Journal of Financial Risk Management
2012. Vol.1, No.3, 27-32
Published Online September 2012 in SciRes (http://www.SciRP.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2012.13005
Gauging Risk Stability: A Simple Test Using Patterns of Workers’
Compensation Claims
Richard J. Butler1, B. Delworth Gardner1, Harold H. Gardner2
1Department of Economics, Brigham Young University, Provo, USA
2Human Capital Management Services, Cheyenne, USA
Received July 10th, 2012; revised August 12th, 2012; accepted August 26th, 2012
Abstract Abstract: In financial risk management, whether for national and international entities, or within a firm,
it is important to be able to decide what risks are altered by past experience (or intervention of a central banker
at the national level, or a firm’s risk manager at the employer level) and what risks do not vary over time (risks
from intrinsic heterogeneity). Policies aimed at changing intrinsic risk will obviously not be cost effective,
though tools for identifying such unchanging risks may help to minimize losses associated with those risks. This
paper outlines a simple test that allows the researcher to distinguish these alternative risk types. We present our
test in the context of patterns of workers’ compensation lost day claims to test whether past experience explains
repeated claims for some individuals, or whether some individuals exhibit an innate heterogeneity in
claims-filing propensities. We find that a previous claim significantly increases claim probabilities in the future
using easy to estimate and interpret “runs” tests on the claims. This suggests, for the risk management problem
examined here, that early intervention to limit the effects of the first lost time claim may produce significant
disability-cost savings with respect to future claims.
Keywords: Risk Measure; Heterogeneity; Runs Test; Workers’ Compensation
Introduction
One of the ongoing lessons from the current international fi-
nancial, banking, and economic crisis is the importance of dis-
tinguishing risks that do not change over time (call this “intrin-
sic heterogeneity”) from risks that are susceptible to change. As
an empirical matter, do risk entities change their behavior
enough in a crisis to justify early intervention, or is the risk of
those entities intransigent, so that such interventions are largely
a waste of resources, and the cost effective policy is to some-
how “isolate” intrinsic risks?
Not just public policy makers, a firm’s risk management also
finds it important to distinguish between intransigent (intrinsic)
heterogeneous risks from risk that is altered by past experience.
We develop a simple test for distinguishing these risk types
when repeated observations on the same entities are available.
We apply this test using patterns of losses from a US firm’s
workers’ compensation (WC) claims. WC is not only expensive
to firms (roughly $80 billion per year, see Ruser and Butler,
2010), and interacts with other employer provided benefits in
ways that affects other program costs (Butler and Gardner,
2011). The US WC system pays virtually all medical expenses
and provides partial reimbursement for lost wages for workers
with on-the-job injuries and for some occupational diseases.
Patterns of Claims: Distinguishing
Heterogeneity from Experience Effects
Our sample comes from a cohort of workers from one firm—
eliminating the problems of differential risk management pol-
icy, alternative benefit programs, and unobserved management
safety culture, relative to a panel across many firms. Following
our panel of workers over time, the distribution of claims ex-
hibits more repeated claims, and more individuals with no
claims, than one would expect if workers’ compensation claims
were just a random Bernoulli process (i.e., the likelihood of a
claims filing was constant across workers and over time). Three
prominent explanations for these distributional results include:
1) residual impairments manifest themselves in repeated claims
(i.e., workers do not fully recover from their injuries); 2) work-
ers are inherently different in their preferences, so that a given
health condition that would potentially qualify for a workers’
compensation claim might elicit differential propensities to file
claims over time, or differ in their intrinsic health (either of
which results in a time-invariant heterogeneity across workers
in claims-filing propensity); and 3) workers are potentially
affected by filing a workers’ compensation claim (injury-
claimant experience) in a way that affects the future likelihood
of filing a claim (even if all workers start with the same filing
propensity initially, that propensity changes for an individual
worker once he or she files a claim). Under all explanations, we
would see claims concentrated among some workers, while at
the same time an unexpectedly large number of workers ex-
perience no claims at all (relative to a constant claims-filing
probability).
In our sample of US workers from one firm, the residual
impairments do not explain the observed patterns. We were
able to match up the claim data with the nature of injury and
injured body part, and create six broad classes of injuries for
these workers: back strains (21 percent), other strains and
sprains (32 percent), cuts (4 percent), fractures (3 percent),
contusions and concussions (23 percent), and other injuries (16
percent). If the residual-impairment explanation of repeated
claims is true, then those who repeat claims will tend to report
the same type of claim last year as they do this year. Relatively
few of the repeat claims, however, are for the same type of

R. J. BUTLER ET AL.
injury as occurred previously. Of the 1105 pairs of consecutive
WC claims for the complete sample, only 25.2 or 22.8 percent
reported injuries in the same broad category for both years.
This is true despite the fact that a cut on the arm in one year is
counted as the same claim type as a cut on the leg next year
(given the broad nature of our six claim groups). The results
hold when also examining claims two years apart, and under a
variety of definitions of claims (whether using “first claim filed
in any given year” or “any claims filed in that category during
the year”). That is, there are relatively few injuries that are
reported as being of the same type—only slightly more than
one would expect if the injury types were random (and again,
these are overstated because of the broad categories used for
injury type).
Hence our inference problem for the bunching of claims re-
duces to the classic inference problem of sorting out heteroge-
neity (each worker has a different but time invariant probability
of filing a claim) from experience dependence (injury-claimant
experience for workers’ compensation, where the likelihood of
future claim-filing depends in part on whether past claims were
filed). Injury-claimant experience effects can result from a
worker’s job-related skills declining with time away from work
on an injury claim, even as worker’s consumption skills and
ability to use the disability system increase, hence lowering the
opportunity cost of filing future claims.
Injury-claimant experience effects, that is, the things learned
from the process of going through a social insurance claim such
as workers’ compensation insurance or unemployment insura-
nce, has been estimated both by examining claimant-duration
patterns and by examining repeat claims. Some claim-duration
studies interpret negative duration dependence as evidence of
injury-claimant experience: a claimant’s probability of exiting
the benefit system declines with time spent in the system as
they become more acclimated to the system. Negative-duration
dependence in benefit programs has been examined in studies
looking at unemployment insurance (Heckman and Borjas,
1980), Aid to Families with Dependent Children (Moffitt,
1992), and workers’ compensation (Butler and Worrall, 1985).
Studies examining the effects of injury-claimant experience by
looking at repeat spells are less common. However, repeat
spells in unemployment insurance have been examined by
Corak (1993), Lemieux and Macleod (1995) and McCall
(1995). Again, our study examines repeated spells in workers’
compensation for employees from one firm in the US. Like the
US unemployment insurance (UI) system, workers’ compensa-
tion indemnity pay for non-work spells is a standard percentage
of the pre-injury wage subject to minimum and maximum
weekly benefits. Unlike UI benefits, workers compensation
(WC) benefits are higher than UI benefits, received tax-free
and potentially are of unlimited duration for serious injuries.
Historically, there are more WC claims than there are UI cla-
ims.
Claim filing due to innate preference differences, determined
before the onset of claims, we will call the heterogeneity effect.
Claim filing due to practice, or experience with the benefit
system, we will call the injury-claimant experience effect. As
mentioned above, if there is heterogeneity in claim filing pro-
pensities between workers, and if this heterogeneity is intrinsic
to the individual and not subject to intervention efforts, then
perhaps the only purpose for targeting repeat users of workers’
compensation is to segregate them into long-term counseling,
or lower-cost chronic health treatments.
If, on the other hand, being on a workers’ compensation
claim increases the likelihood of filing future workers’ com-
pensation claims because of the acquisition of WC claimant
skills, then there is a more compelling role for early, perhaps
aggressive, intervention in risk management. Lowering the
level of dependency may generate significant cost savings in
the future. So knowing whether multiple claims arise from intr-
insic heterogeneity or injury-claimant experience is interesting
from both a policy and scientific perspective.
To understand the different implications of the heterogeneity
versus the injury-claimant experience explanation of multiple
claims, the analogy of three disability lotteries becomes instr-
uctive: the simple lottery, the heterogeneity lottery, and the
injury-claimant experience lottery. In each lottery, a given
worker has his/her own disability lottery urn from which he/she
randomly draws white balls and red balls once a year. If the
worker draws a red ball, he/she files a workers’ compensation
claim. If a white ball is drawn, he/she does not file a claim.
In the simple lottery, we assume that everyone has the same
proportion of red balls in his/her urn and that balls are drawn
with replacement. Each time a ball is taken out, it is put back in
the urn and the balls in the urn randomly shuffled. In the simple
lottery, the composition of red and white balls is constant acr-
oss workers and constant over time. For example, suppose that
the urn contains 100 balls, with 5 red balls and 95 white balls.
Since everyone draws from urns with the same fraction of red
balls, and the composition of the balls in the urn doesn’t change
from draw to draw, there are no heterogeneity or injury- clai-
mant experience effects and everyone has a 5 percent chance of
filing a claim. This is a Bernoulli process. In a large number of
trials, each worker will file a workers’ compensation claim
only about once in every 20 years. But the theoretical outcomes
of a simple lottery model are compared with actual patterns of
claims, there are many more workers with multiple claims in
the empirical data than the simple lottery would predict.
Workers who draw multiple red balls over the course of sev-
eral years can be explained by either of the other two lotteries:
the heterogeneity lottery or the claimant-injury-experience lot-
tery. The difference between these two lotteries is in the way
that draws are made. In the heterogeneity lottery, all individuals
still have their own disability urns, but the proportion of red
balls varies from person to person, perhaps due to intrinsic
health differences. For example, some may have 50 red balls
and 50 white balls, so that a workers’ compensation claim will
be filed, on average, every other year. Some will have 25 balls
and file a claim about once every fourth year. Some may have
only 1 or 2 red balls in their 100 ball urn; they would rarely file
a claim. In the heterogeneity-disability lottery, the probability
of filing a claim doesn’t vary over time for any given individual,
but does vary between individuals. Since the probabilities are
assumed to be intrinsically fixed for any given individual,
though they may vary across individuals, intervention wouldn’t
affect subsequent behavior.
In contrast to the heterogeneity lottery, where initially work-
ers have different proportions of red and white balls in their
urns, the injury-claimant experience lottery initially has the
same proportion of red balls across all workers. Hence, there is
no difference in the initial claims-filing probability (i.e. no
heterogeneity) in the injury-claimant experience lottery. But
now when someone draws a red ball and experiences a disabil-
ity claim, some injury-claimant experience is accumulated that
changes the future probability of claims filing. This injury-
claimant experience may take several forms: the marginal nui-
sance cost of filing a claim falls as more claims are filed, ex-
pertise increases in finding sympathetic claims management or
treating physicians (many employees choose their own treating
28

R. J. BUTLER ET AL.
physicians under WC), or the relative value of work to leisure
falls as work skills depreciate.
In the injury-claimant experience lottery, therefore, instead
of simply replacing the red ball when a claim occurs, we chan-
ge the color composition of the urn by putting additional red
balls in the place of white balls each time a single red ball is
drawn. Suppose that when a red ball is drawn out, we put 21
red balls back while removing 20 white balls-the initial draw of
a red ball raises the probability of drawing a red ball next time
from 5 percent to 25 percent. Over the course of many draws,
initial users of the system will tend to end up in the multi-
ple-claims group because of this injury-claimant experience
effect. This claimant-injury-experience lottery captures the
notion that disability injury-claimant experience changes work-
ers’ future behavior because claimant-consumption skills ac-
cumulate, lowering the cost of filing future claims.
But if early intervention for someone who has drawn a red
ball in the injury-claimant experience lottery can change this
preference (i.e., can mitigate the shift to additional red balls),
such intervention may have a potentially large payoff as it
speeds returns to work not only in the current period but also
reduces the likelihood of filing more claims in the future. But-
ler, Johnson, and Gray (2009) find that an early nurse contact is
an effective risk management strategy as it significantly re-
duces costs in a sample of low back pain claims for one large
corporation. For example, consistent and sincere communica-
tions to the workers about their “temporary work intolerance,”
their importance to the company, and the company’s willing-
ness to modify work until full recovery, may considerably alter
the composition of red balls in the injury-claimant experience
lottery. Instead of replacing the single red ball drawn with 21
more as discussed above, perhaps only 4 more are replaced.
Then the workers likelihood of a claim filing will rise from 5 to
8 percent rather than from 5 to 25 percent.
While the injury-claimant experience and heterogeneity dis-
ability lotteries suggest that repeat usage by some individuals
will be relatively common, the reasons for subsequent use
might vary. In the heterogeneity model, the subsequent use is
the result of innate differences across workers; in the injury-
claimant experience model, it is because their initial experience
develops a stock of claimant skills that lowers the cost of filing
subsequent workers’ compensation claims.
Distinguishing Heterogeneity Patterns from
Claimant-Injury-Experience Patterns
To distinguish between injury-claimant experience and hete-
rogeneity models we need to follow workers over multiple yea-
rs beyond the initial claim. Consider claim patterns for several
years, where in a given year, “0” denotes no claim and “1”
denotes that a workers’ compensation claim has been filed. The
claims’ patterns for any given worker can be written as a string
of zeros and ones moving left to right. In the first four years we
might observe patterns of runs such as (1111) for workers who
file a claim for each of their first four years at work, (0000) for
those filing no claims during their first four years, and (1010)
for those workers in which a claim is filed in the first and third
years of employment.
If one starts with the premise that all urns initially had the
same, relatively small proportion of red balls, a (1111) pattern
might be seen as evidence of either injury-claimant experience
or heterogeneity. Similarly, a (0000) pattern may indicate indi-
viduals with low propensities to file claims, either because
there are few balls in their own urns (heterogeneity) or because
the absence of initial claims never increased their propensity to
file future claims.
In Tables 1(a) and (b), we present some of the runs patterns
for new hires in a single company. The focus on new hires
means that all workers essentially come into our sample with
no prior workers’ compensation experience that we need to
take into account: the first “0” or “1” we observe is their first
on-the-job experience with workers compensation. (That is, to
avoid the “initial conditions” problems that arise from not hav-
ing a complete history of the workers’ claims experience for
each worker, we focus on the record of new hires with the
company.) Additionally, to control for other unobserved factors,
we examine workers in a single blue collar occupation. All
these employees work part-time in a single division of the
company. Hence we are able to control for what typically are
unobserved differences in the demand for labor. In these tests,
we use roughly 9 years of data. In Tables 1(a) and (b), we have
included all those patterns for new hires with at least 5 indi-
viduals in each run. As will become apparent below, patterns of
all zeros or patterns with all ones do not allow us to differenti-
ate between heterogeneity and injury-claimant experience, and
so are excluded from consideration in Tables 1(a) and (b). (For
the Table 2 sample of males, there are 3608 workers with a (00)
pattern, 1510 with a (000) pattern, 916 with a (0000) pattern,
57 with a (11) pattern, 8 with a (111) pattern, and 1 with a
(1111) pattern.)
One way to control for unobservable heterogeneity in the
composition of red balls is based on patterns containing equal
numbers of claims. For example, (001), (010), and (100) all co-
ntain one claim in three years and so are equally likely in terms
of the number of their occurrences as long as there is no clai-
mant-injury-experience effects. If there is no claimant-in-
jury-experience effect, the probability of observing only one
claim in three years should be independent of the year in which
the claim is filed. The Bernoulli model of the simple lottery
with no heterogeneity would also imply that equal probabilities
should be observed for the three patterns (011), (101), and (110).
A formal test of the Bernoulli model can be based on a com-
parison of the actual number of times each of these patterns
occurred with number of times we would expect a pattern to
occur if it were a Bernoulli model. For the female data in Table
1(a), since the (001), (010), (100) patterns are equally likely to
occur in the Bernoulli model (even with heterogeneity across
workers), then on average we expect each pattern to occur 104
times (the average of 83, 157, and 73). A simple chi-square test
comparing the actual number with the expected number yields
a value of 36.37, which rejects the null hypothesis of the Ber-
noulli model at the 1 percent level of statistical significance.
Similarly, the (011), (101) and (110) patterns should each occur
20.333 times (the mean of 27, 7, and 27). Again, the chi-square
rejects the Bernoulli model (at the 1 percent level, as it does for
all of the appropriate combinations of patterns in Tables 1(a)
and 1(b)). The assumption that a simple Bernoulli process is pr-
esent, with or without heterogeneity, is therefore not supported
by the data.
An alternative hypothesis is that there is injury-claimant ex-
perience, so that prior claims experience affects the probability
of filing a claim in the future. We explore the implications of a
general class of claimant-injury-experience models, the linear
experience dependency, or LED, models. In this family of
models, each year in which there is a claim, the likelihood of a
claim the following year increases by β. In each year in which
there are no claims filed, the probability of filing a claim sub-
sequently is reduced by α. If we assume that α = β = 0, then
there are no learning effects, and we get the Bernoulli process

R. J. BUTLER ET AL.
30
Table 1.
(a) Patterns of Workers’ Compensation Claims for New Hires Part-Time, Division A Females; (b) Patterns of Workers’ Compensation Claims for
New Hires Part-Time, Division A Males.
(a)
Pattern Actual Strong Led Rank Weak Led Rank Actual Strong Rank Actual Weak Rank
[01]
[10]
227
198
1
2
1
2
1
2
1
2
[001]
[010]
[100]
83
157
73
1
2
3
-
1
2
2
1
3
-
1
2
[011]
[101]
[110]
27
7
27
1
2
3
1
2
3
1
2
1
1
2
3
[0001]
[0010]
[0100]
[1000]
54
88
78
29
1
2
3
4
-
-
1
2
3
1
2
4
-
-
1
2
[0011]
[0101]
[1001]
[0110]
[1010]
[1100]
14
13
5
30
10
11
1
2
3
4
5
6
-
1
2
1
2
-
2
3
6
1
5
4
-
1
2
1
2
-
[00001]
[00010]
[00100]
[01000]
[10000]
25
30
29
30
7
1
2
3
4
5
-
-
-
1
2
3
1
2
1
4
-
-
-
1
2
(b)
Pattern Actual Strong Led Rank Weak Led Rank Actual Strong Rank Actual Weak Rank
[01]
[10]
401
295
1
2
1
2
1
2
1
2
[001]
[010]
[100]
134
243
102
1
2
3
-
1
2
2
1
3
-
1
2
[011]
[101]
[110]
32
9
33
1
2
3
1
2
3
2
3
1
2
3
1
[0001]
[0010]
[0100]
[1000]
60
101
103
41
1
2
3
4
-
-
1
2
3
2
1
4
-
-
1
2
[0011]
[0101]
[1001]
[0110]
[1010]
[1100]
16
20
6
31
7
7
1
2
3
4
5
6
-
1
2
1
2
-
3
2
5
1
4
4
-
1
2
1
2
-
[00001]
[00010]
[00100]
[01000]
[10000]
24
40
41
40
21
1
2
3
4
5
-
-
-
1
2
3
2
1
2
4
-
-
-
1
2
as a special case. If we assume that α = 0, and β > 0, then we
have a strong form of injury-claimant experience in which a
single claim increases future claim-filing propensities, while
several years of no claim experience doesn’t reduce claims-
filing propensities. Under this STRONG form of the LED
model, we would expect that the data would be ranked as they
are in the second column of Table 1(a). Under the strong form
of the LED model, the likelihood of observing (01) is simply
(1-P) × P; whereas the likelihood of observing (10) is P × (1 –
(P + β)), where P is the initial probably of filing a claim. Hence,
in the strong LED model it is the case that Pr(01) > Pr(10),
where Pr( ) denotes the probability of observing that sequence
of claims experience. Similar calculations within all the blocks
containing the same number of claims, as indicated by the “[ ]”
groupings, yields the ranking in the third column from the left
labeled “STRONG LED Ranks.”
This strong form of the LED model is too restrictive in its
predictions about behavior if continual employment without a
claim tends to lower the propensity of filing workers’ compe-
nsation claims. While there are many weaker versions of in-
jury-claimant experience, the one we find intuitively appealing
assumes that the likelihood of future claims rises more on av-
erage in a year in which there is a workers’ compensation claim
than it fails in a year in which there is no claim. The WEAK
version of the LED is the expected impact of experiencing a
claim is greater than the expected impact of a no-claims ex-
perience, or P × β > (1 – P) × α.
For relatively rare events like workers’ compensation where
P is initially much less than a half, this means that β will be
much greater than α. This simply suggests that experiencing a
claim will shift the likelihood of a future claim up much higher
in absolute terms than will a no-claims experience shift it

R. J. BUTLER ET AL.
downwards. It is relatively easy to show that this condition im-
plies the rankings given in the middle column under the head-
ing “WEAK LED Ranks.”
In general for any n-tuple pattern, the following three results
(which can be shown by some tedious algebra) hold:
RESULT 1: Pr(01,XYZ..) > Pr(10,XYZ..), where “XYZ..”
represents any specific subsequent pattern of zeros and ones, if
P × β > (1 – P) × α.
RESULT 2: Pr(0..0,01) > Pr(0..0,10), where “0..0,” repre-
sents n zeros preceding the last two indicated outcomes, if P ×
β > (1 – P) ·α + n· α · (α + β).
RESULT 3: Pr(1..1,01) > Pr(1..1,10), where “1..1,” repress-
ents n ones preceding the last two indicated outcomes, if P × β
> (1 – P) ·α – n · β ·( α + β).
These results are sufficient to generate most of the WEAK
LED rankings given in Table 2. This also suggests why pat-
terns like (0001) and (0010) cannot be ranked in the WEAK
LED case (result 2): the initial multiple rounds of no claims
experience means the worker is accumulating some “work”
experience that is impossible to weigh against future “claims”
experience without more specific assumptions, and so it is im-
possible to rank these cases under our WEAK rule without
specific knowledge of the values of α and β.
Finally, we are assuming that there is no depreciation of the
experience effect in these runs examples. This turns out, sur-
prisingly, to be a relatively reasonable assumption over our
sample period. We are able to examine this issue with a more
complex econometric analysis in Table 3.
Table 2.
Sample Means (and Standard Deviations).
Male 0.591 (0.47)
Married 0.507 (0.50)
Age 33.02 (6.81)
Tenure 6.41 (1.17)
Tenure Squared 42.30 (15.72)
Sample Size 3059
Table 3.
Workers’ Compensation Claims Logit Regressions.
Logit Regression
Logit Regression with
Random Effects
Intercept –3.188*** (0.34) –2.958*** (0.39)
lag 1 WC 0.508*** (0.10) 0.578*** (0.12)
lag 2 WC 0.487*** (0.10) 0.535*** (0.12)
lag 3 WC 0.453**** (0.10) 0.517*** (0.12)
lag 4 WC 0.618*** (0.10) 0.699*** (0.13)
lag 5 WC 0.490*** (0.12) 0.572*** (0.14)
discipline-New 0.230*** (0.06) 0.254*** (0.07)
discipline-Old 0.040* (0.02) 0.048* (0.03)
division A 0.381** (0.15) 0.434*** (0.17)
Male –0.249*** (–0.08) –0.274*** (–0.08)
Full-Time 0.392*** (–0.13) 0.401*** (0.15)
–2 log Likelihood 5197.93 5195.11
N 7.869 7.869
Notes: All regressions (including the random effects logistic regression) include
year and work site dummy variables that are not reported here. The random ef-
fects model also included other “intercept” values and probability of support
parameters. ***= significant at 1% level; **= significant at 5% level; *= significant
at the 10% level. Tests could not reject the null hypothesis that the lagged WC
injury experience coefficients had the same values (indicates no depreciation of
the injury experience effects).
Sample and Empirical Results
From the sample means presented in Table 2, it is clear that
focusing on new hires results in a working population that is
both relatively young (about 33 years old) and with only 6 or 7
years of experience with the company on average. Besides try-
ing to control for initial conditions and demand-side forces by
looking only at the newly hired, we have focused on just one
blue collar occupational group working for one US firm. The
complete sample has part-time division-A workers, all of whom
qualify for workers’ compensation insurance. Workers are mo-
stly males, about half of whom are married. We chose to ana-
lyze part-time workers in Tables 1(a) and (b) specifically be-
cause they are not eligible for the employer-provided disabil-
ity benefits, thus eliminating another possible confounding in-
fluence of workers’ compensation claims.
The comparison of the expected ranks with the actual ranks
indicates little support for the STRONG version of the LED
model. However, all of our results are consistent with our weak
LED ranks given injury-claimant experience except for the
“[011], [101], and [110]” blocks in Table 1(b) (for males). We
believe that these results are strongly suggestive of injury-
claimant experience, especially as they hold demand heteroge-
neity constant. They imply that experiencing a workers’ com-
pensation claim now has a much greater effect on subsequent
claimant behavior than working now has on the subsequent
likelihood of working. While prior research has found that
males and females differ in their workers’ compensation ex-
perience (Worrall, Appel, and Butler, 1987), ceteris paribus,
we found statistically significant (using chi-square tests) evi-
dence of weak LED ranks supporting injury-claimant experi-
ence, for both males and females.
Regression Model Counterpart
Table 3 expanding the non-parametric runs test in Table 1 to
a parametric setting (logistic regression), indicates that the most
consistent results are that disciplinary action increases the
probability of entering into the disability system, and that prior
use of the system increases the likelihood of filing future claims.
The results in Table 3 indicate that a disciplinary notice (given
for poor job performance, not for health-related reasons) is
likely to increase the probability of filing a WC claim from
about 12 to 15 percent, even after controlling for benefits-con-
sumption-capital effects. Past disciplinary notices also signify-
cantly increase the likelihood of filing a claim, although the
effect is only about one fourth as strong as the effect of a cur-
rent disciplinary notice.
The estimated injury-claimant experience effects are sub-
stantial, even after controlling for heterogeneity using a random
effects model (in the right hand column). Tests indicate that the
effect of prior claims on current claim filing remains strong for
at least 5 years after a claim is filed. The chi-square tests cannot
reject the null hypothesis that the lagged coefficients all have
the same value. Since we cannot reject this null hypothesis,
there appears to be no depreciation in injury-claimant experi-
ence effects for the first five years after a claim. If we take 0.5
as a conservative estimate of prior experience on current claims
probability, then each prior claim increases the current prob-
ability of a claim by slightly more than 5 percent. Those who
have experienced claims in 2 of the past 5 years are almost
twice as likely to file a claim this year as someone who has not
experienced any prior claims.

R. J. BUTLER ET AL.
32
Summary and Conclusions
A common financial risk management problem, both at the
level of nations and for individual firms, is to distinguish risks
that can be changed by some sort of intervention from risks that
cannot be changed. Firms struggling to reduce medical-care
costs or disability costs are searching for ways to manage bene-
fits programs to achieve that end. Crucially important is under-
standing why some employees file disability claims at a much
higher rate than others do. Is it simply an intrinsic difference in
health status or does participation in the disability-insurance
system lead to an injury-claimant experience effect that in-
creases the filing of subsequent claims quite apart from health
status?
To answer this question, we analyzed individual blue-collar
employee data from a large private US firm using “runs” tests
that analyze patterns of claims filings and compares these with
a random Bernoulli process. The runs test indicates that claims
filings are not a simple random lottery nor a heterogeneity lot-
tery (without injury-claimant experience). Therefore, health
status and/or “injury-claimant experience” effects on claims
filings seem to be a potentially significant explanation, a priori.
Though firm characteristics (“demand conditions”) are held
constant because all employees come from the same firm with a
common overall workplace risk environment, these runs test
imposes two restrictive assumptions: 1) differences in workers’
socio-economic characteristics don’t affect outcomes; and 2)
there is no depreciation of the “injury-claimant experience”
effect over time. While our sample of new employees from one
firm offers more advantages over samples ranging across firms,
occupations, and unmeasured differences in the human re-
source/employee benefits environments, the analysis still suffer
from potentially unmeasured, time-varying factors, including
the underreporting of workplace injuries (Boone and van Ours,
2006). Nonetheless, our results suggest that the potential im-
portance of injury-claimant experience in workers’ compensa-
tion warrants the scrutiny of this important result in future re-
search. Clearly, the empirical ideas and models here also may
have application to the behavior of other entities subject to
financial risks, such as banks and countries within a common
currency zone.
These findings have important implications for firm and pub-
lic policy. It would appear that resources invested in reducing
injury-claimant experience effects, as well as improving the
health status of employees, would have large payoffs in reduc-
ing insurance costs and productivity losses (Butler, Johnson,
and Gray (2007) provide analogous results for a different sam-
ple using a different statistical approach). Exactly what the
appropriate early intervention strategy should be, whether ap-
plied internally by the firm and perhaps through changes in the
mandated workers’ compensation system, is a question that
should receive the attention of private managers and public
policy makers.
Acknowledgements
We are grateful for computing support from the Industrial
Relations Center at the University of Minnesota, and the De-
partment of Economics at Brigham Young University. Helpful
comments were received in seminars at the Risk Theory Soci-
ety Meeting, Columbia University, Cornell University, and the
University of Minnesota. We especially wish to thank Steve
Cameron, John Budd, and Brian McCall for comments on ear-
lier drafts.
REFERENCES
Boone, J., & van Ours, J. C. (2006). Are recessions good for workplace
safety? Journal of Health Economics , 25, 1069-1093.
doi:10.1016/j.jhealeco.2006.03.002
Butler, R. J., & Gardner, H. H. (2011). Moral hazard and benefits con-
sumption capital in program overlap: The case of workers’ Com-
pensation. Foundations and Tren ds in Microeconomics, 6, 1-52.
Butler, R. J., & Worrall, J. D. (1985). Work injury compensation and
the duration of non-work spells. Economic Journal, 96, 714-724.
Butler, R. J., Johnson, W. G., & Gray, B. (2007). Timing makes a dif-
ference: Early employer intervention and low back pain. Professional
Case Management Journal, 12, 316-327.
Chamberlain, G. (1980). Analysis of covariance with qualitative data.
Review of Economic Studies, 47, 225-238. doi:10.2307/2297110
Corak, M. (1993). UI once again: The incidence of repeat participation
in the Canadian UI Program. Canadian Public Policy, 19 , 162-176.
doi:10.2307/3551680
Heckman, J. J., & Borjas, G. J. (1980). Does unemployment cause
future unemployment? Definitions, questions and answers from a
continuous time model of Heterogeneity and state dependence. Eco-
nometrica, 47, 247-283.
Lemieux, T., & MacLeod, W. B. (1995). State dependence and unem-
ployment insurance. Human Resources Development Canada, mimeo.
McCall, B. P. (1995). Repeat use of unemployment insurance. Indus-
trial Relations Center, Minnesota: University of Minnesota.
Moffitt, R. (1992). Incentive effects of the US welfare system: A re-
view. Journal of Economic Literature, 30, 1-61.
Ruser, J., & Butler, R. J. (2010). The economics of occupational safety
and health. Foundations and Trends in Microeconomics, 5, 301-354.
Worrall, J. D., Appel, D., & Butler, R. J. (1987) Sex, marital status, and
medical utilization by injured workers. Journal of Risk and Insur-
ance, 54, 27-44. doi:10.2307/252880