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: furlan@stat.unipd.it (Claudia Furlan), guidolin@stat.unipd.it

(Mariangela Guidolin), renato.guseo@unipd.it (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