-
Journal of Health Economics 6 (1987) 305-318. North-Holland
ON THE ESTIMATION OF HOSPITAL COST FUNCTIONS
Donald F. VITALIANO* Rensselaer Polytechnic Institute, Troy, NY
12181, USA
Received March 1987, final version received May 1987
Data from 166 general hospitals in New York State (1981) is used
to estimate a quadratic and logarithmic long-run cost function.
Both equations lit the data very well but give very different
results. The quadratic appears to confirm the commonly-held view of
a shallow U-shaped ave. age cost curve, whereas the log function
indicates significant economies of scale: a total and avr;rage cost
elasticity of 0.9 and -0.10, respectively (using beds or patient
days to measure output). Ramseys RESET test is used to discriminate
between the two models and the quadratic is clearly rejected as a
misspecilication. Scale economies thus exist even where the usual
quadratic suggests otherwise.
1. Introduction
Over the past 20 years a number of empirical studies of hospital
cost functions and scale economies have appeared. A representative
list might include the papers by Carr and Feldstein (1967), Culver
et al. (1978) (U.K.), Evans (1971) (Canada), Feldstein (1968), Lave
and iave (1970) and Sloan and Steinwald (1980). Among the most
recent studies is that by Grannemann et al. (1986), which employs a
multiple-output type of cost function. While it is hazardous (and
perhaps foolhardy) to suggest the existence of anythinp approaching
a consensus among economists, the most recent edition of a leading
textbook on health economics summarizes its survey of the
literature as follows: The shape of the average cost curve is
shallow [U-shaped], that is it does not fall sharply nor is its
minimum point much below that of hospitals on the ends of the curve
[Feldstein (1983, p. 212)].
This paper first replicates the U-shaped cost function and then
goes on to show that the same data set is capable of generating
significantly decreasing unit costs with respect to size. The role
of functional form misspecification and estimation technique in
causing this apparent contradiction is formally explored.
Statistical testing permits the decisive rejection of the U-shape
in
*This paper was written while the author was visiting the
Institute for Research in the Social Sciences and the Department of
Economics and Related Studies at York University, Engl-nd. The
valuable comments and suggestions of Professor J.P. Hutton are
gratefully acknowledged. Professor A.J. Culyer and Dr. Keith
Hartley have also made useful comments. All remaining errors are,
of course, the sole responsibility of the author.
0167-6296/87/%3.50 @ 1987, Elsevier Science ?ublishers B.V.
(North-Holland
-
306 D.F. Vitaliano, Estimation of hospital cost functions
favour of significant economies of scale. Even those who reject
the U-shaped consensus will welcome the strong evidence here about
scale economies which, as Berki (1972, p. 115) remarked, ought to
exist.
Partly owing to the consensus just noted, but also because of a
policy- driven concern with the cost of individual hospital
services, it has become fashionable to estimate multiple-output
cost functions. This new approach is useful in its own way and
welcome, but it would be ill-advised to completely abandon the
estimation of single output functions [see Hombrook and Monheit
(1985)]. For example, the efficient planning choice between a
single 500 bed hospital and two 250 bed units with a similar
complement of facilities requires knowledge of conventionally
measured scale economies in order to balance changes in treatment
costs against changes in the travel costs of patients, visitors and
staff as size varies. Moreover, the multiple output models
typically suffer from difficulty in interpreting their results and
from multicollinearity among the output measures which causes
unreliable parameter estimates, thus weakening much of their policy
usefulness.
In what follows, I present a brief view of selected past cost
studies. There follows a description of the model and data base
employed here. The next section presents the econometric results. A
concluding part assesses the findings and attempts an
interpretation of their significance.
2. Prior studies
Typically, past studies have relied upon single equation,
cross-section multiple regression to estimate hospital cost
functions [Carr and Feldstein (1967)]. A quadratic total cost
function is fitted, with much attention devoted to attempting to
control for the quantity and quality of output (e.g., case- mix or
facilities available). A positive but small coefficient on the
squared term in the quadratrc leading to the inference of a saucer
shaped average cost curve [Carr and Feldstein (1967), Sloan and
Steinwald (1980), Bays (1980)]. Francisco (1970) fitted an average
cost function and reached a similar conclusion. Estimation of a
total rather than an average cost function is preferred on
econometric grounds because the latter introduces the size or
output variable on both sides of the equation. This may cause bias
in parameter estimates of as much as 10% and of unknown direction
[Hough (1985)]. .
Evans (1971) found evidence of a U-shaped average cost curve for
hospitals in Ontario.
The recent paper by Grannemann et al. (1986) typifies the
multiple-output approach in which total cost is regressed on a
vector of output measures in order to estimate separate marginal
costs. Using single equation least- squares, they find important
scale economies for emergency room activity but not for other
outpatient activity. Because of multicollinearity among the
-
D.F. Vitaliano, Estimation of h al cost functions 307
outputs, 30 of 64 reported coefXcients wer wide confidence
intervals around the es hospital outputs.
t statistically significant, with es of marginal cost for
all
One problem with the standard appro that firm data often exhibit
non-constant error variance (heterosceda y) which can cause
statistical tests and goodness of fit measures to incorrect,
leading to incorrect inferences about coefficients and functio form
[Pindyck and Rubinfeld (1981, pp. 14&152)]. Further problems se
with the results that have appeared in the literature when it is
realiz that the use of a single equation model implies either a
reduced form ation or only one endogenous variable. Price, cost and
output are ty lly determined jointly. In such instances, the
interpretation of the c nts of a single equation is particularly
hazardous as they may re a complex of unspecified or unidentified
coefficients from a larger mode ost authors have been content to
merely point out the problem of en y before proceeding to single
equation estimation.
3. A data-consistent model of hospital cost
The data set employed in this study is especially well-suited to
avoid the cndogeneity problem of single equation estimation. New
York State (U.S.A.) has, since 1969, engaged in a comprehensive and
compulsory system of prospective (i.e., ex-ante) hospital rate
regulation of all its non-federal hospitals. In other words, the
prices are set in advance for each hospital by the State Health
Department, much as electricity and telephone rates are set by
regulatory boards [Health Care Financing Administration (1981)].
Prospective reimbursement rates are based on complex formulae
designed to measure efficient levels of cost. Hospitals are grouped
by bedsize, service-mix and teaching status. Costs are classified
as routine or ancillary, with the former on a per diem basis and
the latter per admission. A group mean is calculated after
excluding hospitals above 125% and below 750/, of the raw mean. The
baseline costs thus derived are adjusted to allow for expected
inflation to form the prospective reimbursement rate, which is also
subject to adjustment and penalties for deviation from target
occupancy and utilization levels. This implies that prices are
exogenous to the hospital, much as to a perfectly competitive firm.
In addition, hospitals are similar to electric utilities in that
output is non-storable and supplied on demand to customer-patients.
Together these two factors imply that total revenue is exogenous
and thus use of a single equation, cost-minimizing cost function is
appropriate [Wallis (1979)]. Cost minimization is much more general
than profit maximization and consistent with a variety of
non-profit maximizing models [Cowing et al. (1983, p. 263)].
Although almost all the hospitals included in this study are
not-for-profit, the regulators allow them to keep
-
308 D.F. Vitaliano, Estimation of hospital cost functions
any profit and impose financial penalties for cost overruns.
Thus it is not unreasonable to assume least-cost behaviour on the
part of the hospitals.
The rationale advanced here for the use of a single equation
model is similar to that employed by Nerlove (6963) in his classic
study of returns to scale in the electric power industry. Following
Nerlove, let us define the following generalized Cobb-Douglas
production function:
Q=A Xdfl X$2X$3, (1)
where Q is output, the XS input, A a constant and the ors the
output elasticities. The least cost equation derived from (1) under
the assumption of cost minimization is [Nerlove (1963, p. 54)]
1 lnC=lnk+-lnQ+%nPI+%nP,+olflnP,,
V V V V 12)
where C is total cost, P the unit prices of the inputs and k-
v(Aailti
-
D.F. Vitaliano, Estimation of hospital cost functions 309
cQ2 - a-dX zO.
e=a+bQ+cQ2+dX
Increasing, constant and decreasing costs obtain according as
e$O. We shall employ e later in the paper when comparing (3) and
(4) since the elasticity of total cost e = e + 1 = l/v.
4. Data base and choice of variables
American Hospital Association (1981) and data provided me by the
New York State Health Department are the basic data sources
employed. On& hundred and sixty-six general medical-surgical
(or acute care) hospitals located in upstate, New York State
(U.S.A.) are analyzed. These hospitals represent virtually the
entire universe of acute care hospitals in the upstate region. The
166 units consist of 139 private, not-for-profit hospitals, 23
publicly-owned and operated hospitals and only four for-profit
units. Not included in the data set are specialty hospitals such as
mental institutions and military base and veterans hospitals.
Included are 32 medical school affiliated hospitals.
The New York State rate-setting scheme under which all these
hospitals operate imposes on them a uniform system of cost
accounting. This helps to minimize a source of error common to
cross-section studies arising from non-uniform treatment of costs
(e.g., depreciation) across observations. This is a particular
weakness of prior hospital cost studies that used a sample drawn
from various states.
The choice of an appropriate index of hospital size is the next
issue to be addressed. In this paper I use beds as the measure of
size, and thus the proxy for size-related output. Carr and
Feldstein employed average daily census and Francisco used patient
days to measure hospital size. Culyer et al., Bays and Sloan and
Steinwald used beds as the size variable. Since the general
conclusion of all these authors about costs is similar, the choice
of size index does not appear crucial. Nevertheless, Carr and
Feldbieins (1967, p. 231) argument against use of bed size is
worthy of note: available beds might be defined differently across
hospitals and smaller hospitals are required to keep a larger
fraction of beds vacant in order to assure a given probability of
bed availability. The latter, they allege, distorts the true cost
picture. In our view the latter phenomenon represents a genuine
scale diseconomy, analogous to inventory costs as between small and
large shops. Because all New York hospitals are required to use
uniform procedures to calculate costs and other
*Upstate in the present corztext refers to the area of the state
outside New York City and Long Island. The latter locations are
excluded because the rate-setting procedure varies between upstate
and down, and because this paper is part of a larger project on
hospital location in the upstate region.
-
310 D.F. Vitaliano, Estimation of hospital cost functions
hospital statistics, the probability of a varying definition of
bed capacity across hospitals is low. Another reason to choose beds
as a size measure is that admissions, census and patient-day
measures all reflect short-run output volume variations and
short-run costs that may lie off the long-run locus of interest to
us. Hospital beds better reflect installed capacity, and planning/
location decisions are usually made in terms of bed capacity.
However, as indicated below (see footnote 4), the results of this
paper are not sensitive to the choice between beds and patient
days.
The data base includes hospitals ranging from 23 beds to 1,070
beds, with a mean and standard deviation of 214 and 175,
respectively. Thus, a very wide variation in hospital size is
included.
Besides measurement of size, it is necessary to allow for
non-size related influences on cost. Among these, three in
particular warrant attention: factor prices, facilities and me t.
cal school affiliation.
The most likely source of factor price variation in the present
situation is between hospitals located in rural areas versus
locations in urban areas. An index of the size of the metropolitan
area in which the hospital is located is utilized to capture this
effect. It varies from 0 (rural area) to 6 (population in excess of
2.5 million). The mean value of this index is 2.6, between 100,000
and 500,000 population.
With regard to service-mix, an unweighted index of 11 available
hospital facilities is employed. (The included facilities are shown
in an appendix.) Francisco (1970) has shown that such an index is a
good proxy for the service-output mix. 2 The mean value of this
index is 3.4. The choice of a facilities or services index in
preference to a case-mix variable reflects the important
distinction between the two made by Tatchell (1983). The former
reflects the supply-side, the latter demand influences. The
service-mix approach may better reflect reality in countries such
as the U.S. . . . The extent, degree of sophistication and quality
of facilities and services offered plays an important role in
attracting doctors, and hence their patients, to particular
hospitals (p. 880).
A dummy variable to represent the presence of a medical school
affiliation is used. The teaching-related costs of a medical school
are likely to exert an upshift, ceteris paribus, on hospital costs
[Culyer et al. (1978)]. Normally, the expected sign of the medical
school variable would be positive.
Finally, a variable designed to capture any market-power related
effects on hospital costs is included. A monopsony or oligr
>psony hospital may be able to exert downward pressure on factor
prices. (I%:sumably regulation of price bits monopoly
exploitation.) Market power iG measured by the share of
2Francisco (1970) showed that an unweighted facilities _ .-dex
performed equally well in a multiple regression e service item.
uation 8s a more complex &es of dummy variable,s for each
individual
-
D.F. Vitaliano, Estimation of hospital cost functions 311
beds in its county represented by each hospital. The mean value
of bed share is 0.28.
The dependent variable is total hospital costs, including
payroll an payroll costs (inclusive of interest and historic
depreciation). All the variables described thus far are as defined
in the American Hospital Association
, survey. We may summarize the hypothesis thus far advanced,
C = F(B, F, M, u, s), (61 where
C = total hospital costs, B =number of beds available, F = index
of hospital facilities, M = medical school affiliation (a dummy), U
=index of urban area size, S =market share, the hospitals share of
total beds in the county.
In the next section we use multiple regression to estimate (6)
using alternate functional forms (3) and (4) and estimating
techniques, with attention particularly focused on the effect of
bed size on C. The role of occupancy rates and length of stay is
also discussed in section 5.
5. Econometric results
We begin by first estimating the total cost function using the
quadratic functional form typically found in the literature. Eq.
(7) presents that result (t ratios in parenthesis),
Total cost = - 3,073,130* + 57,477 Beds* + 18.27 Beds2 * *
(-2.46) (5.99) (1.84)
+ 6,733,225 Med. schl. + 1,202,13 1 Facil.* (3.98) (4.78)
+ 682,736 Urban* - 20,07 1 Share, (2.73) (-1.13)
R2 =0.89, F(6, 159) =214.4,
* = signitrl dnt at 95% level, ** = significant at 90%
level.
Many researchers would find (7) quite an acceptable result: most
of the coeficients have the expected signs and are significant at
the 9 the R2 is very high for cross-section data. The coefficients
on th
-
312 D.F. Vitaliano, Estimation of hospital cost functions
is not significant at the 95% level but the null hypothesis of a
zero coefficient can be rejected at the 900/ level. Overall, eq.
(7) broadly conforms with the results widely reported in the
literature. Only the market share variable Share, which was
somewhat speculative to start with, is clearly insignificant.
Dropping this variable from the regression has no effect on the
remaining coefficients.
The Goldfeld-Quandt test of (7) indicates the existence of
heteroscedasticity associated with hospital bed size: a test
statistic in excess of 70 versus a critical value of about 1.5 (95%
level). The Park-Glejser test allows one to estimate the
appropriate weight to use in a weighted least squares regression,
the most common technique for allowing for heteroscedasticity
[Pindyck and Rubinfeld (1981, pp. M-152)]. The test involves
regressing the residuals from (7) on bed size and using the
resultant coefficient as the appropriate weight.3 In the present
instance that weight is 1.26; thus eq. (7) is rerun using weighted
least square and shown below (t ratios in parentheses),
Total cost = - 1,317&U* +64,303 Beds* + 24.57 Beds** (-2.49)
(10.22) (2.30)
+ 5,194,528 Med. schZ.* + 206,373 Urban** + 470,134 Facil?
(3.85) (1.73) (3.03)
- 9,686 Share, (0.99)
R=0.92, F(6, 159) = 371.0, .
* = significant at 95% level, ** = significant at 90/, level.
(8)
In eq. (8) the coefficient on Beds* is now significant and a
shallow b-shaped average cost curve seems clearly confirmed. The
quotes around the R* indicates that it is a pseudo correlation
coeflficient, consisting of the simple correlation between C and
fitted C using (8). This measure is used because there is no
entirely satisfactory measure of R* when weighted least squares is
employed [Pindyck and Rubinfeld (1981, p. 146)]. The high R* in (8)
and (9) combined with only one insignificant coeficient suggests
the absence of any serious multicollinearity among the explanatory
variables.
It should be noted that the negative constant term is not a
problem because inclusion of typical values of Facil., which
represents a further dimen- sion of output, will render the
intercept positive [Klein (1962, p. 120)].
3The result is In e2 = 22.7 + 1.26 In Beds, R2 =0.14,
(18.0) (5.15) where e2 is the squared residuals from (7).
-
D.F. Vitaliano, Estimation of hospital cost functions 313
Utilizing (8) and the elasticity of average cost (S), along with
the mean value of Facil. (= 3.4), the average cost falls up until
bed size of 107 is reached and rises thereafter. At the mean bed
size of 214, the average cost elasticity e = 0.028 and total cost
elasticity e = 1.028.
Turning next to alternate functional forms of the estimating
equation, the log form equation (3) is used to re-estimate the
total cost function (t ratios in parentheses),
In Total cost = 11.2485 + 0.9035 In Beds* (79.6) (24.59)
+ 0.2734 Med. schl.* + 0.02 1 Urban* + 0.059 1 Facil.* (2.42) -
- (1.97) - (4.49)
+ 0.001 Share (1.16)
R2=0.92, F(5, 160)= 15,871,
* = significant at 95% level. (9)
Eq. (9) was fitted using weighted least squares and the same
weight employed in (8). An unweighted version gave quite similar
results but with somewhat lower t ratios on the size and intercept
terms. It clearly indicates significant economies of scale and
decreasing costs, with an elasticity of total cost of 0.90. The
null hypothesis that l/v=e= 1 is rejected at the 95% and 99%
confidence levels (one-tail test). The coefficients on medical
school affiliation, urban size and facilities are all positive, as
a priori reasoning would suggest. In both the log and quadratic
form of the cost function the market share variable S is not
significantly different from zero. The results suggest that perhaps
researchers have not gone far enough in exploring alternative
specifications when estimating hospital cost functions. A given
data set that apparently suggests a conventional U-shaped average
cost curve is shown instead to imply significantly decreasing costs
with respect to hospital bed size.
Differences in capacity utilization and/or average length of
patient stay in hospital might introduce error into the analysis
because, for example, larger hospitals might display lower average
cost per bed because patients stay for longer periods and the later
part of the hospitalization episode consists mostly of hotel costs.
Systematic variations in occupancy rates, with larger hospitals
displaying higher rates, may lead to greater ease in spreading
fixed costs as hospitals grow in size. While a genuine source of
scale economies, one would be interested in clearly identifying and
measuring it. In the event, inclusion of average length of stay or
occupancy rate into eqs. (8) and (9) resulted in insignificant
coefficients on those variables with virtually no
-
314 D.F. Vita!iano, Estimation of hospital cost functions
impact on the other coefficients. The reason for the failure of
length of stay (LOS) or occupancy (OCC) to exert any size-related
effect on hospital costs is undoubtedly because the New York State
regulatory system imposes financial penalties on hospitals that
fail to adhere to predetermined LOS and OCC guidelines [Health Care
Financing Administration (19Sl)].
Although only cost and beds are in log form in eq. (9),
estimation with all right-hand variables (except the medical school
dummy) in logs gives virtually the same results in terms of cost
elasticity. Some economists seem to prefer patient days to beds as
an output measure in cost function estimation in spite of the
reasons for choosing beds discussed above. Consequently, eq. (9)
was run using adjusted patient days (American Hospital Association
definition) instead of beds. Happily, the results are virtually
identical? In the following section an attempt is made to
discriminate between the quadratic and log-form cost functions.
One of the most powerful tests for detecting functional form
misspecifi- cation is RESET (regression specification error test)
developed by Ramsey (1969j; its properties and power were explored
by Thursby and Schmidt (1977).
Consider the standard linear regression model y=/IiXi + u, where
y is the dependent variable, X the explanatory variable (s), u the
disturbance term and /? the coefficients to be estimated. The null
hypothesis of no misspecifi- cation involves E(u 1 X) = 0, whereas
the alternative hypothesis E(u 1 X) = A # 0 involves one or more of
the following misspecification errors: omitted variables, incorrect
functional form, and correlation between X and u mursby and Schmidt
(1977, p. 635)]. Assuming ilk 42, the RESET test involves forming
the augmented regression y= /IX + #Z+ u and testing whether 4=0 in
the usual way. This corresponds to the null hypothesis
E(uIX)=O.
Using Monte Carlo methods, Thursby and Schmidt explored various
candidates for 2 and found, among other things, that powers of
fitted values of the dependent variable (i.e., j2,jj3) performed
very well: a lOOo/, detection rate (95% confidence level) when a
known *true functional form was tested against an alternative
model.
It is a straightforward matter to rerun eqs. (8) and (9) adding
a c2 term to
?he alternative regression (with t ratios in parentheses) is In
Total cost = 6.385* + 0.873 In Patient days* + 0.03 Facil.*
(17.16) (23.6) (2.83) +0.319 Med schf.* +0.046 Urban size*, (10)
(4.50) (4.17)
R2 =0.91, N = 166, RESET test =0.53*, is significant at 95%
level. The Park-Glejser test indicates no heteroscedasticity in
(lo), and the null of equal cost elasticity in (10) and (9) is not
rejected (95% level of confidence). The coincidence between the two
estimates may suggest the existence of long-run equilibrium.
-
D.F. Vitaliano, Estimation of hospital cost functions 315
each, where e is the Wed value of total cost estimated from (8)
and (9), respectively. The results are presented below (t ratios in
parentheses),
Total cost = - 6,486,148 i- 154,683 Beds - 526 Beds2 (- 5.01)
(8.01) (5.43)
- 586,854 Med. schl. + 325,249 Urban + 302,373 Facil. (-2.16)
(1.37) (1.08)
- 9,006 Share + 0. (-0.55) (5.65)
R2 =0.91, I (8 1
In Total cost = 11.20 + 0.933 In Beds + 0.212 Med. schl. (3.17)
(0.97) (0.60)
+ 0.061 Urban + 0.0638 Facil. + 0.001 Share (2.30) (0.93)
(0.75)
-o.7419e2, ( -0.002)
R2 = 0.89. I (9)
The implications of the RESET test are clear: the coefficient of
e2 in the quadratic form is significantly different (99% level of
confidence) from zero and the null hypothesis of no
misspecification is rejected. [The small size of 4 in (8) is due to
the dimensions of e: millions squared.] In contrast the 4
coefficient in (9) is highly insignificant and the null of no
misspecification cannot be rejected. Thus, it seems reasonable to
conclude that general surgical-medical hospitals exhibit
significantly decreasing costs pr patient bed as bed size
increases.
The next thing to be discussed are potential errors or bias
other than functional form that might vitiate the inference of
decreasing costs.
Use of a facilities index is an approximation to some ideal
measure designed to control for the composition of hospital output.
Because larger hospitals will generally deal with more complex and
costly cases, the efFect of failing to fully allow for case-mix is
to ouerstate the costs of larger hospitals. Any bias thereby
introduced thus works to strengthen the conclusion that decreasing
costs obtain in hospitals. In addition to using the Facil. index,
Facile2 was tried in order to capture any non-linear effects, as
well as a bed size facilities interaction term. he FaciL2 usually
performed somewhat better than Fad.
-
316 D.F. Vitaliano, Estimation of hospital cost functions
in the sense of having a smaller standard error, but did not
affect the bed size coefficients in any meaningful way in either
the quadratic or log form of the cost function. The facilities-bed
size interaction was not sign&an different from zero in either
functional form.
It seems safe to conclude that the results presented in eq. (9)
are robust both as to functional form and errors in variables and
that pure size-related decreasing costs exist in the 166 hospitals
herein analyzed. A total cost elasticity of 0.9 and average cost
elasticity of -0.10 is found, which in turn implies a returns to
scale coefficient v = 1.10. Given the small standard error (0.0367)
on the bed size variable in eq. (9), it appears that the case for
rejecting the consensus hypothesis of a U-shaped hospital average
cost curve is strong. Returns to scale of 1.1 are quite significant
and lie at the upper end of the range reported in studies of other
industries [Mansfield (1985, pp. 223-225), Walters (1961)].
6. Conclusion
Using cross-section weighted least squares to estimate a total
cost function for 166 acute care hospitals in New York State in
1981, an elasticity of total cost with respect to bed size of 0.9
and average cost of -0.10 is found.
The reason for overturning the U-shaped long-run average cost
curve in preference for significantly decreasing average costs lies
with the choice of the cost function that is estimated. We have
shown that our own data set is capable of replicating the standard
result very nicely. Rut use of a log form cost function that is
fully consistent with economic theory and the insti- tutional
arrangements in the hospital industry produce results that are far
more satisfactory from an econometric point of view and which are
consistent with the great body of cost studies covering other
sectors of the economy - including regulated and public utility
industries similar to the New York hospitals examined here.
It is worthwhile pondering briefly the possible sources of the
scale economies uncovered in this paper. The most commonly accepted
reason for falling unit costs is indivisibilities of labour and
capital. A hospital is composed of highly specialized personnel and
equipment. To the extent these specialized components reach minimum
costs at different activity levels, average costs for the hospital
as a whole will decline as the scale of activity grows. In
addition, the purely hotel aspects of a hospital (e.g., catering
and cleaning) are probably subject to scale economies, if one is to
judge by the ever-growing size of newly-built commercial hotels.
Average costs are thought to eventually turn up when the preceding
forces are overwhelmed by increased control and decision-making
costs as the unit grows. But use of computers and modern management
methods may have the effect of delaying the point of upturn very
considerably.
-
D.F. Vitaliano, Estimation of hospital cost functions 317
q dixt List of items in facilities index
1. Electroencephalography (EEG) 2. CT. scanner (head unit) 3.
C.T. scanner (body unit) 4. Diagnostic radioisotope facility 5.
Open heart surgery 6. Ultrasound 7. Megavolt radiation therapy 8.
Therapeutic radioisotope facility 9. X-ray radiation therapy
10. Ambulatory surgical services 11. Kidney transplant
References
American Hospital Association, 1981, Annual survey of hospitals
(Chicago, IL). Bays, C.W., 1980, Specification error in the
estimation of hospital cost functions, Review of
Economics and Statistics 62, no. 2, 302-305. Berki, R., 1972,
Hospital economics (Heath, Lexington, MA). Berry, R., 1967, Returns
to scale in the production of hospital services, Health Services
Research
2, Summer, 123-129. Berry, R.E., 1973, On grouping hospitals for
economic analysis, Inquiry 10, Dec., 5-12. Carr, J.W. and P.
Feldstein, 1967, The relationship of cost to hospital size, Inquiry
4, June,
45-65. Cowing, T.G., A.G. Holtmann and S. Powers, 1983, Hospital
cost analysis: A survey and
evaluation of recent studies, in: R.N. Schemer and L. Rossiter,
eds., Advances in health economics and health services research,
Vol. 4 (J.A.I. Press, Greenwich, CT).
Culyer, A.J., J. Wiseman, M.F. Drummond and P.A. West, 1978,
What accounts for the higher cost of teaching hospitals, Social and
Economic Administration 12, no. 1, 20-23.
Evans, R.G., 1971, Behavioural cost functions for hospitals, The
Canadian Journal of Economics IV, no. 2, 198-215.
Feldstein, M., 1968, Economic analysis for health service
efficiency (Markham, Chicago, IL). Feldstein, P., 1983, Health care
economics (Wiley, New York). Francisco, E.W., 1970, Analysis of
cost variations among short-term general hospitals, in: H.
Klarman, ed., Empirical studies in health economics (Johns
Hopkins University Press, Baltimore, MD).
Grannemann, T.W., R.S. Brown and M. Pauly, 1986, Estimating
hospital costs: A multiple output analysis, Journal of Health
Economics 5, no. 2 107-127.
Health Care Financing Administration, 1981, Abstracts of State
Legislated Hospital Cost Containment Programs, Publication no.
03089 (Department of Health and Human Services, Washington,
DC).
Hombrook, M.C. and A.C. Monheit, 1985, The contribution of
case-mix severity to the hospital cost-output relation, Inquiry 22,
Fall, 259-27 1.
Hough, J.R., 1985, A note on economies of scale in schools,
Applied Economics 17, 143-144. Johnston, J., 1984, Econometric
methods, 3rd ed. (McGraw-Hill, New York). Klein, L., 1962, An
introduction to econometrics (Prentice-Hall, Englewood Cliffs, NJ).
Lave, J. and L. Lave, 1970, Hospital cost functions, American
Economic Review 60, no. 3, 379-
395. Mansfield, E., 1985, Microeconomics, 5th ed. (Norton, New
York).
-
318 D.F. Vitaliano, Estimation of hospital cost functions
Nerlove, M., 1963, Returns to scale in electricity supply, in:
C.F. Christ et al., eds., Measurement in economics (Stanford
University Press, Stanford, CA).
Pindyck, R.S. and D.L. Rubinfeld, 1981, Econometric models and
economic forecasts, 2nd ed. (McGraw-Hill, New York).
Ramsey, B.B., 1969, Tests for specification errors in classical
linear least squares regression analysis, Journal of the Royal
Statistical Society, Series B, 31, no. 2, 35&371.
Rao, P. and R.L. Miller, 1971, Applied econometrics (Wadsworth,
Belmont, CA). Sloan, F. and B. Steinwald, 1980, Insurance,
regulation and hospital costs (Lexington Books,
Lexington, MA). Tatchell, M., 1983, Measuring hospital output: A
review of the service-mix and case-mix
approalches, Social Science and Medicine 17, no. 13,871-887.
Thursby, J.G. and P. Schmidt, 1977, Some properties of tests for
specification error in a linear
regression model, Journal of the American Statistical
Association 72, no. 359, Sept., 635-641. Vitaliano, D.F. and S.
Heshmat, 1986, Hospital cost containment regulations and the
diflusion
of the cat scanner: A case study, Journal of Health and Human
Resources Administration 9, no. 2, Sept., 185499.
Wallis, K.F., 1979, Topics in applied econometrics (Blackwell,
Oxford). Walters, A.A., 1961, Production and cost functions,
Econometrica 31, l-66. Watts, @.A. and T.D. Klastorin, 980, The
impact of case mix on hospital cost: A comparative
analysis, Inquiry 17, Winter, 357-367.