1. Risk Analysis, Vol. 36, No. 2, 2016 DOI: 10.1111/risa.12449
An Empirical Analysis of Life Jacket Effectiveness
in Recreational Boating
Christelle Viauroux1,∗
and Ali Gungor2
This article gives a measure of life jacket (LJ) effectiveness in U.S. recreational boating. Using
the U.S. Coast Guard’s Boating Accident Report Database from 2008 to 2011, we find that
LJ wear is one of the most important determinants influencing the number of recreational
boating fatalities, together with the number of vessels involved, and the type and engine of
the vessel(s). We estimate a decrease in the number of deceased per vessel of about 80%
when the operator wears their LJs compared to when they do not. The odds of dying are 86%
higher than average if the accident involves a canoe or kayak, but 80% lower than average
when more than one vessel is involved in the accident and 34% lower than average when the
operator involved in the accident has more than 100 hours of boating experience. Interest-
ingly, we find that LJ effectiveness decreases significantly as the length of the boat increases
and decreases slightly as water temperature increases. However, it increases slightly as the
operator’s age increases. We find that between 2008 and 2011, an LJ regulation that requires
all operators to wear their LJs—representing a 20% increase in wear rate—would have saved
1,721 (out of 3,047) boaters or 1,234 out of 2,185 drowning victims. The same policy restricted
to boats 16–30 feet in length would have saved approximately 778 victims. Finally, we find that
such a policy would reduce the percentage of drowning victims compared to other causes of
death.
KEY WORDS: Life jacket effectiveness; Poisson model; U.S. Coast Guard
1. INTRODUCTION
Attempts to raise risk awareness in recreational
boating and to design effective policies aimed at
reducing the number of accidents took off in the
1990s.(9)
In Ref. 10, Wheeler et al. develop risk-based
measures of effectiveness of the U.S. Coast Guard
Vessel Inspection Program linking categories of root
causes of accidents to inspection activities designed
to reduce the risk of the root causes.
1Department of Economics, University of Maryland–Baltimore
County, Baltimore, MD, USA.
2Standards Evaluation & Analysis Division, United States Coast
Guard Headquarters, 2703 Martin Luther King Jr. Ave. S.E.,
Washington, DC, USA.
∗Address correspondence to Christelle Viauroux, Department of
Economics, University of Maryland–Baltimore County, Balti-
more, MD 21250, USA; ckviauro@umbc.edu.
At the same time, it became obvious that life
jacket (LJ) use was very low for many types of recre-
ational boats despite the legal requirement of car-
rying LJs aboard watercrafts. In 1993, the National
Transportation Safety Board released a study3
ana-
lyzing 281 recreational drowning cases where victims
were not wearing LJs (also referred as personal flota-
tion devices [PFDs]). It was believed that 238 of them
would have survived had they worn their LJs. A 2012
U.S. Coast Guard blog post4
(based on a 7th Coast
Guard District press release), mentions “The Coast
Guard estimates 80 percent of boating fatalities
could have been prevented if boaters wore their life
3Safety Study: Recreational Boating Safety, PB93-917001,
NTSB/SS-93/01.
4http://coastguard.dodlive.mil/2012/05/12-tips-for-12-weeks-of-
summer
302 0272-4332/16/0100-0302$22.00/1 C 2015 Society for Risk Analysis

2. An Empirical Analysis of Life Jacket Effectiveness 303
jackets.” This statement is based on direct calculation
of how many people drown each year, and of those,
how many were not wearing LJs. By themselves,
these quantities do not represent complete measures
of LJ effectiveness, but they clearly indicate a need
for further investigation. Indeed, the 2008–2011 U.S.
Coast Guard’s Boating Accident Report Database
(BARD) shows that only about 19.8% of fatalities
in recreational boating were wearing their LJs. The
wear rate is as low as 15.1% among drowning victims,
representing 2,185 of the total 3,047 fatalities. One of
the reasons that LJs are highly underused may be the
unpopular nature of the LJ itself. In Ref.7, Quistberg
et al. explore behavioral factors and strategies that
encourage consistent LJ usage among adult recre-
ational boaters. Participants in their LJ experiment
report using their LJs only when conditions were
poor. More specifically, they report that barriers to
consistent LJ use include discomfort and the belief
that LJ use indicates inexperience or poor swimming
ability. Participants suggested that the design of more
comfortable, better fitting, or more appealing LJs
may increase LJ usage but that laws requiring LJ use
may be necessary to change boaters’ habits.
One of the primary objectives of this article
will be to assess the impact of an LJ policy on
the recreational boating fatality rate. However,
such a major and controversial policy cannot be
implemented without a thorough investigation of LJ
effectiveness. A lot of the work focusing on reducing
recreational boating fatalities lacked the availability
of LJ use data. For example, in Ref. 4, Duda et al. use
the U.S. Coast Guard 1995–2004 BARD to analyze
factors associated with canoe and kayak fatalities.
Their results found that the more people involved
in the incident, or the longer canoe or kayak, the
lower the fatality rate. Males are more prone to
death in canoe/kayak incidents than are females.
Alcohol/drug use emerged as a factor positively
associated with the fatality rate. They also find that
the states of West Virginia, Maine, and the Pacific
Division (consisting of Alaska, California, Hawaii,
Oregon, and Washington) are more unsafe than the
rest of the United States. Finally, they find that LJ
accessibility is correlated with safer boating. LJ ac-
cessibility, however, is only a prerequisite for LJ use
but does not imply use and hence does not constitute
a good measure of possible life savings from LJs.
A first measure of LJ effectiveness was calcu-
lated in Ref. 8. In his analysis of U.S. fatal boating
accidents observed between 1960 and 1965, Traub
calculated the odds of dying and finds that they are
3.18 times greater for individuals not wearing their LJ
than for those individuals wearing it. He concludes
that if everyone who had fallen in the water and died
had worn an LJ, 60% of them would have survived.
This study, however, was not limited to recreational
boating and included fatal accidents only. In a case
control study on recreational boating,(12)
Yang et al.
estimate that children one to four years old who
wore PFDs when playing near water were less likely
to drown than other children, with an adjusted risk
ratio of 0.43. It is unknown, however, whether this
estimate is relevant for adults or boaters. In Ref. 2,
Cummings et al. use the 2000–2006 BARD and a
matched-cohort design to compare accident out-
comes from people on the same boat who were
involved in recreational incidents resulting in them
being in the water or at risk of drowning. They find
that wearing a PFD (i.e., a 100% wear rate) reduces
the risk of drowning by 49%. However, the authors
warn that substantial bias is possible because of
the small number of vessels (201 vessels involving
497 boaters) that met their criteria: among different
things, these criteria excluded boating accidents
resulting in less than one fatality, or where only
one person ended up in the water. Additionally,
other vessels were excluded because of nonmatching
records or missing data on gender or age of the
persons involved. Using probability theory, the
2008 BARD data, and the NTSB estimate above,
Maxim(6)
calculates that a 43.6% reduction in
drowning (from 250 to 141) would follow an increase
in the wear rate from 17.9% to 70% (corresponding
to 67.7% for a 100% wear rate). His calculation
method, however, assumes that LJ wear is the
only factor explaining the drowning rate and is
limited to open-motorboard-type vessel incidents
in 2008.
This article provides a more comprehensive anal-
ysis of LJ effectiveness for two reasons. First, we
use the more recent 2008–2011 BARD to explain
the number of fatalities and its variation across ves-
sels by many different factors that together influ-
ence the outcome of the accident. Our model allows
us to measure the importance of LJ wear relative
to other influential factors and to identify the most
significant environmental and individual factors ex-
plaining fatalities in recreational boating. Second, we
give a prediction of how much a policy regulating LJ
wear would reduce the number of fatalities observed.
Third, we segment the fatalities database by cause of
death to investigate the role of several factors present
at the time of the accident to explain the number of

3. 304 Viauroux and Gungor
fatalities. We conclude the analysis by showing how
the distribution of causes of death would be affected
by a policy regulating LJ wear.
Our results show that LJ wear is one of the most
influential determinants of the number of fatalities
in recreational boating, together with the number of
vessels involved and the type and engine of the ves-
sel. We estimate that the expected number of de-
ceased per vessel would decrease by about 80% if the
operator wears his LJ. We also find that LJ effective-
ness decreases significantly as boat length increases
and decreases slightly with increase in water temper-
ature. Finally, it increases slightly with the age of the
operator. Our simulation of an LJ policy requiring
all operators to wear their LJs shows that between
2008 and 2011, about 1,721 out of 3,047 total fatalities
could have been prevented, representing 1,234 out
of 2,185 drowning deaths. A similar policy restricted
to 16–30-foot-length boats would have saved approx-
imately 778 victims. Finally, an analysis of causes
of death shows that a policy on LJ wear would re-
duce the proportion of drowning victims compared
to other causes.
The data and the model used to measure the
impact of various interacting factors on the fatality
rate are described in Section 2. Estimation results
are presented in Section 3. In Section 4, the model
presented in Section 2 is used to simulate a policy
aimed at increasing LJ wear; life-saving measures
are reported. In Section 5, we estimate an alternative
model to provide measures of distribution of causes
of death before and after simulation of an LJ wear
policy. Section 6 concludes.
2. DATA AND ESTIMATION PROCEDURE
2.1. Data
Federal and state regulations require boat own-
ers/operators to complete boat accident report forms
and submit them to state boating law administra-
tors within 2–10 days of an accident, depending on
the circumstances. The 50 states, five U.S. territories,
and the District of Columbia submit accident report
data electronically to the U.S. Coast Guard for in-
clusion in the annual boating statistics publication.
These data are then compiled into the Coast Guard’s
BARD. The BARD database provides information
on a general overview of the accident (date, time, lo-
cation, number of deceased and injured on the boat),
on characteristics of operators and vessels involved in
the accident, as well as on more detailed character-
istics of fatalities and casualties. For the purpose of
this study, and its focus on number of fatalities rather
than types of fatalities, we merged the overview and
the vessel tables for the years 2008–2011. The merged
file contains a total of 30,066 vessels (corresponding
to 81,179 persons involved). Data on LJ wear are
available for operators of vessels involved in acci-
dents as well as for fatalities (operators and nonop-
erators). Table I presents LJ wear rates among recre-
ational boating fatalities. The table shows an over-
all wear rate among all fatalities of 19.8%. Drown-
ing victims have the lowest wear rates among all
causes of death, with about 85% of them without an
LJ. LJ wear is higher for trauma victims and other
causes of death.5
For further purposes, we note here
that among fatalities observed, operators’ wear rate
is comparable to the wear rate of a representative vic-
tim.
Let us turn to the more general BARD (includ-
ing fatalities and nonfatalities) and the circumstances
of the accident. Tables A1(a) and A1(b) provide
summary statistics of different factors that could
explain the observed number of deceased on each
boat. It shows that about one fatality was reported
for every 10 vessels involved in an accident (with a
maximum of five fatalities observed) and only one
disappearance was reported for every 100 accidents.
While an average of 4.85 PFDs were present on a
boat, only 46% of vessel operators wore their LJs.
Note that this reported wear rate of 46% among
operators is much higher than the rate observed for
fatalities in Table I, which can be explained two ways.
First, we expect the wear rate to be lower among
dead victims simply because of the protective nature
of the device. Second, the boat owner/operator
may be inclined to misreport this information for
fear of incriminating himself or herself. This would
cause the effect of a regulation aiming at increasing
LJ wear to be underestimated. This variable is,
however, the only one currently available.
Additional descriptive statistics show that in
80% of the accidents, the weather was clear and
that 85% of accidents happened during the day. The
average air temperature at the time of the accident
5The category “Other” includes the following reported causes of
death: “cardiac arrest” (Total: 83, N.W.: 59.7%), “hypothermia”
(Total: 45, N.W.: 44.2%), “carbon monoxide poisoning” (Total:
23, N.W.: 100%), “unknown” (Total: 192, N.W.: 85.9%), and
“other” (Total: 27, N.W.: 84.6%). Note that some columns or
rows may not sum due to rounding.

4. An Empirical Analysis of Life Jacket Effectiveness 305
Table I. Life Jacket Wear Rate by Cause of Death in 2008–2011 Recreational Boating Fatalities
Not Worn Total
Life Jacket (N.W.) Worn (W) Missing (M.D.) Total (w/o M.D.)
All 2,202 544 301 3,047 2,746
% of total w/o m.d. 80.2% 19.8%
All-operators 1,196 296 159 1,651 1,492
% of total w/o m.d. 80.2% 19.8%
Drowning-all 1,730 308 147 2,185 2,038
% of total w/o m.d. 84.9% 15.1%
Drowning-operators 987 171 86 1,244 1,158
% of total w/o m.d. 85.2% 14.8%
Trauma-all 264 162 66 492 426
% of total w/o m.d. 62% 38%
Trauma-operators 96 76 19 191 172
% of total w/o m.d. 55.8% 44.2%
Other-all 208 74 88 370 282
% of total w/o m.d. 73.8% 26.2%
Other-operators 113 49 54 216 162
% of total w/o m.d. 69.8% 30.2%
Source: Boating Accident Report Database (BARD), U.S. Coast Guard.
was about 80 ◦
F, while the water temperature
was 71 ◦
F. Vessels involved in an accident were
mostly open motorboats (46%), followed by cabin
motorboat (15%). Most operators, of average age
40, were male (89%) with low boating experience
(only 25% have acquired more than 100 hours of
experience). Additional statistics are available in the
Appendix.
Unfortunately, Tables A1(a) and A1(b) also
show a large number of missing values for most
strategic variables such as LJ wear of the operator or
his blood alcohol concentration at the time of the ac-
cident. For example, the data set reports LJ wear in
only 4,063 accident cases (out of 30,066 vessels). The
number of PFDs available on a vessel (on average
4.85) is reported in only 1,550 cases. Blood alcohol
concentration is reported in 3,856 of cases.
The problem is that the subsample of accident
reports showing the information on LJ wear may not
give a good representation of the entire set of vessels
involved in accidents. To remedy this issue and im-
prove on the robustness of our results, we construct
an additional data set where a weight is given to each
vessel for which the operator’s LJ wear is collected.
This weight is constructed in order for the final data
set to match the share of vessel types found in the
initial sample so that the weighted sample gives an
accurate representation of boats types involved in
accidents. Although the power of weighting the ob-
servations remains limited by the presence of other
variables with a large number of missing values, the
robustness and possible generalization of our results
is greatly improved by doing so.
In the following section, we present the model
used to measure LJ effectiveness. Descriptive statis-
tics of subsamples of observations used in the esti-
mated models are presented in the Appendix.
2.2. The Model
In this section, we investigate which of the many
different factors involved in an accident explains best
the number of fatalities.
Let yi represent the actual number deceased on
vessel i, and μ be the average number of deceased
per vessel involved in accidents between 2008 and
2011. Let i denote a random unobserved component
that accounts for the unexplained difference between
the average number of deceased per vessel and the
observed number of deceased on vessel i. We assume
that:
yi = μ + i .
Fig. 1 shows the distribution of number of de-
ceased reported in recreational boating between
2008 and 2011. It shows a large number of accidents
with no fatalities and only a small number of acci-
dents resulting in a positive number of fatalities.
We assume that i follows a Poisson distribution
with probability density function:
f ( i ) = f (yi )
=
μyi
exp(−μ)
yi !
,

5. 306 Viauroux and Gungor
Fig. 1. Number of deceased per vessel involved in an accident.
where the first equality follows from the fact that μ is
nonrandom. More specifically, we use a Poisson re-
gression model, an extension of the Poisson distribu-
tion above, by allowing each accident to have a dif-
ferent value of μ. The model assumes that each ob-
served count of fatalities on vessel i is drawn from an
independent and possibly different Poisson distribu-
tion with mean μi , where μi is the predicted average
number of deceased on vessel i, estimated from var-
ious observed factors present at the time of the acci-
dent involving i. These factors include environmental
conditions at the time of the accident (weather, wa-
ter temperature, etc.), as well as the vessel’s intrin-
sic characteristics such as the engine type, the length,
etc., and some socioeconomic characteristics of the
vessel’s operator (age, experience, etc.). We assume:
μi = exp(β0 + βxi ) ≥ 0,
where xi ≡ (1, xi1, ...xik) represents a vector of char-
acteristics of the accident and β ≡ (β0, βi1, ...βik) is
the associated vector of coefficients to be estimated.
Note that the Poisson distribution requires accident
events to be independent and has the major property
that
Var(yi |xi ) = E(yi |xi ) = μi = exp(β0 + βxi ), (1)
which proves to be verified in our data set: Table
A1(a) shows, for example, that E(yi ) = 0.102 is close
to V(yi ) = 0.3432
= 0.117. Table II(b) also reports
the results of an overdispersion test showing that
Equation (1) is valid in our data.
2.3. Estimation Procedure
The first step to understanding which factor
present at the time of the accident mattered most is
to use one-variable regressions to explain the num-
ber of fatalities. A total of 54 one-variable Poisson
regressions (corresponding to 54 candidate factor
variables) were run,6
providing univariate measures
of correlation between the number of fatalities
and each available factor. A sample of them are
reported in Table A2 and commented on below.7
We
henceforth refer to these as models 1 (M1s). Inter-
pretation of the effect of each factor on the number
of deceased is as follows. Let E(y|x, xk) denote
the expected number of deceased per vessel when
factor x takes value xk. Let E(y|x, xk + δ) denote
the expected number of deceased per vessel after
increasing xk by δ units. Then, using Equation (1),
E(y|x, xk + δ)
E(y|x, xk)
= exp (βδ). (2)
For a change of δ in xk, the expected number of
deceased per vessel increases by a factor of exp(βkδ),
holding all other variables constant. This factor is
also known as the incident rate ratio (I.R.R.). Note
that if the change δ = 1, then the I.R.R. is simply
exp(β). For example, in Table A2, an operator wear-
ing his LJ (i.e., “LJ wear” going from no wear (0) to
wear (1)) decreases the expected number of deceased
per vessel by 68.3%.
Among candidate variables for the models
below, those that appear significantly negatively
related to the number of fatalities (i.e., with I.R.R.
< 1) include LJ wear, experience (although not
significantly), increases in water temperature,
increases in number of vessels involved in the ac-
cident, and increases in length of the vessel. The
number of fatalities seem to also be significantly
lower when the accident occurs during the day
or when the weather is clear at the time of the
accident. On the other hand, the number of fatalities
seem to be significantly higher (i.e., with I.R.R.
> 1) when blood alcohol concentration increases,
when the operator is older, when the accident
occurs during a weekday or when the vessel is of
open-motorboard type. One-variable regressions,
however, do not account for the complexity of the
6Note that each regression uses a different number of vessels.
This is because each candidate variable has a different set of
missing values.
7Results of the other ones are available to the reader upon re-
quest.

6. An Empirical Analysis of Life Jacket Effectiveness 307
accident, and hence represent very poor predictors
of the observed variation in number of fatalities
across accidents. This is shown by the very small fit
measure of the regressions (pseudo-R2
) reported in
Table A2. During the accident, many factors are
combined and it is their combination that results in
the unfortunate outcome of fatalities. For example,
it is possible for a factor to significantly affect the
number of fatalities when it is seen as a unique
explanation of the outcome but become insignificant
when other factors are introduced because some of
its effect is subsumed by one or more other variables.
One such occurrence is illustrated in Table A3. Table
A3 reports Poisson estimation results of a model
where blood alcohol concentration and LJ wear are
introduced simultaneously (henceforth, model M2).
As mentioned in Section 2.1, we consider two data
sets: an unweighted data set and a weighted data
set to represent the distribution of vessel types from
the complete sample. Results of (M2) (in Table A3)
show that taken separately, both wearing a LJ
and having a high blood alcohol concentration are
significant in explaining the number of deceased.
Furthermore, the signs and magnitudes of the esti-
mates are intuitive: a 67% decrease in the average
number of fatalities on the vessel and a 28% increase
in the number of fatalities for every 10% increase in
operator’s blood alcohol concentration. However,
combining both factors (see Table A3) shows that
the information on LJ wear may incorporate some of
the behavior found in operators drinking alcohol, as
the latter variable coefficient becomes insignificant.
This result is consistent with the result of Loeb
et al.,(5)
who find that there is no persuasive evidence
of alcohol contributing substantially to operator
fault in fatal accidents.
In the section below, we report the results
associated with the best model specifications (i.e.,
combinations of variables) when several variables
are introduced.
3. ESTIMATION RESULTS
Tables II(a) and II(b) report the estimation re-
sults of two variants of the Poisson model pre-
sented above: one variant uses unweighted data
(M3), while the other (M4) uses the weighted sam-
ple described above.8
A test of overdispersion is re-
8Note that the pseudo-R2 of these two models, respectively, 0.268
and 0.330, cannot be compared as they do not use the same sam-
ple of vessels.
ported at the end of Table II(b) and rules out the
use of a negative binomial distribution in both cases
(i.e., the null hypothesis H0 : α = 0 where α is such
that Var(yi |xi ) = E(yi |xi )(1 + αE(yi |xi )) cannot be
rejected). Additionally, for policy purposes, we fo-
cus on “reportable” accidents as classified by the
U.S. Coast Guard9
by introducing a variable “Re-
portable Accident” as an additional factor.10
Tables
A4 and A5 report descriptive statistics for the vari-
ables used in M3 and M4. All other variables held
constant, estimation results show that the expected
number of deceased per vessel decreases by about
80% (79.4% in M3 and 80.8% in M4) when the op-
erator wears his LJ, compared to when he does not.
This result is highly significant and makes LJ wear
together with the number of vessels involved in the
accident the most important contributors of fatality
reduction. This result, however, is of lower magni-
tude than Traub’s (1989) result, which reports that
the odds of dying are 3.18 times greater for a person
not wearing a PFD than for a person who does (our
result is equivalent to the respective odds of dying of
1.794 in M3 and 1.808 in M4). Several reasons may
explain the difference in findings. First, Traub(8)
in-
vestigates a selected sample of fatal accidents while
we include all accidents; second, the decision to wear
an LJ may depend on some characteristics of the ac-
cident such as weather conditions or the type of ves-
sel involved. These last factors were not included in
Traub’s estimation and may lower our estimate as
well. Third, boating may be safer today than it was
in the 1960s. For example, the use of GPS to deter-
mine the location of an accident may be associated
with faster rescue. Therefore, it may be reasonable
to assume that wearing an LJ was of greater impor-
tance in the 1960s.
Additional results show that more vessels in-
volved in an accident reduces the number of fatali-
ties between 78% (M3) and 83% (M4). This result is
consistent with Duda et al.,(4)
who find that more peo-
ple involved in an accident is associated with lower
fatalities. One could conjecture that more people in-
volved are associated with faster rescue/first aid. Ex-
perience is also found to greatly reduce the number
of fatalities, with a 34% (M4) estimated reduction
9See the 2012 annual statistics report for details, pages 9–11
(www.uscgboating.org/assets/1/workflow_staging/Page/705.
PDF).
10Estimation of the sample selecting only reportable accidents re-
moves an additional 235 observations in M3 and 1,333 in M4.
Estimation results are extremely similar to those of Tables II(a)
and II(b) and for this reason, have not been reported.

7. 308 Viauroux and Gungor
Table II(a). Estimation Results
Model 3 N=2,030 Model 4 N=10,849
Variables Coeff. I.R.R. Coeff. I.R.R.
Length of vessel −0.057*** 0.945*** −0.044*** 0.957***
(0.014) (0.008)
Day (=1)/night −0.611*** 0.543*** −0.501*** 0.606***
(0.158) (0.089)
Operator wears life jacket −1.578*** 0.206*** −1.650*** 0.192***
(0.216) (0.101)
Water temperature −0.007 0.993 −0.015*** 0.985***
(0.005) (0.004)
Reportable accident 0.891*** 2.438*** 1.630*** 5.104***
(0.330) (0.221)
Number vessels involved −1.546*** 0.213*** −1.795*** 0.166***
(0.249) (0.143)
Boat type: open motorboat −0.309* 0.734* −0.435*** 0.647***
(0.172) (0.095)
Engine type: outboard 0.487*** 1.628*** 0.465*** 1.592***
(0.173) (0.101)
Accident on a weekday 0.153 1.166 0.216*** 1.241***
(0.140) (0.068)
Speed 10–20 miles per hour −1.041*** 0.353***
(0.317)
Vessel not moving 0.453*** 1.573***
(0.161)
State: AZ −1.215* 0.297* −1.112*** 0.329***
(0.715) (0.327)
State: FL 0.525** 1.690** 0.980*** 2.665***
(0.233) (0.099)
State: MO −0.678* 0.508* −0.979*** 0.376***
(0.371) (0.209)
State: NJ −0.741 0.476 −0.993*** 0.371***
(0.459) (0.295)
State: NY −0.549** 0.578**
(0.265)
State: OH −0.483 0.617 −1.168*** 0.311***
(0.335) (0.197)
when the operator has more than 100 hours of expe-
rience. However, speed may also change the accident
outcome: the average number of deceased increases
by about 57% (M3) if the vessel is not moving at the
time of the accident and is 65% lower if the vessel
averages a speed of 10 to 20 miles per hour.
Age is found to be slightly positively corre-
lated with the number of fatalities observed: it
increases between 0.8% (M4) and 1.1% (M3) for
every additional year of age of the operator. This
result may capture unobserved characteristics of the
operator such as overconfidence or high risk taking
as experience increases. This intuition is consistent
with another result on boat rentals. We find that the
number of deceased is 22% lower when the boat
has been rented. In this case, the less experienced
operator may be more risk averse, perhaps making
mistakes overall less threatening. The lower number
of deceased may also be due to the fact that rented
boats may be in better condition and that those
renting out boats may require PFD wear.
Fig. 2 (panels a and b, corresponding to estimates
from models M3 and M4, respectively) provides an
illustration of this result. Both panels show the pre-
dicted number of deceased per vessel estimated as
the operator ages, distinguishing between operators
wearing their LJs (black continuous line), and oper-
ators who do not wear their LJs (dashed line). Both
graphs clearly show that the effectiveness of LJ in-
creases with age.
The number of fatalities on a vessel also seems
to be closely related to the vessel’s intrinsic charac-
teristics. We find that it is significantly safer to be on
a longer vessel with a number of fatalities estimated

8. An Empirical Analysis of Life Jacket Effectiveness 309
Table II(b). Estimation Results (continued)
Variables Model 3 Coeff. I.R.R. Model 4 Coeff. I.R.R.
Age of operator 0.011** 1.011** 0.008*** 1.008***
(0.004) (0.002)
Vessel’s number of engines −0.412* 0.662*
(0.249)
Operator experience > 100 hours −0.418*** 0.658***
(0.082)
Vessel was rented −0.256** 0.774**
(0.125)
Air temperature −0.003 0.997
(0.004)
Horsepower −0.002*** 0.998***
(0.000)
Canoe type 0.624*** 1.867***
(0.134)
State: IA 1.280*** 3.596***
(0.467)
State: IL 0.931** 2.538**
(0.456)
State: LA 1.745*** 5.725***
(0.117)
State: MD −0.672*** 0.511***
(0.178)
state: PA 0.409*** 1.506***
(0.130)
State: SC 1.112*** 3.039***
(0.236)
State: UT −0.787* 0.455*
(0.453)
Constant 2.815*** 16.694*** 2.708*** 15.006***
(0.683) (0.402)
R-squared 0.268 0.330
Negative binomial11 α value 2.86e-7 std. err.: 1e-4 5.42e-8 std. err.:2.02e-5
Negative binomial H0 : α = 0 0.0e+00 p=0.5 5.1e-6 p=0.499
p< 0.10, **p< 0.05, ***p< 0.01.
to be between 4.3% (M4) and 5.5% (M3) lower for
each additional foot length.
Fig. 3 (panels a and b) reports the predicted num-
ber of fatalities per length of vessel, distinguishing
between individuals wearing their LJ and those who
do not. Both models M3 and M4 estimate that it is
safer to be on a longer boat and that the effective-
ness of LJ decreases with its size.
The average number of deceased is estimated to
be 1.86 times higher when the vessel is a canoe or a
kayak. It is also more dangerous to be on a powerful
boat, with a 77% increase in fatalities for each addi-
tional engine. In model M4, among open motorboats
with outboard type engine, the average number of
deceased is ((0.647−1)+(1.592−1)) = 23% higher
11We implicitly assume that this policy on mandatory PDF is ac-
companied by full compliance.
than among other types of boats (excluding vessels
with no engine).
Finally, environmental conditions are found to
be important predictors of the number of deceased
on a vessel. All other variables being held constant,
each additional degree Fahrenheit in water temper-
ature decreases the average number of fatalities be-
tween 0.7% (M3) and 1.5% (M4). Panels a and b in
Fig. 4 show that the predicted number of deceased
per vessel decreases as the water temperature in-
creases and varies greatly depending on operators’
willingness to wear their LJs. LJ effectiveness is much
higher in cold water, perhaps reflecting the debilitat-
ing effects of cold shock.
The average number of deceased is 40% lower
when the accident occurs during the day and is es-
timated to be between 24% (M4) and 29% (M3)
higher when the accident occurs during a weekday

9. 310 Viauroux and Gungor
Fig. 2. LJ effectiveness increases with operator’s age: Panel a M3
and Panel b M4.
as opposed to a weekend. Finally, once all the factors
above have been controlled for, results show that the
location of the accident still matters; in particular, it
is more dangerous to boat in LA, IA, SC, IL, and FL
(relative to other states).
4. POLICY IMPLICATIONS
This section uses the estimation results above
to simulate the impact of a policy on LJ wear in
recreational boating. We simulate a policy requiring
all operators to wear their LJs and infer how many
lives could have been saved under such a policy.12
Policy simulation results using estimates from M3
and M4 are reported in Table III, which reports the
12We implicitly assume that this policy on mandatory PDF is ac-
companied by full compliance.
Fig. 3. LJ effectiveness decreases with boat size: Panel a M3 and
Panel b M4.
predicted number of deceased per vessel before and
after the policy. It shows that the policy would de-
crease the number of deceased between 56.5% (M3)
and 62% (M4).
In order to infer how many lives could have been
saved had this policy been implemented, let r denote
the observed wear rate, and let T (respectively, O)
denote the total number of boaters (respectively, op-
erators) involved in recreational accidents. Since T
is not reported, we will use T = T ∗ O, where T is
the reported average number of people on board for
each vessel involved in an accident.
Let T1
(respectively, O1
) denote the number
of individuals (respectively, operators) wearing their
LJs. Note that the wear rate r = T1
T
= O1
+(T1
−O1
)
T
.
In what follows, we calculate the change in wear
rate associated to a full compliance of this policy
by operators. This allows us to link the change

10. An Empirical Analysis of Life Jacket Effectiveness 311
Fig. 4. LJ effectiveness decreases as water temperature increases:
Panel a M3 and Panel b M4.
Table III. Predicted Number of Deceased per Vessel Under
LJ Regulation
Number of Deceased/Vessel M3 M4
1- Current condition
Predicted mean 0.0380 0.0245
Std. error 0.0052 0.0018
2- All operators wear an LJ
Predicted mean 0.0165 0.0092
St. error 0.0034 0.0009
Confidence interval [0.0099 0.02317] [0.0074 0.0112]
3- No operator wears LJ
Predicted mean 0.0801 0.0483
Standard error 0.0114 0.0036
Confidence interval [0.0577 0.1025] [0.0412 0.0554]
4- % change from 1- to 2- −56.5% −62%
Table IV. Calculation of the Change in Wear Rate Associated
to the Change in Number of Deaths
Variables Model 3 Inference
Current Policy Current Policy
O 2,027 2,027 27,661 27,661
T 2.845 2.845 2.7 2.7
T 5,766 5,766 74,684 74,684
O1 958 2,027 12,724 27,661
T1 − O1 1,769 1,769 21,631 21,631
r 0.473 0.658 0.460 0.660
r +18.5% +20%
y −56.5% −56.5%
in number of deceased reported in Table III to
the appropriate change in wear rate. Table IV
details the calculations. The second column of
Table IV indicates that in the final sample of ac-
cidents used in M3,13
there were 2,027 operators;
vessels had, on average, 2.845 people on board (see
Table A4), corresponding to a total recre-
ational boaters involved in accidents of 5,766
(=2,027*2.845). Of 2,027 operators, 47.3%, i.e., 958
operators (see Table A4), report having worn their
LJ at the time of the accident. Assuming the wear
rate is identical among nonoperators, this means
that 1,693 nonoperators were wearing their LJs (for
example, solve for (T1
− O1
) in 0.473 = 958+(T1
−O1
)
5,766
).
In column 2 of Table IV, we assume that the
policy is implemented with full compliance: the num-
ber of operators wearing their LJs is equal to the to-
tal number of 2,027 operators. Assuming the policy
does not affect the wear rate of nonoperators (kept
at 47.3%), the policy increases the overall wear rate
to r = 1,769+2,027
5,766
= 0.658, hence representing an in-
crease of 18.5% in wear rate.
Therefore using M3, we conclude that an 18.5%
increase in wear rate causes a decrease in the num-
ber of fatalities of 56.5%. By means of comparison
with Ref. 6, this means that an increase in the wear
rate by 22.7% (to a rate of 70% as in Maxim’s result)
would decrease the number of fatalities by 69.3%.
Therefore, our result is stronger than the 43.6%
decrease found by Maxim.(6)
The difference may
simply be due to the fact that in his probability cal-
culation, Maxim does not account for the multiple
13We choose to use M3 instead of M4 for this policy simulation
because the number of people on board in M3 (equal to 2.845)
is more representative of the number of people on board in the
total population of boaters (equal to 2.7) than M4, with a number
of 3.234.

11. 312 Viauroux and Gungor
factors involved in accidents, which, combined with
the wear rate decision, could enhance the accident
outcome.
Assuming that the data used in M3 are a random
representation of all boating activity in the country,
it is possible to generalize the results to the overall
population of accidents observed between 2008 and
2011. In the overall sample, Table A1(a) reports that
8% of vessels have no operator. Hence, we count
approximately 27,661 operators (i.e., 27,661 vessels
with an operator), 46% of which wear their LJs (i.e.,
a total of 12,724 operators). With an average number
of people on board of 2.7, the total number of per-
sons involved in accidents was 27,661*2.7=74,685.
Assuming an aggregate wear rate of 46% means that
21,631 nonoperators wore their LJs (0.46=12,724+x
74,684
).
Hence, going from 46% to 27,661+21,631
74,684
= 66%
reduces the number of fatalities by 56.5%.
As a conclusion, between 2008 and 2011, we es-
timate that 1,721 (out of 3,047) fatalities could have
been avoided had a policy increased the wear rate
to about 66%. This would have represented 1,234
out of 2,185 drownings. A more conservative pol-
icy restricting this policy to, for example, 16–30-feet
boats—which counted 1,378 deceased between 2008
and 2011—would still have saved 778 victims.
5. EXTENSION: EXPLAINING CAUSES
OF DEATH
In this section, we refine our analysis to explore
how different factors interact for different causes of
death. To that purpose, we use the restricted sample
of fatalities (as partially described in Table I) instead
of the total sample of accidents as in the preceding
section. We use a standard multinomial logit model
(MNL) to address how some fatalities’ character-
istics such as LJ wear, alcohol use, and the victim’s
role on the boat (passenger/operator) explain causes
of death such as drowning, trauma, or other causes
of death. We predict how the distribution of
causes of death would be altered if a policy similar
to the one above was implemented.
5.1. The Model
Let d denote a random variable indicating the
type of death observed taking on the indexes j =
0, 1, 2 for drowning, trauma, and other causes, re-
spectively. Let x denote a vector of victim-specific
characteristics. Our interest lies in understanding the
main factors that can potentially explain the proba-
bility p of each type of death occurring.
For the ith victim, we assign a function Ui j char-
acterizing the chances of death j occurring as fol-
lows:
Ui j = V (xi ) + i j ,
where V() is a function constructed from observed
variables and i j is an unobserved random compo-
nent characterizing the accident. i j . i j is assumed
to be independent across victims and causes of death
and distributed according to an extreme value type I
distribution.14
Using the distributional properties of i j , the
probability that individual i cause of death j occurs,
i.e., Pi j can be expressed as:
Pi j = P(ci = j|xi ) = Pi j
=
exp(xi βj )
2
h=0
exp(xi βh)
, j = 0, 1, 2.
The parameters of the MNL model are gener-
ally not directly interpretable and are complicated.
In particular, a positive coefficient need not mean
that an increase in the regressor leads to an in-
crease in the probability of that outcome being se-
lected. To see this, we can compute marginal effects,
i.e., the effect of a change in the victim’s charac-
teristics on the probability of a cause of death oc-
curring. For a continuous variable xik of associated
coefficient βjk belonging to the N × K set of vari-
ables xi := (xi1, ...xik, ...xi K) with associated vector of
coefficients βj := (βj1, ...βjk, ...βj K), ∀ j = 0, 1, 2, the
marginal effect of xk on the probability can be written
as:
∂ Pi j
∂xik
= Pi j βjk −
2
h=0
βhkPih .
Note that for any particular xk, ∂ Pi j /∂xik need
not have the same sign as βjk. Furthermore, the
marginal effects vary with the value of x. However,
14The extreme value type I distribution, also known as the
Gumbel distribution, has the probability density function F( )
=exp(− exp(−μ( − η), where η is the location parameter and μ
is the scale parameter. The location parameter determines where
the origin of the distribution will be located, while the scale pa-
rameter determines the statistical dispersion of the probability
distribution.

12. An Empirical Analysis of Life Jacket Effectiveness 313
Fig. 5. The predicted probability of drowning is much lower when
the individual wears his LJ.
when the function Ui j is linear in x, one can show
that
ln
Pi j
Pil
= ln (x) = xi (βj − βl).
Taking the exponential of both sides of the above
equation, we obtain the expression of an odd of dying
of a certain cause, given accident characteristics x:
(x) =exi (βj −βk)
.
If we let xik change by 1 unit, we have:
(xi ,xik + 1) = e(βj1−βl1)xi1
...e(βjk−βlk)xik
e(βj −βl )
×...e(βj K−βlK)xi K
.
Hence, the odds ratio (x,xk+1)
(x,xk)
is equal to:
e(βj1−βl1)xi1
...e(βjk−βlk)xik
e(βj −βl )
...e(βj K−βlK)xi K
e(βj1−βl1)xi1 ...e(βjk−βlk)xik ...e(βj K−βlK)xi K
= e(βj −βl )
.
For a unit change in xk, the odds of outcome j
occurring versus outcome l are expected to change
by a factor e(βj −βl )
, holding all other variables con-
stant. For e(βj −βl )
> 1, one could say that the odds
are “e(βj −βl )
times larger,” or that the odds “increase
by e(βj −βl )
− 1”; for e(βj −βl )
< 1, one could say that
the odds are “e(βj −βl )
times smaller,” or that the odds
“decrease by 1 − e(βj −βl )
.”
5.2. Results
Table V shows that the odds of dying by drown-
ing versus trauma (respectively, other causes) among
deceased wearing their LJs are 61% (respectively,
58%) lower than the odds among deceased who did
Table V. Estimation Results
Dep. Variable: Cause Marginal
of Death Coeff. Odds Ratio Effect
Drowning
Deceased wore PFD −0.773*** 0.462*** −0.092***
(0.191) (0.018)
Deceased used alcohol 0.311 1.365 −0.047**
(0.285) (0.021)
Deceased age −0.034*** 0.967*** 0.000
(0.006) (0.001)
Deceased role: operator 0.355 1.426 0.197***
(0.491) (0.037)
Deceased role: passenger −0.014 0.986 0.085**
(0.494) (0.034)
Constant 5.334*** 207.176*** –
(0.825) –
Other Ref. Ref. Ref.
Trauma
Deceased wore PFD −0.278 0.757 0.061***
(0.214) (0.016)
Deceased used alcohol 0.771** 2.162** 0.064***
(0.304) (0.018)
Deceased age −0.048*** 0.953*** −0.002***
(0.006) (0.000)
Deceased role: operator −1.023** 0.359** −0.193***
(0.506) (0.032)
Deceased role: passenger −0.722 0.486 −0.091***
(0.507) (0.026)
Constant 3.754*** 42.688*** –
(0.888) –
R-squared 0.065
N 2,019
p < 0.10, **p < 0.05, ***p < 0.01.
Fig. 6. The predicted probability of drowning is higher with alco-
hol use until age 63.
not wear an LJ. We also find that the odds of dy-
ing of a trauma versus drowning are 58.4% higher
(i.e., 1.365
2.162
− 1 = 0.584) when the deceased used alco-
hol prior to the accident than when he did not.
Figs. 5 and 6 show how the predicted probability
of drowning changes with age depending on whether

13. 314 Viauroux and Gungor
Table VI. Predicted Probability of Dying by Cause of Death
Cause of Death Observed Prediction Std. Error z p-Value 95% C.I.
Drowning 0.7653 0.79 0.01 81.56 0.00 [0.77, 0.81]
Trauma 0.1723 0.16 0.01 18.37 0.00 [0.14, 0.18]
Other 0.0623 0.05 0.01 9.08 0.00 [0.04, 0.06]
Fig. 7. An LJ policy reduces the number and share of drowning
victims relative to other causes of death. Panel a (N = 2,019): Dis-
tribution before policy and panel b (N = 212): Distribution after
policy.
the deceased did or did not wear a PFD device and
did or did not use alcohol.
We find that the probability of drowning is re-
lated to age through a concave function reaching its
maximum at about 60 years old. This maximum could
be explained by a higher number of individuals boat-
ing around that age, and by additional risk taken by
older operators. Alcohol touches a much younger
population, with a maximum probability of drowning
obtained at age 30.
Table VI shows the distribution of fatalities per
cause of death. The predictive power of our model is
very good although it slightly overestimates drown-
ings compared to other causes.
Finally, Fig. 7 (panels a and b) gives an illustra-
tion of the predicted distribution of causes of death
before and after implementation of the policy on
operators’ LJ wear.15
The policy is shown to reduce
both the total number of victims and the share
of drowning victims compared to other causes of
death.
6. CONCLUSION
In this article, we use the recent U.S. Coast
Guard BARD database to investigate the different
factors explaining the number of fatalities observed
between 2008 and 2011 as well as the effectiveness of
LJ wear. Among many factors present at the time of
the accident, we find that LJ wear is one of the most
influential at explaining the number of fatalities. We
also find that during this period, an estimated 1,721
fatalities, representing 1,234 drownings, could have
been avoided, had LJ wear been increased to 66%
through regulatory LJ wear policy.
One limitation of our study is in the quality of
the data. We remedy the presence of missing values
by weighting the data set in order to make it rep-
resentative of the entire sample of vessel types and
we find that our results from the weighted sample
do not vary much compared to the results found us-
ing the unweighted sample. This suggests that our
conclusions are pretty robust to this issue. Also,
note that improving data quality and precision is
one of the major goals of the U.S. Coast Guard to
achieve 100% boat accident report completeness by
2016.
Second, given the binary nature of the “LJ wear”
variable, we cannot extrapolate the marginal effect
of LJ usage. A quantitative, i.e., continuous, variable
(number of LJ wearers on the boat, for example)
would be required to estimate the functional form of
change in fatalities resulting from a change in LJ us-
age rate. Indeed, the relationship between the inten-
sity of LJ wear and the number of fatalities could be
15The size of the second graph is smaller to illustrate the smaller
number of deaths after implementation of the policy.

14. An Empirical Analysis of Life Jacket Effectiveness 315
of logarithmic form or polynomial form. In case of a
logarithmic relationship, for example, the biggest re-
duction in number of fatalities would be obtained for
the first 20% increase in LJ wear and this reduction
would gradually decrease as the wear rate further
increases.
Finally, because our data are limited to accidents
reported, this study does not measure the fraction
of LJ effectiveness associated with accidents that are
not reported (e.g., person falling in water who can
rescue himself (herself) thanks to the protection of
the LJ). Information about all registered vessels’ ac-
tivity would be required to measure this effect.
ACKNOWLEDGMENTS
The authors are thankful to S. Farrow, three
anonymous referees, and participants at U.S. Coast
Guard seminars and Towson University seminars, as
well as participants at the 2013 Society for Risk Anal-
ysis Annual Meeting for their very insightful com-
ments. This project was supported by Rolling Bay,
LLC.
APPENDIX
Table A1(a). Summary Statistics of the Overall Sample
Variables Count Mean SD Min Max
Accident Characteristics
Number of people on board 27,738 2.70 2.62 0.00 72.00
Number of deceased 29,863 0.102 0.343 0.00 5.00
Number of disappearances 14,620 0.01 0.08 0.00 3.00
Depth of water in feet 2,042 3.84 5.11 0.00 71.00
Depth of water in inches 1,446 6.66 7.61 0.00 84.00
Number of boating citations 346 0.63 1.26 0.00 17.00
Fire extinguishers on board (=1) 30,012 0.04 0.19 0.00 1.00
Number of PFDs on board 1,550 4.85 4.78 0.00 60.00
Dollar amount of vessel property damage 23,997 7,845.85 88,510.99 0.00 9,000,000
Operator Characteristics
Gender (male =1) 20,105 0.89 0.31 0.00 1.00
Age 22,716 40.43 15.86 0.00 95.00
Wore personal flotation device (=2) 4,063 1.46 0.50 1.00 2.00
Blood alcohol concentration (*100) 3,856 2.03 6.57 0.00 160.00
Education: American Red Cross (=1) 30,012 0.00 0.07 0.00 1.00
Education: Informal (=1) 30,012 0.04 0.19 0.00 1.00
Education: None (=1) 30,012 0.42 0.49 0.00 1.00
Education: No operator (=1) 30,012 0.08 0.27 0.00 1.00
Education: State course (=1) 30,012 0.10 0.30 0.00 1.00
Education: U.S. Power Squadron (=1) 30,012 0.02 0.12 0.00 1.00
Education: USCG Auxiliary (=1) 30,012 0.04 0.20 0.00 1.00
Experience: 10–100 hours (=1) 30,012 0.17 0.38 0.00 1.00
Experience: 100–500 hours (=1) 30,012 0.25 0.44 0.00 1.00
Experience: No operator (=1) 30,012 0.08 0.27 0.00 1.00
Experience: No experience (=1) 30,012 0.01 0.09 0.00 1.00
Experience: Over 500 hours (=1) 30,012 0.11 0.32 0.00 1.00
Weather Conditions
Clear (=1) 29,401 0.79 0.41 0.00 1.00
Cloudy (=1) 29,401 0.15 0.36 0.00 1.00
Fog (=1) 29,401 0.01 0.10 0.00 1.00
Rain (=1) 29,401 0.04 0.19 0.00 1.00
Snow (=1) 29,401 0.00 0.05 0.00 1.00
Hazy (=1) 29,401 0.01 0.09 0.00 1.00
Air temperature 25,393 79.53 13.98 0.00 125.00
Water temperature 24,674 71.10 11.36 29.00 108.00
Day (=1)/night 29,917 0.85 0.36 0.00 1.00

15. 316 Viauroux and Gungor
Table A1(b). Summary Statistics of the Overall Sample (continued)
Variables Count Mean SD Min Max
Vessel Characteristics
Year vessel was built 26,411 1,995.81 11.76 1,899 2,011
Number of engines 23,977 1.07 0.71 0.00 90.00
Length in feet 28,125 21.48 16.59 3.00 734.00
Type: Airboat (=1) 29,359 0.01 0.07 0.00 1.00
Type: Auxiliary sail (=1) 29,359 0.05 0.21 0.00 1.00
Type: Canoe (=1) 29,359 0.03 0.18 0.00 1.00
Type: Houseboat (=1) 29,359 0.02 0.12 0.00 1.00
Type: Inflatable (=1) 29,359 0.02 0.15 0.00 1.00
Type: Open motorboat (=1) 29,359 0.46 0.50 0.00 1.00
Type: Other (=1) 29,359 0.01 0.11 0.00 1.00
Type: Personal watercraft (=1) 29,359 0.20 0.40 0.00 1.00
Type: Pontoon (=1) 29,359 0.04 0.19 0.00 1.00
Type: Rowboat (=1) 29,359 0.01 0.10 0.00 1.00
Type: Sail (only) (=1) 29,359 0.01 0.11 0.00 1.00
Type: Sail (unknown) 29,359 0.00 0.02 0.00 1.00
Engine type: Inboard (=1) 28,142 0.41 0.49 0.00 1.00
Vessel has no engine 28,142 0.08 0.27 0.00 1.00
Engine type: Other (=1) 28,142 0.01 0.08 0.00 1.00
Engine type: Outboard (=1) 28,142 0.34 0.47 0.00 1.00
Engine type: Stern drive (=1) 28,142 0.17 0.38 0.00 1.00
Amount of horsepower 21,441 224.30 346.81 0.00 7,000.00
Propulsion: Manual (=1) 28,405 0.06 0.25 0.00 1.00
Propulsion: No propulsion (=1) 28,405 0.00 0.02 0.00 1.00
Propulsion: Other (=1) 28,405 0.00 0.01 0.00 1.00
Propulsion: Propeller (=1) 28,405 0.69 0.46 0.00 1.00
Propulsion: Sail (=1) 28,405 0.02 0.13 0.00 1.00
Propulsion: Air thrust (=1) 28,405 0.01 0.08 0.00 1.00
Propulsion: Water jet (=1) 28,405 0.22 0.42 0.00 1.00
Fuel type: Diesel (=1) 26,924 0.07 0.25 0.00 1.00
Fuel type: Electric (=1) 26,924 0.01 0.09 0.00 1.00
Fuel type: Gasoline (=1) 26,924 0.84 0.36 0.00 1.00
Fuel type: No fuel (=1) 26,924 0.08 0.27 0.00 1.00
Table A2. Sample of One-Variable Poisson Regressions (M1s) Results
Dep. Variable: Number of Deceased per Vessel Coeff. I.R.R. S.E. N pseudo-R2
Operator’s Characteristics
PFD wear (=1) −1.150*** 0.317*** 0.101 4,063 0.045
PFD wear, weighted per vessel type (=1) −1.112*** 0.329*** 0.047 30,250 0.034
Blood alcohol concentration (%) 0.027*** 1.028*** 0.002 3,855 0.027
Experience greater than 100 hours (=1) −0.024 0.976 0.053 18,800 0.000
Age 0.017*** 1.017*** 0.001 22,710 0.011
Accident’s Characteristics
Water temperature −0.033*** 0.968*** 0.001 24,578 0.026
Day (=1)/night −0.612*** 0.542*** 0.042 29,772 0.009
Weekday (=1) 0.342*** 1.408*** 0.036 29,863 0.004
Weather: Clear (=1) −0.395*** 0.674*** 0.041 29,257 0.004
Number of vessels involved −1.879*** 0.153*** 0.057 29,852 0.091
Vessel’s Characteristics
Length −0.042*** 0.959*** 0.002 28,107 0.021
Type: Open motorboat (=1) 0.186*** 1.204*** 0.036 29,311 0.001
p< 0.10, **p< 0.05, ***p< 0.01.

16. An Empirical Analysis of Life Jacket Effectiveness 317
Table A3. Model 2 Estimation Results
Unweighted Sample Weighted Sample
Variables Coef. IRR Coef. IRR
Blood alcohol concentration (BAC) (%) −0.013 0.987 −0.031*** 0.970***
(0.013) (0.006)
Operator wears life jacket −2.629*** 0.072*** −2.888*** 0.056***
(0.345) (0.157)
Constant 2.137*** 8.478*** 2.242*** 9.415***
(0.421) (0.188)
R-squared 0.221 0.219
N 377 2,670
p< 0.10, **p< 0.05, ***p< 0.01.
Table A4. Descriptive Statistics for Variables Used in Model 3
Variables Mean SD Min Max
Number of deceased 0.1064 0.346 0 4
Length of vessel 18.960 10.371 5 120
Accident occurred during the day 0.867 0.340 0 1
Operator wears his life jacket 1.473 0.499 1 2
Accident is reportable 0.884 0.320 0 1
Age of operator 41.021 16.205 9 89
No. of engines of the vessel 1.078 0.351 0 3
Water temperature 72.793 11.353 29 108
No. vessels involved in accident 1.436 0.537 1 5
Vessel type is open motorboat 0.483 0.500 0 1
Vessel engine type is outboard 0.332 0.471 0 1
Accident occurred on a weekday 0.413 0.492 0 1
Speed 10 to 20 miles per hour 0.199 0.399 0 1
Vessel was not moving 0.175 0.380 0 1
State: AZ 0.048 0.214 0 1
State: FL 0.093 0.291 0 1
State: MO 0.071 0.258 0 1
State: NJ 0.063 0.242 0 1
State: NY 0.088 0.283 0 1
State: OH 0.058 0.234 0 1
No. people on board14 2.845 2.688 0 60
N 2,030

17. 318 Viauroux and Gungor
Table A5. Descriptive Statistics for Observations Used in Model 4
Variables Mean SD Min Max
Number of deceased 0.0881 0.325 0 3
Operator wears life
jacket (=2)
1.412 0.492 1 2
Age of operator 42.671 15.827 9 89
Operator has more than
100 hours of
experience
0.625 0.484 0 1
Length of vessel 20.639 11.001 4 120
Vessel was rented 0.133 0.339 0 1
No. vessels involved in
accident
1.369 0.535 1 5
Vessel type is open
motorboat
0.503 0.500 0 1
Vessel engine type is
outboard
0.385 0.487 0 1
Accident is reportable 0.877 0.328 0 1
Accident occurred
during the day
0.854 0.353 0 1
Accident occurred on a
weekday
0.430 0.495 0 1
Water temperature 72.889 11.782 29 98
Air temperature 80.856 13.827 25 113
Vessel’s horsepower 223.827 305.246 0 5,200
Vessel is a canoe or a
kayak
0.023 0.153 0 1
State: AZ 0.043 0.204 0 1
State: FL 0.123 0.329 0 1
State: IA 0.002 0.042 0 1
State: IL 0.000 0.021 0 1
State: LA 0.012 0.110 0 1
State: MD 0.063 0.243 0 1
State: MO 0.092 0.289 0 1
State: NJ 0.060 0.238 0 1
State: OH 0.081 0.273 0 1
state: PA 0.033 0.179 0 1
State: SC 0.003 0.054 0 1
State: UT 0.020 0.142 0 1
No. people on board15 3.234 2.744 0 30
N 10,849

18. An Empirical Analysis of Life Jacket Effectiveness 319
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