Financing medical specialist services in The Netherlands: Welfare implications of imperfect agency

Financing medical specialist services in The Netherlands: Welfare implications of imperfect agency

Available online at www.sciencedirect.com Economic Modelling 25 (2008) 946 – 958 www.elsevier.com/locate/econbase Financing medical specialist servi...

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Available online at www.sciencedirect.com

Economic Modelling 25 (2008) 946 – 958 www.elsevier.com/locate/econbase

Financing medical specialist services in The Netherlands: Welfare implications of imperfect agency Cees Folmer ⁎, Ed Westerhout CPB Netherlands Bureau for Economic Policy Analysis, The Hague, The Netherlands Accepted 20 December 2007

Abstract Since 1995 the financing scheme for medical specialist services in the Netherlands has moved from a fee-for-service scheme to a capitation scheme. This paper analyzes the economic and welfare effects of this policy change. The paper adopts a numerical model that integrates demand and supply considerations and that recognizes the potential roles of moral hazard and supplierinduced demand. The paper finds that the shift in financing regime has been welfare-reducing. The policy change induced medical specialists to lower the supply of the health services which was already lower than optimal before the policy reform. © 2008 Elsevier B.V. All rights reserved. Jel classification: D60; H21; I18 Keywords: Fee-for-service scheme; Lump-sum budget; Medical specialists; Moral hazard

1. Introduction For many years, the services delivered by medical specialists in the Netherlands were financed according to a fee-forservice scheme. Although adjustments were frequently made, the scheme continued to link the income of medical specialists to the volume of their output. In 1995 things started to change. In that year medical specialists, hospitals and health insurers in a number of regions started to experiment with schemes in which medical specialists were given a lump sum budget, i.e. a budget that is independent of the volume of their output. Soon after, the Dutch government encouraged all other medical specialists to follow which most of them did. As the new scheme aimed to change producer incentives only, budgets for medical specialists were set such as to keep aggregate specialist income on its pre-reform level. This paper investigates the economic and welfare effects of the introduction of this capitation system. We adopt a principal-agent approach in which medical specialists take decisions on labour supply and consumption. Specialists

⁎ Corresponding author. CPB Netherlands Bureau for Economic Policy Analysis, P.O. Box 80510, 2508 GM The Hague, The Netherlands. Tel.: +31 70 3383399; fax: +31 70 3383350. E-mail address: [email protected] (C. Folmer). 0264-9993/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2007.12.002

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may act as perfect agents of their patients (which we will call the ethical option) or they may follow their own interests (the financial option). In the latter case specialists incur a utility loss as they deviate from the preferences of their patients. This principal-agent approach implies that on the aggregate level both demand and supply determine medical consumption. So we do justice to empirical evidence that shows that medical consumption is responsive not only to demand factors like the out-of-pocket price of medical consumption and patient income (e.g. Rosett and Huang, 1973; Newhouse and the Insurance Experiment Group, 1993) but also to supply factors like physician income and the number of physicians relative to the population (e.g. Evans, 1974; Fuchs, 1978; Newhouse, 1987). Our model features endogenous switching between the financial option and ethical option. Hence, the weights given to demand and supply factors are not fixed, but endogenous and virtually a function of all model parameters. Our analysis indicates that the financial reform has decreased the consumption of medical specialist services. Furthermore, it finds that patients were hurt by this decline in medial consumption, whereas medical specialists benefited from the concomitant increase in leisure time. On net, society suffered a welfare loss. The reason is that due to (negative) supplier-induced demand, medical consumption was already too low before the financial reform. The reform aggravated this inefficiency by inducing medical specialists to reduce supply, thereby lowering medical consumption still further. These results are robust to significant changes of important parameter values. The numerical configuration of the model is important as theory alone cannot sign the welfare effect of the reform. One reason is that, before the reform, the market for health care services may be in excess supply or excess demand. Therefore, a reduction of supply brought about by the reform may increase or decrease the gap between demand and supply. A second reason is that moral hazard considerations lend support to a fee reduction of a certain size. The fee reduction that is implied by the reform may be either too large or too small. Our approach fits into the literature on the welfare effects of medical insurance (e.g. Feldman and Dowd, 1991; Manning and Marquis, 1996; Zeckhauser, 1970), but extends it by recognizing the independent role of physicians. This extension has an impact on the relation between fee and volume changes as well as on the welfare consequences of the former, as fee changes generally also affect the well-being of physicians. Next, our paper joins the literature on physician responses to fee changes (e.g. McGuire and Pauly, 1991; Rizzo and Blumenthal, 1994), but extends it by including the role of patients. This allows us to demonstrate that supplier-induced demand may help to combat the moral hazard that is due to insurance (see also Wedig et al., 1989). Closest to our paper are Ellis and McGuire (1990, 1993) which also focus on the interaction between demand and supply considerations. Different from these two papers is that our paper explores the effects of a real-world experiment and adopts specifications for the demand and the supply of health care that have a strong empirical base. Furthermore, our paper does not take demand and supply behaviour as independent, but as related, due to the constraint that the financial reform that is analyzed should not change the income of physicians in the aggregate. The setup of our paper is as follows. First, it describes some empirical evidence on the effects of the reform of the financing scheme. Next, it constructs our model which is subsequently used to calculate the effects of the financial reform. Finally, it provides some concluding remarks. 2. Some earlier evidence An analysis of the new financing scheme in five hospitals involved in the first round of experiments indicates that it has changed the behavior of medical specialists. The new system has reduced the probability of an admission and increased the average waiting time (Mot, 2001). In addition, a statistically significant effect has been found for referrals: after the reform, a significantly larger fraction of patients of medical specialists was referred back to a general practitioner (Ziekenfondsraad, 1998; Van den Berg and Mot, 2000). On the other hand, no significant effects upon the average duration of stay in hospitals were found. Aggregate time series data on hospital admissions, outpatient treatments and outpatient visits also suggest that the financial reform had important output effects (Statistics Netherlands, 2000). Hospital admissions grew 1.1% a year during the period 1990–1994, but with the onset of the new financing regime the average yearly rate of growth dropped to − 1.4% (period 1995–2000). Outpatient treatments grew firmly during 1990–1994 at an annual rate of 10%, but slowed down since 1995 to 5.5% a year. Outpatient consultations increased during 1990–1994 at 1.3% a year, but more or less stabilized during 1995–2000 with an annual growth rate of − 0.1%. Although the evidence is not conclusive, it suggests a role for the change in the financing scheme for medical specialists, as demographics did not change dramatically in the period under consideration and also no further major policy reforms took place in this period.

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Summing up, micro evidence on specialist behavior in the hospitals that were the first to experiment with the new financing scheme points to negative output effects. Macroeconomic time series on various output variables in the 1995–2000 period hint in the same direction. 3. A model of medical care 3.1. Medical specialists We describe the behavior of medical specialists with a neoclassical labor supply model, extended with ethical costs in order to capture an agency relationship between the patient and the physician. Imperfect information at the side of the patient allows the medical specialist to deviate from the patient's interest and pursue other (personal) objectives. However, the physician cannot fully neglect the demand of the patient. Reputation considerations, the medical oath, or medical ethics all lead us to regard physicians as (imperfect) agents of patients. This special agency-feature is allowed for in the model by imposing an ethical cost on the professional when she deviates from the patient's best interest, i.e. the action that the patient would have selected under perfect information. Formally, the physician solves a utility maximization problem with physician utility being a function of the consumption of leisure, that of other goods and services and of ethical costs. We denote physician k's utility as vk, her leisure as lk and her consumption of other goods and services as dk. The utility function is specified in CESformat,  1=q vk ðdk ; lk ; ek Þ ¼ wk  ek ¼ adkq þ lkq ek

qN1

ð1Þ

where ek refers to the ethical cost which is imposed on a particular physician if she chooses not to act in the patient's best interest, i.e. if she fails to deliver demand. The physician maximizes her utility subject to a time constraint and a budget constraint. The time constraint defines leisure time as the difference between the total time allotment T and the time allocated to producing services. Denoting the supply of services by s, we have, lk ¼ T  Ask

ð2Þ

where μ measures units of time needed to produce one treatment. Physician consumption or income sums the income from the provision of medical services and the income provided to her by the government: dk ¼ tsk þ h

ð3Þ

where t stands for the fee per service and h is the government income transfer. This income transfer can be positive or negative. In the former case, we will talk about a subsidy, in the latter case of a tax. The income transfer is unrelated to the individual physician's supply of services (lump sum). As to ethical costs, we consider it to be a dichotomous variable: a physician bears ethical costs (if she deviates from patient preferences) or not (if she accommodates patient demand). Obviously, in reality ethical costs may depend on the gap between demand and supply rather than being dichotomous, although it will be difficult to distinguish between fixed and variable ethical costs empirically (see Folmer and Westerhout, 2002). The distinction between fixed and variable costs is not relevant here however as it is aggregate physician labor supply which drives the welfare effects. Below we will see that our results would not change qualitatively if we left out physician welfare completely. For a further discussion on the fixed nature of ethical costs in our model, see Folmer et al. (1997). The dichotomous character of ethical costs implies that the utility maximization problem must be solved in two stages. The first stage is to solve the problem in two distinct cases: first under the condition that the physician will bear ethical costs and second under the condition that she will not bear ethical costs. These two cases will be referred to as the financial option and the ethical option respectively. Second, the physician decides whether or not to bear the ethical costs by choosing for the financial or ethical option. Let us start to describe the first case of the first stage: the physician solves her maximization problem, conditional upon having decided to bear ethical costs.

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Given that ethical costs must be borne, maximization of Eq. (1) boils down to maximization of the utility from consumption and leisure, wk. The interior solution of the maximization problem, denoted ¯s ⁎ , follows from elaborating the corresponding first-order condition, i.e. ∂wk /∂sk = 0. This yields P4

s ¼b

T h  ð1  bÞ A t

ð4Þ

where the auxiliary variable β is defined as b¼

t r1 A1r ar 1 þ t r1 A1r ar

and σ = 1 / (1 + ρ) is defined as the elasticity of substitution between consumption and leisure. One can easily verify that ∂2wk / ∂sk2 | sk = ¯s ⁎ b 0, hence the supply of medical services in Eq. (4) indeed maximizes wk. The Appendix explains in more detail how to derive Eq. (4). Note that ¯s ⁎ can be negative. However, labor supply cannot be negative. Therefore, labor supply obeys the interior solution to the corresponding maximization problem, ¯s ⁎, only if ¯s ⁎ ≥ 0. If ¯s ⁎ b 0, concavity ensures that the corner solution ¯s = 0 applies. Formally, we can then summarize the financial option as ¯s = max(0, ¯s ⁎). The corresponding solutions for non-medical consumption and leisure read as d¯ and ¯l respectively, and follow from substituting the value of ¯s into expressions (3) and (2). The solution for indirect utility exclusive of ethical costs, w ¯ , follows in turn upon substituting d¯ and ¯l into the expression for wk in Eq. (1). Eq. (4) shows that demand for specialist services does not directly affect supply. Hence, under the financial option physicians may supply more or less medical services than demanded, depending on their preferences for consumption and leisure and the incentives they face to supply medical services. In particular, the physician may supply more than demand to raise her income. She may equally well supply less than demand to gain leisure time. In the second case of the first stage, the physician solves her maximization problem, conditional upon having decided not to bear ethical costs. Under the ethical option, a specialist accommodates her supply of services, s˜ , to the corresponding demand, Z/Ns, where Z denotes aggregate demand and Ns denotes the number of medical specialists. Formally, an exception must be made when this behavior would imply negative leisure. In that case, T/μ would replace Z/Ns. This effect does not occur in any of our simulations, however. Under the ethical option patients receive the amount of medical services they would have demanded in the absence of any information imperfections. We use d˜ and ˜l to denote the consumption of non-medical goods and leisure under the ethical option. These two variables are derived by substituting the solution for s˜ into expressions (3) and (2) respectively. Indirect utility under the ethical option, ˜v, follows when the solutions for d˜ and ˜l are substituted in the expression for vk in Eq. (1). The second stage of the physician maximization problem is to decide whether to bear ethical costs and choose for the financial option or whether not to bear ethical costs and choose for the ethical option. The solution to this stage of ¯ and ˜v. the problem is straightforward: the physician compares her level of ethical costs with the difference between w If her ethical costs are lower than the utility differential, she chooses the financial option; if ethical costs are higher, she opts for the ethical option. If her ethical costs happen to be just equal to the utility differential, she is indifferent. Fig. 1 illustrates. The points F⁎ and E⁎ refer to the utility, exclusive ethical costs, and the supply that corresponds to the financial option and ethical option respectively. If the physician's ethical costs are lower than the distance EF⁎-F⁎, then the financial option is seen to generate the highest utility. If her ethical costs exceed EF⁎-F⁎, the ethical option generates the highest physician utility. This can be formalized as follows. Calculate the critical level of ethical costs at which the physician is indifferent between the financial and the ethical option, e⁎, by solving the equality P P w  e4 ¼ v˜ ¼Ne4 ¼ w  v˜

ð5Þ

From Eq. (5) it follows that the critical value of the ethical cost depends on the utility difference between the two options, and hence on all variables and parameters in Eqs. (2)–(4). The second stage of the optimization problem can now be summarized as follows: ek be4 ¼N sk ¼ Ps ek N e4 ¼N sk ¼ s˜

ð6Þ

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Fig. 1. Utility maximization of medical specialists: the financial and ethical option.

Physician k thus prefers the financial option (sk = ¯s ) if e⁎ exceeds her ethical cost variable ek. The ethical option is chosen (sk = ˜s ) whenever e⁎ is below this threshold value. By definition, the physician is indifferent between the two options if ek = e⁎. We assume that physicians are heterogeneous with respect to the value of the ethical cost variable e. Hence, a number of physicians will prefer the ethical option while others will choose the financial option. Denoting the distribution function of e by Gs(e), the supply of medical services of specialists in the aggregate can then be expressed as a weighted sum of supply as defined for the two options: P

P

S ¼ Ns ½Gs ðe4Þ s þ ð1  Gs ðe4ÞÞ s˜  ¼ Ns Gs ðe4Þ s þ ð1  Gs ðe4ÞÞZ

ð7Þ

Eq. (7) indicates that aggregate supply behavior of medical specialists reflects the supply behavior of two types of physicians: one who obeys the demand of the patient, whatever the consequences for her personal income and workload, and another whose behaviour is fully ruled by financial considerations independent of the health care demand of her patients. How does medical supply react to a change in the fee for medical services t? In general, three effects are relevant: the effect of a fee change upon i) the supply of the ethical specialist ii) the supply of the financial specialist and iii) the fraction of financial (ethical) specialists. The supply by ethical specialists is not affected by the fee as it equals demand and all patients are fully insured (see below). Given this, the aggregate supply function depends upon the supply by specialists who have chosen the financial option and the share of specialists Gs(e⁎) who prefer this option. In case of the financial option, we distinguish two direct effects that work in opposite direction. A higher fee makes it financially more attractive to provide medical services (a substitution effect), but also increases the physician's income and thereby her demand for leisure (an income effect). In the numerical version of our model, the substitution effect dominates. Note that these effects may not occur for sufficiently low fee levels. In particular, low fee values may restrict the supply by financial specialists to be zero as supply cannot be negative. The fraction of financial specialists is a positive function of the service fee in deviation from the fee level that equalizes supply and demand. At the latter level, all specialists prefer the ethical option as both options yield the same level of consumption and leisure, but only the financial option includes ethical costs. If the fee deviates from this specific level, the financial option generally corresponds to a different pair of consumption and leisure and a higher level of utility. Hence, the change in the fee away from the equilibrium level drives a wedge between the consumption-leisure pairs that correspond to the ethical and financial option and thus widens the utility gap between both options. Consequently a number of specialists, in particular those with the lowest ethical costs, will switch to the financial option. This argument works also the other way round. Hence, the fraction of financial

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specialists is a U-shaped function of the fee, with a minimum of zero at the fee level that equalizes demand and supply. The impact of an increase in the service fee on medical supply can thus have either sign. Given that the substitution effect dominates the income effect, the effect on the supply of financial specialists is zero or positive. The effect on the fraction of financial specialists can be any however: it depends on whether we move towards or away from the fee level that equalizes demand and supply and whether the ethical or the financial option features the highest supply. 3.2. Patients We postulate that the patient derives utility from the consumption of medical specialist services, z, and the consumption of other goods and services, c. We also assume that preferences are of the linear-quadratic form, 1 1 ui ¼ ci  gc2i þ ei zi  dz2i 2 2

dN0;

ei z0;

0bgb1=ð y  PÞ

ð8Þ

where ui is utility of patient i . y is the income of patients before health care premiums and P is health care premiums. y − P, after-premium income, is also the maximum of non-medical consumption. Hence, the last condition in Eq. (8) ensures that the marginal utility of non-medical consumption is strictly positive everywhere. Our motivation to employ a linear-quadratic specification is twofold. First, we want to allow the marginal utility of medical care to turn negative if medical consumption becomes sufficiently high. This reflects that receiving care brings time costs to patients and that the medical benefits from health care do not need to be positive at all levels of intervention. Second, it is necessary that the marginal utility of medical care can take the zero value in order to obtain a finite solution for demand in case of a zero out-of-pocket price. Rather than using Eq. (8) however, we simplify our exposition by imposing full insurance. The effect of this, given that the marginal utility of non-medical consumption is positive everywhere, is that non-medical consumption equals patient income net of health care premiums: ci = y − P. Now, income is exogenous and, as will become clear below, health care premiums can be treated as exogenous as well in our simulations. Hence, the first two terms at the RHS of Eq. (8) reduce to a constant and maximization of ui in Eq. (8) is equivalent with maximizing uiV in Eq. (9): 1 uiV¼ ei zi  dz2i 2

ð9Þ

To find the demand for specialist services, we elaborate the patient's optimization problem. The first-order condition of this problem is εi − δzi = 0. The corresponding second-order condition for a maximum, i.e. − δ b 0, applies since δ N 0. Hence, the first-order condition describes the amount of health care consumption that yields the maximum level of utility. Rewriting this condition in terms of zi gives us the demand equation: zi ¼

ei d

ð10Þ

Note that since we have assumed εi ≥ 0, z b 0 cannot occur. Therefore, corner solutions do not apply and Eq. (10) characterizes completely the demand for medical services. We assume that patients are heterogeneous in the marginal utility of health care consumption. This may reflect for example heterogeneity in health status. Since the marginal utility of health care reads as ∂ui′/∂zi = εi − δzi, it is clear that we can achieve this by taking εi as a heterogeneous parameter. Using N to denote the population of patients, demand for medical services at the population level can be expressed as follows: E ðei Þ d 3.3. Closure of the model Z¼N

ð11Þ

We close the model by specifying expressions for aggregate specialist income, the government budget constraint, the consumer price of medical services and aggregate health insurance premiums.

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By aggregation of Eq. (3) over all specialists we obtain R R D ¼ Ns dk dGs ðek Þ ¼ tNs sk dGs ðek Þm Ns h ¼ tS þ Ns h

ð12Þ

where aggregate supply S is defined in Eq. (7). Aggregate income for medical specialists sums two components of physician income: i) income derived from the provision of medical services and ii) income from government transfers. The former component is different for physicians that choose the financial and ethical option, the latter is the same for all physicians. Government transfers are financed by levying a tax on medical consumption. Using τ to denote the tax rate on medical consumption, the government budget constraint reads as follows: st S ¼ Ns h

ð13Þ

Due to this tax, the consumer price of medical services, denoted as tc, consists of two components: an exogenous feefor-service to the provider and a tax on medical consumption: tc ¼ t ð1 þ sÞ

ð14Þ

Finally, health care premiums, P, equal aggregate health expenditure, tc S, where S is given by Eq. (7). 3.4. Welfare Individual patient welfare can be derived basically by substituting the supply of medical services into the patient's utility function. Note that supply may deviate from demand at the level of the individual patient. As a rationing rule, we assume that the specialist who prefers the financial option divides her services between all her patients such that each patient faces the same discrepancy between demand and supply in relative terms (proportional rationing). Total patient welfare U is defined as the sum of individual utilities, where the summation runs over consumers who differ in their value for εi: Z U ¼N

l

Z

l

uiVdGðei Þ ¼ N

0

0



 1 2 ei si  dsi dGðei Þ 2

ð15Þ

Similarly, welfare of medical specialists, V, is defined as the sum of the welfare of specialists choosing for the ethical and the financial option: " # Z e4   P P ek dGs ðek Þ ð16Þ V ¼ W þ V˜ −Ns E ðek jek be⁎Þ ¼ Ns ð1  Gs ðeÞÞw þ Gs ðe⁎Þ v˜  0

¯ and V˜ are implicitly defined by the second equality in Eq. (16). Note that ethical costs are only relevant for where W those specialists who choose to bear these costs, i.e. the specialists whose ek is below e⁎. To calculate social welfare, we transform the changes in patient and physician welfare into their consumptionequivalent counterparts. The latter are defined in terms of the non-medical consumption good which is consumed by both patients and specialists. The consumption-equivalent change in social welfare is then the sum of the consumptionequivalent changes of patient welfare and physician welfare. Our working paper (Folmer and Westerhout, 2002) discusses in detail the method of consumption-equivalent welfare changes. Important is that this measure of social welfare neglects distributional concerns. Indeed, our analysis focuses on the efficiency effects of the policy reform, not on any distributional effects. 4. Evaluation of policy changes 4.1. The numerical model The numerical model that we use for our calculations is less stylized than the model described above. In particular, it adds two elements. First, it does not impose full insurance, i.e. it maximizes patient utility defined in Eq. (8) rather than

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the simplified version in Eq. (9). It also allows for co-payment schemes that impose a deductible (a fixed co-payment rate of 100% until a co-payment maximum). This implies that the budget constraint of the patient is kinked: the out-ofpocket price equals the consumer price as long as total expenditures do not exceed the co-payment maximum, and equals zero afterwards. This more realistic assumption severely complexes the theoretical analysis while on the other hand its contribution to the empirical analysis has proven to be very limited. Therefore we have made the assumption of full insurance in the previous section. A consequence is that the impact of the reform on welfare can only be evaluated numerically. The interested reader may find the details in Folmer and Westerhout (2002) and a further elaboration in Westerhout and Folmer (2007). Second, the empirical model decomposes the patient population into a group of people who are covered by public insurance and another group who are privately insured. This distinction was relevant until January 2006. This allows us to do justice to the differences in income and in the distribution of the marginal utility of health care that existed between the two groups. In contrast with the publicly insured, the privately insured faced a co-payment scheme that included deductibles. Consequently, their demand depended on the (out-of-pocket) price of medical services and on income net of health care premiums (see Folmer and Westerhout, 2002 for details). Nowadays all patients face some kind of co-payment scheme. Finally, the numerical model distinguishes between first and subsequent treatments. The former are demand determined as they mainly constitute of referrals from other health care suppliers; the latter are determined by physicians in the way that has been discussed above. These elements add to the realism of the model. Yet, their impact on the numerical simulations is fairly modest. Parameter values are found by a combination of estimation and calibration. Details can be found in the working paper version of this paper (Folmer and Westerhout, 2002). Particularly important are the values of the parameters of our physician model. These parameter values stem from estimating a linearized version of Eq. (7). Due to the fact that we had to use relatively short time series in our regression and that we had to linearize the empirical equation, we should warn that the parameter values used have indicative value only. This also calls for a sensitivity analysis in which the effects of alternative parameter configurations are explored. For a discussion of the results of this sensitivity analysis see the working paper version of our analysis Folmer and Westerhout (2002). 4.2. Simulation approach We evaluate 13 levels for the fee for services t, which we vary from 0 to 1080 euro in steps of 90 euro. This seems to be too general for the purpose at hand; for an evaluation of the financial reform, we only need to compare outcomes before and after the reform (corresponding to fees of t = 360 euro and t = 0 respectively). However, by evaluating a wider range of fee values, we can sketch a broader picture of the effects of the physician financing scheme, which helps us to interpret the effects of the financial reform that we want to analyze. All 13 simulations share the same level of aggregate specialist income. Eq. (12) is then used to calculate the corresponding amount of subsidies to specialists. The constancy of aggregate specialist income is a crucial element of the financial reform. Not only does it imply that government subsidies are a function of the fee-for-service level, it also implies that health care expenditure is invariant to this fee for service. The same holds true for non-medical consumption of patients, c, which equals patient income net of health care expenditure (premiums plus copayments). Note that we have used this result in transforming the utility function of patients (see Eqs. (8) and (9)). Finally, the tax rate and the consumer price of medical consumption are both endogenous. The tax rate follows from the government budget constraint (Eq. (13)), the consumer price from the fee for service and the tax rate (Eq. (14)). We display the results of our numerical simulations graphically. This helps us to get a quicker understanding of the effects of the fee for medical services. For transparency, we have connected the points on the curves in the different figures that correspond with the 13 simulations through straight lines. 4.3. Outcomes We first analyze the supply curves of physicians that prefer the ethical or financial option. As Fig. 2 shows, the supply curve of the ethical specialist is (almost) flat. As the supply of ethical specialists follows demand, the only effect of the fee for services is that which operates through the demand for specialist services. Below we will explain why the curve is not completely flat.

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Fig. 2. Supply of medical specialist services.

The supply curve of financial specialists is more complex. When the fee is below 270 euro, the zero corner solution applies. When the fee is increased beyond the value of 270 euro, supply becomes positive and increasing. This reflects that the substitution effect of an increase in the fee (work becomes more attractive financially) dominates the income effect (physicians demand more leisure when their income increases). Due to the curvature of the utility function of the specialist, the elasticity of labor supply with respect to the fee for services falls when the fee is further increased. One might think that as income effects of fee changes are neutralized by adjustments in government income transfers, the income effect would be nil. However, this is not correct. Indeed, as the income transfer adjustment that compensates for fee changes is the same for both ethical and financial specialists, part of the income effect survives. Supply under the ethical option and under the financial option are equal at a fee value t⁎ of about 630 euro. Hence, the utilities for the two options (exclusive ethical costs) also coincide. The consequence of this is illustrated in Fig. 3 which shows the share of physicians who prefer the financial option. At t = t⁎ = 630 euro this share equals zero. The more the fee t deviates from t⁎, the higher the yield of optimization and the larger the number of medical specialists who prefer the financial option. Fig. 2 demonstrates that the aggregate supply of subsequent treatments is increasing everywhere. That the slope of the aggregate supply curve is positive for low values of the fee (t b 270 euro) follows entirely from the negative relationship between the number of financial medical specialists and the fee (see Fig. 3). The decline in the number of financial physicians increases the weight of ethical specialists who supply more services. For t N 270 euro, the positive slope of the aggregate supply curve must also be attributed to the upward-sloping supply curve of financial physicians. Generally, the consumer price of medical services, tc, increases less than proportionally with the producer price, t. The reasons is that an increase in the producer price increases supply, reduces government subsidies that maintain physician income, and decreases tax rates in order to match falling subsidies to physicians. This tax effect may even be so strong that the consumer price of medical services falls upon an increase of the producer price. This actually happens in our simulation, in which an increase in t makes the consumer price decline, thereby inducing an increase of patient demand. This explains why the supply curve of ethical specialists is slightly upward sloping (Fig. 2). Figs. 4–6 show the corresponding consumption-equivalent changes in patient welfare, specialist welfare and social welfare respectively. Recall that consumption of non-medical services is invariant to fee movements. Hence, changes in patient welfare fully reflect movements in health care consumption. Fig. 4 shows that patient welfare reaches its peak value at t = t⁎, where supply equals demand.

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Fig. 3. Relative weight of the financial option.

How can we explain that patient welfare is highest when supply equals demand? Obviously, we would expect differences between supply and demand to be welfare-reducing, as the patient chooses his demand such as to maximize his utility. So in case supply meets demand, welfare losses due to imperfect agency are zero. However, the moral hazard argument suggests that welfare could be raised by moving supply below demand. The reason why this does not occur lies in our financing rule for specialist income. Normally, the welfare gain from a smaller loss due to moral hazard would be reflected in lower health insurance premiums (and possibly lower co-payments). However, our simulations keep health

Fig. 4. Consumption-equivalent change of patient welfare.

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Fig. 5. Consumption-equivalent change of specialist welfare.

insurance premiums plus co-payments constant by adjusting income transfers to physicians to compensate for fee changes. Hence, any welfare gain from the reduction of moral hazard is transmitted to the group of medical specialists. Fig. 5 demonstrates how the consumption-equivalent change in specialist welfare depends on the fee value. The maximum is achieved by moving to a situation in which the fee equals zero. This is well below the fee that optimizes patient welfare, reflecting the redistribution to physicians of the welfare gains that the elimination of moral hazard brings about. Maximum social welfare is achieved at a fee of 540 euro (see Fig. 6). This value is thus below the level for which supply equals demand. Optimal supply policies reduce supply in order to compensate for the moral hazard effect in the demand for physician services. What has been the impact of the introduction of a capitation system, lowering t from 360 euro to 0? Economically, the reform induced physicians to reduce the supply of medical services. Physicians who prior to the reform preferred

Fig. 6. Consumption-equivalent welfare changes.

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the financial option reduced their supply of services (Fig. 2). In addition, physicians with relatively low ethical costs were induced to switch to the financial option (Fig. 3), thereby also reducing their supply. Patients faced a decline in welfare—due to the fall of medical consumption. In contrast, physicians benefited from the increased amount of leisure time. Social welfare decreased (see Fig. 5). In sum, the policy reform reduced the moral hazard in medical consumption but aggravated the distortion due to imperfect agency. On net, the reform was welfare-reducing. In our discussion paper, we also conducted a sensitivity analysis in order to explore the robustness of our results. In this analysis, we imposed 75% higher and lower values for three important variables of our model: the elasticity of substitution between leisure and consumption in the utility function of medical specialists, the budget of medical specialists and the price elasticity of health care demand. In all alternative scenarios, the financial reform was found to be welfare-reducing as well. 5. Concluding remarks This paper concludes that the reduction of fees for specialist services in the Netherlands reduced social welfare. As the policy change increased the deviation of the actual fee, 360 euro, from its optimal level, 540 euro, it aggravated the welfare loss from a suboptimal financing scheme. This result is robust to a number of alternative assumptions. In particular, our conclusion does not depend on the inclusion of physician welfare in our social welfare function. One may argue that social welfare should be defined exclusive of physicians. Fig. 6 clearly demonstrates that such a change of definition would leave unaltered our finding that the reform imposed a welfare loss. Neither does our conclusion depend upon the definition of the policy change. We have defined the financing scheme that resulted after the reform as being fully lump sum, i.e. with a zero services fee. Van den Berg and Mot (2000) report that in some hospitals, it is agreed that specialist budgets might be increased if specialist production grows faster than expected. To the extent that these agreements are credible, the financial reform may actually have been perceived not as a switch from a fee-for-service scheme to a lump sum scheme, but as a plain reduction of the fee for medical services. It can be seen from Fig. 6 that, if this is true, our calculations overstate the impact of the change in financing scheme. However, it would not affect our finding that the introduction of a lump sum budget for specialist services has reduced social welfare. Noteworthy is the assumption that specialists are risk-neutral. Risk-averse specialists would have experienced a larger drop in welfare because the shift to a capitation system increases the variability of their income net of production costs. This would have reinforced our result that the financial reform was welfare-reducing. In addition, taking patient's time costs to be a function of the average waiting time would not probably change our central finding either. According to our calculations, the shift to a lump sum payment scheme has led to additional excess demand. This could be reflected in an increase in waiting lists. If we had accounted for an increase in time costs, patient welfare would have been further reduced. We did not pay attention to the possibility that the financial reform has induced specialists to engage in risk-selection strategies. Indeed, fee reductions may have induced physicians to intensify their efforts to dump high-risk consumers, i.e. supply no services at all to these patients, see Ellis and McGuire (1993) and Newhouse (1996). If this is the case, the financial reform will have had more adverse welfare effects than recognized in this paper. The results in this paper clearly suggest that the move towards capitation was a bad idea from an efficiency point of view. Going back to the old financing system would undo the welfare loss that the financial reform brought about. One could even achieve an additional welfare gain if the fee for service would be put to 540 euro rather than its pre-reform value of 360 euro. Such a reform would reduce further the excess demand for medical specialist services that is due to an ill-structured financing scheme. It is important to observe that our analysis deals only with efficiency, not with distribution. To the extent that the reform has been used to redistribute towards patients by skimming the incomes of medical specialists, the reform may be judged more positively. Whether the overall evaluation should be positive or negative depends on the weights one attributes to efficiency and redistribution. Acknowledgements Thanks are due to the participants of the iHEA conference in York, July 2001, Peter Kooiman, Esther Mot and an anonymous referee for useful remarks. Ton Brouwer prepared the layout of the graphs.

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Appendix A This appendix show how to derive Eq. (4) in the main text. The first-order condition of the first part of the physician's maximization problem reads as ∂wk /∂sk = 0. Elaboration of this condition yields a relation between supply of medical services and income: at ¼ A

 ð1þqÞ lk dk

ðA1Þ

We can rewrite this condition as an expression for lk as a function of dk. Using Eqs. (2) and (3) in the main text, we then get an equation for sk:  r   r a at t 1r þ A sk ¼ T  h A A

ðA2Þ

where σ = 1 / (1 + ρ) is defined as the elasticity of substitution between consumption and leisure. Let us now define β as below Eq. (4) in the main text. Combining this with Eq. (A2) gives us Eq. (4) in the main text. References Ellis, R.P., McGuire, T.h.G., 1990. Optimal payment systems for health services. Journal of Health Economics 9, 375–396. Ellis, R.P., McGuire, T.h.G., 1993. Supply-side and demand-side cost sharing in health care. Journal of Economic Perspectives 7, 135–151. Evans, R.G., 1974. Supplier-induced demand: some empirical evidence and implications. In: Perlman, M. (Ed.), The Economics of Medical Care. MacMillan, London. Feldman, R., Dowd, B., 1991. A new estimate of the welfare loss of excess health insurance. American Economic Review 81, 297–301. Folmer, C., Stevens, J., van Tulder, F., Westerhout, E.W.M.T., 1997. Towards an economic model of the Dutch health care sector. Health Economics 6, 351–363. Folmer, C., Westerhout, E.W.M.T., 2002. Financing Medical Specialist Services in the Netherlands: Welfare Implications of Imperfect Agency, CPB Discussion Paper no. 6. The Hague. Fuchs, V.R., 1978. The supply of surgeons and the demand for surgical operations. Journal of Human Resources 13, Supplement, 35–56. Manning, W.G., Marquis, M.S., 1996. Health insurance: the tradeoff between risk pooling and moral hazard. Journal of Health Economics 15, 609–639. McGuire, T.h.G., Pauly, M.V., 1991. Physician responses to fee changes with multiple payers. Journal of Health Economics 10, 385–410. Mot, E.S., 2001. The influence of the payment system for medical specialists upon waiting times in the Netherlands. Mimeo. Newhouse, J.P., and the Insurance Experiment Group, 1993. Free for All?. Lessons from the RAND Health Insurance Experiment. Harvard University Press, Cambridge. Newhouse, J.P., 1987. Medical care expenditure: a cross-national survey. Journal of Health Economics 6, 109–128. Newhouse, J.P., 1996. Reimbursing health plans and health providers: efficiency in production versus selection. Journal of Economic Literature 34, 1236–1263. Rizzo, J.A., Blumenthal, D., 1994. Physician labor supply: do income effects matter? Journal of Health Economics 13, 433–453. Rosett, R.N., Huang, L., 1973. The effect of health insurance on the demand for medical care. Journal of Political Economy 81, 281–305. Statistics Netherlands, 2000. Vademecum of Health Statistics of the Netherlands, Voorburg. Van den Berg, B., Mot, E.S., 2000. Honorering, verwijsgedrag en prikkels. Economisch Statistische Berichten 85, 791–793 (in Dutch). Wedig, G., Mitchell, J.B., Cromwell, J., 1989. Can price controls induce optimal physician behavior? Journal of Health Politics, Policy and Law 14, 601–620. Westerhout, E.W.M.T., Folmer, C., 2007. Co-payment Schemes in Health Care: Between Moral Hazard and Risk Reduction. CPB discussion paper, no. 78. Zeckhauser, R., 1970. Medical insurance: a case study of the tradeoff between risk spreading and appropriate incentives. Journal of Economic Theory 2, 10–26. Ziekenfondsraad, 1998. Evaluatie Experiment Specialistenhonorering, report no. 783, Amstelveen (in Dutch).