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date: 20 February 2020

# Price Regulation and Pay-for-Performance in Public Health Systems

## Summary and Keywords

Payment systems based on fixed prices have become the dominant model to finance hospitals across OECD countries. In the early 1980s, Medicare in the United States introduced the Diagnosis Related Groups (DRG) system. The idea was that hospitals should be paid a fixed price for treating a patient within a given diagnosis or treatment. The system then spread to other European countries (e.g., France, Germany, Italy, Norway, Spain, the United Kingdom) and high-income countries (e.g., Canada, Australia). The change in payment system was motivated by concerns over rapid health expenditure growth, and replaced financing arrangements based on reimbursing costs (e.g., in the United States) or fixed annual budgets (e.g., in the United Kingdom).

A more recent policy development is the introduction of pay-for-performance (P4P) schemes, which, in most cases, pay directly for higher quality. This is also a form of regulated price payment but the unit of payment is a (process or outcome) measure of quality, as opposed to activity, that is admitting a patient with a given diagnosis or a treatment.

Fixed price payment systems, either of the DRG type or the P4P type, affect hospital incentives to provide quality, contain costs, and treat the right patients (allocative efficiency). Quality and efficiency are ubiquitous policy goals across a range of countries.

Fixed price regulation induces providers to contain costs and, under certain conditions (e.g., excess demand), offer some incentives to sustain quality. But payment systems in the health sector are complex. Since its inception, DRG systems have been continuously refined. From their initial (around) 500 tariffs, many DRG codes have been split in two or more finer ones to reflect heterogeneity in costs within each subgroup. In turn, this may give incentives to provide excessive intensive treatments or to code patients in more remunerative tariffs, a practice known as upcoding. Fixed prices also make it financially unprofitable to treat high cost patients. This is particularly problematic when patients with the highest costs have the largest benefits from treatment. Hospitals also differ systematically in costs and other dimensions, and some of these external differences are beyond their control (e.g., higher cost of living, land, or capital). Price regulation can be put in place to address such differences.

The development of information technology has allowed constructing a plethora of quality indicators, mostly process measures of quality and in some cases health outcomes. These have been used both for public reporting, to help patients choose providers, but also for incentive schemes that directly pay for quality. P4P schemes are attractive but raise new issues, such as they might divert provider attention and unincentivized dimensions of quality might suffer as a result.

# Introduction

Payment systems based on fixed prices have become the dominant model to finance hospitals across OECD countries. In the early 1980s, Medicare in the United States introduced the Diagnosis Related Groups (DRG) system. The idea was that hospitals should be paid a fixed price for treating a patient within a given diagnosis or treatment. The system then spread to other European countries (e.g., France, Germany, Italy, Norway, Spain, the United Kingdom) and high-income countries (e.g., Canada, Australia). The change in payment system was motivated by concerns over rapid health expenditure growth, and replaced financing arrangements based on reimbursing costs (e.g., in the United States) or fixed annual budgets (e.g., in the United Kingdom).

A more recent policy development is the introduction of pay-for-performance (P4P) schemes, which, in most cases, pay directly for higher quality. This is also a form of regulated price payment but the unit of payment is a (process or outcome) measure of quality, as opposed to activity, that is admitting a patient with a given diagnosis or a treatment.

This article reviews and analyzes hospital incentives induced by fixed price payment systems, either of the DRG type or the P4P type, to provide quality, contain costs, and treat the right patients (allocative efficiency). The focus on these dimensions is justified because quality and efficiency are ubiquitous policy goals across a range of countries. The analysis mostly draws on microeconomic theoretical models that have have investigated the design of payment systems for healthcare providers, with a special focus on hospitals. Some reference to the empirical literature is made where appropriate. Whenever possible healthcare providers are modeled as altruistic, meaning that they have a genuine concern to improve patient health.

Payment systems in the health sector are complex. We address a number of policy-relevant questions that reflect the key features and complexities of such health payment systems. We investigate under what conditions a fixed price regulation induces providers to both contain costs and provide appropriate quality and to treat the right patients, that is those for whom health benefits are higher than costs.

Since its inception, DRG systems have been continuously refined. From their initial (around) 500 tariffs, many DRG codes have been split in two or more finer ones to reflect heterogeneity in costs within each subgroup. The potential benefits and pitfalls of further DRG refinement are addressed. Hospitals may differ systematically in costs and other dimensions, and some of these external differences are beyond their control (e.g., higher cost of living, land, or capital). The adjustments that price regulation can put in place to address such differences are examined. The sections on pay-for-performance derive the implications for the design of monetary incentive schemes, which directly incentivize quality, under the plausible scenarios that not all dimensions of quality are contractible and that providers differ in some unobserved dimensions, such as their degree of motivation.

Reporting of quality indicators in the public domain, through websites, newspapers, and other media, is increasingly popular. Whether public reporting can incentivize providers to increase quality by enhancing reputational concerns is investigated. Given that many indicators of performance are self reported by the provider, some of the information could be misreported to the provider advantage (gaming), which in turn affects the design of the payment system for the funder.

Throughout the article, a contract theory—principal/agent—perspective is adopted, where the purchaser (the principal) decides on key features of the payment system and anticipates their effect on providers’ incentives (the agent). To reflect this focus, each section is structured in three parts: (i) the provider, which investigates incentives for a given payment rule; (ii) the purchaser, which investigates the design of the payment rule; and (iii) the key policy implications that arise from the analysis. Given our applied focus, we mostly look at payment rules that we observe in practice even if this comes at the cost of restricting the contract space. Our approach is both normative and positive. It is normative because we aim at deriving optimal payment rules. It is positive because we investigate scenarios that closely mimic the environment under which the providers operate in order to inform policy with practical recommendations.

The focus is mostly on hospitals, though some of the results derived could be translated to the context of primary care (e.g., GPs paid by capitation and practices with higher quality attracting a larger volume of individuals registered with that practice). We do not discuss in detail issues related to hospital competition because these have been discussed in great detail elsewhere (Gaynor, 2007; Gaynor & Town, 2011).

# Quality and Cost Containment

Quality and efficiency are ubiquitous goals of health policymakers. In this section, we provide a simple model of hospital behavior where the provider can choose both quality of care and cost-containment effort (which can be interpreted more broadly as efficiency). The model helps to understand how hospital payment systems affect provider behavior. We make the following key assumptions, all of which are relaxed below. We assume that (i) demand responds to quality and (ii) there is excess capacity so demand equals supply. Assumptions (i) and (ii) are likely to apply to countries with relatively high levels of funding (e.g., the United States, Germany). The model is based on Ma (1994) and Chalkley and Malcomson (1998a). Moreover, we assume that prices are regulated and thus not determined in the market. This is in line with institutional settings of many OECD countries that regulate prices on hospital services. This includes the Diagnosis Related Groups (DRG) system introduced by Medicare in the United States in the early eighties, and the Payment by Results (PbR) system in England, which is based on Healthcare Resource Groups (HRGs). We do not discuss the scenarios under variable prices, where prices are bargained between the purchaser of health services (a private or a public insurer) and the hospital (Barros & Martinez-Giralt, 2006; Siciliani & Stanciole, 2013; Gaynor, 2007).

## The Provider

Formally, the representative hospital provides quality $q$, and exerts cost-containment effort $e$. It receives a fixed price $p$ for each patient treated, possibly combined with a lump-sum transfer (a fixed budget component) $T$. We assume that the demand function, $n(q)$, is increasing in quality $q$, so that $nq(q)>0$. More patients are willing to get treated when the quality is high. The profit of the hospital is

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where the cost function $C(.)$ is increasing in both the number of patients treated and quality (e.g., investment in machines, etc.), with $Cn>0$, $Cq>0$, and $Cqq>0$, and it is decreasing in cost-containment effort, $Ce<0$. We assume that the hospital treats all patients who demand care, and demand equals supply. We allow for a general cost function that encompasses several plausible scenarios. If there are diseconomies of scale, then the marginal cost of treatment is increasing ($Cnn>0$). This assumption is likely to hold for larger hospitals: the empirical evidence suggests diseconomies of scale arise above 250–300 beds (see, e.g., Aletras, 1999; Folland, Goodman, & Stano, 2004, for literature surveys). The closer a hospital’s production is to capacity, the more costly it is to treat one additional patient. Capacity utilization in hospitals varies across health systems. In more regulated publicly funded health systems (e.g., the United Kingdom, the Scandinavian countries, Spain, Italy), there is typically excess demand (waiting), suggesting that hospitals operate at a steeper part of the marginal cost curve. However, in less regulated systems (e.g., the United States, Germany, France), there is often excess supply, suggesting relatively constant hospital marginal costs. Small hospitals may instead be characterized by economies of scale ($Cnn<0$). Moreover, the model allows for both cost substitutability ($Cnq>0$) and cost complementarity ($Cnq<0$) between quality and number of patients treated. Cost substitutability is plausible if the marginal cost of treating a patient increases with quality (e.g., $C(.)=c(q)n$, with $Cnq=cq>0$). Treating more patients might also improve quality in the presence of “learning-by-doing” effects, leading to complementarity between quality and volume of patients treated ($Cnq<0$).

We assume that providers care directly about quality, not just because quality affects profits. This may be because they are altruistic and care about the effect of quality on patients or are intrinsically motivated. The degree of altruism is $α∈[0,1]$. Patient benefit is $b(q)$, which is increasing in quality, $bq>0$, at a weakly decreasing rate, $bqq≤0$. The assumption is shared within health economics by several authors (e.g., the seminal paper by Ellis & McGuire, 1986; Chalkley & Malcomson, 1998b; Jack, 2005). Although doctors may not act as perfect agents for the patients, it seems plausible that they may act at least as imperfect ones (McGuire, 2000). Becoming a doctor requires several years of demanding training to learn how to improve patient health, and doctors take the Hippocratic Oath. The literature on motivated agents makes a similar assumption (Francois, 2000; Besley & Ghatak, 2005, 2006; Delfgaauw & Dur, 2007, 2008; Prendergast, 2007).

Providers may also incur nonmonetary costs (disutility) from providing quality and effort, which we denote with $φ(q,e)$. Quality generates nonmonetary costs for doctors such as providing a good diagnosis and keeping focused during surgery, $φq>0$, $φqq>0$. Cost-containment effort takes time and energy to identify better management solutions and reduce waste of resources, $φe>0$, $φee>0$. To sum up, the hospital’s objective function is

$Display mathematics$
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The hospital chooses quality $q$ and cost-containment effort $e$ to satisfy the following conditions:

$Display mathematics$
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$Display mathematics$
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Quality is chosen such that marginal benefit from higher revenues and from the altruistic motive is equal to marginal monetary and nonmonetary costs of quality. Cost-containment effort is such that the marginal benefits from lower monetary costs (and therefore higher profits) is equal to the marginal nonmonetary cost of effort.

To assess whether a payment systems provides the right incentives, a benchmark is needed that identifies the desired or optimal quality and cost-containment effort. Here a purchaser perspective is taken. An alternative would be to take a welfare perspective, which we discuss in more detail, and which would give qualitatively similar results.

## The Purchaser

Suppose the purchaser maximizes the difference between patient benefits and the transfer to the provider, formally defined as $W=B(n(q),q)−T−pn(q)$. Patient benefits are $B(n(q),q)$ and encompass both the direct benefits from higher quality, $Bq$, and the indirect ones from higher number of patients treated, $Bnnq$ (and it is therefore different from the benefit function of the provider $b(q)$). The purchaser maximizes $W$ subject to the participation constraint for the provider, $U≥0$. Given that leaving a positive rent to the provider is costly to the purchaser, this constraint is binding with strict equality so that revenues equate costs, and $T+pn(q)=C(n(q),q,e)+g(e,q)−αb(q)$. (In this section, we assume the disutility $g(.)$ is sufficiently high relative to altruism so that the profit constraint is not binding, and can therefore be ignored). By substitution, we obtain $W=B(n(q),q)−C(n(q),q,e)−g(e,q)+αb(q)$. The optimal level of quality and effort from the purchaser’s perspective is given by: (i) $Bq+(Bn−Cn)nq+αbq=Cq+(gq−αbq)$, (ii) $−ce=ge$. By comparing the optimal quality and cost-containment effort condition for the purchaser and the provider, it can be shown that the optimal quality and cost-containment effort can be induced by the purchaser by setting the price at the following level:

$Display mathematics$
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The price should be set equal to the sum of the direct marginal benefit from quality, weighted by the responsiveness of demand to quality, and the marginal benefit from treating patients. The rule highlights the criticality of demand responsiveness to quality. A higher demand responsiveness to quality implies a lower price.

Assumptions (i) and (ii) play a critical role. If demand does not respond to quality then price does not affect quality incentives. Similarly, in the presence of excess demand, hospitals do need to increase quality to attract patients because more patients demand treatment than the hospital can treat (assuming the quality does not drop below a minimum level, which dissuades too many patients from seeking treatment; see Chalkley & Malcomson, 1998a, for a formal analysis); in such cases, the introduction of partial cost reimbursement rules can be welfare improving (Chalkley & Malcomson, 1998b).

## Policy Implications

The model provides some good news in terms of efficiency incentives. It suggests that price regulation induces hospitals to contain costs at the appropriate level. The implications are mixed in terms of quality. Only in countries with excess supply do price incentives give an additional motive to provide quality. For countries with long waiting times and excess demand, this is not the case. Moreover, even in countries with excess supply, demand elasticity is generally low (see Brekke, Gravelle, Siciliani, & Straume, 2014, for a review of the empirical literature). Although the purchaser could compensate for the low elasticity of demand by setting a very high price, in practice this is not observed because DRG systems commonly set price to reflect past average costs. Given that marginal costs are likely to be below average costs for many providers, DRG systems do provide a financial incentive to increase quality. However, given the low demand elasticity this additional incentive may be insufficient. This seems consistent with some empirical evidence from the United States and the United Kingdom, which finds that increases in DRG prices have had no effect on quality (Dafny, 2005; Farrar et al., 2009). It is also consistent with the desire of policymakers to increase quality through other means, such as the development of pay-for-performance schemes that directly pay for higher levels of reported, mostly process, quality measures.

# Patient Heterogeneity

The model in the section “Quality and Cost Containment” focuses on quality and cost-containment incentives at the overall hospital level. It also implicitly assumes that patients are homogenous. In this section, we explore hospital incentives to treat patients under a fixed price system for a given diagnosis (DRG) when patients differ in the degree of severity. Does the DRG price system give the correct incentives to treat patients? If financial incentives are not aligned it may be that some patients who are supposed to be treated are not treated, and some patients who are not supposed to be treated are instead treated. Under a DRG system hospitals receive hundreds of tariffs. Whether the incentives are aligned is likely to depend on the benefit and cost function of treating a patient within a given diagnosis. We now discuss these issues more formally following a sketch of the model outlined by Kifmann and Siciliani (2017). See also Ellis and McGuire (1986), Ellis (1998), and De Fraja (2000) for related models.

## The Provider

Consider patients with a given diagnosis and therefore a given DRG. In each hospital, patients differ in severity of illness $s$, which is distributed over the support $[s_,s¯]$ with density function $f(s)$ and cumulative distribution function $F(s)$. The cost of treating a patient with severity $s$ is $c(s)$, and is increasing in severity, $cs>0$. A patient’s benefit of hospital treatment is given by $b(s)$, which is positive but can increase or decrease with severity, $bs≷0$. If $bs>0$ patients with higher severity have also higher capacity to benefit. For example, patients who suffer from severe arthritis can benefit more from a hip replacement to reduce their pain. If $bs<0$ patients who are more severe may require a complicated surgery from which they are less likely to recover. Both scenarios are plausible depending on the diagnosis and medical condition. We assume that patients’ severity is observed by providers but not by the purchaser, and patients accept to undertake the treatment recommended by the provider. Hospitals receive a DRG price $p$ for patients with the same diagnosis. The DRG price is set according to the average cost of all patients who are treated with the same diagnosis, as we observe in many health systems. We assume that the number of hospitals (which in this model are identical) is sufficiently large that we can ignore any strategic effect of each individual hospital choice on the DRG price.

Hospitals are risk neutral and altruistic. The provider’s altruistic gain from each patient treatment is $αb(s)$, where $α$ denotes altruism (see “Quality and Cost Containment”). The provider treats the patient if the sum of the financial and non-financial benefits from treating the patient are larger than it costs, that is, the DRG price plus the altruistic component covers the cost, $p+αb(s)≥c(s)$. In an interior solution, the marginal patient has severity $s$ implicitly defined by $p=c(s∗)−αb(s∗)$, so that the DRG tariff equates to the marginal “net cost,” where the net cost is defined as the difference in cost and altruistic gain.

Whether the provider treats low-severity or high-severity patients under this interior solution depends on specific assumptions about altruism, the benefit, and the cost function. We distinguish two scenarios. In the first scenario, the net cost increases with severity $(cs−αbs>0)$ so that low-severity patients are treated. This case always arises if patient’s benefit decreases with severity. Because low-severity patients have lower costs and higher benefits, the provider has incentive to treat them for both profit and altruistic reasons. This case also arises if patient’s benefit increases with severity and either altruism or the marginal benefit from higher severity is relatively small. Assuming an interior solution, the optimal provider’s equilibrium severity is characterized by

$Display mathematics$
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It is such that the nonmonetary benefit from altruism and the monetary benefit from the DRG tariff, which is equal to the average cost, is equal to the marginal cost (where note that the marginal cost is always above the average cost).

In the second scenario, the net cost decreases with severity ($cs−αbs<0$) so that high-severity patients are treated. This case arises if patients’ benefit increases with severity and altruism or benefit is sufficiently high. Despite high-severity patients being more costly, the benefit is sufficiently high that the provider prefers to treat patients with high severity.

## The Purchaser

From a policy perspective, the critical question is whether DRG prices give providers the incentive to treat the right patients. Whether it is optimal from the purchaser perspective to treat low- or high- severity patients depends on her assessment of benefits and costs. Suppose that the purchaser is utilitarian, that is, it maximizes the differences between benefits and costs. Then patients should be treated when benefits are (weakly) above costs: $b(s)≥c(s)$. Again, we can identify two cases.

### Low-Severity Patients Should be Treated

This scenario arises when patient benefit is either decreasing with severity or increasing with severity but less steeply than cost: $cs−bs>0$. Assuming an interior solution, the marginal patient is such that $b(sf)=c(sf)$. Patients with severity below first-best severity $sf$ should receive treatment and those with severity above $sf$ should not. We can compare this first-best severity threshold with the severity threshold adopted by the hospital under the DRG payment system. In this scenario, hospital net cost of treating a patient always increases with severity, and severity is characterized by $αb(s∗)+(∫s_s∗c(s)f(s)ds)/F(s∗)=c(s∗)$. If altruism is low, too few patients are treated as long as $s∗: it would be optimal from a welfare perspective to treat also patients with intermediate severities in $(s∗,sf]$. If altruism is high, too many patients are treated, and this is always the case for very high altruism, for example, $α=1$: some patients with high severity should not be treated but instead are treated.

### High-Severity Patients Should be Treated

This arises when patient benefit increases with severity more quickly than costs: $cs−bs<0$. The marginal patient is still characterized by $b(sf)=c(sf)$ but it is now patients with severity above $sf$ who should be treated. If the net cost increases with severity, hospitals do not treat high-severity patients when altruism is low. This is perhaps the most worrying case because the DRG system gives completely the wrong incentives. For high altruism, only some of the patients who should be treated are actually treated. If the net cost decreases with severity, for low altruism there are some patients with low severity who should not be treated. For high altruism, too many patients are treated.

The analysis assumes that the net cost of treatment either increases or decreases with severity. There may be cases where it increases with severity both for low-severity and high-severity patients, but is decreasing with severity for middle-severity patients. In such cases, it would be optimal to treat middle-severity patients but not low- and high-severity patients.

## Policy Implications

The key policy implications of the analysis is that DRG payments are particularly problematic when provider (net) cost of treating a patient increases with severity because patients with high severity should be treated but they are not treated. One first step in addressing this issue is to identify problematic DRGs, where net cost of treatment is increasing with severity. This would, however, be a demanding exercise. Although costs and benefits of health treatments are measured and employed in economic evaluations of healthcare treatments to decide whether a new treatment should be provided by a public insurer (Drummond, Sculpher, Claxton, Stoddart, & Torrance, 2015), these cover only a subset of treatments, and are generally based on relatively small samples. If the most problematic DRGs could be identified, some regulatory interventions could be developed such as targeted audits for these groups or some further tariff adjustments (on top of current cost outliers reimbursement). Another possibility is to further split DRGs to better reflect different costs.

# Multiple Treatments for a Diagnosis

In “Patient Heterogeneity” we have implicitly assumed that there is just one treatment to cure a medical condition. In this section we relax this assumption by allowing for the presence of multiple treatments for a given diagnosis, with some treatments being more intensive and expensive than others. DRG systems are based on average costs rules. One policy choice is whether DRG prices should refer to the diagnosis, effectively pooling costs across different treatments, or whether the DRG price should refer to the treatment with each price reflecting the average cost within each treatment. Given that treatments tend to vary extensively in costs, several waves of DRG refinements have introduced new DRGs that split old DRGs in more refined categories. DRG split may, however, give incentives to provide the more intensive treatments too frequently contributing to health expenditure growth. In this section we provide a simple model of DRG refinement based on Hafsteinsdottir and Siciliani (2010). See Malcomson (2005) and Siciliani (2006) for related contributions.

## The Provider

Patients with a certain diagnosis receive one of two treatments: $θ_$ is the less intensive treatment, and $θ¯$ is the more intensive treatment. As in “Quality and Cost Containment,” patients differ in severity of illness $s∈[s_,s¯]$, which has density function $f(s)$ and cumulative distribution function $F(s)$. The number of patients treated by each hospital is normalized to one. The benefit from the more intensive treatment for a patient with severity $s$ is $b(θ¯,s)$. For the less intensive treatment it is $b(θ_,s)$. The cost of the less intensive treatment is $c(θ_,s)$ and the cost of the more intensive treatment is $c(θ¯,s)$. Cost of treatment increases with patient severity: $cs(θ,s)>0$. As an example, consider patients with ischemic heart disease, which can cause angina (severe chest pain) due to diminished blood flow. Low-severity patients with mild angina can be treated with medication (e.g., beta-blockers). More severe patients need a coronary bypass or angioplasty, which are more invasive procedures. We also assume that patients’ benefit and the difference in benefit between the two treatments increases with severity, $bs(θ¯,s)≥bs(θ_,s)>0$; and that the cost increases with severity more quickly for the less intensive treatment; $cs(θ_,s)≥cs(θ¯,s)$ (for example, more intensive treatment such as surgical procedures have higher fixed costs and smaller marginal costs).

The provider decides what type of treatment to provide to each patient. There are $H$ identical hospitals. Each hospital $i=1,...,H$, maximizes utility $Ui=αBi+Ti−Ci$, where $α$ is altruism, $Bi$ and $Ci$ are the total benefit and cost of treating patients, and $Ti$ is the payment to the hospital. We assume that patients’ severity of illness is observed by the provider but not by the purchaser. The treatment instead is known to both the provider and the purchaser. We assume that hospitals must treat all patients and cannot dump patients.

We define $zi$ as the cut-off severity point above which the more intensive treatment is provided. For simplicity, we refer to the low-intensity treatment as the medical treatment, and to the high-intensity treatment as the surgical treatment. The proportion of medical treatments is $n_i=∫s_zif(s)ds=F(zi)$, and the proportion of surgical treatments is $n¯i=1−F(zi)$. The total cost of treatment is the sum of the cost of providing the medical treatment, $C_i(zi)$, and the surgical treatment, $C¯i(zi)$, and similarly, for total benefit, $Bi(zi)$.

$Display mathematics$
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Under a DRG payment system, prices are set equal to the average cost. If prices are unrefined the purchaser pays the same price $p$ for the medical and the surgical treatment, and this reflects the average cost across the two treatments:

$Display mathematics$
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If the purchaser instead decides to refine prices, the purchaser sets two different prices for the medical and surgical treatment:

$Display mathematics$
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Hospital $i$ maximizes utility, $Ui=αBi+Ti−Ci$, with respect to the optimal cut-off point $zi$, where $Ti=p×ni$ if prices are unrefined, and $Ti=p_×n_i+p¯×n¯i$ if prices are refined. We assume that the number of hospitals is sufficiently large so that $H−1H≈1$, and we can ignore the effect of each individual hospital choice of the severity cut-off on the price levels so that hospitals effectively treat prices as exogenous.

Suppose that prices are unrefined. If an interior solution arises, then the optimal severity cut-off point chosen by the hospitals is such that

$Display mathematics$
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where the severity threshold $zu$ is such that the difference in benefit, weighted by altruism, between a surgical and medical treatment is equal to the difference in costs. Intuitively, with unrefined prices the purchaser pays the same price for both treatments and the optimal cut-off point for the semi-altruistic hospital is strictly greater than zero, resulting in the hospital providing the medical treatment to patients with severity below the optimal cut-off point and the surgical treatment to patients with severity above the optimal cut-off point. For sufficiently low altruism, the cut-off point is set at the highest level, so that the medical treatment is provided to all patients.

Suppose now that prices are refined. To avoid corner solutions, we assume that for patients with lowest severity, the medical treatment is more beneficial than the surgical treatment, that is, $b(θ_,s_)>b(θ¯,s_)$, which is plausible. The optimal severity cut-off point $zr>s_$ satisfies:

$Display mathematics$
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The cut-off point is such that the marginal benefit for the patients from an additional medical treatment, rather than a surgical one, is equal to the reduction in profits. When DRG prices are refined, there are strong incentives to provide the surgical treatment to the point where some patients would actually benefit more from a medical treatment but are instead given a surgical one. This is because when prices are refined, the provider has a positive profit margin on the patient with marginal severity when the surgical treatment is provided ($p¯>c(θ¯,zr)$) and a negative profit margin when the medical treatment is provided ($p_). In both cases, with or without price refinement, profits are zero in equilibrium because prices are set equal to the average costs.

## The Purchaser

Suppose that the purchaser maximizes welfare given by $W=Bi(zi)−(1+λ)Ci(zi)$. This specification can be justified in the case of a utilitarian purchaser (which maximizes the sum of patient benefit and provider profit), the presence of a positive opportunity cost of public funds, and no double counting of provider altruistic component. Differently from elsewhere we generalize the welfare function by allowing for the presence of distortionary taxation and introduce the parameter $λ>0$, which denotes the shadow cost of public funds, that is, for each \$1 levied to fund healthcare expenditure, distortionary taxation generates $(1+λ)$ disutility for the taxpayers. The first-best cut-off severity point $z∗$ satisfies the following condition:

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The optimal cut-off point is such that the additional marginal benefit from the surgical treatment is equal to the social marginal cost. Under minimal regularity conditions, it is possible to show that there is an overprovision of more intensive treatments if the purchaser refines the prices: $z∗>zr$. Instead, there is an underprovision of the more intensive treatment if the purchaser does not refine the price when the degree of altruism is sufficiently small $(1/(1+λ)>α)$, so that $zu>z∗$.

The purchaser obtains a higher welfare when prices are refined if $W(zr)>W(zu)$ or more extensively if

$Display mathematics$
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Intuitively, welfare is higher under refinement when the difference between benefit and cost for the marginal patients is higher when the surgical treatment is provided rather than the medical treatment. Refinement is optimal when the additional benefit for the patients with severity $s∈[zr,zu]$ receiving a surgical treatment rather than a medical treatment is higher than the corresponding additional cost.

## Policy Implications

The key policy implication of the analysis is that refining DRGs by splitting a tariff into finer tariffs that better reflect costs is not always desirable. Policymakers face a difficult choice. By not splitting DRGs, purchasers give strong incentives to contain costs, but in some cases patients will receive too little treatment. By splitting DRGs, the purchaser may give providers an incentive to provide too much care to the point where benefits are below costs. The analysis suggests that the trade-off between the risk of over- versus under-treatment needs to be assessed on a one-to-one basis. An alternative solution would be to split the DRG but to set the price difference between the more and less intensive treatment below the difference in the cost of the two treatments. This approach is reminiscent of a mixed payment system where only a proportion of the costs are reimbursed (Ellis & McGuire, 1986). Other considerations are also important. Splitting DRGs has the advantage that it protects better the provider against financial losses, especially when volumes are low (e.g., in one year the provider treats few patients whose cost is above the tariff). But it also has the disadvantage of increasing the scope for misclassifying patients in more remunerative groups, a practice that is also known as upcoding (Silverman & Skinner, 2004; Dafny, 2005) and to which we return in Section 9.

# Provider Heterogeneity Along Observable Dimensions

Previously we have assumed that hospitals are identical. In some cases we have allowed for heterogeneity in patient severity within the hospital. But there are many dimensions of heterogeneity also across hospitals, some of which may be observable to the regulator (and some unobservable). In this section we explore one source of heterogeneity, that is, differences in costs that are exogenous to the hospital. For example a hospital located in London is likely to have higher costs than hospitals located in other areas of the country (e.g., the Midlands area). Differences in costs are important because if not accounted for some hospitals could face larger deficits. Moreover, there is a wealth of information on costs and this can be used by regulators to refine the payment system.

One option is to allow the DRG fixed price payment system to vary across hospitals, as we observe in some institutional settings. For example, under Payment by Results (PbR) in England, hospitals are paid a Health Resource Group (HRG) price (the English version of DRG prices) based on national average costs adjusted by a provider-specific index, the Market Factor Forces (MFF). The MFF adjusts the national price for local unavoidable differences in costs due to factor prices for staff, land, and building costs. Similarly, the DRG payment system in the United States adjusts the fixed price based on some providers’ characteristics, for example to control for wage variation, cost variations between urban and rural areas, and teaching status. In this section, we discuss the extent to which price should be adjusted. As an extension, we also investigate how equity considerations affect price adjustment. The analysis is based on Miraldo, Siciliani, and Street (2011). To make the analysis more salient and policy oriented, we also introduce the realistic assumption that hospitals are paid only through the price system, that is, no fixed budget—or lump-sum transfer—is used, which is in line with several health system arrangements (see also Mougeot & Naegelen, 2005, for a related analysis).

## The Provider

Define $n$ as the number of patients treated by the provider. As usual, the provider receives a fixed price $p$ per patient treated (e.g., for a coronary bypass). Providers differ in (exogenous) costs, for example due to land costs, and this is captured by the parameter $θ$. The cost function is $C(θ,n)$ and is increasing in number of patients treated at an increasing rate, $Cn>0$ and $Cnn>0$. Moreover, hospitals with higher exogenous unavoidable costs $θ$ also have a higher marginal cost, in addition to overall cost, $Cnθ>0$ and $Cθ>0$. The cost index $θ$ is observable to the purchaser and can be used for price adjustment.

Each provider decides how many patients to treat by maximizing its profit $π(θ,n)=pn−C(θ,n)$ so that the price equals the marginal cost, $p=Cn(θ,n)$. The number of patients treated increases with the DRG price and decreases with unavoidable costs, $np=1/Cnn>0$, $nθ=−Cnθ/Cnn<0$. Moreover, providers with higher costs respond less to an increase in price than providers with lower costs if $npθ=CnθCnnn/Cnn3−Cnnθ/Cnn2<0$.

## Purchaser

The purchaser buys healthcare from the provider and has to decide the price $p$. We assume that the purchaser’s utility is a weighted sum of patients’ benefits and hospital utility net of the transfer to the provider, the latter weighted by the opportunity cost of public funds (as in “Multiple Treatments for a Diagnosis”). In more detail, define $B(n)$ as patients’ benefit, with $Bn>0$ and $Bnn<0$: benefit is increasing in the number of patients treated at a decreasing rate; and $λ>0$ as the shadow cost of public funds. The purchaser’s utility is then $W(θ,n)=B(n)+π(θ,n)−(1+λ)pn$, which after substitution of $π$ gives $W(θ,n)=B(n)−λpn−C(θ,n)$. It can be shown that it is optimal for the purchaser to set a price $p∗$ equal to:

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The optimal price is set below the marginal benefit. The first term is the marginal benefit from treatment discounted for the opportunity cost of public funds. Since leaving a rent to the provider is costly, the second term is negative and implies a lower price. A higher responsiveness of activity to price, $np$, implies a higher optimal price. The optimal price is decreasing in the shadow cost of public funds $λ$: the higher the shadow cost, the higher is the overall cost of provision as well as the cost of leaving a rent to the provider. The purchaser is therefore less willing to pay a higher price.

How does the price differ according to unavoidable cost type $θ?$ By the implicit function theorem we have $dp∗/dθ=−Wpθ/Wpp$. Totally differentiating with respect to $θ$ we obtain:

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There are three main terms. The first term is positive. Because high-cost providers provide lower activity, the marginal benefit from treating patients is higher and therefore the price is higher (treatment effect). The second term is also positive. Again, because high-cost providers provide lower activity, the rent from a marginal increase in price is lower. Therefore the price should be higher (rent effect). The third term is negative whenever high-cost providers respond less to an increase in price, that is, when $npθ<0$, which is the case for many well-behaved cost functions. Given that an increase in price is less effective in boosting activity for high-cost providers (and higher activity is valuable), then the optimal price should be lower (responsiveness effect). Therefore, the price for high-cost providers is higher than for low-cost providers only if the first two effects dominate the third.

The rent and the responsiveness effect are only relevant when the opportunity costs of public funds are strictly positive. Otherwise the purchaser is not concerned about leaving rents to the providers, and always adjusts upward the price for high-cost providers. The rent and responsiveness effects go in opposite directions. Suppose that costs behave according to the power function: $C(θ,n)=θnω/ω$, with $ω>1$. Then, the rent effect is exactly offset by the responsiveness effect, and the optimal price adjustment is:

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Hospitals with higher costs receive a higher price. Moreover, the price adjustment is partial, that is, it covers only a share of the additional marginal cost. The steeper is the marginal benefit curve, the higher is the adjustment. The result that the rent and the responsiveness effect cancel each other out does not hold in general. To illustrate this, suppose that the cost function is additively separable: $C(θ,n)=c(θ)n+g(n)$, with $cθ>0$, $gn>0$ and $gnn>0$. This specification implies that the marginal monetary cost of treatment is constant, the marginal non-monetary cost (or disutility) is increasing, and that the unavoidable cost parameter affects the monetary cost and not the non-monetary one. This seems a plausible assumption within the MFF price adjustment scheme, which compensates mainly for differences in monetary costs (land, building, and staff costs) as opposed to nonmonetary ones. In this case the rent effect is larger than the responsiveness effect, and the optimal price adjustment is even larger:

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The shape of the cost function can be estimated empirically. For example, the power function $C(θ,n)=θnω/ω$, is equivalent to a log-log specification for the estimation of a cost function (taking logs, we have $logC=logθω+ωlog(n)$, where $ω$ is the elasticity of costs with respect to quantity and $(logθω)$ is the constant term in the regression equation).

### Equity

Price regulation purely on efficiency grounds could potentially lead to a large gap in healthcare utilization between high- and low-cost providers. Equity is a key concern in many publicly funded systems, and has implications for price regulation. We conclude this section by investigating how a higher degree of inequality aversion affects the degree of price adjustment. We assume that the purchaser has an overall fixed budget $Z$. The purchaser problem now determines prices to maximize patients’ benefit

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subject to the budget constraint: $∫θ_θ¯p(θ)n(p(θ),θ)f(θ)dθ≤Z$, where $ρ$ is an index of inequality aversion. To obtain an analytical solution, suppose that both the benefits and the costs are specified as a power function, $C=θnω/ω$ with $ω>1$, $B(n)=nε/ε$ with $0<ε≤1$, and that the distribution of cost types is uniform, $f(θ)=1/(θ¯−θ_)$. The optimal equilibrium prices and volume of treated patients are $p∗(θ,μ,ρ)=θ(ε−ρθμω)−ω−1ω−ε(1−ρ)$, $n∗(θ,μ,ρ)=(ε−ρθμω)−1ω−ε(1−ρ)$ where $μ$ is the multiplier associated with the budget constraint. It can be shown that $∂p∗/∂θ>0$ and $∂n∗/∂θ<0$, and as expected, high-cost providers receive a higher price and treat fewer patients in equilibrium.

How does inequality aversion affect the inequality of patients treated across providers and in prices? A standard method within the health economics literature to measure the degree of inequality in the receipt of healthcare is the concentration curve (see Wagstaff & van Doorslaer, 2000 for a review). Define $Kn(g)$, $Kp(g)$ as the concentration curve for volumes of patients and prices, where $g=F(θ)$ is the cumulative percentage of providers with lowest costs (with $0≤g≤1$). The concentration curve plots the cumulative percentage of volume or price against the cumulative percentage of providers ranked by cost type $θ$, beginning with the provider with the lowest costs, and ending with the provider with highest costs. The concentration curve for volumes and prices is, respectively:

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where $β=ω−1−ε(1−ρ)ω−ε+ερ$ and $σ=ω+1−2ε(1−ρ)ω−ε+ερ$. Because low-cost providers treat more patients the concentration curve of volumes lies above the unit diagonal. In contrast, because they are paid lower prices, the concentration curve of prices lies below the diagonal. Differentiating with respect to the degree of inequality aversion, it can be shown that: $∂Kp(g)/∂ρ<0$, $∂Kn(g)/∂ρ<0$. Higher inequality aversion implies higher concentration of prices and lower concentration of volumes of patients treated. Higher inequality aversion implies that high-cost providers are paid higher prices, which shifts the concentration curve of prices downward. Because the concentration curve of prices lies below the diagonal, this implies overall a higher concentration in prices. As a result of the higher prices for the high-cost providers, their volume is also higher. The concentration curve of volumes also shifts downward when inequality aversion is higher. However, because now the concentration curve lies above the diagonal, this implies overall a lower concentration in volumes.

In summary, the analysis suggests that when inequality aversion is higher, the purchaser would like to reduce disparities in volumes of patients treated among providers by increasing the difference in price between high- and low-cost providers.

## Policy Implications

The analysis provides several practical policy insights. It suggests that in most realistic scenarios the price adjustment should be partial, that is, cover a proportion of differences in costs across hospitals. A key parameter in the degree of adjustment is the marginal benefit from treating additional patients. A steeper marginal benefit curve increases the scope for price adjustment and reduces dispersion in utilization across hospitals. A constant marginal benefit curve can be consistent with no price adjustment where the same DRG price is paid to each hospital and with large dispersion in utilization across hospitals. The results also generally hold when the purchaser is restricted to the use of a fixed price to pay hospitals—and no other forms of payments are allowed—with further adjustments upward or downward (depending on the details of the cost function) to avoid hospitals holding excessive rents. Finally, and perhaps most importantly, a higher degree of inequality aversion increases the scope for further price adjustment: by having a steeper price adjustment, higher-cost hospitals receive a relatively higher price, which contributes to reduce the gap in healthcare utilization between high- and low-cost providers.

# Pay-for-Performance

We have highlighted that DRG payment systems may give weak incentives to provide quality, and this may be so in particular when demand elasticity to quality is low and in health systems with large excess demand and long waiting lists. In turn, this implies that policymakers could pursue alternative policy levers to increase quality. The development of information systems has made possible the development of a number of quality indicators. It is no surprise that some policymakers have considered incentivizing quality by directly paying for it.

Such policy interventions are commonly referred to as Pay-for-Performance (P4P). They however come with several criticisms. A common one is that P4P encourages tunnel vision. By incentivizing some dimensions of quality, other non-incentivized ones may suffer as a result. Economists have long investigated this issue within the principal-agent literature on multitasking, starting with the seminal paper by Holmstrom and Milgrom (1991), then adapted by Eggleston (2005) and Kaarboe and Siciliani (2011) to the health sector. We follow the latter to illustrate how the presence of multitasking affects the design of P4P schemes. Other common criticisms of P4P is that it may be subject to gaming and that financial incentives might crowd out intrinsic motivation or altruism (Siciliani, 2009).

## The Provider

Differently from “Quality and Cost Containment,” we allow quality to be multidimensional. For expositional simplicity, we consider two dimensions of quality, $q1$ and $q2$, where quality 1 is verifiable and quality 2 is not. Provider disutility function (non-monetary cost) from providing quality is $C(q1,q2)$, which is increasing in quality at an increasing rate, $Cqi>0$, $Cqiqi>0$. If the two dimensions of quality are substitutes (complements), then an increase in quality 1 increases (decreases) the marginal disutility of quality 2 and $Cq2q1>0$ ($Cq2q1<0$). Quality dimensions can be substitutes when they are time consuming for the doctor. They can be complements in the presence of scope economies or learning by doing effects. Patients’ benefit $B(q1,q2)$ increases in both dimensions of quality at a (weakly) decreasing rate, $Bqi>0$, $Bqiqi≤0$. If $Bq1q2<0$ ($Bq1q2>0$) then an increase in quality 1 decreases (increases) the marginal benefit of quality 2, and the two dimensions of quality are substitutes (complements) in benefits.

The incentive scheme is based only on the verifiable dimension of quality 1. Verifiable quality is rewarded through a payment $p$ for each unit of quality. The provider also receives a positive lump-sum payment $T$. As in “Quality and Cost Containment,” the provider is altruistic and altruism is captured by $α$. Provider’s utility is $U=T+pq1+αB(q1,q2)−C(q1,q2)$. Optimal qualities are such that $p+αBq1(q1,q2)=Cq1(q1,q2)$, $αBq2(q1,q2)=Cq2(q1,q2)$. The marginal monetary benefit (for verifiable quality) and nonmonetary benefit (for both qualities) is equal to its marginal disutility.

What is the effect of increasing the price or introducing a P4P scheme on qualities?

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An increase in price increases the incentivized quality 1. It also decreases (increases) non-verifiable quality 2 if qualities are substitutes (complements) in patients’ benefit and in provider’s disutility. It is the overall effect $(αBq1q2−Cq1q2)$ that determines the relationship between quality dimensions. It could be, for example, that qualities are complements in patients’ benefit but substitutes in provider’s disutility.

## Purchaser

The purchaser maximizes the difference between patients’ benefit and the transfers to the provider $B(q1,q2)−T−pq1$ subject to the participation constraint $U≥0$. It can be shown that the optimal price is:

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The optimal price is equal to marginal benefit of the verifiable quality and it is critically adjusted to take into account the effect of verifiable quality on non-verifiable quality and the associated marginal benefit. If qualities are substitutes, the price is adjusted downward: $p∗. We refer to this incentive scheme as low-powered. As a special case, if the marginal benefit from the non-verifiable quality is very high, then the optimal price can drop to zero. The purchaser is better off by not introducing a P4P scheme. If qualities are independent, then the price is equal to the marginal benefit of quality 1: $p∗=Bq1(q1(p∗),q2(p∗))$, which is consistent with the result obtained in “Quality and Cost Containment.”. If qualities are complements, the price is set above the marginal benefit of quality 1: $p∗>Bq1(q1(p∗),q2(p∗))$. The incentive scheme is now high-powered.

Kaarboe and Siciliani (2011) also show that there is another case when it is optimal to set the price equal to the marginal benefit of verifiable quality, a high-powered incentive scheme. This arises if the non-verifiable quality drops quickly to zero as the price increases. When quality 2 is at its lowest level, a marginal increase in price generates benefits that are larger than provider disutility. The scenario could arise when both altruism and benefits from the unverifiable quality are low. The purchaser is then better off when unverifiable quality is at its minimum level, the verifiable quality is high, and the price is equal to the marginal benefit of quality 1, $p∗=Bq1(q1(p∗),0)$, compared to a scenario where both quality dimensions are positive but low, and the price is set below the marginal benefit of quality 1.

The model highlights the critical role of the degree of substitution or complementarity between different dimensions of quality in designing an incentive scheme in the health sector. If non-contracted measures of quality are also not observable, it is challenging for empirical work to inform the design of the schemes. A recent exception is Sutton, Elder, Guthrie, and Watt (2010) in relation to P4P schemes for family doctors (GPs), which provides some evidence of complementarities in qualities (though an earlier survey suggests that GPs think that qualities may be substitutes, and patients with acute conditions would deteriorate as a result of the increase in quality for chronic conditions [Whalley, Gravelle, & Sibbald, 2008]). Future work may be able to shed light if this finding can be extended to other institutional contexts and different types of providers, such as hospitals.

## Policy Implications

Pay-for-Performance is popular among policymakers, despite possible reservations regarding tunnel vision, that is, the potential for P4P to crowd out other important dimensions of quality. Within the hospital sector, the evidence seems to suggest that providers respond only to a small extent to such incentives, though we may be at too early a stage to draw general conclusions (Cashin, Chi, Smith, Borowitz, & Thomson, 2014). One possible reason for the lack of the effectiveness of such schemes is that the payments made to reward quality are still relatively small, often below 5% of the revenues. The small payments may be the result of multitasking concerns and are consistent with the theory outlined that suggests that the power of the incentive scheme should be low-powered when qualities are substitutes. But the small payments may also be the reason for the small take up in quality. One possible solution to the multitasking issue is to ensure that performance indicators cover all key areas of care based on best practice and available empirical evidence. In those cases there may be a stronger rationale for increasing the prices as suggested, for example, by Kristensen, Siciliani, and Sutton (2016) in relation to a P4P scheme on stroke patients that covered all key dimensions of validated process measures of quality.

# Provider Unobserved Heterogeneity

We have investigated how payment systems should be corrected in the presence of provider heterogeneity along some observable dimensions. In this section, we investigate how to adjust the payment scheme in the presence of unobservable dimensions. We focus on the derivation of optimal schemes to incentivise quality, in line with “Pay-for-Performance” (though the model can be readily re-interpreted in terms of volumes of patients, as in “Provider Heterogeneity Along Observable Dimensions”). The assumption that quality is perfectly contractible is admittedly strong, because quality metrics can be noisy and not comprehensive of all dimensions of care. However, process measures of quality for both primary and secondary care are commonly used to incentivize care (e.g., the Quality and Outcome Framework for primary care, and best practice tariffs in secondary care in England) and the optimal scheme derived here could be appropriate in such settings.

In line with some of the previous models, we assume that the provider is altruistic because, as shown in this section, the degree of altruism has implications for the power of the incentive scheme. With a large number of providers, it is unlikely that the purchaser of health services can distinguish between more and less efficient or able providers. Providers’ ability to provide quality care can therefore be considered private information. Does the presence of unobserved heterogeneity imply that the incentive scheme is high-powered or low-powered? Should there be large differences in transfers between providers with different levels of reported quality? We provide a model to answer these questions based on Makris and Siciliani (2013) (see Jack, 2005; Chone & Ma, 2011; Makris, 2009 for related contributions). It builds on the traditional principal-agent model (Baron & Myerson, 1982), which predicts that the optimal incentive scheme is high-powered in the presence of heterogeneity, private information (adverse selection), and profit-maximizer providers (these properties may be different if regulation is based on cost reimbursement rules, as in Laffont & Tirole, 1993).

## The Provider

Providers differ in efficiency $θ$, for example, due to differences in ability of doctors. Efficiency is private information and takes two values ${θ_;θ¯}$. The inefficient (efficient) provider is denoted with $θ¯$ ($θ_$), and $θ¯>θ_$. The probabilities of types $θ¯$ and $θ_$ are common knowledge and equal to $γ$ and $(1−γ)$. The contract offered by the purchaser specifies a fixed payment $T(θ)$ in return for a given quality $q(θ)$. Profit is $π(θ)=T(θ)−C(q(θ),θ)$, where $C(q,θ)$ is the total monetary cost of provider $θ$ for a given quality $q$. The marginal cost of quality is positive and increasing, $Cq>0$, $Cqq>0$. More inefficient providers have higher total and marginal cost of treatment, $Cθ>0$ and $Cθq>0$. Analogously to previous sections, $α$ is a positive parameter denoting the degree of altruism. Provider utility is the sum of profit and the altruistic component: $U(θ)≡π(θ)+αB(q(θ))$, where $B(q)$ is benefit from quality with $Bq>0$, $Bqq<0$. For notational simplicity we define $T¯≡T(θ¯)$, $q≡q(θ¯)$, $T_≡T(θ_)$, $q_≡q(θ_)$, $π¯≡π(θ¯)$, $π_≡π(θ_)$, $U_≡αB(q_)+T_−C(q_,θ_)$ and $U¯≡αB(q¯)+T¯−C(q¯,θ¯)$.

## The Purchaser

The purchaser is utilitarian and maximizes welfare $W$ defined as the sum of patients’ benefit net of the transfer to the provider, weighted by the opportunity costs of public funds, plus the utility of the provider, which gives $W(q,T,θ)=B(q)−C(q,θ)−λT$, where $λ$ is the opportunity cost of public funds. To ensure that the provider accepts the contract, the participation constraint has to hold for each type: $U(θ)≥0$. There is also a limited liability constraint: the provider cannot make losses (as in Choné & Ma, 2011; Besley & Ghatak, 2006): $π(θ)≥0$. Therefore, we assume purchasers face an institutional constraint that restricts them from requiring providers to self-finance parts of the monetary costs; the offered transfer has to be weakly higher than the monetary cost of providing quality; limited liability effectively protects (altruistic) providers from being exploited by purchasers.

The participation constraint is never binding in the presence of altruism if the limited liability constraint is binding. Moreover, the purchaser needs to satisfy incentive-compatibility conditions to ensure that the efficient (inefficient) provider has no incentive to mimic the inefficient (efficient) provider:

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The optimal contract depends on the degree of altruism. Let $Ψ(q¯)≡C(q¯,θ¯)−C(q¯,θ_)>0$ be the gain for the efficient provider from pretending that she is inefficient. A first key result is that for moderate altruism, that is, $α^≡C(q¯f,θ¯)−C(q¯f,θ_)B(q_f)−B(q¯f)≤α≤C(q_f,θ¯)−C(q_f,θ_)B(q_f)−B(q¯f)≡α¯$, the full-information contract with no informational rents can be implemented. Under this contract profits are zero, $π_f=π¯f=0$, and quality is such that the marginal benefit is equal to the weighted marginal cost

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and the more efficient provider has higher quality, $q_f>q¯f$. Transfers are equal to the cost of treatment, $T_∗=C(q_f,θ_)$, $T¯∗=C(q¯f,θ¯)$. The intuition for this key result is as follows. The efficient provider does not mimic the inefficient one, because the higher quality gives extra utility due to altruism. The inefficient provider does not mimic the efficient one because it is too costly to do so.

The results are different when altruism is low, and $0<α<α^$ and in line with the traditional model without altruism (Baron & Myerson, 1982; Laffont & Martimort, 2003). The altruistic motive is not enough to prevent the efficient provider to pretend being inefficient. The optimal quality of the inefficient type is distorted downward. It can be shown that the quality of the efficient provider is also distorted but upward, which is in contrast with the traditional model where “no distortion at the top” arises (and the quality of the efficient provider is not distorted even in the presence of private information). Due to the provider being altruistic, information rents can also be reduced by distorting upward the quality of the efficient provider. The efficient type may hold an informational rent. The inefficient type holds zero rent.

If altruism is high and $α>α¯$ then it is the inefficient provider who has an incentive to mimic the efficient provider to be able to provide the higher quality. In turn, it can be shown that this implies that the purchaser has to distort both qualities and may need to leave a rent to the inefficient type.

A critical role in the analysis is played by the limited liability constraint, $π(θ)≥0$. The earlier analysis by Jack (2005) shows that if only the participation constraints need to be binding, then the incentive scheme is high powered, and as in the traditional model, the efficient provider always has an incentive to mimic the inefficient one.

## Policy Implications

Overall, the analysis provides good news in terms of policy. It suggests that for intermediate ranges of altruism, it may be possible to implement incentive schemes that encourage more able providers to provide higher quality without holding informational rents: the transfers to providers simply reflect the cost of quality provision. Therefore, P4P schemes that encourage quality provision do not need to be high powered with more efficient providers making strictly positive profits. The result has also positive equity implications, because there will be a smaller dispersion in quality across providers under this scheme, compared to a higher-powered one.

# Public Reporting and Reputation Concerns

We have mentioned that there is a proliferation of quality measures that can be used to give financial incentives to improve quality either directly, through pay-for-performance schemes (“Pay-for-Performance”), or indirectly through higher demand (“Quality and Cost Containment”). In this section we discuss whether the mere publishing of quality indicators in the public domain can affect behavior even when demand is completely inelastic to quality and no P4P scheme is in place. The argument is that providers may still care about their image in front of society—patients and their family and friends, doctors’ peers—and less motivated providers may make additional effort to improve quality as a result. The model is based on Olivella and Siciliani (2017).

## The Provider

As usual we define $q$ as quality of care. The players are a doctor, a third-party payer (a public or private insurer), and society. Doctors differ in altruism, which takes two values $α∈{α_;α¯}$ with $α_<α¯$, and altruism is private information. We refer to the more altruistic provider as the good doctor, and to the less altruistic provider as the bad doctor. The prior probability that the doctor is good is common knowledge and equal to $γ≥0$. Both types of doctor have the same costs of providing quality, $C(q)$, with $Cq>0$ and $Cqq≥0$, and include both monetary and nonmonetary costs (e.g., diagnostic effort and time spent with the patient).

Patients observe quality and update their beliefs to decide whether the doctor is good or not. We denote these (posterior) beliefs as $γS(q)$, which is the probability that the doctor is good after observing quality $q$. The expected type of a doctor is given by $αS(q)=γS(q)×α¯+(1−γS(q))×α_$. If there is no updating, then the expected type is simply the expected type in doctors’ population ($E(α)=γα¯+(1−γS)α_$). If updating occurs such that the doctor is good (bad), then the expected type is $α¯$ ($α_$) and $γS=1$ ($γS=0$).

Doctors’ utility function is given by

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where $V(q)=π(q)+αB(q)$ is the sum of profits and the altruistic component, and doctors profits are $π(q)=T−C(q)$, where $T$ is a lump-sum payment (e.g., capitation).

Differently from other sections, we allow doctors to care about their own reputation. The parameter $R$ conveys the extent to which the doctor cares about what others think of her. This reputation component is more important the larger is the number of people who directly learn about the quality of the doctor’s care through family, friends, word of mouth, and social networks. Reputation can also be affected by policy. Policymakers can change and amplify reputational concerns by publishing and disseminating an extensive range of quality indicators through websites, newspapers, and leaflets. The model assumes that if no new information is revealed by the quality provided by the doctor, then the doctor’s reputation remains the same. If all doctors provide the same quality, quality is not informative and there is no reputational gain or loss. If observing some (low) quality generates posterior beliefs that the doctor is bad, then the reputational payoff is negative.

The equilibrium concept to solve the model is the Perfect Bayesian Equilibrium (PBE). Beliefs are restricted to satisfy two properties: Monotonicity (beliefs on altruism are not decreasing in quality) and Pessimism (beliefs for out-of-equilibrium actions are the most pessimistic). These imply that society does not raise its beliefs that the doctor is good when observing quality levels that are higher than the quality chosen by the good doctor in equilibrium. Even imposing monotonicity and pessimism, there is a large multiplicity of PBEs. We focus on equilibria where the good doctor chooses the quality that maximizes the non-reputational payoff, $V(q)$, and the bad doctor may mimic such quality.

## The Purchaser

The choice variable of the purchaser is the extent to which disseminating quality indicators in the public domain affects the parameter $R$. Define $q∗(α)$ as the quality level satisfying $αBq=Cq$, that is, the optimal quality of doctor with altruism $α$ facing no reputational concerns. If reputational concerns are small (for $0≤R≤τ=[V(q∗(α_)|α_)−V(q∗(α)|α_))]/(α¯−α_)$), a separating equilibrium arises where the good doctor provides a higher quality than the bad doctor, $qE(α¯)=q∗(α¯)>qE(α_)=q∗(α_)$. The good doctor enjoys a reputation gain while the bad doctor suffers a reputation loss. The parameter $τ$ conveys the cost of the bad doctor of disguising as a good doctor.

If reputational concerns are high (for $R≥τ/γ$), a pooling equilibrium arises where the bad doctor has an incentive to mimic the good doctor, $qE(α¯)=qE(α_)=q∗(α¯)$. Because doctors provide the same quality, observing the high quality is not informative and patients (and society) cannot distinguish between good and bad doctors: neither type of doctor gains or loses any reputation. The bad doctor suffers a mimicking cost, which he is willing to incur to avoid a reputation loss. If reputational concerns are intermediate (for $τ), a semi-separating equilibrium arises where the good doctor provides the high quality and the bad doctor randomizes between high and low quality.

## Policy Implications

Consider a policy that introduces public reporting. In the status quo there is limited availability of quality reports; the reporting, if it occurs, is at a higher organization level so that doctors do not feel directly exposed to this information; and the reports are difficult to access and not widely disseminated. With public reporting, there is a plethora of quality metrics; these are provided at doctor level and are widely disseminated through websites, newspapers, and leaflets. The analysis suggests that such policies will have the intended effect of raising quality by amplifying nonmonetary reputational concerns, and this arises even in the absence of monetary mechanisms (that is, quality measures do not affect patient demand and when they are not directly used to pay the provider for higher quality).

# Gaming

We have so far assumed that healthcare payment systems, either a DRG payment for hospitals or P4P schemes, are robust and independent from provider behavior. In practice, healthcare payment systems are complex and such complexity can be used to the provider advantage, for example by allocating patients to most remunerative tariffs, which is sometimes referred to as upcoding. More broadly any payment system is based on some measure of performance. These are often based on activity reports from the provider and as such may be subject to payment manipulations. Common forms of gaming or manipulation include billing services that were not delivered, upcoding of services into more complex diagnostic groups with higher tariffs, splitting or unbundling of a treatment episode into separate ones that lead to additional reimbursement. In these instances, the purchaser pays for activity at excessive rates.

In this section we explore the implication of gaming for the design of the incentive scheme. Does the presence of game imply that it is not optimal to pay hospitals through a fixed price scheme? If a price system is to be retained, how does gaming affect the optimal price? To address these questions we provide a stylized model based on Kuhn and Siciliani (2013), which expands the analysis in “Quality and Cost Containment” by allowing the provider to game the system.

## The Provider

Define $n$ as the reported number of patients treated, $q$ as quality of treatment and $m$ as a measure of upcoding effort. We assume, as in “Quality and Cost Containment,” that higher quality increases demand and therefore the reported number of patients treated $n(q,m)$, with $nq>0$. Higher manipulative effort also increases reported output, for example by stimulating unnecessary treatments, splitting cases and upcoding, $nm>0$. The provider receives from the purchaser a tariff $p$ for each unit of output provided and a lump-sum transfer (or fixed budget component) $T$. The monetary and nonmonetary cost is $C(n(q,m),q,m)=C(q,m)$, with $Cq=∂C/∂q+(∂C/∂n)nq>0$, $Cm=∂C/∂m+(∂C/∂n)nm≥0$. Quality raises costs both directly and indirectly through triggering a higher number of cases. Manipulation has a direct effect on cost and possibly an indirect effect through higher activity.

We allow for the provider being subject to an audit either from the purchaser or a contracted auditor. We assume, realistically, that audits are not always informative: the auditor may not find manipulation even when there is some (type 1 error). We define $a$ as audit intensity, with higher intensity translating into a higher probability of the audit being informative. Upon discovery of manipulation, the provider is fined according to an exogenous function $ϕ(m)$, with the fine increasing with the degree of manipulation uncovered, $ϕm≥0$.

Providers maximize their expected surplus $U=T+pn(q,m)−C(q,m)−aϕ(m)$, where $aϕ(m)$ denotes the expected fine. The optimal number of reported patients treated and manipulation are

$Display mathematics$
(28)

$Display mathematics$
(29)

The reported output $nc$ is chosen to equalize price with marginal cost. The level of manipulation $mc$ is such that the marginal cost savings from a reduction in quality are equal to the expected marginal cost from manipulation, which includes the direct cost of manipulative effort and the increase in the expected fine.

## The Purchaser

The purchaser’s benefit is given by the function $B(q)$, and encompasses both direct benefits from higher quality and indirect benefits (through higher demand, as in “Quality and Cost Containment”). The audit cost function is $K(a)$, which exhibits positive and increasing marginal cost, $Ka≥0$, $Kaa>0$. A low auditing intensity, for instance, would involve an administrator browsing through a provider’s billing accounts checking for inconsistency in DRG assignment. A high audit intensity would correspond to an expert team for an in-depth look at the financial reports. We assume that a share $S∈[0,1]$ of the fine is reinstituted to the purchaser.

We assume that the purchaser can commit to an audit intensity. The purchaser chooses price and audit intensity, taking into account its effect on provider reported output, quality, and manipulation. The purchaser maximizes the sum of the benefit and expected share of the fine net of the audit cost and transfer to the provider. After substituting for the participation constraint, we can write the purchaser problem as

$Display mathematics$
(30)

where $qc(p,a)$ and $mc(p,a)$ are the provider’s best responses. Optimal price and audit intensity satisfy:

$Display mathematics$
(31)

$Display mathematics$
(32)

The optimal intensity of the audit is such that the marginal benefit from a lower level of manipulation equals its marginal cost. The marginal benefit includes two components. First, a greater audit intensity reduces costly manipulation. Second, audit intensity may change also the provision of quality. Because there is under-provision of quality in the presence of manipulation, that is, $Wq>Cq$, the marginal benefit from auditing is reduced (increased) if quality and manipulation are complements (substitutes). The marginal cost of auditing includes the marginal audit cost, $Ka$, and the marginal loss on fines, $(1−S)ϕ(m)$.

The optimal price in the absence of manipulation ($∂mc/∂p=0$) reduces to $pc=Wq/nq$, and is proportional to the marginal benefit of quality and to the inverse of the responsiveness of output to quality (as in “Quality and Cost Containment”). The presence of manipulation reduces the optimal price, $pc. More broadly it reduces the power of the incentive scheme. Because manipulation is wasteful and increases overall costs of provision, the purchaser finds it optimal to reduce the price to contain manipulation. It is straightforward to see this when the purchaser cannot recover the fines, that is, $S=0$. But it is possible to show that the result still holds in the general case $(0≤S≤1)$ where the purchaser can recover part or all of the fines (as the term in the numerator is a second order effect).

This model assumes a representative hospital. Kuhn and Siciliani (2013) investigate the effect of manipulation on the power of the incentive scheme when providers differ in costs along some unobserved dimensions, in a set-up similar to “Provider Unobserved Heterogeneity.” They show that the presence of manipulation can provide a rationale for quality ceilings. Despite being derived in a very different set-up, this results also suggests that the presence of manipulation broadly reduces the power of the optimal incentive scheme.

## Policy Implications

The key policy insight of this section is that the optimal price used to pay the provider is lower in the presence of gaming. Higher prices induce the provider to improve quality and treat more patients, but also to game more. The presence of gaming can be mitigated by auditing mechanisms that reduce the scope for gaming. But auditing itself is a costly activity for the purchaser, and therefore the benefits from lower gaming have to be traded off against the cost of auditing. Health systems that can rely on efficient and effective auditing mechanisms are likely to benefit from less gaming and will be able to use prices to a greater extent. The result that gaming implies a lower-powered incentive scheme is analogous to the result obtained for pay-for-performance schemes where qualities are substitutes. The mechanism is, however, different. Gaming, an unobserved provider action, generates no benefits to the purchaser but increases costs. It is such higher cost that makes it optimal to reduce the price. With multitasking, unobserved quality generates benefits to patients, and it is the concern about potential reductions in benefits that makes it optimal to reduce the price.

# Conclusions

This section draws the main policy lessons of this article in relation to three policy objectives, namely cost containment, quality, and allocative efficiency (i.e., treating the appropriate number of patients). We discuss each of these three in turn. In relation to cost containment, fixed price regulation induces prima facie strong incentives to contain costs. Given providers are residual claimants and can appropriate or reinvest surpluses, any effort to contain costs will translate into a higher financial surplus, giving them strong incentives to contain costs.

There is, however, one important caveat. Patients can receive different treatments within the same diagnosis, and within the same treatment or diagnosis they may be classified as with or without comorbidities and complications. Fixed tariffs (of the DRG type) differ across treatments and severity groups, and this is even more so as they are continuously refined to reflect finer cost groups. In turn, this gives a financial incentive to providers to either provide more expensive treatments with higher markups or to classify patients in the more remunerative groups. This may contribute as a result to higher growth in health expenditure.

The rationale for splitting DRGs into finer groups is that this allows prices to better reflect costs, reduce uncertainty, and avoid providers being exposed to losses or to gain rents. Hospitals are, however, large organizations, and this concern is diminished for hospitals with large volumes of patients within a DRG or across many DRGs. Regulators may therefore want to refrain from further refining DRG prices and to restrict them to those with low expected volumes with a high variance in costs. Auditing or monitoring mechanisms may also need to be put in place to minimize the extent of these practices, though these regulatory interventions are likely to be expensive.

In relation to quality, fixed price payment of the DRG type can give incentives to increase quality, but these are likely to be weak in particular for countries with tighter capacity constraints. We have shown that incentives to provide quality will be stronger the higher is the demand elasticity to quality and the higher is the price paid for each patient treated. The intuition is simple. Providers that increase quality can attract more patients and will be rewarded so with higher revenues and financial surpluses (if prices are strictly above marginal treatment costs). But the empirical literature suggests that the demand elasticity to quality is low, and so will be the incentive to increase quality. Although the regulator could potentially compensate a lower demand elasticity by setting a higher price, this is not what we observe in practice. DRG payment systems are based on average-cost pricing rules, and I am not aware of policy examples that include demand elasticity considerations into the price setting. The incentive to provide quality is likely to be weaker for systems with large excess demands that translate into long waiting lists. In the presence of excess demand, hospitals do not need to attract additional patients, and any attempt to do so will translate into longer waiting times.

The limited ability of DRG payments to sustain quality improvements may be the reason for policymakers to increasingly pay for quality directly. The development of information technology has allowed the construction of a plethora of quality indicators, mostly process measures of quality and in some cases health outcomes. These incentive schemes raise new issues. A key concern in this area is that pay-for-performance schemes might divert provider attention so that unincentivized dimensions of quality might suffer as a result. Further refining the quality metrics can ensure that no important dimensions of quality remain unmeasured. There are some concerns that so far such incentive schemes, with few exceptions, have led to relatively small quality improvements though that may be the result of the relatively low prices attached to such schemes. The idea of paying directly for quality seems attractive, but it remains to be seen the extent to which these schemes can be usefully employed.

The development of quality metrics can also serve other purposes. A number of quality measures are increasingly available in the public domain through websites and other media, and this may help patients to compare hospitals. It may also induce providers to compare each other’s performance, and put pressure on low-performing providers to catch up and engage in dialogues with high-performing ones to identify best practices. It has also the advantage of improving transparency and accountability to the general public.

In relation to the last policy objective, that is, to treat the appropriate number of patients, the analysis highlights that fixed price systems give financial incentives to avoid costly patients. This is particularly a concern when costly patients are also those who benefit more from health care. The issue is potentially mitigated in the presence of altruistic motives, and additional payments for cost outliers. But regulators may want to target DRGs with high positive correlation between benefits and costs and introduce additional regulation either through payment corrections or auditing mechanisms. Finally, hospitals may differ systematically in some dimensions of costs, which are beyond their control (e.g., higher cost of living). Prices need to reflect such differences, at least to some extent, with greater corrections in the presence of steeper marginal benefit curve and higher inequality aversion.

Fixed price regulation remains at the core of paying healthcare providers, and this is likely to remain so in the future. There are several advantages from fixed price regulation but also great scope for further improvements.

Barros, P. P., & Martinez-Giralt, X. (2002). Public and private provision of health care. Journal of Economics and Management Strategy, 11(1), 109–133.Find this resource:

Barros, P. P., & Martinez-Giralt, X. (2008). Selecting health care providers: “Any willing provider” vs. negotiation. European Journal of Political Economy, 24(2), 402–414.Find this resource:

Barros, P. P., & Olivella, P. (2005). Waiting lists and patient selection. Journal of Economics and Management Strategy, 14, 623–646.Find this resource:

Biglaiser, G., & Ma, C. T. (2007). Moonlighting: Public service and private practice. RAND Journal of Economics, 38(4), 1113–1133.Find this resource:

Di Giacomo, M., Piacenza, M., Siciliani, L., & Turati, G. (2017). Do public hospitals respond to changes in DRG price regulation? Health Economics, 26(S2), 23–37.Find this resource:

Jack, W. (2005). Purchasing health care services from providers with unknown altruism. Journal of Health Economics, 24(1), 73–93.Find this resource:

Januleviciute, J., Askildsen, J. E., Kaarboe, O., Siciliani, L., & Sutton, M. (2016). How do hospitals respond to price changes? Evidence from Norway. Health Economics, 25, 620–636.Find this resource:

Longo, F., Siciliani, L., & Street, A. (forthcoming). Are costs differences between specialist and general hospitals compensated by the prospective payment system? European Journal of Health Economics.Find this resource:

Ma, C. T. (2003). Public rationing and private cost incentives. Journal of Public Economics, 88, 333–352.Find this resource:

Ma, C. T., & Grassi, S. (2011). Optimal public rationing and price response. Journal of Health Economics, 30, 1197–1206.Find this resource:

Ma, C. T., & Mak, H. (2014). Public report, price, and quality. Journal of Economics & Management Strategy, 23, 443–464.Find this resource:

Makris, M., & Siciliani, L. (2013). Optimal Incentive Schemes for Altruistic Providers. Journal of Public Economic Theory, 15(5), 675–699.Find this resource:

Siciliani, L. (2006). Selection of treatment under prospective payment systems in the hospital sector. Journal of Health Economics, 25, 479–499.Find this resource:

Siciliani, L. (2007). Optimal contracts for health services in the presence of waiting times and asymmetric information. The B.E. Journal of Economic Analysis & Policy, 40, 1–25.Find this resource:

Street, A., Mason, A., Miraldo, M., & Siciliani, L. (2009). Should prospective payments be differentiated for public and private healthcare providers? Health Economics, Policy and Law, 4, 383–403.Find this resource:

## References

Aletras, V. H. (1999). A comparison of hospital scale effects in short-run and long-run cost functions. Health Economics, 8, 521–530.Find this resource:

Baron, D., & Myerson, R. (1982). Regulating a monopolist with unknown costs. Econometrica, 50, 911–930.Find this resource:

Barros, P. P., & Martinez-Giralt, X. (2006). Models of negotiation and bargaining in health care. In A. Jones (Ed.), The Elgar companion to health economics (chap. 21, pp. 231–239). Cheltenham, UK: Edward Elgar.Find this resource:

Besley, T., & Ghatak, M. (2005). Competition and incentives with motivated agents. American Economic Review, 95, 616–636.Find this resource:

Besley, T., & Ghatak, M. (2006). Sorting with motivated agents: Implications for school competition and teacher incentives. Journal of the European Economics Association (Papers and Proceedings), 4, 404–414.Find this resource:

Brekke, K., Gravelle, H., Siciliani, L., & Straume, O. R. (2014). Patient choice, mobility and competition among health care providers. In R. Levaggi & M. Montefiori (Eds.), Health care provision and patient mobility (pp. 1–26). Developments in Health Economics and Public Policy 12. Milan, Italy: Springer-Verlag.Find this resource:

Cashin, C., Chi, Y.­L., Smith, P., Borowitz, M., & Thomson, S. (2014). Paying for performance in healthcare: Implications for health system performance and accountability. Buckingham, UK: Open University Press.Find this resource:

Chalkley, M., & Malcomson, J. M. (1998a). Contracting for health services with unmonitored quality. Economic Journal, 108, 1093–1110.Find this resource:

Chalkley, M., & Malcomson, J. M. (1998b). Contracting for health services when patient demand does not reflect quality. Journal of Health Economics, 17, 1–19.Find this resource:

Choné, P., & Ma, C. A. (2011). Optimal health care contracts under physician agency. Annales d’Economie et de Statistique, 101/102, 229–256.Find this resource:

Dafny, L. S. (2005). How do hospitals respond to price changes? American Economic Review, 95, 1525–1547.Find this resource:

De Fraja, G. (2000). Contracts for health care and asymmetric information. Journal of Health Economics, 19(5), 663–677.Find this resource:

Delfgaauw, J., & Dur, R. (2007). Signaling and screening of workers’ motivation. Journal of Economic Behavior and Organization, 62, 605–624.Find this resource:

Delfgaauw, J., & Dur, R. (2008). Incentives and workers’ motivation in the public sector. Economic Journal, 118, 171–191.Find this resource:

Drummond, M. F., Sculpher, M. J., Claxton, K., Stoddart, G. L., & Torrance, G. W. (2015). Methods for the economic evaluation of health care programmes (4th ed.). Oxford, UK: Oxford University Press.Find this resource:

Eggleston, K. (2005). Multitasking and mixed systems for provider payment. Journal of Health Economics, 24, 211–223.Find this resource:

Ellis, R. (1998). Creaming, skimping and dumping: Provider competition on the intensive and extensive margins. Journal of Health Economics, 17, 537–555.Find this resource:

Ellis, R. P., & McGuire, T. (1986). Provider behavior under prospective reimbursement: Cost sharing and supply. Journal of Health Economics, 5, 129–151.Find this resource:

Farrar, S., Yi, D., Sutton, M., Chalkley, M., Sussex, J., & Scott, A. (2009). Has payment by results affected the way that English hospitals provide care? Difference-in-differences analysis. British Medical Journal, 339, b3047.Find this resource:

Folland, S., Goodman, A. C., & Stano, M. (2004). The economics of health and health care. Upper Saddle River, NJ: Prentice Hall.Find this resource:

Francois, P. (2000). “Public service motivation” as an argument for government provision. Journal of Public Economics, 78, 275–299.Find this resource:

Gaynor, M. (2007). Competition and quality in health care markets. Foundations and Trends in Microeconomics, 2, 441–508.Find this resource:

Gaynor, M., & Town, R. (2011). Competition in health care markets. In M. Pauly, T. McGuire, & P. P. Barros (Eds.). Handbook of health economics (pp. 499–637). Amsterdam, The Netherlands: North-Holland.Find this resource:

Hafsteinsdottir, E., & Siciliani, L. (2010). DRG prospective payment systems: Refine or not refine? Health Economics, 19, 1226–1239.Find this resource:

Holmstrom, B., & Milgrom, P. (1991). Multitask principal-agent analyses: Incentive contracts, asset ownership, and job design. Journal of Law, Economics and Organization, 7, 24–52.Find this resource:

Kaarboe, O., & Siciliani, L. (2011). Quality, multitasking and pay for performance. Health Economics, 2, 225–238.Find this resource:

Kifmann, M., & Siciliani, L. (2017). Average-cost pricing and dynamic selection incentives in the hospital sector. Health Economics, 26(12), 1566–1582.Find this resource:

Kristensen, S., Siciliani, L., & Sutton, M. (2016). Optimal price-setting in pay for performance schemes in health care. Journal of Economic Behavior & Organization, 123, 57–77.Find this resource:

Kuhn, M., & Siciliani, L. (2009). Performance indicators for quality with costly falsification. Journal of Economics and Management Strategy, 18, 1137–1154.Find this resource:

Kuhn, M., & Siciliani, L. (2013). Manipulation and auditing of public sector contracts. European Journal of Political Economy, 32, 251–267Find this resource:

Laffont, J. J., & Martimort, D. (2003). The theory of incentives: The principal-agent model. Princeton, NJ: Princeton University Press.Find this resource:

Laffont, J. J., & Tirole, J. (1993). A theory of incentives in procurement and regulation. Cambridge, MA: MIT Press.Find this resource:

Ma, C. A. (1994). Health care payment systems: Cost and quality incentives. Journal of Economics & Management Strategy, 3, 93–112.Find this resource:

Makris, M. (2009). Incentives for motivated agents under an administrative constraint. Journal of Economic Behavior and Organization, 71, 428–440.Find this resource:

Malcomson, J. M. (2005). Supplier discretion over provision: Theory and an application to medical care. RAND Journal of Economics, 36, 412–432.Find this resource:

McGuire, T. (2000). Physician agency. In A. Culyer & J. P. Newhouse (Eds.), Handbook of health economics (pp. 461–536). Amsterdam, The Netherlands: Elsevier.Find this resource:

Miraldo, M., Siciliani, L., & Street, A. (2011). Price adjustment in the hospital sector. Journal of Health Economics, 30, 112–125.Find this resource:

Mougeot, M., & Naegelen, F. (2005). Hospital price regulation and expenditure cap policy. Journal of Health Economics, 24, 55–72.Find this resource:

Olivella, P., & Siciliani, L. (2017). Reputational concerns with altruistic providers. Journal of Health Economics, 55, 1–13.Find this resource:

Prendergast, C. (2007). The motivation and bias of bureaucrats. American Economic Review, 97, 180–196.Find this resource:

Siciliani, L. (2009). Pay for performance and motivation crowding out. Economics Letters, 103, 68–71.Find this resource:

Siciliani, L., & Stanciole, A. (2013). Bargaining and the provision of health services. European Journal of Health Economics, 14, 391–406.Find this resource:

Silverman E., & Skinner, J. (2004). Medicare upcoding and hospital ownership. Journal of Health Economics, 23, 369–389.Find this resource:

Sutton, M., Elder, R., Guthrie, B., & Watt, G. (2010). Record rewards: The effect on risk factor monitoring of the new financial incentives for UK general practices. Health Economics, 19, 1–13.Find this resource:

Wagstaff, A., & van Doorslaer, E. (2000). Equity in healthcare finance and delivery. In A. J. Culyer & J. P. Newhouse (Eds.), Handbook of health economics (pp. 1803–1862). Amsterdam, The Netherlands: Elsevier.Find this resource:

Whalley, D., Gravelle, H., & Sibbald, B. (2008). Effect of the new contract on GPs’ working lives and perceptions of quality of care. British Journal of the General Practice, 58(546), 8–14.Find this resource: