DEPARTMENT OF ECONOMICS
ISSN 1441-5429
DISCUSSION PAPER 05/12
Are fluctuations in production of renewable energy permanent or transitory?
Hooi Hooi Lean* and Russell Smyth†
Abstract
This study examines the integration properties of total renewable energy production, as well as
production of biofuels and biomass in the United States. To do so we employ Lagrange Multiplier
(LM) univariate unit root tests with up to two structural breaks. We conclude that each production
series contains a unit root. This result suggests that random shocks, including regulatory changes, to
renewable energy production may lead to permanent departures from predetermined target levels.
Furthermore, this result implies that positive shocks associated with a permanent policy stance
(such as renewable portfolio standards) that increases the production of renewable energy resources
will realize more in terms of positively altering the energy mix between renewable energy and
energy from fossil fuels than temporary policy stances (such as investment tax credits over a
predetermined time horizon).
*
Economics Program, School of Social SciencesUniversiti Sains Malaysia, Malaysia
Email: [email protected]
†
Department of Economics, Monash University, Australia.
Email : [email protected]
© 2012 Hooi Hooi Lean and Russell Smyth
All rights reserved. No part of this paper may be reproduced in any form, or stored in a retrieval system, without the prior written
permission of the author.
1
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1. Introduction
Renewable energy is most commonly taken as energy that is naturally replenished within a
biological (ie. non-geologic) time frame where the source is capable of being provided in a
sustainable manner [24, 25]. In the United States, in 2010 renewable energy represented
about 8 per cent of overall energy consumption and 10 per cent of electricity generation [80].
There are, however, increasing calls to make renewable energy a larger share of the energy
mix in response to concerns about energy security and the environmental consequences of
greenhouse gas emissions resulting from burning fossil fuels [26, 27]. At the federal level,
recent initiatives to stimulate the use of renewable energy include the Energy Policy Acts of
2002 and 2005 and the Federal Energy Independence and Security Act of 2007, which have
created renewable energy production tax credits, federal income tax credits for renewable
energy systems and financial incentives for the expansion of biofuels [21].
In his 2011 State of the Union address, President Obama proposed that by 2035, 80 per cent
of United States electricity should come from clean energy sources, including nuclear, highefficiency natural gas generation, clean coal and renewables [28]. To meet this proposed
target, the production of renewable energy in the United States is expected to grow
substantially in coming years. Specifically, the International Energy Outlook [29] predicts
that renewable energy will be the fastest growing energy source for electricity use over the
next two and a half decades, growing at approximately 3 per cent per annum until 2035. At
the sub-national level, several states are taking steps to implement specific targets in raising
the share of renewable energy. For example, the state of New Mexico requires electric
utilities to produce, or purchase, 20 per cent of their sales from renewable resources by 2020
[30]. Several states have also adopted the renewable portfolio standard and require a variety
of mechanisms (eg. tradeable renewable energy credits) to meet the standard [31].
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Common renewable sources are solar, biomass, geothermal, hydropower and wind. In the
United States, in 2010, the breakdown of renewable energy sources was biomass 53 per cent,
hydropower 32 per cent, wind 11 per cent, geothermal 3 per cent and solar 1 per cent [80].
The Energy Information Administration divides biomass into three categories; namely,
biomass waste, biofuels and wood. In 2010, wood represented approximately 47 per cent of
biomass, biofuels represented 43 per cent of biomass and biomass waste represented 10 per
cent of biomass [80]. A common view is the biomass industry in the United States has
emerged due to the fact that, compared with other forms of renewable energy, such as solar
and wind, it is easy to use [17]. It has also benefited from generous financial incentives,
particularly in the 2005 Energy Policy Act [17]. The United States has set a target for
biofuels as a share of transport energy of 20 per cent by 2022 [24]. However, one major
concern with biofuels, and biomass more generally, is that they take a lot of energy to
produce [54] and, in some cases, can actually contribute more to global warming than the
fossil fuels that they are intended to replace [55, 58, 59]. Critics of biomass point out that
conversion of ecologically vulnerable wetlands, rainforests, peatlands, savannas and
grasslands into new croplands would potentially create large biofuel carbon debts by
releasing quantities of carbon dioxide that far exceed the reduction in emissions from
replacing fossil fuels [57, 59]. Thus, it has been suggested that biomass has a decade-long
window of opportunity, during which fossil fuel prices remain volatile, to evolve into a global,
interdependent energy system, assuming that sustainability issues can be addressed [24, 56].
While there are a growing number of studies that have examined different aspects of
renewable energy in the United States (for recent examples see [25, 28, 30, 32, 33, 34, 35, 36,
37]), more research is needed. As Arent et al. [24, p.592] put it: “Clearly further research and
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analysis is needed to improve our understanding of the potential of renewable energy
technologies with a more diverse energy economy”. The purpose of this study is to examine
whether shocks to renewable energy production in the United States are permanent or
temporary. In addition to production of renewable energy as a whole, we consider production
of biomass and biofuels as a subcategory of biomass. Biomass has the largest share of
renewable energy production and biofuels by themselves represent about a quarter of the
production of renewable energy in the United States [80]. To address the possibility that
failure to reject the unit root may be attributable to the omission of structural breaks, as
suggested by Perron [38], we use the Lagrange Multiplier (LM) unit root test with up to two
breaks, proposed by Lee and Strazicich [39]. The LM unit root test with up to two breaks has
been applied to analyse time series properties in a range of other fields such as
macroeconomic variables (see, eg, [40, 41]), international tourist arrivals (see eg. [42]) and
housing prices [43] as well as energy variables (see eg. [4, 8, 11, 14, 15, 19, 22, 23]).
The issue of whether production of renewable energy contains a unit root is important for
several reasons. First, if renewable energy production is stationary, shocks to renewable
energy production will be temporary, but if renewable energy production contains a unit root,
shocks will have a persistent effect. Second, to the extent that the renewable energy sector is
integrated into the wider economy, if shocks to renewable energy production are persistent,
such shocks may be transmitted to other sectors of the economy and key macroeconomic
variables. In this respect, taking the approach in [4, 5, 6] consider the following production
function, linking the supply of renewable energy and economic activity:
Y = f (K,L,RE)
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Here Y is output, K is capital, L is labour and RE is the supply of renewable energy. Assume
that output is sold for a nominal price of P dollars per unit, that workers are paid a nominal
wage, W, that the nominal cost of energy is Q and that capital is rented at a nominal rate, r.
This implies that the profits of a representative firm can be calculated as follows:
PY-WL-rK-QRE
A price-taking profit maximizing firm will purchase renewable energy up to the point where
the marginal product of renewable energy is equal to its relative price as follows:
FE(L,K,RE) = Q/P
Here FE(L,K,RE) represents the partial derivative of F(.) with respect to RE. Multiplying both
sides of the equation by RE and dividing by Y, one gets the following expression:
 lnF/ lnRE = QRE/PY
Thus, the elasticity of output with respect to a given change in renewable energy use can be
inferred from the dollar share of renewable energy expenditure in total output. Although, this
figure is currently not high in the United States relative to fossil fuels, it can be expected to
increase. Conservative estimates suggest that global primary energy consumption will
increase from approximately 500 EJ (EJ=exajoule=1018) with over 80 per cent of energy
consumption being fossil fuels in 2008 to 800-1000 EJ in 2050 in a business-as-usual world
[52]. As Moriarty and Honnery [52, p.245] noted: “If CO2 levels are already too high and
nuclear energy can at best be only a minor contributor to the future energy mix, then the
various forms of renewable energy will have to provide the bulk of future energy needs”.
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Third, whether production of renewable energy contains a unit root is important in modelling
renewable energy. Some studies have started to model the relationship between renewable
energy, economic growth and other variables within a unit root, cointegration and Granger
causality framework [44-51]. The correct approach to modelling Granger causality between
such variables depends on whether renewable energy contains a unit root. While most
studies using this framework proxy energy with energy consumption, some studies have
proxied energy using energy production (see [76-78]). Finally, whether production of
renewable energy contains a unit root has implications for forecasting future production of
renewable energy. If production of renewable energy is stationary, it is possible to forecast
future production based on past production, but if production of renewable energy contains a
unit root then past production is of no value in forecasting future production (see [1, 7]).
2. Existing literature
Beginning with Narayan and Smyth [1], over the last five years a sizeable literature has
emerged which specifically examines the unit root properties of energy consumption or
production. Aslan and Kum [14, p.4256] go as far as to describe this as “a new branch of
research in [the] economics literature”. Table 1 summarizes the findings from studies which
have specifically tested for a unit root in energy consumption or production. In addition to the
studies mentioned here, there are a number of studies which have tested for a unit root in
energy consumption as the first step before proceeding to test for cointegration and Granger
causality with economic growth (for recent surveys of this literature see [60-62]).
One strand of the literature uses conventional univariate unit root tests, with and without
structural breaks, to test for a unit root in energy consumption or production [1, 8, 10, 14, 19,
22, 23]. A second strand of the literature has employed panel unit root tests, with and without
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structural breaks, to test for a unit root in energy consumption or production [1, 2, 3, 4, 6, 11,
12, 19]. Overall, the results from both strands of literature are mixed, although generally there
is more evidence of stationarity from studies that have employed panel tests and/or allowed
for structural breaks. A third strand of the literature has applied non-linear unit root tests to
energy consumption and production [5, 14, 15, 18]. The results from these studies is also
mixed, although there has tended to be less evidence of stationarity. A fourth strand of the
literature has tested for fractional integration, with and without structural breaks [7, 16, 17, 20,
21]. This literature has tended to find evidence of long memory (persistence).
Compared with the literature that has tested for a unit root in energy consumption, relatively
few studies have tested for a unit root in energy production. Examples of the latter are [4, 5,
16]. In terms of type of energy analysed, most studies have focused on aggregate energy [1-3,
6, 10, 14, 18, 19, 23]. This might be one reason for inconclusive findings. A focus on
aggregate energy ignores the likelihood that disaggregated energy sources might exhibit
different unit root behaviour [63, 64]. In response some studies have started to focus on
disaggregated energy. However, most of these focus on fossil fuels (coal, natural gas or oil)
[4, 5, 7, 8, 11, 12, 15, 16]. There are only two studies, of which we are aware, which consider
renewable energy sources and these studies focus on consumption, not production, of
renewable energy [17, 20]. To summarize, the findings from the extant literature are, at best,
mixed, suggesting further studies are needed before any sort of consensus on this issue can be
realized. Moreover, there are relatively few studies which examine energy production or
consider renewable energy and no studies which consider the unit root properties of
renewable energy production. This is a gap which this study seeks to address.
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3. Econometric methodology
We apply LM univariate test to production of renewable energy, biomass and biofuels. The
LM family of unit root tests consist of the Schmidt and Phillips [65] LM unit root test with no
structural breaks and the univariate LM unit root tests with one and two structural breaks
proposed by Lee and Strazicich [39]. We first present the Schmidt and Phillips [65] LM unit
root test with no structural breaks to provide a point of comparison for the univariate LM unit
root tests with structural breaks. Similar studies to this which have applied LM unit root tests
with structural breaks to energy consumption or production have either used an Augmented
Dickey-Fuller (ADF) [79] unit root test as a benchmark for their results (see eg. [19]) or not
presented the results of a unit root test without structural breaks at all (see eg. [14, 15]). We
present the Schmidt & Phillips [65] LM unit root test rather than an ADF [79] unit root test,
or nothing at all, to provide a consistent set of unit root tests throughout. The rationale for so
doing is that we believe it makes more sense to provide tests from the same family of unit
root tests (ie. the LM family of unit root tests) from no breaks through to two breaks, rather
than switch from one family of unit root tests (ADF unit root tests) for the no break case to
another (LM unit root tests) for the one and two break cases.
The univariate LM unit root tests developed by Lee and Strazicich [39] represent a
methodological improvement over ADF-type endogenous break unit root tests proposed by
Zivot and Andrews [66] and Lumsdaine and Papell [67] which have the limitation that the
critical values are derived while assuming no break(s) under the null hypothesis. Nunes et al.
[68] showed that this assumption leads to size distortions in the presence of a unit root with
structural breaks. Thus, with ADF-type endogenous break unit root tests, one might conclude
that a time series is trend stationary, when in fact it is non-stationary with break(s), meaning
9
that spurious rejections might occur. In contrast to the ADF-type endogenous break tests, the
LM unit root test is unaffected by structural breaks under the null hypothesis [69].
The Schmidt & Phillips [65] LM unit root test is based on the following equation:
yt   Zt  et , et   et 1   t .
(1)
Here, yt is the production of renewable energy in period t, Z t consists of exogenous variables
and  t is the error term. Building on the Schmidt and Phillips [65] test, Lee and Strazicich [39]
developed two versions of the LM unit root test with one structural break, commonly known
as Models A and C. Models A and C differ in terms of whether the break is in the intercept or
intercept and slope of renewable energy production. Model A allows for one structural break
in the intercept. Model A can be described by Zt  1, t , Dt  , where Dt  1 for t  TB  1, and
'
zero otherwise and TB is the date of the structural break. Model C allows for one break in
both the intercept and slope of renewable energy production and can be described by
Zt  1, t , Dt , DTt  , where DTt  t  TB for t  TB  1, and zero otherwise.
'
Lee and Strazicich [39] also developed a version of the LM unit root test to accommodate
two structural breaks. These are commonly known as Models AA and CC and also differ in
terms of whether the break is restricted to the intercept or extends to the intercept and slope.
Model AA, as an extension of Model A, allows for two breaks in the intercept and is
described by Zt  1, t , D1t , D2t  where D jt  1 for t  TBj  1, j  1, 2, and 0 otherwise. TBj
'
denotes the date when the structural breaks occur. Model CC, which is as an extension of
Model C, incorporates two structural breaks in the intercept and the slope and is described by
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Zt  1, t , D1t , D2t , DT1t , DT2t  , where DT jt  t  TBj for t  TBj  1, j  1, 2, and 0 otherwise. The
'
LM unit root test statistic is obtained from the following regression:
yt   Z t  S t 1  t
(2)
where S t  yt ˆ x  Z t ˆ t , t  2,...,T ; ̂ are coefficients in the regression of yt on Z t ;
̂ x is given by yt  Z t  ; and y1 and Z1 represent the first observations of y t and Z t
respectively. The most important parameter in Equation (2) is . The LM test statistic is the tstatistic for testing the unit root null hypothesis that   0 . The location of the structural
break is determined by selecting all possible break points for the minimum t-statistic. The
search is carried out over the trimming region (0.1T, 0.9T), where T is the sample size.
4. Data
Data for biofuels, biomass and total renewable energy production for the United States is
from the Energy Information Administration. All data were transformed to natural logs prior
to undertaking the analysis. Data is both monthly, measured in trillion btu, and annual,
measured in billion btu. We use the longest sample period for which data is available from
the Energy Information Administration and this differs according to series. For the monthly
data the sample period is January 1981 to September 2011 for biofuels (T = 369) and January
1973 to September 2011 for biomass and total renewable energy (T = 465). For the annual
data it is 1981 to 2010 for biofuels (T = 30) and 1949 to 2010 for biomass and total
renewable energy (T = 62). Figure 1 plots the monthly time series of biofuels, biomass and
total renewable energy production in the United States. From Figure 1 we can see clearly the
existence of a seasonal pattern. The seasonal pattern was removed from the monthly data
with the United States Census Bureau’s X12 seasonal adjustment procedure.
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5. Results
The results for the Schmidt and Phillips [65] LM unit root test are reported in Table 2. There
are two test statistics, Z(ρ) and Z(τ). According to both test statistics, the unit root null
hypothesis fails to be rejected for production of renewable energy as a whole, biomass and
biofuels with both annual and monthly data. Thus, on the basis of the Schmidt and Phillips
[65] LM unit root test, shocks will have a permanent effect on renewable energy production.
This result potentially reflects failure to allow for a structural break(s) in the series. Hence, in
Tables 3 and 4 we present the results of Lee and Strazicich’s [39] Models A and C, which
accommodate a structural break in the intercept and intercept and slope respectively. Lee and
Strazicich’s [39] Model A provides slightly more evidence of stationarity than the Schmidt
and Phillips [65] LM unit root test in that biofuels is stationary at 5 per cent with annual data.
However, the other series continue to be non-stationary and each of the series, including
biofuels with annual data, are non-stationary in Lee and Strazicich’s [39] Model C.
Given that the results of Model A and Model C differ with respect to biofuels with annual
data, it is useful to pause and consider whether Model A or Model C is preferable. Sen [70]
argued that Model C is preferable to Model A when the break date is treated as unknown.
Further evidence from Monte Carlo simulations, reported in Sen [71], show that Model C will
yield more reliable estimates of the breakpoint than Model A. Hence, between Model A and
Model C, the results for Model C appear preferable. Based on the no-break and one-break
case, shocks will result in permanent effects on production of renewable energy.
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Tables 5 and 6 present the results of Lee and Strazicich’s [39] Models AA and CC, which
accommodate two structural breaks in the intercept and intercept and slope respectively.
Models AA and CC paint a similar picture to Model A and C. Specifically, Model AA
suggests that biofuel production is stationary with annual data, but none of the other series are
stationary. Meanwhile, Model CC suggests that none of the series are stationary. While Sen
[70, 71] suggested that Model C is preferable to Model A in the one break case, no such clear
cut claims can be made in the two break case. As Lumsdaine and Papell [67] noted in the
context of developing their ADF-type unit root test with two structural breaks, while it would
be desirable to have a concrete statistical method for choosing between Models AA and CC,
no such method exists in the literature. Overall, though, we prefer the results from Model CC
over Model AA because Model CC is the more general case and has the advantage that it
encompasses Model AA. Thus, on the basis of the LM unit root test with up to structural
breaks we conclude that shocks to production of renewable energy, as well as biomass and
biofuels, will result in permanent deviations from the long-run growth path.
Turning briefly to the location of the breakpoints, most of the breakpoints fall into one of four
periods; namely early 1980s, late 1980s/early 1990s, mid 1990s and late 1990s/early 2000s.
The breakpoints in the early 1980s and late 1980s/early 1990s coincided with oil price spikes
which resulted in short episodes of increased R&D expenditure on renewable energy in
OECD countries [72]. In the United States, the breaks in the late 1970s and early 1980s also
coincided with the Energy Tax Credit (1978), Energy Tax Act (1978) and Energy Security
Act (1980), while the breaks in the late 1980s and early 1990s coincided with the Clean Air
Act Amendments (1990) and Energy Policy Act (1992), each of which provided financial
incentives for investment in renewable energy. In particular, concern over energy security
resulting from the first Gulf War (1990-91) was a catalyst for the Energy Policy Act (1992).
13
Many of the provisions of the Energy Policy Act (1992) penalized fossil fuels, while
providing tax breaks for investment in renewable energy [73]. The breaks in the mid-1990s
coincided with various initiatives such as the Federal production tax credit, introduced as part
of the Energy Policy Act (1992) in 1994 and the introduction of net metering laws in many
states in 1996. The breaks in the late 1990s and early 2000s coincided with what has been
described as a new phase for renewable energy in the United States, which started around
1997 [74]. By then, some of the uncertainty surrounding electricity reform had begun to
lessen, and state renewable energy policies that were enacted during restructuring started to
take effect. Most notably, these state policy innovations included renewable portfolio
standards, which required utilities to generate or purchase minimum levels of renewable
energy. These were enacted in 18 states and Washington DC in the mid-to-late 1990s [74].
6. Conclusion
The potential for renewable energy sources to take a greater share of the energy mix in the
coming decades has attracted the interest of academics and policy makers. In this paper, we
have added to the burgeoning literature on the unit root properties of energy production and
consumption by examining the unit root properties of total renewable energy production as
well as biomass and biofuels production in the United States. To this point, two studies have
examined the unit root properties of renewable energy consumption in the United States [17,
21]. Apergis and Tsoumas [17] found evidence of stationarity, while Barros et al. [21] found
more evidence of persistence in renewable energy consumption. The results reported here are
more in line with the findings of Barros et al. [21] than Apergis and Tsoumas [17].
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The existence of a unit root in renewable energy production suggests that random shocks,
including regulatory changes, to renewable energy production may lead to permanent
departures from predetermined target levels. Barros et al. [21] distinguished between
permanent and temporary policy stances on renewable energy production. An example of the
former is renewable portfolio standards at the state level, which mandate for the states to
achieve a certain percentage of electricity generation from renewable sources. An example of
the latter is production and/or investment tax credits granted over a predetermined time
horizon. In stark contrast with the findings in Apergis and Tsoumas [17], but quite consistent
with the findings in Barros et al. [21], our results paint a rosy picture for the upside potential
of a permanent policy stance designed to increase production of renewable energy. That our
results suggest production of renewable energy contains a unit root implies that positive
shocks associated with a permanent policy stance that increases the production of renewable
energy resources will realize more in terms of positively altering the energy mix between
renewable energy and energy from fossil fuels than temporary policy stances [21].
The results here also suggest that shocks to renewable energy production may impact on the
real economy and, in particular, employment and output. The extent to which this occurs will
depend on the dollar share of renewable energy expenditure in total output. While this figure
is currently rather low, relative to fossil fuels, it can be expected to increase sharply in
coming decades. Finally, the permanent character of the shocks implies that there is a positive
role for Keynesian demand management policies, both in the aggregate economy and in
specific sectors, such as renewable energy [75]. This result suggests that aggregate demand
shocks, such as the economic stimulus package passed by the United States Congress in 2009,
will be effective in stimulating economic recovery from the Global Financial Crisis.
15
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21
Table 1
Existing studies examining the unit root properties of energy consumption and production
Study
Narayan & Smyth [1]
Coverage
182 countries,
1979-2000
Energy Type
Energy
consumption per
capita
Chen & Lee [2]
Seven regional
panels 1971-2002
Hsu, Lee & Lee [3]
Five regional
panels 1971-2003
Narayan, Narayan &
Smyth [4]
Panels of 60
countries, 19712003
Energy
consumption per
capita
Energy
consumption per
capita
Crude oil and NGL
production
Maslyuk & Smyth [5]
17 countries
1973-2007
Crude oil
production
Mishra, Sharma &
Smyth [6]
Panel of 13
Pacific Island
countries 19802005
United States,
1973-2008
Energy
consumption per
capita
Lean & Smyth [7]
Apergis & Payne [8]
States of United
States 1960-2007
Gil-Alana, Loomis &
Payne [9]
United States
electric power
sector 1973-2009
Narayan, Narayan &
Popp [10]
States in
Australia
1973-2007
States of United
States 1982-2007
States of United
States 1980-2007
Portugal, 19772003
Apergis, Loomis,
Payne [11]
Apergis, Loomis,
Payne [12]
Pereira, Belbute [13]
Aslan, Kum [14]
Turkey, 19702006
Aslan [15]
States of United
States 1960-2008
Disaggregated
petroleum
consumption
Petroleum
consumption
Consumption of
various
disaggregated
energy sources
Energy
consumption per
capita by sector
Coal consumption
Natural gas
consumption
Consumption of
various
disaggregated
energy sources
Energy
consumption per
capita by sector
Natural gas
consumption
Unit Root Test/Findings
(a) Univariate tests without structural
breaks – mixed evidence of stationarity
(b) Panel test without structural breaks
– evidence of stationarity
Panel test with structural breaks –
evidence of stationarity
Panel test without structural breaks –
mixed evidence of stationarity
(a) Panel test without structural breaks –
mixed evidence of stationarity.
(b) Panel test with structural break –
evidence of stationarity
Univariate non-linear unit root test –
mixed evidence of unit roots and partial
unit roots.
Panel test with structural breaks –
evidence of stationarity
Fractional integration – mixed evidence
of fractional integration, nonstationarity and stationarity.
Univariate unit root tests with structural
breaks – evidence of stationarity in
majority of cases.
Fractional integration with structural
break – evidence of fractional
integration.
Univariate unit root tests with up to two
structural breaks – evidence of
stationarity.
Panel test with structural breaks –
evidence of stationarity
Panel test with structural breaks –
evidence of stationarity
Non-parametric persistence tests –
evidence of persistence.
(a) Univariate unit root tests with up to
two structural breaks – evidence of
stationarity.
(b) Non-linear unit root test- evidence
of non-stationarity
Non-linear unit root test – mixed
evidence of stationarity.
22
Table 1 continued:
Barros, Gil-Alana &
Payne [16]
OPEC countries,
1973-2008
Crude oil
production
Apergis & Tsoumas
[17]
United States,
1989-2009
Hasanov & Telatar
[18]
178 countries,
1980-2006
Agnolucci & Venn
[19]
Apergis & Tsoumas
[20]
Industrial
subsectors in the
United Kingdom,
1970-2004
United States,
1989-2009
Consumption of
disaggregated solar,
geothermal and
biomass energy by
sector
Energy
consumption per
capita
Energy
consumption per
capita
Barros, Gil-Alana &
Payne [21]
United States,
1981-2010
Kula, Aslan & Ozturk
[22]
OECD countries,
1960-2005
Ozturk, Aslan [23]
Turkey, Sectors,
1970-2006
Disaggregated
fossils, coal and
electricity retail
consumption
Renewable energy
consumption
Electricity
consumption per
capita
Energy
consumption per
capita
Fractional integration with structural
breaks – mixed evidence of fractional
integration and non-stationarity
Fractional integration with and without
structural breaks – mixed evidence of
order of integration depending on
energy type and sector.
Univariate unit root tests which allow
for non-linearities and structural breaks
– mixed evidence of stationarity
(a) Univariate tests with structural
breaks – evidence of stationarity.
(b) Panel test with structural breaks –
evidence of stationarity
Fractional integration with structural
breaks – mixed evidence of order of
integration depending on energy type
Fractional integration – evidence of
nonstationarity with mean-reverting
behaviour.
Unit root tests with structural breaks –
evidence of stationarity
Unit root tests with structural break –
evidence of stationarity
23
Table 2
Results of LM test with no break (Schmidt and Phillips [65])
Lag
Stat.
0
Z(ρ)
Z(τ)
Z(ρ)
Z(τ)
Z(ρ)
Z(τ)
Z(ρ)
Z(τ)
Z(ρ)
Z(τ)
1
2
3
4
Biofuel
T = 30
-1.9808
-0.9950
-2.7828
-1.1794
-3.2702
-1.2785
-3.6306
-1.3471
-3.9202
-1.3998
Yearly Data
Biomass
T = 62
-3.1278
-1.2564
-3.8517
-1.3942
-4.4600
-1.5003
-5.2288
-1.6244
-6.0404
-1.7460
Total
T = 62
-7.8603
-2.0319
-7.8116
-2.0256
-8.3984
-2.1003
-8.7160
-2.1396
-9.2160
-2.2001
Biofuel
T = 369
-0.3981
-0.4456
-0.4327
-0.4646
-0.5341
-0.5162
-0.6330
-0.5620
-0.7266
-0.6021
Monthly data
Biomass
Total
T = 465
T = 465
-15.4663
-13.1408
-2.8013
-2.5788
-11.6904
-11.4457
-2.4354
-2.4067
-8.4783
-9.3434
-2.0740
-2.1745
-7.0096
-8.2268
-1.8858
-2.0404
-6.5300
-8.1740
-1.8202
-2.0339
Notes: critical values based on Schmidt and Phillips [65, pp.264-265, Tables 1A & 1B].
24
Table 3
Results of LM test with one break in the intercept (Lee and Strazicich [39] - Model A)
Biofuel (yearly data)
TB
1995
k
4
Biomass (yearly data)
1993
4
Total (yearly data)
2000
0
Biofuel (monthly data)
7/97
12
Biomass (monthly data)
9/99
11
Total (monthly data)
3/96
12
St-1
**
-0.1474
(-3.9215)
-0.1179
(-3.0257)
-0.1890
(-2.5232)
-0.0095
(-1.6041)
-0.0165
(-1.4513)
-0.0272
(2.0091 )
Bt
***
-0.4493
(-6.3029)
0.1104**
(2.2322)
-0.2172***
(-4.2470)
-0.3348***
(-5.4685)
-0.2191***
(-5.4330)
-0.0671**
(-2.0125)
Notes: TB is the date of the structural break; k is the lag length; St-1 is the LM test statistic; Bt is the dummy
variable for the structural break in the intercept. Figures in parentheses are t-values. Critical values for the LM
test statistic are from Lee and Strazicich [39]. Critical values for other coefficients follow the standard normal
distribution. (**) *** denote statistical significance at the 5% and 1% levels respectively.
25
Table 4
Results of LM test with one break in the intercept and slope (Lee and Strazicich [39] - Model C)
Biofuel (yearly data)
TB
1994
k
4
Biomass (yearly data)
1957
4
Total (yearly data)
1982
4
Biofuel (monthly
data)
Biomass (monthly
data)
Total (monthly data)
7/97
12
1/90
12
3/00
12
St-1
-0.3945
(-3.9221)
-0.1643
(-3.4414)
-0.3988
(-3.4308)
-0.0173
(-1.9092)
-0.0391
(-2.4195)
-0.0727
(-3.2469)
Bt
0.0877
(0.7667)
-0.0328
(-0.7484)
0.1231**
(2.2746)
-0.3375***
(-5.5178)
0.0340
(0.8524)
0.0832**
(2.4490)
Dt
-0.3482***
(-3.0482)
0.0254
(1.1270)
-0.0094
(-0.6736)
-0.0104
(-1.1368)
-0.0145**
(-2.3639)
-0.0163**
(-2.5638)
Critical values
location of break, λ
0.1
1% significant level
-5.11 -5.07 -5.15 -5.05 -5.11
5% significant level
-4.50 -4.47 -4.45 -4.50 -4.51
0.2
0.3
0.4
0.5
10% significant level -4.21 -4.20 -4.18 -4.18 -4.17
Notes: TB is the date of the structural break; k is the lag length; St1 is the LM test statistic; Bt is the dummy
variable for the structural break in the intercept; D t is the dummy variable for the structural break in the slope.
Figures in parentheses are t-values. The critical values for the LM test statistic are symmetric around λ and (1-λ).
Critical values for other coefficients follow the standard normal distribution. ( **) *** denote statistical
significance at the 5% and 1% levels respectively.
26
Table 5
Results of LM test with two breaks in the intercept (Lee and Strazicich [39] - Model AA)
TB1
TB2
K
Biofuel (yearly
data)
Biomass (yearly
data)
Total (yearly data)
1995
2000
4
1988
1993
4
1968
2000
0
Biofuel (monthly
data)
Biomass (monthly
data)
Total (monthly
data)
5/97
7/97
12
3/96
9/99
10
12/89
9/99
12
St-1
-0.1833**
(-3.8508)
-0.1316
(-3.0677)
-0.2323
(-2.7367)
-0.0118
(-1.8402)
-0.0242
(-1.7159)
-0.0350
(-2.2191)
Bt1
-0.4663***
(-5.8712)
0.0735
(1.5442)
0.0657
(1.3105)
-0.1737***
(-2.7867)
-0.2020***
(-5.2504)
-0.0946***
(-2.8170)
Bt2
-0.2003**
(-2.2316)
0.1134**
(2.1675)
-0.2227***
(-4.2859)
-0.3706***
(-6.0031)
-0.2185***
(-5.3502)
-0.1097***
(-3.2303)
Notes: TB1 and TB2 are the dates of the structural breaks; k is the lag length; St-1 is the LM test statistic; Bt1 and
Bt2 are the dummy variables for the structural breaks in the intercept. Figures in parentheses are t-values. Critical
values for the LM test at 5% and 1% significance levels are -3.842 and -4.545. (**) *** denote statistical
significance at the 5% and 1% levels respectively.
27
Table 6
Results of LM test with two breaks in the intercept and slope (Lee and Strazicich [39] - Model CC)
TB1
TB2
k
Biofuel
1987 2000 3
(yearly
data)
Biomass
1974 1994 4
(yearly
data)
Total
1957 1982 4
(yearly
data)
Biofuel
7/85
4/01 12
(monthly
data)
Biomass
2/80
1/01 12
(monthly
data)
Total
10/81 6/00 12
(monthly
data)
Critical values for the LM test
λ2
St-1
-1.1963
(-3.3542)
Bt1
0.2566
(1.5631)
Bt2
-0.1571
(-1.4649)
Dt1
-0.7473***
(-3.2784)
Dt2
0.2009***
(4.3580)
-0.3270
(-4.9633)
-0.1475***
(-3.4405)
0.0467
(1.1070)
0.1250***
(5.4129)
-0.1088***
(-4.3156)
-0.6116
(-4.1621)
0.0144
(0.2672 )
0.1524***
(2.7087)
0.0093
(0.3254)
-0.0779***
(-3.9167)
-0.1222
(-3.8900)
0.0158
(0.2730)
0.0034
(0.0580)
-0.0585***
(-4.3381)
0.0202***
(2.9080)
-0.1771
(-4.5523)
-0.0264
(-0.6753)
0.0202
(0.4945)
0.0379***
(3.5696)
-0.0291***
(-3.6432)
-0.1367
(-4.5339)
-0.0570
(-1.6974)
0.0097
(0.2800)
0.0180***
(3.1053)
-0.0260***
(-3.6362)
0.4
0.6
0.8
λ1
1%
5%
10%
1%
5%
10%
1%
5%
10%
0.2
-6.16
-5.59
-5.27
-6.41
-5.74
-5.32
-6.33
-5.71
-5.33
0.4
-
-
-
-6.45
-5.67
-5.31
-6.42
-5.65
-5.32
0.6
-
-
-
-
-
-
-6.32
-5.73
-5.32
Notes: TB1 and TB2 are the dates of the structural breaks; k is the lag length; St-1 is the LM test statistic; Bt1 and
Bt2 are the dummy variables for the structural breaks in the intercept. D t1 and Dt2 are the dummy variables for the
structural breaks in the slope. Figures in parentheses are t-values. λj denotes the location of breaks. *** denotes
statistical significance at the 1% level.
28
Figure 1
Monthly time series of biofuels, biomass and total renewable energy production in US
900
800
700
600
500
400
300
200
100
0
1975
1980
1985
1990
1995
biofuels trillion (btu)
biomass trillion (btu)
total trillion (btu)
2000
2005
2010