Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach

G Model

ARTICLE IN PRESS

SOCSCI-1386; No. of Pages 10

The Social Science Journal xxx (2017) xxx–xxx

Contents lists available at ScienceDirect

The Social Science Journal journal homepage: www.elsevier.com/locate/soscij

Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach Yanming Sun a , Yihua Yu b,∗ a b

School of Urban and Regional Science, East China Normal University, 3663 North Zhongshan Rd., Shanghai 200062, China School of Economics, Renmin University of China, 59 Zhongguancun Str., Beijing 100872, China

a r t i c l e

i n f o

Article history: Received 29 August 2016 Received in revised form 13 February 2017 Accepted 20 February 2017 Available online xxx JEL classifications: L52 Q41 Q48 Q58 Keywords: Electricity consumption Residential sector Price elasticity Income elasticity Dynamic partial adjustment model

a b s t r a c t In recent years, price policies and price changes derived from environmental regulations have played a more important role to promote residential energy conservation. Using recent annual state-level panel data for 48 states, we estimate a dynamic partial adjustment model for electricity demand elasticities on price and income in the residential sector. Our analysis reveals that in the short run, one unit price increase will lead to 0.142 unit of reduction in electricity use after controlling for the endogeneity of electricity price. Thus, raising energy price in the short run will not give consumers much incentive to adjust their appliances to reduce electricity use. However, in the long run, one unit price increase will lead to almost one unit consumption reduction, ceteris paribus. In addition, we find new evidence that for states of higher per capita GDP, raising the electricity price may be more effective to ensure a cut in consumption. © 2017 Western Social Science Association. Published by Elsevier Inc. All rights reserved.

1. Introduction In the United States, residential buildings account for roughly 22% of primary energy consumption and over 37% of total electricity use.1 Their dominance in the total electricity use has made them a focus of efforts to reduce greenhouse gas (GHG) emissions2 and improve

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Sun), [email protected] (Y. Yu). 1 According to the 2015 Monthly Energy Review data and 2015 Electric Power Monthly data by the EIA, in 2014, the residential, commercial, industrial and transportation sectors account for 37.68%, 36.46%, 25.66% and 0.21% of total electricity use, respectively. 2 In the U.S., primary sources of GHG emissions include electricity production (approximately 67% of electricity comes from burning fossil fuels,

energy efficiency.3 During the last three decades, electricity demand in the residential sector has grown constantly,

mostly coal and natural gas), transportation (burning fossil fuel for cars, trucks, planes, ships and trains), industry, commercial and residential (burning fossil fuels for heat and other end uses), agriculture, land use and forestry. Among these factors, increasing residential demand for electricity, especially what people are using electricity for relative to what they used to use it for, e.g., moving to bigger houses, serves as an important component. For example, in 2014, the increase of GHG emissions was mainly due to cold winter conditions resulting in an increase in fuel demand, especially in residential and commercial sectors (EPA, 2016). 3 Energy efficiency is recognized as one of the lowest-cost options to reduce emissions. Climate mitigation scenarios with higher levels of energy efficiency show lower total costs. In an analysis of the costs of climate mitigation, Fraunhofer ISI (2015) demonstrated that a scenario with significant energy efficiency adoption was at least 2.5 trillion US dollars less costly by 2030 than other more energy-intensive mitigation scenarios. This sets the stage for greater prominence of energy efficiency in the

http://dx.doi.org/10.1016/j.soscij.2017.02.004 0362-3319/© 2017 Western Social Science Association. Published by Elsevier Inc. All rights reserved.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS

2

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

although the growth has slowed progressively since 1990’s due to energy efficiency investments. The annual energy outlook by the EIA predicted that considering extended policies, which includes additional rounds of appliance standards and building codes in the future, residential electricity use will continue to grow, by 0.2% per year from 2012 to 2040, spurred by population growth and continued population shifts to warmer regions with greater cooling requirements (Energy Information Administration, 2015). Aiming to reduce the GHG pollution and promote energy efficiency and conservation among consumers’ energy use,4 multiple policy instruments and stimulus projects have been implemented by government in recent years. In 2009, the Stimulus Bill urged by President Barack Obama allocated $27.2 Billion for energy efficiency and renewable energy research and investment. Moreover, as of June 2013, more than 25 states have fully-funded policies in place that establish specific energy savings targets (Energy Efficiency Resource Standard, EERS) that utilities or non-utility program administrators must meet through customer energy efficiency programs.5 Yet, in spite of cost-effective circumstances for energy saving improvements, projects and regulations are still far from being an obvious success. Proponents of government intervention believe that substantial market barriers prevent socially desirable levels of investment in energy efficiency, so it is unlikely that any future market structure for the utility industry will ameliorate these “market barriers to energy efficiency.” Ideally, homeowners would spontaneously make energy-efficiency investments in their homes, were they aware of future energy savings. In practice, it is often observed that consumers give up opportunities to make energy-efficiency investments. The literature on the so-called “rebound effect” holds that efficiency improvements can paradoxically lead to higher ¨ 2008). Potential explanations include energy use (Kristrom, consumers’ budget constraints, their uncertainty about energy prices in the future, lack of information in the energy market, high rates of intertemporal preferences, distrust in engineering estimates of the cost savings, and misplaced incentives (Alberini, Gans, & Velez-Lopez, 2011; Golove & Eto, 1996; Jaffe & Stavins, 1994; Metcalf & Hassett, 1999). Given the ambiguous effects of direct efforts for energy efficiency, more and more attention has been paid to price policies. Price changes derived from environmental regulations have played a more important role in energy conservation. Many previous studies find that policies aiming to promote renewable resources and reduce GHG emissions, including Renewable Portfolio Standards and

policy mix as governments work to achieve their contributions to the Paris Agreement in December 2015 (IEA, 2016). 4 According to the literature, policies for energy efficiency have been strengthened the most in the residential sector, suggesting this is a key factor driving improvements. From 2000 to 2015, increasing population and the move to larger dwellings have especially contributed to the increasing energy consumption in this sector (IEA, 2016). 5 The EERS requires that electric utilities achieve a percentage reduction in energy sales from energy efficiency measures. The strongest EERS requirements exist in Massachusetts and Vermont, which require almost 2.5% savings annually.

emissions trading schemes, raise economic costs and electricity prices (Fischer, 2006; Frondel, Schimidt, & Vance, 2012). In addition, with more rigid air quality standards and environmental regulations for power plants, there have been more beliefs that the cost of electricity delivered to final consumers is expected to increase. In general, the policy influence of increased electricity prices is twofold. Besides promoting energy conservation and reducing emissions, one other important effect of raising electricity rates is that it will inevitably affect the welfare of the household, with differentiated effects on different groups, such as consumers from states of relatively higher income levels versus from states of relatively lower income levels. Quantitatively assessing these policy effects requires good estimates of residential consumption responsiveness to the electricity price changes or price changes derived from regulation policies (for instance, the carbon emissions tax and the renewable percentage requirement). In this paper, using recent state-level panel data on residential electricity retail sales, revenue, average retail prices and residential natural gas prices from the Energy Information Agency (EIA), we estimate a dynamic partial adjustment model for residential electricity demand elasticities on price and income. Specifically, we estimate our model by applying the Bias Corrected LSDV (Alberini & Filippini, 2011; Kiviet, 1995) and the system GMM procedures (Blundell & Bond, 1998), and further instrument for both the lagged consumption and the price of electricity with lags. We further explore the electricity elasticities across states of different income levels. This would allow a clearer characterization of the different effects of a price increase and a price increase derived from regulations such as a carbon tax, on electricity consumption for groups of different income levels. Previous works have applied different methods to measure the responsiveness of residential electricity consumption to the price, and have produced a wide range of estimations (from zero to −1.30), with diverse types of data used (time-series, cross-sections and panel) in variant geographical levels and time periods covered. Existing studies can be broadly classified into one of three categories: (i) those based on national level time-series data (Dergiades & Tsoulfidis, 2008; Kamerschen & Porter, 2004); (ii) those using household-level data (Alberini et al., 2011) but typically involving imputed data or are constrained to geographically narrow regions or with some important information missing, and (iii) those based on state-level panel data or county-level panel data for a state (Alberini & Filippini, 2011; Bernstein & Griffin, 2005; Paul, Myers, & Palmer, 2009). This paper on residential electricity consumption using state-level panel data with dynamic partial adjustment model differs in several ways from the existing literature. First, we are using a more recent data set, the state-level residential electricity retail sales, revenue, average retail prices and residential natural gas prices from the EIA. In Alberini and Filippini (2011), their data cover the time period of 1995–2007, which is the most recent data in prior studies with dynamic panel data models. However, there are a number of important changes in the U.S. electricity

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

system after 2007. The American Clean Energy and Security Act of 2009 and The American Power Act of 2010 by the U.S. Congress established an economy-wide cap and trade program and created other incentives and standards for increasing energy efficiency and low-carbon energy consumption.6 Both these energy bills approve subsidies for new clean energy technologies and energy efficiency, require electric utilities to meet 20% of their electricity demand through renewable sources and energy efficiency by 2020 (EPA, 2009, 2010).7 These changes not only affect energy price to consumers, but also influence households’ consumption behavior. Previous studies find that policies including emissions trading schemes and Renewable Portfolio Standards which are usually done at the state level, raise residential electricity rates (Fischer, 2006; Frondel et al., 2012). Tightened environmental regulations on emissions are also expected to increase the price of energy to consumers (Basheda, Chupka, Fox-Penner, Pfeifenberger, & Schumacher, 2006). When prices increase, households tend to adjust their consumptions and choose less energyintensive appliances and dwellings (Webster, Paltsev, & Reilly, 2008). Fell, Li, and Paul (2014) conduct a policy study to simulate the U.S. Climate policy legislation H.R. 2454 (U.S. Congress, 2009), and the outcomes show that federal climate policy will engender a significantly greater reduction in electricity use when consumers are more price elastic. These changes, therefore, can yield a quite different result from analysis of previous data. In fact, the 2010 Annual Energy Outlook of the EIA adopts an electric elasticity of −0.30 in anticipation of improved consumer awareness resulting from smart grid projects,8 different from its historically employed price elasticity of −0.15 in the short run (EIA, 2010). Second, in order to solve the autocorrelation problem caused by the lagged electricity consumption on the righthand side of the demand equation, one method is to employ estimation techniques other than the LSDV (fixed effect) procedure. However, most of prior studies with dynamic panel models have not addressed or paid enough attention to this problem, which makes their estimates of the electricity demand elasticity questionable. In this paper, we adopt the Bias Corrected LSDV and the system GMM procedures to estimate our partial adjustment model. Because our data is relatively more recent with longer time period, this could improve the precision of our estimation. Last but not the least, one limitation of most above studies is that their analyses do not give enough attention to the electricity demand elasticity for different income groups, which is of great interest from a policy perspective. Regarding groups of relatively higher and lower income levels, for policy makers, a greater deal of interest should focus on: for which group the increase of electricity price will be more effective to ensure a cut in consumption, so that the price policy design may be heterogeneous accordingly across

6 Under the cap and trade program, the government sets a limit (cap) on the total amount of greenhouse gases that can be emitted nationally. 7 The American Clean Energy and Security Act of 2009 also sets a 17% target for emission reductions from 2005 levels by 2020. 8 These projects were funded under the American Recovery and Reinvestment Act of 2009.

3

states of different income levels. To address this problem, this Fseessler paper also estimates electricity elasticities for 21 states with very high income levels and for 19 states with very low income levels in our sample.

2. Model and methodologies 2.1. Modeling issues In the residential sector of the U.S., electricity and natural gas are the most important fuels used by households. 100% of the households use electricity, and natural gas is served for 60% of the households. In this study, we assume that a household combines electricity, natural gas and appliances for a composite energy commodity. The residential demand for electricity means the consumer’s demand is derived from the demand of heating, cooking, lighting and so on, and “can be specified using the basic framework of household production theory” (Alberini & Filippini, 2011). Assume the utility function of the representative household is formed as: U = U(N(E, G, CS), X ; Z, W), where E is electricity, G is gas, and CS is the capital stock of appliances. The composite energy service N = N(E, G, CS) is an argument. X is the aggregate consumption bundle. Z and W denote household characteristics and the weather in the residing area of the household, respectively. They both influence the utility function. The household utility is maximized subject to a budget constraint: Y = PN × N + X, where Y is the income, and the price of the composite energy service is PN . The price for aggregate consumption bundle is assumed as one. The long-run equilibrium demand of the household can be solved by the optimization problem. The Marshallian demand functions can be written as: E* = E*(PE , PG , PCS , Y ; Z, W), G* = G*(PE , PG , PCS , Y ; Z, W), CS* = CS*(PE , PG , PCS , Y ; Z, W), X* = X*(PE , PG , PCS , Y ; Z, W). Following the specification of Alberini and Filippini (2011), we further use a linear double-log form with income per capita, average electricity price, average price of natural gas (as the alternative fuel) and a number of socioeconomic factors as independent variables to specify the electricity demand. The basic model of electricity consumption is specified as, ln (Eit ) = ˇ0 + ˇPE ln (PEit ) + ˇPG ln (PGit ) +ˇINCOME ln (INCOMEit ) + ˇFS ln (FSit ) + ˇHDD ln (HDDit )

(1)

+ˇCDD ln (CDDit ) + vi + εi where Eit is the aggregate electricity consumption per capita in state i at year t, PEit and PGit are the real average price of electricity and the real average price of natural gas in state i at year t, respectively. INCOMEit is the per capita GDP in state i at year t. FSit is the household size or family size. HDDit and CDDit are the heating and cooling degree days in state i at year t. i is the state-fixed effect, which is controlled to eliminate unobserved statespecific effects, such us geography and demographics that may be correlated with independent variables and affect residential electricity demand.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS

4

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

This model is static in the sense that it assumes the representative household can instantly adjust both the use of electricity and the stock of appliances to new equilibrium values when price and income change. Hence, there is no difference for the consumption responsiveness to change of prices in the short run and long run. In practice, electricity demand changes when consumers are allowed to adjust their stock of appliances and make energy efficiency and conservation investments. Actual electricity consumption and the long-run equilibrium demand may not be the same during a period of time when households have not fully adjusted their capital stock. Following Alberini and Filippini (2011) and Houthakker (1980), a partial-adjustment model takes into account this situation. This model assumes that the change in log actual electricity demand between any two periods t − 1 and t is only some fraction () of the difference between the logarithm of actual demand in period t − 1 and the log of long-run equilibrium demand in period t. That is, the relationship is shown as ln(Et ) − ln(Et −1 ) = (ln(Et *) − ln(Et −1 )), where 0 <  < 1, and  is the partial adjustment parameter. The higher the value of  means the closer the change in log actual electricity consumption between two periods t − 1 and t is to the difference between the log of consumption in period t − 1 and the log of long-run equilibrium demand. This further implies that assuming there is an optimal though unobservable level of electricity demand, actual demand just gradually converges towards that optimal level between any two time periods. Assume the optimal (desired long-run equilibrium) electricity consumption can be expressed as Et ∗ = ˛(PE) (PG) eX , where  and  are the long-run elasticities with respect to the price of electricity and natural gas,9 and X is a set of variables including income per capita, climate, household characteristics, etc. Combining the above two equations and removing Et * by substitution, we have ln(Et ) − ln(Et−1 ) = ln(˛) + ln(PE) + ln(PG) + X − ln(Et−1 ), which forms the basis for the following regression model, ln (Et ) = ln (˛) + ln (PE) +ln (PG) + X + (1 − )ln(Et −1 ) + ε

(2)

Eq. (2) can be further written as (1/)[(ln(Et ) − ln(Et −1 )) + ln(Et −1 )] = ln(˛) + ln(PE) + ln(PG) + X + ε/, or ln(Et * ) = ln(˛) + ln(PE) + ln(PG) + X + ε/. From Eq. (2), the short-run price elasticities are the regression coefficients on log prices, whereas the long-run price elasticities can be obtained by dividing the coefficients on the log prices (short-run elasticities) by the estimate of .  can be calculated as 1 minus the coefficient on ln(Et −1 ). Therefore, the dynamic model of electricity consumption based on the partial adjustment hypothesis is formed

9 Assume the Marshallian demand function for electricity is Et∗ =  ˛(PE) (PG) eX , then  is the long-run elasticity with respect to the price

of electricity, because  =

∂E ∗ t

∂PE

·

PE E∗ t



= ˛(PG) · eX ·  · (PE)−1 ·

PE E∗

. Simi-

t

larly,  is the long-run elasticity with respect to the price of natural gas.

as, ln (Eit ) = ˇ0 + ˇE ln(Ei,t −1 ) + ˇPE ln (PEit ) + ˇPG ln (PGit ) +ˇINCOME ln (INCOMEit ) + ˇFS ln (FSit ) +ˇHDD ln (HDDit ) + ˇCDD ln (CDDit ) + i + εit

(3)

where Eit is the aggregate electricity consumption per capita in state i at year t. PEit and PGit are real average prices of electricity and natural gas in state i at year t, respectively. In the remainder of this paper, we estimate the basic and dynamic partial adjustment model, respectively, for the representative electricity residential consumer in the U.S. We will see the change in estimates of elasticites when alternative estimation methodologies are deployed for the dynamic partial adjustment model and the heterogeneous demand responsiveness for states of different income levels. 2.2. Estimation issues To estimate static panel data models of electricity demand, the fixed effects or random effects are often implemented to account for the unobserved individual effect that may or may not be correlated with regressors in the model. The corresponding estimation techniques that are often used are the LSDV (for the fixed effects model) and GLS (for the random effects model), respectively. However, to estimate dynamic panel data models, several econometric problems may arise, for instance, (i) the lagged dependent variable, ln(Ei,t −1 ), on the right-hand side gives rise to autocorrelation, which makes the LSDV and GLS estimators biased and inconsistent; (ii) simultaneity problems are present between the marginal electricity price and consumption since there is reverse causality between demand and price in Eqs. (1)–(3). For the first issue, we adopt properly both the Bias Corrected LSDV (Kiviet, 1995) and the system GMM (Blundell & Bond, 1998) to estimate our dynamic models. In these two rounds of estimation, the real average price of electricity, the real price of natural gas, GDP per capita, cooling degree days, heating degree days, and family size are treated as exogenous variables. for the second issue, we use the EIA reported average price of electricity to residential sectors, which is considered exogenous here. However, from previous studies (Alberini & Filippini, 2011; Fell et al., 2014; Uri, 1994), another problem, namely measurement error of prices, yet exists because of the way that the EIA calculates the electricity price used in our estimations. The measurement error makes state-level electricity prices endogenous.10 To solve this problem, Alberini and Filippini (2011) suggest a strategy to get around the measurement error problem. Suppose another measure of price can be found, which is also affected by the measurement error. Let pit be the true price and p* = pit + eit be the observed price, where eit is a classical measurement error with mean zero and constant variance. Assume rit * = pit + uit is the

10 Uri (1994) discussed problems arose from measurement error in the data on the estimated price elasticities of electricity demand in the US agricultural sector.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

5

Table 1 Descriptive statistics of variables (obs. = 768). Variable

Description

Mean

Std. dev.

Min

Max

E PE PG POP FS INCOME HDD CDD

Electricity consumption per capita (KWh per person) Price of electricity for the residential sector (1982–1984 dollars per KWh) Price of natural gas (1982–84 dollars per thousand cubic feet) Annual estimates of state population State population divided by state housing units State real GDP per capita (1982–1984 dollars per person) Heating degree days (base: 65 ◦ F) Cooling degree days (base: 65 ◦ F)

4,617.15 0.049 5.35 5.93e + 06 2.32 19,771.83 5,134.97 1,130.97

1,241.01 0.013 1.48 6.34e + 06 0.15 3,610.08 2,013.91 808.784

2,184.04 0.029 2.62 4.78e + 05 1.83 12,963.88 542 135

7,424.45 0.094 10.68 3.73e + 07 2.93 33,858.11 10,745 3,875

additional proxy for price, with the classical measurement error uit . Then the covariance between the two mismeasured prices can be shown to be the true price’s variance, Var(pit ). This can be used to correct the bias caused by the mismeasurement error of prices. Another efficient approach is to use rit * to instrument for p* and generate consistent estimated coefficient on p*. Therefore, in the third round of estimation, we decide to use lagged levels of electricity prices to instrument for the current level of electricity price by applying the Blundell–Bond system GMM to estimate the differenced form of Eq. (3). This makes the endogenous variable pre-determined and thus not correlated with the error terms in Eq. (3). 3. Data sources The analysis of this paper combines several different types of data set. The main data set we use is the state level data of electricity retail sales, revenue, average retail prices and residential prices of natural gas, which are provided by the Energy Information Agency. The annual estimates of the state population and housing units are obtained from the U.S. Census Bureau. The nominal GDP data by state is from the Bureau of Economic Analysis. We then convert the nominal GDP and prices into real GDP and prices by using the consumer price index provided by the Bureau of Labor Statistics. We calculate the typical size of a family by dividing the estimate of state population by the estimate of housing units in the state. The annual heating and cooling degree days in each state are calculated from the monthly degree day data of the National Climatic Data Center, National Oceanic and Atmospheric Administration. The degree day data are presently available for the 48 conterminous states with the District of Columbia treated as part of Maryland. We are now able to construct a panel dataset by compiling annual state level data in the United States from 1995 to 2010. We further drop Alaska and Hawaii due to their incomplete information on heating and cooling degree days. Table 1 presents summary statistics for 48 states from 1995 to 2010. The residential electricity price is a key variable in our analysis. The EIA provides the average retail price of electricity at the state level for the residential sector in the U.S., which is calculated by the EIA as the retail revenue of utilities for the residential sector divided by retail sales distributed to the residential sector. It is documented by utilities in the Form EIA-861, “Annual Electric Power Industry Report”.

In studies using household-level data, it is often theoretically assumed that households know their marginal rate structure and thus optimize their consumption by responding to marginal electricity prices (Herriges & King, 1994; Reiss & White, 2005). However, when using state level panel data, considering properties of residential electricity consumption, the assumption that consumers respond to marginal prices may not be appropriate for the average consumer.11 This has been demonstrated by many empirical studies (Borenstein, 2009; Ito, 2014; Paul et al., 2009; Shin, 1985). Many states experienced the transition from rate-of-return regulated electricity pricing to deregulated electricity markets since 1990’s. Paul et al. (2009) treat electricity prices largely determined by regulation and are thus exogenous in the demand function. They argue that for those states with ongoing rate-of-return regulation, prices of electricity from EIA database of utility sales and revenue are based on expectations of total costs and demand informed by data from past test years and are therefore contemporaneously exogenous. In addition, Borenstein (2009) also finds that comparing to the marginal price, the average price is a better indicator in estimating the response of households’ electricity consumption. Fig. 1 presents real average electricity prices and consumption quantities per person for seven states that have the largest number of population and housing units (California, Florida, Illinois, New York, Ohio, Pennsylvania and Texas). In Fig. 1, the electricity price changes over time for each state, and it differs a lot across states. Many states underwent the transition from regulated electricity pricing to deregulation of electricity markets since 1990’s. However, the provision and retail prices of electricity to the residential sector are supervised by the state public utility commission, and exogenous price caps are simultaneously stipulated.

11 There are two primary features of consumers’ behaviour in electricity consumption that need to be considered. First, it is not realistic that consumers can always keep track of or control their electricity use at any time point during a billing period. Even they can do so, it is still hard for them to optimize their consumption according to the marginal rate in reality. The second is that block tariffs are applied by many utilities, where the household’s actual quantity of electricity consumed determines the marginal price for this household. Knowing the rate structure based on an electricity bill is not that easy, since the bill usually arrives sometime after the consumption has been finished. Hence, consumers are often not very conscious of their rate structure or the marginal electricity price they face during a billing period (Fell et al., 2014).

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS

6

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

Table 2 Static model estimation results (dependent variable: ln(E)). Variable

ln(PE) ln(PG) ln(FS) ln(INCOME) ln(HDD) ln(CDD) Constant No. of obs.

FE(within)-LSDV

RE-GLS

Coefficient

t stat.

Coefficient

z stat.

−0.1714 0.0741 −0.8075 0.311 0.2265 0.0897 2.8437 768

−10.84 9.00 −11.25 13.46 12.34 11.59 9.41

−0.2079 0.078 −0.8497 0.257 0.1487 0.0982 3.8942 768

−11.67 8.22 −10.73 9.94 7.76 11.19 11.74

4. Estimation results We first provide results of the static model in Table 2. As expected, electricity prices contribute negatively to consumer’s consumption, with the fixed effect coefficient of −0.1714 and the random effect coefficient of −0.2079. The other estimated parameters also have the expected signs and are statistically significant. The fixed effect estimates and the random effect estimates are very close. The estimated coefficients on ln(PG) have the expected positive signs, which suggests there is a substitution relationship between electricity and natural gas. The coefficients on the family size variable indicate that more family members decline the electricity consumption for each person. The income elasticity of electricity consumption is 0.311 in the LSDV model and 0.257 in the GLS model. Our results are consistent with results in previous studies by Alberini and Filippini (2011), Borenstein (2009), and Ito (2014), where their electricity price elasticity estimates in regard to the average price range from −0.10 to −0.25. Next, we provide the estimation results of the dynamic partial adjustment models (Table 3). In the second and the third columns, we provide the conventional LSDV and the Bias Corrected LSDV model results. The estimates from the conventional LSDV are expected to be biased, and we still report it here for comparison reason. The fourth column presents results when using the system GMM model, where the lagged ln(E) is instrumented up to the third lag. The last column gives results from another version of the system GMM model where the electricity price is assumed to be endogenous with measurement error, and both the

lagged ln(E) and the electricity price variable are instrumented up to the second lag. In the second column of Table 3, although estimated parameters from the LSDV generally have expected signs and are statistically significant, we expect coefficients from this model to be biased and inconsistent, since the lagged dependent variable is correlated with the error term. As expected, estimates of price elasticity in the Bias Corrected LSDV model, the system GMM1 (when using the system GMM model to deal with the autocorrelation problem) and the system GMM2 (applying the Blundell–Bond system GMM to solve the measurement error problem) models show negative contribution of electricity prices to residential consumptions, which are all significant in the 5% significance level. The Bias Corrected LSDV produces a negative coefficient on the gas price variable, which is statistically insignificant. The other coefficients from the three models generally have expected signs and are statistically significant. In Table 3, we also notice that the Bias Corrected LSDV and the system GMM1 generate close estimates of the electricity price responsiveness, −0.0964 and −0.0732. Moreover, the absolute value of coefficients on the ln(PE) from the Bias Corrected LSDV and the system GMM1 are smaller than what is obtained from the system GMM2, −0.1421. These imply that the short-run price elasticities are close when using the Bias Corrected LSDV and the system GMM1 techniques, and they are smaller than the short-run elasticity generated from the system GMM2 technique by 32.16% and 48.49%, respectively. As we expect, a larger family size or more family members decline the electricity use for each person. Small households use more electricity per person than large families. Increasing the family size by one person results in a 13%–23% decline in the electricity consumption for a member of the family. Our estimated coefficients on ln(PE) are slightly smaller than the estimates in Alberini and Filippini (2011), and many of their estimated parameter on the gas price, per capita income and household size variables are not statistically significant in their experiment with the Blundell–Bond GMM technique. Because our data is relatively more recent with longer time period, this improves

Average Prices (1982-1984 $/KWh) 0.1

8000

0.08

Consumption Quantity (KWh per person)

6000

0.06 4000 0.04 2000 CA OH

FL PA

IL TX

NY 0

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

0

CA NY

FL OH

IL PA

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

0.02

Fig. 1. Average electricity prices and quantities for selected states.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model

ARTICLE IN PRESS

SOCSCI-1386; No. of Pages 10

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

7

Table 3 Dynamic model estimation results (dependent variable: ln(E)). Variable

LSDV

Bias corrected LSDV

System GMM1

System GMM2

Coefficient

z stat.

Coefficient

z stat.

Coefficient

t stat.

Coefficient

t stat.

Lagged ln(E) ln(PE) ln(PG) ln(FS) ln(INCOME) ln(HDD) ln(CDD) Constant

0.5789 −0.1358 −0.0269 −0.1952 0.0953 0.1146 0.0872

20.29 −9.77 −2.34 −3.18 4.94 7.27 13.87

0.8516 −0.0964 −0.0192 −0.1955 0.0979 0.1109 0.0940

10.63 −5.54 −1.56 −2.91 4.69 5.83 11.93

0.9224 −0.0732 0.0197 −0.1386 0.0197 0.0199 0.0324 −0.0293

32.29 −2.61 1.65 −3.07 1.70 3.52 7.04 −0.14

0.8576 −0.1421 0.0435 −0.2234 0.0327 0.0153 0.0395 0.2019

33.90 −4.87 2.91 −4.58 2.03 1.97 8.53 0.71

Year effects Hansen test AR(1) test AR(2) test

Yes

Yes

[0.000] [0.280]

[0.000] [0.280]

Yes [0.571] [0.000] [0.280]

Yes [0.905] [0.000] [0.230]

Notes: p values are reported in brackets.

the consistency of our estimation and produces more reasonable estimates. Now we are able to calculate the long-run price elasticities based on the coefficients on the lagged dependent variable (the estimated partial adjustment parameters). As analyzed in Section 2.1, when consumers are allowed to adjust their stock of appliances and make energy efficiency investments, the short-run own price elasticities are the regression coefficients on log prices, and the longrun own price elasticities can be determined by dividing short-run price elasticities by the estimate of one minus the coefficient on the lagged dependent variable. In Table 4, we present our estimates of price elasticities and income elasticities in the short run and long run, based on the consistent estimators in Table 3. In the short run, the estimated electricity price elasticity ranges from −0.073 to −0.142, which is much smaller comparing to the estimates in the long run. Thus, we can infer that consumers do not respond dramatically to price changes or price changes derived from regulation policies at least in the short run, which is expected (partly because people need time to change their appliances). Yet in the long run, a price change will affect residential electricity demand. The estimated long-run price elasticity ranges from −0.6493 to almost −1.0 when applying the three techniques. The Bias Corrected LSDV provides an own price elasticity of −0.6493, which is the smallest in terms of the absolute value among the three techniques. The corresponding estimate from the system GMM2 is −0.9972, of which the magnitude is larger than the other two, though it is close to the estimate in the system GMM1. These differences can be primarily explained by differences in the estimated coefficients of the lagged dependent variable. Since the measurement error of prices can make the state–level electricity price endogenous, and the electricity price variable is instrumented in the system GMM2 model, we consider the estimated coefficient from this technique to be the most reliable. The high magnitude of electricity price elasticity in the system GMM2 implies that in the long run, consumers do respond to price changes of electricity with declined consumption levels. The estimated partial adjustment parameter in the system GMM2 is 0.1424, which

suggests that the change in log actual electricity consumption between two periods t − 1 and t is 14.24% of the difference between the log of actual demand in period t − 1 and the log of long-run optimal demand in period t. Therefore, by making adjustment of stock of appliances and energy efficiency investments, consumers decline their electricity use with the increase of electricity prices derived from regulations such as an emissions tax and the consumers’ renewable quota obligation. Further, the higher electricity price induced from regulation policies gives consumers much incentive to adjust their stock of appliances and make energy efficiency investments, which makes their electricity consumption less. In Alberini and Filippini (2011), their estimated own price elasticities in the short term vary between −0.08 and −0.16, and long-term own price elasticities range from −0.43 to −0.73. Thus, we estimate a slightly smaller shortrun electricity price elasticity and a larger long-run price elasticity comparing to their result. Last, we examine the heterogeneous electricity demand responsiveness for states of different income levels, we further leave out 8 states (Arizona, Indiana, Iowa, Michigan, Ohio, Oregon, South Dakota and Wisconsin) whose GDP per capita are close to the sample median, and do two separate estimations for 21 states with very high income levels and for 19 states with very low income levels. We report results from the system GMM models in Table 5. Table 5 suggests that when using the system GMM1 technique, the short-run price elasticity is −0.0888 for states of very higher income levels and −0.0825 for states of very lower income levels. When applying the system GMM2 model, the short-run price elasticities for two respective groups of states are −0.1242 and −0.0723, respectively. The former is about 1.72 times the latter. The long-run price elasticities are calculated to be −0.9976 for states of higher income levels, and −0.8358 for states of lower income levels, based on results from the system GMM2. Since the measurement error of prices can make the state-level electricity price endogenous, and the electricity price variable is instrumented in the system GMM2 model, we still consider the estimated coefficient from this technique to be the most reliable.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS

8

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

Table 4 Short-run and long-run demand elasticities from the dynamic partial adjustment model. Bias corrected LSDV

Short run Long run

System GMM1

System GMM2

Price elasticity

Income elasticity

Price elasticity

Income elasticity

Price elasticity

Income elasticity

−0.0964 (0.0174) −0.6493 (0.2516)

0.0979 (0.0209) 0.6597 (0.2754)

−0.0732 (0.0280) −0.9427 (0.3646)

0.0197 (0.0116) 0.2539 (0.2346)

−0.1421 (0.0292) −0.9972 (0.1907)

0.0327 (0.0162) 0.2296 (0.1420)

Notes: standard errors are reported in parentheses.

Table 5 Dynamic model estimation results for states of different income levels (dependent variable: ln(E)). Variable

States of higher income levels System GMM1

States of lower income levels System GMM2

System GMM1

System GMM2

Coefficient

t stat.

Coefficient

t stat.

Coefficient

t stat.

Coefficient

t stat.

Lagged ln(E) ln(PE) ln(PG) ln(FS) ln(INCOME) ln(HDD) ln(CDD) Constant

0.9086 −0.0888 0.0321 −0.1189 0.0291 0.0217 0.0347 −0.1235

18.16 −2.10 2.49 −0.88 1.59 1.14 4.56 −0.24

0.8755 −0.1242 0.0480 −0.1612 0.0353 0.0146 0.0365 0.3633

38.52 −4.30 3.13 −1.86 1.78 1.04 5.57 0.12

0.9035 −0.0825 0.0089 −0.2140 −0.0091 0.0201 0.0399 0.4130

18.28 −1.81 0.35 −2.23 −0.35 1.72 5.89 0.78

0.9135 −0.0723 0.0071 −0.1938 −0.0106 0.0206 0.0386 0.3641

26.39 −1.99 0.27 −2.50 −0.48 2.04 5.87 0.91

Year effects Hansen test AR(1) test AR(2) test

Yes [1.000] [0.001] [0.365]

Yes [1.000] [0.000] [0.346]

Yes [1.000] [0.000] [0.500]

Yes [1.000] [0.000] [0.490]

Notes: p values are reported in brackets.

These results have several important implications. First, for states of higher income levels, more capital stock is as likely, and public and private savings could be higher because of consumption and price levels. For example, many states, like California, have public-benefit funds dedicated to promoting energy efficiency. These funds are usually funded through a mandatory service charge on consumer electricity bills or through mandatory contributions by utilities. The funds are then used for energy efficiency purposes, including lighting rebate and efficiency loan programs. Many states have also authorized Property Accessed Clean Energy (PACE) financing, allowing property owners to finance energy efficiency upgrades through assessments on their tax bill. Therefore, facing a price increase derived from regulations like an emissions tax or the consumers’ renewable quota obligation, consumers in rich states with more capital stock and savings could have more incentive to adjust their appliances and make energy conservation investments to decline electricity use. Second, states of relatively higher income levels are more price elastic than states of relatively lower income levels. Our results show that electricity demand of states of higher per capita GDP is about 1.72 times and 1.19 times more price-elastic when compared to states of lower per capita GDP in the short run and the long run, respectively. As income increases, people might make intra-fuel substitutions and switch from one heating system to another that is likely to be more efficient. They can afford to use combinations of energy and energy efficient capital ¨ 2008). goods as substitutes for the input of time (Kristrom, Thus, compared to states of relatively lower income levels, the stock of high efficiency appliances for households in

rich states could also be higher, which makes them more responsive to electricity price changes. For these states, raising the electricity price may be more effective to ensure a cut in consumption. Another useful insight from economic theory is that income encompasses many of the attitudinal factors and ¨ public awareness that affect demand (Kristrom, 2008). As income rises, the demand for environmental quality increases at a more-than-proportional rate (Turner & Hanley, 2011). In states where a large proportion of households have high awareness of environmental quality, they are more likely to invest in energy conservation as income increases.

5. Concluding remarks In this paper, using the recent annual state-level panel data for 48 states over 16 years, we estimate a dynamic partial adjustment model for electricity demand elasticities on price and income in the residential sector. The static model estimation shows that the income elasticity of electricity consumption varies between 0.257 and 0.311, and the price elasticity ranges from −0.17 to −0.21. These results are consistent with previous studies, where electricity price elasticity estimates in regard to the average price ranges from −0.10 to −0.25 (Alberini & Filippini, 2011; Borenstein, 2009; Ito, 2014). Prior works on residential energy demand with dynamic panel data models often use the LSDV (fixed effect) estimation and suffer from the endogeneity problem caused by the lagged demand on the right-hand side of demand equation. We estimate our model by applying the Bias Corrected

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

LSDV and the system GMM procedures and compare results generated by different techniques. In addition, though we use the average price of electricity for residential sector reported by the EIA, potential measurement error on the electricity price can make it econometrically endogenous. To address this problem, we further use a dynamic specification that instrument for both the lagged consumption and the electricity price with their lags within the system GMM estimation. We generally have three findings based on our estimation methodologies, compared with results in previous studies: First, results vary according to estimation techniques. Our analysis with the dynamic partial adjustment model reveals that in the short-run, price elasticities vary between −0.073 (system GMM1) and −0.142 (system GMM2), and income elasticities vary between 0.02 (system GMM2) and 0.098 (bias corrected LSDV). In the long run, price elasticities range from −0.65 (bias corrected LSDV) to −0.997 (system GMM2), and income elasticities range from 0.23 (system GMM2) to 0.66 (bias corrected LSDV). Changing the estimation methodology changes the estimated shortrun and long-run price elasticities by 48.49% and 53.58%, respectively. Second, consistent with the strategy in Alberini and Filippini (2011), the system GMM2 with the endogeneity of electricity price controlled is considered to be the “safest” and most reliable among the three estimation techniques used. Because our data is relatively more recent with longer time period, this improves the consistency of our estimation, comparing to results of Alberini and Filippini (2011). Our results reaffirm that ignoring the endogeneity of electricity price would understate responses to price changes. In fact, when the measurement error is corrected for by instrumenting for the lagged consumption and price, the demand is more price responsive in the long run, comparing to −0.7, a consensus on the long-run price elasticity in ¨ 2008). previous studies (Kristrom, Third, our results reveal that states of higher GDP per capita are 1.72 (1.19) times more price elastic than states of lower GDP per capita in the short run (long run). In general, for rich states, more capital stock is as likely, and public and private savings could be higher. Consumers in these states could have more incentive to adjust their appliances and make energy conservation investments to decline electricity use, facing the price increase derived from regulations. Compared to states of relatively lower income levels, the stock of high efficiency appliances for households in rich states could also be higher, which makes them more responsive to electricity price changes. In terms of policy implications, our findings based on the system GMM2, with the endogeneity of price controlled, suggest that even though consumers are not very price elastic in the short run, the impact of electricity price increase resulted from regulations on electricity use holds promise in the long run. Moreover, for states of higher income levels, raising the electricity price may be more effective to ensure a cut in consumption. Within an electricity system under environmental regulations to mitigate greenhouse gas emissions, the increase of electricity price can be obtained by the establishment of an emissions trading scheme or obliging the consumer’s renewable per-

9

centage requirement usually done at the state level (EPA, 2009, 2010). Under these situations, it is expected that an increase of the electricity price has an important impact on energy conservation and gains additional reductions in greenhouse gas emissions. This impact varies across states of different income levels, and may be stronger for rich states. Acknowledgements We thank an editor and anonymous referees for helpful comments and suggestions. We are also grateful for comments from Kevin Currier, Bidisha Lahiri, Keith Willett, Art Stoecker in Oklahoma State University, and the conference participants at the 33rd USAEE/IAEE North American Conference in Pittsburgh, PA. We acknowledge the publication support provided by the Overseas Publication Funding for Humanities and Social Sciences Research of East China Normal University (41300-542500-15301/003/061) and the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (13XNJ017). References Alberini, A., & Filippini, M. (2011). Response of residential electricity demand to price: The effect of measurement error. Energy Economics, 33(5), 889–895. Alberini, A., Gans, W., & Velez-Lopez, D. (2011). Residential consumption of gas and electricity in the U.S.: The role of prices and income. Energy Economics, 33(5), 870–881. Basheda, G., Chupka, M., Fox-Penner, P., Pfeifenberger, J., & Schumacher, A. (2006). Why are electricity prices increasing? An industry-wide perspective. Washington DC: Edison Foundation. Bernstein, M. A., & Griffin, J. (2005). Regional differences in the price elasticity of demand for energy. The RAND Corporation Technical Report. Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143. Borenstein, S. (2009). To what electricity price do consumers respond? Residential demand elasticity under increasing-block pricing. University of California-Berkeley Working Paper. Dergiades, T., & Tsoulfidis, L. (2008). Estimating residential demand for electricity in the United States, 1965–2006. Energy Economics, 30(5), 2722–2730. EIA (Energy Information Administration). (2010). Annual energy outlook 2010. Washington DC: Energy Information Administration. EIA. (2015). Annual energy outlook 2015. Washington DC: Energy Information Administration. EPA (Environmental Protection Agency). (2009). EPA analysis of the American Clean Energy and Security Act of 2009, H.R. 2454 in the 111th congress. tech. rep. U.S. Environmental Protection Agency. EPA. (2010). EPA analysis of the American Power Act in the 111th congress. tech. rep. U.S. Environmental Protection Agency, Office of Atmospheric Programs. EPA. (2016). Sources of greenhouse gas emisRetrieved on 12 December 2016 from sions.. https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emissions Fell, H., Li, S., & Paul, A. (2014). A new look at residential electricity demand using household expenditure data. International Journal of Industrial Organization, 33(1), 37–47. Fischer, C. (2006). How can renewable portfolio standards lower electricity prices? Resources for the Future Discussion Paper. Fraunhofer ISI. (2015). How Energy Efficiency Cuts for a 2-Degree Future.. Available at Costs www.climateworks.org/wp-content/uploads/2015/11/Report How-Energy-Efficiency-Cuts-Costs-for-a-2-Degree-Future.pdf Frondel, M., Schimidt, & Vance, C. (2012). Emissions trading: Impact on electricity prices and energy-intensive industries. Intereconomics, 47(2), 104–111. Golove, W., & Eto, J. (1996). Market barriers to energy efficiency: A critical reappraisal of the rationale for public policies to promote energy efficiency. Lawrence Berkeley Laboratory report. UC Berkeley.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004

G Model SOCSCI-1386; No. of Pages 10

ARTICLE IN PRESS

10

Y. Sun, Y. Yu / The Social Science Journal xxx (2017) xxx–xxx

Herriges, J., & King, K. (1994). Residential demand for electricity under inverted block rates: Evidence from a controlled experiment. Journal of Business and Economic Statistics, 12(4), 419–430. Houthakker, H. S. (1980). Residential electricity revisited. Energy Journal, 1(1), 29–41. IEA (International Energy Agency). (2016). Energy efficiency market report 2016. Paris: IEA/OECD Publishing. Ito, K. (2014). Do consumers respond to marginal or average price? Evidence from nonlinear electricity pricing. American Economic Review, 104(2), 537–563. Jaffe, A., & Stavins, R. (1994). The energy efficiency gap. What does it mean? Energy Policy, 22(10), 804–810. Kamerschen, D., & Porter, D. (2004). The demand for residential, industrial and total electricity, 1973–1998. Energy Economics, 26(1), 87–100. Kiviet, J. (1995). On bias, inconsistency, and efficiency of various estimations in dynamic panel data models. Journal of Econometrics, 68(1), 53–78. ¨ Kristrom, B. (2008). Residential energy demand. OECD Journal: General Papers, 2008(2), 95–115. Metcalf, G., & Hassett, K. (1999). Measuring the energy savings from home improvement investments: Evidence from monthly billing data. Review of Economics and Statistics, 81(3), 516–528.

Paul, A., Myers, E., & Palmer, K. (2009). A partial adjustment model of U.S. electricity demand by region, season and sector. Resources for the future discussion paper. Reiss, P., & White, M. (2005). Household electricity demand, revisited. Review of Economic Studies, 72(3), 853–858. Shin, J. (1985). Perception of price when price information is costly: Evidence from residential electricity demand. Review of Economics and Statistics, 67(4), 591–598. Turner, K., & Hanley, N. (2011). Energy efficiency, rebound effects and the environmental Kuznets curve. Energy Economics, 33(5), 709–720. Uri, N. (1994). The impact of measurement error in the data on estimates of the agricultural demand for electricity in the USA. Energy Economics, 16(2), 121–131. U.S. Congress. (2009). American Clean Energy and Security Act of 2009. H.R. 2454, 111th Congress. Webster, M., Paltsev, S., & Reilly, J. (2008). Autonomous efficiency improvement or income elasticity energy demand: Does it matter? Energy Economics, 30(6), 2785–2798.

Please cite this article in press as: Sun, Y., & Yu, Y. Revisiting the residential electricity demand in the United States: A dynamic partial adjustment modelling approach. The Social Science Journal (2017), http://dx.doi.org/10.1016/j.soscij.2017.02.004