Aboki, peter maisaje

2.5.1.2 Co-integration

A time series is stationery if it is I (0), and non stationary if I(1), that is they have stochastic trend. Hence a linear combination can cancel out the stochastic trends in the two series that are I (1), and we do not have a spurious regression. In which case we say the two variables are co-integrated. From the economic point of view two series are co- integrated if they have a long-term, or equilibrium relationship between them. Therefore the traditional regression methodology applies including the t and F tests. As Granger puts it “a test for co- integration” can be thought of as a pre-test to avoid nonsensical regression situations. Some sample tests for certification are the Engle-Granger (EG) or Augmented Engle-Granger (AEG) test which has its roots in ADF (Ali & Rahaman, 2009). The co-integrating Regression Durbin–Watson (CRDW) test, whose critical values were provided by Sargen and Bhargana, used the Durbin – Watson d- statistic obtained from the co-integrating regression (Gujarathi, 2007).

2.5.1.3 Co-integration and Error correction Mechanism (ECM)

Co-integration implies a long term or equilibrium relationship between two variables. In the short run, there may be disequilibrium. Here we can treat the error term in the co integrated variables regression as equilibrium error. This error can be tied to the short run behaviour of the series (or variable) to its long term value. This was used by Engle and Granger to correct for disequilibrium. As Granger puts it, if two variables Y and X are co-integrated, the relationship between the two can be expressed as ECM given as

∆Y_t = a₀ + α_1t∆X_t + α₂μ_t-1 + ε_t …………….. 2.14

2.5.1.4 The Johansen Trace test

The Johansen test (Bivariate and multivariate) are based on vector auto regressive (VAR) model; a reduced form which avoids the problem of simultaneity (Asche et al, 1999; 2005). The Johansen trace test detects the number of co integration vectors that exists between two or more integrated series. The test follows the maximum likelihood estimation procedure that provides estimates of all co-integration vectors existing among a group of variables. The presence of co-integration among for instance pairs of price series shows the existence of integration among the series. A further test of residuals and test for variable exclusion confirms the existence of market integration between spatially differentiated markets. The Johansen bi-variate and multivariate tests (Johansen 1998; Johansen & Juselius 1992; Asche et al, 1999; Asche , 2005) has gained popularity; and is widely used for the test of the Law of one price (LOP) in agriculture and food markets and is preferred to the Engel–Granger procedure(Okoh & Egbon 2005; Asche et al, 2005)

2.6 Problems of Agricultural Processing Industry

There are peculiar problems associated with agricultural processing which make it different from other forms of businesses. Most raw materials are perishable and will quickly deteriorate if not processed immediately. Special and speedy transportation and processing facilities are required to maintain the quality of both the raw materials and the processed products (Fellows & Hampton, 1997). The cost of these facilities could be prohibitive for small- scale processors.

For crop and animal products, seasonality is a critical factor in the capacity utilization of processing machines and increases in unit cost of production (Brown, 1986). Seasonality of raw materials means that they can only be processed for part of the year, while the plants may be idle at some other periods. During the peak season, supplies waiting to be processed can even deteriorate, and high risk of plant breakdown due to intensive operations (Browm, 1986; Austin, 1992). Plants that can handle a variety of crops can be installed to reduce risk.

Technological incompatibility and technical incompetence have brought so much to bear on ago- processing industry. Most processing machines are operated by unskilled personnel, which reduce the efficiencies of these machines and consequent poor quality of the products. Traditions can simply not allow some technologies to flourish (Barau, 1979; Brown, 1986). In addition to operating frequently in economically hostile environment, majority of food processing enterprises are small-scale and within the informal sector hence have little economic powers. These include poor access to credit and infrastructure (Fellows and Hampton, 1997).

Brown (1986) outlined two types of labour related problems in the World Bank assisted agro-industries; (i) for public enterprises there is pressure to absorb excess labour, though economically beneficial, can inflate labour cost to the financial detriment of the enterprises; and (ii) low labour turn over. In the same study he observed that in their locations (rural areas), agricultural industries suffered from lack of access to rail system, water supply, electricity and facilities for waste disposal. Financial management and process management are closely related and in the World Bank lending to agro-industries have been serious problems; in which Brown (1986) and Austin (1992) suggested adequate financial planning that actually takes care of inventory management as it affects raw material supplies and liquidity management.

It was specifically observed by Brown (1986) that high level of optimism regarding the supply of raw material markets led to wide spread under capacity utilization in agro-industrial projects. Several agro- allied industries have collapsed due to irregular supplies and shortage of raw material. A typical case is that of Cadbury tomato processing plant located in Zaria that had to close down on the 25^th May, 1978 due to lack of raw material for processing(Orewa, 1978).

Crop processing is an activity traditionally undertaken by women (Clarke, 1987; Paris, 1988). The techniques are quite arduous, involving large investment of time for a little result. Two categories of women are involved. The farm women who process their own crops for family consumption, and the landless women or wives of marginal farmers who process other people’s crops as a means of supplementing family income (Clarke, 1987). Even then the development of modern processing and its wide spread had destroyed millions of part- time jobs for the poorest section of the society. Some 7 to 8 million women were estimated to have lost their jobs following mechanization of rice in Java. In Bangladesh, each new rice mill is said to put about 350 women out of part-time employment (Clarke, 1987; Austin, 1992).

2.7 Theoretical Framework

Theoretical perspective for this research is the value chain analysis or value addition concept. The value chain analysis is a concept based on the economic value of a product to the consumer. It is a business concept concerned with creating and sustaining superior performance. A product gains value as it passes through stages of activities in the value chain, as it moves from producer to the ultimate consumer. Michael Porter of Harvard University proposed the value chain as a tool for identifying ways to create more customer value. According to this model, every firm is a synthesis of activities performed to design, produce, market, and support its product (Kotler & Keller, 2006). The ultimate goal is maximization of value creation, which culminates into cost minimization and profit maximization.

Of course marketing involves satisfying consumers’ needs and wants; therefore the task of any business is to deliver customers’ value at a profit (Kotler & Keller, 2006). In that perspective, Kotler & Armstrong (2008) emphasized the following: (i ) creating values for customers to capture values from customers in return;(ii) building and managing strong value creating brands; (iii) managing returns from marketing to recapture value; (iv) harnessing new marketing technologies and; and (v) marketing in a socially responsible way around the globe.

In analyzing the value delivery (value chain) process, Kotler & Keller (2006) made two observations. Firstly, the traditional view of marketing in which the firm makes a product and sells it. In this view, marketing takes place in the second half of the process, that is, after the product had been made. Here, the company knew what to produce and the market would buy enough units for the firm to make profit. Market institutions or agencies that subscribe to this approach can best succeed in economies marked by goods shortages, where consumers are not fussy about quality, features, or style. Examples are the markets for basic staple goods in developing countries or evolving markets. Secondly, in developed economies, where people face abundant choices, the traditional views of the business process will not work. Here, the “mass market” is actually splintering into numerous micro-markets, each with its own wants, perceptions, preferences, and buying criteria. Therefore, the belief at the core of the new view of business process is proper definition of target markets. This places marketing at the beginning of planning. In the value delivery process, firms see themselves as part of the chain instead of emphasizing making and selling. Nimalya Kumar (2004) put forth ‘3Vs’ approach to value delivery in marketing; (i) define the value segment or customers; (ii) define the value proposition; and (iii) the value network that will deliver the promised service. Other similar views expressed by Webster (1997) are; (i) value defining process, e g market research and company self-analysis; (ii) value developing process, example new product development, sourcing strategy and vendor selection; and (iii) value delivery process such as advertising and managing distribution.

The value chain as proposed by Michael Porter (1985) is shown in figure 2.2. In this model, the value chain identifies nine strategically relevant activities that create value and cost in a specific business. These value creating activities consist of five primary activities and four supportive activities (Kotler & Keller, 2006). The primary activities cover the sequence of bringing materials into the business(in-bound logistics), converting them into products(operations), shipping out final products (out-bound logistics), marketing them(marketing and sales), and servicing them(service); while the supportive activities include procurement, technology development, human resources management, and firm infrastructure. These are handled by specialized departments or elsewhere. Note the firm’s infrastructure covers general management such as planning, finance, accounting, legal, and government affairs.


Firm infrastructure




Human resources management

Margin



Technology development

Procurement

Inbound logistics

Operations

Marketing & Sales

Services

Outbound logistics

Margin

Figure 2.2: The generic value chain of Michael E Porter adapted from Kotler & Keller (2006)

2.7.1 Value chain in agricultural processing and marketing

Value chain optimization can be an efficient tool in the development of food processing and marketing (Hagelaar, 1994). The improvement of each step in the food marketing chain needs to be analyzed and monitored in relation to other links in the chain. This calls for good cooperation between the different actors in the chain. An important aspect of chain optimization is chain marketing, defined as cooperation in marketing through the whole chain. The management of improvement in the value delivery network is called chain management (Bruinsma, 1999). This will develop as agricultural production becomes more market driven than production driven. A flow chart of a typical agricultural value chain is shown in figure 2.3.

In an analysis of development in food chain in Europe, Bruinsma (1999) in quoting Zuurbiov (1981) noted some reasons for greater emphasis on cooperation with other actors in the food marketing chain most of which are applicable in Africa. They include: (a) reduction of transaction and coordination costs through better organization; (b) greater access to information about new technologies as well as the technologies themselves; (c) reduction in uncertainty about actions that other individuals or groups in the chain may take; (d) possible increased competitiveness; and (e) reduction in logistical problems regarding the handling of perishables which otherwise may lead to loss of product quality. Another concept that is of great importance to the optimization of the food marketing chain is quality assurance. Instituting quality assurance measures at all stages (production, processing and trade) of the marketing chain will ensure that the marketed product is demanded by consumers and is also safe for consumption.

Critical factors or approaches that underline the understanding of value delivery network and eventual successful operation of agro-processing enterprises as set out by Brown (1986), Austin (1992); Brown, Deloitte, and Touche (1994) include; (i) raw material supply and procurement, (ii) processing component, and (iii) marketing. Although this is the operational order of the material flow in the production chain, the marketing factor is the logical starting point, because it will make no economic sense to invest in processing a product that there is no demand for it.

Figure 2.3: Flow chart of Agro-processing value chain

Source: Adapted from Austin (1992)

2.8 Analytical Framework

The analytical framework for this research is based on the optimization of value chain from Groundnut processing through products marketing. Production efficiency and profitability analysis models of the firms in groundnut oil processing and product marketing, market co-integration analysis and the law of one price (LOP) as a measure of market efficiency were also adopted. Hypotheses were tested appropriately as required.

2.8.1 Stochastic frontier production function

This was used to evaluate the production efficiency of groundnut oil and groundnut cake together. Production has been defined by Olayide & Heady (1982) as a process whereby some goods and services referred to as inputs are transformed into other goods and services called output. In agricultural processing this changing of input form into output involves changing of farm produce into another form desired by consumers or manufacturers (Austin, 1992; Olukosi & Isitor, 1990). Brown et al (1994) observed this activity adds more value to the raw farm produce. The technical efficiency involved in changing the input into output as well as factors that determine the inefficiency were analysed using the stochastic frontier production function.

The stochastic frontier analysis (SFA) is based on the premise which represents an improvement over the traditional production function and deterministic functions using mathematical programming to construct production frontiers. It recognizes the possibility that a firm’s performance may be affected by factors completely outside its control, such as bad weather and input supply breakdowns as well as factors under its control. To lump the effects of exogenous shocks, both favourable and unfavourable to the firm together with the effects of measurement errors and efficiency into a single one- sided error term is incorrect, as is the case with deterministic frontiers. Again, in the statistical noise that every econometric empirical relationship carries, the standard interpretation is that, first, there may be measurement errors on dependent variables; secondly, the equation may not be completely specified due to omitted variables. This argument holds for production functions as it is for any other equations assuming a one - sided noise. The essential idea in stochastic frontier model as put forward by Aigner, Lovell & Schmit (1977) and Meuesen & van den Brook (1977) is that the error term is composed of two parts, the effects of measurement error, other statistical noise, and random shocks outside the firm’s control. The original specification which involved a production function for cross-sectional data had an error term with two components, one to account for random effects and another to account for technical inefficiency. Several specifications of the frontier production function have been developed by Battese & Coelli (1992, 1995). For this research the model is given as,

Yi = X_i β+ (v_i-u_i) …………………. 2.15

i =1, ……, N

Where,

Y_i = the production (or logarithm of production) of the ith firm;

X_i = kx1 vector of (transformation of the) input quantities of the ith firm;

β = vector of unknown parameters;

V_i = random variables which are assumed to be iidN (0, σ v²) and independent of the

U_i which are non-negative random variables that are assumed to account for technical inefficiency in production and are said to be iid, │N (0, σv²)│.

Equation (1) above can also be approximated in a translog form (Karagiannis & Sarris 2005; Amefula et al, 2009) as follows

Y_it = β₀ + βγ_t +1/2βγγt² +∑β_jx_jit + 1/2∑∑β_jkx_kit +∑β_jtx_jitt +e_it …………………….. 2.16

Where Y_it is the logarithm of the observed output by the ith firm at period t, x_jit is the logarithm of the quantity of the jth input used by the firm at period t, β is a vector of parameters to be estimated. Symmetrically imposed, β_ij = β_kj and e_it = v_it- u_it being a composite error term. The v_it term corresponds to white noise and represents those factors that cannot be controlled by processors, such as weather conditions, labour market conflicts, access to credit as well as measurement error and omitted explanatory variables. On the other hand U_it term is a non negative random variable associated with technical inefficiency. The v_it and the u_it are assumed to be independently distributed from each other. The technical inefficiency effects u_it, can be replaced with a linear function of explanatory variables (Battese & coelli, 1995). The technical inefficiency effects are assumed to be independent and non negative truncations (at zero) of normal distribution with unknown mean and variance. Specifically,

U_it = δ₀ + ∑δ_mz_mi + w_{it……………………} 2.17

Where z_mi a column vector of hypothesized explanatory variables associated with technical inefficiency; δ₀ and δ_m (m=1...h) are parameters to be estimated, and u_it is independently and identically distributed with N (0, σ_u²) random variable truncated at – (δ₀ + ∑δ_mz_mi) from below. Equation (3), an average level technical efficiency measured by mode of truncated normal distribution (i. e, U_it) has been assumed to be function of socio-economic factors (Kumbhakar & Heshmati, 1995; Yau and Liu, 1998; Ogundele & Okoruwa, 2006). If u_it does not exist or u_it =0, the stochastic frontier production function reduces to the traditional production function of Cobb-Douglas. The distributional parameters U_it and δu² are hence inefficiency indicators of the processor, indicating the level of technical inefficiency and later dispersion of inefficiency level across observable units (Battese & Coelli, 1995; Bamire, Oluwasola & Adesanya, 2007). Together, equations (2) and (3) can be estimated by means of the computer programme FRONTIER version 4.1c developed to obtain the maximum likelihood estimates of the Frontier production model detailed in Battese & Coelli (1988,1992, 1995) and Coelli (1996), Battese, Coelli & Colby (1989) which are special cases of Coelli(1992). The programme can accommodate panel data, time-varying and invariant efficiencies; cost and production functions; half normal and truncated normal distribution; and functional forms which have a dependant variable in logged or original units.

Hypotheses can be tested using the generalized likelihood ratio test statistic λ = - 2{lnL (H₀) – lnL(H₁), where L(H₀) and L(H1) are values of the likelihood function under the null H₀ and the alternative H₁ hypotheses respectively. If γ= δ₀ = δ_m (m=1 …….h), then inefficiency effects are not present and consequently each firm in the sample operates on the frontier. It should be noted that γ=0 if there is no difference between the null and alternative hypotheses, and if not the likelihood function (LF) will diverge. Asymptotically the λ follows the χ² (mixed χ²) distribution hence the statistical significance can be tested at a chosen α with degree of freedom equal number of restrictions.

Coelli (1996) also observed that this model has been used in a vast number of applications over two decades. That the original version has been altered and extended in many ways which include more general specification of distributional assumptions for the non-negative random variables which account for technical inefficiency; consideration of panel data and time varying technical efficiency, and the extension of the method to cost functions and estimation of systems of equations among many. A comprehensive review of literature on the model can be found in Forsund, Lovell & Schmit(1980), Baur(1990) and Greene(1993).

2.8.2 Profitability analysis

The profit function was employed to estimate the profitability of resource input in groundnut processing enterprise. These inputs include variable (groundnut, firewood, water, salt, grinding) and fixed input (frying equipment, pressing equipment, kneading surface) and labour. The profit function was used because of its importance in diagnostic analysis reflecting marginal resource profitability at mean level on input price.

Following Sankhayan (1981), Olayide & Heady (1982) and Arene (2002), the linear profit function analytical model is stated thus: Given a production function in which m variable inputs, x₁, x₂ ….x_m; Z₁, Z₂ …Z_n, are related to Y as follows,

Y= f(x₁, x₂, x_m; Z₁, Z₂…Z_n) ………………………….. 2.18

In the short run, the opportunity cost of fixed inputs is zero. Therefore the processor needs only to maximize the returns to variable inputs, that is, the sales value of output less the cost of variable inputs, called the variable cost. The resulting returns also called the variable profit (π), the variable inputs in respect to the production function given in (2.18) above can be written as: π = Py f(x₁, x₂… x_m; Z₁, Z₂….Z_n) - ∑ P_ix_i ………….. 2.19

Where Py is the price of output and Pi is the output per unit price of the ith variable inputs, i = 1, 2…m.

For profit maximization of π in the short run, the first order partial derivative with respect to the variable inputs equated to zero are each taken (Olayide & Heady, 1982). Hence the partial derivative from (2.19) with respect to X_i, i=1, 2 …., m, equated to zero is given by

δy/δx₁ = P_y f_i = p_i ……….. 2.20,

where f_i denotes the first order partial derivative with respect to the ith input. Since from (2.18), f(x₁, x₂… x_m; z₁, z₂ …Zn) is equal to Y, (2.20) can also be written as

pyδy/δx₁ = pi or δy/δx₁ = p_i/p_y, i=1, 2 ….m …………… 2.21.

There will thus be m simultaneous equations in m unknowns, which can be solved to obtain the optimum input quantities X*_i, I = 1, 2 ….m, given by

X_i*= X_i*(py,p₁, p₂, ….pm,z₁ ,z₂, ….z_n), i = 1, 2,……m ……….2.22

Equation (5) gives the demand function for the ith variable input.

Substituting the demand functions given by (2.22) and (2.20), what is obtained is given as

π* = P f(x_i*x₂*,…x*_m; z₁,z₂,…...,z_n) - ∑p_ix_i* …………..2.23,

Where x_i* (i=1, 2….m) is the optimum quantity of the ith variable input and π* corresponds to the amount of maximum variable profits or gross margin (GM). Obviously however, π* with a harsh in (2.23) is expressed as a function of the price of inputs and the fixed inputs quantities. Given that the alternative use of fixed input is zero in the short run, that is profit horizon, the interest is on the analysis of variable input to be used in groundnut oil processing. Thus

π* = π*(p_y, p₁, p₂… p_m; z₁, z_2, …….,z_n) …………….2.24.

2.8.3 Measurement of co-integration and the law of one price (LOP)

The law of one price (LOP) captures the existence of equilibrium due to efficient commodity arbitrage between two or more trading markets. It assumes that if markets are integrated, price change in one market will be transmitted on a one-for-one basis to other markets instantaneously (Chirwa, 2000).

This can be written as

P_tⁱ = α +βP_t^j …………………… 2.25

Where,

P_t^j and P_t^j are the natural logarithm of prices of homogeneous goods in markets i and j respectively. In empirical work, evidence of how price change in one market generate price changes in another market so as to bring about long run equilibrium relationship (Asche et al 2005), can be written as

P_t ¹ – β₀- B₁ P_t² = e_t ……………………… 2.26

where,

P_t is the logarithm of the price observed in market i at time t, β₀ is a constant term that captures transportation, or transaction cost and other quality differences, and β₁ gives the relationship between the processes. If β = 0 there is no relationship between the two price series, if β₁ =1, the LOP holds and the relative price is constant. If β₁ is different from 0 but not equal to 1, there is relationship between the prices, the relative price is not constant and the markets are not fully integrated. If P_t¹ and P_t² are co-integrated, the error term, e_t, will be stationary. This forms the basis of Engle and Granger test for co-integration and the unit root test by performing the Augmented Dickey-Fuller (ADF) unit root test (Asche et al, 2005). Due to the weakness inherent in the Engle–Granger procedure, it is replaced by the more powerful Johansen trace test in the analysis of co-integrated markets (Chirwa, 2000; Okoh & Egbon, 2005; Gujarathi, 2007).

2.8.3.1The unit root problem

Random walk process may have no drift, may have drift or may have both deterministic and stochastic trends. For these reasons, the actual procedure of ADF test for unit root on the price series will require estimation of the three models for the three possibilities (Gujarathi, 2007; Ali & Rahaman, 2009). These are:

the random walk (RMW) without drift,

∆Y_t = δy_t-1 + α_t∑∆Y_t-1 + e………………… 2.27;

the random walk with drift,

∆Y_t = β₁+ δY_t-1 + α₁∑∆Y_t-1 +e ………… 2.28; and

the random walk with drift around a deterministic trend,

∆Y_t = β_t + β_2t + δY_t-1 + α∑∆Y_t-1 + e ………… 2.29;

where,

Y_t = price series in market Y during period t,

∆Yt = first difference of series Y, ie Y_t-Y_t-1,

t = trend variable (1, 2, 3… n) n being the length of data series in years; m = no of lagged difference; and

e = Error.

Β₁, β₂, δ, α = parameters to be estimated.

2.8.3.2 Unit root test

Unit root test is a test of stationarity (non stationarity) required to avoid spurious regression. Given that equation (2.29)

Yt = ρY_{t- 1} + U_t …….. 2.30 -1 ≤ ρ ≤ 1

Where Ut is a white noise error term; recall that if ρ= 1, a case of unit root, equation (2.30) an RWM is I (1). We regress Y_t on its lagged value Y_t-1 and see if estimated ρ is statistically equal to 1. If so, then Y_t is non-stationary. If we subtract Y_t-1 from both sides of equation (2.30), we obtain

Y_t – Y_t–1 = ρY_t-1- Y_t-1 + U_t …………….. 2.31

= (ρ-1) Y_t-1 + U_t

Which can be written alternatively as

∆Y_t = δY_t-1 + U_t ……………… (2.32)

Where δ = (ρ-1) and ∆ is the first difference operator. In practice equation (2.32) is estimated to test the (null) hypothesis that δ = 0. If δ = 0 then ρ = 1, hence we have a unit root which means the time series under consideration is non-stationary. If negative, it is stationary. Note also that if δ = 0, equation (2.32) becomes

∆Y_t = (Y_t-Y_t-1) = U_t ……………………. 2.33.

Here U_t is white noise error term and stationary, which implies that the first difference of a RWM time series is stationary.

Testing the null hypothesis of non stationary against the alternative of stationary, the Augmented Dickey - Fuller (ADF) and Phillips Perron (PP) tests are applied. The ADF is a parametric tests, whereas the PP test statistics uses a non parametric modification of the Dickey – Fuller test. Under the null hypothesis that δ = 0 (ie ρ = 1), the t-value of the estimated coefficient of y_t-1 does not follow the t-distribution even in large samples, that is it does not have asymptotic normal distribution. The Dickey- Fuller statistic has shown under the null hypothesis that δ = 0 and the estimated coefficient of y_t-1 in equation (2.33) follows the τ (tau) statistic. If the hypothesis δ = 0 is rejected, the series is stationary. The Augmented Dickey- Fuller (ADF) is based on statistics obtained from applying the OLS method to the following equation (Gujarathi, 2007; Ali & Rahaman 2009)

P_t = μ + β_t + ΦP_t-1 + ∑d∆P_t-1 + ε_t ………………… 2.34

Where P_t = price series, t = time trend; ∆P_t-1 = P_t-1- P_t-1+1; ε_t ̴ iid(0, σ²)

To determine whether P_t is non- stationary, the unit root test statistic is calculated and tested as above.

In addition, the Dickey-Fuller (DF) test assumption is the error terms, U_t, being white noise. The ADF adjusts it to take care of possible serial correlation in the error terms by adding the lagged difference terms of the regressand. Phillips and Perron (Gujarathi, 2007) used non-parametric statistical methods to take care of the serial correlation in the error term without adding lagged difference terms. Asymptotically, the Phillips – Perron test is the same as ADF test statistic.

2.8.3.3 Co-integration: The Johansen test

The multivariate Johansen model can be expressed as follows. Let X_t denote an nx1 vector, where the maintained hypothesis is that X_t follows an unrestricted vector auto regression (VAR) in the levels of the variables (Asche et al, 2005).

X_t = П₁X_t-1 + …..+ П_kX_t-k + ФDt + μ +ε_t ……….. 2.35

where each П_t is an nxn matrix of parameters, μ a constant term, and ε_t ̴ iid (0,σ²) matrix Ω. In (ECM) or difference equation (10) can be written as

∆X_t = Ґ_t ∆X_t-1 + …….. + Ґ_k-1 ∆X_t-1+1 +ПX_t-k + ψDX_t + ε_t ………… 2.36

With Ґ_i = -1 +П₁ + ……. + П_i, i =1 ……k-1

П_i = -1 + П₁ + …..+ Пk. Hence Π is the long run “level” solution to equation (2.35).

Given that X_t is a vector I(1) variables, the left hand side and the first (k-1) elements of equation (2.36) are I(0), and the kth element of equation (2.36) is linear combination of I(1) variables. If the assumptions on error term holds, the kth element must also be I (0); П_t-k ̴ I(0). Thus either X_t contains a number of co-integration vectors, or П be matrix of zeros.

A 2 variable system model of the Johansen VAR procedure (Chirwa, 2000) is given as ECM

∆X_t = μ + ∑Ґ∆t-1 + ПX_t-1 + ε ………………. 2.37

Where X_t is nx1 vector containing the series of interest (spatial prices); Ґ and П are the matrices of parameters, k is asymptotic to capture the short run dynamics of the underlying VAR and to produce normally distributed white noise residuals, and ε_t is the vector of the white noise error.

Given that rank (П) = r; П, r, indicates the number of linear combinations of X_t that are stationary. If r = n, the variables in levels are stationary; if r = 0 so that П = 0, none of the linear combinations are stationary. When 0

The Johansen procedures involves two tests for the number of co-integration vectors in the system, that is whether the П matrices in equation (2.35) has less than full rank using the maximal eigenvalue (2.36) and the trace test (2.37). These are given (Hjalmarsson &Osterholm, 2007) as

J_max = - Tln (1- λ_r+1) …………………………. 2.38

J_trace = -T∑ⁿ_i-r+1 ln (1-λ_i)…………………………. 2.39

T is sample size, and λ is the i:th largest canonical correlation (largest eigenvalue). The trace test tests the null hypothesis of r co-integrating vectors against the alternative hypothesis of n co-integrating vectors. The maximum eigenvalues test on the other hand tests the null hypothesis of r co-integrating vectors against the alternative hypothesis of r + 1 co-integrating vectors

A wide range of hypothesis testing on the coefficients α and β, is allowed by the Johansen procedure, using the likelihood ratio test (Johansen and Juselius 1990). If the LOP hypothesis is of interest, it is the restrictions on the parameters in the co-integration vector β that is to be tested. Where there are two price series in X_t vector, and provided that these series co-integrate, the rank of П = αβʹ is equal to 1 and α and β are 2x1 vectors. A test of LOP is actually a test of whether βʹ = (1,-1)ʹ. If a group of goods are to be in the same market, all prices must be pair –wise co-integrated. This allows a multivariate test of LOP, since it implies only one common stochastic trend in the system, and therefore with n prices in the system, there must be n-1 co-integration vectors (Asche et al, 1999; Gonzalez- Rivera & Helfand 2001; Asche at al, 2005). Generally, in a system with n data series and r co-integration vectors, there will be n-1 different stochastic trends.

2.8.3.4 Determinants of co-integration

Market integration is consequent of activities of participants and the operating environment defined by government policies, and infrastructural development among others. The cost of carrying out marketing functions of transportation, processing and storage as well as profit margin, of traders is central to the concept of spatial arbitrage. Several factors influencing the extent of market integration have been identified in literature to include market infrastructure, production differentials and shocks, and the policy environment (Golletti et al, 1995, Felchamps & Gavien 1996; Chirwa, 2000; Kindie, Verbeke & Viaene, 2005; Asche, Gutternsen, Sebulonsen and Sissener, 2005; Ali & Rahaman, 2009).

CHAPTER THREE
METHODOLOGY
3.1 Study Area
The location for this research is the geo-political area described as North Central Nigeria. North Central Nigeria politically comprises Benue, Kogi, Kwara, Nasarawa, Niger, Plateau States and the Federal Capital Territory (FCT). This area is located between longitudes 4^o35’E and 9^o4’E and latitudes 7^o 09’ N and 9^o53’N (Phillips, 1996). This area lies within the guinea savanna zone of Nigeria. The vegetation is characteristic of the tropical, deciduous forests that existed centuries ago, with interspersion of thicket, grassland, fringing forests and woodland or gallery forest along the river valleys (Iloeje, 1985). Some areas in some of the seven states such as Kogi, Benue and Kwara fall within the tropical rain forest zone of Nigeria.

The north central Nigeria (NCN) has an estimated population of 21, 682, 776 people as estimated by 2006 population census, with land area of 242, 425 km². The selected states of Nasarawa, Benue and Niger have a combined population of 11, 121, 989 people with a land mass of 137, 536km² (Wikipedia, 2013). The major regional markets include Gboko, Makurdi, Otukpo and Zaki Biam in Benue State; Lafia. Keffi, Nasarawa Eggon and Mararaba in Nasarawa state; Suleija, Bida, Minna and Kontagora markets in Niger State; Lokoja, Okenne and Anyangba in Kogi State; Jos and Shendam markets in Plateau State; Offa and Ilorin in Kwara State; and Wuse and Gwagwalada markets in the Federal Capital Territory (FCT). These markets are noted for trade in agricultural commodities. The zone links the north and the southern parts of the country. Major roads and railway lines pass through these states from north to southern Nigeria. The two rivers, Niger and Benue and their tributaries run through the zone and provide potentials for in-land water ways and ports for trading activities.

The North Central States are known for the production of crops including yam, rice, groundnut, cassava, beans, maize, citrus, cashew, cocoa and variety of other fruits. These crops form the basis of trade within the region and with other parts of the country. Livestock production is also vibrant here (Agboola, 1979; Iloeje, 1985; Olam, 2006). Groundnut processing and processed products marketing are very vibrant business activity involving men, women and youths; both in traditional and modern processing in this area. Generally small-scale industries, especially agro-based provide impetus for economic growth and development of the area.

3.2 Sampling Technique

The population for this study comprised traditional and modern groundnut oil processors in North Central Nigeria. Four groundnut producing states (Nasarawa, Plateau, Benue and Niger) and the FCT were identified as reported by RMRDC (2004). Three groundnut producing states were randomly selected for the study. The LGAs were purposively selected based on groundnut processing and marketing activities, while the respondents were taken randomly. The formula applied is as given below

SS = SP / ZP x TS

Where,

SS = state sample size selected,

SP = state total sampling frame, and

ZP = zonal total sampling frame (selected states).

TS = Total sample size.

Sampling from the two producing LGAs of each state, given as

LS = LT/ST x TL,

Where

LS = LGA sample size selected,

LT = total LGA sampling frame,

ST =state total sampling frame (selected LGAs), and

TL = total sample size.

The samples were randomly and proportionally taken based on the estimated population of traditional processors in the selected LGAs of the States. The estimated populations (sampling frame) of processors were Nasarawa State 350; Benue State, 225; and Niger State, 300; obtained from Agricultural Development Programmes (ADPs), Ministry of Commerce and Industries and groundnut oil (GNO) processors in the states. The distribution of the proportionately selected samples for the states was Nasarawa state 70; Benue State 45 state; Niger State 60; and the total sample for North Central Nigeria was 175, (Table 3.1). The active population of modern processors in the selected states within the zone was 17 and all were taken for the study.

Table 3.1: Population and sample selection for the study

State	Population	Sample	LGA	LGA Sample
Nasarawa	350	70	Lafia	30
			N/Eggon	40
Niger	300	60	Bida	36
			Chachaga(Minna)	24
Benue	225	45	Gboko	20
			Makurdi	25
Total	875	175		175

3.3 Data Collection

Primary data were used for this study. These were collected through survey by means of structured and pre-tested questionnaires. Personal interview was used to administer the questionnaires. Observations were employed for on the spot assessment of processing and marketing activities at various processing sites and markets where possible (Alamu & Olukosi, 2008). Price data chart was used to collect price data.

Socio-economic characteristics such as age, sex, experience, cooperatives participation, and educational attainment were covered. Data on procurement of groundnut for processing, processes involved in processing of the groundnut into oil and cake and costs involved at each stage were obtained as well as other inputs used, their respective quantities and prices. Quantities and values of oil and cake sold by processors were also collected. Processing cost and other charges involved also obtained from the respondents, and many others. Data collection took place between December 2010 and November 2011. Weekly price data on market prices of groundnut oil (GNO) and groundnut cake (GNC) were collected for 52 weeks from December 2010 t0 May 2011 in six strategic markets. These were Lafia, Nasarawa –Eggon in Narawa state; Minna (Chachaga) and Bida in Niger state, Makurdi in Benue State and Wuse in the Federal Capital Territory (FCT).

3.4 Data Analysis

Data were analyzed by means of descriptive and inferential statistics. Descriptive statistics was used to achieve objectives 1, and 6. Objective 2 was attained with stochastic frontier analysis. Gross margin and profit function were used to achieve objective 3 and t-test was used to achieve objective 4. Objective 5 was realized with the Johansen test for co-integration analysis.

3.4.1. Stochastic frontier model

The Stochastic frontier production function was used to evaluate the processing efficiency involved in traditional and modern groundnut oil processing. This enabled the attainment of objective two of the study. The model for traditional processing is specified as follows:

LnY =β₀+ β₁lnX₁ + β₂lnX₂+ β₃lnX₃ +β₄lnX₄ + (v_ij – U_ij)………….. 3.1

Where,

Y = output of processors (GNO +GNC) (kg)

X₁ = Raw groundnut seeds (kg)

X₂ = Labour (hours)

X₃ =Fuel-wood (N)

X₄ =salt (kg)

Vij = random effect which are assumed to be iid N (0, σ)

U_ij = technical inefficiency effect, which is assumed to be independent of V_ij. If U_ij=0, then there is no technical inefficiency occurring, therefore the production lies on the stochastic frontier. IF U_ij >0, then the production lies below the frontier and is inefficient.

The absolute value of U_ij is expressed as follows:

U_ij=δ₀ +δ₁Z₁ +δ₂Z₂ +δ₃Z₃ +δ₄Z₄ + δ₅Z₅₊ δ₆Z₆₊ δ₇Z_{7 …………….}3.2

where,

U_ij= technical inefficiency or characteristics related to inefficiency;

Z₁ =age of processors in years

Z₂ = level of education (years of formal education)

Z₃ = years of experience in GNO processing;

Z ₄ = gender (1 male, 0 female);

Z₅ = household size (actual number of members);

Z₆ = marital status (1 married, 0 otherwise)

Z₇ = Cooperative participation (1menber, 0 otherwise)

The model used to evaluate the efficiency in modern processing is presented below.

LnY =β₀+ β₁lnX₁ + β₂lnX₂+ β₃lnX₃ +β₄lnX₄ + (v_ij – U_ij)………….. 3.3

Where,

Y = output of processors (GNO +GNC) (kg)

X₁ = Raw groundnut seeds (kg)

X₂ = Labour (hours)

X₃ =Maintenance of equipment/machines (N)

X₄ = Price of raw groundnut (N)

The inefficiency model was given as follows:

U_ij=δ₀ +δ₁Z₁ +δ₂Z₂ +δ₃Z_{3 …………………….}3.4

where,

U_ij= technical inefficiency or characteristics related to inefficiency;

Z₁ = level of education (years of formal education)

Z₂ = years of experience in GNO processing;

Z ₃ = gender (1 male, 0 female);

The maximum likelihood estimation of the βs and δs coefficients above was done simultaneously using the Frontier 4.1c computer programme by Coelli (1996). Hypotheses were tested using the generalized likelihood ratio test statistic λ = - 2{lnL (H₀) – lnL(H₁), where L(H₀) and L(H1) are values of the likelihood function under the null (H_0:) and the alternative (H_1:) hypotheses respectively. If γ= δ₀ = δ_m (m=1 …….h), then inefficiency effects are not present and consequently each firm in the sample operates on the frontier. It should be noted that γ=0 if there is no difference between the null and alternative hypotheses, and if not the likelihood function (LF) will diverge. Asymptotically the λ follows the χ² (mixed χ²) distribution hence the statistical significance can be tested at a chosen α with degree of freedom equal number of restrictions.

3.4.2 Profit Function Analysis

As a prelude to the estimation of the profit function, gross profit margin was adopted to estimate the average costs and returns per week to the processors who processed groundnut oil for the achievement of part of objective three. The model is given as;

GM = TR – TVC ………….. .. 3.5

Where,

GM= Gross margin (in Naira); TR = Total Revenue (in Naira); TVC = Total Variable Cost (in Naira).

The generalized profit function model is expressed thus:

π* =π*(p_y1p_y2, p₁, p_2,p₃;z₁,z₂) ……………….3.6

Where;

π* = amount of maximum variable profits (GM) from sales of GNO and GNC per week

p_y = price of output GNO and GNC (N)

p₁= per unit price of groundnut (N)

p₂= per unit price of labour (N/man hour)

p₃=per unit price of fuel wood (N)

p₄=per unit price of packaging (N)

p₅= per unit price of transportation cost (N)

P₆ = per unit price of salt (N)

Zs are fixed cost items and so were not anaysed because the analysis is based on the short run effects of input costs, Arene (2002). The result of the regression analysis was evaluated on the basis of the coefficient of multiple determination (R²), t-values and the F-values for the respective states studied.

3.4.3 Value addition model

Value addition is the difference in value of agricultural product before and after processing (Gitinger 1972; Brown, 1986). Brown et al, (1994) explained further that the difference between the cost of ingredients and the ex-factory or post processing price of the finished product is the value added through processing. This could be gross value added or net value added. It was applied to achieve part of objective 4.

In this study the gross value added was determined as follows:

Va = Vp – Vb ……………….. 3.7

Where

Va = Value added to raw groundnut after processing (N/tonne)

Vp = value of processed groundnut products (GNO and GNC) from one tonne of groundnut (N)

Vb = value of unprocessed groundnut per tonne (N)

This can also be presented in percentage as follows

Va% = Vp – Vb/Vp x100 …………………. 3.8

A test of significance was done to verify the null hypothesis (H₀: X̄₁ = X̄₂), given as

t = X̄₁ – X̄₂/√σ²₁ +σ²₂/N₁ +N₂ -2 …………………. 3.9

Where

t = test statistic

X̄₁ = mean value of groundnut before processing

X̄₂ = mean value of processed groundnut products (GNO&GNC).

σ¹ = variance of value of groundnut before processing

σ²= variance of Value of groundnut products (GNO&GNC)

N₁ and N₂ are equal sample sizes

When the value of input used in processing is subtracted from va in equation (3.7) above, we obtain net value added. This principle can be applied at any point in the value chain to determine value added at that point.

3.4.3 Johansen trace test (a measure of market integration)

This is based on the maximum likelihood estimation of the error correction model. This is for the attainment of part of objective 5 of the study, (Chirwa, 2000; Asche et al, 2005). The model underlining the co-integrating VAR option is given by the VECM thus:

∆X_t = a_0t + αβX_t-1 + ∑Г_i∆X_t-1 + U_t ………………….. 3.10

Where,

X_t = wholesale (processors) prices in market i) with respect to GNO, GNC per week;

m_t x1 vector of jointly determined I (0) variable.

a_0t = intercepts, an m_t x1 vector

αβ = the long run multiplier matrix of order mx1(ECM)

Г_i = mx1 (n=number of lagged difference of X_t) coefficients of lagged X_t variables

∆ = change operator

U_t = error term

The ECM model estimation was preceded by Augmented Dickey-Fuller (ADF) unit root test, to test the non-stationarity of the series or otherwise.

The Johansen trace statistic for testing the null hypothesis of r co-integration relationships was given as LR_trace(r/k) = -T∑_r+i log (1-λ_i), where λ is the largest eigenvalue of the П matrix, and T is the sample size.

3.4.4 Determinants of market integration

An empirical model for analysing the determinants of market integration for the attainment of part of objective 5 in this study is expressed as follows:

Y_ij = a_o + β₁x₁ + β₂X₂ + β₃X₃ +β₄X₄ + ε …………………. 3.11

Where

Y_ij = the Johansen bi-variate trace statistics for paired markets as a measure of market integration for GNO and GNC

X₁ = the shortest distance between market i and market j (km) proxy for transport cost,

X₂ = the number of telephones owned by processors in markets i and j,

X₃ = average no of groundnut processing facilities in markets i and j,

X₄ = membership of groundnut processing associations in districts of markets i and j,

X₅ = administrative regulations on groundnut oil (dummy) in markets i and j, and

ε = error term.