Exploratory Model of the Impact of Agriculture on Nigerian Economy

This paper explored four models in determining the impact of four agricultural sub-sectors of on the Nigerian GDP. The data is on the contribution of four different sub-sectors of agriculture on Nigerian Economy and was obtained from Central Bank of Nigeria statistical bulletin. The findings revealed that ridge regression and PCR are good regression estimation methods for predicting GDP. From the models there is strong indication that fish production in Nigeria is too insufficient to sustain her ever increasing population and improve her economy. Also, the ever increasing demand for fish by Nigerians due to high cost of meat in the market is clearly shown in the models and this stands to say that a lot need to be done to improve fish production in Nigeria to ensure sustainable growth and development. KEYWORD : Gross Domestic Product (GDP), Agriculture, Economy, Crop production, Livestock production, Fishery, Forestry, Multicollinearity, Ridge regression, PCR, Adjusted R-squared, Standard error of the estimate


Introduction
Agriculture is the process of producing food, feed, fiber, fuel, medicinal plants and other goods by cultivation and breeding of plants and animals. One of the critical sectors that deserve attention in any country's economy, especially the developing countries such as Nigeria, is agricultural sector. Agriculture in Nigeria is a branch of the economy in Nigeria that provides employment for about 30% of the population as of 2010 (Wikipedia).
Nigeria's agricultural development policy over the years has been formed by the belief that the development of agriculture is a sine-qua-non for the overall growth and development of the economy. Agricultural development efforts have been to enhance and sustain the capacity of the sector in order to ensure growth with emphasis on the attainment of a sustainable level in the production of basic food commodities, especially those in which the country has comparative advantage. It also involve developing the capacity to increase the production of agricultural raw material to meet the growing needs of an expanding industrial sector, as well as the production and processing of the exportable cash crop to boost the nation's non-oil foreign exchange capacity. Agricultural sector is seen as an engine that contributes to the growth of the overall economy of Nigeria. Despite this, the sector is still characterized with low input, limited areas under cultivation, poor agricultural machinery, and low input, which are caused by government overdependence on monocultural economy based on oil sector.
Many researchers have statistically analyzed the contribution of agricultural sector on economic growth of Nigeria. Sertoglu et al (2017) empirically examines the impact of agricultural sector on the economic growth of Nigeria, using time series from 1981to 2013 and discovered that Real Gross Domestic Product (RGDP), agricultural output and oil rents have a long-run equilibrium relationship. They recommended that Government and policy makers should embark on diversification and enhance more allocation in terms of budgeting to the agricultural sector. Izuchukwu (2011) analyzed the contribution of agricultural sector on the Nigerian economic development using panel data sources from the statistical bulletin of the Central Bank of Nigeria and World Bank's development indicators and discovered a positive relationship between Gross Domestic Product vis-a-vis domestic saving, government expenditure on agricultural and foreign direct investment between the period of 1966-2007. This paper aimed at determining the impact of crops, livestock, fisheries, and forestry sub-sectors on the economic growth and development of Nigeria.

Agriculture and Nigerian Economy
Noko (2017) stated that agriculture is estimated to be the largest contributor to the non-oil foreign exchange. According to him a strong agricultural sector is essential to economy development both in its own rights and to simulate and support the growth of  In 1990, policy measures were initialized and strategies designed to propel agricultural development targeting the year 2010. Emphasis was on food, livestock, the fisheries and the forestry.
Food crops constitute the largest component of crops sub-sector of Nigeria's agricultural sector. They are categorized broadly into cereals, roots, tubers, plantain, oil seeds and nuts, pulses, vegetables and fruits, sugar and beverages.
For the purpose of planning of self-sufficiency in livestock production, output in the sector has been categorized into short and long term. Livestock whose sufficiency level could be conveniently attained within five years such as beef, poultry products, goat meat, mutton, and pork were classified as short term while those that would at least in 15years be sufficient were categorized as long term.
Forestry concern is on the preservation and maintenance of economic trees and plants. It also involves the eradication of various forms of resources associated with forest. Agriculturists derived a lot from such plants preserved and they include: timber for plywood, furniture, houses and boats, manufacturing of papers, electric poles etc.
Fishing sub-sector involves breeding and catching fishes from the rivers for human consumption. Fishing constitutes major occupation of river line people. Fish constitute main sources of protein. Ezeokoli (2011) 3

. Data and its Presentation
The data used for this work is mainly secondary data, sourced from the Central Bank of Nigeria statistical bulletin (2014) via: annual report and statement of account. Information on the annual GDP from agricultural sub-sector: food crop production ( ), livestock production ( ), forestry ( ), fishing ( ) and total GDP (Y) were collected for analysis. The period covered is 33 years from 1981to 2013. Below is the contribution of agricultural sector to total GDP for the period of 32 years.  The graphical display of four quarters of 2013 data is presented in figure 3 below to give us an overview of each sub-sectors contribution to the entire GDP from Agriculture. To determine the suitable model we are going to build for our data, the correlation matrix for the data was computed to check for possible correlates. The correlation matrix for the data is shown in Appendix A below.

Collinearity
Collinearity is the existence of near perfect linear relationship among the explanatory variables of multiple regressions. Suppose we have the sum of four explanatory variables + + + as in the case of this our study as a component of a whole, then there is tendency that the variables will be linearly related to one another, thereby creating inaccurate estimate of the regression coefficients. Observe from the correlation matrix in Appendix A that there exists perfect linear relationship between crop production and livestock and near perfect relationship among other variables. This is a case of data that is suffering from multicollinearity. When the Available Online @www.ijtsrd.com multicollinearity occurs, least square estimates are unbiased, but their variances are large so they may be misleading. From Appendix B, the OLS regression of the data produces estimates with very high variance inflation factor. This problem made us to compute the principal component regression PCR which is a biased estimation method often used in overcoming the multicollinearity problem. PCR can lead to efficient prediction of the outcome based on the assumed model (GlitchdataWiki 2016). It tends to perform well when the first principal components are enough to explain most of the variation in the predictors. A significant benefit of PCR is that by using the principal components, if there is some degree of multicollinearity between the variables in your data sets, this procedure should be able to avoid this problem since performing PCA on the raw data produces linear combinations of the predictor that are uncorrelated (Michy 2016). The PCR result of the data in Appendix C was obtained from regressing first principal component that accounted for 99.9% of the total variability in the original data on the response variable. The result produced a model that can efficiently be used in predicting the outcome. The result has the coefficient that is highly significant with a very low VIF, but with a higher standard error and lesser adjusted R-square than that of OLS. This led to computation of another biased regression estimation method for solving the problem of multicollinearity known as ridge regression.

Ridge Regression
Ridge regression is a biased regression technique used in analyzing multiple regression data when the explanatory variables are linearly correlated. When multicollinearity occurs, ordinary least square regression (OLS) may produce estimates with inflated variances thus giving us the model that are not reliable. Ridge regression is like least square but it shrinks the estimated coefficient towards zero by adding a small constant term ≥ 0 to the diagonal element of the ′ before finding it inverse as in the case of OLS. Given a response vector ∈ and a predictor matrix ∈ × the ridge regression estimate is defined as the value of that minimizes the penalized sum of squares ∑ ( − ′ ) + ∑ , that is, The constant ≥ 0 (a pre-chosen constant) is a tuning parameter which controls the strength of the penalty term ∑ . Applying the ridge regression penalty has the effect of shrinking the estimates toward zero; introducing bias but reducing the variance of the estimates. Equation (1) is equivalent to minimization of ∑ ( − ∑ ) subject to ∑ < , that is, constraining the sum of the squared coefficients. Note that  When = 0, we get the linear regression estimate  When = ∞, we get = 0  For in between, we are balancing two ideas: fitting a linear model of y on x, and shrinking the coefficients.
Therefore the ridge regression coefficient can be obtained thus, The variance of the ridge regression estimates is The bias of the ridge regression estimates is The total variance ∑ ( ) is a monotone decreasing function, while the total square bias ∑ ( ) is a monotone increasing sequence with respect to .
The least eigenvalue of the explanatory variables is chosen to be the value of in this study. This value gives better result than other pre-assigned values as suggested by Okeke and Okeke (2015). From Appendix C we have this value to be 0.0001.

Result and Discussion
Four different regression estimation methods were computed in this work due to nature of our data. This is to help us come up with a best model form predicting the GDP of Nigeria. The model (4) showed that crop production, Forestry and livestock production have positive influence on the total GDP of Nigeria. Fisheries have negative influence on GDP. This result goes a long way to say that much work is needed to be done in our fish production in order to improve Nigerian economy. The highest value of the coefficient of crop production indicates that among the four agricultural sub-sectors that crop production has strong influence in her GDP. The very high values of VIF of the coefficients gave rise to PCR.

Results from PCR
The PCR model of the data which was computed using the first principal component was obtained to be = −1.0 + 6.05PC This model has adjusted R-square of 0.994 which is a little lesser than that of OLS, but with very small VIF of 1. The standard error of the model is 997.674 and this is higher than that of OLS which is obtained to be 987.792. The calculated P-value of the PC is 0.000 which indicate that the linear combination (PC) is highly significant in predicting y. The first principal component used is = 0.5000 + 0.5000 + 0.5000 + 0.5000

Result from Ridge Regression
Different values of the tuning parameter k were considered in our effort to build a model that will give us better prediction. The values were: the least, second to the least, the median and highest eigenvalues of the explanatory variables. Observe that the result of ridge regression is almost exactly that of OLS but with little variation on the standard error of the estimate and shrink on the values of the regression coefficients.

Result from Stepwise Regression
The stepwise regression gave the estimated model of the variable Y to be = −7.128 + 3.397 The model has adjusted R-squared value of 0.994. The VIF of the crop production which is the only variable it retained is 1.