an economic analysis of variations in medical expenses and ... · the expense data refer to the...
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This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research
Volume Title: Essays in the Economics of Health and Medical Care
Volume Author/Editor: Victor R. Fuchs, ed.
Volume Publisher: NBER
Volume ISBN: 0-870-14236-4
Volume URL: http://www.nber.org/books/fuch72-1
Publication Date: 1972
Chapter Title: An Economic Analysis of Variations in Medical Expenses and Work-Loss Rates
Chapter Author: Morris Silver
Chapter URL: http://www.nber.org/chapters/c3452
Chapter pages in book: (p. 97 - 118)
es:s.d,bs
An Economic Analysis of Variationsin Medical Expenses and
Rates Morris Silver
1. OBJECTIVES AND ORGANIZATIONThis paper employs a number of the standard tools of economic analy-sis to explore unpublished data on the medical expenses and work-lossdays due to iilness or injury of currently employed persons. Section 2deals with the data, statistical techniques, and variables employed inthe study. The primary objective of Section 3 is to estimate elasticitiesof demand for medical care (totally and by type) with respect to familyincome. Knowledge of these elasticities should contribute to more ac-curate forecasts of the demand for medical care and aid in the formula-
it tion of policy-related judgments concerning the equity of the currentdistribution of medical services.
a Like earlier studies of the demand for medical care1 which haveS NOTE: This paper appeared previously in Herbert E. Kiarman (ed), Em-J pirical Studies in Health Economics; Proceedings 0/ the Second Conference on
a the Economics of Health, Baltimore, Johns Hopkins Press, 1970, pp. 121—40.This research was carried out at the National Bureau of Economic Research
and was supported in part by grants from the Commonwealth Fund and by theNational Center for Health Services Research and Development, Grant1POICHOO374—0l. I am indebted to Richard Auster, Gary Becker, Michael Gross-man, Irving Leveson, Jacob Mincer, Kong-Kyun Ro, and, most of all, to Victor R.Fuchs for many helpful comments. Special thanks are due Mrs. Geraldine A.Gleeson, Chief, Analysis and Reports Branch, Division of Health Interview Statis-tics, National Center for Health Statistics, United States Public Health Service, forproviding me with the work-loss and medical expense data.
1 Paul J. Feldstein and Ruth Severson, "The Demand for MedicalReport of the Commission on the Cost of Medical Care, Chicago, AmericanMedical Association, 1964, pp. 57—76; Grover Wirick and Robin Barlow, "TheEconomic and Social Determinants of the Demand for Health Services," in TheEconomics of Health and Medical Care, ed. S. J. Axeirod, Ann Arbor, The
98 Essays in the Economics o/ Health and Medical Careutilized other bodies of data, the present study utilizes data on medicalexpenses to measure the amount of care received. Expense data areuseful because, unlike the available physical measures, they reflect not honly the quantity but the quality of medical care. On the other hand,the use of expense data creates a number of problems (e.g., free care)which are given detailed consideration in Section 3.
Unlike many previous studies, this study makes use of grouped or"ecological" data. The use of average incomes to estimate income elas-ticities which describe individual behavior can be justified in two ways.First, grouped data should minimize "simultaneous-equation bias."The individual correlation between income and medical care will re-flect not only the effect of income on the amount of medical care de-manded but also the effect of health on income. This problem would bemore severe for individual than for grouped data because individual ehealth is affected not only by differences in "erratic" factors amonggroups but by intragroup variations in such factors. Second, measure-ment errors (including transitory influences) in individual incomes
2would lead to underestimates of regression coefficients even if theseerrors were not correlated with the true (or long-run) individual in-comes.2 Errors of this type often cancel out in grouped data.
One of the important innovations of Section 3 is the inclusion of theearnings rate with family income in the regressions. This allows empiri-cally for the previously ignored possibility that higher-income individualsmay need more medical care or use less patient—time-intensive methodsof dealing with their medical problems.
The mortality rate has been the most widely used measure of healthfor many years, but the recent growth of quantitative interest in thedeterminants of health status has sharply increased the demand formore flexible measures. One of the most promising alternative measures
University of Michigan Press, 1964, Pp. 95—125; Paul J. Feldstein and W. JohnCarr, "The Effect of Income on Medical Care Spending," Proceedings of theSocial Statistics Section of the American Statistical Association, 1964, pp. 93—105.For useful summaries, references to the literature, and discussions of many ofthe relevant issues in the theory and empirical application of the demand formedical services, see Herbert E. Kiarman, The Economics of Health, NewYork, Columbia University Press, 1965, chap. 2; Paul J. Feldstein, "Researchon the Demand for Health Services," Mi/bank Memorial Fund Quarterly 44,July 1966, Pp. 128—62; and Jerome Rothenberg, "Comment," Proceedings of theSocial Statistics Section of the American Statistical Association, 1964, pp. 109—10.See also Part III of this volume.
'J. Johnston, Econometric Methods, New York, McGraw-Hill Book Co., 1963,pp. 148—SO.
I
Medical Expenses and Work-Loss Rates 99
of health is the work-loss rate due to illness or injury. Section 4 at-tempts to test the validity of using the work-loss rate as a measure ofhealth by ascertaining whether variations in work-loss rates reflect dif-ferences in the degree to which individuals can afford to lose income orin the amounts that would be lost, and, if so, the extent to which theydo so. The principal findings of the study are summarized in Section 5.
2. DATA, VARIABLES, AND STATISTICAL TECHNIQUESThe medical expense and work-loss data analyzed are drawn from theNational Health Survey of the National Center for Health Statistics.These data, which are restricted to currently employed persons, are inthe form of averages for each of twenty-four groups, by regions (North-east, North Central, South, and West), age group (17—44, 45—64, and65 and over), and sex.
•
. The information was obtained through household health interviewsand mail-in questionnaires left after completion of the interviews. Theaverages for medical expenses are based on a. sample of about 71,000persons from 22,000 households and include all medical bills paid, orto be paid, by the ill person, his family or friends, and any part paidby insurance. The average work-loss rates are based upon a sample of134,000 persons from 42,000 households. The expense data refer tothe twelve months prior to the interview period of July 1, 1962—Decem-ber 31, 1962, while the work-loss data refer to the interview periodJuly 1962—June
The primary data utilized in the paper are shown in Table 6-1. The
data for the quantitative independent variables are, of necessity, alsoin the form of averages for each of the twenty-four region-age-sex cellsand refer to employed persons at work. However, those averages whichrefer to 1959 or 1960 are derived from a different sample than themedical expenses and work-loss rates, the l-in-1,000 sample of thecensus of
For more detailed discussions of the work-loss and expense data, see U.S.Department of Health, Education, and Welfare, Public Health Service, NationalCenter for Health Statistics, Personal Health Expenses per Capita Annual Ex-penses, United States: July—December 1962, Vital and Health Statistics, series 10,no. 27, Washington, D.C., 1966, and Disability Days in the United States: July1963—June 1964, Vital and Health Statistics, series 10, no. 24, Washington, D.C.,1965.
'U.S. Department of Commerce, Bureau of the Census, Census of Populationand Housing, 1/1,000 and 1/10,000: Two National Samples of the Populationof the United States, Washington, D.C., 1960.
'I
I
100 Essays in the Economics of Health and Medical CareThe more important variables employed in the multiple regressions ii
of Sections 3 and 4 are listed below and discussed when appropriate.
I
tia
d
-4
iit(
TABLE 6-1Selected Data on Medical Expenses and Days Lost from Work, by
Age Group and Sex
RegionAge
Group Sex
Average MedicalExpenses per
Currently EmployedPerson per Year(July—December
1962)
Average Days Lostdue to Illness or
Injury per CurrentlyEmployed Person perYear (July 1962—June
1963)
NENENE
17—44
45—64
65 and
MMM
$106.99
175.12
228.89
3.5
7.1
8.2
NENENE
over
17—44
45—64
65 and
FFF
154.47
193.81
269.79
6.5
8.7
6.4
NCNCNC
over17—4445—6465 and
MMM
90.30161.00190.45
3.96.9
10.6
NCNCNC
over
17—44
45—64
65 and
FFF
129.83
181.17
163.53
5.5
6.7
5.4
S
S
S
over
17—44
45—64
65 and
MMM
95.50
156 .02
175.12
5.4
9.8
13.8
S
S
S
over
17—44
45—64
65 and
FFF
140.95
168.23
142.09
6.5
6.3
7.1
WWW
over
17—44
45—64
65 and
MMM
114.59
192.37
203.94
4.8
6.2
9.8
WWW
over
17—44
45—64
65 and
over
FFF
216.81
249.30
183.05
6.6
6.0
7.5
4.
Medical Expenses and Work-Loss Rates 101
Dependent Variables:Y1, total medical expense per currently employed person per yearY2, hospital expense per currently employed person per yearY3, medicine expense per currently employed person per yearY4, doctor expense per currently employed person per yearY5, dentist expense per currently employed person per yearY8, days lost from work due to illness or injury per currently em-
ployed person per year
Independent Variables:5
Average weekly earnings are obtained by dividing mean total earn-ings for a given cell by its mean number of weeks worked. Earningsper day are estimated by dividing the above quotient by 5; the resultingdollar figure is multiplied by mean work-loss days in the cell to obtainthe value of lost time, which is then added to X15.
X1, adjusted mean total family income for employed persons at workwho are in familiesunadjusted mean total family income for employed persons atwork who are in families
Xld, 0 if adjusted mean total family income for employed persons atwork in families (X1) is below its median value; the actualvalue of X1 when it is above its median
X2, 0 for female, 1 for maleX3, region: 0 for non-South, 1 for SouthX4, age: 0 for 17—44, 1 for 45—64, 2 for 65 and overX3 and X4 are the primary measures of region and age utilized in the
study. The forms of these variables are derived from a priori considera-tions and from a desire to conserve degrees of freedom, to limit multi-collinearity problems, and to avoid exhausting the sample space. Theage variable is the most controversial, but it is important to note thatthe possibility that its use biases the coefficients of the economic vari-ables upon which our interest centers is lessened by the use of a varietyof regression forms. However, as an additional precaution, key resultsare checked by replacing with:
X5, age: 1 if age 17—44, 0 otherwiseand
X5, age: 1 if age 45—64, 0 otherwiseThe following midpoints were assumed for open-ended classes: total family
income of employed persons at work in families (Item 60, Code X), $60,000;total earnings of employed persons at work (Item 39, Code X), $40,000;highest grade of school completed by employed persons at work (Item 26,Code X), 17.5 years.
S
102 Essays in the Economics of Health and Medical CareX7, mean highest grade of school completed by employed persons
at workX8, percentage of employed persons at work residing in rural areas
percentage of employed persons at work residing outside SMSA'sX10, percentage of employed persons at work who are married with
spouse presentX11, percentage of employed persons at work who are NegroX12, earnings per week worked of employed persons at work (esti-
mated by dividing mean total earnings in 1959 for those withearnings by the mean number of weeks worked in 1959 by thosewho worked)
Since the relevant bodies of theory do not specify functional forms,both natural values and a logarithmic transformation are employed.Further, the regressions are run in both unweighted and weighted form,in which the weights are the square roots of the number of persons ineach of the twenty-four region-age-sex cells. The use of weights is de-signed to achieve homoscedasticity and reduce the chances of errorsin regression coefficients caused by large random errors in a smallcell. However, unweighted regressions are run also because relevantinformation might be lost by the assignment of low weights to smallbut extreme cells (e.g., those for the 65-and-over age group).
3. REGRESSION ANALYSIS OF MEDICAL EXPENSES
The primary objective of this section is to estimate elasticities of de-mand for medical care with respect to command over goods and serv-ices. Amounts of medical services received are measured by the meanmedical expenses of currently employed persons in a region-age-sexcell (Y1—Y5), while command over goods and services is measured bya cell's adjusted mean total family income for employed persons atwork who are in families (X1).
An important advantage of expense data is that they reflect both thequantity and quality of medical care, whereas the available physicalmeasures (e.g., physician visits) reflect only the quantity. However, asin previous studies, the use of expenses gives rise to a number of diffi-culties. First there is the (probably minor) problem of "free" carewhich is received by some currently employed persons with very lowincomes but is not included in the expense data. Second, medical careprices may be positively correlated with income because physicianscharge the more affluent higher prices for given services, or because
Medical Expenses and Work-Loss Rates 103
the more affluent are more likely to have health insurance and thosecovered by insurance are charged higher prices.6 Third, and most im-portant, when more affiudnt individuals are ill or undergoing preventivecare, they attempt to maintain their customary living standards bypurchasing amenities and complements to medical care such as private
I hospital rooms and "Park Avenue doctors." As a result, the medicalexpenses of the more affluent overstate the amount of medical carethey have received.
- The available data do not permit dealing with the last two problems.I However, the purchase of amenities is probably most important in the
case of hospital expense, and the data do permit the estimation ofseparate income elasticities for the various components of medical care.
As has been pointed out in Section 1, the use of mean incomes helpsto minimize bias due to errors of measurement and simultaneous-equa-tion problems. However, if variables not included in the statisticalmodel reduced health in certain of our region-age-sex cells and resulted
- in higher medical expenses and lower family income, income elasticitieswould still be biased. In order to deal with this possibility, data for each
i region-age-sex cell on average earnings rates and work-loss days dueto illness or injury were used to estimate the value of working time lost
1due to poor health. These estimates were added to the mean familyincome figure for each of the cells to secure "adjusted" mean total familyincome (X1), which was utilized in the regressions.
Since higher-income individuals can afford to purchase more andbetter medical care and are unlikely to prefer purchases of other types
- of consumer goods when they are ill, and since it seems unlikely that- most consumers regard the services provided by preventive medical
care as lower-quality members of some broader family of services (asis margarine in the family of table fats), there is reason to expect theincome elasticity to be positive. On the other hand, given appropriateassumptions about time preferences, it is possible that those with higherincomes might purchase more preventive care, resulting in lower averagecurrent expenses.7 In the opinion of this writer the arguments suggest-
'These possibilities are mentioned by Victor R. Fuchs in his Comment in- The Economics of Health and Medical Care, 1964, p. 126. It should be noted
that the direction of the bias caused by a sliding scale of fees depends upon theelasticity of demand for medical care with respect to its price. If, as is generally
V assumed, demand is inelastic, a positive correlation between medical care pricese and income would lead to overestimation of income elasticities.
Wirick and Barlow, "The Economic and Social Determinants of the Demandfor Health Services," p. 107.
• 7-
I
104 Essays in the Economics of Health and Medical Careing a positive relationship are far stronger than those supporting anegative one, but in the final analysis the issue must be resolved bythe data.
Previous empirical studies indicate that the income elasticity is posi-tive and somewhat below unity. The latter magnitude is a useful bench- inmark because of the "necessity" character of much, if not most, medicalexpenditure. If we continue to think in terms of the "degree of neces-sity," it seems reasonable to expect the income elasticity of dentist ex- ccpense to be relatively high and that of hospital expense to be relativelylow. This hypothesis receives support from the findings of Feldstein Uiand Severson8 and is reexamined in the present study.
Because of their intrinsic interest and to avoid biased estimation of ni
the income elasticity, a number of additional independent variables are leincluded in the regressions. Dummy variables measuring age, sex, andregion are utilized because they may reflect differences in physiologicalor psychological needs for medical care,9 or perhaps in its cost. Laterin the analysis, the percentage rural, the percentage living outside ci
SMSA's, the percentage Negro, and measures of marital status and edu-cation are included in the regressions. In the final phase the earnings 11
rate is introduced. The studies cited above suggest that being youngerand better educated lowers expenses, while being female raises them.The results of the regressions are presented in Table 6-2.
Regressions 1—4 show that whatever the form employed, the co-efficient of income is positive and statistically significant at conventionallevels.'0 The estimated income elasticities of demand for medical serv- d
ices, which range from 1.4 to 2.0, are quite high in comparison withthose observed in previous studies. t
The inclusion of bills paid by insurance in the expense data, takentogether with a positive correlation between family income and theamount of health insurance (whether directly paid for by the family
See "The Demand for Medical Care."Wirick and Barlow, pp. 101, 104.
10 XId was introduced into the regressions in order to ascertain whether theeffect of income varies with its level. It was found that the coefficient of thisvariable, which measures the difference in the effect of income in the rangebelow its median from that in the range above its median, fluctuates in signand is statistically insignificant.
In practice, the use of '4adjusted" income did not matter very much; whenregression 4 was rerun utilizing unadjusted income the income elasticitywas 2.04 and its computed t value was 5.44, while the adjusted coefficient ofdetermination was 0.89.
II,
V - -
Medical Expenses and Work-Loss Rates 105
a or by third parties), may help to explain the above discrepancy. Alongthe same lines, some studies include insurance coverage as an inde-pendent variable, which causes income elasticities to be underestimatedsince, to a large extent, insurance coverage is a positive function of
h- income. Unfortunately, the data at my disposal do not permit quantita-al tive statements of the role of these factors. Another possibility which
is difficult to test is that preventive care, which is probably more in-come-elastic than care of the curative variety, comprises a larger frac-tion of total medical expenses for the currently employed population
in than for the population as a whole.Since the LW form showed the strongest results, sole reliance was
of now placed upon it. The next step taken was to replace X4 by there less demanding age variables X, and X6 (see regression 5)." Since
the coefficients of these variables were found to be statistically signifi-al cant, to increase the unadjusted coefficient of determination slightly,
and to raise the estimated income elasticity from 2.0 to 2.5, it was de-le cided to retain them in the succeeding regressions. Regressions 6—9 are
for the separate components of medical expense and show the relativemagnitudes of the income elasticities to be consistent with a priori con-siderations and previous empirical work—i.e., the income elasticitiesrange from 1.8 for hospital expense to 3.2 for dentist expense.
The results for the other independent variables utilized in regressions1—9 may be summarized as follows: Other things being equal, the
al proxy for the quantity of medical services is higher for females, South-erners, and older persons (with the exception of dental care) than formales, non-Southerners, and younger persons.12 Some possible interpre-tations are (1) that younger persons and non-Southerners require less
n medical care because they are healthier than older persons andte Southerners, and (2) that for physiological or psychological reasons
females purchase more and/or more expensive medical care than males.In regressions 10—14 some new independent variables are introduced
one at a time into regressions for total expenses. The coefficients of thepercentage rural (X8) and the percentage outside SMSA's (X0) are
is "The coefficients of X, and X0 show how much the level of the entire equa-tion must be adjusted for the influence of the corresponding age groups; theinfluence of the age group sixty.flve and over is reflected in the constant termof the equation.
12 When X4 is used in regressions 6—9 instead of X5 and the ordering ofincome elasticities remains the same while the coefficients of X, are 0.15, 0.16,0.08, and —0.04, respectively. The corresponding computed t values are 4.20,11.67, 3.73, and —1.25, respectively.
TAB
LE 6
-2R
egre
ssio
ns o
f Med
ical
Exp
ense
s per
Cur
rent
ly E
mpl
oyed
Per
son
per Y
ear o
nV
ario
us In
depe
nden
t Var
iabl
es fo
r Tw
enty
-fou
r Reg
ion-
Age
-Sex
1
2
0
Reg
ress
ion
Coe
ffic
ient
and
Com
pute
dV
alue
(in
Pare
nthe
ses)
°
Bia
sed
Co-
effic
ient
of
Determina-
tion
and
Unb
iase
dC
oeff
i-Fo
rm o
fci
ent o
fR
egre
ssio
nb a
ndA
ge (K
4)D
eter
min
a-R
egre
ssio
nD
epen
dent
Inco
me
Sex
Reg
ion
ortio
n (in
Pa-
No.
Var
iabl
e(K
1)(X
2)(X
3)A
ge (X
5)A
ge (X
6)X
r-X
12re
nthe
ses)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
10.
03—
34.9
033
.50
37.1
9.70
Tot. exp. (Y1)
(3.42)°
(—3.
01)°
(1.4
5)(5
.27)
0(.6
3)2
NW
0.03
—43.95
47.33
36.10
.88
Tot. exp. (Y1)
(4.32)0
(2.92)0
(.85)
3LUw
1.55
—0.10
0.12
0.11
.75
Tot. exp. (Y1)
(4.01)0
(_3.61)e
(2.04)
(6.24)°
(.70)
4LW
2.02
—0.14
0.18
0.11
.91
Tot. exp.
(5.61)0
(_7.
64)e
(4.1
6)°
(6.4
0)°
(.90)
5LW
2.53
—0.
140.
24—
0.26
—0.
18.9
2To
t. ex
p. (Y
1)(5
.38)
0(4
.35)
e(_
6.34
)e(.9
0)6
LW1.
82—
0.14
0.17
—0.
32—
0.19
.74
Hos
. exp
. (1'
2)(1
.74)
(—3.
69)°
(1.4
3)(—
3.56
)°(—
1.77
)(.6
7)7
LW2.
23—
0.15
0.29
—0.
34—
0.20
.96
Med
. exp
.(Y
3)(5
.62)
0(—
10.5
2)°
(6.1
6)e
(_1O
.05)
e(_
4.93
)e(.9
5)8
LW2.
88—
0.15
0.29
—0.
21—
0.18
.86
Dr.e
xp.(Y
4)(4
.56)
0(—
6.42
)°(3
.94)
0(.82)
9LW
3.19
—0.
130.
220.
04—
0.04
.71
Den
. exp
. (Y
6)(3.55)e
(3.7
5)°
(2.0
8)(0
.47)
(—0.
44)
(62)
(con
tinue
d)
j.
""ue
n.ex
p. (Y
o)(—
3.75
)(2
.08)
(0.4
7)(—
0 44
)9
(con
tinue
d)
TAB
LE 6
-2(c
ontin
ued)
[Ed.
10LW
2.61
—0,
130.
28—
0.34
—0.
220.
74.93
Tot. exp. (Y1)
(5.4
7)°
(—5.70)°
(4.11)°
(—3.58)°
(1.01)
(.90)
[%
rura
lX.1
11
LW
2.39
—0.13
0.24
—0.26
—0.17
—0.05
.92
Tot. exp. (Y1)
(4.1
2)°
(—5.24)°
(4.17)°
(_6.19)e
(—3.35)°
(—0.43)
(.90)
[%
out.
SMSA
X,]
12LW
2.38
—0.
140.
23—
0.25
—0.
18—
0.04
.93
Tot.
exp. (1's)
(4.16)e
(—7.34)°
(4.08)e
(—3.50)°
(—0.47)
(.90)
[%
mar
ried
X10J
13
LW
2.35
—0.20
0.21
—'0.29
—0.22
0.35
.94
Tot.exp.(Yi)
(5.30)°
(_6.32)6
(4.08)°
(—7.l1)e
(4.59)a
(2.0
6)(.9
2)[%
Neg
roX11]
14
LW
2.29
—0.16
0.27
—0.24
—0.16
—0.11
.93
Tot.
exp.
(4.7
0)6
(_8.
09)e
(4.6
9)6
(_5.
77)e
(—3.
37)°
(—1.
45)
(.91)
[Ed.
X7]
15LW
1.56
—0.19
0.05
—0.08
—0.07
—2.26
.77
Hos.exp.(Y2)
(1.51)
(_3.87)e
(0.34)
(—0.41)
(—0.51)
(—1.44)
(.69)
16
LW2.
37—
0.13
0.36
—0.
48—
0.27
1.26
.97
Med
. exp
. (Y
3)(6
.54)
6(_7.71)e
(6.87)°
(_7.15)a
(_5.
69)e
(2.28)d
(.96)
17
LW3.
06—
0.12
0.38
—0.
39—
0.26
1.59
.88
Dr.
exp. (}'4)
(_4.21)e
(4,35)e
(_3,47)e
(_3.
35)e
(1.7
1)(.8
4)18
LW
3.20
—0.12
0.22
0.02
0.04
0.10
.71
Den. exp. (Y6)
(3.41)
(_2.80)d
(1.67)
(0.15)
(—0.38)
(0.07)
(.60)
(continued)
TAB
LE 6
-2(c
ontin
ued)
I
Reg
ress
ions
of M
edic
al E
xpen
ses p
er C
urre
ntly
Em
ploy
ed P
erso
n pe
r Yea
r on
Var
ious
Inde
pend
ent V
aria
bles
for T
wen
ty-f
our R
egio
n-A
ge-S
ex C
ells
&
0 00B
iase
d C
o-ef
ficie
nt o
fD
eter
min
a-tio
n an
dU
nbia
sed
Form
of
Reg
ress
ionb
and
Reg
ress
ion
Coe
ffic
ient
and
Com
pute
d t V
alue
(in
Pare
nthe
ses)
°C
oeff
i-ci
ent o
fD
eter
min
a-A
ge (X
4)R
egre
ssio
nD
epen
dent
Inco
me
Sex
Reg
ion
ortio
n (in
Pa-
No.
Var
iabl
e(X
1)(X
2)(X
3)A
ge (X
6)A
ge (X
6)re
nthe
ses)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
[% m
arrie
dX
10]
-
19LW
1.28
—0.
310.
10—
0.42
—0.31
1.03
.83
Hos.exp. (Y2)
(1.4
4)(_
4.84
)e(0
.93)
(_3.
15)a
(2.9
7)e
(77)
20LW
2.23
—0.
160.
28—0.34
—0.20
0.01
.96
Med.exp.(Y3)
(5.3
4)a
(_5.
35)e
(579
)e(_
_8.8
8)c
(—4.
41)°
(0.0
5)(.9
5)21
LW2.
57—
0.25
0.25
—0.
28—
0.25
0.60
.91
Dr.
exp.
(Y4)
(467
)e(_
6.30
)e(3
.80)
c(—
5.48
)°(2
.79)
"(.8
7)22
LW3.
33—
0.08
0.24
0.06
—0.
01—
0.28
.72
Den. exp. (Y5)
(3.6
0)e
(—1.
20)
(2.l8
)d(0
.74)
(—0.
09)
(—0.
77)
1%N
egro
X11J
(.62)
23
LW
2.04
—0.13
0.14
—0.34
—0.21
0.10
.75
24
lbs. exp. (Y2)
LW(1
.81)
2.08
(1.05)
(_3.50)e
(—1.83)
(0.58)
—0.16
0.31
—0.33
—0.19
—0.07
(.66)
:96
Med
. exp
. (Y
,)(4 .93)e
(—9 .89)e
(6 .09)e
(—9 .27)e
(—4 .48)a
(—1
.06)
(.95)
25LW
2.35
—0.
180.
36—
0.18
—0.
14—
0.24
.90
Dr.
exp.
(1',)
(4.0
2)°
(_7.
79)e
(5.2
1)°
(_2.
38)d
(—2.
63)"
(.87)
26LW
3.22
—0.
120.
210.
03—
0.04
0.01
.71
Den
. exp
. (Y
6)(3
.28)
6(_
3.20
)e(1
.81)
(0.4
0)(—
0.43
)(0
.10)
jEar
n. ra
te X
12J
(.60)
27LW
1.20
—0.
690.
28—
0.37
—0.
322.
07.9
6To
t. ex
p. (Y
1)(2
.30)
".5
0)'
(6.3
4)'
(—8.
22)'
(—5.
94)'
(358
)'(m
i till
(.94
)
27LW To
t. ex
p. (Y
1)1.
20—
0.69
0.28
—0.
37—
0.32
(2.3
0)d
(_4.
50)e
(634
)e(_
8.22
)e(_
594)
e
(Con
tin
uc(l)
tLar
n. ra
w A
12J
2.07
(3.5
8)6
.96
(.94)
TAB
LE 6
-2(c
oncl
uded
)
obta
ined
from
the
follo
win
g:
Reg
ion
Age
NE
NE
NE
NE
NE
NE
NC
NC
NC
NC NC
NC
No.
of
Sex
Pers
ons
M6,
338
M3,
980
M52
5F
3,03
1F
2,03
6F
190
M7.
372
M4,
236
M58
0F
3,18
1F
1,93
0F
248
No.
of
Sex
Pers
ons
28LW
1.20
—0.
400.
19—
0.37
—0.
250.
96.7
5H
os. e
xp. (
Y2)
(0.7
9)(—
0.89
)(1
.50)
(_2.
82)d
(—1.
61)
(0.5
7)(.6
6)29
LW1.
46—
0.47
0.31
—0.
41—
0.28
1.20
.97
Med
. exp
. (Y
3)(2
.81)
d(_
3.12
)e(7
.03)
6(_
9.08
)e(_
5.21
)e(2
.10)
d(.9
6)30
LW0.
85—
0.99
0.35
—0.
40—
0.40
3.15
.94
Dr.
exp.
(Y4)
(1.3
8)(_
5.43
)e(6
.74)
6(_
7.39
)e(_
6.13
)e(4
.60)
6(.9
2)31
LW2.
39—
0.45
0.24
—0.
03—
0.12
1.24
.72
Den
. exp
. (Y
6)(1
.85)
(—1.
20)
(2.2
2)"
(—03
1)(—
0.03
)(0
.87)
(.62)
For d
etai
led
defin
ition
s of t
he v
aria
bles
em
ploy
ed in
the
regr
essi
ons,
see
Sect
ion
2.b
Nat
ural
unw
eigh
ted,
NU
w; n
atur
al w
eigh
ted,
NW
; log
arith
mic
unw
eigh
ted,
LU
w; l
ogar
ithm
ic w
eigh
ted,
LW
. The
wei
ghts
are
Reg
ion
Age
17—
4445
—64
65—
17—
4445
-64
65—
17—
4445
—64
65—
17—
444
5—64
65—
I
S17
—44
M7,
103
S45
—64
M3,
820
S65
—M
495
S17
—44
F3,
460
S45
—64
F1,
833
S65
—F
181
W17
—44
M3,
977
W45
—64
M2,
205
W65
—M
300
W17
—44
F1,
800
W45
—64
F1,
062
W65
—F
102
The
estim
ated
inco
me
elas
ticiti
es a
t poi
nts o
f mea
ns fo
r the
nat
ural
regr
essi
ons a
re 1
.44
(reg
ress
ion
1) a
nd 1
.83
(reg
ress
ion
2).
dS
tatis
tical
lysi
gnifi
cant
at t
he .0
5 le
vel o
n a
one-
tail
test
for t
he e
arni
ngs r
ate
(X12
) and
on
a tw
o-ta
il te
st fo
r all
othe
r var
iabl
es.
Stat
istic
ally
sign
ifica
nt a
t the
.01
leve
l on
a on
e-ta
il te
st fo
r the
ear
ning
s rat
e (X
12) a
nd o
n a
two-
tail
test
for a
ll ot
her v
aria
bles
.
'1
110 Essays in the Economics of Health and Medical Carefound to be insignificant, and it is wisest to ignore them. The computed
4t value for the education variable (X7) is more respectable but isstatistically insignificant. However, in view of the wide interest in therole of this variable, it is worth noting that its sign is positive, whichmight be interpreted to mean that education leads individuals to takebetter care of their health. The coefficient of the percentage Negro(X11) is negative, which might mean that, other things being equal,Negroes are healthier than whites and therefore require less medicalcare, but is more likely to mean that cultural and other factors resultin Negroes receiving less medical care for a given problem. However,these speculations should not be emphasized, since the coefficient ofX11 is not statistically significant. Finally, the coefficient of the maritalstatus variable (X10) is positive and is in the range of statisticalsignificance. In order to obtain further information on the role of thelast three independent variables, they were included in regressions foreach of the four types of medical expense, with the results shown inregressions 15—26.
The results for the education variable (regressions 15—18) are quiteinteresting: the coefficient of X7 is negative for hospital expenses,positive for medicine and physician expense, and positive but of negligi-ble magnitude for dentist expense. A possible interpretation is that edu-cation results in emphasis being placed on preventive care, which leadsto relatively low hospital and dentist expense and relatively high medi-cine and physician expense.13
The coefficient of the marital status variable is found to be positiveand statistically significant for hospital and physician expense, positivebut insignificant for medicine expense, and negative but insignificantfor dentist expense (regressions 19—22). These results probably meanthat the positive correlation between X10 and total expenses is a reflec-tion of the fact that being married with a spouse present is associatedwith child-bearing expenses for females; child-bearing raises hospitaland physician expenses but does not greatly affect dentist and medicineexpenses.
It is found that the inverse relationship between the percentageNegro and total expenses is derived from a strong negative relationshipfor physician expense and a somewhat weaker negative effect on medi-cine expense (regressions 24 and 25). The basis for the observed
"Caution is justified here, as the computed t values of the education variableare not very large, and there is evidence of harmful multicollinearity in re-gression 15.
4
Medical Expenses and Work-Loss Rates 111
differences in the results for the various components is not apparent tothe present writer.14
To the extent that analysts have been willing to take a position onthis issue, they have tended to interpret positive relationships betweenincome and medical expenses to mean that higher income permitsindividuals and groups to receive the benefits flowing from more andbetter medical care. At the same time, policy-related judgments con-cerning the equity of the current distribution of medical services are inpart based upon the magnitude of the income elasticity. However, asidefrom the problems that arise in using expenses as a measure of theamount of medical care, such interpretations and judgments are spuri-ous to the extent that (1) activities raising money incomes simultane-ously depress health status and consequently increase the demand formedical services, and (2) individuals or groups with higher income useless patient-time-intensive (more medical-goods-and-services-intensive)methods of dealing with their medical problems.
Both of these conditions that give rise to upward-biased incomeelasticities might occur because of a positive correlation between in-come and the earnings rate.'5 A higher earnings rate may reduce healthstatus while raising income by inducing individuals to "work harder,".to go to work instead of staying at home when they are ill, to take moresedentary jobs, or to take more dangerous jobs. Further, it seemsreasonable to believe that an increase in the earnings rate, and hencein income, will lead patients or their physicians to substitute medicalgoods and services for the patient's time in dealing with a given medicalproblem. In recognition of these possible sources of biased incomeelasticities, the earnings rate (X,2) is included in regression 27. It isfound that the coefficient of the earnings rate has the expected positivesign and is statistically significant, while its inclusion lowers the incomeelasticity of total expenses from 2.5 (regression 5) to 1.2 and raisesthe adjusted coefficient of determination from 0.90 to 0.94.
In interpreting the results of the above regression it should be noted"Charlotte Muller suggests that these differences may be explained by the
fact that in the Negro subculture (and in other subcultures of poverty) thereexists a tendency to substitute medicine for the services of physicians (self-medication) and to substitute home remedies for market purchase of medicines.
"Actually, the bias could be downward if (I) an increase in the volume ofmedical services needed to produce a given level of health resulted in a declinein medical expenditures (i.e., the price elasticity of demand for health was nu-merically greater than 1), and (2) health were relatively time-intensive andsubstitution in consumption outweighed substitution in production. These pos-sibilites were called to my attention by Michael Grossman.
4.
112 Essays in the Economics of Health and Medical Care
that the correlation coefficient between the earnings rate and sex vari-ables is in the range of 0.9.16 Intercorrelations of this magnitude oftenproduce highly unstable parameter estimates. A check on the stabilityof the conclusions suggested by regression 27 is provided by regres-sions 28—31, which are for the separate components of medical ex-pense. Although multicollinearity problems are evident in each of theregressions, the results are consistent with expectations: in every casethe coefficient of the earnings rate is positive, and its inclusion in theregression causes a perceptible decline in the estimated income elastic-ity. The explanatory value of the earnings rate is greatest for physicianexpense (the adjusted coefficient of determination rises from 0.82 to0.92) and weakest for hospital and dentist expense (virtually no changeoccurs in the adjusted coefficient of determination). The statisticallyinsignificant result for dentist expense seems reasonable, since it isunlikely that higher earnings rates lead individuals to substitute moneyincome for dental health or to use higher ratios of dental services totheir own time in the production of dental health, A factor whichmay help to explain the exceptional showing of the earnings rate forphysician expense is that in the absence of information about incomedoctors may discriminate in their charges on the basis of occupation,which is more highly correlated with the earnings rate than with income.
With the inclusion of the earnings rate in the regressions, the legiti-macy of interpreting the estimated coefficients of income as "incomeelasticities" is increased. Using expected values, it is found that theelasticity for medical care as a whole is 1.2, while the elasticities for itscomponents range from a low of 0.85 for physician expense to a highof 2.4 or for dentist expense.'8
These results demonstrate that, even when proper account is takenof the earnings rate, command over goods and services as measuredby family income exerts a strong positive influence upon the amountof medical care received by individuals.'9
The correlation between the income and sex variables is only .05, while thatbetween the earnings rate and income is .41.
"The latter value results when the statistically insignificant earnings rate isdropped from the regression.
Medical care is produced by the market goods analyzed above togetherwith the patient's time. The best available measure of the latter input is dayslost from work due to illness or injury per currently employed person (Y,),which in Section 4 is found to have an income elasticity of about 2—i.e., inter-mediate between medicine and dentist expense.
"The reader is reminded that since some free care is available to personswith very low incomes, the income elasticities in the text, which apply to the
9.' . -. .— ' ..
IMedical Expenses and Work-Loss Rates 113
4. REGRESSION ANALYSIS OF WORK-LOSS RATESThe primary objective of this section is to obtain information on thequestion of whether the work-loss rate due to illness or injury is aworthwhile addition to the currently scant stock of quantitative healthmeasures. This purpose is accomplished by testing two hypothesessuggesting that variations in the work-loss rate reflect differences ineconomic variables (health status remaining constant) rather than inthe objective state of health. The primary hypothesis is that the higherthe earnings rate in a region-age-sex cell, the lower its rate of workloss. The secondary hypothesis is that the higher the adjusted meantotal family income in a cell, the higher its work-loss rate.
The prediction concerning the earnings rate flows from both con-sumption and production considerations. The consumption argumentruns as follows: (I) It is more pleasant to recover from an illnesswhile resting at home than while working; (2) the earnings rate canbe considered the price of the consumption good "recovery at home" or"rest"; (3) the "law of demand" predicts an inverse relationship be-tween price and quantity. The production argument is based upon thebelief that individuals with higher earnings rates (or their physicians)substitute medical goods and services for their own time in dealingwith a given medical problem. Since the patient's time input is, atleast in part, reflected in the work-loss rate, the above substitution re-sults in a negative correlation between the earnings rate and the work-loss rate.
The predicted relationship between family income and the work-lossrate rests upon a consumption argument and a mixed consumption-production argument. Stated briefly, the consumption argument is that"recovery at home" or "rest" is a superior consumption good. Themixed argument is based on the assumption that health or "recovery"is a superior consumption good produced according to a productionfunction which is homogeneous of degree one (or of any other formwhich excludes the possibility of "inferior" factors of production).If these assumptions hold, an increase in family income would increasethe demand for health, and hence the demand for all the relevantfactors of production, including the patient's own time. An increasein the patient's time input would be reflected in an increased work-loss rate.
relatively affluent, currently employed segment of the population, overestimateto an unknown degree the differential benefits received by the more affluentmembers of our society.
114 Essays in the Economics of Health and Medical Care
In order to avoid biasing the results and to increase their reliability,dummy variables representing region, age, and sex were included inthe regressions shown in Table 6-3.
Negative regression coefficients for the earnings rate and positiveones for family income20 are observed in three of the four forms utilizedin regressions 1—4. In the fourth case (regression 3) the signs of familyincome, the earnings rate, and the sex variable (positive in the otherthree cases) are reversed. While none of the computed I values areimpressive, the strongest results are obtained in regression 2, in whichthe positive coefficient of income is statistically significant while thenegative one for the earnings rate is insignificant but respectable.
It is well known that high intercorrelations between independentvariables often result in unstable parameter estimates and small com-puted t values. In the present analysis the previously noted deviantresults for regression 3 and generally small computed I values may besymptoms of harmful multicollinearity (primarily) between the earn-ings rate and sex variables whose coefficient of correlation is in therange of 0.9. One method for dealing with this type of problem is tonarrow the scope of the model by removing the less theoretically in-teresting variable, which in this case is the dummy for sex. This is donein regressions 5 and 6 for the weighted forms, which earlier yieldedhigher multiple correlation coefficients than the unweighted forms. Itis found that the coefficients of family income and the earnings ratemaintain the predicted signs and, especially in the case of the LWform, are statistically significant. The results are not greatly affectedby the use of the less restrictive age variables X5 and X6 (see regres-sion 7).
Of course, the danger inherent in the above precedure is that theprice of avoiding harmful multicollinearity may be biased parameterestimates. Little can be done to deal with this possibility beyond run-ning separate regressions for the twelve observations on each sex. Thisis done in regressions 8 and 9, which exclude the family income andregion variables because they are now highly correlated with the earn-ings rate.2' The results are ambiguous: while the coefficient of the male
'° It is worth noting that the simple correlations between family income andwork-loss days are small and negative.
21 Taking all twenty-four observations together, the simple correlations betweenthe earnings rate and the family income and regional variables are 0.41 and—0.31, respectively, while for males the corresponding values are 0.97 and—0.83 and for females, 0.89 and —0.79. The correlation between the earnings rateand age is .06 for all the observations, .21 for males, and close to 0 for females.
A
Medical Expenses and Work-Loss Rates 115
earnings rate is negative and statistically significant, the coefficient forfemales is positive and unreliable.
Obviously, the results are far from conclusive, but in my opinionthey lend some support to the economic arguments presented above.The observed signs of the income and earnings rate variables, togetherwith their relatively high partial correlation coefficients, suggest thatdifferences in work-loss days may be unreliable measures of healthstatus.22 To the extent that the magnitudes of the regression coefficientscan be taken seriously, it appears that the elasticity of the work-lossrate with respect to family income is surprisingly high, while that withrespect to the earnings rate is low.
Turning to the other independent variables, it is found that, otherthings being equal, work-loss rates are higher for males, Southerners,and older persons than for females, non-Southerners, and younger per-sons. Like the findings for medical expenses (see Section 3), the resu.tsare consistent with the view that non-Southerners and younger personsenjoy better health than Southerners and older persons. The generallypositive signs for sex are subject to a variety of interpretations, includingthe notion that females enjoy better health than males.
S. SUMMARY OF MAJOR FINDINGSThe empirical analysis in Section 3 reveals an income elasticity ofdemand of 1.2 for medical care as a whole, while the elasticities for its
22 There are alternative, but in my opinion less plausible, interpretations ac-cording to which the empirical results are consistent with the view that thework-loss rate is a pure measure of health. First, the earnings rate might benegatively correlated with the work-loss rate because the former is an "efficiencyvariable"; that is, market skills might be positively correlated with skill in theproduction of health. Second, even after adjusting for differences in the earningsrate it might be the case that groups with higher incomes have poorer health.
A crude check of the alternative explanations presented above were obtainedby running LW regressions utilizing a less ambiguous measure of health, themortality rate, as the dependent variable. (The mortality data utilized in-clude deaths of persons who were not employed during the relevant period; thedata were taken from the 1962 and 1963 volumes of Vital Statistics of the UnitedStates, from National Center for Health Statistics, Health Insurance Coserage,United States: July 1962—June 1963, Table 13, and from the 1960 Census ofPopulation, vol. 1, Pt. 1, Table 52.) The regressions offered little if any supportfor the alternative interpretations: (1) When the sex variable is included, thecoefficient of income is positive but far from s:atistical significance, while thecoefficient of the earnings rate is positive and insignificant; (2) when sex isdropped from the regression in order to avoid multicollinearity problems, thecoefficient of income becomes negative and insignificant, while the coefficient
ofthe earnings rate is positive and highly significant.
TAB
LE 6
-3R
egre
ssio
ns o
f Day
s Los
t fro
m W
ork
due
to Il
lnes
s or I
njur
y pe
r Cur
rent
lyEm
ploy
ed P
erso
n pe
r Yea
r (Y
8) o
n V
ario
us In
depe
nden
t Var
iabl
esa
a'
Reg
ress
ion
Coe
ffic
ient
and
Parti
al C
orre
latio
n C
oeff
icie
ntB
iase
d C
oeff
icie
nt
Form
of
Reg
ress
ionb
and
(Com
pute
d t
Val
ue in
Par
enth
eses
)of
Det
erm
inat
ion
and
Unb
iase
dC
oeff
icie
nt o
fA
ge (X
4)Ea
rnin
gsR
egre
ssio
nN
umbe
r of
Inco
meo
Sex
Reg
ion
orA
geR
atec
Det
erm
inat
ion
No.
Obs
erva
tions
(X1)
(X2)
(X3)
Age
(Xe)
(X6)
(X7)
(in P
aren
thes
es)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
1NUw
0.001
3.55
2.07
1.42
—0.05
.52
24
0.22
(0.94)
0.26
0.31
(1.14)
(1.39)
0.53
(2.65)d
—0.21
(—0.90)
(.38)
2NW
0.002
3.27
3.23
1.85
—0.08
.74
24
0.43
(2.04)d
0.26
0.56
(1.13)
(2.85)d
0.67
(3.88)°
—0.32
(—1.44)
(.67)
3LUw
—0.05
—0.21
0.15
0.13
0.83
.54
24
—0.01
(—0.06)
—0.23
0.38
(—1.02)
(1.73)
0.67
(3.86)e
0.25
(1.11)
(.41)
4LW
1.96
0.02
0.28
0.12
—0.
42.7
724
0.35
(1.61)
0.02
0.63
(0.10)
(3.44)e
0.66
(3.69)e
—0.10
(—0.42)
(.71)
5N
W0.
001
2.96
2.02
—0.
02.7
324
0.39
0.52
(2.6
6)d
0.71
(4.3
9)e
—0.
40(_
1.92
)d(.6
7)
(continued)
TAB
LE 6
-3 (c
oncl
uded
)
6LW
1.86
0.27
0.12
—0.
33.7
724
0.55
0.64
0.70
—0.
53(.7
2)(2
.91)
e(3.64)e
(4.23)e
(_2.76)e
7LW
2.28
0.32
—0.28
—0.18
—0.33
.78
24
0.53
0.61
—0.
67—
0.45
—0.
54(.7
2)(2
.64)
°(3
.24)
e(—
3.83
)°(—
2.13
)(—
2.76
)°8
LW M
ales
0.24
—0.
86.8
212
0.90
—0.
56(.7
8)(6
.39)
a(_2.04)d
9LW
Fem
ales
0.03
0.24
.18
120.37
0.24
(—.0
0)(1
.20)
(0.73)
For d
etai
led
defin
ition
s of t
he v
aria
bles
em
ploy
ed in
the
regr
essi
ons,
see
Sect
ion
2.b
See
Tabl
e 6-
2, n
ote
b.• T
he e
stim
ated
inco
me
elas
ticiti
es a
t poi
nts o
f mea
ns fo
r the
nat
ural
regr
essi
ons a
re 0
.79
(reg
ress
ion
1), 2
.38
(reg
ress
ion
2),
and
1 .3
2 (r
egre
ssio
n 5)
. The
cor
resp
ondi
ng v
alue
s for
the
earn
ings
rate
are
—0.
66 (r
egre
ssio
n 1)
, —1
.29
(reg
ress
ion
2), a
nd —
0.29
(reg
ress
ion
5).
dS
tatis
tical
lysi
gnifi
cant
at t
he .0
5 le
vel o
n a
one-
tail
test
for i
ncom
e an
d th
e ea
rnin
gs ra
te a
nd o
n a
two-
tail
test
for a
ll ot
her
varia
bles
.St
atis
tical
ly si
gnifi
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118 Essays in the Economics of Health and Medical Care
components range from 0.85 for physician expense to 3.2 for dentistexpense. The ordering of the income elasticities is not unreasonable,and the magnitudes suggest that family income exerts a strong influenceupon the amount of medical care received by individuals. However,an important question for future research is why the income elasticitiesreported in the present study are so high relative to those estimatedfrom other bodies of data. The elasticity of total expenses with respectto the earnings rate is positive and statistically significant and is notnegligible in magnitude—its value is 2.1.
In Section 4 it is seen that the work-loss days due to illness or injuryare usually positively related to family income and inversely related tothe earnings rate, which suggests the tentative conclusion that differ-ences in unadjusted work-loss days may be unreliable measures ofvariations in health status.