4.3.2. Determination of the Lag Order
When environmental regulation returns to the level of social employment, it is first necessary to judge whether environmental regulation has significant nonlinear transformation characteristics for social employment. The AIC and SC criteria in the vector autoregressive model (VAR) are used to select the lag order, and the lag order of the AR part is chosen to be two orders in here. The basic form of the model is as follows:
After the adjustment, the model has low goodness-of-fit, but the fitting effect is not ideal. Therefore, it is tested whether there is a nonlinear relationship between environmental regulation and the employment level of residents, and whether the fitting effect of the model will be greatly improved after the transformation becomes a nonlinear relationship.
According to the test results in
Table 3, when the conversion variable is ΔlnER*, the probability of accepting the linear relationship hypothesis is 4.5991 × 10
−3, which is less than 5%, so the hypothesis about the linear relationship between environmental regulation and employment level can be rejected. The alternative hypothesis, that there is a nonlinear relationship between the two factors, should be taken into consideration. Since the
p value of F3 is the smallest among F4, F3, and F2, the corresponding form of the conversion function is LSTR2.
4.3.3. Determination of Initial Values of Smoothing Parameters and Positional Parameters
It is necessary to estimate the parameters of the STR model after the determination of the conversion form of the function and the conversion variables. According to the systematic grid search method, the chosing of the initial estimate of
(location parameter) and
(smoothing parameter) are performed by selecting different
and
within a certain range so that the sum of squared residuals estimated by the STR model system is the smallest. As shown in
Table 4, the interval of the smoothing parameter
is set to be (0.50, 10), and the interval of the positional parameter
is (−3.38, 3.47) (the smoothing parameter interval and the position parameter interval are set based on the model system data change and the conversion variable empirical data range, respectively), and the value of
and
are both 30, which constitutes a combined point of 30 × 30
. All the two-dimensional space combination points are evaluated one-by-one to find the parameters with the smallest residual square sum as the initial estimate value for further optimization. The initial estimates of
and
are shown in the table below.
Figure 1 and
Figure 2 are contour plots and plans, respectively, under the help of two-dimensional grid search method, and the plan is the inverse of the maximize residuals.
4.3.4. Determination of Model Parameters
The Newton–Paphson method is used to solve the maximum conditional relief function after the determination of the parameters and initial variables. The nonlinear equation parameters φ, θ, γ, and c for environmental regulation and employment levels can be obtained. Detailed results are shown in
Table 5:
The specific form of the LSTR2 model is as follows:
According to the above results, the employment effect of environmental regulation shows a clear transition relationship. This shows the better performance of the LSTR2 model, that is to say, the model can better demonstrate the nonlinear relationship between environmental regulation and employment level, and the estimated coefficient of the model has strong significance.
The nonlinear part obtains the positional parameters
and
, and the transfer function is
. Therefore, when the conversion variable
, the transfer function is
, that is, the nonlinear portion does not exist. The model then only presents as the linear part:
When it comes to the linear part of the model, it is clear that the unemployment rate coefficient is negative, and the government will respond to the current employment problem by taking out the corresponding employment policy in the next year, thereby, the unemployment rate may have a reduction. The policy can solve the unemployment problem in the short-term, but in the long run, the unemployment problem caused by the economic operation has a cumulative effect, so the coefficient of the unemployment rate lags behind the second period is positive. There is a positive correlation between Δln
ER and unemployment rate, with a coefficient of 1.52240, and it is tested at a significance level of 1%, which proves that the implementation of environmental regulation has a loss effect on social employment in the current period. The relationship between ΔlnER(−1) and unemployment rate is negative at a significance level of 1%, the result indicates that the environmental regulation lags behind the first phase has an expansion effect on social employment. By the way of technological innovation and the adjustment of industrial structures, such as paths to reduce the unemployment rate, namely, environmental regulation has a positive effect on employment for a long time. There is a negative correlation between per capita GDP and industrial structure upgrading and unemployment rate. That is, economic development and upgrading of industrial structure can effectively reduce unemployment and promote the improvement of social employment levels. The implementation of environmental regulations will also have a positive impact on economic growth, thereby promoting the level of social employment [
34].
When the conversion variable Δln
ER is equal to the critical value, that is, Δln
ER = −0.08791 or Δln
ER = 0.21572, the transfer function G = 1/2, and the model is in the transition state from the pure linear state to the nonlinear model. The basic form of the model is:
When switching variable Δ ln
ER < −0.08791 or Δ ln
ER > 0.21572; namely, the intensity of environmental regulation is decreased, and the speed of decrease is more than 8.41% [exp(0.08791) −1]; or when the intensity of environmental regulation is rapidly increased, and the speed exceeds 24.07% [exp(0.21572) −1], the nonlinear effects of environmental regulation on employment will change significantly. Then, the basic form of the model is:
When the conversion variable is satisfied with , that is the slow process of environmental regulation, the transfer function value is small, and the conversion variable has small impact on the entire nonlinear part, environmental regulation and employment level (unemployment rate) will maintain the linear relationship. That is to say that environmental regulation will have a negative effect on the unemployment rate with the coefficient of 1.52240, indicating that environmental regulation will increase the unemployment rate, which is not conducive to the improvement of social employment level. The main reason is that the implementation of environmental regulation in the short term will have a phase-out effect on some ‘three high’ enterprises, and the green environmental protection industry in the incubation has not yet formed, resulting in the loss of social employment.
The smoothing parameter of the model is (it is generally considered that the adjustment speed of the nonlinear part is faster when ), indicating that the adjustment speed of the nonlinear part of the model is relatively faster, the conversion function G is an increasing function of the conversion variable , and the conversion function grows as the value of the variable grows, thus, the nonlinear part in the model has a greater influence on the level of social employment.
Figure 3 is a time series diagram of the raw data and simulation data in the model. It can be seen from the following figure that the dynamic characteristics of the data fitted by the STR model have a high degree of coincidence with the dynamic characteristics of the original data, which indicates the effectiveness of the STR model. That is to say, the model can better fit the dynamic relationship between environmental regulation and employment.
Figure 4 and
Figure 5 show schematic diagrams of the model nonlinear function and the transfer function
.
Figure 4 is the result of the transfer function in which
is treated as the conversion variable. The horizontal axis represents the conversion variable
and the vertical axis represents the conversion function
. It can be seen that the value interval of the conversion function
is 0–1, and the symmetry about
.
Figure 5 is the time series diagram of the transfer function, and it clearly shows there are obvious phase characteristics between environmental regulation and social employment. Specifically, it can be divided into three stages: 1990–2004, 2005–2008, and 2009–present. Among them, the values of
in the two periods from 1990 to 2004 and 2009 to present are relatively small and show the linear performance. The lagging period of environmental regulation is negatively correlated with the unemployment rate, which indicates that such environmental regulation is conducive to the improvement of social employment in the long run. In 2005–2008, during the ‘Eleventh Five-Year Plan’ period, there was an obvious nonlinear characteristic between environmental regulation and social employment
. At this time, the coefficient of
is 0.73682, and the coefficient of
is 1.42287. The coefficient of the environmental regulation lags from the first phase is changed from the negative value of the linear part (such as Equation (9)) to the positive value, demonstrating the positive correlation between the environmental regulation lag phase 1 and the social unemployment rate, which is unfavorable to the improvement of the social employment level. We assume that the change in the coefficient is mainly affected by the domestic environmental protection situation. The ‘Eleventh Five-Year Plan’ is the period in which China’s environmental protection situation has taken turns, and the ‘environmental storm’ has become the key word during the ‘Eleventh Five-Year Plan’ period. The five-year environmental plan is considered to be the best environmental plan for the past years at the government work evaluation meeting. During the ‘Eleventh Five-Year Plan’ period, the Ministry of Environmental Protection will not accept and approve the investment of more than 2.9 trillion yuan for 813 projects that do not meet the environmental protection requirements. At the same time, it will investigate and deal with heavy metal pollution, papermaking enterprises, sewage treatment plants, etc., and shut down more than 20,000 illegal sewage companies. The long-term and super-level improvement of environmental regulation has led to a large loss of social employment. Therefore, during the period, whether it is the current period of environmental regulation or the first period of lag, there is a significant positive correlation between the unemployment rate.
4.3.5. Model Stationarity Test
In order to evaluate the stability of the model, the ADF and Philliips& Perron (PP) unit root test method is used to test the stability of the residual term of the regression model. The results of the test are shown in
Table 6. The residual term of the regression model is a stable time series at a significance level of 5%, whether under the ADF test or the PP test.
The ARCH-LM test method is used to test the heteroscedasticity of the model. The corresponding results are shown in
Table 7. The chi-square statistic is 1.4168, the corresponding
p value is 0.4924, and the F-statistic is 0.7492, the corresponding
p value is 0.4839. The null hypothesis is accepted at a significance level of 10%, that is, there is no heteroscedasticity in the residual term.
The results show that the impact of environmental regulation on the rate of unemployment presents a nonlinear conversion relationship according to different intensities of environmental regulation. In the short period, the correlation between environmental regulation and unemployment rate is positive, and environmental regulation will cause the loss of employment; in the long-term, the correlation between environmental regulation and unemployment rate is negative, and environmental regulation will cause the expansion of employment. At the same time, the long-term and high-intensity environmental regulation will contribute to the loss of social employment. In particular, long-term implementation of high-intensity environmental regulation policies will have a major influence on social employment, resulting in a significant reduction in employment.