Creating an efficient market for nursing home care

S~cio-Em~ Ph. Sci Vof. 16. No. 2, pi. 5342,1982 Printed ia Great B&k.

CREATING AN EFFIClEPtT 1MARKET FOR NURSING HCjMIkARE ANDREW J. HOGAN Wisconsin Health Care & ResearchInc., Olde Towne OfficePark, 6417Odana Road Suite A, Madison,WI 53719,

U.S.A. (Received20 November1981)

Abstract-This paper reviews the theoretical foundations of the common Medicaid nursing home reimbursement systems: Reasonable cost related, fixed rate and negotiated rate reimbursement. Each reimbursement system is examined in terms of the four reimbursement system design’goals: Allocative efficiency, appropriateness of care, quality of care and equity of economic rewards. None of the reimbursement approaches are found to be deficient on the theoretical level, but practical problems of implementation are shown to be very ditlicult. As an alternative, a competitive bidding system is proposed which would bring competitive market efficiency to the allocation .of Medica% funds for iitirsing home -care. A mathematical programming model is developed to process the bidding infoprinationand to z#?cate Medidd funds to nursing homes.

1. THEANALYTICS OF NURSING HOMEREIMBURSEMENT SYSTEM because of mtt’nt~lr&r&tion 6r‘psycholbgical disorders, DESIGN then it is .red\on&le IQ I-urnq some physical impair-

ment. Such a. p~ysic~‘impairme~t will represent a ‘considerable.limi~~tion on ‘freedom of choice. Our last recourse to ‘save consumers? sovereignty is to view the nursi$hame care sklection decision as a family decision. Unfoitunattty,: this not a viable argument. First, many r&&g hdme. patients do not have relatives who are able o&lling to m&kethese selection decisions for them. Furthermore, family participation in such decisions may te$r%nt anotherlimitation on freedom of choice. It can easily fiappen that’ the convenience of the family in terms~6f travel time or cost may weigh too heavily in the decition ,process. It is clear that some aider people reside :ig tigr.&g homes @her than with their families @e .to’the ‘wishes o$ the families, not by their own preferen&. In ;urnrn~~y,~.@ finf!.&at many nursing home patients are not m&tall~.Bble or physically free to choose nursing home care.‘l&by of these patients do not have families who are able or willing to make choices for them, and when they do, it is not certain that we can always assume’ that the families are msking choices in the best interest of the patients. For these reasqns, the state governments have set up programs to regulate nursing homes and to guarantee the ,quality of. care provided. Given the inability of most nursing. home patients to exercise .consumer spvereignty in the choice,.of a nursing home, there is”nQbasis upon which to deregulate nursjng home care financing s@ that it. will behave iike a free competitiv~.market. Fort~~~fely, there is an alternatjve. to the present regulatory mechanism +vhich offers. the benefits of market efficiency. Iristead of regulating nursing homes, the State should act as a broker for nursing home patients. Using the same kind of diligence which consumers emplpy:in making purthases, the State should “shop ar$hd” for_the best bargains in terms of both cost and quality of-‘care. Due to the number of individuals and r&sing homes involved; ttiis is riot a simple task, but it is possiblz: if we take advantage of some powerful operations research computer models. A methodology for instituting a “public market for nursing home care” will be

It is unecessary to remind the reader that public expenditures on health care have created a crisis in public finance ([I], pp. l-21. At the Federal level, Medicare/Medicaid costs have been growing at an alarming rate, but at the State level the Medicaid Program is sometimes viewed like a science fiction monster ready to devour the entire State budget. These fears arise not only from the size of the expenditures per se, but from their unyielding rate of growth. Among Medicaid expenditures, the category which seems most intractable is long-term care ([2], pp. 5-10). Nursing home expenditures have been rising faster than any other category and will soon represent the bulk of public health expenditures on health care[3]. The recent disenchantment with regulatory processes and the preference for designing health care systems which rely on economic incentives and competition presents a very serious challenge to public agencies responsible for financing nursing home care. All health care fin~cing systems which hope to achieve efficiency without regulation through competition have to rely on the efficacy of consumer sovereignty. In economics, consumer sovereignty means that consumers know the true price and the qualityof’what they buy and that they are free to choose among the alternatives. Consider foraqoment the nursing home population in the State of Wiscansin. Eighty-five percent of Wisconsin’s nursing home residents are sixty-five years or older. There are many‘elderly peRons who are bright and apt consumers; they @&jnot likely fo be residing in nursing homes, hdwever. Most of ‘the younger nursing home patients ,@dq there because of mental retardation or psychologic& .&orders ([4], p. 1). Even among the subset of nursing home patients who are mentalty, wpable of aprising themselves of the economic features of nursing home care, how many of these are free ‘2c;choose? Freedom to choose nursing home care involves the ability to shop around for alternatives and to’move to another facility. If a person is residing in a skilled or intermediate care facility not 53

54

A. J. HOGAN

presented as soon as we analyse the current practices in nursing home care financing. The goals of a nursing home reimbursement system

In the literature on nursing home reimbursements, one finds a number of confusing statements about efficiency. .In some contexts, pursuing efficiency seems to be equated with cutting costs. In other contexts, it seems to be synonymous with quality. To an economist, efficiency has a very precise meaning and it behooves us to spend, some time examining it. Consider a health care consumer with the following utility function: w = H(S, B) ’ U[Z- R(s)]

(1)

where W is total utility; S is the measure of health care service; 0 is the health status of the individual-a random variable; H(.) is the utility of health as a function of health status and health services; Z is total individual income; R(.) is the cost function of health services; and U(u) is the utility function for income. The utility model (1) emphasizes the role of good health inthe enjoyment of other goods. Thus, a person with a high income but poor health will have a low total satisfaction, just as a person with good health but a low income. With this model, one can characterize the decision to purchase health care. Taking the first derivative of (1) with respect to the level of services (S),
0.

(2)

We can solve (2) for.the marginal cost of health care, giving: aRlas

=

_,

aHas

u[z-NS*)I

autaR

H(S*, e)

(3)

Since aUtaR = - 1, (3ibecomes: aRlaS = aH/aS “~$f(~~)‘.

where R(S) is the revenue function; S is the level of service provided; and C(S) is the cost of producing the service. We can maximize the health care provider’s profit by taking the first derivative of (5) with respect to s: adas=

aRtas-actas=o,

or G$=$$.

(6)

This is the familiar rule of allocative efficiency in economics, the marginal revenue is equal to the marginal cost. Of course, the provider is only able to influence the cost characteristics of the service. The revenue function is the province of the consumer and is determined in (4). Currently, a great deal of time and effort is being expended in the nursing home industry collecting data and estimating the cost function in (5). Clearly, if there were nursing home administrators who were incapable of dealing with these kinds of managerial problems, they have been largely weeded out by now. The same cannot be said for the nursing home care consumer. For reasons stated earlier, there is every reason to believe that the utility optimization process described in (4) is often biased by the mental and physical condition of the patient. In as much as the revenue function (R(S)) in (5) is the product of the individual demand decisions in (4), the criteria for the efficient allocation of resources will not be met in an unregulated market-social optimality cannot be achieved in the absence of consumer sovereignty. The situation just described is known in economics as market failure. The theory of public finance dictates that in the face of market failure, it is appropriate for the government to intervene to restore social efficiency. This is not necessarily an easy process, as the case of nursing home reimbursement proves. In designing a system of nursing home reimbursement, we would like the system to have the same properties as the market has when it functions properly. Buchanan ([2], pp. 25-27) reviewed several sets of goals for nursing home reimbursement systems. What follows is a compilation derived from that analysis: Nursing home reimbursement system design goals

We can interpret (4) as follows: The optimal allocation of the consumer’s income between health.care and other goods and services ischaracterized by the condition that the marginal cost of health .services is equal to the marginal increase in health caused by those services times the ratio of total non-health utility to total health utility. The health consumer optimizes utility when the marginal cost of another unit of health care (JR/&) is equal to the marginal change in utility brought about by the consumption of one more unit of health care times the ratio of total non-health utility to total health utility. The consumer is considered to be economically rational so long as the health care consumption decision meets the criterion specified in (4). As we will see in a moment, the marginal cost of health care (aR/aS) is actually the price the consumer is willing to pay for the service. In a free competitive market, the price covers the cost of the service. Now consider the case of a profit maximizing health care provider. The provider’s profit function can be represented by: rr = R(S) - C(S)

(5)

(1) Allocative efficiency in provision of services; (2) Appropriateness of the care provided; (3) Quality of care provided; (4) Equity in the payment of services rendered. Let us review each goal. Allocative efficiency in the provision of services refers to the property developed in (6); the marginal cost of providing a service should equal the market price. This also includes the concept of technical efficiency-using that technology, managerial practice or social organization which produces the greatest output for any given level of input. Thus, the technically most efficient technology is not necessarily the cheapest; rather it is the technology which produces the most service per dollar of input. Note that the most advanced technology is not necessarily economically efficient. Appropriateness of the care provided rests on the realization that in health care more is not always better. A reimbursement system ought to encourage nursing homes to provide the right amount of care for a patient, neither too little nor too much. Quality of care provided has to do with the conditions and manner in which care is provided. The number and type of services performed may be adequate, but the

55

Creating an efFtcientmarket

manner of this provision could detract from their effectiveness, Lastly, equity in the payment of services rendered refers to the need to prevent the economic exploitation of any of the participants in the nursing home care system. Health care providers and nursing home patients ought to receive and pay prices respectively which are fair under present economic conditions. Equity in the treatment of all partners will bring stability to the reimbursement system. Current r~irnb~r~ernenr methods Let us now look at the three principal approaches to nursing home reimbursement: Reasonable cost-related reimbursement, fixed rate reimbursement and negotiated rate reimbursement. For the purpose of the present discussion, we will assume that all data processing and rate setting problems involved in these reimbursement approaches can be resolved, In the next section, we will discuss the empirical problems of rate setting. Consider first the predominant form of reimbursement: Reasonable cost-related reimbursement. Under this system, the nursing home is repaid the cost of providing care to the patient plus a reasonable rate of return. A simple model of the nursing home profit function is: Maximize v = R(S) - C(S) = (1 t p&Z(S)- C(S)

(7)

Third, to the extent that quality is a function of cost, the quality of care is limited by the cost constraint. With nursing home care, or with the purchase of a large vohrme of any product, quality monitoring is necessary. However,’ with reasonable cost-related reimbursement, the cost function constraint may place an unacceptably lower limit on quality: This is an empirical question to be reviewed later. Lastly, in terms of equity, reasonable cost-related reimbursement achieves this goal if the allowable rate of return, p, is set at the level which the market would have produced under ideal conditions. This is not an easy estimate to make, but it is not theoretically impossible. Now, let us consider fixed rate reimbursement. Here the nursing home is paid a flat rate for each unit of service regardless of cost. We can represent the nursing home’s profit function as: Maximize rr = rS - C(S)

(11)

where r is the fixed rate per unit of service. The prolit maximizing level of service, for the nursing home is characterized by: d97ldS=*r- atlas-0 or

r= atlas. WI

The nursing home will provide service up to the point where the marginal cost of providing the service is equal where p is the predetermined allowable rate of return. to the fixed rate. Clearly, this reimbursement approach In this case, the rate of return is proportional to the level provides exactly the same level of care as the free of expenditures made on behalf of patients. The profit market, if r = aR/aS*, if the flat rate is equal to the ideal maximizing condition for (7) is: market price. Hence, there is no problem with allocative efficiency under the flat rate approach on the theoretical a?r/as = (1 + ~)~C~~S- aeias = 0. (8) level. The only problem is the empirical estimation of the optimal flat rate. Clearly, the profit function is unbounded and the profit If we assume good will on the part of the nursing home maximizing level of services is the largest level possible. administrator, there should be no difficulty with either This, of course, would produce infinite costs. To control appropriateness or quality of care. As a practical matter, costs, states institute some kind of cost containment supervision is necessary to insure appropriateness and procedure-to be discussed below. Thus, (7) can be quality of care. To the extent, that quality involves greater costs, supervisjon will be needed to assure that rewritten to reflect cost containment: sufficient quality is provided. In distinction to reasonable cost-related reimbursement, there will be a tendency to Maximize GT= R(S)- C(S)th[(ltp)C*(S)-R(S)] (9) provide too little service under the fixed rate system economic rents can be earned when r> aC/aS. Again, where c*(S) is the acceptable level of cost for each level even with normal economic activity, it is a good idea to count one’s change after a purchase. of service. We can substitute in the constraint condition, Lastly, there should be no theoretical di~culty with giving the following first order condition: equity, so long as nursing homes are not forced to accept patients whose costs are greater than the flat rate. If the dd&!T=(ltp)$$-$j=O or (10) rate is set too low, then there will be a shortage of nursing home beds open to public pay patients. The negotiated rate reimbursement approach differs In (lo), we equate the marginal cost of providing the service with thy-margina change in the IeveI of reim- from the fixed rate only in that each nursing home is assigned a different rate according to its.special circumbursement. stances. Thus, the profit function for the nursing home Let us now review reasonable cost-related reimbursement in terms of our four reimbursement system goals. becomes: First, reasonable” cost-related reimbursement will Maximize ,r = r( JI)S - C(S) produce allocative efficiency if C”*(S)is a good estimate (13) of the cost fun&on which will prevail in the competitive market. Theoretically, then, there is no problem with this where r((0 is the flat rate as a function of provider approach. We 621 consider the practical problems below. ~ar~cteristics, JI. The first order condition for (13) is: Second, left to their own devices, the nursing homes optimize profits by increasing the level of services proadas = r(ij) - aC/aS = 0 or r(9) = $j. (14) vided. This tendency led to the imposition of the cost constraint. Therefore, appropriateness is guaranteed by Here the nursing home will provide service up to the external supervision.

(*+p)s=$j,

56

k J. HOGAN

point where the marginal cost of the service is~jysteqital to its individualized flate rate. The use of the negotiated flat rate approach recognizes that different nursing homes face different service provision problems. Thus, the marginal cost of providing the 100th bed at one home will differ from its cost in another home. Allocative efficiency will be achieved .when thesemarginal costs are equal .across all nursing homes. Since the marginal cost should equal the price in an efficient market, the use of a negotiated rate,seems to violate the efficiency criterion developed earlier, The justification for the negotiated rate rests ‘on the idea of xrgment4 m.&&--.I large’nur~~n~~homein the city of hl~b~~ukee IS ~LVrn the same market as a small nursing’home in Bloomer (population 5OQq).Since one could not,reasonably expect a nursing’home patient to be willing to,choose between these two nursing homes even if the type and quality of care were equ&alent,,.we must treat each nursing home differently. .At the extreme, this reduces to considering each nursing home separately, and at this point it is difficult to distinguish functionally reasonable cost from negotiated fixed rate reimbursement. The reason for the negotiated rate’ reimbursement approach rests on. the unwillingness of nursing homes to accept public pay patients at.& established flat rate ([Z], pp. 32-33). Part of the negotiation over the rate has to do with the costs of offering appropriate.and quality care. The negotiated rate helps to,.overcome some of the unavoidable problems presented by the heterogeneity of the nursing home experience. The problem in negotiating rates is to know when this heterogeneity is due to poor management and when it is dueLto external,. uncontrollable factors. Theoretically, however, opti~~1 rates can be negotiated. Once negotiated, the tendency will be towardunderservice, as ‘with the:fixed rate, and supervision must be employed. The issue of equity is a difficult one. If-we assume that the State negotiating team extracted all of the concessions which the market would have, then we should find that all nursing homes have essentially the&me profit rate, This, of course, would occur in a market situation only if all ,nursing homes faced thesame service production situation ,with ‘the same. managerial talent and resource base. In the ,real world, we do not expect all businesses to beequally lucky in’ their resource base or service production environment. in the-’face of this heterogeneity, we expect businesses to mak~.s~ecialized adaptations in order to,compete: From these adaptations can come many innovations leading to greater technical efficiency. Thus, while in one sense the goal of the negotiated rate to guarantee aroughly equal profit rate for nursing homes facing different servjce production requirements is fair,.@ another-sense it may reduce the nursing home industry’s need to be innovative and, thereby, discourage the growth of technical efficiency. Related to the negotiated fixed rate is the reasonable cost-related reimbursement conditioned by prdvider characteristics ([lS], p. 60). Under this approach, the cost estimation procedure, .will consider certain provider characteristics in determining the allowable‘fevel of cost. Commonly discussed ,cha~acteristics are ge~aphic location, ownership type, occupancy rates and case mix. We can-include these factors with a simple reformulation of (9): Maximize ?r = R(S) -‘C(S) (15) + A[(1+p)C*(S, $I--R(S)1

where C*(S, ‘) is the acceptable level of cost for each service level S, taking into consideration provider characteristics I++. This reimbursement approach has the same properties in terms of the achievement of reimbursement system design goals as the reasonable cost-refated approach, with the caveats just mentioned for the negotiated fixed rate. This method will not meet the standard criterion for allocative efficiency, but by assuming segmented markets, the criterion is no longer applicable. There will be a tendency to overservice, and supervision will be required to guarantee quality. Equity will be achieved in the sense of allowing for equat profit rates across nursing homes, but technical efficiency may be discouraged in the long run. On the empirical and policy level, it is possible but not trivial to determine which provider characteristics justify a differential reimbursement and what the magnitude of the differential should be. (See [5], for discussion.) The reader conversant with the recent literature on nursing home reimbursement or public health care reimbursement may be experiencing an uneasy feeling about the analyses just concluded. It is common to utter and cost related reimbursement” “reasonable “inflationary” in the same breath. Flat rate reimbursement is virtually synonymous with low quality. What we have been reviewing here are the theoretical foundations of the principle reimbursement approaches in use today. We have not discussed all of the possible hybrid systems (e.g. reasonable cost-related reimbursement with a ceiling) because the general conclusion would be the same. From the point of view of managerial economics, there is nothing inherently inefficient or inequitable in any of the reimbursement systems now in use. Appropriateness and quality of care require supervision under any conceivable payment mechanism; there is no industry which does not employ some form of inspection and quality assurance. The reasons why actual reimbursement systems have not controlled the increase in health care costs are: (1) people want more health care and they are willing to pay for it; (2) actual reimbursement systems are impractical to administer. The first reason seems to be solving itself. People are no longer willing to pay more for health care. The second reason will be discussed more fully in the next section, and a possible solution will be proposed. We saw above that contemporary reimbursement systems can achieve the four goals of a reimbursement system, if certain information can be obtained for the purpose of setting rates or determining costs. In the reasonable cost-related model (91, we need to determine the acceptable level of costs for each level of services (C*(S)) and the acceptable rate of return. In the fixed rate model (1l), we need to determine the fixed rate (r) to be paid per unit of service. Unfortunately, the calculation of these parameters has been agood deal more difficult than was originally believed. The purely technical problem of estimation has been gteatly complicated by the rapid inflation of the 197Os,’especially in health care costs. Inflation confo~ds our ,wncrete measures of allocative efficiency and equity. W&out. firm standards to judge by, the political process becomes more important as a mediation mechanism, which further complicates the technical process of reimbursement. The present preference for so-called “prospective

Creating an efiicientmarket

reimbursement” is almost entirely a product of inflation. Consider an economy with no inflation and with a set of laws and administrative rules governing the type and quality of nursing home services which can be reimbursed. In such a situation, why would a government want to tell nursing homes how much it was willing to pay when it can wait and see how much it will be charged, while all the time vigorously applying cost controls. Under these circumstances, prospective reimbursement would be an invitation to charge up to the limit announced by the government. In the present climate, however, inflation is a “reasonable cost” and inflation factors are built into most health care rate setting procedures [6]. There is little incentive in the retrospective reimbursement mechanism to control inflation; if a nursing home cuts inflation, it may only be rewarded by reduced reimbursement. If the profit rate is proportional to total costs, then the nursing home can make money from inflation (171,p. 34). Prospective reimbursement, then, creates an incentive for health care providers to reduce inflation. If they can reduce costs below the prospectively established rate, they can retain some or all of the differences as a profit. How to set the inflation factor so as to induce maximum reduction in inflation without causing inappropriate or low-q~lity care is yet another of the difficult problems in estimation to which we will now turn. Consider the situation depicted in Fig. 1. On the vertical axis, we measure average cost per patient day and on the horizontal axis we measure the service provided. To simplify the discussion, the service unit will represent a package of different services which could be broken down into components. Now suppose that the economically efficient frontier is described by the cost function C*(S). Any nursing home which has a service-cost combination which lies on C*(S) is economically efficient according to the criterion developed earlier. Suppose there are four nursing homes-A, B, C and X-which have service-cost combinations a, b, c, x respectively. The reader will notice that nursing homes A, B and C are providing service in an economically efficient way, but that nursing home X is inefficient. Let us now examine how the standard reimbursement systems will deal with this simplified nursing home market.

57

The most simple approach within the reasonable costrelated reimbursement‘system is to calculate the average cost per day. The average cost becomes the upper limit on reasonable cost; and. the State offers to pay no more than that (often ‘the,limit is not the average, but rather some fractile limit, i.e. the cost corresponding to the 75th or 90th fractile of the empirical ~is~i~ution of cost, e.g. see [S]). If all .nprsing homes :were forced to charge no more than the average (in Fig: 5, the tine AA); then both nursing homes ‘C.-and.X ,would be forced to reduce their charges. Nursing hoime X_is an inefficient producer and can be forced to reduce costs to the average level with~t chan~g,services. Nursing home C, however, is on the efficie~t;frontier and’cannot reduce the cost of providing its level of service, Thus, nursing home C must move along :C*(S) to the intersection with the average cost line ,AA. As for nursing homes A and B, they are able to maintain their present operations, but there will be little incentive to prevent costs from rising ‘up to the level of average costs. In particular, these nursing homes have little incentive to control cost .i.nflation. Each successive round of inflation will lead homes A and B to deviate further from the’-efficient inR.dionQdj~~kd sod curve. This will tend to push up the j\zrsge cost Izlel faster than necessary. As this happens, home .X will no longer be forced to ‘supply a~level of service which is cost efficient-the avetige cost wih no longer intersect the efficient cost function-.$,,the service level provided, by nursing home X Thus, we’began iGithone inefficient home and ended with three inefficient; only home Cis still on the efficient cost frontier; One strategy:,used to,~~~~ome some of the,diffic~ties presented with. ~~era~ng:~as to~~~up homes according to service leLcls;and then ~mpn~~..averages for each group. The -reader. ca%nverify that such a procedure (grouping,.e&i.,‘l&&s A and B ahd homes C and-X) will result in moving two of the three’efficient homes off of the efficient ‘cost frontier. Furthermore,‘the adjustment to the inefficient behavior of home X is greatly lessenedIt may be that the total deviation from the etlicient cost function is lessened by grouping, ‘but this is not necessarily true. Since vye:presumably,.do not know where the efficient frontier ‘is, we.tlo not know if we should group

C(S) COST

c*(s)

SERVICE

Fig. 1.

A. 1. HOGAN

58

or not, nor which grouping pattern is best. If we knew the efficient frontier, we would, of course, not need to use either grouping or averaging. Another approach to this problem which has been used in empirical analysis and proposed as a rate setting technique is cost function analysis [S]. The conventional approach to estimating the cost function is through some kind of regression model. Ordinary least squares has sometimes been used but found inappropriate due to bias in the residuals. Some form of regression procedure is required to estimate the function. Within the regression model, it is possible to add categorical variables so that ~ouping by provider characteristics is facilitated. When regression analysis is used for rate setting purposes, a bias like that just discussed with averaging arises. In pig. 2, we present the same nursing home market discussed in Fig. 1. C*(S) is again the efficient frontier. Suppose that we estimate C*(S) using the four data points available to us. The presence of the inelhcient nursing home’X is going to bias our regression line and our estimate of the efficient cost frontier will be c”(S). Notice that nursing home A (point a) is above the estimated regression line and homes B and C (points b and c) are below the line. If we use c’(S) as a rate setting instrument, then, nursing home X will be forced to reduce costs. Since home A is on the efficient frontier, it cannot reduce costs but must move to point al, still on the efficient cost frontier. Unfortunately, under this system, nursing homes B and C will be allowed to raise costs up to c’(S). This will result in only one nursing home operating on the efficient frontier. Another bothersome feature with this procedure is that it may lead to a general cost inflation. For example, nursing home X can comply with the estimated cost function rates bg either moving from point ,x ‘vertically down to point x,, or horizontally across to. point x2. Likewise. nursing homes B and C can mov,e up.to c’(S) either vertically or diagonally to points b, or bZ and c1 or c2 respectively. There is in the reasonable cost-related reimbursement system an incentive to increase the level of costs, since the profit rate is proportioned to cost. Hence, it would seem likely’ that this approach will encourage a general growth in the level of service and in corresponding costs. External inflationary pressures will

only worsen this tendency. The net result of this rate setting approach will be the elimination of the low cost/low service intensity provider. The averaging approach tends to discourage the high cost/high service intensity provider. The problem with any statistical approach to rate setting is that it is most effective when it is not needed. The efficient frontier can be estimated without bias only when inefficient producers are excluded from the analysis. If we knew the inefficient producers, we would not need a rate setting procedure. When we use biased statistical procedures, we cannot guarantee that the gains made by partially controlling ine~cient producers will offset the perverse incentive to efficient producers. Statistical procedures are excellent approaches for measuring what is, but they are often difficult to use in determining what should be. Determining the allowable level of costs is only one of the issues in the reasonable cost reimbursement approach. The other has to do with the acceptable rate of return. Here, of course, an immense literature has grown up, especially in the areas of utility and transportation regulation [9]. We would be drawn too far afield to review all of the issues involved. Let us simply conclude that determining the optimal rate of return is possible albeit not trivial, and that much controversy still exists on how this is to be done. Moving to the fixed rate approach, the problem is at least conceptually much easier. We need to fix a rate which will find an adequate nursing home for all those who need it. As we discussed in the negotiated rate case, real markets do not produce uniform prices because of location and other factors which inlluence people’s willingness to pay. For this reason, universal fixed rates tend to be difficult to set, especially when private pay patients compete for the same beds. On the empirical level, the fixed rate estimation process is complicated by bias built into the market by existing regulations. To estimate the rate which would provide an adequate number of beds for public pay nursing home patients, one would need to know the market supply function of the nursing homes and the market demand function of the private pay patients. Of

cecs>

C(S) COST

a

SERVICE

Fig. 2.

59

Creatingan efficientmarket course, the only observable quantities available to us are the number of nursing home beds actually filled and the prices paid for them. Unfortunately, these figures have been conditioned, perhaps significantly, by the existing reimbursement practices of the State. Thus, as with the cost function, a supply function for nursing home beds can be estimated, but it may be of little value for public planning purposes. We cannot discover the “true” market supply function through deregulation because the market will “fail”, as described in the first section of this paper, leading to observed market equilibria different from what the socially optimal market equilibria would be. Fixed rate reimbursement, then, relies principally on estimates of cost and acceptable rates of return. The fixed rate is designed to cover these costs and supply a reasonable cost-related reimbursement, and in fact, prospective reimbursement is only a form of negotiated fixed rate reimbursement with much attention paid of inflation adjustments. Insofar as the fixed rate reimbursement systems are based on cost and rate of return analyses, they are subject to the same biases that we analysed above for the reasonable cost-related reimbursement. Historically, fixed rate reimbursement has been criticized as too ungenerous, leading to inadequate care and/or a shortage of beds for public pay nursing home patients. Even where adequate or average, there is an incentive for nursing homes to turn away expensive patients and to recruit patients with low service requirements. Treating all patients as equals for reimbursment purposes, leads to underservice for some patients. As long as the payment is made on a patient-by-patient basis, there is no incentive for nursing homes to accept the reasoning that on average they receive a fair payment. This system is fair in the aggregate, but it would be fair for a particular nursing home only if it had a representative sample of the whole population upon which the rate was calculated. Thus, the fixed rate introduces a kind of risk into the reimbursement system which nursing home administrators attempt to manage by patient recruitment. This same problem arises, however, when under reasonable cost related reimbursement a nursing home with high service intensity patients is reimbursed for only the average cost. In the fixed rate setting approach, fixed rates for different levels of care are roughly equivalent to the grouping of homes on the basis of costs and levels of service. In summary, while both reasonable cost-related reimbursment and fixed rate reimbursement systems (along with their variants and hybrids) are theoretically capable of achieving the four nursing home reimbursement system design goals, the estimation of the functional relationships required to implement these systems in a socially optimal fashion has been difficult, if not impossible. The nursing home care market is so distorted that it is to be wondered if arty amount of econometric estimation can produce a socially optimal nursing home financing system. 3. A CODER

SYSTEM

FORN~~~G HOMECARE FINANCING Only two courses of action seem capable of producing a long-term care financial program which meets the four goals of allocative efficiency, appropriateness, quality and equity. First, data could be collected and an econometric model of the nursing home market SEPS Vol. 16. No. 2-B

B~D~G

developed which would allow the State to manage the market. in such a way that rates and service levels could be set optimally. Second, the State could create a competitive market for long-term health care. While not rejecting the first alternative, what follows in this paper wilt outline the second alternative, which seems to be more politically and financially feasible in the present context. Earlier, we discussed the causes for market failure in the provision of nursing home care. We saw that these problems derived from the inability of nursing home patients to exercise consumer sovereignty. We can reinstitute 8 competitive market for nursing home care if we can overcomk the limitation on consumer sovereignty. Here it is proposed that the State act as a broker on behalf of nursing home patients. In order for a market to function, there must be a market demand function and a market supply function. Under normal circumstances, the market demand function is the summation of the individual demand functions of consumers, and the market supply function is the summation of the indiyidual homes’ supply functions. The competitive bidding model will generate a virtual market demand function through the specification of a social utility function constrained by a budget. The supply side is generated by requesting a range of bids from each participating nursing home. The set of bids in the context of the bidding model is equivalent to the specification of a piecewise linear supply function, The mathematical solution to the competitive bidding model, then, represents a competitive market equilibrium with the desirable properties of efficiency and equity discussed previously. Furthermore, the representation of this market problem in a mathematical programming framework will allow us to handle such issues as level of care and regional market segmentation in a convenient and useful, m.anner. The competitive bidding model will be an invaluable tool‘ in facilities planning and Iicensure policy development. This model also allows the State to appiy different criteria to homes bf different ownership types, if this were to be considered consistent with health care financing policy. The nursing home competitive bidding model cab be formulated as a linear programming problem. Here, we formulate a model for a market where there are J homes, each of which is requested to supply N different service plan% Maximize

J N’ U = z 2 tJ(i)X,(i) j=c I=,

Subject to i 5 &(i)&(i) z Sk7 k= I,. i=, 8-l

(16)

K (17) (18)

$X,(i)rl r=l

j=l,...,J

(191

where U!(i) is the service rating given to the ith plan submitted by the jth nursing home; U,(i) = F(Sj(i)), where F(v) is the rating function. S,(i) is the ith service proposal for the kth level of care submitted by the jth nursing home; SkT is the State’s service target (e.g. total patient days or nursing home beds) for the kth level of

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care; B,(i)is the budget level requested for the ith service plan from the jth nursing home; BT is the State’s nursing home budget limit: Xi_(i) is the selector or decision variable for the -ith service plan of the jth nursing home. If Xi(i) = 0, the ith service plan is rejected; if Xi(i)= 1, the ith service plan.is rejected; if X,(i) = 1, the ith service plan is accepted. Since CXj(i)I 1, only one service plan per nursing home can be. selected. In the model (16)-(19). the service plan consists of the service proposals offered for each level of care and the budget request. Thus, a service plan could be comprised of 600 patient days of SNF, 1000 patient days of ICF-1, 200 patient days of ICI;-2,460 patient days of ICF-3, IO0 patient days of ICF-4, and 20 patient days of ICE-5, to be provided for a total cost of $15,000. .‘. -. The crucial step in making the model operational is the calculation of the service rating, lY,(i?., Clearly, one patient day at ICF-1 in nursing home a is not necessarily equivalent to a day of KY-l,in nosing home. b:Thus, on a periodic basis, all nursing homes must be inspected and rated. The rating procedure must produce an interval scale score, such that-“ one ICF-2 patient day in nursing home a is equal to 0.85 ICF-2 patient day in nursing home_ b”-is a meaningful statement. Insofar as the service rating procedure is explicit and understandable, the nursing home can choose the quality, as well as the quantity; of service it
services should be purchased through the competitive bidding system. Initially, it seems appropriate to exclude from the service plans episodic health care and special medication. Thus, the service plans would refer to the provision of standard nursing home care appropriate to a patient authorized for that level of care-hotel services, diet, laundry, and standard and regular nursing care. Episodic care should probably be provided either on a fee-for-service basis or through a capitation system with a heavy medical experience or risk adjustment. The actual bidding process will take place in two steps. First, perhaps at the end of the year, each nursing home will submit its set of service plans. The service plans and budget requests will be used in conjunction with the service ratings to generate the bidding model (l&(19). The model will be solved and the initial solution reported to each nursing home. At some later point, a meeting will be called of all nursing home administrators to produce the final solution and sign the service contracts. At this meeting, which could be held simultaneously at different locations with a connection to a central computer facility, nursing home administrators will be allowed the chance to adjust their bids in light of the initial solution and any modification in State nursing home financing policy. The final bids will be submitted at this time, and the final solution produced. The computer can be employed to print out the service contracts, which can be signed by the nursing home administrator and a State official at the conclusion of the meeting. These meetings could be important for the State if the initial solution did not produce a combination of service plans which covered the nursing homes needs of all the public pay patients. These meetings will allow for the kind of negotiation which will prevent the system from becoming too inflexible. It is likely that another meeting will have to be held during the course of the year to take account of changes in the patient population. The same computer network can be used to find care for new patients or to reduce the budget of homes who have lost patients. This will also allow the State the opportunity to reassess the quality of care in each home. Any dramatic change in quality (up or down) would lead to a modification of nursing homes’ budget level. This leads us to a consideration of how the bidding model can be used to control the quality of care without sacrificing patient welfare. If a nursing home were to allow its service to deteriorate, it could happen that the bidding model would choose not to allocate any of the State’s budget to that nursing home. Clearly, the State would not wish to remove all of its public pay patients from the nursing home unless the quality of service had fallen below the minimum safety standard. In these circumstances, we want the bidding model to allow those patients already in the nursing home to remain but to prevent the nursing home from acquiring new public pay patients. Since the turnover rate in Wisconsin nursing homes is about 20% per year (and. thi$ might be accelerated in a specially targeted low quality home), nursing homes with poor quality service woqld be deprived of public pay patients in three or four years. This procedure can be incorporated into the bidding model with the following constraint set: g&(i)X,(i)

2 SjL,-’ k = 1,. . . , K;

j= 1,. ..L,J

(20)

Creatingan efficientmarket where Sii,-’ is the service level (e.g. patient days) for level of care k provided by nursing home j in the last (t - 1) period. In order to discourage nursing homes from allowing short-term, abrupt declines in the quality of care, the service rating for the present period can be based upon a moving average of the service ratings of several prior periods. The moving average could be constructed so that large deviations from past performance count more heavily. Even in a competitive market, it is necessary to monitor performance. Within the competitive bidding system for nursing home financing, it will be necessary to assure contract compliance and to monitor the quality of care. These supervisory system are already in place and only minor modifications in operating procedures will be required. What will not be needed is the monitoring of costs and expenses. The number of patient days actually provided to patients cannot be known with certainty at the time the service contracts are signed due to death, transfer and recovery. We can calculate the budget adjustment directly from the bidding model (16)-(19). The solution of (16)-(19) will produce a dual variable on the budget constraint y = a,V/aB. y measures the change in total utility given a change of one dollar in the budget limit. Therefore, y-’ represents the dollar value of a one unit change in total utility. Let AS, be the deviation in the service plan of nursing home j from its proposed level. Since F(.) is the service rating function: AQ = F(ASj),

(21)

where AUj is the change in the utility of nursing home j service plan caused by the change in the service levels. Since the budget level Br was determined in reference to a particular service plan which has now changed, the budget level should also be changed. The budget adjustment will be: ABj = AlJ,ly (22) If AU, < 0, then the budget of nursing home j will be reduced by the quantity ABi. The budget will be raised if AQ>O. Changes in quality cause changes in the budget level also. If the quality of care over the year was below the level agreed upon in the contracts, then Ur will decline (AUj < 0), and the budget reduction can be calculated as in (21). Using these same properties of the bidding model, facilities planning can be improved. If we specify service targets on regional basis, we can measure the benefits of opening new nursing homes or closing old nursing homes on the attainment of these regional service targets. Specifically, we can estimate the possible effects of changing the nursing home capacity on the budget levels needed to maintain service quality in the region. Through careful facilities planning arid licensure policies.;’an appropriate (non-ruinous) level of competition can be maintained in each region. As with the other’nursing home financing mechanisms analysed earlier ‘in this paper, the efficacy of the competitive bidding system rests on a crucial assumptionthat competition can be successfully induced between nursing homes. If nursing- homes are able to collude either:directly among themselves or through a nursing home association, then the competitive model will per-

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form no better than the present reimbursement system. Unless the State were unaware of the collusion, the competitive bidding system will perform no worse than the actual system. It could become the centerpiece for a bargaining system like those often found in Europe [lo]. Let us return now to the four goals of an ideal reimbursement system: Allocative’efficiency, appropriateness of care, quality of care and equity. In the area of appropriateness of care, the competitive bidding system will reward, appropriateness through the service plan rating mechanism, which will give a low score for both too much and too little service. Since profits are no longer proportional to the level of cost, underservice is more likely to present a problein than overservice. Having agreed to provide a given, amount of service for a given budget level, a nursing home will profit from underservice: This is a problem of contract compliance and not the‘system of payment. At least, the nursing home hasnoexcuse for not delivering the service, since it, not the State, determined that this level of service was economically’ feasible for the budget level proposed. It_ may behoove the state to set up a program of managerial support for nursing home administrators on a cost recovery basis. This will reduce. the number of infeasible service plans submitted and thereby reduce the social disruptions of nursing home bankruptcies. In terms of the quality of care, it will still be necessary to monitor nursing homesto .assurethat minimum health, safety and medical standards are being met. Beyond these minimum standards, it is the nursing home which must decide how to make the trade-off between cost and quality of care. The State in rating each nursing home service plan will be willing to pay for the demonstrated ability to provide greater quality. By its site visit inspection instruments, the. State can define very precisely what it means by quality, and it can change these,instruments in response to’the needs of the nursing home patient population. In this, .the competitive bidding system will have achieved’ a level of integration of cost reimbursement:and quality assurance which surpasses even the most advanced ‘system in place today (see Ohio Am. Sub. 176,in Creasey[ll]). With regard to allocative efficiency, the competitive bidding system will achieve all that can be offered under the competitive-market in a capitalist economy. While design considerations always intervene, on the theoretical plane, the level of ailocative efficiency produced through the competitive bidding system cannot be surpassed by any other reimbursement system. As we have seen, however, all of the reimbursement systems are theoretically efficient. Rather, it has been the practical design features which have led to inefficiency. Perhaps, the strongest feature of the competitive bidding system is its’guarantee, ‘of equity in terms of the rules of econamic behavior accepted in the United States. No nursing home is forced to operate under a service plan which it .has not itself proposed. Each nursing home is responsible for determining what it can and is willing to do and how much it must be compensated. The State, for its part, is not obligated to purchase services from any nursing home when another nursing home will offer the same service at a lower price or a better service at the same price. The State is under no obligation to subsidize a nursing home which cannot compete. Thus, inefficient homes will be forced to improve or leave the market.

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Lastly, the competitive bidding model offers the best possible approach to controlling inflation. At present, inflation is built into the reimbursement system. Most reimbursement systems have an inflation factor which allows nursing homes to pass on the increased cost’s of goods and ,services[6]. Such inflation factors offer no encouragement to reduce price increases and may even offer opportunities to inflate costs more than is required. In the competitive bidding system, a nursing,home which merely passes on cost increases is likely to be outbid by a similar home whose administration has found ways to lessen the impact of general price increases. In this system, the “reasonable” inflation factor is replaced by the “competitive” inflation factor. The competitive bidding system offers some advantages to the State. Principal among these is a much more manageable and less expensive nursing home’care financing system. The vast amount of electronic data processing involved in reimbursing reasonable costs for nursing homes is eliminated. The personnel now employed in reimbursement monitoring can be used for

contract compliance and quality assurance and measurement. Furthermore, the very difficult methodological problems of estimating an optimal flat or negotiated rate or of determining the efficient cost functions are eliminated. The nursing home market created by the competitive bidding system solves these problems by itself. Lastly, the process of facilities planning and licensure are greatly assisted by the information which can be derived from the competitive bidding model. The implication is that facilities planning policy and nursing home care financing policy will be much more closely integrated than is possible under the present system. There are some features of the competitive bidding system which will appeal to the nursing home administrator. There will be a good deal less paperwork and, for the administrator trained in business management, the financing system will become much more rational and l&s arbitra’ry than previously:Nursing home care financing will be conducted with mtich more equity than is presently.the case. Nevertheless, it would be foolish to think that the competition bidding system will be strongly supported by

nursing home administrators or owners. Gone will be the days when all but the most inefficient nursing homes are guaranteed basic financial viability. In a competitive market, inefficiency is punished by economic loss. Gone also will be the days when price inflation can be simply passed through to the patient or Medicaid. The financially viable nursing home will be the one which finds ways to resist price inflation. It is axiomatic in economics that there is no producer in a competitive market who would not prefer to become a monopolist or, failing that, an oligopolist. Thus, the creation of a competitive market for nursing home care is designed principally to benefit the consumer, not the producer, of that care. This is the consequence of restoring consumer sovereignty to the nursing home care market. REFERENCES

M. Koetting, Nursing Home Organization and Ejiciency. Lexington Books, Lexington, MA~(1980). R. T. Buchanan. Health-Care Finance. Lexington Books, Lexington, MA (1981). P. D. Fox and S. B. Clausen, Trends in nursing home expenditures: implications for aging policy. Health Care Fiktcing Reu. 2:65-70 (1980). 4. G. Krc, S. Seigel and T. Tyson, Final Report: Nursing Home Cost/Quality Study. Department of Health and Social Services, State of Wisconsin, Madison, WI (Sept. 1980). 5. C. E. Bishop. Nursing home cost studies and reimbursement issues. He&h Care &umcing Rev. 1,47-64 (1980). 6. P. L. Grimaldi, Inflation factors and nursing home reimbursement. Long Term Care and Health Services Administration Quart. 4, 16-28 (1980).

I. W. L. Dowling, Prospective rate setting: concept and practice. In: Prospective Rate Setting, Aspen System Corporation. Germ&town, MD (1977). 8. G. Tricario and N. H. Shanks. Long-term care reimbursement and regulation: A study of cos< case mix and quality. Health Care Financine Contract Reoort. HCFA. Washinaton. D.C. (March 1981). 9. C. F. Phillips, The Economics of Regulation. Richard D. Irwin, Homewood, IL (1969). 10 W. A. Glaser, Health Insurance Bargaining. Gardner Press, New York (1978). 11. K. B. Creasey, Medical assistance newsletter No. 104. Department of Public Welfare, State of Ohio, Columbus, OH (Aug. 1980). I