132 The Journal of Risk and Insuranceway of financing care

132 The Journal of Risk and Insurance
way of financing care and also to expand
the amount of medical care received by
some parts of the population.
The final consensus of the conference
may be stated in the words of one of the
participants, "When I came into the con-
ference the other day I said We are going
to come out of here with a recommenda-
tion that the situation be further stud-
ied.'"^ With the unresolved questions
concerning this type of program still be-
fore us, it is hoped many of these studies
will be completed before the politicians
make their decision.
This is a most useful book for any
person interested in the implications of
a national health insurance program.
Many changes have taken place since
November 1970, but the conference pro-
ceedings provide a most helpful source
of information.
INFLATION, TECHNOLOGY AND
GROWTH: POSSIBLE LONG RANGE
IMPLICATIONS FOR INSURANCE. By
Robert I. Mehr and Seev Neumann. Grad-
uate School of Business, Bloomington,
Indiana: Division of Research, Indiana

University, 1972, $15.00.
Reviewer: J. D. Hammond, Professor of
Business Administration, The Pennsyl-
vania State University.
The general title of this new book sug-
gests a rather traditional macro level re-
view of the insurance industry as it is
beset by economic and technological
forces. Such is not the case. Professor
Mehr, the senior author of the book, and
Professor Neumann have employed the
Delphi technique in an attempt to iden-
tify various characteristics of the insur-
ance industry in the year 2000. Although
the cynic may suggest this to be an easy
task for the insurance industry, the Mehr
'Page 259.
and Neumarm approach is a serious at-
tempt to apply a relatively new forecast-
ing device (the Delphi Technique) to a
particular set of questions about the in-
surance industry. As such, it deserves seri-
ous attention.
The volume was written as a part of
the 1970 Sesquicentennial celebration of
Indiana University. The Mehr-Neumann
volume is one of four companion pieces
representing the School of Business con-
tribution to the celebration. The three
other works are not identified. Financial
assistance for the series came from sev-

eral grants from insurance companies. The
stated purpose of the book "is to make
some cautious, documented speculations
about the long-range effects of infiation,
technology, and growth on private insur-
ance in the United States." Its objective,
we are told, "is to identify both the pres-
ent characteristics that are hkely to pre-
vail until the end of the century and any
new characteristics that are Hkely to
emerge sometime between now and then."
A statement by a University executive
in the foreword gives added scope. Mr.
George Pinnell, Vice President and Treas-
urer of Indiana University states: "I fully
anticipate that in the years to come these
volumes will be increasingly useful to
planners and will clearly demonstrate the
insight and vision of the authors. Whether
time will corroborate their projections and
prophesies is a matter that we will watch
with fascination." Thus, there is the hope
by at least one person that the Mehr-
Neumann book and its companion vol-
umes will be of use to planners in the in-
surance world. It is a fair assessment of
the most likely use of the book.
The book contains 319 pages of text
with an additional 184 pages of support-
ing material in several appendixes. The
authors have assembled 111 tables, 88 of
which contain data generated by the
study. Graph lovers will be disappointed

Publications 133
to find only one graph. Labor economists
will be pleased, however. It has a Phillips
curve.
The entire findings of the research rest
upon the use of the Delphi method. So
far as the reviewer knows, this is the first
application of the Delphi method in any-
thing which might be called the insurance
literature. Basically, the technique pro-
vides for a systematic method of eliciting
expert opinion. It was developed by the
Rand Corporation as a device to be used
for long-range forecasting, a situation
where extrapolation of statistieal series is
of doubtful value. The procedure calls for
a group of experts to be polled repetitively
concerning their opinions on a particular
forecast. For example, such a group might
be asked their opinion about various ef-
fects of say, women's liberation, preemp-
tive nuclear strikes, or the ecumenical re-
ligious movement. In general, past use of
the Delphi Teehnique has centered upon
those questions where the use of statistical
data is not possible or inappropriate. In
any event, the opinions are compiled and
are fed back to the panel for another
round of opinion response. The feed-back
procedure is then repeated until consen-
sus is apparent. The technique is thus
characterized by the need to develop con-

sensus through a series of iterative exer-
cises and by the use of experts.
Mehr and Neumann have adhered
strictly to the Delphi procedure. Invita-
tions were sent to a group of 70 experts
to participate in the study. Of this num-
oer, 64 accepted and 58 eventually com-
pleted the project. It is not unreasonable
to think that the six drop-outs r^ulted
from exhaustion. After receiving detailed
inputs of background information on the
American economy and possible techno-
logical developments (panelists were also
'fee to develop additional background in-
formation in these areas), each panel
' ' b received a 25-page questionnaire
containing 73 questions about various as-
pects of the insurance business. A sum-
mary of these first round responses was
then compiled and sent to eaeh panel
member. Each panelist had the chance to
reconsider and revise his first round re-
sponse and was asked to explain why his
judgments deviated from the norm of the
round one responses.
Second round responses were then cir-
culated again to eaeh panel member, to-
gether with a summary of the reasons
underlying the deviating opinions. Mem-
bers were asked to reconsider their sec-
ond round opinions in light of the new
information and again to revise their re-
sponse to the question if that was felt

necessary. For the atypical third round
responses, members were asked to explain
why they were unimpressed with the
stated reasons underlying such responses.
These responses were again summarized
and returned to the members where each
had a final opportunity to modify his re-
sponse. At this point, the median of the
fourth round response was taken to be
the consensus of the panel.
The 58 finishers represented a cross-
section of expert opinion. The oracles rep-
resented universities, government bodies,
corporate insurance buyers, journalists,
and executives from both property-liabil-
ity and life insurance.
Two of die first three chapters of the
book are devoted to the presentation of
background material on technology and
the economy. The first chapter discusses
the difficulties of long-range prediction
and a discussion of the Delphi method.
The remaining eight chapters are devoted
to the presentation of the research re-
sults. Here, we are able to learn the panel
responses to sets of questions dealing with
the entire industry, life insurance, health
insurance, the property and liability in-
surance industry, automobile insurance,
property and liability insurance lines ex-

capt auto. A summary is presented in the
final chapter.
The general tone of most of the ques-
tions asked of the panel can be seen from
a sample of the responses. We learn that
the panel consensus sees social insurance
to be the dominant insurance form in the
year 2000; that the purchase of life in-
surance policies characterized by high and
moderate savings wQ! decline; that the
percentage share of health insurance pre-
miums written by private insurers wHI in-
crease (from 53.7 to 60 percent); that the
premiums to policyholder surplus ratio
for property and liability insurers will in-
crease only slightly; that the percentage
of total auto premiums written by the top
ten insurers wiU increase; and that direct-
writing insurers will further increase their
share of the market.
All responses are given in terms of a
point estimate but the authors have also
provided a statement of the response vari-
ance about the estimate. For example,
panel members were asked to forecast the
premiums to policyholder surplus ratio
and the 1966 value of that ratio was taken
as the starting point—about 1.4. The con-
sensus forecast value was 1.7. The 95 per-
cent confidence interval presented in the
results is 1.65 to 1.91.
So much for the content and the ap-

proach of the book. Though the approach
is innovative for the insurance literature,
it is not without some Hmitations.
While the Delphi Technique is gen-
erally recognized as a useful forecasting
device, the value of using experts has
been subject to question. Stated differ-
ently, if one were to use any reasonably
intelligent group of people, the consensus
answers finally arrived at may be little
different than those generated by the ex-
perts. It is an interesting possibiHty and
one which has some support in the Delphi
Hterature.
A second problem concerns any fore-
cast for the year 2000. The rate of change
in all things affecting any institution—in-
cluding insurance—is so high that any
forecast by any method must be suspect.
Most Delphi research has dealt with ques-
tions not amenable to traditional statis-
tical analysis and where long-range pre-
dictions deal more with shifts in values
rather than time-series projections. For
example, Delphi studies have dealt with
anticipated changes in American values
in the year 2000 and with changes in the
goals of educational institutions. The
Mehr-Neumann work does not deal with
those or similar phenomena directly. In-
stead, panelists were asked to forecast a
particular point value for several eco-
nomic projections deaHng with insurance.

Although considerations of value changes
and similar shifts within the economy
were considered in arriving at forecast
values, the consideration was not syste-
matic. The resulting forecast for various
time series for a point 30 years in the fu-
ture is an exercise requiring more faith in
judgment than even actuarial science.
The investment in time by panel mem-
bers precludes the asking of questions to
satisfy every reader. Still, some areas were
omitted from consideration. For example,
there is no direct consideration of lapse
rates nor of the distribution costs in life
insurance. The related major problem of
turnover among life insurance agents was
not included. If one is interested in panel
consensus, on such problems, he must in-
fer them from questions dealing with gen-
eral operating efficiency or the prospec-
tive growth in group coverage. Such
questions were more directly considered
for property and Hability insurance than
for life insurance. Still, it is diBBcult to
fault a 73 item questionnaire for a Delphi
process for errors of omission.
It would be very helpful to know th«
identity of the panelists. We are assured
they are experts but nonetheless one would
like to make his own assessment of such
quaHfications. Further, the number of eJi'
perts from each of the categories repiC'
sented is not given. Thus, we do not know

Publications 135
if all of the areas are equally represented
or whether one group might have a dis-
proportionate impact on the process. Since
the Mehr-Neumann questionnaire is so
comprehensive, one wonders whether
each of the experts is expert in all of the
aspects of the insurance covered in the
investigation. One suspects not.
The book is interesting to read and in-
tellectual curiosity is stimulated by the
large number of questions and the re-
sponses of the panel. The reader cannot
help but project his own responses and
compare them with those of the panel.
Herein lies the chief value of the book.
While the panel projections for a point
nearly 30 years distant are simply too
speculative for use by executives or regu-
lators, one would hope that sueh groups
would study the research. They may dis-
agree with the projections or feel insulted
at not being consulted, but a serious read-
ing of the book where one role-plays the
panel may be for insurance executives,
policy-makers,—and educators too—a
unique thinking experience.
Professors Mehr and Neumann have
provided us with a thorough application
of a relatively new research tool which
has not previously appeared in the insur-

ance literature. The research methodology
is detailed and sound and its presentation
clear and concise. The projected values
of the research will not likely serve as
diiect inputs to corporate planning models
is insurance (there may be none) but it
cannot help but make planners better
thinkers.
^DAMENTALS OF RISK AND IN-
SURANCE. By the late Curtis M. Elliott
ind Emmett J. Vaughn, John Wiley and
5ons, Inc., 1972, x and 703 pages.
^viewer: William M. Howard, Professor
f Finance and Insurance, University of
fundamentals of Risk and Insurance is
i for use in a college-level survey
course in risk and insurance. The stated
intent of the authors has been to create a
text that is consumer oriented. The types
of consumer the authors apparently have
in mind are individuals and families. For
example, there is an entire chapter of 24
pages on general liability insurance for
the individual. Chapters on property and
liabiHty insurance for business firms,
surety bonds and credit insurance are
largely independent of other chapters and
may be omitted.
The section on life and health insur-
ance, 7 chapters, seems to be aimed al-
most exclusively at individuals and fam-

ilies. Only two and a half pages are allotted
to forms of group life insurance and group
annuities. Group health insurance is men-
tioned casually in a paragraph on meth-
ods of marketing health insurance.
The authors have recognized the prob-
lem of handling the subject of risk
management in an elementary text and
have chosen to avoid extensive treatment
of statistical techniques and utility theory.
A 15-page chapter entitled "Risk Manage-
ment" describes the nature and function
of risk management. It appears to be ade-
quate for individuals and families; it pro-
vides an introduction of the subject to
those who may pursue it more deeply,
and is consistent with the stated purpose
of the book.
What knowledge may the authors of
insurance texts reasonably assume their
readers bring to the subject? Can they
assume a knowledge of elementary prob-
ability, principles of statistics and busi-
ness law? EUiott and Vaughn assume no
knowledge of probability and statistics.
They include just enough on these sub-
jects to allow the reader to understand
the nature of insurance. A chapter on
"Negligence and Legal Liability" makes
one wonders again why teachers of insur-
ance (including this reviewer) seem to
feel that students must understand the
causes of liability losses but not neces-
sarily of property losses. Most of us—in-

1
4
Title of Paper
Your Name
Rasmussen College
COURSE#: Course Title
Professor’s Name
Assignment Due Date
Thesis Statement:
Title of Paper: Outline
I. Introduction
A. Attention grabbing sentence about topic
B. Thesis statement
II. First paragraph main point – topic sentence
A. Supporting details (in-text citation for outside resource used
as support/evidence)
1. Details about the supporting details
B. Supporting details (in-text citation)
C. Transition sentence
III. Second paragraph main point – topic sentence
A. Supporting details (in-text citation)

IV. Third paragraph main point – topic sentence
A. Supporting details (in-text citation)
V. Conclusion
A. Summary of main points/Restatement of thesis statement
B. Sentence to state a judgment on topic, make a prediction, or
call the reader to action
References

336 The Journal of Risk and Insn^rance
TEACHERS, COMPUTERS,
AND TEACHING
James A. Wickman
An increasingly familiar sight along the
the paths of academia are a number of
hunched figures with output paper and
punch cards askew, invoking "do-loops,"
"diagnostics" and "Hollerith counts."
Computer technology is an unsettling
innovation to many who have only re-
cently acquired creditable speed and ac-
curacy in using a desk calculator. Fur-
thermore, the reactions of colleagues and
students can often be predicted by refer-
ence to the "Cee Whiz Syndrome." The
nature of the "Cee Whiz Syndrome" can
be approximated by imagining the follow-
ing conversation:
COMPUTER USER: "I wrote this pro-
gram in FORTAN, rather than FAP
becau. . ."
LISTENER: "Cee whiz!"
COMPUTER USER: ". . . so it took me
twelve runs to de-bug this.. ."
LISTENER: "Cee Whiz!"
COMPUTER USER: ". . . and now I

can do two plus two three thousand times
in 37 microseconds."
LISTENER: "CEE WHIZ!"
On the other hand, worship of peri-
pheral input-output devices and central
processing units is not the inevitable result
of using the high speed data-manipulation
powers of data processing systems. The
relative newness of computers and the
obvious complexity of their inner mechan-
isms do seem to reduce some causal users
of computer facilities to a state of hysteria
bordering upon absolute reverence.
One can raise psychological defenses
against these forms of idol-worship by in-
sisting and believing that the modem
computer is essentially a large, ultra-high
speed, printing calculator with logical ca-
pacity to make "yes-no" decisions. A com-
puter can be instructed to do various com-
putational series, has the power to remem-
ber what it has calculated and to use these
values in later calculations. These com-
prise a fair intuitive understanding of
the basic elements of raodern computer
technology. Increasing familiarity with
computers can even breed a feeling akin
to "contempt" when the computer slav-
ishly follows illogical instructions to pro-
duce meaningless answers. To student and
professor alike, there is utility (and per-

haps sanity) in becoming acquainted with
the powers and shortcomings of data proc-
essing equipment.
Becoming a Computer User
Happily, it is not necessary to become
a computer programmer to be a success-
ful and prolific computer user, any more
than it is necessary to become a proficient
automobile mechanic to be a capable auto-
mobile driver. One who wants to try his
hand at using the computer will often find
that an existing set of computer instruc-
tions can be utilized to solve his problem.
There are a great many such "canned pro-
grams" available which will solve general
or specialized types of problems.
Information About Programs
One of the more useful "families" of
"canned" programs is the BMD series of
computer programs.^ These cover a broad
range of typical statistical computations,
as well as several advanced statistical com-
putation programs.
An eflBcient index to many existing com-
puter proigrams is the Key-Word-In-Con-
text (KWIC) Index published by IBM.
This source lists programs in a format
which emphasizes each key word in the
^ These programs are described in BMD—
Biomedical Computer Programs, W. J. Dixon,

editor. The latest edition was published January
1, 1964, by the Health Sciences Computing
Facility, Department of Preventive Medicine and
Public Health, School of Medicine, University of
California, Los Angeles.
Communications 337
title, resulting in an ability to scan the
index rapidly in search of a program or
programs which have sought-for capabil-
ities. Each program is also described in a
brief abstract in another section of this
publication, along with instructions for
ordering a copy of the program.
Many campus computer installations
have acquired some of these programs as
a service for their users. Additional pro-
grams can be acquired and made availa-
ble on request. Typically, the computer
installation will also maintain a library of
lists and indexes regarding available pro-
grams.
A special-purpose index of "canned"
programs dealing with insurance and risk
problems, for research or classroom dem-
onstration purposes, would be useful.
While none is known to exist at the pre-
sent time, the American Risk and Insur-
ance Association, in the author's opinion,
should consider creating a clearinghouse
for information about existing programs.

Perhaps space in this Journal could be
devoted to brief listings so that interested
teachers could be informed of the eflForts
of others.
"Canned^' Programs and Teaching
"Canned" programs offer many oppor-
tunities to a teacher to develop a variety
of classroom demonstrations which would
otherwise represent a prohibitive invest-
ment of time and energy to perform the
calculations. Supplied with these demon-
strations, a teacher can concentrate his
major eflEorts on explaining the rationale
of methodology and the interpretation of
results to students. Students can also use
such programs to work problems that
would have been inappropriate if the com-
putational work had to be done by hand
or by desk calculator.
Even if a "canned program" is not read-
ily available, a teacher still does not have
to develop programming ability himself.
He can describe the desired computations
and the desired format of results to a
qualified programmer.^ The programmer
then takes over the "ritualistic" task of
preparing a formal set of computer in-
structions to solve the problem and com-
municate the results. In this fashion, a
teacher can avoid getting involved in the
mechanical aspects of computer program-
ming and reserve his time for concentrat-

ing on analytic method.
Additional Computer Features
Beyond the saving in computational
time offered by computer programs,
"canned" or otherwise, additional features
must be considered in assessing the teach-
ing usefulness of the computer. Today's
technology will be widely available on the
campus tomorrow (three to five years) to
allow the instructor to communicate with
the computer from the classroom. He can
ask the proper questions of the central
computing facility and get an immediate
response in the form of printed output,
displays of frequency distributions on a
cathode-ray tube, etc., using pre-stored
programs and data. Or the students can
do so.
The computer can be told what pro-
gram to use; it will ask the students for
appropriate information, do the computa-
tions, and report the results. AH of this
can occur simultaneously in many class-
rooms on the same campus. Actually, the
computer will work on the problem for
one class for a few thousandths of a sec-
ond, go to the next, and so on through
the list of problems and back to the be-
ginning of the circuit.^ The effect of this
time-switching arrangement on computer
^ "Qualified programmer," in a pragmatic
sense, means someone who is able to "perform

the ritual" of expressing instructions in appro-
priate language for the computer. Students make
excellent "qualified" programmers.
^ Several imiversides are adopting remote con-
soles and time-switching arrangements within the
next year; among these are MIT, Carnegie, and
Michigan.
speed is virtually undiscernible in the
classroom. Thus neither the students nor
the instructor need to know programming
(but the instructor may need to know a
programmer).
Even without these "Gee Whiz" addi-
tions to computer technology, special pro-
grams can be incorporated along with
computational instructions to portray the
results of calculations in graphic form.
The calculational results and graphic out-
put can be reproduced for classroom dis-
tribution using additional features of the
normal computer installation.
Risk and Insurance Courses
In teaching risk and insurance courses,
the instructor must refer frequently to sta-
tistical concepts and measures. The
teacher who wants to include course ma-
terials dealing with the application of

basic and advanced statistics to risk man-
agement and insurance concepts faces
two major difficulties, here referred to as
the "capital investment" and "statistical
block" problems.
"Capital Investment"
First of all, "capital investment" by the
instructor in developing illustrations which
show the application of statistics will be
great. Developing any one illustration will
involve a lot of calculational time. Even
slight variations in the assumptions under-
lying the illustration will usually require
complete recalculation. At this rate, it will
take a long time for an instructor to de-
velop a reasonably complete kit of illustra-
tions to cover even one course. "Canned"
programs, such as the one described be-
low, can be used to reduce the "capital
investment" required of any single in-
structor.
"Statistical Block"
Secondly, many students are not able
or willing to utilize their prior training in
statistics to investigate risk and insurance
principles because their prior training in
statistics is clouded with a "statistical
block." Their first training in statistics did
not "take" as well as might be hoped, giv-
ing these students great difficulty in ap-
plying a statistical frame of reference to

the principles and problems of a different
subject matter area.*
A risk and insurance teacher can avoid
confronting this awkwardness by eliminat-
ing all but the mildest of statistical refer-
ences in his course materials. In doing so,
the instructor may weaken significantly
the vigor of the course. A more satisfac-
tory way of dealing with both of these
problems lies in using the computational
power of computer programs, "canned" or
otherwise, to alleviate tedious calcula-
tions and allow greater emphasis on inter-
preting the results.
Illustrative Teaching Problem
For example, basic statistics can be in-
tegrated with risk and insurance problems
by exploring the common observation that
"the mortality table portrays a risk con-
verging on a certainty over time." This ob-
servation is intuitively correct, as will be
explained, but how does a teacher effec-
tively communicate this understanding to
a non-intuitive student? The phrase can
be repeated again and again, using differ-
ent words, but this pedagogical device
may not be too helpful.
The formal reasoning lying behind this
observation could be explored and ex-
plained verbally:
A mortality table displaying number of

deaths by age is a specialized portrayal of
a frequency distribution. As with many
other frequency distributions, it is possible
and logical to compute the mean. The mean
in this instance represents the average age
at death for those at the initial age of the
mortality table. For each greater age the
frequency distribution is obtained by trun-
cating to eliminate earlier ages from con-
sideration. The mean of e;ach such distribu-
^ Editor's note: At some universities, of course,
statistics is not a prerequisite to courses in risk
management and insurance.
Communications 339
tion is the average age at death for each
new initial age.
The average age at death is a useful meas-
ure for many purposes, but it does not
adequently demonstrate that some people
die well before attaining the average age
and others live considerably longer than
the average age at death for persons in
their group. There is, therefore, risk in such
a situation since actual ages at death are
dispersed around the most likely result, the
average age at death. To understand the
statement that 'the mortality table por-
trays a risk converging on certainty over
time,' the dispersion of actual ages at death
should be examined to see if this dispersion
does in fact narrow or converge, over time,

upon the average age at death.
The standard deviation is a common meas-
ure of dispersion. The standard deviation
can be used to measure and express the
concentration or scatter of data around
its mean value. By calculating, for each
age, the standard deviation as well as the
average age at death, absolute dispersion
can be expressed. Confidence intervals can
be estimated.
Another way of looking at variability in a
set of data uses the coeiBcient of variation
as an indicator of relative dispersion or
scatter. The standard deviation is divided
by the mean to calculate the coefficient of
variation. A decreasing coefficient of varia-
tion signifies that the relative dispersion is
lessening.
Computing the standard deviation and the
coefficient of variation should show that as
age increases actual deaths occur more and
more closely to the average age at death.
The coefficient of variation approaches
zero as a limit. Thus, 'mortality is a risk
converging upon a certainty over time.'
To express sucb a line of reasoning
verbally in a classroom without specific
measures of tbe mean, standard deviation,
and coefficient of variation would be fool-
hardy. On the other band, the calcula-
tional work will be extensive and tedious.
Table 1 and Chart 1 are exact reproduc-
tions of the output of a computer pro-
gram, LFXP, written to perform this
multitude of calculations.' An instructor

^ This program, written by the author, derives
its code name from LiFe EXPectation. Purists
can use reproductions of this tabular and
graphic output to demonstrate the results
of the calculation process as well as the
logic of the argument. By using the same
computer program but different mortality
tables, certain of the differences between
mortality tables can be demonstrated and
examined.
Appendix A presents an abbreviated
description of the computer program used
to calculate and produce the information
contained in Table 1 and Chart 1. Addi-
tional computer programs are being pre-
pared to investigate and demonstrate
other applications of mortality tables.*
Summary
Rapid evolution of computer technol-
ogy, although often bewildering, need
not be terrifying. Teachers and students
both will benefit from a thorough exploita-
tion of the high speed data manipulating
capacity of modern computers. Teaching
many of the statistical aspects of risk and
insurance can be highlighted and assisted
through the use of prepared computer
programs with tabular and graphic pre-
sentation of output. The use of such pro-
grams does not require programming abil-
ity. By avoiding the monumental task of

hand calculation, the instructor can con-
centrate on demonstrating the relevance
of statistical measures to risk and insur-
ance problems with less effort and greater
probable success.
Appendix A
LFXP is relatively simple to use. Four
mortality tables are "built in" the pro-
may object to the use of upper-case letters in
place of the customary lower-case form of actu-
arial notation. This is defended pragmatically on
grounds of second-best. Computer-related print-
ers only print in upper-case; the choice is to
have no symbols, or to have symbols in uncon-
ventional form.
* Perhaps to be published, ultimately, as "Ex-
ploring Mortality Tables with Punch Card and
Computer."
gram;'' others may provide the data for
calculations at the instructor's option. A
single card is prepared to instruct the
program what to do; this problem card
selects the mortality table, specifies the
confidence limits desired for graphic out-
put, and specifies the age-interval for tab-
ular output. This problem card is included
with the program deck and submitted to
the campus computer installation for proc-

essing.
The first calculation performed by the
program computes the complete expecta-
tion of life, beginning with initial age
equal to birth and then increasing initial
age by one until the limiting age of the
mortality table is reached. The complete
expectation of life for each initial age is
added to the initial age to estimate the
average age at death.
Next, the standard deviation around the
average age at death is calculated for each
initial age. This is used to compute the
coefficient of variation and to estimate the
confidence limits.
If graphic output is requested by the
user, the program next calls upon the plot-
ting subroutine to prepare and print out
the requested graph. Following this, the
program instructs the computer to print a
'These are: 1941 CSO; 1958 CSO; 1937
Standard Annuity, set back five years; and 1959-
61 U.S. Life Table for the Total Population.
tabular summary. At this point the main
work of the program is completed. The
computer is instructed to check for an-
other problem to be run, performing the
same sequence of operations on a differ-
ent set of data. When no further problems
are requested, the computer turns its at-
tention to other jobs waiting for process-

ing.
LFXP is written in the FORTRAN IV
language. Version 13, for the IBM 7094-
7040 DCS system at the Research Com-
puter Laboratory of the University of
Washington. The program uses several
standard systems routines in performing
the calculations. The graphic output is
obtained by calling on the UM PLOT sub-
routine.^ as modified for the University of
Washington system. The graph of output
is optional with the user.
This brief discussion deals with the ma-
jor aspects of the program. More extensive
documentation may be obtained by writ-
ing to the author. Progiram listings and
punched-card decks (approximately 500
cards) of the source program can be ob-
tained for the cost of materials and mail-
ing charges. Within limits, the author will
attempt to assist interested instructors in
adapting the program to be compatible
with their campus computer requirements.
8 SHARE, Distribution No. 1085.
Communications 341
Chart 1
AVERAGE AGE AT DEATH FOR PERSONS NOW AGE X
dASED UPON THE 1958 CSO MORTALITY TABLE

( 95.000 0/0 CONFIDENCE LIMITS)
1 00 .0 + U U- + ---.i^.^-..-..-.-.- ... .( ... U--^-
A
V
E
R
A
G
E
83.a
66.3
49.5
I
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I
32.7 L-
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*
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u uI U U
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* • *
* # • I
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. J,
IJ 1
U U
I U U U U I
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I »
I *
» * t
* 1
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[ U L
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[ *
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L

KEY TO PLOTTING CHARACTERS
# = AVERAGE AGE AT DEATH
U = UPPER CONFIDENCE LIMIT
LOWER CONFIDENCE LIMIT I
25 50
- PRESENT AGE -
75 100
SOURCE — LFXP
342 The Journal of Risk and Insurarwe
Table 1
AVERAGE AGE AT DEATH FOR PERSONS NOW AGE X
BASED UPON THE 1958 CSO MORTALITY TABLE
f. .--
I AGE
[ <X)
I 0-
: 5
: 10
: 15

[ 20
25
30
35
40
45
50
55
60
65
70
75
80
]
85 I
90 :
95 :
100 ]
I

I NUMBER ALIVE
I AT AGE X
t L(X)
I 10000000
: 9868375
: 9805870
: 9743175
9664994
9575636
9480358
9373807-
9241359
9048999
8762306
8331317
7698698
6800531
5592012
4129906

2626372
1311348
,468174
97165
0
I
.1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

I
I
I
I
II
I
I
I
I
I
I
I
I
I
I
I
I
I
I
NUMBER DYING
WHILE AGE X
D(X)
70800
13322
1 1865
14225
17300

18481
20193
23528
32622
48412
72902
108,307
156592
215917
278426
303011
288648
211311
106809
34128
0
I
I
I

I
I
I
I
I
I
I
I
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I
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I

I
I
I
I
I
I
1
H
AVERAGE AGE
AT DEATH
68.3
69.2
69.6
70.0
70.4
70.8
71.3
71.7
72.2
72.8
73.6
74.7 I

76.1 I
77.9 :
80.1 I
82.8 I
.85.9
89.3 I
93.1 I
96.8 ]
0.0 I
), -„.
COEF. OF
VARIATION
V(X)
0.266
0.239
0.228
0.218
0.207
0.196

0.186
0.176
0.167
0.1 5fe
0.144
0.130
0.114
0.098
0.081
0.065
0.050
0.037
0.026
0.014
0.000
+
•-••

1
I
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—. +
YEARS OF LIFE' I
REMAINING
E<X>
68.3
64.2
59.6
55.0
50.4
45.8
41.3
36.7
32.2
27.8

23.6
19.7
16.1
12.9
10.1
7.8
5.9
4.3
3.1
1 •B
0.0
]
i
—t
I
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I
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i
I

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.1
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1
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•I
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I
I
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I
SOURCE — LFXP

C© Risk Management and Insurance Review, 2005, Vol. 8, No.
1, 141-150
THE COLUMBIA SPACE SHUTTLE TRAGEDY:
THIRD-PARTY LIABILITY IMPLICATIONS
FOR THE INSURANCE OF SPACE LOSSES
Piotr Manikowski
ABSTRACT
Space flights are no longer rare events, but the commonplace is
not necessarily
safe. When disaster strikes, as in the Columbia Space Shuttle
disaster of 2003,
third parties as well as those directly involved are financially
affected. This
article considers how these issues are treated under
international law. It also
analyzes what products the insurance markets offer as
protection against such
third-party liabilities.
INTRODUCTION
On February 1, 2003 the Columbia space shuttle, the oldest of a
fleet of four, was destroyed
during reentry into the earth’s atmosphere, causing the death of
all seven crew. The total
damage is estimated at about US$3 billion. During the
International Space Insurance
Conference that took place in Florence (April 3–4, 2003), Paul

Pastorek, General Counsel
of U.S. space agency NASA reported the latest findings of the
investigations into the
loss of the Columbia space shuttle (Stahler, 2003). NASA had
recovered 45,000 pieces
of wreckage from an area 100 miles long and 10 miles wide.
The material recovered
comprised in terms of weight almost half the lost shuttle. The
initial suspicion was that
one of the brittle ceramic tiles on the underside of the wing had
been damaged during
take-off, allowing heat to enter into the wheel chamber. A video
tape was recovered, but
this stopped transmitting shortly before the crew realized that
there were problems with
the re-entry. NASA subsequently recovered an instrument used
on the shuttle to record
a multitude of technical data during each flight. These data
revealed that the build-up of
heat inside the right wing came from the leading edge of the
wing, which was made of
an extremely hard and tough material. The initial ceramic-tile
theory thus seemed to be
disproved. However, the official report has yet to be released.
Was Columbia the victim
of a collision with space debris, of which thousands of items are
now littering the earth’s
orbital paths? It may never be established with absolute
certainty what really happened
Piotr Manikowski is with the Poznań University of Economics,
Insurance Department,
al. Niepodleglosci 10, 60-967 Poznań, Poland (e-mail:
[email protected]). This ar-
ticle was subject to anonymous peer review.
The author wishes to thank Peter Birks for his language revision

of the text.
141
142 RISK MANAGEMENT AND INSURANCE REVIEW
at a speed of 21,000 kilometers an hour in the upper layers of
the atmosphere above
Texas.
Debris from the space shuttle fell to the ground, but did not
cause serious damage.
However, it remains possible that space exploration could
inflict harm on third parties
on the ground. This could evoke the civil liability of the guilty
party. It is possible to buy
third-party liability insurance for space losses.
GENESIS OF SPACE (SATELLITE) INSURANCE
Until the mid-1960s the insurance market was not interested in
the space industry, since
it had been focused on the military aims of the United States
and the Soviet Union.
The launching of the first artificial earth satellite on October 4,
1957 and the sending of
the first man—Yuri Gagarin—into space on April 12, 1961,
accelerated the development
of the space industry—including its commercial arm. It became
clear to the insurance
industry that there would soon be a commercial space market
available for exploitation.
Insurance for space activities has evolved over many years
through the collaboration

of aerospace clients, brokers, and the underwriting community
worldwide. The goal of
that work was to provide flexible forms of insurance for a
volatile class of exposure,
which was not yet quantified by loss data.
In the formative years of the space age, projects were
uninsurable: launch vehicles were
unreliable and most of the payloads were experimental —the risk
was self-insured by
governments and space agencies that financed the flights. The
first company to devote
its attention to the use of this new technology for commercial
purposes and to show
an interest in obtaining insurance protection was American
Communication Satellite
Corporation (ACSC), founded in 1962. On April 6, 1965 ACSC
obtained the first space
insurance policy to protect the first commercial geostationary
communication satellite
Early Bird (Intelsat I-F1). The policy covered only material
damages to the satellite prior
to lift-off (pre-launch insurance for US$3.5 million) and third-
party liability insurance
for US$ 5 million (Daouphars, 1999).
In time, and with increasing experience of insurers and the
insured, the insurance market
developed a wider scope of space insurance cover. There are
currently three basic groups:
1. Property insurance: (pre-launch, launch, in-orbit insurance);
2. Third-party liability insurance;
3. Warranty insurance (loss of revenue, launch re-flight (risk)

guarantee, incentive
payments insurance).
The third group is supplementary to property cover. In this
study only third-party li-
ability insurance is taken into consideration. It should be
emphasized that, since the
early days of satellite insurance, little notice has been taken of
the issues connected with
liability for space damages.
RISK OF THIRD-PARTY LIABILITY FOR LOSSES MADE BY
SPACE OBJECTS
Space activity and the use of spacecraft entail the possibility of
inflicting damage on third
parties, for which the owner or the user of a satellite is usually
responsible. In the event
THE COLUMBIA SPACE SHUT TLE TRAGEDY 143
of the explosion of a rocket only a few meters above the ground,
the potential loss could
be enormous.
In connection with the specificity of space activity and its
“over-territorial” character, it
was decided that the responsibility for damages should be
regulated by international
law. From the late 1960s a series of five treaties and
conventions were agreed upon that
covered the exploration of space and the legal ramifications for
events on the ground:
� The Treaty on Principles Governing the Activities of States

in the Exploration and
Use of Outer Space, including the Moon and Other Celestial
Bodies (the “Outer
Space Treaty,” adopted by the General Assembly in its
resolution 2222 (XXI)),
opened for signature on January 27, 1967, entered into force on
October 10, 1967,
98 ratifications and 27 signatures (as of January 1, 2003);
� The Agreement on the Rescue of Astronauts, the Return of
Astronauts and the
Return of Objects Launched into Outer Space (the “Rescue
Agreement,” adopted by
the General Assembly in its resolution 2345 (XXII)), opened for
signature on April
22, 1968, entered into force on December 3, 1968, 88
ratifications, 25 signatures, and
1 acceptance of rights and obligations (as of January 1, 2003);
� The Convention on International Liability for Damage Caused
by Space Objects
(the “Liability Convention,” adopted by the General Assembly
in its resolution 2777
(XXVI)), opened for signature on March 29, 1972, entered into
force on September
1, 1972, 82 ratifications, 25 signatures, and 2 acceptances of
rights and obligations
(as of January 1, 2003);
� The Convention on Registration of Objects Launched into
Outer Space (the “Reg-
istration Convention,” adopted by the General Assembly in its
resolution 3235
(XXIX)), opened for signature on January 14, 1975, entered i nto
force on September
15, 1976, 44 ratifications, 4 signatures, and 2 acceptances of

rights and obligations
(as of January 1, 2003);
� The Agreement Governing the Activities of States on the
Moon and Other Celestial
Bodies (the “Moon Agreement,” adopted by the General
Assembly in its resolution
34/68), opened for signature on December 18, 1979, entered
into force on July 11,
1984, 10 ratifications and 5 signatures (as of January 1, 2003).
These acts constitute the bulk of what is referred to as “space
law,” intended as that branch
of public law that deals with activities which occur outside the
earth’s atmosphere. From
a practical point of view, the effect of these treaties is
somewhat limited. The main reasons
for their ineffectuality is that they mostly deal with issues of
principle and not with the
day-to-day activities of aerospace companies (d’Angelo, 1994).
The first of these acts (“Outer Space Treaty”) already includes
article VII, which concerns
third-party liability and states that: “Each State Party to the
Treaty that launches or
procures the launching of an object into outer space, including
the moon and other
celestial bodies, and each State Party from whose territory or
facility an object is launched,
is internationally liable for damage to another State Party to the
Treaty or to its natural
or juridical persons by such object or its component parts on the
earth, in air or in outer
space, including the moon and other celestial bodies.”

That basic rule was even enlarged upon in the “Liability
Convention,” according to
which the signatory states are responsible for all acts and
omissions of their government
agencies and of all their natural or juridical persons. Article II
of the “Liability Conven-
tion” states that: “A launching State shall be absolutely liable to
pay compensation for
damage caused by its space object on the surface of the earth or
to aircraft flight.” There
is no limit to the amount of indemnity, but compensation is
restricted to damage caused
directly by space objects. In addition, damage on the earth is
clearly distinguished from
damage in outer space. The first applies if a space object
inflicts damage on the surface
of the earth or to aircraft in flight. In such a case the liability of
a launching state shall be
absolute. However, liability for damage to other space objects
in outer space is based on
fault (Articles III, IV, VI). In consequence such regulations of
space law usually cause the
necessity of buying an insurance policy against third-party
liability. Also, treating dam-
age on the earth and damage in outer space differently is very
important when assessing
the liability risk, because, according to Kowalewski (2002), the
intra-space liability based
on fault creates a less-intensive risk of third-party liability.
Moreover, this distinction in space law also requires a
definition of where “outer
space” starts. Here there are many different opinions, and this

has created both sci-
entific and legal problems. Simply speaking, outer space begins
where airspace finishes
(Antonowicz, 1998). Another definition is that outer space
begins at the lowest altitude
at which it is technically feasible for a satellite to orbit the
earth, which is currently
about 80 kilometers above sea level (Space Flight and
Insurance, 1992). According to
this definition, the true birth of space flight was in 1942 when a
German A-4 (also called
V2) rocket was launched, because its altitude exceeded 80
kilometers. Another source
(Encyklopedia Geograficzna Świata, 1997) announces that space
begins at about 180 kilo-
meters, which is where the density of atmosphere becomes so
thin that it is possible for a
few days’ free flight around the earth. Although there is no
clear-cut lower limit of outer
space, international practice assumes that outer space “begins”
at the altitude of about
100 kilometers above see level (Antonowicz, 1998).
The compensation provided for in the “Liability Convention,”
depends on the identifica-
tion of the space object that is responsible for the damage. It is
to assure that such identifi-
cation is possible that a “Registration Convention” demands
that each state launching an
object into outer space register the said object. If it is possible
to confirm who launched the
given space object, the injured party can claim its compensation
on the basis of principles
given in the “Liability Convention” (Articles VIII–XX).
Damages inflicted on third parties occur more often on the

earth. During take-off, there
is a possibility that the launch vehicle or its parts (e.g., external
tanks, strap-on boosters)
can cause damage to any objects on the ground, sea, or to
aircraft in flight. For this reason,
satellites are usually launched in a seaward direction,
sometimes indeed from a platform
on the sea (e.g., a Sea Launch rocket). Shipping lanes nearby
and airspace in the region of
the launch are closed during launching time. If a launch vehicle
deviates from its nominal
trajectory and threatens to cause damage, it can be blown up by
a built-in self-destruction
device, thus minimizing the risk of damage. The most dangerous
are those accidents that
arise on the launch pad or within a minute or thereabouts of
take-off. This happened in
1986 when a Titan rocket exploded at a height of only 240
meters, destroying both the
launch pad and the launch facilities. In another case a farmer
from Georgetown in Texas
had a 500-pound fuel tank from a Delta II booster rocket land
nearly intact just 150 feet
from his house (Coffin, 1997). Other examples include:
1. the failure of a Long March 3B in 1996, which pitched over
before clearing the launch
tower. It crashed into a hillside 22 seconds into flight, killing at
least 100 people and
destroying the attached Intelsat 708 satellite (Anselmo, 1999);
2. the second stage of a Thor Able Star rocket fell to the ground

in Cuba and killed a
cow—the U.S. Government had to pay to Cuba US$2 million in
compensation, thus
creating one of the more expensive cows in history (Bulloch,
1988);
3. the failure of a Proton launcher on July 7, 1999, which
resulted in an 80-ton
rocket fragment plummeting to the ground, 6 miles from the
town of Salamalkol
(Kazakhstan), with a further 440-pound piece falling into a yard
of a home in a
nearby village—Kazakh authorities presented a claim to the
Russian Government
in the amount varying between US$270,000 and US$288,000;
4. another failure of a Proton rocket on October 27, 1999, 3
minutes 40 seconds into
its flight, with the reported claim paid by Russia to Kazakhstan
in the region of
US$400,000 (for these and more examples of accidents, see
Schmid, 2000);
5. at least 21 people were killed in August 2003 in Alcantara
(Brazil) after the explosion
of a VLS-3 rocket on the launch pad. The rocket booster was
mistakenly ignited
during tests, three days prior to the scheduled launch.
It is also possible during the operation of spacecraft for harm to
be inflicted on third
parties. Damages in outer space are usually connected with
either a collision or through
electromagnetic interference in transmissions of one satellite or
terrestrial radio links
caused by the system of another satellite. However, there is no

doubt that a guilty party
is obligated to compensate for that damage.
A spacecraft could suffer damage (both partial and total loss) as
a result of collision with
another object. A crash is possible with three kinds of objects:
� with another operating satellite;
� with space debris;
� with a heavenly body such as a meteor, in which case there
would be no liability.
The chance of a collision between two operating spacecrafts is
small. These objects are
under the constant control of ground stations that track their
orbits. It has been rec-
ommended for several years that satellites that have reached the
end of their working
life-span be moved away from their geostationary orbit.
Satellites from low orbits are
usually de-orbited. They partly or completely burn up in the
atmosphere, with any debris
theoretically falling into oceans. One example of a space object
being treated in this way
was the Space Station MIR, taken out of commission in 2001.
Other satellites are shifted
to higher orbits. In the second case the altitude increase should
be at least 150 kilometers.
The fuel required for that operation is equivalent to the amount
needed for six weeks
active station-keeping (Blassel, 1985).
Human activity in outer space has resulted in the appearance of
many objects orbiting
the earth. The majority no longer serve any useful purpose—old
satellites, fragments of

rockets—but are a danger to functioning spacecrafts. One
example occurred in August
1997, when a 500-pound discarded rocket motor floating in
earth’s orbit passed within
2.5 kilometers of an ozone-measuring satellite worth tens of
millions of dollars. NASA
alerts its space shuttles of a possible collision when any other
object comes within 50
kilometers of the orbiters (Coffin, 1997).
Article II of the “Registration Convention” imposes on launch
operations the obligation
to catalogue all objects sent into space. Since 1957 about 9,000
objects have been logged
that are still being tracked. More than 100,000 bits of debris are
still in space that are too
small to follow. Such debris includes pieces of aluminum
chuffed from satellite boost
stages, blobs of liquid metal coolant that leaks from discarded
space reactors, debris
resulting from satellite explosions, and lens covers and other
hardware discarded during
normal satellite operations. Some of this material w ill remain in
earth orbit for hundreds
or even thousands of years (Ailor, 2000). However, only 7
percent of the registered
objects are still functioning—the rest are nonfunctional
satellites (20 percent), rockets’
upper stages (16 percent), remains after missions (12 percent),
and different fragments
(45 percent). This means that over 90 percent of objects sent

into outer space are now
nonfunctional debris. Space (orbital) debris is technically
defined as any man-made
earth-orbiting object, which is nonfunc tional with no reasonable
expectation of assuming
or resuming its intended function or any other function for
which it is or can be expected
to be authorized, including fragments and parts thereof (Flury,
1999).
Currently, the possibility of an operational satellite being
damaged or destroyed by
space debris is small (estimated by actuaries at about 0.01
percent), but as the amount
of debris in space increases, the possibility of an operational
satellite being hit is rising.
This process is irreversible, since the cleaning-up of space is
economically (and also
technically) unfeasible. Most space debris is located in orbital
regions that are frequently
used for a multitude of applications (low orbits: 800 to 1,600
kilometers and geostationary
orbit of about 36,000 kilometers above the earth’s surface).
For large close-to-earth orbiting spacecraft and for space debris
there is a risk of a fall to
earth. The lower the orbit and the greater the mass, the greater
the chance of a reentry.
A satellite falling to the earth has the same effect as a natural
meteor. When it passes
through the atmosphere, huge heat and pressure develops and
the object is broken up
into numerous pieces, most of which are completely burnt up.
Only a very few large
pieces survive to reach the ground. Some examples of reentries
from outer space:

1. the spent stage of a Saturn V rocket, weighing about 22 tons,
which fell into the
Atlantic Ocean east of the Azores in January 1978;
2. the American Skylab, weighing approximately 80 tons,
crashed over the western
coast of Australia in July 1979 (Space Flight and Insurance,
1992).
However, in reality, despite the large size of these objects, the
risk of damage to the earth
is quite low—over two-thirds of the earth’s surface is sea and
much of the land is sparsely
populated.
What causes more concern is the environmental damage that can
be caused by space-
craft with nuclear power generators on board. On January 24,
1978 the Russian satellite
Cosmos 954 crashed in Northwest Canada, contaminating large
areas with radioactivity.
Based on the provisions of the “Liability Convention” and
general principles of inter-
national law, a claim in the total amount Can$6.04 million was
submitted, although the
matter was settled some time later following negotiation, in the
amount of Can$3 million.
There are still spacecraft that use nuclear materials for power
supplies. This constitutes
a serious risk.

The service and/or repair of spacecrafts in orbit could cause
liability of the owner of the
device for potential damage. It is unclear what would happen if,
during replacement of a
broken part, the astronaut-mechanic destroyed the repaired
module. How can companies
that have spent huge sums of money in the manufacturing of
such equipment protect
themselves against the risk of sharing multipurpose platforms or
space stations? How
can the “earth” (national) law be applied to these situations?
International space law has
not solved this problem yet. This matter should engage not only
lawyers, but also other
interested parties, including the insurance community.
SPACE THIRD-PARTY LIABILITY INSURANCE IN THE
WORLD INSURANCE MARKET
The need to procure third-party liability insurance is based on
protection against fi-
nancial claims resulting from certain fundamental principles of
international space law
(mainly the “Outer Space Treaty” and the “Liability
Convention”) as well as national leg-
islation, executive orders, administrative regulations, and
judicial decisions that control
or otherwise influence the conduct of activities in space
(Meredith, 1992). The require-
ment for and scope of liability cover is dependent on the Launch
Services Contract with
the launching agency. In some cases the satellite owner is
responsible for the purchase
of insurance, but the majority of launch suppliers now include
the arrangement of the
appropriate coverage as part of the launch services supplied by
them.

In general, liability insurance covers the insured against
potential claims and ensures
compensation for the victim. Therefore, liability insurances
fulfill a double protection
function. Space third-party liability insurance has the same
purpose.
It covers the legal liability arising from damage to a third party
during the preparations
for launch, the lift-off itself, in-orbit operations of a satellite
program, and finally the
reentry. This type of insurance will provide compensation in the
event of personal injury
and property damage to third parties, both on the ground and in
space, caused by the
launch vehicle sections or the satellite. So the space third-party
liability insurance applies
to damages to a third party in connection with such events as:
falling of a satellite or
a rocket or elements thereof on the ground, fire during ignition,
explosion of a satellite
in orbit, collision with another spacecraft, etc. (Zocher II, 1988;
Zocher IV, 1988). The
launch pad is usually not covered. Neither is damage to
payloads, since there is often a
clause in the underlying contracts in which all parties agree to a
cross-waiver of liability.
According to Pino (1997) this applies also even in the case of
gross negligence. Therefore,
insurance covers the period from the delivery of a spacecraft to
a launch pad till the day
of expiration of that policy or the destruction of the satellite,
whichever comes first.
Contracts are extended to the end of a spacecraft’s life.

The launch service providers typically purchase third-party
liability insurance for the
launch of a satellite and for a set period thereafter. They will
add the satellite operator to
the liability insurance they hold as an additional named insured.
The satellite operator
will also occasionally purchase in-orbit third-party cover, which
comes into operation
when the launch coverage expires. This insurance is taken out
either to comply with leg-
islation in certain countries, or for the satellite operator’s own
peace of mind. Sometimes
producers, launching states, or other related organizations could
be coinsured.
Exclusions that are typically applied to a third-party liability
policy, include (Margo,
2000):
� war risks;
� claims caused by radioactive contamination of any nature
whatsoever;
� noise, pollution, and related risks;
� any obligation of the insured to his employees or any
obligation for which the
insured or any carrier as his insurer may be liable to his own
employees, under any
workers’ compensation, death, or disability benefits law, equal
opportunity laws,
or under any similar law;

� any damages to the property of the insured;
� claims resulting from an interruption in telecommunications
service to satellites,
whatever cause thereof;
� liability of any insured as a manufacturer;
� claims made for the failure of the spacecraft to provide
communications service.
The limits recently purchased vary from around US$60 million
to US$500 million. For
example, in the United States, the government has renewed
legislation that limits com-
mercial operations liability for damage caused by a launch
failure to US$200 million,
with the U.S. government responsible for the balance of up to
US$1.5 billion in liability
specified by international treaties (Pagnanelli, 2001).
Rates differ considerably. They are affected by trends in the
overall liability market and
the capacity required as well as specific liability issues. In the
context of the launch (14
percent to 18 percent of the sum insured) and in-orbit (2 percent
to 4.5 percent of the sum
insured) premiums, liability premiums are relatively small
amounts and are typically at
a level of around 0.1 percent (per year) of the required limit of
liability (Space Insurance
Briefing, 2001). However, when Russians protected themselves
against the failure of
the falling of the MIR Station into the Pacific ocean (March 23,
2001), they had to pay
about US$1 million premium for US$200 million limit of
responsibility. The high level of
premium required could have shown the degree of confidence of

the insurance market
in the reliability of MIR.
CONCLUSIONS
Thus far there have been only a few cases of third-party liability
for space losses. It should
also be noted that there has never been a substantial claim on a
space liability insurance
policy. It remains to be seen if this type of coverage would
remain available if a major
accident was to occur. The tragedy of the Columbia space
shuttle shows that potential
damage could be enormous (if the catastrophe had occurred
above a city). The debris
of the orbiter fell on a sparsely populated area near the
Texas/Arizona border. In total,
NASA received 66 claims for property damage and loss of
cattle, totaling US$500,000.
The corridor of debris passed 15 miles south of Houston and
Fort Worth. However, it
also has to be said that the debris of the space shuttle Columbia
did not hit or hurt a
single person. According to Mr. Pastorek, NASA self-insures
what it flies (Stahler, 2003).
So again it should be emphasized—with the development of
space transportation—both
commercial and noncommercial (governmental, scientific,
etc.)—issues of risk manage-
ment are very important in view of the considerable financial
commitments of launch

participants and the enormity of damages that may occur. In
addition to the risk involved
in the loss or failure of spacecraft that we have frequently
observed, space activities cre-
ate exposure to potentially “astronomical” (or even “out of this
world”) liability to third
parties injured by the malfunctioning spaceship or rocket
boosters.
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Anselmo, J., 1999, Cox: Companies Broke Law—and Knew It.
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Antonowicz, L., 1998, Podręcznik prawa międzynarodowego
(Warsaw: Wyd. Prawnicze
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Associated Risks. The Geneva Papers
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d’Angelo, G., 1994, Aerospace Business Law (Westport:
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merciale de l’Espace (Paris: LITEC).
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(Krakow: Tom VIII—Wszechświat,
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Spacecraft? In: Commercial and
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cywilnej, Prawo Asekura-
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Aviation Insurance, Including
Hovercraft and Spacecraft Insurance, 3rd edition (London,
Edinburgh, Dublin: Butter-
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for the Practitioner: Imple-
menting a Telecommunications Satellite Business Concept
(Amsterdam: Martinus Nijhoff
Publishers).
Pagnanelli, B., 2001, Space Insurance Towards the Next
Decade. In: Commercial and In-
dustrial Activities in Space—Insurance Implications (Trieste:
Generali), pp. 25-33.
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Satellite Industry will En-
counter new Frontiers in the Legal Claims Area. In: Commercial

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in Space Insurance Implications (Trieste: Generali), pp. 189-97.
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Liability Claims, In: The 9th
International Space Conference (London: IBC).
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Space Insurance Briefing, 2001, (London: Marsh Space Projects
Ltd.).
Stahler, W., 2003, Of New Risks, Unknown Risks and
Uncertainty. Risk Management, 33:
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Raumfahrt und ihrer
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Raumfahrt und ihrer
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The effect of ambiguity on risk management choices:
An experimental study

Vickie Bajtelsmit1 & Jennifer C. Coats1 & Paul Thistle2
Published online: 24 July 2015
# Springer Science+Business Media New York 2015
Abstract We introduce a model of the decision between
precaution and insurance
under an ambiguous probability of loss and employ a novel
experimental design to test
its predictions. Our experimental results show that the
likelihood of insurance purchase
increases with ambiguous increases in the probability of loss.
When insurance is
unavailable, individuals invest more in precaution when the
probability of loss is
known than when it is ambiguous. Our results suggest that
sources of ambiguity
surrounding liability losses may explain the documented
tendency to overinsure against
liability rather than meet a standard of care through precaution.
The results provide
support for our theoretical predictions related to risk
management decisions under
alternative probabilities of loss and information conditions, and
have implications for
liability, environmental, and catastrophe insurance markets.
Keywords Liability. Imperfect information . Design of
experiments . Laboratory
experiments
JEL Classifications K130 . D81 . C9 . C920
Two apparently conflicting puzzles consistently arise out of the
empirical observation
of insurance markets. Both involve a tendency to make

suboptimal insurance decisions
and have important implications for environmental risk
mitigation, consumer decision
making, public finance, and firm profit maximization. First,
there is substantial evi-
dence that individuals and businesses underinsure catastrophe
risk (Kunreuther and
J Risk Uncertain (2015) 50:249–280
DOI 10.1007/s11166-015-9218-3
* Jennifer C. Coats
[email protected]
Vickie Bajtelsmit
[email protected]
Paul Thistle
[email protected]
1 Department of Finance and Real Estate, Colorado State
University, Fort Collins, CO 80523, USA
2 Department of Finance, University of Nevada Las Vegas, Las
Vegas, NV 89154, USA
http://crossmark.crossref.org/dialog/?doi=10.1007/s11166-015-
9218-3&domain=pdf
Pauly 2004; 2005). The devastating cost of a failure to insure
against catastrophe is
highlighted repeatedly with each natural disaster. Second,
individuals and firms pur-
chase liability insurance even when neither law nor contract
requires they do so. Given
that injurers are held liable under U.S. law only if they have
failed to meet a reasonable
standard of care, expenditure on care could be a less expensive
alternative to purchasing

actuarially unfair liability insurance. In the absence of the
ability to take precaution
against accident, theory suggests that risk-averse individuals
will fully insure when
actuarially fair insurance is available. In situations where
insurance is not fairly priced
or where precaution is an alternative, the optimal choice
depends on risk aversion,
insurer profit and risk loading, and the cost of precaution.
Although negligence liability can be avoided by exercising an
appropriate level of
care, there are many sources of uncertainty that could explain
the existence of the
thriving liability insurance market in the U.S. The theoretical
literature suggests that
insurance demand may be explained by uncertainty regarding
one’s own risk type
(Bajtelsmit and Thistle 2008; 2015), the mechanics of the
pooling mechanism
(DeDonder and Hindriks 2009), the cost of taking precaution
(Bajtelsmit and Thistle
2009), potential for errors by the courts (Sarath 1991), and the
risk of momentary lapses
in judgment by oneself or others (Bajtelsmit and Thistle 2013).
Uncertainty may be
especially profound in the face of environmental risks. Riddel
(2012) notes that
environmental gambles involve greater uncertainty surrounding
the probability,
severity, and welfare loss effects of outcomes. In a
comprehensive overview of
environmental risk management, Anderson (2002) highlights the
extensive degree of
ambiguity surrounding potential environmental losses, even
from the standpoint of

risk-neutral corporations. In addition to the usual risks related
to property, liability, life
and health, environmental risks may include ethical, cultural,
business, reputational,
and regulatory uncertainty. Anderson also notes that the
interpretation of preventive
measures under environmental liability is particularly vague
compared to other liability
standards. Therefore, the degree of ambiguity that surrounds the
court’s judgment of
whether a defendant has met the standard of care is likely to be
higher in environmental
liability cases than under other liability cases. We view a
greater understanding, in
general, of precaution and insurance decisions under ambiguity
as a crucial step
towards understanding these tradeoffs under particular types of
ambiguity, such as that
created by environmental risks.
In this paper, we show theoretically that, when the probability
of loss is more
ambiguous, the demand for insurance increases. However, the
ambiguity may increase
or decrease expenditure on precaution, depending on
assumptions related to the cost
and benefit of precautionary spending. We test these results
empirically in a laboratory
experiment in which participants make decisions about
insurance and precaution under
different ambiguity conditions.
We extend the literature on the market for insurance in several
dimensions.
First, we develop a model which includes mistakes as a source
of ambiguity

underlying the decision between precaution and insurance and
shows that
ambiguity aversion increases insurance demand. Second, we
employ a novel
experimental design to test the predictions of the model. To our
knowledge,
ours is the first study to model the effect of ambiguity on
precaution and
insurance in this way and to use the experimental method to
investigate the
choice between precaution and insurance. Third, the
experimental design also
250 J Risk Uncertain (2015) 50:249–280
allows us to test previous theoretical findings related to the
choice between
precaution and insurance by individuals with heterogeneous
probabilities of
loss. In particular, Bajtelsmit and Thistle (2008) show that the
optimal insur-
ance contract leads individuals with high probability of loss to
meet the
standard of care and thereby avoid liability, whereas individuals
with low
probability of loss prefer to purchase insurance and take less
precaution. Their
results imply that individuals who have a preference for taking
full precaution
when insurance is unavailable will switch to insurance if it
becomes available
at a comparable cost. Finally, our design, parameters, and
framing allow us to
contribute additional evidence to existing mixed results related

to the decision
to insure against low-probability, high-severity losses.
Our primary motivation is to test whether ambiguity
surrounding the prob-
ability of a loss impacts the demand for precaution and
insurance, as suggested
by our theoretical model. To our knowledge, ours is the first
laboratory study to
allow a choice between buying insurance and exercising a level
of precaution
to achieve a desired level of risk of a loss. 1 The experimental
design requires
participants to make precaution and insurance decisions under
different condi-
tions, some of which involve risks with known probability
distributions and
others in which the probability of loss is unknown or ambiguous
to both the
experimenter and the participant. Participants make decisions
under conditions
of low and high probability of loss. In some treatments,
participants can pay for
a desired level of precaution and, in others, they can choose to
buy insurance
or alternative levels of precaution. To determine whether
ambiguity of the loss
distribution affects participants’ precaution and insurance
decisions, in some
treatments the participants are subject to an additional unknown
risk of loss.
By using a similar experimental design, as well as similar
parameters and
framing, we confirm the experimental results of Laury et al.
(2009) that
individuals are more likely to purchase insurance in the low

probability treat-
ments, after controlling for other factors such insurance pricing
and loss
severity. Empirical analysis of participant decisions under
conditions of known
versus ambiguous loss probabilities shows that the likelihood of
insurance
purchase increases with ambiguous increases in the probability
of loss and that,
when insurance is unavailable, individuals invest more in
precaution when
probability of loss is known than when it is unknown. Our
results also provide
support for theoretical findings in Bajtelsmit and Thistle
(2008): in the absence
of ambiguity, participants are more likely to purchase insurance
in the low
probability treatments and those who prefer full precaution
when insurance is
unavailable switch to insurance when it is available.
The next section reviews the theoretical and experimental
literature related to the
purchase of insurance against liability and catastrophe losses
and presents a theoretical
model to analyze the impact of ambiguity on insurance and
precaution decisions. The
laboratory experiment, which closely follows the theory setup,
is described in Section 2.
We formalize our hypotheses in Section 3, summarize the
empirical analysis and results
in Section 4 and provide conclusions in Section 5.
1 However, several papers do examine risk mitigation or
endogenous risk, without considering the role of
insurance—such as Fiore et al. (2009) and Harrison et al.

(2010).
J Risk Uncertain (2015) 50:249–280 251
1 Background and theory
1.1 Background
The extensive theoretical literature on insurance demand
provides several explanations
for the purchase of liability insurance. Under the standard
model of expected utility
theory, these include risk aversion of agents,
uncertainty/ambiguity related to proba-
bility of loss, cost of care, and operation of the legal system.
This literature has
generally distinguished individual insurance decisions from
corporate insurance deci-
sions. Theoretically, risk neutral corporations should not be
willing to buy insurance at
actuarially unfair prices. However, agency theory suggests that
risk-averse managers
might be motivated to do so on behalf of the firm, in order to
protect their own
employment and/or reputations (see, for example, Greenwald
and Stiglitz 1990; Han
1996; Mayers and Smith 1982).
A second strand of the insurance literature, also based on
standard expected
utility theory, focuses on individual decision-making under
ambiguity (when the
probability of loss is not objectively known). Although the risk
of negligence

liability can be avoided by exercising an appropriate level of
care, there are many
sources of ambiguity related to understanding the risk,
satisfying the negligence
standard, and judicial enforcement of the standard. For example,
potential injurers
may face uncertainty about their own risk type (Bajtelsmit and
Thistle 2008), the
mechanics of the pooling mechanism (DeDonder and Hindriks
2009), or the cost of
taking precaution to avoid risks (Bajtelsmit and Thistle 2009).
Shavell (2000)
illustrates that uncertai nty regarding negligence standards
results in a level of care
that exceeds a socially optimal level. The potential for errors by
the courts (Sarath
1991) and the possibility of injuries caused by momentary
lapses in judgment, either
one’s own mistakes or another agent’s (Bajtelsmit and Thistle
2013), theoretically
have been shown to justify a market for insurance.
A more generalized stream of research investigates decision-
making under risk and
uncertainty according to both standard and non-standard risk
preferences. While there
are many potential sources of ambiguity in a liability case, as
discussed above, our
experimental design and analysis adopts Camerer and Weber’s
(1992) definition of
ambiguity: Buncertainty about probability created by missing
information that is rele-
vant and could be known^ (p. 330). They note further that Bif
ambiguity is caused by
missing information, then the number of possible distributions .
. . might vary as the

amount or nature of missing information varies^ (p. 331). In
several treatments in our
experiment, participants make decisions that depend on
outcomes whose probabilities
they have estimated with varying degrees of missing
information, but are unknown at
the time either to themselves or the experimenters.
A vast literature related specifically to risk preferences suggests
that Bnonstandard^
features, not included in expected utility theory, drive behavior.
Non-expected utility
theories include alternative decision-weighted probability
models, prospect theory by
Kahneman and Tversky (1979), and Tversky and Kahneman’s
cumulative prospect
theory (1992), which combine probability-weighting with
different risk preferences
over gains and losses. 2 Prospect theory suggests that
individuals underestimate or
2 See Starmer (2000) for a review.
252 J Risk Uncertain (2015) 50:249–280
ignore very low probability events and the primary explanation
in the literature given
for underinsurance of catastrophic loss is that individuals may
ignore probabilities
below a certain threshold.3
Laboratory experiments on insurance purchase decisions under
different risk and
ambiguity conditions have been conducted under a wide variety

of designs and
protocols and the results are highly inconclusive. 4 A few
experimental studies
(Ganderton et al. 2000; Laury et al. 2009; McClelland et al.
1993; Slovic et al. 1977)
test the tendency to underinsure against low-probability high-
severity losses. However,
the differences in designs, procedures, and parameters employed
across the studies limit
the ability to generalize conclusions from their results. The
Laury et al. experimental
design, discussed in detail below, implements a choice task to
investigate the phenom-
enon of underinsurance for low-probability, high-severity
losses, and produces results
that are counter to the notion that individuals ignore very low
probabilities.5
1.2 The theoretical effect of ambiguity on precaution and
insurance decisions
The underlying theory is based on the standard model of
accidents in the law and
economics literature. In the absence of the ability to take
precaution against accident,
theory suggests that risk-averse expected utility maximizers will
fully insure when
actuarially fair insurance is available. In general, the
assumption of risk aversion
implies that individuals will be willing to pay some level of
load or risk premium to
avoid risk. Thus, when insurance is not fairly priced, the
optimal choice depends on
the level of risk aversion and the insurance loading factor.
We assume that individuals are expected utility maximizers with

increasing
concave von Neumann-Morgenstern (vNM) utility u. Individuals
have exogenous
initial wealth w and face a potential loss d<w with probability
π. Expenditure on
precaution or care is denoted c (c ≥ 0) and the risk of a l oss is a
decreasing,
convex function of c. Individuals have either a high or low
probability of loss,
where πH(c) > πL(c) for any expenditure on precaution. We
assume 0 ≤ π(c) < 1,
that is, it is possible to reduce the risk of loss to zero through
expenditure on
precaution. We also assume precaution has a lower marginal
impact on the
probability of loss for low-probability risks than for high
probability risks, 0 >
π′L(c) > π′H(c). We assume each person knows whether they
face high or low risk
and understands how the level of precaution affects the
probability of loss. An
insurance policy consists of a premium, pi, paid whether or not
loss occurs, and an
indemnity, qi, paid in the event that the loss occurs. The first
best levels of
precaution are ci* = argmin ci + πi(ci)d, i = H, L.
3 The behavioral literature also suggests that certain behavioral
biases, such as overconfidence or optimism, as
well as the tendency to overreact to recent events, may explain
under- and overinsurance for certain types of
losses. See, for example, Kunreuther et al. (2001).
4 See Jaspersen (2014) for a comprehensive review.
5 Many studies attempt to explain insurance markets by
designing the experiments as auctions rather than
choice tasks. See, for example, Camerer and Kunreuther (1989)

and Hogarth and Kunreuther (1989).
Although this design may work well as a mechanism for
eliciting willingness to pay for insurance, and under
a double auction, studying both sides of the insurance markets,
the results are not necessarily generalizable to
the insurance marketplace in which consumers face choice tasks
rather than pricing tasks, as explained in
Laury et al. (2009).
J Risk Uncertain (2015) 50:249–280 253
If insurance is not available, then expected utility is
Ui cið Þ ¼ 1−πi cið Þð Þu w−cið Þ þ πi cið Þu w−ci−dð Þ ð1Þ
The individual chooses the level of precaution, ci
0, that maximizes expected utility.
Because the individual is risk averse, she is willing to pay some
amount PiU to avoid
the risk of loss. The results in Bajtelsmit and Thistle (2008)
imply that the willingness
to pay to avoid the risk is given by u(w − PiU)=Ui(ci
0). Willingness to pay can be
written as PiU=ci
0+πi(ci
0)d+ρiU, where ρiU is a risk premium.
Now assume that insurance is available, that insurers can
determine risk type ex
ante, and that the expenditure on precaution is observable. In
general, the insurance

premium can be written as pi=λπi(ci)qi, where λ is the loading
factor; the insurance
premium is actuarially fair if λ=1 and unfair if λ>1. The
individual who buys the
insurance policy (pi, qi) and spends ci on care has expected
utility given by
Ui pi; qi; cið Þ ¼ 1−πi cið Þð Þu w−pi−cið Þ þ πi cið Þu
w−pi−ci−d þ qið Þ ð2Þ
for i=H, L.
The risk of negligence liability presents a special case. If
liability is determined
by a negligence rule, individuals who exercise a Breasonable^
level of care will
have a zero probability of loss. More specifically, under a
negligence rule where
the negligence standard of care is z, an individual is liable for
damages if their
level of precaution is less than the negligence standard, ci<z
and is not liable for
damages if their level of precaution meets the negligence
standard, ci≥z. Meeting
the negligence standard yields utility u(w − z). If insurance is
available at
actuarially fair prices, the individual can also eliminate the risk
by fully insuring;
this yields utility u(w − c* - π(c*)d). The individual will choose
whichever
alternative is less expensive. With a premium loading, the
insurance decision will
depend on the relationship between the cost of the insurance
relative to the cost of
precaution. If the premium is not actuarially fair, the individual
will not choose full
insurance. This yields utility u(w − ĉi − λπ (ĉi) q
̂ i − ρi), where

ρi is the risk
premium for the residual uninsured risk. The individual will
choose insurance if
ĉi + λπ (ĉi) q
̂ i + ρi<z, that is, if the cost of insurance and
precaution is sufficiently
less than the cost of meeting the negligence standard.
Individuals will not choose
to insure if the cost of doing so is greater than the cost of
meeting the negligence
standard. The size of the insurance loading factor relative to
expected loss and cost
of precaution makes a difference in the predicted decision
between insurance and
precaution. For example, for low frequency, low severity risks,
expected loss may
be so small that even a modest profit and risk charge will tilt
the scale toward
taking care instead of buying insurance.
In most analyses of liability, as in the analysis described above,
the probability of an
accident is a function of care or precaution and is deterministic.
Now suppose that it is
possible to make a mistake that, despite expenditure on care,
can result in an accident.
We can think of this as a momentary lapse in judgment, such as
a driver glancing away
from the road just before a dog crosses the street or an oil rig
worker failing to notice a
worn valve. Despite effort and expenditure on compliance,
managers cannot predict
precisely how the courts will assess liability and damages from
environmental losses.
As discussed at length in Anderson (2002), these types of losses
expose firms to a great

254 J Risk Uncertain (2015) 50:249–280
deal of uncertainty. Therefore, we model the case in which
individuals and firms know
that there is a random chance of a mistake, but they do not
know exactly how it will
impact the probability of loss.
Thus, denote ~m as the probability of a mistake, independent of
expenditure on care
or precaution, which results in loss d, and assume that the
probability of a mistake is
unknown. We deliberately do not distinguish the sources of this
mistake. It could be
one’s own mistake, the mistake of another agent, or an error by
the courts. The fact that
the probability of a mistake is unknown introduces ambiguity.
Letting m = E ~mf g be
the expected probability of a mistake, expected utility is given
by:
Ui cim
� �
¼ 1−m
� �
1−πi cð Þð Þu w−cið Þ þ πi cið Þu w− ci−dð Þ½ � þ m u w−
ci−dð Þ ð3Þ
for i=H,L. The optimal expenditure on care decreases with
increasing expected prob-
ability of mistake. As m approaches 1, expected utility is
optimized with zero expen-

diture on care. For a very small expected probability of a
mistake, the problem reduces
to Eq. (1) and the individual will select the level of care that
minimizes total cost of loss
and precaution.
If the individual is ambiguity averse, then decisions are made
according to the
second order expected utility function
Vi cið Þ ¼ E Φ Ui ci; ~m
� �� n o
¼ E Φ 1−~m
� ��
1−πi cð Þð Þu w−cið Þ þ πi cið Þu w− ci−dð ÞÞ½ � þ ~m u
w−ci−dð Þ
n o ð4Þ
where the expectation is over the distribution of mistakes
(Klibanoff et al. 2005;
Neilson 2010). The vNM utility function u captures the attitude
toward risk while Φ
captures the attitude toward ambiguity. If the individual is
ambiguity neutral then Φ is
linear and if the individual is ambiguity averse then Φ is
concave. An ambiguity-averse
individual is willing to pay to eliminate the risk; the willingness
to pay to avoid the risk
is given by Φ(u(w − PiV)=max E{Φ(Ui(ci, ~m). We show that
ambiguity aversion
increases the willingness to pay to avoid the risk,
PiV ≥PiU ; ð5Þ
the proof is given in Appendix 1.6 In sum, ambiguity aversion

is shown to increase the
demand for insurance.
The effect of ambiguity aversion on the optimal level of
precaution is theoretically
indeterminant and depends on the fine detail of the theoretical
model. Snow (2011)
shows that if individuals have unbiased beliefs (i.e., E{π(c,
~m)} equals the objective
loss probability), then the loss probability must be either
multiplicatively separable
(π(c, ~m)=α(c)π(~m)) or additively separable (π(c,
~m)=π(~m)+β(c)). Snow further shows
that multiplicative separability implies ambiguity aversion
increases the expenditure on
care. Snow (2011) and Alary et al. (2010) show that additive
separability decreases the
expenditure on care. The effect of ambiguity aversion on the
expenditure on care is
therefore an empirical question. However, decreased willingness
to pay for small
6 Alary et al. (2010) and Snow (2011) show that ambiguity
aversion increases the willingness to pay to avoid
the risk when the distribution of the risk is fixed. Their result
does not apply directly here because individuals
can shift the distribution of risk by exercising care.
J Risk Uncertain (2015) 50:249–280 255
reductions in risk seems at odds with an increased willingness
to pay to avoid the risk
and implies a discontinuity in behavior between small risk
reductions and risk elimi-

nation. This suggests that ambiguity will lead to lower
expenditures on care.
Now consider the same case when insurance is available. If an
individual’s proba-
bility of loss depends both on risk type and the chance of
mistake, then the expected
utility for a person who buys the insurance policy (pi, qi) and
spends ci on care is given
by:
Ui pi; qi; ci; m
� �
¼ 1−m
� �
1−πi cið ÞÞ½ u w−pi−cið Þ þ πi cið Þu w−pi−ci−d þ qið Þ
þ m u w−pi−ci−d þ qið Þ
ð6Þ
For an individual who is ambiguity averse, the second order
expected utility is V(pi, qi,
ci)=E{Φ(Ui(pi, qi, ci, ~m)}. Given the risk of mistakes, the
actuarially fair premium is
pi=(πi + m (1 − πi))d. If the premium is actuarially fair, then the
individual will fully
insure (q=d), and receive utility u(w − ci* − pi).
In the following section we discuss our use of the experimental
method to investi-
gate the theoretical predictions developed above and formally
present a set of testable
hypotheses in the context of the experimental design. To
summarize, under a setting of

a clearly-defined negligence standard with no risk of mistakes,
we test the predictions
that individuals will not insure if it is more efficient to simply
meet the standard of care,
and that individuals are less likely to insure as the size of the
insurance loading factor
increases. We introduce mistakes into the design, and
investigate the impact of ambig-
uous increases in the probability of loss on insurance and
precaution decisions.
2 Experimental design and procedures
In this section we present the experimental design and briefly
discuss the procedures
that were used to implement the design in the laboratory. Where
applicable, the design
and procedures follow those used in the Laury et al. (2009)
experiments. In our within-
subject design, each participant made independent decisions in
twenty treatments. A
random draw of one treatment at the end of the experiment
determined actual payoffs.
The risk of loss was implemented as a computer-generated
random number—
explained with the analogy of a random draw from 100 white
and orange ping pong
balls, where a draw of an orange ball resulted in a loss of a
specific dollar amount from
their experiment earnings. Participants were told the probability
of loss through a
description of the number of orange and white balls respectively
in each treatment as
well as the numerical probability of loss. In some treatments
they could reduce their

probability of loss by paying for units of precaution, described
as the option to pay to
replace orange balls with white balls. In other treatments,
participants could choose
between precaution, insurance, and no risk mitigation. An
actuarially fair premium in a
competitive insurance market is based on the expected loss in a
population of
policyholders in which some face higher risks of loss than
others. Therefore, the
insurance load associated with a single premium will vary
across individuals. In our
main treatments, we hold constant the loss severity, insurance
premium, and cost per
unit of precaution, which implies the insurance (or equivalent
precaution) load will
necessarily be higher in treatments with a lower initial risk of
loss than treatments with
256 J Risk Uncertain (2015) 50:249–280
a higher initial risk of loss, all else equal. To introduce
ambiguity and determine
whether the chance of mistakes changes participants’ choices
over precaution and
Table 1 Experimental treatments and corresponding initial
probabilities of loss prior to risk mitigation, by
ambiguitya and risk type
Panel A: Main Treatments
Level of ambiguity
in treatment

Loss
amo-
unt
($)
Risk mitigation
alternatives
available
Initial probability of loss
Treatment
#
Low Risk/
High
Load
Treatment
#
High Risk/
Low
Load
No ambiguity-known
probability
45.00 Precaution only #1 0.10 #2 0.32
No ambiguity-known
probability
45.00 Precaution or
insurance

#3 0.10 #4 0.32
Ambiguity due to unknown
probability of own
mistake
45.00 Precaution only #5 ≥0.10 #6 ≥0.32
Ambiguity due to unknown
probability of own
mistake
45.00 Precaution or
insurance
#7 ≥0.10 #8 ≥0.32
Ambiguity due to
unknown probability
of other’s mistake
45.00 Precaution only #9 ≥0.10 #10 ≥0.32
Ambiguity due to
unknown probability
of other’s mistake
45.00 Precaution or
insurance
#11 ≥0.10 #12 ≥0.32
Panel B: Replication treatmentsb
Level of ambiguity

in treatment
Loss
amo-
unt
($)
Risk mitigation
alternatives
available
Initial probability of loss
Treatment
#
High Load Treatment
#
Low Load
No ambiguity-
known probability
45.00 Insurance only #13 0.01 #17 0.01
No ambiguity-
known probability
4.50 Insurance only #14 0.10 #18 0.10
No ambiguity-
known probability
60.00 Insurance only #15 0.01 #19 0.01

No ambiguity-
known probability
6.00 Insurance only #16 0.10 #20 0.10
a In the no ambiguity treatments, prior to making the risk
mitigation decision, participants are given the initial
probabilities and the effect that their risk mitigation decision
will have on the probability of loss. In the Own
Mistake treatments, participants know the initial probability of
loss, but are subject to an additional unknown
risk of loss that depends on their own performance on the
driving quiz. In the Others’ Mistake treatments,
participants know the initial probability of loss, but are subject
to an additional unknown risk of loss that
depends on the performance of another participant on the
driving quiz. Because the secondary risk is
participant-specific, the probability of loss for the ambiguity
treatments is not known for certain but is
greater than or equal to the initial probability of loss that is
given in the treatment
b The replication treatments use the loss amounts and
probabilities given in Laury et al. (2009). These
treatments were included in the experiment for purposes of
validation of the experimental design, but are not
used in any of the main empirical models in this paper
J Risk Uncertain (2015) 50:249–280 257
insurance, in some treatments the draw of a white ball could
still result in a loss,
depending on mistakes made during the earnings task. These
elements of the experi-
ment are described more fully in this section.

2.1 Earnings task
Similar to Laury et al. (2009), participants received earnings in
several installments. We
paid a $15 participation payment in cash at the start of the
experiment, and collected a
signed receipt from each participant. We encouraged them to
put this money away and
emphasized that the $15 was payment for their participation and
would not be at risk in
the experiment. We also clearly framed the risky environment to
require decisions over
losses of their earnings, rather than gambles over gains. This
design feature was
intended to more closely resemble decision-making in the actual
insurance market.
Prior to receiving any instructions or information about the risk
management and
insurance task, participants earned their endowment by
successfully completing an
earnings task, which required taking a written quiz covering
basic knowledge about
state driving rules. Upon completion of the driving quiz, they
were asked to estimate
their own score and the average score for the group. 7
Following the earnings task, they
received instructions and completed an assessment to ensure
that they fully understood
the decisions they would be asked to make in the experiment.
After the assessment,
they reviewed their earnings task answers and estimated scores
and entered them into
computers. Lastly, they participated in the precaution and
insurance decision-making
task which, together with chance, determined whether they

132 The Journal of Risk and Insuranceway of financing care

132 The Journal of Risk and Insuranceway of financing care

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