CHAPTER THREE
METHODOLOGY
Methodology refers to the steps taken by the researcher to solve the
problems posed in the research question. The method chosen for this
research is the econometric method, the use of regression analysis. This tells
us the relationship that exists between variables specified in the econometric
models.
The ordinary least squareS (OLS) technique of estimation would be used in
estimating the models. This technique is preferred because its parameter
estimators have optimal properties that are best, linear, unbiased estimators
known as BLUE properties.
3.1 MODEL SPECIFICATION
While the literature dwells on the existent relationship as regards monetary
policy and inflation in Nigeria, the pioneering theoretical has always been
traced to the Keynesian and neoclassical simple Polynesian models. For the
purpose of this study, the simple monetary policy function shall be employed.
From the foregoing discussion, we hereby specify the following model.
Ms = F (inF, MRR, OMO) .......................................3.1
where
Ms = Broad money supply
InF = Inflation rate
Omo = Open market operation proxied with value of treasury bill.
u = Random variable
MRR = Central Bank Minimum Rediscount rate.
u satisfies the assumption of zero mean, last variances and no
multicollinearity.
3.2 MODEL SELECTION
Equation 3.1 represents the functional form of the model. The mathematical
or the equation form of the model is written as:
Ms =
The log value of money supply and the value of treasury bill (VTB) can be
taken due to the large magnitude of the data. Hence, we specify our model as
follows:
log. Ms =
The expected apriori sign are as follows:
> 0 i.e positive
< 0 i.e negative
< 0 i.e negative
3.3 METHOD OF ESTIMATION
The procedure for estimation adopted in this study is the Ordinary Least
Suare (OLS) because of its small sample properties of BLUE. This method
attributed to Carl Fried-Rich Gauss, a German mathematician is preferred
because it is easy to understand, simple in its computational procedure plus
its parameter estimates, which have some optimal properties of linearity,
unbiasedness and minimum variance among a class of unbiased estimates.
Due to the limited knowledge of applied macro-econometrics the researcher
is hampered in investigation of the detailed econometric analysis. The
regression results will be weighed basically on two criteria, economic criteria
and econometric criteria
3.4 TECHNIQUES FOR EVALUATION OF RESULTS
The purpose of evaluation is to know whether the parameter estimates are
theoretically meaningful and statistically satisfactory. We shall rely on
secondary data sources for the necessary information. The publications of the
Central Bank of Nigeria statistical bulletin, Federal Office of Statistics and
other related publications would be considered.
The variables used in the estimation are real variables only, having properly
adjusted them for price changes where applicable, the natural logarithms of
the variables are used in order to ensure better estimation. The data on Broad
money supply, minimum rediscount rate and value of treasury bill was
obtained from the Central Bank of Nigeria statistical bulletin while data on
inflation was obtained from the Federal Office of Statistics from (1970-2003)
3.5 ECONOMIC TEST (APRIORI EXPECTATION)
This criterion is determined by the principle of economic theory and refers to
the sign and size of the economic relationship of the parameters. The
economic coefficient of models are the constant of economic theory. If the
sign and size of the parameters do not conform to economic theory, reject
unless there is a cogent reason to believe that in a particular instance, the
principle of economic theory do not hold.
3.6 STATISTICAL CRITERIA (First Order) Test
This criteria aims at evaluating the statistical reliability of the parameters
estimated and are determined by statistical theory. The coefficient of multiple
determination (R) and the standard error are the most widely used criteria.
These estimates are obtained from the variables used while the accuracy of
the model is determined by sampling theory. The R is computed from the
data and shows the percentage of the total variation of the dependent
variable being explained by the effect of changes in the explanatory variable.
The T-test and F-test determines the level of significance of each variable as
well as the overall significance of the model respectively. The parameter
estimates should be rejected if it has a wrong sign or (size) even though there
is high correlation coefficient or the error term suggests that the parameters
are statistically significant.In such cases, the parameters though statistically
satisfactory are theoretically farfetched, that is they make no sense on the
basis of apriori theoretically economic criteria. In other words, it is a spurious
regression.
(A) STUDENTS TEST: This tests the significance of each of the explanatory
variables on the dependent variables.
(B) The F-TEST : This tests the overall significance of the explanatory
variables on the dependent variable.
(C) THE COEFFICIENT OF MULTIPLE DETERMINATION (R2) : This tests
the goodness of fit of the estimated regression. That is it tells how well the
variables in the dependent variable areexplained by the independent variable.
ECONOMETRIC CRITERIA (Second Order) TEST
Here, we try to investigate whether the assumption of econometric method
employed are satisfied or not and are set by econometric theory. In eria other
words,they determine the reliability of the statistical criteriamas well as the
standard error of the parameter estimates. They help us establish whether
the estimates have the desirable properties of unbiasedness, consistency.If
the assumptions of econometrics applied are satisfied or that the estimated
parameter possess the desirable operties (e.g biasedness) or that the
statistical criterion becomes unreliable for the determination of the
significance of these estimates. We say that the econometric criteria strives
to detect the violation of the assumption of the econometric method
employed.
1. TEST FOR AUTOCORRELATION
There is a problems associated with the time series econometrics. We
employ the Durbin-Watson (DW) Statistics test to test for autocorrelation. If
the DW is close to 2.00, it is accepted that there is absence of
autocorrelation.
2. TEST FOR STATIONARITY
The unit root is used to test for the stationarity of the variables used in the
econometric models. By this, we mean that the mean value, variance and co-
variance are constant over time. For this reason, we will use the augmented
Dickey-fuller test (ADF) to test for the stationarity.
3. TEST FOR MULTICOLLINEARITY
This test is carried out using the correlation matrix, this suggests that if
the correlation coefficient is in excess of 0.8, then there is a serious
multicollinearity problem. If the coefficient is less than 0.8, we conclude that
there is no multicollinearity.
4. TEST FOR NORMALITY
The Jarque-Bera is used to test for normality by testing the asymptotic or
large sample data. The chi-square distribution is used to test if the error term
is normally distributed.
5. TEST FOR HETEROSCEDASTICITY
This is used to verify the OLS assumption of homoscedasticity (i.e equal
variance)
CHAPTER FOUR
PRESENTATION AND ANALYSIS OF RESULTS
4.1 PRESENTATION OF REGRESSION RESULTS
The result of the model was arrived at by estimating version forms of the
model equation thereby general to specific approach to model selection.
However our analysis is based in equation 3.3 and the result are presented in
the table below. The modelling procedure employed is the OLS and the
econometric software package used is E-views 3.1.
TABLE 4.1
REGRESSION RESULTS
DEPENDENT VARIABLE
L0G (MS)
Variables Coefficients Std Error T-stat T-prob
Constant -6.2576 0.3542 -17.6678 0.0000
INF 0.0013 0.0039 0.3313 0.7428
MRR -0.0154 0.0201 -0.7561 0.4555
LOG (VTB) 1.0246 0.0505 20.2843 0.0000
4.1.1 INTERPRETATION OF RESULTS
As previously discussed in chapter 3, the R2 is used to test the overall
goodness of fit, while the F-statistic is used to test the overall impact of the
independent variable on the dependent variable. The results shown above
shows that the coefficient of inflation is (0.0013). This denotes that if inflation
increases by 1 percent, on the average, the level of money supply increases
by (0.0013 x 100) = 0.13 percent. The result also show us that the coefficient
of minimum rediscount rate (MRR) is (-0.0166). This implies that MRR
increases by 1.66 percent. We also see from the result that as log value of
Treasury bill (VTB) increases by 1 percent, on the average, money supply
also increase by 1.03 percent.
4.2.1 ECONOMIC CRITERIA
Here, we examine whether the estimated coefficients agree with
theoretical apriori expectation both in terms of size and sign. The log
variables are interpreted as elasticity while other variables not logged are
interpreted on absolute term, inadequate sensitization of the public on the
use of treasury bills reduces the level of awareness which critically inhibit how
inflation rate is curbed. Hence, we can give a summary of the expected and
obtained sign from the result.
TABLE 4.2
EXPECTED AND OBTAINED SIGNS
Variables Expected sign Obtained sign Remarks
INF >0 (positive) >0 (positive) Conforms
MRR <0 (negative) <0 (negative) Conforms
LOG(VTB) <0 (negative) >0 (positive) Did not conform
The coefficient of inflation rate conform to the apriori expectation because it
is expected that if CBN increases money supply, other things remaining
constant, inflation will also increase. Hence, it conforms to the apriori
expectation. The value 0.001 means that as inflation increases by 0.001 x 100
= 0.1 percent. The coefficient of minimum rediscount rate agrees with the
apriori expectation because iys expectation lies on the fact that if money
supply increases as stated in IS-LM model,interest rate will fall. Then the
negative expected negative relationship was achieved. The value 0.015
means that as minimum rediscount rate increases by 1 percent average,
money supply declines by about 0.015 x 100 = 1.5 percent. Finally, the open
market operation represented by the value of treasury bill did not conform
with the apriori expectation. The value 1.024 shows that as value of treasury
bill increases by 1 percent. On average money supply increases by about 1.1
percent.
What could be the cause of this?
As the money supply increase, the tendency for the government to use open
market operation to control increase in money supply increases. The action
results in order to decrease inflation or to keep inflation at a certain level. The
result of the model and the analysis show that inflation and monetary policy
is negatively related.
4.2.2 STATISTICAL TEST
i THE COEFFICIENT OF MULTIPLE DETERMINATION (R2)
From money supply function, we can observe that the lag value of
treasury bill, minimum rediscount rate and inflation together explained about
94% variation in money supply from (1970-2003)
ii T- TEST
This test is based on statistical decision theory. This test is carried out in
order to check the significant influence of the independent variables. The test
shall be carried out under the following hypothesis.
H0 ; = 0
H1 ; = 0
At 5% level of significance to.025 = 2.04
DECISION RULE
Reject H0 at 5% significance if /t cal > /t and accept if otherwise
t1 (inflation) = 0.3435
t0.025 = 2.04
Thus since /t / > /t1/, we accept H0 and conclude that the inflation is not
statistically significant.
t2 = -0.8133
t0.025 = -2.04
Since /-2.04/ > /-0.8133/, we accept H0 and conclude that the minimum
rediscount rate (MRR) is not statistically significant.
T3 = 20.303
T0.025 = 2.04
Since /20.303/ > /2.04/, we reject the null hypothesis and conclude that the
value of treasury bill is statistically significant.
iii F-TEST ANALYSIS
The F-test analysis shall be carried out under the following hypothesis.
H0 : (all scope coefficients are simultaneously zero)
H1 : (all slope coefficient are not simultaneously zero)
DECISION RULE
Reject H0 if Fcal > F (k-1, n-k) df and accept H0 if otherwise
Fcal = 420.8050
F (3.31) = 2.92
Since Fcal > Ftab i.e 420.80 > 2.92, we reject H0 and accept the alternative.
On this ground, we also conclude that the slope coefficients of the money
supply functions are not zero and that the model is not of good fit. The
implication is that the overall model is significant.
4.2.3 ECONOMETRIC CRITERIA
Under this test, we are interested to know whether the assumption of the
ordinary least squared method adopted in this analysis. The tests are
presented below.
A. TEST FOR AUTOCORRELATION
The presence of absence of autocorrelation is detected by the use of Durbin
Watson statistic. The test is carried out under the following hypothesis
H0 : P = 0 (No autocorrelation)
Against
H1 : P 0 (Positive autocorrelation)
At = 5%
Decision rule:
Reject H0 if dv < d < 4-di (No autocorrelation). Otherwise accept H0
NB dl = 1.271, du = 1.652, d* = 1.14213
n = 4, k = 3
4-dl = 2.729
du < d* < 4-dl i.e +.652 <
= 1.652 < 1.14213 < 2.729
1.652 < 1.14213 < 2.729, we reject H0
There is positive autocorrelation
B. TEST FOR HETEROSCEDASTICITY
We are interested in checking whether the variance is constant 02 hence
we shall use the white’s general test. The hypothesis under this test is
H0 : There is no heteroscedasticity
H1 : There is heteroscedasticity
DECISION RULE
If the calculation value exceeds the critical square value at 5% level of
significance, we reject the null hypothesis otherwise accept it.
X2o.o5(6) = 12.5916
X21 = 2.670956
Since X20.05 > X12 we accept the null hypothesis that there is no
heteroscedasticity in the model.
C. TEST FOR MULTICOLLINEARITY
This test is carried out in order to detect whether there is presence of
multicollinearity in the explanatory variable.
Variables r2 Remark
X1X2 0.330450 No multicollinearity
X1X3 -0.130053 No multicollinearity
X2X3 0.537787 No multicollinearity
X1 = Value of Treasury bill
X2 = Inflation rate
X3 = Minimum rediscount rate
NM = No multicollinearity
4.3 EVALUATION OF WORKING HYPOTHESIS
These test are based on statistical decision theory on hypothesis testing. For
the reliability or significance of the included explanatory variables in the
model, we shall assess this based on the t-test.
Null hypothesis B1 = 0, where = 0
At 5% level of significance t0.025 = +2.042
We can conclude that the constant and the log of value of treasury bill is
statistically significant while inflation rate and minimum rate is not
statistically significant.
The summary can be presented below
Variables Two tail test Decision
Inf Statistically insignificant Accept H0
MRR Statistically insignificant Accept H0
LOG (VTB) Statistically insignificant Accept H0
4.4 EVALUATION OF THE WORKING HYPOTHESIS
The results of the model and the analysis show that inflation and monetary
policy is negatively related. This can be illustrated by the aggregate demand
and aggregate supply function.
