BARGAINING WITH OPTIMISM: IDENTIFICATION AND ESTIMATION OF A MODEL OF MEDICAL MALPRACTICE LITIGATION

• Date: 01 August 2019
• Published date: 01 August 2019
• Author: Xun Tang,Antonio Merlo
• DOI: http://doi.org/10.1111/iere.12378

INTERNATIONAL

ECONOMIC

REVIEW

August 2019

Vol. 60, No. 3

DOI: 10.1111/iere.12378

BARGAINING WITH OPTIMISM: IDENTIFICATION AND ESTIMATION OF A

MODEL OF MEDICAL MALPRACTICE LITIGATION∗

BYANTONIO MERLO AND XUN TANG1

Rice University, U.S.A.

We study a model of bargaining with optimism where players have heterogeneous beliefs about the final

resolution. Beliefs and bargaining surplus are identified from the settlement probability and the distribution of

accepted transfers. Using data from medical malpractice lawsuits in Florida, we estimate doctor and patient be-

liefs and the distribution of potential compensation. We find that patients are more optimistic and doctors more

pessimistic when the severity of injury is higher, and the joint optimism diminishes as severity increases. We quan-

tify the increase in settlement probability and the reduction in accepted settlement offers under counterfactual

caps on the total compensation.

1. INTRODUCTION

Optimism is often invoked as a possible explanation for why parties involved in a negotiation

sometimes fail to reach an agreement even though a compromise could be mutually beneficial.

For example, consider a medical malpractice dispute where a patient (the plaintiff) suffered

a damage allegedly caused by a doctor’s (the defendant’s) negligence or wrongdoing. If the

plaintiff and the defendant are both overly optimistic about their chances of getting a favorable

jury verdict, there may not be any settlement that can satisfy both parties’ exaggerated expec-

tations. The general argument dates back to Hicks (1932) and was later developed by Shavell

(1982), among others, in the context of legal disputes. A recent theoretical literature originated

by the work of Yildiz (2003, 2004) extends this insight and studies a general class of bargaining

models with optimism (see Yildiz, 2011, for a survey). These models have also been used in a

variety of empirical applications that range from pretrial negotiations in medical malpractice

lawsuits (Watanabe, 2006) to negotiations about market conditions (Thanassoulis, 2010) and

cross-license agreements (Galasso, 2012).

Despite the recent surge of interest in the theory and application of bargaining with optimism,

none of the existing contributions formally addresses the issue of identification in this class

of models. That is, under what conditions can the structural elements of the model (beliefs

and bargaining surplus) be unambiguously recovered from the history of bargaining outcomes

reported in the data? In a typical context of negotiations, the beliefs of both parties interact

∗Manuscript received May 2017; revised September 2018.

1We thank seminar participants at Brown, CEMFI (Madrid), CREST (Paris), Emory, HKUST, LSE, Ohio State,

Princeton, SUFE (Shanghai), Texas A & M, TSE (Toulouse), Tsinghua, UCL, U Wisconsin (Madison), and attendants

of 2014 Econometric Society North America Summer Meeting, 2015 Cowles Foundation Conference, and the 11th

World Congress of Econometric Society (Montreal 2015) for feedback. This research is funded by NSF Grant #

SES-1448257. We thank Devin Reily, Michael Shashoua, and Michelle Tyler for capable research assistance. Special

thanks to Ms. Ying Xu, a practicing attorney from the Law Offices of Eric K. Chen, for sharing her knowledge about

the institutional details related to medical malpractice litigation. Please address correspondence to: Xun Tang, Rice

University, Economics Dept., MS-22, 6100 Main St., Houston, TX 77005. E-mail: xt9@rice.edu

1029

C

(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1030 MERLO AND TANG

with the bargaining surplus to determine the outcome. As a result, the distribution of bargaining

outcomes reported in a typical data environment is conditional on events involving these model

elements. Such a selection issue causes major challenges in the identification of this class of

models. One of the contributions of this article is to deal with these challenges in identification

using a minimum set of nonparametric assumptions.

We consider a bilateral bargaining environment where players hold optimistic beliefs about

whether a stochastic outcome favors them if they fail to reach an agreement. The players have

a one-time opportunity for reaching an agreement at an exogenously scheduled date during the

bargaining process and make decisions about whether or not to settle and, if so, the amount

of the settlement based on their beliefs, the bargaining surplus, and the time discount factor.

We show that all structural elements in the model are identified nonparametrically from the

probability of reaching an agreement and the distribution of transfers in the final resolution

of the dispute. The identification strategy is robust in the sense that it does not rely on any

parametrization of the distribution of beliefs or bargaining surplus.

We apply this model to analyze medical malpractice disputes in the State of Florida between

1984 and 1999. In his seminal work, Sloan et al. (1993) provides a thorough empirical analysis of

medical malpractice litigation using this source of data. Sieg (2000) is the first structural paper

that estimated a bargaining model to understand the incentives of patients and doctors during

medical malpractice disputes. Sieg (2000) is also the first paper that structurally estimates a

bargaining model with asymmetric information. In comparison, we use a qualitatively different

model to study how optimism in beliefs impact the final outcome. In addition to establishing

the nonparametric identification of this model, we are interested in the following questions:

How do the characteristics of lawsuits affect the litigation outcome through their impact on

the parties’ beliefs (and optimism)? To what extent are these beliefs consistent with the actual

pattern of jury decisions observed in court? How does the total potential compensation for the

alleged malpractice depend on these characteristics? What are the consequences of a tort reform

that restricts the maximum compensation possible? To answer these questions, we propose a

Maximum Simulated Likelihood (MSL) estimator based on flexible parametrization of the

beliefs of both sides in the litigation. We then use the structural estimates for the belief and

compensation distribution to quantify their relation to the case characteristics and to evaluate

the impact of the proposed tort reform.

The bargaining environment we consider is simpler than the one studied by Yildiz (2004).

Instead of allowing for multiple rounds of offers and counteroffers, in our model there is a

single settlement opportunity for the players to reach an agreement. Hence, in our case there

are no dynamic “learning” considerations in the players’ decisions, and the dates of the final

resolution of the bargaining episodes are solely determined by the players’ optimism, their

patience, and their perception of the surplus available for sharing. Following Sieg (2000), we

model the medical malpractice lawsuits as bargaining episodes with one-time opportunities for

the players to settle out of court.2

Our specification of the bargaining environment is motivated by both theoretical and empiri-

cal concerns. First, data limitation would prevent us from deriving robust (parametrization-free)

arguments for the identification of structural elements in general models of bargaining with op-

timism that admit multiple rounds of offers and counteroffers. For instance, none of the data

sets that are used in empirical applications of bargaining models with optimism contains infor-

mation on the sequence of proposers in a negotiation or the timing and size of rejected offers. By

abstracting from the dynamic learning aspects (which would be introduced into the theoretical

analysis if we were to consider a more general bargaining environment with multiple rounds of

unobserved offers and counteroffers), we take a pragmatic approach and specify a model that

is identifiable under realistic data requirements and mild econometric assumptions. Second,

despite this simplification, our model captures the key insight of bargaining with optimism in

2Da Silveira (2017) also uses a one-shot bargaining model with asymmetric information to study the outcome of

plea bargaining between a prosecutor and a defendant in criminal cases. His analysis provides conditions for the

nonparametric identification of that model.

BARGAINING WITH OPTIMISM:IDENTIFICATION AND ESTIMATION 1031

that the incidence of agreement is determined by the players’ optimism and their patience.

Thus, our work represents a first important step toward addressing the issue of nonparametric

identification in more general models of bargaining with optimism.3Third, our modeling choice

is motivated by the specific empirical context of medical malpractice disputes in Florida. The

law of the State of Florida (Florida Statues, Title XLV, Chapter 766, Section 108), requires that

a one-time, mandatory settlement conference between the plaintiff and the defendant be held

“at least three weeks before the date set for trial.” The settlement conference is scheduled by the

county court, is held before the court, and is mediated by court-designated legal professionals.

Our identification method consists of two steps. First, we recover the settlement probability

and the distribution of transfers conditional on the unreported wait time between the scheduled

settlement conference and the court trial. To do so, we tap into a recent literature that uses

eigenvalue decomposition to identify finite mixture models or structural models with unob-

served heterogeneity (see, for example, Hall and Zhou, 2003; Hu, 2008; Hu and Schennach,

2008; Kasahara and Shimotsu, 2009; An et al., 2010; Hu et al., 2013). In particular, we exploit

the institutional details in our environment to group lawsuits into clusters defined by the county

and the month in which the lawsuit is filed. We argue that the lawsuits within each cluster can

be plausibly assumed to share the same, albeit unobserved, wait time. We then use the cases

in the same cluster as instruments for each other and apply eigenvalue decomposition to the

joint distribution of settlement decisions and accepted offers within the cluster. This identifies

the probability for settlement and the distribution of accepted settlement offers conditional on

unreported wait time. A novel feature in our first step of identification is that we show how the

major identifying assumptions for models with unobserved heterogeneity (e.g., rank conditions

in Hu, 2008, and invertibility conditions in Hu and Schennach, 2008) are implied by intuitive

restrictions on structural primitives in our model.

Second, we identify all structural elements of the model by exploiting the interaction between

the length of wait time, the beliefs, and the potential compensation in the outcome of settle-

ment decisions and accepted offers. To do so, we use the conditional distribution of outcomes

recovered from the first step and take full advantage of two implications of the model: (i) With

orthogonality between beliefs and potential compensation, the distribution of transfers to the

plaintiff as ruled by the court is directly related to the marginal distribution of potential compen-

sation and the settlement probability; (ii) the distribution of accepted offers under settlement

is based on an additive transformation of the beliefs and potential compensation distribution.

Our structural estimates show that on average the potential compensation decreases with the

patient’s age, but increases with the severity of injury due to the alleged malpractice and the

median household income in the county where the lawsuit is filed. As for the beliefs about jury

verdict, we find that patients tend to be relatively more optimistic and doctors relatively more

pessimistic for the cases with higher severity. This is consistent with the effect of severity on court

decisions observed in the data. Our estimates also show that the patient’s and the doctor’s beliefs

are negatively correlated and that the optimism diminishes as severity increases. In addition,

we find that doctor qualification (i.e., the doctor’s board certification status and educational

background) affect the beliefs of both parties in ways that are inconsistent with their actual

marginal effects on jury verdicts observed in the data.

We use our structural estimates to predict the probability for settlement and the distribution

of accepted offers under hypothetical caps on potential compensation. For each level of severity,

we impose a cap equal to the 75th empirical percentile of compensations paid by defendants

following jury verdicts in the data. Although these caps only increase the probability for set-

tlement by small margins, they lead to sizeable reductions in the accepted settlement offers on

average. For example, among the lawsuits against board certified doctors, the rates of reduction

in the mean of accepted offers under the caps vary between 15% and 22%, depending on the

severity level. For the other cases involving doctors with no board certification, this range is

between 16% and 20%.

3Watanabe (2006) studies medical malpractice disputes in the context of a dynamic model of bargaining with

optimism and learning. His analysis is fully parametric and does not address the issue of identification.