SWEATING IT OUT:
THE RESPONSE OF SUMMER ELECTRICITY DEMAND TO INCREASES IN
PRICE
A Thesis
Presented to the faculty of the Department of Economics
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF ARTS
in
Economics
by
Zephaniah K. Davis
FALL
2013
© 2013
Zephaniah K. Davis
ALL RIGHTS RESERVED
ii
SWEATING IT OUT:
THE RESPONSE OF SUMMER ELECTRICITY DEMAND TO INCREASES IN
PRICE
A Thesis
by
Zephaniah K. Davis
Approved by:
__________________________________, Committee Chair
Craig Gallet, Ph.D.
__________________________________, Second Reader
Smile Dube, Ph.D.
____________________________
Date
iii
Student: Zephaniah K. Davis
I certify that this student has met the requirements for format contained in the University
format manual, and that this thesis is suitable for shelving in the Library and credit is to
be awarded for the thesis.
__________________________, Graduate Coordinator
Kristin Kiesel, Ph.D.
Department of Economics
iv
___________________
Date
Abstract
of
SWEATING IT OUT:
THE RESPONSE OF SUMMER ELECTRICITY DEMAND TO INCREASES IN
PRICE
by
Zephaniah K. Davis
This study examines the own price elasticity of demand for electricity in the Greater
Sacramento Area.
Data corresponded to customer billing information from the
Sacramento Municipal Utility District for Summer 2012. Both linear and logarithmic
functional forms, as well as fixed and random effects models, were estimated to examine
the effects of price changes on usage. A number of other variables, such as temperature, a
one-period lag in use, and various binomial event indicators, were also included as
determinants of daily electricity usage. The results indicate that the daily price elasticity
is in the range of -0.0210 to -0.0702 for the double log model, while the linear estimates
range from -0.0037 to -0.2726, with temperature playing an important role in both
models.
__________________________________________, Committee Chair
Craig Gallet, Ph.D.
v
ACKNOWLEDGEMENTS
I would like to thank Professor Craig A. Gallet for all of his support and guidance in
writing this thesis, Professor Smile Dube for additional guidance and diligence, and
Kristin Kiesel for serving as my graduate coordinator.
I would also like to thank my parents, particularly my Dad, who have guided me,
supported me and opened every door they could for me throughout my life.
vi
TABLE OF CONTENTS
Page
Abstract ..........................................................................................................................v
Acknowledgements ...................................................................................................... vi
List of Tables ............................................................................................................. viii
List of Figures .............................................................................................................. ix
Chapter
1. INTRODUCTION.………………………………………………………………..1
2. LITERATURE REVIEW ........................................................................................4
3. METHODS ............................................................................................................20
4. ESTIMATION RESULTS .................................................................................... 35
5. CONCLUDING REMARKS ................................................................................ 48
Work Cited ...................................................................................................................51
vii
LIST OF TABLES
Tables
Page
1.
Comparison of the Empirical Results for Energy Demand ........... …………….5
2.
Price Elasticities by Household Income and Electricity Consumption ………14
3.
Variable Means ........................................................ ………………………….16
4.
Variables and Definitions ........................................ ………………………….21
5.
Summary Statistics................................................... ………………………….22
6.
Descriptive Statistics for Electricity Use in Each Quartile .......... …………….25
7.
Electricity Rates by Rate Code and Usage .................................. …………….26
8.
Model 1 Estimation Results ......................................................... …………….37
9.
Model 2 Estimation Results ......................................................... …………….38
10.
Model 3 Estimation Results ......................................................... …………….40
11.
Model 4 Estimation Results ......................................................... …………….42
12.
Quartile Estimation Results for Fixed-Effect Double Log Model 3 .... ……….46
viii
LIST OF FIGURES
Page
1.
Increasing-Block Pricing……………… ........ .……………………………….12
2.
Estimated Distribution of California Household’s Electricity Price
Elasticities .................................................................................... …………….13
3.
Histogram of the Daily Average of the Total Electricity Use per Household..23
4.
Typical Daily Household Electricity Use during Each Month .... …………….27
5.
Average Daily Usage and Average Daily Temperature .............. …………….31
ix
1
Chapter 1
INTRODUCTION
During the 1970s and 80s the United States saw rapidly increasing energy costs
and subsequent government, firm and consumer concerns. Accompanying these concerns
about energy conservation during this period came a large number of studies of
residential electricity usage conducted to measure and support critical elements in the
energy policy dialogue. Since this period, we have seen steady growth in both studies
and debate over energy efficiency and conservation, and concerns over global climate
change and energy security have only intensified the issues.
Further complicating
matters is the fact that electricity cannot be stored, so strict regulation has been put into
place to assure that quantity supplied always meets or very slightly exceeds quantity
demanded to prevent disruptions in service. This regulation comes at a price, namely
inefficient prices resulting in deadweight loss. However, consequences of this are not
limited to deadweight loss. Due to immense demand and the shutdown of nuclear power
plants due to environmental activism, we find ourselves in short supply of electricity,
particularly in California. This issue was made very prominent during the Energy Crisis
of 2000 and 2001 when utilities were unable to make electricity supply meet demand in
California and other western markets, resulting in brownouts and other disruptions in
power delivery during times of high demand. While California has not had a crisis of this
magnitude since, the California Energy Commission (2013) predicts a 13% statewide
increase in electricity demand from 2012 through 2024.
2
To address this issue, in recent years many utilities have been implementing timebased pricing programs in which they charge more money during times in which
electricity demand is high and less during times in which it is low to get consumers to
substitute towards cheaper electricity in ‘off’ times by reducing demand during critical
times.
Many advocates and policymakers hold that reducing the demand for energy is
essential to mitigating concerns, and accumulated literature and analyses over the past 30
years overwhelmingly find that demand reductions can be a cost-effective means of doing
so.
However, given the extremely complicated nature of electricity production,
distribution and pricing, it is vital to understand consumer’s responsiveness to electricity
price changes. Understanding these behaviors can help municipalities, utility companies
and policy makers predict future energy needs and design pricing and taxation policies.
This interest in accurate pricing reflects a general desire of policymakers, electricity
producers, utilities and end-users to improve the efficiency of electricity markets. How
new pricing mechanisms would affect households’ consumption and expenditures is still
a matter of considerable uncertainty in many markets, however.
Facing possible
volatility in electricity price, consumers may decide to modify their demand profile to
reduce electricity costs. Therefore, it will be necessary to estimate and quantify how
consumers respond to price changes. This work is valuable for policymakers in
developing more effective electricity pricing schemes.
For these reasons, in this thesis we ask two research questions. First, what are the
short-run and long-run price elasticities of demand for electricity in the Greater
3
Sacramento area? That is, what is the magnitude of the relationship between a price
increase and the diminished response in purchasing by consumers? Second, do temporary
events, such as particularly hot days or social energy-saving events, cause temporal
changes in the level of demand, as well as the price elasticity?
We create a panel dataset using electricity consumption data for 665 residential
households, each with 121 daily observations spanning June 1, 2012 through September
30, 2012. To this we add calculated price data, temperature data and binomial indictors
of temporary events aimed at reducing electricity consumption and improving air quality.
We also include interactions of price with these variables to estimate changes in
elasticities due to these events. Our estimates are based on commonly-used double log
and linear models, the double log being of most interest as it is easy to estimate and
yields elasticities directly from coefficients. We specify fixed and random effects models
to account for unobserved heterogeneity. Briefly, we find that price elasticities are stable
across models with a fixed effects specification yielding price elasticities that range from
-0.0037 to -0.1022 in the short-run and .0024 to -0.0594 in the long-run.
The remainder of this thesis is organized as follows. In the following chapter we
review previous studies of the price elasticity of demand in electricity markets. Chapter 3
details our empirical specification, while Chapter 4 provides the estimation results. The
thesis concludes with a summary in Chapter 5.
4
Chapter 2
LITERATURE REVIEW
Since the 1950s numerous studies have examined the demand for electricity, with
many of them focused on estimating the price elasticity of demand. For instance, in what
is likely the first study of its kind, Houthakker (1951) applied generalized least squares
(GLS) to a panel of data to analyze domestic electricity demand over several months
(assuming a stable demand function).
The data came from surveys of 42 British
households for the years 1938-9 and included variables for the marginal price of
electricity, annual usage of electricity, average monthly income per household, the
marginal price of gas (considered a substitute) and the average holdings of heavy
domestic equipment per consumer. Using a double-log functional form of demand,
Houthakker estimated the price elasticity to be -0.89. Being in the inelastic range, his
results suggest electricity demand modestly responds to price changes.
Since the publication of Houthakker’s study, a multitude of other studies have
used various techniques and data to estimate the price elasticity for single- and mixedenergy sources, as well as household-level and economy-wide demand. As an indication
of the variation in price elasticity estimates, Lee and Lee (2010) surveyed 16 of these
studies and discussed key differences in the literature. According to Table 1 below, some
studies (e.g., Pindyck, 1979) report price elasticities which lie in the elastic range,
whereas other studies (e.g., Li and Maddala, 1999) report price elasticities which lie in
the inelastic range. Although we will discuss several of these studies later in the chapter,
a perusal of Table 1 shows that (i) periods examined tend to be over multiple years, (ii)
5
short-run price elasticities are smaller in absolute value compared to long-run price
elasticities and (iii) price elasticities estimated with cross-sectional data tend to be larger
in absolute value than those derived from panel data.
Table 1. Comparison of the Empirical Results for Energy Demand
Empirical
Income
Authors
Subject
Period
Method
Elasticity
Denmark
19481990
Short-run:
0.67; longrun 1.21
Time-series
model
Denmark
19601996
1.29
Time-series
model
Nepal
19801999
3.04
Bentzen and
Engste (1993b)
Time-series
model
Bentzen and
Engste (2001)
Dhungel (2003)
Price
Elasticity
Short-run:
-0.14;
long-run: 0.47
-1.03
-3.45 ~ 1.65
Short-run:
-0.24 ~ 0.18; longrun -0.59 ~
-0.44
Fatai et al.
(2003)
Time-series
model
New
Zealand
19601999
Short-run:
0.34 ~ 0.46;
long-run
0.81 ~ 1.44
Field and
Grebenstein
(1980)
Cross-sectional
model
United
States
1971
--
-1.65 ~ .054
Mexico
19652001
0.45 ~ 0.64
-0.43 ~ 0.07
California
19831997
Insignificant -0.132
Taiwan
19571995
1.57
-0.15
Time-series
model
India
19701995
0.67 ~ 1.57
-0.66 ~ 0.12
Time-series
model
United
States
19701990
0.38 ~ 1.18
-0.08 ~ 0.48
23 OECD 1978countries 1999
Short-run: 0.08 ~ 1.15;
long-run 0.26 ~ 4.20
Short-run: 0.17 ~ 0.16; longrun -0.52 ~
-0.59
Galindo (2005)
Garcia-Cerrutti
(2000)
Holtedahl and
Joutz (2004)
Kulshreshtha
and Parikh
(2000)
Li and Maddala
(1999)
Liu (2004)
Time-series
model
Dynamic
random
variables
Time-series
model
Dynamic panel
model
6
Authors
Empirical
Method
Subject
Period
Income
Elasticity
Mandala et al.
(1997)
Shrinkage
estimators
U.S. - 49
states
19701990
Short-run:
0.39; longrun 0.89
Narayan and
Smyth (2005)
Time-series
model
Australia
19692000
Short-run:
0.01 ~ 0.04;
long-run
0.32 ~ 0.41
Olatubi and
Zhang (2003)
Dynamic panel
model
U.S. - 16
states
19771999
0.4
Pindyck (1979)
Cross-sectional
model
OECD
19591973
0.7 ~ 0.8
Prosser
Time-series
model
OECD
19601982
1.02
Price
Elasticity
Short-run:
-0.185;
long-run 0.263
Short-run:
-0.27 ~ 0.26; longrun -0.47 ~
-0.54
-0.32
Residential
sector: 1.25 ~ -1.0
industrial
sector: 1.17 ~ .022
Short-run:
-0.22 longrun -0.4
Note: A~B means the numbers range from A to B.
Source Lee and Lee (2010) P. 2-3
Fisher and Keysen (1962) examined changes in stock and usage of in-home
electrical appliances in an effort to explain differences in price responsiveness of
household electricity demand across various time horizons. In particular, they utilized a
series of lag terms to estimate a double-log specification of demand, and thus devoted
substantial effort to examining price elasticities in the short- and medium-run, -0.16 and 0.24, respectively.
Soon after Fisher and Keysen (1962), partial-adjustment models
7
became popular due to the researchers assuming that current electricity use may differ
from desired use over different time horizons (Hudson and Jorgenson, 1974).1
During the 1970s and 1980s several studies examined the determinants of
residential electricity demand, often following Fisher and Keysen’s (1962) focus on
household appliance energy usage. For instance, Wilder and Willenborg (1975) used
cross-sectional household-level data to examine the relationship between electricity
consumption, price, household income, size of household and stock of electrical
appliances. By estimating a double-log specification of demand using two-stage least
squares (2SLS), their price elasticity estimate of -1 is larger in absolute value compared
to the literature in general but similar to price elasticity estimates obtained from other
studies using cross-sectional data (see Table 1). 2 Unlike previous studies, however,
Wilder and Willenborg (1975) used average price instead of marginal price stating that
“the consumer responds to his total monthly bill and rarely knows what the marginal rate
is.” (Wilder and Willenborg, 1975; Page 212). Simply put, the consumer makes his
choices based on the period’s total cost. Wilder and Willenborg also state that similar
estimates could be achieved using marginal price data, albeit the demand intercept would
differ from the average price model.
1
Hudson and Jorgenson (1974) estimated a transcendental logarithmic functional form
for demand. By doing so, they were able to estimate the influence of other factors, such
as substitutes and complements on the demand for electricity. Amongst other results,
they estimated the price elasticity for electricity to be approximately -0.2.
2
They also estimated demand using ordinary least squares (OLS) and reported a price
elasticity of -2.65, an elastic range. This suggests that results may be sensitive to the
chosen estimation method.
8
Hsiao and Mountain (1985) extended the home appliance model of electricity
demand by utilizing panel data methods and taking a more in depth look at the role of
income. They found the income elasticity of demand roughly equaled 0.17. Later,
Branch (1993) modeled demand for electricity partially as a function of the utilization of
appliances and their electrical draw. Using a GLS model, he determined that electricpowered stoves, water heaters and freezers were prone to significantly higher electricity
usage than those homes equipped with natural gas-driven versions of those appliances.
The overall price elasticity of demand was estimated to be -0.2.
Griffin (1974) relied on changes in price, among many other variables, to estimate
electricity demand using time-series data applied to a polynomial-distributed lag model.
He did this for both the short- and long-run versions of demand, finding that short-run
price elasticities are small (that is, in the range of -0.06 to -0.04), yet long-run price
elasticities are more substantial (that is, in the range of -0.51 to -0.52). Similar to Wilder
and Willenborg (1975), Griffin used the average price of electricity instead of
approximate marginal tariffs.
Objections to this specification usually stem from
simultaneous equation bias (Griffin, 1974). However, this is dealt with by using 2SLS as
the estimation method.
Although the majority of studies have relied on double-log versions of demand to
estimate price elasticities of electricity, Chang and Hsing (1991) used a complicated
transformation to test the appropriateness of the double-log version, compare to a semilog version of demand (which allows price elasticities to vary over time). Regarding the
price elasticity of demand, their estimates fall in the range of -0.1354 to -0.3643, with
9
higher absolute values corresponding to the double-log specification. Although the
authors reject the log-log and linear forms at the 0.01 and 0.05 levels, they imply in their
discussion that due to the log-log model imposing a constant elasticity over time that this
specification may not be appropriate for long-period data. The authors also find that a
one-period lag in consumption is a statistically significant explanatory variable in all their
models, thus indicating there is habit persistence in the consumption of electricity.
Indeed, the significance of this lag variable is corroborated by Athukorala and Wilson
(2010) and RAND (2006). .85
Many studies suffer from a lack of available data, which often limits their
specifications of demand to one or two explanatory variables. For instance, Al-Zayer and
Al-Ibrahim (1996) only included temperature as a determinant of household electricity
demand, while Dincer and Dost (1997) merely included real income as a determinant of
demand. Yet other studies (for example, Al-Faris, 2002) have been able to model the
demand for energy as a function of own-price, a substitute price and real income, yet not
temperature. However, any reasonable specification of household electricity demand
over shorter periods of time, especially during the winter and summer months, should
control for temperature.
Indeed, utilities often structure their pricing seasonally to
account for the increased need for electric heating and cooling in homes during particular
periods. Thus, if price and temperature are correlated, yet temperature is omitted from
the specification of demand, then the estimates of price elasticity may suffer from omitted
variable bias.
In fact, Narayan and Smyth (2005) and the California Public Utilities
Commission (CPUC) (2012) point out that such biases are particularly troublesome with
10
long-run price elasticity estimates. This has led the CPUC to take the position that
temperature is so important in determining electricity demand, due to the large variations
in electricity use via home heating and cooling elements, that it requires energy
evaluators to incorporate heating and/or cooling degree hours or days into their models.3
To illustrate this, imagine a home with electric heat and air conditioning. During summer
when the outside air temperature is very warm and the consumer wants some comfort,
thus he or she will most likely turn on the air conditioner (cooling degree) and consume
more electricity than he or she would have on a more temperate day. Conversely, this
also applies to heaters in the winter months. While studies examining the use of various
home heating and cooling appliances indirectly capture temperature variation, the use of
CDH or HDH is recommended for academic studies and mandatory for professional
studies (for examples see CPUC, 2012; RAND, 2006).
Fortunately, not all studies have overlooked temperature as a vital explanatory
variable as Reiss and White (2005), Lavin et al. (2011), RAND (2006), Branch (1993)
and Barnes et al. (1981) incorporate explanatory variables to control for temperature in
3
Degree days and hours are essentially a simplified representation of outside airtemperature data. They are widely used in the energy industry for calculations relating to
the effect of outside air temperature on building energy consumption. “Heating degree
days” (HDD) are a measure of how much (in degrees) and for how long (in days, D or in
hours, H) the outside air temperature was lower than a specific “base temperature” (or
“balance point”). “Cooling degree days” (CDD) are a measure of how much (in degrees)
and for how long (in days) the outside air temperature was higher than a specific “base
temperature”. Thus, HDD (CDD) is an indicator of energy consumption needed to heat
(cool) a building.
11
their models.
4
For instance, Reiss and White (2005) use Residential Energy
Consumption (REC) survey data to examine the price and income elasticity of 1,307
California households. Households from an assortment of service providers, climate
zones, household appliances and incomes were selected, all with a two-tier pricing
system called ‘increasing-block pricing.’ In this type of system, the consumer is charged
one rate per kWh up until a usage threshold is reached, after which the price increases to
another figure.
Both standard and low income schedules were included, totaling
altogether 189 rate schedules from 1993 to 1997. Added to the data were income,
structure characteristics and appliance stock data from REC as well as and weather data
(heating and cooling degree days) from the closest National Weather Service station to
the household.
4
In all cases, the coefficients of these variables were significantly different from zero.
12
Figure 1. Increasing-Block Pricing.
Figure 1 illustrates three-tiered increasing-block pricing. The consumer pays one
price, P1, as long as they use less than or equal to Q1 quantity of electricity (700kWh)
over the billing period. Should the consumer use more than Q1 amount of electricity
(>700kWh) he or she will then pay a higher price, P2 and so on. In theory, the price
increase or threat thereof compels consumers to use less electricity than they would
without.
Reiss and White (2005) then used both generalized method of moments (GMM)
and OLS to calculate the demand elasticities for each of the 1,307 households. Across
the households, the average price elasticity was estimated to be -0.39, with electric
heating and cooling elements playing a significant role in determining the household’s
overall price elasticity.
By estimating individual household demand, instead of a panel data version of
demand (for example, fixed-effect model), this allowed Reiss and White (2005) to
13
examine how the price elasticity of demand was distributed (see Figure 2 below). For
instance, as indicated below, while the bulk of households have price elasticities in the
inelastic range, some households have price elasticities in the elastic range.
Figure 2. Estimated Distribution of California Household’s Electricity Price Elasticities.
Source: Reiss and White (2005) Figure 2. P. 870
As Reiss and White (2005) discuss, household location in this distribution is a
function of income and other demographic characteristics.
Because regulatory
commissions provide subsidized tariffs to low-income households and are thus concerned
with income-related consumption levels, Reiss and White (2005) separate their data into
both income and consumption quartiles for further analysis (see Table 2 below). Price
elasticities in the consumption quartiles are positive in the first two quartiles, then
14
negative in the fourth. The authors note that while these results are consistent with their
constructed distribution, the magnitude of the differences is less than expected.
15
Table 2. Price Elasticities By Household Income And Electricity Consumption
Price elasticitya
Quartile
Quartile range
GMM method
OLS method
b
By household annual income level:
1-st
Less than $18,000
-0.49
0.15
2-nd
$18,000 to $37,000
-0.34
0.17
3-rd
$37,000 to $60,000
-0.37
0.14
4-th
More than $60,000
-0.29
0.017
By household annual electricity consumption:
1-st
Less than 4450kWh
-0.46
0.37
2-nd
4450 to 6580kWh
-0.35
0.04
3-rd
6580 to 9700kWh
-0.32
0.00
4-th
More than 9700kWh
-0.33
-0.08
a
Mean annual electricity price elasticity for households within each quartile.
Approximate California household income quartiles, in 1998 dollars.
b
Source: Reiss and White (2005); Figure 2. P. 871
This study was later critiqued by Alberini et al. (2011) using a mixed panel
covering 50 large metropolitan areas in the United States that the authors divide into
quartiles by household income. They then examine price elasticity in each quartile,
finding the elasticity to be between -0.68 and -0.64 and decreasing very slightly through
the successive quartiles.
As suggested previously, Narayan and Smyth (2005) note that many studies omit
obvious variables. Also, researchers often fail to reach ideal empirical specifications due
to data constraints.
Typical studies of residential electricity demand model the
relationship between electricity use and variables such as price, stock of household
appliances, household income, other household characteristics and weather data (CPUC,
2012). Although this study focuses on the price elasticity of demand, it is common to
find studies estimating both price and income elasticity. Also common, some studies
often estimate both short and long-run elasticities, with the latter typically constructed
16
from models that assume the consumer uses a two-stage budgeting process (for example,
see Faruqui and Sergici 2011).
To summarize the extant literature, Espey and Espey (2004) completed a metaanalysis of 36 studies. Espey and Espey (2004) provide summary statistics of variables
contained in a meta-regression model (See Table 3). For instance, given the means of
key variables indicated in Table 3, the majority of price elasticity estimates in the
literature come from double-log specifications of demand which are estimated with panel
data. Furthermore, most price elasticity estimates pertain to the U.S., and were estimated
in the 1970s, a period corresponding to notable oil price fluctuations that obviously
contributed to increased attention given to exploring the determinants of energy demand.
Also, relevant to this thesis, far less attention has been given in the literature to exploring
price sensitivity over very short periods of time, say day-to-day.
Although the mean short-run (long-run) price elasticity estimate in the literature is
-0.35 (-0.85), there is substantial variation in these estimates, as elasticities overall fall in
the range of -0.04 to -2.25. Both Espey and Espey (2004) and the CPUC explain that
specification, data characteristics, time and location and the estimation techniques all
greatly influence the observed variation in price elasticity estimates. Indeed, Reiss and
White (2005) further explain that within California alone price elasticities vary across
studies, depending upon a number of factors, such as geographic region, as well as data
quality and statistical techniques.
17
Table 3. Variable Means
Variable
Elasticity
Demand specification
Reduced form
Structural
Static
Dynamic
Lag dependent variable
Other lag
Stock included
Substitutes included
Temperature included
Household size
Double log model
Non-double log model
Data characteristics
Household level
Time Series
Cross sectional
Cross sectional time series
Monthly
Annual
Average
Marginal
Increasing block
Decreasing block
Time and location
Aggregate
Regional
United States
Non-United States
Pre-1972
1972-1981
Post-1981
Publication year
Estimation technique
Ordinary least squares
Non-ordinary least squares
Short-run
price
elasticity
-0.35
Long-run
price
elasticity
-0.85
0.77
0.23
0.6
0.4
0.61
0.54
0.53
0.047
0.85
0.16
0.56
0.34
0.1
0.13
0.46
0.92
0.08
0.49
0.11
0.3
0.59
0.41
0.59
0.36
0.64
0.07
0.39
0.56
0.11
0.33
0.08
0.92
0.7
0.27
0.6
0.6
0.64
0.95
0.05
0.34
0.85
0.11
1983
0.26
0.74
0.92
0.08
0.82
0.82
0.11
1982
0.37
0.63
0.08
0.92
Note. Adapted from "Turning on the Lights: A Meta-Analysis of Residential Electricity Demand
Elasticities," by Espey, James A. and Espey, Molly (2004) Journal of Agricultural and Applied
Economics, vol. 36(01), p. 69.
18
Regarding California-specific studies, Lavin et al. (2011) examine price elasticity
with careful attention given to price endogeneity. Specifically, Lavin et al. (2011) use a
two-stage budget model with both double-log and linear demand specifications, which
are similar to those used by Hewitt et al. (1995). Using REC survey data, as well as
controlling for household characteristics, demographics, and weather conditions, Lavin et
al. (2011) estimate the short run price elasticity for the double-log model to be -0.11;
whereas for the linear model the price elasticity (evaluated at the means) is estimated to
be -0.41. The authors mention that these estimates are somewhat lower than previous
studies, which they suggest indicates that price may not be as effective a policy tool as
resource managers believe.
In an extensive study conducted by the RAND Corporation and published by the
National Renewable Energy Laboratory (2006) both the residential and commercial
electricity price elasticity was estimated at the national, state, regional and utility-level,
utilizing one- and two-way fixed effects regressions. In both the double-log and linear
models, independent variables included current period and one-year lagged price,
population, income. In addition, current period climate data in the form of HDH and
CDH was included as were fixed-effect indicator variables. The dataset, spanning the
years 1977-2004, was constructed from several sources, including state energy reports,
the Bureau of Economic Analysis, the U.S. Energy Information Administration, the
National Oceanographic Atmospheric Administration, and data purchased from McGrawHill Construction Dodge. National-level residential short and long-run price elasticity
results were estimated to be -0.20 and -0.32 respectively, which are in the range of other
19
studies. Also price elasticities were found not to vary across years but did vary across
regions. In particular, the California-specific short-run price elasticity was estimated to be
roughly -0.29, while the long-run price elasticity fell in the range of -0.25 to -0.50.
Interaction terms appear in some studies, most notably in Faruqui and Sergici
(2011) as a way of measuring event or time period-specific effects on price elasticity.
This is included so that the model captures not the amount electricity demanded (demand
shift), but the changes in consumer responsiveness to price due to them. That is, does the
price elasticity of demand change (the demand curve rotates) during those events?
Faruqui and Sergici (2011) interact price with temperature and various dummy variables
indicating an assortment of time periods to measure price responsiveness over the course
of their lengthy experiment.
Their results indicated very minor but statistically
significant fluctuations in responsiveness.
20
Chapter 3
METHODS
3.1
Empirical Specification
This study considers both linear and logarithmic regression models to measure the
impact of a price increase on electricity consumption, as our key interest is on how
sensitive consumers are to day-to-day changes in price. To begin, consider the following
linear model:
Useit = 0 + 1Priceit + 2Useit-1 + 3Temperatureit + 4SpareAirit + 5CriticalPeakit +
6FlexAlertit + it
(1)
where i indexes the individual household and t indexes the day. Useit designates the daily
use of electricity by each household on each day, while it is an error term. With results
provided in the next chapter, different versions of the demand specification are estimated.
For instance, one version is represented by equation (1), whereby electricity use is
regressed on the price of electricity, its one-day lagged value, daily temperature, and
dummy variables used to account for various energy-savings programs utilized by
SMUD. All of these variables are defined in Table 4 below.5
While most studies reviewed in the previous chapter use ordinary least squares
(OLS) to estimate electricity demand, this study will use entity-fixed and random effects
5
A log version of demand is also estimated. For example, in the log version of equation
(1), the log of electricity use is regressed on the log of price, the log of the one-day lag in
use, the log of temperature, and the three energy-savings dummy variables. The log
specification is particularly convenient, as the coefficient of the log of price corresponds
to the price elasticity of demand for electricity.
21
models to estimate demand at the household level. Such effects control for additional
variation across households that are time invariant. 6
Hausman tests will then be
conducted in order to select the most appropriate model.
Regarding the explanatory variables used in this study, they are similar to those
that have been explored in the existing literature. It is expected that a higher price will
reduce daily electricity use (that is, following the law of demand, as the price of a good
increases a consumer will demand less of the good, all other things being equal). It is
also expected that the one-day lag in electricity use will have a positive impact on current
use, as there is a habitual nature to the demand for electricity (for example see Reiss and
White, 2005; RAND, 2006).7 We also expect temperature to have a positive impact on
electricity use, particularly among households with electric heat and air conditioning, as
these devices are used to mitigate the effects of uncomfortable outside air temperatures
(RAND, 2006).
Energy-saving programs (which are SpareAir, CriticalPeak, and
FlexAlert) are all binomial variables related to programs administered by SMUD. They
are designed to encourage customers to conserve energy, and thus could have a negative
effect on electricity use. However, they may also simply signal days in which electricity
use is predicted to be abnormally high (that is, beyond that captured by our measure of
6
Given the short time span we are considering (described in Section 3.2), household
effects control for a variety of factors, including household income, wealth, and features
of each residence (e.g., square footage, use of air conditioning, quality of insulation, etc.).
7
For instance, since our data corresponds to the warmer months of the year, given that
consumers often leave the setting of their thermostat unchanged, prior electricity use will
influence current electricity use. Furthermore, by including lagged use in the
specification of demand, we can estimate both “short-run” and “long-run” price
elasticities.
22
temperature, such as during periods of above-normal humidity), and thus could in fact be
positively correlated with electricity use. The remainder of this chapter discusses these
various variables in greater detail.
3.2
Variables and Data
In this section we discuss the variables used in the empirical model as well as
provide and discuss various descriptive statistics for these variables. Table 4 below
provides a list of the dependent and explanatory variables used in this thesis, along with
their respective definitions. In the following paragraphs the variables will be discussed in
more detail.
Table 4. Variables and Definitions
Variable
Definition
Dependent:
Use
Total daily household electricity use (kWh)
Explanatory:
Price
Average daily price of one kilowatt hour (kWh)
Use(-1)
A lag term corresponding to the previous day’s electricity use
Temperature
A temperature variable in the form of cooling degree hours
SpareAir
Dummy variable set equal to 1 for Spare the Air days
CriticalPeak
Dummy variable set equal to 1 for Critical Peak days
FlexAlert
Dummy variable set equal to 1 for Flex Alert days
The total sample includes 665 households, each with 121 daily observations
spanning June 1, 2012 through September 30, 2012. This totals 80,465 observations.
Table 5 below shows various descriptive statistics (i.e., mean, standard deviation,
kurtosis, skewness, minimum, and maximum) of the variables from Table 5.
23
Table 5. Summary Statistics
Variable
Mean
Use
1.16
Price
0.11
Temperature
214.29
SpareAir
0.05
CriticalPeak
0.10
FlexAlert
0.03
St. Dev.
0.82
0.03
97.20
0.22
0.30
0.18
Kurtosis
4.52
0.43
-0.02
15.39
5.28
25.54
Skewness
1.67
1.02
0.34
4.17
2.70
5.25
Minimum Maximum
0.06
7.84
0.06
0.20
5.90
485.80
0
1
0
1
0
1
As mentioned, the dependent variable in our regression is “Use.” Since it is
infeasible for this study to present summary statistics for this variable for each of the 665
households in the study, Table 5 presents the average daily consumption of all
households in the study. When used in the empirical model, Use will be defined as the
total daily kWh usage for each household. This usage data was taken from SMUD
customer billing data, and along with SMUD rate schedules, was used to calculate
average daily price, which is the price paid for each kWh on that respective day.
Temperature is accounted for in the form of cooling degree hours (CDH). CDH are the
maximum of outside air temperature minus the base (typically taken as 65), times the
number of hours during the day that the air temp is above 65, or zero. SpareAir,
CriticalPeak, and FlexAlert are binomial variables indicating if a particular day was
categorized as a Spare the Air day, a Critical Peak Pricing day, or a Flex Alert day. As
indicated in Table 5, 10 percent of the observations occurred during CPP days, while only
3 percent of the observations occurred during Flex Alert days.
Since we seek to primarily explain the relationship between price and quantity
consumed, we will begin by examining our dependent variable (daily use) and its pricing
structure. Usage data came from a random sample of regular and low income households
24
provided by the Sacramento Municipal Utility District (SMUD).
The raw data,
corresponding to an hourly report of the amount of electricity used by each household,
was summed across all hours of the day to obtain total daily use data for each household.
As indicated in Table 6, while mean usage is 1.16, the distribution is peaked (a kurtosis
of 4.52) and somewhat skewed to the right (skewness of 1.67), which is indicated below
in Figure 3.
Figure 3. Histogram of the Daily Average of the Total Electricity Use per Household
Number of households
120.00
100.00
80.00
60.00
40.00
20.00
0.08
0.28
0.48
0.68
0.88
1.08
1.28
1.48
1.68
1.88
2.08
2.28
2.48
2.68
2.88
3.08
3.28
3.48
3.68
3.88
4.08
4.28
4.48
4.68
4.88
-
Average daily usage in kWh
Each household’s use was summed across the entire 122-day period then divided
by 122. Figure 3 presents the frequency (vertical axis) in which a particular average
value (horizontal axis) appears in the distribution. According to the figure, electricity use
is positively skewed, with a relatively small number of households accounting for a high
percentage of electricity use during the period. This indicates that more households use
much more electricity than the average household, whereas very few use less. Intuitively,
this makes sense as most homes contain similar appliances (such as a refrigerator,
25
television, dishwasher, and a washer and dryer), and somewhat regular use of these items
is to be expected. Though unusual, some households contain high electricity-demand
items such as computer servers, kilns or manufacturing equipment whose energy use can
very quickly cause the mean to exceed the median and/or mode. 8
Due to this variation in use across households, the demand for electricity might
differ between low-use and high-use consumers. Accordingly, in addition to regressions
which pool all 665 households together, we also split the households into quartiles by
average daily use (similar to Reiss and White (2005)), whereby quartile 1 consists of
households with average daily use under 0.69, quartile 2 consists of households with
average daily use between 0.69 and 1.021, quartile 3 consists of households with average
daily use between 1.021 and 1.47, and quartile 4 consists of households with average
daily use beyond 1.47. Table 6 below gives descriptive statistics for electricity usage for
each of these quartiles as well as the entire sample.
8
While this is not an exact normal distribution, we have a very large number of
observations. Thus, following the central limit theorem, in the estimation of our
regression models we assume the parameter estimates adhere to a normal distribution.
This is in keeping with previous work in this area, as well as standard convention in the
economics literature when estimating electricity demand functions.
26
Table 6. Descriptive Statistics for Electricity Use in Each Quartile
Quartile
Quartile
Quartile
Quartile
1
2
3
4
0.688 1.021 Range
< 0.688
> 1.174
1.021
1.474
Mean
0.465
0.845
1.229
2.102
Standard Deviation
0.149
0.100
0.130
0.612
Coefficient of variation
0.32
0.12
0.11
0.29
Kurtosis
-0.77
-1.25
-1.11
5.26
Skewness
-0.36
0.09
0.22
2.04
kWh as Percentage of
10%
18%
26%
45%
Total
Count
166
166
166
167
Correlation with price
-0.06
0.01
0.01
0.1
Correlation with
0.34
0.57
0.56
0.44
temperature
Complete
Sample
.06 – 7.84
1.16
0.82
0.71
4.52
1.67
100%
665
0.36
0.29
We see that for quartiles 1-3 kurtosis and skewness are closer to the normal
distribution than the overall sample. Yet for the fourth quartile this is not the case.
Accordingly, much of the imbalance in the overall sample is tied to those households
with much higher electricity use. We also see that the range in use is highest for the
fourth quartile, as is the correlation between price and use (albeit positive for quartiles 24). Furthermore, the first quartile has the highest coefficient of variation and is the only
one to have a negative correlation with price, which is similar to results reported in Reiss
and White (2005).9
The average price paid by each household for each day of the 122 days in the
sample was calculated using SMUD’s residential rate schedule. Standard residential
9
As mentioned, we expect price and consumption to be negatively correlated. Thus,
finding a positive correlation between these two variables is not consistent with our
expectations. However, given that we intend to estimate a multiple regression, it is best
to wait until the multiple regression results are presented in Chapter 4 to fully discuss the
relationship between price and electricity use.
27
rates, SMUD rate codes Residential Standard General service (RSGH) and Residential
Standard Open Electric-heated (RSEH), are subject to SMUD’s residential rate schedule.
However, if they meet low- income requirements, customers can enroll in an assistance
program where they receive a 35% discount on their base usage and a 30% discount on
600kWh past base usage. The customer is charged the full price for any electricity
purchased in addition to the base plus 600kWh.
This creates a two-block pricing
structure for regular customers and a three-block structure for low-income customers,
indicated below in Table 7.
Table 7. Electricity Rates by Rate Code and Usage
Monthly Usage
<700kWh
>=700kWh
Rate Code
Regular
RSGH and
RSEH
Low Income
RSGH_E and
RSEH_E
>=1350kWh
Weekday
Weekend
Weekday
Weekend
Weekday
Weekend
0.10778
0.0846
0.179
0.166
-
-
0.07005
0.05499
0.1253
0.1162
0.179
0.166
Note: Prices in dollars per kWh.
For example, consider a ‘regular’ household that uses 956kWh of electricity over
the course of a billing cycle, usually 30 days. The household will be charged either
$0.10778 or $0.0846 (depending upon the day of the week) for the each of the first
700kWh consumed, then $0.179 or $0.166 per kWh (again, depending upon the day of
the week) for the remaining 256kWh. This increasing-block pricing structure utilizes the
economics principle that consumers will purchase less of a good as the prices increases,
28
thus leading to a reduction in energy use. This can be illustrated by examining changes
in daily usage of a typical household throughout the month (see Figures 4 a-d below).
Figures 4 a-d. Typical Daily Household Electricity Use during Each Month
Figure 4 b. July
Daily Use
Daily Use
Figure 4 a. June
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Day of the Month
1 3 5 7 9 1113151719212325272931
Day of the Month
Figure 4 d. September
Daily Use
Daily Use
Figure 4 c. August
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Day of the Month
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Day of the Month
Above are graphs of 30 randomly selected households whose total daily kWh use
have been averaged by month. In the above figures, the typical household generally
surpasses the 700kWh threshold between the sixteenth and seventeenth day of any given
month. Interestingly, notice that (i) average hourly usage is slightly higher prior to the
threshold and (ii) there is a decline in usage beyond the threshold level of consumption.10
Rate information is publicly displayed on SMUD’s website and is also provided on all
SMUD bills. Given that SMUD sets its rates well in advance, similar to the existing
literature, we treat price as exogenous in the models we estimate.
10
29
Spare the Air, Critical Peak Pricing and Flex Alerts are all binomial variables that
are district-specific and are designed to help reduce electricity use and promote a cleaner
environment. Spare the Air days are event days called by regional air districts and
promoted on television, radio and other media outlets in an effort to reduce harmful
particles in the air. The program is administered by local air quality districts and is
designed to improve air quality by reducing automobile usage, wood burning and other
activities that release unhealthy particulate matter into the air. This may lead consumers
to avoid driving on those days (and thus use more electricity at home) or perhaps lead
them to conserve electricity in the home if they perceive doing so indirectly reduces
particulate matter. Accordingly, the impact of such announcements could increase or
decrease electricity demand.
Critical Peak Pricing (CPP) and Flex Alerts could also have positive or negative
influences on household electricity demand depending on the story. For instance, if both
signal unusually uncomfortable weather (beyond that accounted for by cooling degree
hours), then it could be that electricity use is simply higher on such days due to weather
conditions. Alternatively, as the intent of these mechanisms is to reduce electricity usage
on such days, their impacts on electricity demand could be negative. For instance, CPP is
a program instituted by SMUD, which monitors enrolled household electricity use on a
real-time basis, such that when a CPP day is announced enrolled households are charged
during the peak time of the day a rate 75% above that charged during a similar time
period on a non-CPP day. Although the sample used in this thesis does not include such
30
households, any spillover effects could influence households in our sample even though
they follow a different rate structure.
Unlike CPP, Flex Alerts are designed to affect all households consuming
electricity. California’s Energy Conservation Network administers Flex Alerts, usually a
day ahead of time as another effort to reduce peak electricity demand. Households are
asked to turn off any unnecessary appliances that use electricity or to use them after 6
pm. While this may cause households to shift their electricity use on any given day to
after 6 pm, and thus its effect on electricity use for the entire day may remain unchanged,
it could also lead households to shift their consumption away from such days towards
other days, thus decreasing demand on that day.
As indicated in Figure 5 below, temperature is highly correlated with electricity
use on any given day. As mentioned in the previous chapter, most home energy use
studies since 1970 incorporate a temperature variable in their models. Recent studies
(such as Alberini et al. (2011), Bratch (1993), and Faruqui and Sergici (2011)) as well as
the majority of studies reviewed in the previous chapter, utilize heating and cooling
degree hours (CDH) or days instead of outside air temperature in their models. In this
study, CDH on any given day t is defined as the summation of the maximum of:
CDHt = ∑ maximum [(O.A.T. – 65) × (hours in dayt temp>65), zero]
(1)
This is the same construction as used by the U.S. Department of Energy and is
recommended by the CPUC (2012), RAND (2006), as well as most other governmental
and research agencies. The rationale behind this is that this measure is more likely to
accurately explain home energy use rather than a simple outdoor air temperature reading.
31
An outdoor air temperature of roughly 65 is not likely to result in households using either
a heater or an air conditioner, However, this study examines homes in the Sacramento
valley during the summer months when outside air temperatures average in the mid-90s
(National Oceanic and Aeronautical Association 2013). Temperatures this far above 65
compel most households to use electric air conditioners, fans, and other means of space
cooling to avoid discomfort, all resulting in large amounts of electricity being consumed.
Indeed, this relationship can be seen in Figure 5 below, which charts CDH and average
daily energy use over the period analyzed, summer 2012.
Figure 5. Average Daily Usage and Average Daily Temperature
2.5
21.0
2
16.0
1.5
11.0
1
0.5
6.0
0
1.0
CDH
Average Daily Use
3
Average Daily Use (kWh)
CDH
Figure 3 illustrates the strong positive correlation in electricity use and cooling
degree hours throughout this four month period. Accordingly, any regression model
seeking to explain daily fluctuations in electricity demand should control for the
temperature in some form or another.
3.3
Alternative Specifications of Electricity Demand
32
We estimate several fixed and random effects variants of the linear and doublelog versions of equation (1). Specifically, we begin by estimating fixed and random
effects models of basic versions of our model, where use is regressed only on price:
Levels:
Useit = 0 + 1Priceit + it
(2)
Logs:
Ln(Useit) = 0 + 1 ln(Priceit) + it
(3)
These models are designed to investigate the relationship between price and use with no
other explanatory variables.
Building on that model, we then introduce one-day lag use and temperature
variables, (consistent with Reiss and White, 2005; RAND, 2006, CPUC, 2012 and
others).
Levels:
Useit = 0 + 1Priceit + 2Useit-1 + 3Temperatureit + it
(4)
Logs:
Ln(Useit) = 0 + 1 ln(Priceit) + 2ln(Useit-1) + 3ln(Temperatureit) + it
(5)
Building further, we incorporate our remaining explanatory variables: Spare the
Air, Critical Peak and Flex Alert. Thus,
Levels:
Useit = 0 + 1Priceit + 2Useit-1 + 3Temperatureit + 4SpareAirit + 5CriticalPeakit +
6FlexAlertit + it
Logs:
(6)
33
Ln(Useit) = 0 + 1 ln(Priceit) + 2ln(Useit-1) + 3ln(Temperatureit) + 4SpareAirit +
5CriticalPeakit + 6FlexAlertit + it
(7)
This concludes the list of explanatory variables. However, we wish to further examine
electricity demand. We do so by interacting price with the temperature, Spare the Air,
Critical Peak Pricing and Flex Alert variables. By doing this, we hope to capture events
that may temporarily change the slope of the demand curve.
Levels:
Useit = 0 + 1Priceit + 2Useit-1 + 3Temperatureit + 4SpareAirit + 5CriticalPeakit +
6FlexAlertit + 7(Priceit × Temperatureit) + 8(Priceit × SpareAirit) + 9(Priceit ×
CriticalPeakit) + 10(Priceit × FlexAlertit) + it
(8)
Logs:
Ln(Useit) = 0 + 1 ln(Priceit) + 2ln(Useit-1) + 3ln(Temperatureit) + 4SpareAirit +
5CriticalPeakit + 6FlexAlertit + 7(lnPriceit × lnTemperatureit) + 8(lnPriceit ×
SpareAirit) + 9(lnPriceit × CriticalPeakit) + 10(lnPriceit × FlexAlertit) + it
(9)
This is similar to what Faruqui and Sergici do in their (2011) study. Both studies
interact price with temperature, but this study is more concerned with an event rather than
a time period affecting price elasticity so we will use event dummy variables instead of
month dummy variables. Temperature may play a key component in household behavior,
for as the temperature increases electricity becomes more necessary (as there is greater
need for cooling), causing demand to become more inelastic.
Finally, due to the variation in the quartiles (by use) we will also segregate
households into their respective quartiles and then analyze their demand characteristics
34
with the preferred model(s) from the previous regressions in the same way that Reiss and
White (2005) conducted their study.
35
Chapter 4
ESTIMATION RESULTS
This chapter presents and discusses the results from the estimation of the various
models provided in the previous chapter. As previously mentioned, several versions of
electricity demand are estimated.
First, we estimate a simple static specification,
whereby electricity usage is regressed solely on price, utilizing fixed and random effects.
Second, we estimate a dynamic version of demand by adding our measure of temperature
(i.e., cooling degree hours) and one-day lagged usage to the simple regression model.
Third, we further extend the analysis by adding as regressors three dummy variables
representing Spare the Air, Critical Peak, and Flex Alert days. Fourth, we account for
possible changes in consumer preferences tied to cooling degree hours, as well as Spare
the Air, Critical Peak Pricing, and Flex Alert days, by interacting the price of electricity
with these variables.11 Lastly, while initial estimations rely on data pooled across all
households, to assess differences in electricity demand within our sample we split
electricity usage into quartiles and then estimate our preferred specification for each of
these quartiles.
Given our emphasis is on the impact of price on demand, for each regression we
report short-run and long-run (in the dynamic specifications) price elasticities of demand.
11
For instance, it might be that on unusually hot and humid days electricity demand is
less sensitive to price (i.e., the price elasticity of demand is lower in absolute value), as
consumers find it more necessary to use air conditioning on such days. Alternatively,
during Spare the Air, Critical Peak Pricing, and Flex Alert days, if consumer preferences
change in response to information tied to such events, it may be that not only does
demand for electricity shift but price responsiveness may change as well.
36
For the double-log form, the price elasticity is simply the estimated coefficient of the log
of price. For the linear form, the price elasticity is evaluated at the means of use and
price by multiplying the coefficient of price by the mean price-to-use ratio. In dynamic
specifications, both short-run and long-run price elasticities are provided. For instance,
consider the following specification:
LogUsei,t = β0 + β1LogPricei,t + β2LogUsei,t-1 + β3LogTemperaturei,t.
(1)
In this case, the short-run price elasticity is β1, while the long-run price elasticity is
β1/(1- β2). Given that our data is daily, though, we do caution the reader that the “longrun” price elasticity is nonetheless measuring price responsiveness over a very short
period of time.
To begin, Table 8 below shows the results for the simple specification of demand,
under the different panel data treatments (i.e., fixed and random effects) as well as the
two functional forms (i.e., double-log and linear). As with all regressions in this thesis,
we utilize Eicker-Huber-White heteroskedastic-consistent standard errors.
As provided at the bottom of Table 8, the R-squared for both the double-log and
linear forms is quite high. Also, the coefficient of the price variable in each regression is
negative and significantly different from zero. As for the estimated price elasticities, they
all lie in the inelastic range, with the linear estimates being roughly 50% larger in
magnitude compared to the double-log estimates. Furthermore, these estimates are much
lower in absolute value compared to the literature in general (e.g., see Espey and Espey,
2004). However, since there is a high likelihood of omitted variable bias associated with
these simple regressions, the reader is cautioned in attaching too much importance to
37
these price elasticity estimates. Indeed, in the regressions that follow we wish to see
whether the inclusion of additional variables affects the magnitude of the price elasticity.
Table 8. Model 1 Estimation Results
Double-Log
Variables
Log Price
Fixed Effects Random Effects Fixed Effects
-0.0702***
(0.00576)
-0.247***
(0.0129)
Random
Effects
-0.0643***
(0.00854)
Price
Constant
Linear
-0.234***
(0.0315)
-1.079***
(0.0737)
-0.956***
(0.106)
1.280***
(0.00839)
1.267***
(0.0289)
Observations
81,130
81,130
81,130
81,130
R-squared
0.744
0.714
Short-run Price
-0.0702
-0.0643
-0.1022
-0.0906
Elasticity
Note: Hausman test of random versus fixed effects is not feasible for these regressions
due to estimated negative variance of difference in fixed and random effects coefficients.
Robust standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.10.
Building on the simple regression, we now incorporate into the specification of
demand base-65 cooling degree hours (labeled as temperature in the remaining tables)
and the one-day lag of use. Given that studies typically find these variables are important
determinants of household electricity demand, we expect their inclusion to significantly
raise explanatory power, as well as possibly influence the price elasticity estimates (in the
event of omitted variable bias in their absence). Indeed, as the results in Table 9 below
show, R-squared has increased in both fixed effects models, indicating that adding these
38
two variables explain roughly an additional 10% of the movement in electricity use
across households and days. Furthermore, the Hausman test confirms the preference of
fixed effects over random effects estimation.
Table 9. Model 2 Estimation Results
Double-Log
Random
Fixed Effects
Variables
Effects
Log Price
-0.0311***
0.0894***
(0.00440)
(0.00751)
Log Use(-1)
0.476***
0.859***
(0.00395)
(0.00703)
Log Temperature
0.193***
0.145***
(0.00222)
(0.00374)
Price
Use(-1)
Temperature
Constant
Observations
R-squared
Hausman Test
(p-value)
-1.124***
(0.0149)
80,465
0.849
-0.568***
(0.0218)
80,465
Linear
Fixed Effects
-0.281***
(0.0550)
0.441***
(0.00480)
0.00175***
(1.53e-05)
0.306***
(0.00815)
80,465
0.843
Random
Effects
1.491***
(0.0654)
0.826***
(0.00921)
0.00126***
(3.73e-05)
-0.233***
(0.0113)
80,465
30717.65
30661.85
(0.00)
(0.00)
Short-run Price Elasticity
-0.0311
0.0894
-0.0266
0.1414
Long-run Price Elasticity
-0.0594
0.6340
-0.0476
0.8126
Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.10
Examining the coefficients of one-day lagged use and temperature, results are
similar in that as expected the coefficients are positive and significantly different from
zero in all four regressions. Accordingly, similar to other studies (e.g., see Faruqui and
Sergici, 2011), an increase in outside temperature above 65 causes households to
increasingly condition their indoor air, using more electricity in the process. Also, the
coefficients on one-day lagged use fall within the zero-one interval, which is consistent
39
with studies that examine the habitual nature of demand for a variety of goods.
Interestingly, though, the coefficient of lagged use is nearly twice as large in the random
effects regressions as compared to the fixed effects regressions, which does affect the
long-run price elasticity estimates.
Turning to the price elasticity estimates, given that Model 2 is a dynamic version
of household electricity demand, we can estimate both short-run and long-run price
elasticities. As we see at the bottom of Table 9, the price elasticities corresponding to the
two fixed effects regressions are not only negative, but in the case of the short-run
estimates they are more than 50% smaller in magnitude compared to the values reported
in Table 8.12 Furthermore, as expected long-run estimates are slightly larger in absolute
value compared to the short-run estimates. Nonetheless, the price elasticity estimates are
very close to zero, which indicates consumers are nearly unresponsive to price changes
on a day-by-day basis.13
Unexpectedly, the random effects regressions yield positive and significant
coefficients on price, which as reported at the bottom of Table 9 lead to positive price
elasticity estimates. However, as mentioned, the Hausman test strongly favors using
12
Accordingly, finding a large increase in R-squared when temperature and one-day
lagged use are added to the regression, coupled with large decreases in the price
coefficients, lends support to there being omitted variable bias in the simple regressions
reported in Table 8.
13
Our estimated price elasticities are close to others obtained in the literature. For
instance, Fisher and Keysen (1962) obtained similar results when they incorporated
lagged terms into their double-log models. Griffin (1994) also obtained similar results,
reporting short-run price elasticities in the -0.04 to -0.06 range. In their study of daily
household electricity demand in Baltimore, Faruqui and Sergici (2011), reported a daily
price elasticity during the extreme weather periods (i.e. summer months) equal to -0.034,
which falls within the range of our estimates for summer months in Sacramento.
40
fixed effects over random effects. Also, other studies of daily household electricity
demand (e.g., Faruqui and Sergici, 2011) utilize fixed effects procedures. Accordingly,
we favor the fixed effect price elasticity estimates over the random effects estimates.
In Model 3, we incorporate dummy variables into the demand specifications to
account for whether particular days were Spare the Air, Critical Peak Pricing, or Flex
Alert days. Results are provided below in Table 10.
Table 10. Model 3 Estimation Results
Double-Log
Fixed
Random
Variables
Effects
Effects
Log Price
-0.0220***
0.0893***
(0.00443)
(0.00757)
Log Use(-1)
0.461***
0.860***
(0.00409)
(0.00706)
Log Temperature
0.182***
0.148***
(0.00228)
(0.00374)
Spare Air
0.0534***
-0.0495***
(0.00488)
(0.00470)
Critical Peak
0.0300***
-0.0116***
(0.00336)
(0.00320)
Flex Alert
0.0928***
0.0275***
(0.00591)
(0.00534)
Price
Use(-1)
Temperature
Constant
Observations
R-squared
Hausman Test
(p-value)
-1.058***
(0.0152)
-0.585***
(0.0224)
80,465
0.850
80,465
Linear
Fixed Effects
Random
Effects
0.00721
(0.00692)
-0.0141***
(0.00444)
0.0609***
(0.00894)
-0.242***
(0.0550)
0.438***
(0.00491)
0.00173***
(1.66e-05)
0.307***
(0.00834)
-0.103***
(0.00735)
-0.0436***
(0.00414)
0.00172
(0.00774)
1.447***
(0.0654)
0.829***
(0.00914)
0.00138***
(3.86e-05)
-0.248***
(0.0117)
80,465
0.843
80,465
31207.46
30095.43
(0.00)
(0.00)
Short-run Price Elasticity
-0.0220
0.0893
-0.0229
0.1371
Long-run Price Elasticity
-0.0408
0.6379
-0.0408
0.8017
Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.10
41
Although the coefficients of these additional variables are most often significantly
different from zero, their impact on R-squared is negligible. Also, similar to the results
from Model 2, the Hausman test indicates a strong preference of fixed effects over
random effects estimation.
Concerning the individual coefficients, the coefficient estimates on the price, oneday lagged use, and temperature variables are nearly identical to those in the previous
model. The coefficients of two of the newly-introduced variables (Spare Air and Flex
Alert) are positive and largely significant in the fixed effects regressions, while the
coefficient of Critical Peak is negative in three of the four regressions. 14 As for the Flex
Alert coefficient, when SMUD calls a Flex Alert event it asks customers to curtail
electricity use as much as possible until after 6 PM the day of the event, in an effort to
reduce load on the grid during high use times. Since most of our Flex Alert coefficient
estimates are positive and significant, this suggests that this program has the opposite of
its intended effect. However, since this study uses total daily usage instead of hourly
usage as its dependent variable, it is quite possible that users in fact did curtail use prior
to 6 PM, by shifting their usage to after 6 pm. In the end, it could still be that total usage
on such days is higher simply because of extreme conditioning of indoor air.
As for the price elasticity estimates, the calculated values are very similar to those
obtained from Model 3. In particular, they lie well within the inelastic range, with the
14
Recall that critical peak pricing coincides with a temporary 75% increase in price on
critical use days, which generally occur on the hottest days in the summer. At least for
three of the four regressions, consumers are reducing their electricity demand on such
days, which suggests there may be non-linear responses to price increases.
42
short-run estimates being lower in absolute value compared to the long-run estimates, and
in the case of the fixed effects (random effects) regression they are significantly negative
(positive). Given the Hausman test favors using fixed effects over random effects,
however, we do favor the theoretically-consistent estimates associated with the fixed
effects regressions.
In Model 4, we introduce a set of interaction terms. Specifically, similar to
Faruqui and Sergici (2011), we interact price with temperature.15 We go a step further,
though, and also interact price with the Spare the Air, Critical Peak Pricing, and Flex
Alert dummy variables. The inclusion of these additional terms allows the price elasticity
to vary depending on the variables interacted with price.
Table 11. Model 4 Estimation Results
Double-Log
Fixed
Random
Variables
Effects
Effects
Log Price
-0.0413
0.0914*
(0.0386)
(0.0502)
Log Use(-1)
0.461***
0.861***
(0.00409)
(0.00706)
Log Temperature
0.190***
0.147***
(0.0163)
(0.0215)
Spare Air
0.125**
-0.116**
(0.0494)
(0.0536)
Critical Peak
0.0270
0.0626
(0.0379)
(0.0421)
Flex Alert
0.0717
0.0788
(0.0657)
(0.0615)
15
Linear
Fixed Effects
-0.0975**
(0.0439)
-0.0564
(0.0345)
0.00402
(0.0577)
Random Effects
-0.0107
(0.0415)
-0.147***
(0.0362)
-0.0866*
(0.0470)
In the case of Faruqui and Sergici (2011), they obtained a negative coefficient on the
term interacting price and temperature. Yet, as we suggested earlier, we expect the price
effect to drop during periods of unusually hot weather as conditioning indoor air becomes
more of a necessity, thus lowering the price elasticity in absolute value. Accordingly,
Faruqui and Sergici (2011) obtain results which run counter to this argument.
43
Table 11. Model 4 Estimation Results cont.
Double-Log
Random
Fixed Effects
Variables
Effects
Log Price x
0.00365
-0.000636
Log Temperature
(0.00739)
(0.00961)
Log Price x
0.0315
-0.0293
Spare Air
(0.0218)
(0.0238)
Log Price x
-0.00108
0.0329*
Critical Peak
(0.0167)
(0.0188)
Log Price x
-0.00977
0.0223
Flex Alert
(0.0278)
(0.0260)
Price
Use(-1)
Temperature
Price x
Temperature
Price x
Spare Air
Price x
Critical Peak
Price x
Flex Alert
Constant
-1.101***
(0.0853)
-0.580***
(0.111)
Linear
Fixed Effects
Random Effects
-2.934***
(0.125)
0.429***
(0.00486)
0.000311***
(6.31e-05)
0.0132***
(0.000593)
1.127***
(0.432)
0.316
(0.334)
1.013*
(0.613)
0.609***
(0.0144)
-0.424**
(0.174)
0.827***
(0.00892)
0.000388***
(9.79e-05)
0.00914***
(0.000918)
-0.817**
(0.402)
0.939***
(0.334)
1.123**
(0.485)
-0.0416**
(0.0162)
Observations
80,465
80,465
80,465
80,465
R-squared
0.850
0.845
Hausman Test
30827.56
31037.64
(p-value)
(0.00)
(0.00)
Short-run Price
-0.0211
0.0906
-0.0037
0.1488
Elasticity
-0.0392
0.6518
-0.0065
0.8892
Long-run Price
Elasticity
Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.10. Price
elasticities are calculated at the means of Temperature, Spare Air, Critical Peak, and Flex
Alert.
44
Perusing Table 11, we see the addition of these interaction terms has changed Rsquared very little. Furthermore, the Hausman test continues to favor using fixed effects
or random effects. As for the interaction terms, we see the effects of these variables are
not significant in the double-log model. Yet several interactions in the linear model are
significant. The positive interaction of price and temperature does not match Faruqui and
Sergici’s (2011) results, but does match our expectations. Indeed, for the Sacramento
Valley as outdoor temperature increases, household electricity demand becomes slightly
more inelastic. Examination of both Faruqui and Sergici (2011) and this study’s average
temperatures and cooling degree days (NOAA 2113) during their respective sample
periods reveal higher average temperatures and cooling degrees in the Mid-Atlantic
region, suggesting that households in that region are more acclimated to warmer
temperatures and are thus less responsive to increases in outside air temperature.
Interacting price with Critical Peak yielded mixed results between the models.
For instance, with respect to the fixed effect results, on CPP days the linear model
showed a more inelastic price effect, whereas the log model showed a less inelastic price
effect, albeit in both cases though the coefficients are statistically insignificant.
Additionally, for the linear random effects model, which is the only one for which all
four interaction terms are significant, we see that price elasticities generally become more
(less) inelastic on Flex Alert (Spare the Air) days, indeed potentially becoming positive
on Flex Alert days.
45
Regarding the price elasticities, similar to prior models, they become negative
when demand is estimated with fixed effects, yet positive when demand is estimated with
random effects. Furthermore, the double-log price elasticity estimates are similar in
magnitude to those reported in Tables 9 and 10. As for the linear specification, the price
elasticity estimates are lower in absolute value for the fixed effect regression. Again,
since the Hausman test favor using fixed effects over random effects, coupled with the
theoretically-consistent estimates obtained from the fixed effect regressions, we favor the
fixed effect price elasticity estimates.
In Section 3.1 of Chapter 3, Table 6 splits the household data into quartiles
depending upon the average amount of electricity used each day by household. To see
whether the price elasticity estimates differ across we consider estimating separate
regressions on each of these quartiles. Specifically, given the Hausman test favors fixed
effects over random effects, we eliminate the random effects specifications from further
consideration. Also, since the double-log specification is convenient in that the estimated
price coefficient is the price elasticity of demand, coupled with the interaction terms
being insignificant in Table 11, we settle on estimating the double-log fixed effect
specification in Table 10 (i.e., column 1) for each quartile. This is similar to an approach
taken by Reiss and White (2005) to examine differences in price elasticities within their
sample. The results are provided in Table 12 below.
To begin, across all four regressions, R-squared is higher with the 1st and 4th
quartile regressions, compare to the 2nd and 3rd quartiles. Also, many of the coefficients
are significantly different from zero across the regressions.
46
Table 12. Quartile Estimation Results for Fixed Effect Double-Log Model 3
Variables
Quartile 1
Quartile 2
Quartile 3
Quartile 4
Log Price
Log Use(-1)
Log Temperature
Spare Air
Critical Peak
Flex Alert
Constant
0.0151
(0.0143)
0.279***
(0.00686)
0.0627***
(0.00297)
-0.00451
(0.0138)
0.0199***
(0.00763)
0.0184
(0.0158)
-1.074***
(0.0361)
-0.00545
(0.00543)
0.0749***
(0.00314)
0.0374***
(0.00172)
0.0246***
(0.00564)
0.0216***
(0.00356)
0.0246***
(0.00685)
-0.469***
(0.0151)
-0.00456
(0.00353)
0.0835***
(0.00307)
0.0495***
(0.00183)
0.0219***
(0.00419)
0.00240
(0.00289)
0.0305***
(0.00480)
-0.0946***
(0.0122)
-0.0145***
(0.00439)
0.223***
(0.00542)
0.149***
(0.00409)
0.0255***
(0.00442)
-0.00156
(0.00335)
0.0525***
(0.00522)
-0.219***
(0.0222)
Observations
20,170
20,163
20,106
20,026
R-squared
0.685
0.252
0.242
0.659
Short-run Price
0.0151
-0.0055
-0.0046
-0.0145
Elasticity
0.0209
-0.0059
-0.0050
-0.0187
Long-run Price
Elasticity
Note: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.10
Estimation results for the 4th quartile, the quartile with the greatest average daily
use, most closely resemble those of the preferred Model 3, albeit with minor differences
(most notably the decreased magnitude of the lagged use coefficnet). In addition to being
the only quartile exhibiting a statistically significant response to price, quartile 4 also is
the most responsive to temperature, Spare the Air, and Flex Alerts.
Although the only statistically significant price coefficient occurs with the 4th
quartile, we our results are similar to those of Reiss and White (2005), in that their OLS
method estimated the price elasticity to decrease from 0.37 to -0.08 when comparing the
47
1st to the 4th quartiles. Accordingly, given the price responsive is insignificantly different
from zero for quartiles 1 through 3, coupled with the associated exceptionally small
short-run and long-run price elasticities, it appears that much of our prior results are
driven by behavior among higher users of electricity. And so, individuals in the 4th
quartile are reacting to price quite differently from users in other quartiles. Perhaps such
individuals have a better understanding of factors influencing their energy bill and react
to price changes accordingly. Interestingly, if the intent of pricing policy is to reduce
overall electricity use during peak periods, much of the response to such a policy comes
from high-end users and not low-end users. Thus, there are distributional issues to
consider when evaluating the efficacy of such peak load pricing programs. In the next
chapter, we summarize our results and provide concluding comments.
48
Chapter 5
CONCLUDING REMARKS
As we observed in Table 1 from Chapter 2, studies utilizing cross-sectional data
tend to report higher absolute price elasticities than studies utilizing panel data. The
primary result of this study, which also uses panel data, is consistent with previous
results, as our price elasticities are on the lower end and fall in the range of other panel
data studies of household electricity demand. Indeed, the double-log estimates range
from -0.0210 to -0.0702, while the linear estimates range from -0.0037 to -0.2726, with
both models yielding relatively consistent estimates across the various models. Also,
both double-log and linear specifications show that long-run estimates are slightly less
inelastic than short-run estimates, which is in keeping with studies of short-run and longrun price elasticities for other goods.16
Additional explanatory variables added meaningfully to our model. While the
effects of Spare the Air, Critical Peak Pricing and Flex Alert days added statistically
significant explanatory power, their magnitudes are smaller than expected. Both Spare
the Air and Flex Alert had small positive impacts on electricity use, ever though the latter
was implemented to help reduce energy consumption. Both of these are likely caused by
A “standard” story told is that over a longer period of time consumers are more easily
able to respond to price changes as they are better-able to find substitutes. In our case,
given we are utilizing daily data, our results do not imply there is greater price
responsiveness over a two-day period because consumers are finding substitutes. All we
can say, regardless of the story, is that we find consumers are slightly more responsive to
price over a slightly longer period of time. If data of a sufficient time span were available,
a more detailed analysis would consider differences between the impact of price changes
today on consumption today compared to consumption over a longer period, say a month
or two.
16
49
households shifting the time of their use from peak hours to off-peak hours (after 6 PM)
and subsequently using more overall energy than they otherwise may have.17
Including one-day lagged use and cooling degree hours (temperature) to the
model added significant explanatory power to the regressions, and their estimates were
significant and consistent across each of the models. The coefficient estimates for lagged
use were approximately 0.5 for the double-log and linear models, while the coefficients
of temperature were approximately 0.18 and 0.0017 for the double-log and linear models,
respectively. Theoretically, both of these variables should increase the use of electricity
due to the fact that home energy use is relatively stable from day-to-day and as outside air
temperatures increase above 65 households are more likely to use their air conditioning
units to cool themselves down.
The results of this thesis suggest several avenues for future research to consider.
First, although future research done on this topic will likely incorporate double-log and
linear specifications, coupled with fixed or random effects if estimated with panel data,
future researchers may wish to consider alternative functional forms of demand. For
instance, given that the double-log and linear forms do not ensure theoretically-consistent
parameter estimates (such as ensuring normal demands are homogeneous of degree zero),
provided data can be obtained, perhaps future research should consider estimating
household electricity demand with theoretically-consistent specifications (such as the
17
Additionally, we see that price elasticities generally become less elastic on Spare the
Air days, but more elastic on Flex Alert days.
50
almost ideal demand system or other forms commonly used in the literature today).
Second, although data was lacking for this thesis, future research may wish to consider
including other variables of interest in the model, such as household income, home
square footage, and information about appliances in the household (specifically those
used for indoor climate control). Third, if data of a longer time span were available,
researchers could consider assessing changes in the price elasticity over a longer time
span to more effectively gauge differences between short-run and long-run price
elasticities. Fourth, if SMUD were to implement a dynamic pricing program (in which
the price of electricity varies constantly throughout the day), that data would greatly
increase price variability and likely lead to better estimates of the price elasticity of
demand for its customers, reducing uncertainty. Furthermore, while we assume price is
exogenous, customers do influence the price they pay depending on their choice of
electricity use. Thus, future research should explore the endogeneity of price in greater
detail.
Lastly, given that we find differences in demand across households (i.e.,
quartiles), there are distribution issues to consider when contemplating pricing programs,
such as peak load pricing, since the benefits and costs of such policies are not equally
shared across households.
51
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