The paper develops frequency distribution of annual health expense for a variety of family compositions. The basic data resource was a sample of claims for a large group of federal employees in 1977. The primary data were compared in several aspects against three other sources of reference data on expenses by the non-aged population; the comparisons were reassuring. The method of convolution is used to obtain family frequency distributions from the distribution for individual adults and children. This technique is necessary when the claims data do not record family com-position. In consequence, the results may not be nationally representative of households which are relatively large or affected by unemployment. Aside from this special reservation, the experience of the non-elderly federal employee families seems to be a useful resource for policy analysis.

Bernard Friedman

English

Research Papers in Economics

NBER WORKING PAPER SERIES
DISTRIBUTIONS OF FAMILY HOSPITAL
AND PHYSICIAN EXPENSES
Bernard Friednan
Working Paper No. 510
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
CambridgeMA02138
July 1980
Martin Feldstein gave substantial advice. Francis Atorick of Aetna
Life and Casualty and Richard Hanschu of Michigan Blue Cross
Associationgenerously contributed data resources and helpful
discussions. The research reported here is part of the NBER's
research project in health insurance. Any opinions expressed are
those of the author and not those of the National Bureau of
Economic Re search.NBER Working Paper #510
July, 1980
Distributions of Family Hospital
and Physician Expenses
ABSTRACT
The paper develops frequency distribution of annual health expense
for a variety of family compositions. The basic data resource was a
sample of claims for a large group of federal employees in 1977. The
primary data were compared in several aspects against three other sources
of reference data on expenses by the non—aged population; the comparisons
were reassuring.
The method of convolution is used to obtain family frequency distri-
butions from the distribution for individual adults and children. This
technique is necessary when the claims data do not record family com-
position. In consequence, the results may not be nationally representative
of households which are relatively large or affected by unemployment.
Aside from this special reservation, the experience of the non—elderly
federal employee families seems to be a useful resource for policy analysis.
Bernard Friedman
Department of Economics
Northwestern University
Evanston, Illinois 60201
(312) 492—5690March, 1980
Distributions of Family Hospital and
Physician Expenses
Bernard Friedman *
NorthwesternUniversity
The purpose of this report is to develop and discuss some new frequency
distributions of family health expenses. Such distributions, if nationally
representative of non-aged, non-poor, households wculd be useful for eval-
uating proposals for new health insurance programs.
Ideally, these distributions would be obtained from a large sample of
families, using insurance company and household records under the following
conditions: the composition of each enrolled family is known; all families
have the same insurance coverage that is extensive by current standards;
there was no selection bias in the observed population. These ideal require-
ments cannot be met with any single available data resource. There are a
variety of imperfect data resources, any of which should be used only with
caution and after cross-checking for significant discrepancies.1"
In this report, expenditure distributions are developed from the claims
experience of a large group of federal employees in 1977. Several character-
istics of this data will be compared with other sources such as per capita
spending computed at HEW, claims experience at Blue Cross-Blue Shield of
Michigan, and claims experience of Metropolitan Life employees. The compar-
isons are rather reassuring.
*The research reported here is part of an NBER project on health insurance.
nyopinionsexpressed are those of the author and not those of the National
Bureau of Economic Research. Martin Feldstein gave substantial advice. Francis
Atorick of Aetna Life and Casualty and Richard Hanschu of Michigan Blue Cross
Association generously contributed data resources and helpful discussions.-2-
Some interesting questions about the impact of new insurance
programs would require much more disaggregated detail than is attainable
with present resources. For example, the sources of family income,
education, age and occupation of members are likely to affect the responses
of sub-populations to insurance changes. Also, health care supply conditions
vary geographically and therefore consequences of insurance innovation will
also vary with location. The present resources and analysis allow direct
disaggregation only by family size, and are primarily relevant to aggregate
budgetary and service demand consequences of insurance changes.
Sampled Population nd Insurance Coverage
In 1977, there were approximately 862,000 persons insured under the
high-option Indemnity Plan (Aetna Life and Casualty) for federal employees.
The persons insured are either enrollees (employees and annuitants), spouses,
or dependent children under age 19 or full-time students to age 23 or disabled
children with no age limit.
Each enrollee represents a "contract." There were about 274,000
contracts headed by an enrollee under age 65. These contracts, contain-
ing about 452,000 adults and 277,000 children are the reference population
for the ensuing analysis. The enrollees had a choice of several insurance
plans, each having an experience-rated premium paid partly by the enrollee.
The 1977 premium (including both employer and subscriber payments) for family
coverage was 960 per year for the Aetna plan, which was somewhat lower than
the premium for the more popular Blue Cross-Blue Shield option. The BCBS
plan has more complete "first-dollar" coverage than the Aetna, but the two
are comparable in the coverage of large expenses. The possible selection
bias is that Aetna families may expect to incur fewer moderate health care
needs than the average federal employee family.-3-
Virtually all health care expenses are covered in the Aetna plan
except dentistry, routine checkups or well-baby care, eye glasses or
eye examinations. The family is responsible for 207 of hospital room
and board expenses after 2000, 207,, of all other hospital expenses, the
first 75 and then 207 of ambulatory care. Family copayment ends when
l0,00O of gross expense is exceeded. This is a clear instance of
"catastrophic" coverage. Further general information on enrollment and
coverage may be found in publications of the U.S. Civil Service Commission.
(Annual Reports, booklet BR1 41-24, and Federal Fringe Benefit Facts, 1978)
Claims Experience
The Aetna company has prepared a l07 sample of all contracts with
claims for occurrences in 1977. The resulting file contains the annual
experience of each of 25,197 persons under age 65. The exact family
composition of each claimant contract is unknown, as is commonly the
case in insurance claim statistics. Therefore, the size distribution
of expense for a particular family composition cannot be simply observed.
Instead, each family composition must be synthesized from the individual
distributions for adults and children. This procedure will be addressed
in a later section.
The average annual covered expense appearing on claims was approximately
279 per insured person. Persons not submitting claimsmay have had some
expense. This average is only 5% lower than the experience of Blue Cross-
Blue Shield of Michigan (BCBSM) with more than 2 million regular (non-aged)
contracts in force. More specifically, for BCBSM the average claimed
charges per person insured in 1977 were 296. Health care prices in
Michigan are slightly higher than the national average, and there are more-4-
blue-collar worker families than in the federally employee population.
This comparison is therefore somewhat reassuring about the national
representativeness of the Aetna data.
The upper tail of the distribution of claimed expenses is a matter
of great interest for current policy discussions. In Table 1 below, the
Aetna and BCBSM results are compared in a gross fashion permitted by
published data.
Table I
Distribution of Contracts with Claims
Expense Category Relative Frequency
_______ Aetna BCBSM
a0-10,000 .9826 .9862
10 -50,000 .0171 .0135
50,000 + .0002 .0002
(Spurce for BCBSM: Blue Cross Association, Perspective, Spring, 1979,
and private communication)
These data again do not suggest serious incompatibility between the
reference population and Michigan families. Apparently, the Aetna group
had relatively more large claims, but because of greater "first-dollar"
coverage or other factors, the average expanse for families in the lower
category was higher in Michigan.
A second population with which the Aetna group may be compared is
the population of employees of Metropoligan Life, whose headquarters is
in New York City. The Metropolitan claims experience for 1965-1975 has
been applied in policy analysis by the Congressional Budget Office.
Table II compares the upper tail of claimed expenses for Aetna
federal employees and Metropolitan employees. The crudest comparison
between the first and third columns, shows a greater proportion of expenses-5-
in the upper tail of the Aetna group. Partly, this is due to the
increase in per capita hospital and physician expenses of 227,, between
1975 and 1977. Also, the Metropolitan plan has more "first-dollar"
coverage. After adjusting all Aetna claims proportionally for inflation,
the two distributions are quite comparable.
Table II
Expenses in the Upper Tail of Contracts
Proportion of Expenses in Contracts
over Limit
adjusted for Metropolitan
Limit Expense Aetna, 1977 inflation 1975
5,000 .398 .328 .284
10,000 .223 .169 .154
15,000 .140 .110 .092
50,000 .011 .011 NA
The size distribution of expenses for an individual is reported in
Table III. Spouses have been omitted, but their average expense was only
47, greater than that of enrolled adults. All non-claiming adults were
assumed to have 34 in ambulatory medical expenses. This amount is
derived from results of the Current Medicare Survey, a panel study using
diaries of expense for individuals who do not meet a deductible on
comprehensive ambulatory services. Children without claims were assumed
to have 40 in routine uncovered expense.-6-
TABLE III: SIZE DISTRIBUTION OF EXPENSES FOR INDIVIDUALS
*
Expense Enrolled Adult Child
Category Avg. Freg. Avg. Freg.
O- 50 34 .5882
' 39 .7067
-100 77 .0438
: 75 .0687
-250 168 .1235 162 .llO9
-500 356 .0891 348 .0553
-1,000 705 .0564 716 .0313
-2,500 1602 :0524
,1,514 .0194
-5,000 3493 .0280 '3,343 .0047
—7,500 6003 .0078
,6,029 .0011
-10,000 8712 .0041
'8,639 .0004
-15,00O 11757 .0037
,12,592 .0006
-25,000 18763 .0022 18,824 .0003
-50,000 32229 .0007
•35,484 .0003
50,000-I- 82746 .0000 80,077 .0000
Number of claimants in Sample: 12,365 ,10,151
107, of covered persons: 27,400 '27,758
Mean Expense: 490 fl87
*under age 65-7-
The mean results in Table III can be compared with official estimates
of national per capita expense in 1977. For the national per capita
expense in Table IV below, dentistry, eyeglasses and nursing home care have
been eliminated, and the fiscal year rather than calendar year is available.
TABLE IV: MEAN EXPENSES PER PERSON, 1977
National Aetna
under 19 2l4 fl87 (-137.)
19-64 581 49O (-16%)
(Source for national data: R. Gibson and C. Fisher,
"Age Differences in Health Care Spending, Fiscal
Year 1977." Social Security Bulletin, January, 1979.)
The table shows, presumably, the net effect on the two populations of
differences in geographic concentration, age, income, education, insurance
coverage, health status or other factors. The apparent difference between
the groups would be narrowed if an appropriate share of drugs and other
health services (e.g., psychiatric) were deducted from the national means.
In some previous investigations, federal employee group expenses have been
said to overestimate national averages. The present analysis may have
reversed this perception by using an age limit. It is noteworthy that the
Michigan experience would also tend to fall short of the national averages
in Table II. These findings suggest that private insurance data would
tend to underestimate the experience of persons eligible for comprehensive
Medicaid assistance.-8-
Family Expenses
In the previous section I explained why family experience cannot be
simply tabulated from claims records. In this section, family experience
is estimated by the method of convolution. The method of coavoluting inde-
pendent random variables is as follows. Consider a two-person family, so
that family expense, Ef is the sum of expense for individual 1 and
individual 2.
Ef =E1+ E2
x
Then Prob [Ef=X}=EProb [E1 =Z}Prob {E2 =X-Z}
z=O
Inthe case of independent distributions, a family distribution for any
particular composition is easily synthesized by a sequence of pairwise con-
volutions. There are, however, reservations that should be attached to the
independence assumption. Contagious disease and accidents suggest a positive
correlation among the expenses of family members. Also, conformity of
decision-making in the family suggests a positive correlation. If we took a
sample of individuals living alone and estimated family experience using the
independence assumption, we would expect to underestimate the variance of
family expense because of positive intra-family correlation. Our sample is
not individuals living alone, so there is not necessarily a distorted result.
The problem of bias from the independence assumption is more acute the
farther we depart from modal family size in the sample (which has a mean of
3.3 persons per contract). In the case of large families, it is quite pos-
sible that average family expense will be overestimated. There may be economies
of scale in knowledge and treatment as in other areas of family life. Also,
if there is a general association of larger family size with lower income this-9-
would suggest reduced health expense per person.
Families with a composition close to the sample mode can be estimated
with unknown but perhaps tolerable bias until better data are available.
Tables Va through Vf below present a variety of family distributions
synthesized from the Aetna individuals.
The hazards of the independence assumption have this implication for
analysis of new insurance programs: effects on small, very large, or
unemployed households are not confidently predicted by the Aetna federal
employee experience. However, for medium-sized households in the non-elderly
employed population, the Aetna data seem to be a valuable research resource.Table Va
Expenditure Distribution: One Adult and One Child
Relative Cumulative Share
Expense Interval Average Fregency of Expenses
-250 111 .65598 117.
-500 386 .11771 17.9
1,000 719 .09529 . 28.2
2,500 1629 .07617 46.9
-5,000 3568 .03275 64.5
-7,500 6051 .00932 73.0
-10,000 8755 .00458 79.0
-15,000 11978 .00446 87.1
-25,000 18896 .00249 94.1
-50,000 33411 .00098 99.2
50,001 + 81420 .00008 100.2
.9998 1
Mean Expense =663Table Vb
Expenditure Distribution: One Adult and Four Children
Relative Cumulative Share
Expense Interval Average Fregency of Expenses
-250 235 .26884 5.67.
-500 378 .22603 13.3
-1,000 737 .25604 23.9
-2,500 1718 .16661 49.5
-5,000 3760 .04799 65.7
-7,500 6131 .01500 74.2
-10,000 8862 .00632 79.0
-15,000 12453 .00676 86.5
-25,000 19249 .00353 92.6
-50,000 34934 .00188 98.4
50,001 + 80892 .00021 100
.99921
Mean Expenseft117Table V
Expenditure Distribution: TwoAdults
- 1,000
-2,500
-5,000
-7,500
-10,000
-.15,000
-25,000
-50,000
Average
111
386
714
1658
3600
5998
8756
11906
18934
32582
81981
Relative
Frequency
.55560
.12787
.11516
.10767
.05326
.01787
.00863
.00788
.00458
.00141
.00008
1.00001
Cumulative Share
of Expenses
6.87.
12.3
21.4
41.1
54 .1
66.0
74.3
84.7
94.3
99.4
100
Mean Expense =904
Expense Interval
-250
-500
50,001 +Table Vd
Expenditure Distribution: Two Adults and One Child
Relative Cumulative Share
Expense Interval Average Frequency of Expenses
-250 56 .45479 6.1Z
-500 398 .15594 11.5
-1,000 737 .15232 21.2
-2,500 1693 .13425 40.9
-5,000 3669 .05765 59.2
-7,500 6034 .02007 69.7
-10,000 8796 .00930 76.8
-15,000 12059 .00871 85.9
-25,000 19060 .00497 94.1
-50,000 33328 .00171 99.1
50,001 + 81363 .00013 100
.99984
Mean Expense =1154Table Ve
Expenditure Distribution: TwoAdultsand TwoChildren
Expense Interval
-250
-500
-1,000
-2,500
-5,000
-7,500
-10,000
-15,000
-25,000
-50,000
50,001 +
Average
179
355
748
1723
3732
6066
8826
12192
19170
33852
81109
Relative
Frequency
.26753
.25989
.19652
.16369
.06245
.02240
.01002
.00958
.00535
.00202
.00017
.99962
Cumulative Share
of Expenses
3.67
10.6
21.6
42.9
60.4
70.6
77.3
86.1
93.8
99.0
100
Mean Expense = 1328Table Vf
Expenditure Distribution: Two Adults and Four Children
- 500
-1,000
-2,500
-5,000
-7,500
-10,000
-15,000
-25,000
-50,000
Mean Expense =1675
Average
358
788
1784
3856
6141
8897
12447
19405
34681
80952
Relative
Frequency
0
.3 7308
.26385
.23046
.07233
.02750
.01165
.0 1132
.00616
.00263
.00025
.99923
8. 07
20.4
44. 9
61.6
71.6
77.8
86.2
93.3
99.5
100.7
Expense Interval
- 250
Cumulative Share
of Expenses
0
50,001 +NOTES
1/
During the 1980's more ideal data files should become
available from a major project of the National Center for
Health Statistics. Results of the Health Insurance
Experiment conducted by the Round Corporation will also be
forthcoming and should clarify the importance of selection
bias in insured groups.
2/
Indirect methods of disaggregated analysis are possible.
For example, experimental results or other studies may yield
reliable models of the effect of income and other variables on
health care demands, independent of insurance coverage. Then
the reported distributions in this paper could be used to
synthesize distributions for particular subpopulations.
3/
See U.S. Congressional Budget Office, "Catastrophic Health
Insurance," Budget Issue Paper (January, 1977). Analysis of the
Metropolitan claims was performed 'inder contract by Gordon Trapnell
who kindly provided the data presented in this paper.

Distributions of Family Hospital and Physician Expenses

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