## Introduction

Modeling the demand and supply of crude oil in international and regional markets has many benefits. The models provide policymakers with information to predict the fluctuations in supply and demand, and adopt policies to cushion the local economy from external shocks. Moreover, the models give vital information regarding consumer demand and the impact of energy prices on consumer income (Bayar 67).

Such information helps determine the past and future trends in demand and supply, the determinants of consumer demand, and the relationships between energy supply and demand. While consumer income, tastes/preferences, and market prices determine energy demand, supply is determined by processing costs, transportation costs and technological factors.

In modeling, the theoretical relationships between energy demand and supply are converted into equations or models. However, the fact that demand is determined by market prices makes this transformation difficult as prices keep on fluctuating.

Moreover, the varied number of energy pricing approaches, including “two-part tariffs, seasonal pricing, average rates, and block rates among others” complicates the modeling process. Also, variation in sampling, data collection and statistical analyses affect model estimates of demand and supply. Thus, a model’s suitability is determined by its theoretical foundations, period/season under consideration and robustness of the model.

## Types of Demand and Supply Models

Statistical analyses for energy demand and supply use two kinds of energy models: time series models and cross-sectional models (Bayar 34). Time series models examine the trends in demand and supply over time while cross-sectional models explore the correlations among different factors over a specified duration.

Thus, cross-sectional models identify the causes and determinants of energy demand or supply. In an industry, a cross-sectional model can be employed to determine the energy demand variables by considering economic factors (output rates and oil prices) and technical/engineering factors such as the size/number of boilers required. In this regard, these models give significant statistical information that is relevant and specific at a particular period. Therefore, their predictive ability is limited.

On the other hand, time series models examine the demand or supply variables over a given period of time. Thus, past and future trends in demand and supply can be determined using time series models (Bayar 56). Time series models are important in demand or supply forecasting as they rely on historical data to make such predictions.

Although they provide a useful approach for estimating the correlations between demand and supply, data availability reduces their applicability. The development of these models involves two approaches: the econometric approach and the ‘time series’ approach (Harvey 78).

The first approach relies on the economic theory to measure the demand/supply relationships over time. It considers factors such as consumer income, market prices and climatic factors. Econometric models facilitate empirical testing of postulated hypotheses and serve as a basis for making predictions. On the other hand, the ‘time series’ approach involves extrapolation of the current relationships. They involve statistical equations (moving averages) that analyze stochastic variables to determine future trends through extrapolation.

## Energy Demand Models

The demand for natural gas can be determined based on a number of energy models that rely on sociological, economic and technical/engineering variables. Studies usually use econometric approaches to determine natural gas demand as such approaches consider shifts in market prices. Moreover, data from the Department of Energy has made researchers to use econometric analyses to predict trends in the demand for natural gas.

A study by Kydes, Shaw and McDonald focused on modeling of the residential energy demand. It grouped models into five main classes: (1) qualitative choice models; (2) translog models; (3) end-use models; (4) log-linear/double-log models; (5) cross-sectional/time series models (45). Most industries prefer the log-linear/double-log models as they are relatively easy to use.

They can be represented using two gas use equations: log D = β_{0} + β_{1}P + β_{2}Y + β_{3}W + β_{4}X and log D = β_{0} + β_{1}logP + β_{2}logY + β_{3}logW + β_{4}logX, where D = demand, Y = income, P = price, W = weather, X = structural variables and β = measurement parameters (49). The income and price elasticity of demand can be computed from the price and income parameter estimates respectively. Hisnanck and Kyier made an assumption that current gas prices determine future prices and demand (125).

However, transforming the demand into consumption variables using this approach was problematic. Using this approach, Hisnanck and Kyier were able to estimate the price elasticity related to gas demand. They found it to range between -0.58 and -0.69, which were statistically significant results (131). The model could explain the energy usage in different states as well as their future energy demand.

The translog models were developed in 1960s to measure industrial energy demand, including the electric power demand. It comprises of a quadratic function that involves a logarithmic notation for each element, and a Cobb-Douglas function, which estimates energy production by allowing for changes in production inputs.

Translog approaches, unlike the log-linear models take into account the utility function, which helps in estimating the price elasticity of demand. Moreover, translog models are more flexible, which facilitates a more accurate estimation of the utility function. However, these models have some disadvantages that limit their usage. First, the models are complex, which makes the interpretation of results difficult. Second, a large amount of data is needed when using these models.

Third, these approaches cannot be used in time series analyses, hence cannot be used to predict future trends in demand and supply (Olatubi and Zhang 207). Translog models are expressed as: log D = β_{0} + β_{1}logP + β_{11 }(logP)^{2} + β_{12}(log P)(log Y) + β_{13}(log P)(log W) + β_{14}(log P)(log X) + β_{2}logY + β_{22}(log Y)^{2} + β_{23}(log Y)(log W) + β_{24}(log Y)(log X) + β_{3}logW + β_{33}(log W)^{2} + β_{34}(log W)(log X) + β_{4}logX + β_{44}(log X)^{2} (Olatubi and Zhang 207).

One advantage of a translog model is that it is built on the economic theory, which allows for the analysis of specific demand factors and substitutions.

The qualitative choice approaches measure the utilization of resources or energy based on discrete values. Thus, these models use discrete variables (dependent) to determine the choice (negative or positive). A negative choice (no choice) is denoted by 0, while a positive choice is denoted by 1 (Hisnanck and Kyier 128).

Other factors that affect the choice are estimated by the independent variables. These models can be expressed as: y = x β + e, where x = independent variables, y = dependent (discrete) variables, β = parameters/coefficients and e = normal distribution error (129). These models are useful in measuring consumer behavior and purchase decisions. They require comprehensive data (consumer surveys), which limits their use.

## Conclusion

There are several modeling approaches for energy demand and supply. Each model has its advantages and disadvantages that limit its usage. The log-linear/double-log, translog and qualitative choice are the most common types of models. For the linear/double-log models, it is easy to interpret the price elasticity of demand.

However, unrealistic elasticity assumptions and lack of consistency limit its usage. On the other hand, the translog models derive from the economic theories, which facilitate the estimation of demand variance. Qualitative choice approaches work well when the dependent variable assumes discrete values, which allow for estimation of consumer choices.

## Works Cited

Bayar, Ali. *Energy and Environmental Modeling*. Florence: EcoMod Press, 2007

Harvey, Andrew. *Forecasting, Structural Time Series Models and the Kalman Filter.* Cambridge: Cambridge University Press, 1989.

Hisnanck, John and Ben, Kyier. Assessing a disaggregated energy input using confidence intervals around a translog elasticity estimates. *Energy economics* 17. 2 (1995): 125-132.

Kydes, Andy, Susan, Shaw and Douglas, McDonald. Beyond the Horizon: Recent Directions in Long-Term Energy Modelling. *Energy* 20.2 (1995): 31-149.

Olatubi, William and Yang, Zhang. A Dynamic Estimation of Total Energy Demand for the Southern States.* The Review of Regional Studies* 33.2 (2003): 206-228.