1.1 Monthly estimates
The first step in analysis of longitudinal studies is the examination of the stationarity of variables. Due to high variation in investigated variables during the course of study, all variables were used in logarithmic form. To check variables stationarity, the Augmented Dickey-Fuller test was used. The null hypothesis in this test implies the existence of a single root for each variable, which in nature is a non-stationary variable. Consequently, this study carried out these unit root tests on the log of pollution (average across 19 stations), fuel prices, and weather variables with linear time trend. Table 2 represents the results of stationarity test.
Table 2. Results of stationarity test.
|
Variable
|
|
Test statistics (pc)
|
|
Test result
|
Lna CO
|
|
-1.62 (0.46)
|
|
Non-stationary
|
Δb Ln CO
|
|
-7.13 (0.00)
|
|
stationary
|
Ln NO2
|
|
-2.80 (0.058)
|
|
Non-stationary
|
Δ Ln NO2
|
|
-12.4 (0.00)
|
|
stationary
|
Ln PM10
|
|
-4.67 (0.00)
|
|
stationary
|
Ln GP
|
|
-2.40 (0.14)
|
|
Non-stationary
|
Δ Ln GP
|
|
-11.66 (0.00)
|
|
stationary
|
Ln DP
|
|
-2.31 (0.16)
|
|
Non-stationary
|
Δ Ln DP
|
|
-11.45 (0.00)
|
|
stationary
|
Ln Temp
|
|
-2.01 (0.4)
|
|
Non-stationary
|
Δ Ln Temp
|
|
-5.31 (0.00)
|
|
stationary
|
Ln Rain
|
|
-2.00 (0.65)
|
|
Non-stationary
|
Δ Ln Rain
|
|
-2.33 (0.00)
|
|
stationary
|
Ln wind
|
|
-1.12 (0.14)
|
|
Non-stationary
|
Δ Ln wind
|
|
-2.11 (0.00)
|
|
stationary
|
Holi
|
|
-2.71 (0.059)
|
|
Non-stationary
|
Δ Holi
|
|
-12.4 (0.00)
|
|
stationary
|
a denote logarithm; b denote the difference between variable logarithm in time t and t-1; c P value
According to the results in table 2, all variables become stationary after one- differentiating (I(1)) except for PM10. PM10 were stationary at level (I (0)). Therefore, it can be concluded that the relationship between the time series is sufficient, so the results of the regression are to be true.
Since variables in this study, are a combination of different stationary (I (0) and I (1)), the use of the auto regressive distributed lag (ARDL) method is more preferable with respect to other methods. In this model, the Hannan-Quinn criterion (HQ) was used to determine the optimum length of lags. The optimum lags for variables in each models reported in parenthesis in table 3. The optimum lags for models with CO, PM10, and NO2 dependent variables were (1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0), and (1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0). The first numbers in parenthesis refer to optimum lag number of dependent variables, and other numbers refer to independent variables optimum lags. The optimum lags for all dependent variables were one, so we included all dependent variables with one lag. In model with CO dependent variable, the optimum lags for variables "Ln Temp" and "Ln Trend" was two, so in this model we apply "Ln Temp (-1)", "Ln Temp (-2)", "Ln Trend (-1)", and "Ln Trend (-2)". In other hand, the optimum lag for other explanatory variables was zero, so we included these variables in non-lag form.
Table 3. Results of short-term estimations for models with three different pollutants (CO, NO2, and PM10)
Dependent variable
|
Ln CO
|
|
Dependent variable
|
Ln PM10
|
|
Dependent variable
|
Ln NO2
|
Optimum lag
|
(1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0)
|
|
Optimum lag
|
(1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0)
|
|
Optimum lag
|
(1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0)
|
|
coefficient
|
t- value (p)
|
|
|
Coefficient
|
t-value (pa)
|
|
|
Coefficient
|
t-value (pa)
|
Ln CO (-1b)
|
0.48
|
6.005 (0.00)
|
|
Ln PM10 (-1 b)
|
0.41
|
5.005 (0.00)
|
|
Ln NO2 (-1 b)
|
0.61
|
8.77 (0.00)
|
Ln MPI
|
0.67
|
-1.75 (0.08)
|
|
Ln MPI
|
0.17
|
-1.83 (0.07)
|
|
Ln MPI
|
0.79
|
0.97 (0.33)
|
Ln Rain
|
0.01
|
2.39 (0.11)
|
|
Ln Rain
|
-0.007
|
2.93 (0.02)
|
|
|
0.36
|
1.26
(0.2)
|
Ln Temp
|
-0.006
|
2.33 (0.02)
|
|
Ln Temp
|
-0.09
|
3.33 (0.01)
|
|
Ln MPI(-2 b)
|
-1.96
|
-2.45 (0.01)
|
Ln Temp (-1b)
|
-0.002
|
-0.52 (0.59)
|
|
Ln Temp (-1 b)
|
-0.002
|
-0.52 (0.59)
|
|
Ln Rain
|
0.01
|
1.1
(0.1)
|
Ln Temp (-2 b)
|
0.005
|
1.78 (0.07)
|
|
Ln VAT
|
0.04
|
2.12 (0. 3)
|
|
Ln Temp
|
-0.001
|
1.29 (0.19)
|
Ln VAT
|
0.01
|
-0.25 (0.8)
|
|
ln GP
|
-0.012
|
-1.97 (0.05)
|
|
Ln VAT
|
1.39
|
-1.51 (0.13)
|
ln GP
|
-0.02
|
-1.97 (0.05)
|
|
Ln Trend
|
0.05
|
-2.23 (0.2)
|
|
Ln VAT (-1 b)
|
1.9
|
2.03 (0.04)
|
Ln Trend
|
0.1
|
-2.23 (0.02)
|
|
Ln Trend (-1 b)
|
0.13
|
2.33 (0.02)
|
|
Ln GP
|
0.011
|
1.34 (0.18)
|
Ln Trend (-1 b)
|
0.13
|
2.33 (0.02)
|
|
Ln Trend (-2 b)
|
-0.12
|
-2.56 (0.01)
|
|
Ln GP (-1 b)
|
0.016
|
-1.91 (0.05)
|
ln Trend (-2 b)
|
-0.009
|
-2.56 (0.01)
|
|
Ln DP
|
-0.02
|
1.43 (0.06)
|
|
Ln Trend
|
0.001
|
0.06 (0.04)
|
ln DP
|
-0.008
|
1.43 (0.06)
|
|
DUM
|
-0.24
|
2.24 (0.02)
|
|
Ln DP
|
-0.015
|
-1.9 (0.05)
|
DUM
|
-0.24
|
2.24 (0.02)
|
|
Ln Wind
|
-0.44
|
-5.04
(0.00)
|
|
DUM
|
-0.03
|
0.38 (0.69)
|
Ln Wind
|
-0.11
|
2.5
(0.01)
|
|
|
|
|
|
Ln Wind
|
-0.09
|
2.5
(0.01)
|
Holi
|
-0.11
|
3.05 (0.00)
|
|
Holi
|
-0.07
|
0.2 (0.3)
|
|
Holi
|
-0.09
|
3.24 (0.01)
|
C
|
8.001
|
0.98 (0.3)
|
|
C
|
9.1
|
0.5 (0.2)
|
|
C
|
-7.44
|
-0.95 (0.33)
|
Diagnostic tests
|
|
Diagnostic tests
|
|
Diagnostic tests
|
|
statics
|
p
|
|
|
statics
|
p
|
|
|
statics
|
p
|
R2
|
0.80
|
-
|
|
R2
|
|
-
|
|
R2
|
0.80
|
-
|
Durbin-Watson
|
2.05
|
-
|
|
Durbin-Watson
|
2.01
|
|
|
Durbin-Watson
|
1.91
|
|
Autocorrelation test
|
078
|
0.66
|
|
Autocorrelation test
|
0.68
|
0.76
|
|
Autocorrelation test
|
0.72
|
0.48
|
Ramsey’s RESET Test
|
0.59
|
0.44
|
|
Ramsey’s RESET Test
|
0.4
|
0.54
|
|
Ramsey’s RESET Test
|
0.74
|
0.46
|
Jarque -Bera
|
1.77
|
0.41
|
|
Jarque -Bera
|
1.23
|
0.52
|
|
Jarque -Bera
|
1.65
|
0.39
|
Engle’s ARCH LM
|
0.64
|
0.42
|
|
Engle’s ARCH LM
|
0.74
|
0.39
|
|
Engle’s ARCH LM
|
1.19
|
0.27
|
a P value; b lag number
In model with PM10 dependent variable, the optimum lag for variables "Ln Temp" and "Ln Trend" were 1 and 2 respectively, so in this model we apply "Ln Temp (-1)", "Ln Trend (-1)", and "Ln Trend (-2)". In other hand, the optimum lag for other explanatory variables was zero, so we included these variables in non-lag form.
Also, in model with NO2 dependent variable, the optimum lag for variables "Ln VAT", "Ln MPI", and “Ln GP” were two, one, and one, respectively. Therefore, in this model we apply "Ln VAT", "Ln VAT (-1)", "Ln VAT (-2)", "Ln MPI (-1)", and "Ln GP (-1)". In other hand, the optimum lag for other explanatory variables was zero, so we included these variables in non-lag form.
The findings on dynamic models (short- term) showed that change in gasoline fuel price has greater impact on CO concentration than other pollutants. According to the results of short run, one percent change in gasoline fuel prices lead to 0.02, 0.012, and 0.011 percent change in CO, PM10, and NO2 concentrations, respectively. Also, one percent increase in diesel fuel prices lead to 0.008, 0.02, and 0.015 percent decrease in CO, PM10, and NO2 concentrations, respectively. The findings indicated that diesel price had greater impact on NO2 and PM10 concentrations and gasoline fuel price had greater impact on CO concentration than diesel fuel.
The findings on weather variables revealed that rainfall had no significant impacts on CO and NO2 concentrations. However, rainfall had a significant negative impact on PM10 concentration. Higher temperature was also associated with less air pollution. Wind blow had a significant effect on the concentration of all pollutants, and this relationship was inverse. That is one percent increase in wind speed resulted in 0.11, 0.09, and 0.44 percent decrease in the concentration of CO, NO2, and PM10, respectively.
The findings revealed that time trend had positive impacts on CO and NO2 concentrations in a significant manner but no significant effect on PM10 concentration was observed. In other words, an increase in the population and change in fuel quality led to an increase in concentrations of CO and NO2.
The findings also indicated that coefficient of log VAT and MPI had positive impacts on air pollutant concentration, but not a significant effect.
In regards to the holidays, the findings indicated that an increase in number of holidays and weekends in each month had a negative impact on the concentrations of CO, NO2, and PM10; so that, one percent increase in the number of holidays in each month, led to 0.11, 0.09, and 0.07 percent decrease in CO, NO2, and PM10 concentration, respectively. However, this effect was not significant for PM10 concentration.
In this study the coefficient of determination (R2) in all models was near 1.00 (R2= 0.8), which indicates that the models had a relatively high explanatory power. Also, the Durbin-Watson statistics in all three models were near two, which mean no autocorrelation problem was present in the models.
This study implemented several diagnostic tests to ensure models appropriateness, such as 1-test for the correctly specified model (Ramsey’s RESET Test), 2- serial correlation (LM test), 3-heteroscedasticity (ARCH test) and 4-normality (Jarque -Bera (N)). The diagnostic tests results showed that there are no problems associated with the correctly specified model, serial correlation, normality or heteroscedasticity. Table 3 shows the results of the dynamic equation estimation for three pollutants in three columns along with several diagnostic tests to ensure the accuracy of estimation models.
Furthermore, this study conveyed cumulative sum control chart (CUSUM) test to investigate stability of the model’s coefficients. In this test, the confidence interval is two straight lines that show 95% confidence level. If the test statistics were located between these two lines, then the null hypothesis would not be rejected (H0: stability of parameters). The findings of this test indicated that all estimated parameters were stable at 5% significant level. Based on Figure 3, value for the CUSUM tests in all models were located between these two lines, which indicates the stability of the parameters in all models.
Also, The Boundary test was used to investigate existence of cointegration and the long- term relationship between variables. In this method, two critical bounds are presented, upper bound for time series I(1) and lower bound for series I(0). In this test, if the F statistic is greater than the upper bound value, the null hypothesis (lack of cointegration) is rejected; and if F statistic is less than the lower bound value, the null hypothesis is confirmed. Moreover, if the F statistic locates between two bounds, no conclusions can be made. Results of boundary test showed that F statistic is higher than upper bound, which is provided by Pesaran et al. consequently, there is a long- term relationship between variables. Table 4 shows the results of Boundary test for models.
The long – term results of the models showed that, one percent increase in gasoline fuel price lead to 0.027 and 0.016 percent decrease in concentrations of CO and PM10, respectively; and 0.02 percent increase in NO2 concentration. However, the impact on PM10 was not significant in the long term. Furthermore, one percent increase in diesel fuel price leads to 0.011, 0.024, and 0.029 percent decrease in concentrations of CO, NO2, and PM10, respectively. Therefore, in the long term, fuel price changes had a greater impact on the concentrations of pollutants compared to the short run. In the short term however, changes in gasoline fuel prices had greater impact on the concentration of pollutants, than diesel fuel prices.
Table 4. Boundary test results for the models
|
|
F-statistic
|
|
critical bounds at 5% Significant level
|
|
|
Lower bound I(0)
|
Upper bound I(1)
|
|
Model with PM10 dependent variable
|
|
5.14
|
|
2.01
|
3.05
|
|
Model with NO2 dependent variable
|
|
4.98
|
|
2.01
|
3.05
|
|
Model with CO dependent variable
|
|
6.15
|
|
2.01
|
3.05
|
|
|
|
|
|
|
|
|
|
|
|
Other variables such as VAT and MPI had a positive impact on the concentration of all air pollutants in significant manner. So that one percent increase in VAT causes a 0.31, 0.31, and 1.21 percent increase in CO, NO2, and PM10 concentrations, respectively. Also, one percent increase in MPI causes a 2.96, 2.96, and 0.88 percent increase in CO, NO2, and PM10 concentrations, respectively. Consequently, these two variables had greater impacts in the long term compared to the short term.
For other coefficients related to weather variables, the findings revealed that rainfall, wind blow, and temperature had no significant impacts on pollutant concentration except for PM10. That is one percent increase for rainfall and temperature leads to 0.01 percent decrease in PM10 concentration in the long term. The stated coefficients were greater in the long term than for the short term.
The findings also indicated that time trend had maximum impacts on all pollutant concentrations in the long- term. This means the increase in the population and decrease in fuel quality in the long- term, lead to 1.78, 1.93, and 0.05 percent increase in CO, NO2, and PM10 concentration respectively. Table 5 shows the results of long- term relationship between variables for models with three different dependent variables (i.e. CO, NO2, and PM10).
Table 5. Results of long-term estimations for models with three different pollutants (CO, NO2, and PM10)
|
Model with dependent variable:
|
|
Ln CO
|
Ln NO2
|
Ln PM10
|
Variable
|
Coefficient (p)
|
Coefficient (p)
|
Coefficient (p)
|
Ln DP
|
-0.011 (0.002)
|
-0.024 (0.002)
|
-0.029 (0.03)
|
Ln GP
|
-0.027 (0.01)
|
0.02 (0.01)
|
-0.016 (0.27)
|
Ln MPI
|
2.96 (0.007)
|
2.96 (0.007)
|
0.88 (0.001)
|
Ln Rain
|
0.008 (0.62)
|
0.008 (0.62)
|
-0.01 (0.01)
|
Ln Temp
|
-0.07 (0.14)
|
-0.07 (0.14)
|
-0.01 (0.05)
|
Ln Wind
|
-0.1 (0.1)
|
-0.52 (0.2)
|
-1.07 (0.06)
|
Ln VAT
|
0.31 (0.05)
|
0.31 (0.05)
|
1.21 (0.01)
|
Ln Trend
|
1.78 (0.01)
|
1.93 (0.01)
|
0.05 (0.00)
|
Holi
|
-0.8 (0.04)
|
-0.8 (0.07)
|
-0.92 (0.07)
|
DUM
|
-1.1(0.5)
|
-1.0 (0.5)
|
-0.93 (0.4)
|
C
|
-10.91 (0.49)
|
-10.91 (0.49)
|
-16.15 (0.3)
|
1.2 Sub-period analysis gasoline- Compressed Natural Gas (CNG) substitution
Over the past decade, the Iranian government has paid a lot of attention to the production of CNG vehicles in order to reduce gasoline consumption and air pollution. As part of such plan, gasoline-fueled vehicles have been converted to CNG and, the number of CNG stations has been increased around the nation. However, the CNG-fueled vehicles emit less CO and more NO2 than the gasoline powered vehicles. In order to increase the validity of the results, the models were studied in two different periods – during 01. 2009– 03.2013 (period 1) and 04. 2013-12.2019 (period 2) (Table 6).
Results showed that an increase in gasoline price leads to an increase in NO2 concentration in recent years and the second period of study as well. Based on substitution between gasoline and CNG, an increase in gasoline fuel price lead to increases in CNG consumption and consequently increases NO2 emission.
Table 6. Fuel price affects CO, NO2, and PM10 during period (1) and period (2)
|
|
Model with dependent variable
|
Variable
|
|
CO
|
|
NO2
|
|
PM10
|
|
Period 1
|
|
Period 2
|
|
Period 1
|
|
Period 2
|
|
Period 1
|
|
Period 2
|
Ln DP
|
|
-0.02
|
|
-0.018
|
|
-0.019
|
|
-0.019
|
|
-0.26
|
|
-0.027
|
Ln GP
|
|
-0.02
|
|
-0.029
|
|
-0.016
|
|
0.014
|
|
-0.016
|
|
-0.019
|
R2
|
|
0.8
|
|
0.8
|
|
0.8
|
|
0.79
|
|
0.81
|
|
0.81
|