# The Effects of Increasing Penalties in Drunk Driving Laws—Evidence from Chile

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## Abstract

**:**

## 1. Introduction

## 2. Institutional Background

## 3. Materials and Methods

#### 3.1. Data and Descriptive Statistics

#### 3.2. Empirical Methods

#### 3.2.1. Negative Binomial Regressions

- Marginal effect of the ZTL in month t:$$\mathsf{\Delta}\%E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}$$
- Marginal effect of EML in month t:$$\mathsf{\Delta}\%E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}$$

#### 3.2.2. Generalized Linear Models

#### 3.2.3. Censored Quantile Regressions

## 4. Results

#### 4.1. Accidents, Injuries and Deaths

#### 4.2. Blood Alcohol Content

## 5. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ZTL | Zero Tolerance Law |

EML | Emilia’s Law |

BAC | Blood Alcohol Content |

DUI | Driving Under the Influence |

GLM | Generalized Linear Model |

OLS | Ordinary Least Squares |

## Appendix A. Derivation of Dynamic Effects

- Marginal effect of ZTL in month t.The change in $E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}$ between no law and ZTL can be written as:$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}-E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=0,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}\hfill \end{array}\hfill \phantom{\rule{1.em}{0ex}}& =exp\left(\right)open="["\; close="]">\alpha +\eta t+{\beta}_{1}+{\beta}_{2}(t-{t}_{1})+{\mathbf{z}}_{i,t}\gamma -exp\left(\right)open="["\; close="]">\alpha +\eta t+{\mathbf{z}}_{i,t}\gamma \hfill $$Then, the corresponding percentage change is given by:$$\begin{array}{c}\hfill \mathsf{\Delta}\%E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}\phantom{\rule{1.em}{0ex}}\\ ={\displaystyle \frac{E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}}{-}}E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=0,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}\hfill \end{array}$$
- Marginal effect of EML in month t.The change in $E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}$ between the ZTL and EML can be written as:$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=1,{\mathbf{x}}_{-d,i,t}-E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}\hfill \end{array}\hfill \phantom{\rule{1.em}{0ex}}& =exp\left(\right)open="["\; close="]">\alpha +\eta t+{\beta}_{1}+{\beta}_{2}(t-{t}_{1})+{\delta}_{1}+{\delta}_{2}(t-{t}_{2})+{\mathbf{z}}_{i,t}\gamma \hfill $$Then, the corresponding percentage change is given by:$$\begin{array}{c}\hfill \mathsf{\Delta}\%E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathbf{x}}_{i,t}\phantom{\rule{1.em}{0ex}}\\ ={\displaystyle \frac{E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=1,{\mathbf{x}}_{-d,i,t}}{-}}E\left(\right)open="["\; close="]">{y}_{i,t}|{\mathrm{ZTL}}_{t}=1,{\mathrm{EML}}_{t}=0,{\mathbf{x}}_{-d,i,t}\hfill \end{array}$$

## Appendix B. Zero-Inflated Negative Binomial Regression

Negative Binomial | Logit (Inflate) | |
---|---|---|

(1) | (2) | |

Trend | −0.0076 | 0.0305 |

(0.0047) | (0.0522) | |

Post ZTL | −0.2364 | −2.6494 * |

(0.1609) | (1.4847) | |

Post ZTL × Trend | 0.0119 | 0.1606 |

(0.0087) | (0.1060) | |

Post EML | −0.2410 | −0.9074 |

(0.1648) | (2.0402) | |

Post EML × Trend | −0.0011 | −0.2305 ** |

(0.0087) | (0.1005) | |

Police Stops | 0.0028 * | 0.1731 * |

(0.0016) | (0.1006) | |

Gas Sales | 0.0065 | −0.4890 *** |

(0.0046) | (0.1582) | |

Alcohol Accidents | −0.9134 ** | |

(0.4255) | ||

Constant | −0.8052 *** | 3.3788 ** |

(0.3062) | (1.3558) | |

$ln\left(\theta \right)$ | −1.7136 *** | |

(0.2508) | ||

Observations | 1650 | |

Pseudo-${R}^{2}$ | 0.1666 | |

Wald test | 407.47 | |

p-value | 0.0000 |

## Appendix C. Robustness Checks

#### Appendix C.1. Generalized Poisson Regressions

Accidents | Injuries | Deaths | ||||
---|---|---|---|---|---|---|

All | Minor | Moderate | Severe | |||

(1) | (2) | (3) | (4) | (5) | (6) | |

Trend | 0.0062 *** | 0.0007 | 0.0005 | 0.0011 | −0.0018 | −0.0074 |

(0.0015) | (0.0019) | (0.0020) | (0.0029) | (0.0024) | (0.0046) | |

Post ZTL | −0.4112 *** | −0.4115 *** | −0.4290 *** | −0.4306 *** | −0.2985 *** | −0.2405 |

(0.0487) | (0.0658) | (0.0637) | (0.1081) | (0.0854) | (0.1602) | |

Post ZTL × Trend | 0.0119 *** | 0.0141 *** | 0.0162 *** | 0.0107 * | 0.0117 *** | 0.0117 |

(0.0026) | (0.0034) | (0.0034) | (0.0056) | (0.0044) | (0.0087) | |

Post EML | −0.2547 *** | −0.2180 *** | −0.2337 *** | −0.2314 ** | −0.0784 | −0.2389 |

(0.0473) | (0.0598) | (0.0621) | (0.0963) | (0.0750) | (0.1622) | |

Post EML × Trend | −0.0047 * | −0.0055 * | −0.0069 ** | −0.0076 | −0.0060 | 0.0007 |

(0.0025) | (0.0033) | (0.0032) | (0.0055) | (0.0042) | (0.0087) | |

Police Stops | 0.0009 * | −0.0005 | -0.0001 | −0.0017 | −0.0003 | 0.0030 * |

(0.0005) | (0.0007) | (0.0007) | (0.0011) | (0.0009) | (0.0016) | |

Gas Sales | 0.0097 *** | 0.0086 *** | 0.0095 *** | 0.0032 | 0.0061 * | 0.0072 |

(0.0021) | (0.0025) | (0.0026) | (0.0042) | (0.0032) | (0.0046) | |

Constant | 1.8471 *** | 2.1784 *** | 1.8581 *** | −0.0043 | 0.4849 *** | −1.1389 *** |

(0.0954) | (0.1149) | (0.1215) | (0.1862) | (0.1413) | (0.2881) | |

$ln\left(\theta \right)$ | −3.8199 *** | −3.2158 *** | −3.1509 *** | −2.7129 *** | −3.2387 *** | −2.3911 *** |

(0.0838) | (0.0636) | (0.0648) | (0.1274) | (0.1229) | (0.2230) | |

Observations | 1650 | 1650 | 1650 | 1650 | 1650 | 1650 |

Pseudo-${R}^{2}$ | 0.2026 | 0.1532 | 0.1603 | 0.1530 | 0.1898 | 0.1557 |

Wald test | 9432.48 | 5029.93 | 4598.63 | 1189.11 | 2059.08 | 589.39 |

p-value | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

#### Appendix C.2. First Full Month of Enforcement

Accidents | Injuries | Deaths | ||||
---|---|---|---|---|---|---|

All | Minor | Moderate | Severe | |||

(1) | (2) | (3) | (4) | (5) | (6) | |

Trend | 0.0043 *** | −0.0017 | −0.0016 | −0.0009 | −0.0035 | −0.0099 ** |

(0.0015) | (0.0017) | (0.0018) | (0.0029) | (0.0022) | (0.0044) | |

Post ZTL | −0.3117 *** | −0.2807 *** | −0.3036 *** | −0.3156 *** | −0.2060 ** | −0.0689 |

(0.0484) | (0.0624) | (0.0620) | (0.1070) | (0.0853) | (0.1548) | |

Post ZTL × Trend | 0.0112 *** | 0.0129 *** | 0.0148 *** | 0.0090 * | 0.0113 *** | 0.0078 |

(0.0026) | (0.0032) | (0.0033) | (0.0055) | (0.0044) | (0.0083) | |

Post EML | −0.2106 *** | −0.1489 *** | −0.1669 *** | −0.1654 * | −0.0526 | −0.1172 |

(0.0464) | (0.0561) | (0.0599) | (0.0964) | (0.0756) | (0.1606) | |

Post EML × Trend | −0.0025 | −0.0031 | −0.0043 | −0.0044 | −0.0040 | 0.0062 |

(0.0025) | (0.0031) | (0.0032) | (0.0054) | (0.0043) | (0.0086) | |

Police Stops | 0.0010 ** | −0.0004 | −0.0002 | −0.0018 | −0.0003 | 0.0029 * |

(0.0005) | (0.0006) | (0.0006) | (0.0011) | (0.0009) | (0.0016) | |

Gas Sales | 0.0085 *** | 0.0073 *** | 0.0082 *** | 0.0030 | 0.0059 * | 0.0070 |

(0.0019) | (0.0022) | (0.0023) | (0.0041) | (0.0031) | (0.0046) | |

Constant | 1.8840 *** | 2.2332 *** | 1.9064 *** | 0.0320 | 0.5167 *** | −1.0962 *** |

(0.0956) | (0.1126) | (0.1199) | (0.1864) | (0.1408) | (0.2875) | |

$ln\left(\theta \right)$ | −2.5939 *** | −1.9083 *** | −1.9078 *** | −1.8280 *** | −2.3415 *** | −1.5643 *** |

(0.0949) | (0.0727) | (0.0754) | (0.1381) | (0.1365) | (0.2340) | |

Observations | 1650 | 1650 | 1650 | 1650 | 1650 | 1650 |

Pseudo-${R}^{2}$ | 0.1968 | 0.1487 | 0.1533 | 0.1417 | 0.1771 | 0.1439 |

Wald test | 9952.24 | 5282.90 | 4775.47 | 1174.39 | 2044.36 | 579.03 |

p-value | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

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**Figure 1.**Plots for alcohol-related accidents, injuries and deaths, along with cubic fits. Each dot represents the regional average of events in a given month. The first and second vertical lines represent the enactment month of the Zero Tolerance Law (ZTL) and Emilia’s Law (EML), respectively.

**Figure 2.**Kernel density plots for blood alcohol content (BAC) tests. For ease of exposition, only $0<\mathrm{BAC}\le 0.4$ are included. The numbers of observations are 24,255, 17,431 and 22,191 for the no law, ZTL only and ZTL & EML periods, respectively. The Epanechnikov kernel is used, and bandwidth selection follows Silverman [39].

Mean | SD | Min | Max | |
---|---|---|---|---|

Data from Carabineros de Chile: | ||||

All Accidents | 407.79 | 528.67 | 6.00 | 3225.00 |

Alcohol Accidents | 28.84 | 25.40 | 0.00 | 152.00 |

All Injuries | 28.33 | 23.04 | 0.00 | 124.00 |

Minor Injuries | 21.15 | 17.70 | 0.00 | 104.00 |

Moderate Injuries | 2.65 | 2.74 | 0.00 | 17.00 |

Severe Injuries | 4.53 | 4.28 | 0.00 | 27.00 |

Deaths | 0.92 | 1.36 | 0.00 | 16.00 |

Police Stops | 41.29 | 33.26 | 1.78 | 168.04 |

Data from the National Energy Commission: | ||||

Gas Sales | 21.83 | 32.93 | 1.30 | 174.69 |

Data from Servicio Médico Legal: | ||||

BAC Test | 0.03 | 0.06 | 0.00 | 0.64 |

Male Proportion | 0.82 | 0.39 | - | - |

Accidents | Injuries | Deaths | ||||
---|---|---|---|---|---|---|

All | Minor | Moderate | Severe | |||

(1) | (2) | (3) | (4) | (5) | (6) | |

Trend | 0.0063 *** | 0.0006 | 0.0006 | 0.0012 | −0.0018 | −0.0075 |

(0.0014) | (0.0017) | (0.0018) | (0.0029) | (0.0023) | (0.0046) | |

Post ZTL | −0.4103 *** | −0.4071 *** | −0.4250 *** | −0.4295 *** | −0.2979 *** | −0.2407 |

(0.0475) | (0.0612) | (0.0609) | (0.1079) | (0.0854) | (0.1601) | |

Post ZTL × Trend | 0.0118 *** | 0.0143 *** | 0.0161 *** | 0.0107 * | 0.0117 *** | 0.0118 |

(0.0026) | (0.0032) | (0.0033) | (0.0056) | (0.0044) | (0.0087) | |

Post EML | −0.2469 *** | −0.2079 *** | −0.2249 *** | −0.2295 ** | −0.0788 | −0.2400 |

(0.0456) | (0.0554) | (0.0591) | (0.0961) | (0.0750) | (0.1621) | |

Post EML × Trend | −0.0052 ** | −0.0064 ** | −0.0075 ** | −0.0077 | −0.0060 | 0.0007 |

(0.0025) | (0.0031) | (0.0031) | (0.0054) | (0.0042) | (0.0087) | |

Police Stops | 0.0011 ** | −0.0004 | −0.0001 | −0.0017 | −0.0003 | 0.0030 * |

(0.0005) | (0.0006) | (0.0006) | (0.0011) | (0.0009) | (0.0016) | |

Gas Sales | 0.0086 *** | 0.0074 *** | 0.0083 *** | 0.0030 | 0.0061 * | 0.0073 |

(0.0019) | (0.0022) | (0.0023) | (0.0041) | (0.0032) | (0.0046) | |

Constant | 1.8500 *** | 2.1930 *** | 1.8680 *** | −0.0034 | 0.4859 *** | −1.1388 *** |

(0.0953) | (0.1126) | (0.1200) | (0.1862) | (0.1412) | (0.2881) | |

$ln\left(\theta \right)$ | −2.6346 *** | −1.9314 *** | −1.9304 *** | −1.8503 *** | −2.3507 *** | −1.5758 *** |

(0.0977) | (0.0735) | (0.0763) | (0.1405) | (0.1373) | (0.2368) | |

Observations | 1650 | 1650 | 1650 | 1650 | 1650 | 1650 |

Pseudo-${R}^{2}$ | 0.1989 | 0.1505 | 0.1550 | 0.1429 | 0.1779 | 0.1446 |

Wald test | 10,169.41 | 5350.44 | 4869.16 | 1190.76 | 2066.18 | 590.25 |

p-value | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Months after Enactment | 0 | 6 | 12 | 18 | 24 |
---|---|---|---|---|---|

Panel A: Marginal effect of ZTL | |||||

Accidents | −33.66 | −28.78 | −23.55 | −17.93 | −11.90 |

Injuries | −33.45 | −27.50 | −21.02 | −13.97 | −6.28 |

Panel B: Marginal effect of EML | |||||

Accidents | −21.88 | −24.26 | −26.57 | −28.81 | −30.98 |

Injuries | −18.77 | −21.82 | −24.75 | −27.57 | −30.29 |

OLS | GLM | |||
---|---|---|---|---|

(1) | (2) | (3) | (4) | |

Post ZTL | −0.0067 *** | −0.0013 ** | −0.0077 *** | 0.0002 |

(0.0004) | (0.0005) | (0.0005) | (0.0011) | |

Post EML | −0.0023 *** | −0.0023 *** | −0.0028 *** | −0.0032 *** |

(0.0004) | (0.0005) | (0.0004) | (0.0009) | |

Male | 0.0184 *** | 0.0228 *** | 0.0187 *** | 0.0213 *** |

(0.0002) | (0.0004) | (0.0002) | (0.0004) | |

Post ZTL × Male | −0.0066 *** | −0.0080 *** | ||

(0.0005) | (0.0011) | |||

Post EML × Male | −0.0000 | 0.0005 | ||

(0.0005) | (0.0010) | |||

Observations | 358,460 | 358,460 | 358,460 | 358,460 |

Pseudo-${R}^{2}$ | 0.0148 | 0.0151 | 0.0152 | 0.0153 |

Wald test | 8391.13 | 8536.22 | 4760.68 | 4935.85 |

p-value | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Quantile | |||
---|---|---|---|

85th | 90th | 95th | |

Post ZTL | −0.0000 | −0.0000 | 0.0034 |

(0.0000) | (0.0039) | (0.0407) | |

Post EML | 0.0000 | −0.0000 | −0.0162 |

(0.0000) | (0.0039) | (0.0229) | |

Male | 0.1210 *** | 0.1640 *** | 0.0923 *** |

(0.0011) | (0.0008) | (0.0048) | |

Post ZTL × Male | −0.0300 *** | −0.0170 *** | −0.0176 |

(0.0019) | (0.0041) | (0.0198) | |

Post EML × Male | −0.0050 ** | −0.0010 | 0.0080 |

(0.0025) | (0.0043) | (0.0239) | |

Constant | 0.0000 | 0.0000 | 0.1108 *** |

(0.0000) | (0.0000) | (0.0053) | |

Observations | 358,460 | 358,460 | 358,460 |

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## Share and Cite

**MDPI and ACS Style**

García-Echalar, A.; Rau, T.
The Effects of Increasing Penalties in Drunk Driving Laws—Evidence from Chile. *Int. J. Environ. Res. Public Health* **2020**, *17*, 8103.
https://doi.org/10.3390/ijerph17218103

**AMA Style**

García-Echalar A, Rau T.
The Effects of Increasing Penalties in Drunk Driving Laws—Evidence from Chile. *International Journal of Environmental Research and Public Health*. 2020; 17(21):8103.
https://doi.org/10.3390/ijerph17218103

**Chicago/Turabian Style**

García-Echalar, Andrés, and Tomás Rau.
2020. "The Effects of Increasing Penalties in Drunk Driving Laws—Evidence from Chile" *International Journal of Environmental Research and Public Health* 17, no. 21: 8103.
https://doi.org/10.3390/ijerph17218103