# Statistical Modeling of the Early-Stage Impact of a New Traffic Policy in Milan, Italy

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## Abstract

**:**

## 1. Introduction

**Hypothesis**

**1.**

**Hypothesis**

**2.**

## 2. Materials and Methods

#### 2.1. Data

#### 2.1.1. Air Quality and Weather Monitoring Network in Milan

#### 2.1.2. Temporal Coverage, Pollutants, and Weather Measures

#### 2.1.3. Anthropogenic Activities

#### 2.2. Methods: Average and Median Difference before and after the Policy

#### 2.3. Methods: Time Series Modeling Using a State Space Approach

#### 2.3.1. Basic Structural Model for Air Quality Data

#### 2.3.2. Three-Step Model Selection

#### 2.3.3. Policy Intervention Analysis

#### 2.3.4. Software

## 3. Results

#### 3.1. Average and Median Differences

#### 3.2. Model Selection

#### 3.2.1. Step 1: Detection of the Seasonal Components

#### 3.2.2. Step 2: Detection of the Counter-Factual Component

#### 3.2.3. Step 3: Detection of the Weather and Calendar Factors

#### 3.2.4. Final Model Specification

#### 3.3. Basic Structural Model and Policy Intervention

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Annual average NO${}_{2}$ concentrations ($\mathsf{\mu}$g/m${}^{3}$) in Europe during 2018. Levels are expressed in $\mathsf{\mu}$g/m${}^{3}$. Source: European Environmental Agency

**Figure 2.**Monitoring system in Milan. Air quality stations (blue points): Marche (501), Verziere (528), Senato (548), Liguria (539) and Città Studi (705). Weather stations (red points): Lambrate (100), Zavattari (503), Brera (620), Feltre (869), Rosellini (1327), Juvara (502), and Marche (501).

**Figure 3.**Georeferentiation of counter-factual candidates. Geographical positioning of the counter- factual candidates with respect to Milan.

**Figure 4.**Pollutant levels in Milan ($\mathsf{\mu}$g/m${}^{3}$). Observed concentrations levels of NO${}_{\mathrm{x}}$ and NO${}_{2}$ between 2014 and 2019 with yearly average and median values. Values are expressed as $\mathsf{\mu}$g/m${}^{3}$.

**Figure 5.**Model selection-Step 1-NO${}_{\mathrm{x}}$. Seasonal component selection for the five nitrogen oxides stations in Milan. Left panel: 10-steps-ahead MSFE in log-scale as function of the number of harmonics. Right panel: AICc and BIC pairs for each model.

**Figure 6.**Model selection-Step 1-NO${}_{2}$. Seasonal component selection for the 5 nitrogen dioxide stations in Milan. Left panel: 10-steps-ahead MSFE in log-scale as function of the number of harmonics. Right panel: AICc and BIC pairs for each model.

**Figure 7.**Model selection-Step 2-NO${}_{\mathrm{x}}$. Counter-factual term selection for the five nitrogen oxides stations in Milan. Left panel: 10-steps-ahead MSFE in log-scale as function of the candidate. Right panel: AICc and BIC pairs for each model.

**Figure 8.**Model selection-Step 2-NO${}_{2}$. Counter-factual term selection for the five nitrogen dioxide stations in Milan. Left panel: 10-steps-ahead MSFE in log-scale as function of the candidate. Right panel: AICc and BIC pairs for each model.

**Table 1.**Differences between the average concentration level of the sub-period 2014–2018 and the treatment period 2019. Differences are expressed in $\mathsf{\mu}$g/m${}^{3}$.

Station Name | Nitrogen Oxides | Nitrogen Dioxide | ||
---|---|---|---|---|

${\mathit{d}}_{\mathit{AVG}}$ | ${\mathit{d}}_{\mathit{MED}}$ | ${\mathit{d}}_{\mathit{AVG}}$ | ${\mathit{d}}_{\mathit{MED}}$ | |

Milano city stations | ||||

Città Studi | 0.94 | −0.43 | −2.63 | −4.26 |

Liguria | −25.59 | −26.91 | −19.49 | −20.71 |

Marche | −17.29 | −22.00 | −11.53 | −13.37 |

Senato | −14.99 | −13.84 | −10.46 | −9.73 |

Verziere | −2.66 | −5.00 | −4.35 | −5.78 |

Other urban centres in Lombardy | ||||

Bergamo | −11.56 | −8.90 | −5.11 | −4.07 |

Brescia | −4.61 | −6.39 | −3.46 | −4.12 |

Cremona | 3.47 | 1.10 | 1.53 | 0.85 |

Lodi | −5.99 | −7.62 | -1.85 | −2.57 |

Pavia | −14.75 | −17.77 | −7.75 | −9.28 |

Saronno | −7.96 | −7.84 | −8.66 | −8.87 |

Treviglio | 0.06 | −3.71 | 2.25 | 0.39 |

**Table 2.**Model selection-Step 3-NO${}_{\mathrm{x}}$: Best subset of covariates using backward-forward stepwise algorithms for NO${}_{\mathrm{x}}$.

Marche | Verziere | Senato | Liguria | Citta Studi | ||||||
---|---|---|---|---|---|---|---|---|---|---|

AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | |

Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Week-End | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Saturday:Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | |||||

Sunday:Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Wind speed Q${}_{\mathrm{NE}}$ | ||||||||||

Wind speed Q${}_{\mathrm{SE}}$ | ✓ | |||||||||

Wind speed Q${}_{\mathrm{SW}}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Wind speed Q${}_{\mathrm{NW}}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

Temperature | ||||||||||

Rainfall | ✓ | ✓ | ✓ | ✓ | ||||||

Global radiation | ✓ | ✓ | ||||||||

Humidity |

**Table 3.**Model selection-Step 3-NO${}_{2}$: Best subset of covariates using backward-forward stepwise algorithms for NO${}_{2}$.

Marche | Verziere | Senato | Liguria | Citta Studi | ||||||
---|---|---|---|---|---|---|---|---|---|---|

AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | |

Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Week-End | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Saturday:Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||

Sunday:Holidays | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |

Wind speed Q${}_{\mathrm{NE}}$ | ||||||||||

Wind speed Q${}_{\mathrm{SE}}$ | ||||||||||

Wind speed Q${}_{\mathrm{SW}}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Wind speed Q${}_{\mathrm{NW}}$ | ✓ | ✓ | ||||||||

Temperature | ||||||||||

Rainfall | ✓ | ✓ | ||||||||

Global radiation | ✓ | ✓ | ✓ | ✓ | ||||||

Humidity | ✓ | ✓ |

Parameter | Marche | Citta Studi | Liguria | Verziere | Senato | |
---|---|---|---|---|---|---|

log(Pavia) | $\theta $ | 0.51 *** | 0.93 *** | 0.73 *** | 0.66 *** | 0.57 *** |

(0.01) | (0.02) | (0.02) | 0.02 | (0.01) | ||

Holidays | ${\varphi}_{1}$ | −0.06 *** | −0.02 | −0.05 * | −0.10 *** | −0.09 *** |

(0.03) | (0.04) | (0.03) | (0.03) | (0.03) | ||

WeekEnd | ${\varphi}_{2}$ | −0.11 *** | −0.09 *** | −0.09 *** | −0.17 *** | −0.15 *** |

(0.01) | (0.02) | (0.01) | (0.01) | (0.01) | ||

Saturday:Holidays | ${\varphi}_{3}$ | 0.10 | 0.17 | 0.04 | 0.10 | 0.14 *** |

(0.08) | (0.13) | (0.10) | (0.14) | (0.05) | ||

Sunday:Holidays | ${\varphi}_{4}$ | 0.09 ** | 0.09 | 0.12 * | 0.08 | 0.10 *** |

(0.05) | (0.08) | (0.06) | (0.05) | (0.03) | ||

WindSpeed Q${}_{\mathrm{SW}}$ | ${\varphi}_{5}$ | −0.44 *** | −0.20 *** | −0.56 *** | −0.30 *** | −0.27 *** |

(0.01) | (0.02) | (0.02) | (0.02) | (0.01) | ||

WindSpeed Q${}_{\mathrm{NW}}$ | ${\varphi}_{6}$ | −0.31v*** | −0.27 *** | −0.12 *** | −0.20 *** | −0.12 *** |

(0.01) | (0.02) | (0.01) | (0.01) | (0.01) | ||

Level variance | ${\sigma}_{\eta}^{2}$ | 0.0047 | 0.0065 | 0.0037 | 0.0038 | 0.0027 |

Slope variance | ${\sigma}_{\zeta}^{2}$ | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Seasonality variance | ${\sigma}_{\omega}^{2}$ | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Error variance | ${\sigma}_{\epsilon}^{2}$ | 0.0298 | 0.0745 | 0.0437 | 0.0370 | 0.0308 |

Parameter | Marche | Citta Studi | Liguria | Verziere | Senato | |
---|---|---|---|---|---|---|

log(Pavia) | $\theta $ | 0.36 *** | 0.85 *** | 0.69 *** | 0.65 *** | 0.55 *** |

(0.01) | (0.02) | (0.02) | (0.02) | (0.01) | ||

Holidays | ${\varphi}_{1}$ | −0.06 *** | −0.08 *** | −0.08 *** | −0.10 *** | −0.08 ** |

(0.02) | (0.03) | (0.02) | (0.02) | (0.03) | ||

Week-end | ${\varphi}_{2}$ | −0.06 *** | −0.10 *** | −0.09 *** | −0.14 *** | −0.11 *** |

(0.01) | (0.01) | (0.01) | (0.01) | (0.01) | ||

Saturday:Holidays | ${\varphi}_{3}$ | 0.06 | 0.18 *** | 0.06 | 0.14 ** | −0.09 *** |

(0.05) | (0.08) | 0.07 | (0.06) | (0.02) | ||

Sunday:Holidays | ${\varphi}_{4}$ | 0.08 *** | 0.11 *** | 0.11 *** | 0.06 | 0.10 *** |

(0.03) | (0.05) | (0.04) | (0.03) | (0.03) | ||

WindSpeed Q${}_{\mathrm{SW}}$ | ${\varphi}_{5}$ | −0.35 *** | −0.13 *** | −0.42 *** | −0.23 *** | −0.18 *** |

(0.01) | (0.01) | (0.01) | (0.01) | (0.01) | ||

WindSpeed Q${}_{\mathrm{NW}}$ | ${\varphi}_{6}$ | −0.17 *** | −0.16 *** | −0.08 *** | −0.13 *** | −0.08 *** |

(0.01) | (0.01) | (0.01) | (0.01) | (0.01) | ||

Level variance | ${\sigma}_{\eta}^{2}$ | 0.0051 | 0.0065 | 0.0046 | 0.0044 | 0.0024 |

Slope variance | ${\sigma}_{\zeta}^{2}$ | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Seasonality variance | ${\sigma}_{\omega}^{2}$ | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Errors variance | ${\sigma}_{\epsilon}^{2}$ | 0.0093 | 0.0282 | 0.0182 | 0.0154 | 0.0114 |

**Table 6.**Estimated permanent and transitory effects in log scale on NO${}_{\mathrm{x}}$ and NO${}_{2}$ for each station.

Stations | Effect | Nitrogen Oxides | Nitrogen Dioxide | ||||
---|---|---|---|---|---|---|---|

Estimate | S.E. | t-Statistic | Estimate | S.E. | t-Statistic | ||

Senato | Perm. eff. ${\delta}_{1}$ | 0.38 | 0.19 | 2.03 ** | 0.29 | 0.12 | 2.40 ** |

Trans. eff. ${\delta}_{0}$ | −0.12 | 0.16 | −0.76 | −0.14 | 0.11 | −1.25 | |

Verziere | Perm. eff. ${\delta}_{1}$ | 0.26 | 0.21 | 1.27 | 0.22 | 0.15 | 1.50 |

Trans. eff. ${\delta}_{0}$ | −0.01 | 0.18 | −0.05 | −0.06 | 0.14 | −0.40 | |

Liguria | Perm. eff. ${\delta}_{1}$ | 0.12 | 0.22 | 0.54 | 0.20 | 0.16 | 1.25 |

Trans. eff. ${\delta}_{0}$ | −0.02 | 0.19 | −0.10 | −0.10 | 0.15 | −0.67 | |

Marche | Perm. eff. ${\delta}_{1}$ | 0.15 | 0.19 | 0.80 | 0.23 | 0.13 | 1.82 * |

Trans. eff. ${\delta}_{0}$ | −0.11 | 0.17 | −0.63 | −0.19 | 0.13 | 1.56 | |

Citta Studi | Perm. eff. ${\delta}_{1}$ | 0.35 | 0.29 | 1.19 | 0.25 | 0.19 | 1.30 |

Trans. eff. ${\delta}_{0}$ | 0.08 | 0.25 | 0.30 | 0.02 | 0.18 | 0.10 |

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## Share and Cite

**MDPI and ACS Style**

Maranzano, P.; Fassò, A.; Pelagatti, M.; Mudelsee, M. Statistical Modeling of the Early-Stage Impact of a New Traffic Policy in Milan, Italy. *Int. J. Environ. Res. Public Health* **2020**, *17*, 1088.
https://doi.org/10.3390/ijerph17031088

**AMA Style**

Maranzano P, Fassò A, Pelagatti M, Mudelsee M. Statistical Modeling of the Early-Stage Impact of a New Traffic Policy in Milan, Italy. *International Journal of Environmental Research and Public Health*. 2020; 17(3):1088.
https://doi.org/10.3390/ijerph17031088

**Chicago/Turabian Style**

Maranzano, Paolo, Alessandro Fassò, Matteo Pelagatti, and Manfred Mudelsee. 2020. "Statistical Modeling of the Early-Stage Impact of a New Traffic Policy in Milan, Italy" *International Journal of Environmental Research and Public Health* 17, no. 3: 1088.
https://doi.org/10.3390/ijerph17031088