1.5 Experiments
2.1.3 Histograms
The representation of the GARCH (p, q) is given as:
Yt= α + b1Yt-1+ b2Yt-2+Ɛi
(Autoregressive process) ………… (21) And the variance of random error is:
2t=0+12t-1+22t-1……….. (22)
2t =+∑ i2t-i+∑ iƐ2t-i(23) Where, Ytis the price in the ithperiod of the ith market, p is the order of the GARCH term and q isthe order of the ARCH term. The sum of (α + β) gives the degree of persistence of volatility in the series. The closer is the sum to 1; the greater is the tendency of volatility to persist for a longer time. If the sum exceeds1, it is indicative of an explosive series with a tendency to meander away from the mean value.
Results and Discussion Lag Selection Criteria
Before we construct the conditional mean, the first thing to do is to find the right lag of VAR model in order to ensure that the errors are Gaussian white noise and obtain more interpretable parsimonious results devoid of biases due to sensitive nature of time series data to lag length (Table 1). A reasonable strategy of how to determine the lag length of the VAR model is to fit VAR (p) models with different orders p = 0,…,pmaxand choose the value of p which minimizes some model selection criteria. Model selection criteria for VAR (p) are based on Akaike information criterion (AIC), Schwarz-Bayesian information criterion and Hannan-Quinn (HQ) information criterion. A cursory review of the results shows that Akaike and Hannan-Quinn information criteria advised for the selection of lag 4 while Schwarz-Bayesian information criterion chose lag 1 as indicated by the asterisks ascribed to the criterion. And by applying democratic principle the decision of two criteria viz. Akaike and Hannan-Quinn information criteria supersedes that of the latter, therefore lag 4 was chosen as the optimum lag truncation length that is
appropriate for all the models to be used in subsequent analysis.
Table 1: Lag selection criteria
Lag(s) AIC BIC HQC
1 42.88 43.62* 43.01
2 43.09 44.28 43.29
3 43.45 45.09 43.72
4 41.89* 43.98 42.24*
Test of Unit Roots
Before conducting cointegrating tests, there is a need to examine the univariate time-series properties of the data and confirm that all the price series are non-stationary and integrated of the same order. This can be established analytically by using the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and GLS-ADF tests. The results of the unit root tests using ADF, PP and GLS-ADF tests are shown in Table 2. A perusal of Table 2 shows that the ADF test results applied at the level for all the price series variables did not reject the null hypothesis of non-stationarity as indicated by the tau-statistics which were greater than the t-critical at 5% significance level. But at the succeeding stage (1st difference) the applied ADF test results for all the price series variables rejected the null hypothesis and accepted the alternative hypothesis of the stationarity of the price series as indicated by the tau-statistics which were lower than their respective critical values at 5% significance level. Furthermore, because of the inherent weaknesses of the ADF test: the underlying distribution theories assume that the residual errors are statistically independent and have a constant variance which may not be true for many time series data; it tends to lost its power to test for stationarity if the lag length is too long, it tends to lost its power to test for stationarity if the data have structural break points and also if it contains more than one unit root it tends to lost its power to test for stationarity- its validity and robustness was verified using GLS-ADF test which overcomes this short-coming.
The results of the PP test which is a non-parametric model conform to the results of the ADF test at the level and at first difference.
Also, the results of the GLS-ADF test applied at level and at first difference accepted the null hypothesis of non-stationarity as indicated by tau-statistics in absolute value which were lower than the t-critical at 5% significance level and rejected the null hypothesis in favour of the alternative hypothesis of stationarity of the data as indicated by tau-statistics in absolute value which were higher than the t-critical at 5% significance level, respectively.
Since these results were in conformity with the earlier results produced by ADF-test, thus, it can be adjudged that the obtained ADF test results were robust and valid for the subsequent analysis. Because of these inherent weaknesses, great econometric scholars:
Maddalla and Kim (1998) as cited by Gujarati et al.(2012), Maddalla and Lahiri (2013) suggested that all the traditional unit root test models (DF, ADF and PP tests) should be discarded despite being the most widely used unit root test models. Given that all the price series are now integrated of the same order I(1) as evidenced by ADF, PP and GLS-ADF tests, it became possible to conduct the cointegration tests. It should be noted that since these variables were non-stationary at levels, any attempts to use them will lead to spurious/nonsense regression which is not ideal for policy making and cannot be used for long run prediction.
Table 2: Unit root tests
Tests Stage Ivory-Coast Ghana Nigeria Remarks
-stat P<0.05 -stat P<0.05 -stat P<0.05
ADF Level -1.76 0.688 -2.42 0.361 -3.30 0.07 Non-stationary
1stdiff. -5.40* 0.002 -3.98* 0.009 -3.75* 0.04 Stationary
-stat -critical -stat -critical -stat -critical
PP Z(t) Level -0.217 -3.00 -2.267 -3.600 -1.76 3.00 Non-stationary
1stdiff. -5.19* -3.00 -4.825* -3.600 -3.67* 3.00 Stationary Z(rho) Level -0.629 -12.50 -7.636 -17.90 -6.48 -12.50 Non- stationary
1stdiff. -22.10* -12.50 -24.41* -17.90 -16.67* -12.50 Stationary
ADF-GLS Level -1.92 -3.19 -2.42 -3.19 -2.14 -3.19 Non- stationary
1stdiff. -5.66* -3.19 -4.55* -3.19 -3.91* -3.19 Stationary
Note: * indicate that unit root at the level or at first difference was rejected at 5 per cent significance.
Multivariate market Cointegration Test Results
The results of cointegration using Johansen’s Jusleius maximum likelihood tests are presented in Table 3. To investigate the first null hypothesis that the variables were not cointegrated (r = 0), both the estimated trace and Eigen-value statistics rejected the null hypotheses as their respective test statistic values were higher than their corresponding critical values at 5% significance level and accepted the alternative of one or more cointegrating vectors. Furthermore, the null hypothesis r 2 from both the trace and maximum Eigen-value tests statistics were accepted and their alternative hypotheses (r = 2) were rejected as their respective test statistic values were less than their corresponding critical values at 5%
significance level. Both these tests confirmed that all the three selected tea markets had one cointegrating vectors out of 3 cointegrating equations, indicating that they were weakly integrated and price signals were not fully transmitted from one market to the other to ensure efficiency. On the whole, the results of cointegration tests indicated that the regional tea markets were weakly integrated in the long run, as only one out of the three markets were cointegrated. This also indicates that there are two common stochastic trends; hence two independent markets exist among the three markets. Therefore, it can be deduced that the law of one price between these markets was poor, implying that the price differences between these spatially separated markets were not equal to transaction costs i.e. there exist arbitrage in these markets. Thus, Johnson cointegration test has shown that despite that
these selected regional tea markets in West Africa are geographically isolated and spatially segmented; they were fairly connected in terms of tea prices, implying that they have long-run price linkage across them.
Also, it can be inferred that the spatial market integration conceptualized as tradability for these markets was consistent with market efficiency as their prices equilibrate across the markets while trade occurs.
Table 3: Multivariate market cointegration test results
H0 H1 Eigen value Trace test P-value Lmax test P-value
r = 0 r≥1 0.867 46.29** 0.0002 36.272** 0.0001
r≤ 1 r≥2 0.368 10.01 0.2848 8.272 0.3598
r≤ 2 r≥3 0.092 1.74 0.187 1.742 0.187
Note: **denotes rejection of the null hypothesis at 5 per cent level of significance Pair-wise market Cointegration Test
Results
The results of pair-wise cointegration across the markets are presented in Table 4. A perusal of the Table showed that the market pairs Ivory Coast – Ghana and Ivory Coast -Nigeria, had one cointegrating vectors, indicating that these market pairs were well-cointegrated and there exists long-run price association between them. Furthermore, it implies that the law of one price prevails between these market pairs, meaning that price differences between these market pairs are equal to the transaction cost. Therefore, the spatial market integration conceptualized as tradability for these market pairs are consistent with market efficiency as prices equilibrate across them while trade occurs. On the other hand, the market pair: Ghana- Nigeria market pair had no cointegrating vector, implying non-existent of any cointegration between them and thus, no long-run price association exists between this two market pair. It can be deduced that the law of one price did not prevail between this market pair, and the price difference between them is not equal to transactional costs, thus, market inefficiency between them. Furthermore, the spatial market integration conceptualized as tradability for
this market pair is not consistent with market efficiency as prices did not equilibrate across this market pair while trade occurs. However, the market inefficiency between Ghana – Nigeria market pair can be attributed to several factors that undermine the degree of market integration and generate discontinuities in the price responses to exogenous shocks.
The first one is the presence of high transaction costs relative to the price differential between this market pair, resulting in an autarkic market. Other factors include the presence of barriers to entry, risk aversion and information failures. Some characteristics of agricultural production, commercialization, and consumption, such as inappropriate transportation infrastructure, entry barriers and information failures, may create more friction in the arbitrage process. Also, it can be deduced that the power of these markets was concentrated in the hand of few traders, low quality and quantity of arrivals in these markets, thereby causing imperfection in these markets. Overall, the results show that the tea markets across the region were integrated as two out of the three relationships were cointegrated, indicating a high level of integration in the tea markets in West Africa.
Table 4: Pair-wise market Cointegration Test Results
Market pair H0 H1 Trace test P-value Lmax test P-value CE
Ivory Coast- Ghana r = 0 r≥1 22.79** 0.02 15.21** 0.06 1CE
r≤ 1 r≥2 7.58 0.10 7.58 0.10
Ivory Coast- Nigeria r = 0 r≥1 16.59** 0.087 15.87** 0.074 1CE
r≤ 1 r≥2 0.722 0.396 0.722 0.395
Ghana - Nigeria r = 0 r≥1 17.298 0.123 11.49 0.225 NONE
r≤ 1 r≥2 5.810 0.213 5.81 0.213
Note:**denotes rejection of the null hypothesis at 10 per cent level of significance CE- Cointegration Equation
Multivariate Vector Error Correction Model Results
Price changes in one market will be transmitted on a one-to-one basis to the other market either instantaneously (short-run integration) or over a number of lags (long-run integration), following an adjustment process toward the long-run equilibrium relationship between the price series. The coefficients of ECTs indicate the speed of adjustment of any disequilibrium towards the long-run equilibrium. These coefficients apparently reflect the long-run deviations of the system from the long-run equilibrium level as a result of shock(s) originating from short-run equilibrium. A cursory review of the results shows negative ECTs for all the markets, indicating that the long-run disequilibrium adjustment process would lead to stable long-run prices in all of the selected markets (Table 5). However, the results show that the long-run adjustment coefficients (ECTs) of Ghana and Nigeria markets) were statistically insignificant in explaining the price changes in other markets. The long-run dynamics of tea prices in Ivory-Coast market measured by the ECT display negative and statistically significant attractors. The speed of adjustment (-0.345) is statistically significant at 5%
significance level, meaning that, a price shock that induces price deviations from their equilibrium level would induce traders to respond to the shock in a way that prices would converge toward their equilibrium value. In other words, it implies that 34.5% of the previous deviation in the prices of tea in Ivory-Coast market due to short-run shocks is corrected annually in order to establish equilibrium in the long-run. However, the
adjustment rate was very slow as it would take approximately 7.9 months to restore back to equilibrium in the long run if eventually, the shocks originate from any of the short-run equilibrium. This coefficient, known as the attractor, helps absorb the effects of shocks and keeps prices in a long-run equilibrium relationship. The higher the attractor in absolute value, the faster would be the speed of adjustment of the prices towards the equilibrium level. However, such an adjustment occurs only if there is a linear and symmetric relationship between the price series of the markets. Furthermore, there were delays in the short-run price transmission except for lagged one price of tea at Ghana market as the coefficients of the lagged price differences were not statistically significant.
The prices of tea in Ghana market at lagged one in the short-run was instantly transmitted as indicated by the estimated price coefficient which was significant at 5% significance level.
Also, the prices of tea in Ivory- Coast and Ghana markets at lagged one were instantly transmitted to Ghana market as evidenced by the price coefficients which were significant.
These negative coefficients indicate that in addition to spatial price differences, some unknown factors have a predominant role in spatial price transmission.
Generally, the long-run price integration of regional tea market in West Africa is noticeable as all the attractor coefficients tend to be negative; indicating that long-run changes in prices in all the markets may lead to a long-run equilibrium in the system. The levels of regional causality appeared to exist to some extent in these spatially separated markets, which shows that the trade barriers
are not restricting regional free trade and the price signals transient through these West Africa regional markets. To strength the linkage and interconnectedness between these regional markets for faster transmission of price and management of tea commodity from the surplus area to deficit area, the clarion call
is to enhance the development of market infrastructure, use of information and technology in the transaction of goods, processing, transportation and other back-end supply chain. This would definitely help in the development of a single integrated economic market in the West Africa region.
Table 5: Multivariate VECM of the selected tea markets in West Africa
Variable D(Ivory-Coast) D(Ghana) D(Nigeria)
ECTt-1 -0.345 (0.119)** -0.119 (0.078)NS -0.078 (0.416)NS D[Ivory-Coastt-1] 0.156 (0.288)NS 0.437 (0.188)** 0.274 (1.01)NS D[Ivory-Coastt-2] 0.44 (0.36)NS 0.396 (0.235)NS -0.229 (1.26)NS D[Ivory-Coastt-3] 0.32 (0.33)NS 0.278 (0.214)NS 0.525 (1.148)NS D[Ghanat-1] -1.65 (0.58)** -0.785 (0.381)* -1.679 (2.045)NS D[Ghanat-2] -1.08 (0.68)NS -0.616 (0.441)NS -0.119 (2.368)NS D[Ghanat-3] -0.93 (0.52)NS -0.184 (0.337)NS -1.10 (1.81)NS D[Nigeriat-1] 0.002 (0.085)NS 0.070 (0.056)NS 0.134 (0.299)NS D[Nigeriat-2] 0.089 (0.094)NS 0.068 (0.061)NS 0.03 (0.329)NS D[Nigeriat-3] 0.013 (0.102)NS -0.006 (0.067)NS 0.01 (0.358)NS Note: *** ** * implies significance at 1%, 5% and 10% respectively
NS: Non-significant (): implies Standard error Granger Causality Test
The Granger causality helps in establishing the direction of causation (if any) between the variables and thus helps in predicting the value of one variable on the basis of other variable.
The results of the granger causality tests presented in Table 6 shows that only one F-statistics for each of the causality tests of the prices in Ivory-Coast and Ghana markets on other market were statistically significant, while Nigeria market had none of its F-statistics significant. A perusal of Table 6 shows that there exists bidirectional causality between Ivory Coast-Ghana market pair, meaning that, the former market granger causes the price formation in the latter market which in turn provides the feedback to the former market as well. This implies that this market pair is efficient with no consequence of leverage condition. Further, two market pairs, Ivory Coast- Nigeria and Ghana-Nigeria had no direct causality between them, indicating that neither Ivory Coast nor Ghana market granger causes the price formation in Nigeria market; nay the Nigeria market granger causes the price formation in Ivory Coast and Ghana
markets. In other words, there is no long-run price association between these market pairs.
From these results, it can be deduced that Ivory Coast-Ghana market pair exhibit strong endogeneity, while prices of tea in Nigeria market exhibited super exogeneity with its counterparts, indicating that the prices of tea in Nigeria market were absolutely exogenous and were determined outside the system perhaps by quality, price intervention, and to some extent by export demand. The exogenity test helps to identify whether the flow of price information is unidirectional or bidirectional.
The Wald test for the regional markets signified the dominant role played by the tea prices of Ivory Coast and Ghana markets in the regional tea market in West Africa.
Therefore, it can be inferred that Ivory-Coast and Ghana markets are more operational and price efficient when compared to their counterpart, and tea prices in these markets adjust according to demand and supply situation in the international market. The poor market efficiency of Nigeria market is not far from the low quantity of arrivals in the market, poor quality of the commodity, market power
concentration in the hand of few traders, poor market infrastructure and market information failure. All these inhibiting factors affecting the efficiency of tea market in Nigeria are due
to lack of political will and almost total neglect of agricultural sector by the government since the adoption of structural adjustment programme in the country.
Table 6: Pair-wise Granger causality among selected major palm oil markets
H0 t-stat Prob.(P<0.05) Granger cause Direction
Ivory Coast→ Ghana 9.71 0.014** Yes Bidirectional
Ivory Coast← Ghana 4.86 0.050** Yes
Ivory Coast→ Nigeria 5.65 0.238 No None
Ivory Coast← Nigeria 0.49 0.745 No
Ghana→ Nigeria 2.25 0.199 No None
Ghana← Nigeria 1.37 0.363 No
Note:**denotes rejection of the null hypothesis at 5 per cent level of significance Impulse Response Functions
The results of impulse response functions presented in Figure 1 shows how and to what extent a standard deviation shock in one of the tea markets affects the current as well as future prices in all the integrated markets over a period of ten years. A perusal of the diagrammatic figure shows that an unexpected shock that is local to the Ivory-Coast market will have a transitory effect on the prices of Ghana and Nigeria markets i.e. the effect of the shock will die out over time. Also, an orthogonalized shock to the price of tea in Ghana market has a transitory effect on the prices of tea in Ivory Coast and Nigeria markets. However, unexpected shocks that are local to the tea prices in Nigeria market will have a transitory effect on the tea prices that will be obtained in Ivory Coast and Ghana
market, while it will have a permanent effect on its own market i.e. the price effect will not die out over time. Therefore, it can be deduced that none of the selected markets have a dominant effect over its counterpart in the region i.e. the market impulse response confirm that the price transmission from one market to the other markets and vice versa occur in small proportions. Furthermore, it implies that the prices of tea in these regional markets seemed to be exogenous and will be determined outside the system perhaps by quality, price intervention, and to some extent by export demand. Therefore, all these selected regional tea markets in West Africa are relatively market followers and do not play a significant role in the world internationaltea market.
Figure 1: Impulse response of markets to innovation/shocks Decomposition of Variance for the selected
regional Tea Markets in West Africa
The results of variance decomposition for the selected regional tea markets are given in Table 7. The decomposition detailed for the selected markets are as follows: For Ivory-Coast market, in the short-run (first quarter), a shock to the price of tea in Ivory-Coast market will account for 75.15, 24.68 and 0.17%
variations of fluctuation in prices at Ivory-Coast (own shock), Ghana and Nigeria markets, respectively; while in the long-run (last quarter), a shock to the price in the same market will account for 73.44, 23.80 and 2.77% variation of fluctuation in prices at Ivory-Coast (own shock), Ghana and Nigeria markets, respectively. Based on this outcome it can be deduced that the effect of the shock on Nigeria market is very marginal when compared to the resultant transmission effect in Ghana market, thus, indicating that Nigeria market is inefficient. In the case of Ghana market, in the short-run, an impulse to the price of tea in Ghana market can cause 45.03, 39.67 and 15.30% of variation in the fluctuation of prices in Ivory-Coast, Ghana (own shock) and Nigeria markets,
respectively; while in the long-run (last quarter), an impulse to the price in Ghana market can cause 32.72, 51.92 and 15.36% of variation in the fluctuation of prices in Ivory-Coast, Ghana (own shock) and Nigeria markets, respectively. It is evident that Ghana market will be comparatively competent, and this may be due to its geographical position-the centre-most among position-the selected tea markets of the region as the price signals in Ghana market would be quickly transmitted to other markets and vice versa. Therefore, the geographical situation and optimal distance between the market places will hold the mutual forces on commodity movements and price formation. In the case of Nigeria market, in the short-run (first quarter), an innovation to the price of tea in Nigeria market can cause 1.00, 3.27 and 95.73% of variation in the fluctuation of the prices in Ivory-Coast, Ghana and Nigeria (own shock), respectively; while in the long-run (last quarter), an innovation to the price in Nigeria market can cause 0.90, 5.27 and 93.83% of variation in the fluctuation of tea prices in Ivory-Coast, Ghana and Nigeria (own shock), respectively. Based on these findings it is obvious that Nigeria market
-50 0 100 50 150 200 250 300 350 400 450
0 2 4 6 8 10 years
Ivorycoast -> Ivorycoast
-150-100-50 50 0 100 150 200 250 300
0 2 4 6 8 10 years
Ghana -> Ivorycoast
-200-150 -100-50 50 0 100 150 200
0 2 4 6 8 10 years
Nigeria -> Ivorycoast
-100-50 50 0 100 150 200 250 300 350 400
0 2 4 6 8 10 years
Ivorycoast -> Ghana
-100-50 50 0 100 150 200 250 300
0 2 4 6 8 10 years
Ghana -> Ghana
-150-100-50 50 0 100 150 200
0 2 4 6 8 10 years
Nigeria -> Ghana
-1000-800-600-400-200 200 400 600 0
0 2 4 6 8 10 years
Ivorycoast -> Nigeria
-1000-800-600-400-200 200 400 600 0
0 2 4 6 8 10 years
Ghana -> Nigeria
-400-200 0 200 400 600 800 1000
0 2 4 6 8 10 years
Nigeria -> Nigeria
will be inefficient which may be due to poor quality, low quantity of arrival, market information failure, poor infrastructure and oligopolistic tendency. However, it was observed that the shock originating from
Ivory-Coast and Nigeria markets at both time periods is more pronounce on the respective market itself when compared to its effect on other markets.
Table 7: Decomposition of variance for the selected tea markets in Nigeria
Ivory-Coast (IVC) Ghana Nigeria
P IVC Ghana Nigeria P IVC Ghana Nigeria P IVC Ghana Nigeria
1 100.00 0.00 0.00 1 20.51 79.49 0.00 1 0.94 0.04 99.01
2 78.97 20.85 0.18 2 40.56 52.99 6.45 2 0.46 3.32 96.22
3 75.15 24.68 0.17 3 45.03 39.67 15.29 3 1.00 3.27 95.73
4 72.03 25.76 2.21 4 48.02 36.59 15.39 4 0.85 3.09 96.06
5 70.40 26.10 3.50 5 45.36 39.96 14.69 5 1.04 3.29 95.67
6 70.72 26.28 3.00 6 40.34 45.50 14.16 6 0.94 3.06 95.997
7 72.91 24.20 2.89 7 36.88 49.58 13.54 7 0.84 3.47 95.69
8 74.54 22.53 2.94 8 35.06 50.95 13.98 8 0.83 4.07 95.10
9 75.46 21.69 2.85 9 34.40 50.62 14.98 9 0.81 4.64 94.55
10 73.44 23.80 2.77 10 32.72 51.92 15.36 10 0.90 5.27 93.83
Source: Computed from GRETL computer printout Diagnostic Testing
The results of diagnostic statistics of VECM model for the selected regional tea markets are shown in Table 8. The autocorrelation tests indicate that the residuals were not serially correlated as evidenced from the Ljung-Box Q-statistics which were not different from zero at 10% probability level (p>0.10), thus the acceptance of null hypothesis of no autocorrelation. The Arch test results revealed that the variance of the current residuals and that of the lagged residuals do not correlate as evidenced from the Lagrange multiplier (LM) test statistics which were not different from zero at 10% probability level (p>0.10), thus the acceptance of null hypothesis of Arch effects are not present.
The stability tests indicated that none of the models was misspecified as evidence from the Eigen-values which shows that none of the remaining Eigen-values appears close to the unity circle. Furthermore, the result of normality test shows that the residuals are not normally distributed as evidence from Doornik-Hansen test 2 which is different from zero at 10% probability level (p<0.10).
However, when dealing with time series data, non-normality of the residuals is not considered a serious problem, because in most cases these data are not normally distributed.
Therefore, based on the outcome of the diagnostic statistics, it can be inferred that all the results were valid and the VECM model used was the best fit.
Table 8a: VECM Diagnostic checking Test
Statistic P-value Autocorrelation
Ljung-Box Q (Eq1)
6.06 0.195
Ljung-Box Q (Eq2)
2.47 0.651
Ljung-Box Q (Eq3)
0.79 0.939
Arch effect LM-Test 1.43 0.84
(Eq1) LM-Test (Eq2)
1.20 0.88 LM-Test
(Eq3)
0.80 0.94 Normality
Doornik-Hansen test
23.92 0.0005
Eigen-values 1 0.541
2 0.99
3 1.47
Source: Computed from GRETL computer printout