PRICE DYNAMICS OF LOCAL AND IMPORTED RICE IN RURAL AND URBAN MARKETS OF LAGOS STATE, NIGERIA

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INTRODUCTION
Global demand for agricultural products is expanding rapidly and the demand for food products is foreseen to continue to grow for several decades as a result of a combination of population growth, rising per capita incomes and urbanization (Nasirin et al., 2015). In developing countries, approximately 60 % of total calories consumed are derived directly from cereals, among which rice is the most important source of calories for humans. Rice is the most important staple food for about half of the human race (Imolehin and Wada, 2000). In Nigeria, rice was primarily an urban middleclass product, but has now become a more widely consumed staple food. Nigeria currently is leading in terms of per capita consumption of rice in sub-Sahara Africa with about 10% of the 2000 average daily calorie intake (Mohanty, 2013). According to Federal Ministry of Agriculture and Rural Development (FMARD, 2011), there is an increasing demand for rice in Nigeria, as rice consumption was 5 million metric tons in 2010 and is expected to reach 36 million metric tons by 2050. Nigerian economy relies heavily on the importation of food to supplement domestic food production and rice is one of the most important food commodities in the country's food import basket (Onu et al., 2015). The alarming increase in prices over time is an issue of great importance as it causes food insecurity as most people go hungry because they cannot get food at affordable prices (Oyinbo et al., 2013). The objectives of the study were to: i. describe the trend in the prices of local and imported in rural and urban markets; ii.
ascertain the market that causes movement in the prices of local and imported rice; and iii.
estimate the extend of price relationship between integrated markets in the short run. β = ( ϕ -1), and ∆ is the first difference operator; thus in practice, equation 3 is estimated and the null hypothesis of β = 0 is tested against the alternative hypothesis of β ≠ 0. If, β = 0, then ϕ =1, it implies that there is unit root problem and Yt is nonstationary; but when β ≠ 0, then ϕ <1 and the series Yt is stationary. But according to Erdogdu (2007), the t-value of the estimated coefficient of Yt-1 does not follow the t-distribution even in large samples, therefore the decision to reject or accept the null hypothesis of β = 0 is based on the critical values of the tau statistic in the Dickey Fuller (DF) test. The DF test is based on the assumption that the error terms are not serially corrected, however in practical sense they show evidence of serial correlation, therefore the ADF test was developed to resolve this problem. In the ADF test, the lags of the first difference are included in the regression equation in order to whiten the noise of the error term et, the equation is presented as: ∆Yt = β Yt-1 + ϕi ∑ =1 ∆Yt-1+ et …(4) When intercept and time trend are added, the model becomes ∆Yt = α1 + α2 t+ β Yt-1 + ϕi ∑ =1 ∆Yt-1+ et …(5) where; α1 and α2 are constant and coefficient of time trend, respectively.
The ADF test was carried out on equations 3, 4 and 5, where; Yt represents a random walk without drift, a random walk with drift, and a random walk with drift around a deterministic trend.
With regards to causality of market prices, objective ii was achieved by the use of Granger causality test to determine the lead market between rural and urban markets that is the direction in which the price is moving. The Granger model for the study as adopted from Izekor et al. (2016) is represented as: − + …(6) where; n = number of observations, M = number of lag, RPt = rural market price, UPt = urban market price, α and β = parameters to be estimated and εt = error term. The study tested hypothesis are: H0: price of rice in one market does not determine the price of rice in the other market H1: price of rice in one market determine the price of rice in the other market.
On extent of price relationship, objective iii was achieved by the use of Index of Market Concentration (IMC). This was used to measure the degree of short-run price relationship between integrated markets. The model is specified below for both local and imported rice as follows; R1t = price of local rice in rural market (N/kg), R2t = price of local rice in urban market (N/kg) R3t = price of imported rice in rural market (N/kg), R4t = price of imported rice in urban market (N/kg), R1t-1 = lag price of local rice in rural market (N/kg), R3t-1 = lag price of imported rice in rural market (N/kg). β0 and α0 = intercept, ε = stochastic term. IMC = 1 3 is for local rice, IMC < 1 implies high short-run market integration, IMC > 1 implies low short-run market integration, IMC ∞ 1 implies no market integration, and IMC = 1 implies moderate short-run market integration

RESULTS AND DISCUSSION
The summary statistics for the price series as revealed by Table 1 shows that the maximum price for local rice in the area for the period under study is N274.48 and N283.07 in rural and urban markets, respectively. The maximum prices for imported rice in Lagos were N400.52 and N 485.89 in rural and urban markets, respectively. The skewness of both prices of local and imported rice shows that it is positively skewed with many small values, since the values were all greater than zero. The kurtosis value (Table 1) indicates that flat peaks for local rice prices and sharp peaks for imported rice prices, though the prices of local rice which is more closer to 3 seems to be normally distributed than that of imported rice. The result (Table 2) of ADF test for the price series which include price of local rice at rural and urban markets as well as price of imported rice in rural and urban as indicated by tstatistics and t-critical value (5%) became significant after the first differencing for all the estimated equations (no intercept, with intercept and with intercept and trend). The result of ADF with intercept and trend as reported is in agreement with the findings of Ohen et al. (2007) and Mkpado et al. (2013) who observed that rural and urban market price of rice became stationary after the first differencing and also that of Ojo et al. (2015) in the study of rural and urban rice market in Niger state and find out that unit root was eliminated after the first difference, the result also conforms with those of Moses (2017) who observed that rural and urban market prices of maize in Gombe state were stationary at first differencing and also Chen and Saghaian (2016) who observed that the monthly series of rice in Thailand and United states are integrated of I(1).
To achieve objective i of the study which is trend in prices. The trend was achieved by a graphical presentation of the price series, where the prices were compared graphically for rural and urban markets to see their movement pattern. Source: Data analysis, 2018 The graph of trend in the price of local rice in rural and urban markets of Lagos State as visualized in Figure 1, shows that the price of local rice in both rural and urban markets was increasing and moving up in an irregular pattern. This implies that there is information flow between the two markets, which enable marketers to know about price change in one market and it is easily reflected in the other market, this will make marketers apprised on prices and take decisions quickly.
The graph in Figure 2 shows that the price of imported rice was increasing in both rural and urban market of Lagos State between the period under study, Akande and Akpkodje (2003) finds out that average monthly retailed prices of imported rice was increasing. The prices got to it peak at the end of 2016 were price per kg of imported rice got close to N500.

Figure 2: Trend in price of imported rice in rural and urban markets of Lagos state
The result (Table 3) of Granger causality test for Lagos State price shows that all the prices paired together granger causes each other as shown by the probability which rejected the null hypothesis at 1% (P≤0.01) for all the price pairs except for the pairs of PLUL to PLRL, PLRI to PLRL, PLRI to PLUL and PLUL to PLUI which were rejected at 5% (P≤0.05). Source: Data analysis, 2018 The result of Table 3 implies that there exist a bilateral or bi-directional relationship between all the price pairs and these further justify the existence of perfect price transmission or simultaneous feedback relationship in Lagos State markets, and that prices of rice both local and imported in rural markets can be used to predict the prices in urban markets and prices in urban markets can also be used to predict prices in rural market. These means that the prices move together and any change in one market is quickly transmitted to the other market and this conforms with the findings of Ohen et al. (2007), and Mohammed and Wim (2010) who studied the evaluation of rice market in Banglandesh and Adeoye et al. (2011) who observed a bidirectional causality or simultaneous feedback in Oyo State Nigeria.
The IMC for local rice prices in rural and urban markets of Lagos State as revealed in Table 4 shows a value of 2.795 which is greater than 1 means a low short-run market integration for local rice prices between rural and urban markets of Lagos State. This further means that price transmission mechanism in Lagos State markets is low which may be attributed to inadequacy in the flow of market information in the short run period. This was also observed by Akintunde et al. (2012) in the study of long run price integration of grains in Oyo State. Note: *** significant at 1%, * significant at 10%, IMC =2.795 >1, that is low short run market integration.

Source: Data analysis, 2018
The result of IMC in Table 5 shows a value of 2.581 which is greater than 1, this imply low short run market integration for imported rice prices in Lagos state markets. That is, there is low flow of market information from rural market to urban market and also from urban market to rural markets in the short run. This is in contrast with the findings of Akpan (2014), who observed a high short run market integration between prices in rural and urban market. 2.30 Note: *** significant 1%; ** significant 5%; * significant 10% and IMC = 2.581 >1, that is low short run market integration Source: Data analysis, 2018

CONCLUSION AND RECOMMENDATIONS
The study concludes that prices of both local and imported rice in rural and urban markets were seen to be increasing at an irregular pattern, the maximum price for local rice in rural and urban markets in the study are N274.48 and N283.07, respectively, while that of imported rice was N400.52 and N485.89 for rural and urban markets, respectively. All prices were integrated of I(1) and there is a bi-directional causality relationship between all the price pairs. The IMC shows a low short run relationship for both local and imported rice. It is recommended that the flow of information should be enhanced between spatially separated markets and also firm policies should be implemented on prices to minimized irregularities in rice prices across board.