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Cost-shifting under cost reimbursement and prospective payment
Journal of Health Economics 4 (1985) 261-271. North-Holland
COST-SHIFTING UNDER COST REIMBURSEMENT AND PROSPECTIVE PAYMENT
Richard W. FOSTER* University nf Colorado at Denver, CO 80202, USA Received September 1984, final version received March 1985 Cost-shifting is seen as a three-way phenomenon involving hospital interests as well as those of government and private patients. Without economies of scale, private patients are indifferent to government policies unless underpayment leads to hospital bankruptcy. In the presence of economies of scale, private patients benefit from reductions in government payment under either cost reimbursement or prospective payment. Their interest in a shift to prospective payment depends upon the hospital’s location on its cost curve. Hospitals benefit from increases in payment rates in all cases, but benefit from a shift to prospective payment only if operating in a region of dtslining average costs. The conventional view of cost-shifting is inconsistent with profit maximization and may be inappropriate for many voluntary hospitals as well.
1. Intrah!tion
The passage of legislation mandating a new method of reimbursement for inpatient services to Medicare beneficiaries has set off a new wave of concern about cost-shifting. The discussion is clouded by a failure to specify the nature of the phenomenon. It is generally regarded as a consequence of government ‘underpayment’, but criteria for underpayment vary. To some, underpayment occurs when ‘hospitals charge some patients more for the same service than they charge others’ [Meyer (1983, p. G)]. Hay (1983), on the other hand, argues that ‘genuine’ cost-shifting occurs only when government pays less than average cost, and shows that differential pricing may occur without this. Hay’s criterion is appealing in that it implies cross-subsidies. Sloan and Becker (1984) employ yet another criterion: to them, cost-shifting occurs if reductions in the government payment rate lead to increases in the orices charged to private pay patients. This criterion is appealing in implying that private patients are made worse off by the cost-shift. While most discussions emphasize this impact on private patients, concern is sometimes also expressed that government underpayment threatens hos*I would like to thank Joel Hay, James Morris, Norman We&, and the editor and referees for coraments on various drafts of the paper. 01’57-6296/85/$3.30 0
1985, Elsevier Science Publishers R.Y. (North-Holland)
R.W Foster, Cost-shijting, cost reimbursement, prospective payment
262
pit&’ financial viability. These concerns are sometimes expressed in aggregate terms, while at other times the threat is said to be more severe for hospitals with higher proportions of government patients [Hadley, Mullner and Feder (1982)]. In this paper, I examine these propositions for the simple but important case of a profit-maximizing hospital. I shall generally adopt Hay’s criterion for underpayment, but I shall be attentive to whether costs are shifted to private pay patients or hospital owners. It is shown that Hay’s criterion may be satisfied when the Sloan-Becker criterion is not. Indeed, a profitmaximizing hospital will not generally practice cost-shifting in the SloanBecker sense. I also distinguish the cases in which the deficit from treating government patients grows as a result of a reduction in the government payment rate or as a result of an increase in the number of government patients treated. The cases are shown to be quite different, with the latter conforming more closely to conventional discussions of cost-shifting. The effects of reductions in government payment rates and of increases in government patient loads are qualitatively the same under cost reimbursement and prospective payment. The effects of a shift to prospective payment depend upon the hospital’s location on its average cost curve. Long-run effects &zuW >R negligible. In the short run, hospitals and private patients are both likely to benefit, while government program costs are likely to increase. Govermnent underpayment will generally iead hospitals to practice ‘demarketing’. In the short run, though, some hospitals may actively recruit government patients in spite of underpayment. Some of these conclusions contradict widely held views of cost-shifting. The empirical evidence for such cost-shifting is weak, however. Thus it remains unclear whether it is the conventional view of cost-shifting or the conventional view of hospital pricing which should be rejected. At a minimum, cost-shifting discussions should carefully distinguish investorowned and non-profit hospitals. 2. Formulation of the model The hospital is assumed to maximize profits,
max7~=
P,Q,
+ aCQG - C(Q, + QG) -
%'QG
where
QP =volume
of private use, QG =volume of government patient use, 5 = Pp(Qp) = price paid by private patients,
cR,
R.U! Foster, Cost-shifting,cost reimbursement,prospectivepayment
263
C = C(Q) + Qo) = average cost of producing services at volume Q, + QG, CR = CR(QG- QGo)= total cost of marketing efforts to achieve volume QG of government patients, of government patients which would arrive with no marketing QGO =vohme effort, Q =fraction of average cost reimbursed for government patients. In addition, I assume P
ap,
p=aQp
(downward sloping private demand),
Pp+~pQp>O
(private monopolist’s marginal revenue positive),
2Pp+P;Qp<0
(private monopolist’s marginal revenue falling),
C+c’(Q,+Q&O
(marginal cost of production positive),
2c’ + C”(Q, + QG)2 0
(marginal cost of production rising),
CL=0 >O
for for
QG-QGO=O QG-QGO>O
CO for
QG-QoO
c;>o
(marginal cost of moving QG away from QGOis positive), (marginal cost of moving Qo away from QGOincreases with distance from QGO),
O
(government ‘underpayment’).
The model should also incorporate the constraint K20, but I shall omit this for simplicity, simply referring in the text to situations in which the constraint may prove binding. Two aspects of this formulation warrant particular discussion. The first is the assumption of profit maximization and the second is the structure of marketing costs. Profit maximization is clearly the appropriate objective for the important and rapidly growing investor-owned se ent of the hospital industry. Furthermore, the implications of the profit-maximization rule are of interest for voluntary hospitals for a number of reasons. First, profit maximization is the most widely used criterion in explicit
264
R.W Foster, Cost-shijling,
costreimbursement, prospective
payment
models of hospital pricing behavior [see, for example, Damon (1982), Hay (1983)]. Hence, if implications of profit maximization could be rejected, this would be of interest 111forcing a reconsideration of much of the pricing Iiteratutie. Secondly, there are a number of cases in which non-profits will behave like profit maximizers. Hay (1933), for example, shows that some of the conclusions reached here are also valid for a hospital which maximizes the incomes of its physician staff. Dran and Campbell (1981) argue that. non-profit hospitals should maximize profits on profitable services, using the proceeds to undertake projects which are not self sustaining. This makes profitmaximizing pricing rules appropriate for much of the hospital’s business. Finally, many hospital leaders are concerned about access to capital and have urged non-profit hospitals to improve profitability in order to enter debt markets on favorable terms [Special Committee on Equity of Payment (1983)]. Thus, differences in pricing behavior between for profit and nonprofit hospitals may be diminishing. The introduction of marketing or recruiting into the model permits the hospital to adjust its government patient load, but such adjustments are made subject to a penalty function of the conventional form. Recruiting costs are zero at Qo=Qo,,, which will depend primarily on the demographic character of the hospital’s service area (though changes in government program eligibility criteria could also shift QGO).IA order to attract more government patients than this, the hospital must incur positive recruiting costs which may take the form of advertising, outreach programs, cultivation of referral networks, and the like. Reducing Qo below QGO(‘demarketing’ is the current buzzword) likewise requires the hospital to incur costs. These may take such forms as development of referral mechanisms or damage to the hospital’s reputatior. as it becomes known for ‘dumping’. The marginal cost of such adjustments is assumed to increase as the magnitude of the adjustment increases in either direction. This formulation of recruiting costs places the model in an intermediate position between those of Danzon (1982) and Hay (1983). Danzon assumes the volume of government patients is exogenously determined, while Hay assumes that the hospital can costlessly adjust its government patient load to any desired level. The first-order conditions for an interior solution to the hospital’s problem are
(1) (2) The marginal conditions state the familiar result that the marginal revenue
R.W Foster, Cost-shijkg, cost reimbursement,prospective payment
265
must equal the marginal cost for each class of patient. The expression on the right-hand side in each of (1) and (2) is the marginal cost of production, assumed equal for the two classes of patients. The first two terms in the expression for the marginal Lyevenuefrom private patients @eft-hand side of eq. (l)] simply give the marginal revenue for the textbook monopolist. The third term, &‘QG, reflects the fact that if an additional private patient changes the average cost this will affect the hospital’s revenue through a change in its reimbursement for government patients. The same term appears in the expression for marginal revenue from government patients @eft-hand side of eq. (2)]: any change in average cost can be thought of as altering the reimbursement for all other government patients. In addition, the term -CR reflects the fact that net marginal revenue is reduced if costs must be incurred to recruit the marginal government patient (or, alternatively, net marginal revenue is increased if costs of discouraging government patients are avoided by allc sing volume to increase). 3. Cost-shifting with cost reimbursement Since the empirical evidence suggests few if any economies of scale (except at very small sixes or for some specialized services) [Lave and Lave (1979)], I shall take the case of C’=0 and C” = 0 as representative of the long run. For this case, eqs. (1) and (2) reduce to
Pp+ ppQ, = G
(3)
aC=C+C;p.
(4)
The solution is illustrated in fig. 1. Notice that as long as average cost is insensitive to total volume, eq. (3) will yield an optimal Q,=Q,* (and hence -P,*)which is insensitive to the parameters (a) and Qoo. an optimal PpPrivate pay patients are indifferent to government payment policies even though they pay more than the government pays for identical services and even if government ‘underpays’ (a < 1). The hospital, however, is not indifferent to government payment policies. With LIc 1, eq. (4) requires CRCO. With government underpayment, then, the hospital will practice ‘demarketing’ in an effort to reduce government patient volume. If it could adjust government volume costlessly, it would treat no government patients at all, a case which is not observed in practice. It can easily be shown that reductions in (a) or increases in Qoo will reduce rc. Hence, if government underpayment is taken as the criterion for cost-shifting, then costs are shifted to the hospital rather than to private pay
266
R.W!Foster, Cost-shifting, cost reimbursement,prospectivepayment
Fig. 1. Longrunequilibrium withcost reimbursement. patients. Thus the Hay criterion for cost-shifting is satisfied, but the Sloan-
Becker criterion is not. Evidence of this kind of cost-shifting is offered by Hadley, Mullner and Feder (1982), who find hospital profits are lower where the proportion of government patients is higher (due, presumably, to cross-sectional variation in Qcd The effect on hospital profits means that the indifference of private pay patients to government payment policies must be qualified. To this point I have assumed an interior solution, ignoring the constraint x20. It is clear, though, that for sticiently low (a) and sufficiently high Qo,,, the constraint could become binding, and the hospital would be forced to bankruptcy. Private pay patients would be made worse off by being forced to more distant or otherwise less satisfactory hospitals. In the short run private pay patients are affected by government payment policies even if the hospital remains solvent. Absent economies of scale, short run responses for a hospital initially at optimum capacity are given by the case of C’=0, C” > 0 (with declining long-run average costs, a hospital at optimal capacity has c’ CO, C” > 0, a case which is discussed below). These effects, however, are inconsistent with the conventional view of costshifting. It is a relatively straightforward exercise in comparative statics to show that a reduction in the proportion of costs reimbursed for government patients will actually reduce the price charged to private patients. The intuition for this result is that, by reducing marginal revenue from government patients, the reimbursement change induces the hospital to reduce total volume. This reduces marginal cost, so that private marginal revenue is equated with marginal cost at a lower level. The presence of the aC’Q, term in eq. (1) only partially compensates for this.
R. W!Foster, Cost-shifting, cost reimbursement,prospective payment
267
This decline in total volume with decreases on (a), combined with a history of apparently declining (a), suggests that many hospitals may be operating in a region of declining average costs. Certainly the Tax Equity and Fiscal Responsibility Act of 1982 must have reduced (a), so that many hospitals faced declining average costs in the short run at the onset of prospective payment. The comparative statics show that, again in this case, a reduction in (a) leads to lower private prices, contrary to the conventional wisdom. Such a short-run equilibrium is illustrated in fig. 2. (Those who believe in significant economies of scale may also regard this as a possible long-run equilibrium.) From eq. (I), the private monopolist’s marginal revenue must exceed marginal cost by -aC’Qo. We may think of a decline in (a) causing volume to decline with this relationship being maintained until marginal cost - uC’Qo is simultaneously equal to UC- CR as required by eq. (2). While this scenario of falling (a) suggests &>O, the case of Ck
Fig. 2. Equilibrium with declining average costs.
268
R.W Foster, Cost-shying, cost reimbursement, prospective payment
price charged to private patients. The price increase occurs because the hospital is led to operate at higher volume and hence at higher marginal cost. It is possible that an increase in government patient demand might actually increase hospital profits. This could occur if the hospital was initially operating in an area of declining average costs and was actively seeking government patients, as describd above. 4 Introduction of prospectivepayment I assume in this section that government introduces a new payment system under which hospitals will be paid a fixed prospective rate Po for each unit of service to government patients. Consistent with the principle of budget neutrality, the level of PG is set equal to the rate which the government was paying under the old system. That is, PG is set equal to the previous equilibrium level of UC. The new expression for profit is
aud the new marginal conditions are
PG-C;(=C+C'(Qp+QG).
(6)
Combining (5) and (6) gives P, +
PpQ,= PG- CL.
Consider first the case of C’=O. Comparison of eq. (1) with eq. (5) and comparison of eq. (2) with eq. (6) reveals that when PG is set equal to the previous level of UC, neither marginal condition is disturbed. Thus the shift to prospective payment does not affect anyone: hospital profits, private prices, and volume of service rendered to government beneficiaries all remain unchanged. This is even true in the short run, as long as the hospital is operating at the optimal scale for its volume before the shift (assuming no long-run economies). I argued earlier, though, that many hospitals are likely to face declining average costs in the short run. Comparison of eqs. (1) and (5) and of eqs. (2) and (6) with C’
R.R! Foster, Cost-shifting, cost reimbursement,prospective payment
269
Consider first the case of QG. If Qo were to fall or remain the same, then -CL would be greater than or equal to its previous level. But eq. (7) would then require PP+PPQ, greater than or equal to its previous level, and hence Q, less than or equal to its previous level. But this would contradict the conclusion that total volume must rise, so the supposition of stable or falling Qo must be false. Given the increase in Qo, we have -CR less than before. Eq. (7) then requires PP+ PLQ, smaller than before, so that Qp must also rise. In the short run, then, a shift to prospective payment is likely to increase hospital profitability and government spending while reducing prices charged to private patients. It should be noted, though, that this describes a ‘pure’ shift to prospective payment: I have assumed Po= UC and no change in volume measures. The prospective payment system actually introduced was more complicated. The assumption of Po= aC is reasonable given ‘budget neutrality’. But Medicare not only switched from cost reimbursement to prospective payment, but also simultaneously switched from a patient day basis of payment to an admission basis. Note in particular that this latter switch provides the hospital with an incentive to reduce length of stay. This could dominate the increase in Qo noted above SC that government volume could fall when measured in patient days (it should still rise in terms of admissions). Further discussion of this switch from a patient day to an admission basis is given by Hay and Ernst (1984). 5. Cost-shifting with prospective payment For the constant returns to scale case, reductions in the prospective rate Po will reduce hospital profits and service to government program beneficiaries, leaving private price and volume unchanged. The logic for this result is the same as in the cost reimbursement case: neither marginal cost nor marginal revenue from private patients is altered by the change in government payment rates. The indifference of private patients to the government’s choice of Po is again subject to the qualification that low government payment rates could force hospital bankruptcies. With economies of scale, the hospital will respond to a reduction in Po by reducing prices to private patients. Hospital profits and service to government program beneficiaries will fall. As in the cost reimbursement case, reduced marginal revenue from services to government patients causes the hospital to reduce the volume of output. The resulting reduction in marginal cost causes marginal cost and private marginal revenue to be equated at a lower price to private patients. Constant returns to scale also find private patients indifferent to the volume of government patients, again subject to hospital survival. With
270
R.W!Foster, Cost-shifting, cost reimbursement,
prospective
payment
economies of scale, though, increases in QGOlead to higher private prices. Hospital profits will fall unless declining average costs and a low initial QoO caused the hospital to recruit government patients. 6. Summary
Qualitative effects of reductions in government payment rates and of increases in government patient loads are the same under prospective payment as under cost reimbursement. The etrects on hospital profits and on government patients are generally consistent with conventional expectations, although hospitals may actively recruit government patients in spite of underpayment in the short run. The effects on private patients generally run counter to conventional expectations. In the long run, private patients are indifferent to government payment policies unless such policies drive the hospital to bankruptcy. In the short run, increases in government patient demand have the expected effect of driving up private prices, but reductions in government payment rates actually reduce private prices. For hospitals operating at minimum average cost, the shift to prospective payment has no effect by itself. The introduction of prospective payment is likely to have found many hospitals operating on the downward sloping portions of their short-run average cost curves, however. In these cases, the shift to prospective payment sl.ould increase hospital profits and the volume of government patients treated, while reducing prices charged to private pay patients. The effects of government payment polic.ies on hospital profits and government program beneficiaries are generally consistent with expectations. They are consistent with a self-interest explanation for the hospital associations’ complaints of underpaymentand their support of the shift to prospective payment. Effects on private patients are another matter. Private insurers’ claims that reducing government payment rates and shifting to prospective payment will raise private prices are not legitimate for profit-maximizing hospitals. Their legitimacy for non-profit hospitals is unclear. The conventional arguments may rest on an assumption of target income pricing, which is seldom made explicit. There is little empirical evidence available. Payment. differentials are well established, but this does not imply government payment at less than cost and even government underpayment does not imply that private patients are injured by government payment policies. The most relevant evidence to date is that of Sloan and Becker (1984). Theirs is a cross-sectional study, relying on multiple payers as a source oi variation in (a). Although their underpayment variable incorporates dif-
R.II! Foster, Cost-shifting,cost reimbursement,prospectivepayment
271
ferences in QGOand in P,, as well as in (a), they include payer mix variables as controls and use an instrumental variables method for the underpayment variable. The payer mix variables are treated as exogenous, however, and are included among the instruments as well as the controls. While the Sloan-Becker results support the conventional view of costshifting, they cannot be considered definitive. A recent study by Hadley and Feder (1984) attempts to relate changes over time in private patient markups to changes in an index of ‘need to cost-shift’, but finds no significant relationship. Like the Sloan-Becker underpayment variable, the HadleyFeder index of need to cost-shift incorporates both changes in (0) and changes in QoO.Their results suggest a more skeptical view of cost-shifting. Further work along these lines would be valuable. References Danzon, Patricia Munch, 1982, Hospital ‘profits’:The effects of reimbursement policies, Journal of Health Economics 1, no. 1,29-52. Dran, John J., Jr. and Brian E. Campbell, 1981, Hospital investment and Medicare reimbursement, Journal of Financial Research 4, summer, 147-160. Hadley, Jack and Judith Feder, 1984, Hospital cost shifting: An analysis of hospitals’ markups and financial needs, unpublished manuscript (Center for Health Policy Studies, Georgetown University, Washington, DC). Hadley, Jack, Ross Mullner and Judith Feder, 1982, Special report: The financially distressed hospital, New England Journal of Medicine 307, no. 20,1283-1287. Hay, Joel W., 1983, The impact of public health care financing policies on private-sector hospital costs, Journal of Health Politics, Policy and Law 7, no. 4,945-952. Hay, Joel W. and Richard Ernst, 1984, Hospital DRGs, prospective reimbursement, and Medicare cost-shift, unpublished manuscript, Project HOPE. Lave, Judith R. and Lester B. Lave, 1979, Empirical studies of hospital cost functions: A review, in: George K. Chacko, ed., Health handbook (North-Holland, Amsterdam). Meyer, Jack A., with William R. Johnson and Sean Sullivan, 1983, Passing the health care buck: Who pays the hidden cost? (American Enterprise Institute, Washington, DC). Sloan, Frank A. and Edmund R. Becker, 1984, Cross-subsidies and payment for hospital care, Journal of Health Politics, Policy and Law 8, no. 4, 660-685. Special Committee on Equity of Payment for Not-For-Profit and Investor-Owned Hospitals, 1983,Report to the Board of Trustees (American Hospital Association, Chicago, IL).
COST-SHIFTING UNDER COST REIMBURSEMENT AND PROSPECTIVE PAYMENT
Richard W. FOSTER* University nf Colorado at Denver, CO 80202, USA Received September 1984, final version received March 1985 Cost-shifting is seen as a three-way phenomenon involving hospital interests as well as those of government and private patients. Without economies of scale, private patients are indifferent to government policies unless underpayment leads to hospital bankruptcy. In the presence of economies of scale, private patients benefit from reductions in government payment under either cost reimbursement or prospective payment. Their interest in a shift to prospective payment depends upon the hospital’s location on its cost curve. Hospitals benefit from increases in payment rates in all cases, but benefit from a shift to prospective payment only if operating in a region of dtslining average costs. The conventional view of cost-shifting is inconsistent with profit maximization and may be inappropriate for many voluntary hospitals as well.
1. Intrah!tion
The passage of legislation mandating a new method of reimbursement for inpatient services to Medicare beneficiaries has set off a new wave of concern about cost-shifting. The discussion is clouded by a failure to specify the nature of the phenomenon. It is generally regarded as a consequence of government ‘underpayment’, but criteria for underpayment vary. To some, underpayment occurs when ‘hospitals charge some patients more for the same service than they charge others’ [Meyer (1983, p. G)]. Hay (1983), on the other hand, argues that ‘genuine’ cost-shifting occurs only when government pays less than average cost, and shows that differential pricing may occur without this. Hay’s criterion is appealing in that it implies cross-subsidies. Sloan and Becker (1984) employ yet another criterion: to them, cost-shifting occurs if reductions in the government payment rate lead to increases in the orices charged to private pay patients. This criterion is appealing in implying that private patients are made worse off by the cost-shift. While most discussions emphasize this impact on private patients, concern is sometimes also expressed that government underpayment threatens hos*I would like to thank Joel Hay, James Morris, Norman We&, and the editor and referees for coraments on various drafts of the paper. 01’57-6296/85/$3.30 0
1985, Elsevier Science Publishers R.Y. (North-Holland)
R.W Foster, Cost-shijting, cost reimbursement, prospective payment
262
pit&’ financial viability. These concerns are sometimes expressed in aggregate terms, while at other times the threat is said to be more severe for hospitals with higher proportions of government patients [Hadley, Mullner and Feder (1982)]. In this paper, I examine these propositions for the simple but important case of a profit-maximizing hospital. I shall generally adopt Hay’s criterion for underpayment, but I shall be attentive to whether costs are shifted to private pay patients or hospital owners. It is shown that Hay’s criterion may be satisfied when the Sloan-Becker criterion is not. Indeed, a profitmaximizing hospital will not generally practice cost-shifting in the SloanBecker sense. I also distinguish the cases in which the deficit from treating government patients grows as a result of a reduction in the government payment rate or as a result of an increase in the number of government patients treated. The cases are shown to be quite different, with the latter conforming more closely to conventional discussions of cost-shifting. The effects of reductions in government payment rates and of increases in government patient loads are qualitatively the same under cost reimbursement and prospective payment. The effects of a shift to prospective payment depend upon the hospital’s location on its average cost curve. Long-run effects &zuW >R negligible. In the short run, hospitals and private patients are both likely to benefit, while government program costs are likely to increase. Govermnent underpayment will generally iead hospitals to practice ‘demarketing’. In the short run, though, some hospitals may actively recruit government patients in spite of underpayment. Some of these conclusions contradict widely held views of cost-shifting. The empirical evidence for such cost-shifting is weak, however. Thus it remains unclear whether it is the conventional view of cost-shifting or the conventional view of hospital pricing which should be rejected. At a minimum, cost-shifting discussions should carefully distinguish investorowned and non-profit hospitals. 2. Formulation of the model The hospital is assumed to maximize profits,
max7~=
P,Q,
+ aCQG - C(Q, + QG) -
%'QG
where
QP =volume
of private use, QG =volume of government patient use, 5 = Pp(Qp) = price paid by private patients,
cR,
R.U! Foster, Cost-shifting,cost reimbursement,prospectivepayment
263
C = C(Q) + Qo) = average cost of producing services at volume Q, + QG, CR = CR(QG- QGo)= total cost of marketing efforts to achieve volume QG of government patients, of government patients which would arrive with no marketing QGO =vohme effort, Q =fraction of average cost reimbursed for government patients. In addition, I assume P
ap,
p=aQp
(downward sloping private demand),
Pp+~pQp>O
(private monopolist’s marginal revenue positive),
2Pp+P;Qp<0
(private monopolist’s marginal revenue falling),
C+c’(Q,+Q&O
(marginal cost of production positive),
2c’ + C”(Q, + QG)2 0
(marginal cost of production rising),
CL=0 >O
for for
QG-QGO=O QG-QGO>O
CO for
QG-QoO
c;>o
(marginal cost of moving QG away from QGOis positive), (marginal cost of moving Qo away from QGOincreases with distance from QGO),
O
(government ‘underpayment’).
The model should also incorporate the constraint K20, but I shall omit this for simplicity, simply referring in the text to situations in which the constraint may prove binding. Two aspects of this formulation warrant particular discussion. The first is the assumption of profit maximization and the second is the structure of marketing costs. Profit maximization is clearly the appropriate objective for the important and rapidly growing investor-owned se ent of the hospital industry. Furthermore, the implications of the profit-maximization rule are of interest for voluntary hospitals for a number of reasons. First, profit maximization is the most widely used criterion in explicit
264
R.W Foster, Cost-shijling,
costreimbursement, prospective
payment
models of hospital pricing behavior [see, for example, Damon (1982), Hay (1983)]. Hence, if implications of profit maximization could be rejected, this would be of interest 111forcing a reconsideration of much of the pricing Iiteratutie. Secondly, there are a number of cases in which non-profits will behave like profit maximizers. Hay (1933), for example, shows that some of the conclusions reached here are also valid for a hospital which maximizes the incomes of its physician staff. Dran and Campbell (1981) argue that. non-profit hospitals should maximize profits on profitable services, using the proceeds to undertake projects which are not self sustaining. This makes profitmaximizing pricing rules appropriate for much of the hospital’s business. Finally, many hospital leaders are concerned about access to capital and have urged non-profit hospitals to improve profitability in order to enter debt markets on favorable terms [Special Committee on Equity of Payment (1983)]. Thus, differences in pricing behavior between for profit and nonprofit hospitals may be diminishing. The introduction of marketing or recruiting into the model permits the hospital to adjust its government patient load, but such adjustments are made subject to a penalty function of the conventional form. Recruiting costs are zero at Qo=Qo,,, which will depend primarily on the demographic character of the hospital’s service area (though changes in government program eligibility criteria could also shift QGO).IA order to attract more government patients than this, the hospital must incur positive recruiting costs which may take the form of advertising, outreach programs, cultivation of referral networks, and the like. Reducing Qo below QGO(‘demarketing’ is the current buzzword) likewise requires the hospital to incur costs. These may take such forms as development of referral mechanisms or damage to the hospital’s reputatior. as it becomes known for ‘dumping’. The marginal cost of such adjustments is assumed to increase as the magnitude of the adjustment increases in either direction. This formulation of recruiting costs places the model in an intermediate position between those of Danzon (1982) and Hay (1983). Danzon assumes the volume of government patients is exogenously determined, while Hay assumes that the hospital can costlessly adjust its government patient load to any desired level. The first-order conditions for an interior solution to the hospital’s problem are
(1) (2) The marginal conditions state the familiar result that the marginal revenue
R.W Foster, Cost-shijkg, cost reimbursement,prospective payment
265
must equal the marginal cost for each class of patient. The expression on the right-hand side in each of (1) and (2) is the marginal cost of production, assumed equal for the two classes of patients. The first two terms in the expression for the marginal Lyevenuefrom private patients @eft-hand side of eq. (l)] simply give the marginal revenue for the textbook monopolist. The third term, &‘QG, reflects the fact that if an additional private patient changes the average cost this will affect the hospital’s revenue through a change in its reimbursement for government patients. The same term appears in the expression for marginal revenue from government patients @eft-hand side of eq. (2)]: any change in average cost can be thought of as altering the reimbursement for all other government patients. In addition, the term -CR reflects the fact that net marginal revenue is reduced if costs must be incurred to recruit the marginal government patient (or, alternatively, net marginal revenue is increased if costs of discouraging government patients are avoided by allc sing volume to increase). 3. Cost-shifting with cost reimbursement Since the empirical evidence suggests few if any economies of scale (except at very small sixes or for some specialized services) [Lave and Lave (1979)], I shall take the case of C’=0 and C” = 0 as representative of the long run. For this case, eqs. (1) and (2) reduce to
Pp+ ppQ, = G
(3)
aC=C+C;p.
(4)
The solution is illustrated in fig. 1. Notice that as long as average cost is insensitive to total volume, eq. (3) will yield an optimal Q,=Q,* (and hence -P,*)which is insensitive to the parameters (a) and Qoo. an optimal PpPrivate pay patients are indifferent to government payment policies even though they pay more than the government pays for identical services and even if government ‘underpays’ (a < 1). The hospital, however, is not indifferent to government payment policies. With LIc 1, eq. (4) requires CRCO. With government underpayment, then, the hospital will practice ‘demarketing’ in an effort to reduce government patient volume. If it could adjust government volume costlessly, it would treat no government patients at all, a case which is not observed in practice. It can easily be shown that reductions in (a) or increases in Qoo will reduce rc. Hence, if government underpayment is taken as the criterion for cost-shifting, then costs are shifted to the hospital rather than to private pay
266
R.W!Foster, Cost-shifting, cost reimbursement,prospectivepayment
Fig. 1. Longrunequilibrium withcost reimbursement. patients. Thus the Hay criterion for cost-shifting is satisfied, but the Sloan-
Becker criterion is not. Evidence of this kind of cost-shifting is offered by Hadley, Mullner and Feder (1982), who find hospital profits are lower where the proportion of government patients is higher (due, presumably, to cross-sectional variation in Qcd The effect on hospital profits means that the indifference of private pay patients to government payment policies must be qualified. To this point I have assumed an interior solution, ignoring the constraint x20. It is clear, though, that for sticiently low (a) and sufficiently high Qo,,, the constraint could become binding, and the hospital would be forced to bankruptcy. Private pay patients would be made worse off by being forced to more distant or otherwise less satisfactory hospitals. In the short run private pay patients are affected by government payment policies even if the hospital remains solvent. Absent economies of scale, short run responses for a hospital initially at optimum capacity are given by the case of C’=0, C” > 0 (with declining long-run average costs, a hospital at optimal capacity has c’ CO, C” > 0, a case which is discussed below). These effects, however, are inconsistent with the conventional view of costshifting. It is a relatively straightforward exercise in comparative statics to show that a reduction in the proportion of costs reimbursed for government patients will actually reduce the price charged to private patients. The intuition for this result is that, by reducing marginal revenue from government patients, the reimbursement change induces the hospital to reduce total volume. This reduces marginal cost, so that private marginal revenue is equated with marginal cost at a lower level. The presence of the aC’Q, term in eq. (1) only partially compensates for this.
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This decline in total volume with decreases on (a), combined with a history of apparently declining (a), suggests that many hospitals may be operating in a region of declining average costs. Certainly the Tax Equity and Fiscal Responsibility Act of 1982 must have reduced (a), so that many hospitals faced declining average costs in the short run at the onset of prospective payment. The comparative statics show that, again in this case, a reduction in (a) leads to lower private prices, contrary to the conventional wisdom. Such a short-run equilibrium is illustrated in fig. 2. (Those who believe in significant economies of scale may also regard this as a possible long-run equilibrium.) From eq. (I), the private monopolist’s marginal revenue must exceed marginal cost by -aC’Qo. We may think of a decline in (a) causing volume to decline with this relationship being maintained until marginal cost - uC’Qo is simultaneously equal to UC- CR as required by eq. (2). While this scenario of falling (a) suggests &>O, the case of Ck
Fig. 2. Equilibrium with declining average costs.
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price charged to private patients. The price increase occurs because the hospital is led to operate at higher volume and hence at higher marginal cost. It is possible that an increase in government patient demand might actually increase hospital profits. This could occur if the hospital was initially operating in an area of declining average costs and was actively seeking government patients, as describd above. 4 Introduction of prospectivepayment I assume in this section that government introduces a new payment system under which hospitals will be paid a fixed prospective rate Po for each unit of service to government patients. Consistent with the principle of budget neutrality, the level of PG is set equal to the rate which the government was paying under the old system. That is, PG is set equal to the previous equilibrium level of UC. The new expression for profit is
aud the new marginal conditions are
PG-C;(=C+C'(Qp+QG).
(6)
Combining (5) and (6) gives P, +
PpQ,= PG- CL.
Consider first the case of C’=O. Comparison of eq. (1) with eq. (5) and comparison of eq. (2) with eq. (6) reveals that when PG is set equal to the previous level of UC, neither marginal condition is disturbed. Thus the shift to prospective payment does not affect anyone: hospital profits, private prices, and volume of service rendered to government beneficiaries all remain unchanged. This is even true in the short run, as long as the hospital is operating at the optimal scale for its volume before the shift (assuming no long-run economies). I argued earlier, though, that many hospitals are likely to face declining average costs in the short run. Comparison of eqs. (1) and (5) and of eqs. (2) and (6) with C’
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Consider first the case of QG. If Qo were to fall or remain the same, then -CL would be greater than or equal to its previous level. But eq. (7) would then require PP+PPQ, greater than or equal to its previous level, and hence Q, less than or equal to its previous level. But this would contradict the conclusion that total volume must rise, so the supposition of stable or falling Qo must be false. Given the increase in Qo, we have -CR less than before. Eq. (7) then requires PP+ PLQ, smaller than before, so that Qp must also rise. In the short run, then, a shift to prospective payment is likely to increase hospital profitability and government spending while reducing prices charged to private patients. It should be noted, though, that this describes a ‘pure’ shift to prospective payment: I have assumed Po= UC and no change in volume measures. The prospective payment system actually introduced was more complicated. The assumption of Po= aC is reasonable given ‘budget neutrality’. But Medicare not only switched from cost reimbursement to prospective payment, but also simultaneously switched from a patient day basis of payment to an admission basis. Note in particular that this latter switch provides the hospital with an incentive to reduce length of stay. This could dominate the increase in Qo noted above SC that government volume could fall when measured in patient days (it should still rise in terms of admissions). Further discussion of this switch from a patient day to an admission basis is given by Hay and Ernst (1984). 5. Cost-shifting with prospective payment For the constant returns to scale case, reductions in the prospective rate Po will reduce hospital profits and service to government program beneficiaries, leaving private price and volume unchanged. The logic for this result is the same as in the cost reimbursement case: neither marginal cost nor marginal revenue from private patients is altered by the change in government payment rates. The indifference of private patients to the government’s choice of Po is again subject to the qualification that low government payment rates could force hospital bankruptcies. With economies of scale, the hospital will respond to a reduction in Po by reducing prices to private patients. Hospital profits and service to government program beneficiaries will fall. As in the cost reimbursement case, reduced marginal revenue from services to government patients causes the hospital to reduce the volume of output. The resulting reduction in marginal cost causes marginal cost and private marginal revenue to be equated at a lower price to private patients. Constant returns to scale also find private patients indifferent to the volume of government patients, again subject to hospital survival. With
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prospective
payment
economies of scale, though, increases in QGOlead to higher private prices. Hospital profits will fall unless declining average costs and a low initial QoO caused the hospital to recruit government patients. 6. Summary
Qualitative effects of reductions in government payment rates and of increases in government patient loads are the same under prospective payment as under cost reimbursement. The etrects on hospital profits and on government patients are generally consistent with conventional expectations, although hospitals may actively recruit government patients in spite of underpayment in the short run. The effects on private patients generally run counter to conventional expectations. In the long run, private patients are indifferent to government payment policies unless such policies drive the hospital to bankruptcy. In the short run, increases in government patient demand have the expected effect of driving up private prices, but reductions in government payment rates actually reduce private prices. For hospitals operating at minimum average cost, the shift to prospective payment has no effect by itself. The introduction of prospective payment is likely to have found many hospitals operating on the downward sloping portions of their short-run average cost curves, however. In these cases, the shift to prospective payment sl.ould increase hospital profits and the volume of government patients treated, while reducing prices charged to private pay patients. The effects of government payment polic.ies on hospital profits and government program beneficiaries are generally consistent with expectations. They are consistent with a self-interest explanation for the hospital associations’ complaints of underpaymentand their support of the shift to prospective payment. Effects on private patients are another matter. Private insurers’ claims that reducing government payment rates and shifting to prospective payment will raise private prices are not legitimate for profit-maximizing hospitals. Their legitimacy for non-profit hospitals is unclear. The conventional arguments may rest on an assumption of target income pricing, which is seldom made explicit. There is little empirical evidence available. Payment. differentials are well established, but this does not imply government payment at less than cost and even government underpayment does not imply that private patients are injured by government payment policies. The most relevant evidence to date is that of Sloan and Becker (1984). Theirs is a cross-sectional study, relying on multiple payers as a source oi variation in (a). Although their underpayment variable incorporates dif-
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ferences in QGOand in P,, as well as in (a), they include payer mix variables as controls and use an instrumental variables method for the underpayment variable. The payer mix variables are treated as exogenous, however, and are included among the instruments as well as the controls. While the Sloan-Becker results support the conventional view of costshifting, they cannot be considered definitive. A recent study by Hadley and Feder (1984) attempts to relate changes over time in private patient markups to changes in an index of ‘need to cost-shift’, but finds no significant relationship. Like the Sloan-Becker underpayment variable, the HadleyFeder index of need to cost-shift incorporates both changes in (0) and changes in QoO.Their results suggest a more skeptical view of cost-shifting. Further work along these lines would be valuable. References Danzon, Patricia Munch, 1982, Hospital ‘profits’:The effects of reimbursement policies, Journal of Health Economics 1, no. 1,29-52. Dran, John J., Jr. and Brian E. Campbell, 1981, Hospital investment and Medicare reimbursement, Journal of Financial Research 4, summer, 147-160. Hadley, Jack and Judith Feder, 1984, Hospital cost shifting: An analysis of hospitals’ markups and financial needs, unpublished manuscript (Center for Health Policy Studies, Georgetown University, Washington, DC). Hadley, Jack, Ross Mullner and Judith Feder, 1982, Special report: The financially distressed hospital, New England Journal of Medicine 307, no. 20,1283-1287. Hay, Joel W., 1983, The impact of public health care financing policies on private-sector hospital costs, Journal of Health Politics, Policy and Law 7, no. 4,945-952. Hay, Joel W. and Richard Ernst, 1984, Hospital DRGs, prospective reimbursement, and Medicare cost-shift, unpublished manuscript, Project HOPE. Lave, Judith R. and Lester B. Lave, 1979, Empirical studies of hospital cost functions: A review, in: George K. Chacko, ed., Health handbook (North-Holland, Amsterdam). Meyer, Jack A., with William R. Johnson and Sean Sullivan, 1983, Passing the health care buck: Who pays the hidden cost? (American Enterprise Institute, Washington, DC). Sloan, Frank A. and Edmund R. Becker, 1984, Cross-subsidies and payment for hospital care, Journal of Health Politics, Policy and Law 8, no. 4, 660-685. Special Committee on Equity of Payment for Not-For-Profit and Investor-Owned Hospitals, 1983,Report to the Board of Trustees (American Hospital Association, Chicago, IL).