Hospital Investment Decisions and the Cost of Capital
Author(s): Gerard J. Wedig, Mahmud Hassan, Frank A. Sloan
Source: The Journal of Business, Vol. 62, No. 4 (Oct., 1989), pp. 517-537
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/2353364
Accessed: 29/07/2009 01:21
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=ucpress.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the
scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that
promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].
The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The
Journal of Business.
http://www.jstor.org
Gerard J. Wedig
Boston University
Mahmud Hassan
Nashville, Tennessee
Frank A. Sloan
Vanderbilt University
Hospital Investment Decisions
and the Cost of Capital*
I. Introduction
Hospital investmentdecisions depend on several
factors that are not relevant to the typical forprofitfirm.First, most hospitalsare not-for-profit
organizations.Roughly 60%are privatelyowned
not-for-profits(NFPs); about 25% are operated
by public agencies (AmericanHospital Association 1984). The remaininghospitals are run on a
for-profit (FP) basis. NFPs have no clearly
defined objectives, and there is no consensus
about their objective function (Newhouse 1970;
Lee 1971;Feldstein 1977; Sloan 1988).
Second, virtuallyall paymentsto hospitals, especially for inpatientcare, come from third parties rather than directly from the recipient of
care. There are substantial intertemporal and
geographicdifferences in the methods third parties use to pay for hospital care, as well as their
generosity (Sloan and Becker 1984). Some plans
pay on the basis of the price set by the hospital
* This researchwas supportedin partby grant18-P-98267/
1-02 from the U.S. Health Care FinancingAdministration
(HCFA)to the Centerfor HealthEconomicsResearchwith a
subcontractto VanderbiltUniversity. We wish to thankparticipantsin the MicroeconomicsWorkshopat Vanderbiltand
ProfessorsJ. S. Butler, Cliff Huang,and V. KerrySmithfor
helpful suggestions. An appendixis availableon request.
(Journal of Business, 1989, vol. 62, no. 4)
? 1989 by The University of Chicago. All rights reserved.
0021-9398/89/6204-0005$01 .50
517
This study addresses
two issues conceptually
and empirically.How
does hospital ownership type affect hospital investment
choices? How do differences in the way
hospitalsare paidcost- versus chargebased reimbursement-affect hospital
investment?We compute cost-of-capital
measuresfor both forprofitand not-for-profit
hospitals. Whetheror
not hospital dependence on cost-based
payment stimulatesinvestment depends on
the generosity of such
paymentrelative to the
economic cost of capital. Empirically,we
find that for-profithospital exit/entry decisions are guidedby the
generosity of payment
to a greaterextent than
the not-for-profits.
518
Journal of Business
(subjectto discounts) while others pay "retrospectivecosts" in which
the insurer compensates the hospital for the "reasonable" costs incurred on behalf of the persons they insure. Yet another system of
payment establishes price prospectively, either by formula, negotiation, or a combination of these methods. Medicare, for one, has
switched from a retrospective cost to a prospective payment system
for paying hospital operating cost, but it still pays capital cost on a
limited retrospective basis.
At the very least, these features complicate the task of modeling
investment behavior. This perhaps accounts for the limited work on
hospital investment to date, an exception being the work of Ginsburg
(1970).
The hospital investmentprobleminvolves a wide varietyof issues of
intrinsicinterestto economists as well as a uniqueexperimentalsetting
in which to analyze these issues. First, there is the opportunityto study
the effects of organization(NFP) status on investmentflows. The fact
that NFPs coexist with proprietaryhospitals offers an ideal "controlled" setting in which to study the question. Second, there is the
opportunityto study the effects of forms of demandregulationas well
as third-partypayment on investment. The issues are similarto those
in regulatedindustries, such as public utilities, and yet unique in the
sense that cost-based reimbursementis "mixed" with other forms of
reimbursement.Insights gleaned here may thus be applied to other
industries, such as defense contracting,where cost-based paymentalgorithms by some government agencies are mixed with charge-based
payment by private customers and some governmentsas well.
This study thus addresses these issues. How does NFP status-in
particular,differencesin organizationalobjectives from theirfor-profit
(FP) counterparts-affect hospitals' investmentdecisions?How do the
unique sources of hospital revenue affect investmentby both hospital
types? Does cost-based reimbursementencouragecapital acquisition,
as argued by many in the industry?Finally, how is the trend toward
paying hospitals on a prospective basis likely to affect investment?
Section II presents the model for FP and NFP hospitals separately
and solves for key features of their investmentand financialbehavior.
The focus is on how cost-based reimbursementaffects the hospital's
cost of capital and on differencesin decisions about investmentacross
ownership. Section III deals with specific aspects of NFP hospital
investment, emphasizing important differences unique to the NFPownershipform. Section IV describes our method for developingempiricalestimates of the cost of capitalfor both FP and NFP hospitalsby
state and year over the time interval 1974-82. Section V presents
econometrictests of the role of the cost of capitalon hospitalentry/exit
and investment. Finally, Section VI concludes the articlewith a discussion of the theoreticaland policy significanceof our work. We exclude
analysis of public hospital behavior in what follows.
519
Hospital Investment
II.
The Model
The assumptionsthat define both FP and NFP investmentmodels are
similarand are presented simultaneouslyin orderto facilitatecomparison.
1. Objectives. FP hospitals maximize the marketvalue of the hospital as defined by the summed market value of hospital debt and
equity; however, NFP hospitals maximize the discounted present
value of the flows of utilities realized by hospital administrators,the
board, and medical staff, where utility is a function of both quantity
and quality of output (as defined below).1 The discount rate used to
discount flows of utility in the NFP case need not be the same as the
rate used to capitalize proprietarycash flows. In what follows we distinguishbetween these two rates usingR to denote the FP discountrate
and R' to denote the NFP time rate of preferencefor utility.
2. Demand. The hospital's inverse demandcurve for services is a
weighted average of the demand of three types of payers: (1) insured
charge-basedpayers, who pay the hospital a price which is a decreasing function of the quantityof charge-basedpatients served as well as
quality, as defined below; (2) cost-based payers, who reimbursethe
hospital for its variable costs and reimbursehospitals for their capital
costs according to a preset formula; and (3) self-insured(uninsured)
payers, who also pay accordingto the hospital's chargeschedulebut at
a greater discount than insured charge-payingpatients (Ginsburgand
Sloan 1984).Traditionally,charge-payinginsurancehas been less complete than the cost-based variety. For this reason, consumerscovered
by charge-basedinsurance are responsive to price. Thus, the insured
charge-baseddemandcurves, as well as the uninsureddemandcurves,
slope downwardfor the usual reason.2We assume that the cost-based
demand curve has an elasticity of zero. Mathematically,the formula
for the hospital's inverse demandcurve is given by
P
=P(.)+
A
( X
+
r K)
+
a)+ (1 -
-
p )p,
(1)
where
p' = weighted average price;
P = proportionof hospital receipts from charge-basedpayers;
p = marketprice of output (charge-basedprice);
1. This is the same assumptionmade by Newhouse (1970)and Feldstein(1977).For
the sake of focus, we do not consider the possibility that administrators,boards, and
medical staff have differentor conflictingobjectives.
2. Since 1982, there has been growthin charge-payinginsurers;e.g., health maintenance organizationsand preferredprovider organizations,which obtain sizable discounts from charges. These insurers had negligible market shares duringthe period
covered by this study and thereforeare not consideredhere. We treat Medicarereimbursementas cost-based.
Journal of Business
520
(x = proportionof hospital receipts from cost-based payers;
w = wage rate;
L = level of labor input;
X = quantity of output;
r = weighted averagereturnon debt and equitypaidby cost-based
payers;
q = price of capital good;
K = level of capital inputs;
Zi = present value of depreciationreimbursedby cost-basedpayers
per dollar of investment;
I = level of investment expenditure;and
,r= proportionof p paid by uninsuredpatients.
Both NFP and FP hospitals face the same inverse demandcurve.3
3. Production. Both types of hospitalsuse capital(K) and labor(L)
to produce quantity(X) and quality (Y) with productiontechnologies
X = F(K,L)
(2)
and
Y = G(k,O),
(3)
where k = KIX (capital intensity) and f = LIX (laborintensity).4
4. Finance. Investment capital for FP hospitals may be obtained
from any of three sources: (1) retainedearnings,(2) stock issue, or (3)
debt issue. However, we assume perfect certainty;the hospital's optimal mix of fundingdepends on the associated tax liabilitiesof investors and its level of tax shields (DeAngelo and Masulis 1980). We
assume that all investment expendituresby FPs are financedwith the
optimal mix of funding so defined.5 Funds for investment for NFP
hospitals can be generated from either of two sources, (1) retained
earningsor (2) debt issuance. Technicallyspeaking,NFP hospitalscan
also obtain investment funding from government grants or philanthropy, but these sources of funding have largely disappeared
(Cohodes and Kinkead 1984)and thus are not considered here.6
3. In the calculationsthatfollow, the payer sharesare assumedto be optimizedat the
marginin order to maximize average revenues. Moreover, an internalsolution to the
problemis assumedto exist so that, e.g., P,, = 0 at all pointsin time. The significanceof
this assumptionlies in the fact that the envelope theoremimplies that if hospitalscontinuouslymaximizewith respect to payer shares, these sharescan be treatedas exogenous in the derivationof optimalcapitalstock. Thispointis reiteratedin the calculations.
4. This input-orientedspecificationof quality has been used by Newhouse (1970),
Feldstein (1977), and others in studies of hospitalbehavior.
5. Under a more realistic scenarioincorporatinguncertainty,the risks of bankruptcy
would also have an impact on the funding decision (see Wedig, Sloan, Hassan, and
Morrisey1988).However, this addedrefinementwould not affect any of the key results
to follow.
6. Failureto measurethe cost andlevel of philanthropyshouldnot bias our measureof
the cost of capitalbecause (1) the shareof philanthropyis very small, and (2) hospitals
set the marginalcost of philanthropyequalto cost of otherfundingsources, the costs of
which we do measure.
Hospital Investment
521
The Proprietary Case
Given assumptions 1-4 above, the FP hospital's investment problem
can be solved using the technique of optimal control. Without any
theory to guide the costs of adjustment, the technique chosen here
ignores such costs. We estimate the costs of adjustmentempirically,
using a distributedlag as in Jorgenson(1963).
The FP hospital is like any other firm with respect to its financing,
and this behavior is alreadywell understood. For-profitfinancingproceeds according to the standardtheory of optimal capital structure,
which in turn determinesits cost of funds, R.
Under our model, the FP hospital's problemcan be written as
max
T)[p'F(K,L)
-
e-Rt{(1
- wL]
- q(1 - 4j)I + TZqI}dt,
subject to
K = I - SK,
(4a)
and where
+ = investment tax credit available to FP hospitals;
Z = present value of depreciationallowance for corporatetax purposes (distinct from Z');
and
(, =
qZ1I
X ) + (1 - a - Pap.
+
XP
(1)
Equation (4a) gives the basic differentialequation guiding movements in the stock of capital, while (1) reiterates the basic demand
constraintfacing hospitals.
The solution to (4) subject to the constraints(4a), incorporatingthe
above assumptions, yields this first-ordercondition for the hospital's
stock of capital:
pFK + py YkX + PXXKX
- TZ) -(1-
q(R + 8)(1
qV
(1
-
)[I3
+
(1
)ot[r + Z' (R + 8)]
-
-
(5)
13)r]
Details of the derivationof marginalconditions for capital in both FP
and NFP sectors are presented in an appendix availablefrom the authors.
Intuitively, equation (5) instructs the hospital to set the marginal
revenue product of capital equal to its marginalinputprice. The right
side of (5) represents a modifiedcost of holding capital inputs, where
Journalof Business
522
the modificationincorporatesthe peculiarelements of cost-basedreimbursement.The firstterm in the numeratoron the rightside of (5) is the
standard Jorgenson cost of capital, incorporatingthe various taxrelated incentives to hold capital as well as the interest and depreciation rates, while the second numeratorterm measures the reimbursement that cost-based payers allow for capital expenses. If there were
no cost-based reimbursement,a would equal zero, and the hospital's
cost of capital would just be Jorgenson's cost of capital.
Equation (5) can be further refined to account for some additional
institutionalcharacteristicsof hospital payment. Blue Cross, the main
privateinsurerthat often reimburseson cost, sometimespays a plus (-y)
on reasonable cost (excluding cost of equity) as a partial return on
equity. In addition,mainlybecause of bad debts, insuredcharge-based
patients paid 96% and uninsured patients only paid 72% of hospital
chargesin 1981(Ginsburgand Sloan 1984).Althoughthese percentages
have undoubtedlyvaried over time, no data are availableto document
this. Equation (5) then can be rewrittenas
EK + Py YkX + PXXKX
-
_
P
((R + 8)(1
-
-/Z)
(1 -v)
-(1
- T)(Ot + y
[.9613+ (1 -
a
-
BC)[r + Z' (R + 8)]
13)(0.72)]
p
(5a)
where BC equals the proportion of revenue from Blue Cross costbased plans, and (cip) is henceforth referredto as the cost of capital.
The effect of cost-based payer dependence on capital acquisitionis
ambiguous. Its sign depends on the relative generosity of cost-based
payment comparedto the hospital's true economic or "Jorgensonian"
cost of capital. Specifically, it can be shown that if the effective return
that the hospital's cost-based payers allow exceeds the hospital's
Jorgensonian cost of capital, then marginalincreases in cost-based
share should stimulatecapital acquisitionand vice versa.7 Intuitively,
this occurs because a marginalincrease in cost-based share represents
7. This can easily be shown by differentiatingthe rightside of (5) with respect to the
proportionof cost-based payers, at. This result stands in interestingcontrast to the
prevailingwisdom held by industry"practitioners,"which holds that cost-basedreimbursementreduces the hospital's cost of capital and hence always encouragescapital
acquisition.The present result shows that such a claim rests on the assumptionthat
eithercost-basedpayment(a) reducesfinancialrisk(a factornot consideredin our model
of perfect certainty)or (b) is paid so generouslythat it exceeds the economic cost of
capital.
523
Hospital Investment
a substitutionof cost-based for charge-basedrevenues. Wheneverthe
cost-based returnon capital exceeds its Jorgonsoniancost, cost-based
payers return more than charge-basedpayers at the marginand the
substitution encourages capital acquisition. While cost-based reimbursementpossibly introducesa distortionon capitalinputuse, there is
no parallel distortion on the labor side (except throughthe insurance
effect on quantity and quality) since the cost payer always pays the
market wage, no more or no less. Thus, one implication of this
modified Averch-Johnson(1962) result is that cost-based payers who
pay the hospital somethingother than its Jorgensoniancost of capital
induce the hospital to use an allocatively inefficient capital-to-labor
ratio.
III.
Extensions to Not-for-Profit Hospitals
Perhaps the biggest obstacle in extending the FP hospitals results is
delimitingthe numberof possible objectives that NFPs may have. A
general approach, and the one utilized here, is to extend Feldstein's
(1977)model of quantityand quality maximization.Using his assumption that NFP hospitals maximize a utility function in the quantityand
quality of care, we model the effects of reimbursementmethods on
investment and compare the results to those obtained under profit
maximization.
Formally, then, we assume that hospital behavior and constraints
are summarizedby the above assumptions.Thus the hospital chooses
quantity (X) and quality (Y) to
max
{
eR'tU(X,
Y)dt,
(6)
subject to a break-evenconstraint
p' + d =AC,
(6a)
where d equals the hospital's net borrowingper unit of output[D/F(-)],
and AC equals average cost:
AC
(X
wL+
X
+
TB
X)'(b
~~~~~~(6b)
where T equals the market interest rate on debt, and B equals the
hospital's stock of debt.
Finally, (6) is also constrainedby the differentialequations
K = I - AK,
(6c')
B = D.
(6c")
and
Journal of Business
524
Substituting (6b) and (1) into (6a), the constraints defined above
collapse into a single constraint expressing the hospital's labor-tooutput ratio (or labor intensity) as a function of its level of investment
net borrowingand other variables. Thus, (6a)-(6b) and (2) become
-e [a + (1-
(6d)
- P)ir]p + o(rb + Zqi) + d - qi-rb
Finally, substitutingthis constrainttogether with (6c) and the production function relationships(2)-(3) into the originalobjective function, the NFP hospital's problemcan be rewrittenas
00
e R t ufF(K,L),
max
?0
G kg [I + (I - ot - P~lp
(6e)
L_
+ ot(!rb+ Zqi) + d - qi - !rb dt
subject to constraints (6c') and (6c").
The NFP hospital's first-ordercondition for capital is
u>2,
(U1 I XKX + U2TYk +
=
q(R' + 8)
f
-
+ (1
U2Ye(PXXKX+ p y YkX)
o[Z(R' + 8)]
-
)
(7a)
a-
where
i
=
In+ (1
- a -
)s
Its marginalcondition for borrowingis
R
= (1 - a)r.
(7b)
As in the proprietarycase, equation(7a) instructsutility-maximizing
hospitals to set the marginalvalue (in this case, utility)of capitalequal
to its marginalcost or shadow price. The differencein this case is that
the marginalvalue of capitalis measuredby its contributionsto hospital quantity and quality, adjusted by the factor (wIU2Ye)to convert
utility units into dollar terms. The tax policy parametersfor the NFP
hospital are zero.
Like the proprietaryhospital, the NFP institution'scost of capitalis
a modifiedJorgensoniancost, where, as before, the hospital's reliance
on cost-based payers ambiguouslyaffects the shadow price of capital.
Indeed, the only difference between the right side of (5) comparedto
the right side of (7a) are (i) the absence of tax parametersand (ii) the
absence of an explicit returnon assets paid by cost-based payers.8As
8. Of course, cost-basedpayersdo allow a "pass through"of debt service and in this
sense allow a returnon assets. This returndoes not appearon the right side of (7a)
because the modeldoes not makethis paymentcontingenton the level of physicalassets
Hospital Investment
525
before, the effects of cost-based reimbursementon capital acquisition
are ambiguous, the sign dependingon the relative generosity of costbased reimbursementcompared to the true economic cost of holding
capital (R' + 8).
Condition (7b), which gives the hospital's marginalcondition for
borrowing,indicatesthat the hospitalsets the marginalcost of debt and
equity financingequal to one another in deciding its optimal funding
mix. The interestingaspect of this conditionis the fact that the cost of
debt is discountedby (1 - a) in comparingit to the opportunitycost of
hospital-generatedequity. This reflects the simple fact that cost-based
payers do not pay NFP hospitals a returnon invested equity although
debt expenses are passed through.9Thus the effective cost of debt is
discounted by a factor equal to (1 - oa).
More important are the effects of these unique characteristicsof
hospital finance on the hospital's investment decisions. Inspection of
(7a) shows that the NFP cost of funds differs from the normalproprietary case in that it is measuredby the discount rate appliedto utility
flows. Assuming that the costs of debt and equity are equal at the
margin,this parameteris an accurate measure of the overall marginal
discountrate appliedto utilityflows. Clearlythis measureof the cost of
funds may differfrom the FP hospital's measure,which is constructed
from the average tax-adjustedcosts of debt and equity. Specifically,
the NFP hospital's tastes for immediate consumption of utility will
tend to raise its costs of fundingand vice versa.
Finally, in the absence of significantlevels of risk, (7b) may not hold
as an equality with (1 - ot)T< R' at the margin. If so, hospitals would
use 100%debt finance, and their cost of funds would be the cost of
debt. 'O
IV.
Cost of CapitalEstimates
We developed cost of capitalestimatesfor FP and NFP hospitalsbased
on equations (5) and (7a). Measures of (cip) were developed for 49
states (excludingAlaska and Hawaii but includingthe District of Columbia)for the years 1974-82, separatelyfor FP and NFP hospitals.
Parametersthat vary over time and by state are the frequencydistri-
the hospitalholds. In realitythe debt expenses associatedwith physicalassets only are
allowed in that a complicated series of rules disallows earningson financialassets.
Below, the calculationof the NFP cost of capitalacknowledgesthis by includingthe debt
service paymentin the cost-based reimbursementlevel for physicalassets.
9. We discuss the natureof the bias cost-basedpayers inject into the NFP hospital's
borrowingdecision in greaterdetail in a recent article. See Wediget al. (1988).
10. The theoreticalpossibilityof 100%debt financeand its implicationsfor the cost of
fundingare emphasizedhere to reflectthe fact that so muchof recent NFP fundinghas
been throughthe use of debt. See Cohodesand Kinkead(1984)for a discussionof trends
in hospitaldebt-versus-equityfinancing.
Journal of Business
526
bution of payer shares by type of payer (commercialinsurers, which
always pay charges; Blue Cross, which is classified according to
whether the plan paid cost or charges;Medicareand Medicaid,which
always paid cost; and self-pay), output price, and-,forBlue Cross cost
plans, depreciationpolicy and the plus factor.
Data on payer shares came from several sources. Data on private
payer benefit payments for hospital care came from annual issues of
the Health InsuranceAssociation of America's Source Book of Health
InsuranceData (1974-82). Data on paymentsfor hospitalcare by Medicare and Medicaidwere drawnfrom variouspublicationsby the Social
Security Administrationand the Health Care Financing Administration. Data on spendingfor hospital care, needed to computethe payer
shares, came from American Hospital Association's (AHA) "Annual
Hospital Survey" (1974-82). We determinedwhether the Blue Cross
plan paid on a cost- or charge-basisand the Blue Cross plan depreciation policy and plus factor from unpublishedsurveys of Blue Cross
plans.11Although there has been considerableinterstate variationin
the cost-based share for decades, there was no trend in this share
during 1974-82, but the share of revenue from self-pay sources increased.
The outputprice came from unpublished"AnnualHospital Survey"
(1974-82) data aggregatedby state and year with 1977 = 1.0 and New
York the base state. Our index of investment-goodprices is by region
and year. We used unpublishedconstruction-costdata by nine census
divisions and years from the U.S. Bureau of Economic Analysis. We
used annual data for the equipmentcomponent of the index from the
Survey of Current Business. Equipment prices do not vary by region.
We assigned weights derivedfrom investmentdatafrom the 1982"Annual Hospital Survey" to combine the construction and equipment
indexes and set the MiddleAtlantic census division and 1977equal to
1.0.
We computed the real cost of funds from
R = Wd[(l - T)i - I] + (I
-
Wd)e,
(8)
where
Wd = debt as a proportionof sum of debt and equity;
Ir = inflationrate (percent change in ConsumerPrice Index);
e = real cost of equity; and
i = effective interest rate (weighted average of taxable and taxexempt bond rate).
11. Data on Blue Cross plans came from periodic surveys of Blue Cross plans conducted by the AmericanHospitalAssociationfor 1974, 1976, 1979, 1981,and 1983.We
had to interpolatevalues for the interveningyears.
Hospital Investment
527
For proprietaries,we calculatedthe real cost of equity using a dividend growthmodel, which is based on dividendand growthin earnings
of five large hospital companies.12The real cost of equity capital for
NFP hospitals presumablyreflects the opportunitycost to the hospital
of investing in itself rather than outside the hospital. We took the
Moody's AAA bond yield to representthis opportunitycost.13 If measurementof equity cost to a for-profitorganizationis controversial,the
underlyingissues are even less settled in the context of nonprofitinstitutions.
Estimates of several tax-related parameterswere needed for calculatingthe cost of capital to proprietaries.To compute the corporate
tax rate (X),we assumed a constant rate of 0.4. To derive this rate, we
examinedeffective corporatetax rates for the five largesthospitalcompanies from 10-K reports and found very small intertemporalor intercompany differences about 0.4. Values of t, the investmenttax credit
(ITC)term, were obtainedfrom 10-K reportdata on the effective relationship of credits to net investmentfrom one largehospitalcompany.
We allowed the ITC to vary by year. Finally, to calculate the present
value of depreciationper dollarof investmentfor tax purposes(Z), we
assumed hospitals used an accelerated depreciation method and we
took allowable useful lives for plant and equipmentfrom Commerce
ClearingHouse (1983).
Next, measures of the parametersof cost-based paymentwere constructed. Estimates of the present value of depreciationpayments(Z')
vary by payer. Medicare and Medicaid depreciationpolicy was uniform duringthe observationalperiod, but policies of Blue Cross plans
varied markedly, both cross-sectionally and over time. In addition,
both FP and NFP hospitals had their debt expenses passed through
although Medicare-Medicaid'sexplicit payment on equity was reserved for proprietaries.Blue Cross, on the other hand, granteda costplus factor to all hospitals in some states.
Annual estimates of the cost of capital are shown in figure 1. The
cost of capital generallydeclined duringthe 1970s, largelydue to substantialincreases in the outputprice (p). Feldstein (1982)found similar
trends in cost of capitalduringmuch of the 1970sfor the economy as a
whole. The estimated cost of capital to FP hospitals is sensitive to the
methodused to compute the cost of equity capital. Using the dividendgrowth model yields a very low cost of equity capitalto FP hospitals.
With a bond-based measure of equity cost, trends for the FPs and
12. To calculate the equity cost from the dividendgrowthmodel, we used a 3-year
moving averageof earningsgrowth.
13. The simplecorrelationof this series with the dividend-to-equityratio(bookvalue)
for the UnitedStates as a whole, 1974-82, is 0.23. A dividendratiohas often been used to
representthe cost of equitycapitalin studiesof the U.S. economy (see Bosworth1985).
Journal of Business
528
c/p
(%/)
212019
1816 -
For-profit
1514131210
Non-profit
9
8
1974 1975 1976 1977 1978 1979 1980 1981 1982 YEAR
FIG.
1.-The cost of capital,1974-82
NFPs are similar even though the cost of capital to FPs is generally
appreciablyhigher. We found substantialinterstatedifferencesin cost
of capitalwith states with high proportionsof cost-basedpayers generally having the highest values.
Given the many variablesthat enter our cost-of-capitalcalculation,it
is difficultto deduce which variablesaccount for most of the variation
in (cip). To assess sources of variation in (cip), we estimated (cip)
equationsseparatelyfor FP and NFP hospitals. Judgingby the levels of
statistical significancein the two equations for (cip), the most important variables are the cost-based revenue share (a), a positive effect,
outputprice (p), a negative effect, the real cost of funds (R), a positive
effect and the self-pay proportionof total hospital revenue, a positive
effect. The cost-based share has the greatest explanatorypower. With
this variable entered alone, the R2 is 0.38, in the FP (cip) equation,
comparedto 0.84, with all components of the cost of capital formula
added, and 0.48, in the NFP hospital (cip) equation, out of a total
explained variationof 0.75. Furtherdetails on our calculationsof the
cost of capital are available from the authors.
Hospital Investment
V.
529
Empirical Analysis
Exit-Entry: Rationale and Specification
We divided our empiricalwork into two broad parts. First, we tested
the hypotheses that proprietary hospital investment decisions are
guided by the cost of capital measure developed above and that NFP
investment preferences are interdependentwith FP behavior. To test
these hypotheses, we ran tests of both the likelihood that proprietary
hospitals are found in given states as well as their share of beds in a
given state as a function of the state-specificcost of capital prevailing
in the area.
More specifically,we related (1) the probabilitythat proprietaryhospitals will locate in a state and year and (2) the fractionof proprietary
beds to total beds in the state and year to several explanatoryvariables: cost of capital (cip); state regulatoryprograms;real state per
capita income; and a measure of state liberalism.The regulatoryvariables describe the share of hospital revenue covered by young (less
than 3 years of age) or mature (older than 3 years) state prospective
payment programs (price control programs over hospitals) and by
certificate of need programs of various ages (entry controls). All of
these programsare described in more detail elsewhere (Sloan 1981).
State liberalismis a proxy for politicalbias againstcorporatemedicine
and was measured by the fraction of votes by state against George
McGovern in the 1972 presidentialelection.
The probability equations were estimated with probit. One timeseries cross-section bed-share regression included state binary variables (fixed-effectsmodel). Data on beds came from reportspublished
annuallyby the AmericanHospital Association (now publishedannually in Hospital Statistics). Using this fixed-effects specification, we
accounted for various historicalreasons for hospitallocation decisions
that have nothing to do with cost of capital or the other included
independent variables. We had to drop the state variables from the
probit analysis because there was too little intertemporalvariationin
the presence or absence of FP hospitalsin a state. We emphasized1982
in our empiricalwork since this is the most recent year in our data set.
We also compared mean values of (cip) for hospitals in different
ownership categories and by whether they were affiliatedwith a chain
or were independent.To the extent that FP hospitals' investmentdecisions are particularlysensitive to the cost of capital, they should be
concentrated in areas with low (cip). Therefore, we would expect
mean (cip) to be relatively low for proprietaryhospitals. Data for this
test came from unpublishedmicrodatafrom the 1982 AHA "Annual
Hospital Survey" and from a special survey of multihospitalsystems
conducted in 1983-84 by the AmericanHospital Association.
Journal of Business
530
TABLE 1
Empirical Results: Proprietary Hospital Bed Share
Probability That
State Has
Proprietary Bedsa
Explanatory
Variables
c/p
1982
(1)
(2)
(3)
(4)c
(5)
(6)
- 2.846*
- 13.444**
(6.191)
-.411*
(.104)
-.115*
(.023)
-.914*
(.475)
-.909***
(.533)
- 39.306
- .088**
- .015
...
...
1.981
(1.285)
(53.415)
.704
1.142
(.441)
(1.331)
PRO
PRECON
- .432
CONNEW
- .380
RINC (000)
REPUB
CONS
(.295)
.171
(.254)
-.346*
- .023
(.014)
(5.990)
- 1.399
(5.391)
(.022)
.015
(.019)
-.180
...
1.154
(3.246)
4.071
(6.581)
...
...
F-statistic
...
...
49
.019*
(.008)
001
(.005)
-.002
(.007)
203
- .043
(.057)
- .106
- .121
(.079)
-.037
(.070)
(.083)
-.041
(.072)
-.008
...
-.002
...
-.114
(.018)
(.005)
...
.286*
(.041)
.21
7.55
(.050)
(.005)
-.
...
.029
(.050)
- .045
- .001
(.029)
(.346)
343
- .027***
(.029)
1.001
R2
N
- .110*
- .029
(.098)
3.324*
(.655)
(.011)
(.040)
...
(.300)
CONOLD
1982
1976-82
1976-82
(1.057)
PRY
Proprietary Share (Share > 0)b
.225*
(.072)
.97
206.81
203
(.138)
.315*
(.163)
.37
.35
3.19
30
2.12
30
NOTE.-c/p = real cost of capital;PRY = fractionof hospitalrevenues covered by mandatory
prospective paymentprogramless than three years of age; PRO = fractionof hospitalrevenue
covered by mandatoryprospectivepaymentprogramthreeyears of age or older;PRECON= 1 for
the yearbeforea certificate-of-need
programwas implementedandthe firstyearpastimplementation;
CONNEW = 1for the secondandthirdyearsof a certificate-of-need
program;CONOLD= 1for the
fourthand subsequentyears afterimplementationof certificateof need;RINC = percapitapersonal
incomedeflatedby a state priceindex;REPUB = fractionof the vote againstMcGovernin the 1972
presidentialelection; CONS = intercept.SEs are given in parentheses.
a
Estimatedwith probit.
b
Only states with positive proprietarysharesin all years are included.
c Variantcontainsstate dummies.
* Statisticallysignificantat 1%level (two-tailedtest).
** Statisticallysignificantat 5%level (two-tailedtest).
* Statisticallysignificantat 10%level (two-tailedtest).
Exit-Entry: Empirical Results
The cost of capital affects both the probabilitythat a state had any
proprietaryhospital beds (regressions 1 and 2, table 1), and for those
states with beds, the share of total beds in nonfederal,short-termgeneral hospitals (a category that includes most hospitals but excludes
hospitals with mean lengths of stay of over 30 days) under FP ownership. Although the coefficients of (cip) vary in table 1, this variable
has a statistically significanteffect at the 5%level or better in five out
of six regressions(two-tailedtest) andis significantat the 10%level in a
Hospital Investment
531
1982single cross-section of bed-shareregressions(regression6), which
is based on many fewer degrees of freedom. Elasticities computed at
the mean are - 0.448, - 0.125, - 0.757, and - 0.753 for the third
through sixth regressions, respectively. The lowest elasticity is from
the fixed effects specification(regression4). We were concerned that
results on (cip) may merely reflect omitted state effects, but the result
stands even in the fixed-effects model. There is some indicationthat
price regulation of hospitals retardedproprietaryshare (see table 1,
nos. 3 and 4) but, as in past studies, certificate-of-needprograms,
which requirehospitals to obtain formal approvalfrom a state agency
before entering, have no influence on either dependent variable (see
Sloan [1981, 1982]for a review).
We also estimated share equations for NFP hospitals. The (cip)
variable consistently had a significantly positive effect on market
share. An explanationfor this result is that the residual claimantsof
NFP hospitals, local community leaders, board members, doctors in
the community, and local philanthropistsdo not compare returns of
alternative investments geographically and over time. Rather, they
pick up the slack of FP lack of entry resultingfromhigh values of (cip).
Surely residual claimants living in Peoria would not be indifferentbetween two hospitalsin Peoria, one in Tampaand one in Peoria, andtwo
in Tampa. The owners of a hospital company would prefer two in
Tampaand none in Peoriaif the pricesjustifiedthis allocationdecision.
We comparedthe mean cost of capitalin 1982by hospitalownership
and affiliationin order to furthertest the hypothesis that proprietary
hospitals locate where this cost is lowest. The measure of (cip) for
proprietarieswas used for all hospital types so as not to introduce
variationin the means from this source. Our cost of capital measures
for the two ownership types are highly correlated(corr = 0.9).14 As
seen in table 2, the mean (cip) for proprietaryhospitalchainswas much
less than the (cip) for all other hospitals, including independent
nonprofithospitals and hospitals owned, sponsored, or leased by an
outside nonprofitorganization(nonprofitchain). Moreover, the mean
value of (cip) was significantlyhigher(5%level or higher)for independent nonprofithospitalsthanfor the other hospitaltypes shown in table
2. Finally, the 1982(clp) of hospitals contractmanagedby proprietary
organizationswas almost the same as the value for hospitals contract
managed by private nonprofit organizations and over a percentage
point higher than (cip) for the proprietarychains. This is not at all
14. This correlationis very high even though the for-profitand NFP cost of capital
were computedusing differentassumptionsaboutthe cost of equity. We also computed
two sets of cost of capitalestimatesfor for-profithospitalsusingalternativesas the bond
rate and the dividendgrowthmodels, and estimateswere very close. The two series are
available from the authors. As noted above, the main source of variationin (cip) is
attributableto differencesin the cost-base share. This variableis well measured.
Journalof Business
532
TABLE2
Mean Cost of Capitalby HospitalOwnership,1982
PrivateNonprofit
Independent
.109
(.076)
Proprietary
Chain
Contract
Managed
Independent
Chain
Contract
Managed
.090*
(.039)
.085*
(.026)
.088*
(.040)
.072a*
(.020)
.086*
(.035)
NOTE.-SESare given in parentheses.
aMeansignificantlydifferentfrom meanfor private,not-for-profitchainhospitals.
*Mean significantlydifferentfrom mean for private, not-for-profitindependenthospitals (5%
level).
surprisingsince such companies managesuch hospitalsfor a fee; they
do not invest in them. Thus, results from table 2 strongly supportthe
table 1 findingsbased on regression analysis.
Net Investment per Private Not-for-Profit Hospital:
Rationale and Specification
Althoughwe felt we could learn a lot about investment behavior and
the importanceof our cost of capital measureto FP hospitals by looking at the probit and share equations, we also sought to validate the
relevance of our cost of capital measure for NFP hospitals directly.
Thus, in the second partof our empiricalwork, we estimatedequations
for real net investment per hospital for NFP hospitals only. Unpublished investment data by state and year, 1976-82, derivedfrom "Annual Hospital Surveys," were obtained from the American Hospital
Association. A parallelanalysis for FP hospitals was not possible because there were so many nonresponses to the surveys.
We broughtthe marginalconditiongiven in equation(7a) into operation by assumingthat the marginalproductof capitalin the production
of both quantity and quality is an exponentialfunction of the ratio of
quantityto capital, that is,
XK = YK -
(
FX
)P
'
(9)
where p is some arbitraryparameter.Holdingthe output-to-laborratio
constant, this assumptiongenerates an investment specificationthat is
identical to a Jorgenson-type flexible accelerator (Jorgenson and
Stephenson 1967) using a Cobb-Douglasor CES technology, where
or = 1/(1 + p) is the elasticity of substitution.
We specifiedthe dependentvariableto be meanNFP hospitalinvestment expendituresdeflatedby a Bureauof LaborStatisticsinvestmentgoods price index. We consideredtwo alternativemeasuresof hospital
output-adjusted patient days (the adjustment converts outpatient
visits into inpatientequivalents) and real hospital revenue, where the
deflatorwas a measure of cost of living in the state with New York in
Hospital Investment
533
1977 = 1.0. The revenue measurerecognizes qualitativedifferencesin
output of the type that our nonprofitmodel sought to capture.
Ratherthanestimate nonlinearregressions,we estimatedinvestment
equationsby ordinaryleast squares, assumingalternativevalues for or.
Likelihood-ratiotests were then performedto test for differences in
results based on alternativevalues of or.
Since the flexible acceleratormodel includesoutputterms, (cip) only
affects capital stock via a substitutioneffect. But the cost of capital
may also affect quantity (and quality). Finally, note that the hypothesized effect of the cost of capital measureon NFPs is not unrelatedto
the findingsin the first part of our work. As noted above, a findingthat
NFPs respond to the behavior of proprietarieswould tend to diminish
the anticipatednegative impact of the cost of capital on their investment flows.
Net Investment per Private Not-for-Profit Hospital:
Empirical Results
We appliedthe flexible acceleratormodel (Jorgensonand Stephenson
1967)in the analysis of real net investment per NFP hospital by state
and year 1976-82, using asset data from 1974 and 1975 for lagged
variables and allowing the elasticity of substitutionparameters,a, to
vary between zero and one (table 3). The odd-numberedregressions
are based on output measuredby the change in adjustedpatientdays.
Even-numbered regressions use real revenue-based output change.
The results, based on a specification with as set equal to one, show
negative output change terms and are implausiblewith either output
measure. Conversely, the real revenue change results for oaequal to
zero are plausible, but the adjustedpatient-daychange terms are implausiblynegative. Far better results on adjustedpatient-daychangein
terms of the estimated coefficients and statistical significance were
obtainedwith a-assumed to be greaterthan zero and less than 0.2. The
even-numberedregressions are about the same with cr in the 0-0.15
range. The coefficients on lagged investment are uniformlynegative,
statistically significant,and stable across regressions. The size of the
coefficient (-0.4) implies that the capital stock value converges to a
new equilibriumvalue after the hospital system has been subjectedto
an exogenous perturbation.
We performed a likelihood-ratiotest to determine whether the uequal-to-one specification could be rejected in favor of a technology
with a lower c, but the x2s were always below the thresholdfor statistical significanceat conventional levels. We suspect the reason is that
the state dummyvariablespicked up most of the unexplainedvariation
due to misspecification. In any case, it seems best to rely on the
specificationsbased on relativley low a, as these specificationshave
more plausible coefficients. In earlier specifications,we also included
the regulatoryvariablesshown above in table 1. These variables,taken
Journal of Business
534
00 C.,
en
n nm
OCO)
"C'ctn-WC))
M 1t
CT
m
V)
6 .5
C'S
c 00
Cd
C's
0
ON 't
-en
r-
00
r- 00
W)00
00
.I-
"C 't
0
Cd
en
00 c
E
Cd
W)
".C
rq 00 a-, -t
oo
kn
C,
rc Z
c
t- a-,
en
W)
CN
00
rq rq
W
00
r- 00
00 ON00 c
0
a-,
00
a-,
C:
Cd
0
V)
Z
CNW)00
en
C-i
rq
en
00
(= 00
en 00
00
cq
',C
t00
r- 00
C) CN rq CN
00
ON
CN
W)
en
en
>1
.0
C) - 't
1_1
en
en
00
00
C,
W)
C) CN 00 en C)
rq oo
00 ICZ
00 en
00 W)
CN C)
00
r- 00
Cd
1.0
4-4
0
rq CN
(5
rq rq rq C) 00 W) rl
(= rq- 00- '-;"C'.nc
0WO)
00
00
C'i4
0
2
4>1
0
Cd
en 00
CN.I-
W)00
0
Cd
C) 00
en
'O
00
0
cd
cd
4,
(Z4.0
00
cg
w
>
-1
-1
>
z
z
z
U
C)
0
cd
C:
C's
C) to
Hospital Investment
TABLE 4
535
Real Net Investment per Private Not-for-Profit Hospital
Alternative Specifications
(N=
336)
Explanatory
Variables
A(clp)
A(clp)_1
NINV1
CONS
R2
F(52,284)
(1)
(2)
996,894
(1,301,920)
- 1,428,176
(1,051,497)
-.354*
(.057)
2,093,883
(485,114)
...
.291
2.29
- 1,711,954**
(983,306)
-.352*
(.057)
2,095,407*
(484,758)
.290
2.32
NOTE.-Coefficienton state dummiesand time dummyfor 1978includedin both the regressions
but not presentedhere in the table.
*Significantat the 1%level (two-tailedtest).
**Significant at the 8%level (two-tailedtest).
as a group, did not reduce unexplained variance by a statistically
significantamount and were subsequentlydropped.
With low values of o-, there is a small substitutioneffect from the
cost of capital operating on desired capital stock. To determine the
effects of the cost of capitalon real investmentper NFP hospitalwhen
(cip) is allowed to affect output (uncompensatedfor output change),
we estimated investment equations with the change in (cip) and its lag
(table 4). With both (cip) change variables included, the (cip) parame-
ter estimates vary in sign. With only lagged (cip) included,the cost-ofcapitalis negative and statisticallysignificantat the 8%level (elasticity
= -0.014 at mean real investment for a 1%change in [cAp]).
These findingsare not surprising,given the results of the shareequations. That is, the expected negative impactof the cost of capitalmeasure is at least partiallyconfoundedby the fact that NFPs take up the
slack left by exiting proprietaries.The fact that a marginalnegative
effect persists in the NFP investment equations attests to the validity
of the cost-of-capitalmeasureas well as the fact that proprietaryhospitals are a minorityin the industry,so that theirinvestmentdecisions do
not completley confound the results found for the NFPs.
VI. ConcludingRemarks
The expressed purpose of this study has been to answer a numberof
importantquestions about the investment behavior of the hospital industry. These included the question of how not-for-profitorganizations' objectives affect the costs as well as the incentives for undertaking investments and also the question of how the unique payment
mechanismsused in the industryaffect its investmentflows.
536
Journal of Business
Most of what was learnedabout the effects of paymentmechanisms
on investment incentives was presented in the theoretical section.
Here, a modified Averch-Johnson(1962) result was derived that accountedfor mixed forms of paymentand emphasizedthe importanceof
the relative generosity of capital payment algorithmscomparedto the
hospital's true economic cost of capital in derivingthe effects of costbased reimbursementon investment. Another notable result was the
fact that the more generalobjectives pursuedby NFP hospitals do not
affect their cost of capital;ratherit was found to be of the same general
form as for the proprietaries'cost. Althoughobjectives plausiblydiffer
between the FP and NFP forms, as we have shown, standardinvestment theory can provide a way to identifyfactors that affect for-profit
and not-for-profitgrowth in both cases.
Conversely, most of what was learned about the effects of hospital
preferences on the marginalvalue placed on capital was found in the
empirics. Here we found that proprietariesbehave very much according to the neoclassical theory of the firm, enteringand existing areas
accordingto the relative magnitudeof the cost-of-capitalmeasurecomputed in the theory section. Perhapsmore interesting,our results also
indicated that NFP hospitals make up the slack left by exiting proprietaries,providingsome evidence that their investmentpreferences
are at least partially guided by the behavior of their proprietary
counterparts.
Finally, the results obtained here are of potential value for understandingthe likely effects of the growinguse of stringentprospective
payment systems of payment, as characterized,for example, by Medicare's Prospective Payment System. There is widespreadconcern in
the industry that not-for-profitinstitutions will suffer the burdens of
reduced payments by such payers disproportionatelycompared to
their proprietarycounterparts.This concern is based on the assumption that proprietariesare better able to adaptto such changes and are
more financiallyviable institutionsto start with.
Ourresults at least partiallyconfirmthese concerns in the sense that
we see strong evidence of capital mobility on the part of proprietary
hospitals. The logical implication of these results suggests that forprofit hospitals would increasinglylocate in areas less subject to prospective payment (i.e., areas with small elderly populations)leaving
their NFP counterpartsto deal with the difficultiesof increasinglyless
generous sources of payment.
References
AmericanHospitalAssociation(AHA). 1984.Hospital Statistics, 1984.Chicago:AHA.
Averch, H., and Johnson, L. 1962. Behaviorof the firmundera regulatoryconstraint.
American Economic Review 52 (December): 1052-69.
Hospital Investment
537
Bosworth, B. P. 1985. Taxes and investmentrecovery. BrookingsPaper on Economic
Activity, no. 1, pp. 1-45.
Cohodes, D. R., and Kinkead, B. M. 1984. Hospital Capital Formation in the 1980s.
Baltimore:Johns Hopkins UniversityPress.
Commerce Clearing House, Inc. 1983. Medicare and Medicaid Guide, 1645-3 to 1648
(clause no. 4696), Chicago.
DeAngelo, H., and Masulis, R. 1980. Optimalcapital structureunder corporateand
personal taxation. Journal of Financial Economics 8 (March): 3-30.
Feldstein, M. 1977. Qualitychange and the demandfor hospitalcare. Econometrica45
(October):1681-1702.
Feldstein, M. 1982. Inflation,tax rules and investment:Some econometricevidence.
Econometrica 50 (July): 825-62.
Ginsburg,P. B. 1970.Capitalin Non-profitHospitals.Ph.D. dissertation,HarvardUniversity, Cambridge,Mass.
Ginsburg,P. B., and Sloan, F. A. 1984.Hospitalcost shifting.New EnglandJournalof
Medicine 310 (April 5): 893-98.
Jorgenson,D. W. 1963. Capitaltheory and investmentbehavior.AmericanEconomic
Review 53 (May): 247-59.
Jorgenson,D. W., and Stephenson,J. A. 1967.Investmentbehaviorin U.S. manufacturing, 1947-60. Econometrica35 (April):169-220.
Kamien, M. I., and Schwartz, N. L. 1981. Dynamic Optimization: The Calculus of
Variations and Optimal Control in Economics and Management. New York: North
Holland.
Lee, M. L. 1971.A conspicuousproductiontheory of hospitalbehavior.SouthernEconomic Journal 38 (July): 48-58.
Newhouse, J. P. 1970.Towarda theoryof nonprofitinstitutions:An economicmodelof a
hospital. American Economic Review 60 (March): 64-74.
Sloan, F. A. 1981.Regulationand the risingcost of hospitalcare. Review of Economics
and Statistics 63 (November): 479-87.
Sloan, F. A. 1982.Governmentand the regulationof hospitalcare. AmericanEconomic
Review 72 (May): 196-201.
Sloan, F. A. 1988.Propertyrightsin the hospitalindustry.In H. E. Frech (ed.), Health
Care in America: The Political Economy of Hospitals and Health Insurance. San
Francisco:PacificResearchInstitutefor PublicPolicy.
Sloan, F. A., and Becker, E. R. 1984. Cross-subsidiesand paymentfor hospitalcare.
Journal of Health Politics, Policy, and Law 8 (Winter): 660-85.
Wedig, G.; Sloan, F. A.; Hassan, M.; and Morrisey, M. A. 1988. Capital structure,
ownership,and capitalpaymentpolicy: The case of hospitals.Journalof Finance 43
(March):21-40.