INTRODUCTION
Nigeria is the second largest producer of natural rubber in Africa after Cote d’Ivoire and the eleventh in the world, with average annual production of crumb is 143,500 t CBN^{1}, out of which about twothird of it is exported, contributing 1.3% of the world’s output of natural rubber FAOSTAT^{2}.
Currently the rubber industry in Nigeria is facing constraints, which require urgent solutions. Rubber has the potential to help in poverty reduction, but the current production, processing and marketing techniques being used, do not maximize the potential gains to be realized by farmers, who cultivate and market rubber products. The efficiency of the marketing system is crucial in determining the profits from the products. An efficient marketing system is an important means for raising the income levels of farmers and for promoting the economic development of a country Abolagba et al.^{3} and an encouraging factor to improve production. Nigeria has a lot of smallholder rubber farmers, who depend solely on the industry as their main source of income. The growers have to depend on various marketing agencies to get a remunerative price for their produce, who in turn depend on rubber processors for affecting their sales. Constraints such as inadequate market information due to lack of marketing research, might have hindered the much anticipated rapid expansion of natural rubber production. It is obvious that the natural rubber sector needs a good marketing system. Market integration analysis will help in analyzing the rubber market performance. Market integration can be measured in terms of the strength and speed of price transmission between markets across various states of the country^{4 }.
Previous studies in natural rubber focused mainly on its production^{58,} constraints to production^{9,10} and rubber seed processing^{11}. However, very little worked on its marketing was done yet. Rubber marketing in Nigeria, was studied only by Giroh et al.^{12}, who focused on estimating costs and returns from rubber marketing and examined market structure, whereas Mesike et al.^{13}, focused on the supply response of rubber farmers to prices and other factors in Nigeria were analyzed using cointegration and vector error correction technique. But no one take a holistic economic analysis of the complete marketing system. This study fills that gap. It expanded the existing literature and the subject of market integration analysis in Nigeria and also shed light on required efforts to enhance the production and utilization of rubber at larger scale to bring about economic development in the area.
The information generated will be useful to a number of organizations including: Research and development organizations, marketers, producers, processors, policy makers, government and nongovernmental organizations to assess their activities and redesign their mode of operations and ultimately influence the design and implementation of policies and strategies.
This study was however, carried out to determine longrun and shortrun rubber market price integrations and transmission between local markets in Edo, Delta and AkwaIbom states.
MATERIALS AND METHODS
Area of study: The study was conducted in three selected states in SouthSouth Nigeria, namely Edo, Delta and AkwaIbom states in 2016. The State covers a land area of about 17,902 km^{2} with a population of 3,218,332 (NPC^{14}). Delta State presently covers a land area of about 18,050 km^{2} out of which more than 60% is land with a population of 4,098,391 people (NPC^{14}). AkwaIbom State presently covers a land area of 7,081 km^{2} with a population estimate of 4,805,451 (NPC^{14}). Notable food crops cultivated in the study area include: Cassava, maize, yam, cocoyam, cowpea, vegetables and cash crops such as rubber, oil palm, cocoa, kola nut, citrus, coffee, cashew and mangoes.
Data collection: Secondary data on monthly average rubber price (N/kg) in Edo, Delta and AkwaIbom markets from January, 2005 to December, 2015 were sourced from Rubber Research Institute of Nigeria, Edo, Delta and AkwaIbom states’ Agricultural Development programs, the various issues of Central Bank of Nigeria (CBN) and Food and Agriculture Organization (FAO) publications.
Analytical procedure: Data were analyzed using EViews software and statistical processes were employed in order to achieve an appropriate analysis. The data collected was analyzed using cointegration, Granger causality and vector error correction model. The cointegration analysis was achieved using augmented dickeyfuller test (ADF), Johansen’s maximum likelihood test, Granger causality and the vector error correction model (VECM) to analyze the timeseries data.
The first step was to examine the stationary properties of the various prices using the ADF test. If a series, say P_{t}, is stationary, invertible and stochastic after differencing d times, it is said to be integrated of order d and denoted by P_{t} = I(d). The statistical tests to determine whether the economic
variables were 1(0) or 1(1) using the Johansen test. Alufohai and Ayantoyinbo^{15}, formulation test on residual from the cointegration regression was given in Eq .1.
where: t is time e_{t} is residual error term assumed to be distributed identically and independently,P_{t1}, P_{t2} and P_{t3,} are rubber price series in three markets in Edo, Delta and AkwaIbom market states.
The null hypothesis of nonstationary could not be rejected, when, the absolute value of the ADF statistic is smaller than the critical ADF value and the next stage will be to test whether the first differences are stationary. If the null hypothesis of nonstationarity could not be rejected, then the series is still not stationary. Therefore, differencing continues until the series becomes stationary and order noted. The process is considered stationary if/δ/<1, thus testing for stationary is equivalent with testing for unit roots (δ<1) under the following hypotheses:
• 
Ho: δ = 0 the price series is nonstationary or there is existence of unit root 
• 
H1: δ ≠ 0 the price series is stationary or there is white noise in the series 
The hypothesis of nonstationarity will be accepted at 0.01 or 0.05 levels if ADF is greater than the critical value. The residuals from the Eq.1 were considered to be temporary deviation from the long run equilibrium.
Consider a pair of variables p_{t1} and p_{t2} each of which is integrated of ordered their linear relationship can be given by Eq 3^{17}.
In order to conclude that the price series were cointegrated the residuals from the equation had to follow stationarity. If the residual errors were stationary then the linear combination of the two prices is stationary (co integrated). If the tstatistic of the coefficient did not exceed the critical value the residuals, eˆ_{t1} from the cointegration equation were stationary^{18} and thus the price series p_{1t} and p_{2t} are cointegrated. Cointegration between time series evident that there must be an identification of a single market.
Granger causality test: This test was used to test the existence and the direction of longrun causal price relationship between the markets (Granger^{19}). The Granger causality test was used to determine the leading markets between three states markets. Granger causality provides additional evidence as to whether and in which direction, price integration and transmission is occurring between three price series or market levels. The test was based on the following pairs of OLS regression Eq .46 through a bivariate VAR:
Where:
n 
= 
Number of observation 
M 
= 
Number of lag 
Ep_{t} 
= 
Edo State market price 
Dp_{t} 
= 
Delta State market price 
Ap_{t} 
= 
AkwaIbom State market price 
α and β 
= 
Parameters to be estimated 
Error correction model (ECM): The ECM was applied to investigate further on shortrun interaction causality between variables and ability to correct long run deviation in the shortrun.
Where:
β_{1}, β_{2} and β_{3} 
= 
The estimated short run counterparts to the long run solution 
k 
= 
The lag length of the time, 
δ 
= 
The speed of adjustment parameter, which indicates how fast the previous moves back towards long run equilibrium in case of deviation in the previous time period 
ε_{t} 
= 
Is the stationary random process capturing other information not contained in either lagged value of p_{1t} and p_{2t} 
e_{t1} 
= 
Errorcorrection term, obtained from the cointegration equation captures the deviation from longrun equilibrium 
RESULTS AND DISCUSSION
Testing for stationarity: To ascertain whether the variables were stationary or not, the ADF unit root test was applied at ground levels and first differences of the price series. The results were presented in Table 1. The empirical evidence suggested that price series were not stationary in their level form and any attempt to use the nonstationary variables could lead to spurious regression and such results could not be used for prediction in the long run. The null hypothesis stated that the prices of natural rubber in one state/market did not t determine prices in another state/market so it could not be rejected at p<0.05.
When first differenced, however, the null hypothesis of nonstationarity was rejected in favour of the alternative as the values of the ADF tstatistics were greater in absolute term than the critical value. This result was necessary and sufficient for a test of cointegration of the price series.
Cointegration test results: Both trace and maximum eigenvalue statistics indicate the existence of cointegration relationship at 5% significant level for natural rubber. To check the first null hypothesis that the variables were not cointegrated (r = 0), trace and eigenvalue statistics were calculated, results showed that the maximum eigenvalue and trace test statistics values were higher than 5% critical values. Therefore, the null hypothesis was rejected and the alternative accepted for one or more cointegrating vectors (Table 2).
Similarly, the null hypotheses: r = 0 and r<1 from both statistics were rejected against their alternative hypotheses of r>1. The null hypothesis r >2 from both tests (trace test and maximum eigenvalue test) were accepted and their alternative hypotheses (r = 3) were rejected as the trace value and maximum eigenvalue were well below their corresponding critical values at 5% of significance. Both tests confirmed that all the three selected rubber producing states/markets had 2 cointegrating vectors out of 3 cointegrating equations, indicating that they were well integrated and price signals were transferred from one market to the other to ensure efficiency. Thus, Johnson cointegration test showed that though the selected natural rubber states/markets in Nigeria were geographically remote areas and spatially segmented, they were wellconnected in terms of prices of natural rubber, demonstrating that the selected states/markets during the study period were cointegrated and had longrun price linkage across them. Thus, the Edo, Delta and AkwaIbom States markets were cointegrated and there existed longrun equilibrium. This was supported by earlier studies carried out by Mesike^{20}, who concluded that cocoa and rubber market price within Nigeria are highly integrated and the findings of Emokaro and Ayantoyinbo^{21 }the result indicated that rice markets in Osun State were cointegrated and there existed longrun equilibrium.
Short run cointegration relationship: The VECM was employed in order to analyze the shortrun dynamics of the effects of natural rubber prices in the selected markets, having established that a long run relationship existed between the variables. The result of the VECM showed that if there is a positive deviation from the long run equilibrium the market tends to respond with a decrease or increase in the other market.
Table 1:  ADF unit root test results in levels and first differences 

1(0), price level and 1(1), first differences 
Table 2:  Testing for numbers of cointegration relations in the study area 

*Denotes rejection of the null hypothesis at 5 percent level of significance 

Fig. 1: 
Granger causality directions between the market pairs 
Table 3:  Pairwise Granger causality test for natural rubber market 

***Significant at 1% probability level, **Significant at 5% probability level, Computed from secondary data, 2017^{22} 
The Delta State price appears to respond faster than the Edo and AkwaIbom price. The adjustment coefficient was statistically significant at 1% for Delta market price for rubber suggesting that the Edo and AkwaIbom price exogenous weakly. This implies that movement in the Edo and AkwaIbom was less affected by price in the Delta market while movement in the Delta price was dictated by events in the Edo and AkwaIbom markets. This means that the longrun equilibrium in the natural rubber after an exogenous shock was restored primarily by corrections made by the Delta market prices.
The coefficient of the error correction term, which signified the speed at which rubber price in the selected states adjust to their longrun equilibrium level, was negative and statistically significant. The significant coefficient of the error correction term confirms the existence of a longrun equilibrium relationship of price for natural rubber in Nigeria. The coefficient of the error correction term of 0.325550 implies that, the feedback into the shortrun dynamic process from the previous period is 32.55% and the negative sign suggests that the adjustment formed a higher price shock (price rise) to the longrun price level. This means that the adjustment from the shortrun to longrun equilibrium was about 32.55% which was relatively weak compared with the perfect adjustment of 100% threshold. It suggests that the price in Edo, Delta and AkwaIbom states adjust partially to its longrun level after a price rise (shock). The error correction term had important feature for determining the time period after any deviation from long run equilibrium.
Granger causality test: The data in Table 3 showed unidirectional causalities between the market pairs: AkwaIbomDelta markets, meaning that a price changed in the former market in each pair granger caused the price formation in the latter market, whereas the price change in the latter market is not feedback by the price change in the former market in each pair. There was also bidirectional causality between EdoDelta and EdoAkwaIbom market pairs as shown in Fig. 1. In these cases, the former market in each pair Granger caused the price formation in the latter market which in turn provides the feedback to the former market as well. The longrun and shortrun null hypotheses that rubber market prices were not integrated and a price change in a market was not immediately transmitted to other markets, respectively, was rejected.
The results showed that there exist both longrun and shortrun market integrations between Edo, Delta and AkwaIbom State/markets. Thus, changes in the price of rubber in one market would cause the price of rubber in other markets to adjust immediately and the estimated speed of adjustment was about 32.55%. However, Beag and Naresh^{17} found out that apple market pairwise cointegration test confirmed that the pairs of Ahmedabad–Kolkata and BengaluruKolkata markets do not have any price association between them. Moreover, Granger causality tests indicated that there was no causality direction on price formation between them.
CONCLUSION
The findings of the study found out that Delta State price appears to respond faster than the Edo and AkwaIbom price, changes in the price of rubber in one market would cause the price of rubber in another state to adjust immediately and that can be beneficial for agricultural policy makers and the government developmental reforms program, revenue will be greatly enhanced with such incentives by government to intensify their production and marketing of natural rubber which create greater opportunities for economic growth and development and eventually improve market efficiency and increased technical efficiency of rubber producers.
SIGNIFICANCE STATEMENTS
The findings of the study provide relevant information in formulating policies relating to government developmental reforms program In addition, the findings will equip agricultural policy makers and extension agents in addressing the major barriers facing farmers in making decisions in rubber prices and marketing.
ACKNOWLEDGMENTS
The authors sincerely appreciate the genuine efforts of the authorities of the Rubber Research Institute of Nigeria and the tree crop units of the Ministry of Agriculture and Natural Resources in Edo, Delta and Akwa Ibom States for the support during this study.