An Econometric Assessment of Electricity Demand in the United States Using Panel Data and the Impact of Retail Competition on Prices


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1 9 June 2015 An Econometric Assessment of Electricity Demand in the United States Using Panel Data and the Impact of Retail Competition on Prices By Dr. Agustin J. Ros This paper was originally presented at the Rutgers University Center for Research in Regulated Industries, 34th Annual Eastern Conference. Introduction Since the early 1970s electricity demand in the United States has been growing at an average annual rate of approximately 2%. In that period there have been major developments in the electricity sector including significant technological changes in generation services and the development of wholesale and retail competition. In this paper I use panel data covering 72 electricity distribution companies in the United States during the period from to econometrically estimate structural demand equations separately for residential, commercial, and industrial customers and to examine the impact that retail competition has had on electricity prices. I find the ownprice elasticity of demand for residential, commercial, and industrial consumers that are generally consistent with the published economics literature, ranging between and for residential demand, for commercial demand, and ranging between and for industrial demand. Regarding retail electricity competition, I econometrically examine the impact of the restructuring of the retail electricity sector in the US from the mid1990s. Since this period and up to 2009, a total of 21 states permitted retail customers (some states permitting only large industrial customers and some states also permitting smaller commercial and residential customers) to select their electricity generation supplier (retail competition) from a firm other than the incumbent electricity distribution company. As of 2009, 17 and 15 states still permitted retail competition for large and smaller customers, respectively. I estimate reducedform static and dynamic price equations controlling for demand and supply factors, and include a binary variable for those states and time periods where retail competition was permitted. I test the null hypothesis that retail competition had no statistically significant impact on real electricity prices. I find that retail electricity competition is associated with lower electricity prices for each customer class with the magnitude of the impact being greater for the larger customer classes.
2 Literature Review There is a large economic literature on electricity demand in the US and other countries. Using data on US residential electricity demand for , Silk and Joutz (1997) find that a 1% increase in electricity prices reduces electricity consumption by 0.62%. With respect to disposable income, they find a 1% increase in income leads to a 0.82% increase in electricity consumption. Using data on residential demand for electricity in the US, Dergiades and Tsoulfidis (2008) find short and longrun price elasticities of demand to be % and %, respectively. With regard to income, they find short and longrun income elasticities of demand to be 0.101% and 0.273%, respectively. Paul, Myers, and Palmer (2009) find US shortrun price elasticities of demand ranging between and (depending on customer class and region of the country), and longrun price elasticities of demand ranging between and (depending on customer class and region of the country). In the same paper, they summarize the results from previous studies, which I summarize below in Table 1. Table 1. Summary of OwnPrice Elasticities of Demand from the Literature Customer Class Reference Short Run Long Run Bohi and Zimmerman (1984) (consensus) Dahl and Roman (2004) Residential Supawat (2000) Espey and Espey (2004) Bernstein and Griffin (2005) Commercial Bohi and Zimmerman (1984) Bernstein and Griffin (2005) Bohi and Zimmerman (1984) Industrial Dahl and Roman (2004) Taylor (1977) All Dahl and Roman (2004) Source: Paul, Myers and Palmer (2009), Table 5 Finally, using data from the Korean service sector, Lim and Lim (2014) find the shortand longrun price elasticities of electricity demand to be and , respectively, and find short and longrun income elasticities of electricity demand to be and 1.090, respectively. With regard to the impact of electricity competition, a number of studies are focused on the wholesale sector but few studies focus on the retail sector. Regarding the former, Kleit and Terrell (2001) find that by eliminating technical inefficiencies, gasfired generation plant could reduce costs by up to 13%. Fabrizio et al. (2007) found evidence of reduced fuel and nonfuel expenses in fossilfueled plants in states that restructured their wholesale markets. Zhang (2007) finds that, in states that have restructured nuclearfueled plants, utilization is higher and operating costs are lower. 2
3 Regarding the impact of retail competition, a recent paper by Su (2014) uses a differenceindifference approach to estimate the policy impact for US states that restructured their electricity retail markets. Su finds that only residential customers have benefitted from significantly lower prices but not commercial or industrial customers. Furthermore, this benefit is transitory and disappears in the long run. Swadley and Yücel (2011) find that retail competition makes the market more efficient by lowering the markup of retail prices over wholesale costs, and it generally appears to lower prices in states with higher customer participation rates in retail choice. Data I use several different data sources for my study: (I) FERC Form 1 data that contains information on residential, commercial, and industrial revenues and sales volume; (II) data from the bureau of labor statistics on price indices used for deflating prices and other relevant variables; and (III) inputs and results from a total factor productivity study containing information on cost indices, and total factor productivity for the 72 US electricity firms that I use in this study. 1 In Table 2 below, I provide a description of the variables and data sources used for this study using average revenue per unit as a proxy for price. 2 Table 2. Description of Variables Variable Name Description Data Source Lntfp Natural log of index of total factor productivity TFP Study ln_rpres Natural log of deflated residential revenue per unit sales volume FERC Form 1, TFP Study, and author s calculations using US census region cpi and urban consumer as deflator ln_rpcom Natural log of deflated commercial revenue per unit sales volume FERC Form 1, TFP Study, and author s calculations using US census region cpi and urban consumer as deflator ln_rpindus Natural log of deflated industrial revenue per unit sales volume using FERC Form 1, TFP Study, and author s calculations US census region cpi and urban consumer as deflator ln_qres Natural log of residential sales volume FERC Form 1, TFP Study, and author s calculations ln_qcom Natural log of commercial sales volume FERC Form 1, TFP Study, and author s calculations ln_qindus Natural log of industrial sales volume FERC Form 1, TFP Study, and author s calculations labprcindex Real labor cost index FERC Form 1 and TFP Study caprcindex Real capital cost index FERC Form 1 and TFP Study t_hdd State heating degree day index National Oceanic and Atmospheric Administration t_cdd State cooling degree day index National Oceanic and Atmospheric Administration ln_pop Natural log of state population Bureau of Economic Analysis ln_income Natural log of real state personal income using US census region Bureau of Economic Analysis cpi and urban consumer as deflator ln_price_natural gas Natural log of real state natural gas price index using US census US Energy Information Administration region cpi and urban consumer as deflator compl Indicator variable 1 if competition for large industrial Author s construct customers is permitted comps Indicator variable 1 if competition Author s construct for residential and commercial customers is permitted ratecap Indicator variable 1 if state that permitted competition had a rate cap for residential and commercial customers Swadley and Yücel (2011) Table 1 3
4 In Table 3 below, I present summary statistics of the variables. Mean values over the period for deflated residential, commercial, and industry prices were kwh, 8.91 kwh, and 6.16 kwh, respectively. And over the time period, there was a downward trend in deflated prices for all customer classes beginning in the late 1980s and lasting through the early 2000s. Approximately 14% and 13% of observations of the data reflect retail competition for large and residential and commercial customers, respectively. Table 3. Summary Statistics Variable Obs Mean Std. Dev. Min Max lntfp unem ln_pop ln_rpres ln_rpcom ln_rpindus ln_qres ln_qcom ln_qindus labprcindex caprcindex t_hdd t_cdd ln_income ln_price_natural gas Compl Comps Rate cap Econometric Models Econometric estimation of US electricity demand I estimate demand equations for US electricity distribution services for a 72company panel sample from 1972 to 2009 to determine the price elasticity of demand, as well as the effects of other factors. I estimate demand equations separately for residential, commercial, and industrial electricity demand. In these demand equations, output (sales volume) is the lefthand side dependent variable. I am measuring how electricity output changes when other variables, such as price and income, change. The basic model is of the form: (1) y it = Y it γ + X it β + μ i + υ it 4
5 Where y it is the dependent variable (electricity consumption), Y it is a 1 x g 2 vector of observations on g 2 endogenous variables included as covariates (in my demand models, g 2 =1 since I assume that price is the only endogenous variables), and these variables are allowed to be correlated with the υ it, X it is a 1 x k 1 vector of observations on the exogenous variables included as covariates (such as income, population, price of natural gas, and heating and cooling degree days), γ is a g 2 x 1 vector of coefficients, β is a k 1 x 1 vector of coefficients, μ i is the individuallevel effect (i.e., the unobservable companylevel effects), and υ it is the disturbance term. I estimate demand models for each type of customer using four different estimators: fixedeffects, randomeffects, firstdifference, and the ArellanoBond estimator for dynamic models. The fixedeffect estimator fits the model after sweeping out the μ i by removing the panellevel means from each variable. The randomeffects estimator treats the μ i as random variables that are independent and identically distributed (i.i.d.) over the panels. The firstdifference estimator removes the μ i by fitting the model in first differences. The ArellanoBond model is a linear dynamic paneldata model that includes p lags of the dependent variables as covariates and contains unobserved panellevel effects, fixed or random. 3 I expect price to be endogenous, and for instruments I use data from the TFP Study of US distribution companies. Specifically, I use a deflated labor price index and a deflated capital price index. These two variables reflect changes in input costs for the 72 distribution companies over the period and are thus good candidates for instruments. In addition to price, I expect electricity demand to be positively related to population, real income, the state heating degree day index, the state cooling degree day index, and the deflated price of natural gas. 4 To capture the possibility of changing demand preferences over time, I include three decade binary variables. Residential demand models The first three models are static demand models, while the ArellanoBond model is a dynamic demand model. Table 4 contains the results of my static and dynamic residential demand equations. Since the lefthand side dependent variable is the log of residential demand, the coefficient on residential prices is the price elasticity of demand. The fixedeffects and randomeffects estimators provide very similar results for the price elasticity of demand and for all the variables in the model. The price elasticity of demand using the fixedeffects estimator is estimated to be and statistically significant (t statistic = 3.65). The price elasticity of demand using the randomeffects estimator is estimated to be and statistically significant (t statistic = 3.57). When I use the firstdifference estimator, the price elasticity of demand increases to (t statistic = 3.23). Finally, when I use the ArellanoBond dynamic estimator, the price elasticity of demand is estimated to be , and is estimated very precisely. 5 The econometric evidence, therefore, supports a price elasticity of demand for residential customers ranging between and These estimates are within the range found in the economic literature (see Section 2 above). With respect to the income elasticity of demand, the fixedeffects and randomeffects estimators also provide very similar results. The income elasticity of demand using the fixedeffects estimator is estimated to be and statistically significant (t statistic = 5.51). The income elasticity of demand using the randomeffects estimator is estimated to be and statistically significant (t statistic = 5.64). When I use the firstdifference estimator, the 5
6 income elasticity of demand decreases to (t statistic = 1.90). Finally, when I use the ArellanoBond dynamic estimator, the income elasticity of demand is estimated to be and is estimated very precisely. To control for changes in quantity demanded over time, I included three decade binary variables. All the decade variables are positive and statistically significant. Specifically, using the results from the fixedeffects estimator I find that, compared to the 1970s and holding all factors constant, residential demand in the 1980s, 1990s, and 2000s was approximately 10%, 12%, and 13% higher, respectively. The similarity in the coefficients suggests that, holding all factors in the model constant, residential demand has not changed much since Other variables in the model are population, the price of natural gas, and the heating and cooling degree day indices. With respect to population, the four models provide similar results: a 1% increase in population results in an increase in residential demand ranging between 0.786% and 0.873% and is estimated very precisely (in each case a pvalue of less than 0.001). I find natural gas to be a substitute for residential electricity consumption. A 1% increase in the real price of natural gas results in an increase in residential electricity consumption of approximately 0.090%. Finally, I find that the heating and cooling degree days index positively affects the demand for residential electricity. Table 4. Estimation of Static 2SLS and Dynamic Residential Demand Equations Using Panel Data Variable Fixed Effects Random Effects First Difference ArellanoBond ln_rpres *** *** *** decade_80s *** *** *** decade_90s *** *** *** decade_2000s *** *** ** ln_pop *** *** *** t_hdd *** *** *** t_cdd *** *** *** ln_income *** *** *** ln_price natural gas *** *** ln_rpres_cpi D ** decade_80s D decade_90s D decade_2000s D ln_pop D *** t_hdd D *** t_cdd D *** ln_income D ln_price natural gas D ln_qres L *** _cons *** *** *** *** N Wald χ 2 Prob > χ Prob > χ Prob > χ Prob > χ *p<0.05; **p<0.01; ***p<
7 Commercial demand models Table 5 contains the results of my static and dynamic commercial demand equations. The fixedeffects and randomeffects estimators provide very similar results for the price elasticity of demand and for all the variables in the model. The price elasticity of demand using the fixedeffects estimator is estimated to be but is not estimated precisely (t statistic = 1.71). The price elasticity of demand using the randomeffects estimator is estimated to be and is also not statistically significant (t statistic = 1.71). When I use the firstdifference estimator, the price elasticity of demand decreases to but is estimated with very poor precision (t statistic = 0.39). Finally, when I use the ArellanoBond dynamic estimator, the price elasticity of demand is and estimated very precisely. 7 The econometric evidence, therefore, supports a price elasticity of demand for commercial customers of , also within the findings in the economics literature (see Section 2). With respect to the income elasticity of demand, the fixedeffects and randomeffects estimators also provide very similar results. The income elasticity of demand using the fixedeffects estimator is estimated to be and statistically significant (t statistic = 3.90). The income elasticity of demand using the randomeffects estimator is estimated to be and statistically significant (t statistic = 3.98). When I use the firstdifference estimator, the income elasticity of demand decreases to (t statistic = 4.98). Finally, when I use the ArellanoBond dynamic estimator, the income elasticity of demand is estimated to be and is estimated very precisely. The econometric evidence thus supports an income elasticity of residential electricity demand ranging between and These estimates are within the range found in the economic literature (see Section 2). To control for changes in quantity demanded over time, I included three decade binary variables. All the decade variables are positive and statistically significant. Specifically, using the results from the fixedeffects estimator I find that, compared to the 1970s and holding all factors constant, commercial demand in the 1980s, 1990s, and 2000s was approximately 14%, 23%, and 20% higher, respectively. Other variables in the model are population, the price of natural gas, and the heating and cooling degree day indices. With respect to population, a 1% increase in population results in an increase in commercial demand ranging between 0.472% and 0.767%, depending on the model, and is estimated precisely, in three cases with a pvalue of less than I find evidence that natural gas is a substitute for commercial electricity demand in two of the four models, with a 1% increase in the real price of natural gas resulting in approximately a 0.10% increase in commercial demand. And I find some evidence that the heating and cooling degree days index positively impacts the demand for commercial electricity. 7
8 Table 5. Estimation of Static 2SLS and Dynamic Commercial Demand Equations Using Panel Data Variable Fixed Effects Random Effects First Difference ArellanoBond ln_rpcom_cpi *** decade_80s *** *** ** decade_90s *** *** * decade_2000s ** ** ln_pop *** *** *** t_hdd 4.084e e e06 t_cdd 1.707e e *** ln_income *** *** ** ln_price natural gas * * ln_rpcom_cpi D decade_80s D decade_90s D decade_2000s D * ln_pop D * t_hdd D * t_cdd D *** ln_income D *** ln_price natural gas D ln_qcom L *** _cons *** *** *** N Wald χ 2 Prob > χ Prob > χ Prob > χ Prob > χ *p<0.05; **p<0.01; ***p<0.001 Industrial demand models Table 6 contains the results of my static and dynamic industrial demand equations. The price elasticity of demand using the fixed and randomeffects estimator is contrary to economic theory, showing a positive price elasticity of demand. I therefore rely on the results from the firstdifference and ArellanoBond models. When I use the firstdifference estimator, I find the price elasticity of demand to be (t statistic = 2.80). When I utilize the ArellanoBond dynamic estimator, the price elasticity of demand is estimated to be and is estimated precisely. 8 The econometric evidence, therefore, supports a price elasticity of demand for industrial customers between and , also within the findings in the economics literature (see Section 2). With respect to the income elasticity of demand, the fixedeffects and randomeffects estimators also provide very similar results. The income elasticity of demand using the fixedeffects estimator is estimated to be and statistically significant (t statistic = 4.95). The income elasticity of demand using the randomeffects estimator is estimated to be and statistically significant (t statistic = 5.02). The income elasticity of demand using the 8
9 firstdifference estimator is significantly lower at (with a student t statistic = 4.26). When I use the ArellanoBond dynamic estimator, the income elasticity of demand is estimated to be 1.58 and is estimated precisely and closer to the estimates found from the fixed and randomeffects estimators. To control for changes in quantity demanded over time, I included three decade binary variables. The results are mixed. Three of the four models suggest that industrial electricity demand was lower in the 1980s (than in the 1970s) but higher in the 1990s and 2000s. The remaining model, however, suggests that industrial electricity demand was lower in each decade compared to the 1970s. Other variables in the model are population, the price of natural gas, and the heating and cooling degree day indices. With respect to population, the fixed and random effects model finds that a 1% increase in population results in an increase in industrial demand of 0.361% and 0.338%, respectively while for the firstdifference model a 1% increase in population results in an increase in industrial demand range of 0.882%. I find evidence in the ArellanoBond model that natural gas is a complement for industrial electricity consumption. A 1% increase in the real price of natural gas results in a decrease in industrial electricity consumption of approximately 1.236%. Finally, I do not find strong evidence that the heating and cooling degree days index impacts the demand for industrial electricity. Table 6. Estimation of static 2SLS and dynamic industrial demand equations using panel data Variable Fixed Effects Random Effects First Difference ArellanoBond ln_rpindus_cpi *** *** * decade_80s ** ** *** decade_90s ** ** *** decade_2000s *** ln_pop ** ** t_hdd e e06 t_cdd e06 ln_income *** *** * ln_price natural gas * ln_rpindus_cpi D ** decade_80s D ** decade_90s D * decade_2000s D * ln_pop D ** t_hdd D e06 t_cdd D ln_income D *** ln_price natural gas D ln_qindus L *** _cons *** N Wald χ 2 Prob > χ Prob > χ Prob > χ Prob > χ *p<0.05; **p<0.01; ***p<
10 Econometric Estimation of US Electricity Price Equations In this section, I estimate reducedform price equations for residential, commercial, and electricity customer classes. The lefthand side dependent variable is log of real price and is the same price variable that I used above for the demand equations. The righthand side independent variable comps is a binary variable with a value of one if the state permitted retail competition for residential and commercial (small) customers. I use this variable for the residential and commercial price equations. For the industrial price equations, the variable compl is a binary variable with a value of one if the state permitted retail competition for industrial (large) consumers. I estimate fixed and random effects models assuming that comps and compl are exogenous. In addition, I again estimate dynamic models using the ArellanoBond estimator and provide two results: the first treats the competition variable as exogenous, and the second assumes it is endogenous and uses the lagged values of the competition variable as instruments. Other independent variables in my reducedform price equation include binary variables for the 1980s, 1990s, and 2000s, log of population, log of the firm s total factor productivity (lntfp), heating and cooling degree day indices, real personal income, and the log of real price of natural gas. I also include the variable ratecap to control for the fact that some of the states that permitted competition imposed a rate cap on electricity prices for small customers (residential and commercial) for a period of time. Thus, it is important to control for this effect, otherwise the effect would be included within the comps coefficient. The variable ratecap is a binary variable with one in those states that permitted competition and had a rate cap in the year in question. Residential price equations Table 7 contains the results of my residential price model. The fixed and random effects estimators provide very similar results (and each having a pvalue of less than 0.001): holding all other factors constant, residential prices were approximately 8% lower in those states that permitted retail competition for residential and commercial consumers. The ArellanoBond estimator assuming that comps is exogenous (model 3) indicates that residential prices were approximately 3% lower in those states that permitted retail competition for residential and commercial consumers, but the effect was not significant. When I use the ArellanoBond estimator and consider comps as endogenous, I find the impact is practically zero and is not estimated precisely. Based upon these results, while there is some evidence that residential electricity competition is associated with lower residential prices, additional work should be performed on finding suitable instruments for the comps variable in order to ensure that the parameter estimates for comps are unbiased. Other significant findings include the impact of lntfp and personal income on residential electricity prices. In each of the models, an increase in tfp of 1% results in a decrease in residential prices, ranging from % to %. In each of the models, an increase in personal income results in a decrease in prices, ranging from % to %. 10
11 Table 7. Estimation of Static and Dynamic Residential Price Equations Using Panel Data Variable Fixed Effects (1) Random Effects (2) ArellanoBond (3) ArellanoBond (4) comps .089*** .084*** ratecap .105*** .101*** .085*** .081*** decade_80s.045***.043***.02***.02*** decade_90s .057*** .065*** decade_2000s .075*** .098***.06***.056*** ln_pop *** Lntfp .22*** .253*** .087*** .084*** t_hdd 2.2e05* 1.2e05* 6.78e e06 t_cdd 4.3e05*** 5.2e05*** 2.15e05* 2.5e05* ln_income .338*** .258*** .186*** .191*** ln_price natural gas .079*** *.045* ln_rpres_cpi L1..773***.780*** _cons ** 1.53** N *p<0.05; **p<0.01; ***p<0.001 Commercial price equations Table 8 contains the results of my commercial price model. The fixed and randomeffects estimators provide very similar results (each having a pvalue of less than 0.001): holding all other factors constant, commercial prices were approximately 16% lower in those states that permitted retail competition for residential and commercial consumers. The ArellanoBond estimator, assuming that comps is exogenous (model 3), indicates that commercial prices were approximately 19% lower in those states that permitted retail competition for residential and commercial consumers (with a pvalue of less than 0.001). When I use the ArellanoBond estimator and consider comps as endogenous, the impact is approximately 19%. Based upon these results, there is evidence that commercial electricity competition is associated with lower commercial prices. Other significant findings include the impact of lntfp and personal income on residential electricity prices. In each of the models, an increase in tfp results in a decrease in prices, ranging from % to %. In each of the models, an increase in personal income results in a decrease in prices, ranging from 0.68% to 0.29%. 11
12 Table 8. Estimation of Static and Dynamic Commercial Price Equations Using Panel Data Variable Fixed Effects (1) Random Effects (2) ArellanoBond (3) ArellanoBond (4) comps .176*** .171*** .038*** .035*** ratecap * decade_80s decade_90s .108*** .119*** decade_2000s .105*** .134***.051***.05*** ln_pop.075*.079*** lntfp .236*** .278*** .058*** .056** t_hdd 2.5e05** 1.0e e e06 t_cdd 3.2e e05* 2.2e e05 ln_income .683*** .567*** .296*** .292*** ln_price natural gas .087** * ln_rpcom_cpi L1..811***.821*** _cons 3.89*** 2.55*** 2.09*** 2.06*** N *p<0.05; **p<0.01; ***p<0.001 Table 9 contains the results of my industrial price model. The fixed and randomeffects estimators provide very similar results (each having a pvalue of less than 0.001): holding all other factors constant, industrial prices were approximately 24% lower in those states that permitted retail competition for industrial consumers. The ArellanoBond estimator indicates that industrial prices were approximately 30% lower in those states that permitted retail competition for industrial consumers (with a pvalue of less than 0.001). When I use the ArellanoBond estimator and consider compl as endogenous, the impact is approximately 29%. Based upon these results, there is evidence that industrial electricity competition is associated with lower industrial prices. Other significant findings include the impact of tfp and personal income on residential electricity prices. In each of the models, an increase in tfp results in a decrease in prices, ranging from % to %. In each of the models, an increase in personal income results in a decrease in prices, ranging from % to %. 12
13 Table 9. Estimation of Static and Dynamic Industrial Price Equations Using Panel Data Variable Fixed Effects (1) Random Effects (2) ArellanoBond (5) ArellanoBond (6) Compl .269*** .263*** *** *** decade_80s.0861***.0844*** decade_90s *** *** decade_2000s *.0813***.0799*** ln_pop.175***.0967*** Lntfp .193*** .263*** .075** ** t_hdd 3.0e05* 8.8e e e06 t_cdd 4.5e e05* 1.1e e05 ln_income .811*** .616*** .379*** .376*** ln_price natural gas .149*** ln_rpindus_cpi L1..791***.803*** _cons 3.38*** 2.44*** 3.39*** 3.37*** N *p<0.05; **p<0.01; ***p<0.001 References T. Dergiades and L. Tsoulfidis, Estimating residential demand for electricity in the United States, , Energy Economics, K. Lim and S. Lim, Short and longrun elasticities of electricity demand in the Korean service sector, Energy Policy, A. Paul, E. Myers, and K. Palmer, A Partial Adjustment Model of US Electricity Demand by Region, Season and Sector, Resources for the Future Discussion Paper, Available at J. Silk and F. Joutz, Short and long run elasticities in US residential electricity demand: a cointegration approach, Energy Economics, X. Su, Have Customers Benefited from Electricity Retail Competition, Journal of Regulatory Economics, 2015 (forthcoming). A. Swadley and M. Yücel, Did residential electricity rates fall after retail competition? A dynamic panel analysis, Energy Policy,
14 Notes 1 I was the coauthor (with Jeff Makholm) of an expert report entitled Total Factor Productivity in the United States Electricity Sector from We were expert witnesses on behalf of the Alberta Public Utility Commission in a proceeding in 2012 whose objective was setting tariffs for electricity and gas distribution companies. Our analysis was used to establish the Xfactor in a price cap plan. Throughout this paper, I refer to the study as TFP Study. 2 I did not have data on actual tariffs for the different customer classes over the time period. Instead, I use average revenue per unit as a proxy for price and assume that some errors exist in variable (EIV). Nevertheless, EIV should not present a significant problem because I treat the price variable as (jointly) endogenous in my structural demand equations, and I explicitly model price in my reducedform price equations. 3 The model is constructed so that by definition the unobserved panellevel effects are correlated with the lagged dependent variables, thus making standard estimators inconsistent. Arellano and Bond derived a consistent generalized methodofmoments (GMM) estimator for the parameters of the model. 4 I consider natural gas as a substitute for electricity and expect the crossprice elasticity of demand to be positive. 5 The total effect is /( ). 6 I also estimate every model by including interaction terms between the price variable and each decade variable to test whether there is evidence that the price elasticity of residential electricity demand changed significantly during the decades. For the fixedeffects model, the price elasticity of demand for the 1980s, 1990s, and 2000s ranged between to , similar to the models without the interaction effects but the parameters were not estimated precisely, none being significant at the 5% level of statistical significance. Results for the randomeffects estimator are similar. 7 The total effect is /( ). 8 The total effect is /( ).
15 About NERA NERA Economic Consulting (www.nera.com) is a global firm of experts dedicated to applying economic, finance, and quantitative principles to complex business and legal challenges. For over half a century, NERA s economists have been creating strategies, studies, reports, expert testimony, and policy recommendations for government authorities and the world s leading law firms and corporations. We bring academic rigor, objectivity, and real world industry experience to bear on issues arising from competition, regulation, public policy, strategy, finance, and litigation. NERA s clients value our ability to apply and communicate stateoftheart approaches clearly and convincingly, our commitment to deliver unbiased findings, and our reputation for quality and independence. Our clients rely on the integrity and skills of our unparalleled team of economists and other experts backed by the resources and reliability of one of the world s largest economic consultancies. With its main office in New York City, NERA serves clients from more than 25 offices across North America, Europe, and Asia Pacific. Contact For further information and questions, please contact the author: Dr. Agustin Ros Vice President The opinions expressed herein do not necessarily represent the views of NERA Economic Consulting or any other NERA consultant. Please do not cite without explicit permission from the author.
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