Uncovering state-level heterogeneity: The case of U.S. residential electricity demand

Transcription

1 Ohio University From the SelectedWorks of Daniel H Karney June 6, 2016 Uncovering state-level heterogeneity: The case of U.S. residential electricity demand Daniel H Karney Available at:

2 Uncovering state-level heterogeneity: The case of U.S. residential electricity demand Daniel H. Karney Department of Economics Ohio University Athens, OH June 2016 Abstract This paper employs recently developed panel estimators to uncover state-level heterogeneity in U.S residential electricity demand. The common correlated effect and cross-sectionally augmented distributed lag estimation procedures yield consistent state-specific elasticity estimates that are averaged to produce a national estimate. Allowing for state-level heterogeneity economically affects results; for instance, if residential electricity prices rise due to forthcoming U.S. climate policy, then calculated aggregate consumer surplus falls by 2-5 times more with statespecific elasticities compared to a single, national elasticity value. The empirical techniques highlighted can accurately measure heterogeneity in many settings with limited cross-sectional units but a large time dimension. JEL Codes: D2, Q4, Q5 Key Words: Residential electricity, Demand elasticity, Panel data, Heterogeneity, Common correlated effects, Consumer surplus address: [email protected]. I am grateful for comments and suggestions from Joshua Austin, Glenn Dutcher, and Harold Winter, and from the participants of the 2015 Heartland Workshop at the University of Illinois Urbana/Champaign. All mistakes are my own

3 -1-1 Introduction Accounting for heterogeneity can affect economic results both theoretically (e.g., Adner and Levinthanl (2001), Serfes (2005), Jackson and Yariv (2015)) and empirically (e.g., Heckman et al (2006), Petrin and Levinsohn (2012), Schaner (2015)). While this paper focuses on estimating residential electricity demand elasticities using aggregate panel data, the empirical techniques highlighted in this paper can accurately measure U.S. state-level heterogeneity underlying other economic issues as many prominent U.S. longitudinal data series are reported at the state level. Indeed, the empirical methodologies demonstrated in this analysis can uncover heterogeneity in a variety of settings using datasets with limited cross-sectional units but a large time dimension. The analysis here finds that net benefit calculations from pending U.S. climate change policy are affected when allowing for state-level heterogeneity in residential demand elasticities. 1 The Clean Power Plan (CPP) could be the first nationwide policy limiting carbon dioxide (CO 2 ) emissions from power plants in the United States (U.S. EPA, 2015). 2 Burtraw et al (2014) finds that achieving a comparable CO 2 emission reduction target to that of the CPP yields significant net benefits but requires increasing electricity prices by 2-9 percent. Their analysis highlights distributional effects and shows that residential consumers bear a large share of the burden in most policy scenarios. Indeed, the residential electricity sector s price responsiveness 1 The state-specific residential demand elasticity estimates presented in this paper can be used in disaggregated computational general equilibrium (CGE) models to perform policy analysis. However, comparing results from a CGE model with and without state-specific elasticities is beyond the scope of this paper. 2 Although pending legal challenges may delay or void CPP implementation, economists and policymakers are examining its potential impacts on the economy and environment, and calculating its net benefits (e.g., Bushnell et al, 2015).

4 -2- is an important factor in determining the CPP s net benefit and associated distributional effects. 3 In the context of climate policy, the long-run, own-price elasticity of demand is the relevant measure of consumer responsiveness. This paper provides new estimates of the long-run U.S. residential demand elasticity at both the state and national levels, and shows that accounting for state-level heterogeneity dramatically impacts aggregate consumer surplus loss when electricity prices increase relative to assuming a single, national demand elasticity. The new estimates are found by employing recently developed panel estimators designed for data structures similar to U.S state-level aggregate data; specifically, the common correlated effects (CCE) mean group estimator for static models (Pesaran, 2006) and the cross-sectionally augmented distributed lag (CS-DL) mean group estimator for dynamic models (Chudik et al, 2015). Critically, both estimators account for cross-sectional dependence from unobserved common factors. The estimation procedures yield consistent state-specific elasticity estimates that can be averaged to find a single, national elasticity estimate. The CCE and CS-DL approaches originated in the empirical macroeconomics literature to fit panel datasets with a limited number of cross-sectional units N along with a relatively large time T dimension. 4 Monte Carlo simulations demonstrate that CCE and CS-DL mean group estimators perform well under finite samples with reasonable minimum size guidelines for N and T (Pesaran, 2006; Chudik et al, 2015), and annual state-level data for the lower 48 U.S. states during the years match these criteria. The CCE and CS-DL mean group estimators also help address any lingering concerns about endogeneity due to simultaneity bias beyond the standard identifying assumptions that the average price is the relevant price for residential consumers (Ito, 3 In 2014, U.S. residential electricity customers purchased 37.4 percent of all retail sales (U.S. EIA, 2015). 4 See Eberhardt and Teal (2012) for a full discussion of so called macro-panel estimators.

5 ) and that the average state price is exogenous when examining state-level aggregate data (Alberini and Filippini, 2011). Neither the CCE nor CS-DL approaches have been used to estimate electricity demand elasticities. 5 The national elasticity estimates reported in this paper are at the low-end of prior estimates. Espey and Espey (2004) conduct a meta-analysis and report a sample mean of for U.S. long-run price elasticity with a range of -2.5 to Dahl (2011) surveys crosscountry estimates and finds as the average long-run elasticity with an inter-quartile range of to Paul et al (2009) uses a fixed-effect approach with U.S state-month data to estimate a dynamic model and reports a national elasticity value of for residential electricity demand (with regional values that range from to -0.14). Alberini and Filippini (2011) use a generalized method of moments (GMM) approach with U.S. state-year data for the years and their preferred dynamic specification yields a long-run elasticity value of Using a similar approach but with U.S. household-level data, Alberini et al (2011) reports a long-run, own-price electricity demand elasticity. Fell et al (2014) finds an elasticity of with household-level expenditure data also using a GMM approach. 6 This analysis shows that the CS-DL approach estimating a dynamic model yields a larger (i.e. more elastic) elasticity than the CCE approach estimating a static model. The preferred CCE specification has a national elasticity point estimate of with a 95 percent confidence 5 The CCE mean group estimator has been used in other literatures including the analysis of spatial housing prices (Holly et al, 2010; Holly et al, 2011), the cross-country environmental Kuznets curve (Arouri et al, 2012), and cross-country health care expenditures (Baltagi and Moscone, 2010). 6 Early work in this literature includes Halvorsen (1975), Taylor (1975), Houthakker (1980), Shin (1985), Flaig (1990), Kamerschen and Porter (2004), and Reiss and White (2005). See Alberini et al (2011) for a literature review of the contemporary literature.

6 -4- interval of [-0.185, ]. Meanwhile, the CS-DL approach leads to national elasticity estimates that have a mean for the set of six preferred specifications. Also, the range of state-specific elasticity estimates is larger for the CS-DL approach than the CCE approach, but the estimates in both cases are reasonable with no elasticity statistically greater than zero and no point estimate less than minus one. Allowing for different state elasticities, compared to assuming the same elasticity for all states, affects consumer surplus calculations when electricity prices rise as might occur under climate policy. Indeed, aggregate consumer surplus falls by 2-5 times (or $2-4 billion) more when allowing for heterogeneous elasticities across states relative to using a single, national elasticity value for all states assuming that electricity prices rise by a uniform percentage in all states. Furthermore, the gap increases as the range of the state elasticities increases. The methodology to calculate consumer surplus losses follows Borenstein (2012) and Davis (2014) by assuming a constant elasticity of demand functional form. The paper proceeds as follows. Section 2 discusses the full-adjustment and partialadjustment models that underlie the static and dynamic empirical specifications, respectively. Section 3 presents the data and reports results of empirical tests providing evidence for crosssectional dependence in the data. Section 4 provides results for the baseline fixed-effect approach and the CCE mean group estimator. Section 5 presents results using CS-DL mean group estimator under a wide range of specifications. Section 6 explores the consumer surplus implications of the heterogeneous elasticity estimates. Section 7 briefly concludes. 2 Theoretical Models The elasticity estimations are based on two theoretical models. The first model is the fulladjustment (FA) model derived from the long-run equilibrium conditions. The second model is the partial-adjustment (PA) model that assumes the capital stock adjusts slowly to changes in the

7 -5- electricity price. The long-run elasticity can be estimated with either the FA model or the PA models as the underlying theory Full-Adjustment Model Under standard utility maximizing assumptions, the household demand for electricity can be expressed as a function of the weather, exogenous household characteristics, income, and the prices of energy services. The set of energy prices includes the electricity price and the prices of substitutes (or complements) such as the natural gas price. 8 The full-adjustment (FA) model assumes a household can perfectly adjust both the electricity utilization and the stock of electricity-utilizing capital in response to price changes. Thus, the FA model describes the longrun equilibrium behavior of a household. Let E! be the long-run equilibrium quantity demanded for electricity at time t, such that: E! = E P!, I! ; Z, W! (1) where P! is a vector of energy prices, I! is household income, Z is a vector of exogenous, timeinvariant household characteristics, and W! is a vector of exogenous weather conditions. The FA model is static with no lagged variables appearing on the right-hand side. 2.2 Partial-Adjustment Model The partial-adjustment (PA) model does not assume that households can easily adjust the stock of electricity-utilizing capital. That is, the stock of capital in the short-run only partially adjusts to price changes, and thus leads to a divergence between the short- and long-run quantities. Expressed in terms of elasticities, this means that the short-run, own-price elasticity of demand 7 See Alberini and Filippini (2011) for a further discussion of both models. 8 In cold-weather states, natural gas heating is a substitute for electric heating.

8 -6- for electricity is smaller (i.e. less elastic) than the long-run elasticity. The PA model assumes that the difference in actual demand between periods t and t-1 is some fraction λ of the difference between the actual demand in period t-1 and the optimal long-run demand at time t. The model specifies the fractional difference in logarithms and thus the partial adjustment is formally defined as: ln E! ln E!!! = λ ln E! ln E!!! (2) where 0 < λ < 1 is an adjustment coefficient, E! and E!!! are the actual quantities of electricity demanded at time t and t 1, respectively, and E! is the long-run quantity demand from the FA model. Thus, the observed short-run difference on the left-hand side of equation (2) is smaller than the theoretical long-run difference on the right-hand side under full adjustment. 9 Next, following Alberini and Filippini (2011), assume the long-run electricity demand has the functional form E! = αp ρ! exp σv!, where ρ and σ are vectors of long-run parameters and V! = I! Z W!. Substituting the functional form assumption into (2) and rewriting yields: ln E! = α + λρ ln P! + λσv! + φ ln E!!! (3) with α = λ ln α and φ = 1 λ. Importantly, lagged electricity consumption appears on the right-hand side of equation (3) making it a dynamic model. The vectors λρ and λσ are interpreted as short-run elasticities. Thus, estimation of equation (3) directly provides the shortrun elasticities while the associated long-run elasticities are recovered by dividing the short-run elasticities by λ, which is one minus the coefficient of the lagged consumption variable. 9 Note that the PA model collapses to the FA model when λ = 1 or full-adjustment.

9 -7-3 Data This section details the data sources, provides summary statistics, and demonstrates crosssectional dependence between states with respect to electricity prices and quantities. On an annual basis the U.S. Energy Information Agency (U.S. EIA) collects and reports on a state-bystate basis total residential electricity sale receipts (i.e. revenue), electricity quantity purchased, number of residential customers, and average retail price paid by the residential customers. 10 This study uses all currently available state-level data covering the years The data are collected for the lower, contiguous 48 states and thus excludes the states of Alaska and Hawaii, and the District of Columbia. The sample has 1200 state-year observations. Other important data for control variables come from a variety of sources including: personal income (PI) by state (U.S. Bureau of Economic Analysis [BEA]); residential natural gas prices by state (U.S. EIA); population by state (U.S. Census); and, heating and cooling degreedays by state (National Oceanographic and Atmospheric Administration [NOAA]). Cooling and heating degree-days are measures of above and below a normal temperature, respectively. Specifically, cooling degree-days (CDD) for a given day are calculated as the average daily temperate minus 65 degrees Fahrenheit, where the average daily temperature is the mean of the daily maximum and minimum temperature, and so a large CDD number implies a hot day that requires cooling to maintain a normal temperature. An analogous, but reversed, definition applies to heating degree-days (HDD). The annual values for CDD and HDD are the sum of the daily values. Importantly, this particular NOAA degree-days data weights the dispersed weather station data by population to better represent the weather experienced by state residents. All 10 The U.S. EIA calculates the average price by dividing total revenue paid to utilities by the total quantity consumed.

10 -8- nominal prices are converted into 2014 dollars (2014$) using the All Items, =100, Consumer Price Index (U.S. Bureau of Labor Statistics [BLS]). Table 1 provides summary statics across states and years. In this time period, the average U.S. household consumed megawatt-hours (MWh) of electricity per year. In contrast to pervious work, this study interprets the number of residential retail customers as the number of households. Under this interpretation, the average state during the sample period had 2.37 million households with an average household size of 2.40 that is calculated dividing total population by the number of households. 11 Table 1 also reports electricity consumption on a per capita basis with the average person using 4.53 MWh per year. The average electricity price is cents per kilowatt-hour (2014$), although the minimum (7.05) and maximum (22.43) values demonstrate that residential electricity prices can vary greatly across states and time. The regressions below include four main control variables with the following mean values: $12.03 per 1000 cubic feet of natural gas; $95,604.0 real personal income per household; cooling-degree days; and, heating degree-days. [Insert Table 1 here.] Figure 1 plots the evolution of electricity consumption per household for the first ten states selected alphabetically (Alabama, Arizona, Arkansas, etc.), where the horizontal axis denotes the year and the vertical axis measures the natural log of consumption. Figure 1 demonstrates significantly more variation in consumption across states within a given year than within a state across years. The figure also suggests that per household electricity consumption 11 The average household size of 2.40 is close to the value other researchers find; for instance, Alberini and Filippini (2011) report that dividing population by the number of detached houses yields an average household size of 2.35 individuals for the contiguous 48 U.S. states during the years

11 -9- is increasing over time. Indeed, 42 of 48 states have a statistically significant, but unconditional, positive linear trend in consumption. 12 For the same ten states, Figure 2 plots the evolution of the real residential electricity price. Figures 1 and 2 have the same vertical axis log scale for comparability. Figure 2 demonstrates substantial within state price variation over the period. Furthermore, the price evolution is non-linear for many states as the real electricity price generally declines in the first half of the sample, but increases over the second half. Finally, it is clear the prices move together for some states due, in part, to regional electricity markets. [Insert Figure 1 here.] [Insert Figure 2 here.] The cross-sectional dependence test (or CD-test) from Pesaran (2004) formally checks if a variable exhibits cross-sectional dependence in a panel setting, where the null hypothesis is cross-sectional independence with the test statistic distributed N(0,1). The test is robust to nonstationarity and structural breaks. When applied to the consumption and price variables for the full dataset, the CD-test strongly rejects the null in both cases indicating cross-sectional dependence and a positive correlation. The cross-sectional dependence test statistic for the log of the price variable [ln(pr_elec)] is 83.7 with a correlation of 0.50, and the test statistic for the log of the consumption variable [ln(q_hh)] is similarly large at 77.9 with a 0.46 correlation. The main estimation techniques the CCE and CS-DL approaches take into account the cross- 12 For each state, the following estimation is performed: ConsumptionPerHousehold = α + τ Year. Linear trend statistical significance is evaluated using inference on τ and three additional states have statistically significant (unconditional) negative linear trends. However, many of the linear trends become statistically insignificant conditional on controls such as income.

12 -10- sectional dependence of the data and post-estimation application of the CD-test checks for crosssectional dependence of the residuals. 4 Static Specifications This section applies static techniques to estimate the full-adjustment model. Ordinary least square (OLS) estimation provides baseline results for a fixed-effects specification while the common correlated effect (CCE) approach is the preferred methodology. 4.1 Static Fixed-Effect Specification and Results Ordinary least square estimation provides baseline results. Let s = 1,, N index the crosssectional units (i.e. 48 states) and let t = 1,, T index time (i.e. years ), where the full fixed-effect specification is given: ln Y!" = α + β ln P!" + γx!" + δ! + ω! + η! t + ε!" (4) and, Y!" = Q!" HH!" (5) such that the dependent variable Y!" is the ratio of total electricity consumption Q!" divided the number of households HH!" by state s and year t. Recall the theoretical models are formulated with respect to household consumption. On the right-hand side, ln P!" is the natural log of the average residential electricity price. Thus, equation (4) comprises a standard log-log formulation, where β is the coefficient of interest and measures the long-run, own-price elasticity of electricity demand. This empirical specification fits a single elasticity common to all states. The matrix X!" provides additional time-varying controls with γ representing a vector of coefficients (with bold notation indicating a vector or matrix depending on context). The full specification in equation (4) includes state fixed effects δ! to control for time-invariant, state-

13 -11- specific characteristics, year fixed effects ω!, and state-specific linear time trends η!. The error ε!" is assumed random conditional on the covariates. In terms of the variables defined by Table 1, the dependent variable is given Y!" = Q_HH, and the right-hand side variables are given P!" = PR_ELEC and X!" = ln PR_GAS PI_HH CDD HDD. 13 Errors are clustered by state. Before reporting OLS regressions results, concerns regarding simultaneity bias in the demand-supply setting and the overall issue of identification must be addressed. To start, the average price is the relevant price for consumers in the residential electricity market (Ito, 2014). Next, the literature commonly employs the assumption that the average electricity price for statelevel aggregate data can be considered exogenous (Shin, 1985). As Alberini and Filippini (2011) observe, [The] potential for the [state average] price to be endogenous with consumption is mitigated by the presence of many different pricing levels and schemes at different locales. Therefore, if the state-average price is exogenous, then OLS yields unbiased estimates for the coefficient of interest β. However, if the endogeneity is not fully mitigated, then OLS estimates are biased, although the CCE approach in the next section addresses this concern. Table 2 reports the results from four OLS estimations. Panel A details results for the long-run elasticity estimate while Panel B reports the controls and summary information for each specification. Column (1) records an elasticity estimate in a specification with only state fixed effects and time-varying controls. 14 The coefficient is statistically significant with a t-statistic of and a 95% confidence interval (C.I.) of [-0.272, ]. The elasticity 13 The non-price variables in the control matrix are not log-transformed to coincide with the function form assumption in section 2.2. The main results are robust to log-transformations of the non-price controls as shown in the Online Appendix. 14 In contrast, a specification with neither controls nor fixed effects, the elasticity value is quite large (-0.769) and adding time-varying controls alone has little effect on the estimated value.

14 -12- estimation becomes slightly more negative when adding year fixed effects. Column (3) reports results for the full specification that includes state-specific linear trends. The full specification yields an OLS estimate of with a 95 percent C.I. of [-0.247, ] and has a within R 2 statistic of for 1200 state-year observations. However, column (4) shows that the coefficient estimate shrinks to when the observations are weighted by the average number of households by state over the sample period, and thus indicating that large states pull the estimate toward zero. Panel C demonstrates that control coefficients are stable across specifications with the exception of the natural gas price variable that become statistically insignificant when year fixed effects are included. Panel D reports the results of applying Pesaran (2004) s cross-sectional dependence (CD) test to the residuals and null hypothesis of independence is rejected for all but one specification. [Insert Table 2 here.] 4.2 CCE Model Before providing the specification for the common correlated effect (CCE) mean group estimator, the basic model underlying the CCE estimations that follows assumes: ln Y!" = β! ln P!" + u!" (6) where u!" = α!! + θ!! f!!! + e!" (7) ln P!" = α!! + θ! f!! + θ! f!!! + e!" (8) where Y!" and P!" are observable data on electricity consumption per household and average residential retail electricity prices, respectively. The model can also include a matrix of other observable, time-varying covariates X!" as controls, but omitted here for ease of exposition. Given the log-log setup in equation (6), then β! is directly interpreted as a long-run, own-price elasticity for state s. The unobservable u!" specified in equation (7) contains time-invariant

15 -13- heterogeneity α!! and a vector of time-dependent factors denoted f!! that are common across the cross-sectional units. The model allows for heterogeneous loading θ!! such that the common factors affect cross-sectional units differently. Importantly, f!! appears in both equations (7) and (8) accounting for endogeneity when a common factor influences both the price and quantity. As equation (8) shows, the electricity price is influenced by another vector! of common factors f! with heterogeneous loading that can also differ by cross-sectional unit θ!!!. Furthermore, some elements of the vector f! can appear in f! and thus a common factor can differentially influence price and quantity. Eberhardt and Teal (2012) point out a series of studies demonstrating that the common factors in the CCE model can be linear or nonlinear, stationary or non-stationary, and cointegrated or not cointegrated (Coakley et al, 2006; Kapetanios et al, 2011; Pesaran and Tosetti, 2011). The vectors of common factors are theoretically not limited in size despite remaining unobserved. These unobserved factors could represent many phenomena including countrywide macroeconomic shocks and local spillover effects from regionally integrated electricity markets. 15!! The terms e!" and e!" are assume to be random shocks. 4.3 CCE Specification The common correlated effect (CCE) mean group estimator introduced by Pesaran (2006) estimates the model in equations (6)-(8) but extended to include time-varying covariates. The CCE mean group estimation procedure generates consistent estimates for state-specific 15 The one caveat is that the CCE approach can only account limited number of strong common factors such as the Great Recession, but can still account for an unlimited number of small or weak common factors. See Eberhardt (2012) for a further discussion of the CCE model.

16 -14- elasticities β! and also yields an asymptotically unbiased estimate of a single, national elasticity value denoted β!!". The estimation proceeds as follows: (1) Run N auxiliary state-specific, augmented regressions using OLS with the specification for each state s given by: ln Y!" = α! + β! ln P!" + γ! X!" + κ! ln Y! + κ! ln P! + κ! X! + ε!" (9) where augmented means inclusion of the cross-sectional averages of the regressand and regressors as denoted by the bar notation and off set by parentheses. The resulting β! are consistent estimates of the state-specific elasticities. State-specific linear trends can be added to the auxiliary regression. 16! (2) Collect the β! estimates and calculate β!!" = 1 N!!! β!. Here, β!!" is an asymptotically unbiased estimate of a single, national long-run elasticity value, and, if relevant, a weighted average can be calculated. The coefficients of the augmenting regressors in equation (9), denoted by the κ parameters, have no direct meaning but instead filter out the common correlated effects. Standard inference tests can be applied to both the β! estimates and β!!" estimate, and the CCE approach works well for samples such as N = 30 and T = 20. The CCE mean group estimator is robust to serial correlation and heteroskedasticity in the errors (Pesaran, 2006) The auxiliary regressions include state-specific intercepts that have a similar impact as state fixed effects in OLS specifications. That is, the auxiliary regressions account for within state variation only. 17 The asymptotic properties of panel estimators developed for microeconomic datasets generally require the number cross-sectional units to become large relative to a fixed time dimension. In contrast, the CCE and CS-DL mean

17 CCE Results Table 3 reports estimates of the single, national long-run elasticity value using the CCE mean group estimator. Panel A reports an un-weighted β!!" while Panel B reports a weighed average β!!" with the weights being the average number of total households by state over the observation period. In contrast to the OLS results, across all specifications the un-weighted and weighted elasticity estimates are similar and thus weighted results are omitted going forward. Without time-varying controls or state-specific trends, column (1) records a highly significant unweighted, long-run elasticity estimate of (where a z-statistic is reported since β!!" is an average of normal distributions). Column (3) reports the same un-weighted, long-run elasticity estimate as column (1) given a specification that includes state-specific trends. Columns (2) and (4) report results from specifications including the time-varying controls. Panel C records specification summary information while Panel D reports coefficient estimates for the additional controls. The covariate coefficients reported are similar to those from the OLS results and calculated in same manner as the main elasticity estimate. Importantly, including the timevarying controls leads to the residuals failing to reject the null of cross-sectional independence for the CD test (see Panel E), since they provide more information to filter out the unobserved common correlated effects. The full specification reported in column (4) yields an un-weighted, long-run elasticity estimate of with a 95 percent C.I of [-0.185, ] and it is the preferred CCE specification. Overall, the national estimates using the CCE approach is similar to the OLS estimates. [Insert Table 3 here.] group estimators have asymptotic properties derived allowing for N and T to jointly tend to infinity (Pesaran, 2006; Chudik et al, 2015).

18 -16- Unlike OLS estimates with the fixed-effect specification, the CCE approach allows for state-level heterogeneity. Figure 3 plots the state-specific, long-run elasticity estimates β! along the national elasticity estimate β!!" for the preferred CCE specification. The β! estimates are sorted most-to-least elastic and plotted with dots. The state-specific estimates range from to None of the positive elasticity estimates are statistically different from zero as the whiskers off each dot are the 95 percent confidence intervals by state. The national estimate of is denoted by the solid, horizontal line with the 95 percent C.I. marked by dashed lines, and 16 of the 48 state-specific elasticity point estimates fall within 95 percent C.I of the national estimate. [Insert Figure 3 here.] Figure 4 plots the state-specific elasticities for the preferred specification against the average annual cooling degree-days (CDD) for the sample period. The figure shows that the state-specific estimates do not appear to be systematically biased in an obvious manner as the five states with the most elastic estimates Washington (WA), Massachusetts (MA), Illinois (IL), Virginia (VA), and Alabama (AL) do not cluster geographically or with respect to the average annual CDD. A trend line is not statically significant if the outlier states of Arkansas (AR) and Florida (FL) are excluded. That is, electricity demand in hot states does not seem to be more inelastic than cool states. All state-specific elasticity estimates are available in the Online Appendix. [Insert Figure 4 here.]

19 CCE Robustness Year Ranges. Figure 5 shows that the national elasticity estimate is robust to different year ranges across specifications with and without state-specific trends (although the variance increases as the sample size decreases). The full dataset cover yielding 25 observations for each state. On Figure 5, the national elasticity point estimates from Table 3 columns (2) and (4) are plotted with the x and, respectively, above the 25 on the horizontal axis indicating all 25 years of data are included in the estimation. The x is for specifications without state-specific trends and the o is for specifications with state-specific trends, although all specifications include the time-varying controls. The vertical axis measures the elasticity value. Then, one can construct two 24-year ranges, and , given 25 years of data, and thus Figure 5 plots four national elasticity estimates above the 24 due to running two specification on two data subsets. This procedure is repeated and results plotted for three 23-year ranges, four 22-year ranges, and five 21-year ranges. The national elasticity estimate is similar for all year ranges. The Online Appendix reports additional robustness checks and demonstrates that overall results are not affect by outlier states, alternative covariate specifications, or consumption measured on a per capita basis. [Insert Figure 5 here.] 5 Dynamic Specifications This section applies dynamic techniques to estimate the partial-adjustment model. Lagged consumption is included as a regressor as required for the dynamic specifications. The dynamic fixed-effect specification gives baseline results while the cross-sectionally augmented distributed lag (CS-DL) approach provides the main results.

20 Dynamic Fixed-Effect Specification and Results The dynamic fixed-effect specification is given: ln Y!" = α + φ ln P!" + γx!" + δ! + ω! + η! t + φ ln Y!"!! + ε!" (10) where φ = 1 λ. Recall λ is the adjustment coefficient from the partial-adjustment model. The coefficient on ln P!" is designated φ and here interpreted as the short-run, own-price elasticity. A post-estimation calculation using the delta method yields the long-run, own-price elasticity β estimate; specifically, β = φ 1 φ. It is well known that OLS estimation of dynamic models with fixed effects yields biased estimates due to serial correlation (Nickell, 1981). Thus, bias correction techniques are applied to (some) estimations; specifically, the correction uses Bruno (2005) s approximations building on Kivet (1995) employing the Blundell and Bond (1998) GMM estimator. The specification in (10) does not allow for state-level heterogeneity. Table 4 columns (1) and (2) report uncorrected OLS estimates of equation (10) without and with state-specific trends, respectively. Columns (3) and (4) report results using the bias correction technique described above. All short-run elasticity estimates are smaller than the long-run elasticity estimates as expected, and similar for all specifications and estimation procedures with point estimates that range from to However, the long-run elasticities significantly differ across specifications; for instance, Panel B column (3) reports an elasticity estimate of while column (4) reports (with non-overlapping confidence intervals). Interestingly, the bias corrected estimates are similar to the uncorrected estimates, and all specifications and estimation procedures yield residuals that reject the null of cross-sectional independence. [Insert Table 4 here.]

21 CS-DL Specification Chudik and Pesaran (2015) extends Pesaran (2006) s CCE mean group estimator to a dynamic setting using the cross-sectionally augmented autoregressive distributed lag (CS-ARDL) approach. Similar to the CCE approach, the CS-ARDL approach controls for unobserved common factors using cross-sectional averages in auxiliary regressions as in equation (9), but also includes the lagged dependent variable. The CS-ARDL approach yields short- and long-run elasticity estimates in the same way as the estimation procedures in section 5.1; that is, the longrun estimate is post-estimation calculation using the short-run elasticity and coefficient of the lagged depended variable. However, the CS-ARDL approach still requires bias correction procedures and requires T 40 to yields reliable results (Chudik and Pesaran, 2015). Unfortunately, the data for this study are only observed annually for 25 years and this means the CS-ARDL approach is not viable. Fortunately, Chudik et al (2015) develops the cross-sectionally augmented distributed lag (CS-DL) approach and show that is yields reliable results when T 30 without the need for bias correction procedures. This analysis assumes that 25 observations per cross-sectional unit is close enough to T = 30 for the CS-DL approach to be viable. Also, the CS-DL approach is robust to serial error correlation and misspecification of the dynamics, while the CS-ARDL approach is not robust on these dimensions (Chudik et al, 2015). Also, the CS-DL approach does not limit the number of unobserved common factors controlled by the augmentation of the auxiliary regressions. One drawback of the CS-DL approach is that short-run elasticity cannot be recovered and instead the long-run elasticity is directly estimated, although this study focuses on estimating the long-run elasticity and so this downside is mitigated.

22 -20- As with the CCE mean group estimation procedure described in section 4.3, the CS-DL mean group estimator requires a two-step approach. To start, using OLS run N augmented auxiliary regressions with the specification for each state s given:!!! ln Y!" = α! + β! ln P!" + γ! X!" + δ!!" Δ ln P!,!!!!!!!!!!!!!!! + δ!!" ΔX!,!!!!!! (11) + κ!,!" ln Y!!!!!! + κ!,!" ln P!!!!!! + κ!,!" X!!! + ε!"!!! where again the coefficients on the cross-sectional averages κ have no direct interpretation but absorb the unobserved common factors (as in the CCE estimator). Meanwhile, the difference term parameters δ account for the short-run effects consistent with the partial-adjustment model. The coefficient of interest β! it still interpreted as the long-run, own-price elasticity of demand for state s. Chudik et al (2015) recommends setting n! equal to the integer part of T!!, so that T = 25 implies setting n! = 2. Also, Chudik et al (2015) set n = n! = n! and n! = 0. However, given five right-hand side variables the electricity price and four controls it is not possible follow these recommendations while including all the regressors due to insufficient degrees of freedom in the auxiliary regressions (even though n! = 0 is set to all specifications). As with the CCE estimation, collect the β! estimates from the auxiliary regressions and calculate! β!"#$ = 1 N!!! β! to find a single, national elasticity value. Chudik et al (2015) shows that the CS-DL approach yields consistent estimates for both β! and β!"#$. 5.3 CS-DL Results Tables 5a reports results for specifications setting n! = 2 such that that auxiliary regressions include two lags (but one control variable at most). With two lags the number of observations per cross-sectional unit falls to 23 and the simplest specification with no additional control

23 -21- variables still requires 8 regressors in the auxiliary regressions. In this case, the national elasticity estimate is with a 95% C.I. of [-0.347, ]. Column (2) - (5) then report results for specifications that each use one of the control variables and find statistically significant elasticity estimates with overlapping confidence intervals. Using the state-specific elasticity estimates underlying the results reported in column (1), Figure 6 mimics Figure 3 in plotting the state-specific elasticity estimates along with the national elasticity estimate (noting the figures are plotted with the same vertical scale for ease of comparison). The state-specific estimates are more dispersed and nosier under the CS-DL approach compared to the CCE approach. That is, the CS-DL approach yields a wider range of state elasticity estimates and fewer of the state-specific estimates fall within the 95 percent confidence interval of the national elasticity estimate compared to the CCE approach. [Insert Table 5a here.] [Insert Figure 6 here.] Tables 5b reports results for specifications again setting n! = 2 but now allowing for two control variables. The six columns come from the six combinations of two control variables from the pool of four. The CS-DL approach with three right-hand side variables, the electricity price and two controls, requires 20 regressors per auxiliary regression and thus leaves only three degrees of freedom. This small number of degrees of freedom accounts for the relatively low z- statistics across all specifications with one estimation yielding a non-significant point estimate. The root mean square errors are similar across all specifications and all but one set of residuals fails to rejects the null hypothesis of cross-sectional independence. Without a prior to select among the specifications, one can consider all six specifications reported in Table 5b as the set of preferred specifications using the CS-DL approach. The set has a range of point estimates from

24 to with a mean of , which is approximately twice the magnitude of the preferred CCE point estimate of Overall, the CS-DL approach estimating a dynamic model leads to long-run elasticity estimates that are large in magnitude than the CCE approach estimating a static model. The CS-DL results are also robust to alternate year ranges, outlier states, and alternative control transformations. [Insert Table 5b here.] 6 Consumer Surplus Implications The empirical results above show that elasticities for U.S. states vary and may be different than the national average. The exercise below demonstrates the potential importance of accounting for this heterogeneity. Given a uniform electricity price increase in all states, accounting for state-level heterogeneity leads to consumer surplus falling by 2-5 times (or $2-4 billion) more than when assuming a single, national elasticity. The methodology here follows Borenstein (2012) and Davis (2014) by assuming a constant elasticity of demand function with the form q! = A! p!!!, where q! is the total quantity demand in state s, p! is the state average electricity price, A! is a state-specific scale parameter, and β! is the state-specific elasticity. Let q!! be the observed quantity demanded for state s calculated as the average over the observation period ( ). Similarly, let p!! be the observed average electricity price (in real dollars) over the same period. Using the observed data and an estimated elasticity value, the state-specific scale parameter can be recovered by!! rearranging the demand function such that A! = q!! p!!!. The change in consumer surplus for each state s is then calculated by the integral:

25 -23- and evaluating the integral leads to:!!!! CS! = A! p!!!!! dp! (12) CS! = A! 1 + β! p!!!!!! p!!!!!! (13) where p!! > p!! and thus CS! < 0 for β! > 1. Here, p!! is set at 10 percent greater than p!! to reasonably approximate the electricity price increase expected under policies to limit carbon dioxide emission from U.S. power plants (Burtraw et al, 2014). A 5 percent difference is also evaluated. The level of consumer welfare loss increases with the price difference. The consumer surplus calculation is performed for six scenarios that vary with respect to assumptions about the elasticity values. Scenario A uses the state-specific elasticity values from the preferred CCE specification as plotted in Figure 3. The change in surplus is calculated for each state using equation (13) and then summed across all states to find the aggregate consumer surplus loss. Scenario B is similar to Scenario A, but the nine positive point estimates shown in Figure 3 are set to zero and thus yields a conservative welfare loss amount. 18 Scenario C sets all state elasticities equal to the national estimate from the preferred CCE specification; specifically, β! = for all s. Scenario D is similar to Scenario A, but uses instead the state-specific elasticity values from the CS-DL specification whose estimates are plotted in Figure 6, while Scenario E again sets positive point estimates to zero. Scenario F uses the national estimate from the same dynamic specification, see Table 5a column (1), and thus sets β! = for all s. 18 The demand scalars are elasticity specific and so the scalars are recalculated when the β! values change.

26 -24- Table 6 summarizes the results from the welfare calculations for each scenario given a uniform 5 or 10 percent increase in state prices. 19 Panel A provides information on the scenario details including information about the elasticity values, zero upper-bound criteria, and estimation approach used to determine the elasticity values. Panel B reports results for the 10 percent price increase while Panel C does so for the 5 percent price increase. In addition to the consumer surplus lost reported in dollars, the Herfindahl-Hirschman Index (HHI) provides a measure of loss concentration across states (where the HHI here ranges from zero to 10,000). [Insert Table 6 here.] For scenario A, the consumer surplus loss for a uniform 10 percent price increase in all states is almost $24 billion with an HHI value of 3,383 indicating a significant degree of concentration. While the $24 billion in surplus loss seems large, Burtraw et al (2014) report consumer surplus losses of $33 billion (in 2010 dollars) for a 9 percent price increase. However, the concentration of losses seems unreasonable with $12.5 billion coming from Florida and $5.5 billion attributable to Arkansas; that is, over 76 percent of the aggregate loss come from two states in Scenario A. This occurs because Florida, in particular, is a large state with a positive elasticity point estimate (although not statistically different than zero). Scenario B yields a much lower aggregate consumer surplus loss of $6.2 billion because the positive elasticity point estimates are set to the zero upper bound. Indeed the surplus loss in Florida shrinks to $1.2 billion when the zero elasticity bound is imposed. The HHI value also falls to 882 indicating relatively dispersed surplus losses across states. Scenario C has the smallest surplus loss using the static model estimates ($3.9 billion) with Scenario B s aggregate loss almost twice a large. 19 The assumption of uniform price increase in all states is employed for simplicity. Rather, the price increase from climate policy is likely to be different across states and a function of the demand elasticity.

27 -25- The relatively small aggregate loss with the single, national elasticity value arises because surplus loss is convex with respect to the elasticity value (as Figure 7 below demonstrates). Unsurprisingly, the single elasticity value leads to a lower HHI too. The 5 percent price increase results in Panel C mimic the pattern of results in Panel B, but with a lower absolute level of surplus loss due to the smaller price increase. Scenarios D-F find a similar pattern of results using elasticity results from the dynamic estimation procedure. However, the surplus losses in Scenario E are almost five times greater than Scenario F due to the greater range of state-specific elasticities generated by the CS-DL approach. The dollar value difference between scenarios B and C, and scenarios E and F, range from $2-$4 billion depending on the price increase and elasticity estimation approach. [Insert Figure 7 here.] Figure 7 plots aggregate consumer surplus loss for different average elasticity values using the methodology of Scenario C for a 10 percent uniform price increase. 20 In fact, the $3.9 billion in surplus loss from Scenario C is plotted for the elasticity value of Figure 7 demonstrates that aggregate consumer surplus change is a convex function with respect to changes in the elasticity value. Indeed, changes in the elasticity value have little effect on the magnitude of surplus loss when elasticity values are close to minus one. In contrast, small changes in the elasticity value have a large effect on the magnitude of surplus loss when the elasticity is close to zero. If all states were assigned a zero elasticity of demand, then the consumer surplus loss from a 10 percent uniform price increase is almost $15 billion, while the 20 The figure looks almost identical if the total surplus change is calculated using national aggregate consumption and average price instead of summing up changes in surplus on a state-by-state basis.

28 -26- surplus loss falls to $0.8 billion when then elasticity reaches -0.3 and it is lower than $0.1 billion for elasticities of -0.6 to Conclusion This study presents new estimates of the long-run, own-price elasticity of U.S. residential electricity consumers using annual aggregate state-level data, but employing state-of-the-art panel estimators designed for datasets with a limited cross-sectional units and a relatively large time dimension. Specifically, the common correlated effect (CCE) mean group estimator fits a static model (Pesaran, 2006), while the cross-sectionally augmented distributed lag (CS-DL) mean group estimator fits a dynamic model (Chudik et al, 2015). Both estimators have attractive features such as accounting for unobserved shocks common amongst the cross-sectional units (i.e. states) and allowing for state-level heterogeneity. Neither of these estimators previously has been employed to estimate the elasticity of demand for residential electricity. The preferred specification using the CCE mean group estimation yields a point estimate of with a 95 percent confidence of [-0.185, ]. The set of six preferred specifications for CS-DL mean group estimation has a range of to with a mean of Both estimation approaches yield elasticity estimates at the low-end of prior estimates. In additional, the estimators yield state-specific elasticities and considering this heterogeneity dramatically impacts consumer surplus calculations when electricity prices change uniformly across states. The statespecific elasticity estimates arising from the CCE and CS-DL approaches can be employed in disaggregated computational general equilibrium models and doing so would likely impact the quantitative and qualitative results relative to using a common elasticity value for all states. The estimation techniques can be applied to many other settings with limited cross-sectional units but a large time dimension to uncover underlying heterogeneity.

29 -27- References Adner, Ron and Daniel Levinthal (2001), Demand heterogeneity and technology evolution: Implications for product and process innovation, Management Science, 47(5): Alberini, Anna, and Massimo Filippini (2011), Response of residential electricity demand to price: The effect of measurement error, Energy Economics, 33(5): Alberini, Anna, Will Gans, and Daniel Velez-Lopez (2011), Residential consumption of gas and electricity in the U.S.: The role of prices and income, Energy Economics, 33(5): Arouri, Mohamed El Hedi, Adel Ben Youssef, Hatem M henni, and Christophe Rault (2012), Energy consumption, economic growth and CO 2 emissions in Middle East and North African countries, Energy Policy, 45: Baltagi, Badi H., and Francesco Moscone (2010), Health care expenditure and income in the OECD reconsidered: Evidence from panel data, Economic Modelling, 27(4): Blundell, Richard, and Stephen Bond (1998), Initial conditions and moment restrictions in dynamic panel data models, Journal of Econometrics, 87(1): Borenstein, Severin (2014), The redistributional impact of nonlinear electricity pricing, American Economic Journal: Economic Policy, 4(3): Bruno, Giovanni S. F. (2005), Approximating the bias of the LSDV estimator for dynamic unbalanced panel data models, Economics Letters, 87(3): Burtraw, Dallas, Josh Linn, Karen Palmer, and Anthony Paul (2014), The costs and consequences of Clean Air Act regulation of CO 2 from power plants, American Economic Review: Papers & Proceeding, 104(5):

30 -28- Bushnell, James B., Stephen P. Holland, Jonathan E. Hughes, and Christopher R. Knittel (2015) Strategic Policy Choice in State-Level Regulation: The EPA's Clean Power Plan, NBER WP#21259, Cambridge MA Chudik, Alexander, Kamiar Mohaddes, M. Hashem Pesaran, and Mehdi Raissi (2015), Long- Run effects in large heterogeneous panel data models with cross-sectionally correlated errors, Federal Reserve Bank of Dallas, Globalization and Monetary Policy Institute, Working Paper No Chudik, Alexander, and M. Hashem Pesaran (2015), Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors, Journal of Econometrics, 188(2): Coakley, Jerry, Ana-Maria Fuertes, and Ron P. Smith (2006), Unobserved heterogeneity in panel time series models, Computational Statistics & Data Analysis, 50(9): Davis, Lucas (2014), The economic cost of global fuel subsidies, American Economic Review: Papers & Proceeding, 104(5): Dahl, Carol A. (2011), A global survey of electricity demand elasticities, Paper presented at the 34 th IAEE International Conference: Institutions, Efficiency, and Evolving Energy Technologies, Stockholm School of Economics. Eberhardt, Markus (2012), Estimating panel time-series models with heterogeneous slopes, The STATA Journal, 12(1): Eberhardt, Markus, and Francis Teal (2012), Structural change and cross-country growth empirics, The World Bank Economic Review, 27(2):

31 -29- Espey, James A., and Molly Espey (2004), Turning on the lights: A meta-analysis of residential electricity demand elasticities, Journal of Agricultural and Applied Economics, 36(1): Fell, Harrison, Shanjun Li, and Anthony Paul (2014), A new look at residential electricity demand using household expenditure data, International Journal of Industrial Organization, 33(1): Flaig, Gebhard (1990), Household production and the short- and long-run demand for electricity, Energy Economics, 12(2): Halvorsen, Robert (1975), Residential demand for electric energy, The Review of Economics and Statistics, 57(1): Heckman, James J., Sergio Urzua, and Edward Vytlacil (2006), Understanding instrumental variables in models with essential heterogeneity, The Review of Economics and Statistics, 88(3): Holly, Sean, M. Hashem Pesaran, and Takashi Yamagata (2010), A spatio-temporal model of house prices in the USA, Journal of Econometrics, 158(1): Holly, Sean, M. Hashem Pesaran, and Takashi Yamagata (2011), The spatial and temporal diffusion of house prices in the UK, Journal of Urban Economics, 69(1): Houthakker, Hendrik A. (1980), Residential electricity revisited, Energy Journal, 1(1): Ito, Koichiro (2014), Do consumers respond to marginal or average price? Evidence from nonlinear electricity pricing, American Economic Review, 104(2): Jackson, Matthew O., and Leeat Yariv (2015), Collective dynamic choice: The necessity of time inconsistency, American Economic Journal: Microeconomics, 7(4):

32 -30- Kamerschen, David R., and David V. Porter (2004), The demand for residential, industrial, and total electricity, , Energy Economics, 26(1): Kepetanios, George, M. Hashem Pesaran, and Takashi Yamagata (2011), Panels with nonstationary multifactor error structures, Journal of Econometrics, 160(2): Kivet, Jan F. (1995), On bias, inconsistency, and efficiency of various estimators in dynamic panel data models, Journal of Econometrics, 68(1): Nickell, Stephen (1981), Biases in dynamic models with fixed effects, Econometrica, 49(6): Paul, Anthony, Erica Meyers, and Karen Palmer (2009), A partial adjustment model of U.S. electric demand by region, season, and sector, Resources for the Future Discussion Paper 08-50, Washington, D.C. Pesaran, M. Hashem (2004), General diagnostic tests for cross section dependence in panels, CESifo Working Paper #1229, Munich, Germany. Pesaran, M. Hashem (2006), Estimation and inference in large heterogeneous panels with a multifactor error structure, Econometrica, 74(4): Pesaran, M. Hashem, and Elisa Tosetti (2011), Large panels with common factors and spatial correlations, Journal of Econometrics, 161(2): Petrin, Amil, and James Levinsohn (2012), Measuring aggregate productivity growth using plant-level data, The RAND Journal of Economics, 43(4): Reiss, Peter C., and Matthew W. White (2005), Household electricity demand, revisited, Review of Economics Studies, 72(3):

33 -31- Schaner, Simone (2015), Do opposites detract? Intrahousehold preference heterogeneity and inefficient strategic savings, American Economic Journal: Applied Economics, 7(2): Serfes, Konstantinos (2005), Risk sharing vs. incentives: Contract design under two-sided heterogeneity, Economics Letters, 88(3): Shin, Jeong-Shik (1985), Perception of price when price information is costly: Evidence from residential electricity demand, Review of Economics and Statistics, 67(4): Taylor, Lester (1975), The demand for electricity: as survey, The Bell Journal of Economics, 6(1): U.S. Energy Information Agency [U.S. EIA] (2015); U.S. Environmental Protection Agency [U.S. EPA] (2015), Regulatory Impact Analysis for the Clean Power Plan Final Rule, Washington, DC.

34 -32- Tables and Figures Table 1: Summary Statistics Across States and Years ( ) Variable Description [Abbreviation] Unit Mean Std. Dev. Min. Max Electricity Consumption per Household [Q_HH] MWh/HH Electricity Consumption per Capita [Q_POP] MWh/POP Real Electricity Price Cents/kWh [PR_ELEC] (2014$) Real Natural Gas Price [PR_GAS] Real Personal Income (PI) per Household [PI_HH] Real Personal Income (PI) per Capita [PI_POP] $/1000ft 3 (2014$) $/HH (2014$) $/POP (2014$) , , , , , , , ,863.6 Cooling Degree Days [CDD] Count 1, ,799 Heating Degree Days [HDD] Count 5, , ,761 Households [HH] Millions Population [POP] Millions Household Size [HHSize] Count Notes: Data for contiguous U.S. states and thus excludes Alaska, Hawaii, and the District of Columbia. MWh equals megawatt-hour. kwh equals kilowatt-hour.

35 -33- Table 2: Static Fixed-Effects Estimates of Long-Run, Own-Price U.S. Residential Electricity Demand Elasticity ( ) [Dependent variable: ln(q_hh)] (1) (2) (3) (4) Panel A: Elasticity Estimate [ln(pr_elec)] t-stat % Confidence Interval [-0.272, ] [-0.398, ] [-0.247, ] [-0.200, ] Panel B: Controls and Summary Information State Fixed Effects Yes Yes Yes Yes Time-Varying Controls Yes Yes Yes Yes Year Fixed Effects Yes Yes Yes State-Specific Trends Yes Yes Weighting by # Households Yes Cross-sectional Units Observations Within R Panel C: Additional Covariate Estimates (Std. Err.) ln(pr_gas) 0.061*** (0.017) (0.039) (0.013) (0.014) PI_HH/ *** 0.020** 0.030*** 0.031*** (0.004) (0.008) (0.005) (0.006) CDD/ *** 0.118*** 0.115*** 0.117*** (0.011) (0.010) (0.006) HDD/ *** 0.034*** 0.041*** (0.005) (0.007) (0.003) Panel D: Cross-Sectional Dependence Test on Residuals (Un-weighted) [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value < Correlation Note: Standard errors clustered by state. *** Significant at 1% level ** Significant at 5% level * Significant at 10% level (0.006) 0.036*** (0.004)

36 -34- Table 3: Common Correlated Effect (CCE) Mean Group Estimates of Long-Run, Own- Price U.S. Residential Electricity Demand Elasticity ( ) [Dependent variable: ln(q_hh)] (1) (2) (3) (4) Panel A: Elasticity (Un-weighted) Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.248, ] [-0.187, ] [-0.244, ] [-0.185, ] Panel B: Elasticity (Weighted) Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.265, ] [-0.199, ] [-0.246, ] [-0.188, ] Panel C: Controls and Summary Information Time-Varying Controls Yes Yes State-Specific Linear Trend Yes Yes Cross-sectional Units Observations Root Mean Squared Error Panel D: Additional Covariate Estimates (Std. Err.) ln(pr_gas) (0.014) (0.012) PI_HH/ *** 0.022*** (0.006) (0.006) CDD/ *** 0.114*** (0.004) HDD/ *** (0.003) Panel E: Cross-Sectional Dependence Test on Residuals (Un-weighted) [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation *** Significant at 1% level ** Significant at 5% level * Significant at 10% level (0.006) 0.051*** (0.003)

37 -35- Table 4: Dynamic State Fixed-Effects Estimates of Short-Run (SR) and Long-Run (LR), Own-Price U.S. Residential Electricity Demand Elasticity ( ) [Dependent variable: ln(q_hh)] (1) (2) (3) (4) Panel A: Short-Run Elasticity Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.167, ] [-0.180, ] [-0.144, ] [-0.166, ] Panel B: Long-Run Elasticity Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.484, ] [-0.268, ] [-0.486, ] [-0.261, ] Panel C: Controls and Summary Information State Fixed Effects Yes Yes Yes Yes Time-Varying Controls Yes Yes Yes Yes Year Fixed Effects Yes Yes Yes Yes State-Specific Linear Trend Yes Yes Bias Corrected 1 Yes Yes Cross-sectional Units Observations Within R Panel D: Cross-Sectional Dependence Test on Residuals [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation Note: Standard errors clustered by state. 1 See section 4.1 for details on the bias correction procedure.

38 -36- Table 5a: CS-DL Estimates of Long-Run, Own-Price U.S. Residential Electricity Demand Elasticity ( ) with 2 Lags and Up to 1 Control [Dependent variable: ln(q_hh)] (1) (2) (3) (4) (5) Panel A: Elasticity Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.347, ] [-0.442, ] [-0.426, ] Panel B: Additional Covariates Included Yes Yes [-0.323, ] [-0.235, ] ln(pr_gas) PI_HH CDD Yes HDD Yes Panel C: Summary Information Total Observations Cross-sectional Units Cross-sectional Obs Regressors Root Mean Square Error Panel D: Cross-Sectional Dependence Test on Residuals [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation Table 5b: CS-DL Estimates of Long-Run, Own-Price U.S. Residential Electricity Demand Elasticity ( ) with 2 Lags and 2 Controls [Dependent variable: ln(q_hh)] (1) (2) (3) (4) (5) (6) Panel A: Elasticity Estimate [ln(pr_elec)] z-stat % Confidence Interval [-0.682, [-0.273, [-0.557, [-0.621, [-0.433, [-0.378, ] ] ] ] ] 0.058] Panel B: Additional Covariates Included ln(pr_gas) Yes Yes Yes PI_HH Yes Yes Yes CDD Yes Yes Yes HDD Yes Yes Yes Panel C: Summary Information Total Observations Cross-sectional Units Cross-sectional Obs Regressors Root Mean Square Error Panel D: Cross-Sectional Dependence Test on Residuals [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation

39 -37- Table 6: Consumer Surplus Changes for Difference Elasticity Scenarios Scenario: A B C D E F Panel A: Elasticity Value Varies by Varies by Varies by Varies by State State State State Zero Upper-Bound No Yes n/a No Yes n/a Estimation Approach CCE CCE CCE CS-DL CS-DL CS-DL Panel B: 10% Price Increase Consumer Surplus Loss ($ millions) 23, , , , , ,102.5 Loss Concentration (HHI) 3, , , Panel C: 5% Price Increase Consumer Surplus Loss ($ millions) 11, , , , , Loss Concentration (HHI) 3, , ,

40 -38- Figure 1: Natural Log of Residential Electricity Consumption per Household for 10 States ( ) Notes: The states plotted are the first 10 alphabetical states: Alabama (AL), Arizona (AZ), Arkansas (AR), California (CA), Colorado (CO), Connecticut (CT), Delaware (DE), Florida (FL), Georgia (GA), and Idaho (ID).

41 -39- Figure 2: Natural Log of Real State Average Residential Electricity Price (2014$) for 10 States ( ) Notes: The states plotted are the first 10 alphabetical states: Alabama (AL), Arizona (AZ), Arkansas (AR), California (CA), Colorado (CO), Connecticut (CT), Delaware (DE), Florida (FL), Georgia (GA), and Idaho (ID).

42 -40- Figure 3: State-Specific, Long-Run, Residential Electricity Demand Elasticities Ordered Lowest-to-Highest from Common Correlated Effect (CCE) Mean Group Estimation Using the Preferred Specification

43 -41- Figure 4: State-Specific, Long-Run, Residential Electricity Demand Elasticities Plotted by State Annual Average Cooling Degree Days (CDD) from Common Correlated Effect (CCE) Mean Group Estimation Using the Preferred Specification

44 -42- Figure 5: Common Correlated Effect (CCE) Mean Group Estimates of Long-Run, Own- Price U.S. Residential Electricity Demand Elasticity for Different Sub-Sample Year Ranges

45 -43- Figure 6: State-Specific, Long-Run, Residential Electricity Demand Elasticities Ordered Lowest-to-Highest from Cross-sectionally Augmented Distributed Lag (CS-DL) Mean Group Estimation with 2 Lags

46 -44- Figure 7: Aggregate Consumer Surplus Loss for Various Average Elasticity Values for a 10% Uniform Price Increase Across All States

47 -45- Online Appendix Other CCE Robustness Checks Outlier States. One concern is that outlier states may be disproportionately impacting the national elasticity estimate. To check for this concern, the preferred CCE specification is rerun 48 times leaving out one state each time. These 48 leave-one-state-out estimations yield a range of national elasticity point estimates given by [-0.152, ] with similar standard errors. Thus, the full sample point estimate of reported in Table 3 column (4) is robust to outlier states since the CCE mean group estimate β!!" is the average of 48 state-specific estimates. Alternative Specifications. The results in Table 3 come from estimations that use the control matrix X!" = ln PR_GAS PI_HH CDD HDD when time-varying controls are included as regressors. Table A-1 starts with column (1) reporting all coefficient estimates from the preferred specification and corresponding to the result in Table 3 column (4). Note that the first row of Panel B provides an alternate representation of the result in Panel A. However, the literature often uses log-transformations of all control variables. Column (2) shows that the elasticity estimate is stable given the log-transformation for all control variables. The signs and statistical significance of the control variable coefficients are similarly stable. However, the residual fail the CD-test in that the null hypothesis of cross-sectional independence is rejected (see Panel D). Column (3) keeps the non-price controls in levels and adds quadratic terms. In this case, the elasticity estimate rises in magnitude to but interestingly the income controls are non-significant. Finally, column (4) reverts to the specification of column (1) but uses the lagged electricity price. This lagged specification yields an estimate of and thus provides suggestive evidence that household respond more to the current-year price rather than the previous-year price (although the confidence intervals overlap).

48 -46- [Insert Table A-1 here.] Per Capita Estimation. The literature commonly estimates elasticities with aggregate variable such as electricity consumption converted into per capita measures. This study differs from many pervious studies by employing per household normalization despite the fact that the household is the decision-making unit for consumption. The specifications from Table 3 are rerun using per capita measures, where now Y!" = Q_POP and X!" = ln PR_GAS PI_POP CDD HDD. The additional regressor ln HHsize is included in all specifications where HHsize is the average household size by state and year. Table A-2 reports the per capita national elasticity estimate in Panel A and the household size elasticity in Panel B. Column (4) is the preferred specification that includes the time-varying trends and state-specific trends. For the preferred specification in column (4), the elasticity per capita yields a slightly smaller elasticity estimate of compared to the per household specification estimate of reported in Table 3, although the 95 percent confidence intervals overlap to a large degree. The household size elasticity is negative as expected since multiple individuals can share common benefits of electricity consumption (e.g. lighting). The point estimate of in column (4) is similar to the results in Alberini and Filippini (2011). [Insert Table A-2 here.] The derivation below shows the household and per capita specifications equivalently identify the long-run, own-price electricity demand elasticity. Let (A.1) represent a household normalized specification given by: ln Q_HH = α + β ln PR_ELEC + γ PI_HH (A.1)

49 -47- where, the consumption and income variables are normalized by household counts. The coefficient of interest is β and note that equation (A.1) is a simplified version of equation (4) with the error term omitted. Next, observe that total population is equal to the number of households times the average household size; that is POP = HH HHsize. Thus, (A.1) can be rewritten as: ln Q POP + ln HHsize = α + β ln PR_ELEC + γ HHsize PI POP (A.2) and then moving ln HHsize to the right-hand side yields: ln Q_POP = α + β ln PR_ELEC + γ PI_POP + δ ln HHsize (A.3) where γ = γ HHsize and δ is the coefficient on the household size variable. Since ln HHsize is moved from the left-hand side of (A.3) to the right-hand side, then it is expected that δ < 0 (as found in Table 5). Importantly, the transformation between per household specification in (A.1) to the per capita specification in (A.3) does not affect the identification of β.

50 -48- Table A-1: Common Correlated Effect (CCE) Mean Group Estimates of Long-Run, Own- Price U.S. Residential Electricity Demand Elasticity ( ) with All Covariate Coefficients and Alternate Controls [Dependent variable: ln(q_hh)] (1) (2) (3) (4) Panel A: Elasticity Estimate z-stat % Confidence Interval [-0.185, ] [-0.292, ] [-0.238, ] [-0.124, ] Panel B: Covaraite Coefficient Estimates (Std. Err.) Ln(PR_ELEC) Lag Ln(PR_ELEC) *** (0.024) *** (0.024) *** (0.033) Ln(PR_GAS) (0.012) (0.011) (0.021) PI_HH/ *** (0.005) (0.091) (PI_HH/10000) (0.005) CDD/ *** 0.074* (0.006) (0.039) (CDD/1000) (0.035) HDD/ *** 0.099** (0.003) (0.045) (HDD/1000) ** (0.006) Ln(PI_HH) 0.213*** (0.052) Ln(CDD) 0.111*** Ln(HDD) (0.135) 0.223*** (0.016) Panel C: Summary Information *** (0.017) * (0.011) 0.024*** (0.005) 0.110*** (0.007) 0.055*** (0.003) Cross-sectional Units Observations State-Specific Linear Trend Yes Yes Yes Yes Root Mean Squared Error Panel D: Cross-Sectional Dependence Test on Residuals [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation *** Significant at 1% level ** Significant at 5% level * Significant at 10% level

51 -49- Table A-2: Common Correlated Effect (CCE) Mean Group Estimates of Long-Run, Own- Price U.S. Residential Electricity Demand Elasticity ( ) Using Per Capita Normalization [Dependent variable: ln(q_pop)] (1) (2) (3) (4) Panel A: Elasticity Estimate z-stat % Confidence Interval [-0.253, ] [-0.151, ] [-0.292, ] [ ] Panel B: ln(hhsize) Coefficient Estimate z-stat % Confidence Interval [-1.086, 0.369] [-1.041, ] [-0.932, 0.039] [-1.109, ] Panel C: Controls and Summary Information Time-Varying Controls 1 Yes Yes State-Specific Linear Trend Yes Yes Cross-sectional Units Observations Root Mean Square Error Panel D: Cross-Sectional Dependence Test on Residuals [H 0 : Cross-Sectional Independence ~N 0,1 ] z-stat p-value Correlation Time-varying controls include: log of real natural gas price, personal income per household, and the count of heating and cooling degree days.

52 -50- Table A-3: State-Specific Elasticity Estimates from Preferred CCE Specification State Elasticity Std. Err. 95% C.I. Low 95% C.I. High Alabama (AL) Arkansas (AR) Arizona (AZ) California (CA) Colorado (CO) Connecticut (CT) Delaware (DE) Florida (FL) Georgia (GA) Iowa (IA) Idaho (ID) Illinois (IL) Indiana (IN) Kansas (KS) Kentucky (KY) Louisiana (LA) Massachusetts (MA) Maryland (MD) Maine (ME) Michigan (MI) Minnesota (MN) Missouri (MO) Mississippi (MS) Montana (MT) North Carolina (NC) North Dakota (ND) Nebraska (NE) New Hampshire (NH) New Jersey (NJ) New Mexico (NM) Nevada (NV) New York (NY) Ohio (OH) Oklahoma (OK) Oregon (OR) Pennsylvania (PA) Rhode Island (RI) South Carolina (SC) South Dakota (SD) Tennessee (TN) Texas (TX)

53 -51- Utah (UT) Virginia (VA) Washington (WA) West Virginia (WV) Wisconsin (WI) Wyoming (WY) National Source: Authors calculations.

54 -52- Table A-4: State-Specific Elasticity Estimates from CS-DL Specification with 2 Lags and No Controls State Elasticity Std. Err. 95% C.I. Low 95% C.I. High Alabama (AL) Arkansas (AR) Arizona (AZ) California (CA) Colorado (CO) Connecticut (CT) Delaware (DE) Florida (FL) Georgia (GA) Iowa (IA) Idaho (ID) Illinois (IL) Indiana (IN) Kansas (KS) Kentucky (KY) Louisiana (LA) Massachusetts (MA) Maryland (MD) Maine (ME) Michigan (MI) Minnesota (MN) Missouri (MO) Mississippi (MS) Montana (MT) North Carolina (NC) North Dakota (ND) Nebraska (NE) New Hampshire (NH) New Jersey (NJ) New Mexico (NM) Nevada (NV) New York (NY) Ohio (OH) Oklahoma (OK) Oregon (OR) Pennsylvania (PA) Rhode Island (RI) South Carolina (SC) South Dakota (SD) Tennessee (TN)

55 -53- Texas (TX) Utah (UT) Virginia (VA) Washington (WA) West Virginia (WV) Wisconsin (WI) Wyoming (WY) National Source: Authors calculations.