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Energy Policy 138 (2020) 111246
Available online 22 January 2020
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From frugal Jane to wasteful John: A quantile regression analysis of Swiss
households’ electricity demand
☆
Ivan Tilov
*
, Mehdi Farsi, Benjamin Volland
Institute of Economic Research (IRENE), University of Neuch^
atel, Switzerland
ARTICLE INFO
JEL classication:
Q400
Q410
D120
Keywords:
Electricity demand
Households
Prices
Quantile regression
Panel data
ABSTRACT
In this article, we investigate the heterogeneity in the responsiveness of Swiss household electricity demand to
changes in prices and income. We focus on segments of consumers with different intensities of electricity con-
sumption by using a panel quantile regression approach. This estimation strategy is applied to a rich micro-level
longitudinal data set of 3880 observations from more than 1400 households, matched with a unique price data
set extracted from the Swiss electricity regulator’s online sources. While the ndings show an inelastic electricity
demand across all groups, an interesting pattern of variation emerges between lower and upper quantiles of
electricity demand, respectively frugal and intensive users. Results show that households in the rst conditional
quartile and at the median react signicantly to changes in prices, while those at the lowest quantile and upper
quantiles exhibit insignicant price elasticities. The main policy implications of this work concern the design of
price-based measures for reducing electricity consumption in the residential sector and the possibility of ac-
counting for individual responses in tailoring policies for specic consumer segments.
1. Introduction
The notion of “average economic agent”, “representative consumer”
or “typical household” plays an essential role in applied economics. It is
used to aggregate population attributes into a single representative en-
tity in order to measure its sensitivity to changes in its characteristics or
environment. Although bringing computational and interpretational
convenience, and usually being related to lower policy-implementation
costs, the focus on the “typical consumer” is nevertheless likely to
conceal some important differences among sub-groups in the population
under study. Yet, knowledge about how responsiveness varies between
these sub-groups could be used to design specic instruments which
achieve policy goals with a better investment-impact ratio, in shorter
time periods and with less welfare distortions, compared to “one-size-
ts-all” interventions based on the reactivity of the “average Joe”. The
study of population heterogeneity is thus a necessary rst step in
assessing the efciency and the equity dimensions of policy in-
terventions (Gillingham, 2014; Wadud et al., 2009).
In residential energy demand, the interest in the sensitivity of the
average consumer to tax and wealth increases has triggered a vast body
of scientic literature focusing mean price and income elasticities. This
effort has been justied by the willingness of national governments to
curb GHG pollution levels and to ensure energy independence, by
simultaneously pursuing better life standards for their populations.
However, previous estimations of average price and income elasticities
have been found to vary dramatically across studies (Espey and Espey,
2004; Fan and Hyndman, 2011; Sanquist et al., 2012). Qualied as
“mixed” and “inconclusive”, these results have been attributed to dif-
ferences in data aggregation levels, empirical methods and time hori-
zons, but also to heterogeneity of responses across countries and within
populations (Jessoe and Rapson, 2014; Miller and Alberini, 2016).
Despite a general agreement that electricity consumption is indeed
characterized by signicant variability which might severely bias
average estimations (Jaffe and Stavins, 1994; Lind�
en et al., 2006; Ran-
dolph, 2008), differences in the responsiveness of various population
groups to changes in prices and income have hitherto received little
attention from researchers.
The variation of electricity consumption within populations can be
readily related to two major sources. Namely, households vary signi-
cantly both in their available electric appliances and in the way they use
☆
This title draws on the title of an earlier article by Binder and Coad (2011) analyzing the determinants of happiness. Any resemblance with actual persons is
purely accidental!.
* Corresponding author. Institute of Economic Research, University of Neuch^
atel, A.-L. Breguet 2, CH-2000, Neuch^
atel, Switzerland.
E-mail address: ivan.tilov@unine.ch (I. Tilov).
Contents lists available at ScienceDirect
Energy Policy
journal homepage: http://www.elsevier.com/locate/enpol
https://doi.org/10.1016/j.enpol.2020.111246
Received 8 April 2019; Received in revised form 21 October 2019; Accepted 4 January 2020
Energy Policy 138 (2020) 111246
2
them. The rst of these aspects captures not only the number and the
type of electronic durables, but also their technical characteristics, such
as efciency. The second aspect is related to appliance-specic utiliza-
tion behaviors, such as how often a given device operates or the fre-
quency of leaving it on standby. Previous analyses (among others
Frondel et al., 2017; Hendricks and Koenker, 1992; Reiss and White,
2005) indeed observe important heterogeneity in residential electricity
demand originating from the ownership, type and usage of various ap-
pliances. In particular, Reiss and White (2005) nd differences between
households’ electricity price elasticities in terms of electric appliances
and their usage, with owners of larger appliances being more
price-sensitive compared to households with a regular set of electronic
devices. These authors also address differences between price elasticities
within the population directly, by focusing on tiers of electricity con-
sumption. This method has the advantage of providing a more general
picture of the intensity of electricity demand because it considers the
global household stock and usage of electronic devices and does not
focus on them individually. However, as outlined by Koenker and Hal-
lock (2001), an unconditional “truncation of the dependent variable”
suffers from sample selection problems (see p. 147). Their proposed
quantile regression approach provides a solution to avoid this bias by
dening different consumption quantiles conditional on various
household characteristics. Quantile regressions also allow to account for
unobservable differences related to energy intensity between house-
holds. For these two reasons, it is particularly well-suited for the analysis
of the responsiveness of electricity consumption across population
groups with different levels of electricity consumption. Despite the ex-
istence of prior research applying quantile analysis on residential elec-
tricity demand (Hendricks and Koenker, 1992; Huang, 2015; Kaza,
2010; Niu et al., 2016; Sardianou, 2008), panel data applications remain
scarce, especially in relation with electricity price.
This paper contributes to the understanding of the heterogeneity in
the price and income elasticities of electricity demand across various
groups of Swiss households. For this purpose, we apply a panel quantile
regression with correlated random effects (Wooldridge, 2010) in order
to assess and compare the price and income sensitivities of the average
electricity consumer (“average Joe”), the parsimonious one (“frugal
Jane”) and the intensive user (“wasteful John”). We nd that while in-
come does not have a signicant impact across the spectrum of elec-
tricity demand, households at the lowest decile of the consumption
spectrum or those who use electricity intensively do not react signi-
cantly to changes in prices, in contrast to households at the 25th and
50th conditional percentiles who exhibit price elasticities signicantly
different from zero. More generally, these ndings suggest important
heterogeneity between electricity consumers and could be used to draw
some policy conclusions.
The rest of the paper is organized as follows. Section 2 discusses prior
ndings on heterogeneous price and income elasticities and outlines the
importance of investigating heterogeneity in the context of Switzer-
land’s recent energy policies. The datasets we rely upon and related
descriptive statistics are introduced in Section 3, while section 4 outlines
our econometric strategy. The results from our estimations are presented
and discussed in Section 5. Section 6 concludes and provides policy
recommendations.
2. Literature review and background
2.1. Literature review
Research in the domain of residential energy demand has repeatedly
assessed the average effects of prices and income on household elec-
tricity demand. Although residential electricity consumption has been
generally estimated to be price- and income-inelastic, previous ndings
have been described as “inconsistent” or exhibiting an important degree
of variation (Espey and Espey, 2004; Fan and Hyndman, 2011; Lab-
andeira et al., 2017; Sanquist et al., 2012). On average, in the case of
developed countries,
1
income is found to have a null or small positive
impact on electricity consumption, with income elasticities being lower
than 0.10 in magnitude (Alberini et al., 2011; Bedir et al., 2013; Brounen
et al., 2012; Grønhøj and Thøgersen, 2011; Kavousian et al., 2013; Leahy
and Lyons, 2010; O’Doherty et al., 2008; Sanquist et al., 2012), whereas
the most frequent estimates of price elasticities for electricity demand
are between 0.4 and 0.2 on the short, and 0.7 and 0.5 on the long
run (Dennerlein and Fleig, 1987; Dennerlein, 1990; Fan and Hyndman,
2011; Reiss and White, 2005; Labandeira et al., 2017). However, Espey
& Espey (2004) observe that earlier research reports price elasticities in
a wide interval of values spanning from 2.01 to 0.08 to in the short run,
and from 2.5 to 0.07 on the long run. More recently, a meta-analysis
on the price elasticities of electricity demand by Labandeira et al. (2017)
nds an even more dramatic variation between 24.0 to 4.2. According
to Miller and Alberini (2016) and Jessoe and Rapson (2014) this can be
attributed not only to differences in data aggregation levels, empirical
methods and time horizons, but also to heterogeneity of responses be-
tween and within populations.
Several prior studies examine the heterogeneity in different domains
of household energy demand by applying a quantile regression method.
2
In her analysis of residential heating demand in Greece, Sardianou
(2008) uses conditional quantile analysis among other standard
regression techniques. Her results reveal that income plays a signicant,
albeit not different role for high and low heating consumers. Here, the
effect of energy prices is measured indirectly through households’
willingness to restrict heating fuel consumption in case of a fuel price
increase. The author concludes that intensive heating consumers are less
inclined to reduce their energy use, compared to more frugal house-
holds. Somewhat similarly, Frondel et al. (2012) and Gillingham (2014)
observe that households who use intensively energy for private car
transportation are signicantly less price-reactive compared to their
more frugal counterparts. This is explained by the possibility that more
intensive energy consumers are more dependent on the services pro-
vided by the energy-using device, thus limiting their sensitivity to price
variations. However, it is also conceivable that households with high
levels of energy consumption exhibit higher price elasticities because of
the important amount of discretionary usage of durables, as suggested
by Gillingham et al. (2015) and Wadud et al. (2010).
If it concerns the heterogeneity in household electricity demand, an
important point of reference for our analysis is the previously mentioned
study by Reiss and White (2005) which uses two waves of a residential
energy consumption survey covering 1300 Californian households. This
work estimates elasticities of income and prices in terms of appliance
holdings and usage. Signicant heterogeneity is observed in terms of
price-, but not of income-responsiveness between households. More
precisely, the authors nd that while price variations have an insignif-
icant effect on electricity usage, intensive electricity consumers (i.e.,
users with space or water electric heating systems) are more sensitive to
changes in prices than frugal ones (owning only a set of universally
owned electronic durables), with most price elasticities falling in the
interval 0.4 and 0.2. Yet, their estimated empirical elasticity distri-
bution shows that 44% of households are characterized by a nil price
sensitivity on the short-run, while only about 13% are price-elastic.
These authors also investigate price sensitivities across quartiles of in-
come and electricity demand and nd that wealthier households are less
1
Zhou and Teng (2013) provide a list with prior estimation for developing
countries, where not surprisingly price and income are overall higher. It could
be expected that the price and income sensitivities in developed economies are
lower due to the satiation of electricity demand in these countries.
2
Other strategies for addressing heterogeneity in household energy con-
sumption comprise the use of interaction terms, splitting population in tiers
according to different household characteristics other than energy consumption
(e.g., income levels, age) or cluster analysis (Gillingham, 2014; Romero-Jord�
an
et al., 2016; Zhou and Teng, 2013).
I. Tilov et al.
Energy Policy 138 (2020) 111246
3
price-reactive than their poorer counterparts. Concerning price esti-
mates for quartiles of electricity usage, Reiss and White (2005) notice
that “elasticities are lower for households that use high amounts of electricity,
despite the fact that households with energy-intensive electric space hea-
ting/cooling systems have much greater electricity price sensitivity ceteris
paribus.” (p.871). They attempt to explain this by their previously ob-
tained result that as income rises, households move to less price-elastic
electricity uses, and by the weak correlation between income and the
ownership of heating/cooling systems. Nevertheless, the difference be-
tween the point estimates in each quartile is not tested. Moreover, the
works of Koenker and Hallock (2001) and Heckman (1979) show that
such a procedure leads to a selection bias due to the simplistic seg-
mentation of the response variable. Instead, they suggest that the esti-
mation of the conditional quantiles of demand provides a better
approach to assessing parameters at different parts the consumption
distribution.
Hendricks and Koenker (1992) use a quantile regression to investi-
gate the heterogeneity in electricity demand of about 340 households in
Chicago, with a rather technical goal, i.e., testing the use of nonpara-
metric hierarchical spline models for conditional quantiles. The authors
use socio-demographic, dwelling and electronic durable attributes as
explanatory variables, but do not control for price and income charac-
teristics. They nd that higher quantiles of demand are signicantly
inuenced by household features and appliance ownership in contrast to
lower ones. This leads them to suggest when using a “representative
consumer” for estimating “baseload” electricity demand (i.e., low elec-
tricity consumption levels), demographic factors can be ignored, for
electricity usage is supposed to be more inuenced by behavioral
characteristics.
Also by using a quantile regression method, Kaza (2010) addresses
space heating and cooling, as well as the energy used by appliances and
for warm water, where the use of electricity might be supposed pre-
dominant. The analysis shows that the housing type, size and neigh-
borhood density have substantially different impacts at the tails of the
distribution of household energy demand in the US, compared to the
conditional average. Kaza (2010) also observes that energy prices have a
stronger impact at the upper spectrum of energy demand for cooling and
other uses (i.e., electricity). This result leads him to conclude that
different increases in the energy prices in tiers of energy consumption
are likely to be more efcient for reducing energy usage than uniform
increases such as a single electricity tax. However, this work uses an
aggregated price measure for all energy domains. The author also nds
that low-income consumers exhibit lower income elasticities at lower
conditional quantiles of electricity use. On the other hand, home owners,
which can be supposed to be more afuent, consume more energy for
heating, warm water and appliances. Kaza (2010) suggests that while
wealthier households are more likely to have more energy efcient
durables, they also probably own more devices.
Several more recent studies also address residential electricity con-
sumption by applying a quantile regression analysis, but focus on the
effects of non-price factors on conditional electricity quantiles (Huang,
2015; Niu et al., 2016; Schleich et al., 2013; Valenzuela et al., 2014). An
exception is Niu et al. (2016) who surprisingly do not nd a signicant
effect of prices across levels of electricity usage in China. None of the
previously discussed studies has used household level panel data, with
estimations being overwhelmingly based on household-level cross-sec-
tional data. This is problematic for the identication of structural co-
efcients. Indeed, price elasticities for cross-sectional estimates reect
price-related differences in electricity consumption between house-
holds, rather than changes in electricity consumption by households
facing changing prices.
In the face of these ndings, our contribution to the existing litera-
ture is namely to focus on the price and income elasticities across
different quantiles of household electricity consumption in Switzerland
by using a panel dataset containing a rich set of covariates.
2.2. Background
Similarly to analyses applied to other countries, earlier studies for
Switzerland have extensively focused on the estimation of average price
and income impacts on electricity demand. These works have mainly
relied on cross-sectional aggregated data (Boogen et al., 2017; Denner-
lein and Fleig, 1987; Zweifel et al., 1997), with only few using
household-level analysis (Boogen et al., 2014; Filippini, 1999, 2011).
Most of these studies nd average price elasticities of about 0.3 and
insignicant effect of income on electricity demand. To our knowledge,
no previous works address heterogeneous price and income elasticities
across Swiss households.
Yet, such an investigation is important in the context of Switzerland’s
recent energy policies for two reasons. First, the government’s long-term
Energy Strategy 2050 foresees the introduction of an energy tax in order
to achieve a viable energy transition after the nuclear phase-out decision
following the 2011 Fukushima nuclear power plant accident. With nu-
clear energy currently accounting for one-third in Swiss electricity
production and private households being responsible for 60% of the
increase in the national electricity consumption since 2000 (OFEN,
2017), it is necessary to assess the effectiveness of a price-based policy
instrument. As argued in the introduction of this article, the analysis of
the responsiveness of different household groups to variations in prices
is a rst step in this direction.
A second reason relates to the current liberalization of the electricity
market in Switzerland. The most recent development in this area con-
sists of deregulating the electricity market for private households and
small rms that will have the possibility of selecting their supplier or
electricity mix. It is expected that the customers inuence the devel-
opment of electricity supply by enabling innovative products and ser-
vices. The competition between electricity providers is likely to increase
the interest in identifying heterogeneous segments of residential
consumers.
3. Data
3.1. Data sources
The analysis presented in this article relies on a panel dataset of Swiss
households surveyed online in four consecutive years between 2015 and
2018. The dataset, known as the Swiss Household Energy Demand
Survey (SHEDS), covers the entire geographical space of Switzerland,
except the canton of Ticino, and is conceived as a rolling panel dataset
consisting of about 5000 respondents per wave. Its main objective is to
collect rich information on Swiss household’s energy consumption be-
haviors from a demographic, economic, sociological and psychological
perspectives. Household members aged 18 years old or more, and at
least partially responsible for the household, are interviewed about their
electricity usage and behaviors during the one-year period prior to the
survey.
3
In addition to SHEDS, we use price data from the Swiss Federal
Electricity commission (ElCom) at the zip code level. These price data
are carefully extracted from the ElCom’s price platform which allows
comparisons between electricity prices across providers, household
types and years.
4
Prices are given as weighted averages for each one of
the eight household categories (consumption proles) separately by zip
3
These data have been used in previous research among others, by Hille et al.
(2017) and Blasch et al. (2017). Further details about SHEDS are given in
Weber et al. (2017).
4
The ElCom’s price platform is available at: https://www.prix-electricite.elc
om.admin.ch/BaseDataSelection.aspx. The underlying database not directly
available to us, we extracted the data using a Java code written by Crispin
Kirchner. Compared to the data provided in spreadsheets publicly available at
ElCom’s website, the constructed data provide a better disaggregation level.
I. Tilov et al.
Energy Policy 138 (2020) 111246
4
code and two product types (green or standard). ElCom denes these
eight price categories, referred to as “consumption proles”, based on
dwelling attributes, such as the possession of specic electronic dura-
bles, the number of rooms in the dwelling, and the building type (an
apartment or a house). Since these features are also available in the
SHEDS, we are able to match households with their local electricity
providers based on the zip codes and the specic survey year.
5
This
helped us to create a unique dataset and achieve an excellent household-
provider zip code matching: only 70 households (less than 2% of ob-
servations) in our datasets were not directly matched. We proceed by
attributing to those the electricity prices of the closest zip-code neighbor
within the same price category.
6
It is important to note that the price
measures are partly selected by each individual household mainly
because of their choice in the selection of multi-tariff (day/night) pricing
as well as a range of “green” products generally available in Switzerland.
However, the temporal variation remains largely exogenous.
3.2. Dependent variable
We use the logarithm of annual household electricity use (kWh) as
response variable in our QR model. We exclude households who do not
report electricity consumption from a bill and those who report an
annual consumption below 200 kWh or above 30 000 kWh.
7
The nal
panel data set is a sample of 3856 observations corresponding to a total
of 1483 households for which data is available for at least two waves of
the SHEDS. Table 1 displays descriptive statistics for this dataset.
As shown in Table 1, the annual residential electricity use is char-
acterized by substantial variation. The average values are slightly lower
in comparison to ofcial energy statistics from the Swiss Federal Ofce
of Energy, which reports an average household annual residential
electricity consumption of 5096 kWh in 2015–5311 kWh for 2018
(OFEN, 2019). A possible explanation for this discrepancy with ofcial
statistics is that the SHEDS does not cover the canton of Ticino, situated
in the south of Switzerland, characterized by a milder climate and by a
generalized use of electrical resistance heaters by households, thus
leading to about 30% more electricity consumption with respect to the
rest of the country (Eymann et al., 2014).
3.3. Model specication
We consider three major sets of control variables: (1) socioeconomic
and sociodemographic determinants (income, prices, household
composition, age, gender, education), (2) dwelling characteristics
(dwelling location, dwelling age), (3) weather-related controls (heating
and cooling degree days), and (4) psychological factors (environmental,
altruistic, egoistic and hedonic). In addition, we add canton xed effects
and year dummies in order to control for unobserved characteristics.
Moreover, as explained later, we use econometric models that account
for many time-invariant factors and omitted variables.
Our particular interest is on the impact of electricity prices and in-
come. The measure of average electricity prices (and its components)
obtained from the electricity regulator ElCom is a simplication of a
complex construct of base prices, taxes and tariffs that change over time
and across different areas and various users. Whether individuals are
sufciently aware of prices is an important empirical question. Prior
research, both within Switzerland and abroad, shows that differences in
electricity consumption tend to be related to differences in electricity
prices, and that changes in electricity prices are accompanied by
changes in consumption in a way that is consistent with economic theory
(Espey and Espey, 2004; Labandeira et al., 2017), i.e., consumers behave
as if they are aware of prices and price changes.
8
Moreover, households obtain information on electricity prices
regularly from grid operators, ElCom and the Swiss media. Therefore,
there are good reasons to assume that Swiss consumers have at least a
general idea about the evolution of the electricity prices, which is an
important topic of public discussion. There are no reasons to believe that
lack of awareness causes a delay between billing cycles and actual
consumption. In fact, ElCom sets a deadline (the 31st of August) for
electricity providers to announce their new electricity tariffs (for the
upcoming year) to the regulator and their customers. According to
Elcom,
9
only about 8% of all grid operators do not meet this deadline,
but this does not impact any overall price-related statistics and analyses
given the small sizes of the areas served by these operators. Information
about changes in the electricity prices (which occur on annual basis in
Switzerland) are made public not only directly by the providers, but also
by various media. The majority of customers receive their electricity
bills every 3 or 4 months, before receiving a nal summary bill of their
annual electricity consumption at the end of the year.
10
An analysis by
Gilbert and Graff Zivin (2014) has recently shown that households
respond to changes in prices within a week after the reception of their
energy bill. It could be therefore supposed that Swiss households can
make a timely adjustment in their consumption in reaction to price
changes. These responses could however be limited to short and medium
terms. Long-term responses might require investment in energy ef-
ciency that could take longer periods.
Fig. 1 provides a log-log plot of electricity consumption and price.
However, the observed negative relationship between electricity de-
mand and price could be due to omitted variables and endogeneity. For
instance, households with higher consumption are probably more likely
to adopt more economical double-tariff models and/or standard elec-
tricity as opposed to more expensive green products. However, to the
extent that these selection patterns are stable over time, longitudinal
variations can help overcome such biases. In this paper, we adopt
econometric approaches to account for all time-invariant selection
patterns.
Our second determinant - gross income - is obtained as the mid-point
of the reported income interval. For open-ended income categories we
use the Pareto-curve-based procedure suggested by Celeste et al. (2013).
We also assume that the respondent’s sociodemographic attributes, like
gender, age and education provides information about the household’s
corresponding characteristics. A similar approach is adopted with
respect to participants’ individual attitudes towards various psycho-
logical factors, although more complex interactions between household
members may determine distinguishable psychological characteristics
of the household as an inseparable entity (Volland, 2017). Similar to
prior analyses we include distinctive measures for hedonic, egoistic,
altruistic, and biospheric values (Steg et al., 2014). These attributes are
surveyed using various batteries of questions from the psychological
5
The matching in terms of number of rooms is not perfect for 2 household
types: those living in a 3-room apartment and those with more than 5 rooms, in
which we used average prices of the corresponding categories matching in other
variables that is, year, zip-code and product type (standard/green). Detailed
information about the consumption proles used by ElCom are provided at: htt
ps://www.prix-electricite.elcom.admin.ch/BaseDataSelection.aspx.
6
We include a dummy variable to control for this imputation strategy. The
effect of this dummy is invariably small and statistically insignicant across all
regressions.
7
We follow Boogen et al.’s (2014) strategy for excluding extreme observa-
tions. Alternative strategies for excluding outliers (e.g., dropping observations
with electricity consumption below 300 kWh and above 200000 kWh or Tukey’s
strategy for excluding data points standing further than 1.5 quartile ranges from
the rst and third quartiles) conrm our fundamental results.
8
Although economic theory suggests that consumers respond to marginal
prices, it has been recently shown that electricity consumers respond to average
electricity prices and not to marginal or expected marginal prices (Ito, 2014).
9
This information is available on Elcom’s website https://www.elcom.admi
n.ch/elcom/fr/home/documentation/medienmitteilungen.msg-id-72073.html.
10
This information is available on the web pages of big electricity providers
such as SIG, BKW, Groupe E and Romande �
Energie.
I. Tilov et al.
Energy Policy 138 (2020) 111246
5
module of the SHEDS. Given the available data, we control for the
household’s environmental, altruistic and hedonic attitude, as well as
for its aspiration for social power. Using principal component analysis
(PCA), we reduced the question batteries into four continuous variables.
However, in order to provide a ready interpretation of the coefcients of
our psychological variables, we prefer to use binary controls
Table 1
Descriptive statistics.
Year 2015 2016 2017 2018
Continuous variables Mean Std. Mean Std. Mean Std. Mean Std.
Annual electricity consumption (kWh) 4367 4135 4028 3938 4061 4117 4012 4115
Electricity price (in Swiss Franc cents) 20.34 3.15 20.22 3.37 19.93 3.56 20.41 3.53
Monthly gross income (Swiss Francs) 8811 4381 8900 4631 9048 4588 9068 4566
Age of ref. person 56.05 14.10 53.71 14.55 54.04 14.72 55.06 14.73
Number of household members 2.294 1.183 2.230 1.141 2.275 1.185 2.256 1.163
Vintage of dwelling (years) 44.423 36.890 46.622 43.856 48.160 44.950 48.30 43.97
Heating degree days (HDD) 3235 574.32 3432 553.41 3375 517.04 3024 517.45
Cooling degree days (CDD) 239.4 71.46 146.23 60.10 205.1 77.79 218.060 89.311
Binary variables Mean Mean Mean Mean
Pro-environmental attitude: yes 0.885 0.863 0.856 0.879
Altruistic attitude: yes 0.761 0.737 0.745 0.724
Aspiring for social power: yes 0.126 0.104 0.103 0.095
Hedonic attitude: yes 0.671 0.622 0.678 0.619
Imputed electricity price: yes 0.025 0.013 0.011 0.007
Gender: female 0.371 0.398 0.397 0.405
Education: tertiary 0.404 0.449 0.500 0.493
Location: city 0.439 0.471 0.458 0.459
Location: agglomeration 0.327 0.300 0.307 0.311
Location: countryside 0.234 0.229 0.235 0.230
Canton: ZH 0.190 0.220 0.195 0.221
Canton: BE 0.162 0.161 0.166 0.165
Canton: LU 0.038 0.054 0.058 0.045
Cantons: UR, SZ, OW, NW, GL, ZG 0.046 0.046 0.049 0.046
Canton: FR 0.028 0.032 0.032 0.033
Canton: SO 0.031 0.031 0.024 0.030
Cantons: BS, BL 0.064 0.053 0.053 0.046
Canton: SH, TG 0.041 0.033 0.035 0.039
Cantons: AR, AI 0.006 0.009 0.008 0.013
Canton: SG 0.025 0.020 0.029 0.027
Canton: GR 0.080 0.084 0.082 0.085
Canton: AG 0.102 0.095 0.105 0.096
Canton: VD 0.033 0.037 0.034 0.031
Canton: VS 0.036 0.025 0.031 0.021
Cantons: NE, JU 0.042 0.035 0.042 0.044
Canton: GE 0.074 0.064 0.056 0.056
Observations 636 1059 1081 1080
Fig. 1. Relationship between electricity demand and electricity prices (3856 observations).
I. Tilov et al.
Energy Policy 138 (2020) 111246
6
corresponding to the principal components with the highest loadings.
11
The third category of determinants considered in relation with
annual electricity usage contains dwelling-related characteristics.
Similar to income, a mid-point interval method is used to create a
continuous variable containing the construction year of the dwelling,
from which its age is then calculated. Guided by several preliminary
regressions, we decided to exclude other residence characteristics such
as type (house or apartment), size and ownership status, as well as the
number of electronic durables and the use of electricity for heating,
cooling or warm water. As described in sub-section 3.2, electricity prices
for different household groups are dened on some dwelling and device
characteristics and therefore adding them to our model could lead to
multicollinearity.
12
Moreover, adding the set of various electronic du-
rables could lead to an endogeneity problem due to omitted variable bias
(Boogen et al., 2014).
Heating degree days (HDD) and cooling degree days (CDD) are ob-
tained from M�
et�
eoSuisse - the Swiss Federal Ofce of Meteorology and
Climatology - for 159 whether stations.
13
We could not have a one-to-
one matching between zip code areas and weather stations. Given
Switzerland’s topography and the presence of strong temperature dif-
ferentials in relatively small weather pools, we decided against linear
interpolation. Thus we consider that the closest station (in straight-line
distance) to the household’s zip code area provides the best measure of
the aforementioned variables.
14
Finally, we control for unobservable characteristics by including
year dummies and canton xed effects. Since for some cantons (e.g., Uri,
Obwalden, Nidwalden) the proportion of observations in the SHEDS is
too small for sound econometric analysis, we proceed by grouping
households from the closest geographic areas together. A time dummy
allows us to capture unobservable time-variant effects.
4. Econometric approach
In order to evaluate the effect of socio-economic factors on electricity
demand, we use the following regression model:
lnðkWhitÞ ¼ β0þβ1lnðPit Þ þ β2lnðIit Þ þ X
n
l¼3
ðβlXlitÞ þ aiþ
ε
it;(1)
where kWhit is electricity consumption of household i in year t, Pit is the
electricity price that household i is facing and Iit is its disposable income.
Households’ demographic and psychological characteristics, weather
variables, as well as dwelling features, canton and year dummies are
individually captured by X3it ;…;Xnit . ai and
ε
it are stochastic terms
distributed respectively, at the household an observation levels.
We estimate the average impacts of the variables in equation (1) both
by correlated random effect (CRE) and xed effect (FE) models.
15
Both
models allow us to use the available dataset to control for endogeneity of
unobservable characteristics which do not vary across periods. The CRE
provides simultaneously the FE estimates of controls with sufcient
within variation (namely electricity prices, gross income, dwelling age,
age of the reference person, HDD and CDD) and the coefcients of
variables which do not vary between clusters, such as gender, or exhibit
little within variation, such as education (Allison, 2009; Schnuck, 2013).
Because many of the variables included in (1) can be considered as
time-invariant (e.g., education, environmental attitude), the CRE has the
advantage of quantifying the impact of these variables as well.
In order to address the possibility of heterogeneous price and income
elasticities, we apply the quantile regression (QR) method developed by
Koenker and Bassett (1978). QR addresses namely the question of
whether an explanatory variable has different impacts across condi-
tional quantiles of consumption. Thus, it is an important complement to
estimations of the price and income elasticities of the “average Joe” in
the sense that it provides a more complete picture of the relationship
between the dependent measure and the set of covariates under study.
16
In particular, we use QR models adapted for panel data analysis. In line
with Bache et al., 2013 and Abrevaya and Dahl (2008), we operation-
alize a CRE quantile estimation by including the time averages of the
basic time-variant covariates in (1), and by applying a pooled quantile
regression to this extended model specication (Wooldridge, 2010). In
order to provide more robust estimation results, we cluster the error
terms by household (Machado and Silva, 2013).
Despite the existence of alternative approaches to panel quantile
regression with xed effects (Machado and Santos Silva, 2019; Canay,
2011; Koenker, 2004; Powell, 2016), we do not rely on them because of
their restrictive assumptions about individual xed effects. In particular,
as pointed out by Powell (2016), in order to interpret the marginal ef-
fects at various consumption quantiles, we need to keep the quantiles
unconditional to individual xed effects. This is only possible in Powell’s
model that proved to be quite sensitive when applied to our data.
17
5. Empirical results
Table 2 presents results from two statistically equivalent linear
regression models (CRE and FE). The two estimators differ negligibly in
our case due to the slightly different specication of panel averages in
the CRE model. The CRE model in column (2) includes the sample means
of variables that represent genuine longitudinal variation. In particular,
in order to avoid multicollinearity in the presence of year dummies, we
exclude means of the temporal variables such as the two age variables.
These models conrm several previously well-documented phenomena.
First, an increase in electricity prices has a signicant, negative impact
of on electricity consumption. Our FE estimate of average price elasticity
(0.30), precisely in the middle of the interval of most frequent short-
and medium-run estimates (0.2 to 0.4) suggested by previous studies
(Fan and Hyndman, 2011; Reiss and White, 2005). Our average price
elasticity is practically the same as the elasticities reported in earlier
studies for Switzerland (Boogen et al., 2017; Filippini, 1999). More
generally, in line with previous ndings, our results conrm that elec-
tricity demand is inelastic with respect to prices, at least in the short-run.
This is consistent with the fact that electricity can be considered as a
basic good.
18
In line with previous works in similar set-ups (Alberini
11
Although the Kaiser–Meyer–Olkin statistic (KMO 0:7) indicates a good
quality of the continuous measures, the adopted single components seem to be
sufcient. Our various analyses show that replacing the binary indicators with
corresponding PCA continuous measures does not alter our fundamental results.
12
We are indebted to an anonymous reviewer for emphasizing this issue.
13
HDD is dened as the annual sum of the daily difference between the
threshold temperature of 20 C and the average outside daily temperature when
it is below 12 C. Similarly, CDD is measured as the annual sum of the differ-
ence between the average daily temperature and the threshold of 18.3 C.
14
The average distance between the household’s zip code and the weather
station’s zip code is about 8 km. Detailed information about the location of
M�
et�
eoSuisse weather stations is available at https://www.meteosuisse.admin.
ch/home/valeurs-mesurees.html?param¼messnetz-automatisch.
15
These approaches lead to the same xed effect estimates, as shown by
Schnuck (2013).
16
A short discussion of a basic quantile regression model is provided in the
appendix.
17
Another alternative is Machado and Silva (2019) but not appropriate for
short panels. In order to allow for reliable inference even with moderate
number of time periods, we implement the split-panel jackknife bias correction
suggested by Dhaene and Jochmans (2015). The results conrm in general our
ndings especially concerning the pattern of estimated price elasticities. We are
grateful to Joao Santos Silva for providing us with the code for the imple-
mentation of the jackknife correction bias. Results of both analyses are avail-
able upon request.
18
It is also interesting to note that a substantial number of sampled house-
holds use electricity for heating: about 25% report to rely on electricity as a
primary heating source, while 37% use electricity for generating hot water.
I. Tilov et al.
Energy Policy 138 (2020) 111246
7
et al., 2011; Bedir et al., 2013; Grønhøj and Thøgersen, 2011; Kavousian
et al., 2013; Leahy and Lyons, 2010; O’Doherty et al., 2008), we nd an
insignicant short-term impact of income on electricity consumption.
In agreement with other studies (e.g., Bartusch et al., 2012), we nd
that the vintage of the dwelling has a positive effect on the consumption
of electricity. The age of the reference person is also related to higher
electricity usage, probably due to more sedentary lifestyles at later
stages of life, to increased need of thermal comfort, or to possession of
different (less efcient, different type) electronic durables by the elderly
(Bardazzi and Pazienza, 2017; McLoughlin et al., 2012; Meier and
Rehdanz, 2010). It is important to note that a model, where both age
variables are combined with household-specic means and time
dummies, could represent a multicollinearity problem. However, alter-
native model specications show that including both effects (average
age of reference person and building) does not affect our results.
The average estimates listed in Column (1), also show that house-
holds living in non-urban locations consume signicantly higher
amounts of electricity compared to city-dwellers, namely about 27% and
45% more for people living in agglomerations and those residing in the
countryside, respectively. One possible explanation for this is the urban
heat-island effect, characterizing urban areas which are warmer
compared to neighboring rural regions due to the higher concentration
of human activities (Arneld, 2003). Cities also benet from public
lighting and from district heating services, both of which could be
related to lower personal use of electricity.
An additional household member increases the total electricity usage
(by approximately 20%), whereas a households with a female head use
consume (about 13%) less electricity than their male counterparts -
ndings similar to those of Brounen et al. (2012) and Grønhøj and
Thøgersen (2011). With respect to gender, the latter authors explain that
women report to do more efforts to save electricity than men. Yet, an
earlier work by Karjalainen (2007) suggests that women prefer higher
heating temperatures which could lead to higher consumption of elec-
tricity, if for instance additional electric radiators are used.
The estimated coefcients of weather variables - HDD and CDD, are
statistically insignicant. However, it is likely that year dummies and
individual xed effects (embedded in the CRE model) capture most of
weather variations. Alternatively, the insignicant effect could be also
explained by the fact that HDD and CDD are measured at the weather
station and do not represent household-specic variations (as explained
in Section 3.3).
Table 3 provides the correlated random effect quantile regression
(CRE QR) results for ve quantiles of the conditional distribution of
electricity consumption. This analysis completes the picture of the
“average Joe” covered by the CRE linear model. Our QR model uses the
same set of variables as those previously discussed in the CRE setup.
Exploring the heterogeneity among households, we observe that elec-
tricity prices play a statistically signicant role only at the lower spec-
trum of the distribution of electricity demand, but an insignicant one at
its upper part. That is, the estimated QR coefcients of prices become
signicant at generally accepted signicance levels only at the median
and the rst quartile of the conditional distribution, where the estimated
price elasticity is approximately 0.41 and 0.57. Yet, we nd that
households in the lowest decile do not react signicantly to price
changes. The same applies for intensive electricity consumers, situated
namely at the third quartile and the 90th percentile of the conditional
distribution.
This nding corresponds to Reiss and White (2005) observation that
price elasticities are higher at the lower-end of the (unconditional)
electricity distribution. Hence, a policy measure, which based on an
average estimation establishes higher electricity prices (at a at rate) for
all consumers runs the risk of affecting disproportionately frugal and
intensive users. Therefore, our analysis suggests that taxes should have
different behavioral and welfare effects in different consumer groups.
While showing an inelastic demand similar to other quantiles, parsi-
monious users are relatively responsive to price changes, hence a greater
potential for reducing consumption. However, from an equity perspec-
tive, they should not be the focus of policies aiming at demand reduc-
tion, not only because they are frugal in the rst place, but also because
the undesired impact on their welfare could be greater. This is especially
valid if reducing energy demand would require investment in efciency
with greater income effect for low-income households. These undesired
effects could however be resolved by coupling taxes with subsidies
Table 2
CRE and FE linear regressions.
(1) (2)
CRE FE
Electricity price (ln) 0.312** 0.296**
(0.1418) (0.1358)
Gross income (ln) 0.0225 0.0321
(0.0394) (0.0379)
Heating degree days (HDD) 0.0000001 0.00009
(0.0001) (0.0001)
Cooling degree days (CDD) 0.00004 0.00002
(0.0003) (0.0004)
Year: 2016 (ref. 2015) 0.0116 0.0208
(0.0366) (0.0390)
Year: 2017 (ref. 2015) 0.0358 0.0287
(0.0249) (0.0257)
Year: 2018 (ref. 2015) 0.0568** 0.0126
(0.0286) (0.0285)
Age of ref. person 0.0106***
(0.0012)
Vintage of dwelling 0.000848***
(0.0003)
Number of household members 0.177***
(0.0157)
Gender: female 0.117***
(0.0338)
Education: tertiary 0.0405
(0.0291)
Location: agglomeration (ref. city) 0.242***
(0.0417)
Location: countryside (ref. city) 0.375***
(0.0474)
Pro-environmental attitude: yes 0.00671
(0.0280)
Altruistic attitude: yes 0.0315
(0.0206)
Aspiring for social power: yes 0.00847
(0.0313)
Hedonic attitude: yes 0.00246
(0.0167)
Imputed electricity price: yes Yes No
Average electricity price (by household) Yes No
Average gross income (by househole) Yes No
Average HDD (by household) Yes No
Average CDD (by household) Yes No
Canton dummies Yes No
Constant Yes Yes
Observations 3856 3856
Households 1483 1483
Observations per household:
min 2 2
max 4 4
average 2.6 2.6
R
2
:
within 0.0088 0.0055
between 0.4113 0.0842
overall 0.3782 0.0810
Clustered standard errors (by household) in parentheses.
**p <0.05, ***p <0.010.
I. Tilov et al.
Energy Policy 138 (2020) 111246
8
targeting low-income households, and/or with additional non-price
measures specically designed for intensive users.
19
We are however cautious about this interpretation of our results for
policy guidance. In fact, Table 3 shows that “frugal Janes” in the lowest
conditional decile are also price-insensitive. The most parsimonious and
most intensive consumers might be non-reactive to price variations for
very different reasons though. It is conceivable that since the former
already use as little electricity as possible, there is no further possibility
(or willingness) to reduce electricity as prices increase. As soon as those
households start having “less basic” uses of electricity perhaps they also
become more sensitive to price variations. On the other hand, “wasteful
Johns” might be characterized by non-discretionary electricity usage
(for instance heat pumps) which does not allow them to decrease con-
sumption at their will. Hence, our ndings point more generally to
heterogeneous price elasticities across the conditional electricity dis-
tribution, thereby calling for more targeted policy measures.
The results displayed in Table 3 also indicate different impacts across
the consumption spectrum for variables with little or no within variation
such as gender and living area. For instance, households with a female
reference person use signicantly less electricity at low levels of elec-
tricity usage, whereas gender does not affect high consumption levels. If
women are more energy-conscious than men, as suggested by Thøgersen
and Grønhøj (2010), they could perform better at reducing energy when
energy reduction is possible (discretionary electricity usage). However,
it is also possible that the negative impact of female dummy on
Table 3
Quantile analysis (CRE QR).
Correlated random effects quantile regressions
q0.10 q0.25 q0.50 q0.75 q0.90
Electricity price (ln) 0.442 0.571** 0.409** 0.322 0.515
(0.3109) (0.2508) (0.1685) (0.2390) (0.3008)
Gross income (ln) 0.00802 0.0133 0.0261 0.00371 0.0329
(0.0949) (0.0667) (0.0497) (0.0612) (0.0713)
Heating degree days 0.000068 0.00017 0.000084 0.00022 0.00015
(0.0002) (0.0001) (0.0001) (0.0002) (0.0002)
Cooling degree days 0.00057 0.000001 0.00067 0.00019 0.00159
(0.0008) (0.0007) (0.0005) (0.0008) (0.0010)
Year: 2016 (ref. 2015) 0.0856 0.0165 0.100 0.0894 0.185
(0.0940) (0.0712) (0.0517) (0.0975) (0.1027)
Year: 2017 (ref. 2015) 0.118** 0.0303 0.0887** 0.132** 0.122
(0.0576) (0.0503) (0.0349) (0.0587) (0.0655)
Year: 2018 (ref. 2015) 0.0399 0.0905 0.142*** 0.0419 0.0712
(0.0565) (0.0616) (0.0470) (0.0593) (0.0791)
Age of ref. person 0.0103*** 0.0102*** 0.0106*** 0.0119*** 0.0135***
(0.0017) (0.0015) (0.0013) (0.0015) (0.0029)
Vintage of dwelling 0.000128 0.000481 0.000361 0.000903 0.00135
(0.0006) (0.0006) (0.0004) (0.0006) (0.0010)
Number of household members 0.232*** 0.233*** 0.239*** 0.234*** 0.203***
(0.0209) (0.0217) (0.0193) (0.0221) (0.0302)
Gender: female 0.121** 0.127*** 0.0965*** 0.0994** 0.0435
(0.0494) (0.0472) (0.0334) (0.0443) (0.0721)
Education: tertiary 0.0734 0.0480 0.0278 0.00368 0.0367
(0.0462) (0.0460) (0.0365) (0.0439) (0.0663)
Location: agglomeration (ref. city) 0.166*** 0.147*** 0.192*** 0.313*** 0.518***
(0.0579) (0.0519) (0.0408) (0.0627) (0.1256)
Location: countryside (ref. city) 0.212*** 0.306*** 0.431*** 0.496*** 0.543***
(0.0725) (0.0656) (0.0487) (0.0548) (0.0948)
Pro-environmental attitude: yes 0.0753 0.0505 0.0278 0.0825 0.00615
(0.0508) (0.0415) (0.0411) (0.0605) (0.0834)
Altruistic attitude: yes 0.0562 0.0269 0.0720 0.0653 0.128
(0.0477) (0.0406) (0.0369) (0.0394) (0.0679)
Aspiring for social power: yes 0.0770 0.0375 0.0411 0.126 0.0540
(0.0578) (0.0538) (0.0410) (0.0667) (0.0813)
Hedonic attitude: yes 0.0298 0.0302 0.0236 0.0369 0.0837
(0.0408) (0.0330) (0.0279) (0.0371) (0.0568)
Imputed electricity price: yes Yes Yes Yes Yes Yes
Average electricity price (by household) Yes Yes Yes Yes Yes
Average gross income (by household) Yes Yes Yes Yes Yes
Average HDD (by household) Yes Yes Yes Yes Yes
Average CDD (by household) Yes Yes Yes Yes Yes
Canton dummies Yes Yes Yes Yes Yes
Constant Yes Yes Yes Yes Yes
Observations 3856 3856 3856 3856 3856
Households 1483 1483 1483 1483 1483
Observations per household:
min 2 2 2 2 2
max 4 4 4 4 4
average 2.6 2.6 2.6 2.6 2.6
Pseudo R
2
0.3574 0.3754 0.3756 0.3791 0.3598
Clustered standard errors (by household) in parentheses.
**p <0.05, ***p <0.010.
19
Non-price measures could consist of recommendations, nudges, information
labels, but also standards and stringent regulation. Utilities could for instance
send messages to intensive users reminding them they are using too much
electricity, by comparing them with a typical household or with their neigh-
bors, by informing them about saving possibilities (electricity-related and
nancial) or by sending them targeted ads for efcient appliances.
I. Tilov et al.
Energy Policy 138 (2020) 111246
9
electricity consumption suggests that the lower quantiles have a
disproportionate share of single-member female households. It is also
interesting to notice that in comparison to city-dwellers, non-urban
households use much higher amounts of electricity at the upper-end of
the conditional electricity distribution. As argued before, it is likely that
areas outside cities are characterized by a more limited heating and
lighting options and the increasing magnitude of the location coefcient
could simply translate this decreasing level of discretionary electricity
usage.
In order to test the robustness of the main results of the previous, we
perform several additional robustness checks by dropping households
who move across communal or cantonal borders in order to alleviate the
effects of important life-style changes that cannot be accounted for, by
restricting our sample to a balanced panel, or by imposing different
restrictions for outliers. These results point to a slightly higher and
statistically signicant (at 5%) average price elasticities (between 0.4
and 0.5), and conrm our result that the estimated price elasticities are
signicant for lower quantiles of electricity usage.
5.1. Caveats
Our analysis bears a number of caveats that can be addressed in
further research. First, while our ndings provide evidence of hetero-
geneity of price responses among consumption quantiles, the estimated
pattern of variation across quantiles seems to be sensitive to model
specication. In particular, our QR analyses with alternative condi-
tioning on time-invariant factors especially individual xed effects,
suggest that the pattern of relatively high elasticity in lower quantiles
might not live up to rigorous robustness tests. Such assessments require
more exible QR models that could provide a general framework for
condition quantiles without relying on xed effects in line with Powell
(2016).
Secondly, most Swiss households can choose their electricity prod-
uct, with a usually low fraction opting for more expensive “green”
electricity. Our estimates should not be affected to the extent that this is
a time-invariant factor that does not inuence our longitudinal price
variation. However, given that over time some households might switch
to different products (without necessarily adapting their consumption),
our estimates of price effects could be biased. Third, due to the lack of
price data on alternative heating fuels, we do not consider cross-price
elasticities in our model specication. Since, most electricity-saving
behaviours are by substitution with other energy sources, a complete
picture of price responses requires a full analysis of alternative energy
prices. Fourth, due to the limited longitudinal income variations in a
relatively short panel data set, the analysis does not allow to identify
long-term income effects.
Finally, we focus on the heterogeneity of price responses across
different groups of consumers according to their intensity of consump-
tion. Alternative grouping methods could be used in order to investigate
the heterogeneity in price and income responses, in particular different
income groups and dwelling locations. These elements present possi-
bilities for future research about the long-term effect of prices and in-
come on household electricity demand across different groups of
households.
6. Conclusion and policy implications
In this article, we analyze the heterogeneity in price and income
elasticities of the residential demand for electricity in Switzerland. In
particular, we are interested in price and income effects for different
levels of usage intensity. For this purpose we use a four-year panel
dataset obtained from the Swiss Household Energy Demand Survey
(SHEDS). We combine these data with a unique price data set retrieved
from the Swiss electricity regulator (ElCom) and weather data from the
Swiss federal ofce of Meteorology and Climatology (M�
et�
eoSuisse). Our
estimation strategy consists of applying correlated random effects (CRE)
quantile regression models. The results show that for many covariates,
average CRE represents only lower quantiles of electricity consumption,
namely, “frugal” consumers. With respect to prices, the elasticities found
in the linear CRE model mirrors the estimated inuence of prices in the
lower tail of the electricity distribution. In fact, our QR model shows that
up to the sample median households react to changes in prices, but in
upper quantiles, price-elasticities are statistically insignicant, with an
expected negative sign. Concerning the income effect, our average es-
timations truthfully reect the non-signicant effect of this variable
across the conditional distribution of household electricity demand. The
CRE method also allows us to estimate the impact of time-invariant
covariates, some of which also exhibit different effects across the elec-
tricity consumption spectrum. The main results concerning electricity
prices and income hold when we use alternative control variables and
sample restrictions.
Overall, our results suggest that the “average Joe” differs from the
“frugal Jane” and the “wasteful John” in a variety of aspects. Under-
standing response heterogeneity between consumers could be used not
only to assess the distributive effects of various policies but also for
guiding policies targeting various groups of consumers. With respect to
policy implications, our ndings suggest that when designing policy
measures price and income effects should be considered based on
household heterogeneity. In particular, even the average inelastic
response to price changes, mask some groups of consumers with negli-
gible or little responsiveness to prices. This implies that for instance, if a
tax can be used to curb the household’s electricity consumption, the
effect is probably limited in a selection of households. This not only
limits the effectiveness of price measures, but might compromise the
equity considerations of tax policies. As pointed out by our results, taxes
could impact the frugal usage of electricity with a relatively high welfare
impact, but could leave out the intensive electricity consumers, the very
consumers that should be targeted. In order to overcome these undesired
effects, policy makers could couple taxes with subsidies for potentially
penalized groups and/or non-price measures for those that are less
responsive to price changes.
Acknowledgments
We are grateful to two anonymous referees for their constructive
comments. We would like to thank Crispin Kirchner for his excellent
assistance in extracting the ElCom price data from the agency’s price
platform, Olivier Duding from M�
et�
eoSuisse for providing us with annual
weather data, and Joao Santos Silva for his insightful discussion on
quantile methods applied to panel data. This research is part of the ac-
tivities of the Swiss Competence Center for Energy Research SCCER
CREST, which is nancially supported by Innosuisse, under Grant KTI.
115500015.
Appendix
A starting point for quantile regression is the notion of conditional quantiles, as illustrated by Koenker and Hallock (2001) in their discussion of the
determinants of infant birthweight. In order to generalize a linear model (adapted to sample means) to conditional quantiles, consider a generic matrix
representation of equation (1),
I. Tilov et al.
Energy Policy 138 (2020) 111246
10
yi¼X’
iβþ
ε
i:(2)
From (2), the estimated coefcients vector b
β at the q
th
quantile of yi (q2 ð0;1ÞÞ, hereafter expressed as b
βq, are obtained by minimizing the
asymmetric loss function given as:
X
N
i:yiX’
iβ
q�
�yiX’
iβq�
�þX
N
i:i<X’
iβ
ð1qÞ�
�yiX’
iβq�
�:(3)
Quantile regression allows a ready interpretation of the estimated coefcients b
βq as marginal effects within their respective quantiles (Angrist and
Pischke, 2009). Apart from characterizing the marginal effects over the entire conditional distribution of the dependent variable, QR provides a robust
estimator. As opposed to OLS estimators, QR is more robust to outliers, and to the distribution of error terms.
As demonstrated by Bache et al. (2013) and Abrevaya, J., & Dahl (2008), panel data models such as xed effects formulation and the correlated
random effects (CRE) in line with Wooldridge (2010), can be applied to QR models. In particular using data simulations, Bache et al. (2013)
demonstrate that similar to a linear model, a CRE-QR model can be implemented directly by including sample panel means of time-variant variables.
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