3.1. 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 stationarity, the Augmented Dickey-Fuller test and the Phillips-Perron test were used. The null hypothesis in both tests 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 22 stations), fuel prices, and weather variables with linear time trend. Table (1) represents the results of stationarity test.
According to the results in table (1), 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 findings on dynamic models (short run) showed that change in gasoline fuel price has greater impact on CO concentration than the other pollutants. According to the results of short run, one percent increase in gasoline fuel prices lead to 0.02, 0.011, and 0.012 percent decrease 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.
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 the 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 air pollutants respectively. However, this effect was not significant for PM10 concentration.
In this study the coefficients of determination (R2) in all models was 0.8, which indicates that the models had a relatively high explanatory power. Also, the Durbin-Watson statistics in all three models were near 2, which means 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 (2) 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 are 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 (6), value for the CUSUM test is located between these 2 lines, which indicates the stability of the parameters.
The Boundary test was also used to investigate existence of cointegration and the long-run 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 was higher than upper bound which is provided by Narayan and Pesaran et al. consequently, there is a long run relationship between variables. Table 3 shows the results of Boundary test for models.
Table 1
Results of stationarity test.
variable
|
Test statistics (p-value)
|
Test result
|
Ln CO
|
-1.62 (0.46)
|
Non-stationary
|
Δ 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 gasoline price
|
-2.40 (0.14)
|
Non-stationary
|
Δ Ln gasoline price
|
-11.66 (0.00)
|
stationary
|
Ln diesel price
|
-2.31 (0.16)
|
Non-stationary
|
Δ Ln diesel price
|
-11.45 (0.00)
|
stationary
|
Mean temperature
|
-2.01 (0.4)
|
Non-stationary
|
Δ Mean temperature
|
-5.31 (0.00)
|
stationary
|
Rainfall
|
-2.00 (0.65)
|
Non-stationary
|
Δ Rainfall
|
-2.33 (0.00)
|
stationary
|
wind speed
|
-1.12 (0.14)
|
Non-stationary
|
Δ wind speed
|
-2.11 (0.00)
|
stationary
|
Number of holidays and weekend days
|
-2.71 (0.059)
|
Non-stationary
|
Δ Number of holidays and weekend days
|
-12.4 (0.00)
|
stationary
|
Table 2
Results of dynamic relationship for models with three different pollutants (CO, NO2, and PM10)
Dependent variable
|
lnCO
|
Dependent variable
|
LnNO2
|
Optimum lag
|
(1, 0, 0, 2, 0, 0, 2, 0)
|
Optimum lag
|
(1, 2, 0, 0, 1, 1, 0, 0)
|
|
Coefficient
|
t-value (prob)
|
|
Coefficient
|
t-value (prob)
|
lnCO (-1)
|
0.48
|
6.005 (0.00)
|
lnNO2 (-1)
|
0.61
|
8.77 (0.00)
|
lnMPI
|
0.67
|
-1.75 (0.08)
|
lnMPI
|
0.79
|
0.97 (0.33)
|
lnRain
|
0.01
|
2.39 (0.11)
|
|
lnTempreture
|
-0.006
|
2.33 (0.02)
|
lnMPI(-1)
|
0.36
|
1.26
|
lnTempreture (-1)
|
-0.002
|
-0.52 (0.59)
|
|
-0.2
|
lnTempreture (-2)
|
0.005
|
1.78 (0.07)
|
lnMPI(-2)
|
-1.96
|
-2.45 (0.01)
|
lnVAT
|
0.01
|
-0.25 (0.8)
|
lnRain
|
0.01
|
1.1
|
ln Gasoline price
|
-0.02
|
-1.97 (0.05)
|
-0.1
|
lnTrend
|
0.1
|
-2.23 (0.02)
|
lnTempreture
|
-0.001
|
1.29 (0.19)
|
lnTrend (-1)
|
0.13
|
2.33 (0.02)
|
lnVAT
|
1.39
|
-1.51 (0.13)
|
ln Trend (-2)
|
-0.009
|
-2.56 (0.01)
|
lnVAT (-1)
|
1.9
|
2.03 (0.04)
|
ln Diesel price
|
-0.008
|
1.43 (0.06)
|
ln Gasoline price
|
0.011
|
1.34 (0.18)
|
DUM
|
-0.24
|
2.24 (0.02)
|
ln Gasoline price (-1)
|
0.016
|
-1.91 (0.05)
|
Wind
|
-0.11
|
2.5
|
lnTrend
|
0.001
|
0.06 (0.04)
|
-0.01
|
ln Diesel price
|
-0.015
|
-1.9 (0.05)
|
Number of holidays and weekend days
|
-0.11
|
3.05 (0.00)
|
DUM
|
-0.03
|
0.38 (0.69)
|
C
|
8.001
|
0.98 (0.3)
|
Wind
|
-0.09
|
2.5
|
R2
|
0.8
|
|
-0.01
|
Diagnostic tests
|
Number of holidays and weekend days
|
-0.09
|
3.24 (0.01)
|
Durbin-Watson
|
2.05
|
C
|
-7.44
|
-0.95 (0.33)
|
stat
|
R2
|
0.8
|
|
Autocorrelation test
|
078 (0.66)
|
Diagnostic tests
|
Ramsey’s RESET Test
|
0.59 (0.44)
|
Durbin-Watson
|
1.91
|
Jarque -Bera
|
1.77 (0.41)
|
Stat
|
Engle’s ARCH LM
|
0.64 (0.42)
|
Autocorrelation test
|
0.72 (0.48)
|
|
|
|
Ramsey’s RESET Test
|
0.74 (0.46)
|
|
|
|
Jarque -Bera
|
1.65 (0.39)
|
|
|
|
Engle’s ARCH LM
|
1.19 (0.27)
|
Table 3
Boundary test results for the models
F-statistic
|
critical bounds for Narayan
|
critical bounds for Pesaran
|
Significant level
|
model with CO dependent variable
|
model with NO2 dependent variable
|
model with PM10 dependent variable
|
6.15
|
4.98
|
5.14
|
I(0)
|
I(1)
|
I(0)
|
I(1)
|
|
|
|
2.01
|
3.05
|
1.92
|
2.89
|
10%
|
2.33
|
3.45
|
2.17
|
3.21
|
5%
|
3.02
|
4.35
|
2.73
|
3.9
|
1%
|
Table 4
Long run estimations for the models
|
Model with dependent variable:
|
|
CO
|
NO2
|
PM10
|
Variable
|
Coefficient (P-Value)
|
Coefficient (P-Value)
|
Coefficient (P-Value)
|
lnDieselprice
|
-0.011 (0.002)
|
-0.024 (0.002)
|
-0.029 (0.03)
|
lnGasolineprice
|
-0.027 (0.01)
|
0.02 (0.01)
|
-0.016 (0.27)
|
lnMPI
|
2.96 (0.007)
|
2.96 (0.007)
|
0.88 (0.001)
|
lnRain
|
0.008 (0.62)
|
0.008 (0.62)
|
-0.01 (0.01)
|
lnTemreture
|
-0.07 (0.14)
|
-0.07 (0.14)
|
-0.01 (0.05)
|
Wind
|
-0.1 (0.1)
|
-0.52 (0.2)
|
-1.07 (0.06)
|
lnVAT
|
0.31 (0.05)
|
0.31 (0.05)
|
1.21 (0.01)
|
lnTimetrend
|
1.78 (0.01)
|
1.93 (0.01)
|
0.05 (0.00)
|
Number of holidays and weekend days
|
-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)
|
Table 5
Fuel price impacts on 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
|
lnDieselprice
|
|
-0.02
|
|
-0.018
|
|
-0.019
|
|
-0.019
|
|
-0.26
|
|
-0.027
|
lnGasolineprice
|
|
-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
|
The long run results of the models showed that, one percent increase in gasoline fuel price lead to 0.027 and 0.016 percent decrease in the 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 run. 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 run, 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 a greater impact on the concentrations of pollutants, than diesel fuel prices.
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 run compared to the short run.
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 in the amount of rainfall and temperature leads to 0.01 percent decrease in PM10 concentration in the long run. The stated coefficients were greater in the long run than for the short run.
The findings also indicated that time trend had maximum impacts on all pollutant concentrations in the long run. This means the increase in the population and decrease in fuel quality in the long run, lead to 1.78, 1.93, and 0.05 percent increase in CO, NO2, and PM10 concentration respectively. Table (4) shows the results of long run relationship between variables for models with three different dependent variables (i.e. CO, NO2, and PM10).