.
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018102
International Journal of Energy Economics and
Policy
ISSN: 2146-4553
available at http: www.econjournals.com
International Journal of Energy Economics and Policy, 2018, 8(6), 102-113.
Inequalities in Energy Transition: The Case of Network Charges
in Germany
Lisa Schlesewsky, Simon Winter*
University of Münster, Center for Interdisciplinary Economics, Scharnhorststraße 100, 48151 Müster, Germany.
*Email: simon.winter@wiwi.uni-muenster.de
Received: 18 July 2018 Accepted: 28 September 2018 Doi: https://doi.org/10.32479/ijeep.6917
ABSTRACT
The German energy transition and the rising share of renewable energies in electricity generation have led to an increase in network costs and to higher
network charges in recent years. We use socioeconomic data in order to investigate distributional effects within the period 2010-2016, and employ three
different inequality metrics – the Gini coefficient, the Theil Index and the Atkinson index – all of which unambiguously indicate regressive effects of
network charges. Most recently, the three metrics show an increase of economic inequality of at least 0.67% when accounting for network charges.
This finding is due to (1) the relative inferiority of electricity, (2) the regressive impact of a fixed component of network charges, (3) considerable
regional disparities, and (4) the higher prevalence of prosumers within high-income households.
Keywords: Network Charges, Renewable Energies, Economic Inequality
JEL Classifications: D63, Q40, Q42
1. INTRODUCTION
German energy policy has changed dramatically in recent years.
Federal government stated in its “Energiekonzept 2050” that up
to 80% of electricity should be renewably generated by 2050
(Bundesregierung, 2010). This goal induces a structural change
which not only includes power generation and technologies
themselves, but also the need for an efficient and capable electricity
grid. New challenges arise from decentralized power generation
through photovoltaic (PV) systems and wind mills, which are often
not located in load centers, thus necessitating quantitatively more
and more capable transmission grids. The costs of this network
expansion have to be borne ultimately by the customers, since the
grid costs are reflected in the network charges which in Germany,
are a component of the electricity bill. However, network charges
are lower for industrial users and even differ for private households
– so-called prosumers (i.e., households with roof-top PV systems
or interruptable consumption systems) are partially exempt from
paying the charge. Furthermore, network charges are defined
locally by the distribution system operators (DSOs), which have
to pay network charges to the transmission system operators
(TSOs) themselves. This induces substantial regional disparities
in the financial burden exerted by network charges – for example,
households in regions with a low population density have to pay
for a relatively costly grid. As a consequence, different households
in different regions of Germany are charged differently for the
maintenance and extension of the grid. This finding has been
further aggravated by rising network charges in recent years and
had induced households to pay a considerable proportion of their
disposable income for network charges.
The distributional effects of different energy-market policies
have been investigated extensively in the past. In a cross-country
comparison, Flues and Thomas (2014) find that taxes on electricity
are more regressive than those on other energy sources. Concerning
Germany in particular, the distributional effects of the EEG
feed-in tariff – which is a subsidy to producers of renewable
energies financed by a surcharge on the electricity price – have
This Journal is licensed under a Creative Commons Attribution 4.0 International License
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 103
been analyzed at length (Löschel et al., 2012; Neuhoff et al.,
2012; Techert et al., 2012; Grösche and Schröder, 2014; Többen,
2017). Hence, distribution issues are an essential component of the
scientific and public debate on the energy transition and pose the
question how the costs arising from the ecological transformation
of electricity generation are distributed among the population.
Yet, the distribution of the increasing grid costs has solely been
investigated at a regional level (Hiersig and Wittig, 2015). Hinz
et al. (2018) forecast future regional disparities in network charges,
depending on various tariff designs. They find that regional average
network charges will diverge further by 2025, if the current tariff
design is maintained. Households in Mecklenburg-Vorpommern
would have to pay 12.1 ct/kWh (+41% compared to 2015), whereas
those in Berlin would be charged only 6.5ct/kWh (+10%).
Indeed, the literature described above neither calculates the
financial burden of network charges at a household level, nor does
it link this burden to household income in order to test whether
the charges are characterized by substantial regressive effects.
Nevertheless, this form of analysis is promising and goes beyond
other studies concerning the regressive effects of electricity prices
or feed-in tariffs, since network charges firstly consist of a two-part
tariff and secondly differ regionally. Both of these characteristics
might affect the regressiveness of the charges.
The present study firstly examines how much German households
effectively pay for network charges annually – in absolute and
relative terms measured as a share of income. Secondly, we
quantify the distributional effects on overall economic inequality.
In order to address these issues, we analyze data on network
charges for households during the period 2010-2016 and match
them with socio-economic panel data. We exclude both commercial
customers and indirect effects from our analysis. These might
additionally affect redistributive effects. We find that the regional
definition of network charges leads to a substantial gap between
the North and East of Germany on the one hand, and the South
and West of Germany on the other hand. Since the total financial
burden exerted by network charges increased by approximately
16% between 2010 and 2016, these regional disparities are gaining
importance. The average German household had to pay 218€ in
2016 for network charges – but only about 150€ in some regions
and up to 300€ in others. In addition, different quintiles of the
income distribution spend considerably different shares of their
income on network charges – 1.6% in the lowest quintile and 0.4%
in the highest. In addition, we observe that households in urban
areas had to pay about 30€ less than those in rural areas. We employ
three different inequality metrics – the Gini coefficient, the Theil
index and the Atkinson index – in order to derive the overall impact
of network charges on the distribution of disposable incomes. As
a result, we notice an unambiguously regressive effect of network
charges, as all metrics increase by at least 0.63% when accounting
for network charges. This yields an additional (and increasing)
welfare loss due to increased economic inequality.
We proceed as follows: Section 2 describes the tariff structure of
network charges in Germany, Section 3 derives three hypotheses
concerning the distributional effects of network charges. Section
4 presents our methodology and the underlying datasets and in
Section 5, we test our hypotheses empirically. Finally, Section 6
concludes.
2. FINANCING DISTRIBUTION GRIDS IN
GERMANY
The German Energiewende triggered tremendous changes in
energy policy in order to start the transition from fossil and
nuclear to renewable energy. The objective of this transition is to
revolutionize the German energy system. The installation of new
generation plants for renewable power generation has led to a
rising emphasis on the electricity distribution grid in recent years.
This is a result of the increasing share of renewable energy in gross
electricity consumption, which already represented 33.1% in 2017
(Statistisches Bundesamt, 2018). Hence, renewable energy already
constitutes the largest share of gross electricity consumption and
is planned to reach a share of 80% in 2050 (Bundesregierung,
2010). In this section, we focus on the reasons for the recent rise
in network charges and on the definition and tariff structure of
these network charges. Finally, we define the customer group on
which we concentrate in our empirical investigation.
The focus on renewable energy (especially on onshore
windpower systems and PV systems), and the resulting increase
of decentralized energy supply as well as the regional shift of
generation systems, have led to higher (technical) requirements
for the German electricity grid (Bundesnetzagentur, 2015. p. 9).1
Thus, the transmission and distribution grids need to be extended
and their capacity increased in the future. Studies on different
expansion scenarios until 2020 (the share of renewable energy
in gross electricity consumption in 2020 is predicted to be about
39%) forecast grid-expansion costs between 0.9 and 1.6 bn. €/a
(Deutsche Energie-Agentur 2010. p. 13). The responsibility for
these grid-expansion measures rests (analogous to the Renewable
Energy Sources Act, EEG) with the four German TSOs for the
transmission grid and more than 800 DSOs for the distribution
grid. The increase in network costs and charges and the regional
differences are caused by various factors.
Firstly, the development of network costs depends on the
urbanization level. The unequally distributed settlement of
industrial locations and agglomeration areas leads to a different
utilization rate of the grid. The per capita costs and network
charges increase with a decreasing number of users of a particular
regional grid area. Hence, people in rural areas have to bear
higher network charges than those in urban areas, because fewer
people have to bear the costs of the grid. Furthermore, the German
electricity infrastructure comprises grids of different ages. The
older grid in Western Germany, with its lower residual value, has
1 The regional shift of generation systems follows from two different
factors. Firstly, it is more efficient regarding the environmental and legal
preconditions for onshore wind power systems to become established in the
northern part of Germany (it is, for example, more difficult to build wind
power systems in Bavaria, because of the 10-h-rule); the same holds true
for PV sytems in South and East Germany. Secondly, there are still a few
nuclear power plants in southern Germany which will gradually disappear
from the grid.
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018104
lower network costs than the newer grids in Eastern Germany.
Potential future modernization measures could turn this cost
situation around.
Secondly, the rise of renewable energy generation is associated
with rising network costs. The connection and integration of
renewable energy systems (e.g., the connection of off-shore
wind power systems) are accompanied by higher costs for the
TSOs. Furthermore, because of the increase in renewable energy
generation plants, the amount of energy which is fed in to the lower
voltage grid levels of the distribution grid rises (especially in low
and medium voltage levels). This lowers the current consumption
from upstream transmission grid levels so that the average costs
of the transmission grid per kWh increase and network charges
consequently rise. In addition, the quality of the electricity grid
cannot withstand the heavy load fluctuations from renewable
energy generation (especially from very volatile onshore wind
power systems) and needs to be strengthened and modernized.
This scenario leads to rising costs. Especially the rising power
generation from renewable energy is resulting in a massive and
cost-intensive network expansion in North, East and Southern
Germany. Finally, decentralized energy generating systems feed
in electricity in lower voltage levels and can therefore avoid
upstream network charges. The avoided network charges lead to
increasing costs, due to the rising number of renewable energy
generating systems.
Thirdly, the TSOs have to ensure supply reliability and avoid and
face network bottlenecks. Therefore, the TSOs have to intervene
via redispatching measures and back up power resulting in higher
network costs.2
The rising costs of the expansion and maintenance of the
transmission and distribution grid are passed on to electricity
consumers via network charges (Bundesnetzagentur, 2015.
p. 13). Basically, network charges are a fee paid by the network
users for the transport of electricity within the transmission and
distribution grid. The TSOs raise these charges to cover the costs
resulting from the network. Network charges at the TSO level
are highly regulated by the German Federal Network Agency
(Bundesnetzagentur, BNetzA) via a revenue cap system (RAP,
2014. p. 7. et seq.; Bundesnetzagentur, 2016a. p. 3). Downstream
DSOs calculate their costs and charges based on reported network
charges of the TSOs and invoice the electricity consumers for
the final charge.
In general, network costs can be covered via different mechanisms
involving all or subsets of network users. A key aspect is whether
the network charge is split into a load (L) and a generation (G)
cost component. The L-component allocates the network costs to
the electricity consumers, whereas the G-component forces the
electricity producers to bear part of the costs. Network costs in
Germany consist mainly of an L-component.3 Households and
2 For the total list of reasons for rising network costs, Hinz (2014:40. et seq.)
and Bundesnetzagentur (2015. p. 19. et seqq.; 2016b).
3 In eleven European countries, a G-component is raised in addition to the
L-component (Haucap and Pagel, 2014. p. 11). Additionally, in Great
industrial customers pay for a substantial part of the network costs,
whereas energy producers only pay the costs of connection to the
network, or for voltage transformation substations (Haucap and
Pagel, 2014. p. 5). German households pay the network charges
via their electricity bills. The charges are paid to the DSOs and in
part passed on to the TSOs. The network charges (including meter
operation, meter reading and billing) comprised nearly 30% of the
electricity price net of value-added tax (Mehrwertsteuer, VAT) in
2017 (Bundesnetzagentur and Bundeskartellamt, 2017. p. 254).
Due to different customer profiles, the billing of the network
charges also differs. There are two different customer groups,
namely customers with consumption metering and customers
without consumption metering. The former have to transmit their
consumption data every 15 min to the respective grid operator and
are mainly major or industrial customers who are also connected to
higher voltage levels. They pay a power price in €/kW (for the peak
load within one billing period) on the one hand, and a price given
in ct/kWh depending on actual consumption on the other hand.
This customer group can be separated further, according to their
usage period – i.e., whether they use the grid for less or more than
2,500 h/a. The latter group includes households as well as small
industrial and agricultural customers. For some DSOs, there is a
maximum consumption of about 10,000 kWh/a as an upper limit.
Customers without consumption metering – the focused of the
following analysis – have to pay a fixed component (Grundpreis,
€/a) and a variable component (Arbeitspreis, ct/kWh).
The increase in network charges in recent years, as well as their
considerable share in the electricity price and corresponding
importance for customers make an empirical analysis of the burden
of these network costs relevant. In particular, we take a closer look
at the distributional effects on a household level. Accordingly, we
derive three hypotheses in Section 3 stating that network charges
should exert substantial regressive effects with respect to the
distribution of disposable incomes.
3. HYPOTHESES
Each household i in region j at time t is assumed to have a
disposable income of yij,t. In addition, monthly electricity costs
eij,t are given, as well as the monthly demand for electricity, dij,t.
The electricity price pj,t depends on regionally determined network
charges nj,t which consist of two parts – a fixed component
(Fj,t) paid annually (with fj,t = Fj,t/12 as the monthly share) and
a variable component (vj,t) paid per kWh. These components
in Germany correspond to the Grundpreis and Arbeitspreis
(Section 2). Additionally, we must adjust for the regionally
defined concession fee (kj,t; Konzessionsabgabe). This fee differs
regionally (contingent upon community size) and is a further price
component paid for using public infrastructure, i.e., the electricity
grid. The national average electricity price pt , the national average
network charge nt , the national average concession fee kt , as well
Britain, Norway and Sweden, for example, the G-component varies with the
choice of location of electricity producers (Grimm et al., 2015. p. 14). For an
international comparison of network charges, also Hinz et al. (2018. p. 98).
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 105
as the regional network charge, define the final average electricity
price (FAEP) of household i in region j at time t:
p p n v k k
f
dij t t t j t t j t
j t
ij t
, , ,
,
,
.= − + − + + (1)
All values are gross, i.e., they include the 19% VAT. The electricity
costs eij,t of a household can be defined as the product of the FAEP
and electricity consumption.
e f d p n v k kij t j t ij t t t j t t j t, , , , ,( ).= + − + − + (2)
The partial derivative of electricity costs with respect to income
yields.
∂
∂
= − + − +
∂
∂
e
y
p n v k k
d
y
ij t
ij t
t t j t t j t
ij t
ij t
,
,
, ,
,
,
( ) . (3)
As we assume electricity to be a normal good (i.e., ∂dij,t⁄(∂yij,t)>0), this
term can be expected to be positive. Additionally, the income share
of electricity costs can also be differentiated with respect to income:
∂
∂
=
∂
∂
−
∂
e
y
e
y
e
y
y
ij t
ij t
ij t
ij t
ij t
ij t
ij t
,
,
,
,
,
,
,
.
(4)
Furthermore, assuming electricity to be a relatively inferior good4
leads to a negative link between income and the income share of
electricity costs. The numerator of Equation (4) has to be negative
accordingly. The income elasticity of electricity costs is positive,
but smaller than one and as a consequence:
, ,
,
, ,
(0,1).ij t ij te y
ij t ij t
e y
y e
ε
∂ ∂
= ∈
∂ ∂
(5)
Total network charges paid by the household are:
N f v d
f p n k k v e
p n vij t j t j t ij t
j t t t t j t j t ij t
t t j
, , , ,
, , , ,
= + =
− − +( )+
− + ,, ,t t j tk k− +
(6)
Where dij,t can be derived from Equation (2) as:
d
e f
p n v k kij t
ij t j t
t t j t t j t
,
, ,
, ,
.=
−
− + − +
(7)
4 This assumption is supported by robust empirical evidence from throughout
the world (see most recently for Germany: Schulte and Heindl, 2017;
Jamaica: Campbell, 2018; Singapore: Loi and Le Ng, 2018) estimating
the income elasticity of electricity demand between 0 and 1. For a meta-
analysis on the income elasticity of electricity demand, Espey and Espey
(2004). Fouquet (2014) finds that the income elasticity of electricity
demand followed an inverted U-shaped curve over the past 200 years –
which results in relatively inelastic electricity demand in industrialized
countries nowadays.
The income share of total network charges ( )/
, , ,
N N yij t ij t ij t= can
be differentiated with respect to income:
∂
∂
=
∂
∂
−
−
−
N
y
v
e
y
e
y
f
p n
ij t
ij t
j t
ij t
ij t
ij t
ij t
j t
t
,
,
,
,
,
,
,
,
tt t j t
ij t
t t j t t j t ij t
k k
y
p n v k k y
− +
− + − +
,
,
, , ,
( )
(8)
As both the denominator and the subtrahend in the numerator
are positive, this expression is below zero, especially when the
minuend of the numerator is negative. This is true in our case,
because of the relative inferiority of electricity consumption (i.e.,
0<εe,y<1). Therefore, income and the income share of total network
charges are negatively associated. This effect can be attributed to
two components: Firstly, electricity costs as a share of income
decrease with rising income. Secondly, the fixed component of
network charges plays a minor role, due to fixed cost degression
once a household consumes a substantial amount of electricity
– which occurs especially in high-income households. Thus, the
income share of total network charges not only decreases with
income, because electricity is a relatively inferior good (minuend
in the numerator), but also because the marginal network charge
is smaller than the average network charge, because of the fixed
component (subtrahend in the numerator). The latter effect would
vanish if network charges consisted only of a variable component.
We can therefore now derive Hypothesis 1 for our empirical
analysis.
Hypothesis 1: A household’s financial burden via network charges
is regressive. This regressiveness can be expected to be stronger,
especially if the fixed component of network charges is higher:
2
, ,
, , ,
0 0.ij t ij t
ij t ij t j t
N N
y y f
∂ ∂
< ∧ <
∂ ∂ ∂
Furthermore, regional disparities might lead to a correlation
between income and the variable component of network charges. In
rural areas, incomes are usually lower and network charges higher;
this generally also applies to the new federal states of Germany
(East Germany). Accounting for a relationship v v yj t j t ij t, , ,( )=
modifies Equation (8):
∂
∂
=
∂
∂
−
−
−
N
y
v
e
y
e
y
f
p n
ij t
ij t
j t
ij t
ij t
ij t
ij t
j t
t
,
,
,
,
,
,
,
,
tt t j t
ij t
t t j t t j t ij t
j t
ij t
t t
k k
y
p n v k k y
v
y
p n
− +
− + − +
+
∂
∂
− −
,
,
, , ,
,
,
( )
kk k
p n v k k y
dt j t
t t j t t j t ij t
ij t
+
− + − +
,
, , ,
,
( )
.
(9)
The derivation of Equation (9) can be found in Appendix A. With
∂vj,t⁄∂yij,t=0, the second summand disappears, leaving Equation (8) as
a special case of Equation (9). Otherwise, Hypothesis 2 is as follows:
Hypothesis 2: The regressiveness of network charges increases
(decreases) if income and the variable component of network
charges are negatively (positively) correlated, i.e., if.
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018106
, ,
, ,
0 0j t j t
ij t ij t
v v
y y
∂ ∂
< > ∂ ∂
Additionally, prosumers are not charged any network tariffs for
the share of their electricity demand which they have themselves
produced. If the feeding-in of PV electricity is distributed equally
along household incomes, this has no implications at all for the
incidence of network charges. However, when there is a positive
relationship between household income and the use of PV
systems, high-income households are on average faced with a
lower burden from network charges than low-income households.
This once again increases the regressiveness of network charges.
Hypothesis 3 summarizes this issue.
Hypothesis 3: Since monthly net demand for electricity is
calculated as the difference between consumed and fed-in
electricity, network charges can be avoided by producing
electricity. The regressiveness of network charges increases
(decreases) if the feeding-in of PV electricity and income are
positively (negatively) correlated.
4. METHODOLOGY AND DATA
4.1. Methodology
In order to quantify the overall impact of network charges on
economic inequality, we employ three different distribution
metrics: The Gini coefficient, the Theil index and the Atkinson
index. Furthermore, we vary the parameters of the Theil and
Atkinson index in order to test the robustness of our results. This
selection of inequality metrics basically follows the approach of
Grösche and Schröder (2014), who analyze the distributional effects
of the German feed-in tariff. We only omit the 90/10 percentile
ratio, since it does not include the entire distribution data, but
only measures the relationship between two points within the
distribution. As a percentile ratio, it is very selective and limited
in scope. An axiomatic comparison of the inequality metrics can
be found in the aforementioned study (Grösche and Schröder,
2014. p. 1363. et seq.) as well as in Sen (1973). A brief definition
of the three chosen inequality metrics for weighted survey data
can be found in Appendix B.
4.2. Data
The underlying data consists of two merged datasets: Socio-
economic household data from the German Socio-Economic
Panel (SOEP) (SOEP, 2018, version v33.1) on the one hand and
panel data on regional network charges from ene’t GmbH (2018)
on the other hand.
From SOEP data, we include monthly net household income
(inc) and electricity expenditures (elec) as financial variables in
our analysis. Furthermore, we include the household’s number of
persons aged 14 or above (adult14) and the number of remaining
persons, i.e., children aged 13 or below (children). These variables
are needed so as to calculate equivalent incomes according to the
OECD-modified equivalization scale. We include binary variables
for the existence of PV electricity generation (solar) in our analysis.
Each household is assigned either to a rural or urban area (rural)
and to a Raumordnungsregion5 (ROR).
However, our analysis has to focus on the period 2010-2016,
since electricity expenditure was not surveyed before 2010.
Additionally, monthly electricity costs are only available for rental
households, whereas households with home ownership were asked
to specify their annual electricity costs in the previous year. We
include the latter by dividing these costs by 12 and accounting
for the annual increase in electricity prices in the corresponding
year. The data appears to be comparable, although households
with home ownership paid on average 80.18€ per month in 2016
which is 20.59€ or about a third more than rental households.
Nevertheless, this seems plausible when taking into account the
fact that at the same time, the average household income of owners
(3,162€) was 47 % higher than that of rental households (2,152€).
Additionally, the average number of persons in the household
(2.2 compared to 1.8) and the dwelling size (122.3 compared to
72.8 m2) were considerably higher for households which owned
their own housing. Ultimately, owners spent about 3.2% of their
income on electricity, whereas rental households paid 3.5%. This
finding conforms perfectly to our assumption of electricity as a
relatively inferior good.
Finally, there are 101,597 observations which include information
on electricity costs – equivalent to 13,913 (2016)-17,297 (2013)
observations per year. In 2015, owners were not asked to give
their electricity costs: The costs are only available for 9,021
rental households. Therefore, 2015 is excluded from our analysis
at every point for which we do not control for ownership.
Furthermore, the number of observations does not allow a more
detailed geographic division: A valid statement on the average
burden exerted by network charges in each of the over 11,000
communities (LAU 2) or 400 districts (NUTS 3) could not be
made because of the sample size. At the ROR level, there are on
average 150-180 annual observations which might be sufficient
for a quantitative analysis of regional disparities. However, there
are still eight RORs which exhibit <50 observations in at least
1 year (leaving out 2015 data).6 As a consequence, single values
should be interpreted with caution and the emphasis should rather
be on the overall picture.
From ene’t data, we include network charges for the period 2010-
2017, which consist of the fixed component (GP) and the variable
component (AP). Furthermore, we include the regional concession
fee (KA, measured in ct/kWh). Network charges as well as the
concession fee, are available at LAU 2 level, and are aggregated
by calculating weighted averages for RORs. This enables us to
match households and the corresponding network charges.
Merging the datasets further allows us to calculate electricity
consumption according to Equation (7) and the total burden of
5 A Raumordnungsregion which can be translated as “spatial planning
region,” is a German geographic division standard somewhere between
the NUTS 2 (Regierungsbezirke/government regions) and NUTS 3 level
(Kreise/districts). In total, there are 96 RORs across Germany.
6 The overall response rate for 2010-2014 and 2016 amounted to 87.1%,
which yields a representative analysis.
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 107
network charges according to Equation (6). Since the electricity
price is taxed at 19% VAT, the effective burden must include the
additional tax burden. Therefore, as already explained in Section
3, network charges are gross values in the following analysis.
5. RESULTS
5.1. Descriptive Statistics
As shown in Figure 1, network charges increased substantially
in recent years. The federal average network charge for a
representative household with annual electricity consumption
of 3,500 kWh amounted to 7.44 ct/kWh in 2016, compared to
6.13 ct/kWh in 2010, which corresponds to an increase of 21.3%.
Even after accounting for inflation (7.7%), a real increase in
effective network charges of 12.7% remains. This development is
caused by both an increase in the variable and the fixed component:
Whereas the Arbeitspreis rose from 5.73 ct/kWh in 2010 to 6.34ct/
kWh in 2016 (+10.7%), the Grundpreis even grew more strongly
and nearly tripled (from 14.03€/a in 2010 to 38.32€/a in 2016,
+173.2%). Whereas the Grundpreis grew gradually, the Arbeitspreis
reached a peak in 2013 and remained at a high level from then on.
Also, the distribution of network charges has changed: Network
charges increased especially in the Northeast and in the Southwest
of the country. The Northeast is especially affected by the
modification and expansion of the grid, due to the connection of
renewable energies and having been a region with a relatively
low level of network density. In the Southwest, costs are in part
driven by a well-advanced diffusion of PV systems. The Gini
coefficient measuring the inequality of average network charges
across communities increased from 9.6% in 2010 to 11.3% in
2016. This means that network charges tended to increase more
in communities where they were also higher in 2010. Looking at
the long term, this trend became even more intense over the last
decade (2007: 7.3%; 2017: 12.0%).
In order to display regional income disparities, we equivalize
household net income by applying the OECD-modified scale.
According to this procedure, each member of the household is
assigned a certain value (first adult 1, other adults 0.5, children <14
years 0.3) and the household net income is finally divided by the
sum of these values. The equivalization is better able to account for
the different needs of households with a different composition. Net
equivalent household income (OECD-modified scale) increased
by 11.2% in the period 2010-2016, which corresponds to an
annual growth rate of 1.8%. Since inflation amounted to 7.7%,
real incomes also increased on average. However, huge income
differentials appear when analyzing average incomes at the ROR
level. Income is unequally distributed across RORs in germany.
The gini coefficient (weighted by the number of ROR inhabitants)
measuring regional income inequality was mainly between 7.6%
and 8.0% in recent years and exhibited a moderate downward
trend (2010. p. 8.8%; 2016. p. 8.0%). In 2016, average equivalent
incomes reached from 1,311€ in Prignitz-Oberhavel to 2,280€ in
Ingolstadt. This heterogeneity is persistent over time and extends
back to the division of Germany into GDR and FRG until 1990.
Even over 25 years later, the East-West income differential is
substantial, is decreasing very slowly and easily can be seen in
Figure 2.
In 2016, monthly electricity costs amounted to 68.86€ on average,
which was about 3.4% of net household income. These costs are
used to calculate electricity consumption and the network charge
burden according to the procedure in Equations (6) and (7).
The burden exerted by network charges increased by 16%
– from 188.11€ in 2010 to 217.97€ in 2016. Most recently,
the regional disparities were quite considerable - ranging from
about 148€ in Berlin and Bremen to 301€ in Bremerhaven.7 The
7 It may seem obvious that these huge regional disparities stem from small
samples at the ROR level. However, the inequalities persist when analyzing
network charge burdens at a federal state (Bundesland) level: Whereas
households in Bremen or Berlin only spent about 150€ on network charges
in 2016 and households in Bayern, Sachsen and Thüringen spent between
200€ and 210€, households in Brandenburg and Schleswig-Holstein had to
pay more than 250€.
Figure 1: Average gross network charges (ct/kWh) in 2010 (left) and 2016 (right) for a representative household with electricity consumption of
3,500 kWh/a at the community level
Source: Own illustration and calculation based on ene’t (2018)
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018108
disparity is also large when expressed as a share of income:
People in Ingolstadt spent 0.63% of their income on network
charges, whereas those in Prignitz-Oberhavel paid 1.54%.8
When analyzing relative burdens at a federal level, the North
and East are charged disproportionately compared to the South
and West of Germany (Figure 3). But the burden also increased
at a household level: Whereas 28% of households had to spend
more than 1% of their income on network charges in 2010, this
share increased to 31% in 2016. On the other hand, the share
of households paying <0.5% also decreased from 28% to 24%.
These findings motivate the following analysis which is an
attempt to determine the overall impact of network charges on
economic inequality in Germany.
5.2. Impact on Economic Inequality
First of all, we have to test whether electricity is a relatively
inferior good in our data, as assumed in Hypothesis 1 and in the
literature described in Footnote 4. We regress our estimate of log
8 At the federal state level, this share ranged from about 0.7% in Bremen and
Berlin, to above 1.2% in Brandenburg and Sachsen-Anhalt.
electricity consumption on the logarithm of equivalent income in
a two-way fixed-effects weighted least squares model.9 We find
that the income elasticity of electricity consumption is slightly
but significantly above zero (0.049), even when accounting
for heteroskedasticity robust standard errors. Consequently, we
confirm the results of previous studies, and electricity appears to
be a relatively inferior good.
As assumed in Hypothesis 2, the variable component of the
network charge is negatively correlated with income. Whereas
the lowest income quintile had to pay 5.35 ct/kWh in 2016,
the highest income quintile only had to pay 5.26 ct/kWh. This
difference is small, but persistent over time,10 which can only
9 This technique is most able to extract the ceteris paribus influence of
income on electricity consumption: Time-fixed effects such as efficiency
gains and societal changes in consumption habits are represented, as well
as entity-fixed effects such as individual usage behavior and wastefulness.
10 Actually, this gap amounted to higher values in the past: 0.27 ct/kWh in
2010, 0.22 ct/kWh in 2012, and 0.17 ct/kWh in 2014. In addition, we have
to keep in mind that these values are net of VAT and that these gaps increase
with the factor of 1.19 when calculating effective financial burdens.
Figure 2: Average monthly net equivalent household income (€, OECD-modified scale) in 2010 (left) and 2016 (right) at Raumordnungsregion level
Source: Own illustration and calculation based on SOEP (2018, wave v33.1).
Figure 3: Average annual network charge burden (% of net household income) in 2010 (left) and 2016 (right) on Raumordnungsregion level
Source: Own illustration and calculation
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 109
be explained by regional disparities, since the Arbeitspreis does
not vary within a region but only across regions. This result is
somewhat in line with our previous findings: Households in
rural areas usually have lower incomes, but have to pay for a
grid used by relatively few people, due to the low population
density in rural areas. This finding is also supported by the
conditional means of the variable network charge, given a certain
urbanization level. In 2016, households in rural areas had to pay
on average 5.7 ct/kWh. By contrast, people in urban areas had
to pay only 5.2 ct/kWh.11
The use of rooftop PV systems is indeed correlated with household
income as assumed in the context of Hypothesis 3: Whereas only
3.5% of households in the lowest income quintile produced solar
power in 2016, it was 9.2% in the third, and up to 14.1% in the
fifth quintile.
As all the assumptions underlying our hypotheses are met and
can be found in our data, we expect network charges to display
considerable regressive effects. In a first step, we calculate total
annual network charges and the income share of annual network
charges for each quintile of the distribution of net equivalent
incomes. As shown in Table 1, the absolute financial burden of
network charges increased for all households by about 2-3€ per
month, which corresponds to an annual additional burden of
about 30€. Independent of the year, the income share of network
charges is decisively lower in higher income quintiles: Whereas the
lowest quintile has to pay more than 1.6 % of income for network
charges, the highest quintile has to spend <0.5 %. When analyzing
the intertemporal development of relative financial burdens, we
conclude that the increase in network charges in the period under
11 This also holds for the fixed component: The Grundpreis in rural areas
amounted to 36.80€/a, but only to 30.07€/a in urban areas. In the end,
households in rural areas (239€ in 2016) pay about 30€ more annually than
households in urban areas (208€).
consideration mainly affected the lower quintiles, inducing them
to spend higher shares of their incomes on network charges. By
contrast, the income shares of network charges remained nearly
constant in higher quintiles.
These findings can be attributed to multiple causes. Firstly, the
relative inferiority of electricity induces a sub-proportional
increase in electricity consumption with rising incomes. As
time goes by, this leads to a higher additional burden in lower
quintiles during periods of extensive economic growth. Secondly,
the relevance of the fixed component of the network charges
increased, thus strengthening its regressive impact. Thirdly, the
regional disparities of network charges increased as outlined in
Section 4. Since network charges are negatively correlated with
incomes, this promotes the regressive effects of network charges
once more. And fourthly, incomes grew sub-proportionately in
the lowest quintile (by 7.5% compared to 10.3-13.8% in higher
quintiles).
In order to quantify the impact of network charges on economic
inequality, and following the approach of Grösche and Schröder
(2014), we finally calculate different inequality measures of
equivalent incomes – gross and net of network charges. We employ
the Gini coefficient, the Theil T and L index and the Atkinson index
– the latter with different parameters.12 The results are shown in
Table 2 for the years 2010 and 2016 as an example.
All indices suggest that economic inequality is amplified by
network charges. In 2010, inequality metrics increased by 0.63-
1.55 % when accounting for network charges. Looking at the Theil
and Atkinson indices, we conclude that this effect is qualitatively
12 The underlying formulas are defined in Subsection 4.1. Note that we
interpret these metrics only as a positive measure of inequality and not as a
normative criterion. Thus, we only state that inequality rises or declines and
do not assess whether this finding can be treated to be fair.
Table 1: Monthly financial burden of network charges by quintiles of net equivalent income distribution
Quintile 2010 2016
Borders Mean Total network
charges
… as a share
of income (%)
Borders Mean Total network
charges
… as a share
of income (%)
1 <934€ 717€ 14.71€ 1.54 <1,000€ 771€ 16.62€ 1.63
2 934€–1,233€ 1,092€ 15.16€ 0.96 1,000€–1,400€ 1,235€ 17.89€ 1.02
3 1,233€–1,600€ 1,421€ 15.96€ 0.77 1,400€–1,800€ 1,617€ 18.64€ 0.82
4 1,600€ –2,067€ 1,835€ 15.92€ 0.60 1,800€–2,333€ 2,056€ 18.15€ 0.63
5 > 2,067€ 2,995€ 16.56€ 0.43 >2,333€ 3,302€ 19.38€ 0.45
Source: Own calculation based on SOEP (2018, wave v33.1) and ene’t GmbH (2018)
Table 2: Impact of network charges on economic inequality measured by different inequality indices
Index 2010 2016
Inequality of
equivalent income
… net of network
charges
Percentage
change (%)
Inequality of
equivalent income
… net of network
charges
Percentage
change (%)
Gini 0.2769 0.2787 +0.6286 0.2761 0.2779 +0.6662
Theil’s L (α=0) 0.1291 0.1310 +1.4112 0.1345 0.1302 +1.5130
Theil’s T (α=1) 0.1392 0.1409 +1.2084 0.1345 0.1363 +1.2963
Atkinson (ε=0.5) 0.0642 0.0650 +1.2554 0.0631 0.0640 +1.3479
Atkinson (ε=1) 0.1211 0.1227 +1.3208 0.1204 0.1221 +1.4166
Atkinson (ε=2) 0.2246 0.2281 +1.5481 0.2259 0.2296 +1.6277
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018110
independent of the chosen parameter (α, ε), although it increases
with an increasing inequality aversion. In 2016, this inequality-
promoting effect even grew stronger: Inequality metrics increased
by 0.67-1.63% when accounting for network charges. Looking at
the years in between, this development reflects an ongoing trend.
Consequently, network charges have a positive and increasing
impact on inequality and thereby exert a regressive impact on the
distribution of disposable incomes.
5.3. Welfare Loss
Finally, we attempt to estimate the additional welfare loss caused
by the regressiveness of network charges according to the
definition in Appendix B. The results are shown in Table 3.
The welfare loss for German households which can be derived
from the Atkinson index depends crucially on the presumed
inequality aversion parameter. The additional welfare loss which
is due to unequally distributed network charges amounted to
at least several million Euros per year, but the estimates have
a large variance: At ε = 2, the additional welfare loss is about
5 times as high as at ε = 0.5. As a consequence, the absolute level
of this measure should not be overstated, but the time trend is
interesting: The welfare loss increases substantially over time.
Assuming an inequality aversion of 0.5 or 1, the welfare loss
increased by about a quarter in the period under consideration,
whereas it still increased by more than a fifth with an underlying
inequality aversion of 2.
6. CONCLUSION
Network costs increased substantially in recent years and have
been passed on to electricity customers in the form of higher
network charges. We show that in absolute terms, the average
German household paid 218€ for network charges in 2016 starting
from about 188€ in 2010. As a component of the electricity
price, these charges exert regressive effects on the distribution of
disposable incomes net of network charges due to four reasons.
Firstly, electricity is a relatively inferior good so that the income
share of electricity is negatively related to income. Secondly,
the fixed component of network charges leads to lower average
network charges for households with higher electricity demand.
Thirdly, network charges differ regionally. Both the variable and
the fixed component of network charges are negatively correlated
with regional average income. This leads to a higher burden for
(relatively poor) households in regions with higher network
charges. Fourthly, prosumers are exempt from network charges,
but are high-income households, in many cases. As a consequence,
low-income households are de facto often faced with higher costs
due to network charges although network charges are not de jure
contingent upon income.
As a result, households pay on average a share of 0.9% of
their income for network charges. But different quintiles of the
income distribution spend significantly different shares of their
income on network charges – 1.6% in the lowest quintile and
0.4% in the highest quintile. Because of the negative regional
correlation of network tariffs and income, even households
with similar economic preconditions are charged differently
in different parts of the country. Households had to pay only
150€ in some regions and up to about 300€ in others. Finally,
there are apparent differences between rural and urban areas:
Households in rural areas paid nearly 239€/a and about 208€/a
in urban areas. This corresponds to higher network costs per
household in rural areas.
Using different inequality metrics, we find that network charges
increase overall inequality of disposable incomes net of network
charges by at least 0.6%. This effect has increased since 2010 as
network charges have also increased substantially in the respective
period. As network costs are expected to increase further in the
near future, distribution issues will become increasingly important
in this area.
The maintenance and expansion of the distribution grid is
essential for the integration of renewable energies in order
to fulfill the requirements of the Energiewende. Thus, the
distribution of the corresponding costs among the population is
a fundamental determinant for the political acceptance of such
an energy transition. To the best of our knowledge, the present
study is the first to analyze the relative financial burden imposed
by increasing network charges to households. It shows that
the tariff structure and the regional differentiation of network
charges are able to exert significant (regressive) effects on
the distribution of disposable incomes. Consequently, they
have the potential to jeopardize the political feasibility of the
German Energiewende and have to be analyzed thoroughly.
These concerns regarding the social sustainability of the energy
transition grow further once other empirical studies including
subsidies for renewable energies are taken into account (e.g.,
Grösche and Schröder, 2014).
Yet, these findings do not suggest automatically that the
distribution of the financial burden of network charges can
be treated as unfair. On the one hand, we did not include
Table 3: Welfare loss of income inequality and relative welfare loss, due to inequality-promoting network charges
Index 2010 2016
Welfare loss
without network
charges
Welfare loss
including network
charges
Additional
welfare loss of
network charges
Welfare loss
without network
charges
Welfare loss
including
network charges
Additional
welfare loss of
network charges
Atkinson (ε=0.5) 4,175M€ 4,198M€ 24M€ 4,742M€ 4,771M€ 29M€
Atkinson (ε=1) 7,874M€ 7,923M€ 49M€ 9,045M€ 9,107M€ 62M€
Atkinson (ε=2) 14,597M€ 14,722M€ 125M€ 16,968M€ 17,121M€ 153M€
Source: Own calculation based on SOEP (2018, wave v33.1) and ene’t GmbH (2018)
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 111
commercial customers to our analysis. However, their share in
financing the grids is considerable and it appears to be promising
to analyze this “functional” inequality. On the other hand, there
is an emerging debate in the literature concerning distribution
issues and whether or how far fairness norms should be applied
to the realm of energy policy (Gawel and Korte, 2012; Gawel
et al., 2015). In the context of network charges, a more detailed
discussion of relevant normative criteria is still pending. This
will be an interesting challenge for future research in order
to scrutinize the current tariff design of network charges
and to make useful policy recommendations. Furthermore, a
comparative analysis of the distributional effects of various
tariff designs in different countries appears to be promising.
This might lead to the identification of best practices. However,
this firstly relies on a normative evaluation of distributional
effects and secondly poses the question how far tariff designs
of some countries can be transferred and implemented in other
countries and how far different systems are able to learn from
each other, accordingly.
7. ACKNOWLEDGMENTS
Special thanks go to the SOEP study and ene’t GmbH for providing
the underlying datasets of this study as well as Tobias Kreuz and
his valuable help in gathering the data. We are also grateful to
Brian Bloch for proofreading.
REFERENCES
Atkinson, A.B. (1970), On the measurement of inequality. Journal of
Economic Theory, 2(3), 244-263.
Bundesnetzagentur, Bundeskartellamt. (2017), Monitoringbericht
2017. Bonn. Available from: https://www.bundesnetzagentur.de/
SharedDocs/Downloads/DE/Allgemeines/Bundesnetzagentur/
Publikationen/Berichte/2017/Monitoringbericht_2017.pdf. [Last
retrieved on 2018 Mar 27].
Bundesnetzagentur. (2015), Netzentgelt systematik Elektrizität.
Bonn. Available from: https://www.bundesnetzagentur.de/
SharedDocs/Downloads/DE/Sachgebiete/Energie/Unternehmen_
Institutionen/Netzentgelte/Netzentgeltsystematik/Bericht_
N e t z e n t g e l t s y s t e m a t i k _ 1 2 - 2 0 1 5 . p d f . [ L a s t r e t r i e v e d o n
2018 Mar 27].
Bundesnetzagentur. (2016a), Hinweise für Verteilnetzbetreiber zur
Anpassung der Erlösobergrenze für das Kalenderjahr 2017.
Available from: https://www.bundesnetzagentur.de/DE/Service-
Funktionen/Beschlusskammern/Beschlusskammer8/BK8_01_
Aktuelles/Downloads/EOG_Hinweise_2017.pdf. [Last retrieved
on 2018 Mar 27].
Bundesnetzagentur. (2016b), Netzentgelt: Was ist ein Netzentgelt (Auch
als Netznutzungsentgelt Bezeichnet)? Available from: https://www.
bundesnetzagentur.de/SharedDocs/FAQs/DE/Sachgebiete/Energie/
Verbraucher/Energielexikon/Netzentgelt.html. [Last retrieved on
2018 Mar 27].
Bundesregierung. (2010), Das Energiekonzept 2050. Available from:
http://www.bundesregierung.de/Content/DE/HTML/Breg/Anlagen/
infografik-energie-textversion.pdf. [Last retrieved on 2017 Feb 06].
Campbell, A. (2018), Price and income elasticities of electricity demand:
Evidence from Jamaica. Energy Economics, 69, 19-32.
Deutsche Energie-Agentur. (2010), dena-Netzstudie II: Integration
Erneuerbarer Energien in die Deutsche Stromversorgung bis 2020.
Available from: https://www.shop.dena.de/fileadmin/denashop/
media/Downloads_Dateien/esd/9105_Fachbroschuere_dena-
Netzstudie_II.pdf. [Last retrieved on 2018 Mar 27].
ene’t GmbH. (2018), Datenbank Netznutzung Strom Deutschland.
Hückelhoven: Ene’t GmbH.
Espey, J.A., Espey, M. (2004), Turning on the lights: A meta-analysis of
residential electricity demand elasticities. Journal of Agricultural
and Applied Economics, 36(1), 65-81.
Flues, F., Thomas, A. (2014), The Distributional Effects of Energy Taxes.
OECD Taxation Working Papers No: 23.
Fouquet, R. (2014), Long-run demand for energy services: Income and
price elasticities over two hundred years. Review of Environmental
Economics and Policy, 8(2), 186-207.
Gawel, E., Korte, K. (2012), Verteilungseffekte des EEG: Kritik an den
falschen stellen. Wirtschaftsdienst, 92(8), 512-515.
Gawel, E., Korte, K., Tews, K. (2015), Energiewende im Wunderland:
Mythen zur Sozialverträglichkeit der Förderung erneuerbarer
Energien durch das EEG. UFZ Discussion Papers No: 2/2015.
Gini, C. (1912), Variabilità e Mutabilità: Contributo allo Studio delle
Distribuzioni e delle Relazioni Statistiche. Bologna: C. Cuppini.
Grimm, V., Zöttl, G., Rückel, B., Sölch, C. (2015), Regionale
Preiskomponenten im Strommarkt: Gutachten im Auftrag der
Monopolkommission. Available from: http://www.wirtschaftstheorie.
wiso.uni-erlangen.de/wp-content/uploads/2016/02/gutachten_
regionale-preiskomponenten07.10.15.pdf. [Last retrieved on
2018 Mar 27].
Grösche, P., Schröder, C. (2014), On the redistributive effects of
Germany’s feed-in tariff. Empirical Economics, 46(4), 1339-1383.
Haucap, J., Pagel, B. (2014), Ausbau der stromnetze im rahmen
der energiewende: Effizienter netzausbau und effiziente
struktur der netznutzungsentgelte. DICE Ordnungspolitische
Perspektiven, 55, Available form: https://www.econstor.eu/
bitstream/10419/91596/1/777566125.pdf.
Hiersig, R., Wittig, D. (2015), Gestaltung einer fairen lastenverteilung
in den netzkosten-und netzentgeltstrukturen. Energiewirtschaftliche
Tagesfragen, 65(7), 13-16.
Hinz, F. (2014), Netznutzungsentgelte-Konzepte und regionale
Verteilungseffekte. In: Möst, D., Schegner, P., editors. Energiewende
Sachsen-Aktuelle Herausforderungen und Lösungsansätze
Schriften des Lehrstuhls für Energiewirtschaft. Dresden: TU
Dresden. p39-49. Available from: https://www.researchgate.net/
profile/Dominik_Moest/publication/281525332_Energiewende_
Sachsen-Aktuelle_Herausforderungen_und_Losungsansatze_
Beitrage_der_Abschlusskonferenz_des_ENERSAX-Projektes/
links/55ec77d408aeb6516268c9c7.pdf#page=47. [Last retrieved
on 2018 Mar 27].
Hinz, F., Schmidt, M., Möst, D. (2018), Regional distribution effects
of different electricity network tariff designs with a distributed
generation structure: The case of Germany. Energy Policy, 113,
97-111.
Loi, T.S.A., Le, N.J. (2018), Analysing households’ responsiveness
towards socioeconomic determinants of residential electricity
consumption in Singapore. Energy Policy, 112, 415-426.
Löschel, A., Flues, F., Heindl, P. (2012), Das erneuerbare-energien-gesetz
in der diskussion. Wirtschaftsdienst, 92(8), 515-519.
Neuhoff, K., Bach, S., Diekmann, J., Beznoska, M., El-Laboudy, T.
(2012), Steigende EEG-Umlage: Unerwünschte Verteilungseffekte
können vermindert werden. DIW Wochenbericht, 41, 3-12.
RAP. (2014), Netzentgelte in Deutschland. Herausforderungen und
Handlungsoptionen: Studie im Auftrag von Agora Energiewende.
Berlin: RAP. Available from: https://www.agora-energiewende.
de/fileadmin/downloads/publikationen/Analysen/Netzentgelte_
in_Deutschland/Agora_Netzentgelte_web.pdf. [Last retrieved on
2018 Mar 27].
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018112
APPENDIX A: DERIVATION OF
HYPOTHESIS 2
The income share of total network charges is given by:
N
f p n k k v e
p n v k k y
ij t
j t t t t j t j t ij t
t t j t t j t
,
, , , ,
, ,
� =
− + +( )+
− + + +( ) iij t, .
Differentiating with respect to income yields:
∂
∂
=
− + + +( )
∂
∂
+
N
y
p n v k k y
v
y
e v
ij t
ij t
t t j t t j t ij t
j t
ij t
ij t j
,
,
, , ,
,
,
, ,,
,
,
, , ,
t
ij t
ij t
t t j t t j t ij t
e
y
p n v k k y
∂
∂
− + + +( )2 2
−
− + +( )+
− + + +( )+
f p n k k v e
p n v k k
y
j t t t t j t j t ij t
t t j t t j t
ij
, , , ,
, ,
,,
,
,
, , ,
t
j t
ij t
t t j t t j t ij t
v
y
p n v k k y
∂
∂
− + + +( )2 2
=
∂
∂
+
∂
∂
−
− + +( )v
y
e v
e
y
f p n k k
y
j t
ij t
ij t j t
ij t
ij t
j t t t t j t
ij
,
,
, ,
,
,
, ,
,tt
j t
ij t
ij t
t t j t t j t ij t
v
e
y
p n v k k y
−
∂
∂
− + + +( )
,
,
,
, , ,
−
− + +( )+
∂
∂
− + +
f p n k k v e
v
y
p n v k
j t t t t j t j t ij t
j t
ij t
t t j t t
, , , ,
,
,
,
++( )k yj t ij t, ,
2
=
∂
∂
−
−
− + +
v
e
y
e
y
f
p n k k
yj t
ij t
ij t
ij t
ij t
j t
t t t j t
ij
,
,
,
,
,
,
,
,tt
t t j t t j t ij tp n v k k y− + + +( ), , ,
−
∂
∂
− + +
− + + +
−
−
v
y
p n k k
p n v k k
f e
p n
j t
ij t
t t t j t
t t j t t j t
j t ij t
t t
,
,
,
, ,
, ,
++ + +( )v k k yj t t j t ij t, , ,
=
∂
∂
−
−
− + +
v
e
y
e
y
f
p n k k
yj t
ij t
ij t
ij t
ij t
j t
t t t j t
ij
,
,
,
,
,
,
,
,tt
t t j t t j t ij t
j t
ij t
t t t j t
t t
p n v k k y
v
y
p n k k
p n
− + + +( )
+
∂
∂
− + +
− +
, , ,
,
,
,
vv k k
d
j t t j t
ij t
, ,
,
.
+ +
APPENDIX B: DEFINITION OF
INEQUALITY METRICS FOR WEIGHTED
SURVEY DATA
The Gini Coefficient
The Gini coefficient (Gini, 1912) is probably the most common
inequality measure in economics. It can be derived from the Lorenz
curve which plots the cumulative income share of the bottom x% of the
population. The Gini coefficient is normalized to the interval (0,1), with
0 indicating perfect equality (every household has the same income)
and values close to 1 indicating perfect inequality (only one household
has a positive income).13 For weighted survey data, it is defined as:
=
−
= =∑ ∑i
n
j
n
i j i jy y
y
1 1
2
ω ω
(10)
Where yi is the income of household i y y
i
i i, = ∑ω is its weighted
mean, n the total number of observed households and ωi=wi⁄(∑iwi)
the relative weight of household i (with wi as the projection factor).
The Theil Index
The Theil index (Theil, 1965) is a special case of the generalized
entropy index family stemming from information theory. Originally, it
measured the informational content of a number of observations. This
content is assumed to be minimal if every observation has the same
probability – the entropy reaches its maximum value. By contrast,
13 Note that the Gini coefficient cannot reach a value of 1 for finite populations,
as this is a limit value.
Schulte, I., Heindl, P. (2017), Price and income elasticities of residential
energy demand in Germany. Energy Policy, 102, 512-528.
Sen, A. (1973), On Economic Inequality. Oxford: Oxford University Press.
SOEP. (2018), Data from 1984-2016. DOI: 10.5684/soep.v33.1. Available
from: https://www.diw.de/de/diw_02.c.240089.de/hinweise_fuer_
autoren.html#493461.
Statistisches Bundesamt. (2018), Bruttostromerzeugung in Deutschland
für 2015 bis 2017. Available from: https://www.destatis.de/DE/
ZahlenFakten/Wirtschaftsbereiche/Energie/Erzeugung/Tabellen/
Bruttostromerzeugung.html. [Last retrieved on 2018 Mar 27].
Techert, H., Niehues, J., Bardt, H. (2012), Ungleiche belastung durch die
energiewende: Vor allem einkommensstarke haushalte profitieren.
Wirtschaftsdienst, 92(8), 507-512.
Theil, H. (1965), The information approach to demand analysis.
Econometrica, 33(1), 67-87.
Többen, J. (2017), Regional net impacts and social distribution effects of
promoting renewable energies in Germany. Ecological Economics,
135, 195-208.
Schlesewsky and Winter: Inequalities in Energy Transition: The Case of Network Charges in Germany
International Journal of Energy Economics and Policy | Vol 8 • Issue 6 • 2018 113
the informational content increases with decreasing entropy. This
measure has been applied to the empirical investigation of economic
inequality. The ”informational content” of an income distribution
increases the more it differs from perfect equality (i.e., with lower
entropy). Usually, the Theil L (α = 0) and the Theil T (α = 1) index
are distinct from one another. These indices are defined as:
1
1
ln 0,
ln 1
n
i
i i
n
i i
i
i
y
if
y
y y
if
y y
α
ω α
ω α
=
=
=
=
=
∑
∑
(11)
With the definitions from above. Generally, the Theil T index is
more common in empirical economics (e.g., Grösche and Schröder,
2014. p. 1346). The Theil indices can take any nonnegative value
and increase with inequality.
The Atkinson Index
The Atkinson index (Atkinson, 1970) defines the maximum share
of mean income a society would be willing to give up in order
to reach perfect income equality. As this depends on the level of
inequality aversion ε this implies a social welfare function which
is concave in individual incomes:
1
0
1
1
1
\ 1,
1
( )
ln 1
n
i
i
i
n
i i
i
y
w if
W
w y if
ε
ε
ε
ε
ε
−
>
=
=
−
∈
−
=
=
∑
∑
y
(12)
where y is the vector of household incomes. Based on this social
welfare function, we can define the corresponding equally
distributed equivalent income yε – i.e., household income in a
perfectly equal society, which is associated with the same level
of social welfare as the actual income distribution.
1
1
1
0
1
1
\ 1,
1, i
n
i i
i
n
i
i
y if
y
y if
ε
ε
ε
ω
ω ε
ε
−
−
>
=
=
∈ =
=
∑
∏
(13)
Which yields the weighted geometric mean for ε = 1. Finally, we
normalize:
ε
ε= −1
y
y
(14)
Since, for concave social welfare functions (i.e., for a positive
inequality aversion ε > 0, the equally distributed equivalent income
yε is always smaller than the weighted mean y , the Atkinson
index is normalized to ε ∈[ ]0 1, with higher values denoting
higher inequality.
Consequently, we are able to calculate a “welfare loss” arising
from income inequality. This welfare loss is the difference of
mean and equally distributed income at a household level or
L w y y w y
i
n
i
i
n
iε ε ε= − =
= =
∑ ∑
1 1
( ) (15) at an aggregate level. It can be
interpreted as society’s willingness to pay for eliminating income
inequality, and is calculated for our purposes in Subsection 5.3.