PM2.5 Pollution and Inhibitory Effects on Industry Development: A Bidirectional Correlation Effect Mechanism

In this paper, a vector autoregression (VAR) model has been constructed in order to analyze a two-way mechanism between PM2.5 pollution and industry development in Beijing via the combination of an impulse response function and variance decomposition. According to the results, long-term equilibrium interconnection was found between PM2.5 pollution and the development of primary, secondary, and tertiary industries. One-way Granger causalities were found in the three types of industries shown to contribute to PM2.5 pollution, though the three industries showed different scales of influences on the PM2.5 pollution that varied for about 1–2 years. The development of the primary and secondary industries increased the emission of PM2.5, but the tertiary industry had an inhibitory effect. In addition, PM2.5 pollution had a certain inhibitory effect on the development of the primary and secondary industries, but the inhibition of the tertiary industry was not significant. Therefore, the development of the tertiary industry can contribute the most to the reduction of PM2.5 pollution. Based on these findings, policy-making recommendations can be proposed regarding upcoming pollution prevention strategies.


Introduction
Haze pollution is a serious problem in China. For example, in 12-17 January 2018, Beijing and its surrounding areas suffered from severe regional heavy haze pollution, where the highest concentrations of PM 2.5 reached over 900 µg/m 3 [1]. Numerous studies in China have revealed that there is mutual influence between industry development (mostly in the form of economic growth) and haze pollution; however, particular relationships between different industry sectors and haze pollution differs. The classification of different industry sectors is defined by the National Bureau of Statistics of China, which divides industry into primary, secondary, and tertiary industry according to their economic activities [2]. The primary industry refers to agriculture, forestry, animal husbandry, and fishery (excluding relevant services, which belongs to the tertiary industry). The secondary industry refers to the mining industry (excluding mining assistance services), manufacturing (excluding metal-related production services, machinery, and equipment repair services, etc.), energy production and supply (e.g., electricity, heat, gas, and water), and architecture, engineering, and construction. The tertiary quarter of 2017, a VAR model has been established in this paper. By utilizing the impulse response function and variance decomposition, the dynamic interconnection between the PM 2.5 pollution levels and the development of the three main industry sectors has been analyzed. This study can offer a new perspective for studying the relationship between haze pollution and economic development, and it can provide new ideas for haze pollution management as well.

A Vector Autoregression (VAR) Model
Sims [53] introduced a popular VAR model to econometrics in 1980, and the VAR model has been widely used since then [54,55]. In the VAR model, endogenous variables were used to regress the lag value of each variable in the system for studying the dynamic relationship between these system variables and the endogenous variables. The p-order VAR model is denoted as VAR (p), which is generally given in (1).
where T is the sample size. Y t = (y 1,t , y 2,t , · · · , y k,t ) T is a k dimensional endogenous variable vector. X t = (x 1,t , x 2,t , · · · , x d,t ) T is a d dimensional endogenous variable vector. Π 1 , Π 2 , · · · , Π p are the unknown k × k parametric matrices. H is a k × d dimensional estimated coefficient matrix. U t = (u 1,t , u 2,t , · · · , u k,t ) T is a k dimensional random error vector (i.e., a white noise process). It satisfies: where Σ = σ 2 i I k ; i = 1, 2, · · · , k; and σ 2 i = Var(u i,t ). k is a k-th order identity matrix. Determining the optimal lag order is especially important for establishing the VAR model. Increasing the lag order appropriately can increase the autocorrelation in the error term, but it also easily affects the degree of freedom of the model. Therefore, a comprehensive method was proposed to determine the lag order of the model, based on the likelihood ratio (LR) test statistic, final prediction error (FPE), Akaike information criterion (AIC), Schwarz information criterion (SC), and Hannan-Quinn (HQ) information criterion.

Stability Test
The stability is characterized by the variation in the values of the parameters in a given model. When p = 1, the characteristic equation of the VAR model shown in (1) is shown in (3).
For the VAR model, an equivalent condition for the stability can be defined because the solutions of Equation (3) are within the unit circle.
When p > 1, the following equation can be established: . . .  (3) and (4) can lead to (5). Given: Equation (5) can be written as a VAR model of a one-order partitioned matrix, as shown in (7): where the characteristic equation is shown in (8).
For the VAR model, an equivalent condition for the stability was that the solutions of Equation (8) were within the unit circle.

Cointegration Test
The cointegration relationship expresses the long-term dynamic equilibrium relationship between the multiple economic variables interacting with each other and their evolution [56]. Typical cointegration test methods mainly include the Engle-Granger (E-G) two-step method and the Johansen-Juselius (JJ) test method [57,58]. Compared with the EG method, the JJ method cannot only test the multi-cointegration relationship, but also impose constraints on the cointegration relationship, which was therefore employed in this paper.
Assume that the series Y t = (y 1,t , y 2,t , · · · , y k,t ) T is an h order integration. If there exists a k dimension vector β, such that βY t is an h − b order integration, i.e., 0 ≤ b ≤ h, then Y t = (y 1,t , y 2,t , · · · , y k,t ) T is an (h, b) order cointegration and β is a cointegration vector.
For instance, when h = 1, the series Y t = (y 1,t , y 2,t , · · · , y k,t ) T is integrated of order one. After the differential transform, Equation (1) can be rewritten as (9). where is a vector of order zero, whether a cointegration relationship exists or not depends on the rank of Ω, as explained below.
Denote the rank of Ω by r. When r = 0, Ω is a null matrix, so there is no cointegration relationship between variables. When r = k, Ω is a full rank matrix, then Y t is a stationary series, which contradicts with hypotheses. When 0 < r < k, there exist r cointegration relationships. The matrix Ω can be written as in (10).
where both the ranks of α and β are r. By inserting Equation (10) into Equation (9), it yields: where β T Y t−1 refers to the vector of cointegration relationship. β refers to a matrix of cointegration vectors.
The number of eigenvalues of Ω is usually judged from the trace test and the max-eigenvalue test. The eigenvalues of Ω are λ 1 , λ 2 , · · · , λ k , where λ 1 > λ 2 > · · · > λ k . The null hypothesis was that there existed r cointegration relationships at most; the alternative hypothesis was that there existed r + 1 cointegration relationships at least. The statistics of the trace test and max-eigenvalue test are shown in (12) and (13), respectively.
At significance level α, the values of statistics η r and ξ r were compared with the corresponding critical values from r = 0. The null hypothesis was accepted if the values of statistics were smaller than the critical values, which meant that there existed r cointegration relationships at most. Otherwise, the null hypothesis was rejected, which meant that there existed r + 1 cointegration relationships at least. The order r was increased in turn until the null hypothesis was accepted.

Granger Causality Test
For economic variables, some were highly correlated, but this did not necessarily mean there was a causal relationship between them. The causal relationship was defined as follows [59]: if x is the cause of the change in y, then when regressing y on its past values, additional past values of x will remarkably improve the explanatory power of the regression.
Given a k-dimensional VAR(p) model, as shown in (14): the variable y j was not the Granger cause of the variable y i if and only if ∀q ∈ [1, p], q ∈ N, and it holds that π (q) ij = 0. Therefore, the null hypothesis of the test was π (q) ij = 0, q = 1, 2, · · · , p; the alternative hypothesis was that there at least existed a q, such that π (q) ij = 0. The statistic is written as (15).
where SSR 1 is the residual square sum of y i in Equation (14). SSR 0 is the residual square sum of y i without the lagged variable y j . T is the sample number, and p is the lag order. At significance level α, the value of S was compared with the critical value. When S was smaller than the critical value, the null hypothesis was accepted, which meant that the variable y j was not the Granger cause of y i ; otherwise, the null hypothesis was rejected (i.e., the variable y j was the Granger cause of variable y i .)

Stationary Sequences
In a stationary sequence the statistical law does not change over time. For a time series generated from a random process, {x t }(t = 1, 2, · · · , T), if the sequence is stationary, the following conditions must be satisfied: (1) ∀t, E(x t ) = µ; (2) ∀t, Var(x t ) = σ 2 ; (3) ∀t, Cov(x t , x t+k ) = γ k , where γ k is only related to k. In practical applications, the economic and financial sequences encountered are often non-stationary time series. If they are forced to return, they may lead to "false return" problems. Therefore, stationary data needs to be tested before modeling. Stationary sequences were examined by the augmented Dickey-Fuller (ADF) test method.
An ADF test is used to control a higher order correlation by adding the lag difference term of x t on the right side of the regression equation. Consider the following three models: where a is a constant term. bt is a linear trend function. u t is a random error term. p is the lag order, which is usually determined by AIC. Subtract x t−1 from both ends of Equations (16)- (18),  (20) contained intercept items without time trend items, while Model (21) contained both intercept and time trend terms. In practical applications, Model (21) was usually established to test the significance of intercept and trend terms. If they were significant, then they can be retained; otherwise, they should be rejected, and the model can be simplified to the form of (19) or (20).
The null hypothesis of this test was η = 0; that is, there existed a unit root in the sequence. The alternative hypothesis was η < 0; that is, there existed no unit root. The test statistic is shown in (22).
whereη is the estimate of η, and S(η) is the standard deviation ofη. At significance level α, if the null hypothesis was not rejected, there was a unit root in the sequence; otherwise, this sequence was stationary.

Impulse Response Function
An impulse response function was employed to study the dynamic effects of disturbance items on the current and future of endogenous variables. It was also employed to analyze the influential relationships between variables, since exogenous variables were not affected by system shocks [60]. Consider the VAR(p) model in (1) without exogenous variables, as shown in (23): where T is the sample size. Y t = (y 1,t , y 2,t , · · · , y k,t ) T is a k dimensional endogenous variable vector.Π 1 , Π 2 , · · · , Π p are k × k estimated coefficient matrices. U t = (u 1,t , u 2,t , · · · , u k,t ) T is k dimensional random error vector. Equation (23) can be rewritten as an infinite-order vector moving average model, as in (24).
where L is a casual operator. Θ i satisfies: (24) can be transformed into: According to Equation (25), the following holds: Then the element of the i th row and the j th column of Θ s can be denoted as below: where θ is an element of matrix Θ. This indicated that on the condition that other error terms remain unchanged, it would have an impact on endogenous variable y i at time t + s when u j received a shock at time t. However, the covariance matrix was not necessarily a diagonal matrix; that is, the elements in the random error term changed with a certain element, which contradicted with the assumption of the impulse response function. Therefore, by introducing a transformation matrix, the covariance matrix can be converted into a diagonal matrix, so as to achieve the goal of orthogonalizing the error term.

Variance Decomposition
Variance decomposition was used to analyze the contribution of each endogenous variable to the variance decomposition, so as to reveal the relationship between the variables in the system. According to Equation (25), it holds that: Assume that the covariance matrix Σ of U t is a diagonal matrix. By applying E(U t ) = 0, the variance of y i can be obtained as: where σ jj are the elements of the covariance matrix ∑.
In this way, the variance of y i is decomposed into k unrelated effects. Then the relative variance contribution rate is defined as in (30).
The relative variance contribution rate describes the contribution of the disturbance term to variables. The larger RVC j→i is, the greater the influence of the j th disturbance on the i th variable.

Empirical Analysis
Results of the empirical analysis are presented in this section, including data sources, implementation of the VAR model, model checking, the impulse response function, and variance decomposition.

Data Sources and Data Manipulation
Bidirectional correlation effect between PM 2.5 pollution and industrial development in Beijing has been analyzed in this paper. In addition to 35 air quality automatic monitoring stations with observational hourly concentration data in Beijing set by the Beijing Environmental Protection Monitoring Center [61], PM 2.5 data released from the US embassy were also adopted. On one hand, the VAR model constructed in this paper required a longer time span to include a larger number of parameters. The earliest date of the PM 2.5 data that can be used from the 35 monitoring stations was in December 2013. The US embassy's monitoring data began in April 2008, which can meet the model needs with a larger sample capacity. On the other hand, the data from the US embassy was as representative as those from 35 monitoring stations. The monthly average PM 2.5 concentrations between the US Embassy and 35 monitoring stations (from January 2014 to June 2017) was compared in Figure 1. The overall trends for the two sets of observational data were basically the same, with a high correlation coefficient of 0.986 ( Figure 1). Liang et al. [62] also compared the two sets of monitoring data, and observed the same result. Therefore, it was reasonable to adopt the US Embassy monitoring data with a longer query period, which was effective and representative.
representative as those from 35 monitoring stations. The monthly average PM2.5 concentrations between the US Embassy and 35 monitoring stations (from January 2014 to June 2017) was compared in Figure 1. The overall trends for the two sets of observational data were basically the same, with a high correlation coefficient of 0.986 ( Figure 1). Liang et al. [62] also compared the two sets of monitoring data, and observed the same result. Therefore, it was reasonable to adopt the US Embassy monitoring data with a longer query period, which was effective and representative.  I  II  III  IV  I  II  III  IV  I  II  III  IV  I  II   2014

PM 2.5 and the Trends of the Three Industries
There was a clear seasonal variation of PM 2.5 pollution, where the most serious pollution appeared in winter ( Figure 2). The main reason was because the bad meteorological conditions impeded the diffusion and dilution of pollutants. During the winter season, water vapor in the air was prone to super-saturation, and it condensed into fog because of the large difference between day and night temperatures, relative high humidity, and static wind.
The annual average concentration of PM 2.5 in Beijing showed a general downward trend (Figure 3a). With the adjustment of industry structures, the output values of the primary, secondary, and tertiary industry also changed. The proportion of the output value of primary industry sharply decreased from 0.9% in 2010 to 0.43% in 2017 (Figure 3b). The proportion of secondary industry gradually dropped from 24.12% in 2010 to 18.97% in 2017 (Figure 3c). On the contrary, the proportion of tertiary industry increased from 74.98% in 2010 to 80.60% in 2017 (Figure 3d). The structural ratios of the three industry output values were 0.43%, 18.97%, and 80.60%, respectively.

PM2.5 and the Trends of the Three Industries
There was a clear seasonal variation of PM2.5 pollution, where the most serious pollution appeared in winter ( Figure 2). The main reason was because the bad meteorological conditions impeded the diffusion and dilution of pollutants. During the winter season, water vapor in the air was prone to super-saturation, and it condensed into fog because of the large difference between day and night temperatures, relative high humidity, and static wind.

Data Test
The yearly growth rate of PM2.5 concentration was abbreviated as RPM. The yearly growth rates of the primary, secondary, and tertiary industry production were respectively denoted by RPI, RSI, and RTI. The time series variation of each variable is drawn in Figure 4.

Data Test
The yearly growth rate of PM 2.5 concentration was abbreviated as RPM. The yearly growth rates of the primary, secondary, and tertiary industry production were respectively denoted by RPI, RSI, and RTI. The time series variation of each variable is drawn in Figure 4.
The seasonal effects of the variables were firstly tested through the stable seasonality test and the parameter-shift seasonality test using the X-12-ARIMA seasonal adjustment method. According to the results shown in Table 1, none of the four series had a stable seasonality nor a moving seasonality.
proportion of the tertiary industry GDP.

Data Test
The yearly growth rate of PM2.5 concentration was abbreviated as RPM. The yearly growth rates of the primary, secondary, and tertiary industry production were respectively denoted by RPI, RSI, and RTI. The time series variation of each variable is drawn in Figure 4. The seasonal effects of the variables were firstly tested through the stable seasonality test and the parameter-shift seasonality test using the X-12-ARIMA seasonal adjustment method. According to the results shown in Table 1, none of the four series had a stable seasonality nor a moving seasonality.  In order to avoid the problem of false return, an ADF test was then adopted to examine the smoothness of the time series data. Models (20)- (22) were established for each of the four sequences in turn, to examine the significance of the trend item and the intercept item, so the stationary type could be determined. According to the specific test results shown in Table 2, the unit root test of RPM, RPI, RSI, and RTI sequences rejected the null hypothesis. Thus, it was able to consider that all four sequences were stationary sequences, and a VAR model for direct analysis could be established.

Establishing the VAR Model
Before establishing a VAR model, it was required to determine the optimal lag order of the model based on criteria such as LR statistics, FPE, AIC, SC, and HQ. The optimal lag order was four for the FPE, AIC, and HQ, one for the LR, and zero for the SC, respectively (in Table 3). Considering the validity of the model construction, the lag order was set to four for the VAR model, so a VAR(4) model for RPM, RPI, RSI, and RTI was established. As the VAR model was a non-theoretical model, its coefficients had no economic significance. When the VAR model was analyzed, the magnitudes or the positive and negative influences of one variable on another were not emphasized. Therefore, the significance of the coefficients was not analyzed here.  "C", "T", and "K" represent constant term, time trend, and lag order, respectively; "*" and "**": reject the null hypothesis at the 10% and 5% significance level, respectively.

Checking the Model
The stability of the model by the unit root diagram of the VAR model is examined in Figure 5. The unit roots of the model all fell within the unit circle, indicating that Model (33) was stationary and effective [64].

Checking the Model
The stability of the model by the unit root diagram of the VAR model is examined in Figure 5. The unit roots of the model all fell within the unit circle, indicating that Model (33) was stationary and effective [64].
Since each variable examined by the ADF test was a zero-order integrated sequence, as shown in Table 2, the JJ cointegration tests were performed. According to the results shown in Table 4, two cointegration relationships between variables in the model were found at the 5% significance level, which implied a long-term equilibrium relationship between PM 2.5 pollution and the economic growth of the three industries. The first cointegration relationship is standardized as: where T is a trend variable. According to Equation (33), the PM 2.5 concentration increased with the economic growth of the primary and secondary industries; whilst the economic growth of the tertiary industry had an inhibitory effect on PM 2.5 emissions. The tertiary industry had the greatest impact on PM 2.5 among the three industries, whereas the primary industry had the least.
Through the Granger causality test, a causal relationship between two variables was further considered, as shown in Table 5; that is, all three industries had a one-way Granger causal relationship with PM 2.5 at the 5% significance level. There existed a one-way Granger cause from three industries to PM 2.5 , which suggested the development of the three industries in Beijing had a significant impact on PM 2.5 pollution.

Impulse Response Function
To avoid the order effect of variables on the results of the VAR(4) model, a lag period of 15 (i.e., a quarter) was selected using a generalized impulse response function [65,66] for analyzing the dynamic interconnections of PM 2.5 pollution to the development of the three industries. In Figures 6-8, the trajectory of the shock response was analyzed and illustrated between the level of PM 2.5 pollution and the development of three industries. According to Figure 6a, the impact of PM2.5 on the primary industry was rather complex, which had both positive and negative effects. PM2.5 began to decline in the first period, and dropped to the lowest point of −0.057 in the third period. Then it rose sharply to the peak value of 0.191 and quickly fell back to a very low point. After that, positive effects were depicted in the 8th and 9th periods, but they turned back to negative again in the 10th period. In the final stage, the trend followed fluctuations around zero with a cumulative value of 0.075, which indicated that the development of the primary industry had a weak effect on PM2.5 pollution because the source of PM2.5 emissions from the primary industry was very limited. Besides, the primary industry accounted for a rather small proportion of the total industry (only 0.43% by 2017). Thus, the development of the primary industry eventually played a minor role resulting in PM2.5 pollution.
According to Figure 6b, the response value of the primary industry to PM2.5 shocks was mainly negative after a positive impact by PM2.5. The primary industry fell to −0.023 in the first period, then rose to −0.018 in the second period. It again sharply dropped to the lowest point of −0.059 in the third period, and increased again to −0.0004 in the fourth period. There was also a gradual fluctuation around zero with a cumulative value of −0.230, which suggested that PM2.5 pollution had a certain inhibitory effect on the economic growth of the primary industry. Research in the field of agriculture has demonstrated that high levels of PM2.5 can lead to crop yield loss and quality reduction [7]. According to Figure 7a, influences of PM2.5 on the secondary industry were generally positive. The response value of PM2.5 dropped to −0.055 in the first period, then it rapidly increased to the peak value of 0.205 in the second period. It decreased to 0.003 in the third period, and then rose again to 0.038 in the fourth period. After that, the response value began to drop to −0.047 again in the eighth period. This repeated negative effect depicted that the continuous action of energy conservation and of industrial structure optimization in the secondary industry was assumed. Finally, the response value kept fluctuating around zero with a cumulative value of 0.215, indicating that the economic growth of the secondary industry exacerbated PM2.5 pollution to a certain extent. Although the proportion of the secondary industry to total industries dropped to 18.97% by 2017, it was still the largest source of PM2.5. The strong effect was concentrated on several sectors, such as secondary industry pollutants, exhaust emissions, and construction dust.
The response value of PM2.5 to the impact of the second industry was all negative in the first five periods, shown in Figure 7b. The lowest point of −0.039 appeared in the first period, and reached the peak value of 0.018 in the sixth period. Then it fluctuated around zero with a cumulative value of −0.075, which demonstrated that PM2.5 pollution hindered the economic growth of the second According to Figure 8a, the response of PM2.5 to the impact of the tertiary industry was mainly inhibited. The response value of PM2.5 rose to 0.017 in the first period, fell to the lowest value of −0.211 in the second period, and rose to −0.020 in the third period. After the fourth period it experienced a From Figure 8b, it was found that the response of PM2.5 to the tertiary industry alternated between positive and negative impacts. The tertiary industry reached a peak at 0.019 in the first period and fell to the lowest point of −0.020 in the third period. It then rose to 0.009 in the fourth period. After that, it gradually fluctuated around zero with a cumulative value of the first five periods of −0.009. It indicated that in the short term, PM2.5 pollution had a certain inhibitory effect on the tertiary industry, but it was not significant and had a weak driving effect on the tertiary industry in the long term.  According to Figure 6a, the impact of PM 2.5 on the primary industry was rather complex, which had both positive and negative effects. PM 2.5 began to decline in the first period, and dropped to the lowest point of −0.057 in the third period. Then it rose sharply to the peak value of 0.191 and quickly fell back to a very low point. After that, positive effects were depicted in the 8th and 9th periods, but they turned back to negative again in the 10th period. In the final stage, the trend followed fluctuations around zero with a cumulative value of 0.075, which indicated that the development of the primary industry had a weak effect on PM 2.5 pollution because the source of PM 2.5 emissions from the primary industry was very limited. Besides, the primary industry accounted for a rather small proportion of the total industry (only 0.43% by 2017). Thus, the development of the primary industry eventually played a minor role resulting in PM 2.5 pollution.
According to Figure 6b, the response value of the primary industry to PM 2.5 shocks was mainly negative after a positive impact by PM 2.5 . The primary industry fell to −0.023 in the first period, then rose to −0.018 in the second period. It again sharply dropped to the lowest point of −0.059 in the third period, and increased again to −0.0004 in the fourth period. There was also a gradual fluctuation around zero with a cumulative value of −0.230, which suggested that PM 2.5 pollution had a certain inhibitory effect on the economic growth of the primary industry. Research in the field of agriculture has demonstrated that high levels of PM 2.5 can lead to crop yield loss and quality reduction [7].

Dynamic Relationship between PM 2.5 Pollution Level and the Development of Secondary Industry
According to Figure 7a, influences of PM 2.5 on the secondary industry were generally positive. The response value of PM 2.5 dropped to −0.055 in the first period, then it rapidly increased to the peak value of 0.205 in the second period. It decreased to 0.003 in the third period, and then rose again to 0.038 in the fourth period. After that, the response value began to drop to −0.047 again in the eighth period. This repeated negative effect depicted that the continuous action of energy conservation and of industrial structure optimization in the secondary industry was assumed. Finally, the response value kept fluctuating around zero with a cumulative value of 0.215, indicating that the economic growth of the secondary industry exacerbated PM 2.5 pollution to a certain extent. Although the proportion of the secondary industry to total industries dropped to 18.97% by 2017, it was still the largest source of PM 2.5 . The strong effect was concentrated on several sectors, such as secondary industry pollutants, exhaust emissions, and construction dust.
The response value of PM 2.5 to the impact of the second industry was all negative in the first five periods, shown in Figure 7b. The lowest point of −0.039 appeared in the first period, and reached the peak value of 0.018 in the sixth period. Then it fluctuated around zero with a cumulative value of −0.075, which demonstrated that PM 2.5 pollution hindered the economic growth of the second industry in a short term. Such a short-term response can be explained as temporarily limited or ceased production of relevant emission enterprises.
3.6.3. Dynamic Relationship between PM 2.5 Pollution and the Development of Tertiary Industry According to Figure 8a, the response of PM 2.5 to the impact of the tertiary industry was mainly inhibited. The response value of PM 2.5 rose to 0.017 in the first period, fell to the lowest value of −0.211 in the second period, and rose to −0.020 in the third period. After the fourth period it experienced a temporary positive effect, and gradually stabilized at zero over time with a cumulative value of −0.189, which shows=ed that the development of the tertiary industry alleviated the PM 2.5 pollution to some extent. Meanwhile, the temporary positive effect demonstrated that some sectors promoted PM 2.5 emissions, for example, the motor vehicle exhaust emissions and dust emission in transportation, postal trades, etc.
From Figure 8b, it was found that the response of PM 2.5 to the tertiary industry alternated between positive and negative impacts. The tertiary industry reached a peak at 0.019 in the first period and fell to the lowest point of −0.020 in the third period. It then rose to 0.009 in the fourth period. After that, it gradually fluctuated around zero with a cumulative value of the first five periods of −0.009. It indicated that in the short term, PM 2.5 pollution had a certain inhibitory effect on the tertiary industry, but it was not significant and had a weak driving effect on the tertiary industry in the long term.

Variance Decomposition
Variance decomposition was performed in order to analyze the degree of mutual contribution between the development level of the three industries and the level of PM 2.5 pollution based on the VAR(4) model. Therefore, a lag period of 5 was chosen. The results of the Cholesky decomposition method were very sensitive to the order of variables, and thus this method limited the causal order of variables over the same period. Therefore, based on the research purpose, the corresponding economic theory, as well as the results of the Granger causality test in Table 5, we determined the order of variables as RTI > RSI > RPI > RPM, as shown in Table 6. According to the variance decomposition result of PM 2.5 , the contribution rate of the primary industry gradually increased and peaked at 37% in the fifth period, and then gradually stabilized to 34%. The contribution rate of the secondary industry gradually decreased from 66% and stabilized at 18%. The contribution of the tertiary industry reached the peak of 73% in the second period, then gradually decreased, and tended to stabilize. It was apparent that the impact of the primary and tertiary industrial developments had a certain lag effect on PM 2.5 emissions. The secondary industry was responsible for PM 2.5 emissions from the very beginning, since it contained almost all the high energy consumption industries that led to heavy pollution. However, its role in raising PM 2.5 gradually weakened. Thus, the main factor affecting the level of PM 2.5 pollution was the secondary industry in the early period, and then it turned to the primary and tertiary industries for the rest of the periods, as shown in Table 6.
The impact of PM 2.5 in the first period was zero, demonstrating that PM 2.5 pollution had a lagging effect on the development of the three industries. This result was quite in line with the real practice of "treatment after pollution". The contribution rate of PM 2.5 pollution to the secondary industry was the largest, reaching 1.6% in the 8th period. The contribution rate to the tertiary industry was only 0.4%, whereas to the primary industry is was less than 0.2% for the same period. Hence, the boost in secondary industry in Beijing was most sensitive to PM 2.5 . This observation was rational since the secondary industry mainly influenced air pollution.

Discussion
The impulse response function indicated that economic growth of the primary and secondary industries can raise PM 2.5 emissions, whilst the tertiary industry had an inhibitory effect. This result is consistent with the findings of Cao [67] and Zhao [68]. Therefore, it can be found that industry improvement (defined as economic growth) is an important factor affecting the intensity and direction of PM 2.5 emissions. More efforts should be undertaken to implement innovation-driven development strategies, promote industry transformation and upgrade, vigorously develop the tertiary industry, and actively cultivate high-end service industries in order to mitigate PM 2.5 pollution.
In addition, PM 2.5 pollution itself can hinder the development of the primary and secondary industries. In the long run, it can promote the development of the tertiary industry, which reveals that PM 2.5 pollution can influence industry growth as well. With the intensification of pollution and the enhancement of environmental awareness, the advancement of tertiary industry would become one of the most effective ways to alleviate PM 2.5 pollution.
Liu et al. [48], Duan et al. [52], and Li et al. [69] all observed that indicators of economic growth had good predictions of environmental pollution, while indicators of environmental pollution had less ability to interpret the variance of economic growth. Results indicated by variance decomposition is supported by their studies, which shows that the industry development of Beijing leans over the cost of PM 2.5 pollution. Capital and labor input are important driving forces for the improvement of Beijing's industries, whereas the impact of PM 2.5 pollution is relatively small. Environmental quality preference will also restrict the adverse effects of PM 2.5 pollution on industry growth. Therefore, while the industry is developing rapidly, it is necessary to pay attention to alleviating the negative effects of environmental pollution.
Nonetheless, results in this paper were based on statistical characteristics of the data, which were limited by the characteristics of the VAR model, and were not closely integrated with related economic theories. Additionally, several impact factors of industry development and PM 2.5 pollution, such as policy environment and environmental quality preference, are not considered in this paper. Therefore, the explanation of impact mechanisms in this paper can be further investigated with in-depth data mining. Overall, conclusions drawn in this paper emphasized the economic losses caused by PM 2.5 as well as the interaction of PM 2.5 with industry development, which cannot be overlooked.

Conclusions
From the perspective of industry development, a VAR model has been proposed in this paper to examine the dynamic relation between the level of haze pollution and industry progress in 2010-2017 through an impulse response function and a variance decomposition method. Results have shown that a long-term equilibrium relationship existed between PM 2.5 pollution and the improvement of the primary, secondary, and tertiary industries.
The three industries are the one-way Granger causes of PM 2.5 . The development of the three industries have shown different degrees of impact on the PM 2.5 pollution, with the duration of about one to two years. The development of the primary and secondary industries would increase PM 2.5 emission, whilst the tertiary industry would reduce.
The research work in this paper focuses on analyzing the two-way mechanism between PM 2.5 pollution and the three industries from the perspective of time dynamics, so as to provide theoretical support for Beijing's industry development and environmental planning. The foundation of haze management is to adjust industrial development to promote industry transformation and upgrade. Emergency measures, such as suspending the production of heavy polluting enterprises and restricting motor vehicle operation in the city, can only alleviate heavy pollution in the short-term. The long-term solution to the problem of haze requires transforming the extensive economic development model, optimizing the industry structure, vigorously developing the tertiary industry, and forcing the transformation and upgrade enterprises so as to achieve coordinated economic and environmental development.