4.3.1 Unit Root Test
It has been discovered in studies that Non-stationary variables produces spurious regression; hence the result may be misleading. Therefore, it is important to test and solve the stationarity of data. This was carried out using the Augmented Dickey-Fuller (ADF) unit root test with constant and trend.
Table 4.2 presented the unit root tests conducted on the variables at level. The Table also included the critical values and the ADF test statistic values.
Table 4.2: Unit Root Tests at Level
Variables Critical Values ADF Test Statistic
Remarks 1% 5% 10%
Real GDP -4.26 -3.55 -3.21 2.56 Not Stationary Market Capitalization -4.26 -3.55 -3.21 -1.34 Not Stationary Volume of
Transactions
-4.37 -3.60 -3.24 0.90 Not Stationary
Number of Deals -4.37 -3.60 -3.23 -7.55 Stationary Inflation -4.33 -3.59 -3.23 -3.01 Not Stationary
Source: Researcher Computations (September, 2015) using E-views 8.
From Table 4.2 showed that all the variables are non-stationary at level except number of deals that is stationary at level at 5% level of significance. This can be verified from the ADF test statistic values, which are lower than the 5% critical values. The implication of these results is that almost all the variables means and variances are not constant over time and it can lead to spurious estimation if used without resolving the problem of stationarity of the variables.
Table 4.3 presented the unit root tests conducted on the variables at first difference.
The Table also included the critical values and the ADF test statistic values.
Table 4.3: Unit Root Tests at First Difference
Variables Critical Values ADF Test Statistic
Remarks 1% 5% 10%
Real GDP -4.27 -3.56 -3.21 -3.56 Stationary
Market Capitalization -4.31 -3.57 -3.22 -5.44 Stationary Volume of
Transactions
-4.37 -3.60 -3.24 -8.39 Stationary
Number of Deals -4.37 -3.60 -3.24 -4.51 Stationary Inflation -4.31 -3.57 -3.22 -5.35 Stationary
Source: Researcher Computations (September, 2015) using E-views 8.
Table 4.3 reported that all the variables are stationary at first difference. This can be verified from the ADF test statistic values, which are higher than the 5% critical values. The implication of these results is that almost all the variables means and variances are constant over time. It is also important to test whether the variables will converge at the long-run by using Johansen Co-integration Test. Against this background, the short-run dynamics will be carried out to ascertain the effect of short-run effects of the relationships of variables.
4.3.2 Co-Integration
The essence of co-integration test is to ascertain if a long-run equilibrium relationship exist among variables of the model.
Table 4.3 Johansen Co-integration Result follows.
The table below shows the summary of result from analysis conducted on the specified model. The variables are real GDP, market capitalization, value of transactions, number of deals and inflation.
Unrestricted Co-integration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.809950 102.3757 69.81889 0.0000 At most 1 * 0.513507 49.24072 47.85613 0.0368 At most 2 0.358089 26.18368 29.79707 0.1233 At most 3 0.312321 11.99788 15.49471 0.1570 At most 4 0.000500 0.016017 3.841466 0.8991
Trace test indicates 2 co-integrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level
Source: Researcher Computations (September, 2015) using E-views 8.
Table 4.3 showed that at none the trace statistic of 102.38 is greater than 5%
critical value of 69.82. Also, at most 1 the trace statistic of 49.24 is greater than 5% critical value of 47.86. This showed the existence of a long-run equilibrium relationship among the variables. The respective co-integration equation is specified below:
Table. 4.4: Normalized co-integrating coefficients (standard error in parentheses)
RGDP MCAP VTS ND INF 0.469204 2.917209 210008.4 -3.69E+09 (0.04445) (0.41016) (186985.0) (1.5E+09)
Note: RGDP is the dependent; the standard error statistics attached to each variable are in parenthesis.
Source: Researcher Computations (September, 2015) using E-views 8.
The results of the normalized co-integration showed a long-run equilibrium relationship among variables. It indicates that coefficient of MCAP is positive (0.47). This implies that there exists a positive relationship between MCAP and GDP in the long-run. A unit increase in MCAP leads to an increase in GDP by 0.47 units. The coefficient of VTS and ND - 2.92 and 210008 respectively implies that each of these variables affect real GDP positive, while the coefficient of INF, -3.69E+09 indicates that any increase in inflation, real GDP will deflate by N3.69 billion. Any attempt to increase any of these variables in the long-run, GDP will enhance an increase in GDP.
4.3.4 Error Correction Mechanism
The error correction mechanism estimated the parsimonious model, where active and effective short-run variables were estimated. It introduces short-run dynamism into the long-run equilibrium and show the speed of adjustment in correcting the associated error.
Table 4.5 Error Correction Model
Variable Coefficient Std. Error t-Statistic D(Market capitalization) 0.002 0.001392 1.577214 D(Value of transactions) 0.066* 0.033536 1.981877 D(Number of deals) -43399.17** 20933.02 -2.073239
D(Real GDP(-1)) 0.690*** 0.134907 5.116785
Error Correction Term (-1) -5.88E+10** 2.92E+10 -2.013862
C 5.78E+09* 3.25E+09 1.781437
R-squared 0.742263 F-statistic 14.98***
Adjusted R-squared 0.692699 Durbin-Watson stat 2.263235
Note: 1st differenced of real GDP is the dependent variable. *, ** and *** are 10%, 5% and 1% level of significance respectively. D denote first differenced and (-1) is lagged value.
Source: Researcher Computations (September, 2015) using E-views 8.
The ECM otherwise known as speed of adjustment is significant with the appropriate negative sign. This can be seen on the over-parameterized ECM that shows ECM value of -5.88E+10. This implies that the present value of GDP adjust rapidly to changes in market capitalization, value of transactions, number of deals, and inflation. This is showed in the lagged value of ECM which indicates a feedback of or an adjustment of N58.8 billion from the previous period disequilibrium to the present level of GDP in the determination of causality between the past level of GDP and the present and past level of the explanatory variables.