are fluctuations in production of renewable energy permanent or transitory?

8/11/2019 Are fluctuations in production of renewable energy permanent or transitory?

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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 resourceswill 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] 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 writtenpermission of the author.


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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, high-

efficiency 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 andRE 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

HereFE(L,K,RE) represents the partial derivative ofF(.) with respect toRE. Multiplying both

sides of the equation byRE 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


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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:

t t ty Z e ,

1t t te e . (1)

Here,ytis the production of renewable energy in period t, tZ 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 '

1, ,t tZ t D , where 1tD for 1,Bt T 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

'

1, , ,t t tZ t D DT , where t BDT t T for 1,Bt T 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 '

1 21, , ,t t tZ t D D where 1jtD for 1, 1, 2,Bjt T j and 0 otherwise. BjT

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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'

1 2 1 21, , , , ,t t t t t Z t D D DT DT , where jt BjDT t T for 1, 1, 2,Bjt T j and 0 otherwise. The

LM unit root test statistic is obtained from the following regression:

tttt SZy 1 (2)

where ttxttZyS , T,...,t 2 ; are coefficients in the regression of ty on tZ ;

x is given by tt Zy ; and 1y and 1Z represent the first observations of ty and tZ

respectively. The most important parameter in Equation (2) is . The LM test statistic is the t-

statistic 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 BureausX12 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() and Z(). 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 Strazicichs [39] Models A and C, which

accommodate a structural break in the intercept and intercept and slope respectively. Lee and

Strazicichs [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 Strazicichs [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 Strazicichs [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).


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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.


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Table 1

Existing studies examining the unit root properties of energy consumption and production

Study Coverage Energy Type Unit Root Test/Findings

Narayan & Smyth [1] 182 countries,

1979-2000

Energy

consumption percapita

(a) Univariate tests without structural

breaksmixed evidence of stationarity(b) Panel test without structural breaks

evidence of stationarity

Chen & Lee [2] Seven regional

panels 1971-2002

Energy

consumption per

capita

Panel test with structural breaks


Hsu, Lee & Lee [3] Five regional

panels 1971-2003

Energy

consumption per

capita

Panel test without structural breaks

mixed evidence of stationarity

Narayan, Narayan &

Smyth [4]

Panels of 60

countries, 1971-2003

Crude oil and NGL

production

(a) Panel test without structural breaks

mixed evidence of stationarity.(b) Panel test with structural break


Maslyuk & Smyth [5] 17 countries

1973-2007

Crude oil

production

Univariate non-linear unit root test

mixed evidence of unit roots and partial

unit roots.

Mishra, Sharma &

Smyth [6]

Panel of 13

Pacific Island

countries 1980-2005

Energy

consumption per

capita



Lean & Smyth [7] United States,

1973-2008

Disaggregated

petroleum

consumption

Fractional integrationmixed evidence

of fractional integration, non-

stationarity and stationarity.

Apergis & Payne [8] States of United

States 1960-2007

Petroleum

consumption

Univariate unit root tests with structural

breaksevidence of stationarity in

majority of cases.Gil-Alana, Loomis &Payne [9]

United Stateselectric power

sector 1973-2009

Consumption ofvarious

disaggregated

energy sources

Fractional integration with structuralbreakevidence of fractional

integration.

Narayan, Narayan &

Popp [10]

States in

Australia

1973-2007

Energy

consumption per

capita by sector

Univariate unit root tests with up to two

structural breaksevidence of

stationarity.

Apergis, Loomis,

Payne [11]

States of United

States 1982-2007

Coal consumption Panel test with structural breaks


Apergis, Loomis,

Payne [12]

States of United

States 1980-2007

Natural gas

consumption



Pereira, Belbute [13] Portugal, 1977-

2003

Consumption of

variousdisaggregated

energy sources

Non-parametric persistence tests

evidence of persistence.

Aslan, Kum [14] Turkey, 1970-

2006

Energy

consumption per

capita by sector

(a) Univariate unit root tests with up to

two structural breaksevidence of

stationarity.(b) Non-linear unit root test- evidence

of non-stationarity

Aslan [15] States of United

States 1960-2008

Natural gas

consumption

Non-linear unit root testmixed

evidence of stationarity.


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Table 1 continued:

Barros, Gil-Alana &

Payne [16]

OPEC countries,

1973-2008

Crude oil

production

Fractional integration with structural

breaksmixed evidence of fractionalintegration and non-stationarity

Apergis & Tsoumas

[17]

United States,

1989-2009

Consumption of

disaggregated solar,geothermal and

biomass energy by

sector

Fractional integration with and without

structural breaksmixed evidence oforder of integration depending on

energy type and sector.

Hasanov & Telatar

[18]

178 countries,

1980-2006

Energy

consumption per

capita

Univariate unit root tests which allow

for non-linearities and structural breaks

mixed evidence of stationarity

Agnolucci & Venn

[19]

Industrial

subsectors in the

United Kingdom,

1970-2004

Energy

consumption per

capita

(a) Univariate tests with structural

breaksevidence of stationarity.

(b) Panel test with structural breaks


Apergis & Tsoumas

[20]

United States,

1989-2009

Disaggregated

fossils, coal and

electricity retailconsumption

Fractional integration with structural

breaksmixed evidence of order of

integration depending on energy type

Barros, Gil-Alana &

Payne [21]

United States,

1981-2010

Renewable energy

consumption

Fractional integrationevidence of

nonstationarity with mean-reverting

behaviour.

Kula, Aslan & Ozturk

[22]

OECD countries,

1960-2005

Electricity

consumption per

capita

Unit root tests with structural breaks


Ozturk, Aslan [23] Turkey, Sectors,1970-2006

Energyconsumption per

capita

Unit root tests with structural breakevidence of stationarity


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Table 2

Results of LM test with no break (Schmidt and Phillips [65])

Yearly Data Monthly data

Lag Stat. Biofuel

T = 30

Biomass

T = 62

Total

T = 62

Biofuel

T = 369

Biomass

T = 465

Total

T = 465

0 Z() -1.9808 -3.1278 -7.8603 -0.3981 -15.4663 -13.1408

Z() -0.9950 -1.2564 -2.0319 -0.4456 -2.8013 -2.5788

1 Z() -2.7828 -3.8517 -7.8116 -0.4327 -11.6904 -11.4457

Z() -1.1794 -1.3942 -2.0256 -0.4646 -2.4354 -2.4067

2 Z() -3.2702 -4.4600 -8.3984 -0.5341 -8.4783 -9.3434

Z() -1.2785 -1.5003 -2.1003 -0.5162 -2.0740 -2.17453 Z() -3.6306 -5.2288 -8.7160 -0.6330 -7.0096 -8.2268

Z() -1.3471 -1.6244 -2.1396 -0.5620 -1.8858 -2.0404

4 Z() -3.9202 -6.0404 -9.2160 -0.7266 -6.5300 -8.1740

Z() -1.3998 -1.7460 -2.2001 -0.6021 -1.8202 -2.0339

Notes: critical values based on Schmidt and Phillips [65, pp.264-265, Tables 1A & 1B].


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Table 3

Results of LM test with one break in the intercept (Lee and Strazicich [39] - Model A)

TB k St-1 Bt

Biofuel (yearly data) 1995 4 -0.1474(-3.9215)

-0.4493(-6.3029)

Biomass (yearly data) 1993 4 -0.1179

(-3.0257)

0.1104

(2.2322)

Total (yearly data) 2000 0 -0.1890

(-2.5232)

-0.2172

(-4.2470)

Biofuel (monthly data) 7/97 12 -0.0095

(-1.6041)

-0.3348

(-5.4685)

Biomass (monthly data) 9/99 11 -0.0165

(-1.4513)

-0.2191

(-5.4330)

Total (monthly data) 3/96 12 -0.0272

(2.0091 )

-0.0671

(-2.0125)

Notes: TB is the date of the structural break; kis the lag length; St-1 is the LM test statistic; B t 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.


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Table 4

Results of LM test with one break in the intercept and slope (Lee and Strazicich [39] - Model C)

TB k St-1 Bt Dt

Biofuel (yearly data) 1994 4 -0.3945(-3.9221) 0.0877(0.7667) -0.3482(-3.0482)

Biomass (yearly data) 1957 4 -0.1643

(-3.4414)

-0.0328

(-0.7484)

0.0254

(1.1270)

Total (yearly data) 1982 4 -0.3988

(-3.4308)

0.1231

(2.2746)

-0.0094

(-0.6736)

Biofuel (monthly

data)

7/97 12 -0.0173

(-1.9092)

-0.3375

(-5.5178)

-0.0104

(-1.1368)

Biomass (monthly

data)

1/90 12 -0.0391

(-2.4195)

0.0340

(0.8524)

-0.0145

(-2.3639)

Total (monthly data) 3/00 12 -0.0727

(-3.2469)

0.0832

(2.4490)

-0.0163

(-2.5638)Critical values

location of break, 0.1 0.2 0.3 0.4 0.5

1% significant level -5.11 -5.07 -5.15 -5.05 -5.11



Notes: TB is the date of the structural break; kis the lag length; St1 is the LM test statistic; Btis 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 and (1 -).

Critical values for other coefficients follow the standard normal distribution. (**

)***

denote statistical

significance at the 5% and 1% levels respectively.


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Table 5

Results of LM test with two breaks in the intercept (Lee and Strazicich [39] - Model AA)

TB1 TB2 K St-1 Bt1 Bt2

Biofuel (yearly

data)

1995 2000 4 -0.1833

(-3.8508)

-0.4663

(-5.8712)

-0.2003

(-2.2316)

Biomass (yearly

data)

1988 1993 4 -0.1316

(-3.0677)

0.0735

(1.5442)

0.1134

(2.1675)

Total (yearly data) 1968 2000 0 -0.2323

(-2.7367)

0.0657

(1.3105)

-0.2227

(-4.2859)

Biofuel (monthly

data)

5/97 7/97 12 -0.0118

(-1.8402)

-0.1737

(-2.7867)

-0.3706

(-6.0031)

Biomass (monthly

data)

3/96 9/99 10 -0.0242

(-1.7159)

-0.2020

(-5.2504)

-0.2185

(-5.3502)

Total (monthly

data)

12/89 9/99 12 -0.0350

(-2.2191)

-0.0946

(-2.8170)

-0.1097

(-3.2303)

Notes:TB1and TB2are the dates of the structural breaks; kis the lag length; St-1is the LM test statistic; Bt1 and

Bt2are 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.


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Table 6

Results of LM test with two breaks in the intercept and slope (Lee and Strazicich [39] - Model CC)

TB1 TB2 k St-1 Bt1 Bt2 Dt1 Dt2

Biofuel

(yearlydata)

1987 2000 3 -1.1963

(-3.3542)

0.2566

(1.5631)

-0.1571

(-1.4649)

-0.7473***

(-3.2784)

0.2009***

(4.3580)

Biomass

(yearly

data)

1974 1994 4 -0.3270

(-4.9633)

-0.1475***

(-3.4405)

0.0467

(1.1070)

0.1250***

(5.4129)

-0.1088***

(-4.3156)

Total(yearly

data)

1957 1982 4 -0.6116(-4.1621)

0.0144(0.2672 )

0.1524***

(2.7087)

0.0093(0.3254)

-0.0779***

(-3.9167)

Biofuel

(monthly

data)

7/85 4/01 12 -0.1222

(-3.8900)

0.0158

(0.2730)

0.0034

(0.0580)

-0.0585***

(-4.3381)

0.0202***

(2.9080)

Biomass

(monthlydata)

2/80 1/01 12 -0.1771

(-4.5523)

-0.0264

(-0.6753)

0.0202

(0.4945)

0.0379***

(3.5696)

-0.0291***

(-3.6432)

Total

(monthly

data)

10/81 6/00 12 -0.1367

(-4.5339)

-0.0570

(-1.6974)

0.0097

(0.2800)

0.0180***

(3.1053)

-0.0260***

(-3.6362)

Critical values for the LM test

2 0.4 0.6 0.8

1 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: TB1and TB2are the dates of the structural breaks; kis the lag length; St-1is the LM test statistic; Bt1 and

Bt2are the dummy variables for the structural breaks in the intercept. Dt1 and Dt2are the dummy variables for the

structural breaks in the slope. Figures in parentheses are t -values. jdenotes the location of breaks.***

denotes

statistical significance at the 1% level.


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Figure 1

Monthly time series of biofuels, biomass and total renewable energy production in US

0

100

200

300

400

500

600

700

800

900

1975 1980 1985 1990 1995 2000 2005 2010

biofuels trillion (btu)

biomass trillion (btu)

total trillion (btu)

are fluctuations in production of renewable energy permanent or transitory?

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