2. Methods
2.1. Functional forms We estimate regression models that express fatality rates as functions of beer taxes or
prices, as socioeconomic characteristics, and as a set of variables describing the legal environment. These models take the following form:
y
it
5 x
it
b 1 w
it
; i 5 1, 2, . . . 48;
t 5 1982, 1983, . . . 1990, 1
where y
it
is the possibly transformed fatality rate for state i in year t, x
it
is the vector of right-hand side variables, b is a vector of coefficients to be estimated, and w
it
is an unobserved disturbance term representing unmeasured factors affecting fatalities.
A common specification for the dependent variable employs the logistic transformation of the death rates. That is, if r
it
is the fatality rate i.e., deaths divided by population, then the dependent variable in the regression is defined by
y
it
5 ln
r
it
1 2 r
it
Logistic Model where ln is the natural logarithm function. An advantage of the logistic form is that it restricts
predicted fatality rates to their natural range: 0 –1. However, this study’s measures of the fatality rates also include 0s for some states in some years. There is nothing untoward about
these 0s in and of themselves; they simply indicate that there were no fatalities of a particular type in a particular state in a particular year. For example, in North Dakota in 1982, no
18 –20-year-old dead drivers were tested for alcohol. Unfortunately, the logistic transfor- mation cannot be applied when the fatality rate is 0, because the natural logarithm of 0 is
minus infinity. Thus, this dependent variable cannot be computed for some of the observa- tions.
This study has adopted two approaches to this problem. One is simply to assume that at least one person of each type died in each state-year. When the data are adjusted accordingly,
the death rates are always .0 and the logistic transformation can be computed. As an alternative, this study also estimates regression models in which the dependent variable is
simply the fatality rate, rather than its logistic transformation. The regressions using un- transformed fatality rates are referred to as linear models.
y
it
5 r
it
Linear Model The linear models also provide a check on whether estimated results depend on the somewhat
arbitrary assumptions about functional form.
3
The use of two functional forms somewhat complicates the interpretation of the results
3
The linear model has the potential disadvantage that predicted values could fall outside the 0 –1 range, but, in fact, this never occurs in the first-stage regressions see the discussion of weighting below. Because the
outcomes of interest fatalities are actually count data, still another approach would be to estimate a Poisson model.
109 D.J. Young, T.W. Likens International Review of Law and Economics 20 2000 107–126
since the exact meanings of the coefficients differ. In the linear models, the coefficient on the beer tax or price is the estimate of the absolute change in fatalities per 1,000 population from
a 1 increase in the tax. For example, a coefficient of 20.1 would indicate that a 1 increase in the tax on a case of beer would reduce fatalities 0.1 per 1000, or about 1 per 10,000 people.
In the logistic models, the coefficient on the beer tax indicates the approximate propor- tional change in fatalities from a 1 increase in the tax. For example, a coefficient of 20.1
would imply that fatalities would be reduced by approximately 10 if the tax were increased by 1 per case. This approximation, while very useful in most instances, is less useful if the
coefficient exceeds about 0.2 in absolute value.
4
2.2. Weighting The linear and logistic forms imply that some observations are more reliable have smaller
variances than others. Let p
it
be the population of a state in a particular year, and r
it
be the probability of dying in a motor-vehicle accident. Then the variances of the disturbances for
the two functional forms are given by the following
5
: Logistic
Var~w
it
5 1
p
it
rp
it
~1 2 rp
it
, and
Linear Var~w
it
5 rp
it
~1 2 rp
it
p
it
. Efficient estimation procedures weight the observations inversely with the variances given
immediately above. Thus, both functional forms weight the data from more populous states more heavily than the data from less populous states. The two functional forms differ,
however, in how the probability of a fatality affects the weighting. In the logistic model, state-years with higher probabilities receive more weight, while in the linear model state-
years with higher probabilities receive less weight.
6
In practice, the differences in population levels across states are the dominant influences on the weights.
Operationally, the models are first estimated using just population for the weights, and then the predicted values for fatality rates from these first-round estimates, say, are used to
construct the weights defined above. These constructed weights are used in computing the second-round estimates reported in this article.
7
4
A closer approximation can be obtained for large negative coefficients: The percent change approximately equals exp{b} 2 1100 where b is the coefficient and exp denotes exponentiation. For example, if b 5 20.2,
the approximate reduction is 18.
5
See William H. Greene 1990, Chapter 14 and especially Section 3.1b of Chapter 20.
6
Actually, the weights are symmetric about a fatality rate of 0.5, but because all the fatality rates are very close to 0, the text statement is true within the range of the data.
7
Amemiya 1981, pp. 1498 –1501. Greene 1990 also recommends this procedure. 110
D.J. Young, T.W. Likens International Review of Law and Economics 20 2000 107–126
2.3. State-specific effects We assume that there may be unmeasured factors affecting fatalities that are unique to
each state but that are constant over time within states. Examples might be the percentages of driving that are done on various types of roads such as mountainous, curving, two-lane,
or gravel roads, or the percentage of driving that is done during daylight hours. Effects of this type are easily incorporated into models that utilize pooled time-series cross-section data.
The disturbance term for a model with state-specific effects, a
i
, i 5 1,2, . . . 48, may be written as
w
it
5 a
i
1 e
it
. Thus, the a’s represent factors that are unmeasured i.e., not in x and are constant over time,
although they vary across states. Operationally, the state-specific effects are accounted for by including one dummy variable for each of the states.
In summary, we estimate the relationships between motor-vehicle fatality rates and beer taxes, prices, and other explanatory variables using data across states and over time in the 1980s. Our
specification is very similar to that of Chaloupka et al. 1993 and several other studies, with the following differences: 1 we estimate state-specific fixed effects, while several other studies use
ordinary least squares; 2 we estimate both logistic and linear functional forms—in part because the logistic form cannot be computed for some observations and, in part, to determine whether
the estimates are robust to functional form; and 3 we employ technically superior weights computed from the fitted values of first-stage regressions.
8
2.4. Control variables This study employs a large number of socioeconomic and legal variables in addition to beer
prices and taxes.
9
There are two reasons to include many “control” variables. First, estimators of the tax andor price coefficients may be biased if adequate controls are not included. For example,
if states with high taxes on alcohol are also states with populations that eschew alcohol in the first place, then the deterrent effect of taxes will be overestimated. A similar bias occurs if states that
have increased taxes also have implemented other policies that deter drunken driving, but these other policies are not accounted for in the model specification. On the other hand, the effective-
ness of taxes may be understated if states levy high taxes in response to unmeasured factors that result in high fatalities. These kinds of biases are minimized by including a large number of
control variables.
10
The second reason for including measures of other policies toward drunken driving is because they are of interest themselves. Although this article focuses primarily on taxes
8
Our specification is also very close to Ruhm 1996 whose data cover the 1982– 88 period.
9
The variable list is nearly identical to the “limited specification” of Chaloupka et al. 1993 to make comparisons of our findings easy. However, we were not able to fully reproduce the results of Chaloupka et al.
1993. See our companion piece Young Likens, 1994. Details of sources are provided in the Appendix.
10
Of course, the number of control variables is limited by the number of degrees of freedom available, and including too many controls can result in intractable multicollinearity problems. A still better approach would be
to treat the laws as endogenous in a simultaneous equations framework, if such a model could be identified. 111
D.J. Young, T.W. Likens International Review of Law and Economics 20 2000 107–126
and prices, the drinking age, breath tests, fines for driving under the influence DUI, and other policies are also examined.
2.5. Data Table 1 provides descriptive statistics on the variables used in this study.
11
The first four lines refer to the fatality rates. The first of these, DALLPOP, is the total number of
motor-vehicle fatalities per 1,000 population. The national average of slightly less than 2 fatalities per 10,000 people displayed little trend over the sample period, but there is
considerable variation across state-years.
The next variable, DDALCPOP, is the number of “alcohol-involved” driver deaths per 1,000 population. Alcohol involvement is estimated in the following way.
12
For each state and year, the following totals are counted: dead drivers; dead drivers who were tested and for
whom the result of a blood alcohol content BAC result is known; and dead drivers tested whose BAC is 0.05. Only a fraction of dead drivers are tested, and this fraction varies
from state to state, especially in the early years of the study. The number of dead drivers in alcohol-involved accidents is then computed as the fraction of tested drivers with
BACs0.05 times the total number of dead drivers. For example, if 1,000 drivers died, 500 were tested, and 300 of those tested had BACs of at least 0.05, then the estimated number
of dead drivers in alcohol-involved accidents would be 600 51,000300500.
This method for estimating alcohol involvement may be biased. Particularly in the early years of the study, testing was neither random nor complete. Tests were probably more likely
to be performed on drivers whom the police suspected were, in fact, drunk. For example, alcohol odor or the presence of alcoholic beverage containers may well have triggered
testing. If this is the case, our estimates of alcohol involvement are likely to be biased upward. But no clearly superior alternative exists.
The remaining fatality rates in Table 1 refer to the 18 –20-year-old population. DALL1820 is the total number of motor-vehicle fatalities for drivers aged 18 –20 divided by the number
of persons in the population aged 18 –20. DDALC18 is the corresponding fatality rate based on estimated alcohol involvement. Fatality rates for this age group are more than twice those
of the general population, and a number of policies have been specifically aimed at reducing teenage fatalities.
The first variable in Table 1 after the fatality rates is RTAXB, the beer tax calculated by summing federal and state excise taxes. The tax is measured in dollars of 1982–1984
purchasing power per case of 24 12-ounce cans.
13
The price of beer, RPRICEB, is measured
11
The means are weighted by total population, except that the youth fatality rates are weighted by the population aged 18 –20. There are 432 observations 48 states times 9 years: 1982–1990, except that price data
were only available for 397 state-years.
12
This is the method used by Chaloupka et al. 1993.
13
Dollars of 1982–1984 purchasing power are the basis for the Consumer Price Index of the U.S. Bureau of Labor Statistics. To convert to current 1998 dollars, multiply by about 1.65 to account for inflation since the
1982–1984 period. 112
D.J. Young, T.W. Likens International Review of Law and Economics 20 2000 107–126
Table 1 Variable definitions and descriptive statistics
a
Variable Definition
Mean SD
Min Max
DALLPOP Total motor vehicle fatalities per 1,000 population
0.19 0.05
0.08 0.43
DDALCPOP Estimated alcohol-involved driver deaths per 1,000
population 0.06
0.02 0.02
0.18 DALL1820
Total motor vehicle fatalities of 18–20-year-olds per 1,000 population aged 18–20
0.44 0.12
0.20 1.13
DDALC18 Estimated alcohol-involved deaths of 18–20 year old
drivers per 1,000 population aged 18–20 0.15
0.06 0.00
0.52 RTAXB
Sum of federal and state excise taxes on beer, in 1882– 1984 dollars per 24 can case, divided by state cost of
living index 1.01
0.47 0.49
3.24 RPRICEB
Retail price of beer, in 1982–1984 dollars per six-pack, divided by state cost of living index.
REALINC Per capita personal income in thousands of 1982–1984
dollars, divided by state cost of living index 13.21
1.33 8.85
16.16 SPEED65
Percentage of vehicles exceeding 65 MPH in 55-MPH zones
10.48 3.65
2.70 27.30
VMTLIC Vehicle miles traveled in thousands per licensed driver
11.70 1.61
7.75 17.50
PLIC25 Percent of licensed drivers under age 25
17.70 2.36
7.60 28.20
SEATBELT Dummy variable equals 1 if mandatory seatbelt use law
0.46 0.49
0.00 1.00
UNEM Unemployment rate
7.06 2.32
2.20 18.00
PCTDRY Percent of population residing in dry counties
4.78 9.02
0.00 45.97
PMOR Mormon population as percent of total
1.21 5.44
0.10 65.82
PSBA Southern Baptist population as percent of total
6.80 9.15
0.00 30.36
PCAT Catholic population as percent of total
21.00 12.60
1.64 63.81
PPRO Other Protestant population as percent of total
20.17 8.29
1.46 46.14
DRINKAGE Minimum legal age for purchase and consumption of
beer .3.2 20.57
0.89 18.00
21.00 BREATH
Dummy variable equals 1 if police are authorized to administer a preliminary breath test
0.43 0.39
0.00 1.00
DRAMSHOP Dummy variable equals 1 if state law permits lawsuits
against servers of alcohol 0.81
0.39 0.00
1.00 ADMINPS
Dummy variable equals 1 if state requires administrative driver’s license suspension or
revocation after first arrest for DUI 0.18
0.39 0.00
1.00 ADMINPEN
Mandatory minimum administrative driver’s license action, days
14.33 51.00
0.00 365.00
DUIFINE Dummy variable equals 1 if a fine is required on first
conviction for DUI 0.35
0.48 0.00
1.00 RDUIFINE
Mandatory minimum fine upon first conviction for DUI, in 1982–1984 dollars
91.75 135.90
0.00 721.85
DUILIC Dummy variable equals 1 if state requires license
suspension or revocation upon first conviction for DUI
0.32 0.47
0.00 1.00
DUILICD Mandatory minimum license suspension or revocation
upon first conviction for DUI, days 30.50
74.30 0.00
365.00
a
Sample consists of the 48 contiguous United States from 1982 through 1990 432 observations, except that the price of beer RPRICEB is missing for 35 cases. Sample means are weighted by population in each state-year,
except for youth fatality rates, which are weighted by the youth ages 18 –20 population. See text and Appendix for details, SD, standard deviation.
113 D.J. Young, T.W. Likens International Review of Law and Economics 20 2000 107–126
in 1982–1984 dollars per six-pack.
14
Both the tax and price variables are divided by a cost-of-living index that is specific to each state McMahon et al., 1991. Thus, the beer tax
and price variables are each expressed relative to the overall cost of living in each state and year.
The price data are from surveys of a wide variety of consumer items conducted by the American Chamber of Commerce Research Association ACCRA. The correlation between
the tax and price variables is 0.40.
15
Consequently, the tax variable and the price variable convey somewhat different information about the prices people actually pay. Taxes may not
be a good indicator of actual transaction prices, because they represent ,10 of price; thus, variations in other factors that affect price could “swamp” variations due to taxes. On the
other hand, the ACCRA data are also imperfect measures of price. While the price data consistently refer to a particular brand and size across states and over time, and the
establishments from which prices are gathered are mostly constant over time within states, there is considerable variation in the types of establishments sampled across states.
The control variables include real per capita income, the percentage of vehicles that exceed 65 miles per hour MPH in 55-MPH zones, vehicle miles traveled per licensed
driver, the percentage of licensed drivers under age 25, a dummy variable for mandatory seatbelt usage, the unemployment rate, the percentage of population residing in “dry”
counties, and the percentages of the population who are, respectively, Mormon, Southern Baptist, Catholic, and other Protestant.
Other policies are aimed particularly at drinking and driving. These include the minimum legal drinking age for beer, a dummy variable indicating that police can administer prelim-
inary breath tests, and a dummy variable if servers of alcohol can be sued for damages resulting from motor-vehicle accidents a “dram-shop” law. Three legal penalties for driving
and drinking are represented by pairs of variables. The first variable is a dummy for the existence of a mandatory minimum penalty, and the second variable indicates the magnitude
of the penalty, if it exists. Pairs are defined for mandatory administrative license suspension or revocation after first arrest for DUI and for mandatory fines and license suspension upon
a first conviction for DUI.
3. Results
Kategori