS results are in Appendix III.) The new equation can be denoted as d )] [log( M 2 t = 0.00644-0.25612 [log( M 2)] t 2 (1.82) *() t-value, critical value = 2.0 d + 0.29048d [log( M 2)] t 3 (1.04) (-2.31) (3.1) GDP + 0.28265d[log( M 2)] t 4-0.50495 [log( )] t 1 (-1.64) (1.7) 0.78468d [log( GDP)] (eq 4) + t 3 d The best results of difference-formed variables and difference-log-formed variables are compared below in table 6. 14

d(m) is dependent variable Independent variables in model Intercept d(gdp1) d(gdp3) d(m2) d(m3) d(m4) t-value 1.3-2.6 2.96-2.06 1.57 1.62 Pr > t 0.2022 0.0138 0.0057 0.0474 0.1265 0.1143 standard error 48.24423 0.11834 0.14303 0.16561 0.17022 0.16516 Variance Inflation 0 1.35801 1.98787 1.54976 1.61153 1.5325 R-square 0.4199 Adj R-square 0.332 AIC 331.26 d[log(m)] is dependent variable Independent variables in model Intercept d[log(gdp1)] d[log(gdp3)] d[log(m2)] d[log(m3)] d[log(m4)] t-value 1.04-2.31 3.1-1.64 1.7 1.82 Pr > t 0.3063 0.0278 0.0041 0.1109 0.0983 0.0777 standard error 0.00619 0.21903 0.25349 0.15619 0.1706 0.15507 Variance Inflation 0 1.33755 1.79509 1.26915 1.47225 1.25311 R-square 0.3739 Adj R-square 0.2761 AIC -350.2 * critical t value= 2.0 and critical p value = 0.05 Table 6 After comparing the results from the best equations selected by SAS, we find that difference-formed equation(eq 3) is more preferable than the difference-log-formed equation (eq 4) in terms of the values of R-square, adjusted R-square, and t-statistics of all the 15

parameters. Based on the observation of R-square and adjusted R-square, it is obvious that both R-square and adjusted R-square of difference-formed equation are greater than the R-square and adjusted R-square values of the difference-log-formed equation, which intimates that the model with difference- formed variables is more statistically favorable than the model consisting of difference-log-formed variables. Furthermore, by considering t-statistics of every independent variable in each equation, we notice that difference-formed equation includes more variables with t-values greater than 2 comparing with the difference-log-formed equation. It means the difference-formed equation has more significant variables, and this model is statistically preferred to the model of difference-log-form. Therefore, on the ground of the statistic indicators discussed above, we regard equation 3 as the optimal equation estimated. 4.4 Interpretation Since d(gdp) and d(m2) indicate the difference of GDP s and M2 s between two adjacent quarters, the estimated equation can be implicated as the change in M2 is affected by the changes of GDP of 1 and 3 quarters ago as well as influenced by the changes of M2 of the last second, third and fourth quarters simultaneously. Furthermore, with other variables constant, if the GDP growth of last quarter was 1 billion USD, the M2 growth this quarter will fall by 0.30798 billion USD; if the GDP growth of the past third quarter was 1 billion USD, M2 growth this quarter will decrease by 0.42308 billion USD; when M2 growth of the former 2nd quarter reached 1 billion USD, current M2 will decline by 0.34105 billion USD; if M2 growth three quarters ago was 1 billion USD, M2 will go up by 0.26681 billion USD; and M2 of the same quarter last year raised by 1 billion USD, the M2 in this quarter will raise by 0.26794 billion USD. For instance, the M2 of first quarter in the year of 2007 will increase by 63.08428 billion USD when the changes of GDP of the year 2006 Q4 and Q2, and the change in M2 of the year 2006 Q3, Q2, and Q1 were 1 billion USD. 16

Alternatively, it can also be understood as that the targeted money supply is determined by previous money supply and economic behavior. More precisely, Fed s expected change of M2 this quarter is influenced by the actual M2 growth of last second, third and fourth quarters and GDP growth of 1 and 3 quarters ago. As mentioned in section 3, we apply reduced form approach to evaluate the relationship between M2 and GDP. The result indicates that it is the lagged change in GDP and lagged change in M2 that affect actual money supply. However, the previous theoretical analysis highlights the transmission from the change of money supply to the output. In fact, Frederic S. (2007, p.606) states that If most of the correlation between M and Y occurs because of the Fed s interest-rate target, controlling the money supply will not help control aggregate output, because it is actually Y that is causing M rather than the other way around. The structural approach, which studies every channel that money supply has impact on output, only considers the natural market reaction to the change in money supply. Nevertheless, in the US the fed targets the federal funds rate to control the economy by adjusting money supply. When the FOMC is determining the money supply, the decision process usually takes the performance of output into consideration, as well as the statistics of other economic indicators. Therefore, despite what the structural approach tries to argue, with the intervention of targeting federal funds rate by the Fed, the change in money supply is actually affected by the change in GDP. 5 Prediction According to the optimal equation (eq3), we are able to project the change of M2 in the first quarter of 2011. The calculation is illustrated below. d( M 2) 2011Q1 = 62.77548 0.30798d( GDP) 0.34105d( M 2) 2010Q3 2010Q4 + 0.26681d ( M 2) + 0.42308d( GDP) 2010Q2 2010Q2 + 0.26794d( M 2) 2010Q1 d( M 2) 2011Q1 = 62.77548 0.30798(141.2) + 0.42308(151.5) 0.34105(36.3) + 0.26681(34.7) + 0.26794(34.1) 17

d( M 2) 1 2011 Q = 89.40027 The estimated change of M2 in 2011 quarter one will be approximately 89.40 billion USD. Based on this estimated d(m2), we can also calculate other estimated economic indicators such as M2 in 2011 Quarter one. Since d ( M 2) 2011 Q1 is the difference between M 22011 Q1 and 22010Q4 M, we can then calculate M 22011 Q1 with the value of M 22010Q4. M 22011 Q1 = 22010Q4 M + d ( M 2) 2011 Q1 M =8781.3 + 89.4 22011 Q1 M = 8870.7 22011 Q1 The estimated M2 of 2011 quarter one is 8870.7 billion USD. The positive USD89.4 billion increase in projected M2 of the first quarter in 2011 implies that the Fed will continue raising money supply and applying the loose monetary policy in stimulating the economy. This prediction is consistent with the presumption in the theoretical analysis section that the Fed will endure the loose monetary policy and focus on fighting the unemployment and boost the economy. 6 Conclusion and limitation 6.1 Conclusion In this paper we discuss the relationship between money supply and GDP in the US. Through FOMC, the Fed comes out monetary policies and fiscal policies to control the economy. Among its monetary policies, the most effective policy is to control the money supply via interest rate (ffr) in its Open Market Operations. By targeting an ffr in the fund market, the Fed controls the amount of fund circulating in the money market and further controls the 18

economic performance. To further study this relationship between money supply and economy, we conduct qualitative and quantitative analysis in this paper by adopting M2 measuring money supply and GDP measuring economic performance. The theoretical analysis indicates that the change of M2 will lead to a change of GDP. Traditionally, IS-LM, and AD-AS results shows that the change of money supply in money market will lead to the change of interest rate and a shift of LM curve. Consequently, the new intersect of IS and LM curves indicates the new equilibrium of output. In goods market, this change in output results in a shift of AD curve which changes the price level in the long term, but the price stays constant in the short run due to its stickiness in the short term. Hence, theoretically, it is obvious that the change of money supply leads to the change in output in the same direction. In reality, by applying its tight and loose monetary policies, the Fed controls the money supply and achieving the target interest rates by buying and selling Treasuries and other government bonds in money market, and then to control the whole economy. Based on the conclusion in the theoretical section, in statistical analysis section we then try to generate a more precise relationship of money supply and the economy by estimating an equation of the relevant indicators. According to the theoretical conclusion in theoretical analysis, in this section we firstly apply statistical tests to examine the causality between M2 and GDP, and then estimate an equation of money supply and the output using data from IFS and website of St. Louis Federal Reserve Bank. Inspired by the paper of Feldstein and Stock (1994), we apply a simple VAR as the original model in estimating the quantitative relationship of M2 and GDP. After examining the t-test result in OLS, we select d(m2), d(gdp) and their lagged terms as the optimal variables. The optimal lag of 4 is obtained after another comparison of VAR results. After the Augmented Dickey-Fuller test we discover that the residual of d(m2) and d(gdp) does not have a unit root, and the Granger Causality test is available to conduct. The Granger Causality result shows that d(m2) does not Granger Cause d(gdp), and d(gdp) Granger Cause d(m2). Therefore we simplify the model as model 2 with d(m2) as dependent variable and lagged d(m2) and lagged d(gdp) as independent 19

variables, and conduct OLS in SAS, and obtain the optimal result. This estimated equation indicates that the change of M2 in current quarter is influenced by the fluctuation of GDP in last quarter and the last third quarter, as well as affected by the variation of M2 in the last second, third and fourth quarters. We also project the change of M2 and M2 of 2011 quarter one by plugging d GDP), d( GDP), d M 2), ( 2010Q4 2010Q2 ( 2010Q3 d ( M 2) 2010 Q1 and ( M 2) 2010 Q2 d in the estimated equation (eq 3). 6.2 Limitations To bring the conclusion to a dialectically completion, in this section, we will discuss the endogenous limits of the models and tests we have adopted in statistical analysis. One problem in our study is the limitation of Granger Causality that it does not perfectly indicate the causality. Albeit the Granger Causality test results show that d(m2) does not Granger Cause d(gdp) and d(gdp) Granger Causes d(m2), it does not necessarily prove that d(m2) does not cause d(gdp) or d(gdp) does cause d(m2). Dr. Roland Füss in his lecture on Vector Autoregressive Models mentioned that Granger Causality is a much weaker argument than normal causality. Instead of stating that d(gdp) and its lags determine the change of M2, the Granger Causality result of d(gdp) Granger Causing d(m2) could be more properly understood as that d(gdp) and its lag terms influence the change of M2 in a certain degree, which could be either significant or insignificant. Besides Granger Causality, another pitfall in the statistical analysis section is that in the estimated equation of d(gdp) and d(m2), the t-values of d(m2) 3, d(m2) 4, and the constant are slightly smaller than 2 which makes these coefficients of corresponding variables not statistically significant in explaining the relationship of the variables. To find out a reasonable explanation to this flaw, we first examine the existence of multicollinearity, which could cause insignificant t-test results, by checking the VIF of each variable. Nevertheless, the VIF of every 20

variable is smaller than 2 which is less than the benchmark of a critical value of 5 in defining whether multicollinearity being high. Therefore the multicollinearity is not high among the selected variables in the estimated equation, and the insignificant t-values are not caused by multicollinearity. After considering the study of Hoover and the others on the causes and effect of U.S. M2 we conclude that this insignificance is likely to be caused by other indicators not included in the estimated equation whose change would also contribute to the change in M2, such as inflation, unemployment and price-earnings ratio (Hoover, Demiralp and Perez 2008). 21

References Abel, A., Bernanke, B. and Croushore, D. (2008) Macroeconomics. 6 th Ed. Greg Tobin. A Day in the Life of the FOMC. An Inside Look at the Federal Reserve s Monetary Policymaking Body (2008) Federal Reserve Bank of Philadelphia December 2008. Akhtar, M. (1997) Understanding Open Market Operations. Federal Reserve Bank of New York. Bai, Z., Li H., Wong, W. K., and Zhang, B. (2010) Multivariate Causality Tests with Simulation and Application. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1626782 [accessed 25/04/2011]. Dotsey, M. and Otrok, C. (1994) M2 and monetary policy: A critical review of the recentdebate.economic Quarterly - Federal Reserve Bank of Richmond, Winter 1994, pp. 41-49. Economic Research Centre of the Deutsche Bundesbank (2000)The Relationship between the Federal Funds Rate and the Fed s Federal Funds Rate Target: Is it Open Market or Open Mouth Operations? http://www.bundesbank.de/download/volkswirtschaft/dkp/2000/200009dkp.pdf [accessed 02/01/2011]. Fair R. (2001)Forecasting Growth over the Next Year with a Business Cycle Index Actual Federal Reserve Policy Behavior and Interest Rate Rules. http://www.ny.frb.org/research/epr/01v07n1/0103fair.pdf[accessed 02/01/2011]. Feldstein, M. and Stock, J. H. (1994) The Use of a Monetary Aggregate to Target Nominal GDP National Bureauof Economic Researchp. 7-69 FRBSF Economic Letter:U.S. Monetary Policy: An Introduction. Part 3: How does monetary policy affect the U.S. economy?(2004) http://www.frbsf.org/publications/economics/letter/2004/el2004-03.html [accessed 02/01/2011]. Frumkin, N. (1990) Guide to Economic Indicators. New York: M. E. Sharp, Inc. FüssR. (2007) Vector Autoregressive Models. http://www.empiwifo.uni-freiburg.de/lehre-teaching-1/winter-term/dateien-financial-data-ana lysis/chapter4.pdf [accessed 25/04/2011] Hanssens D. (1980) Bivariate time-series analysis of the relationship between Advertising 22

and Sales.. Applied Economics, Vol 12, No 3, pp. 329-339. Hoover, K., Demiralp, S., and Perez, S. (2008). Empirical Identification of the Vector Autoregression: The Causes and Effects of U.S. M2inthe Conference in Honour of David F. Hendry, 2007, Oxford University. Hung, B. (2010) VAR, Error Correction, Co-intergration, ARCH, GARCH Models. Economic and Business Forecasting, Hong Kong Baptist University, 6 th December 2010. Johansen S. (2002) The interpretation of cointegrating coefficients in the cointegrated vector autoregressive model. http://www.math.ku.dk/~sjo/papers/coefficients.pdf [accessed 25/04/2011]. Lang, D. and Lansing K. (2010)Forecasting Growth over the Next Year with a Business Cycle Index. http://www.frbsf.org/publications/economics/letter/2010/el2010-29.html [accessed 05/01/2011]. Leduc S. (2010)Confidence and the Business Cycle. http://www.frbsf.org/publications/economics/letter/2010/el2010-35.html [accessed 05/01/2011]. Mishkin, Frederic S. (2007) The Economics of Money, Banking and Financial Markets. 8th Ed., Boston: Pearson Education,. Studenmund, A. (2006) Using Econometrics A Practical Guide. 5 th Ed. Daryl Fox. Shrestha B., (2010) Impact of Money Supply on GDP and Price: Case of Nepal. M. Phil. Nepal: Tribhuvan University. Wong, S. (2009) The Fed Today (II) IV. The Fed s Role in Making and Setting. Model Federal Reserve, Universtiy of San Francisco, 16 th November 2009. 23

Appendix I Figure 2. (Frederic S., 2007, p.619) 24

Table 1.Unit Root Test Result Augmented Dickey-Fuller Test t-statistic Prob.* Augmented Test critical values Dickey-Fuller 1% level 5% level 10% level test statistic GDP -0.42245-3.59662-2.93316-2.60487 0.8959 M2 0.025055-3.60099-2.935-2.60584 0.9554 log(gdp) -0.74521-3.59662-2.93316-2.60487 0.8239 log(m2) -1.88401-3.60099-2.935-2.60584 0.3363 d(gdp) -3.33762-3.59662-2.93316-2.60487 0.0193 d(m2) -6.38222-3.60099-2.935-2.60584 0 25

Table 2. VAR Result 1 2 3 4 5 6 7 8 9 obs regressors R-squared Adj. R-squared AIC t-stat F-stat 1 d_gdp d_gdp(-1) 0.359985 0.327164 11.73161 4.11086 10.96805 (lag=1) d_m2(-1) 0.7888 d_m2 d_gdp(-1) 0.034207-0.015321 11.61545-0.77717 0.690669 d_m2(-1) 0.20967 2 d_gdp d_gdp(-1) 0.390635 0.322928 11.80178 3.25525 5.769484 (lag=2) d_gdp(-2) 0.00907 d_m2(-1) 0.66974 d_m2(-2) 0.04288 d_m2 d_gdp(-1) 0.265702 0.184113 11.46588-1.82456 3.2566 d_gdp(-2) 0.84808 d_m2(-1) -0.14821 d_m2(-2) -2.11464 3 d_gdp d_gdp(-1) 0.427823 0.323791 11.86951 2.93548 4.112406 (lag=3) d_gdp(-2) 0.59172 d_gdp(-3) -1.39788 d_m2(-1) 0.71415 d_m2(-2) 0.43341 d_m2(-3) -0.80321 d_m2 d_gdp(-1) 0.39576 0.285898 11.40028-2.29641 3.602339 d_gdp(-2) -0.30366 d_gdp(-3) 2.56863 d_m2(-1) -0.86117 d_m2(-2) -2.83266 d_m2(-3) 0.9536 4 d_gdp d_gdp(-1) 0.433139 0.281976 11.97963 2.75146 2.865374 (lag=4) d_gdp(-2) 0.10641 d_gdp(-3) -0.96631 d_gdp(-4) -0.03732 d_m2(-1) 0.55421 d_m2(-2) -0.13008 d_m2(-3) -0.71847 26

d_m2(-4) -0.55042 d_m2 d_gdp(-1) 0.436636 0.286405 11.45623-2.20304 2.906438 d_gdp(-2) 0.21696 d_gdp(-3) 1.93451 d_gdp(-4) 0.49602 d_m2(-1) -0.87124 d_m2(-2) -1.28146 d_m2(-3) 0.65639 d_m2(-4) 1.57805 27

Table 4. Augmented Dickey-Fuller test Null Hypothesis: D(GDP) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic -3.33762 0.0193 Test critical values: 1% level -3.59662 5% level -2.93316 10% level -2.60487 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 04/13/11 Time: 11:30 Sample (adjusted): 2000Q3 2010Q4 Included observations: 42 after adjustments Variable Coefficient Std. Error t-statistic Prob. D(GDP(-1)) -0.41844 0.125372-3.33762 0.0018 C 47.67811 19.6223 2.429792 0.0197 R-squared 0.217829 Mean dependent var -2.34286 Adjusted R-squared 0.198275 S.D. dependent var 91.67427 S.E. of regression 82.08431 Akaike info criterion 11.69982 Sum squared resid 269513.4 Schwarz criterion 11.78257 Log likelihood -243.696 Hannan-Quinn criter. 11.73015 F-statistic 11.13973 Durbin-Watson stat 1.910139 Prob(F-statistic) 0.001835 Null Hypothesis: D(M2) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic -6.38222 0 Test critical values: 1% level -3.60099 5% level -2.935 10% level -2.60584 28

*MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(M2,2) Method: Least Squares Date: 04/13/11 Time: 11:30 Sample (adjusted): 2000Q4 2010Q4 Included observations: 41 after adjustments Variable Coefficient Std. Error t-statistic Prob. D(M2(-1)) -1.22464 0.191884-6.38222 0 D(M2(-1),2) 0.424172 0.146566 2.894063 0.0063 C 117.5682 21.41973 5.488783 0 R-squared 0.533611 Mean dependent var 1.078049 Adjusted R-squared 0.509064 S.D. dependent var 102.6372 S.E. of regression 71.9146 Akaike info criterion 11.45919 Sum squared resid 196525 Schwarz criterion 11.58457 Log likelihood -231.913 Hannan-Quinn criter. 11.50485 F-statistic 21.7385 Durbin-Watson stat 1.890259 Prob(F-statistic) 0.000001 Null Hypothesis: D(RESID) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic -11.2369 0 Test critical values: 1% level -3.60559 5% level -2.93694 10% level -2.60686 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID,2) Method: Least Squares Date: 04/13/11 Time: 12:00 Sample (adjusted): 2001Q1 2010Q4 Included observations: 40 after adjustments 29

Variable Coefficient Std. Error t-statistic Prob. D(RESID(-1)) -1.51802 0.135093-11.2369 0 C 1.398632 15.31904 0.0913 0.9277 R-squared 0.768669 Mean dependent var -4.12321 Adjusted R-squared 0.762581 S.D. dependent var 198.7379 S.E. of regression 96.83628 Akaike info criterion 12.03263 Sum squared resid 356336.1 Schwarz criterion 12.11707 Log likelihood -238.653 Hannan-Quinn criter. 12.06316 F-statistic 126.2667 Durbin-Watson stat 2.25929 Prob(F-statistic) 0 30

Appendix II The SAS System The REG Procedure Model: MODEL1 Dependent Variable: D _M2 Number of Observations Read 48 Number of Observations Used 39 Number of Observations with Missing Values 9 Number in Model C(p) R-Square AIC Variables in Model 5 3.893 0 4 4.193 1 4 4.356 9 5 4.431 2 0.4199 331.259 8 0.3767 332.060 4 0.3736 332.252 4 0.4098 331.933 3 D_GDP1 D_GDP3 D_M2 2 D_M2 3 D_M2 4 D_GDP1 D_GDP3 D_M2 2 D_M2 4 D_GDP1 D_GDP3 D_M2 2 D_M2 3 D_GDP1 D_GDP3 D_M2 1 D_M2 2 D_M2 4 4 4.432 0 0.3722 332.340 D_GDP1 D_GDP3 D_M2 1 D_M2 2 1 31

Number of Observations Read 48 Number of Observations Used 39 Number of Observations with Missing Values 9 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 5 101355 20271 4.78 0.0022 Error 33 140044 4243.74742 Corrected Total 38 241399 32

Root MSE 65.14405 R-Square 0.4199 Dependent Mean 94.59487 Adj R-Sq 0.3320 Coeff Var 68.86637 Variable DF Parameter Estimate Parameter Estimates Standard Error t Value Pr > t Variance Inflation Intercept 1 62.77548 48.24423 1.30 0.2022 0 D_GDP1 1-0.30798 0.11834-2.60 0.0138 1.35801 D_GDP3 1 0.42308 0.14303 2.96 0.0057 1.98787 D_M2_2 1-0.34105 0.16561-2.06 0.0474 1.54976 D_M2_3 1 0.26681 0.17022 1.57 0.1265 1.61153 D_M2_4 1 0.26794 0.16516 1.62 0.1143 1.53250 33

Obs Dependent Variable Predicted Value Output Statistics Std Error Mean Predict Residual Std Error Residual Student Residual -2-1 0 1 2 Cook's D 1....... 2 17.5000...... 3 83.3000...... 4 114.9000...... 5 146.6000...... 6 64.0000 68.5705 21.7023-4.5705 61.423-0.0744 0.000 7 179.1000 71.3186 13.3769 107.7814 63.756 1.691 *** 0.021 8 130.5000 124.5829 19.5289 5.9171 62.148 0.0952 0.000 9 58.8000 94.7610 21.9829-35.9610 61.323-0.586 * 0.007 10 14.1000 46.1702 18.4921-32.0702 62.464-0.513 * 0.004 11 109.3000 122.4720 15.4136-13.1720 63.294-0.208 0.000 12 161.1000 131.0237 17.1080 30.0763 62.857 0.478 0.003 13 73.2000 68.5972 20.5188 4.6028 61.828 0.0744 0.000 14 109.4000 45.5769 16.3283 63.8231 63.065 1.012 ** 0.011 15 68.8000 100.7993 14.2139-31.9993 63.574-0.503 * 0.002 16 34.6000 63.3080 24.5349-28.7080 60.347-0.476 0.006 17 67.7000 89.2331 12.9033-21.5331 63.853-0.337 0.001 18 102.7000 147.7472 19.1172-45.0472 62.276-0.723 * 0.008 19 58.6000 79.5775 15.3173-20.9775 63.318-0.331 0.001 20 113.9000 78.5309 14.4120 35.3691 63.530 0.557 * 0.003 21 17.7000 105.1219 15.3329-87.4219 63.314-1.381 ** 0.019 22 46.3000 67.6421 18.9740-21.3421 62.320-0.342 0.002 23 75.5000 142.7915 21.3920-67.2915 61.532-1.094 ** 0.024 24 121.9000 112.2463 18.9936 9.6537 62.314 0.155 0.000 25 88.2000 58.6225 19.1946 29.5775 62.252 0.475 0.004 26 53.4000 66.3519 21.5194-12.9519 61.487-0.211 0.001 27 69.3000 108.4637 14.8834-39.1637 63.421-0.618 * 0.004 28 185.0000 181.7330 24.4493 3.2670 60.382 0.0541 0.000 29 107.1000 97.6871 12.6963 9.4129 63.895 0.147 0.000 30 78.6000 22.1244 20.1852 56.4756 61.938 0.912 * 0.015 31 96.2000 93.9228 23.0009 2.2772 60.948 0.0374 0.000 32 146.3000 143.2245 21.3138 3.0755 61.559 0.0500 0.000 33 222.7000 131.1700 16.9090 91.5300 62.911 1.455 ** 0.025 34

Obs Dependent Variable Predicted Value Output Statistics Std Error Mean Predict Residual 34 10.7000 111.6437 16.1926-100.943 7 Std Error Residual Student Residual -2-1 0 1 2 Cook's D 63.099-1.600 *** 0.028 35 90.7000 63.7818 26.1881 26.9182 59.648 0.451 0.007 36 417.8000 169.4068 28.0350 248.3932 58.803 4.224 ****** 0.676 37 207.5000 245.4917 50.8759-37.9917 40.686-0.934 * 0.227 38-14.8000-3.5261 47.1355-11.2739 44.967-0.251 0.012 39-54.7000 8.2061 49.5677-62.9061 42.270-1.488 ** 0.508 40 145.4000 150.5642 47.4327-5.1642 44.653-0.116 0.003 41 34.1000 76.5699 41.2179-42.4699 50.446-0.842 * 0.079 42 34.7000-23.5221 36.8510 58.2221 53.719 1.084 ** 0.092 43 36.3000 103.3316 33.7507-67.0316 55.719-1.203 ** 0.089 44 127.5000 123.8814 16.1461 3.6186 63.111 0.0573 0.000 45. 81.2772 22.0145.... 46....... 47....... 48....... Sum of Residuals 0 Sum of Squared Residuals 140044 Predicted Residual SS (PRESS) 218882 Number of Observations Read 48 Number of Observations Used 39 Number of Observations with Missing Values 9 Source DF Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model 8 105403 13175 2.91 0.0159 Error 30 135995 4533.1802 9 Corrected Total 38 241399 35