The Effect of Motorcycle Helmet Use on the
Probability of Fatality and the Severity of Head And Neck
Injuries
by Jonathan P. Goldstein, Ph.D.
"A Tradeoff Between Head and Neck
Injuries Confronts a Potential Helmet User"
Helmet Study Outline:

Highlights of the Study
 I. Introduction
 II. Overview
 III. The Econometric Model
 A. Fatality Model
 B. Head Injury Severity
Model
 C. Neck Injury Severity
Model
 IV. The Data
 V. Results
 A. Fatality Model
 B. Head Injury Severity
Model
 C. Neck Injury Severity
Model
 D. The Nature of the Tradeoff
 VI. Conclusions and Policy
Implications

Appendix A

Appendix B

Footnotes

Bibliography

Special Thanks
I. Introduction
The repeal or weakening of motorcycle helmet use laws in
thirtyone states between 1976 and 1983 has generated a vigorous
debate over the effectiveness of helmets in the prevention of
fatalities and the reduction of injury severities. Statistical
studies that have explored these issues have suffered from the
lack of an accurate and detailed data set and, more importantly,
have neglected to integrate causal models into their analysis.
While the former problem has been alleviated by the extensive
data collection techniques employed by Hurt, et al. (1981a), the
latter problem has not been addressed. The statistical
techniques employed fail to control for the multifacted and
interrelated factors involved in motorcycle fatalities and
injuries and thus conflate the effects of such factors and
erroneously assign them to helmet use.
The purpose of this paper is to develop, estimate, and
statistically test three causal models for: (1) the probability
of a fatality; (2) the severity of head injuries; and (3) the
severity of neck injuries, where each dependent variable is
conditional on the occurrence of a motorcycle accident. A latent
variable framework is employed in each case and particular
attention is paid to the effectiveness of helmets in each
instance.
In contrast to previous findings, it is concluded that: (1)
motorcycle helmets have no statistically significant effect on
the probability of fatality; and (2) past a critical
impactspeed' measured by the normal component of velocity to
the helmet, helmets increase the severity of neck injuries. It
is also shown that helmets reduce the severity of head injuries.
Thus, an individual or legislator is faced with a tradeoff
between head and neck injuries in deciding whether or not to
wear or mandate helmet use. Further analysis reveals that all
possible combinations of the intensityof the tradeoff, defined
in terms of the severity of head injuries forgone and the
severity of neck injuries incurred from helmet usage, are
equally likely.
The arguments in this paper are presented in five remaining
sections. Section II presents an overview of existing
statistical studies. The next section develops the basic model
and its variants. Section IV discusses the data. Section V
presents our results. Finally, Section VI contains our
conclusions and their policy implications.
II. Overview
Existing statistical research on helmet effectiveness employs
two alternative methodologies to analyze accident data. These
techniques test the differencebetween death rates. injury
rates, location rates of injuries, and severity rates of
particular types of injuries. These rates are compared either
for a similar period of time before and after helmet law repeal
or for helmeted riders and nonhelmeted riders during a single
time period subsequent to helmet law repeal.^{1}
In each case statistically significant differences are
attributed to helmet use or nonuse. Typical results associated
with this literature are death and injury rates two to three
times greater for nonhelmeted riders and increases in
occurrence rates in repeal years that range from 19% to 63%.
The major limitation of previous studies is the lack of an
effective control for other factors that concurrently determine
death and injury rates. On one hand, helmetnonhelmet
comparisons fail to consider differences in these two categories
of riders. The most plausible hypothesis is that helmeted riders
are more risk averse and thus: (1) have lower precrash and
thus crash speeds; (2) are less likely to be involved in
accidents; (3) and are less likely to combine alcohol
consumption and driving.^{2}
Such behavior rather than helmet use per se may dramatically
reduce the probability of a fatality or the severity of an
injury.
On the other hand, before and after designs fail to control
for dramatic trends in the data. In particular trends towards:
(1) lower median age of motorcycle owners; (2) higher average
annual miles traveled; (3) lower average experience levels of
riders: and (4) higher displacement machines, are not
considered.^{3}
Given the relationships between engine displacement and
potential speed, age and riskaversion, and riskaversion, crash
speeds, and alcohol ingestion, simple beforeafter comparisons
cannot be expected to isolate the effectiveness of helmet use.
In the next section we develop an econometric model that
considers the determinants of the probability of death, and the
severity of head and neck injuries. This approach allows us to
isolate the individual effect of helmet use on the variables in
question.
III. The Econometric Model
Variations of one basic model are employed for each of the
three dependent variables considered. The classification of
explanatory variables into three broad groups facilitates the
development of the model. This typology consists of: (1) factors
governed by the laws of physics; (2) physiological factors; and
(3) human factors and operator characteristics. We consider each
of these categories in order.
An informative method for understanding motorcycle trauma is
to consider it as the result of uncontrolled mechanical energy
transfer.^{4}
Motorcycle accidents result in serious injuries because of the
speeds involved and the associated energy that the laws of
physics tell us must be dissipated in the crash. In this light,
the input energy and circumstances surrounding the dissipation
of that energy are the crucial physical factors associated with
injury severity.
Besides a measure of the energy transferred to the motorcycle
operatorthe potential for bodily damagesuch factors as the
compressibility or deformability of the impacted object,
employment of a helmet as an energy handling device and the
engineering and design limitations of such devices must be
considered. The compressibility of an impacted object determines
the amount of kinetic energy utilized to deform that object and
thus not available to injure the rider. Helmets, in turn,
control or mediate within bounds the transfer of impact energy
to the head. The current engineering design, safety standards,
and production techniques applicable to motorcycle helmets place
limits on the energy dissipating capacity of these protective
devices.^{5}
If sufficient energy is involved to overcome these capabilities,
damage to the head and possibly the neck may occur. This implies
that the effectiveness of the helmet is mediated by the force
applied to the helmet.
As a measure of input energy, we employ two variants of the
kinetic energy of the motorcycle operator that results from a
collision. The formula for kinetic energy can be expressed as
K=1/2mv^{2}, where m is the mass of the operator and v
is the velocity assumed by that mass. Given the availability of
data, two variants of the velocity variable are used. These
variables are first approximations of v based on physical laws.
The first measure (K1) is simply the crash speed of the
motorcycle. In the alternative specification (K2), v is assigned
either the relative impact velocity of the motorcycle and other
crashinvolved vehicle, or the motorcycle crash speed.^{6}
The former is assigned when the injury mechanism associated with
the rider's most severe injury is the other vehicle, while the
latter is employed in all other circumstances.^{7}
It is assumed that the dependent variable is positively related
to K1 and K2.
The effect of helmets is modeled through two variables: a
qualitative variable, HI, that distinguishes between helmet use
and nonuse and an interaction term, HI, constructed from the
product of H and the normal component of impact velocity to the
helmet. This specification implies that the overall
effectiveness of the helmet decreases with impact speed. Helmet
engineering considerations lead us to expect a negative
coefficient for HI and a positive coefficient for H.
Finally, a compressibility variable is not included in our
final specification. The results from estimated equations that
include such a variable, not reported, find the coefficient to
be insignificant in all cases.^{8}
Deletion of this variable from the appropriate equations results
in changes in the coefficients and standard errors of all other
variables that are negligible.
The physiological factors considered are the effect of age
and alcohol consumption. Individuals can be considered to have
an "injury threshold" which is based on physiological
parameters. Those parameters in turn depend on an individual's
age in such a manner that older people have a reduced resistance
to injury.^{9}
Alcohol ingestion affects the severity of injuries in two ways.
First, the presence of alcohol hinders not only the clinical
diagnosis of injuries but the selfdetection of injuries.^{l0}
More importantly, the cardiovascular effects of alcohol
significantly inhibit the process of homeostasis, especially the
dynamic management of circulatory stability.^{ll}
These two physiological variables are respectively denoted by A
and BA and the expected signs of their coefficients are
positive.
Other physiological factors considered but not included in
the final equations include drug involvement, and permanent
physiological impairment. The estimated coefficients of these
variables were statistically insignificant in all cases and
deletion of these variables from the equations resulted in
negligible changes in the remaining coefficients and their
standard errors.
While many human factors and operator characteristics were
analyzed, the final equations include only two: the amount of
rider onroad experience, EX , and a binary variable, EA, which
establishes whether or not (EA = 1, or EA =0) the rider had
taken the correct evasive action for the particular accident
situation. A special case of a linear spline, one where the
slope of the linear segment beyond a critical experience level
is constrained to be zero is used to model the experience
variable. This implies that EX = EX for 0 < EX < EX* and
EX = EX* otherwise, where EX* is the critical experience level.
This specification is theoretically justified by marginal
returns from additional experience which approach zero past some
critical experience level, but is also necessitated by the
nature of the data (discussed below). The expected signs for the
EX and EA coefficients are negative.
Other factors considered include driver training, the
operator's past accident and violation history, the height and
weight of the operator, and whether or not the rider voluntarily
separated from the motorcycle before impact. In all cases and in
all equations the coefficients of these variables were
statistically insignificant and their deletion did not alter in
any significant way the remaining coefficients or standard
errors.
Finally, in order to control for any influences of risk
aversion not captured by K1, K2, BA. or H and thus to avoid
specification bias, proxy variables such as income, number of
children, marital status, and education were included in our
equations. These variables were singularly and in all possible
combinations statistically insignificant and were eliminated
from the equations with the same results as other such
variables. Also considered and eliminated in similar fashion
were measures of traffic density and a coefficient of braking
friction.
The major limitation of our specification is the exclusion,
due to data limitations, of a variable that captures the quality
and expeditious delivery of medical services. While the problem
of specification bias is unlikely, the statistical and
quantitative importance of such a variable cannot be
established.
A. Fatality Model
In order to model the probability of a fatality, we define a
dichotomous variable, D_{i}, where D_{i} = 1 if
the operator died given that an accident occurred and D_{i}
= 0 otherwise. We also specify a latent variable D_{i}
an individual's propensity to die conditional on the occurrence
of an accident. For notational simplicity and ease of
exposition, we drop all references in the remainder of the text
to the conditional nature of the three dependent and latent
variables. We assume that
where X_{i} is a vector of independent variables, ß
is a vector of unknown parameters, and E is a random error term.
It is assumed that E_{i} are i.i.d. drawings from
In
this model X_{i} includes K in one of its two forms. H,
HI, A, BA, EA, EX and a constant term. D_{i} can now be
defined in terms of _{
} in
the following manner:
where Z* is a threshold beyond which an individual expires.
Given this specification the probe ability that D_{i} =
1 can be expressed as
where F is the standard normal distribution function. The
maximum likelihood (ML) probit estimates for the parameters of
this model are reported in section V.A. below.
B. Head Injury Severity (HIS) Model
In this model the dependent variable, HS, is the sum of
squared severities for all head injuries sustained by the
driver, where the severity of each injury is measured by the
Abbreviated Injury Scale (AIS).^{12}
Although the dependent variable is continuous, the large number
of limit observations,^{13}
suggest a Tobit specification. We define a latent variable, _{
}, the
sum of squared severities for all head injuries, and assume that
where ß, X_{i}, and E_{i} are as defined in
the fatality model. HS_{i} can now be defined in terms
of HSi in the following fashion
Given this specification the regression function can be
written as
where f is the density function of the standard normal
variable. The ML Tobit estimates for the parameters of this
model are reported below.
C. Neck Injury Severity (NIS) Model
The dependent variable in this case is NS, the sum of squared
severities for all neck injuries.^{14}
Given the large number of limit observations, a Tobit
specification is utilized.^{l5}
Let _{}
be the sum of squared severities from all neck injuries and
assume that
where ß and E_{i} are defined as in the previous
models. One additional explanatory variable (HW) is included in
X_{i}. This variable is an interaction variable and is
formed as the product of H and the weight of the helmet.
The inclusion of both the HI and HW interaction variables in
the neck equation are justified by the laws of physics. Impacts
to the helmet are capable of causing a flexure or extension
displacement (cervical stretch) of the neck and the prospect of
a related neck injury. While a helmet may attenuate head impact
and thus the extensionflexsion response of the neck, this
result can only be expected to occur until some critical impact
speed beyond which the energy absorbing capabilities of the
helmet are surpassed. Beyond that speed, the added mass of the
helmet increases the inertial and postimpact response of the
neck and is theoretically related to the severity of neck
injuries.^{16}
Expressing NS_{i} in terms of _{
} we
obtain:
Given this specification the regression function can be
written as
The ML Tobit estimates for the parameters of the model when
HW_{i} is both included and excluded from X_{i}
are reported below.
IV. The Data
The data used was collected from the onscene indepth
investigations of 900 motorcycle accidents, in the Los Angeles
area, supervised by Hurt et al. (1981a). Each accident was
completely reconstructed and 1,045 data elements covering
accident characteristics, environmental factors, vehicle
factors, motorcycle rider, passenger, and other vehicle driver
characteristics, and human factors including both injuries and
protection system effectiveness were recorded. The data was
collected by a multidisciplinary research team which insured
more accurate and detailed information than is typically
available from police and hospital records.^{17}
A subsample of 644 cases was selected based on our twofold
treatment of missing data. In general, cases with missing data
on the independent variables were dropped from the sample. In
the case where such a deletion would result in possible
selection bias or the significant loss of data, missing values
were assigned the mean value of the variable in question.^{18}
As argued above, one limitation of the data directly affects
the specification of our model. While the use of a linear spline
to model the effects of EX is theoretically justified, it is
also necessitated by the truncated range used to record that
variable: values of EX > 96 months were assigned a value of 97.
While different critical values of EX < 96 were used, the best
fit, occurred when EX* = 96. While it was not possible to test
critical points above 96 to determine if a better fit existed,
the EX variable was insignificant in all but the HIS model. And
deletion of this variable in other models had negligible
influence on all results.
The definition, construction, units of measurement, and
sample means for all variables in our final equations are
contained in Appendix A.
V. Results
The results of the fatality model and the HIS and NIS models
are respectively reported in Tables I, III, and IV. Estimates
are based on the 644 cases remaining after the treatment of the
missing values. For each model two equations corresponding to
the two variants of K are reported. In the NIS model an
additional two equations associated with the inclusionexclusion
of the HW variable are reported.
A. Fatality Model
The results in
Table I reveal that the coefficients of all variables
take on their expected signs. Both the H and HI variables are
insignificant, indicating that:
Helmet use has no statistically
significant effect on the probability of death.
The major determinants of the probability of a fatality are
the kinetic energy imparted to the riderthe potential for
bodily damageand the operator's blood alcohol level. The
results also reveal that the proper execution of evasive action,
an individual's age, and experience level have no statistically
significant impact on the probability of a fatality. Deletion of
all insignificant variables with the exception of H and HI from
the equation produces negligible changes in the remaining
coefficients and their standard errors. Finally, on the basis of
comparisons between the log of the likelihood function, 1,
equation 1 better fits the data.
The quantitative importance of the statistically significant
variables is best understood through the total effects of
relevant changes in those variables on the probability of death,
holding all other variables at their sample means. Such results
are reported in Table II.^{l9}
A change in BA from 0 to 10 (sober to legally intoxicated in
most states) increases the probability of a fatality
dramatically from .0207 to .0853 or from .0233 to .1131
depending on which equation is employed. In the same vain, an
increase in the relevant crash speed from 40 to 60 mph increases
the probability from .0708 to .3632 or from .0446 to .1230.
Table
II  Total Effects On P(D = 1X) 


Eq. 1 
Eq. 2 






All 
X' = X' 
.0228 

.0262 

BA 
BA = 0 
.0207 

.0233 




.0646 

.0898 

BA = 10 
.0853 

.1131 







K 
M = 5.01^{a} 
.0091 

.0166 


V = 0 mph 







.0071 

.0051 

M = 5.01 
.0162 

.0217 


V = 20 mph 













.0546 

.0229 

M = 5.01 
.0708 

.0446 


V = 40 mph 







.2924 

.0784 

M = 5.01 
.3632 

.1230 


V = 60 mph 










^{a}The average weight and mass
are respectively 161.19 and 5.01. 
These results clearly establish that:
Crash speed and the blood alcohol
level of the rider are the most important determinants of
fatalities, while helmets are shown to have no statistically
significant effect on the Probability of survival.
B. Head Injury Severity Model
Parameter estimates associated with the HIS model are
reported in
Table III. As in the previous model, the
statistically most significant determinants of the severity of
head injuries are the rider's kinetic energy and blood alcohol
level. In sharp contrast to the previous model, methods for the
reduction of the gravity of head injuries exist. The most
effective one is the energy absorbing capability of the helmet.
The statistical significance of the H variable and
insignificance of the interaction term (HI) imply that not only
do helmets reduce head injuries, but they do so at almost all
realistic impact speeds to the helmet.^{20}
For example in equation 3 at the average impact speed of 10.13
mph to riders experiencing an impact to the helmet, MS is
reduced by 12.68. Other deterrents to head injuries include
execution of the proper evasive action and rider experience. A
rider with the average level of road experience receives a 2.99
reduction in HS while the reduction for a properly executed
evasive action is 5.31. Finally, as in the fatality model,
equation 3 better fits the data.
C. Neck Injury Severity Model
The results associated with the NIS model are reported in
Table IV. The inclusion of the HW variable in the
equations results in four variants of the model. As in the
previous models K and BA are important determinants of injury
severity, but in addition we find that:
Past a critical impact velocity to the
helmet, measured by the normal component of velocity, helmet
use has a statistically significant effect which exacerbates
the severity of neck injuries.
Using the point estimates in equations 58 and the average
weight of the helmet (2.70), estimates of this critical impact
speed are around 13 mph. Beyond this realistically attained
critical speed the energy absorbing ability of the helmet which
is capable of reducing the extension flexsion response of the
neck to head impacts are surpassed. Under these circumstances,
the inertial and postimpact response of the neck are
intensified due to the added mass of the helmet and neck
injuries result. An impact to the head whose normal component of
velocity is 20 mph will increase the severity of neck injuries
by around 10. Equations 7 and 8 also reveal that marginal
increases in helmet weight do not have a statistically
significant effect on the severity of neck injuries. This
finding along with the acceptance of the zero constraints in
equations 5 and 6 imply that it is the added mass of a helmet
and not its specific weight that is responsible for exacerbating
neck injuries.
Reductions in the severity of neck injuries are achieved
through helmet use but only when impact velocities to the helmet
are below the critical velocity. The proper execution of evasive
action is also an effective deterrent to neck injuries. While
the coefficient of EX in this model takes on an unexpected sign,
the coefficient is not significantly different from zero.
Finally, on the basis of likelihood comparisons, equation 5
better fits the data.
The most important finding generated by the HIS and NIS
models is that:
A tradeoff between head and neck
injuries confronts a potential helmet user.
Past a critical impact speed to the helmet, which is likely
to occur in real life accident situations, helmet use reduces
the severity of head injuries at the expense of increasing the
severity of neck injuries. We now consider the qualitative
nature of this tradeoff to discern if a helmet user forgoes
either severe or minor head injuries in order to incur either
severe or minor neck injuries.
D. The Nature of the Tradeoff
To gain insight into the nature of the headneck injury
tradeoff associated with helmet use, we specify and estimate two
probit equations. The first considers the determinants of the
probability that a rider's most severe head injury is either
critical or fatal (AIS > 5), while the second analogously
considers a rider's most severe neck injury. In each respective
case the vector of independent variables is the same as in the
HIS and NIS models. We thus define HD = 1 if AIS_{MH}
> 5 and HD = 0 if 0 < AIS_{MH} < 5, where the
subscript MH refers to the rider's most severe head injury.
Analogously, ND = 1 if AIS_{MN} > 5 and ND = 0 if
0 < AIS_{MN} < 5.^{21}
Given that HD and ND are conditional on the occurrence of an
accident, the sample size is the same as in the previous models.
The estimates for these basic equations are reported in
Table V.^{22}
These results indicate that the only statistically
significant determinants of the probability that an individual's
most severe head or neck injury will be severe (critical or
fatal) is the rider's blood alcohol level and kinetic energy
which is dominated by the crash speed. With respect to helmets,
this finding implies that both helmeted and nonhelmeted riders
are equally likely tohave their most severe head and neck
injuries classified as severe or minor. This further suggests
that, ceteris paribus, an individual who decides to wear a
helmet and who experiences an impact velocity to the head
greater than the critical level may forego either severe or
minor head injuries and incur either a severe or minor neck
injury; all forms of the tradeoff are equally likely to occur.
VI. Conclusions and Policy Implications
From our empirical results we conclude that helmet use has no
statistically significant effect on the probability of a
motorcycle fatality and that helmet users face a tradeoff
between reductions in the severity of head injuries and
increases in the severity of neck injuries. It is also shown
that all possible combinations of the intensity of this tradeoff
are equally likely to occur. In addition, it is found that the
major determinants of injury and death are speed and blood
alcohol level.
If a major concern of policy makers is the prevention of
fatalities, our results imply that helmet legislation may not be
effective in achieving that objective. Alternatively if the 
overall costs to society in the form of health care costs and
lost productive output are at issue, our results imply that
existing costbenefit analyzes which fail to consider the injury
tradeoff are inappropriate for policy guidance.^{23}
Until studies are adequately designed and completed, the passage
of helmet use laws which may seriously jeopardize the health and
earning capacities of an individual is not a viable policy
option. Even in the event that costbenefit studies show a net
benefit to society from helmet legislation, the existence of
externalities and high marginal disutilities associated with
helmet use for all or a subset of motorcyclists may imply a net
cost to the individual and thus raise questions about the
redistribution of income resulting from helmet legislation.^{24}
Furthermore, alterations in driving behavior in response to
mandatory helmet use laws, predicted by the theories of risk
compensation and risk homeostasis, may dissipate the net
benefits to society from regulation.^{25}
Under these circumstances mandatory helmet use laws cannot be
considered as an effective method to eradicate the slaughter and
maiming of individuals involved in motorcycle accidents. A more
viable policy approach would be two pronged. On one hand, policy
must address the causes of motorcycle accidents. On the other
hand, since all accidents are not preventable, policy must
consider the major determinants of death and injury and
effective methods for their reduction.
Although our empirical results do not shed light on the
causes of accidents, other evidence leads us to suggest the
following policies: (1) the education of the general driving
public about the coexistence of heterogeneous road users; (2)
education of a younger and more inexperienced population of
motorcyclists on the issues of accident avoidance and the proper
use of all too often overpowered machines; and (3) stricter
enforcement of drunk driving laws, an increase in the legal
drinking age, and alcohol awareness programs to reduce the
accident rate.
With respect to the second type of policy, our results show
that the major determinants of death and injury are speed and
alcohol consumption. Policies aimed at the former problem range
from stricter enforcement of speed limits to horsepower
restrictions on the vehicle population.^{26}
In the latter case policy options are the same as those
mentioned above. Finally, a viable alternative to helmets as a
means for reducing the severity of head injuries exists.
Mandatory driver training and education programs which emphasize
the proper execution of evasive action in accident situations
can effectively serve this purpose.