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We have investigated the interactions between economic growth and industrial wastewater discharge from 1978 to 2007 in China’s Hunan Province using cointegration theory and an errorcorrection model. Two main economic growth indicators and four representative industrial wastewater pollutants were selected to demonstrate the interaction mechanism. We found a longterm equilibrium relationship between economic growth and the discharge of industrial pollutants in wastewater between 1978 and 2007 in Hunan Province. The errorcorrection mechanism prevented the variable expansion for longterm relationship at quantity and scale, and the size of the errorcorrection parameters reflected shortterm adjustments that deviate from the longterm equilibrium. When economic growth changes within a short term, the discharge of pollutants will constrain growth because the values of the parameters in the shortterm equation are smaller than those in the longterm cointegrated regression equation, indicating that a remarkable longterm influence of economic growth on the discharge of industrial wastewater pollutants and that increasing pollutant discharge constrained economic growth. Economic growth is the main driving factor that affects the discharge of industrial wastewater pollutants in Hunan Province. On the other hand, the discharge constrains economic growth by producing external pressure on growth, although this feedback mechanism has a lag effect. Economic growth plays an important role in explaining the predicted decomposition of the variance in the discharge of industrial wastewater pollutants, but this discharge contributes less to predictions of the variations in economic growth.
The impact of economic growth on the environment is an emerging and popular issue in resource, environmental, and ecological economics. Resource depletion and pollutant discharge that result from economic growth will inevitably lead to environmental degradation; however, technological progress, economies of scale, and the increased income that result from economic growth can be used to reduce pollutant discharge and ultimately to improve environmental quality. In 1991, Grossman and Kreuger [
Since then, many empirical studies have shown that linear, Ushaped, Nshaped, and inverted Nshaped relationships may also exist between the indices of environmental pollution and those of economic growth. Coondoo
The nature of the EKC is that it measures the impact of economic growth on the environment. In terms of the approach to measurement, researchers have developed a range of models based on different assumed conditions and different dominant factors. The most common equation form used in these models is a quadratic equation for the relationship between income and the resource environment. Sometimes an obviously inverted Ushaped curve can be achieved using a quadratic equation of the logarithm to highlight the curve’s characteristic shape. In contrast, an Nshaped cubic equation shows that there are many fluctuations in any realworld system.
Most current models are simple measurements based on single equations, and suggest that the environment has no feedback effect on economic growth. The unidirectional hypothesis, in which the economy influences the environment but the environment does not influence the economy leads directly to inaccurate assessments because it is based on an unrealistic assumption. As Dinda [
Hu
There are two main methods to account for endogeneity biases. First, the analysis can be performed by establishing simultaneous equations to produce a dynamic structural formula. For example, Huang and Shaw [
The selection of VAR models for use in analyses of the relationships between environmental and economic parameters offers the following advantages: First, there are fewer constraints based on existing theories and assumptions. All the variables in the VAR system are regarded as endogenous and can enter every assessment equation symmetrically. Analysis of the effects of different variables on environmental changes and economic growth would be facilitated in terms of their longterm dynamics, and the problem of variable default would be avoided. Because it is difficult to analyze the economic meaning of test results obtained by direct application of VAR models, the impulseresponse function is frequently used for analysis.
In this context, the aim of the present study was to investigate the mutual relationships and interactions between economic growth and the environment (here, using the discharge of industrial waste pollutants as a proxy), and to demonstrate how this analysis could be used in a case study in China’s Hunan Province. We attempted to resolve some of the problems discussed earlier in this paper by using cointegration and error correction models (ECMs). We hope that this study will improve our knowledge of the relationships between economic growth and industrial pollution.
A VAR model is not based on economic theory, but is instead a regression that investigates the dynamic relationships among all the endogenous variables in a system based on hysteresis effects between changes in the values of each endogenous variable in the model and the resulting changes in the other endogenous variables; that is, there are interactions and pathdependence in these changes. There is no precondition (
This function can also be written as VAR (
If
where Δ is the rank difference operator:
The VECM is a type of VAR model, but with a restriction: it includes a cointegration relationship when it explains the variables [
We adopted the following indicators in our analysis of the discharge of industrial wastewater: the amount of industrial wastewater generated, the amount discharged, the contaminant removal rate, and the amount of pollutants discharged in the industrial waste. Our case study was based on data from Hunan Province in southern China, where annual rainfall is high, and we assumed that the amount of pollutants discharged in industrial waste would have serious effects on the quality of the ecological environment. We adopted the following pollutant parameters (discharge amounts) as proxies for the impact of economic growth on the environment: chemical oxygen demand (COD), ammonia nitrogen (AND), petroleum pollutants (PPD), and heavy metals (HMD).
We obtained timeseries data from 1978 to 2007 from the Statistical Yearbook of Hunan Province and the China Environment Yearbook for each year and parameter. We chose two economic growth indicators based on the availability of data and the popularity of these indicators in previous research. On this basis, we chose the
To make the six variables comparable under the same coordinate, we normalized the values using version 6.0 of the Eviews software (
To confirm the degree of stability of the sequence, we analyzed the series for each of the six variables independently. We used the augmented Dickey–Fuller test (ADF) for this analysis. The results of the ADF test showed that the firstorder difference in the economic environment and the economic growth variables had been taken logarithm. The obvious level was less than the critical value for the ADF unit root test, indicating that the following variables belonged to a firstorder integration process I, which means that under the same unit root, the following variables would become a stationary series after single difference.
Cointegration only reflects the longterm dynamic equilibrium among the variables, and the longterm elasticity of the dynamic equilibrium has a positive (or negative) relationship among the variables. The inadequacies of the longterm static model can be compensated for using a correction mechanism when shortterm values deviate from the longterm equilibrium, and the correction is implemented using a shortterm dynamic model; that is, an error correction model (ECM) can be constructed between the economic and environmental parameters. The error correction can adjust the longterm model for shortterm fluctuations in economic growth, and implies that pollution amounts have clear effects on economic growth because of the twoway relationship between economic and environmental parameters. This conclusion must be further confirmed using the Granger causality test.
To model the parameters with more explanatory power and simultaneously eliminate autocorrelation of the error terms while keeping reasonable freedom, we chose 3 as the maximum lag order. The optimal lag order for a VAR model ranges from level 3 to level 1, in descending order. Akaike’s information criterion (AIC) and the SC information norm and likelihood ratio (LR) statistics were used as the testing standard for choosing the optimum lag order. In addition, we used the
The trace test and the MaxEigenvalue test of Johansen showed that at
The VECM had a loglikelihood value of 209.41, which was sufficiently high to provide confidence that the model was reliable. Simultaneously, the AIC and SC values for the VECM were −;16.34 and −;12.64, respectively; both were sufficiently small to indicate that the whole model was wellfitted and had comparatively good explanatory power (
The cointegration among variables only tells us that there is also a longterm causal relationship among the variables. Because the specific direction of the causality (unidirectional or bidirectional) is still unknown, it is necessary to carry out causality tests to define the nature of the relationships among the variables. To do so, we chose the Granger causality test to identify any causality between the indices of economic growth and the pollution discharge indices. The theorem of Engle and Granger states that if there is cointegration among the variables of the VAR model, we can then establish an ECM, which includes error correction terms, and judge the causality among variables based on the VECM. The general form of the VECM, including double variables, is:
where Δ denotes the Dvalue,
We draw the following conclusions from the test results in
The impulse response function describes the response of an endogenous variable to the impact of error terms. The impulse response function based on the VAR model can be used to measure the impact of a change of 1 standard deviation in one variable that results from stochastic disturbance on the current and future values of the other variables, and can be used to analyze the whole process of how a disturbance of any variable in the VAR model will influence the other variables and ultimately the variable itself. We used general impulse response analysis in this part of our analysis. Its main function is to provide a more prudent scheme for the orthogonalization process than in the traditional impulse response analysis, and its main value is that it can provide a more prudent conclusion based on orthogonality of the impulses and no connection with the order in which the variables are arranged.
During the whole impulse response period, the response curve for COD to a oneunit response of GDP was Nshaped: the response value of COD in terms 1 and 2 was positive, decreased towards zero in terms 3 to 5, became positive again in terms 5 to 8, then finally decreased to remain around zero from terms 8 to 12. This suggests that the overall influence of GDP on COD was to increase this discharge, and the cumulative response was 0.186, which indicates that economic growth increases COD.
The impulse response for NAD approximately resembled an Nshaped curve. The response value in terms 1 to 3 was positive, decreased towards zero from terms 3 to 5, was positive in term 6, was negative in terms 7 and 8, and then remained near zero from term 9 to 12. The impulse response of NAD to GDP was generally an increase in NAD, and the cumulative response was 0.034. The economic meaning of this result is that economic growth would increase NAD and that increased NAD would slow the rate of economic growth.
The impulse response of PPD to GDP also took on an Nshaped curve. The response value of PPD during terms 1 to 3 changed from negative to positive, decreased to remain near zero in terms 3 to 8, and then became positive again from terms 9 to 12. The cumulative response was 0.027. Economic growth would therefore increase PPD.
The impulse response of HMD to GDP took on a double Ushaped curve. The response values of HMD to GDP were initially positive then decreased to become negative in term 1, then increased to become positive in term 3 (the first U), then decreased from term 3 to term 7 and increased again to near zero by term 10 (the second U); thereafter, it remained stable near zero. The cumulative response was 0.215, which indicates that economic growth increases HMD.
The response of GDP to pollutant discharge took on an inverted Ushaped curve. This demonstrates the adverse effects of environmental degradation and pollutant discharge on economic growth: As environmental quality deteriorated and pollutant discharge increased, changes in human preferences related to environmental quality and modulation of the industrial structures imposed external pressure on the mode of economic growth. At the beginning of economic growth, the effects of pollutant discharge on economic growth were small. Therefore, during the first three terms, the GDP curve increased rapidly, and all pollutant discharge response values reached their maximum value, step by step. With continuous economic growth, the discharge slowly became a constraint on economic growth and slowed the rate of economic growth. Thus, when GDP was close to a certain saturated level, during the third to sixth term, the response changed to a nearly horizontal line. From the eighth term onwards, the response of GDP to waste discharge was to decrease, which means that waste discharge became a significant constraint on economic expansion, a constraint on economic expansion until wastewater treatment capacity increased. The contradiction between economic growth and waste discharge then moderated, and GDP once more grew at a good pace, until a new round of adjustment began.
Decomposition of variance refers to calculation of the mean square error of the impact of a variable into the contribution created by a random impulse from various variables, followed by calculation of the relative importance of each variable’s impulse (
Because of space constraints, we will use decomposition of variance for
Cointegration relationships represent a kind of longterm statistical interpretation that balances the relationships among nonstable variables. The cointegration represents a certain linear combination of pairs of nonstable variables, and offers a certain degree of stability. The cointegration analysis tests whether there is a stable linear combination of relationships among nonstable variables and seeks a cointegrated relationship among the variables [
We used the JarqueBera test for normality of the residual error because our analysis showed that when the remaining sequence of each regression equation met the condition of normality (
Under normal circumstances, with more than one cointegration relationship among the variables, the first cointegration equation correctly reflects the longterm relationship among the variables [
An impulse response function based on the VAR model can be used to measure the effects of the impact of a onestandarddeviation random disturbance term on all the current and future values of the variables. This function can be used to analyze how a disturbance of any variable in the VAR model would affect other variables in the model, finally resulting in feedback that affects the variable itself [
In general, the decomposition result for comprehensive variance showed that economic growth played an important role in explaining various proportions of the predicted variance based on pollutant discharge indicators. Economic growth caused a predicted variance for COD, NAD, PPD, and HMD that together exceeded 72%. The results showed that economic growth in Hunan Province accompanied by increased wastewater discharge became an important factor in damage to the ecological environment. Comparatively speaking, the discharge of industrial wastewater accounted for a relatively small impact on economic growth. The contribution of COD was only 16.8%, which was much lower than that of the discharge of industrial wastewater. The influences of NAD and PPD were also relatively weak. One reason for this may be that as a result of maturation of Hunan Province’s economic development, the province increased its pollution control measures and its treatment of NAD and PPD. However, another possible reason is that during the process of data calculation, statisticians may make the statistical data lower than the actual due to subjective differences or governmental directives.
We have conducted a dynamic econometric analysis of Hunan Province’s economic growth and its discharge of industrial wastewater based on timeseries data from 1978 to 2007. To do so, we used a cointegration test, impulse response analysis, and variance decomposition. The results showed a longterm balance between economic growth and the discharge of industrial wastewater. Active and positive effects of economic growth on this discharge and a feedback effect of wastewater discharge on economic growth were both clearly revealed.
This work was supported by the Key Supporting Project of Ministry of Science and Technology of China (2007BAC28B04) and Foundation of Chongqing University of Arts and Sciences (No.RCYJ2011006).
Results of the VECM.
Impulse responses of GDP and CPI and of the four pollutant discharges.
The decomposition of variance for GDP.
The decomposition of variance for COD.
Results of the unit root tests.
Variance  Test method  ADF test value  Critical value  Critical value  Conclusion 

ΔlnGDP  (C,T,0)  −3.1593  −2.9762  −3.6998  stable 
ΔlnCPI  (C,T,0)  −2.6692  −2.6299  −2.9810  stable 
ΔlnCOD  (C,T,0)  −6.0544  −2.9763  −3.6998  stable 
ΔlnNAD  (C,T,0)  −4.8663  −2.9762  −3.6998  stable 
ΔlnPPD  (C,T,0)  −6.4657  −2.9762  −3.6998  stable 
ΔlnHMD  (C,T,0)  −3.7614  −2.9762  −3.6998  stable 
Results of the Johansen test for cointegration.
No. of CEs  Trace statistic  Trace test

MaxEgon  MaxEgon test
 

5% critical value  Prob  5% critical value  prob  
None  132.7742  95.7536  0.0000  55.5041  40.0776  0.0005 
At most 1  77.2701  69.8189  0.0113  35.5217  33.8769  0.0316 
At most 2  41.7484  47.8561  0.5934  24.1177  27.5843  0.1307 
At most 3  17.6306  29.7971  0.6736  11.4452  21.1316  0.6029 
Normalized cointegration equations.
GDP  CPI  COD  NAD  PPD  HMD 

1.0000  −1.0297  0.5513  0.7715  0.2110  0.2107 
0.2010  0.4655  0.0128  0.4314  0.6138 
Results of the Granger causality tests.
Pollutant  Lag order  Short term  Long term  

 
H_{0}: GDP does not Granger cause ED  H_{0}: ED does not Granger cause GDP  H_{0}: GDP does not Granger cause ED  H_{0}: ED does not Granger cause GDP  
COD  4  4.596 (0.061)  4.403 (0.828)  6.894 (0.049)  3.408 (0.433) 
NAP  5  2.891 (0.426)  3.363 (0.848)  4.369 (0.317)  3.612 (0.249) 
PPD  3  4.635 (0.158)  5.452 (0.719)  3.312 (0.543)  2.612 (0.342) 
HMD  3  5.159 (0.023)  4.605 (0.256)  5.894 (0.249)  3.408 (0.437) 