Physician Behavior under Prospective Payment Schemes-Evidence from Artefactual Field and Lab Experiments.

Recent experimental studies analyze the behavior of physicians towards patients and find that physicians care for their own profit as well as patient benefit. In this paper, we extend the experimental analysis of the physician decision problem by adding a third party which represents the health insurance that finances medical service provision under a prospective payment scheme. Our results show that physicians take into account the payoffs of the third party, which can lead to underprovision of medical care. We conduct a laboratory experiment in neutral as well as in medical framing using students and medical doctors as subjects. Subjects in the medically framed experiments behave weakly and are more patient orientated in contrast to neutral framing. A sample of medical doctors exhibits comparable behavior to students with medical framing.

1. Introduction

Understanding physicians’ reactions to incentives is crucial for the design of health care markets. In the seminal theory works on physician behavior of Arrow [1] and later McGuire [2], physicians are modeled to face a trade-off between personal profit and patient health. Following these early theoretical approaches, this trade-off has since been analyzed in empirical research (see Chandra et al. [3] for an introduction). Recent studies show that physicians perform more invasive treatments if this increases reimbursement [4,5] and increase consultation frequency not to improve treatment quality but to increase reimbursement [6]. There is also a growing amount of literature on experiments in health economics which shows that subjects playing the physician’s role care for patients to different extents [7,8,9,10,11,12].

Seminal laboratory experiments on physician behavior focus on settings, where physicians face a trade-off between their own payoff and patient well-being (see for example Hennig-Schmidt et al. [7], Brosig-Koch et al. [13], and Di Guida et al. [14]). These experiments are mainly conducted using medical framing and student subject pools. In this paper, we contribute to the growing experimental literature on physician behavior in three ways: First, we extend the physician decision problem by adding an insurer that finances medical service provision. Second, we conduct our laboratory experiment in neutral as well as medical framing to identify behavioral effects of contextual framing. Third, our subject pool consists of students as well as medical doctors which allows us to analyze whether professional experience in the relevant area influences decisions in the lab.

The division between receivers of services (patients) and those who pay for it (usually a health insurance) is an important feature of many health care systems. Such a third party that finances medical care does not only influence patients’ demand for services (most notably through moral hazard), but also the quality and quantity of care physicians supply. In their model of physician behavior, Chandra and Skinner [15] assume that medical care—although not payed for by the patient—is always subject to constraints, for example, to a lack of resources or ethical norms against spending too many resources. A qualitative study by Hassell et al. [16], a survey by Tilburt et al. [17], and a discrete choice experiment by Pedersen et al. [18] all indicate that physicians take into account the costliness of their services and the scarcity of available resources for treating patients. We analyze physician behavior when an insurer finances medical service provision. This extends the seminal works of Hennig-Schmidt et al. [7] and Brosig-Koch et al. [13] which focus on the bilateral relationship between physicians and patients, in particular with respect to physician payment schemes. We add an insurer that provides a budget for treatment. Such a change can influence individual decisions in experiments as the number of affected agents increases [19,20]. We model the financing of medical care as a prospective payment scheme (PPS) where the budget physicians can spend is determined by the patient’s diagnosis. In most PPS, physicians report patient type by ICD-codes and receive a budget based on a classification algorithm ([21], p. 43ff.). This is not the only common way to organize hospital reimbursement, and physician behavior under PPS has also been subject to many economic studies (e.g., Davis and Rhodes [22], Moreno-Serra and Wagstaff [23], Cutler [24]). The evidence is accruing that physicians over-report patient severity under PPS in order to increase reimbursement (see results from administrative data in Dafny [25], Silverman and Skinner [26], Jürges and Köberlein [27], Fang and Gong [28], Reif et al. [29], and the recent laboratory experiment by Hennig-Schmidt et al. [30]). There is however mixed evidence on whether the extra reimbursement is used to improve care, enrich the physician, or both. We contribute to the literature by modeling the patient–physician–insurance relationship with a PPS to analyze physician behavior in such a more complex decision problem. More specifically, our physicians observe a patient’s medical needs and report the severity of the patient’s sickness to the insurer. The insurer then provides a budget for treatment dependent on the reported diagnosis. In turn, this budget can be spent by the physician to provide medical care to the patient. As the physician is the only agent that makes decisions in our setting, we technically implement a three-person dictator game. Among the first to implement such a design were Charness and Rabin [31] as well as Engelmann and Strobel [32] who find that dictators want to avoid extreme inequality among the subjects. In a meta-study on dictator games, Engel [33] finds that dictators in total give more if there is more than one recipient.

The choices of subject pool and framing are crucial for the design of economic experiments. In studies that analyze physician behavior, the most common choice is a student subject pool with medical framing (See, for example, Lagarde and Blaauw [34], Brosig-Koch et al. [9], Brosig-Koch et al. [35], Brosig-Koch et al. [13], Keser et al. [10], Hennig-Schmidt et al. [7], and Kairies and Krieger [36]). Abbink and Hennig-Schmidt [37] and Gneezy et al. [38] emphasize that contextual framing has advantages as well as disadvantages, and therefore the framing choice depends on the underlying question. In particular for studies on physician behavior, framing might induce experimental subjects to behave as they expect physicians to behave [39]. However, neutral framings might induce varying contexts in the subjects’ mind, which can affect decisions but are unobservable to the researcher. For example, Kimbrough and Vostroknutov [40] find that individual norms correlate with pro-social behavior and Kesternich et al. [41] show in an experiment with medical students that changing perceived context by inducing professional norms influences how subjects distribute stakes between group members. We therefore want to explicitly analyze how changing context framing affects behavior in laboratory experiments. When it comes to choosing a subject pool, Harrison and List [42] suggest that not only students but also professionals should take part in experimental studies. The results from Brosig-Koch et al. [35] show that in the experimental analysis of physician behavior the decisions of business and economics students are similar to those of medical doctors. In contrast, Wang et al. [43] find that medical doctor subjects provide less patient benefit. In general, Engel [33] shows that non-student subjects give more in dictator games. We contribute to both the discussion on framing as well as on subject pool by conducting our experiment with three different subject pools: a student sample in neutral framing, a student sample with medical framing, as well as a sample of medical doctors with medical framing.

We find that physicians trade-off between their own payoff and patient utilities as well as the payoff of the third party. Additionally, we show that concern for patients is higher when the experiment is framed in a medical context. Our results also suggest that medical doctors behave similar to students in laboratory experiments.

The remainder of the paper is structured as follows. In the next Section 2, we introduce our experimental design. The results from our experiments are presented in Section 3, and in the final part Section 4 we conclude.

2. Experimental Design

We conduct artefactual field and lab experiments to analyze physician behavior. Physicians observe the medical needs of a Patient, report the severity of his/her illness to an Insurer, and use the budget from the Insurer to provide Medical Services to the Patient. The third party that finances the Medical Service provision and the related reporting stage are the two main design extensions to the seminal works of Hennig-Schmidt et al. [7] and Brosig-Koch et al. [13], where physicians observe patient severity and then directly provide Medical Services.

2.1. Framing and Subject Pool

In order to identify behavioral effects of framing, we conduct our experiment in a neutral setting as well as in a setting with medical context. Subjects in our experiment take on the roles of either Patients, Physicians, or Insurer. Naming of participant types varies between neutral and medical framing. We call them Participant A, B, and C in the neutral framing, whereas in the medical framing we call them Patient, Physician, and Insurer, respectively. The framing does not influence the underlying mechanism of the experiment. Therefore, for ease of readability, we will use the medical terms to describe the experimental design. Subjects in our experiment were a sample of students as well as a sample of medical doctors. This allows us to analyze whether professional experience in the relevant area influences the decisions in the lab.

2.2. Group Composition and Roles

At the beginning of each experimental session, we divide subjects randomly and anonymously into groups of three. The group composition remains unchanged throughout the whole experiment. Subjects do not know the other two group members but they know that the composition of the groups will not change during the experiment. There is no interaction across groups, thus the outcomes of the members of one group only depend on the decisions of the members within this group.

Only the Physician makes decisions that can influence his/her own payoff and determines the payoff of the other participants within their group. Patient and Insurer will not make any decisions in the experiment (Hennig-Schmidt et al. [7] and Brosig-Koch et al. [13] operationalize patient needs by giving the patient payoff to charity. While this approach has many advantages, it is less suitable in our setting. It would not make much sense to use charity giving for the insurance and consequently, if only the Patient would be represented by donations to charity, Physician behavior can be influenced by whether they prefer donating to a charity or to another subject in the lab. In order to avoid such incentives, we have all three group members represented by subjects in our lab.).

First, every participant makes decisions, as if he/she was in the role of the Physician. After all participants made their decisions, we announce the random assignment of the participants to the roles of Patient, Physician, and Insurer. Only the decisions of the group member who is assigned to the role of the Physician are payoff relevant for the members of the respective group. The decisions of the participants who are assigned to the roles of Patient or Insurer are irrelevant for the group members (Even though the decisions of the participants who are assigned to the roles of Patient or Insurer are irrelevant for the final payoff of their respective group members, we can use their decisions in a strategy method sense for our analysis of Physician behavior. Although this form of strategy method might itself increase pro-social behavior, it is an unproblematic choice in our setting as we have no reason to believe that the effect of the strategy method differs by treatment. Further, Brandts and Charness [44] show in their survey article that treatment effects obtained from strategy method experiments are also obtained using direct-response designs.).

2.3. Relationship between the Group Members

Physicians have to provide Medical Services to the Patients. The provision of Medical Services is associated with costs and, in order to cover costs, the Physician has to request a budget from the Insurer. Physicians request a budget by reporting information about the Patient to the Insurer and the reported information determines the size of the budget. Subsequently, the Physician decides on how many Medical Services he/she wants to provide to the Patient. Figure 1 illustrates the relationship between the group members.

Figure 1

Relationship between the group members.

2.4. Roles and Payoffs

We will now, step by step, introduce the three roles (Patient, Physician, and Insurer) in detail.

2.4.1. Patient

Every Patient’s payoff can either be 0 or 90 Taler (our experimental currency). The Physician’s decision on the number of Medical Services provided determines the probability to earn 90 Taler. We implemented a probabilistic relationship between Patient payoff and Physician’s decision, as we consider it to be more realistic than a deterministic relationship. In reality, the health outcome of a Patient is influenced by the Physician’s decision to a great extent. However, other factors can also have an influence (e.g., the predisposition of a Patient or the effectiveness of prescribed drugs), in order to ensure in our experimental design that sickness of the Patient after a medical intervention cannot unambiguously be traced back to misbehavior of the Physician. Huck et al. [45] use a similar mechanism and Martinsson and Persson [46] show that Physicians’ decisions are similar in a probabilistic and in a deterministic setting.

The severity of a Patient’s illness can influence Physician behavior [9,29]. In order to allow for such heterogeneity in our experiment, we introduce three types of Patients—low type (L), medium type (M), and high type (H)—which represent different severities of Patient’s illness.

The three types of Patients need different numbers of Medical Services in order to maximize their probability of receiving the payoff of 90 Taler. The highest probability of receiving a payoff is 95%. Two units of Medical Services are optimal for L type Patients, whereas M type Patients need four and H type Patients six units. Providing too many Medical Services is equally harmful for the Patient as providing too few Medical Services. The probability to earn 90 Taler is reduced to 65%/35%/5%, when the number of Medical Services provided is one/two/three or more unit(s) above or below the optimum, respectively.

Table 1 shows the Patient type-specific connection between number of provided Medical Services and the probability to earn 90 Taler.

Table 1

Patient payoff probabilities in %.

		Number of Services Provided
		1	2	3	4	5	6
	L	65	95	65	35	5	5
Patient Type	M	5	35	65	95	65	35
	H	5	5	5	35	65	95

Notes: Patient’s probability to earn 90 Taler for three types of Patients (low type (L), medium type (M) and high type (H)).

At the end of the experiment, the Patient learns about his/her final payoff. The Patient does not learn about his/her type or the number of Medical Services provided by the Physician. We consider this design choice to be a realistic representation of actual doctor–patient relationships where asymmetric information is present. The Patient does not make any decisions in the experiment.

2.4.2. Physician

Every Physician faces the task to provide Medical Services to each Patient type, L, M, and H, consecutively (In each treatment, one-third of the subjects faced the sequence L-H-M, M-L-H, and H-M-L, respectively. To ensure comparability across treatments, we kept this sequence pattern constant for all subjects in all experimental sessions.). The different Patient types are independent—the provision of services to one Patient has no effect on the budget or Medical Service provision of another Patient. The potential number of Medical Services provided is an integer between one and six and is associated with costs. Every unit of Medical Services provided costs 15 Taler. In Table 2, we give an overview on the potential number of Medical Services and the associated costs.

Table 2

Costs of provided services.

	Number of Services Provided
	1	2	3	4	5	6
Costs	15	30	45	60	75	90

In order to cover costs, the Physician has to request a budget by reporting a Patient type to the Insurer (see decision screen on Figure A2). The Physician can report any type of Patient (L, M, or H) independently of the true type of the Patient. Therefore, it is possible to report false information—which we call misreporting (Two recent papers, Hennig-Schmidt et al. [30] and Groß et al. [47], provide an experimental investigation specifically on misreporting by physicians.). Two kinds of misreporting are possible—overreporting and underreporting. Overreporting (underreporting) refers to the case where the Physician reports a higher (lower) type than the true Patient type to the Insurer. An example of overreporting would be if the true Patient type is L whereas the reported type is M. We summarize the possible reporting behavior of the Physician in Table 3.

Figure A2

Reporting stage.

Table 3

Reporting options of the Physician.

		Reported Patient Type
		L	M	H
	L	Truthful	Overreporting	Overreporting
True Patient Type	M	Underreporting	Truthful	Overreporting
	H	Underreporting	Underreporting	Truthful

The reported Patient type determines the assignment to a budget group and therefore the size of the budget, comparable to diagnosis related groups in PPS.

Physician payoff can either be determined by a fee for service payment system (FFS) where the number of Medical Services provided determine the payoff of the Physician or a capitation payment system (CAP), where the payoff of the Physician is independent of the number of Medical Services provided. Under FFS, the Physician receives 15 Taler per unit of Medical Service provided. Under CAP he/she receives 50 Taler in any situation. We present an overview of the two Physician payment systems in Table 4. FFS represents the case where the Physician acts on his/her own bill, while in CAP the Physician receives a fixed wage from a hospital.

Table 4

Physician payoff by service provision.

		Number of Services Provided
		1	2	3	4	5	6
Payment System	Fee For Service	15	30	45	60	75	90
	Capitation	50	50	50	50	50	50

2.4.3. Insurer

One participant in the experiment represents the Insurer, which is endowed with 130 Taler for each Patient in all experimental conditions. Dependent on the Patient type reported by the Physician, the budget for the Physician is withdrawn from the endowment of the Insurer. We implement a budget scheme with two groups, where type L and M Patients are assigned to budget group I (45 Taler), which is sufficient to cover costs for the average Patient of type L or M. This design feature reflects a crucial aspect of many PPS, namely, that costs for an average Patient are reimbursed, and consequently not enough budget is available if Patient severity is at the upper end of a budget group definition. If an H type Patient is reported, budget group II (90 Taler) is provided, which covers the cost for optimal Medical Service provision. In case the budget is not fully spent (Physician reports L/M/H and provides less than 2/4/6 Medical Services), the unused budget benefits none of the three group members. This is comparable to actual PPS, where “unused” budget benefits the hospital in general, but not the physician in charge or the insurer. With this design choice, we shut down the possibility for the Physician to cross subsidize between Patients, where medical service provision choices could be influenced by endogenous preferences towards low or high severity Patients (Actually, PPS are designed in a way where hospitals make profits on some patients and losses on others, and are thus incentivized to reduce average costs. There is also a feedback mechanism which adjusts future budgets to actual average costs that could result in strategic reporting. To keep our experimental design as simple as possible, we leave these channels to future research.).

Table 5 summarizes the information of the budget groups and available budgets dependent on the reported Patient type.

Table 5

Assignment of budget groups and costs for optimal number of services.

(Reported) Type	L	M	H
Costs for optimal service	30	60	90
Budget Group	I		II
Available Budget	45		90

2.5. Physician Decision Problem and Conjectures

In total, we implemented six treatments with different combinations of our experimental variations. Table 6 shows an overview of our treatments including their respective abbreviation and the number of subjects in each treatment.

Table 6

Treatment overview.

Treatment	Payment System	Framing	Subjects	N
CNS	Capitation	Neutral	Students	27
CMS	Capitation	Medical	Students	24
CMD	Capitation	Medical	Doctors	12
FNS	Fee For Service	Neutral	Students	27
FMS	Fee For Service	Medical	Students	27
FMD	Fee For Service	Medical	Doctors	9

An overview of the potential payoffs of Physicians and Insurer, as well as the expected payoffs of the Patient, is given in Table 7.

Table 7

Payoff of subjects.

		Patient Payoff				Physician Payoff			Insurer Payoff
Services Provided		L	M	H		FFS	CAP		L	M	H
1		58.5	4.5	4.5		15	50		85	85	40
2		85.5	31.5	4.5		30			85	85	40
3		58.5	58.5	4.5		45			85	85	40
4		31.5	85.5	31.5		60	50				40
5		4.5	58.5	58.5		75					40
6		4.5	31.5	85.5		90					40

Notes: Payoff of respective subject. Column 1 describes the number of Medical Services provided. Columns 2–4 present the expected Patient payoffs for the respective Patient type. Columns 5–6 show the Physician payoff in the Fee For Service and the Capitation treatments. Columns 7–9 show the Insurer payoff, dependent on the reported Patient type. Dots indicate non-achievable outcomes. The dashed line indicates the possible number of services provided into the amount achievable when the physician reports patient type L or M (1–3 units). When patient type H is reported, the budget is sufficient to provide up to six units of medical services.

We implemented three forms of experimental variation: First, we vary the Physician payment system, which is either dependent (fee for service) or independent (capitation) of the provision behavior of the Physician. This is our baseline variation which is closely related to the previous literature. Second, we use two different types of framing: one introducing a medical context and a neutral one without context. Third, we vary the subject pool, where participants of the experiment are either medical doctors or students.

We now derive conjectures about the behavior of the Physician under our three experimental variations. In all treatments, the payoffs for all three group members are solely determined by the Physician. Reported Patient type is the only factor that affects the payoff for the Insurer, as the assigned budget is subtracted from its initial endowment. The Payoff of the Insurer is therefore independent of subsequent Medical Service provision. Although only the provision of Medical Services affects Physician’s and Patient’s payoffs, the preceding reporting decision plays an indirect role for their payoffs by the possible restriction to the number of affordable Medical Services.

Ultimately, the decisions of the Physician depend on how he/she values the well-being of all three group members. Generally, if he/she attaches a high value to the Payoff of the Insurer, he/she reports a low Patient type. If he/she however attaches a high value to the Patient payoff, he/she reports a type such that the provided budget is sufficient for the optimal number of Medical Services. In the capitation system, the Physician only faces the possible trade-off between Insurer and Patient payoff. In contrast, in the fee for service system he/she also influences her own payoff. If he/she attaches a high value to his/her own payoff he/she will report a high Patient type and subsequently provide a high number of Medical Services. As our Physician payment system induces different personal incentives, we expect participants to behave differently across fee for service and capitation systems. Following the theoretical predictions in Ellis and McGuire [48] and findings from previous health economic experiments [7,11], we expect more overreporting and overprovision of Medical Services in the fee for service system. We do, however, not expect the different payment systems to affect the Physician’s preferences towards either Insurer or Patient payoff (Differences in the reporting and provision behavior in fee for service in contrast to capitation systems that favor either Insurer or Patient payoff can be explained by the presence or absence of own pecuniary incentives of the Physician.).

A fee for service Physician payment system leads ceteris paribus to overprovision of Medical Services, compared to a capitation payment system.

Our second experimental variation affects the presentation of our experimental setting, which is framed either in a neutral or a medical way. In the neutral framing, subjects either face a trade-off between “Participant A” and “Participant C” (capitation) or their own payoff as well as the payoff of “Participant A” and “Participant C” (fee for service). In the medical framing, subjects make decisions which can affect themselves, the Patient, and the Insurer. Findings of an earlier health economic experiment suggest that economics students “[...] allocate in less own payoff maximizing ways [...]” when they are in a medically framed setting ([39], p. 6). We therefore expect the decision of the Physician to be more Patient-oriented in the capitation case by introducing a medical framing compared to the neutral framing, as this is more in line with professional norms of Physicians whose main purpose is to restore the health of her Patients. In line with this, in the fee for service systems we expect that Physicians will behave less selfishly, which leads to lower harm for the Patient compared to neutrally framed fee for service systems.

The medical framing induces ceteris paribus more Patient-oriented behavior, while the neutral framing leads to more selfish, own payoff maximizing behavior.

Our third experimental variation is the subject pool, which consists either of students or medical doctors. With this variation we can test whether the norms induced by the medical framing lead to behavioral differences between students without medical background and trained medical doctors. Brosig-Koch et al. [35] show that medical doctors behave in a similar way as students but are on average more concerned with Patient payoff, while Wang et al. [43] show that medical doctors are slightly less Patient-oriented. As the differences in these two studies were small we expect no difference between subject pools.

Medical doctors behave similarly compared to business and economics students.

2.6. Experimental Protocol

Our computerized experiment was conducted at the Laboratory for Experimental Research (LERN) in Nuremberg, Germany. The experiment was programmed and conducted using z-Tree [49], and ORSEE [50] was used to recruit the student subjects. In total, 105 students and 21 medical doctors participated in our experiment (CNS, FNS—27 students; CMS—24 students; FMS—27 students; CMD—12 medical doctors; FMD—9 medical doctors. The sample size allows for a minimal detectable effect size (MDES) for and of 0.5 for the student samples and a MDES of 0.9 for the doctor sample. This is in the range of effect sizes reported in previous experiments on physician behavior.). The average age of our student sample is 23 years and the average age of our medical doctors is 38 years. We do not observe significant age differences across our treatments for students or medical doctors. In total, 13 medical doctors are male and 8 are female. Sixty-one students are female and while 44 are male.

Our student sample consists mainly of undergraduates in economics and business administration. The medical doctors were recruited at a teaching day of an advanced education program in management, which took place in the same building where our laboratory is located (Approximately 90% of our student sample consists of economics and business administration students and 10% are students in Engineering, Law, or study to become a teacher. A sample of doctors that are about to obtain a business degree is clearly not a representative sample of the doctor population. In the existing literature, real doctors behave in a more patient-oriented manner than students. Results from this selected sample are therefore giving a lower bound on the true effect.). We implemented a between subjects design—each subject participated in one treatment only and each treatment was conducted in a separate session. The experimental procedure was identical for all sessions. Upon arrival at the laboratory, subjects were randomly allocated to partitioned computer terminals and given hard copy instructions (Translated screen shots of the experiment as well as the translated instructions and the control questions can be found in the Appendix C, Appendix D, Appendix E, Appendix F and Appendix G. The original German materials are available upon request.). After having read the instructions, subjects had to answer a set of control questions.

The experiment did not begin until all subjects answered all questions correctly. When subjects revealed a lack of understanding, the experimenters explained the respective problem to them personally. Subjects could take as long as they needed to make decisions, to view result screens, and to complete the control questions. All subjects made their decisions in full anonymity.

Sessions lasted approximately one hour. Earnings were expressed in Taler which were exchanged for cash at the end of the session for 1 EUR per 10 Taler for the student subjects and 4 EUR per 10 Taler for the medical doctor subjects (These different exchange rates are comparable to the implementation of Brosig-Koch et al. [35]. Differences in exchange rates are implemented to account for different opportunity costs of different subject pools.). Student (medical doctor) subjects earned an average of 10.26 (44.57) EUR, including the show-up fee of 4 (16) EUR.

3. Results

In this section, we present the experimental results for physicians provision behavior. We compare the provision behavior across physician payment systems, framings, and subject pools. We continue with a regression analysis in order to compare conditional means of the payoffs for the group members. Results for the corresponding reporting decisions are presented in Appendix A.

3.1. Average Provision Behavior

Figure 2 shows the average deviation from optimal Medical Service provision for each Patient type across the experimental treatments. Here, negative values indicate average underprovision, while positive values indicate average overprovision of Medical Services. As in Figure A1, the first row shows deviation from optimal treatment for the CAP and the second row for FFS. Columns indicate Patient types, and within each subfigure each bar represents students in the neutral framing, students in the medical framing, and doctors in the medical framing, respectively. In the CAP treatments, medical service provision is on average optimal for type L Patients and there is underprovision for M and H Patients, independent of subject pool and framing. For L Patients in the FFS treatments, there is most overprovision for students in the neutral framing and some overprovision for students in the medical framing. If we look at type M Patients, there is some overprovision for students in the neutral framing, on average optimal provision for students in the medical framing and underprovison for the doctor sample. H type Patients receive on average fewer than optimal Medical Services for both student samples and the optimal number of services in the doctor sample.

Figure 2

Average deviation from optimal treatment across experimental conditions. Notes: This figure illustrates average deviation from optimal treatment and 95% confidence intervals across experimental conditions. The values are standardized such that optimal Medical Service provision is 0; positive (negative) values indicate overprovision (underprovision). Each subject decided on the reporting and provision of (medical) services of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9. Table A7, Table A8 and Table A9 (in the Appendix B) contain the average deviation from optimal treatment and tests for significant differences.

Figure A1

Average misreporting across experimental conditions. Notes: This figure illustrates average misreporting and 95% confidence intervals across experimental conditions. Misreporting refers to the case where the reported Patient type differs from the true Patient type. Positive misreporting corresponds to overreporting, while negative misreporting corresponds to underreporting. Each subject decided on the reporting and provision of (medical) services of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9. Table A4, Table A5 and Table A6 (in the Appendix B) contain the average misreporting values and tests for significant differences.

In the following subsections, we present the results in more detail by comparing average provision behavior across experimental conditions. For hypothesis testing, we use Mann–Whitney U tests. First, we focus on the difference between the physician payment systems (Section 3.2), second on the difference between neutral and medical framing (Section 3.3), and third on the difference between student and medical doctor subject pool (Section 3.4).

3.2. Differences between Fee For Service and Capitation

There are clear differences between the physician payment systems in the provision of Medical Services (Table 8). While there is barely any deviation from optimal Medical Service provision for type L Patients in the capitation systems, there is significant overprovision in the fee for service systems in the student samples (CNS 0.04 vs. FNS 2.11 and CMS 0.08 vs. FMS 0.96). Participants from our sample of medical doctors always provide the optimal number of Medical Services for type L Patients.

Table 8

Deviation from optimal treatment between fee for service and capitation.

		Payment System
Patient	Fram.-Subj.	FFS	CAP	U-Test
L	Neutr.-Stud.	2.11	0.04	***
	Med.-Stud.	0.96	0.08	***
	Med.-Doc.	0	0
M	Neutr.-Stud.	0.44	−1	***
	Med.-Stud.	−0.04	−0.83	**
	Med.-Doc.	−0.89	−1.08
H	Neutr.-Stud.	−0.26	−0.63	**
	Med.-Stud.	−0.33	−0.54
	Med.-Doc.	0	−0.75

Notes: Average provision of Medical Services across experimental conditions. Positive values indicate an overprovision of Medical Services. Negative values indicate underprovision of Medical Services. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of misreporting/provided Medical Services between experimental conditions. * p < 0.1, ** p < 0.05, *** p <  0.01. Each subject decided about the reporting and provision of (medical) services of every Patient type. Therefore the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

On average, medical service provision is lower than optimal for type M Patients in all experimental conditions apart from the neutrally framed student sample with fee for service. It is significantly lower for both student samples when the capitation physician payment system was implemented (CNS −1 vs. FNS 0.44 & CMS −0.83 vs. FMS −0.04. This indicates that type M Patients are better off in the fee for service system. However, when we look at the absolute deviations from the optimum, displayed in Table A11 in the Appendix B, we see that this is not the case, as there is both under- and overprovision of Medical Services.).

Table A11

Absolute deviation from optimal treatment of Type M Patients across experimental conditions.

Treatment	Avg. Maltreatment		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	1 ***		CNS
CMS	0.83 ***		CMS
CMD	1.08 ***		CMD
FNS	1.41 ***		FNS	***	***
FMS	1.15 ***		FMS		*
FMD	0.89 ***		FMD				*

Notes:Left table: Average absolute deviation from optimal treatment across treatments. Stars indicate p-values of one-sided t-tests, testing whether the mean absolute provision of medical services differs significantly from 0 (optimal number of provided services). Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided medical services between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

The pattern is similar for our sample of medical doctors, although the difference is not significantly different from zero (CMD −1.08 vs. FMD −0.89). When participants reported truthfully, the available budget is not sufficient to provide the optimal number of services for type M Patients. As many participants reported the true type of type M Patients, it is not surprising to observe high levels of underprovision for type M Patients in the capitation setting.

For type H Patients in the student samples, we observe significant underprovision of services in both payment systems. The underprovision is more pronounced in the capitation system, although the differences are only significantly different from zero in the comparison of the neutrally framed students (CNS −0.63 vs. FNS −0.26), while the difference is small and insignificant for medically framed students (CMS −0.54 vs. FMS −0.33) and insignificant for medical doctors (CMD −0.75 vs. FMD 0). Such underprovision neither benefits the Physician (who receive a fixed income under capitation) nor the Insurer as the budget is withdrawn independent of actual services provided. Harming the Patient by underproviding medical services can thus be seen as a choice that makes the (expected) payoff of all three participants more equal.

We find significant behavioral differences between capitation and fee for service systems, independent of Patient type and framing. Subjects in fee for service systems are more likely to overreport and overprovide for L and M type Patients, while they are less likely to underreport and underprovide for type H Patients. The overall effect sizes of the fee for service payment on medical service provision are 0.93 for students under neutral framing, 0.55 for students under medical framing, and 0.38 for our sample of doctors. Qualitatively, this is in line with the findings of Brosig-Koch et al. [13] and Brosig-Koch et al. [35], although the effect sizes are only half as large in our setting with a third party as well as a second decision stage in our experiment.

The different physician payment systems have a significant influence on the reporting and provision behavior. The fee for service system induces more selfish Physician behavior in the student samples.

3.3. Differences between Neutral and Medical Framing

When we compare the provision behavior between neutral framing and medical framing, the only significant difference we find is for type L Patients in the fee for service setting, where the overprovision of Medical Services is higher in the neutral framing (Table 9). This is in line with results from Kesternich et al. [41] who show that salience of professional norms increases pro-patient behavior of physicians. Our second overall result is therefore:

Table 9

Deviation from optimal treatment between Neutral and Medical Framing.

		Framing
Patient	Payment System	Neutral	Medical	U-Test
L	FFS	2.11	0.96	**
	CAP	0.04	0.08
M	FFS	0.44	−0.04
	CAP	−1	−0.83
H	FFS	−0.26	−0.33
	CAP	−0.63	−0.54

Notes: Analysis only for student subject sample. Average provision of Medical Services across experimental conditions. Positive values indicate an overprovision of Medical Services. Negative values indicate underprovision of Medical Services. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided Medical Services between experimental conditions. * p < 0.1, ** p < 0.05, *** p < 0.01. Each subject decided about the provision of (medical) services of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

The medical framing induces a slightly more Patient-oriented behavior of the Physicians.

3.4. Differences between Student and Physician Samples

As a last comparison, we evaluate the effects of different subject pools by comparing the medically framed experiments of student and medical doctor subjects (Table 10). The provision of Medical Services also hardly differs between the subject groups. Again, the only significant difference is for type L Patients in the fee for service setting, where students overprovide significantly in contrast to the doctors who provide the optimal number of services. This is in line with results from Brosig-Koch et al. [35] who also find slightly more patient-oriented behavior for a sample of doctors compared to students. Our third overall result is therefore:

Table 10

Deviation from optimal treatment between student and medical doctor samples.

		Subjects
Patient	Payment System	Students	Doctors	U-Test
L	FFS	0.96	0	**
	CAP	0.08	0
M	FFS	−0.04	−0.89
	CAP	−0.83	−1.08
H	FFS	−0.33	0
	CAP	−0.54	−0.75

Notes: Analysis only for treatments with medical framing. Average provision of Medical Services across experimental conditions. Positive values indicate an overprovision of Medical Services. Negative values indicate underprovision of Medical Services. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided Medical Services between experimental conditions. * p < 0.1, ** p < 0.05, *** p < 0.01. Each subject decided about the reporting and provision of (medical) services of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

Behavior of medical doctors and medically framed students is not significantly different for type M and H Patients. We do find a significant difference for type L Patients in Fee For Service, where Students behave more selfishly.

3.5. Regression Analysis—Payoffs and Experimental Variations

Reporting and provision of Medical Services ultimately results in different payoffs for Patient, Physician, and Insurer. In order to analyze how the different experimental variations influence the trade-off between the participants, we conduct a regression analysis. Linear regression models allow us to identify differences in the conditional means of each experimental variation while keeping constant the other variations. As the payoffs of Patient, Physician, and Insurer are interdependent by design, we apply a seemingly unrelated regression model, to take the resulting cross equational error correlation into account ([51], pp. 333–335). Table 11 summarizes the regression results. The dependent variables of one set of seemingly unrelated regressions are the expected payoff of the Patient, the payoff of the Physician, and the remaining endowment of the Insurer (The actual payoff of the Patient is zero or 90. As the provision of Medical Services determines the probability of receiving a payoff, we use the expected payoff of the Patient.). We estimate separate sets of seemingly unrelated regressions for the different Patient types. As explanatory variables we use dummies for the variations in Physician payment systems (“Fee For Service”), type of framings (“Medical Framing”) and subject pools (“Medical Doctor”). (We also estimate the models controlling for subject characteristics. We control for age and gender of the subjects, as well as measures for risk preferences and social value orientation. This does only marginally influence the results for our student sample, while there are some differences for the Physician sample driven by the small sample size given the number of variables in the regression models (see Table A15 in the Appendix B).

Table 11

Regression results—payoff for different participants by patient type.

		Patient	Physician	Insurer
PatientType L	Fee For Service	−28.57 ***	−0.51	−10.51 ***
		(3.82)	(2.97)	(2.72)
	Medical Framing	11.02 ***	−8.76 ***	7.52 **
		(4.18)	(3.25)	(2.97)
	Medical Doctor	11.94 **	−5.68	4.23
		(5.56)	(4.32)	(3.96)
	Constant	74.79 ***	56.09 ***	77.76 ***
		(3.48)	(2.70)	(2.48)
PatientType M	Fee For Service	−7.32 ***	10.46 ***	−15.27 ***
		(2.66)	(2.56)	(3.52)
	Medical Framing	5.72 **	−3.64	−3.96
		(2.91)	(2.80)	(3.85)
	Medical Doctor	−0.74	−5.37	9.30 *
		(3.88)	(3.73)	(5.12)
	Constant	56.66 ***	53.10 ***	77.64 ***
		(2.43)	(2.33)	(3.21)
PatientType H	Fee For Service	8.66 **	36.30 ***	−2.85 *
		(4.16)	(1.65)	(1.69)
	Medical Framing	−0.31	−0.59	−0.65
		(4.55)	(1.80)	(1.85)
	Medical Doctor	1.93	2.27	0.09
		(6.06)	(2.40)	(2.46)
	Constant	71.17 ***	49.91 ***	43.93 ***
		(3.79)	(1.50)	(1.54)

Notes: Coefficients of seemingly unrelated regressions; Standard errors in parentheses; Number of observations in each estimation: 126. The table shows estimation results of three seemingly unrelated regressions, where each regression is either run with Patients of type L, M, or H; * , ** , *** .

Table A15

Regression results—payoff for different participants by Patient Type.

		Patient			Physician			Insurer
PatientType L	Fee For Service	−28.57 ***	−29.06 ***		−0.51	−0.46		−10.51 ***	−10.91 ***
		(3.82)	(3.83)		(2.97)	(2.96)		(2.72)	(2.72)
	Medical Framing	11.02 ***	10.75 **		−8.76 ***	−9.29 ***		7.52 **	7.28 **
		(4.18)	(4.31)		(3.25)	(3.33)		(2.97)	(3.06)
	Medical Doctor	11.94 **	9.50		−5.68	−4.35		4.23	6.18
		(5.56)	(9.26)		(4.32)	(7.15)		(3.96)	(6.57)
	Age	-	0.25		-	−0.16		-	−0.08
		-	(0.52)		-	(0.40)		-	(0.37)
	Female	-	6.92		-	−7.04 **		-	4.73
		-	(4.27)		-	(3.29)		-	(3.03)
	Pro Social	-	−4.24		-	1.75		-	−4.11
		-	(4.02)		-	(3.10)		-	(2.85)
	Risk	-	0.43		-	−0.24		-	0.41
		-	(0.89)		-	(0.69)		-	(0.63)
	Constant	74.79 ***	64.98 ***		56.09 ***	64.59 ***		77.76 ***	76.79 ***
		(3.48)	(12.90)		(2.70)	(9.96)		(2.48)	(9.15)
PatientType M	Fee For Service	−7.32 ***	−7.55 ***		10.46 ***	11.12 ***		−15.27 ***	−15.80 ***
		(2.66)	(2.60)		(2.56)	(2.51)		(3.52)	(3.50)
	Medical Framing	5.72 **	5.83 **		−3.64	−2.90		−3.96	−4.72
		(2.91)	(2.93)		(2.80)	(2.82)		(3.85)	(3.94)
	Medical Doctor	−0.74	11.15 *		−5.37	5.36		9.30 *	−4.33
		(3.88)	(6.29)		(3.73)	(6.06)		(5.12)	(8.47)
	Age	-	−0.77 **		-	−0.81 **		-	0.99 **
		-	(0.35)		-	(0.34)		-	(0.47)
	Female	-	3.98		-	−5.30 *		-	3.76
		-	(2.90)		-	(2.79)		-	(3.90)
	Pro Social	-	−5.29 *		-	2.43		-	−0.96
		-	(2.73)		-	(2.63)		-	(3.67)
	Risk	-	0.49		-	−0.40		-	0.12
		-	(0.60)		-	(0.58)		-	(0.81)
	Constant	56.66 ***	72.18 ***		53.10 ***	75.29 ***		77.64 ***	52.82 ***
		(2.43)	(8.77)		(2.33)	(8.44)		(3.21)	(11.80)
PatientType H	Fee For Service	8.66 **	6.84 *		36.30 ***	36.03 ***		−2.85 *	−2.71
		(4.16)	(4.09)		(1.65)	(1.65)		(1.69)	(1.71)
	Medical Framing	−0.31	−3.97		−0.59	−1.05		−0.65	−0.14
		(4.55)	(4.61)		(1.80)	(1.86)		(1.85)	(1.92)
	Medical Doctor	1.93	2.06		2.27	5.91		0.09	3.95
		(6.06)	(9.88)		(2.40)	(3.99)		(2.46)	(4.13)
	Age	-	0.02		-	−0.25		-	−0.26
		-	(0.55)		-	(0.22)		-	(0.23)
	Female	-	−3.21		-	−0.90		-	0.93
		-	(4.55)		-	(1.84)		-	(1.90)
	Pro Social	-	−11.80 ***		-	−2.07		-	0.48
		-	(4.29)		-	(1.73)		-	(1.79)
	Risk	-	0.60		-	0.22		-	0.17
		-	(0.95)		-	(0.38)		-	(0.40)
	Constant	71.17 ***	77.16 ***		49.91 ***	56.37 ***		43.93 ***	48.13 ***
		(3.79)	(13.77)		(1.50)	(5.57)		(1.54)	(5.75)

Notes: Coefficients of seemingly unrelated regressions; Standard errors in parentheses; Number of observations in each estimation: 126. The table shows estimation results of three seemingly unrelated regressions, where each regression is either run with Patient of type L, M, or H; * p < 0.1, ** p < 0.05, *** p < 0.01. Description of additional variables: “Pro Social” (subjects with a cooperative/pro social attitude obtained from social value orientation slider measure [52], the reference category are subjects with individualist preferences), “Risk” (subjects where asked the following question: “Are you generally willing to take risks or are you trying to avoid risks?” Possible answers ranged from zero to ten, where zero represents “not willing to take risks” and ten represents “very willing to take risks”).

In regressions with low and medium Patient types, the Fee For Service coefficient is negative and significant for the Patient and Insurer, indicating that the Physicians are willing to harm both other participants to increase her personal payoff. This is clearly visible for M type Patients where the Fee For Service coefficient for the Physicians is significantly positive. Whereas for L type Patient, the fixed payment under Capitation is comparably high such that Fee For Service does not induce a significant difference in the payoff of the Physicians. For H type Patients, we observe a higher Patient payoff in the Fee For Service setting. The payoff for the Physicians is also significantly higher in the Fee For Service setting for type H Patients, while the Insurer payoff is lower. In line with Result 1 in a Fee For Service physician payment system, we find more selfish behavior of the Physicians at the expense of Patient and Insurer.

When we look at the effects of different framings, we see that for type L Patients, a medical framing induces a higher payoff for both the Patient and the Insurer. For M type Patients, the payoff for the Patient is higher in the medical framing, while the Insurer payoff is lower. Physician payoff in medical framing is lower, however this difference is only statistically significant for L type Patients. For H type Patients, we find no significant effect of the medical framing on any of the three payoffs. This shows that—in line with Result 2—medical framing induces Physicians to behave in a more Patient-oriented manner, at their own cost and expense of the Insurer.

Looking at the different subject pools reveals only minor differences between students and medical doctors. The only significant differences are a higher Patient payoff for L type Patients and a higher Insurer payoff for M type Patients in the medical doctor sample. All other differences between subject pools are small and not significantly different from zero. This is also in line with Result 3, as students and medical doctors behave rather similar, with medical doctors caring slightly more about the Patient payoff.

4. Discussion and Conclusions

We conduct a controlled laboratory experiment to investigate how Physicians trade-off between their own, their Patients’, and the Insurers’ benefits under prospective payment schemes. We modify the experimental design of the seminal works by Hennig-Schmidt et al. [7] and Brosig-Koch et al. [13] and introduce a third party that provides a budget for Medical Service provision. A further contribution to the literature is our variation of framings and subject pools.

Even though we introduce a third party in our experiment, our results on the differences between a capitation and a fee for service physician payment system are similar to other experimental studies. Capitation systems are more beneficial for Patients with a low severity of illness, while in fee for service systems, Patients with low severity of illness are harmed due to overprovision of Medical Services. For Patients with a high severity of illness, the fee for service system is more beneficial, as the personal financial incentive of the Physician to provide more services is aligned to the higher demand for Medical Services of those Patients.

In addition, we show that Physicians care about the payoff of a third party that finances medical service provision, an observation in line with results from surveys of physicians. This care for the third party can lead to underprovision of Medical Services to save costs for the third party. This is in particular the case where Physicians are not incentivized to provide many Medical Services. Previous experimental studies on physician behavior were not able to identify such concerns.

In our experiment, the behavior of participants is similar across framings and subject pools. Nevertheless, there are some differences. We find that neutrally framed experiments induce more selfish behavior, while participants in the medically framed experiments did care more about the Patient payoff. For our sample of medical doctors, we observe the most Patient-oriented behavior.

Our results show that direct financial incentives shape the behavior of Physicians. Nevertheless, distributional concerns regarding costs for the Insurer and well-being of the Patients play an important role in our controlled experiment. However, from an experimental research perspective, two main aspects of our paper need further investigation. First, the external validity of our experiment is limited. The patient–physician relationship is much more complex in the real world setting compared to our simplification. This simplification is especially important when it comes to patient payoff. In our experiment, patient well-being is represented by a stochastic payment to the participant. This modeling choice is a strong abstraction from actual patient well-being. Field experimental studies can provide a more externally valid assessment of medical care provision. Second, the health insurance in our experiment is represented by a single participant. Further research on efficiency and equality preferences within the pool of insured individuals is needed for a complete assessment of incentives and preferences in reimbursement schemes. From a policy perspective, further research on the interaction of Physician payment and budget provision is needed to improve current incentive structures in the medical sector.

Table A1

Misreporting between fee for service and capitation.

		Payment System
Patient	Fram.-Subj.	FFS	CAP	U-Test
	Neutr.-Stud.	1	0.22	***
L	Med.-Stud.	0.44	0.13	*
	Med.-Doc.	0	0
	Neutr.-Stud.	0.56	0.04	***
M	Med.-Stud.	0.52	0.33
	Med.-Doc.	0.33	0.08
	Neutr.-Stud.	0	−0.15	*
H	Med.-Stud.	−0.04	−0.04
	Med.-Doc.	0	−0.08

Notes: Average misreporting across experimental conditions. Zero misreporting refers to the case where the true type equals the reported type. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). Columns 5 and 8: U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of misreporting/provided Medical Services between experimental conditions. * p < 0.1, ** p < 0.05, *** p < 0.01. Each subject decided on the reporting of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

Table A2

Misreporting between neutral and medical framing.

		Framing
Patient	Payment System	Neutral	Medical	U-Test
L	FFS	1	0.44	**
	CAP	0.22	0.13
M	FFS	0.56	0.52
	CAP	0.04	0.33	**
H	FFS	0	−0.04
	CAP	−0.15	−0.04

Notes: Analysis only for student subject sample. Average misreporting across experimental conditions. Zero misreporting refers to the case where the true type equals the reported type. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). Columns 5 and 8: U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of misreporting Medical Services between experimental conditions. * p < 0.1, ** p < 0.05, *** p < 0.01. Each subject decided on the reporting of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

Table A3

Misreporting between student and medical doctor samples.

		Subjects
Patient	Payment System	Students	Doctors	U-Test
L	FFS	0.44	0	*
	CAP	0.13	0
M	FFS	0.52	0.33
	CAP	0.33	0.08
H	FFS	−0.04	0
	CAP	−0.04	−0.08

Notes: Analysis only for treatments with medical framing. Average misreporting across experimental conditions. Zero misreporting refers to the case where the true type equals the reported type. Bold formatted values are significantly different from zero (one-sided t-tests, p < 0.1). U-Test: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of misreporting between experimental conditions. * p < 0.1, ** p < 0.05, *** p < 0.01. Each subject decided on the reporting of every Patient type. Therefore, the total number of observations is 126. Number of observations in respective treatments: CNS—27, CMS—24, CMD—12, FNS—27, FMS—27, FMD—9.

Table A4

Misreporting of Type L Patients across experimental conditions.

Treatment	Avg. Misreporting		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	0.22 **		CNS
CMS	0.13 *		CMS
CMD	0		CMD
FNS	1 ***		FNS	***	***	***
FMS	0.44 ***		FMS		*	*	**
FMD	0		FMD				***	*

Notes:Left table: Average misreporting across treatments. Zero misreporting refers to the case where the True Type (L) equals the Reported Type (L). Overreporting by one/two refers to the case where M/H is reported, whereas the True Type is L. Stars indicate p-values of one-sided t-tests, testing whether there is statistically significant overreporting. Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of (mis)reporting between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A5

Misreporting of Type M Patients across experimental conditions.

Treatment	Avg. Misreporting		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	0.04		CNS
CMS	0.33 ***		CMS	**
CMD	0.08		CMD
FNS	0.56 ***		FNS	***		***
FMS	0.52 ***		FMS	***		**
FMD	0.33 **		FMD	*

Notes:Left table: Average misreporting across treatments. Zero misreporting refers to the case where the True Type (M) equals the Reported Type (M). Overreporting/underreporting by +1/−1 refers to the case where H/L is reported, whereas the True Type is M. Stars indicate p-values of one-sided t-tests, testing whether there is statistically significant overreporting/underreporting. right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of (mis)reporting between treatments. * p  < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A6

Misreporting of Type H Patients across Experimental Conditions.

Treatment	Avg. Misreporting		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	−0.15 *		CNS
CMS	−0.04		CMS
CMD	−0.08		CMD
FNS	0		FNS	*
FMS	−0.04		FMS
FMD	0		FMD

Notes:Left table: Average misreporting across treatments. Zero misreporting refers to the case where the True Type (H) equals the Reported Type (H). Underreporting by one/two refers to the case where M/L is reported, whereas the True Type is H. Stars indicate p-values of one-sided t-tests, testing whether there is statistically significant underreporting. Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of (mis)reporting between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A7

Deviation from optimal treatment of Type L Patients across experimental conditions.

Treatment	Avg. Misreporting		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	0.04		CNS
CMS	0.08		CMS
CMD	0		CMD
FNS	2.11 ***		FNS	***	***	***
FMS	0.96 ***		FMS	***	***	***	**
FMD	0		FMD				***	**

Notes:Left table: Average provision of (medical) services across treatments. Positive values indicate an overprovision of (medical) Services. Negative values indicate underprovision of (medical) services. Stars indicate p-values of one-sided t-tests, testing whether the mean provision of (medical) services differs significantly from 0 (optimal number of provided Services). Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided (medical) services between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A8

Deviation from optimal treatment of Type M Patients across experimental conditions.

Treatment	Avg. Maltreatment		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	−1 ***		CNS
CMS	−0.83 ***		CMS
CMD	−1.08 ***		CMD
FNS	0.44 *		FNS	***	***	***
FMS	−0.04		FMS	***	**	**
FMD	−0.89 ***		FMD				**

Notes:Left table: Average provision of (medical) services across treatments. Positive values indicate an overprovision of (medical) Services. Negative values indicate underprovision of (medical) services. Stars indicate p-values of one-sided t-tests, testing whether the mean provision of (medical) services differs significantly from 0 (optimal number of provided Services). Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided (medical) services between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A9

Deviation from optimal treatment of Type H Patients across experimental conditions.

Treatment	Avg. Maltreatment Treatment	CNS	CMS	CMD	FNS	FMS
CNS	−0.63 ***		CNS
CMS	−0.54 **		CMS
CMD	−0.75 *		CMD
FNS	−0.26 *		FNS	**
FMS	−0.33 **		FMS
FMD	0		FMD	*

Notes:Left table: Average provision of (medical) services across treatments. Positive values indicate an overprovision of (medical) services. Negative values indicate underprovision of (medical) services. Stars indicate p-values of one-sided t-tests, testing whether the mean Provision of (medical) services differs significantly from 0 (optimal number of provided services). Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of provided (medical) services between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A10

Absolut Misreporting of Type M Patients across Experimental Conditions.

Treatment	Avg. Maltreatment		Treatment	CNS	CMS	CMD	FNS	FMS
CNS	0.11 **		CNS
CMS	0.33 ***		CMS	*
CMD	0.08		CMD
FNS	0.63 ***		FNS	***	**	***
FMS	0.52 ***		FMS	***		**
FMD	0.33 **		FMD

Notes:Left table: Average absolute misreporting across treatments. Zero misreporting refers to the case where the True Type (M) equals the Reported Type (M). Stars indicate p-values of one-sided t-tests, testing whether there is statistically significant misreporting. Right table: Stars indicate p-values of Mann–Whitney U-tests of pairwise comparisons of misreporting between treatments. * p < 0.1, ** p < 0.05, *** p < 0.01. No star means no significant difference at p < 0.1. Dots indicate comparisons already represented by other combinations of rows and columns.

Table A12

Reporting and provision of medical services for Type L Patients.

Treatment	Reported Type	Provided Services
		1	2	3	4	5	6	Obs.
	L	0	23	0				23
CNS	M	0	1	1				2
	H	1	0	1	0	0	0	2
	L	0	22	0				22
CMS	M	0	1	0				1
	H	0	0	0	1	0	0	1
	L	0	12	0				12
CMD	M	0	0	0				0
	H	0	0	0	0	0	0	0
		1	2	3	4	5	6	Obs.
	L	1	4	8				13
FNS	M	0	0	1				1
	H	0	0	1	0	0	12	13
	L	2	8	10				20
FMS	M	0	0	2				2
	H	0	1	0	0	0	4	5
	L	0	9	0				9
FMD	M	0	0	0				0
	H	0	0	0	0	0	0	0

Notes: Dots indicate non-achievable outcomes. Bold formatted values represent the optimal number of medical services for the Patient of type L.

Table A13

Reporting and provision of medical services for Type M Patients.

Treatment	Reported Type	Provided Services
		1	2	3	4	5	6	Obs.
	L	0	0	1				1
CNS	M	0	1	23				24
	H	0	0	1	1	0	0	2
	L	0	0	0				0
CMS	M	0	0	16				16
	H	0	2	0	6	0	0	8
	L	0	0	0				0
CMD	M	0	2	9				11
	H	0	0	0	1	0	0	1
	L	1	0	0				1
FNS	M	0	0	10				10
	H	0	0	0	2	3	11	16
	L	0	0	0				0
FMS	M	0	2	11				13
	H	0	0	1	3	5	5	14
	L	0	0	0				0
FMD	M	0	1	5				6
	H	0	0	1	2	0	0	3

Notes: Dots indicate non-achievable outcomes. Bold formatted values represent the optimal number of medical services for the Patient of type M.

Table A14

Reporting and provision of medical services for Type H Patients.

Treatment	Reported Type	Provided Services
		1	2	3	4	5	6	Obs.
	L	1	0	0				1
CNS	M	0	0	2				2
	H	0	0	0	1	4	19	24
	L	0	0	0				0
CMS	M	0	0	1				1
	H	1	0	1	1	0	20	23
	L	0	0	0				0
CMD	M	1	0	0				1
	H	0	0	1	0	1	9	11
	L	0	0	0				0
FNS	M	0	0	0				0
	H	1	0	0	1	0	25	27
		1	2	3	4	5	6	Obs.
	L	0	0	0				0
FMS	M	0	1	0				1
	H	0	0	0	1	3	22	26
	L	0	0	0				0
FMD	M	0	0	0				0
	H	0	0	0	0	0	9	9

Notes: Dots indicate non-achievable outcomes. Bold formatted values represent the optimal number of medical services for the Patient of type H.