Stochastic convergence in per capita fossil fuel consumption in U.S. states

    Stochastic convergence in per capita fossil fuel consumption in U.S. states James E. Payne, Maruˇska Vizek, Junsoo Lee PII: DOI: Reference:

S0140-9883(16)30061-5 doi: 10.1016/j.eneco.2016.03.023 ENEECO 3308

To appear in:

Energy Economics

Received date: Revised date: Accepted date:

1 March 2016 17 March 2016 21 March 2016

Please cite this article as: Payne, James E., Vizek, Maruˇska, Lee, Junsoo, Stochastic convergence in per capita fossil fuel consumption in U.S. states, Energy Economics (2016), doi: 10.1016/j.eneco.2016.03.023

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Stochastic Convergence in Per Capita Fossil Fuel Consumption in U.S. States

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James E. Payne Dean and Professor of Economics J. Whitney Bunting College of Business Georgia College & State University Milledgeville, GA 31061 [email protected]

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Maruška Vizek Deputy Director for Research and Senior Research Associate The Institute of Economics Zagreb Zagreb, Croatia [email protected]

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Junsoo Lee Professor of Economics and Rick and Elaine Horsley Faculty Fellow Department of Economics, Finance and Legal Studies University of Alabama, Tuscaloosa, AL 35486 [email protected]

Revised and Resubmitted April 8, 2016

Energy Sector Convergence Symposium

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ACCEPTED MANUSCRIPT Stochastic Convergence in Per Capita Fossil Fuel Consumption in U.S. States Abstract

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This study examines the stochastic convergence of per capita fossil fuel consumption across U.S. states (including the District of Columbia) utilizing LM and RALS-LM unit root tests with allowance for endogenously determined structural breaks. Our results indicate that with the exception of Nevada, the evidence from two-break and one-break LM and RALS-LM unit root tests reject the null hypothesis of a unit root in the relative per capita fossil fuel consumption in the U.S. This finding indicates the presence of stochastic convergence in relative per capita fossil fuel consumption in the U.S. states.

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JEL Classification Codes: C22, E4

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Keywords: Per Capita Fuel Consumption, Convergence, Unit Roots, Trend-shifts

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ACCEPTED MANUSCRIPT Stochastic Convergence in Per Capita Fossil Fuel Consumption in U.S. States 1. Introduction

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According to the Energy Information Administration, primary energy consumption in the U.S. is largely driven by fossil fuels with petroleum representing 34.8%, natural gas

With concerns regarding energy security, carbon emissions, and global

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respectively.

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27.5%, and coal 17.9% whereas renewable energy and nuclear energy are 9.6% and 8.3%,

warming, the U.S. has responded with a number of federal policies to reduce fossil fuel

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consumption, especially in the aftermath of the oil crises that occurred in the 1970s. In 1975, the Energy Policy and Conservation Act set forth the first automobile fuel economy standards. Shortly thereafter, the extensive National Energy Act of 1978 created a number

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of statues to promote energy conservation and greater use of domestic and renewable

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energy sources under the Public Utility Regulatory Policy Act. The Energy Tax Act utilized tax credits to encourage a shift from oil and gas supply toward energy conservation to enhance

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fuel efficiency and renewable energy use. The National Energy Conservation Policy Act

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focused on energy demand management; the Power Plant and Industrial Fuel Use Act restricted the use of oil and natural gas in new power plants; and the Natural Gas Policy Act initiated the deregulation of gas well head prices.

In 1980, the Energy Security Act

authorized the use of synthetic fuels as an alternative to fossil fuels along with providing loan guarantees for biomass and alcohol fuel-based projects. With over a decade since the legislation introduced in the 1970s, the Energy Policy Act of 1992 amended utility laws and set forth goals to increase clean energy use and improve overall energy efficiency, not to mention lessen the U.S.’s dependence of imported energy through additional incentives for renewable energy and the promotion of energy conservation in buildings. The Energy Policy Act of 2005 extended tax incentives for energy 3

ACCEPTED MANUSCRIPT conservation and expand the use of alternative fuels. In 2007, the Energy Independence and Security Act established corporate average fuel economy standards for cars and light trucks

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along with minimum efficiency standards for appliances, equipment, and lamps while encouraging the further development of biofuels. More recently, the American Recovery

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and Reinvestment Act of 2009 included funding to modernize the country’s electric smart grid and tax credits for the renewable energy sector and further enhancement of energy

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efficiency.

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In addition to the federal policies that support energy conservation and improved energy efficiency, energy policies at the state level have also promoted the use of renewable energy sources over fossil fuel sources as reflected in such policy tools as renewable

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portfolio standards, feed-in tariffs, net metering, tax incentives, and public benefit funds. Currently, 29 U.S. states and the District of Columbia have set forth renewable portfolio

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standards with another 8 states implementing voluntary renewable portfolio standards.1 In

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light of the efforts to curtail fossil fuel consumption, this study explores the convergence of

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per capita fossil fuel consumption across the 50 U.S. states including the District of Columbia. Indeed, such policies at the federal and state level which are targeted to decrease energy intensity, enhance energy efficiency, and reductions in carbon emissions from fossil fuels may contribute to the convergence of fossil fuel consumption across the U.S. states. Convergence with respect to the energy sector draws from the income and growth convergence literature set forth by Baumol (1986) and Barro and Sala-i-Martin (1991; 1992) in the examination of β- and σ-convergence. We focus our attention on stochastic convergence in following Meng et al. (2013), Mishra and Smyth (2014; 2016), Fallahi and

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See Dincer et al. (2014), and citations therein, on the variation of renewable portfolio standards across states. Regarding policies to reduce petroleum consumption associated with transportation see Knittel (2012).

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ACCEPTED MANUSCRIPT Voia (2015), and Lean et al. (2016)

in the use of unit root tests with endogenously

determined structural breaks to examine stochastic convergence for each of the 50 U.S.

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states and the District of Columbia.2 Specifically, we employ the newly developed RALS-LM (Residual Augmented Least

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Squares–Lagrange Multiplier) unit root tests with trend-breaks, as suggested by Lee et al. (2012). There are two main advantages of these new tests. First, we can control for the

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effects of structural changes that might have occurred in the data, especially in terms of

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trend-shifts. The usual LM and other unit root tests can depend on the location of breaks, but the suggested transformed LM tests are designed not to depend on the location but to depend only on the number of trend-shifts. As such, there will be no additional nuisance

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parameters with these new tests. Thus, the new tests can be combined with the RALS

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procedure of Im and Schmidt (2008) and Meng, Im, Lee and Tieslau (2014) such that the information of non-normal errors can be utilized to improve the power of the unit root tests.

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In general, standard unit root tests are not affected by the presence of non-normal errors,

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but it does not mean that the information on non-normal errors should be ignored and not utilized. The RALS procedure provides a convenient way to utilize the information to increase the power of the standard unit root tests. Thus, we wish to control for and utilize important components of a time series with these new RALS-LM unit root tests with trendshifts.

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In the context of the growth literature, β-convergence occurs when poor countries grow faster than rich countries. Of which there is absolute β-convergence in which the growth rate of a country declines as the country approaches its steady state growth path and conditional β-convergence in which countries exhibit βconvergence but conditional on other variables remaining constant. On the other hand, σ-convergence occurs with the reduction in the dispersion of the level of income across countries. Evans (1996), Evans and Karras (1996), Quah (1996), among others, have suggested that unit root based tests of stochastic conditional convergence circumvent issues with standard tests of convergence.

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ACCEPTED MANUSCRIPT Section 2 provides a brief survey of the convergence literature pertaining to energy consumption. Section 3 presents the methodology while Section 4 discusses the data and

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the empirical results. Concluding remarks are given in Section 5.

2. Literature Review

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Early studies regarding energy convergence have focused on either energy intensity

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or energy productivity.3 Energy intensity is defined as the ratio of energy consumption relative to output while energy productivity is the ratio of output relative to energy Mielnik and Goldemberg (2000) investigate the convergence of energy

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consumption.

intensity utilizing the purchasing power parity measure of each country’s GDP over the period 1971 to 1992 for 41 countries.

Their analysis shows that developing and

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industrialized countries are converging to a common pattern of energy use with 18

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industrialized countries showing a decreasing trajectory while the 23 developing countries follow an increasing energy intensity path.

Miketa and Mulder (2005) examine the

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convergence in energy productivity for 56 countries in 10 manufacturing sectors over the

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period 1971 to 1995. Their results reveal that, for most sectors, cross-country differences in absolute energy productivity levels decline, more so in less energy intensive industries with the exception of non-ferrous metals which exhibits divergence. Moreover, the results from tests of β-convergence indicate that energy productivity growth in all sectors is relatively high for countries that have lagged behind, lending support for the catch-up hypothesis. There is also persistence in cross-country differences in energy productivity as countries converge to different steady states. Miketa and Mulder (2005) also find that energy price,

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Though unit root based tests of energy consumption to determine the presence of unit roots have been extensively examined in the literature (for a survey of the literature, see Smyth, 2013), these tests do not explicitly test for convergence. Furthermore, another stream of the convergence literature examines the convergence in emissions (see List, 1999; Strazicich and List, 2003; Aldy, 2007; Barassi et al. 2008; Lee and Chang, 2008; Payne et al. 2014, among others).

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ACCEPTED MANUSCRIPT the investment ratio, and fuel mix impact country-specific energy productivity growth rates to a limited extent. Markandya et al. (2006) examine the convergence of energy intensity for

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12 transition countries of Eastern Europe relative to EU15 countries over the period 1992 to 2002. Their results support conditional β-convergence with the rate of convergence in

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energy intensity varying among transition countries.

Ezcurra (2007) explores the cross-sectional distribution of energy intensity for 98

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countries over the period 1971 to 2001 within a nonparametric framework to find the

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presence of convergence. Mulder and de Groot (2007) investigate cross-country convergence of energy and labor productivity for 13 sectors in 14 OECD countries over the period 1970 to 1997.

In terms of σ-convergence their results show that productivity

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performance varies across sectors and the level of aggregation whereas β-convergence for

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most sectors of lagging countries catch-up with technological leaders in terms of energy productivity. Liddle (2009) examines electricity and energy intensity convergence for 22

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industrialized countries over the period 1960 to 2005 to find convergence within the end-use

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sectors varies across countries. Commercial electricity intensity convergence reflected a bellshaped distribution; industrial electricity intensity bimodal convergence concentrated in high and low electricity intensity; and residential electricity consumption per capita convergence into three groups: no growth, slow growth, and rapid growth. Le Pen and Sevi (2010) investigate the stochastic convergence of energy intensity for a sample of 97 countries from 1971 to 2003 through the use of unit root and stationarity tests using the pair-wise benchmark free approach advanced by Pesaran (2007). Their results based on unit root and stationarity tests without structural breaks uniformly reject convergence for regional groups and the full sample of countries.

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ACCEPTED MANUSCRIPT Liddle (2010) utilizes two large data sets (111-country sample from 1971 to 2006 and 134-country sample from 1990 to 2006) to examine the convergence of energy intensity at

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the world and regional level. Liddle (2010) finds that although there is evidence of energy intensity convergence for the world as a whole, there are geographical differences in energy

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intensity convergence. OECD and Eurasian countries demonstrate continued convergence while Sub-Sahara African countries reveal convergence among themselves at a slower rate

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than OECD and Eurasian countries. However, Latin America and Caribbean and Middle East

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and North African countries do not show convergence in energy intensity. Jakob et al. (2012) apply a difference-in-differences estimator to a panel of 30 developing and 21 developed countries over the period 1971 to 2005 to investigate how energy use patterns change in the

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economic development process. With respect to developing countries, the results suggest

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that as these countries caught up economically to the world average, their energy use patterns were not less energy or carbon intensive than in industrialized countries. In the case

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of industrialized countries the results indicate partial decoupling between economic growth

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and energy usage with above average rates of economic growth accompanied by improvements in energy efficiency. Herrerias (2012) examines the distributional dynamics of several energy intensity measures for 83 countries from 1971 to 2008 to show significant differences in the convergence process between developed and developing countries. For developed countries the evidence suggests two convergence clubs with multiple convergence clubs among developing countries. Mulder and de Groot (2012) evaluate the convergence of energy intensity for 50 sectors across 18 OECD countries over the period 1970 to 2005. Their analysis indicates that aggregate energy intensity patterns are explained by changes in the sectoral composition of the respective countries. Cross-country variation in aggregate energy intensity decreases 8

ACCEPTED MANUSCRIPT since 1995 attributed to the convergence in the manufacturing sector along with strong convergence in the service sector. Moreover, aggregate convergence patterns are due to

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the convergence of within-sector energy intensity levels and not by convergence of the sectoral composition in the respective countries. Zhang (2013) tests for convergence in

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manufacturing energy intensity for 28 Eastern European and Central Asian countries over the period 1998 to 2008. The results support convergence which is driven by increases in

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economic growth and energy prices. Further decomposition analysis suggests the decline in

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energy intensities is primarily due to more efficient energy use. Csereklyei and Stern (2015) in their investigation of the decoupling of energy use and economic growth for 93 countries from 1971 to 2010 reveal that the growth of per capita energy use can be attributed to

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economic growth, convergence in energy intensity, and evidence of weak decoupling. In addition to studies pertaining to energy intensity and energy productivity, more

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recent studies have examined the convergence of energy consumption measures.4 Maza and

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Villaverda (2008) apply nonparametric techniques to residential per capita electricity

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consumption for a sample of 98 countries to investigate the distributional convergence over the period 1980 to 2007. With respect to traditional measures of convergence, σ and β, the results indicate convergence. However, the shape of the distribution of residential per capita electricity consumption has changed over time. Mohammadi and Ram (2012) examine cross-country convergence of energy and electricity usage per capita for 108 countries from 1971 to 2007 through tests of unconditional and conditional β-convergence along with σconvergence utilizing quantile regression analysis. Mohammadi and Ram (2012) find weak evidence of convergence in per capita energy usage, but stronger evidence of convergence

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Regarding the examination of convergence in energy consumption rather than energy intensity, Mohammadi and Ram (2012) note that energy intensity is a joint study of the distributions of GDP and energy usage, thus the convergence structure for the two variables may be different.

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ACCEPTED MANUSCRIPT in per capita electricity usage. Energy convergence in the top and bottom quantiles is rather weak with electricity convergence appearing in the top quantile, but not in the bottom

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quantile. In the context of conditional β-convergence, Mohammadi and Ram (2012) show that urbanization yields a positive and significant coefficient to indicate that as urbanization

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increases there is an increase in both energy and electricity usage. However, for the top

statistically significant for the bottom quantile.

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quantile, the coefficient for urbanization is statistically insignificant, while positive and

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Meng et al. (2013) apply LM and RALS-LM unit root tests with endogenously determined structural breaks to examine the convergence of per capita energy use for 25 OECD countries over the period 1960 to 2010. Their results support convergence in per

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capita energy use for a majority of the OECD countries once structural breaks are Anoruo and DiPietro (2014) examine the stochastic

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incorporated in the analysis.

convergence of per capita energy consumption for 22 African countries from 1971 to 2011

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utilizing conventional panel unit root tests alongside a sequential panel selection procedure.

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While the conventional panel unit root tests indicate convergence, upon closer inspection, the use of the sequential panel selection procedure reveals 15 of the 22 countries exhibit convergence while the remaining countries show divergence with respect to per capita energy consumption. Mishra and Smyth (2014) apply panel unit root and stationarity tests with allowance for structural breaks to a panel of five ASEAN countries over the period 1971 to 2011 to find stochastic convergence in per capita energy consumption. Roboredo (2015) examines the convergence of renewable energy as a share of energy supply for 39 developed and emerging market countries from 1990 to 2010 using a pooled mean group estimator. Roboredo (2015) finds heterogeneity in the results with divergence evident in most countries while convergence is observed in only eight countries. 10

ACCEPTED MANUSCRIPT Fallahi and Voia (2015) extend the work of Meng et al. (2013) and Mishra and Smyth (2014) in the use of confidence intervals associated with unit root tests in the examination of

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stochastic convergence in energy use per capita for 25 OECD countries over the period 1960 to 2012. Their results show that 13 of the 25 OECD countries exhibit convergence. Lean et

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al. (2016) utilize a GARCH-based unit root test to investigate conditional convergence of disaggregated petroleum consumption across five U.S. sectors using monthly data from

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1973:1 to 2014:6. Their results suggest the presence of conditional convergence for total

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petroleum consumption in each of the five sectors: residential, commercial, industrial, transport, and electric power. However, the results are mixed with respect to the other sectors at the disaggregated level. Mishra and Smyth (2016) apply recently developed LM

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and RALS-LM unit root test with endogenously determined structural breaks to relative per

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capita energy consumption across seven sectors in the case of Australia. Based on annual data from 1973 to 2014, Mishra and Smyth (2016) find stochastic convergence in relative per

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capita energy consumption across all sectors.

Kim (2015) examines convergence with

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respect to energy intensity and per capita electricity consumption for 109 countries over the period 1971 to 2009 to find the absence of convergence in per capita electricity consumption to a common component for all 109 countries whereas energy intensity is captured by a single component model. However, for both energy indicators, there is a tendency toward a common stochastic trend among the 24 industrialized countries along with the decline over time in cross-country dispersion. The results also indicate club convergence of per capita electricity consumption.

3. Methodology

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ACCEPTED MANUSCRIPT In this study, we adopt the LM based unit root tests, which are based on a two-step procedure, and extend them to incorporate structural changes with trend-shifts and utilize

difference (

) of a time series on the first difference (

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the information on non-normal errors. The first step involves a regression of the first ) of a set of exogenous variables

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which include a constant, trend and dummy variables reflecting structural changes. (1)

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, in which we allow for up-to two trend-shifts with

,

, and zero otherwise, and

for

, and zero otherwise. Then, we denote the estimated coefficient as

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,

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, for

where

(2)

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and construct the de-trended series as

(3)

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.

. The unit root test statistics are then obtained from the following

where

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regression:

,

(4)

As explained in Lee et al. (2012), the usual LM unit root test statistic statistic for

, will depend on the parameter indicating the location of breaks,

denotes the fraction of sub-samples in each regime such that

replace

for in regression (4) with

, or

, which

,and

. We follow Lee et al. (2012) and utilize the transformation, ,

, which is the usual t-

for

for . Then, we

where we add the augmented terms as well to

correct for autocorrelated errors. 12

ACCEPTED MANUSCRIPT . The t -statistic for

is the LM unit root statistic for which we denote it as

. The

are provided in Lee et al. (2012) for the models with one and two trend-

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critical values of

(5)

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shifts.

In order to utilize the information of non-normal errors for more powerful tests, we

where

(6)

,

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modify the above testing regression with

is the residual augmented term which captures the moment conditions using the

are uninformative if

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higher moments

]’.

. (7)

reflect the redundancy condition that knowledge of

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The moment conditions,

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second and third moments of the residuals of the regression (5) with

, which holds only for the normal

distribution but not for any non-normal distributions. Thus, in the presence of non-normal

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errors, the added augmented term

helps to improve the efficiency of the estimators, and

thus increase the power of the underlying unit root tests. We denote the corresponding tstatistic for

as

. The asymptotic distribution of

is given by as

. The corresponding critical values are given for the values of = 0.1, .., 0.9, in Meng, Im, Lee and Tieslau (2014) for the models with no breaks, and Meng et al. (2016) for the models with trend-shifts. 4. Data and the Empirical Results Annual data on primary fossil fuel consumption defined in trillion Btu for each of the 50 U.S. states and the District of Columbia were obtained from the U.S. Energy Information

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ACCEPTED MANUSCRIPT Administration from 1970 to 2013 while state population data defined in thousands was obtained from the Federal Reserve Bank of St. Louis, FRED II. Table 1 reports the summary

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statistics associated with per capita fossil fuel consumption for each state and the District of Columbia. As shown in Table 1 there is a great deal of variation across states as the highest

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mean per capita fossil fuel consumption is observed in Wyoming and the lowest mean per capita fossil fuel consumption in the District of Columbia. The variability in per capita fossil

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variability with Oregon and Vermont the least.

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fuel consumption (standard deviation) varies as well with Wyoming exhibiting the greatest

[Insert Table 1 here] For each state i, we examine the natural logarithm of the ratio of per capita fossil fuel

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consumption (FFC) relative to the average of all states including the District of Columbia as

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follows:5

(8)

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In the context of unit root testing, if relative per capita fossil fuel consumption defined above

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follows a stationary process (does not contain a unit root), shocks will be transitory, lending support for stochastic convergence. Table 2 displays results obtained from applying the twobreak LM (

) and RALS-LM (

) unit root tests on the natural logarithm of the ratio

of per capita fossil fuel consumption in each of the U.S. states to the average per capita fossil fuel consumption for all U.S. states from 1970 to 2013. The LM unit root test results indicate the null hypothesis of a unit root in relative per capita fossil fuel consumption is rejected at the 10 percent significance level in 42 states (including the District of Columbia). The RALSLM unit root test results confirm the rejection of the unit root hypothesis in an additional 4 5

As noted by Meng et al. (2013), the equation suggests that shocks of the same percentage common to all states would leave relative fossil fuel consumption unchanged. Thus, structural breaks from the LM and RALSLM tests are state-specific.

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ACCEPTED MANUSCRIPT states (in total 46 states including the District of Columbia). Thus, judging from the twobreak unit root tests, we can conclude that in 46 states (including the District of Columbia)

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there is an indication of stochastic convergence in relative per capita fossil fuel consumption. Of these 46 states, both trend-break points are statistically significant in 40 states, thus

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affirming the appropriateness of the two-break unit root test. However, in the remaining 6 states in which the null hypothesis of a unit root is rejected (the District of Columbia, Hawaii,

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Louisiana, Michigan, Tennessee, and West Virginia), only one break point is significant at 10

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percent significance level. The states of Nebraska, Nevada, New Hampshire, North Dakota, and Texas fail to reject the null hypothesis of a unit root based on either the LM or RALS-LM unit root tests with two structural breaks.

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[Insert Table 2 here]

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In order to investigate the effects of allowing for one structural break instead of two structural breaks, we apply the one-break LM and RALS-LM unit root tests to each of the

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states and the District of Columbia. The results are shown in Table 3. In 28 cases both tests

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reject the null hypothesis of a unit root in relative per capita fossil fuel consumption. The RALS-LM unit root test rejects the null hypothesis of a unit root in 9 additional cases, while the LM unit root test rejects the null hypothesis of a unit root in 2 additional cases. For the states which failed to reject the null hypothesis of a unit root based on the two-break tests, both the LM and RALS-LM unit root tests with one-break reject the null hypothesis of a unit root in North Dakota and Texas. In addition, the LM test rejects the null hypothesis in New Hampshire, while the RALS-LM does the same for Nebraska. Regarding the states (the District of Columbia, Hawaii, Louisiana, Michigan, Tennessee, and West Virginia) in which the results from the two-break unit root tests indicate that only one structural break is statistically significant, both the LM and RALS-LM unit root tests with one-break reject the 15

ACCEPTED MANUSCRIPT null of unit root in cases of Louisiana and Michigan, while only the RALS-LM unit root test with one-break rejects the null hypothesis of a unit root for the District of Columbia and

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West Virginia. However, one-break unit root tests could not reject the null hypothesis of a unit root in case of Hawaii and Tennessee, for which two-break tests suggested there may be

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just one break in relative per capita fossil fuel consumption. Thus, combining both the twobreak and one-break unit root test results indicate that relative per capita fossil fuel

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consumption contains a unit root in only Nevada.

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[Insert Table 3 here]

Table 4 presents no-break test results. The number of states for which the null hypothesis of a unit root in relative per capita fossil fuel consumption is rejected (13 states

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according to either the LM or RALS-LM tests and 12 additional states according to the ADF

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test) is decidedly smaller when compared to the one-break and two-break tests. This difference clearly reflects the pitfalls of applying no-break unit root tests in presence of

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trend-breaks in the time series. All three no-break unit root tests fail to reject the null

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hypothesis of a unit root in relative per capita fossil fuel consumption for Nevada, which in turn suggests that this state is the only U.S. state that does not exhibit convergence in relative per capita fossil fuel consumption. [Insert Table 4 here] Overall, our empirical evidence provides clear support for stochastic convergence of per capita fossil fuel consumption among a majority of U.S. states (including the District of Columbia). As rejection of the unit root null hypothesis is overwhelmingly more frequent when one allows for two breaks, we visualize our findings by superimposing the level and trend breaks and estimating associated linear trends between breaks with ordinary least squares. Figure 1 displays relative log of per capita fossil fuel consumption with two breaks 16

ACCEPTED MANUSCRIPT and associated trend lines for each state. Combining the visual representation of relative per capita fossil fuel consumption with results presented in Table 2 suggest the structural breaks

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either coincide with or take place within a few years after oil price shocks or in response to federal and state energy related legislation and policies to curtail fossil fuel consumption.

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[Insert Figure 1 here]

Thus, in 10 states we detect a structural breaks within 5 years after the 1973 oil

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shock. In 28 states a structural break took place within 5 years after the 1979 oil crises

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prompted by the Iranian revolution. Moving to more recent periods, in 13 states we find evidence of a structural change in relative fossil fuels consumption within five years after the 1990 oil shock caused by the 1990-1991 Gulf War, while the 2000 oil crisis was accompanied

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by structural change in 17 states. From 2003 to 2008 oil prices exhibited a pronounced

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upward trend and reached a peak in 2008. The oil price bubble collapsed in the second half of the 2008, coinciding with the onset of the Great Recession. However, we find only one

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structural break that we can associate with that year and not one break in the remaining

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part of the period under examination. When comparing the number of break dates obtained from the two-break tests occurring each year of the sample period, it becomes apparent that structural breaks in relative fossil fuel consumption are less frequent since the onset of the 1990s. [Insert Figure 2 here] Figure 2 presents the distribution of breaks across the time period analyzed. From Figure 2 one can notice a more pronounced clustering of breaks in the aftermath of 1979 and 2000 oil crisis. One can also observe that in more recent periods breaks are becoming less frequent. During the 1970s and 1980s each year witnessed on average 3.6 and 4.2 breaks in relative per capita fossil fuel consumption in U.S. states, respectively. However, in 17

ACCEPTED MANUSCRIPT the 1990s, structural breaks took place on average in 2.7 states each year, while in 2000s an average of 2.3 breaks occurred.

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5. Concluding Remarks

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In this study, we analyze the stochastic convergence of per capita fossil fuel consumption across the 50 U.S. states and the District of Columbia. In order to achieve this,

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we employ newly developed LM and RALS-LM unit root tests with endogenously determined trend-breaks. While the LM test depends only on the number of trend-shifts, thus containing

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no additional nuisance parameters associated with the break location, the RALS-LM test utilizes otherwise ignored information on non-normal errors to increase the power of the

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test. Thus, these unit root tests allow us to control for and utilize important components of the time series on relative per capita fossil fuel consumption. Increasing the power of the

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test is of particular importance in this context, as the sample size in most energy

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consumption convergence analysis is usually quite small and contains on average from 30 to 50 annual observations.

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Results from the two-break LM and RALS-LM unit root tests provide strong support for the presence of stochastic convergence of relative per capita fossil fuel consumption among the U.S. states and the District of Columbia. The two-break tests successfully reject the null hypothesis of a unit root in 46 out of 50 states and the District of Columbia, thus indicating the presence of stochastic convergence in per capita fossil fuel consumption. Out of those 46 states, in 40 states both trend-break locations are statistically significant. The one-break tests rejected the null hypothesis of a unit root in 4 out of 6 states for which twobreak tests also rejected the null hypothesis of a unit root, but thereby rendering one of the trend-breaks locations statistically insignificant. Moreover, one-break tests detected 4

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ACCEPTED MANUSCRIPT additional states for which we failed to reject the null hypothesis of a unit root with the twobreak test that yield relative per capita fossil fuel consumption stationary. Thus, after

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allowing for structural breaks, we were unable to reject the null hypothesis of a unit root only in the case of Nevada, while in the case of Hawaii and Tennessee, the results suggest

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that relative per capita fossil fuel consumption is stationary when allowing for two breaks. However, as one out of two breaks is statistically significant, there is ambiguity with regards

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to appropriateness of two-break test specification. After applying the no-break unit root

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test, the null hypothesis is also rejected for Hawaii and Tennessee, which in turn suggests that Nevada is the only state for which we fail to reject the null hypothesis of a unit root across the various unit root test specifications.

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As the inability to reject the null hypothesis of a unit root occurred only for one

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state, we have sufficient evidence to conclude that relative per capita fossil fuel consumption in 49 U.S. states and the District of Columbia exhibit convergence.

We can

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also conclude that shocks to relative per capita fossil fuel consumption in all states, except

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Nevada, should only yield temporary effects. Hence, the difference between state per capita fossil fuel consumption and average per capita fossil fuel consumption in all states, except Nevada, should be deterministic and predictable as the long-run forecast of that difference should tend to zero as the forecasting horizon increases, as noted by Fallahi and Voia (2015). The results of this study also demonstrate that policies at the federal and state level targeted at decreasing energy intensity, enhancing energy efficiency, and reducing carbon emissions from fossil fuels may have contributed to the stochastic convergence of relative per capita fossil fuel consumption across the U.S. states over time. Indeed, federal and state policies oriented toward the expansion of the renewable energy sector in the U.S. may also be a contributing factor in the convergence of relative per capita fossil fuel consumption as well. 19

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CR

IP T

Anoruo, E. and W.R. DiPietro (2014), “Convergence in Per Capita Energy Consumption using African Countries: Evidence from Sequential Panel Selection Methods,” International Journal of Energy Economics and Policy, 4, 568-577.

US

Barassi, M.R., M.A. Cole, and R.J.R. Elliott (2008), “Stochastic Divergence or Convergence of Per Capita Carbon Dioxide Emissions: Re-examining the Evidence,” Environmental and Resource Economics, 40, 121-137.

MA N

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ED

Baumol, W.J. (1986), “Productivity, Growth, Convergence, and Welfare: What the Long-Run Data Show,” American Economic Review, 76, 1072-1085.

PT

Carlino, C. A. and L. O. Mills (1993), “Are US Regional Incomes Converging?,” Journal of Monetary Economics, 32, 335-46.

CE

Csereklyei, Z. and D.I. Stern (2015), “Global Energy Use: Decoupling or Convergence?,” Energy Economics, 51, 633-641.

AC

Dincer, O., J.E. Payne, and K. Simkins (2014), “Are State Renewable Portfolio Standards Contagious,” American Journal of Economics and Sociology, 73, 325-340. Evans, P. (1996), “Using Cross-Country Variances to Evaluate growth Theories,” Journal of Economic Dynamics and Control, 20, 1027-1049. Evans, P. and G. Karras (1996), “Convergence Revisited,” Journal of Monetary Economics, 37, 249-265. Ezcurra, R. (2007), “Distribution Dynamics of Energy Intensities: A Cross-Country Analysis,” Energy Policy, 35, 5254-5259. Fallahi, F. and M. Voia (2015), “Convergence and Persistence in Per Capita Energy Use among OECD Countries: Revisited Using Confidence Intervals,” Energy Economics, forthcoming. Herrerias, M.J. (2012), “World Energy Intensity Convergence Revisited: A Weighted Distribution Dynamics Approach,” Energy Policy, 49, 383-399. Im, K.S. and P. Schmidt (2008), “More Efficient Estimation under Non-Normality when Higher Moments Do Not Depend on the Regressors, Using Residual-Augmented Least Squares,” Journal of Econometrics, 144, 219-233. 20

ACCEPTED MANUSCRIPT Jakob, M., M. Haller, and R. Marschinski (2012), “Will History Repeat Itself? Economic Convergence and Convergence in Energy Use Patterns,” Energy Economics, 34, 95-104. Kim, Y.S. (2015), “Electricity Consumption and Economic Development: Are Countries Converging to a Common Trend?,” Energy Economics, 49, 192-202.

IP T

Knittel, C.R. (2012), “Reducing Petroleum Consumption from Transportation,” Journal of Economic Perspectives, 26, 93-118.

CR

Lean, H.H., V. Mishra, and R. Smyth (2016), “Conditional Convergence in U.S. Disaggregated Petroleum Consumption at the Sector Level,” Applied Economics, forthcoming.

US

Lee, C.-C. and C.-P. Chang (2008), “New Evidence on the Convergence of Per Capita Carbon Dioxide Emissions from Panel Seemingly Unrelated Regression Augmented Dickey-Fuller Tests,” Energy, 33, 1468-1475.

MA N

Lee, J., Strazicich, M., Meng, M. (2012), “Two-Step LM Unit Root Tests with Trend-Breaks,” Journal of Statistical and Econometric Methods, 1(2), 81-107. Le Pen, Y. and B. Sevi (2010), “On the Non-Convergence of Energy Intensities: Evidence from a Pair-Wise Econometric Approach,” Ecological Economics, 69, 641-650.

ED

Liddle, B. (2009), “Electricity Intensity Convergence in IEA/OECD Countries: Aggregate and Sectoral Analysis,” Energy Policy, 37, 1470-1478.

PT

Liddle, B. (2010), “Revisiting World Energy Intensity Convergence for Regional Differences,” Applied Energy, 87, 3218-3225.

CE

List, J.A. (1999), “Have Air Pollutant Emission Converge Amongst U.S. Regions? Evidence form Unit Root Tests,” Southern Economic Journal, 66, 144-155.

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Markandya, A., S. Pedroso-Galinato, and D. Streimikrene (2006), “Energy Intensity in Transition Economies: Is There a Convergence towards the EU Average?,” Energy Economics, 28, 121-145. Maza, A. and J. Villaverde (2008), “The World Per Capita Electricity Consumption Distribution: Signs of Convergence?,” Energy Policy, 36, 4255-4261. Meng, M., J.E. Payne, and J. Lee (2013), “Convergence in Per Capita Energy Use Among OECD Countries,” Energy Economics, 36, 536-545. Meng, M., K. Im, J. Lee, and M. Tieslau (2014), “More Powerful LM Unit Root Tests with Nonnormal Errors,” A Festschrift in Honor of Peter Schmidt, Econometric Methods and Applications, Springer Pub. Co. Meng, M., J. Lee and J.E. Payne (2016), “RALS-LM Unit Root Test with Trend Breaks and NonNormal Errors: Application to the Prebisch-Singer Hypothesis,” Working paper. Mielnik, O. and J. Goldemberg (2000), “Converging to a Common Pattern of Energy Use in Developing and Industrialized Countries,” Energy Policy, 28, 503-508.

21

ACCEPTED MANUSCRIPT Miketa, A. and P. Mulder (2005), “Energy Productivity across Developed and Developing Countries in 10 Manufacturing Sectors: patterns of Growth and Convergence,” Energy Economics, 27, 429-453.

IP T

Mishra, V. and R. Smyth (2014), “Convergence in Energy Consumption Per Capita among ASEAN Countries,” Energy Policy, 73, 180-185.

CR

Mishra, V. and R. Smyth (2016), “Conditional Convergence in Australia’s Energy Consumption at the Sector Level”, Energy Economics, forthcoming. Mohammadi, H. and R. Ram (2012), “Cross-Country Convergence in Energy and Electricity Consumption, 1971-2007,” Energy Economics, 34, 1882-1887.

US

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MA N

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ED

Pesaran, H. (2007), “A simple panel unit root test in the presence of cross-section dependence,” Journal of Applied Econometrics, 22, 265-312.

PT

Roboredo, J.C. (2015), “Renewable Energy Contribution to the Energy Supply: Is There Convergence across Countries?,” Renewable and Sustainable Energy Reviews, 45, 290-295.

CE

Quah, D. (1996), “Empirics for Economic Growth and Convergence,” European Economic Review, 40, 1353-1375.

AC

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22

ACCEPTED MANUSCRIPT

Standard deviation

Minimum

Maximum

411.0

57.0

288.1

501.9

311.9

30.9

256.4

377.7

334.1

78.3

193.1

489.8

197.0

23.4

158.4

245.7

227.9

17.1

186.9

266.6

New Mexico

447.6

51.1

364.0

565.1

302.9

New York

170.6

23.1

131.9

220.0

413.8

North Carolina

227.4

21.1

168.9

264.3

70.7

243.4

North Dakota

725.2

230.0

334.4

964.5

17.5

167.2

241.3

Ohio

317.6

27.6

259.6

369.4

265.2

23.2

194.2

299.7

Oklahoma

418.5

19.5

369.3

460.8

228.2

24.5

176.4

267.9

Oregon

174.3

15.5

146.3

208.4

Idaho

184.4

28.6

149.5

243.6

299.4

25.6

260.2

358.8

Illinois

273.8

31.5

237.8

335.2

Rhode Island

174.5

27.9

124.2

233.5

Indiana

449.2

26.8

387.3

PT

Pennsylvania

496.1

South Carolina

238.9

18.4

204.7

278.7

Iowa

323.2

36.0

266.7

396.1

South Dakota

245.4

21.0

199.7

277.3

Kansas

401.0

29.8

335.2

492.8

Tennessee

276.8

25.4

207.4

318.0

Kentucky

404.4

41.4

338.9

460.5

Texas

561.7

69.2

416.6

680.8

Louisiana

825.8

68.0

AC

Table 1. Descriptive Statistics of Fossil Fuel Consumption Per Capita (in millions of Btus) State

Mean

Standard deviation

Minimum

Maximum

Alabama

372.7

30.0

299.5

412.1

Montana

Alaska

908.7

196.0

566.5

1171.0

Nebraska

Arizona

233.4

26.0

190.0

293.2

Nevada

Arkansas

305.3

18.0

266.8

343.3

New Hampshire

California

192.7

30.5

147.6

252.6

New Jersey

Colorado

278.8

17.5

247.5

312.5

Connecticut

173.9

51.1

104.5

Delaware

330.7

61.2

192.1

District of Columbia

127.9

39.0

Florida

202.3

Georgia Hawaii

688.7

992.2

Utah

346.0

33.5

280.3

397.2

Maine

223.9

31.1

162.7

296.9

Vermont

151.5

15.5

113.1

180.6

Maryland

207.2

28.7

144.2

275.7

Virginia

216.1

19.9

173.8

252.8

Massachusetts

199.7

25.8

146.5

256.5

West Virginia

198.6

21.3

153.1

243.1

Michigan

269.0

22.3

221.8

313.3

Washington

656.9

56.7

544.0

763.3

Minnesota

264.7

20.6

221.8

294.1

Wisconsin

255.2

16.9

223.9

280.8

Mississippi

300.8

26.7

252.7

357.4

Wyoming

1304.2

238.1

837.2

1586.9

Missouri

290.3

18.1

261.6

319.9

Mean

CE

ED

MA

NU

SC RI

PT

State

23

ACCEPTED MANUSCRIPT

Table 2. Two-Break LM and RALS-LM Unit Root Test Results RALS-LM LM RALS-LM TB k TB 2 2 State τ*LM τ*RALS−LM δ State τ*LM τ*RALS−LM δ Alabama -5.92*** -6.07*** 0.94 1980 1993 2 Montana -5.89*** -6.65*** 0.81 1981 1998 Alaska -5.99*** -6.13*** 0.93 1980 1984 3 Nebraska -3.88 -3.89 0.96 1990n 2006 Arizona -6.91*** -7.80*** 0.72 1984 1996 5 Nevada -3.28 -3.46 0.96 1977 2005n Arkansas -5.66*** -5.21*** 0.96 1979 1987 3 New Hampshire -4.13 -4.05 0.99 2001 2004 -7.24*** -7.11*** 0.95 0 -5.77*** -4.49** 0.94 California New Jersey 1980 1998 1978 1993 Colorado -4.30 -4.27* 0.96 1999 2002 4 New Mexico -4.73** -6.98*** 0.55 1978 1984 Connecticut -4.78** -6.27*** 0.55 1982 1990 0 New York -6.92*** -7.50*** 0.73 1981 1998 Delaware -5.81*** -6.36*** 0.74 1977 1986 1 North Carolina -4.41* -4.19* 0.99 1977 2004 District of Columbia -4.75** -4.25** 0.86 1982 1992n 3 North Dakota -3.92 -3.91 0.97 1977 1987 Florida -6.05*** -6.26*** 0.92 1980 1985 0 Ohio -6.05*** -6.02*** 0.96 1980 1994 Georgia -4.92** -5.36*** 0.67 1986 2001 6 Oklahoma -6.30*** -6.92*** 0.77 1983 2003 -4.92** -3.79* 0.71 6 -4.33 -4.06* 0.95 Hawaii Oregon 1987n 1999 1996 1999 Idaho -5.47*** -5.49*** 0.92 1987 2001 5 Pennsylvania -5.42*** -5.90*** 0.83 1980 1983 Illinois -5.36** -5.36*** 0.88 1977 1991 6 Rhode Island -6.01*** -7.96*** 0.55 1989 1998 Indiana -3.89 -4.84*** 0.75 1981 1985 0 South Carolina -5.63*** -5.33*** 0.86 1991 2002 Iowa -5.46*** -4.69** 0.92 1982 1991 3 South Dakota -6.51*** -7.15*** 0.70 1984 1997 Kansas -6.36*** -6.50*** 0.81 1984 2000 3 Tennessee -5.08** -5.11*** 0.90 1989 2001n Kentucky -6.04*** -7.86*** 0.65 1978 1989 0 Texas -4.07 -3.68 0.89 2003 2008 -5.88*** -6.03*** 0.88 5 -4.71** -4.82** 0.94 Louisiana Utah 1987n 1999 1985 1989 Maine -5.09** -6.57*** 0.54 1981 1984 3 Vermont -6.18*** -8.54*** 0.41 1989 2003 Maryland -5.87*** -6.63*** 0.63 1978 1991 6 Virginia -4.55* -4.73** 0.93 1980 2006 Massachusetts -5.37*** -4.87*** 0.84 1982 1996 6 West Virginia -4.44* -5.40*** 0.78 1982n 2000 Michigan -4.96** -5.27*** 0.85 1983n 2004 5 Washington -6.00*** -6.02*** 0.96 1993 2007 Minnesota -2.40 -3.86** 0.41 1977 1981 0 Wisconsin -6.22*** -5.97*** 0.99 1993 2004 Mississippi -7.15*** -7.63*** 0.84 1997 2002 0 Wyoming -7.71*** -6.83*** 0.96 1982 1991 Missouri -5.68** -6.68*** 0.78 1983 1999 5 Notes: since LM test and RALS-LM test share the same procedure when searching for the break point and the corresponding optimal lags, we only report one time to save the space; as maxF can detect the break with 100 percent accuracy when break is relatively large, we use exogenous critical values (for details see Lee et al. 2012); k is the optimal number of lagged firstdifferenced terms; TB denotes the estimated break point; n denotes that the identified break point was not significant at the 10% level. τ*LM and τ*RALS−LM denote the test statistics for the LM and RALS-LM tests, respectively (since we use transformed test, the test statistics are invariant to the location of trend breaks); *, ** and *** denote the test statistic is significant at 10%, 5% and 1% levels, respectively.

AC

CE

PT

ED

MA

NU

SC RI

PT

LM

24

k 6 0 0 0 6 6 5 3 0 3 3 3 3 5 1 4 5 1 5 6 0 6 1 0 0

ACCEPTED MANUSCRIPT

Table 3. One-Break LM and RALS-LM Unit Root Test Results

AC

CE

PT

ED

MA

NU

SC RI

PT

LM RALS-LM LM RALS-LM TB k TB k 2 2 State τ*LM τ*RALS−LM δ State τ*LM τ*RALS−LM δ Alabama -5.13*** -5.26*** 0.79 1990 2 Montana -3.18 -3.36 0.87 2007 1 Alaska -2.44 -2.22 0.52 2004 0 Nebraska -2.64 -3.50* 0.80 2006 0 Arizona -4.02** -3.97** 0.98 1991 5 Nevada -2.80 -1.96 0.71 2008 5 Arkansas -3.65 -3.59* 0.93 1981 5 New Hampshire -4.21** -3.37 0.99 2001 1 -3.52 -3.90*** 0.45 1993 4 -4.95*** -4.98*** 0.88 1980 3 California New Jersey Colorado -4.29** -4.73*** 0.80 1999 2 New Mexico -4.34** -3.98** 0.96 2001 6 Connecticut -3.42 -3.03 0.86 1983 0 New York -3.29 -3.45* 0.95 1993 5 Delaware -4.51** -5.22*** 0.65 1995 1 North Carolina -4.18** -4.41*** 0.82 2004 3 District of Columbia -3.26 -3.63** 0.70 1982 3 North Dakota -4.40** -4.25** 0.98 2001 4 Florida -4.20** -3.48* 0.94 1996 0 Ohio -3.09 -4.47*** 0.39 1987 3 Georgia -2.36 -1.53 0.77 1986 0 Oklahoma -3.89* -4.42*** 0.85 2003 3 -3.62 -2.86 0.90 2006 2 -4.84*** -5.51*** 0.69 1989 3 Hawaii Oregon Idaho -4.23** -4.99*** 0.58 1993 6 Pennsylvania -2.09 -0.90 0.69 2000 2 Illinois -3.67 -4.01** 0.81 1997 5 Rhode Island -2.76 -2.68 0.83 1983 0 Indiana -3.83* -4.47*** 0.73 2000 6 South Carolina -3.89* -3.71* 0.99 2002 0 Iowa -4.37** -4.65*** 0.67 1991 3 South Dakota -5.49*** -5.76*** 0.92 1984 4 Kansas -3.77* -3.61* 0.98 1986 0 Tennessee -1.78 -2.37 0.50 2005 6 Kentucky -4.58** -4.50*** 0.99 1978 0 Texas -3.74* -3.54* 0.86 1983 6 -4.00** -4.51*** 0.80 2004 5 -3.30 -2.82 0.77 1985 1 Louisiana Utah Maine -4.43** -4.15** 0.92 1982 6 Vermont -1.70 -1.65 0.68 1986 6 Maryland -3.85* -3.75* 0.98 1991 6 Virginia -3.75* -3.72** 0.53 1990 4 Massachusetts -4.15** -2.82 0.83 1989 6 West Virginia -3.53 -3.47* 0.97 2000 2 Michigan -4.21** -3.56* 0.95 2004 5 Washington -5.27*** -5.26*** 0.64 2001 1 Minnesota -3.38 -5.69*** 0.30 1997 5 Wisconsin -3.76* -6.17*** 0.45 1983 6 Mississippi -5.18*** -5.32*** 0.91 1997 3 Wyoming -5.69*** -5.19*** 0.98 1989 0 Missouri -3.52 -3.30* 0.71 1999 5 Notes: since LM test and RALS-LM test share the same procedure when searching for the break point and the corresponding optimal lags, we only report one time to save the space; as maxF can detect the break with 100 percent accuracy when break is relatively large, we use exogenous critical values (for details see Lee et al. 2012); k is the optimal number of lagged firstdifferenced terms; TB denotes the estimated break point; n denotes that the identified break point was not significant at the 10% level. τ* LM and τ*RALS−LM denote the test statistics for the LM and RALS-LM tests, respectively (since we use transformed test, the test statistics are invariant to the location of trend breaks); *, ** and *** denote the test statistic is significant at 10%, 5% and 1% levels, respectively.

25

ACCEPTED MANUSCRIPT

0.93 0.56 0.93 0.65 0.57 0.68 0.91 0.68 0.82 0.79 0.93 0.34 0.87 0.95 0.95 0.90 0.91 0.97 0.88 0.92 0.78 0.53 0.98 0.51 0.64 0.98

3 0 4 5 1 0 0 2 0 0 0 5 4 3 6 0 2 1 4 0 5 6 5 0 1 0

SC RI

-0.49 -1.16 -2.28 -5.09*** -1.28 -1.54 -1.82 -2.65 -2.18 -2.27 -1.24 -4.53*** -2.61 -1.52 -1.77 -1.25 -0.91 -1.46 -3.25** -2.22 -1.50 -3.80*** -4.45*** -2.51 -1.89 -1.62

State Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia West Virginia Washington Wisconsin Wyoming

NU

-0.54 -1.64 -1.89 -3.94*** -1.39 -1.87 -1.99 -1.50 -1.67 -2.86 -1.63 -3.32** -2.29 -1.21 -1.97 -1.59 -1.22 -1.44 -3.05 -2.55 -2.25 -2.61 -4.60*** -1.53 -1.41 -1.49

δ

MA

4 0 0 5 1 0 0 2 2 0 0 0 0 4 1 0 2 1 4 0 0 0 5 0 1 0

τ*RALS−LM

k

ED

τ*LM

2

PT

-1.07 -2.73* -1.81 -3.21** -2.41 -2.83* -1.23 -0.32 -1.44 -1.72 0.2 -1.68 -3.09** -2.48 -3.47** -0.09 -1.07 -1.79 -3.48** -2.98** 0.01 -2.38 -1.73 -2.21 0.06 -1.48

k

RALS-LM

CE

State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri

τADF

LM

AC

ADF

PT

Table 4. ADF and No-Break LM and RALS-LM Unit Root Test Results ADF

LM

RALS-LM

τ*LM

k

τ*LM

τ*RALS−LM

-1.59 0.68 0.19 -2.78* -2.12 -2.44 -2.77* -0.29 -5.31*** -2.46 -1.74 -3.51** -2.14 -2.17 -1.96 -0.89 0.3 -1.35 -3.63*** -4.23*** -2.40 -1.55 -3.32** -2.61* -2.59

0 0 6 1 0 6 6 3 0 2 0 0 2 0 0 0 1 1 1 2 0 0 0 0 2

-2.97 -1.94 -0.71 -1.90 -2.93* -3.46** -1.78 -2.66 -2.60 -1.71 -1.82 -2.61 -1.15 -1.96 -1.99 -2.42 -2.89* -2.30 -2.65 -2.29 -1.78 -2.41 -3.16** -2.61 -1.41

-3.23** -1.85 -0.88 -2.14 -3.45** -4.55*** -2.21 -3.90*** -2.57 -1.89 -2.50 -2.46 -0.34 -1.75 -1.69 -2.44 -3.33** -1.92 -1.67 -2.35 -2.73* -2.11 -3.28** -2.73 -3.05**

k

2

δ

0.91 0.83 0.39 0.64 0.60 0.70 0.87 0.58 0.99 0.83 0.77 0.96 0.63 0.85 0.91 0.75 0.91 0.88 0.83 0.98 0.53 0.92 0.84 0.92 0.57

1 5 5 1 3 0 0 3 3 0 0 0 2 0 0 0 0 1 5 0 0 0 0 0 3

Notes: k is the optimal number of lagged first-differenced terms. τADF represents the augmented Dickey–Fuller statistic while τLM and τRALS−LM denote the test statistics for the LM and RALS-LM tests, respectively. *, ** and *** denote the test statistic is significant at the 10%, 5% and 1% levels, respectively.

26

ACCEPTED MANUSCRIPT Figure 1. Log of Relative Per Capita Fossil Fuel Consumption with Two Trend Breaks 0.200

1.2

0.175

1.1

0.150

1.0

T

0.125 0.9 0.100

IP

0.8 0.075 0.7

CR

0.050 0.6

0.025

0.5

0.000 -0.025

0.4

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

NU S

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- ALABAMA

- ALASKA

-0.1

0.05

-0.00

MA

-0.2

-0.05

-0.3

-0.10

ED

-0.4

-0.5

PT

-0.6

-0.15

-0.20

-0.25

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

CE

- ARIZONA

-0.2

AC

-0.3

-0.4

-0.5

-0.6

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- ARKANSAS

-0.075 -0.100 -0.125 -0.150 -0.175 -0.200 -0.225 -0.250

-0.7 -0.275 -0.8

-0.300 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- CALIFORNIA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- COLORADO

27

ACCEPTED MANUSCRIPT

-0.0

0.3 0.2

-0.2 0.1 -0.4

-0.0

T

-0.1 -0.6

-0.8

IP

-0.2 -0.3

-0.5 -1.2

-0.6 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- DELAWARE

NU S

- CONNECTICUT

CR

-0.4 -1.0

-0.25

-0.35

-0.40

-0.50

MA

-0.45

-0.75

-0.50

-1.00

ED

-0.55

-1.25

-1.50

-0.60

-0.65

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- DISTRICT OF COLUMBIA

CE

-0.0

-0.1

AC

-0.2

-0.3

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- FLORIDA

-0.20

-0.25

-0.30

-0.35

-0.40

-0.45

-0.50

-0.4 -0.55

-0.5

-0.60 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- GEORGIA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- HAWAII

28

ACCEPTED MANUSCRIPT

-0.2

-0.00

-0.05 -0.3 -0.10 -0.4

-0.20

IP

-0.5

T

-0.15

-0.25 -0.6 -0.30

CR

-0.7 -0.35

-0.8

-0.40 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- ILLINOIS

NU S

- IDAHO

0.34

0.20

0.15

0.32

0.10

MA

0.30

0.05

0.28

-0.00

-0.05

0.26

ED

-0.10 0.24

0.22

-0.15

-0.20

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- INDIANA

CE

0.40

0.35

0.30

AC

0.25

0.20

0.15

0.10

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- IOWA

0.30

0.25

0.20

0.15

0.10 0.05

0.00

0.05 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- KANSAS

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- KENTUCKY

29

ACCEPTED MANUSCRIPT

1.10

-0.1

1.05

-0.2

1.00 -0.3

T

0.95 -0.4

IP

0.90 -0.5 0.85

0.75

CR

-0.6

0.80

-0.7 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- MAINE

NU S

- LOUISIANA

-0.2

-0.2

-0.3

-0.3

-0.4

MA

-0.4

-0.5

-0.5

-0.6

ED

-0.6

-0.7

-0.8

-0.7

-0.8

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- MARYLAND

CE

-0.05

-0.10

AC

-0.15

-0.20

-0.25

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- MASSACHUSETTS

-0.150

-0.175

-0.200

-0.225

-0.250

-0.275

-0.300

-0.30 -0.325

-0.35

-0.350 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- MICHIGAN

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- MINNESOTA

30

ACCEPTED MANUSCRIPT

0.10

-0.075

-0.100

0.05

-0.125 -0.00 -0.150

T

-0.05 -0.175

IP

-0.10 -0.200 -0.15

-0.250

-0.25

-0.275 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- MISSOURI

NU S

- MISSISSIPPI

CR

-0.225 -0.20

0.4

0.3

0.2

0.3

MA

0.1

0.2

0.0

0.1

ED

-0.1

0.0

-0.1

-0.2

-0.3

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- MONTANA

CE

0.4 0.3 0.2

AC

0.1 -0.0 -0.1 -0.2 -0.3

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NEBRASKA

-0.30

-0.35

-0.40

-0.45

-0.50

-0.55

-0.60

-0.65

-0.4 -0.5

-0.70 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NEVADA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NEW HAMPSHIRE

31

ACCEPTED MANUSCRIPT

-0.20

0.55 0.50

-0.25 0.45 -0.30

0.40

T

0.35 -0.35

-0.40

IP

0.30 0.25

0.15 -0.50

0.10 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NEW MEXICO

NU S

- NEW JERSEY

CR

0.20 -0.45

-0.4

-0.25

-0.30

-0.5

MA

-0.35

-0.6

-0.40

-0.45

-0.7

ED

-0.50

-0.8

-0.9

-0.55

-0.60

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- NEW YORK

CE

1.2

1.0

AC

0.8

0.6

0.4

0.2

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NORTH CAROLINA

0.10

0.05

-0.00

-0.05

-0.10

-0.15

0.0

-0.20 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- NORTH DAKOTA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- OHIO

32

ACCEPTED MANUSCRIPT

0.325

-0.45

0.300 -0.50 0.275 0.250

-0.55

T

0.225 -0.60

0.175

IP

0.200 -0.65

0.150

CR

-0.70 0.125 0.100

-0.75 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- OREGON

NU S

- OKLAHOMA

0.05

-0.3

-0.4

-0.00

-0.5

MA

-0.05

-0.6

-0.10

-0.7

-0.15

ED

-0.8

-0.20

-0.25

-0.9

-1.0

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- PENNSYLVANIA

CE

-0.225 -0.250 -0.275

AC

-0.300 -0.325 -0.350 -0.375 -0.400

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- RHODE ISLAND

-0.10

-0.15

-0.20

-0.25

-0.30

-0.35

-0.40

-0.45

-0.425 -0.450

-0.50 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- SOUTH CAROLINA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- SOUTH DAKOTA

33

ACCEPTED MANUSCRIPT

-0.05

0.8

-0.10

0.7

-0.15 0.6

T

-0.20 0.5

IP

-0.25 0.4 -0.30

-0.40

CR

0.3

-0.35

0.2 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- TEXAS

NU S

- TENNESSEE

0.20

-0.60

-0.65

0.15

-0.70

MA

0.10

-0.75

0.05

-0.80

-0.85

0.00

ED

-0.90 -0.05

-0.10

-0.95

-1.00

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- UTAH

-0.35

-0.40

-0.45

-0.50

AC

-0.30

CE

-0.25

-0.55

-0.35

-0.40

-0.45

-0.50

-0.55

-0.60

-0.65

-0.70

-0.60

-0.75 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- VIRGINIA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- VERMONT

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- WEST VIRGINIA

34

ACCEPTED MANUSCRIPT

0.80

-0.150 -0.175

0.75 -0.200 0.70

-0.225

T

-0.250 0.65

0.60

IP

-0.275 -0.300

-0.350 0.50

-0.375 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

- WISCONSIN

NU S

- WASHINGTON

CR

-0.325 0.55

1.6

1.5

MA

1.4

1.3

1.2

ED

1.1

1.0

0.9

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

PT

- WYOMING

6

AC

7

CE

Figure 2. Occurrence of Structural Breaks in Relative Per Capita Fossil Fuels Consumption (Two Break Cases)

5 4 3 2 1

2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977

0

35