An Experimental Analysis of Patient Dumping Under Different Payment Systems

Massimo Finocchiaro Castro; Domenico Lisi; Domenica Romeo

doi:10.1515/bejeap-2022-0419

Article

An Experimental Analysis of Patient Dumping Under Different Payment Systems

Massimo Finocchiaro Castro , Domenico Lisi and Domenica Romeo

Published/Copyright: December 11, 2023

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From the journal The B.E. Journal of Economic Analysis & Policy Volume 24 Issue 1

Abstract

Physicians behave differently depending on the payment systems, giving rise to several problems such as patient dumping in which patients are refused because of economic or liability reasons. This paper tests whether and to which extent the adoption of either fee-for-service or Salary system induces physicians to practice patient dumping. Through the combination of an artefactual field experiment and a laboratory experiment, we test whether the risk of being sued for having practiced dumping can affect physicians’ behavior. Dumping is more often observed under Salary than under FFS. The introduction of dumping liability only mildly reduced dumping practice, though the provision of services increased. Our findings call for healthcare policy makers looking at the interplay between remuneration schemes and liability risks, and accounting for the trade-off between the reduction of the risk of being sued for patient dumping and the increase of the costs of the provision of medical services.

Keywords: framed field experiments; patient dumping; medical liability; physicians’ decision making

JEL Classification: C72; C93; D83; I12

Corresponding author: Massimo Finocchiaro Castro, Department of Law, Economics and Social Science, Mediterranean University of Reggio Calabria, Reggio Calabria, Italy; Health Econometrics and Data Group, University of York, York, UK; and Institute for Corruption Studies, Illinois State University, Normal, USA, E-mail: massimo.finocchiaro@unirc.it

Acknowledgments

We thankfully acknowledge valuable feedback from the editor Prof. Sandra Ludwig, two anonymous referees, and Peter Martinsson, Mariana Blanco and Calogero Guccio. We would like to thank participants at the EUHEA Conference 2022 in Oslo, in particular Johanna Kokot, Luigi Siciliani, Matteo Lippi Bruni and Mathias Kifmann, for their helpful comments. Finally, we are grateful to the G.O.M. Grande Ospedale Metropolitano in Reggio Calabria, in the persons of Francesco Araniti and Giuseppina Albanese.

Appendix A: Theory Model in Explicit Form

In this Appendix, we revisit the theoretical model in Section 3 by using the explicit functional forms employed in the experiment. Although less general, this revisitation sheds more light on the link between the theory of physicians’ behavior and the choice setting for participants in the experiment.

Physician’s profit can be represented as follows:

Π q = p q − c q 2 under FFS L − c q 2 under Salary

where p is the fee for each medical service provided under FFS, L is the fixed salary paid under the Salary system, and c is the marginal cost parameter.

Patient’s benefit resulting from medical treatment is given by B q , j + ε , where ɛ refers to the random component (due to the unavoidable uncertainty surrounding the provision of medical care) following a standard logistic distribution, ɛ ∼ Logistic(0, 1). The deterministic component of patients’ benefit is given by:

B j q = B 0 j + q if q ≤ q * B 1 j − q if q ≥ q *

with B 0 j = 1 = 7 , B 0 j = 2 = 5 , B 0 j = 3 = 3 and B 1 j = B 0 j + 2 q * . The optimal quantities of medical services are thus given by q* = 3 for low (j = 1), q* = 5 for intermediate (j = 2), and q* = 7 for high severity (j = 3).

The probability of being sued for medical malpractice is given by:

P r j q = λ j 1 − q 10

in which λ ^j=1 = 0.3, λ ^j=2 = 0.4, and λ ^j=3 = 0.5. Therefore, for each quantity of medical services, a higher severity (i.e. from low to intermediate, as well as from intermediate to high severity) increases the probability of being sued for malpractice of 10 %, that is:

∂ Pr j ∂ j = 0.1

Finally, the probability of being sued for dumping is given by d j = 1 = 0.1 , d j = 2 = 0.15 , d j = 3 = 0.2 . This implies that a higher severity (i.e. from low to intermediate, as well as from intermediate to high severity) increases the probability of being sued for dumping of 5 %, that is:

∂ d j ∂ j = 0.05

Considering the above explicit function forms, the physician’s utility functions under FFS and Salary system, respectively, are given as follows:

U q FFS = if patient is treated p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + ε if patient is dumped − d j D

U q Salary = if patient is treated L − c q 2 + α B 0 j + q − λ j 1 − q 10 H + ε if patient is dumped L − d j D

where α ∈ [0, 1] measures the rate at which the physician is willing to give up one euro of profit for one euro of patient benefit. Then, H is the disutility coming from a malpractice litigation; similarly, D is the disutility coming from complaints for patient dumping.

Physicians facing a patient make two sequential choices:

1) they decide if taking charge of the patient or dumping him.
2) in case of admission, they choose the quantity of medical services to provide.

As usual in sequential choice models, we solve the model through backward induction (i.e. starting from the last decision to be made and then going backwards).

In case of a patient being treated, the first order conditions for the optimal quantity of medical services under the two payment systems, q FFS * and q Salary * , are given by:

∂ U q FFS ∂ q = p − 2 c q FFS * + α + λ j 10 H = 0

∂ U q Salary ∂ q = − 2 c q Salary * α + λ j 10 H = 0

which imply that

q FFS * = p + α + λ j 10 H 2 c

q Salary * = α + λ j 10 H 2 c

Hence, in case of a patient being treated, we have that q FFS * > q Salary * (Behavioral Hypothesis 3).

Then, going backwards at the second-to-last decision, the physician chooses to treat patient j over to dump him provided that U if patient is treated > U if patient is dumped , that is:

Pr treat j FFS = Pr p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + ε > − d j D = Pr ε < p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D = e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D

Pr treat j Salary = Pr L − c q 2 + α B 0 j + q − λ j 1 − q 10 H + ε > L − j D = Pr ε < − c q 2 + α B 0 j + q − λ j 1 − q 10 H + j D = e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D

where we exploit the fact that ε ∼ Logistic 0,1 . These represent the probabilities for patient j of receiving treatment (i.e. not being dumped) under FFS and Salary system, respectively.

Comparing the above probabilities of being treated, we can thus investigate the impact of the payment system on the physicians’ practice of patient dumping. For each q, it is immediate to see that Pr treat j FFS > Pr treat j Salary , in fact:

e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D > e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D

e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D > e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D

p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D > − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D

p q > 0

Moreover, physicians choose a higher level of services under FFS, q FFS * > q Salary * , which implies that the probability of facing a malpractice litigation should be lower under FFS, further reducing the incentive to dump patients in FFS with respect to the Salary system. Therefore, the level of dumping achieved under Salary is higher than the one reached under FFS (Behavioral Hypothesis 1).

Then, we can examine whether the introduction of dumping liability affects physicians’ attitude toward dumping. Differentiating the probability of being treated in the two payment systems, we get:

∂ Pr treat j FFS ∂ d = Pr treat j FFS D 1 + e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D > 0

∂ Pr treat j Salary ∂ d = Pr treat j Salary D 1 + e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D > 0

Hence, when physicians can be sued for dumping, the probability of treating patient j should increase, and thus the level of dumping decrease in both payment systems (Behavioral Hypothesis 2).

Differentiating with respect to j, we can also inspect how the probability of being admitted, and thereby the dumping practice, changes with respect to the degree of patient severity:

∂ Pr { treat j } FFS ∂ j = Pr treat j FFS p 0.02 c H − 2 c q 0.02 c H + α 0.02 c H − 2 − H 1 − q 10 − λ j 1 − 0.01 c + 0.05 D 1 + e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D ⋛ 0

∂ Pr { treat j } Salary ∂ j = Pr treat j Salary − 2 c q 0.02 c H + α 0.02 c H − 2 − H 1 − q 10 − λ j 1 − 0.01 c + 0.05 D 1 + e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D ⋛ 0

Therefore, we can see that how dumping practice changes with respect to j is highly ambiguous.

Finally, integrating Pr treat j over the distribution f j of patient’s severity in the population, we obtain the equilibrium level of dumping as a proportion of patients being dumped in the population:

Dumping FFS = 1 − ∫ j e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e p q − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D f j d j

Dumping Salary = 1 − ∫ j e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D 1 + e − c q 2 + α B 0 j + q − λ j 1 − q 10 H + d j D f j d j

These equations give us the equilibrium level of dumping as a function of the physicians’ payment system (i.e. either FFS or Salary), as well as the risk of being sued for both malpractice and dumping.

Appendix B: Instructions

Welcome to Our Experiment

You are going to join an experiment on individual decision-making. Instructions are straightforward and, if you pay close attention, you may gain a monetary amount that will be paid to you in corresponding meal tickets at the end of the experiment. The amount of cash you may win depends only on your decisions and will not be affected by other participants’ decisions. Your monetary gains, measured in Experimental Crown (EC), will be converted into Euro at the following exchange rate 1 EC = 0.45 Euro. For example, if, at the end of the experiment, you achieve 40 EC, you will receive a 18 Euro meal ticket.

Experimental Design

The experiment lasts approximately 30 min and is divided into two stages. You will receive detailed instructions at the beginning of each stage. Please, remind that the decisions taken in one stage of the experiment do not have effects on the decisions that you will have to take in the following stage of the experiment.

Stage I

Please, read carefully the following instructions regarding stage I. If anything in the instructions is not clear please raise your hand and one of the experimenters will approach you. From this moment onward, you cannot communicate with any other participant. If you fail to do so, you will be asked to leave the room.

Figure B.1:

Example situation. Screenshot from z-Tree.

If you decide to treat the patient you then have to decide how many medical prescriptions to provide to patients. In other words, you have to decide on the level of medical care (in terms of drugs, diagnostic exams, …) to provide to patients according to their severity of illness. Thus, you will face nine patients. When taking the decision on patient’s medical care, you can choose among 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 prescriptions per patient. If you decide not to treat the patient you will skip to the following period. If you decide otherwise to treat the patient, after the decision on the level of medical prescriptions to provide, the patient could sue you for medical malpractice with probability Pr, which depends on the level of medical prescriptions already provided.

The following table shows the relationship between patient’s severity of illness and your profit, if you decide not to treat the patient.

Severity of illness	Your profit
Low (1)	0
Medium (2)	0
High (3)	0

The other tables we will provide before taking your decision, show the relationship between provided prescriptions and the probability of being sued.

Earnings

In each period of stage I, you will be paid according to the FFS payment system. Your earnings increase together with the number of medical prescriptions that you provide to patients. Moreover, you bear a cost due to the level of effort devoted to visiting each patient that depends on how many medical prescriptions you provide to patients. If you get sued by a patient, you will incur a fixed monetary loss equal to the profits earned in the same period you are sued. Hence, your profit in each period is computed as the payment you receive from the FFS system minus the cost due to the provision of medical services minus, if sued, the monetary loss due to being sued by the patient.

Each level of medical prescription provided accrues a certain level of benefit to patient according to her/his severity of illness. Therefore, your choice on the quantity of medical prescriptions to provide determines both your profits and the patients’ benefits.

In each period, you will see on the screen (see below) all the information regarding the patient you currently face: his diagnosis, the associated severity of illness, your earning according to the payment system in use, the related costs, the probability of being sued for each possible level of medical prescriptions, the monetary loss due to being sued, your profits and the corresponding patient’s benefits.

Stage II

Stage II lasts for nine periods. In each period, you will play in the role of a physician and you will have to decide whether to take charge of an already diagnosed patient. In each period you will face a patient with a different diagnosis. Each diagnosis is associated with a different level of severity of illness (low, medium, high). If you decide to treat the patient you then have to decide how many medical prescriptions to provide to patients. In other words, you have to decide on the level of medical care (in terms of drugs, diagnostic exams, …) to provide to patients according to their severity of illness. Thus, you will face nine patients. When taking the decision on patient’s medical care, you can choose among 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 prescriptions per patient.

If you decide not to treat the patient, before skipping to the following period, you may be sued with probability d, which depends on the patient’s severity of illness. If you decide otherwise to treat the patient, after the decision on the level of medical prescriptions to provide, the patient could sue you for medical malpractice with probability Pr, which depends on the level of medical prescriptions already provided.

The following table shows the relationship between the probability of being sued for not treating the patient, d, and the patient’s severity of illness.

Severity of illness	Probability d	Your profit
Low (1)	10 %	−10
Medium (2)	15 %	−10
High (3)	20 %	−10

Earnings

In each period of stage II, you will be paid according to the FFS payment system. Your earnings increase together with the number of medical prescriptions that you provide to patients. Moreover, you bear a cost due to the level of effort devoted to visiting each patient that depends on how many medical prescriptions you provide to patients. If you decide not to treat the patient and you get sued for that, you will incur a loss as shown in table and your profit will be simply equal to it. If you decide to treat the patient and you get sued by a patient for malpractice, you will incur a fixed monetary loss equal to the profits earned in the same period you are sued. Hence, if you treat the patient, your profit in each period is computed as the payment you receive from the FFS system minus the cost due to the provision of medical services minus, if sued, the monetary loss due to being sued by the patient.

Patient with illness 1:

Patient with illness 2:

Patient with illness 3:

Stage I (for a Different Pool)

Stage I lasts for nine periods. In each period, you will play in the role of a physician and you will have to decide whether to take charge of an already diagnosed patient. In each period you will face a patient with a different diagnosis. Each diagnosis is associated with a different level of severity of illness (low, medium, high). If you decide to treat the patient you then have to decide how many medical prescriptions to provide to patients. In other words, you have to decide on the level of medical care (in terms of drugs, diagnostic exams, …) to provide to patients according to their severity of illness. Thus, you will face nine patients. When taking the decision on patient’s medical care, you can choose among 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 prescriptions per patient.

If you decide not to treat the patient you will skip to the following period. If you decide otherwise to treat the patient, after the decision on the level of medical prescriptions to provide, the patient could sue you for medical malpractice with probability Pr, which depends on the level of medical prescriptions already provided.

The following table shows the relationship between patient’s severity of illness and your profit, if you decide not to treat the patient.

Severity of illness	Your profit
Low (1)	10
Medium (2)	10
High (3)	10

The other tables we will provide before taking your decision, show the relationship between provided prescriptions and the probability of being sued.

Earnings

In each period of Stage I, you will be given a fixed salary. Your remuneration does not vary with the quantity of medical services provided. Your profit in each period is computed as your fixed salary equal to 10, minus the cost due to the provision of medical services if you treat the patient, minus, if sued, the monetary loss due to being sued by the patient.

Stage II (for a Different Pool)

The following table shows the relationship between the probability of being sued for not treating the patient, d, and the patient’s severity of illness.

Severity of illness	Probability d	Profit
Low (1)	10 %	0
Medium (2)	15 %	0
High (3)	20 %	0

The other tables we will provide before taking your decision, show the relationship between provided prescriptions and the probability of being sued.

Earnings

In each period of Stage II, you will be given a fixed salary. Your remuneration does not vary with the quantity of medical services provided. If you decide not to treat the patient and you get sued for that, you will incur a loss as shown in table and your profit will be simply equal to it. Otherwise, your profit in each period is computed as your fixed salary equal to 10, minus the cost due to the provision of medical services if you treat the patient, minus, if sued, the monetary loss due to being sued by the patient.

Payment

At the end of the experiment, for each session, one period will be randomly drawn. The profit achieved in that period will be paid to you in corresponding meal tickets. While you in this stage have decided in the role of physician on service provision for hypothetical patients, real patients’ health outside the lab is affected by your choices. The overall benefits accruing to patients will be converted into Euro and donated to the charity ‘Per Mano onlus’, https://permanoonlus.wixsite.com/per-mano-onlus. To verify that the monetary amount corresponding to the sum of the patients’ benefits in a session is transferred, one of the subjects will be randomly chosen to be a monitor. When the experiment is over, the monitor will verify that one of the experimenters will transfer the monetary amount through credit card payment on the Per Mano ONLUS website. The money will support the charity assisting people affected by Duchenne Muscular Dystrophy.

Questionnaire

Before starting the experiment, we kindly ask you to answer some simple questions aiming at checking your comprehension of the design of stage I and of the profit generation mechanism.

If you have any question regarding the questionnaire, please raise your hand and one of the experimenters will come to your seat. Stage I will start only when all the participants answer to all questions correctly.

Table C.1:

Parameter values.

		Quantity (q)
Treatment	Variable	0	1	2	3	4	5	6	7	8	9	10
FFS	R ^FFS	0	2	4	6	8	10	12	14	16	18	20
Salary	R ^Salary	10	10	10	10	10	10	10	10	10	10	10
all	c	0	0.1	0.4	0.9	1.6	2.5	3.6	4.9	6.4	8.1	10
FFS	π	0	1.9	3.6	5.1	6.4	7.5	8.4	9.1	9.6	9.9	10
Salary	π	10	9.9	9.6	9.1	8.4	7.5	6.4	5.1	3.6	1.9	0
all	Pr_j=1	30 %	27 %	24 %	21 %	18 %	15 %	12 %	9 %	6 %	3 %	0 %
	Pr_j=2	40 %	36 %	32 %	28 %	24 %	20 %	16 %	12 %	8 %	4 %	0 %
	Pr_j=3	50 %	45 %	40 %	35 %	30 %	25 %	20 %	15 %	10 %	5 %	0 %
all	B _j=1	7	8	9	10	9	8	7	6	5	4	3
	B _j=2	5	6	7	8	9	10	9	8	7	6	5
	B _j=3	3	4	5	6	7	8	9	10	9	8	7
		Patient dumping (d _j=1 = 10 %; d _j=2 = 15 %; d _j=3 = 20 %)
FFS with d.l.	π if not sued	0	0	0	0	0	0	0	0	0	0	0
Salary with d.l.	π if not sued	10	10	10	10	10	10	10	10	10	10	10
FFS with d.l.	π if sued	−10	−10	−10	−10	−10	−10	−10	−10	−10	−10	−10
Salary with d.l.	π if sued	0	0	0	0	0	0	0	0	0	0	0

FFS, fee-for-service; R, revenue; C, total cost; π, profit; Pr, probability of being sued for malpractice; B, patients’ health benefit; d, probability of being sued for dumping.

Regressions reported in Table D.1 focus on the deviation from the efficient quantity, by participants’ type.^[37] Specifically, following the extensive literature on health economics (e.g. Brosig-Koch et al. 2017; Chalkley and Malcomson 1998; Ellis and McGuire 1986, 1990; Ma and Mak 2015), the efficient quantities of medical services in our experiment are implicitly defined by Δ B q E = Δ C q E ; therefore, they are equal to q ^E = 3 for low x and q ^E = 5 for medium y and high z severities.

Table D.1:

Deviation from the efficient quantity ( q − q e ) by participants’ type.

	Physicians (n = 36)			Students (n = 64)
	(1)	(2)	(3)	(1)	(2)	(3)
2.degreeofillness	−0.313	−0.211	−0.335	−0.464***	0.0753	0.0839
	(0.300)	(0.306)	(0.279)	(0.149)	(0.180)	(0.180)
3.degreeofillness	0.413	0.547*	0.429	1.003***	2.385***	2.395***
	(0.318)	(0.310)	(0.279)	(0.258)	(0.260)	(0.260)
FFS	0.954*	1.154*	0.991	1.505***	1.109**	1.387***
	(0.541)	(0.642)	(0.687)	(0.362)	(0.447)	(0.478)
Dumping	0.380***	0.349***	0.521***	0.238**	−0.0227	0.139
	(0.0825)	(0.0867)	(0.127)	(0.117)	(0.171)	(0.221)
Age		0.0251	0.0189		0.198*	0.253**
		(0.0291)	(0.0236)		(0.0982)	(0.102)
Male		0.493	1.392**		−0.849*	−1.182**
		(0.647)	(0.603)		(0.447)	(0.461)
Emergency department		−0.646	−0.334
		(0.685)	(0.692)
Riskseeking^a		−0.0914	0.752		1.079	−0.0204
		(0.680)	(0.747)		(0.800)	(0.483)
Male*Riskseeking			−2.207*			2.809***
			(1.109)			(0.618)
FFS*Dumping			−0.263			−0.306
			(0.179)			(0.339)
Constant	−0.704	−1.925*	−2.021**	0.381	−4.459*	−5.657**
	(0.475)	(1.066)	(0.942)	(0.230)	(2.180)	(2.253)
Observations	500	483	483	1075	457	457

Clustered standard errors at the individual level in parentheses; ***p < 0.01, **p < 0.05, *p< 0.1. 2.degreeofillness and 3.degreeofillness are dummy variables equal to 1 if patient’s severity of illness is either intermediate or high and 0 if the severity is low. FFS is a dummy variable equal to 1 if subjects are paid by FFS and 0 if they are paid by Salary. Dumping is a dummy variable equal to 1 if subjects joined a session where dumping liability has been implemented and 0 otherwise. Male is a dummy variable equal to 1 if the subject is male and 0 otherwise. Physician is a dummy variable equal to 1 if the subject is a physician and 0 otherwise. Emergency department is a dummy variable equal to 1 if the physician works at the Emergency department and 0 otherwise. Riskseeking is a dummy variable equal to 1 if the subject is classified as risk-lover according to Holt and Laury (2002)’s questionnaire and 0 otherwise. ^aThe lower number of observations is due to the exclusion of subjects whose inconsistent choices in the HL questionnaire have prevented them from being classified as either risk-seeker, risk-neutral or risk-averse.

Overprovision is more often observed for high severity patients. Additionally, the deviation from the efficient quantity increases under FFS. However, physicians show a more optimizing behavior than students, balancing patient’s health benefit and treatment costs. Physicians working in the hospital, in fact, always face the trade-off between benefits and costs of each treatment decision. Also dumping liability is found to increase the deviation from the efficient quantity; however, as usually found in the analysis, dumping liability is more salient to physicians.

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Received: 2022-11-22

Accepted: 2023-11-22

Published Online: 2023-12-11

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Articles in the same Issue

https://doi.org/10.1515/bejeap-2022-0419

Keywords for this article

framed field experiments; patient dumping; medical liability; physicians’ decision making