ASSESSMENT OF THE IMPACTS OF OIL PRICES ON NIGERIA ECONOMY USING COBB-DOUGLAS PRODUCTION FUNCTION

Fluctuations in oil prices have been a global issue over the years. Although many studies have been carried out the majority of those studies relating to oil prices focused more on its effects on oil-consuming nations than oil-producing ones. This study, however, examines the vulnerability of the economy of the oil-producing country to oil price changes using Nigeria being an OPEC member as a case study. The Cobb-Douglas production function was used to formulate the appropriate model that relates oil prices with the economy of Nigeria. However, the close to close (standard deviation) volatility method was used to measure the amount of variability in oil prices. Nevertheless, the perpetual inventory method was used to estimate the accumulated physical capital of Nigeria and the problems of multicollinearity inherent in the data were attenuated using ridge regression techniques as capital cannot be left out while dealing with production.


Introduction
Crude oil has been the major source of Nigeria income after its discovery in 1956, which led to less concentration on agricultural products that used to be contributing about 70% to the growth of Nigeria gross domestic product (GDP) in the early 1950s (Alley et al., 2014 andNBS, 2018). Though Nigeria has achieved tremendous growth due to the high production of oil which has led to higher revenue for the country when the oil price was moving to its peak, and that contributed about 8.4% to the growth of GDP in 2009(World Bank, 2018. Nevertheless, it is quite unfortunate to see Nigeria as one of the richest countries in Africa, and still among the country battling extreme poverty and economic mess. Without a doubt, Nigeria is a country currently in dire need of high and sustainable economic growth that is capable of engendering rapid economic development and reducing poverty but, its monoproduct (crude oil) economic practice has allowed its growth to be highly vulnerable to the movements in oil prices over time. (Nwoba et al., 2017).
Hence, there is a need for the Nigerian government to diversify the economy. In 2015, the Federal Government of Nigeria came up to diversify the economy of the country to the agricultural sector. After about four years of flagging off the diversification policy, it is pertinent to examine the responsiveness of the economy concerning international oil price changes. This study, therefore, attempts to verify the vulnerability of Nigeria's economy to oil price through production function, putting into consideration, some economic indicators such as Real GDP, Gross National Income (GNI), Physical Capital (Capital Stock), and Working Age Population (Labour).
Traditionally, there are specific approaches used in analyzing the effect of oil price changes which include non-structural models which solely depend on the theory of exhaustible resources as the root for understanding the oil market. Structural supply/demand framework that uses behavioral equations and factors that link oil demand and supply to its various determinants and the informal approach that can be studied by analyzing oil price movements within specific contexts and episodes of oil market history (Bassam, 2007).
Most studies on oil prices literature have been using structural methods with the use of Augmented Dickey-Fuller, Cointegration, and Granger Causality and high numbers of them have used Gross fixed capital formation as a proxy for capital accumulation (stock). For example, Taofik (2018), Birouke et al. (2012), Aljebrin (2013), Kathleen et al. (2012), Maku et al. (2018), and Alley et al. (2014) Likewise, the informal approach which only describes some economic indicators during the volatility period has been used by a set of economic organizations among which include International Monetary Fund (IMF, 2000) and US Energy Information Administration (EIA, 2018). While few studies have used the non-structural approach, for example, Bassam (2007), in his article "the drivers of oil prices: the usefulness and limitations of non-structural models" describe oil price based on historical, projected prices, and future speculations.
Therefore, this paper adopted structural methods and has a paired distinct contribution to Nigeria's government, stakeholders, and citizens in general to have a view of the recent performance of the economy. This will allow the government to know their stands whether they are getting it right or there is a need to re-strategize. On the other hand, the paper makes a great contribution to research methods on oil price, production function with the usage of estimated capital stock, and addressed the collinearity issues while dealing with time series.

Methodology
Given the Cobb-Douglas production function (1) where, t Y = Total production (GDP) of Nigeria for year t. = Physical capital of Nigeria for year t, t L = Total labor employed in year t, t = Time (Year), A = Efficiency of the function, α = Elasticity of output relative to the physical capital, β = Elasticity of output about workers. Hence, α + β = 1, would suggest that an increase in production would be by the increasing rate of inputs. α + β > 1, would suggest that an increase in production would supersede proportional inputs increase. α + β < 1, would mean that an increase in production would falloff to inputs increasing rate. Assuming, Oil Price = P where P is not directly related to GDP. Because neoclassical production theory only described the general production function as ( ) , = Y F K L meaning that the output is the function of capital and labor. Due to scarcity of data on physical capital "Kt", is estimated using investment capital "It" of the country by Perpetual Inventory Method used by Berlemann (2014). And from (1), if = t A P , then by linearizing (1) it gives (2) where t P is Oil Price in year t, likewise 1 a and 2 a are constants and coefficients of parameter P in equation (2) respectively. Although from the literature, at the beginning of desired period t, the net capital stock t K , can be written as a function of the net capital stock at the beginning of the previous period t-1, 1 − t K , gross investment capital in the current period, t I , and consumption of fixed capital, If the geometric depreciation of fixed capital D at a constant rate is denoted by δ, then equation (3) becomes where t K = Physical capital of year t, 1 − t K = Physical capital of previous year t-1, δ = Capital depreciation rate, and t I is the investment (gross fixed capital formation) of year t. But (4) can be estimated such that It is the investment (gross fixed capital formation) of year t and gGDP is the growth rate of GDP. Because neoclassical growth theory assumed that; if the economy under consideration is in its steady-state, the gross domestic product will be rising at the same rate as the capital stock and the growth rate of the capital stock can be approximated by the growth rate of investments. Therefore, looking at the trend of Nigeria's growth rate which has been somehow like a wave around equilibrium over decades World Bank (2019), the 1 − t K was estimated by gross fixed capital formation growth rate (investment growth rate) with the assumption that the economy is not in steady-state. Such that = (6)

Volatility
Volatility has been the word used to describe the fluctuations in the price of commodities over time and it is usually in form of a comparison of historical changes in the price of such commodity and current price. It should be noted that high variability does not connote high price but rather give the yearly amount of variability in oil price. Hence, the close-to-close volatility method is considered the simplest and most used for the test. It can be estimated by multiplying standard deviation by the square root of working days or number sample. That is: where 'n' is the number of trading days in a year and is the log return of OPEC daily oil price (Pt), which is calculated by: for Pt-1 = oil price of the previous day.

Cursed Economy
An economy is said to be cursed if the growth of per capita income is negatively correlated with the share of labor in the primary sector (Thirlwall, 2011). The scattered plot is used to determine the situation of this and as well determine the accountability of the share of labor in agriculture to the growth of Gross National Income (GNI) by testing through SPSS at a 5% significant level.

Effects of Oil Price on Nigeria Economy
In many cases, time-series data always have some problems such as multicollinearity, nonstationary, autocorrelation among others which is contrary to the assumptions of ordinary least square (OLS) regression. Due to this fact, performing (OLS) regression may lead to the superiority of the model and make some important variables insignificant. Therefore, Ridged regression shall be used as a substitute for the OLS during the analysis. Note: overall regression being significant and insignificant of almost the entire individual test will signify the existence of multicollinearity. Likewise, the high correlation between the independent variables may also be a signal of multicollinearity. For more about the condition of multicollinearity see Gujarati (2004).

Ridge regression
Ridge regression is like the OLS method because it assumes three out of the BLUE assumptions of the OLS except for an unbiased estimator, as it introduces a small amount of bias to the model. Theoretically, Hoerl et al. (1970), define ridge regression as a regression technique used to solve the problems of multicollinearity in the data set under study. The advantage of this technique is it is capable of producing a result with a minimum standard error by standardizing all of the variables included in the model, Normalize the data towards zero which will automatically take care of non-stationary problems, and as well accounting for the effect of outliers in the data sets (NCSS, 2018). In general, we can say that ridge regression is the best substitute for OLS when the variables are suffering from multicollinearity (Hoerl et al. 1970). Mathematically, OLS regression coefficients are usually estimated using (8) Here,  β is a p×1 coefficient matrix of the least-squares, ' X X is p×p matrix of the square of independent variables and ' X Y is a p×1 matrix resulting from the multiplication of dependent and independent variables. The ridge regression coefficients estimation is a little bit different due to standardized variables used to perform the regression and it added a very small value say λ to the correlation matrix of the independent variables in equation (8) such that if ' = X X R , where R denotes design matrix of independent variables, then the estimate of the coefficient for ridged regression is given by Where are the coefficients of ridge regression, R is the design matrix of the independent variables, I is p×p identity matrix and ' X Y is p×p matrix of the square of independent variables likewise, λ is a positive quantity usually ranges between 0 and 1 but, the lower the value of λ, the smaller the introduction of bias to the model. Although, there are several ways of determining the value of λ which can be used to conduct the ridge regression to have better results. One of the popular ways is to plot the Ridge Trace and choose the value of λ which the coefficient line settled. It is done by plotting the coefficients of ridge regression against each value of λ assumed. But in this study, since we have prior knowledge of coefficients of the model, we will select the best minimum value of λ that produces the accurate results based on the theory and with the technological improvement in the field of machine learning and statistical computing, STATA shall be used to run the regression for this study with (ridgereg) function and the results are interpreted by OLS method.

Nigerian Economic Data
Between 1988 and 1999 as shown in Figure 1, the oil price has been floating around $14.24 per barrel to $22.26 per barrel, which seems unfavorable to the economy of Nigeria. However, since 2003 Nigeria's economy continues to grow steadily until 2013 when the oil price has again been fallen till it dropped to $40.68 per barrel in 2016. Since 2017, Nigeria has also been experiencing economic growth as the oil price rose to USD 52.51 per barrel. In summary, Nigeria's economy (GDP) virtually moves together with the oil price. Hence, it is very imperative to check if Nigeria's economy is among the cursed economy in the world. (See Figures 1 & 2). In terms of employment, Nigeria's employment has mostly been from the agricultural and services sector over time and her unemployment rate has reached 23.1% National Bureau of Statistics (NBS, 2018). Meanwhile, an industry which oil sector fell into has not been creating employment opportunities for the population under the labor force even though much attention of government is in this sector since the late 1980s and based on a survey conducted by the national bureau of statistics in 2013 on job creation, it was reported that oil sector only accounts for about 0.01% of total employment in Nigeria. As depicted from Figure 3, since the late 1980s agricultural sector take close to 60%, the service sector covers over 30% and the industrial sector accounted for less than 10% of the total employment in Nigeria. Due to the oil prices boom that started in 2001 (as shown in Figure 1), many Nigerians who are in the agricultural sector begin to lose their jobs because of government negligence of the agricultural sector and that reduced the percentage of employment in the agriculture sector meanwhile the sector is currently accounting for less than 40% of the total employment in Nigeria.

Nigeria Physical Capital
Nigeria's capital stock has been increasing over time. It was estimated to be 66.92 trillion Naira in 1988 and 170.70 trillion in 2017 if assumed that Nigeria's capital depreciation rate is 4%. For the uniqueness of the results, the analysis was tested with different depreciation rates which are 7%, 8%, 10%, 20%, 25%, and 30% respectively. Here the higher the depreciation rate of the country, the lower the amount of physical capital and vice versa. These results are presented in Table 1.

Results and Discussion
Based on the analysis, it was discovered that Nigeria's economy is not cursed and the share of labor in agriculture does account for GNI growth in Nigeria. This is due to the insignificant negative correlation that exists between GNI growth and the share of labor in agriculture (evident from Figure 4). On the other hand, Nigeria economy is highly vulnerable to oil price changes especially in the years 2008, 2009, 2015, and 2016 where oil price was highly varied with the amount of 41%, 34%, 35%, and 42% respectively, except in 2013 where the number of oil prices changes was only 12%. The values of variance inflation factors of the collinearity diagnosis are all less than 5 and the respective R 2 for different models conducted has been minimized. Thus, the models are no more biased, and the collinearity has been eliminated and we can say that the independent variables (factors of productions) account for about 61% on average to changes in Nigeria economy. Also, going by the assumption made by Berlemann et al. (2014), with a hundred-year interval of depreciation rate for physical capital, if we assume 4% as the depreciation rate of Nigeria capital, then the resulting equation of the Nigeria production function as shown in Table 2  Meaning that the elasticity of output relative to capital (α) is 0.5879 and the elasticity of output relative to labor employed (β) is 0.5238. Therefore, since α+β = 0.5879 + 0.5238= 1.1117 > 1, then we conclude that the rate of increase in production (Nigeria economy) will be more than the rate of increase in the input of both capital and labor. That is, a 10% increase in both capital and labor will increase Nigeria's real GDP by 111%.
Similarly, both capital and oil prices are highly significant to the economy of Nigeria at a 1% significance level, but the labor is significant at 5%. This means that Nigeria is a capital-intensive country and is largely driven by the oil price. However, Nigeria has not been able to utilize its labor to its fullest like most developed countries.

Conclusion
Based on the results obtained from the analysis, it can be deduced that the contribution of oil to the growth of Nigeria's economy has not anyway been limited, and is still largely driven by oil price and capital. Therefore, it is highly recommended for the government to put more effort towards economic diversification and make sure oil revenue is reinvested into the economy by the building of refineries, sustainable infrastructures, and the development of other sectors of the economy. Because in the long run, if the developed oil buyers (countries) eventually implement the use of solar power, electric cars, and automobile, the economy of Nigeria will be in trouble and worse-off even more than its current situation. Also, with the low rate of the manufacturing industry in Nigeria which has not been providing employment opportunities to many citizens under the working-age population, the government of Nigeria should use the opportunity of belt and road initiatives of the People's Republic of China to improve the employability of Nigerians, as China has emerged as the most frequent country Nigeria is trading with. Although, there has been a lot of conspiracy on to whether the belt and road initiatives of China is a symptom of colonialism, nevertheless, it is economically recommended for the government of Nigeria not to only look at the financial aspect of these initiatives but also, find a way of attracting productive industries for it to maximally utilize its working-age population to improve the productive capacity of the country. And that will not only increase the employability of Nigerians but also increase its revenue generation from other sectors of the economy. Furthermore, Nigeria needs to focus on real productive industries which can make use of the raw materials produced from the agricultural sector after the diversification has been effective. This is the way to achieve a balance within the industrial and agricultural sectors as there will be an increase in return not only to labor but also to the industry. Lastly, based on economic theory, many scholars agreed that for the economy to move away from stagnating, there is a need for having the right institution to set up political and economic policy and as well as to install the restriction to the political power and controlling the behavior of the citizens. Therefore, it is greatly recommended to emulate fast-growing economy countries such as China in terms of restructuring of policies and constitutions, as much of the Nigeria capital has sunk into the pocket of political leaders over time.