Discrete Dynamics in Nature and Society

Volume 2018, Article ID 5350308, 11 pages

https://doi.org/10.1155/2018/5350308

## VECM Model Analysis of Carbon Emissions, GDP, and International Crude Oil Prices

Changzhou College of Information Technology, Changzhou 213100, China

Correspondence should be addressed to Xiaohua Zou; moc.361@uoz.auhx

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

Academic Editor: Emilio Jiménez Macías

Copyright © 2018 Xiaohua Zou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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

#### 1. Introduction

Global warming caused by greenhouse effect has become one of the major concerns for human survival. Some scientists predict that if humans do not take immediate measures to reduce greenhouse gas emissions, it is possible that surface temperature of the earth will increase by 4°C as early as 2050. This can lead to adverse weather and sea level rise of at least dozens of meters. And series of catastrophes may bring about the coming of “the end of the world” described in movies. Some researches show that greenhouse effect mainly attributes to excessive use of fossil energy in modern industrial society and the massive emission of carbon dioxide gas into the atmosphere.

Since the 1990s, the international community had recognized the seriousness of global warming issue and argued that the reduction of greenhouse gas emissions, especially CO_{2}, is the best way to solve global climatic and ecological issues. And some measures gradually come into use in order to reduce carbon emissions. However, economic development cannot be separated from energy consumption. As a kind of scarce natural capital, energy presents more and more obvious constraint effects on economic growth. And energy consumption is the major source of greenhouse gas emissions. This brings about the problems of the relationships among energy consumption, carbon emissions, and economic growth, which is worthy of long-term attention.

Empirical study on the relationship between energy consumption and economic growth began in the 1970s. J. Kraft and A. Kraft [1] firstly conducted a pioneering research on the relationship between energy consumption and economic growth in 1978, based on the data of the US from 1947 to 1974, and found the one-way causal relationship between GNP and energy consumption; namely, economic growth could drive the increase of energy consumption. At present, common research methods adopted to study on this issue can be mainly classified into two categories. The first one is the Kuznets curve method. For example, Hiroki Iwata et al. [2] proved the existence of inverted “U” type “environmental Kuznets curve (EKC)” through an empirical analysis of France’s carbon dioxide emissions. Wu Zhenxin et al. [3] supplemented the factor of industrial structure based on environmental Kuznets curve (EKC) and established the individual fixed effect model based on the panel data of 30 provinces in China from 2000 to 2009, to explore the effects of economic growth and industrial structure on carbon emissions. The results showed that there respectively existed cointegration relations between carbon emissions and economic growth, as well as between carbon emissions and industrial structure; the relationship between carbon emissions and economic growth presented inverted “U” type characteristics. Lin Boqiang et al. [4] put forward the Kuznets curve of CO_{2} emissions by the method of time series analysis and forecast China’s CO_{2} emissions in the future. Ren Zhong and Zhou Yunbo [5] investigated the relationship between per capita GDP and industrial waste gas emissions in the Bohai Rim region and argued that the relationship between the two factors showed overall upward inverted “N” type curve characteristics.

The second one is the regression model method. For instance, Ugur Soytas et al. [6] studied the Granger causality relationships among the US income, energy consumption, and carbon emissions based on the Vector Autoregression Model (VAR). In this model, labor force and gross fixed capital were taken into account. It was found that, in the long run, income is not the Granger cause of carbon emissions, so income itself could not become a means to solve environmental problems. Niaz Bashiri Behmiri et al. [7] discussed the influences of changes in crude oil prices, natural gas prices, coal prices, and electricity prices on carbon dioxide emission quota price distribution in the US, on the basis of the quantile regression model. It was indicated that, in the condition of high carbon prices, the price increasing of crude oil would cause the sharp drop in carbon prices. Shawka Hammoudeh et al. [8] utilized VAR and VECM (vector error correction model) to analyze the short-term dynamic influence of changes in oil prices, coal prices, natural gas prices, electricity prices, and carbon emissions quota on carbon emissions prices. One important found conclusion is that a positive impact of the crude oil price will produce a negative effect on the approved price of carbon emissions. Meanwhile, they discovered that energy price impacts will have continual influence on the approved price of carbon emissions. Rajaratnam Shanthini [9] demonstrated the long-term equilibrium relationship between CO_{2} emissions and GDP (i.e., 1% increase in GDP led to 3.2% increase in CO_{2} emissions), via marginal testing method of the autoregressive distributed lag model. Furthermore, it was revealed that long-term decrease of CO_{2} emissions was related to price increasing of crude oil and technical progress, despite their small extent. Min Jisheng and Hu Hao [10] examined the dynamic evolution relationship between China’s carbon emissions and economic growth between 1994 and 2007 by means of the VAR method and proposed that economic growth was the main reason of carbon emission increasing. Economic growth led to the rising of carbon emissions, and the increasing of carbon emissions reversely inhibited the rate of economic growth, with certain lag period. Jing Luo [11] conducted an empirical research on the alterable relation between China’s per capita GDP and carbon dioxide emissions. He adopted the time series data from 1978 to 2008 on the basis of the optimal regression model, to reveal the long-term and short-term influence of China’s economic growth on carbon dioxide emissions. Fu Jiafeng [12] examined the correlation between CO_{2} emissions per unit of GDP and GDP per capita, collecting the panel data of 44 countries between 1990 and 2004. The study indicated that EKC existed between the two factors. Han Yujun [13] carried out an empirical analysis based on the data from 165 countries, and maintained that EKC differed among countries with different income levels. Zhang Xingping et al. [14] utilized the multivariable model, considering the economic growth, energy usage, carbon emissions, capital and city population, to survey the existence and effects of Granger causal relationships among China’s economic growth, energy consumption, and carbon emissions. The research showed that, within the past 47 years in China, the economic growth was not caused by carbon emissions or energy consumption. From this, it can be presumed that the conservative energy policies and emission reduction policies which adopted by Chinese government will not impede the economic growth in the long run.

It can be seen that regression models are commonly utilized to study energy and economy problems, and research contents mostly concentrate upon the correlation among energy consumption, carbon prices, carbon emissions quota, and other aspects. However, there is no relevant literature which directly studies the three aspects of actual carbon emissions, oil prices, and GDP. Therefore, this paper took the US as an example to study volatility transmission mechanism of a closed economy and the interactive relationships among oil prices, GDP, and carbon emissions, with the VEC model. Primary energy carbon emissions, gross domestic product (GDP), and international crude oil prices from 1983 to 2013 in the US were selected as sample data to evaluate whether there was cointegration relationship based on the VAR model, and the VEC model was also built. In this paper, the main study objectives were as follows: ① to analyze whether the three variables have cointegration relationship, i.e., whether there is a long-term equilibrium relationship; ② to test whether there is a causal relationship among the three variables; ③ to establish an impulse response function to describe short-term dynamic relationship over time among the three variables based on the VEC model.

#### 2. VECM

Modern econometricians point out a method to establish the relational model among economic variables in a nonstructural way. They are vector autoregressive model (VAR) and vector error correction model (VEC).

The VAR model is established based on the statistical properties of data. In the VAR model, each endogenous variable in the system is considered as the lagged value of all endogenous variables in the system; thus the univariate autoregressive model is generalized to the “vector” autoregressive model consisting of multivariate time series variables. In 1980, Sims (Christopher Sims) introduced VAR model into economic field and promoted the widespread application in dynamic analysis of economic system.

Engle and Granger combined cointegration and error correction models, to establish the trace error correction model. As long as there is a cointegration relationship between variables, the error correction model can be derived from the autoregressive distributed lag model. And each equation in the VAR model is an autoregressive distributed lag model; therefore, it can be considered that the VEC model is a VAR model with cointegration constraints. Because there is a cointegration relationship in the VEC model, when there is a large range of short-term dynamic fluctuation, VEC expressions can restrict long-term behavior of the endogenous variables and be convergent to their cointegration relation.

Assuming as k-dimensional stochastic time series, and , each is affected by exogenous time series of d-dimension ; then the VAR model can be established as follows:

If is not affected by exogenous time series of d-dimension , then the VAR model of formula (1) can be written as follows:

With cointegration transformation of formula (2), we can get that

where

If has cointegration relationship, then ~ and formula (3) can be written as follows:

where is the error correction term, which reflects long-term equilibrium relationships between variables, and the above formula can be written as follows:

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

#### 3. The Causal Relationship between Carbon Emissions, International Crude Oil Prices, and GDP

##### 3.1. Data Source

This paper selected the conversion prices of international crude oil and the domestic annual primary energy carbon emissions of the US to make an empirical analysis. Since the carbon emissions are converted by year according to the energy consumption and current verifiable carbon emissions are calculated by year, in order to maintain the consistency of data sequences, this paper calculated the carbon emissions into the quarterly primary energy consumption since 1983. In addition, international crude oil price data in each trading day were unfixed. Therefore, in order to ensure the consistency of sample data, the adopted international crude oil prices in this paper come from quarterly conversation data of Crude Oil Prices in EIA (Energy Information Administration) database. GDP quarterly data also come from EIA. The sample interval ranges from June 1983 to December 2013. The data source is shown in the following links: primary energy consumption data of America comes from https://www.eia.gov/totalenergy/data/annual/; international crude oil prices data comes from https://www.eia.gov/petroleum/data.php#prices.

##### 3.2. Empirical Test

###### 3.2.1. Stationarity Test

The commonly accepted ADF (Augmented Dickey-Fuller) and PP (Phillips-Perron) unit root test are adopted to stationary test of carbon emissions (), oil prices (), and GDP () series. The test results are shown in Table 1.