Energy is life; seen ab initio only in the form of light (Genesis 1: 2–3) but has since been in divers’ forms. Modern science and economics underscore the importance, essentiality and existence of forms of energy and that energy resources belong to the category of scarce goods despite being naturally available but essential factor of production according to  characterized by monopolies or oligopolies rather than perfect competition especially in developing nations , scarcely located, determine the economic progress of countries and require huge resources for their exploration, development, distribution, and creates negative environmental externalities etc., . To accentuate this, the Nigerian energy sector is a mix of energy sources - renewable energy (solar, wind, generated waste and hydroelectricity) and non-renewable energy (coal, petroleum, natural gas)  and largely influenced by reforms and several government policies over the years ,. Crude oil is a hydrocarbon compound in form of chemical energy that exists in liquid natural state under the ground, rock or the ocean with deposits unevenly found globally . Nigeria is a leader amongst the oil-producing countries with enviable proven reserve , ,  while from scientific knowledge of physics, electricity is based on the invisible movement of positive or negative charges (electrons or proton) that is conducted through cables (wires) to equipment through generated through different sources and conversion processes such as from coal, gas, crude oil, water, wind and solar energy sources , ,.
However, being faced by market risks such as price volatile and uncertainty according to, crude oil price, natural gas price and electricity tariff poses challenges to government policies leading to cash flow uncertainty, low productive economic activities and hence poor welfare outcomes especially in developing economies like Nigeria, which is a net crude oil exporting country and where resource income constitute larger share of government revenue. The pass-through mechanism of crude oil price affects electric power tariff and output has remain uncertain and generated discrete debate over the years.  attributed it to the non-renewable energy fossil fuel (crude oil) conversion to electricity supply because most generating plants are thermal plants (natural gas being a part derivative from crude oil exploration) and that both experience various common price factors such as Market forces and structure, monetary and fiscal policies of domestic economies, cost of infrastructure (equipment) and technology, requirement for statutory regulations, exchange rate etc., according to , . Besides, an increasing competitive energy sources (Substitute Products) such as solar electric system, compressed natural gas (CNG) and fuel cell vehicles sold in developed countries is likely to slow crude oil demand growth globally hence compelling a causative relationship of crude oil and electricity pricing across economies with attendant effects.
As earlier noted energy resources have attracted value that necessitates their prices and pricing mechanism as proprietary factors ,  noted factors determining Crude Oil Prices(which are also common to natural gas) include monetary, fiscal, technical, political and structural factors such as property and quality of the crude oil, market forces of supply and demand, new technology in oil exploration and production, production capacity and cost, membership of OPEC and the cartel’s decision, criminality, insecurity and crisis factors etc. leading to two (2) basic pricing models/formations - the spot price (sp) and forward price (fp) . Similarly, , ,  observed that determinants of electrical power tariff are market-driven including price of natural gas because most generating plants are thermal plants, cost and financing of provision and maintenance of infrastructures and equipment, statutory regulations framework, class of customers, inflation and exchange rate.
With Nigerian experience, negative crude oil price, as posited by  exerts negative, cyclical, asymmetric and unequal pressures on natural gas price and virtually all other economic sectors including electric power supply, pump price of petroleum products and with overall macroeconomic performances . However, positive crude oil price has significant relationship with natural gas supply and pricing, budget allocation , foreign exchange rate  etc. Theoretically, positive crude oil and or natural gas price translates into higher revenue to government but higher production cost to industries and manufacturing firms passed as consumers price hike on goods and services, high cost of living and lower standard of living while a negative price declines causes cut in public revenue and aggregate income, shift in consumption and investment expenditure patterns, fall in the employment level etc. The peculiarity of the electricity tariff changes (increases/decreases) is attributed mostly to factors either endogenous or, but mostly exogenous to the Nigerian power subsector,  such as fluctuating international price of natural gas, market policy shocks, energy consumption imbalances. Electricity tariff mechanism in Nigeria rallied around exogenous factors observed like fixed charge/cost (cost of natural gas- capital costs recovery), variable costs/charge (variable recovery), and endogenous factors such as system applied charge/cost (demand load amount) and or marginal costs.
Globally, little or no famous studies have shown the effects and relationship between the trio of crude oil price, natural gas price and electric power tariff on the economy particularly Nigeria but much has been done on the electricity supply shortage, consumption, demand and so on , , . Probably because electricity tariff is relatively stable, enjoys state incentives like subsidy and being regarded as social services, despite being a factor input into production etc.
This study is premised on Asymmetric Price Transmission(APT) theory that accentuates Rocket and Feather Effect (RFE), and dwells on the pass-through mechanism of changes in the price of energy resources such as crude oil to the price of gasoline due to changes in other input costs commonly attributed to . More over  simply put RFE shows that as prices rise like rockets when input costs increase but fall like feathers when input costs decrease mathematically expressed as in equation i, for two variables model where Y varies directly to Q while k is the constant;
y = kq # 1
In three variable model, where y varies directly to q and z while k is the constant;
y = kqz # 2
This APT is amenable to price changes of commodities that are cross elastic demanded, substitutionary and homogeneous especially in a perfect market structure. For example, the prices of the pair of crude oil and natural gas influences each other (and electricity tariff) asymmetrically and hence obeys the rocket and feather hypothesis according to  with other factors at constant . Further  had argued that the APT effect affects consumers welfare disparities with respect to the speed of adjustment prices as input cost increases or decreases noting that some market participants are disadvantaged in price changes.
Asymmetric Price Transmission(APT) theory emphasizes prices changes in perfect market structure and market Structure dwell on structural characteristics (e.g. producers and consumers) of an industry in any economy ,  generally influenced by theories of demand and supply leading to pricing and price equilibrium simply expressed thus;
Qd = Qs = (P t ) # 3
Unique about a competitive market is the dynamics of price (P) that assumes the determinant of producer profit and consumer utility leading to social welfare (SW) function expressed thus;
P = CS (pt) + PS (pt) = SW # 4
The energy prices, like the trio of crude oil and natural gas prices and electricity tariff, as a segment of energy market economy, ,  changes due to many other factors that are both structural and market inclined, exerts direct and indirect effects.
In Nigeria, like most other net energy export and import economies crude oil and natural gas prices greatly influences the performance of the economy especially in meeting government economic responsibilities  and hence influences prices of other goods and service.
However, critics of the rocket and feather hypothesis (RFH) and market structure assumptions in Nigerian economy like  and  argue that law of equilibrium price may fail due to factor pricing, heterogeneity of product, price and state policies, which also affects social capital investment. However, this study assumes that the trio of crude oil and natural gas prices and electricity tariff exert shocks with effects on each and one another to translate to performances in Nigeria.
Preponderance of studies on energy resources across economies include  who studied the long- and short-term response of natural gas consumption in Pakistan with respect to changes in price and other variables like real GDP per capita and income changes, using a single equation cointegration model of econometric estimation technique for a period between 1978 and 2011 and found that Natural gas demand has significant and positive relationship with income, price of natural gas and price of substitutes. For , who used SVAR method relationship between crude oil prices on gasoline prices in the USA and obtained evidence of the asymmetric effects. Recent work of Chen & Sun, (2021) also examined the pass-through effect of crude oil prices on gasoline prices in Chinese economy and found that gasoline price responded asymmetrically to crude oil price for the period of 2000 to 2017. However,  study in South Africa using a single-step nonlinear autoregressive distributed lag (ARDL), rejected the acclaimed asymmetric response of gasoline prices to international crude oil prices in developed countries like US. These works reviewed discloses that different data frequencies and methods were employed though hence the different results obtained on the relationship between positive and negative energy resources prices.
In Nigeria,  studied the impact of electricity supply on economic growth in Nigeria between 1980–2010 by using an error correction method applied variable such as per capita income, electricity consumption, government expenditure and investment etc, showed that there was no long run relationship between per capita income and the explanatory variables, thereby recommended a check on malpractices in the power sector.  view on Energy Pricing Policy and Environmental Quality in Nigeria using dynamic Computable General Equilibrium Approach of social accounting matrix found that fuel subsidy policy hamper efforts at environmental sustainability and the level of carbon emissions in Nigeria. Since good and quality environment improves welfare and wellbeing of the people, partial, gradual and complete removal of fuel tariff showed carbon emissions marginally suggesting that removal of fuel subsidy was not sufficient to guarantee quality environment improves welfare and wellbeing of the people, but must be accompanied with supporting policies.  studied Crude Oil Price Fluctuations and Nigeria Economic Growth between 1997–2015 and observed mixed findings in Nigerian economy. They, with a view to determining whether the Dutch disease theory application in Nigeria, used time series data on crude oil price, Gross Domestic Product, Exchange rate, Government expenditure and Unemployment from 1997–2015, and adopted regression analysis technique to estimate the relationship between and effects of the variables. The study discovered that Crude oil price has positively insignificant effect on Gross Domestic Product and unemployment but expressed positive and significant effect on Government expenditure, thus recommended that economic diversification by focusing on non – oil revenue like agriculture and mining sectors. Also,  also investigates the impact of electricity consumption on Nigerian economy between 1986 and 2018 using time series data on electricity consumption, cost of fuel/gas and economic growth rate employing Autoregressive Distributed Lag Model estimation technique. The study result show that both electricity consumption and economic growth rate are positively and significantly correlated in the short-run but in the long-run and therefore recommended policies that will enhance efficient electricity consumption measures towards increasing economic growth in Nigeria. Further  estimated natural gas demand elasticity in Nigeria by examining the responsiveness of natural gas demand to changes in price of natural gas, income and prices of other energy products, adopting the bound testing approach to cointegration within the framework of ARDL annual time series data of 33 years (1984–2016) and found that the elasticity of natural gas demand is relatively price inelastic in both short and long run despite of substitute energy products to natural gas in Nigeria and recommended natural gas price as a tool for increasing the quantity demanded of natural gas in Nigeria. Lately,  studied the asymmetric response of petroleum product prices to international crude oil prices by employing the hidden cointegration approach on quarterly data and found that positive and negative components of both the crude oil and petroleum prices move together in the long and short runs, suggesting evidence existence of the rocket and feather hypothesis in the retail energy market in Nigeria and recommended for government intervention in the energy market to reduce the welfare loss. Recently,  analyzed the Nigerian Natural gas consumption between 1990–2020 by adoption relationship between variable like natural gas consumption, natural gas price, crude oil price, using Vector Error Correction model (VECM) and found the presence of a strong positive correlation between the variables though the price of natural gas is not consumption determined, implying that economic policies that encourage production of goods and services in Nigeria will tend to boost natural gas consumption and suggested influx of foreign investment into Nigeria influenced by international crude oil price and not necessarily by the Nigerian natural gas consumption.
Most other studies in Nigeria like and  have concentrated more on the effect of oil price shocks on macroeconomic variables such as output, inflation, stock market and exchange rate. Specifically, most of the studies reviewed focused their analysis on energy resources - crude oil, natural gas and electricity price, consumption, supply and the economy using different methodologies and estimation techniques. However, seldom mentioned in studies is related to crude oil price, natural gas price and electricity tariff nexus in Nigeria. Though  study crude oil price fluctuation however but was not related to electricity tariff in Nigeria while study by  has no link with electricity price and crude oil pricing. These show that there is paucity and gaps in literature in this area, which this study intends to fill especially by applying econometric models and estimation techniques.
In order to achieve the objectives of this study, plethora of related literature reviewed have buttressed qualitatively the relationship between either the pair of crude oil prices and natural gas price and or crude oil price and electricity tariff or electricity tariff and natural gas price through differing mechanisms. The quantitative analysis follows the theoretical endogenous framework model of  with modification of some set of variables empirically used a simple long run model thus;
P P t = α0 + αi CPt +Ɛt # 5
where PPt and CPt are petroleum and crude oil prices, respectively, α0 is the intercept, αi is the slope that measures the long-run effect of crude oil prices on petroleum prices and Ɛt is the residual term. The time series secondary data used were sourced as follows; Electric Energy Tariff (per kilowatt hour) obtained from Nigerian Electricity Regulatory Commission (NERC), Crude Oil Price (per Barrel) and Natural gas price ((per Million Btu) from Henry Hub Natural Gas Spot and wellhead Prices on (United States Energy Information Agency (EIA)) spanning the period between years 1980–2021.
Arising from the theoretical and empirical frameworks and findings of  as discussed above, this study modified the frameworks and the model specifications in order to make them conceptually and realistically relevant to this study. In this study, the linear endogenous model function specified for the estimation as in Eq. 6;
EET = f (COPB + NGP) # 6
expressed mathematically and in econometric as in Eq. 7 below,
EET = β 0 + β1 COPB + β2 NGP +ɛt # 7
Where: EET = Electric Energy Tariff (in Naira),
COPB = Crude Oil Price per Barrel (in US Dollar)
NGP = Natural Gas Price
Where, β0 = Intercept term, β1 = Coefficient of COPB, β2 = Coefficient of Natural Gas Price and ɛt = Stochastic or disturbance term.
Equation 8 is the lagged expression of the model
EET t −1 = β0 + β1 COPBt −1 + β2 NGP t −1+ɛt # 8
This study adopted Eq. 8 as the static and long run relationship of the variables to test for the co-integration of the variables by way of Bound test approach of Autoregressive Distributed Lag (ARDL) to determine the relationship between the variables. Bound test is a type of ordinary least square model, useful and applicable to variables at varied and or similar order of integrations.
Following the result of the preliminary test, this study further employed Vector Autoregressive (VAR) model for its estimation using appropriate Lag criteria adopting the equations 9a, b, and c.
EET = β0 + β1 COPBt −1 + β2 NGPt −1 + β3 EET t −1 +ɛt # 9a
NGP = β0 + β1 COPBt −1 + β2 NGPt −1 + β3EET t −1 +ɛt # 9b
COPB = β0 + β1 COPBt −1 + β2 NGPt −1 + β3EET t −1 +ɛt # 9c
β3 = Coefficient of Electric Energy Tariff. On a priori ground the various theoretical expectations explained above are:
β0 > 0, β1 > 0, β2 > 0, β3 > 0.
VAR is statistical model for economic multivariate times series variables that theoretically exhibit relationship amongst them, capable of forecasting and to produce a bi-directional model (i.e. variable affected by itself and another or both) . In VAR model, no variable is exogenous because of simultaneity between several variables and that each variable is expressed as lagged function of its value in a model.
To further test for the relationship between the variables, causality test was employed, that describes the cause and effect i.e. the direction of causal relationship between two sets of variables. The equation for general Pairwise Granger causality test can be specified as follows:
µ Δy t = ΣδZt-1 + Σ ψ ΔXt-1+ ei # 10
Where Y, Z an X are any of the series variables assumes status of a vector alternatively and uncorrelated, and at appropriate number of lags and Granger-cause one another, δ, ψ and µ are their coefficients, not equal to zero to give bi-directional situations. The null hypothesis of no causality between two variables cannot be rejected if the probability value of the F-statistics is > 0.05 (P > 0.05). Contrarily, the null hypothesis is rejected if the probability value is ≤ 0.05 (P ≤ 0.05).