Estimating the Price Elasticity of Natural Gas and Electricity in Pacific Northwest

: This paper estimates the price elasticity of electricity and natural gas in the Pacific Northwest. Electricity and natural gas are substitutes; and demands of different classes of consumers for the energy are price-inelasticity. The results are when the price of retail electricity and natural gas changes, consumers would choose the cheaper one to make up for the increased cost of another energy price. Consumers' demand for energy is mainly stable, they won’t affect a lot by the change in energy prices.


Introduction
Electricity can be produced by fossil fuels, including natural gas, coal, and petroleum.According to the EIA, natural gas was the largest source-about 38%-of U.S. electricity generation in 2021, and both steam turbines and gas turbines can generate electricity.If the price of natural gas changes, the price of electricity will also be affected correspondingly.Knowing how changes in electricity prices affect the consumption of consumers becomes significant in the area of energy policy model (Manne et al., 1979), electric utility resource plans (Wilkerson et al., 2014), demand reponse (EPA, 2008), and so on.
This study echoes the global carbon emission reduction objective.For example, assumed 10% electricity rate increase an immaterial CO 2 emission decline of 620 to 2,786 t for the Pacific Northwest.(Woo et al., 2017).The estimated price elasticity may serve as a well-grounded justification for policy makers to implement price management policies.For instance, CMU (2011)assess the price and income elasticity for household electricity consumption in the U.S. and found that price elasticity estimates range from −0.21 to −0.25.The results confirm most previous studies that have found inelastic values for both price and income elasticity.(Azevedo et al., 2011).While another study also supported this argument that Pacific Northwest's own-price elasticity estimates are larger in size than California's (−0.0323, −0.0144, and −0.0348 for the residential, commercial, and industrial sectors), they indicate that retail electricity and natural gas demands are highly price-inelastic.(Woo et al., 2017).
For the long-run effect, a study used national-level data for a sample of 44 countries to estimate the price and income elasticities of natural gas demand.It presented both single-equation results and results instrumenting natural gas prices with proved natural gas reserves.They concluded that the long-run price elasticity of natural gas demand point estimates is around −1.25.(Burke et al., 2016).
Our exploration estimates the price elasticity of natural gas and electricity in the Pacific Northwest (Idaho, Oregon, and Washington) using monthly data from 2001.01 to 2022.08 to determine the nexus between consumption and the price of major end-use consumers for residential, commercial, and industrial purposes.Our findings are: The following sections are organized as: Section 2 introduces methodology and background, section 3 presents key results with discussions while section 4 concludes.

Regression Model
We use a CES (constant elasticity of substitution) system to estimate how the price change in retail electricity would response to the change in natural gas demand.This system was previously used to estimate how timevarying price causes peak and off-peak demand change (Woo et al., 2013a).
CES system constructs the equation as: ln(X j /Y j ) = α j + α EGj ln(E j /G j ) + Z j + μ j (1) (Note: Residential: j =1, Commercial: j = 2, Industrial: j = 3) In the equation, ln(X j /Y j ) is the natural log of class j's ratio of electricity and natural gas consumption and ln(E j /G j ) is the natural log of class j's ratio of electricity and natural gas price.We predict that as α EGj j will be negative, ln(X j /Y j ) will move in the different dirctions with ln(E j /G j ).When α EGj equals to zero, the price of electricity and natural gas consumption will have no relationship with the demand.
We use Z j to consider the elements other than price in the Pacific Northwest, including time line, real GDP, and weather variables (CDD -cooling degree days; HDDheating degree days).In order to avoid zero values in the weather variables, we add one for each number and apply natural log -ln(CDD + 1)/ ln(HDD + 1).
The own-price elasticities of demand can be found through the CES system's price coffecients, α EG j.Since the class j's electricity demand is related to the price ratio rather than the price levels, we can calculate the own-price elasticity of electricity as Suppose the μ j is correlated in the system of equations, we can consider three sections together by using ITSUR estimation (iterative seemingly unrelated regressions) in STATA and robust SE (Wooldridge, 2010).

Data Discription
The data of energy consumption, price and weather comes directly form the EIA (the U.S. Energy Information Administration) website from January 2001 to August 2022.The GDP data comes form BEA (an official website of the United States government) from January 2001 to June 2022.
(Note: The ending data is the latest data at the time we writing the paper.) • The monthly electricity and natural gas consumption • The monthly electricity and natural gas retail price data • The monthly weather data by census region including CDD and HDD • The monthly real GDP data.We calculate it from the quarterly GDP: Monthj GDP = first-quarter GDP × [(Month j employment × days)/ Month j employment × 31 days + Month j+1 employment × days + Month j employment × days)]. (6)

Results and Discussion
Table 1 shows the ITSUR regression results from the view of consumption.The regressions' adjusted R 2 values are in the interval of 0.69 and 0.94, which means they fit the model good.The estimates for α EG j are all negative, which prove our hypothesis that electricity and natural gas are substitutes in the area of Pacific Northwest.But we can know from the small number that the price sensitives are quite low.What's more, as the real GDP and the weather changes, retail energy consumption ratios are change with the time trend.Table 2 shows the own-price elasticity estimates for the Pacific Northwest area's retail electricity demands are -0.0284,-0.0009, -0.0197 for the residential, commercial and industrial classes, which means that retail electricity and natural gas demands are inelastic for price.

Conclusion
The results conclude that when the price of retail electricity and natural gas changes, consumers will choose the cheaper one to make up for the increased cost of another energy price.Consumers' demand for energy is mainly stable, they won't affect a lot by the change in energy prices.
) It can be seen that ε EEj = -ε EGj (3) The own-price elasticity equals to the negative value of the cross-price elasticity.The absolute value of them are equal | ε EEj| = | ε EGj|.

Table 1 .
ITSUR regression results of the CES system

Table 2 .
ITSUR regression results of own-price elasticity;