Crime and Punishment: The Case of Alcohol...reaction to increased national awareness of the...

Crime and Punishment: The Case of Alcohol David Turner Advisor: Stefano DellaVigna Economics Senior Honors Thesis

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Introduction:

Drinking and Driving is an important problem within the United States. In 2004,

16,694 drivers died in alcohol related accidents and some estimate that driving drunk

increases the likelihood of an accident by over seven times. 1 National attention to this

problem began early, around the time of prohibition. Modern regulations originated in

1964, when a study in Grand Rapids, Michigan first identified a link between Blood

Alcohol Content (BAC) and automotive accidents. This study helped initiate the passage

of numerous Driving Under the Influence (DUI) laws. These laws are classified as �per

se� laws, which mean that one is a criminal by simply falling in a certain classification.

That is by having a certain BAC and driving a car one is offending, regardless of any

other actions. DUI laws were soon passed in every state.2

DUI laws are associated with falling drunk fatalities across the United States,

although it has been argued that their deterrence effect is outweighed by enforcement

cost.3 In 1984 congress passed the Federal Uniform Drinking Age, which raised the

national drinking age to 21. This represented shifting political intentions and was also

found to have a significant effect on drunk driving.4 Yet most DUI laws still did not

differentiate between drivers aged 21 and younger. Therefore, in 1995 an amendment

was added to National Highway Systems Designation Act, in which states were required

to adopt �Zero Tolerance� (ZT) laws for underage drunk driving by fiscal year 1999 or

forfeit federal highway funds.

Zero Tolerance laws make it illegal, as is, for any driver under the age of 21 to

have any measurable amount of alcohol in their blood. The law was passed after a study

compared states with zero tolerance laws and those without, and in which the authors

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found a significant decrease in alcohol related youth fatalities at night.5 Yet this study

was essentially cross-sectional, and subject to confounding by regional characteristics.

Although they attempted to alleviate this problem by comparing two neighboring states,

this is a poor solution at best because regional characteristics depend on more than

geography. They also only looked at the numbers of drinking fatalities, and while this

variable seems relevant, it could reflect other factors. Carpenter (2004) tried to answer

how these laws worked by finding a reduction in self reported heavy episodic drinking.6

But this does not address the criminality inherent in drunk driving. Because the choice to

drink and drive is in its very nature a criminal decision, it should then be analyzed as a

crime.

This paper uses a crime economic framework to identify the specific impact that

Zero Tolerance laws have. Using Blood Alcohol Content (BAC) data on fatal accidents,

I will estimate the relative criminal propensity by the proportion of the population that

responded to stricter laws. The federal requirement provides a natural experiment with

which to study ZT laws because of the different times in which each state passed the

required legislation. In 1994, 20 states had them before the law was passed; and by the

end of 1998 all 50 states had passed ZT laws. I will use a cross sectional time series

approach to analyze the impact of the laws. The dependant variables will be the

distributions of BAC by age. I will use a similar model to Lee and McCrary7, who

looked at the drop in arrest rates on the 18th birthday when penalties rose discontinuously.

Using this framework I will find the change in probability of committing an offence to

identify the comparable distributions punishment and criminal utility.

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Model:

I will use a version of Becker�s initial model used by Lee and McCrary (2005). A

rational individual will only commit a crime when the utility of the crime is greater than

the utility of not committing the crime.

ptUt(p) + (1- pt)Ut(np) > Ut(nc)

(1)

Where pt is the probability of apprehension. Ut(p) is the utility of punishment, Ut(np) is

the utility of committing the crime and receiving no punishment, and Ut(nc) is the utility

of not committing the crime. And the index t is the age of the individual. Solving for pt

produces the reservation probability of committing the crime.

pt,r = Ut(np) - Ut(nc) / Ut(np) - Ut(p)

(2)

The individual commits a crime when probability of apprehension is less than the

reservation probability, assuming that U(p)<U(nc)<U(np)

Lee and McCrary assumed each individual samples from a distribution of

criminal �opportunities.� They also assumed that the general reservation probability

stays the same. But it is logical to assume that each person�s relative utility causes the

decision to commit the crime. I then adjust the model so that an individual commits a

crime when their reservation probability is below the general probability of getting

caught and each individual has different reservation probability. Therefore, the degree of

violation depends on the relative utilities. In this model the individual commits the

crime, drives drunk, until their reservation probability equals their chances of getting

caught.

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p(apprehension) = pt,r

Assuming the probability of apprehension is constant across age groups. Than the

frequency at which each group violates the law depends on the proportion with a low

enough pt,r. Therefore, the distribution of utilities determines the rates of criminal

behavior.

Pt(committing crime) = Fg(pc)

(3)

With Fg as the cumulative distribution function of group g and pc is the chance of

apprehension, as a function of m.

Identification Strategy:

My identification strategy uses the time of Zero Tolerance laws throughout the

United States. These laws expand the penalties of a DUI to minors (hereafter defined as

under 21), who have any measurable trace of alcohol (BAC usually above .02).

Previously, DUI law did not discriminate by age. Both a 20-year-old caught with a .05

BAC and a 21-year-old with the same BAC would be allowed to drive home. After the

law was passed the 20-year-old is now arrested for a DUI. The year by year change in

distribution of offending by age will then give an idea as to the relative efficacy of these

laws.

The National Highway Transportation Safety Administration (NHTSA),

administers the Fatal Accident Reporting System (FARS). They compile data on every

accident that involved a fatality in the United States. These statistics are compiled yearly

from state reports and include data on a variety of factors, included data on the driver.

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The statistics generally give the state, age, sex, hour of accidents, and Blood Alcohol

Content of each driver. I will use the BACs indexed by state and year, to identify relative

criminal frequencies of each age group.

By 1995, when the Federal government required states to pass ZT laws, only

twenty states had them. By the end of 1998 all 50 states had zero tolerance laws. This

provides a natural experiment with which to study the impacts of these laws. Each state

that passed the laws did so because of an exogenous federal requirement (punishable by

withheld federal highway funds). This helps account for internal factors affecting the

drunken driving rate. Previously states that passed ZT laws might also have a greater

internal concern for minor drunk driving, and this social concern could also be the reason

for decreased accidents documented by the original study of Hinsgon, Hereen, and

Winter(1994). Therefore this natural experiment is perfect for analysis using panel data

regression.

Crash statistics have an advantage over arrest statistics because it reduces effects

from varying enforcement. If ZT laws are associated with vigorous enforcement than

arrest statistics will be directly related, but crashes will only be affected by how much

people react to the increase in enforcement. So the effect is diluted and directly

correlated to the underlying factor. This helps eliminate bias from the data.

This sample is not random�drivers killed in auto-accidents tend to be aggressive,

reckless, or poor drivers, characteristics which might be correlated with drinking and

driving. In addition it has been well documented that alcohol increases the likelihood of

an accident by as much as ten times. Levitt and Porter attempted to identify the number

of drivers on the road using crash statistics. However, they also showed that the

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increased likelihood was similar across age groups (10.13 times for over 25, and 10.88

for under). Therefore both factors will increase BAC averages but the effects which

cause the exaggeration are similar across relevant age groups. Therefore while the

sample is biased toward drunk and especially very drunk drivers, this bias is not likely to

be effected by the timing of ZT laws and is therefore uncorrelated with the independent

variable. But it will cause somewhat of a bias in the estimates of the changes in the

dependant variable.

Other studies have documented increases in drunk driving deaths immediately

following the age of 21, which the authors attributed to inexperience while driving

drunk.8 While interesting, this should not affect the results. I am looking at the change in

underage drinking and driving after the law is passed. Therefore the inexperience effect

will not be large because only those who turn 16 in the next year would be affected. So

only the 16-year-olds whom the law impact (ie those willing to drive with some alcohol),

would internalize the inexperience effect, and it would not be noticed until five years

later when they turned 21. Therefore, the immediately post year change would not be

impacted by a reduction in experience.

Exactly how to apply the BAC data depends on whether or not individuals are

capable of targeting their drinking to the desired concentration. Few would doubt that a

person is capable of targeting their drinking to a desired level of intoxication; perceived

intoxication might be different from relative BAC level. One reason is the BAC is based

on numerous factors other than number of drinks, including weight, sex, time drinking,

and metabolism of alcohol9. However, a small level study done at Bradley University

found that students were fairly capable at identifying their BAC level.10 Therefore it

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seems logical that an individual�s decision to drink and drive is cognizant of this level.

However, it is common knowledge that alcohol impairs judgment, and this would be a

judgment call. So I will attempt to relax this assumption later on.

Assuming BAC is a rational choice, I would expect that the amount of minors

driving under .08 BAC to drop. All of a sudden their previous action is illegal, so those

whom the penalties would deter no longer drive drunk. This effects the reservation

probability, because it changes the utility for the marginal drunk driver. All of a sudden

their reservation probability is higher, and the individual no longer commits the crime.

The relative number of those who no longer offend can give an indication to the impact

the law has on the utilities.

This effect might capture more than just the specific reaction to the details of the

law, it could capture a shift in political intention. For instance part of the logic behind the

zero tolerance law is that if alcohol is illegal to consume for minors, than consistency

merits punishment even if they are safe to drive.11 Additionally the law was also in

reaction to increased national awareness of the consequence of drunk driving. Therefore

the reaction to the law may also be a signal of political intentions to enforce underage

drinking. However by isolating the states and looking at different years I can identify the

specific effect of law.

Essentially, before the law the probability of driving under .08 was simply:

Prob(DD)<21 = P[Ut(np) > Ut(nc)]

But after the law is passed it becomes essentially equation (3).

Prob(DD)<21 = P[pcUt(p) + (1- pc)Ut(np) > Ut(nc)]

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and U(p) is always less than U(np) so the probability must be less as well. One would

expect to see a discontinuity after the law is passed, when a previously illegal action

becomes legal and the size of the change would be Ut(np) � [pcUt(p) + (1- pc)Ut(np)] =

pcUt(np) - pcUt(p) =

pc[Ut(np) - Ut(p)]

(4)

Which is the change in the probability of offending. Therefore if I find the change in this

probability along with the probability of apprehension, I can find the difference in the

two utilities.

In order to find the change in probability, I will use two proxies for criminal

offending: DrunkFraction and AllFraction. DrunkFraction is equal to the number of

BAC�s in the .01 to .081 range over the total number of drunk accidents, and AllFraction

is equal to the number of BACs between .01 and .08 over all accidents where a BAC was

recorded. DrunkFraction is used under the assumption of BAC targeting. If individuals

target BAC�s then after the law is passed this proportion should decrease because drivers

either drink more or don�t drink at all. AllFraction relaxes this assumption because,

while it is still identifying the decrease within the targeted range, it also reflects a

decrease in overall drinking and driving. If drivers who were over the .08 range were

under the impression they were under it, then DrunkFraction would underestimate the

actual effect of the law. Therefore AllFraction identifies the real change in those

breaking the law, out of the entire sample. The reason I still used the .01 to .08 range is

there is significantly less bias due to impaired driving ability. AllFraction attempts to

1 At the time many states had a DUI limit of .10 BAC not .08. But information was difficult to obtain on the specifics, but all were at least .08. Therefore, any reduction in the under-.08 range will still indicate propensity.

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find a better estimate for the actual number. While it only divides by the number where a

BAC was recorded this number is also influenced by the bias towards drunk accidents,

which pull AllFraction in each direction. So bias is difficult to determine. Using

DrunkFraction (DF) to estimate the proportion of drunk drivers who drop out of criminal

behavior, I use the following framework.

Prob(BAC(drunk)<.08) = (L + A)/T = DrunkFraction (5)

L = the drivers who drive drunk when it is legal

A = Those who drive below .08 anyway, regardless of the law

T is the total number of drunk drivers.

Because the total number of drunk drivers is difficult to estimate the proportion L/T is

more useful. The change in DF gives us an indication. In period 1, DF1 = (L+A)/T, and

in period 2, DF2 = A/(T-L). L/T then equals.

L/T = (DF1� DF2) / (1 � DF2)

AllFraction (AF) gives a similar determinate. Define P as the population.

Prob(BAC(drunk)<.08) = (L + A)/P

But because P already contains A and L either way the change is much simpler

L/P = (AF1� AF2) (6)

The change in L/T and L/P will give us a value for the change in the reservation

probability.

To solve for the appropriate values I will need to identify the effect of the law on

DF and AF. I will use the difference in difference technique for panel data to find the

change in DF, = ∆DF, and use the average value of the post-ZT states to estimate DF2

(with an identical approach for AF). In the pseudo-experimental framework, I will use a

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panel regression model with fixed effects to identify the effect of ZT laws. I will use a

binary variable as my independent variable, Xsy, which equals one when the state, s, at

the year, y, had a Zero Tolerance law, and equals zero otherwise.

I will solve the following regression:

DFsy = β0 + γs + γy + τ Xsy + εsy

qsy = empirical proportion

β0 = Intercept for all states and times

γs = Fixed effect per state

γy = Fixed effect by year

εsy = Error term under basic linear assumptions, the proportions will be weighted by the

number of observations to account for heteroskedasiticy.

τ Xsy = Effect of the Zero Tolerance law on proportion, X is a dummy that is zero for

when the state does not have a zero tolerance law, and one when it does. (because most

states passed the law in the first six months X is also one during that year)

Because the τ identifies the change in DF (or AF) due to the law passed I can find

the proportion that stopped drinking and driving. In this case -τ is (DF1� DF2), because τ

represents the change to period 2, then its negative is (DF1� DF2). In order to find (1 �

DF2) I need to estimate the �constant� proportion after the law is passed, in this case β0 +

τ could serve as a proxy. Note that due to selection bias all DF�s are likely to

underestimate their real value, as high BAC crashes are much more likely. Therefore the

actual ratio L/T will be different. If a is the scaling factor that represents the under

prediction of DF, then

L/Tactual = (aDF1� aDF2) / (1 � aDF2) = aτ/(1-a β0)

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To find a I would need to find the relative propensities to crash. Fortunately Levitt and

Porter estimated the relative risk of a legally drunk driver crashing to a sober driver as

13.24 and 14.39, for two and one-car crashes respectively, and the effect of any drunk

driver to a sober driver is 7.51 and 7.45 (Levitt and Porter 2001). Therefore legally drunk

drivers are 1.76 to 1.93 times more likely to crash than and under .08 BAC driver. They

are slightly under two times more likely to end up in the sample. DF would be low by

that factor.

AllFraction, however, has two contradicting impulses. One is that because .01 to

08 BACs are more likely to crash, therefore their proportion is overrepresented and the

numerator is large. But the denominator is the total number of BAC�s in which alcohol is

more likely to be represented, so the effects will pull in opposite directions. Hence the

value is going to have error but it is difficult to tell if L/Pactual would be smaller or larger

than it should be.

I use this change in the probability of offending, τ, to solve for the relative

utilities. The difference in utility before and after is:

τ = pc[Ut(np) - Ut(p)]

Ut(np) - Ut(p)= τ/ pc

Which can gives an indication of the deterrence effect.

Data:

I used the Fatal Accident Reporting System (FARS), for the statistics on fatal

accidents. This database records accident information for every fatal vehicle accident

within the United States. The data is categorized yearly, and each set contains

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information on the person who died in the accident. Among the factors recorded are age,

sex, person type (driver or passenger), whether the accident was alcohol related, the

Blood Alcohol Content (BAC) in percent, and the state in which the accident took place.

Table 0 documents the basic summary statistics for this data set.

Yearly Statistics(1) (2) (3) (4) (5) (6) (7) (8)

Year:1994 92,761 23,016 9,542 1,770 60,357 31,013 18.5% 7.7%

1995 95,423 25,387 9,511 1,837 62,192 31,938 19.3% 7.2%

1996 96,888 23,680 9,516 1,860 62,619 32,873 19.5% 7.9%

1997 95,810 23,588 8,872 1,711 61,303 33,056 19.3% 7.3%

1998 94,782 23,239 8,766 1,702 60,859 32,675 19.4% 7.3%

1999 94,375 23,634 8,780 1,709 61,009 32,103 19.5% 7.2%

2000 94,422 24,079 9,022 1,750 61,475 31,739 19.4% 7.3%

2001 94,852 24,493 9,043 1,774 61,926 31,599 19.6% 7.2%

2002 95,423 25,387 9,511 1,837 62,192 31,938 19.3% 7.2%

2003 95,496 25,324 9,328 1,788 61,980 32,309 19.2% 7.1%

All 950,232 241,827 91,891 17,738 615,912 321,243 19.3% 7.3%

Table 0: Summary Statistics

Notes: The Demo version of Stat Transfer was used to convert the data. This version transfers 15 of 16 cases, therefore the absolute numbers need to be multiplied by 1.07 to get the approximate real value. Because I was using the crashes as a pseudo random sample, the nature of stat transfer does not affect my analysis.

Accidents with Male Drivers

Accidents with

female Drivers

Drunk Fraction

All Fraction

Total Accidents

Accidents where a BAC was recorded

Recorded BAC over

0

Recorded BAC .01

to .08

I looked at the years from 1994 to 2003, because prior to 1994 the data

categorized differently. The BAC information indicates a possible systematic error, as

you can see less than a third of the accidents recorded one. Also, one can see a slight

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yearly effect as the numbers decline in the late 90�s and then began to rise in 2000.

These changes are notable in that they vary less than one percent from year to year,

which indicates the self selection within the sample is relatively constant from year to

year. 1994 represents somewhat of an outlier in terms of DrunkFraction and AllFraction,

as the initial value is very different from subsequent years. Notice that DrunkFraction

rises while AllFraction falls. This shows that these values are not necessarily equivalent

and might represent other factors. Also among the genders, male drivers are consistently

twice as likely as female drivers to be involved in accidents.

In order for the natural experiment to be effective the relative reasons behind the

passage of Zero Tolerance laws must be random. The introduction of the federal

requirement ensures that internal concerns are somewhat controlled for by an overriding

federal one. Additionally the states which were affected need to be relatively randomly

selected. Table 1 shows the state and the year in which they passed the Zero Tolerance

law.

Year1993 or earlier

1994

1995

1996

1997

1998www.nhtsa.dot.gov

Table 1: State and Year it Passed Zero Tolerance Law

StateArizona, Maine, Maryland, Oregon, New Jersey, Arkansas, Nebraska, Tennessee, and Minnesota

Massachusetts, Virginia, West Virginia, Michigan, Ohio, New Hampshire, Nebraska, Idaho, New Mexico, California, and Washington.Iowa, Illinois, Connecticut, Rhode Island, Delaware, North Carolina, and MontanaNew York, Kentucky, Pennsylvania, Missouri, Alabama, Oklahoma, and AlaskaNorth Dakota, Colorado, Texas, Georgia, Kansas, Indiana, Florida, Vermont, Wisconsin, Louisiana, Nevada, and Hawaii

Wyoming, South Dakota, South Carolina, and Mississippi

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The states do not appear to have a geographical correlation, with the exception that 1997

and 1998 seem to contain a large number of generally conservative states, judging by

recent election results. It is possible than that the later states might be more reluctant and

one would see less of an effect. However, this law was passed by a Democrat House and

signed by a Democrat President, therefore the reluctance could be a partisan concern, not

related to the law itself. However, 1995 and 1996 contain a significant number of

generally liberal states, so any partisan or political effect would be mitigated.

Additionally 1993 and earlier seems to have an eclectic mix of geography and politics,

which imply that ZT laws are not a polarizing political issue.

One of the assumptions of the model is that bias in the dependant variable

(DrunkFraction or AllFraction) is systematic and does not significantly differ across age

groups. One problem is that BAC is recorded for less than a third of the accidents, to

identify if any bias existed I compared the subset of BAC data to the general sample. A

comparable statistic is whether or not the accident was determined to involve alcohol.

According to Levitt and Porter, this is generally determined by the officer on the scene.

So it is a different, although more subjective, measure of alcohol Figure 1 shows the

distribution of the two measures, both graph the percentages of fatalities that involved

alcohol. As you can see, there is a clear bias in BAC subset, all the percentages are

higher, but fortunately the shape appears to be the same. See Appendix II for the

distribution of BAC averages by age, which follows approximately the same shape.

Figure 1

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In order to better see if any bias exists per age group, I calculated the chance that a BAC

test was performed given that alcohol was determined to have been involved. The data

was aggregated across all years.

Figure 2

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It appears that in nearly 80% of cases a BAC test was performed. This means that the

distribution of BAC�s is a very good representation of the actual accident BACs, and that

most selection bias is then due to the greater likelihood of crashing while drunk.

Figure 1 also indicates that Drunk Driving is a criminal behavior. The

distribution of percentages follows a standard age-crime curve documented by David

Farrington.12 These curves represent the likelihood of criminal behavior by age and are

typified by a quick early rise followed by a declining effect with age. The type of trend

in most of Farrington�s analysis is clearly visible in figure 1. This lends credibility to the

use of BAC�s as a proxy for the probability of offending. Notice also the discontinuities

at age�s 21 and 18. This discontinuity at age 21 is evidence that underage drinking laws

have an effect on driving behavior.

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Another source of error could arise from the driving ability of those in the sample.

From appendix I, one can see the distribution of accidents across age groups. While this

does not control for the amount of drivers on the road, it shows that those under 21 are

much more likely to crash than any other age group. Fortunately my analysis uses

proportions instead of absolute numbers, which account for the inexperience effect.

The regression indexes DrunkFraction and AllFraction by state and year. In order

to initially see if any effects were present I combined the states by the year they passed

the law. Figure 3 shows the DrunkFraction per year for the sample.

Figure 3

There appears to be no clear trend, but there is a lot of variation in the data. In order to

better see if a trend existed, I grouped the DrunkFraction and AllFraction values before

the law on one side, and after the law on the other. The line indicates the trend. (Larger

graphs are available in appendix III and IV)

Figure 4

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Therefore you can see that the average DrunkFraction and AllFraction values dropped

after the Zero Tolerance laws were passed. The decrease in the values gives an indication

that the laws had an effect, but does not say whether or not it was significant.

Results:

Table 3 summarizes the general results for the regression analysis. Each column

represents a different control or restriction in the model. Column 1 is a standard Ordinary

Least Squares (OLS) without controls, state and year fixed effects are added for

increasing columns. Also note that two different types of estimates were used, MLE and

OLS. One is a fixed effects model which clustered the errors by state, but estimated the

coefficients using maximum likelihood and the other did not cluster the others but used

least squares (see notes for an expanded discussion). One can see then, significant

variation in the intercepts and significance of each specification. The variety in

significance and intercept show the need to cluster errors, as state effects have significant

internal correlation. MLE then, better estimates the model, and under certain

assumptions on the normality of the errors is the same as OLS. These assumptions

appear to be valid for the majority of the regressions. Therefore, the result for column 6

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would be the most reliable estimate for the model. Yet the estimates for intercept

indicate a possible problem with the model, because they are so much higher for

AllFraction, when the average is closer to 10%. The software seems to pick the highest

value as its intercept and each state effect then subtracts from this (see notes). For fitting

the model the intercept for the no effects specification is used because it provides a more

general average. Also, the MLE and OLS estimates return a different value of fit - OLS

returns R squared, and MLE returns the Aikake Information Criterion (AIC). The AIC

has no absolute interpretation rather it describes relative goodness of fit and penalizes for

using too many estimations, a lower value indicates a better model. In this case it helps

identify if the year effects are important for the model. If the addition of year effects

reduces the AIC then that model is a better fit. In Table 3, one sees that when the effect

is significant, the AIC is indeed lower.

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(Binary = 1 for (1) (2) (3) (4) (5) (6)Zero Tolerance Law)Intercepts 0.098*** 0.102** 0.304*** 0.110** 0.112*** 0.427***All Drivers -0.0042 -0.0083 -0.2302 0.0026 -0.0020 -0.1481

N = 35,923 (0.0051) (0.0049)* (0.0201)*** (0.0065) (0.0067) (0.0274)***0.00002 0.20629 -12.24 0.01807 0.21746 -59.61

MLE X XOLS X X X XState Fixed Effects X X X XYear Fixed Effects X X X

Intercepts 0.289*** 0.300*** 0.336*** 0.312*** 0.318*** 0.403***All Drivers -0.0011 -0.0187 -0.0381 0.0177 -0.0077 0.0015

N = 11,764 (0.0127) (0.0131) (0.0331) (0.0166) (0.0183) (0.0437)AIC or R2 0.00002 0.20629 355.52 0.01807 0.21746 373.31

Intercepts 0.092*** 0.097** 0.078*** 0.091** 0.093*** 0.078***All Drivers 0.0023 -0.0042 0.0170 0.0108 0.0015 -0.0016

N = 48,298 (0.0040) (0.0040) (0.0074)** (0.0051)** (0.0055) (0.0101)0.00475 0.31651 -1126.25 0.02217 0.33474 -1066.22

Intercepts 0.175*** 0.181*** 0.149*** 0.167*** 0.170*** 0.149***All Drivers 0.0118 0.0023 0.0305 0.0188 0.0023 -0.0046

N = 24,713 (0.0076) (0.0073) (0.0126)** (0.0098)* (0.0100) (0.0169)0.00475 0.31651 -609.07 0.02217 0.33474 -559.29

Table 3: Summary of Coefficients

Notes: An observation in the linear probability model is a state and year in one of all 50 US States and the 10 years in the sample The dependant variable is the proportion of drivers who had .01-.08 Blood Alcohol Content(BAC), per the selected group. DrunkFraction is over all drunk drivers, AllFraction is over all drivers, and each hs for a different age group. The independent variable is a binary variables that equals one if the state had Zero Tolerance Laws during that year. Robust standard errors are in parentheses, errors for MLE estimation were clustered by state, errors for OLS were not clustered. The observations are weighted by the number of accidents covered in the sample.

Dep. Var.: DrunkFraction Drivers 16 to 20

* significant at 10%; ** significant at 5%; *** significant at 1%

AIC or R2

AIC or R2

AIC or R2

Dep. Var.: AllFraction Drivers 21 and Older

Dep. Var.: AllFraction Drivers 16 to 20

Dep. Var.: DrunkFraction Drivers 21 and Older

As one can see there is a significant effect on AllFraction from the imposition of

Zero Tolerance laws. According the to the regression, the probability of offending drops

by 14% after Zero Tolerance laws are passed (a standard error of 2.74% gives a 95% CI

of [9.43% , 20.1%]). Even using the lower bound of .09, the change in offending is very

significant. The drop in AllFraction is also significant because there is no corresponding

drop for drivers 21 and older, as the model predicts-there is a one percent increase and it

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is far from significant. Had there been a corresponding drop for older drivers, it could be

attributed to a general reduction in drunk driving. This general reduction would mean

that ZT laws are associated with other DUI legislation or policies. One can see a

significant increase in the proportion before controlling for year effects. This might

internalize a general reduction in excessive drunk driving, by substituting for legal

methods (under .08 BAC). Also, social pressures against drunk driving from groups such

as MADD might also encourage drivers who normally drink and drive, to drink less.

This drop is a strong indication that zero tolerance laws have a direct effect on the

behavior of drivers, yet the other measure of criminal propensity, DrunkFraction, did not

have a corresponding decrease. This could be due to two factors. One, people are very

bad at estimating their BAC and the decrease in AllFraction (.01 to .08 BAC) was

correlated with a drop in over .08 BAC driving as well (and a general decline from all

categories means, that the relative proportions do not change). It is well known that

alcohol impairs judgment, so it is a logical extension that it also impairs ability to

objectively determine intoxication as well. The second explanation is that this general

reduction in drunk driving is due to other social and political pressures that happen to be

correlated with Zero Tolerance laws. This is a less plausible explanation because this

model controls for year effects, and the states imposed ZT laws because of a federal

requirement.

Men and women might respond differently to driving rules and regulations. The

fact that men are twice as likely as women to be involved in a fatal accident indicates that

they might also be differently affected by driving laws. Table 4 summarizes these

differences.

23

Dependant Variable: For ages 16 to 20(Binary = 1 forZero Tolerance Law)

(1) (2) (3) (4)Women 0.10036 0.31040 0.0208615 0.0617996

(0.0491)** (0.0682)*** (0.0106)* (0.0163)***AIC or R2 0.17839 571.38786 0.17622 387.47338

N 1,749 1,749 9,251 9,251

Men -0.02466 0.00863 -0.009842 -0.1141692(0.0193) (0.0499) (0.0083) (0.0252)***

AIC or R2 0.20489 505.53610 0.26891 -113.55587N 10,012 10,012 26,671 26,671

MLE X XOLS X X

X X X X


Table 4: Sex and Reaction to Zero Tolerance Laws

DrunkFraction AllFraction

Notes: To see intercpets and the results for each specification please see the Appendix

State and Year controls

We see a most unusual effect in the data on sex. Women seem to increase their relative

fractions after the ZT laws are passed. They are more likely to drive drunk in the under

.08 range. This result is suspect because the data involving women is not very

comprehensive. There are only 1749 drunk crashes of women within the age group

throughout the entire period. This means 175 per year, or a little over 3 per state.

DrunkFractionwomen will take very discrete values. Thus the sample size is so small that

the effects are going to be widely exaggerated.

One possible explanation is that although women as a whole tend to be safer

drivers, the subset of risky ones might be risk loving, and enjoy the breaking the law.

Another possibility is that because men are much more likely to drive drunk, police

24

officers rarely target female drivers, and are more likely to let them go without arrest.

But even if this is the case its hard to imagine a scenario where women offend more after

a law is passed, unless their utility from violating the law is increasing the probability of

getting caught. Neither explanation is very credible, most likely the small amount of data

caused the unusual result. Men, however seem to represent the decrease quite well. As

you can see from the sample size, men are almost twice as likely to drive drunk as are

women, and their reaction to ZT laws is around 11% (95% CI = [6.47%,16.34%]). This

demonstrates that regardless of the unusual result for women, men are still significantly

affected by the law.

A useful extension of the model is to identify at what times during the day Zero

Tolerance laws are most effective. This could effect allocation of police resources to find

DUI�s. If drivers are more likely to be affected by laws at different times of the day, then

police could devote resources toward times where incidence is high. Over 80% of

alcohol related accidents occur between the hours of 7pm and 4am. Anecdotally this

seems to represent two types of drunk drivers: The first I will call the �Happy Hour�

driver, who drinks early in the evening before going home; the second is the �bar and

club� driver who drinks until late at night before deciding to drive. Table 5 summarizes

the coefficients and specifications for each below.

25

Intercept 0.153*** 0.162*** 0.179*** 0.168*** 0.172*** 0.079***Tau 0.002064 -0.003939 -0.003393 0.013525 0.005114 -0.023583

N = 8,503 (0.0117) (0.0124) (0.0361) (0.0152) (0.0173) (0.0447)AIC or R2 0.00006 0.15341 427.71992 0.01548 0.16593 417.19562

Intercept 0.124*** 0.127*** 0.237*** 0.138*** 0.140*** 0.335***Tau -0.012389 -0.015897 -0.1436395 -0.006601 -0.010582 -0.069783

N = 9,988 (0.0092) (0.0095)* (0.0227)*** (0.0118) (0.0129) (0.032)**AIC or R2 0.00362 0.20918 88.04696 0.04600 0.25056 97.13796


Intercept 0.226*** 0.241*** 0.202*** 0.249*** 0.259*** 0.132***Tau 0.01025 -0.00164 0.04279 0.03042 0.00900 0.04115

N = 5,632 (0.0169) (0.0178) (0.0389) (0.0221) (0.0252) (0.0490)AIC or R2 0.000752 0.158295 466.74439 0.016158 0.169941 489.87554

Intercept 0.337*** 0.350*** 0.376*** 0.349*** 0.364*** 0.499***Tau -0.01523 -0.03320 -0.09324 -0.00593 -0.03096 0.00970

N = 3,496 (0.0213) (0.0226) (0.0453)** (0.0275) (0.0310) (0.0555)AIC or R2 0.00109 0.18162 484.34060 0.03296 0.21439 487.52808

7pm to 11:59pm

DrunkFraction Under 21

AllFraction under 21


Notes: These results are taken from the tables in the back. The equivalent data fro over 21 yeilds no signficance once controls are used.

Table 5: Deterrence effect by hour of the Day

12am to 4am

7pm to 11:59pm

12am to 4am

Results show that the laws have a much more important effect on the happy hour driver

than they do on the bar driver. DrunkFraction increases and again is not significant, but

one can see a significant decrease of around 7% for AllFraction (the 95% CI is [.728%,

13.25%]). The significance can be explained if drivers are more likely to be rational

early in the day. Possible reasons: driving early means less time to get drunk and the

driver is more alert when they do drive home, both of which aid judgment and ability.

26

The hours after 12am are also associated with a large increase in sober accidents, as the

ability to operate machinery declines with alertness. Thus the frame of mind earlier in

the evening is better suited to both drive and follow the laws. This explains how drunk

accidents are actually less of a proportion after midnight than before. If this is the reason

for difference in significance, it shows importance of maintaining rationality for

punishment to work.

Estimating the Model:

Depending on the specification tau takes separate values, 14% for all drivers at all times,

11% for male drivers, and 7% for evening drivers. All three confidence bands contain

10% to 13%. For simplicity I will assume 11%, which is the discontinuous change in

offending before and after the law is .11. Therefore the proportion of the population who

no longer drive drunk = L/P = (AF1� AF2) = .11. Recall equation (4).

pc[U(np) - U(p)] = L/P

pc[U(np) - U(p)] = .11

We can find several different estimates for pc, Levitt and Porter estimate the chance of

being arrested for a DUI as 1/27,000 miles driven drunk. The National Survey on Drug

Use and Health find that for 21 and older, .6% of drivers are arrested for a DUI and 2.9%

of those who report driving under the influence in the pervious year were arrested,13 this

indicates that around 20% drove drunk during the year ([arrest per population] / [arrest

per number who drove drunk] = [number who drove drunk out of population]). Using

Levitt�s estimate, equation (4) equals:

U(np) - U(p)= τ/ pc = 27,000 * .11 = 2970

27

I now attempt to calculate utilities in terms of drunk miles, which seems arbitrary.

Almost by definition utilities are used as relative measures. Therefore I set U(nc) = 0,

which indicates U(p) < 0, and U(np) > 0. The values of the utilities will then give the

drunk miles driven each is valued at. If 2.9% are arrested per year, and the chances of

being arrested is 1 per 27,000 drunk miles:

.029 = (average drunk miles driven per year)/27,000

Solving yields, .029 times 27,000 = 783 miles are driven drunk by the average offender

per year. Recall, Prob(Drunk Driving) = P[pcU(p) + (1- pc)U(np) > U(nc)], or if U(nc) =

0, P[pcU(p) + (1- pc)U(np of 783) > 0]. If I assume then that the average expected utility

is equal to the drunk miles driven, then pcU(p) + (1- pc)U(np) = 783. This is done to

maintain simplicity, in order to not identify functional forms for U and P. Arbitrarily

assigning utilities in units of drunk miles then gives two equations.

U(np) - U(p) = 2970 and pcU(p) + (1- pc)U(np) = 783, with pc = .029

solving for U(np) = U(p) + 2970, then pcU(p) + (1- pc)[U(p) + 2970] = 783

U(p) = 783 � (1-pc)2970

U(p) = -2100 Drunk Miles

Because the utilities were calculated in terms of realized behavior, the deterrence effect

of the DUI punishment is then worth around 2100 drunk miles per person. These

equations assumed arbitrarily simple functional forms for utility and probability, so the

estimated utility should only be used as heuristic to human behavior, not a true measure.

Nevertheless, it does give an indication of the substitution effects of DUI laws.

28

Conclusion:

This paper presents a new way to identify the criminal probability for drunk

drivers. By using crash statistics, I help isolate the effects of penalties alone, without

problems from increase enforcement. Zero Tolerance Laws provide an excellent

experiment to test the efficacy of DUI laws in general. DUI penalties were pseudo-

randomly assigned to different states throughout the time period following the passage of

the Highway Act in 1995. Using this natural experiment, I found DUI laws reduce 10-

14% of drunk driving incidence. Heuristically this indicates DUI penalties are worth

2100 miles of drunk driving to the average potential offender. This has several potential

impacts on public policy. One, DUI penalties have a significant deterrence effect on

drunk driving. While no one doubts penalties deter actions, the relative rates of

deterrence effect policy expenditure. Two, the fact that laws are more effective in the

evening than past midnight indicates that police officers would be able to arrest more

potential offenders after midnight. More arrests late, might effect public perception of

the probability of apprehension. The higher the probability of apprehension will lower

the incidence rate. Finally, the fact that only 10% of a population is deterred by DUI

penalties indicates that the penalties might be to light, given the large negative externality

(estimated by Levitt and Porter as 30 cents a mile). Therefore, policy makers would be

justified in enacting even harsher penalties.

The problems with this study arise from the nature of state-indexed data, and its

large variation of errors. Clustered errors were able to show significance but better

regression forms might be able to identify more information in the data. Additionally the

data on women show that problems exist in the analysis. Nevertheless, Zero Tolerance

29

Laws represent a near ideal natural experiment, and the results are not unusual. DUI laws

should deter drunk driving, and 10% is a likely estimate. Further research should identify

the efficacy in enforcement and policy restrictions as this effects were funds should be

allocated for maximum deterrence. Drunk driving is an important national issue and

research on its efficacy should continue to guide the deterrence laws and policies.

References: 1 Levitt, Steven, Porter, Jack. �How Dangerous Are Drinking Drivers?� Journal of Political Economy. 2001, vol 109, no 6. University of Chicago Press, 2001. 2 Traffic Safety Center. �A History of the Science and Law behind DUI.� University of California, Online Newsletter, Volume 1, No 3. 2003. 3 Sen, Anindya. �Do Stricter Penalties Deter Drinking and Driving?� Canadian Journal of Economics. Vol. 34 No. 1. Canadian Economics Association, 2001. 4 Wilkinson, James, T. �Reducing Drunken Driving: Which Policies are Effective?� Southern Economic Journal. Vol. 54, No. 2. 1987. 5 Hingson R, Heeren T, Winter M. Lower legal blood alcohol limits for young drivers. Public Health Rep 1994;109:738-44. 6 Carpenter, Christopher. �How do Zero Tolerance Drunk Driving Laws Work?� Journal of Health Economics, 2004. 7 Lee, David, McCrary. �Crime, Punishment, and Myopia.� NBER Working Paper No.11491. National Bureau of Economic Research, July 2005. 8 Ash and Levy. �Young Driver Fatalities: The Role of Drinking Age and Drinking Experience.� Southern Economic Journal. Vol 57, No 2. Southern Economics Association, 1990. 9 Brautbar, Nathan. �Principles and Pitfalls in Alcohol Toxicology: Intoxication Defense.� http://www.environmentaldiseases.com/article_alcohol_toxicity.html. 2002. 10 Sage-Bollenbach and Baker. "Friday the 13th.� Study conducted by HEAT (Help, Encourage And Teach), a faculty sponsored campus group. 11 Clinton, William. �Statement on signing the National Highway System Designation Act of 1995.� Weekly Compilation of Presidential Documents, 12/4/1995. US Government Printing Office, 1995. 12 Farrington, David P. �Age and Crime.� Crime and Justice. Vol. 7. (1986). University of Chicago Press. 13�Arrests for Driving Under the Influence among Adult Drivers.� The National Survey on Drug Use and Health Report, Office of Applied Studies. September 2005.

30

Notes:

1. The statistical program used for this analysis was the open-source R, given by the Comprehensive R Archive Network. The specific analysis used the functions lm and lme. lm is a standard OLS function for any given formula, and was used for most of the regressions. Unfortunately lm cannot cluster the standard errors, therefore I used lme, from the package nlme. This was a linear mixed effects model. I set the random effects to 0, and entered the same equation that was used in OLS into the fixed effect formula. There were two problems with this software and the first is the estimates were maximum likelihood, not least squares. Under certain assumptions on the errors, normality and no correlation, these two estimates are identical. And both standard errors were approximately normal, and mostly uncorrelated identified by quantile-quantile plots, for normality, and the Durbin Watson test for auto correlation. Therefore the estimates appeared to be acceptable.

2. Another problem is how well the function handles blank spots in the data. Initially I set the weights to zero for the NA�s, but this produced an error message, therefore I was forced to set the weights to one. How the package ignores NA�s might effect the final estimate if it uses the weights. But for the cases of men, all drivers, 11pm to 2am, and 7pm to 10pm, all had under 1% NA�s. Therefore the significance of these estimates is not in doubt, however, the significance for women is because 69 of the 500 dependant variables returned an NA. More information is needed on how lme reacts to NA�s.

3. The fact the intercepts are much higher for the MLE estimation causes doubt with the model. I do not fully understand how the MLE estimator works, but the state effects all seem to be negative, indicating that the intercept is in fact the highest state value. However, the results given by the change in AllFraction seemed to indicated that after the law the incidence dropped to about 25% depending on specifications. This is close to the 20% nationwide estimate (see model estimation), and lends credence to the use of MLE for both effects and estimate.

31

Appendix: Appendix I

Data for 2003

32

Appendix II

Data for 2003, Ages 16 through 25 can be seen below

33

Appendix III

Appendix IV

34

Appendix V � Complete Tables and Specifications

Table 6: .01 to .08 BAC as a Proportion of Drunk Accidents, age 16 to 21

(Binary = 1 for Drivers 16 to 20Zero Tolerance Law) All (1) (2) (3) (4) (5) (6)Intercept 0.289*** 0.300*** 0.336*** 0.312*** 0.318*** 0.403***Tau -0.00115 -0.01874 -0.03811 0.01772 -0.00767 0.00146

N = 11,764 (0.0127) (0.0131) (0.0331) (0.0166) (0.0183) (0.0437)


0.00002 0.20629 355.51668 0.01807 0.21746 373.31467

Intercept 0.058*** 0.063** 0.029*** 0.069** 0.071*** 0.028***Tau 0.04078 0.01326 0.22235 0.11734 0.10036 0.31040

N = 1,749 (0.0327) (0.0347) (0.0551)*** (0.0432)*** (0.0491)** (0.0682)***0.00362 0.15103 538.67594 0.03363 0.17839 571.38786

Intercept 0.111*** 0.115*** 0.238*** 0.122*** 0.125*** 0.382***Tau -0.00861 -0.02513 -0.01848 0.00147 -0.02466 0.00863

N = 10,012 (0.0133) (0.0139)* (0.0380) (0.0173) (0.0193) (0.0499)0.00084 0.18790 482.00629 0.02143 0.20489 505.53610

Intercept 0.226*** 0.241*** 0.202*** 0.249*** 0.259*** 0.132***Tau 0.01025 -0.00164 0.04279 0.03042 0.00900 0.04115

N = 5,632 (0.0169) (0.0178) (0.0389) (0.0221) (0.0252) (0.0490)0.000752 0.158295 466.74439 0.0161582 0.169941 489.87554

Intercept 0.337*** 0.350*** 0.376*** 0.349*** 0.364*** 0.499***Tau -0.01523 -0.03320 -0.09324 -0.00593 -0.03096 0.00970

N = 3,496 (0.0213) (0.0226) (0.0453)** (0.0275) (0.0310) (0.0555)0.00109 0.18162 484.34060 0.03296 0.21439 487.52808AIC or R2


Notes: An observation in the linear probability model is a state and year in one of all 50 US States and the 10 years in the sample The dependant variable is the proportion of drunk drivers under 21, who had .01-.08 Blood Alcohol Content(BAC). The independent variable is a binary variables that equals one if the state had Zero Tolerance Laws during that year. Robust standard errors are in parentheses, errors for MLE estimation were clustered by state, errors for OLS were not clustered. The observations are weighted by the number of accidents covered in the sample.

AIC or R2

Dependant Variable: DrunkFraction = Proportion of Accidents with .01 to .08 BAC over all Drunk Accidents

Women

AIC or R2

AIC or R2

AIC or R2

Men

1am to 4am

7pm to 11:59pm

35

Table 7: .01 to .08 BAC as a Proportion of Drunk Accidents, age 21 and older

(Binary = 1 for Drivers 21 and olderZero Tolerance Law) All (1) (2) (3) (4) (5) (6)Intercept 0.175*** 0.181*** 0.149*** 0.167*** 0.170*** 0.149***Tau 0.0117767 0.00225147 0.03050433 0.018764 0.002328 -0.004554

N = 24,713 (0.0076) (0.0073) (0.0126)** (0.0098)* (0.0100) (0.0169)


0.00475 0.31651 -609.07059 0.02217 0.33474 -559.29411

Intercept 0.210*** 0.204*** 0.136*** 0.208*** 0.202*** 0.097*Tau -0.000625 -0.0073933 0.05674609 -0.002656 -0.02007 0.0112405

N = 3,329 (0.0182) (0.0195) (0.0376) (0.0237) (0.0272) (0.0487)0.00000 0.16486 345.36816 0.01180 0.17622 387.47338

Intercept 0.169*** 0.177*** 0.122*** 0.160*** 0.165*** 0.117***Tau 0.013954 0.00402112 0.05580207 0.022469 0.006341 0.0264043

N = 21,384 (0.0081)* (0.0078) (0.0147)*** (0.0103)** (0.0107) (0.0195)0.00599 0.29485 -431.43335 0.02682 0.31602 -395.17593

Intercept 0.143*** 0.150*** 0.155*** 0.140*** 0.142*** 0.173***Tau 0.0102546 -0.0016399 0.0427891 0.030422 0.008998 0.0411503

N = 11,598 (0.0169) (0.0178) (0.0389) (0.0221) (0.0252) (0.0490)0.00075 0.15829 466.74439 0.01616 0.16994 489.87554

Intercept 0.180*** 0.184*** 0.190*** 0.155*** 0.157*** 0.205***Tau -0.01523 -0.033202 -0.093244 -0.005932 -0.03096 0.0097035

N = 7,362 (0.0213) (0.0226) (0.0453)** (0.0275) (0.0310) (0.0555)0.00109 0.18162 484.34060 0.03296 0.21439 487.52808

AIC or R2

Men

Dependant Variable: DrunkFraction = Proportion of Accidents with .01 to .08 BAC over all Drunk Accidents

Notes: An observation in the linear probability model is a state and year in one of all 50 US States and the 10 years in the sample The dependant varaible is the proportion of drunk drivers over 21 who had .01-.08 Blood Alcohol Content(BAC). The independent variable is a binary variables that equals one if the state had Zero Tolerance Laws during that year. Robust standard errors are in parentheses, errors for MLE estimation were clustered by state, errors for OLS were not clustered. The observations are weighted by the number of accidents covered in the sample.


AIC or R2

AIC or R2

12 am to 4am

AIC or R2

7pm to 11:59pm

AIC or R2

Women

36

Table 8: .01 to .08 BAC as a Proportion of All Accidents, age 16 to 21

(Binary = 1 for All Drivers 16 to 20Zero Tolerance Law) (1) (2) (3) (4) (5) (6)Intercept 0.098*** 0.102** 0.304*** 0.110** 0.112*** 0.427***Tau -0.004217 -0.008339 -0.23023863 0.0026285 -0.002049 -0.1481416

N = 35,923 (0.0051) (0.0049)* (0.0201)*** (0.0065) (0.0067) (0.0274)***


0.00139 0.30212 -12.23918 0.02505 0.32585 -59.61402

Intercept 0.058*** 0.063** 0.029*** 0.069** 0.071*** 0.028***Tau 0.006145 0.003558 0.03151501 0.020702 0.0208615 0.06179961

N = 9,251 (0.0074) (0.0078) (0.0121)*** (0.0096)*** (0.0106)* (0.0163)***0.00140 0.16822 -638.91932 0.02841 0.19573 -581.69041

Intercept 0.111*** 0.115*** 0.238*** 0.122*** 0.125*** 0.382***Tau -0.007429 -0.011755 -0.13942271 -0.0038316 -0.009842 -0.1141692

N = 26,671 (0.0060) (0.006)* (0.0188)*** (0.0078) (0.0083) (0.0252)***0.00304 0.24995 -59.15374 0.02065 0.26891 -113.55587

Intercept 0.153*** 0.162*** 0.179*** 0.168*** 0.172*** 0.079*Tau 0.002064 -0.003939 -0.00339297 0.0135252 0.0051143 -0.0235835

N = 8,503 (0.0117) (0.0124) (0.0361) (0.0152) (0.0173) (0.0447)0.00006 0.15341 427.71992 0.01548 0.16593 417.19562

Intercept 0.124*** 0.127*** 0.237*** 0.138*** 0.140*** 0.335***Tau -0.012389 -0.015897 -0.14363948 -0.0066014 -0.010582 -0.0697827

N = 9,988 (0.0092) (0.0095)* (0.0227)*** (0.0118) (0.0129) (0.032)**0.00362 0.20918 88.04696 0.04600 0.25056 97.13796

AIC or R2

Men

Dep. Var.: AllFraction = Proportion of Accidents with .01 to .08 BAC over all Accidents

Notes: An observation in the linear probability model is a state and year in one of all 50 US States and the 10 years in the sample The dependant varaible is the proportion of all drivers under 21 who had .01-.08 Blood Alcohol Content(BAC). The independent variable is a binary variable that equals one if the state had Zero Tolerance Laws during that year. Robust standard errors are in parentheses, errors for MLE estimation were clustered by state, errors for OLS were not clustered. The observations are weighted by the number of accidents covered in the sample.


AIC or R2

AIC or R2

12am to 4am

AIC or R2

7pm to 11:59pm

AIC or R2

Women

37

Table 9: .01 to .08 BAC as a Proportion of All Accidents, age 16 to 21

(Binary = 1 for All Drivers 21 and olderZero Tolerance Law) (1) (2) (3) (4) (5) (6)Intercept 0.092*** 0.097** 0.078*** 0.091** 0.093*** 0.078***Tau 0.00231 -0.004203 0.0169759 0.01075015 0.001524 -0.00163427

N = 48,298 (0.0040) (0.0040) (0.0074)** (0.0051)** (0.0055) (0.0101)


0.00067 0.25001 -1126.25319 0.02910 0.27079 -1066.21759

Intercept 0.074*** 0.080** 0.043*** 0.078** 0.083*** 0.046***Tau -0.002926 -0.00929 0.00991676 0.00169052 -0.010629 -0.00654337

N = 9,698 (0.0070) (0.0074) (0.0120) (0.0092) (0.0103) (0.0158)0.00035 0.17249 -622.88557 0.01142 0.18172 -578.16286

Intercept 0.097*** 0.101*** 0.079*** 0.094*** 0.096*** 0.077***Tau 0.003356 -0.002851 0.01937671 0.01243385 0.004551 0.00576389

N = 38,600 (0.0045) (0.0046) (0.0082)** (0.0057)** (0.0063) (0.0111)0.00113 0.20238 -1021.75256 0.03247 0.22843 -966.82074

Intercept 0.118*** 0.125*** 0.120*** 0.113*** 0.117*** 0.118***Tau 0.004763 -0.005856 -0.0150027 0.01380082 -0.002516 -0.02376978

N = 14,270 (0.0081) (0.0087) (0.0139)* (0.0104) (0.0119) (0.0195)0.00070 0.13841 -432.74056 0.02044 0.15695 -371.82475

Intercept 0.108*** 0.110*** 0.064*** 0.095*** 0.097*** 0.061***Tau 0.004923 0.000681 0.03209833 0.00567919 -0.001191 0.02403238

N = 12,414 (0.0076) (0.0082) (0.0157)** (0.0100) (0.0115) (0.0207)0.00084 0.13664 -398.47812 0.02040 0.15816 -348.90738

12am to 4am

AIC or R2

Dep. Var.: AllFraction = Proportion of Accidents with .01 to .08 BAC over all Accidents


AIC or R2

Notes: An observation in the linear probability model is a state and year in one of all 50 US States and the 10 years in the sample The dependant varaible is the proportion of all drivers over 21 who had .01-.08 Blood Alcohol Content(BAC). The independent variable is a binary variables that equals one if the state had Zero Tolerance Laws during that year. Robust standard errors are in parentheses, errors for MLE estimation were clustered by state, errors for OLS were not clustered. The observations are weighted by the number of accidents covered in the sample.

AIC or R2

Women

AIC or R2

7pm to 11:59pm

Men

AIC or R2

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