Research ArticleVECM Model Analysis of Carbon Emissions GDP andInternational Crude Oil Prices

Xiaohua Zou

Changzhou College of Information Technology Changzhou 213100 China

Correspondence should be addressed to Xiaohua Zou xhuazou163com

Received 14 March 2018 Revised 23 June 2018 Accepted 4 July 2018 Published 1 August 2018

Academic Editor Emilio Jimenez Macıas

Copyright copy 2018 Xiaohua ZouThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

As a kind of scarce natural capital energy makes more and more obvious constraint effects on economic growth And energyconsumption is the major source of greenhouse gas emissions This brings about the problems of the relationships among energyconsumption carbon emissions and economic growth which is worthy of long-term attention This paper attempted to explorethe interactive relations among American oil prices carbon emissions and GDP through the data analysis from 1983 to 2013 Thispaper adopted time series vector error correction model (VECM) approach to conduct stationarity test cointegration test stabilitytest and Granger causality test The results indicated that no matter in the short term or long term oil price fluctuation is thereason why carbon emissions change while the GDP fluctuation is not the reason for the growth of carbon emissionsThe oil priceimpacts will have a great influence on GDP and carbon emissions in the short term but the in long term the influence will tendto be gentle

1 Introduction

Global warming caused by greenhouse effect has become oneof the major concerns for human survival Some scientistspredict that if humans do not take immediate measures toreduce greenhouse gas emissions it is possible that surfacetemperature of the earth will increase by 4∘C as early as2050 This can lead to adverse weather and sea level rise ofat least dozens of meters And series of catastrophes maybring about the coming of ldquothe end of the worldrdquo describedin movies Some researches show that greenhouse effectmainly attributes to excessive use of fossil energy in modernindustrial society and themassive emission of carbon dioxidegas into the atmosphere

Since the 1990s the international community had recog-nized the seriousness of global warming issue and arguedthat the reduction of greenhouse gas emissions especiallyCO2 is the best way to solve global climatic and ecolog-ical issues And some measures gradually come into usein order to reduce carbon emissions However economicdevelopment cannot be separated from energy consumptionAs a kind of scarce natural capital energy presents moreand more obvious constraint effects on economic growth

And energy consumption is the major source of green-house gas emissions This brings about the problems ofthe relationships among energy consumption carbon emis-sions and economic growth which is worthy of long-termattention

Empirical study on the relationship between energyconsumption and economic growth began in the 1970sJ Kraft and A Kraft [1] firstly conducted a pioneeringresearch on the relationship between energy consumptionand economic growth in 1978 based on the data of the USfrom 1947 to 1974 and found the one-way causal relationshipbetween GNP and energy consumption namely economicgrowth could drive the increase of energy consumptionAt present common research methods adopted to studyon this issue can be mainly classified into two categoriesThe first one is the Kuznets curve method For exampleHiroki Iwata et al [2] proved the existence of invertedldquoUrdquo type ldquoenvironmental Kuznets curve (EKC)rdquo throughan empirical analysis of Francersquos carbon dioxide emissionsWu Zhenxin et al [3] supplemented the factor of industrialstructure based on environmental Kuznets curve (EKC) andestablished the individual fixed effect model based on thepanel data of 30 provinces in China from 2000 to 2009

HindawiDiscrete Dynamics in Nature and SocietyVolume 2018 Article ID 5350308 11 pageshttpsdoiorg10115520185350308

2 Discrete Dynamics in Nature and Society

to explore the effects of economic growth and industrialstructure on carbon emissions The results showed that thererespectively existed cointegration relations between carbonemissions and economic growth as well as between carbonemissions and industrial structure the relationship betweencarbon emissions and economic growth presented invertedldquoUrdquo type characteristics Lin Boqiang et al [4] put forward theKuznets curve of CO2 emissions by the method of time seriesanalysis and forecast Chinarsquos CO2 emissions in the futureRen Zhong and Zhou Yunbo [5] investigated the relationshipbetween per capita GDP and industrial waste gas emissionsin the Bohai Rim region and argued that the relationshipbetween the two factors showed overall upward inverted ldquoNrdquotype curve characteristics

The second one is the regression model method Forinstance Ugur Soytas et al [6] studied the Granger causalityrelationships among the US income energy consumptionand carbon emissions based on the Vector AutoregressionModel (VAR) In this model labor force and gross fixedcapital were taken into account It was found that in the longrun income is not the Granger cause of carbon emissionsso income itself could not become a means to solve environ-mental problems Niaz Bashiri Behmiri et al [7] discussedthe influences of changes in crude oil prices natural gasprices coal prices and electricity prices on carbon dioxideemission quota price distribution in the US on the basisof the quantile regression model It was indicated that inthe condition of high carbon prices the price increasingof crude oil would cause the sharp drop in carbon pricesShawka Hammoudeh et al [8] utilized VAR and VECM(vector error correction model) to analyze the short-termdynamic influence of changes in oil prices coal prices naturalgas prices electricity prices and carbon emissions quota oncarbon emissions prices One important found conclusion isthat a positive impact of the crude oil price will produce anegative effect on the approved price of carbon emissionsMeanwhile they discovered that energy price impacts willhave continual influence on the approved price of carbonemissions Rajaratnam Shanthini [9] demonstrated the long-term equilibrium relationship between CO2 emissions andGDP (ie 1 increase in GDP led to 32 increase in CO2emissions) via marginal testing method of the autoregres-sive distributed lag model Furthermore it was revealedthat long-term decrease of CO2 emissions was related toprice increasing of crude oil and technical progress despitetheir small extent Min Jisheng and Hu Hao [10] examinedthe dynamic evolution relationship between Chinarsquos carbonemissions and economic growth between 1994 and 2007 bymeans of the VAR method and proposed that economicgrowth was the main reason of carbon emission increasingEconomic growth led to the rising of carbon emissionsand the increasing of carbon emissions reversely inhibitedthe rate of economic growth with certain lag period JingLuo [11] conducted an empirical research on the alterablerelation between Chinarsquos per capita GDP and carbon dioxideemissions He adopted the time series data from 1978 to2008 on the basis of the optimal regression model toreveal the long-term and short-term influence of Chinarsquoseconomic growth on carbon dioxide emissions Fu Jiafeng

[12] examined the correlation between CO2 emissions perunit of GDP and GDP per capita collecting the panel dataof 44 countries between 1990 and 2004 The study indicatedthat EKC existed between the two factors Han Yujun [13]carried out an empirical analysis based on the data from 165countries andmaintained that EKCdiffered among countrieswith different income levels Zhang Xingping et al [14]utilized the multivariable model considering the economicgrowth energy usage carbon emissions capital and citypopulation to survey the existence and effects of Grangercausal relationships among Chinarsquos economic growth energyconsumption and carbon emissions The research showedthat within the past 47 years in China the economic growthwas not caused by carbon emissions or energy consumptionFrom this it can be presumed that the conservative energypolicies and emission reduction policies which adopted byChinese government will not impede the economic growthin the long run

It can be seen that regression models are commonlyutilized to study energy and economy problems and researchcontents mostly concentrate upon the correlation amongenergy consumption carbon prices carbon emissions quotaand other aspects However there is no relevant literaturewhich directly studies the three aspects of actual carbonemissions oil prices and GDP Therefore this paper tookthe US as an example to study volatility transmission mech-anism of a closed economy and the interactive relationshipsamong oil prices GDP and carbon emissions with the VECmodel Primary energy carbon emissions gross domesticproduct (GDP) and international crude oil prices from1983 to 2013 in the US were selected as sample data toevaluate whether there was cointegration relationship basedon the VAR model and the VEC model was also built Inthis paper the main study objectives were as follows Ato analyze whether the three variables have cointegrationrelationship ie whether there is a long-term equilibriumrelationship B to test whether there is a causal relation-ship among the three variables C to establish an impulseresponse function to describe short-term dynamic relation-ship over time among the three variables based on the VECmodel

2 VECM

Modern econometricians point out a method to establish therelational model among economic variables in a nonstruc-tural way They are vector autoregressive model (VAR) andvector error correction model (VEC)

The VAR model is established based on the statisticalproperties of data In the VAR model each endogenousvariable in the system is considered as the lagged valueof all endogenous variables in the system thus the uni-variate autoregressive model is generalized to the ldquovec-torrdquo autoregressive model consisting of multivariate timeseries variables In 1980 Sims (Christopher Sims) intro-duced VAR model into economic field and promoted thewidespread application in dynamic analysis of economicsystem

Discrete Dynamics in Nature and Society 3

Engle and Granger combined cointegration and errorcorrection models to establish the trace error correctionmodel As long as there is a cointegration relationshipbetween variables the error correction model can be derivedfrom the autoregressive distributed lag model And eachequation in the VAR model is an autoregressive distributedlagmodel therefore it can be considered that the VECmodelis a VARmodel with cointegration constraints Because thereis a cointegration relationship in the VECmodel when thereis a large range of short-term dynamic fluctuation VECexpressions can restrict long-term behavior of the endoge-nous variables and be convergent to their cointegrationrelation

Assuming yt = (y1t y2t ykt)1015840 as k-dimensionalstochastic time series t = 1 2 T and yt sim I(1) eachyit sim I(1) i = 1 2 k is affected by exogenous time seriesof d-dimension xt = (x1t x2t xdt)1015840 then the VAR modelcan be established as follows119910119905 = 1198601119910119905minus1 + 1198602119910119905minus2 + sdot sdot sdot + 119860119901119910119905minus119901 + 119861119909119905 + 120583119905

119905 = 1 2 119879 (1)

If yt is not affected by exogenous time series of d-dimension xt = (x1t x2t xdt)1015840 then the VAR model offormula (1) can be written as follows

119910119905 = 1198601119910119905minus1 + 1198602119910119905minus2 + sdot sdot sdot + 119860119901119910119905minus119901 + 120583119905119905 = 1 2 119879 (2)

With cointegration transformation of formula (2) we canget that

998779119910119905 = prod119910119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (3)

where

prod =119901

sum119894=1

119860 119894 minus 119868

Γ119894 = minus119901

sum119895=119894+1

119860119895(4)

If yt has cointegration relationship thenprod ytminus1 sim I(0) andformula (3) can be written as follows

998779119910119905 = 1205721205731015840119910119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (5)

where 1205731015840ytminus1 = ecmtminus1is the error correction termwhich reflects long-term equilibrium relationships betweenvariables and the above formula can be written as follows

998779119910119905 = 120572119890119888119898119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (6)

Formula (6) is the vector error correction model(VECM) in which each equation is an error correctionmodel

Table 1 Unit root test results of sequence level values

Variable ADF PPLevel Level

119888119901119905 -2403899(01492) -4542207(00003)119900119901119905 -0557236(08746) -0413474(09022)119892119889119901119905 1983083(09999) 2061330(09999)

Table 2 Unit root test results of sequence first-order difference

Variable ADF PPLevel Level

119897119888119901119905 -5894742(00000) -3603728(00001)119897119900119901119905 -1005132(00000) -9229024(00000)119897119892119889119901119905 -4615071(00002) -7242270(00000)

3 The Causal Relationship betweenCarbon Emissions International Crude OilPrices and GDP

31 Data Source This paper selected the conversion pricesof international crude oil and the domestic annual primaryenergy carbon emissions of the US to make an empiricalanalysis Since the carbon emissions are converted by yearaccording to the energy consumption and current veri-fiable carbon emissions are calculated by year in orderto maintain the consistency of data sequences this papercalculated the carbon emissions into the quarterly primaryenergy consumption since 1983 In addition internationalcrude oil price data in each trading day were unfixedTherefore in order to ensure the consistency of sampledata the adopted international crude oil prices in thispaper come from quarterly conversation data of CrudeOil Prices in EIA (Energy Information Administration)database GDP quarterly data also come from EIA Thesample interval ranges from June 1983 to December 2013The data source is shown in the following links pri-mary energy consumption data of America comes fromhttpswwweiagovtotalenergydataannual internationalcrude oil prices data comes from httpswwweiagovpetroleumdataphpprices

32 Empirical Test

321 Stationarity Test The commonly accepted ADF (Aug-mentedDickey-Fuller) andPP (Phillips-Perron) unit root testare adopted to stationary test of carbon emissions (119862119875) oilprices (119874119875) andGDP (119866119863119875) seriesThe test results are shownin Table 1

The test results in Table 1 show that level value of thethree sequences is nonstationary and further test indicatesthat 119888119901 119900119901 and 119892119889119901 sequences are first-order differencestationary In order to reduce the fluctuations of the datafirst-order difference is made on the three sequences Thenthree new series 119897119888119901 119897119900119901 and 119897119892119889119901 are obtained and their unitroot test results are shown in Table 2

Discrete Dynamics in Nature and Society 3

Engle and Granger combined cointegration and errorcorrection models to establish the trace error correctionmodel As long as there is a cointegration relationshipbetween variables the error correction model can be derivedfrom the autoregressive distributed lag model And eachequation in the VAR model is an autoregressive distributedlagmodel therefore it can be considered that the VECmodelis a VARmodel with cointegration constraints Because thereis a cointegration relationship in the VECmodel when thereis a large range of short-term dynamic fluctuation VECexpressions can restrict long-term behavior of the endoge-nous variables and be convergent to their cointegrationrelation

Assuming yt = (y1t y2t ykt)1015840 as k-dimensionalstochastic time series t = 1 2 T and yt sim I(1) eachyit sim I(1) i = 1 2 k is affected by exogenous time seriesof d-dimension xt = (x1t x2t xdt)1015840 then the VAR modelcan be established as follows119910119905 = 1198601119910119905minus1 + 1198602119910119905minus2 + sdot sdot sdot + 119860119901119910119905minus119901 + 119861119909119905 + 120583119905

119905 = 1 2 119879 (1)

If yt is not affected by exogenous time series of d-dimension xt = (x1t x2t xdt)1015840 then the VAR model offormula (1) can be written as follows

119910119905 = 1198601119910119905minus1 + 1198602119910119905minus2 + sdot sdot sdot + 119860119901119910119905minus119901 + 120583119905119905 = 1 2 119879 (2)

With cointegration transformation of formula (2) we canget that

998779119910119905 = prod119910119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (3)

where

prod =119901

sum119894=1

119860 119894 minus 119868

Γ119894 = minus119901

sum119895=119894+1

119860119895(4)

If yt has cointegration relationship thenprod ytminus1 sim I(0) andformula (3) can be written as follows

998779119910119905 = 1205721205731015840119910119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (5)

where 1205731015840ytminus1 = ecmtminus1is the error correction termwhich reflects long-term equilibrium relationships betweenvariables and the above formula can be written as follows

998779119910119905 = 120572119890119888119898119905minus1 +119901minus1

sum119894=1

Γ119894998779119910119905minus119894 + 120583119905 (6)

Formula (6) is the vector error correction model(VECM) in which each equation is an error correctionmodel

Table 1 Unit root test results of sequence level values

Variable ADF PPLevel Level

119888119901119905 -2403899(01492) -4542207(00003)119900119901119905 -0557236(08746) -0413474(09022)119892119889119901119905 1983083(09999) 2061330(09999)

Table 2 Unit root test results of sequence first-order difference

Variable ADF PPLevel Level

119897119888119901119905 -5894742(00000) -3603728(00001)119897119900119901119905 -1005132(00000) -9229024(00000)119897119892119889119901119905 -4615071(00002) -7242270(00000)

3 The Causal Relationship betweenCarbon Emissions International Crude OilPrices and GDP

31 Data Source This paper selected the conversion pricesof international crude oil and the domestic annual primaryenergy carbon emissions of the US to make an empiricalanalysis Since the carbon emissions are converted by yearaccording to the energy consumption and current veri-fiable carbon emissions are calculated by year in orderto maintain the consistency of data sequences this papercalculated the carbon emissions into the quarterly primaryenergy consumption since 1983 In addition internationalcrude oil price data in each trading day were unfixedTherefore in order to ensure the consistency of sampledata the adopted international crude oil prices in thispaper come from quarterly conversation data of CrudeOil Prices in EIA (Energy Information Administration)database GDP quarterly data also come from EIA Thesample interval ranges from June 1983 to December 2013The data source is shown in the following links pri-mary energy consumption data of America comes fromhttpswwweiagovtotalenergydataannual internationalcrude oil prices data comes from httpswwweiagovpetroleumdataphpprices

32 Empirical Test

321 Stationarity Test The commonly accepted ADF (Aug-mentedDickey-Fuller) andPP (Phillips-Perron) unit root testare adopted to stationary test of carbon emissions (119862119875) oilprices (119874119875) andGDP (119866119863119875) seriesThe test results are shownin Table 1

The test results in Table 1 show that level value of thethree sequences is nonstationary and further test indicatesthat 119888119901 119900119901 and 119892119889119901 sequences are first-order differencestationary In order to reduce the fluctuations of the datafirst-order difference is made on the three sequences Thenthree new series 119897119888119901 119897119900119901 and 119897119892119889119901 are obtained and their unitroot test results are shown in Table 2

4 Discrete Dynamics in Nature and Society

Table 3 Determine Lag Intervals for Endogenous with Lag Length Criteria

Lag log L LR FPE AIC SC HQ0 -1339964 NA 3426841 2356078 2363278 23590001 -1306761 6407712 2241397 2313615 2342418 23253052 -1286441 3814472 1838370 2293756 2344159 23142123 -1195826 1653319 4395237 2150572 2222577 21797954 -1163171 5786333lowast 2907068lowast 2109071 2202678lowast 2147061lowast5 -1154389 1509897 2925821 2109454 2224662 2156210

Table 4 Estimation results the VAR model

LCP LGDP LOPLCP(-1) -049474[-607864] -4770917[-067701] 0453324[074409]LCP(-2) -043948[-521377] -1274873[-017468] 0828137[131251]LCP(-3) -0408605[-488826] -0968913[-013387] 107866[172394]LCP(-4) 0494223[613818] -598804[-085895] 0714737[118591]LGDP(-1) 000123[101152] 0325012[308585] 0000832[009136]LGDP(-2) 0000341[027147] 0406329[373285] 001335[141863]LGDP(-3) 0001484[116965] -0181356[-165089] -0004641[-048870]LGDP(-4) -0002321[-190644] 0098924[093846] 0018296[200765]LOP(-1) 0009131[066567] 253743[213653] 0270457[263413]LOP(-2) -0022643[-157017] -5005037[-400845] -0585263[-542180]LOP(-3) -0007891[-052668] 2230903[171979] 0066615[059401]LOP(-4) -0026265[-181101] -3091612[-246203] -0394997[-363852]C 0107857[058783] 4284598[269697] -2424158[-176502]

Value in brackets in Table 2 are P value ADF and PPvalues are obviously less than the significant value of 5which indicates that the three sequences are stationary

322 Estimation of VAR Model The first issue of the VARmodel is to determine Lag Intervals for Endogenous Thelarger the Lag Intervals for Endogenous is the more it canentirely reflect the dynamic nature of the model But in thiscase more parameters will be needed to be estimated toconstantly reduce freedom degrees of the model This is acontradiction in the selection of proper Lag Intervals forEndogenous

There are many methods that can determine optimal lagperiod for the VAR model In comprehensive considerationof selecting Lag Intervals for Endogenous this paper adoptedLag Length Criteria and Ar Roots Graph to determine LagIntervals for Endogenous as shown in Table 3

According to Table 3 after the comparison of Lag LengthCriteria it can be found that the optimal lag order for theVAR model is 4 The VAR (lag period is 4th order) modelis established with an econometric software as shown inTable 4

Value of log likelihood function for themodel is relativelylarge and AIC value is small which indicates that theexplanatory ability of the model is very strong

After determining the lag order of 4 the VAR (4th order)model is reestablished Then test stationarities of VAR model

minus15

minus10

minus05

00

05

10

15

minus15 minus10 minus05 00 05 10 15

Inverse Roots of AR Characteristic Polynomial

Figure 1 Unit root test

and mod of AR characteristic root reciprocal of VAR modelare shown as Figure 1 which indicates that mod of reciprocalof each characteristic root is in the circle That is to say lagorder of 4 is appropriate and the established VAR model isstable after going through stability test

Discrete Dynamics in Nature and Society 5

Table 5 Results of cointegration test

(a)

Unrestricted Cointegration Rank Test (Trace)Hypothesized Trace 005No of CE(s) Eigenvalue Statistic Critical Value ProblowastlowastNone lowast 04252 1154481 297971 0At most 1 lowast 02631 500979 154947 0At most 2 lowast 01124 140742 38415 00002Trace test indicates 3 cointegrating eqn(s) at the 005 levellowast denotes rejection of the hypothesis at the 005 levellowastlowastMacKinnon-Haug-Michelis (1999) p-values

(b)

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)Hypothesized Max-Eigen 005No of CE(s) Eigenvalue Statistic Critical Value ProblowastlowastNone lowast 04252 653502 211316 0At most 1 lowast 02631 360237 142646 0At most 2 lowast 01124 140742 38415 00002Max-eigenvalue test indicates 3 cointegrating eqn(s) at the 005 levellowast denotes rejection of the hypothesis at the 005 levellowastlowastMacKinnon-Haug-Michelis (1999) p-values

323 Cointegration Test The key of cointegration test liesin selecting proper form of cointegration test and lag orderCointegration relationship between variables in the VARmodel is generally tested with the Johnsen (1988) and Juselius(1990) method Here the selected sequences are linear trendterms and then the test formof cointegration equation is onlyintercept

Johansen cointegration test on oil prices GDP and carbonemissions (Table 5) shows that in both trace and maximumeigenvalue test test results are to accept the null hypothesisunder the 5 level and two positive relationships exist Thismeans there are stable and long-term equilibrium relation-ships among the variables On the premise of the existenceof cointegration relationships VEC modeling can be furtherconducted

324 VECMEstimation andAnalysis Cointegration analysisdemonstrates that oil prices GDP and carbon emissionsdo have long-run equilibrium relationships but in theshort term the three are in disequilibrium The short-termimbalance and dynamic structure can be expressed asVECMSince the lag order of VAR is 4 VECMrsquos lag order should be 3Accordingly VEC model is established with an econometricsoftware

As the second cointegration equation shows there is nocorrelation betweenGDP and oil prices which is inconsistentwith general economic situation Therefore with first equa-tion treated as the cointegration equation of VEC model theequationrsquos results are shown as Table 6

The cointegration equation is

119897119888119901119905minus1 = minus0015342119897119892119889119901119905minus1 + 0743478119897119900119901119905minus1+ 1126692 (7)

Table 6 Results of cointegration equation

Cointegrating Eq CointEq1LCP(-1) 1LGDP(-1) -0015342[-000491]LOP(-1) 0743478[008675]C 1126692

From this equation it can be seen that other thingsequal each percentage-point increase in oil prices willcause the increase of 073478 percentage points in carbonemissions and each percentage-point increase in GDP willcause the decrease of 0015342 percentage points in carbonemissions

VECM is as follows

[[[[

998779119897119888119901119905998779119897119892119889119901119905998779119897119900119901119905

]]]]

= [[[[

0004707334minus01679

]]]]

+ [[[[

minus09617 40004 13081minus00004 minus06408 minus0029400764 75017 08805

]]]]

[[[[

998779119897119888119901119905minus1998779119897119892119889119901119905minus1998779119897119900119901119905minus1

]]]]

6 Discrete Dynamics in Nature and Society

Table 7 VECM estimation results and test

Error Correction D(LCP) D(LGDP) D(LOP)CointEq1 -0104234 [-258593] -7268381[-224355] -2133611[-790997]D(LCP(-1)) -0961687[-239237] 4000415[123820] 1308053[486264]D(LCP(-2)) -0954550[-240919] 4273666[134204] 0803946[303216]D(LCP(-3)) -0919406[-315065] 4670270[199125] 0556109[284777]D(LGDP(-1)) -0000414[-031978] -0640796[-616527] -0029396[-339685]D(LGDP(-2)) -0000291[-020219] -0152107[-131289] -0014040[-145546]D(LGDP(-3)) 0001903[150015] -0251021[-246167] -0019500[-229678]D(LOP(-1)) 0076443[311551] 7501668[380402] 0880550[536292]D(LOP(-2)) 0045991[236590] 1857454[118885] 0308622[237246]D(LOP(-3)) 0030246[186907] 3918942[301310] 0396354[366007]C 0004684[004941] 0733444[009628] -0167900[-026471]R-squared 0957803 0390277 0551367Log likelihood -1223996Akaike information criterion 2135586Schwarz criterion 2220116

+ [[[[

minus09546 42737 08039minus00003 minus01521 minus0014000460 18575 03086

]]]]

[[[[

998779119897119888119901119905minus2998779119897119892119889119901119905minus2998779119897119900119901119905minus2

]]]]

+ [[[[

minus09194 46703 0556100019 minus02510 minus0019500302 39189 03964

]]]]

[[[[

998779119897119888119901119905minus3998779119897119892119889119901119905minus3998779119897119900119901119905minus3

]]]]

(8)

The data in Table 7 show that fitting degree of VECmodelR2 gt 05 and AIC and SC criteria values are relatively smallwhich indicates the reasonability of the model estimation

Zero average line represents a stable and long-termequilibrium relationship among variables There was a largefluctuation at the end of 2008 which shows that the short-term fluctuation at that period significantly deviated from thelong-term equilibrium relationship The short-term fluctua-tion effect is a sharp drop in international oil prices causedby the financial crisis in 2008 shown as Figure 2

325 Granger Causality Test Cointegration test indicates along-term equilibrium relationship between the two vari-ables but in terms of causal relationship further testing isneeded If variable A is helpful in predicting B namely theregression of B is based on past values of B and past values ofA are added this can greatly enhance the explanatory abilityof the regression Then A can be called Granger cause of Botherwise it can be called non-Granger cause

P value is less than the significant level of 5 whichindicates the need to accept the null hypothesis namely theexistence of Granger cause As the results shown in Table 8

2008 financial crisis

20

10

0

minus10

minus20

minus30

minus4025 50 75 100

Cointegrating relation 1

Figure 2 Cointegration relationship graph

except that LGDP and LCP are not Granger causes of eachother all the others exist Granger causality relationshipTherefore GDP and carbon emission are the Granger causesof oil prices oil prices are the Granger cause of both carbonemissions and GDP Granger causality test shows that thereare Granger causalities among changes in oil prices GDPand carbon emissions in the short term and there is certainreciprocity among the three factors

326 VECM Stability Test Root of 4 residual stability testresults in 1 and root of other residual stability test resultsin less than 1 So the VECM model satisfies the stabilitycondition At the same time variable autocorrelation testshows that except for LCP others do not have autocorrelation

Discrete Dynamics in Nature and Society 7

Table 8 Granger causality test

Dependent variable D(LCP) The primary hypothesisExcluded Chi-sq df ProbD(LGDP) 3337504 3 03425 AcceptD(LOP) 9756523 3 00208 RefuseAll 1611858 6 00131Dependent variable D(LGDP)Excluded Chi-sq df ProbD(LCP) 4679288 3 01968 AcceptD(LOP) 2211808 3 00001 RefuseAll 2650551 6 00002Dependent variable D(LOP)Excluded Chi-sq df ProbD(LCP) 2902233 3 00000 RefuseD(LGDP) 1891076 3 00003 RefuseAll 4291822 6 00000

00

05

10

15

00 05 10 15

Inverse Roots of AR Characteristic Polynomial

minus15

minus10

minus05

minus15 minus10 minus05

Figure 3 Residual stability test of ECMmodel

(Figures 3-4) On the whole the VECM model has goodeffects

327 Impulse Response Function and Variance Decomposition

(1) Impulse Response Function In order to analyze dynamiceffects of the model responding to certain shocks as well ashow the effects are among the three variables further analysisis made through impulse response function and variancedecomposition based onVECM and the results for 10 periodsare obtained

According to Granger test results in consideration of theeffects of standard deviation on oil prices effects of oil priceson GDP and carbon emissions are totally different But ingeneral these fluctuations are divergent that is to say the

impacts of oil price fluctuation onGDP and carbon emissionsare persistent

As shown in Figure 5(a) after analysis of the effects of oilprice shock it is found that positive shock has large impactOil prices decline rapidly after a positive shock reach the low-est point in the third period then rise slowly reach the peak inthe 7th period and then remain at a stable levelThis suggeststhat positive shock of oil prices has significant influence on itsown increasing and the significance influence has relativelylong sustained effectiveness

Figure 5(b) is the impulse response function diagramof GDP changes caused by oil price shocks As seen in thefigure the first positive shock in the first period causes GDPfluctuation and GDP reaches the peak at the second periodThen GDP quickly declines to the lowest point in the thirdperiod and after that returns to a stable conditionThis showsthat oil price shock can be shortly transferred toGDP and hasrelatively large impacts on GDP in the short term but GDPbecomes stable since the fourth period Oil price shock hasthe short-term promoting effect on GDP fluctuation and thiseffect tends to be gentle in the long term

Figure 5(c) is the impulse response function of carbonemission changes caused by oil price shock As shown inthe figure after a positive shock in the first period carbonemissions decline to the lowest point in the third period andbegin to rise slowly Then carbon emissions reach the peakat seventh period and stay at a stable level This shows thata positive shock on oil prices can cause changes in carbonemissions and its effect becomes gentle since the seventhperiod It can be noticed that oil price shock has relativelylarge effect on carbon emissions in the short term and theeffect lasts for seven periods

Generally speaking oil price shock has large effects onGDP and carbon emissions in the short term but the effectsare gentle in the long term

(2) Variance Decomposition Impulse response function isadopted to reflect shock effect of a system on an internalvariable and variance decomposition refers to the decom-position of mean square error into contributions of eachvariable Variance decomposition can be applied to analyzethe influence of each variablersquos update on other variableswhich shows relative effects With an econometric softwarevariance decomposition results are obtained as shown inFigure 6

According to Figure 6(a) in LCP predicted variancecontribution of LCP change begins to gradually decline fromthe first period reaches 92 in the fourth period beginsto rise and gradually returns to a stable level LGDP andLOPrsquos contribution rates respectively rise to 7 and 8at the first and fourth periods and then maintain stabilityuntil the tenth period In Figure 6(b) for predicted varianceof LGDP contribution rate of LGDP change declines from98 in the first period to 84 in the sixth period andthen maintains stability until the tenth period But LCPrsquoscontribution remains at about 4 throughout the periodsLOPrsquos contribution rate slowly rises from the first period to

8 Discrete Dynamics in Nature and Society

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LCPLCP(-i))3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LGDPLGDP(-i))

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LOPLOP(-i))

Figure 4 VECM autocorrelation diagram

12 in the sixth period and then maintains stability until thetenth period In Figure 6(c) for predicted variance of LOPcontribution of LOP declines from 82 in the first periodto 80 in the second period gradually increases to the peakof 83 in the fourth period and then stably declines to 78in the tenth period LGDPrsquos contribution rate gently declinesfrom 18 in the first period to 16 in the third period andthen slightly rises to 19 until the last period Contribu-tion rate of LCP quickly rises from 1 in the first periodto 7 in the second period and then basically maintainsstability

In summary it can be seen that in the short term theoil prices have great influence on GDP and carbon emissionsIn the long run the influence is leveling off As presentedin the model the growth of oil price is related to notonly the current variables but also the variables in the lagperiod

4 Conclusions

This paper established the correlation model of Americanprimary energy carbon emissions GDP and WTI crudeoil prices and examined the causal relationships among thethree factors on the basis of the VEC model The resultsdemonstrate that in both the short term and long term oilprice fluctuation is the reason why carbon emissions changewhile the GDP fluctuation is not the reason for the growth ofcarbon emissions

(1) Through Granger analysis of the VEC model theUS GDP and carbon emissions are not Granger causes ofeach other This shows that the growth of carbon emissionsin the US does not necessarily promote GDP growth andeconomic growth in the country does not intensify theexcessive consumption of energy to cause plenty of carbonemissions This is also proved by the fact that the countryrsquos

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

Discrete Dynamics in Nature and Society 5

Table 5 Results of cointegration test

(a)

Unrestricted Cointegration Rank Test (Trace)Hypothesized Trace 005No of CE(s) Eigenvalue Statistic Critical Value ProblowastlowastNone lowast 04252 1154481 297971 0At most 1 lowast 02631 500979 154947 0At most 2 lowast 01124 140742 38415 00002Trace test indicates 3 cointegrating eqn(s) at the 005 levellowast denotes rejection of the hypothesis at the 005 levellowastlowastMacKinnon-Haug-Michelis (1999) p-values

(b)

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)Hypothesized Max-Eigen 005No of CE(s) Eigenvalue Statistic Critical Value ProblowastlowastNone lowast 04252 653502 211316 0At most 1 lowast 02631 360237 142646 0At most 2 lowast 01124 140742 38415 00002Max-eigenvalue test indicates 3 cointegrating eqn(s) at the 005 levellowast denotes rejection of the hypothesis at the 005 levellowastlowastMacKinnon-Haug-Michelis (1999) p-values

323 Cointegration Test The key of cointegration test liesin selecting proper form of cointegration test and lag orderCointegration relationship between variables in the VARmodel is generally tested with the Johnsen (1988) and Juselius(1990) method Here the selected sequences are linear trendterms and then the test formof cointegration equation is onlyintercept

Johansen cointegration test on oil prices GDP and carbonemissions (Table 5) shows that in both trace and maximumeigenvalue test test results are to accept the null hypothesisunder the 5 level and two positive relationships exist Thismeans there are stable and long-term equilibrium relation-ships among the variables On the premise of the existenceof cointegration relationships VEC modeling can be furtherconducted

324 VECMEstimation andAnalysis Cointegration analysisdemonstrates that oil prices GDP and carbon emissionsdo have long-run equilibrium relationships but in theshort term the three are in disequilibrium The short-termimbalance and dynamic structure can be expressed asVECMSince the lag order of VAR is 4 VECMrsquos lag order should be 3Accordingly VEC model is established with an econometricsoftware

As the second cointegration equation shows there is nocorrelation betweenGDP and oil prices which is inconsistentwith general economic situation Therefore with first equa-tion treated as the cointegration equation of VEC model theequationrsquos results are shown as Table 6

The cointegration equation is

119897119888119901119905minus1 = minus0015342119897119892119889119901119905minus1 + 0743478119897119900119901119905minus1+ 1126692 (7)

Table 6 Results of cointegration equation

Cointegrating Eq CointEq1LCP(-1) 1LGDP(-1) -0015342[-000491]LOP(-1) 0743478[008675]C 1126692

From this equation it can be seen that other thingsequal each percentage-point increase in oil prices willcause the increase of 073478 percentage points in carbonemissions and each percentage-point increase in GDP willcause the decrease of 0015342 percentage points in carbonemissions

VECM is as follows

[[[[

998779119897119888119901119905998779119897119892119889119901119905998779119897119900119901119905

]]]]

= [[[[

0004707334minus01679

]]]]

+ [[[[

minus09617 40004 13081minus00004 minus06408 minus0029400764 75017 08805

]]]]

[[[[

998779119897119888119901119905minus1998779119897119892119889119901119905minus1998779119897119900119901119905minus1

]]]]

6 Discrete Dynamics in Nature and Society

Table 7 VECM estimation results and test

Error Correction D(LCP) D(LGDP) D(LOP)CointEq1 -0104234 [-258593] -7268381[-224355] -2133611[-790997]D(LCP(-1)) -0961687[-239237] 4000415[123820] 1308053[486264]D(LCP(-2)) -0954550[-240919] 4273666[134204] 0803946[303216]D(LCP(-3)) -0919406[-315065] 4670270[199125] 0556109[284777]D(LGDP(-1)) -0000414[-031978] -0640796[-616527] -0029396[-339685]D(LGDP(-2)) -0000291[-020219] -0152107[-131289] -0014040[-145546]D(LGDP(-3)) 0001903[150015] -0251021[-246167] -0019500[-229678]D(LOP(-1)) 0076443[311551] 7501668[380402] 0880550[536292]D(LOP(-2)) 0045991[236590] 1857454[118885] 0308622[237246]D(LOP(-3)) 0030246[186907] 3918942[301310] 0396354[366007]C 0004684[004941] 0733444[009628] -0167900[-026471]R-squared 0957803 0390277 0551367Log likelihood -1223996Akaike information criterion 2135586Schwarz criterion 2220116

+ [[[[

minus09546 42737 08039minus00003 minus01521 minus0014000460 18575 03086

]]]]

[[[[

998779119897119888119901119905minus2998779119897119892119889119901119905minus2998779119897119900119901119905minus2

]]]]

+ [[[[

minus09194 46703 0556100019 minus02510 minus0019500302 39189 03964

]]]]

[[[[

998779119897119888119901119905minus3998779119897119892119889119901119905minus3998779119897119900119901119905minus3

]]]]

(8)

The data in Table 7 show that fitting degree of VECmodelR2 gt 05 and AIC and SC criteria values are relatively smallwhich indicates the reasonability of the model estimation

Zero average line represents a stable and long-termequilibrium relationship among variables There was a largefluctuation at the end of 2008 which shows that the short-term fluctuation at that period significantly deviated from thelong-term equilibrium relationship The short-term fluctua-tion effect is a sharp drop in international oil prices causedby the financial crisis in 2008 shown as Figure 2

325 Granger Causality Test Cointegration test indicates along-term equilibrium relationship between the two vari-ables but in terms of causal relationship further testing isneeded If variable A is helpful in predicting B namely theregression of B is based on past values of B and past values ofA are added this can greatly enhance the explanatory abilityof the regression Then A can be called Granger cause of Botherwise it can be called non-Granger cause

P value is less than the significant level of 5 whichindicates the need to accept the null hypothesis namely theexistence of Granger cause As the results shown in Table 8

2008 financial crisis

20

10

0

minus10

minus20

minus30

minus4025 50 75 100

Cointegrating relation 1

Figure 2 Cointegration relationship graph

except that LGDP and LCP are not Granger causes of eachother all the others exist Granger causality relationshipTherefore GDP and carbon emission are the Granger causesof oil prices oil prices are the Granger cause of both carbonemissions and GDP Granger causality test shows that thereare Granger causalities among changes in oil prices GDPand carbon emissions in the short term and there is certainreciprocity among the three factors

326 VECM Stability Test Root of 4 residual stability testresults in 1 and root of other residual stability test resultsin less than 1 So the VECM model satisfies the stabilitycondition At the same time variable autocorrelation testshows that except for LCP others do not have autocorrelation

Discrete Dynamics in Nature and Society 7

Table 8 Granger causality test

Dependent variable D(LCP) The primary hypothesisExcluded Chi-sq df ProbD(LGDP) 3337504 3 03425 AcceptD(LOP) 9756523 3 00208 RefuseAll 1611858 6 00131Dependent variable D(LGDP)Excluded Chi-sq df ProbD(LCP) 4679288 3 01968 AcceptD(LOP) 2211808 3 00001 RefuseAll 2650551 6 00002Dependent variable D(LOP)Excluded Chi-sq df ProbD(LCP) 2902233 3 00000 RefuseD(LGDP) 1891076 3 00003 RefuseAll 4291822 6 00000

00

05

10

15

00 05 10 15

Inverse Roots of AR Characteristic Polynomial

minus15

minus10

minus05

minus15 minus10 minus05

Figure 3 Residual stability test of ECMmodel

(Figures 3-4) On the whole the VECM model has goodeffects

327 Impulse Response Function and Variance Decomposition

(1) Impulse Response Function In order to analyze dynamiceffects of the model responding to certain shocks as well ashow the effects are among the three variables further analysisis made through impulse response function and variancedecomposition based onVECM and the results for 10 periodsare obtained

According to Granger test results in consideration of theeffects of standard deviation on oil prices effects of oil priceson GDP and carbon emissions are totally different But ingeneral these fluctuations are divergent that is to say the

impacts of oil price fluctuation onGDP and carbon emissionsare persistent

As shown in Figure 5(a) after analysis of the effects of oilprice shock it is found that positive shock has large impactOil prices decline rapidly after a positive shock reach the low-est point in the third period then rise slowly reach the peak inthe 7th period and then remain at a stable levelThis suggeststhat positive shock of oil prices has significant influence on itsown increasing and the significance influence has relativelylong sustained effectiveness

Figure 5(b) is the impulse response function diagramof GDP changes caused by oil price shocks As seen in thefigure the first positive shock in the first period causes GDPfluctuation and GDP reaches the peak at the second periodThen GDP quickly declines to the lowest point in the thirdperiod and after that returns to a stable conditionThis showsthat oil price shock can be shortly transferred toGDP and hasrelatively large impacts on GDP in the short term but GDPbecomes stable since the fourth period Oil price shock hasthe short-term promoting effect on GDP fluctuation and thiseffect tends to be gentle in the long term

Figure 5(c) is the impulse response function of carbonemission changes caused by oil price shock As shown inthe figure after a positive shock in the first period carbonemissions decline to the lowest point in the third period andbegin to rise slowly Then carbon emissions reach the peakat seventh period and stay at a stable level This shows thata positive shock on oil prices can cause changes in carbonemissions and its effect becomes gentle since the seventhperiod It can be noticed that oil price shock has relativelylarge effect on carbon emissions in the short term and theeffect lasts for seven periods

Generally speaking oil price shock has large effects onGDP and carbon emissions in the short term but the effectsare gentle in the long term

(2) Variance Decomposition Impulse response function isadopted to reflect shock effect of a system on an internalvariable and variance decomposition refers to the decom-position of mean square error into contributions of eachvariable Variance decomposition can be applied to analyzethe influence of each variablersquos update on other variableswhich shows relative effects With an econometric softwarevariance decomposition results are obtained as shown inFigure 6

According to Figure 6(a) in LCP predicted variancecontribution of LCP change begins to gradually decline fromthe first period reaches 92 in the fourth period beginsto rise and gradually returns to a stable level LGDP andLOPrsquos contribution rates respectively rise to 7 and 8at the first and fourth periods and then maintain stabilityuntil the tenth period In Figure 6(b) for predicted varianceof LGDP contribution rate of LGDP change declines from98 in the first period to 84 in the sixth period andthen maintains stability until the tenth period But LCPrsquoscontribution remains at about 4 throughout the periodsLOPrsquos contribution rate slowly rises from the first period to

8 Discrete Dynamics in Nature and Society

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LCPLCP(-i))3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LGDPLGDP(-i))

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LOPLOP(-i))

Figure 4 VECM autocorrelation diagram

12 in the sixth period and then maintains stability until thetenth period In Figure 6(c) for predicted variance of LOPcontribution of LOP declines from 82 in the first periodto 80 in the second period gradually increases to the peakof 83 in the fourth period and then stably declines to 78in the tenth period LGDPrsquos contribution rate gently declinesfrom 18 in the first period to 16 in the third period andthen slightly rises to 19 until the last period Contribu-tion rate of LCP quickly rises from 1 in the first periodto 7 in the second period and then basically maintainsstability

In summary it can be seen that in the short term theoil prices have great influence on GDP and carbon emissionsIn the long run the influence is leveling off As presentedin the model the growth of oil price is related to notonly the current variables but also the variables in the lagperiod

4 Conclusions

This paper established the correlation model of Americanprimary energy carbon emissions GDP and WTI crudeoil prices and examined the causal relationships among thethree factors on the basis of the VEC model The resultsdemonstrate that in both the short term and long term oilprice fluctuation is the reason why carbon emissions changewhile the GDP fluctuation is not the reason for the growth ofcarbon emissions

(1) Through Granger analysis of the VEC model theUS GDP and carbon emissions are not Granger causes ofeach other This shows that the growth of carbon emissionsin the US does not necessarily promote GDP growth andeconomic growth in the country does not intensify theexcessive consumption of energy to cause plenty of carbonemissions This is also proved by the fact that the countryrsquos

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

6 Discrete Dynamics in Nature and Society

Table 7 VECM estimation results and test

Error Correction D(LCP) D(LGDP) D(LOP)CointEq1 -0104234 [-258593] -7268381[-224355] -2133611[-790997]D(LCP(-1)) -0961687[-239237] 4000415[123820] 1308053[486264]D(LCP(-2)) -0954550[-240919] 4273666[134204] 0803946[303216]D(LCP(-3)) -0919406[-315065] 4670270[199125] 0556109[284777]D(LGDP(-1)) -0000414[-031978] -0640796[-616527] -0029396[-339685]D(LGDP(-2)) -0000291[-020219] -0152107[-131289] -0014040[-145546]D(LGDP(-3)) 0001903[150015] -0251021[-246167] -0019500[-229678]D(LOP(-1)) 0076443[311551] 7501668[380402] 0880550[536292]D(LOP(-2)) 0045991[236590] 1857454[118885] 0308622[237246]D(LOP(-3)) 0030246[186907] 3918942[301310] 0396354[366007]C 0004684[004941] 0733444[009628] -0167900[-026471]R-squared 0957803 0390277 0551367Log likelihood -1223996Akaike information criterion 2135586Schwarz criterion 2220116

+ [[[[

minus09546 42737 08039minus00003 minus01521 minus0014000460 18575 03086

]]]]

[[[[

998779119897119888119901119905minus2998779119897119892119889119901119905minus2998779119897119900119901119905minus2

]]]]

+ [[[[

minus09194 46703 0556100019 minus02510 minus0019500302 39189 03964

]]]]

[[[[

998779119897119888119901119905minus3998779119897119892119889119901119905minus3998779119897119900119901119905minus3

]]]]

(8)

The data in Table 7 show that fitting degree of VECmodelR2 gt 05 and AIC and SC criteria values are relatively smallwhich indicates the reasonability of the model estimation

Zero average line represents a stable and long-termequilibrium relationship among variables There was a largefluctuation at the end of 2008 which shows that the short-term fluctuation at that period significantly deviated from thelong-term equilibrium relationship The short-term fluctua-tion effect is a sharp drop in international oil prices causedby the financial crisis in 2008 shown as Figure 2

325 Granger Causality Test Cointegration test indicates along-term equilibrium relationship between the two vari-ables but in terms of causal relationship further testing isneeded If variable A is helpful in predicting B namely theregression of B is based on past values of B and past values ofA are added this can greatly enhance the explanatory abilityof the regression Then A can be called Granger cause of Botherwise it can be called non-Granger cause

P value is less than the significant level of 5 whichindicates the need to accept the null hypothesis namely theexistence of Granger cause As the results shown in Table 8

2008 financial crisis

20

10

0

minus10

minus20

minus30

minus4025 50 75 100

Cointegrating relation 1

Figure 2 Cointegration relationship graph

except that LGDP and LCP are not Granger causes of eachother all the others exist Granger causality relationshipTherefore GDP and carbon emission are the Granger causesof oil prices oil prices are the Granger cause of both carbonemissions and GDP Granger causality test shows that thereare Granger causalities among changes in oil prices GDPand carbon emissions in the short term and there is certainreciprocity among the three factors

326 VECM Stability Test Root of 4 residual stability testresults in 1 and root of other residual stability test resultsin less than 1 So the VECM model satisfies the stabilitycondition At the same time variable autocorrelation testshows that except for LCP others do not have autocorrelation

Discrete Dynamics in Nature and Society 7

Table 8 Granger causality test

Dependent variable D(LCP) The primary hypothesisExcluded Chi-sq df ProbD(LGDP) 3337504 3 03425 AcceptD(LOP) 9756523 3 00208 RefuseAll 1611858 6 00131Dependent variable D(LGDP)Excluded Chi-sq df ProbD(LCP) 4679288 3 01968 AcceptD(LOP) 2211808 3 00001 RefuseAll 2650551 6 00002Dependent variable D(LOP)Excluded Chi-sq df ProbD(LCP) 2902233 3 00000 RefuseD(LGDP) 1891076 3 00003 RefuseAll 4291822 6 00000

00

05

10

15

00 05 10 15

Inverse Roots of AR Characteristic Polynomial

minus15

minus10

minus05

minus15 minus10 minus05

Figure 3 Residual stability test of ECMmodel

(Figures 3-4) On the whole the VECM model has goodeffects

327 Impulse Response Function and Variance Decomposition

(1) Impulse Response Function In order to analyze dynamiceffects of the model responding to certain shocks as well ashow the effects are among the three variables further analysisis made through impulse response function and variancedecomposition based onVECM and the results for 10 periodsare obtained

According to Granger test results in consideration of theeffects of standard deviation on oil prices effects of oil priceson GDP and carbon emissions are totally different But ingeneral these fluctuations are divergent that is to say the

impacts of oil price fluctuation onGDP and carbon emissionsare persistent

As shown in Figure 5(a) after analysis of the effects of oilprice shock it is found that positive shock has large impactOil prices decline rapidly after a positive shock reach the low-est point in the third period then rise slowly reach the peak inthe 7th period and then remain at a stable levelThis suggeststhat positive shock of oil prices has significant influence on itsown increasing and the significance influence has relativelylong sustained effectiveness

Figure 5(b) is the impulse response function diagramof GDP changes caused by oil price shocks As seen in thefigure the first positive shock in the first period causes GDPfluctuation and GDP reaches the peak at the second periodThen GDP quickly declines to the lowest point in the thirdperiod and after that returns to a stable conditionThis showsthat oil price shock can be shortly transferred toGDP and hasrelatively large impacts on GDP in the short term but GDPbecomes stable since the fourth period Oil price shock hasthe short-term promoting effect on GDP fluctuation and thiseffect tends to be gentle in the long term

Figure 5(c) is the impulse response function of carbonemission changes caused by oil price shock As shown inthe figure after a positive shock in the first period carbonemissions decline to the lowest point in the third period andbegin to rise slowly Then carbon emissions reach the peakat seventh period and stay at a stable level This shows thata positive shock on oil prices can cause changes in carbonemissions and its effect becomes gentle since the seventhperiod It can be noticed that oil price shock has relativelylarge effect on carbon emissions in the short term and theeffect lasts for seven periods

Generally speaking oil price shock has large effects onGDP and carbon emissions in the short term but the effectsare gentle in the long term

(2) Variance Decomposition Impulse response function isadopted to reflect shock effect of a system on an internalvariable and variance decomposition refers to the decom-position of mean square error into contributions of eachvariable Variance decomposition can be applied to analyzethe influence of each variablersquos update on other variableswhich shows relative effects With an econometric softwarevariance decomposition results are obtained as shown inFigure 6

According to Figure 6(a) in LCP predicted variancecontribution of LCP change begins to gradually decline fromthe first period reaches 92 in the fourth period beginsto rise and gradually returns to a stable level LGDP andLOPrsquos contribution rates respectively rise to 7 and 8at the first and fourth periods and then maintain stabilityuntil the tenth period In Figure 6(b) for predicted varianceof LGDP contribution rate of LGDP change declines from98 in the first period to 84 in the sixth period andthen maintains stability until the tenth period But LCPrsquoscontribution remains at about 4 throughout the periodsLOPrsquos contribution rate slowly rises from the first period to

8 Discrete Dynamics in Nature and Society

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LCPLCP(-i))3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LGDPLGDP(-i))

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LOPLOP(-i))

Figure 4 VECM autocorrelation diagram

12 in the sixth period and then maintains stability until thetenth period In Figure 6(c) for predicted variance of LOPcontribution of LOP declines from 82 in the first periodto 80 in the second period gradually increases to the peakof 83 in the fourth period and then stably declines to 78in the tenth period LGDPrsquos contribution rate gently declinesfrom 18 in the first period to 16 in the third period andthen slightly rises to 19 until the last period Contribu-tion rate of LCP quickly rises from 1 in the first periodto 7 in the second period and then basically maintainsstability

In summary it can be seen that in the short term theoil prices have great influence on GDP and carbon emissionsIn the long run the influence is leveling off As presentedin the model the growth of oil price is related to notonly the current variables but also the variables in the lagperiod

4 Conclusions

This paper established the correlation model of Americanprimary energy carbon emissions GDP and WTI crudeoil prices and examined the causal relationships among thethree factors on the basis of the VEC model The resultsdemonstrate that in both the short term and long term oilprice fluctuation is the reason why carbon emissions changewhile the GDP fluctuation is not the reason for the growth ofcarbon emissions

(1) Through Granger analysis of the VEC model theUS GDP and carbon emissions are not Granger causes ofeach other This shows that the growth of carbon emissionsin the US does not necessarily promote GDP growth andeconomic growth in the country does not intensify theexcessive consumption of energy to cause plenty of carbonemissions This is also proved by the fact that the countryrsquos

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

Discrete Dynamics in Nature and Society 7

Table 8 Granger causality test

Dependent variable D(LCP) The primary hypothesisExcluded Chi-sq df ProbD(LGDP) 3337504 3 03425 AcceptD(LOP) 9756523 3 00208 RefuseAll 1611858 6 00131Dependent variable D(LGDP)Excluded Chi-sq df ProbD(LCP) 4679288 3 01968 AcceptD(LOP) 2211808 3 00001 RefuseAll 2650551 6 00002Dependent variable D(LOP)Excluded Chi-sq df ProbD(LCP) 2902233 3 00000 RefuseD(LGDP) 1891076 3 00003 RefuseAll 4291822 6 00000

00

05

10

15

00 05 10 15

Inverse Roots of AR Characteristic Polynomial

minus15

minus10

minus05

minus15 minus10 minus05

Figure 3 Residual stability test of ECMmodel

(Figures 3-4) On the whole the VECM model has goodeffects

327 Impulse Response Function and Variance Decomposition

(1) Impulse Response Function In order to analyze dynamiceffects of the model responding to certain shocks as well ashow the effects are among the three variables further analysisis made through impulse response function and variancedecomposition based onVECM and the results for 10 periodsare obtained

According to Granger test results in consideration of theeffects of standard deviation on oil prices effects of oil priceson GDP and carbon emissions are totally different But ingeneral these fluctuations are divergent that is to say the

impacts of oil price fluctuation onGDP and carbon emissionsare persistent

As shown in Figure 5(a) after analysis of the effects of oilprice shock it is found that positive shock has large impactOil prices decline rapidly after a positive shock reach the low-est point in the third period then rise slowly reach the peak inthe 7th period and then remain at a stable levelThis suggeststhat positive shock of oil prices has significant influence on itsown increasing and the significance influence has relativelylong sustained effectiveness

Figure 5(b) is the impulse response function diagramof GDP changes caused by oil price shocks As seen in thefigure the first positive shock in the first period causes GDPfluctuation and GDP reaches the peak at the second periodThen GDP quickly declines to the lowest point in the thirdperiod and after that returns to a stable conditionThis showsthat oil price shock can be shortly transferred toGDP and hasrelatively large impacts on GDP in the short term but GDPbecomes stable since the fourth period Oil price shock hasthe short-term promoting effect on GDP fluctuation and thiseffect tends to be gentle in the long term

Figure 5(c) is the impulse response function of carbonemission changes caused by oil price shock As shown inthe figure after a positive shock in the first period carbonemissions decline to the lowest point in the third period andbegin to rise slowly Then carbon emissions reach the peakat seventh period and stay at a stable level This shows thata positive shock on oil prices can cause changes in carbonemissions and its effect becomes gentle since the seventhperiod It can be noticed that oil price shock has relativelylarge effect on carbon emissions in the short term and theeffect lasts for seven periods

Generally speaking oil price shock has large effects onGDP and carbon emissions in the short term but the effectsare gentle in the long term

(2) Variance Decomposition Impulse response function isadopted to reflect shock effect of a system on an internalvariable and variance decomposition refers to the decom-position of mean square error into contributions of eachvariable Variance decomposition can be applied to analyzethe influence of each variablersquos update on other variableswhich shows relative effects With an econometric softwarevariance decomposition results are obtained as shown inFigure 6

According to Figure 6(a) in LCP predicted variancecontribution of LCP change begins to gradually decline fromthe first period reaches 92 in the fourth period beginsto rise and gradually returns to a stable level LGDP andLOPrsquos contribution rates respectively rise to 7 and 8at the first and fourth periods and then maintain stabilityuntil the tenth period In Figure 6(b) for predicted varianceof LGDP contribution rate of LGDP change declines from98 in the first period to 84 in the sixth period andthen maintains stability until the tenth period But LCPrsquoscontribution remains at about 4 throughout the periodsLOPrsquos contribution rate slowly rises from the first period to

8 Discrete Dynamics in Nature and Society

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LCPLCP(-i))3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LGDPLGDP(-i))

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LOPLOP(-i))

Figure 4 VECM autocorrelation diagram

12 in the sixth period and then maintains stability until thetenth period In Figure 6(c) for predicted variance of LOPcontribution of LOP declines from 82 in the first periodto 80 in the second period gradually increases to the peakof 83 in the fourth period and then stably declines to 78in the tenth period LGDPrsquos contribution rate gently declinesfrom 18 in the first period to 16 in the third period andthen slightly rises to 19 until the last period Contribu-tion rate of LCP quickly rises from 1 in the first periodto 7 in the second period and then basically maintainsstability

In summary it can be seen that in the short term theoil prices have great influence on GDP and carbon emissionsIn the long run the influence is leveling off As presentedin the model the growth of oil price is related to notonly the current variables but also the variables in the lagperiod

4 Conclusions

This paper established the correlation model of Americanprimary energy carbon emissions GDP and WTI crudeoil prices and examined the causal relationships among thethree factors on the basis of the VEC model The resultsdemonstrate that in both the short term and long term oilprice fluctuation is the reason why carbon emissions changewhile the GDP fluctuation is not the reason for the growth ofcarbon emissions

(1) Through Granger analysis of the VEC model theUS GDP and carbon emissions are not Granger causes ofeach other This shows that the growth of carbon emissionsin the US does not necessarily promote GDP growth andeconomic growth in the country does not intensify theexcessive consumption of energy to cause plenty of carbonemissions This is also proved by the fact that the countryrsquos

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

8 Discrete Dynamics in Nature and Society

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LCPLCP(-i))3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LGDPLGDP(-i))

3

2

1

0

minus1

minus2

minus32 4 6 8 10 12

Cor(LOPLOP(-i))

Figure 4 VECM autocorrelation diagram

12 in the sixth period and then maintains stability until thetenth period In Figure 6(c) for predicted variance of LOPcontribution of LOP declines from 82 in the first periodto 80 in the second period gradually increases to the peakof 83 in the fourth period and then stably declines to 78in the tenth period LGDPrsquos contribution rate gently declinesfrom 18 in the first period to 16 in the third period andthen slightly rises to 19 until the last period Contribu-tion rate of LCP quickly rises from 1 in the first periodto 7 in the second period and then basically maintainsstability

In summary it can be seen that in the short term theoil prices have great influence on GDP and carbon emissionsIn the long run the influence is leveling off As presentedin the model the growth of oil price is related to notonly the current variables but also the variables in the lagperiod

4 Conclusions

This paper established the correlation model of Americanprimary energy carbon emissions GDP and WTI crudeoil prices and examined the causal relationships among thethree factors on the basis of the VEC model The resultsdemonstrate that in both the short term and long term oilprice fluctuation is the reason why carbon emissions changewhile the GDP fluctuation is not the reason for the growth ofcarbon emissions

(1) Through Granger analysis of the VEC model theUS GDP and carbon emissions are not Granger causes ofeach other This shows that the growth of carbon emissionsin the US does not necessarily promote GDP growth andeconomic growth in the country does not intensify theexcessive consumption of energy to cause plenty of carbonemissions This is also proved by the fact that the countryrsquos

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

Discrete Dynamics in Nature and Society 9

8

6

4

2

0

minus2

minus41 2 3 4 5 6 7 8 9 10

Response of LOP to LOP

(a)

80

40

0

minus401 2 3 4 5 6 7 8 9 10

Response of LGDP to LOP

(b)

08

12

04

00

minus041 2 3 4 5 6 7 8 9 10

Response of LCP to LOP

(c)

Figure 5 Impulse response

economic growth in recent yearsmainly relies on the vigorousdevelopment of high-tech industry

(2) According to impulse response function analysis it isfound that carbon emission and oil prices present negativeeffects A positive shock of oil prices has reverse effecton carbon emissions Influenced by the factor of oil pricethe high oil prices will slow down the increasing speed ofoil demand to further cause the declining proportion ofoil in energy structure Energy consumption will turn tonew energy and renewable energy to replace the energyconversion This is consistent with the energy consumptionin the time of high oil price The rise in oil prices causes thedecline in fossil energy consumption and further leads to thedecline of carbon emissions

(3)TheVEC empirical analysis indicates that the oil priceimpact will produce great influence on GDP and carbon

emissions in the short term but in the long term theinfluence will tend to be gentle

In conclusion the correlations among the US GDP oilprice fluctuations and carbon emissions are relatively com-plex and there exists an asymmetric interaction mechanismA positive shock of oil prices can have a negative impacton carbon emissions and GDP growth does not lead to thegrowth of carbon emissions

Data Availability

The data source is shown in the following links primaryenergy consumption data of America comes from httpswwweiagovtotalenergydataannual international crudeoil prices data comes from httpswwweiagovpetroleumdataphpprices

10 Discrete Dynamics in Nature and Society

Variance Decomposition of LCP

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

LCPLGDPLOP

(a)

Variance Decomposition of LGDP

0

20

40

60

80

100

LCPLGDPLOP

1 2 3 4 5 6 7 8 9 10

(b)

Variance Decomposition of LOP

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

LCPLGDPLOP

(c)

Figure 6 Variance decomposition

Conflicts of Interest

The author declares that there are no conflicts of interest

Acknowledgments

This paper was supported by the National Natural ScienceFoundation of China no 51276081 National Social ScienceFund of China no 12ampZD062 Brand Professional Buildingin Jiangsu Higher Education Institutions PPZY2015A090Science and Technology Support Project (Social Develop-ment) in Jiangsu Province no BE2014692 Science and

Technology Support Plan (Social Development) in ZhenjiangCity no SH2015018

References

[1] J Kraft and A Kraft ldquoOn the relationship between energy andGNPrdquo Journal of Energy and Development vol 3 no 2 pp 401ndash403 1978

[2] H Iwata K Okada and S Samreth ldquoEmpirical study on theenvironmental Kuznets curve for CO2 in France The role ofnuclear energyrdquo Energy Policy vol 38 no 8 pp 4057ndash40632010

Discrete Dynamics in Nature and Society 11

[3] F Zhenxin X Xiaojing and W Shuping ldquoThe Influence ofEconomic Development and Industrial Structure to CarbonEmission Based on Chinarsquos Provincial Panel Datardquo ChineseJournal of Management Science vol 20 no 3 pp 161ndash166 2012

[4] L boqiang and J zhujun ldquoInfluencing Factors and Kuznetscurve prediction of Chinese CO2rdquo Management World vol 4pp 27ndash35 2009

[5] Z Ren and Y-B Zhou ldquoEconomie growth and waste gaspollution in Bohai areardquo China Population Resources and Envi-ronment vol 19 no 2 pp 63ndash68 2009

[6] U Soytas R Sari and B T Ewing ldquoEnergy consumptionincome and carbon emissions in the United Statesrdquo EcologicalEconomics vol 62 no 3-4 pp 482ndash489 2007

[7] N Bashiri Behmiri and J R Pires Manso ldquoCrude oil conser-vation policy hypothesis in OECD (organisation for economiccooperation and development) countries A multivariate panelGranger causality testrdquo Energy vol 43 no 1 pp 253ndash260 2012

[8] S Hammoudeh D K Nguyen and RM Sousa ldquoEnergy pricesand CO2 emission allowance prices A quantile regressionapproachrdquo Energy Policy vol 70 pp 201ndash206 2014

[9] S Rajaratnam ldquoFossil fuel based CO2 emissions economicgrowth and world crude oil price nexus in the United StatesrdquoArticle ID 29574 Munich Personal RePEc Archive 2007 12Paper No29574 httpmpraubuni-muenchende29574

[10] M Jisheng and H Hao ldquoBased on the VAR (vector autoregression) dynamic analysis on the dynamic analysis therelationship between carbon emission and economic growth inChina based on VARrdquo Inquiry into economic issues vol 5 pp20ndash25 2011

[11] J luo ldquoAn empirical investigation of the causal relationshipbetween carbon dioxide emissions and GDP growth in chinardquoJournal of Zhengzhou Institute of Aeronautical IndustryManage-ment vol 10 no 28 pp 24ndash27 2010

[12] F Jiafeng G Qingxian and S Huading ldquoEmpirical Study onthe CO2 Environmental Kuznets Curve Based on Productionand Consumption-based CO2 Emissionsrdquo Advances in climatechange research vol 11 no 4 pp 376ndash381 2008

[13] L Han and L Yang ldquoThe Relationship between EconomicGrowth and Environmental Quality An Empirical Test ofEnvironmental Kuznets Curve of CO2rdquo in EconomicTheory andBusiness Management vol 3 p 11 5 2009

[14] X Zhang and X Cheng ldquoEnergy consumption carbon emis-sions and economic growth in Chinardquo Ecological Economicsvol 68 no 10 pp 2706ndash2712 2009

Discrete Dynamics in Nature and Society 11

[3] F Zhenxin X Xiaojing and W Shuping ldquoThe Influence ofEconomic Development and Industrial Structure to CarbonEmission Based on Chinarsquos Provincial Panel Datardquo ChineseJournal of Management Science vol 20 no 3 pp 161ndash166 2012

[4] L boqiang and J zhujun ldquoInfluencing Factors and Kuznetscurve prediction of Chinese CO2rdquo Management World vol 4pp 27ndash35 2009

[5] Z Ren and Y-B Zhou ldquoEconomie growth and waste gaspollution in Bohai areardquo China Population Resources and Envi-ronment vol 19 no 2 pp 63ndash68 2009

[6] U Soytas R Sari and B T Ewing ldquoEnergy consumptionincome and carbon emissions in the United Statesrdquo EcologicalEconomics vol 62 no 3-4 pp 482ndash489 2007

[7] N Bashiri Behmiri and J R Pires Manso ldquoCrude oil conser-vation policy hypothesis in OECD (organisation for economiccooperation and development) countries A multivariate panelGranger causality testrdquo Energy vol 43 no 1 pp 253ndash260 2012

[8] S Hammoudeh D K Nguyen and RM Sousa ldquoEnergy pricesand CO2 emission allowance prices A quantile regressionapproachrdquo Energy Policy vol 70 pp 201ndash206 2014

[9] S Rajaratnam ldquoFossil fuel based CO2 emissions economicgrowth and world crude oil price nexus in the United StatesrdquoArticle ID 29574 Munich Personal RePEc Archive 2007 12Paper No29574 httpmpraubuni-muenchende29574

[10] M Jisheng and H Hao ldquoBased on the VAR (vector autoregression) dynamic analysis on the dynamic analysis therelationship between carbon emission and economic growth inChina based on VARrdquo Inquiry into economic issues vol 5 pp20ndash25 2011

[11] J luo ldquoAn empirical investigation of the causal relationshipbetween carbon dioxide emissions and GDP growth in chinardquoJournal of Zhengzhou Institute of Aeronautical IndustryManage-ment vol 10 no 28 pp 24ndash27 2010

[12] F Jiafeng G Qingxian and S Huading ldquoEmpirical Study onthe CO2 Environmental Kuznets Curve Based on Productionand Consumption-based CO2 Emissionsrdquo Advances in climatechange research vol 11 no 4 pp 376ndash381 2008

[13] L Han and L Yang ldquoThe Relationship between EconomicGrowth and Environmental Quality An Empirical Test ofEnvironmental Kuznets Curve of CO2rdquo in EconomicTheory andBusiness Management vol 3 p 11 5 2009

[14] X Zhang and X Cheng ldquoEnergy consumption carbon emis-sions and economic growth in Chinardquo Ecological Economicsvol 68 no 10 pp 2706ndash2712 2009

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