Two-tier charging strategies in public hospitals: Implications for intra-hospital resource allocation and equity of access to hospital services

Journal of Health Economics 26 (2007) 447–462

Two-tier charging strategies in public hospitals: Implications for intra-hospital resource allocation and equity of access to hospital services Barbara McPake a,∗ , Kara Hanson b , Christopher Adam c a b

Queen Margaret University College, Edinburgh, Edinburgh, United Kingdom London School of Hygiene and Tropical Medicine, London, United Kingdom c University of Oxford, Oxford, United Kingdom

Received 4 February 2005; received in revised form 4 October 2006; accepted 27 October 2006 Available online 4 December 2006

Abstract Two-tier charging, the practice of offering separate qualities of service at different prices, is a growing practice in public hospitals internationally. This paper models two-tier charging as a Stackelberg game in which the Ministry of Health leads by setting prices and a representative hospital follows by setting quality levels to maximise surplus in response. Whether or not two-tier charging will secure cross-subsidy from superior to basic service users depends on the own and cross-quality effects of the demand functions for the two services. Under a range of assumptions, the policy will evoke cross-subsidy from basic to superior services. © 2006 Elsevier B.V. All rights reserved. JEL classification: I11 Analysis of Health Care Markets; I18 Government policy, regulation, public health Keywords: Two-tier charging; Public–private mix; Equity

1. Introduction Two-tier charging refers to the practice in which hospitals offer two separate qualities of service at different prices. Two-tier charging is widespread in public health systems in both high and low income settings (National Economic Research Associates (NERA) 1995; Carmel and Halevy, 1999; Nolan and Wiley, 2000; Shirom, 2001; Suwandono et al., 2001). In a number of low and middle income countries in particular, governments are actively pursuing two-tier charging ∗

Corresponding author. Tel.: +44 131 317 3490; fax: +44 131 317 3494. E-mail address: [email protected] (B. McPake).

0167-6296/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhealeco.2006.10.011

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ostensibly as a means to bridge the gap between the funding needs of hospitals, the limited ability to pay of the majority of the population, and the restricted capacities of public funds. Hospital officials often justify two-tier pricing on the grounds that by exploiting greater willingness and ability to pay amongst the better off, premium services cross-subsidize the provision of basic (general ward) services. By raising the quality of the basic service, and/or by narrowing the gap between the best and worst quality, this cross-subsidy may be thought of as equitable. But the exclusive focus on quality is only one way of measuring equity. Equity may also be deemed to be served if two-tier pricing lowers the per-unit price of quality for the basic service, either absolutely or relative to that for the premium service. An equivalent way of expressing this is in terms of each service’s contribution to fixed costs in which case two-tier pricing may be deemed equitable if the superior service makes a larger (absolute and relative) contribution to fixed costs than the basic service. There is no guarantee, however, that two-tier pricing necessarily generates a cross subsidy in favour of the basic service. It is possible that this form of discriminatory pricing generates inequitable outcomes; two-tier pricing may equally reduce the absolute and/or relative quality of the basic service, or result in the basic service making a larger contribution to fixed costs. The case of Zambia illustrates many of these issues. The health care financing policy distinguishes services which fall inside a defined essential package of services to be charged at “cost sharing” prices from those to be charged at cost-recovery prices which include services in private wards and clinics. Cost and resource use data from two Zambian tertiary care hospitals indicate that private patients receive more per patient of some (but not all) services and resources. For example, they receive more drugs from hospital dispensaries and achieve better access to minor surgical operations (McPake et al., 2004). A similar cost study in Indonesian hospitals found that the objective of recovering costs on higher priced hospital beds was not achieved (Suwandono et al., 2001). Such examples raise questions about the circumstances under which two-tier charging can lead to greater equity. The key feature of two-tier charging is the separation of demands by quality. The setting of quality levels therefore plays an important role in both the firm’s (hospital’s) strategy, and in the determination of demands for the two services. It follows that a model capable of describing hospital behaviour in these circumstances must incorporate demand functions which are interrelated through cross-quality effects. This inter-relationship between demand functions seems first to have been identified by Dupuit in the 19th century (Phlips, 1983): “It is not because of a few thousand francs which would have to be spent to put a roof over the third-class carriages or to upholster the third-class seats that some company or other has open carriages with wooden benches . . . What the company is trying to do is prevent the passengers who can pay the second-class fare from travelling third class; it hits the poor not because it wants to hurt them but to frighten the rich.” In other words, in order to protect the market for the higher priced product, firms have to avoid substitutes being too close. This requires them to consider the characteristics of both products, and the relationship between their demands. In the case of hospitals, patients will only be persuaded to pay higher prices for services in cases where there is a clear differentiation between the two products. This may tempt hospitals to drive down the quality of the basic service. This relationship between the demands for substitute products is linked to the concepts of price discrimination and product differentiation. The conditions for price discrimination (nontransferability of the commodity and of demand) appear to be met in the hospital services market:

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observation of current practice confirms its divisibility into sub-markets with different price effects, and hospital services generally cannot be re-sold to other consumers. However, price discrimination can also occur in the context of product differentiation of the type identified by Dupuit, above, where the question arises of whether the services are “basically the same.” This would seem to locate the analysis within the class of intra-firm product differentiation such as addressed by Marris (1963). In the context of health services, there is the additional issue of the clinical significance of product differentiation. In principle, basic and premium services are intended to be equally effective and medically appropriate, but amenities such as waiting times and privacy may differ. In practice, however, the medical appropriateness and effectiveness of services for basic service patients is potentially undermined if resources such as drugs and medical personnel are preferentially allocated to patients using the higher priced service. Elements of the literature on price discrimination provide salient insights into the justification for two-tier charging in hospitals. For example Koutsoyiannis (1975) describes the case where the existence of an industry is only made possible by price discrimination and the subsidy of the basic sector by the premium sector. This situation could well apply in low-income contexts, where total demand at a single price may not cover the cost of single-tier service provision. In this case price discrimination may not imply efficiency losses from a neoclassical economic perspective. Against this background, this paper develops a simple model of hospital decision making to examine the equity implications of two-tier charging. The model allows for interdependent demands for basic and premium services and places the hospital in a regulatory environment in which a Ministry of Health sets the prices for these services in order to maximize service utilization, subject to its own budget constraint. Using specific functional forms for demand and cost functions we generate numerical solutions to the model to examine the consequences for service quality, the direction and degree of cross-subsidy, and the effect on total utilization and its distribution between basic and premium services. We examine the effects of altering the characteristics of the demand functions and two policy variables: the weight placed by the government on basic services, and the mechanism through which the hospital receives its budget. The extent to which two-tier charging creates the incentives for the hospital to cross-subsidize from superior to basic service users or vice versa clearly depends on the own and cross-quality elasticity of demand for the two services. Our analysis suggests, however, that, for a plausible range of values characterizing demand, twotier pricing may well induce profit-maximizing hospitals to cross-subsidize from basic to superior services in a manner that threatens not just equity but also the absolute quality of basic services. 2. A two-tier pricing model Our model consists of a representative hospital, operating in competitive markets for inputs and service provision and acting to maximise its surplus, and a Ministry of Health (MoH). The hospital provides two levels of service which are distinguished by their quality and price. We refer to these as basic and premium services respectively. The MoH does not regulate service quality directly. Rather it is assumed to have price-setting authority for these services and may also provide subsidies to (or require cost-recovery from) the hospital, subject to its own budget constraint imposed by the Ministry of Finance. The problem for the MoH is then to use its priceand subsidy-setting powers to influence the level and composition of service demand. Users of each service pay the MoH-mandated prices directly to the hospital and the hospital’s surplus is remitted back to the Ministry. This is consistent with surplus maximising behaviour on the part of the hospital if the hospital is rewarded in some way for the generation of surplus. We assume that the Ministry of Health seeks to maximize overall service utilization but is not indifferent to

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the composition of service provision between basic and premium services. A more conventional assumption would be that the MoH seeks to maximise health, but health is not directly determined in our model. We use utilisation as a (albeit imperfect) proxy for health impact. The preference for utilization of basic over premium services may reflect domestic or external political pressures and hence may vary across countries. We return to this issue in Section 4. Utilization, in turn, is a function of the price and quality of each service and of the price and quality of the alternative service. There is no uncertainty in the model and we assume that the activities of the hospital are fully monitorable by the Ministry of Health. Together with our characterization that the market for health service provision is competitive, these assumptions allow us to abstract from any agency problems between the MoH and the hospital. The model takes the form of a simple Stackelberg game in which the Ministry of Health is the leader and the hospital the follower. This model can be solved in a conventional manner. We start by defining the hospital’s “quality reaction functions” which define its surplus-maximizing level of quality for each service as a function of the structure of demand for the two services and the vector of prices and subsidies set by the Ministry of Health. The Ministry then maximizes its own utility by setting service prices, subject to its own budget constraint set by the Ministry of Finance, while recognizing the hospital’s quality reaction function. We start with the case where the Ministry sets prices but provides only lump-sum subsidies to the hospital, before turning to the case where it can provide an activity-based subsidy to the hospital. 2.1. Service utilization Users’ demands for the two services are indexed i = B, P, where B denotes the basic service and P the premium service, and are functions of own prices and qualities as well as the price and quality of the substitute services: di = di (˜q, p) ˜

i = B, P

(1)

where, q˜ denotes the vector of qualities and p˜ the vector of prices for both services. 2.2. Ministry of Health The Ministry of Health’s objective function is defined as: ˜ + (1 − α)dP (˜q∗ , p) ˜ U = αdB (˜q∗ , p)

(2)

where the weight α reflects the Ministry’s relative preference for the basic service. The MoH sets service prices, p, ˜ to maximize U subject to the constraint that the hospital’s losses do not exceed X: (¯cB + c¯ P ) − (pB − cB (qB ))dB (.) + (pP − cP (qP ))dP (.) ≤ X,

(3)

where ci (qi ) denotes the marginal cost and c¯ i the fixed costs of providing service; and ˜ qi∗ = arg max[π(˜q, p)],

(4)

the quality–choice reaction functions of the hospital, which are derived below. When government subsidises hospital activities, condition (3) limits the hospital’s losses to X; by contrast, if hospital operations were required to make a net contribution to the government budget then X < 0. Notice,

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however, that the constraint (3) is consistent with the hospital making smaller losses (or larger profits) than X. 2.3. The hospital The hospital’s reaction functions, condition (4), define the level of quality for the two services, as a function of the prices mandated by the MoH and the structure of demand. Given our earlier assumptions, we can describe the hospital’s problem as: Max π = (pB − cB (qB ))dB (˜q, p) ˜ + (pP − cP (qP ))dP (˜q, p) ˜ − (¯cB + c¯ P ) + X, (˜q)

(5)

where we assume that the demand functions are twice differentiable. 2.4. Solution To simplify the solution, we assume that pB = 1 (so that we solve for the relative price of the high-quality service), and that cost is a linear function of quality, a formulation consistent with the absence of x-inefficiency. This allows us to write the cost function as: c¯ i + ci (qi ) = c¯ i + qi .

(6)

Letting ηii ≥ 0 be the own-quality elasticity of demand and ηij ≤ 0, i = j, the cross-quality elasticity of demand, the hospital’s optimal quality choices (i.e. the solution to (5)) can be expressed in terms of the following reaction functions for basic and high-cost services:   ηBB + ηPB φ(pP − qP∗ ) ∗ , (7) qB = 1 + ηBB and qP∗

∗ ) pP ηPP + ηBP (1/φ)(1 − qB , = 1 + ηPP



(8)

where φ = (dP /dB ) is the relative scale of the demand for the two services. These reaction functions have standard properties: since the cross-quality elasticities, ηij , are ∗ is decreasing and q∗ increasing in the relative price p , while each quality level is negative, qB P P increasing in the quality of the other. Substituting the reaction functions (7) and (8) into the demand functions (1), and the constraint (3) it is clear that Ministry of Health price-setting choices will impact on utilization through three channels: a direct effect on demand operating through prices; an indirect effect on demand operating through the hospital’s choice of quality for the two services (itself a function of Ministry of Health-set prices); and an indirect effect operating on the Ministry’s budget constraint, again working through the hospital’s quality choices. Hence the Ministry’s problem can be expressed as: direct demand effect

direct demand effect

  ∗ ∗ MaxU = αdB (qB (pP ), qP∗ (pP ), pP ) + (1 − α)dP (qB (pP ), qP∗ (pP ), pP ) pP       indirect demand effect

indirect demand effect

(9)

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subject to the inequality constraint ∗ (¯cB + c¯ P ) − (1 − qB )dB (.) + (pP − qP∗ ))dP (.) ≤ X,   

(10)

constraint effects

and the non-negativity constraints pi , qi∗ ≥ 0. The magnitudes of these separate effects cannot be determined unambiguously but depend on the precise structure of preferences. To focus on the central argument of the paper, we therefore analyse the results in terms of numerical solutions to the Ministry’s optimization based on explicit forms for preferences. Moreover, we restrict our attention to interior solutions to the problem. 2.5. Lump-sum versus activity-based subsidies The set-up above assumes that the Ministry of Health sets the schedule of prices facing users subject to an overall lump-sum subsidy limit. An alternative payment mechanism would involve the Ministry of Health, subject to the same aggregate cost, being able to set prices as before but also provide an activity-based payment in which the subsidy to the hospital for the provision of the basic service reflects the volume of services provided. Such a mechanism can give the payer more leverage over providers (Sussex and Street, 2004). In this case, denoting the subsidy on the basic service as t, the budget constraint facing the Ministry of Health can be written as ∗ ((1 + t) − qB )dB (.) + (pP − qP∗ )dP (.) − (¯cB + c¯ P ) ≥ 0.

(10’)

Hence the hospital receives no lump-sum subsidy, but we assume tdB (·) ≤ X, so that the Ministry of Health has no more resources at its disposal. The corresponding hospital reaction functions become   (1 + t)ηBB + ηPB φ(pP − qP∗ ) ∗ qB , (7’) = 1 + ηBB and qP∗

∗ ) pP ηPP + ηBP (1/φ)((1 + t) − qB , = 1 + ηPP



(8’)

In principle, of course, the Ministry may choose some combination of lump-sum and activitybased subsidy. However, as we argue in the next section, most of the relevant insight from these alternative instruments resides in the polar cases. 3. Model properties and numerical solutions Although the Ministry’s optimization problem defined in (9) and (10) (or (10’)) is straightforward, its solution does not generate simple, readily interpretable analytical results. In order to develop a sense of its properties, and in particular to understand how the key features of the solution depend on the characteristics of demand, we therefore analyse the model through numerical simulation. To do so, we impose specific functional forms on the demand, cost and utility functions, and simulate the model across a range of plausible parameter values for the key elasticities of demand, the weights that the Ministry of Health attaches to the utilization of the basic service

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relative to the premium service, and the form and scale of the subsidy to the hospital. Specifically, we assume that the demand functions are log-linear in prices and qualities (so that own- and cross-price elasticities, and own- and cross-quality elasticities of demand are constant)1 , and continue to maintain the assumption that quality is isomorphic with cost at the margin. The baseline simulation parameters are reported in Appendix A Table A.1. These values are illustrative but are based on results from Hanson et al. (2004). To keep our analysis close to reality we assume that demands are price- and quality-inelastic and more so for the low-cost service.2 In both cases, we assume that cross-price and cross-quality effects are one third of the absolute value of own-price and own-quality effects. For each simulation, we examine: (i) the (optimally chosen) relative price of the two services; (ii) the absolute and relative level of quality embodied in each service; (iii) overall service utilization; and (iv) a set of measures of the cross-subsidization entailed by the pricing structure. Our measures of cross-subsidy merit additional explanation. In all cases, the crude quality ratio (qP /qB ) and the crude price ratio (pP /pB ) will exceed 1 (otherwise the hospital could not or does not charge more for the premium service). However, we are also interested in the relationship between price and quality for each service, To this end we define three further measures: first, the unit price of quality, defined as (pB /qB ) = (1/qB ) and (pP /qP ) respectively; second, the per-unit contribution to fixed costs (pB − qB ) = (1 − qB ) and (pP − qP ). Clearly a decline in the absolute unit price of quality and the per-unit contribution of the basic service correspond to an improvement in absolute equity. Third, we also define the relative unit price of quality, [(pP /qP )/(pB /qB )]. This measure, which we refer to as the value for money index, expresses the price per unit of the premium service as a multiple of the price per unit of the basic service. A value for money ratio of more than one (less than one) implies a progressive (regressive) outcome in the sense that the premium service is making a larger contribution to fixed costs so that a rising value for money index corresponds to an improvement in relative equity. We use these simulations to focus on three features of two-tier pricing. First, to examine Dupuit’s argument regarding the importance of interdependence of demands we examine the effects of varying the own-and cross-elasticities characterising demand. Second, we assess the impact of changing the relative weight government places on the utilization of the two services. In both these cases we base our analysis on the model in which the hospital receives its subsidy in the form of a lump sum. Finally, we investigate the effects of replacing this payment mechanism with an activity-based payment system. 4. Simulation results 4.1. Demand structure, quality and equity Fig. 1a and b provide a stylized illustration of the effects of varying the cross-quality and cross-price elasticities of demand for the two services. The exact numbers on which 1 If all components of users’ total expenditure were also determined by similar constant-elasticity log-linear demand functions, this specification would violate the adding-up property of demands, namely that expenditure shares sum to unity. It is possible, however, to retain this double-logarithmic form if we assume that health expenditures of the form analysed here account for a limited share of users’ total expenditures (Deaton and Muellbauer, 1980). 2 A number of empirical studies find inelastic price and quality elasticities of demand in different contexts (e.g. Heller, 1982; Hanson et al., 2004).

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Fig. 1. (a) The impact of cross-quality elasticities on service price, quality and value for money. (b) The impact of cross-price elasticities on service price, quality and value for money.

the figures are based are reported in Table 1. In both cases, we consider the case where these cross-elasticities vary simultaneously for both services and do so in proportion to each other. In other words, we examine what happens when the demand system as a whole becomes more sensitive to cross-quality or cross-price effects, all other things held

Table 1 Variations in service price, quality, utilization and value for money in response to changes in demand characteristics and MoH preference parametersa Model 1 (lump-sum subsidy to hospitals) Panel A Variations in cross-quality elasticitiesb

Simulation assumptions Cross-price elasticity of demandb Basic service Premium service Cross-quality elasticity of demandb Basic service Premium service MoH weighting of basic servicec Basic service Premium service Solution properties Quality of basic service [qB ] Crude quality ratio (premium:basic) [qP /qB ] Relative price (premium:basic) [pP /pB ] Cross-subsidy/equity measures Unit price of basic service[pB /qB ] Unit price of premium service [pP /qP ] Per unit contribution to fixed costs: basic [pB − qB ] Per unit contribution to fixed costs: bpremium [pP − qP ] Value for money indexd [(pP /qP )/(pB /qB )]

[b]

[c]

[d]

[e]

[f]

[g]

Panel C Variations in MoH weight on basic service utilizationc [h]

[i]

[j]

[k]

[l]

[m]

0.15 0.18

0.15 0.18

0.15 0.18

0.15 0.18

0.13 0.15

0.15 0.18

0.18 0.21

0.20 0.24

0.23 0.27

0.15 0.18

0.15 0.18

0.15 0.18

0.15 0.18

−0.08 −0.15

−0.09 −0.18

−0.11 −0.21

−0.12 −0.24

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

−0.09 −0.18

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.50 0.50

0.55 0.45

0.60 0.40

0.65 0.35

0.16 3.19

0.15 2.80

0.14 2.50

0.13 2.46

0.16 2.38

0.15 2.80

0.14 3.29

0.14 3.50

0.13 4.08

0.15 2.80

0.16 2.31

0.17 1.94

0.18 1.61

1.54

1.31

1.17

1.09

1.22

1.31

1.43

1.50

1.61

1.31

1.19

1.08

1.00

6.25 3.01

6.67 3.12

7.14 3.34

7.69 3.42

6.25 3.21

6.67 3.12

7.14 3.10

7.14 3.07

7.69 3.03

6.67 3.12

6.25 3.22

5.88 3.28

5.56 3.45

0.84

0.85

0.86

0.87

0.84

0.85

0.86

0.86

0.87

0.85

0.84

0.83

0.82

1.03

0.89

0.82

0.77

0.84

0.89

0.97

1.01

1.08

0.89

0.82

0.75

0.71

0.48

0.47

0.46

0.44

0.51

0.47

0.44

0.43

0.39

0.47

0.51

0.56

0.61

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[a]

Panel B Variations in cross-price elasticitiesb

455

456

Panel A Variations in cross-quality elasticitiesb

Service utilization Basic Premium Total Hospital profit a b c d

Panel B Variations in cross-price elasticitiesb

Panel C Variations in MoH weight on basic service utilizationc

[a]

[b]

[c]

[d]

[e]

[f]

[g]

[h]

[i]

[j]

[k]

[l]

[m]

80.03 49.03 129.06

78.95 51.15 130.10

79.18 52.77 131.95

76.94 57.12 134.06

79.40 50.30 129.70

78.95 51.15 130.10

78.66 52.24 130.90

78.70 52.87 131.57

79.09 53.68 132.77

78.95 51.15 130.10

80.10 49.88 129.98

80.99 48.68 129.67

81.77 47.38 129.15

97.61

92.56

91.37

91.10

89.09

92.56

98.29

101.26

106.56

92.56

88.13

83.86

79.81

All other model parameters held at initial calibration values. Cross-quality and cross-price elasticities are adjusted proportionally for basic and premium services. Cross-quality and cross-price elasticities held at baseline values (see columns [b] and [f]. Quality-adjusted price ratio (premium:basic). See text for details.

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Table 1 (Continued )

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constant.3 As Fig. 1a and Panel A of Table 1 clearly show, as the cross-quality elasticities increase in absolute terms, both the crude quality differential chosen by the hospital and the optimal price differential set by the Ministry of Health decline. However, since the price ratio declines proportionally more rapidly than the crude quality ratio, the unit price of the basic service rises, as does the per-unit contribution of the basic service to fixed costs. The unit price of the premium services also rises but more slowly so that the quality-adjusted price ratio (i.e. the value for money index) decreases. Moreover, in this instance, the absolute quality of the basic service is driven downwards as cross-quality effects become stronger. This suggests that the stronger are cross-quality elasticities, the more disadvantageous the system is towards consumers of basic services, both in absolute and relative terms. Before proceeding further it is worth contrasting these results with the outcome under a single tier service with a monopoly government provider. This can be derived as a special limiting case of our model in which we assume the cross-price and cross-quality elasticities are arbitrarily large and the Ministry of Health weight on basic service utilization tends to unity. Although not reported in the table, in this case the quality of the basic service, qb exceeds unity by approximately the size of the subsidy, profits net of the subsidy tend to zero, and utilization shifts almost entirely to the basic service. However, this comparison assumes that this alternative to two-tier pricing – a monopoly public provider – represents a feasible option. Fig. 1b and Panel B of Table 1 repeat the analysis for the case where cross-price elasticities vary. In this case, relative quality and price differentials between the premium and basic services increase rather than decrease. However, since the quality differential rises more rapidly than the price differential, the value for money index actually declines. And since the absolute quality of the basic service also declines, we observe the same outcome as before, namely that consumers of the basic service enjoy lower absolute and real relative quality of service the higher the crossprice elasticity of demands. In both cases, the model confirms the relevance of Dupuit’s conjecture to two-tier pricing strategies; in circumstances where demands are strongly interdependent the optimal response of the surplus-maximizing hospital will be not only to drive up the relative crude quality differential between premium and basic services but also to drive down the absolute quality of the basic service. 4.2. Government preferences for basic service utilization It is often argued that equity in the presence of two-tier service provision is protected by ensuring that the price of the premium service is increased to cover costs. We therefore examine whether a greater Ministry of Health weight on basic service use implies a higher premium service price. Fig. 2 illustrates the effects of increasing the weight attached by the Ministry of Health to basic service utilization. We again focus on the Ministry’s choice of relative prices and the hospital’s choice of qualities and their implications for the absolute quality of the basic service and the value for money index. Fig. 2 reports the results for the case where we increase only the preference weighting on basic service, leaving all other parameters at

3 Similar exercises have been carried out in which we vary the own-price and own-quality elasticities. However, while these alter the specific characteristics of the solution they are less relevant to understanding the characteristics of two-tier pricing that are central to this paper.

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Fig. 2. The impact of the Ministry of Health weighting on basic services on service price, quality and value for money.

their calibration values (again the numerical values are reported in Table 1). However, a more extensive analysis in which we altered other demand structure parameters suggests that the qualitative characteristics of the results presented here are broadly invariant to these changes.4 These results suggest that although it results in a decline in the premium service’s contribution to fixed costs, a greater weight on basic service utilization does promote equity. The mechanism is rather different, however. As the weight is increased, the Ministry of Health will lower the price of the premium service which, given the cost function, will induce the hospital to reduce the quality differential between the premium and basic services and, in addition, raise the absolute quality of the basic service. The value for money index rises, increasing the equity of outcomes. As in the earlier case, however, the value for money index remains below unity, the point at which the price of both services is equal per unit of quality. The Ministry of Health’s increased weight on basic service utilization results in increased use of the basic service and a decline in the utilization of the premium service.5

4 Given the calibration values employed in the simulations, however, values of α greater than 0.65 entail an optimally chosen price for the premium service which is less than that for the basic service and, as such, generate infeasible solutions for the model. An alternative initial calibration could, in principle, be defined to ensure that this infeasibility is not encountered for values of α ≤ 1, but doing so would not alter the qualitative nature of the results presented here. 5 The effect of increasing the Ministry of Health’s weight on basic utilization was also explored at these values in the second model. As with model 1, the effect was to reduce the relative price of the premium service, increase the quality level of the basic service and shift the quality adjusted price ratio in favour of users of the basic service.

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Table 2 The impact of alternative payment mechanisms on service price, quality and value for moneya Model 1 Lump-sum subsidy Solution properties Quality of basic service Quality of premium service Relative price (premium:basic) Crude quality ratio (premium:basic) Quality-adjusted price of basic service Quality-adjusted price of premium service Value for money indexb Service utilization Basic Premium Total

Model 2 Per-unit subsidy

0.15 0.42 1.31 2.80 6.67 3.12 0.47

0.33 0.94 3.03 1.94 3.03 3.22 1.06

78.95 51.15 130.10

97.35 46.75 144.10

Note. Evaluated at calibration values of all parameters (see Table A.1). a See text for description of alternative payment mechanisms. b Quality-adjusted price ratio (premium:basic). See text for details.

4.3. Varying the payment mechanism Finally, we consider the payment mechanism. Our second model examines the case where the lump-sum subsidy is replaced by an activity-based subsidy paid by the Ministry of Health for each unit of basic service utilisation. The intuition behind this is that because the subsidy is only paid per unit of the basic service, the hospital earns more of the subsidy at the margin by allocating more resources to the basic service in order to encourage its demand. The activity-based subsidy increases the price the hospital receives per basic service user, while avoiding the demand depressing effect of increasing the price paid by the basic service user. The subsidy rate is fixed so that the total subsidy paid equals that paid under model 1, allowing for comparison of the two payment mechanisms under constant total subsidy. Table 2 compares the fixed- with activity-based subsidy outcomes. At these values, switching to activity-based payment more than doubles the quality level of the basic service, and also more than doubles the quality level of the premium service. The crude quality ratio increases slightly (a regressive move). However, the switch to a per-unit subsidy produces a sharp increase in the ratio of price-adjusted qualities, causing it to reach a level above 1. This implies that the users of the premium service now pay slightly more for each unit of quality than those of the basic service. Total utilization increases, the result of an increase in the utilization of the basic service and a smaller reduction in the utilization of the premium service. By switching to subsidising marginal activity, rather than paying a lump sum, it is unsurprising that marginal cost/quality increases. What is interesting is the mixed effect on the distribution of benefits: greater efficiency (quality and utilisation levels for the same subsidy value) and benefit for both groups, and better relative value for money for basic service users, are obtained at the expense of equity in the sense of the relative difference between quality levels. 5. Discussion Two-tier charging policies for hospital care are found across a wide variety of countries, but there has been little theoretical or empirical exploration of their effects. While concerns

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about their equity impact have been expressed in high-income contexts, such policies are increasingly being introduced in low-income contexts with the aim of generating income from superior quality services, which can be used to subsidize basic services. Using a simple model of hospital behaviour, this paper has shown that such an equitable cross-subsidy is far from assured, and depends both on characteristics of demand, and on a number of features of the policy environment. Our model of hospital behaviour under a two-tier charging regime indicates that the direction and magnitude of any cross subsidy depends crucially on the magnitude of the cross-price and cross-quality effects in demand. Equity outcomes, expressed in terms of the absolute level of basic-service quality, relative prices, contribution to fixed costs or our “value for money” index, which compares the price-adjusted qualities for the superior and basic services, point in the same direction. Our results confirm Dupuit’s insight into the importance of cross-quality effects, and show that under some circumstances extracting profit from a superior service requires a hospital to drive down the quality of the basic service. A number of testable hypotheses emerge from the analysis, for example that (1) larger cross-effects and (2) increasing the relative price (pP /pB ) of the two services, reduce basic service quality. These provide considerable scope for empirical investigation. The model also examines the effect of the weight placed by the Ministry of Health on basic service utilization relative to that of superior services, finding that a greater weight on basic services leads to a more equitable outcome. The real life analogue of this equity weight might be thought of as being domestically generated through the political process, or in the case of a low-income context, externally imposed through donor conditionality. In either case, the effect of this parameter highlights the role of social and political values in shaping the policy outcome. These values also come into play when assessing the motivation of government to create two-tier services in the first place. While we have focused on the potential for an equitable cross-subsidy, there may be other, unstated objectives of creating two-tier services, such as seeking to ensure the availability of (and, potentially, to subsidise) higher-quality services for politically significant groups, such as civil servants. The model confirms that there is scope for policy leverage over the outcome measured in equity terms. The MoH can change equity outcomes by setting prices that reflect its weights for the two types of utilisation. The model also describes limits to that leverage. The MoH can achieve greater equity, but not absolute equity, or the guarantee of an equitable cross-subsidy. This suggests that evaluation of MoH performance in this respect might compare relative levels of inequity, internationally for example, rather than suppose that any level of inequity identified implies lack of MoH commitment. The final factor we evaluate is the effect of the hospital payment mechanism. Our findings suggest that in a two-tier charging regime, the shift from a lump-sum to an activity-based subsidy can have a dramatic effect both on the absolute quality of the basic service, and on the relative prices of superior and basic services as expressed in the value for money index. In the specific case examined here, such a change was able to produce a distributionally progressive outcome in the value for money index. In contrast to the motivation behind our results, the current policy emphasis on activity-based payment to hospitals appears to be driven primarily by the potential for efficiency gains at the hospital level. While some concern about the effects on access to hospital care, working through the strengthened incentive to increase utilization and thereby reduce waiting lists, has also influenced policy design (Kjerstad, 2004), the connection between hospital payment mechanism and two-tier pricing has not been explored in the theoretical or empirical literatures.

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The importance of payment mechanism, government weight on basic service provision and demand characteristics suggests an explanation of the variable characteristics of two-tier charging systems in different parts of the world, and the potential for different outcomes. This provides further scope for empirical work. At present there are insufficient, internationally comparable data on price elasticities of demand for hospital services, and almost no data on quality, cross-price, or cross-quality elasticities in two-tier charging contexts. There are a number of potential limitations of the analysis presented here. First, our characterization of hospital objectives could be challenged, on the grounds that it is too simplistic (Harris, 1977) or that public hospital decision making may favour altruistic objectives, such as maximization of quality of care for basic services, or demand for basic services. Nonetheless, the proposed maximand is consistent with the range of hospital reforms that have been undertaken in the past decade in a variety of contexts, which have sought to alter the financial incentives facing hospital decision makers. Second, the Ministry of Health’s objectives have also been modelled simplistically, ignoring, for example, potential MoH concerns to avoid the defection of middle and higher income earners from the public to the private system; and we ignore the existence of the private system altogether. These are important issues that future development of the model should address. Third, our results are generated from numerical solutions based on specific parameterization and functional forms, for example log-linear demand functions and a linear cost function for quality. We have chosen parameter values to be consistent with empirical evidence where this exists (e.g. on the price elasticities of demand), but have been limited by the evidence in this area. Nonetheless, given these characteristics, the qualitative results, and therefore the insights regarding the directions of change, are robust to the choice of calibration values even though the actual numerical values are not. Finally, our model is a simple, full information model, with no private information and hence no scope for moral hazard or adverse selection problems. Problems created by strategic behaviour by hospitals, for example manipulating their activity reports in a context of activity-based payment, are ruled out. Indeed, not all such behaviour need be opportunistic: in many contexts there are more fundamental problems of inadequate hospital management information systems, which would preclude any simple shift in hospital payment system. Two-tier charging represents both opportunity and risk to equitable hospital service provision. Our results contradict the na¨ıve assumption that an equitable cross-subsidy is a certain outcome, and identify both demand-side and supply-side factors that are likely to influence this. Acknowledgements At the time of this research, McPake and Hanson worked within the Health Economics and Financing Programme, and McPake is Director of the Health Systems Development Programme, both funded by the UK Department for International Development (DFID). This work was conducted to support a research project ‘Hospital Autonomy in Zambia and the equity implications of the market for hospital services’ funded by DFID and the Swedish International Development Agency. The authors would like to express their thanks to two anonymous reviewers of the paper who have helped considerably in the process of clarifying the model, its implications, and the paper as a whole.

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Appendix A Table A.1 Baseline simulation parameters

Own-price elasticity of demand Cross-price elasticity of demand Own-quality elasticity of demand Cross-quality elasticity of demand MoH weight on service utilization Household income Hospital fixed costs Lump sum subsidy to hospital (Model 1) Per unit subsidy (Model 2)

Total

Basic service

Premium service

– – – – – 1000 20 100 –

−0.50 0.15 0.30 −0.09 0.50 – – – 102.8%

−0.60 0.18 0.60 −0.18 0.50 – – – –

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