Electricity Prices, Income and Residential Electricity Consumption

Transcription

1 Electricity Prices, Income and Residential Electricity Consumption Yanming Sun School of Urban and Regional Science East China Normal University August, 2015 Dr. Yanming Sun School of Urban and Regional Science, East China Normal University 3663, N. Zhongshan Rd., Shanghai, , China Phone: (86) , (86) Abstract In recent years, aiming to reduce the Greenhouse Gas pollution and promote energy efficiency and conservation among consumers energy use, price policies and price changes derived from environmental regulations have played a more important role. In this paper, using the most recent annual state-level panel data for 48 states, I estimate a dynamic partial adjustment model for electricity demand elasticities on price and income in the residential sector. My analysis reveals that in the short run, one unit price increase will only lead to unit of reduction in electricity use after controlling for the endogeneity of electricity price. Thus, raising the energy price in the short run will not give consumers much incentive to adjust their appliances and make energy conservation investments to reduce electricity use. However, in the long run, one unit price increase will lead to almost one unit consumption reduction when the endogeneity of electricity price is controlled. Therefore, in the long run, facing the higher electricity price induced from regulation policies, consumers are more likely to adjust their stock of appliances and make energy efficiency investments, which lowers their electricity consumption. In addition, we find new evidence that states of relatively higher income levels are more price elastic than states of relatively lower income levels in both the short run and long run. Thus, for states of higher per capita GDP, raising the electricity price may be more effective to ensure a cut in consumption. JEL Classification: L52, Q41, Q48, Q5 Keywords: Dynamic Partial Adjustment Estimation, Residential Electricity Consumption, Electricity Price, Income level I am deeply indebted to Dr. Kevin Currier for his support and helpful suggestions. I am very grateful to Dr. Keith Willett, Dr. Bidisha Lahiri and Dr. Art Stoecker for their comments. I also benefited from comments of participants of ECON seminar in Oklahoma State University. All errors are my own. ymsun@re.ecnu.edu.cn. 1

2 1 Introduction In the United States, residential buildings account for roughly 22% of primary energy consumption and over 37% of total electricity use. Their dominance in the total electricity use has made them a focus of efforts to reduce greenhouse gas (GHG) emissions and improve energy efficiency. 1 During the last three decades, electricity demand in the residential sector has grown constantly, 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, 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. 2 Yet, projects and regulations on the energy supply side are still far from being an obvious success. 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. Potential explanations for this paradox include consumers budget constraints, their uncertainty about energy prices in the future and their incomplete information in the energy market (Jaffe and Stavins, 1994; Alberini et al., 2011). Given the ambiguous effects of these direct efforts for energy efficiency, more and more attention has been paid to consumers electricity demand side. Further, price policies and 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 emissions trading schemes, raise economic costs and electricity prices (Fischer, 2006; Frondel et al., 2008). 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 two fold. 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 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 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. 2

3 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 the most 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. The LSDV (fixed effect) estimation is often applied in recent studies on residential energy demand with dynamic panel data models (Bernstein and Griffin, 2005; Paul et al., 2009). These studies do not pay enough attention to the autocorrelation problem caused by the lagged demand on the right-hand side of demand equation. In addition, simultaneity problems exist between the marginal electricity price and consumption. We use the EIA reported average price of electricity to the residential sector, which is considered exogenous in our model. However, previous studies have pointed out that the price of energy tends to suffer the measurement error, which can make the electricity price variable endogenous in the demand function (Alberini and Filippini, 2011; Alberini et al., 2011; Fell et al., 2012). To address these problems, we estimate our model by applying the Bias Corrected LSDV (Kiviet, 1995; Alberini and Filippini, 2011; Branas-Garza et al., 2011) and the system GMM procedures (Roodman, 2006; Alberini and Filippini, 2011; Branas-Garza et al., 2011), and further instrument for both the lagged consumption and the price of electricity with lags. We further study the electricity elasticities across states of different income levels, i.e., states of relatively higher income levels versus states of relatively lower income levels, by introducing a dummy variable and an interaction term in our model. 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 tried 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. Most of prior studies can be classified into one of three categories: (i) those based on national level time-series data; (ii) those using householdlevel data but typically involve 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. The first group of works includes studies of Kamerschen and Porter (2004) where the estimated electricity consumption responsiveness to the price ranges from to -0.94, and Dergiades and Tsoulfidis (2008), who estimate the elasticities to be and in the short run and long run, respectively. For the second group of works, some studies use nationwide dataset but with missing information for some important variables such as the household-level electricity consumption and price. Alberini et al. (2011) employ nationwide household-level data from the American Housing Survey for six periods up to 2007 and find strong household response to energy prices, both in the short run and long run. They compute the average price of certain utilities and impute the consumption of energy as expenditure divided by the average price. However, 3

4 due to the nonlinear pricing scheme usually employed in the retail of electricity, problems of simultaneity and measurement error can be caused by estimations from imputed data. Other studies employ household-level electricity billing information but are usually constrained to limited time periods or narrow geographic scope (Metcalf and Hassett, 1999; Reiss and White, 2005; Borenstein, 2009; Ito, 2012; Fell et al., 2012). In Reiss and White (2005), they use the electricity rate structure information of households in California based on the Residential Energy Consumption Survey (RECS) from the Department of Energy. Each household is matched up with the rate structure applied by the utility that serves in the area. Based on this, they estimate the choice of electricity consumption levels with a GMM model. In Fell et al. (2012), the household electricity demand is estimated with a new GMM strategy by using household-level data from the consumer expenditure survey and utility-level consumption data complementing individual billing data. Their estimated price elasticity is near Nevertheless, their study covers a relatively short period between 2006 and 2008 for only PSU (primary sampling unit) states. Given diversity of pricing structures across the nation and heterogeneity of households in different regions, it is difficult to apply the estimation method and results from specific areas to multiple areas or the whole country. The majority of the third group of studies have used state-level panel data and are differed from one another in the choice of average price or marginal price of electricity, in the time period of data and in the estimation technique. Among them, three studies (Bernstein and Griffin, 2005; Paul et al., 2009; Alberini and Filippini, 2011) based on recent panel data, with period until 2007, have found that in the short run at least, the residential electricity consumption is not very sensitive to the price change. Bernstein and Griffin (2005) examine whether the price elasticity for consumption of electricity and natural gas varies at the state and regional levels. Using the state-level panel data, they employ a partial adjustment model with state fixed effects and estimate electricity price elasticities to be in the short run and in the long run. Thus, they conclude that the electricity consumption in the residential sector is price-inelastic, which is consistent with results in prior studies. Paul et al. (2009) use a partial adjustment model of electricity demand that is estimated in a fixed-effects OLS framework, which allows for the price elasticity to be expressed in both its short-run and long-run forms. The data they use are a state-level panel of monthly observations from 1990 to 2006 that include electricity consumption and prices along with degree days and daylight minites that are assumed to drive consumption. Their estimated national, annual average short-run price elasticity is -0.13, and the long-run elasticity is Broadly consistent with earlier literature, they also find that demand for electricity is price inelastic in both the short run and long run. Since the partial adjustment model includes a lagged dependent variable, the LSDV (fixed-effect) estimates could be biased due to the correlation between lagged consumption and the state fixed effect. They address this problem by reestimating the model with a two-stage least squares method and employing lagged prices and past consumptions as instrumental variables. However, the result is unsatistying, so they just report the LSDV (fixed-effect) estimation results. Being different from the above two studies that use dynamic models with the LSDV (fixed-effect) procedure, 4

5 Alberini and Filippini (2011) have considered the autocorrelation problem caused by the lagged dependent variable and the potential endogeneity of the electricity price. Based on a state level panel data with annual residential energy demand from 1995 to 2007, they estimate with different estimation techniques for a partial adjustment model where the dependent variable is the state-level electricity demand per person. They experiment with bias-corrected LSDV and Blundell Bond GMM estimations, and also consider the situation when the price of electricity is endogenous due to measurement error. Their estimated elasticities range from to in the short term, and from to in the long term. So they get the conclusion that residential demand is not very elastic in the short term, but in the long term, it is relatively sensitive to the price change. This study on residential electricity consumption with dynamic panel data 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 , 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 system after The American Clean Energy and Security Act of 2009 and The American Power Act of 2010 by the U.S. Congress established a economy-wide cap and trade program 3 and created other incentives and standards for increasing energy efficiency and low-carbon energy consumption. 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 (Environmental Protection Agency, 2009; Environmental Protection Agency, 2010). 4 These changes can affect not only energy price to consumers, but also influence households consumption behavior. In addition, during 2008, with the increased delivered fuel costs for electricity generation, many states experienced an increase of electricity price. All these changes can yield a quite different result from analysis of previous data. Second, in order to solve the autocorrelation problem caused by the lagged electricity consumption on the right-hand 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. Although these techniques employed are similar to what Alberini and Filippini (2011) use, their estimated parameter on the gas price, per capita income and household size variables are not statistically significant in their experiment with the Blundle-Bond GMM technique. Most of our estimated coefficients are statistically significant, and we estimate a slightly smaller short-run price elasticity and a larger long-run price elasticity comparing to their result. Because our data is relatively more recent with longer time period, this improves the consistency of our estimation. Last but not the least, one limitation of most above studies is that their analyses do not give enough at- 3 Under the cap and trade program, the government sets a limit (cap) on the total amount of greenhouse gases that can be emitted nationally. 4 The American Clean Energy and Security Act of 2009 also sets a 17% target for emission reductions from 2005 levels by

6 tention to the electricity demand elasticity for different groups, for example, groups of different income levels. Understanding the different effects of a price increase on electricity consumption for groups of different income levels is especially interesting from a policy perspective, and it provides a clearer picture of what is driving the main results generated from the rise of price on electricity use. Regarding the group of relatively higher income levels and the group of relatively lower income levels, for policy makers, a greater deal of interest should focus on the followings: for which group the increase of electricity price will be more effective to ensure a cut in consumption; will it be necessary to design different volumes and rates in each block for each group? To address these problems, this paper also estimates the electricity elasticities across states of different income levels, i.e., states of relatively higher income levels versus states of relatively lower income levels. Our examination suggests that states of relatively higher income levels are more price elastic than states of relatively lower income levels. This result implies that for states of higher income, raising the electricity price may be more effective to ensure a cut in consumption. Consumers in states of higher GDP per capita may have more incentive to adjust their appliances and make energy conservation investments to decline electricity use, facing the price increase derived from regulations like an emissions tax and the consumers renewable quota obligation. Our analysis in this paper generally reveals that in the short run, one unit price increase will only lead to unit of reduction in electricity use after controlling for the endogeneity of electricity price. Thus, raising the energy price in the short run will not give consumers much incentive to adjust their appliances and make energy conservation investments to reduce electricity use. However, in the long run, one unit price increase will lead to almost one unit consumption reduction when the endogeneity of electricity price is controlled. Therefore, in the long run, facing the higher electricity price induced from regulation policies, consumers are more likely to adjust their stock of appliances and make energy efficiency investments, which lowers their electricity consumption. In addition, we find new evidence that consumption responsiveness associated with raising electricity prices vary across states of different income levels. The short-run price elasticity for states of higher income levels is , and for states of lower income levels is The long-run price elasticities are for states of higher income levels, and for states of lower income levels. Thus, for states of higher per capita GDP, raising the electricity price may be more effective to ensure a cut in consumption. The rest of this paper is organized as follows. Section 2 presents the model of residential electricity consumption we use. In Section 3, we provide description of data used and discuss estimation strategies. Section 4 presents the estimation results of the model, and Section 5 concludes. 2 The Model of Residential Demand for Electricity 2.1 Basic Model 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 6

7 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 derived from the demand of heating, cooking, lighting and so on, and can be specified using the basic framework of household production theory (Alberini and Filippini, 2011). Following the specification of Alberini and Filippini (2011), we 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 for the static model of electricity consumption. ln E it = β 0 + β P E ln P E, it + β P G ln P G, it + β Y ln(income it ) + β F S ln F S it +β HDD ln HDD it + β CDD ln CDD it + ν i + ε it (1) where E it is the aggregate electricity consumption per capita in state i at year t, P E, it and P G, it are the real average price of electricity and the real average price of natural gas in state i at year t, respectively. Income it is the per capita GDP in state i at year t. F S it is the household size or family size. HDD it and CDD it are the heating and cooling degree days in state i at year t. ν i is the state-fixed effect, which is controlled to eliminate unobserved state-specific effects, such us geography and demographics that may be correlated with independent variables and affect residential electricity demand. This model is static in the sense that it assumes the household can instantly adjust both the use of electricity and the stock of appliances to price and income changes. Hence, there is no difference for the consumption responsiveness to change of prices in the short run and long run. 2.2 Dynamic Partial Adjustment Model In practice, electricity demand changes when consumers are allowed to adjust their stock of appliances and make energy efficiency and conservation investments. Following Alberini and Filippini (2011) and Houthakker (1980), a partial-adjustment model lets consumers adjust their stock of appliances and energy efficiency investments. This model assumes that the change in log actual electricity demand between any two periods t 1 and t is only some fraction (λ) of the difference between the logarithm of actual demand in period t 1 and the log of long-run equilibrium demand in period t. This relationship is shown as follows: ln E t ln E t 1 = λ(ln E t ln E t 1 ) (2) where 0 < λ < 1, and λ is the partial adjustment parameter. The higher the value of λ 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, 7

8 actual demand gradually converges towards the optimal level between any two time periods. Assume the optimal (desired) electricity consumption can be expressed as Et = α PE σ P µ G exp(xγ), where σ and µ are the long-term price elasticities of electricity and natural gas, and X is a set of variables including income per capita, climate, household characteristics, etc. Substituting this expression into Eq. (2), we have the following equation: ln E t ln E t 1 = λ ln α + λσ ln P E + λµ ln P G + λxγ λ ln E t 1 (3) Re-arranging Eq. (3) and appending an econometric error term, the following regression equation is obtained: ln E t = λ ln α + λσ ln P E + λµ ln P G + λxγ + (1 λ) ln E t 1 + ε (4) Eq. (4) can be further written as 1 λ (ln E t ln E t 1 ) + ln E t 1 = ln α + σ ln P E + µ ln P G + Xγ + ε λ or ln E t = ln α + σ ln P E + µ ln P G + Xγ + ε λ. From Eq. (4), the short-run price elasticities are the regression coefficients on log prices, whereas the longrun price elasticities can be obtained by dividing the coefficients on the log prices (short-run elasticities) by the estimate of λ. λ can be calculated as 1 minus the coefficient on ln E t 1. Therefore, the dynamic model of electricity consumption based on the partial adjustment hypothesis is formed as: ln E it = β 0 + β E ln E i,t 1 + β P E ln P E, it + β P G ln P G, it + β Y ln(income it ) +β F S ln F S it + β HDD ln HDD it + β CDD ln CDD it + ν i + ε it (5) where E it is the aggregate electricity consumption per capita in state i at year t. P E, it and P G, it are real average prices of electricity and natural gas in state i at year t, respectively. 2.3 Heterogeneous Effects of Different Income Levels Since residential electricity consumption may have different patterns among states with different income levels, we examine this heterogeneous effect by estimating the following equation: ln E it = θ 0 + θ 1 ln E i,t 1 + θ 2 ln P E, it Rich it + θ 3 ln P E, it + θ 4 Rich it +θ 5 ln P G, it + θ 6 ln(income it ) + θ 7 ln F S it +θ 8 ln HDD it + θ 9 ln CDD it + ν i + ε it (6) where Rich it is a dummy variable that equals one if the GDP per capita of state i at year t is greater than the sample median of that year. The estimated coefficient of the interaction term between ln P E, it and Rich it captures the difference in price elasticity of the higher-income state compared with the lower-income state. Taking the state of relatively lower 8

9 income as the benchmark, the short-run price elasticity of the lower-income state is estimated by θ 3, and short-run price elasticity of the higher-income state is estimated by (θ 2 + θ 3 ). 3 Data and Estimation Issues 3.1 Data and Summary Statistics 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 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 Table 1: Descriptive Statistics of Variables Variable Description Mean Std. Dev. Min. Max. elec pc elec price gas price Electricity consumption per capita (KWh per person) Price of electricity for the residential sector ( dollars per KWh) Price of natural gas ( dollars per thousand cubic feet) population Annual estimates of state population e+07 family size State population divided by state housing units GDP pc State real GDP per capita ( dollars per person) HDD Heating degree days (base: 65 Deg F) CDD Cooling degree days (base: 65 Deg F) Lnelec pc Natural log of electricity consumption per capita Lnpe Natural log of residential electricity price Lnpg Natural log of residential natural gas price Lnfs Natural log of family size Lnincome Natural log of state real GDP per capita ( dollars per person) Lnhdd Natural log of HDD Lncdd Natural log of CDD Total Observations 768 9

10 The residential electricity price is a key variable in our analysis. The EIA provides the average retail price of electricity for the residential sector of all the states in the U.S., which is documented by utilities in the Form EIA-861, Annual Electric Power Industry Report. It is calculated as the retail revenue of utilities for the residential sector divided by retail sales distributed to the residential sector. Then why is it reasonable to use the average price of electricity here? In theory, it is often assumed that consumers know their marginal rate structure and thus optimize their consumption by responding to marginal electricity prices. However, this may be an unrealistic representation of consumers actual behavior in electricity markets. First, it is not realistic that consumers can always keep track of and 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 reason 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., 2012). With these properties of consumers behavior in electricity consumption, the marginal price may not be an appropriate measure for most consumers, whereas the average price has been shown to be a reasonable indicator, which has been demonstrated by many empirical studies. Shin (1985) investigates the consumer s perception of the electricity price under a declining block rate schedule. The empirical results support the hypothesis that consumers respond to average price perceived from the electricity bill rather than the marginal price whose information is costly. Many states experienced the transition from rate-of-return regulated electricity pricing to deregulated electricity markets since 1990 s. Paul, Myers and Palmer (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. Those states with the transition to electricity market restructuring simultaneously instituted exogenous rate caps. Hence, they regard average prices exogenous in their study. In addition, Borenstein (2009) finds a very smooth distribution of consumption levels where marginal rates increase. 5 He also finds that comparing to the marginal price, the average price is a better indicator in estimating the response of households electricity consumption. Using household-level monthly panel data of two utilities in California, Ito (2012) provides strong evidence that consumers sub-optimize their behavior by responding to average price rather than marginal or expected marginal price in nonlinear price schedules. 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. 5 If households respond to the marginal price of electricity, then in a block tariff pricing structure, there is expected to be a concentration of consumption levels just below the cut-off points for the change of price. However, the evidence from Borenstein (2009) is contrary to what this implies. 10

11 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. Figure 1: Average Electricity Prices and Quantities for Selected States 3.2 Estimation Issues When using panel data to estimate static electricity demand functions, 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 (the Least Square Dummy Variable, or the within estimator for the fixed effects model) and GLS (for the random effects model), respectively. However, several econometric problems may arise from estimating dynamic panel data models. (i) The lagged dependent variable, ln E i,t 1, on the right-hand side gives rise to autocorrelation, which makes the LSDV and GLS estimators biased and inconsistent. According to Kiviet (1995), the estimation is 11

12 asymptotically valid with lagged dependent explanatory variables only when the time dimension (T ) gets large, and the LSDV as well as the GLS estimators remain biased and inconsistent for large N and small T. In Judson and Owen (1999), they show a bias which equals as much as 20% of the true value of the coefficient of interest with a time dimension of 30. To cope with this problem, Kiviet (1995) suggests that to handle dynamic panel bias, one can perform LSDV and then correct results for the bias by removing a consistent estimate of this bias from the LSDV estimator, which is more efficient than various instrumental variable estimators. In addition, an alternative approach to solve this problem is to use first-differences and remove the fixed state-specific effects. First-differencing Eq. (5), it can be transformed into: ln E it = β E ln E i,t 1 + β P E ln P E, it + β P G ln P G, it + β Y ln(income it ) +β F S ln F S it + β HDD ln HDD it + β CDD ln CDD it + ν i + ε it (7) With ν i + ε it = (ν i ν i )+(ε it ε i, t 1 ), the fixed state-specific effect is swiped out, since it does not change over time. The first-differenced lagged dependent variable y i,t 1 is instrumented with y i,t 2 or y i,t 2 (Anderson and Hsiao, 1982). In fact, dependent variables with three or more lags can also be used as instruments so that more instruments than unknown parameters will be available (Branas-Garza et al., 2011). Using the differencing transform and the generalized method of moments (GMM), Arellano and Bond (1991) proposed an approach to obtain all possible instruments. Estimators are obtained using moment conditions between lagged values of the dependent variable (y i,t 2, y i,t 3,...) and ε it. These estimators are named as Arellano-Bond Difference GMM estimators. Arellano and Bond (1991) find their difference GMM estimators exhibit the smallest bias and variance comparing to OLS and within group estimators. Yet in practice, the Arellano-Bond estimator has been shown to be biased in small samples, and the bias increases with the number of instruments (Alberini and Filippini, 2011). Moreover, Judson and Owen (1999) find that the one-step GMM estimator outperforms the two-step estimation. In addition, there are two situations that the difference GMM estimator does not perform well. First, under heteroscedasticity, these estimators are robust but they are downward biased in regard to the approximation of standard errors (Arellano and Bond, 1991). Second, when we use time invariant regressors, the independent variable that does not change over time is eliminated, making this approach useless for estimation. Arellano and Bover (1995) proceeding Blundell and Bond (1998) proposed an alternative system GMM estimation. In this method, in addition to using Eq. (7) and implementing lagged levels of ln E it 1 as instruments of ln E it 1, the model is also stacked with the original equation (Eq. (5)) and the first difference ln E it 1 as instruments of ln E it 1. Hayakawa (2007) shows that in regard to the small sample bias, the system GMM estimator is less biased than the Arellano-Bond estimator. Moreover, Roodman (2006) and Branas-Garza et al. (2011) point out that the system GMM has the advantage that time-invariant variables can be included as 12

13 independent variables. The above mentioned estimators are applicable for panel dataset with large N and small T. In this paper, we have a situation of short time dimension (T = 16) and a modest state dimension which is considered fixed (N = 48). According to Judson and Owen (1999), Kiviet s corrected LSDV estimator for the parameter on the lagged dependent variable is better performed than the Anderson-Hsiao and the Arellano-Bond estimators, in balanced dynamic panels where T 20 and N 50. In addition, we have the time invariant dummy variable Rich in Eq. (6). Thus, considering the system GMM estimator s advantage in including time invariant variables as regressors, we adopt the Bias Corrected LSDV and the system GMM 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, CDD, HDD and family size are treated as exogenous variables. (ii) In Eq.s (1) to (6), simultaneity problems exist between the marginal electricity price and consumption because there is reverse causality between demand and price. We use the EIA reported average price of electricity to residential sectors, which is considered exogenous here. However, from previous studies (Uri, 1994; Alberini and Filippini, 2011; Fell et al., 2012), another problem - namely measurement error of prices yet exists because of the way that the EIA calculates the electricity price used in our estimations, which makes state-level electricity prices econometrically endogenous. 6 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 p it be the true price and p it = p it + e it be the observed price, where e it is a classical measurement error with mean zero and constant variance. Assume rit = p it + u it is the additional proxy for price, with the classical measurement error u it. Then the covariance between the two mismeasured prices can be shown to be the true price s variance, V ar(p it ). 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 it and generate consistent estimated coefficient on p it. Therefore, in our 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 Eq. (7). This makes the endogenous variable pre-determined and thus not correlated with the error terms in Eq. (5). 4 Estimation Results In this section, we discuss estimation results from the above models in details. Section 4.1 provides results from the static model. Section 4.2 discusses results obtained from the estimation of the dynamic partial adjustment model. Results and discussions on consumers responsiveness from states with different income levels to price changes are provided in Section Uri (1994) discussed problems arose from measurement error in the data on the estimated price elasticities of electricity demand in the US agricultural sector. 13

14 4.1 Static Model The estimation results for the static model are presented in Table 2. As expected, electricity prices contribute negatively to consumer s consumption, with the fixed effect coefficient of and the random effect coefficient of 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, and the price responsiveness from the within estimation is a little smaller than what the GLS estimation produces. The estimated coefficients on Lnpg have the expected positive signs, which suggests there is a substitution relationship between electricity and natural gas. Moreover, the estimated substitution effect of natural gas from the within estimation is slightly smaller than what it is in the GLS estimation. The coefficients on the family size variable indicates that more family members decline the electricity consumption for each person. The income elasticity of electricity consumption is in the LSDV model and in the GLS model. Our results are consistent with results in previous studies by Borenstein (2009), Alberini and Filippini (2011) and Ito (2012), where their electricity price elasticity estimates in regard to the average price range from to Table 2: Static Model Estimation Results (Dependent Variable: Lnelec pc) FE (within) - LSDV RE - GLS Variable Coefficient t stat. Coefficient z stat. Lnpe Lnpg Lnfs Lnincome Lnhdd Lncdd Constant No. of observations R square within R square between R square overall Dynamic Partial Adjustment Model Table 3 reports comparisons of estimation results in the dynamic partial adjustment model. In the second and the third columns, we provide estimation results from the conventional LSDV and the Bias Corrected LSDV. 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 Lnelec pc 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 Lnelec pc 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 14

15 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 and the system GMM2 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 addition, the p-value of the test statistic for the AR(1) process in first differences is significant, which means there is first-order autocorrelation. The p-values of the test for AR(2) process in first differences show that there is no significant autocorrelation in levels. The Hansen test of overidentifying restrictions has the null hypothesis that instruments as a group are exogenous. We can infer from p-values of the Hansen test statistic that the null hypothesis is not rejected, and instruments are valid. With a small N (N = 48) in our sample, in order to prevent the weak Hansen test, it is important to keep the number of instruments less than or equal to the number of groups. We try with further lags of the dependent variable as instruments but gets loss of efficiency. We finally use the second and third lags of the dependent variable as instruments for the lagged Lnelec pc in the system GMM1. In the system GMM2, we instrument for the lagged Lnelec pc with the second lag, and the electricity price is instrumented with the first and second lags. In Table 3, we also notice that the Bias Corrected LSDV and the system GMM1 generate close estimates of the electricity price responsiveness, and Moreover, the absolute value of coefficients on the Lnpe from the Bias Corrected LSDV and the system GMM1 are smaller than what is obtained from the system GMM2, 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% to 23% decline in the electricity consumption for a member of the family. Our estimated coefficients on Lnpe 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 Blundle-Bond GMM technique. Because our data is relatively more recent with longer time period, this improves the consistency of our estimation and produces more reasonable estimates. In order to calculate the long-run price elasticities, we need to look at the coefficients on the lagged dependent variable (the estimated partial adjustment parameters). The estimated coefficient of the lagged Lnelec pc in the Bias Corrected LSDV model is 47.1% larger than what it is in the conventional LSDV. The corresponding estimates in the Bias Corrected LSDV and two system GMM models are , and , which are very close. The value of estimate on the lagged Lnelec pc from the system GMM1 is 8.3% higher than the Bias Corrected LSDV estimate, and 7.6% higher than the system GMM2 estimate. The estimates of the partial 15

16 adjustment parameter from the three procedures are , and This means that the change in log actual electricity consumption between two periods t 1 and t is 7.76% to 14.84% of the difference between the log of actual demand in period t 1 and the log of long-run equilibrium demand in period t. Table 3: Dynamic Model Estimation Results (Dependent Variable: Lnelec pc) LSDV Bias Corrected LSDV System GMM1 System GMM2 Variable Coefficient z stat. Coefficient z stat. Coefficient t stat. Coefficient t stat. Lag Lnelec pc Lnpe Lnpg Lnfs Lnincome Lnhdd Lncdd Iyear 1995 Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Iyear Constant Hansen test (p-value) Arellano-Bond AR(1) test (p-value) Arellano-Bond AR(2) test (p-value) Now we are able to calculate the long-run price elasticities based on the above findings. As analyzed in the Section 2.2, when consumers are allowed to adjust their stock of appliances and make energy efficiency investments, the short-run self price elasticities are the regression coefficients on log prices, and the long-run self 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 to -0.15, 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 (for instance, the carbon emissions tax and the renewable percentage requirement) at least in the short run. Raising the energy price will not give them much incentive to adjust their 16