Has the Fukushima accident influenced short-termconsumption in the evolution of nuclear energy?
An analysis of the world and seven leading countries
Claudia Furlana,∗, Mariangela Guidolina, Renato Guseoa
aDepartment of Statistical Sciences, University of Padua, Italy
Abstract
In 2013 registered nuclear power consumption in several countries, including
France, Germany, and other OECD members, declined. In this paper, we focus
on nuclear consumption leaders and explore, through diffusion models, whether
and to what extent Fukushima accident had a short-term effect on these coun-
tries’ consumption dynamics. Safety checks, performed after the accident caused
temporary shutdowns in production but not all of them were significant enough
to modify nuclear energy evolution. Then, we compared the evolutionary behav-
ior estimated through the entire time series and that obtained by excluding the
last three observations (2011−2013): what would the forecasts have been before
Fukushima? Significant short-term effects were identified in 2011− 2013 at the
global level, for France, and South Korea, while they have not been identified for
the US, Germany, and Russia. About the medium-term evolution predicted by
the models, we identified countries with declining consumption (the US, France,
Germany and South Korea) and with increasing consumption (China, Russia,
and Canada). At the global level a declining trend is predicted.
Keywords: Nuclear power, energy policy, Fukushima, diffusion of innovations,
heterogeneity, multi-cycles
∗Corresponding authorEmail addresses: [email protected] (Claudia Furlan), [email protected]
(Mariangela Guidolin), [email protected] (Renato Guseo)
Preprint submitted to Journal of LATEX Templates December 17, 2015
1. Introduction
Of all the forms of energy used to generate electricity, nuclear is probably
the most concerned with safety issues. The history of commercial use of nuclear
fission dates back to the 1950s and has been characterized by three major acci-
dents. The first one, occurred in 1979 at Three Mile Island (USA), fortunately5
had a limited effect, since the amount of radioactivity was under the safety lim-
its. However, the accident received much media attention [8]. Conversely, the
accident that produced catastrophic consequences for nuclear fallout in Western
Union of Soviet Socialist Republics (USSR) and Europe was Chernobyl in 1986.
The Chernobyl disaster is considered the worst ever and has been classified at10
Level 7 on the International Nuclear Event Scale (INES) (maximum level): the
accident was due not only to flawed reactor design but also to dramatic human
errors [40]. The other accident classified at Level 7 is the one that occurred in
Fukushima (Japan) in March 2011.
After the Fukushima accident Japan, from being the world’s third largest nu-15
clear power generator, fell down to the 18th position between 2010 and 2012 due
to the shutdown of all its reactors [36]. According to the IAEA-Pris database
[27] in Japan 11 reactors currently have been shutdown, while 48 are still “op-
erational”, even though 46 are classified as “suspended operation” and have not
generated electricity for years. The disaster changed Japanese public opinion20
about this energy source. In Esteban [14], it is reported that a recent opinion
poll revealed that 70% of Japanese are in favor of a nuclear power phase-out.
Since the Fukushima disaster the Japanese government has launched various
measures to update the electricity sector and diversify the energy mix: before
2011, the energy policy in Japan was essentially led by large power companies25
that persuaded people about the security of nuclear power [14].
As emphasized in Huenteler et al. [16], the Japanese energy strategy was
focused on nuclear power as “a (nominally) cheap, quasi-indigenous and low-
carbon power source”, while renewables played a secondary role. However, in
Huenteler et al. [16], it is also underlined that the Fukushima accident shed30
2
light on the importance of a decentralized and resilient energy supply system:
in particular, photovoltaic energy seems doomed to play a prominent role in
the future of this country [16]. The BP Statistical Review of World Energy,
[3], reported a dramatic increase in photovoltaic (PV) installed power for 2013
(∆%13/12=75.4%). More impressive is the annual absolute installed photo-35
voltaic power in megawatts: 6900 (2013), 1829 (2012), 1296 (2011) and 991
(2010), which denotes a rapid shift toward a decentralized technology.
Outside Japan, it is argued that the disaster was responsible for reconsider-
ation of nuclear power policy in many countries. In particular, many questions
raised about the prevailing decision to implement the uprating process, which40
consists of technical alterations and lifetime extensions of existing reactors. As
reported in Schneider and Froggatt [36], the main reason for reactor uprating
is the economic advantage with respect to building new ones, even though this
strategy implies a lower level of security. Alternatively, small modular reactors
(SMRs) have been proposed as a possible solution to the problems character-45
izing nuclear power, namely economics, safety, waste and proliferation[12]. In
Ramana and Mian [35], the basic features of this technology are discussed and
the authors concluded that the four key problems characterizing nuclear power
(cost, safety, waste and proliferation) cannot be solved by this technology si-
multaneously. In particular, each challenge requires driving the technology in50
different and sometimes conflicting directions [35].
Safety concerns forced national decisions on nuclear energy. For instance,
four days after the accident in Japan, the German government ordered the
shutdown of eight reactors that had started up before 1981 and other countries,
such as Belgium and Switzerland, reconsidered previous decisions to extend55
lifetime of reactors. In Italy, a referendum rejected a plan to build new reactors,
[15]. Thus, the Fukushima accident appears to have affected the energy policies
outside Japan. In 2013, the BP Statistical Review of World Energy [3] reported a
decline in nuclear power consumption in several countries, although it increased
in others.60
In Table 1, we summarize the situation as of 2013 for the seven leading
3
countries, the US, France, Russia, South Korea, China, Canada and Germany.
Together, these countries generate about 75% of all nuclear electricity in the
world. Various percentage changes are outlined in Table 1, in order to appre-
ciate the differences between countries: for instance, the only country that has65
exhibited a steady growth is China. Conversely, a decrease is observed in Ger-
many, France and South Korea. Focusing on the percentage change from 2012
to 2013 there has been a decrease in France, Russia, South Korea, and Ger-
many and an increase in consumption has been reported for the US, China, and
Canada. Should we consider the decline as a post-Fukushima outcome? Was70
growth slowed by the accident? To answer these questions we cannot simply
refer to the change observed in more recent years; we must instead analyze the
complete history of nuclear consumption in these countries (see Fig. 1).
FIGURE 1 ABOUT HERE
The main purpose of the paper is to evaluate, in quantitative terms, the ef-75
fect of the Fukushima accident on the consumption dynamics of nuclear power
in the seven leading nuclear-consuming countries. In particular, this analysis is
aimed at recognizing the short-term effects (3 years) of the accident compared
to the medium-term trend (almost a decade, until 2020), whose behavior may
depend on historical, economic, social and technological aspects, which are gen-80
erally country-specific. In fact, in Hayashi and Hugues [15], it is highlighted that
in addition to short-term effects in Japan, the accident could have had short-
to-medium term effects in other countries, that invested or not in the nuclear
option. In particular, in [15], the authors maintain that the Fukushima acci-
dent occurred during a growth phase for nuclear power, often termed as “nuclear85
renaissance” [33, 41]. However, as reported in Csereklyei [8], a body of litera-
ture questions whether this renaissance really occurred. Among others, Glaser
[18], Guidolin and Guseo [19], Schneider and Froggatt [36] and Thomas [38] ar-
gued that the nuclear renaissance had ended before Fukushima due to economic
and technological problems. Partially building on this literature, we reach con-90
clusions on the impact of Fukushima on nuclear consumption at a global and
4
country level: in investigating this issue, we adopt a statistical approach, to
identify the existence and intensity of short-term effects, by separating them
from the medium-term dynamics of consumption. In particular, we model the
time series of annual consumption of nuclear power for the world and the seven95
countries of Table 1 with innovation diffusion models. Such choice relies on an
increasing literature that uses innovation diffusion models in the energy context,
as will be clarified in Section 2.
The paper is structured as follows. In Section 2 we present the diffusion
models we used in our analyses. In particular, we propose a new approach100
that combines in one model aspects that exist in literature, which are dynamic
market potential [24], heterogeneity of agents [26], and external interventions
[2], allowing for a more flexible parametric structure. Moreover, whenever nec-
essary, in order to capture the behaviors of countries with non-homogeneous
regimes, we expand a single-cycle approach by proposing a two-wave model,105
that generalizes the work of Guseo [21] and Guseo and Guidolin [25], and pro-
vides a more flexible parameter structure between the two waves. In Section 3,
we discuss the results of our analysis at the global level and for the seven leading
countries in energy consumption and evaluate the effects of the Fukushima acci-
dent on the countries’ energy policies from short and medium-term perspectives.110
Conclusions are presented in Section 4.
2. Diffusion models: exogenous shocks, dynamic market potential,
heterogeneity, and two-wave regimes
The pioneering work of the physicist Cesare Marchetti (see for instance [29])
provided a crucial contribution to the understanding of historical dynamics of115
energy systems. Starting with the hypothesis that society as a whole is a system
made of interconnected individuals who share knowledge and generate collective
expectations, he theorized that energy sources are comparable to new commer-
cial products that compete to be accepted by society, whose learning behavior
may be characterized by logistic-like functions. Under this hypothesis, primary120
5
Table 1: Nuclear power consumption: annual nuclear consumption (TWh), 2013 share of total
for the 7 consumption leaders, and percent changes.
2013 share
TWh of total ∆%13/12 ∆%13/11 ∆%13/07 ∆%10/07
US 830.5 33.4 2.6 −0.2 −2.2 0.1
France 423.7 17 −0.4 −4.2 −3.8 −2.8
Russia 173.0 6.9 −2.5 0.1 8.1 6.4
South Korea 138.8 5.6 −7.7 −10.3 −2.9 4.0
China 110.6 4.4 13.6 28.1 78.0 18.9
Canada 102.1 4.1 6.6 7.7 10.0 −3.4
Germany 97.3 3.9 −2.2 −9.9 −30.7 0.1
energy functions may be considered innovations, whose diffusion process has its
own speed and degree of uncertainty depending on technological, socio-economic
and institutional aspects. For instance, Usha Rao and Kishore [39], reported
that nuclear fission was used for the first time in a reactor to produce commer-
cial power 40 years after the discovery. Thus, the adoption of a new energy may125
be a very slow process due to a high degree of uncertainty and public policies
may be an efficient mean of reducing it, by stimulating market formation [17].
However, despite the fundamental contribution of Marchetti’s theories since
the 1980s, the development of studies that combine innovation diffusion mod-
els, mostly introduced in quantitative marketing, with energy themes is quite130
recent. In fact, typical applications of diffusion models have concerned tradi-
tional marketing sectors, such as durable goods, information and communication
technologies, pharmaceuticals, and services (for comprehensive reviews of the
literature, see for instance [30] and [34]).
More recently, we have witnessed increasing interest in the use of these mod-135
els in the energy sector to forecast the evolution of different energy sources, with
growing attention paid to renewable energy technologies (RETs): for instance,
Dalla Valle and Furlan [9] studied the diffusion of wind energy; Dalla Valle and
6
Furlan [10] the diffusion of nuclear energy in some developing countries; Davies
and Diaz-Rainey [11] analyzed the pattern of international diffusion of wind140
energy; Guidolin and Guseo [19] applied diffusion models to the diffusion of nu-
clear power and parallel reactor start-up process; Guidolin and Mortarino [20]
modeled the growth of photovoltaic energy; Guseo [21], Guseo and Dalla Valle
[22], and Guseo et al. [23] studied the oil depletion problem with diffusion mod-
els; Meade and Islam [31] modeled the European usage of renewable energy.145
In particular, consumption dynamics of energy sources have been described
through diffusion models, such as the Bass model, BM, [1] and the General-
ized Bass Model, GBM, [2] under the hypothesis that they are comparable to
commercial products or technologies with a given market potential and a finite
life cycle characterized by innovative and imitative behavior of adopters. The150
GBM has played a prominent role when external interventions, such as political,
economic and environmental changes act on the diffusion process of renewable
and non-renewable energy sources: for instance the GBM has been used in the
oil depletion context in order to account for the effect of the 1970s shocks on
oil production/consumption dynamics [7, 21, 22, 23], and to model the effect155
of incentives in the cross-country growth of photovoltaic [20] and wind energy
[9], the dynamics of reactor startups in the world [19], and the consumption of
nuclear power in developing countries [10].
2.1. The Generalized Bass model, GBM
The GBM is defined with a first-order differential equation,160
z′(t) =
(p+ q
z(t)
m
)(m− z(t))x(t), (1)
where m is the constant market potential (typically expressed in physical vol-
umes), parameters p and q summarize the usual innovative and imitative be-
havior of agents in an economic system, and x(t) is the control function that
includes exogenous shocks, modifying the timing of diffusion. In particular, if
x(t) > 1, we observe an acceleration of the diffusion process, while a delay in165
adoptions is implied by x(t) < 1. The closed-form solution of the GBM under
7
the initial condition, z(0) = 0, is
z(t) = m1− e
−(p+q)∫ t
0x(τ)dτ
1 + qpe
−(p+q)∫ t
0x(τ)dτ
, t > 0, (2)
and zero elsewhere. When there are no external interventions (i.e., x(t) = 1),
the GBM reduces to the standard BM.
2.2. A time-dependent market potential model, GGM170
A well-known limitation of the GBM, and consequently of the BM, postulates
a constant market potential m, which implies that there exists a set of potential
adopters ready to choose the new product or technology as soon as it enters the
market. This theoretical choice may be unrealistic in many situations, especially
for technologies with a high degree of innovation and complexity. A model with175
a time-dependent market potential m(t) was proposed by Guseo and Guidolin
(2009) [24]. This is described with the following first-order differential equation,
z′(t) =
(p+ q
z(t)
m(t)
)(m(t)− z(t)) + z(t)
m′(t)
m(t), (3)
whose general solution for z(0) = 0 and t > 0 is
z(t) = m(t)1− e−(ps+qs)t
1 + qspse−(ps+qs)t
(4)
and zero elsewhere. Equation (4) highlights that the dynamic market potential
m(t) is not forced to have a particular shape. A specific choice has been made180
in [24], where m(t) is function of a latent evolutionary communication network
about an innovation. The model denoted here as the Guseo–Guidolin model
(GGM) has the following structure,
z(t) = K
√1− e−(pc+qc)t
1 + qcpce−(pc+qc)t
1− e−(ps+qs)t
1 + qspse−(ps+qs)t
, (5)
where K is the asymptotic market potential, pc and qc denote the communica-
tion parameters generating the non-constant market potential, and ps and qs185
express the dynamics of adoption. This formulation assumes that a diffusion
8
process is characterized by two separate and complementary phases: communi-
cation and adoption.
As highlighted in Gallagher et al. in [17], knowledge development, knowledge
diffusion through networks and market formation are key functions of innova-190
tion systems. Focusing on the energy context, the communication component
described by parameters pc and qc refers to the spread of technical knowledge
and the parallel creation of shared expectations that are necessary for market
formation and the successive adoption phase, which is described by parameters
ps and qs.195
2.3. A time-dependent market potential model with exogenous interventions,
GGM-R
Equation (5) may be generalized to model processes not only characterized
by a dynamic market potential but also by exogenous interventions [24], intro-
ducing the control function x(t) in the adoption component:200
z(t) = K
√1− e−(pc+qc)t
1 + qcpce−(pc+qc)t
1− e−(ps+qs)
∫ t
0x(τ)dτ
1 + qspse−(ps+qs)
∫ t
0x(τ)dτ
t > 0. (6)
Function x(t) may take different forms to describe the effect of interventions.
A stable perturbation that acts on diffusion for a relatively long period may be
described with a rectangular shock,
x(t) = 1 + c1It≥a1It≤b1 , (7)
where parameter c1 describes the perturbation intensity and may be either posi-
tive or negative, while parameters a1 and b1 define the extremes of the temporal205
interval in which this occurs. The model of Equation (6) with the rectangular
shock of Equation (7), is indicated as GGM-R. For more examples of x(t), see
for instance, [22].
Notice that the GBM is obtained from Equation (6) for m(t) = K, and
the BM for x(t) = 1, and m(t) = K. Moreover, model (6) may be further210
generalized by including an intervention function that acts on communication
dynamics (see [24]).
9
2.4. A time-dependent market potential model with heterogeneity effects, GGBM
A further modeling extension introduced in this paper accounts for the het-
erogeneity among agents underlying the diffusion process [4, 5, 26]. Bemmaor215
[4] and Bemmaor and Lee [5], suggested a flexible approach for explaining the
local changes in the parameter estimates of the Bass model due to the pop-
ulation heterogeneity. They assumed the variation in individual propensities
to adopt to follow a gamma distribution and described the timing of the first
purchase through a shifted Gompertz density. The aggregate diffusion process220
results in a composition of these two densities that we denote as Bemmaor’s
effect. The individual-level model for the adoption time may be specified with
a shifted Gompertz distribution:
y(t) =(1− e−bt
)e−ηe−bt
, t > 0, η, b > 0. (8)
For simplicity, parameter b is assumed fixed. Small values for η denote a low
individual mean adoption time that defines high propensity to buy. If the het-225
erogeneity parameter η varies according to a gamma distribution, G(1/β, α),
with shape parameter α and scale parameter 1/β, the aggregate-level diffusion
model is a mixture described by the distribution function due to Bemmaor
([4, 5])
y(t) =(1− e−bt)
(1 + βe−bt)α , α, β > 0. (9)
Equation (9) may be re-parameterized through b = p + q and β = q/p, thus230
obtaining the following diffusion model,
z(t) = m
(1− e−(p+q)t
)(1 + q
pe−(p+q)t
)α , t ≥ 0, α, p, q > 0. (10)
As is shown, the standard Bass model is obtained for α = 1. As α approaches
zero, the diffusion curve is a special monomolecular model (exponential), and
for larger values of α, α >> 1, it approaches a logistic curve. In particular, high
values of α correspond to a heterogeneous behavior among agents, while small235
values of α, α << 1, describe a homogeneous system.
Notice that Equation (10) may be thought of as a product of two distribution
10
functions resulting, therefore, in a new distribution, which opens the way to new
heterogeneity modeling[26]. Following this suggestion, we extend the GGM by
introducing two parameters that account for heterogeneity both in communi-240
cation and adoption components. The GGM with Bemmaor effects, GGBM,
is
z(t) = K
√√√√√(1− e−(pc+qc)t
)(1 + qc
pce−(pc+qc)t
)Ac
(1− e−(ps+qs)t
)(1 + qs
pse−(ps+qs)t
)As, t ≥ 0, (11)
where Ac, As, pc, qc, ps, qs > 0. In particular, high values of Ac and As denote
heterogeneity, especially within imitators, in communication and adoption, and
determine a delay. Conversely, small values of Ac and As , << 1, reveal high245
homogeneity and, therefore, imply a concentration of adoptions at the beginning
of the process. Reduced versions of model (11) may account for the presence of
parameter Ac or As. In the first case, the reduced model is indicated as GGBMc
(i.e., GGBM with As = 1) to point out the only effect of parameter Ac, while
the corresponding reduced version with only As is called GGBMs (i.e., GGBM250
with Ac = 1).
Model (11) may be further extended to account for the presence of an ex-
ternal shock through intervention function x(t), which may influence the speed
of adoption dynamics, namely,
z(t) = K
√√√√√(1− e−(pc+qc)t
)(1 + qc
pce−(pc+qc)t
)Ac
1− e−(ps+qs)
∫ t
0x(τ)dτ(
1 + qspse−(ps+qs)
∫ t
0x(τ)dτ
)As, t ≥ 0.
(12)
If x(t) is modeled through a rectangular shock, as defined by Equation (7), we255
term the model GGBM-R. Reduced versions of this model with the presence
of only one parameter of heterogeneity are possible: GGBMc-R will include Ac
(As = 1), and GGBMs-R only As (Ac = 1).
11
2.5. A two-wave model, TWM260
The models presented thus far have been conceived to describe a unique life
cycle with modifications that act in different directions. In the GBM, the con-
trol function x(t) may accomodate exogenous interventions that locally modify
timing (or duration) of an adoption or consumption process. Conversely, the
GGM introduces a dynamic market potential that, under convenient parameter265
conditions, generates a significant slowdown depicting a kind of double-peaking
behavior.
In other situations, the local dynamics of an adoption process are much
more separate over time, and are therefore better represented with a multi-wave
approach [21, 25, 32] that is suitable for including different strategic policies or270
regimes over time.
A simple framework in this context is a two-wave model (TWM) with a
constraint in the local behavior of the innovative contributions:
z(t) = mg
(1− e−(p+qg)t
)(1 +
qgp e−(p+qg)t
) +ma
(1− e−(p+qa)(t−ta)
)(1 + qa
p e−(p+qa)(t−ta))It>ta
= mgFg(t) +maFa(t− ta)It>ta , t ≥ 0, ta > 0, (13)
where mg and ma are local fixed market potentials pertaining to the first and
second waves respectively, Fg and Fa are cumulative distribution functions,275
parameters qg and qa represent different local imitative behavior, and ta > 0
denotes the birth date of the second wave. In this model, parameter p, related to
institutional communication, is assumed invariant over the two waves to depict
a common cultural basis. As usual, z(t) represents cumulative adoptions, and
It>ta is an indicator function of event t > ta. Notice that the model differs from280
that proposed in [25], where diffusion parameters are proportional in subsequent
waves, because each wave has its own imitation parameter, namely, qg and qa.
The previous model in Equation (13) may be extended in additional directions,
as described, for instance, in the first part of this section, by considering het-
erogeneity effects.285
12
The rate representation of Equation (13) may be approximated as follows,
z′(t) ≃ mg {Fg(t+ 0.5)− Fg(t− 0.5)}
+ ma {Fa(t− ta + 0.5)− Fa(t− ta − 0.5)} It>ta . (14)
2.6. Model selection
The statistical implementation of the models presented in Section 2 relies on
a nonlinear least squares approach (NLS); in particular, we may consider the
structure of a nonlinear regression model290
w(t) = η(β, t) + ε(t), (15)
where w(t) is the observed response, η(β, t) is the deterministic component,
depending on parameter set β and time t, and ε(t) is a residual term, not
necessarily normal and independent identically distributed (i.i.d.).
To evaluate the performance of an extended model, m2, compared with a
nested one, m1, we may use a squared multiple partial correlation coefficient R2295
in the interval [0; 1], namely,
R2 = (R2m2
−R2m1
)/(1−R2m1
), (16)
where R2mi
, i = 1, 2 is the standard determination index of model mi.
The R2 coefficient has a monotone correspondence with the F -ratio, that is,
F = [R2(n− v)]/[(1− R2)u], (17)
where n is the number of observations, v the number of parameters of the
extended model m2, and u the incremental number of parameters from m1 to300
m2. Under strong conditions on the distributional shape of the error term ε(t),
particularly i.i.d. and normality, the statistic F -ratio is a Snedecor’s F with
u degrees of freedom for the numerator and n − v degrees of freedom for the
denominator, F ∼ Fu,n−v. A common upper critical value for the F -ratio (17)
(without assumptions on error distributions) is 4 for u = 1.305
We highlight that the F -ratio, which is a robust statistic from a distribu-
tional point of view, is extremely useful for comparing nested models. In fact,
13
complex models with v degrees of freedom are penalized for increasing values of
v. Moreover, large differences u of parameter complexity between nested com-
peting models determine a correct penalization for too complex models in favor310
of simpler versions.
3. Results
In this section, we model medium-term consumption dynamics of nuclear
energy and try to identify a short-term effect, if any, of the Fukushima accident
at the global level and on the seven largest global nuclear energy consumers: the315
US, France, Russia, South Korea, China, Canada and Germany. Data about
annual nuclear energy consumption in TWh come from BP Statistical Review
of World Energy [3], while information about the commercial operation state
comes from IAEA PRIS, [27].
Fig. 1 shows the time series of annual consumption for these countries plus320
Japan. The collection period is 1965 − 2013, except for Japan whose period
begins in 1966, Canada in 1971, and South Korea in 1977. For Russia, the first
available value is in 1985, which is not the starting period of Russian nuclear
energy consumption since the first part of the time series is missing. China
began in 1994: China has the shortest nuclear history among the top seven,325
and still in a strong growth phase. Due to missing values or scarcity of data,
China and Russia are analyzed and modeled separately in Subsections 3.7 and
3.8. For the remaining countries, we performed the following analysis.
For each time series we applied the models presented in Section 2, starting
with the simplest ones and increasing in complexity step by step. A test for330
nested models, as described in Equations (16) and (17), is applied to select the
best parsimonious and performing model. The global fitting is measured with
the standard determination index R2, while the improvement obtained with
respect to the simple BM is evaluated through coefficients R2 and F (where
m1 is the BM and m2 is the selected more general model). Notice that the335
NLS algorithm for cumulative data determines high values of R2: a good global
14
performance, when dealing with cumulative data, is characterized, therefore, by
levels higher than 0.99.
To understand if the Fukushima accident has had an impact on the medium-
term evolution of the series of nuclear power consumption, we compared the340
behavior estimated with the entire time series with that obtained by excluding
the last three observations. Therefore, the model previously selected for each
country is fitted again by excluding 2011 − 2013. Let β be the parameter set
of the selected model fitted to the entire series, and β∗ the parameter set of
the model fitted to the truncated series. Let β and β∗ be the corresponding345
estimates. For each country, the two evolutionary patterns are then compared
by testing whether the nuclear diffusion dynamics of a country were changed by
the events of the last three years. To do this, we verify if the parameter set β
is statistically different from β∗ (at the 5% level).
This is done by using the relationship between statistical tests and confidence350
intervals, by verifying if β∗ pertains to the 95% confidence interval of the corre-
sponding β (component by component). If so, the two models are not considered
significantly divergent. Otherwise, a different behavior between the two high-
lights the role played by the last three observations. In the sequel, information
about the nuclear policy at the global and country levels comes from [42] and355
[37].
3.1. World
We started our analysis by studying the consumption dynamics at the global
level. The series began in 1965, apparently reached its maximum around 2006,
and has been on a substantially declining trend since then. In particular, Fig. 2360
shows a quite strong acceleration around the mid 1970s and a slowdown at the
end of the 1980s, probably associated with the Chernobyl disaster, while since
2010, there has been a visible deceleration just partially compensated by the
2013 observation.
FIGURE 2 ABOUT HERE365
15
Table 2: Estimates and marginal linearized asymptotic 95% confidence intervals (in brackets)
for GGBMc fitted to the World, GGM fitted to the US and France, GGM-R fitted to South
Korea, GGBM fitted to Germany, and GGBMs-R fitted to Canada. The entire time series was
used. R2, R2, and corresponding F calculated with respect to the simple BM are provided.
Par. World US France South Korea Germany Canada
K 120726 36257 15975 4395 5555 12630
(117767, (32615, (15622, (4333, (5394, (−44035,
123686) 39899) 16328) 4456) 5717) 69297)
pc 0.00023 0.00035 0.00015 0.00155 0.00004 0.00027
(0.00008, (0.00025, (0.00014, (−0.00061, (−0.00004, (−0.00204,
0.00045) 0.00044) 0.00017) 0.00371) 0.00012) 0.00259)
qc 0.311268 0.11295 0.14269 0.61270 0.19054 0.05859
(0.27175, (0.09895, (0.13890, (0.43301, (0.14515, (0.02192,
0.35078) 0.12696) 0.14648) 0.79240) 0.23594) 0.09526)
Ac 0.57149 0.65512
(0.44485, (0.40077,
0.69812) 0.90947)
ps 0.00205 0.00937 0.00097 0.00117 0.00032 0.00337
(0.00197, (0.00819, (0.00085, (0.00090, (−0.00005, (0.00036,
0.00213) 0.01054) 0.00110) 0.00145) 0.00071) 0.00638)
qs 0.08688 0.13710 0.25298 0.13589 0.30430 0.19088
(0.08412, (0.11962, (0.24351, (0.13382, (0.25288, (0.13449,
0.08965) 0.15459) 0.26245) 0.13795) 0.35571) 0.24727)
As 0.55513 0.56835
(0.37730, (0.34906
0.73295) 0.78763)
a1 8.99733 26.9656
(6.18503, (26.1726,
11.8096) 27.7587)
b1 15.1289 33.624
(14.59820 (32.8456
15.65970) 34.4023)
c1 0.33583 −0.55918
(0.16007 (−0.76713,
0.51158) −0.35124)
R2 0.999991 0.99992 0.99998 0.999989 0.99998 0.99996
R2 0.9932 0.9241 0.9910 0.9848 0.9895 0.9866
F 2107 268 2424 377 994 418
16
Table 3: Models in Table 2 fitted to data until 2010. Estimates, marginal linearized asymptotic
95% confidence intervals (in brackets), and R2 are provided.
Par. World US France South Korea Germany Canada
K 126485 35223 15132 4312 5675 8517
(119211, (28800, (14666, (4205, (5219, (−66708,
133759) 41646) 15598) 4419) 6131) 83744)
pc 0.00040 0.00034 0.00014 0.00149 0.00008 0.00098
(−0.00001, (0.00022, (0.00013, (−0.00062, (−0.0002, (−0.01440,
0.00081) 0.00045) 0.00015) 0.00361) 0.00040) 0.01637)
qc 0.28413 0.11593 0.14983 0.63440 0.17307 0.04504
(0.24030, (0.09452, (0.14568, (0.43199, (0.09108, (−0.09537,
0.32795) 0.13733) 0.15398) 0.83681) 0.25507) 0.18546)
Ac 0.66367 0.75587
(0.48743, (0.20313,
0.83990) 1.30862)
ps 0.00213 0.00959 0.00093 0.00115 0.00026 0.00638
(0.00197, (0.00788, (0.00080, (0.00087, (−0.00013, (0.00006,
0.00225) 0.01131) 0.00105) 0.00142) 0.00066) 0.01270)
qs 0.08284 0.13875 0.26106 0.13732 0.31530 0.144217
(0.07769, (0.11792, (0.25134, (0.13458, (0.24764, (0.06852,
0.08798) 0.15959) 0.27078) 0.14006) 0.38297) 0.21990)
As 0.51730 0.75915
(0.29113, (0.21127
0.74347) 1.30704)
a1 8.99978 26.49950
(6.57856, (25.86070,
11.421) 27.13830)
b1 15.09340 33.54030
(14.64140 (32.83920
15.54540) 34.24140)
c1 0.36428 −0.48071
(0.17486 (−0.84796,
0.5537) −0.11347)
R2 0.99999 0.99989 0.999979 0.999986 0.99998 0.999963
17
To model the evolutionary behavior of the series, we found that the best
model is a GGBMc (i.e., a GGM with Bemmaor effect influencing the commu-
nication component of the process). See Table 2 for the results. The model
reaches a high level of global fitting R2 = 0.999991, and the coefficients R2
and F calculated with respect to the simpler Bass model, R2 = 0.9932432 and370
F = 2107, highlight the strong significance of parameters pc and qc, that is
the presence of a dynamic market potential. This clearly indicates the impor-
tance of communication for the successive adoption of nuclear power, in terms of
technical knowledge and social acceptance. Parameter Ac = 0.57149 indicates
homogeneous behavior during the communication phase. This suggests that375
the process leading to technology development and knowledge growth has been
characterized by a high degree of consensus among countries. This is also con-
firmed by parameter qc = 0.311268, which expresses a strong imitative behavior
in the communication phase of nuclear fission diffusion. Conversely, parame-
ter pc takes a very small value pc = 0.000227785, so that innovative countries380
represent a very limited share.
Japan is among the countries that explored and experienced nuclear fission
technology. Japan has been a leader in developing and adopting the technology
but has also had a central role in recent history with the Fukushima accident.
To evaluate the effect of the accident on the evolution of global consumption,385
we estimated the GGBM without the last three observations (see Fig. 2). Ac-
cording to the results presented in Table 3, all the parameter estimates, except
for K∗, pertain to the 95% confidence interval of the corresponding parameters
of the model fitted to the entire time series. The asymptotic market potential
K is smaller than K∗: this may have accounted for the fact that, in Japan,390
all reactors were temporarily shut down right after the 2011 events. Thus, we
may conclude that the Fukushima accident had an effect at the global level only
on the asymptotic potential K. Nevertheless, the estimated behavior with the
truncated series predicts a declining trend regardless of this crucial event.
Our results provide a statistical and model-based confirmation of the conclu-395
sion in Schneider and Frogatt [36] that “the world nuclear industry already faced
18
daunting challenges long before Fukushima”.
3.2. The US
Nuclear energy in the US has decelerated since 2000 (Fig. 3). The most
evident signal following Fukushima’s accident is the decrease recorded in 2012,400
likely due to the safety checks planned by the government. The recovery in 2013
is unexpected because nuclear energy is becoming less economically competitive
than renewables and natural gas, and safety costs are increasing. However, Fig.
3 shows that the width of variations in 2011− 2013 may not be so important if
we consider the complete US nuclear history.405
FIGURE 3 ABOUT HERE
For the US, the model selection is worthy of discussion. The process has not
yet reached the point at which future dynamics may be predicted reasonably
well. In particular, the contradictory observations in 2012 − 2013 are partially
responsible for this uncertainty. The model selection procedure carried out410
through F -ratios indicates a GGM-R (i.e., a GGM with a rectangular shock)
is the preferred model. As Fig. 3 shows, the model matches very well the in-
credible nuclear expansion before the 1979 Three Mile Island accident, but does
not account for the fall recorded in 2012. The alternative model for this time
series is a GGM, which fits less well before 1979 but is more reasonable for the415
last three observations although it probably tends to close the cycle too quickly.
Since the performance in the last part of the data is very important in the
diffusion model context, for more reliable forecasting, we considered an alter-
native procedure for model selection by using Mean Absolute Percentage Error
(MAPE), which is focused on the forecasting accuracy evaluation. MAPE was420
evaluated in 2011− 2013 for both models, and is 0.4842 for GGM-R and 0.2152
for GGM. These results indicate the GGM is the preferred model. Therefore,
we prefer the GGM between the two for its forecasting performance, although
a more realistic trajectory would probably lie between the trajectories designed
by the two models. Regarding the GGM, the parameter estimates are stable, as425
19
shown by the marginal linearized asymptotic 95% confidence intervals and the
goodness-of-fit is good overall (Table 2).
Table 3 and Fig. 3 show the results of the GGM fitted until 2010. The differ-
ence in terms of estimated evolutionary behavior by excluding what happened
after Fukushima (2011− 2013) is not significant (Fig. 3): the results presented430
in Table 3 show that all the estimates pertain to the 95% confidence intervals
of the corresponding parameters of the model with the entire time series (Table
2). Moreover, marginal confidence intervals essentially overlap in both cases. It
is apparent that the unexpected recovery of 2013 helps eliminate the negative
effect observed in 2012. It may be very informative to see what will change as435
soon as the 2014 observation is available. However, looking at the data and the
information now available, we conclude that the US did not change its nuclear
policy after Fukushima, except for paying more attention to safety, especially
for 60 of the 104 reactors that have an operating license extension.
However, safety has a cost, and this contributed to make nuclear energy less440
economically competitive with not only wind power, but also natural gas, when
gas prices are falling due to shale oil and gas renaissance. Thus, in 2013, four
aging reactors were permanently shut down before their licenses expired: it was
the first time reactors had been shut down since 1998. Uprating, which had a
considerable economic advantage in the past over new reactor building, has not445
been considered thus far (except for a few units), since uprating leads to less
safety and higher operating costs [36].
3.3. France
For France, the GGM is the most parsimonious model. The parameter
estimates are stable, the marginal linearized asymptotic 95% confidence intervals450
are well identified, and the goodness-of-fit is satisfactory, R2 = 0.999979 (Table
2). The high values of R2 = 0.9910 and corresponding F = 2424.19 in Table
2 suggest that the improvement of the GGM with respect to the BM is highly
significant. As Fig. 4 shows, the model accurately captures the behavior of the
data until the very last few observations. The big fall in national consumption in455
20
2009 was followed by a substantial increase in 2010−2011 and by a stabilization
in 2012 − 2013 at the level reached in 2010. This lack of a pattern in the very
last part of the time series causes uncertainty in the modeling.
FIGURE 4 ABOUT HERE
Table 3 and Fig. 4 show the results of the GGM fitted until 2010. In this460
case, while p∗s and q∗s lie inside the confidence interval of ps and qs respectively,
K∗ falls outside the confidence interval of K, p∗c lies outside the confidence
interval of pc (close to the lower limit), and q∗c is outside the confidence interval
of qc (close to the upper limit). Moreover, we note that K is bigger of 842.9 TWh
than K∗, pc is slightly bigger than p∗c , while qc is slightly smaller than q∗c . The465
last three observations have increased the market potential, slightly changed the
dynamic of communication (increasing the innovative attitude and decreasing
the imitative attitude), leaving the dynamic of the adoption component of the
process unchanged. In other words, the government’s energy policy decisions
have increased the market potential but also the speed of the process, delaying470
its inflection time.
France has relied heavily on nuclear energy to produce electricity (over 75%).
The energy mix for the next two decades was discussed in 2003 during the first
national energy debate. In July 2010, the lifetime of existing reactors was ex-
tended to 60 years through a strong and ongoing uprating phase. However,475
growth might have slowed in 2012− 2013 in light of public opinion, which was
influenced by the Fukushima accident. In 2012, the government announced that
two of the oldest reactors would be closed by 2017 for safety evaluations, and
in 2012, President Hollande proposed leading France to a partial nuclear phase-
out by reducing the share of nuclear power in electricity generation from 75%480
to 50%. In 2012− 2013, a new national debate on energy transition took place
to discuss the roles of nuclear and renewables in the energy mix. Meanwhile,
a parliamentary commission was asked to evaluate the timing of the phase-out
since nuclear was the best option for electricity production and other forms of
energy would be more costly and available too late. Finally, Fukushima moti-485
21
vated the government to upgrade the protection of vital functions in all nuclear
reactors. Safety has a cost, but nuclear electricity in France remains cheaper
than in many countries, especially compared to the US, if capital, operations
and maintenance, fuel procurement, back-end cycle and development costs are
considered simultaneously [6].490
3.4. South Korea
The history of nuclear consumption in South Korea is more recent and began
in 1977. Today, there are 23 operating reactors and five under construction.
The data in Fig. 5 indicate that South Korea had various phases of nuclear
technology adoption: the first until 1994, which corresponded to the commercial495
operation of nine reactors; the second in 1995, with the commercial operation of
seven reactors; and the third with another four reactor startups between 2002
and 2005.
FIGURE 5 ABOUT HERE
In this case, a GGM-R (that is, a GGM with a rectangular shock) was500
selected. See Table 2 for the results. This model reaches a very high level of
fitting, R2 = 0.999989. The behavior of the first part of the series, where an
acceleration in consumption occurred, is reasonably related to the first phase of
reactor startups and is captured by the rectangular shock, estimated between
1985 (a1 = 8.99) and 1991 (b1 = 15.1289).505
The model, which highlights the strong dominance of the imitative compo-
nent in both phases of the diffusion process, communication (qc = 0.612708)
and adoption (qs = 0.135891), forecasts a declining trend. Is this decline at-
tributable to a post Fukushima outcome? To answer this question, we estimated
the GGM-R without the last three observations (Table 3) and found that, except510
for K∗, parameter estimates pertain to the confidence interval of the correspond-
ing parameters of the model fitted to the entire time series. Therefore, the two
models differ only in the size of the asymptotic market potential; in particular,
22
the fact that K is bigger than K∗ may be essentially attributed to the jump in
the 2011 observation.515
The nuclear development plan for 2007 − 2011 was to lead South Korea to
be one of the top five in the world. Less than a month after March 2011, the
Korea Electric Power Corporation presented a plan for double-installed capacity.
However, in 2012, a massive quality control scandal emerged and many units
were kept offline, which could explain the subsequent decline observed in 2012520
and 2013.
3.5. Germany
For Germany, the GGBM was selected. The parameter estimates are stable,
except for pc and ps, which show slight instability (Table 2). The two coefficients
Ac and As are less than one, indicating that, in Germany, there has been a kind525
of homogeneous behavior in the access and use of nuclear technology, with good
maintenance services, which led to stability in energy supply. The fitting is
very good (Fig. 6), as indicated by R2 = 0.999981 and R2 = 0.989549. The
huge value of F = 994 emphasizes the great improvement achieved with GGBM
compared to BM. The good performance of the GGBM is explained by the530
evolutionary behavior of the installed capacity over time before and after 2002,
partially compensated by large investments in renewable resources (wind and
photovoltaic) due to the Energiewende policies.
FIGURE 6 ABOUT HERE
Table 3 and Fig. 6 show the results of the GGBM fitted until 2010. The535
events in 2011−2013 have not changed the forecast for nuclear energy consump-
tion in Germany: in fact, all the parameter estimates of the GGBM of Table
3 lie in the confidence interval of the corresponding parameters of the GGBM
fitted to the entire time series (Table 2). This is confirmed by the nuclear phase-
out planned in 2002 with final retreat planned for 2022. In October 2010, the540
government decided to modify the phase-out plan, and extended the reactor
licenses for 12 years. However, a few months later, less than a week after the
23
Fukushima accident, the government restored the nuclear policy signed in 2002.
In addition, the government decided to shut down the eight oldest reactors (of
the 17 operating reactors), before their licences expired, causing a loss of 30%545
in nuclear power generation [28]. This halt may be observed in 2011 in Fig.
6. Germany compensated the loss of nuclear power by increasing the electricity
produced by renewable energy and reducing net electricity exports and domestic
electricity demand [28]. In summary, Fukushima accident slightly accelerated
the phase-out of the oldest reactors to increase safety level, but the retreat plan550
signed one decade earlier remains in effect.
3.6. Canada
The case of Canada is well described with a GGBMs-R (that is, the GGBM
with only the heterogeneity parameter As plus a rectangular shock), which
reaches a good level of global fitting, R2 = 0.999966, R2 = 0.966457 and F =555
418.6667. The results are shown in Table 2 and Fig.7. The parameters are
well estimated, except for parameters K, pc, and qc, whose estimate instability
may be explained by recent history: a halt occurred around 2000, with a re-
start in 2004 characterized by a decreasing trend around 2006 − 2010, and an
increasing trend in 2011− 2013. This contradictory behavior in the last part of560
the serie increased uncertainty in the estimates of the market potential and the
medium-term forecasts. Parameter As indicates a high level of homogeneity in
the adoption phase.
FIGURE 7 ABOUT HERE
The halt occurred around 2000 was caught by a negative shock, which is565
estimated to have occurred between 1997 and 2003, and may be explained by a
1995 maintenance accident that occurred in one of the Bruce A plant reactors,
in which the core was contaminated. A review was then commissioned to check
the safety, maintenance, and refurbishment costs of the Bruce A (four units)
and Pickering A plants (four units). As a consequence, eight reactors were shut570
down in 1995 − 1998 pending refurbishment. Two units of Pickering A were
24
retired, and four units (two of Pickering A and two of Bruce A) were returned
to service in 2003− 2005 with the design bases corrected. The last two units of
Bruce A were authorized to restart in 2012 after refurbishment.
The same model estimated with the truncated time series produces the re-575
sults presented in Table 3 and Fig. 7. The estimates are all contained in the
95% confidence interval of the corresponding parameters of the model presented
in Table 2. However, for the instability of K, pc, and qc we could not state that
no significant changes occurred in the last three years.
Canada had previously reflected on safety, maintenance standards, and up-580
rating 15 years before, after the domestic accident. The difference between the
two models is attributed to the growing trend in the last three observations that
was not evident before 2010. This recent growth is related to the reconnection
of the two units in 2012.
3.7. China585
As of December 1, 2013, 69 reactors were under construction at the global
level. China is a prominent leader, with 29 reactors and a relevant and expand-
ing nuclear policy. Mainland China currently has 20 nuclear power reactors in
operation. The Chinese efforts to increase nuclear power (China’s current share
contributes 1.97% of the total electric energy production) have been motivated590
by air pollution from coal-fired plants (now at a 80% share level). The State
Nuclear Power Corporation (SNPTC) selected the Westinghouse AP1000 as the
reference technology for future development. This is confirmed by the local re-
actor CAP1400, which is based on preserving the intellectual property rights
and characterized by full fuel cycle capacity. In fact, one effect of Fukushima595
has been the choice of the reactor technology for the future and the decision that
no further approval will be given to other type of reactors, as the CPR-1000.
FIGURE 8 ABOUT HERE
The nation’s first plant, Qinshan, became operational in 1991 in Zhejiang
province, followed by Daya Bay plant in Guangdong province in 1994, Ling Ao600
25
Table 4: Estimates, marginal linearized asymptotic 95% confidence intervals (in brackets) and
R2 for TWM fitted to China and Russia, with entire time series (left side). TWM fitted to
data until 2010 (right side). Estimates were performed on rate data.
Par China Russia Par China Russia
mg 320.426 2187.26 m∗g 207.246 2199.67
(−442.448, (1873.63, (46.8405, (1857.63,
1203.3) 2500.9) 367.652) 2541.7
p 0.0083843) 0.0004261 p∗ 0.0298013 0.0004419
(−0.00437, (−0.0000074, (0.01288, (−0.0000399,
0.002114) 0.0008596) 0.04672) 0.000924)
ma 276.099 26691.3 m∗a 279.614 25185.1
(−569.842, (−3420.3, (58.4255, (−5979.7,
1122.04) 56803) 500.803) 56350)
ta 9.00045 31.57 t∗a 9.0768 31.56
(5.01546, (30.93, (8.28625, (30.86,
12.9854) 32.2) 9.86735) 32.26)
qa 0.108741 −0.11335 q∗a −0.18748 −0.10875
(−0.40157 (−0.1442, (−0.37636, (−0.15036,
0.61904) −0.0825) 0.001403) −0.067154)
R2 0.98161 0.97750 0.97330 0.97330
26
plant in 2002, and Tianwan plant in 2006. We observed two separate phases.
The first lasted from 1991 to 2001 with slow increasing electric energy produc-
tion/consumption and the second began in 2002 when 17 new reactors were
connected to the grid. This two-regime behavior is well-recognized in the anal-
ysis of consumption time series, and may be seen a specific characteristic of605
centralized economic policies facing rapid growth in industrial and commercial
sectors. This two-regime behavior does not match similar growth in OECD
countries where the proposed GGM (or its variants based on a single life cycle)
coherently fit the progressive dynamics of nuclear technology since the begin-
ning.610
We tested, with no success, various models based on a single-cycle hypoth-
esis. The major drawback has been the difficulty describing the recent impetus
of nuclear electric energy consumption. Therefore, we examined a TWM that
is much more suitable theoretically and empirically. We applied it to rate data
(Eq. (14)) with a very high determination index, R2 = 0.981607. See Table 4615
for the results (left side). Even if the approximate confidence intervals are quite
large, the change-point time between the two regimes, 2002 (= 1993+ ta), is
in agreement with known facts regarding nuclear power investments. The two
local market potentials, mg = 380.43 and ma = 276.1, signal a surprising con-
traction in consumption that contrasts with the declared effort related to the620
high number of new reactors under construction (29), as well as the huge num-
ber of planned projects. The proposed TWM is consistent, in particular, with
the behavior of the last few observations and related curvature (not recognized
by models grounded on a single cycle).
To examine the role of the Fukushima accident, we excluded the last three625
observations referring to 2011, 2012, and 2013. The determination index is
relevant, R2 = 0.98596, and the change-point time, ta ≃ 9, has been con-
firmed. This exercise has little meaning to identify a short-term effect due to
the Fukushima accident, since from 2010/2011 a new faster growth was observed:
the elimination of the last three years significantly changes the curvature of the630
forecasts in the opposite direction (see Fig. 8 and right side of Table 4). The
27
last three observations are crucial because they confirm the effort to expand the
nuclear power capacity. The nuclear policy had been planned before 2008, with
a projected increase in nuclear generating capacity to 40 GWe by 2020, suddenly
moved toward 70− 80 GWe by 2020. After Fukushima, the target was reduced635
to 60 GWe by 2020 and approval for new plants remained suspended until Oc-
tober 2012. In 2011 − 2012 the feeling was to move to steady development of
nuclear energy but in safety. In fact, safety checks started immediately after the
accident on the operational and under construction reactors and were completed
in October 2011. Then, in 2012 a series of R&D projects was launched to make640
nuclear technology safer.
In conclusion, it is difficult to understand from the data whether the Fukushima
accident induced a negative short-term impact, for the safety checks, which could
have reduced in a certain measure the important growth of more recent years.
However, the accident has had a role in the planning of the nuclear energy policy645
and the technologies for the coming decades.
3.8. Russia
Russia was the first to produce electricity in 1954 with the 5 MWe Obninsk
reactor. Commercial plants opened in 1963− 1964, eventually reaching a total
of 25 power reactors in 1986. The nuclear industry faced different technological650
and managerial problems. The Chernobyl accident in 1986 defined a new period
that concluded in 1995 when only one power plant, the four-reactor Balakovo,
was constructed, and three other units were implemented in the Smolensk plant.
The collapse of the Soviet Union in 1989 created a dramatic shortage of financial
resources for nuclear developments, and numerous projects were canceled. In655
the mid-1990s, the technological sector revived in Russia and abroad through
export activities negotiated with China, India, and Iran. Today, 31 reactors are
in operation and a second phase in nuclear power expansion is evident.
FIGURE 9 ABOUT HERE
28
We adopted a TWMwith difficulty related to the lack of knowledge of specific660
electric energy consumption from the beginning until 1984. We applied a rate
version for TWM (Eq. (14)). The results are summarized in the left side of
Table 4 and in Fig. 9. The determination index is quite high, R2 = 0.97750,
and the approximate confidence intervals are sufficiently stable. The two local
market potentials, mg = 2187.26 and ma = 26691.3, signal an expansion for the665
second phase that began in 1996 (= 1964 + ta). The test based on a reduced
time series, excluding the data from 2011, 2012, and 2013 confirms Russia’s
stable energy policy: the parameter estimates of the reduced series belong to the
corresponding confidence intervals of the complete TWM. This stability reveals
that the Fukushima accident has not played a significant role in changing the670
medium-term evolution of nuclear consumption in Russia.
4. Conclusions
The nuclear history of the world and leading countries was studied in the
context of technology diffusion and the consumption dynamics of nuclear energy
have been modeled to understand, in particular, whether the Fukushima acci-675
dent had a short-term effect on consumption in 2011− 2013; information about
possible policy implications due to Fukushima is provided, country by country.
Moreover, medium-term consumption evolution has been predicted.
Innovation diffusion models were applied to each time series (the World,
the US, France, Russia, South Korea, Germany, Canada, China) starting with680
the simplest and increasing in complexity. The F-ratio test was used to select
the most parsimonious and performing model among nested models. To iden-
tify short-term effects, the selected models were fitted again to the truncated
time series (data until 2010), and the contribution of the last three years after
Fukushima was evaluated to test whether it significantly changed the diffusion685
dynamics of the technology. Table 5 indicates the selected models, short-term
effects in 2011−2013, if any, identified by the models, policy implications due to
Fukushima, and the medium-term evolution predicted by the selected models.
29
Table 5: Brief summary results: model used, short-term effects in 2011 − 2013 identified
by the models, policy implications due to Fukushima, medium-term evolution predicted by
the models. “⋆” indicates when the exercise with the truncated series had little meaning in
detecting short-term effects.
Model Short-term Policy Medium-term
Used Effect Implications Evolution
(3 years) Implications (until 2020)
YES-Negative
World GGBMc Due to the halt of Declining
Japan production.
Safety cost made nuclear
US GGM NO less economically competitive. Declining
Uprating old reactors is not
convenient as in the past.
YES-positive A new national debate and
Nuclear expansion a parlamentary commission
France GGM was planned in 2003. discuss the role of nuclear Declining
Fukushima may have in the energy mix.
slowed the growth.
South YES-positive In 2012− 2013 a massive
Korea GGM-R Due to the high quality control emerged Declining
consumption in 2011. and units were kept offline.
The phase-out of the 8
Germany GGBM NO oldest reactors was Declining
slightly accelerated.
Canada GGBMs-R ⋆ Weakly
growing
The planned increased
⋆ capacity decreased from
China TWM Fukushima may have 70− 80 to 60 GWe by 2020. Strongly
slowed growth. Evaluate which tecnology growing
to use in the coming decades.
Russia TWM NO Growing
30
Overall safety checks, immediately performed after the accident, caused tem-
porary stops in the production (and then consumption) of nuclear energy but690
not all of them were significant enough to modify the diffusion pattern. A sig-
nificant short-term effect was identified in 2011 − 2013 at the global level, for
France, and South Korea, but was not identified for the US, Germany, and
Russia.
At the global level, the short-term is negative due to the cessation of nuclear695
electricity in Japan. For France the short-term is positive because the nuclear
technology was expanding according to the plan signed in 2003. Fukushima may
have slowed growth but it is difficult to statistically separate the two compo-
nents. For South Korea the short-term is positive reflecting that consumption
grew substantially in 2011; however, in 2012-2013 a serious halt occurred due700
to the quality control scandal and thus, with these data, a declining trend has
been predicted.
The models did not identify a short-term effect for the US, Germany and
Russia. In the US, nuclear energy has become less economically competitive
because safety has a cost and after Fukushima, the uprating process requires a705
major level of safety. In fact in 2013 four old reactors were closed before their
life license expired. In Germany, right after Fukushima, the eight oldest reactors
were closed, accelerating their phase-out process, and the proposal expressed in
2010, delaying the phase-out of nuclear energy for a decade was withdrawn.
Finally, Russia does not seem to have been affected by Fukushima.710
For Canada and China the exercise of using the truncated series for isolating
a significant effect had little meaning for the particularity of the last observa-
tions. In particular, Canada already reflected about nuclear safety for the 1995
maintenance accident and this caused a serious halt in the production of nuclear
energy for almost a decade. However, China experienced a new faster growth715
from 2010/2011 and as said before for France, it is difficult to quantify whether
the Fukushima accident slowed China’s growth.
About the medium-term evolution predicted by the models, two main clus-
ters were identified taking into account the current nuclear policy: the declining
31
countries (the US, France, Germany and South Korea) and the growing countries720
(China, Russia, and Canada). At global level a declining trend is predicted.
5. Acknowledgements
This work was supported by the Energy Research Centre Giorgio Levi Cases,
University of Padua, Italy; Grant 2014 “Innovation Diffusion Processes: Com-
petition and Substitution in Energy Technologies”.725
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Figure 1: Observed annual nuclear consumption (TWh) for the US, France, Japan, Germany,
Russia, South Korea, Canada, and China.
Figure 2: World: observed and fitted values of annual nuclear consumptions (TWh). GGBMc:
time-dependent market potential model with heterogeneity effects in the dynamic market
potential component only. Solid line represents the model fitted to the complete time series
(Table 2), and dotted line to the model fitted until 2010 (Table 3).
37
Figure 3: The United States: observed and fitted values of annual nuclear consumptions
(TWh). GGM, time-dependent market potential model, and GGM-R, time-dependent market
potential model with an exogenous intervention. Solid line represents the model fitted to the
complete time series (Table 2), and dotted line to the model fitted until 2010 (Table 3).
Figure 4: France: observed and fitted values of annual nuclear consumptions (TWh). GGM:
time-dependent market potential model. Solid line represents the model fitted to the complete
time series (Table 2), and dotted line to the model fitted until 2010 (Table 3).
38
Figure 5: South Korea: observed and fitted values of annual nuclear consumptions (TWh).
GGM-R: time-dependent market potential model with an exogenous intervention. Solid line
represents the model fitted to the complete time series (Table 2), and dotted line to the model
fitted until 2010 (Table 3).
Figure 6: Germany: observed and fitted values of annual nuclear consumptions (TWh).
GGBM: time-dependent market potential model with heterogeneity effects. Solid line rep-
resents the model fitted to the complete time series (Table 2), and dotted line to the model
fitted until 2010 (Table 3).
39
Figure 7: Canada: observed and fitted values of annual nuclear consumptions (TWh).
GGBMs-R: time-dependent market potential model with heterogeneity effects, in the adop-
tion component only, with an exogenous intervention. Solid line represents the model fitted to
the complete time series (Table 2), and dotted line to the model fitted until 2010 (Table 3).
Figure 8: China: observed and fitted values of annual nuclear consumptions (TWh). TWM:
two-wave model, sum of a Bass model and a translated Bass model. Solid line represents the
model fitted to the complete time series (Table 4, left side), and dotted line to the model
fitted until 2010 (Table 4, right side).
40
Figure 9: Russia: observed and fitted values of annual nuclear consumptions (TWh). TWM:
two-wave model, sum of a Bass model and a translated Bass model. Solid line represents the
model fitted to the complete time series (Table 4, left side), and dotted line to the model
fitted until 2010 (Table 4, right side).
41