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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.
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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 MS1 to MS2 with a constant price level P1 which leads to a drop
in interest rate from r1 to r2, LM curve shifts downward from LM1 to LM2. In IS-LM model, the
downward-shifted LM curve intersects with IS curve at equilibrium with an increased output,
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Y2. In AD-AS model, the new output level shifts AD curve up from AD1 to AD2.
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 Y2. In the long term, since the price is
flexible and the output will ultimately return to the assumed-full-employment level Y1, the
upward-shifted AD curve will intersect with LRAS curve at Y1, but at a higher price level P2.
Due to the return in the output, and the rise in price, LM curve will then shift back to the initial
position LM1, and the interest rate reduces back to the original level r1. 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
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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
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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.
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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.
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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, [Y ]t , [Y ]t −1 , … [Y ]t − k are the 1 × p vector of
variables, and the [ A] , … and [ A ' ] are the 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 6th 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,
m
d (GDP) t = C1 +
n
∑b
∑ a1i d (GDP) t −i +
i =1
i =1
p
d ( M 2) t = C 2 +
∑ a2i d (M 2)t − i +
i =1
1i
d ( M 2) t −i + e1t ……(eq 1)
q
∑b
i =1
2i
d (GDP) t −i + e2t ……(eq 2)
10
Where aij , bij and ci are the parameters to be estimated, and eij ’s are the stochastic
error terms.
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 5th and 6th
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 8th 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
t-Statistic
Test critical values
Augmented
Dickey-Fuller
1% level
test statistic
d(GDP) 1
d(M2)
2
d(resid)
3
5% level
Prob.*
10% level
-3.337624 -3.596616 -2.933158 -2.604867 0.0193
-6.382221 -3.600987 -2.935001 -2.605836
0
-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
2.57393
0.0578
D_GDP does not Granger Cause D_M2
Table 5
12
The probability of not to reject H0: d(M2) does not Granger Cause d(GDP) is 0.6964 which
is larger than confidence interval 0.1, so we do not reject H0, and d(M2) does not Granger
Cause d(GDP); The probability of not to reject H0: d(GDP) does not Granger Cause d(M2) is
0.0578 which is smaller than confidence interval 0.1, so we reject H0, 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
d ( M 2) t = C +
∑ a d (M 2)
i =1
i
l
t −i
+
∑ b d (GDP)
i =1
i
t −i
+ et …… (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-3and
d(M2)t-4as independent variables.
In the result, R-square is 0.4199. The t-statistics of d(GDP)t-1, d(GDP)t-3and d(M2)t-2are
-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-3and
d(M2)t-4with 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 d ( M 2) t − 2 + 0.26681d ( M 2) t −3 + 0.26794d ( M 2) t − 4
(1.30)
(-2.06)
(1.57)
(1.62)
- 0.30798d (GDP) t −1 + 0.42308d (GDP) t −3 …… (eq 3)
(-2.60)
(2.96)
*() t-value, critical t value = 2.0
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 - 0.25612d [log(M 2)]t − 2 + 0.29048d [log(M 2)]t −3
(1.04)
(-2.31)
(3.1)
+ 0.28265d [log(M 2)]t − 4 - 0.50495d [log(GDP)]t −1
(-1.64)
+ 0.78468d [log(GDP)]t −3
(1.7)
…… (eq 4)
(1.82)
*() t-value, critical value = 2.0
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
1.98787
1.54976
1.61153
1.5325
R-square
0.4199
Adj R-square
0.332
AIC
331.26
1.35801
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) 2010Q 4 + 0.42308d (GDP) 2010Q 2
− 0.34105d ( M 2) 2010Q 3 + 0.26681d ( M 2) 2010Q 2 + 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) 2011Q1 = 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) 2011Q1 is the difference between
M 2 2011Q1 and M 2 2010Q 4 , we can then calculate M 2 2011Q1 with the value of M 2 2010Q 4 .
M 2 2011Q1 = M 2 2010Q 4 + d ( M 2) 2011Q1
M 2 2011Q1 =8781.3 + 89.4
M 2 2011Q1 = 8870.7
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) 2010Q 4 , d (GDP) 2010Q 2 , d ( M 2) 2010Q 3 ,
d ( M 2) 2010Q1 and d ( M 2) 2010Q 2 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
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23
Appendix I
Figure 2. (Frederic S., 2007, p.619)
24
Table 1.Unit Root Test Result
Augmented Dickey-Fuller Test
t-Statistic
Augmented
Dickey-Fuller
test statistic
Prob.*
Test critical values
1% level
5% level
10% level
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
-2.60584
-2.935
0
25
Table 2. VAR Result
1
obs
1
2
3
regressors
d_GDP
(lag=1)
d_GDP(-1)
4
5
6
7
8
9
R-squared
Adj. R-squared
AIC
t-stat
F-stat
0.359985
0.327164 11.73161
d_M2(-1)
d_M2
d_GDP(-1)
0.7888
0.034207
-0.015321 11.61545 -0.77717 0.690669
d_M2(-1)
2
d_GDP
(lag=2)
d_M2
3
d_GDP
(lag=3)
d_M2
4
(lag=4)
d_GDP
d_GDP(-1)
4.11086 10.96805
0.20967
0.390635
0.322928 11.80178
3.25525 5.769484
d_GDP(-2)
0.00907
d_M2(-1)
0.66974
d_M2(-2)
0.04288
d_GDP(-1)
0.265702
0.184113 11.46588 -1.82456
d_GDP(-2)
0.84808
d_M2(-1)
-0.14821
d_M2(-2)
-2.11464
d_GDP(-1)
0.427823
0.323791 11.86951
2.93548 4.112406
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_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
d_GDP(-1)
0.433139
3.2566
0.281976 11.97963
2.75146 2.865374
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)
d_M2
d_GDP(-1)
-0.55042
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
Augmented Dickey-Fuller test statistic
Test critical values: 1% level
5% level
-3.33762
-3.59662
-2.93316
-2.60487
10% level
Prob.*
0.0193
*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
D(GDP(-1))
Coefficient Std. Error
t-Statistic
0.125372
19.6223
Prob.
C
-0.41844
47.67811
-3.33762
2.429792
0.0018
0.0197
R-squared
Adjusted R-squared
0.217829
0.198275
Mean dependent var
S.D. dependent var
-2.34286
91.67427
S.E. of regression
Sum squared resid
82.08431
269513.4
Akaike info criterion
Schwarz criterion
11.69982
11.78257
Log likelihood
F-statistic
Prob(F-statistic)
-243.696
11.13973
0.001835
Hannan-Quinn criter. 11.73015
Durbin-Watson stat
1.910139
Null Hypothesis: D(M2) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=9)
t-Statistic
Augmented Dickey-Fuller test statistic
Test critical values: 1% level
5% level
10% level
-6.38222
-3.60099
Prob.*
0
-2.935
-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
D(M2(-1))
D(M2(-1),2)
C
R-squared
Adjusted
R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Coefficient Std. Error
-1.22464
0.424172
117.5682
0.191884
0.146566
21.41973
t-Statistic
-6.38222
2.894063
5.488783
Prob.
0
0.0063
0
0.533611
Mean dependent var 1.078049
0.509064
S.D. dependent var
71.9146
196525
-231.913
21.7385
0.000001
Akaike info criterion
11.45919
Schwarz criterion
11.58457
Hannan-Quinn criter. 11.50485
Durbin-Watson stat
1.890259
102.6372
Null Hypothesis: D(RESID) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=9)
t-Statistic
Augmented Dickey-Fuller test statistic
Test critical values: 1% level
5% level
10% level
-11.2369
-3.60559
-2.93694
-2.60686
Prob.*
0
*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
D(RESID(-1))
C
-1.51802
1.398632
R-squared
Adjusted
R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.135093
15.31904
t-Statistic
Prob.
-11.2369
0.0913
0
0.9277
0.768669
Mean dependent var
-4.12321
0.762581
S.D. dependent var
198.7379
96.83628
356336.1
-238.653
126.2667
0
Akaike info criterion 12.03263
Schwarz criterion
12.11707
Hannan-Quinn criter. 12.06316
Durbin-Watson stat
2.25929
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
Number in
Model
C(p) R-Square
9
AIC Variables in Model
5 3.893
0
0.4199 331.259 D_GDP1 D_GDP3 D_M2__2 D_M2__3
8 D_M2__4
4 4.193
1
0.3767 332.060 D_GDP1 D_GDP3 D_M2__2 D_M2__4
4
4 4.356
9
0.3736 332.252 D_GDP1 D_GDP3 D_M2__2 D_M2__3
4
5 4.431
2
0.4098 331.933 D_GDP1 D_GDP3 D_M2__1 D_M2__2
3 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
9
Number of Observations with Missing Values
Analysis of Variance
Source
Sum of
DF Squares
Mean
Square
F
Value
Pr > F
4.78
0.0022
Model
5
101355
20271
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
Parameter Estimates
Variable
DF
Parameter Standard
Variance
Estimate
Error t Value Pr > |t| 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
Output Statistics
Obs
Dependent Predicted
Std Error
Std Error Student
Variable
Value Mean Predict Residual Residual Residual
Cook's
D
-2-1 0 1 2
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 |
7
179.1000
71.3186
13.3769 107.7814
63.756
1.691 |
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
|
|***
|
|
0.000
0.021
34
Output Statistics
Obs
Dependent Predicted
Std Error
Std Error Student
Variable
Value Mean Predict Residual Residual Residual
Cook's
D
-2-1 0 1 2
16.1926 -100.943
7
63.099
-1.600 |
26.1881
26.9182
59.648
0.451 |
|
169.4068
28.0350 248.3932
58.803
4.224 |
|******|
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
.
.
.
.
.
.
.
34
10.7000
111.6437
35
90.7000
63.7818
36
417.8000
37
***|
|**
|
|
0.028
0.007
0.676
0
Sum of Residuals
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
Analysis of Variance
Source
Sum of
DF Squares
105403
Mean
Square F Value Pr > F
Model
8
13175
Error
30
135995 4533.1802
9
Corrected Total
38
241399
2.91 0.0159
35
Root MSE
67.3289 R-Square 0.4366
0
Dependent Mean
94.5948 Adj R-Sq 0.2864
7
Coeff Var
71.1760
5
Parameter Estimates
Variable
DF
Parameter Standard
Variance
Estimate
Error t Value Pr > |t| Inflation
Intercept
1
92.95119
74.20804
1.25 0.2200
0
D_GDP1
1
-0.44845
0.20356
-2.20 0.0354
3.76138
D_GDP2
1
0.04969
0.22901
0.22 0.8297
4.74742
D_GDP3
1
0.38258
0.19777
1.93 0.0625
3.55794
D_GDP4
1
0.09314
0.18777
0.50 0.6235
3.30383
D_M2_1
1
-0.22413
0.25725
-0.87 0.3905
3.54767
D_M2_2
1
-0.31924
0.24913
-1.28 0.2098
3.28295
D_M2_3
1
0.14469
0.22043
0.66 0.5166
2.52992
D_M2_4
1
0.32461
0.20570
1.58 0.1250
2.22556
Number of Observations Read
48
Number of Observations Used
40
Number of Observations with Missing Values
8
Analysis of Variance
Source
Sum of
DF Squares
Mean
F
Square Value
Model
4
59688
14922
Error
35
184348
5267.08030
Corrected Total
39
244036
2.83
Pr > F
0.0390
36
Root MSE
72.57465 R-Square
0.2446
Dependent Mean
95.89500 Adj R-Sq
0.1583
Coeff Var
75.68137
Parameter Estimates
Variable
Parameter Standard
DF Estimate
Error t Value
Pr > |t|
Variance
Inflation
Intercept
1
127.94606
34.54110
3.70
0.0007
0
D_GDP1
1
-0.57171
0.20425
-2.80
0.0083
3.25937
D_GDP2
1
0.28956
0.16463
1.76
0.0873
2.12335
D_GDP3
1
0.27130
0.16113
1.68
0.1011
2.10702
D_M2_1
1
-0.31737
0.22954
-1.38
0.1755
2.43468
37
Appendix III
The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable:
D_log_M2
Number in
Model
Number of Observations Read
48
Number of Observations Used
38
Number of Observations with Missing Values
10
C(p) R-Square
AIC Variables in Model
5 3.099
3
0.3739 -350.193 D_log_GDP1 D_log_GDP3 D_log_M2_2 D_log_M2_3
1 D_log_M2_4
4 3.544
4
0.3213 -349.127 D_log_GDP1 D_log_GDP3 D_log_M2_3 D_log_M2_4
2
3 3.617
2
0.2767 -348.708 D_log_GDP1 D_log_GDP3 D_log_M2_4
8
4 3.735
7
0.3172 -348.897 D_log_GDP1 D_log_GDP3 D_log_M2_2 D_log_M2_4
4
4 3.836
8
0.3150 -348.776 D_log_GDP1 D_log_GDP2 D_log_GDP3 D_log_M2_4
6
38
Number of Observations Read
48
Number of Observations Used
38
Number of Observations with Missing Values
10
Analysis of Variance
Sum of
DF Squares
Source
Mean
Square F Value Pr > F
Model
5
0.00165 0.0003292
7
Error
32
0.00276 0.0000861
4
Corrected Total
37
0.00440
3.82 0.0079
Root MSE
0.00928 R-Square 0.3739
Dependent Mean
0.01396 Adj R-Sq 0.2761
Coeff Var
66.5051
1
Parameter Estimates
Variable
DF
Parameter Standard
Variance
Estimate
Error t Value Pr > |t| Inflation
Intercept
1
0.00644
0.00619
1.04 0.3063
0
D_log_GDP1
1
-0.50495
0.21903
-2.31 0.0278
1.33755
D_log_GDP3
1
0.78468
0.25349
3.10 0.0041
1.79509
D_log_M2_2
1
-0.25612
0.15619
-1.64 0.1109
1.26915
D_log_M2_3
1
0.29048
0.17060
1.70 0.0983
1.47225
D_log_M2_4
1
0.28265
0.15507
1.82 0.0777
1.25311
39
Output Statistics
Obs
Dependent Predicted
Std Error
Std Error Student
Variable
Value Mean Predict Residual Residual Residual
Cook's
D
-2-1 0 1 2
1
.
.
.
.
.
.
.
2
0.003693
.
.
.
.
.
.
3
0.0174
.
.
.
.
.
.
4
0.0235
.
.
.
.
.
.
5
0.0292
.
.
.
.
.
.
6
0.0125
0.0101
0.002612 0.002357
0.00891
0.265 |
|
7
0.0341
0.0127
0.003263
0.0214
0.00869
2.465 |
|**** |
0.143
8
0.0242
0.0209
0.003136 0.003259
0.00874
0.373 |
|
|
0.003
9
0.0107
0.0167
0.004760 -0.00600
4
0.00797
-0.754 |
*|
|
0.034
10
0.002549
0.007917
0.003430 -0.00536
8
0.00862
-0.622 |
*|
|
0.010
11
0.0195
0.0206
0.003232 -0.00104
0
0.00870
-0.120 |
|
|
0.000
12
0.0281
0.0204
0.002517 0.007688
0.00893
0.861 |
|*
|
0.010
13
0.0125
0.009806
0.002759 0.002716
0.00886
0.306 |
|
|
0.002
14
0.0184
0.007317
0.002737
0.0111
0.00887
1.253 |
|**
|
0.025
15
0.0114
0.0162
0.002457 -0.00475
2
0.00895
-0.531 |
*|
|
0.004
16
0.005693
0.0109
0.004173 -0.00518
5
0.00829
-0.625 |
*|
|
0.017
17
0.0110
0.0138
0.001937 -0.00277
6
0.00908
-0.306 |
|
|
0.001
18
0.0165
0.0230
0.003215 -0.00650
2
0.00871
-0.747 |
*|
|
0.013
19
0.009309
0.0118
0.002313 -0.00248
2
0.00899
-0.276 |
|
|
0.001
20
0.0179
0.0120
0.002238 0.005829
0.00901
0.647 |
|*
|
0.004
21
0.002746
0.0160
0.002376
-0.0132
0.00897
-1.477 |
**|
|
0.025
22
0.007146
0.0110
0.002751 -0.00381
7
0.00886
-0.431 |
|
|
0.003
23
0.0115
0.0206
0.003299 -0.00909
8
0.00868
-1.049 |
**|
|
0.026
24
0.0184
0.0165
0.002880 0.001888
0.00882
0.214 |
|
|
0.001
25
0.0131
0.008139
0.002854 0.004941
0.00883
0.560 |
|*
|
0.005
26
0.007837
0.0107
0.002853 -0.00287
2
0.00883
-0.325 |
|
|
0.002
27
0.0101
0.0161
0.002036 -0.00599
5
0.00906
-0.662 |
*|
|
0.004
|
0.001
40
Output Statistics
Obs
Dependent Predicted
Std Error
Std Error Student
Variable
Value Mean Predict Residual Residual Residual
Cook's
D
-2-1 0 1 2
28
0.0264
0.0256
0.003362 0.000850
0.00865
0.0983 |
|
|
0.000
29
0.0150
0.0136
0.001986 0.001351
0.00907
0.149 |
|
|
0.000
30
0.0109
0.004408
0.002865 0.006446
0.00883
0.730 |
|*
|
0.009
31
0.0131
0.0144
0.002819 -0.00124
9
0.00884
-0.141 |
|
|
0.000
32
0.0196
0.0203
0.002413 -0.00065
6
0.00896
-0.0732 |
|
|
0.000
33
0.0292
0.0181
0.002031
0.0111
0.00906
1.224 |
|**
|
0.013
34
0.001380
0.0153
0.002286
-0.0140
0.00900
-1.552 |
|
0.026
35
0.0116
0.0107
0.002609 0.000930
0.00891
0.104 |
|
36
0.0519
0.0217
0.003886
0.0302
0.00843
3.581 |
|******|
37
0.0248
0.0303
0.006975 -0.00546
9
0.00612
-0.893 |
*|
|
0.173
38
-0.001748
0.002690
0.006217 -0.00443
8
0.00689
-0.644 |
*|
|
0.056
39
-0.006488
0.002913
0.006590 -0.00940
1
0.00654
-1.438 |
**|
|
0.351
40
0.0172
0.0180
0.006243 -0.00085
4
0.00687
-0.124 |
|
|
0.002
41
0.003981
0.007967
0.005902 -0.00398
6
0.00716
-0.557 |
*|
|
0.035
42
0.004035 -0.001809
0.005261 0.005844
0.00765
0.764 |
|
0.046
43
0.004204
0.0130
0.004669 -0.00874
8
0.00802
-1.091 |
|
0.067
44
.
0.0154
0.002662
.
.
.
.
45
.
.
.
.
.
.
.
46
.
.
.
.
.
.
.
47
.
.
.
.
.
.
.
48
.
.
.
.
.
.
.
Sum of Residuals
***|
|*
**|
|
0.000
0.454
0
Sum of Squared Residuals
0.00276
Predicted Residual SS (PRESS)
0.00413
41
Number of Observations Read
48
Number of Observations Used
38
Number of Observations with Missing Values
10
Analysis of Variance
Sum of
DF Squares
Source
Mean
Square F Value Pr > F
Model
8
0.00166 0.0002069
7
Error
29
0.00275 0.0000947
3
Corrected Total
37
0.00440
2.18 0.0591
Root MSE
0.00973 R-Square 0.3761
Dependent Mean
0.01396 Adj R-Sq 0.2039
Coeff Var
69.7410
6
Parameter Estimates
Variable
Parameter Standard
Variance
DF Estimate
Error t Value Pr > |t| Inflation
Intercept
1
0.00677
0.00832
0.81 0.4226
0
D_log_GDP1
1
-0.58180
0.35296
-1.65 0.1101
3.15873
D_log_GDP2
1
0.08143
0.40833
0.20 0.8433
4.23113
D_log_GDP3
1
0.74596
0.35790
2.08 0.0461
3.25405
D_log_GDP4
1
0.04379
0.36155
0.12 0.9044
3.61473
D_log_M2_1
1
-0.05826
0.24496
-0.24 0.8137
2.86579
D_log_M2_2
1
-0.22314
0.23062
-0.97 0.3413
2.51608
D_log_M2_3
1
0.25645
0.21692
1.18 0.2467
2.16460
D_log_M2_4
1
0.31140
0.20421
1.52 0.1381
1.97618
42
Number of Observations Read
48
Number of Observations Used
38
Number of Observations with Missing Values
10
Analysis of Variance
Source
DF
Sum of
Squares
Mean
Square F Value Pr > F
5 0.0009318 0.0001863
2
6
Model
Error
32
0.00347 0.0001084
7
Corrected Total
37
0.00440
1.72 0.1588
Root MSE
0.01041 R-Square 0.2116
Dependent Mean
0.01396 Adj R-Sq 0.0885
Coeff Var
74.6286
0
Parameter Estimates
Variable
Parameter Standard
Variance
DF Estimate
Error t Value Pr > |t| Inflation
Intercept
1
0.01538
0.00493
3.12 0.0038
0
D_log_GDP1
1
-0.71092
0.36131
-1.97 0.0578
2.89050
D_log_GDP2
1
0.46478
0.31014
1.50 0.1438
2.13171
D_log_GDP3
1
0.54133
0.32000
1.69 0.1004
2.27179
D_log_GDP4
1
-0.29008
0.26144
-1.11 0.2755
1.65057
D_log_M2_1
1
-0.09452
0.22899
-0.41 0.6825
2.18709
43