The Value of an Attorney: Evidence from Changes to the Collateral

Source Rule

⇤

Eric Helland†

Claremont McKenna College

Jungmo Yoon‡

Hanyang University

October 13, 2017.

Preliminary. Please Do Not Circulate.

Abstract

One of the more contentious questions in law is the value of lawyers to their clients. Yet asimple comparison of recovery in cases with and without lawyers will not yield a satisfactoryestimate of the value of an attorney since hiring a lawyer is endogenous. We utilize modificationsto the collateral source rule which require that awards at trial be reduced by the amount ofpayments from first party insurance as an instrument. Theoretically these modifications tothe collateral source rule reduce the likelihood a claimant will hire a lawyer and reduce thelikelihood that the lawyer accepts the case. Consistent with our model the modification of theCS rule has a non-trivial e↵ect on the probability of hiring attorneys. There is one problemwith our candidate instrument; modifications to the CS rule that require o↵sets have a directe↵ect on recovery and hence violate the exogeneity requirement for a valid instrument. Wepropose an alternative estimator which bounds the impact of lawyers. We find that the upperand lower bounds of our estimated impact of hiring a lawyer are negative. The reduction intotal payment received from hiring a lawyer range from over $230,879 to approximately $51,407in 2002 constant dollars in contrast to a gain from hiring a lawyer of $22,963 to $33,614 whenestimated using the conventional approach. We also estimate the quantile e↵ect of hiring anattorney. Here the e↵ect for all but the largest claims is close to zero with the estimated boundstypically straddling zero. However for the top 10% of claims we find very large negative impactssuggesting that lawyers actually reduce the client’s recovery relative to the amount they wouldhave received without representation.

⇤First draft: Nov 10, 2016. This version: March 16, 2017. The authors wish to thank seminar participants andGeorge Mason University Law School and Georgetown University School of Law.

†Robert Day School of Economics and Finance, Claremont McKenna College, 500 East Ninth Street, Claremont,California, 91711 (eric.helland@cmc.edu).

‡College of Economics and Finance, 222 Wangsimni-Ro, Seongdong-Gu, Seoul, Korea (jmyoon@hanyang.ac.kr).

1 Introduction and Background

One of the more contentious questions in law is the value of lawyers to their clients.1 Unlike other

services, in which the fact that people are willing to pay for the service strongly suggest that the

service creates value, there are theoretical reasons to believe that lawyers could, in fact, reduce

a client’s expected recovery.2 The most obvious problem is that lawyers could charge more in

fees than the increase in payments from third party source their services generate for their clients.

Beyond their fees lawyer’s presence may generate additional costs to claimants, which would be

passed on to claimants as compensation absent the litigation. This could be the case if, for example,

expert witness testimony generates less on average than its additional cost in recovery. Moreover

since claimants typically lack the experience with or, expertise about, the civil justice system, they

are unable to estimate whether they would be better o↵ without an attorney. Much like doctors,

realtors, mutual fund managers and funeral directors, the client’s lack of expertise necessitates

hiring someone to represent their interests but this also means the potential client is uncertain as

to whether the service is worth the cost.3 In the context of this paper, tort litigation resulting

from auto accidents, major accidents are, thankfully, rare, and therefore the typical person has

very little experience with the complex process of recovery from a third party who may be liable

for their injuries.

Even if lawyers could produce an increase in the value of the claim there are reasons to be

concerned that they lack the incentives to do so once retained. Lawyers in tort cases are paid a

percentage of the proceeds of the litigation when the client recovers. Moreover the typical contract

between lawyer and client does not pay fees for experts and court costs if there is no recovery.

While there are reasons to believe that contingent fee arrangements between lawyers and clients

may be optimal in light of private information on case quality and/or e↵ort, law and economics has

long recognized that under any fee arrangement the lawyer has distinct interests from the client.4

1For an extensive discussion of the literature see Greiner and Pattanayak (2012) and Brinkman (2011).2See Ashenfelter, Bloom and Dahl (2013) and Ashenfelter and Dahl (2012) for an example in which hiring a lawyer

is modeled as a prisoners dilemma game.3For a discussion of each of these professions see Fuchs (1978), Gruber and Owing (1996), Chavalier and Ellison

(1997), Harrington and Krynski (2002), and Levitt and Syverson (2008).4See Rubinfeld and Scotchmer (1993) and Dana and Spier (1993.)

1

These divergent interests generally cover three dimensions: the willing of lawyers to take a case

and bring suits on behalf of a prospective client; the lawyer’s willingness to settle a case before trial

and the lawyer’s e↵ort in pursuing the case.

To understand the divergence of interests the literature has focused on the incentive e↵ects of

the contingent fee contract between the lawyer and client. These contracts typically give the lawyer

one third of the total recovery (often net of costs other than the lawyer’s time) but typically provide

no additional payment for time worked. In this context it is clear that a contingent fee contract

provides better incentives for the lawyer to reveal the value of a claim to a client than an hourly

fee contract. A lawyer on an hourly fee contract has the incentive to take any case regardless of

expected outcome. However a contingent fee contract is not optimal since, in most models, it is

e�cient to bring cases worth more than legal costs meaning that a lawyer on a contingent fee brings

too few cases.5 A similar logic applies to settlement. Lawyers under contingent fee arrangement

want to settle too frequently since they receive only a portion of the proceeds of a trial and yet

in the models the lawyers typically pay all of the litigation costs. Finally, in most models it is

assumed that the client cannot directly observe the lawyer’s e↵ort meaning that under an hourly

fee the lawyer would expend no e↵ort but even under a contingent fee the lawyer will expend less

e↵ort than the plainti↵ would find optimal in a world where e↵ort was observable.6 All of these

incentive e↵ects tend to diminish the value of hiring a lawyer.

One dimension that has not been extensively studied is the lawyers non-labor investment in

the case. Since the lawyer typically pays court costs and expert witness expenses up front and is

then reimbursed out of any recovery. Contingent fees are often based on recovery net of fees. This

introduces a more complex dynamic in which lawyers are sharing the cost of the expenses with

the client unless they do not recover. This would cause lawyers to under invest in value creating

expenses since they bear all the risk in the event of a loss and pay one third of the expenses in the

event of recovery but only recover a third of the benefit of the investment. Engstrom (2009, 2011)

has argued that this incentive has produced “settlement mills”; law firms specializing in settling

5Since the lawyer receives only one third of case value and typically pays all the legal costs, the lawyer will onlywant to accept a case in which a third of the expected value of the case is greater than legal cost.

6Or in which the client could legally sell the case to the attorney: a contingent fee of 100%.

2

auto cases with a minimum investment in the case. To the extent that Engstrom is correct and

settlement mill firms dominate auto accident litigation, we would expect to see lawyers adding very

little value on average as the incentive to invest would be pushed toward the opportunity cost of

lawyer’s time.7

The second factor diminishing the value of a lawyer is that contingent fees allow lawyers to

finance the claims of their capital constrained clients. Since the lawyer is essentially working for

free until the claim is resolved he or she is issuing the client a contingent loan paid back only in the

event the client recovers. Like all investments financed by borrowed money the value of payo↵ must

be net of the borrowing costs. In a world of perfect information and repeated dealings with the civil

justice system, we might expect clients to, at least on average, borrow from plainti↵’s attorneys

only when the expected payo↵ is greater than the lending costs but in the realm of personal injury

litigation these conditions need not be met.8

Models in law and economics typically assume that the value of a lawyer should be measured

relative to a zero recovery. That is, absent bringing a claim the client would recover nothing. Yet

this is often not the case. In the cases examined here, auto accidents, the value of a lawyer needs to

be evaluated relative to what the client would have received in compensation without the lawyer.

For example, it is common in auto accidents for victims to get an o↵er from other parties insurance

company even if the injured party does not retain a lawyer.

The theoretical literature o↵ers no consensus on the value of an attorney suggesting the im-

portance of empirical estimates. Yet the simple comparison of recovery with and without lawyers

will not yield a satisfactory estimate of the value of an attorney since hiring a lawyer is endoge-

nous. Greiner and Pattanayak (2012) survey the empirical literature, which consists of hundreds of

studies. They conclude that beyond the three randomized controlled trials, inclusive of their own

7Engstrom (2011) points out that while settlement mills on average may add very little to the amount clientsrecover, net of fees, beyond what they would recover without the lawyer, these firms may add value in faster recovery,reduced court congestion and other non-recovery dimensions.

8As in most instances of agency problems, the most important check on plainti↵’s lawyers expropriating theproceeds of litigation is a competitive market. There is considerable dispute about whether the market for plainti↵’slawyer is competitive. First, there are the above mentioned information problems. In addition, there is the fact thatlaw school admissions and bar exams represent at least a partial barrier to entry. Of course the lack of a competitivemarket is not required for lawyers to grab a larger share of the litigation surplus.

3

study, the rest of the literature is not worthy of credence.9 The di�culty is that all of the studies

compare the outcome of cases with and without lawyers despite the fact that the decision to hire

a lawyer and the lawyer’s decision to accept the case are endogenous.10

The alternative to a randomized control trial when there are endogenous variables is an instru-

ment that impacts the decision to hire a lawyer but does not impact claim value. Our candidate

instrument is changes to the collateral source (CS) rule (or collateral source doctrine). This eviden-

tiary rule prohibits the admission of evidence of compensation the victim has received from other

sources. For example, the defendant would still be liable for the full amount of the victim’s injury

even if the victim had received payment from their health insurance to cover injuries resulting from

the defendant’s negligence. Beginning in the mid-1970s several states modified this rule to prevent

the plainti↵ from being compensated twice for the same injury and in many cases states mandated

that any award be o↵set by the amount paid to plainti↵s from collateral sources. In Section 2, we

present a simple demand and supply analysis of the decision to hire an attorney and demonstrate

that when the collateral source rule is modified, claimants are less likely to hire an attorney. The

modification of the CS rule, our instrument, has a non-trivial e↵ect on the probability of hiring

attorneys, our treatment. This theoretical prediction is also supported by empirical evidence which

we discuss below. This leads us to conclude that our candidate instrument satisfies the relevance

requirement of being a valid instrument.

One concern is that the law change itself may not be random. Fortunately our data is su�ciently

rich in detail on the history of law changes that it give us an additional source of random variation.

When they introduced modifications to the CS rule some states applied it to all cases, while other

states restricted it to cases involving allegations of medical malpractice. Since we study only auto

accidents, the law change in the latter should have no impact on our cases. Sloan and Chepke

(2008) suggest that scope of the modification, including by implication the decision to include all

cases or just medical malpractice cases, was random and depended on the specific coalitions in

the state that led to passage of the reform. Tort reform primarily arises out of insurance crises

9In fact Greiner and Pattanayak (2012) argue that the problems are so severe as to render their conclusionsuntrustworthy.

10For an example of an alternative approach to the selection issues inherent in litigation data see Ashenfelter andDahl (2012) and Ashenfelter, Bloom and Dahl (2013).

4

a↵ecting doctors but in certain states the coalition supporting reform also included insurers more

broadly. In a subset of these the reform e↵ort was successful. Also in a subset of those successful

states the reform was not overturned by the courts. The end result is that the comprehensiveness

of modifications to the collateral source rule appears to be random. Thus while the modification

itself may not be random, we argue the decision to apply it more broadly or narrowly is random.

Below will provide some statistical evidence that this is the case.

There is a more serious concern with our candidate instrument, however. Specifically modifica-

tions to the CS rule have a direct e↵ect on recovery and hence violate the exogeneity requirement for

a valid instrument. Lawyers are paid a fraction of the eventual recovery, and modifications to the

CS rule also typically have a direct e↵ect on recovery by requiring that collateral source payments

must be o↵set. In the terminology of instrumental variable (IV) estimation method, our candidate

instrument has a direct e↵ect on outcome variables, which makes it a ‘invalid’ instrumental variable.

We solve this invalid instrumental variable problem by considering a potential outcome variable

which blocks the direct e↵ect of instrument on outcome but allows the indirect e↵ect of instrument

through treatment.11 To be specific, we ask what would be the total payment if o↵sets under

the modified CS rule are to impact the decision to hire a lawyer but then did not materialized at

trial. By using this potential payment instead of the observed payment as our outcome measure,

we can define a local average indirect e↵ect that has a causal interpretation. If the direct e↵ect

were blocked, the modification to the CS rule impacts payment only through the decision to hire a

lawyer or not. This would have a causal interpretation.

This potential outcome variable, however, is not directly observed, so the local average indirect

e↵ect may not be identified from data. Fortunately we can link the potential outcome to observed

quantities because o↵sets reduce payments in mechanical ways; it literally reduces the award at trial

dollar for dollar with the payments form relevant collateral sources. By calculating the maximum

o↵sets allowed by the modification enacted in the relevant state, we are able to bound the potential

payment. In this way we can identify a sharp bound on the local average indirect e↵ect. The details

11A quantity like this has been defined and used in the treatment e↵ect literature, mainly outside of economics. Itwas called the pure indirect e↵ect (Robins and Greenland (1992), Robins (2003)), or the natural indirect e↵ect (Pearl(2001)). In economics, Flores and Flores-Lagunes (2010) use the concept to define the mechanism treatment e↵ect.

5

of the estimation strategy can be found in Section 3.

We use the modification of the CS rule as an (invalid) instrument to estimate the value of

attorneys in auto accident claims. Our data, which cover accidents which occurred in the years

1982 to 2002, also contain information on compensation from other sources such as health insurance.

Individuals in our sample can either choose to hire a lawyer in their case against a potentially liable

third party or simply accept whatever payments they would receive from third party insurance

plus their own insurance.12 Consistent with Greiner and Pattanayak (2012), and in contrast to

Hammitt’s (1985) earlier evaluation of auto accidents, we find that the upper and lower bounds

of our estimated impact of hiring a lawyer are mostly negative. The reduction in total payment

received from hiring a lawyer range from over $230,879 to approximately $51,407. This e↵ect is

quite large for an average payment, in 2002 dollars, of approximately $18,680. To find out why

this is the case, we estimate the quantile e↵ect of hiring an attorney. Here the e↵ect for all but

the largest claims is close to zero with the estimated bounds typically straddling zero. However for

the top 10% of claims we find very large negative impacts suggesting that lawyers actually reduce

the clients recovery relative to the amount they would have received without representation. Our

conjecture is that expenses, such as hiring expert witnesses, are not captured in attorney’s fees or

the net recovery to the client. This is also consistent with Hammitt (1985) who also finds that

for very large claims cases with lawyers actually receive less compensation than cases with similar

damages where the claimant does not hire a lawyer.

2 Theory

In this section we examine a simple theoretical model of the decision to hire an attorney. By a

simple demand and supply analysis for attorney’s service, we demonstrate that a modification of

the CS rule, that requires o↵sets of any judgment at trial by the amount the plainti↵ received from

collateral sources, such as their personal health or auto insurance, reduces the likelihood a claimant

retains an attorney. This shows the relevance of the modification of the CS rule as an instrument

12For a more extensive discussion of the compensation of auto accident victims see Hammitt (1985), Rolph et al.(1985) and Hensler et all. (1991).

6

and hence justifies our estimation strategy.

Suppose that the claimant is legally entitled to an amount M in compensation from the defen-

dant assuming the defendant is either found liable or willing to pay (in order to avoid litigation).

This setup abstracts away from the decision to settle or litigate the claim to trial and hence M can

be thought of as the expected outcome of successful litigation.

Suppose that the claimant will receive M from the (potential) defendant or his/her insurer with

probability P0 if no lawyer is hired. If the claimant hires an attorney, he faces a probability P1 of

recovering M . We assume that P1 > P0. Assume that the attorney, if he/she agrees to take the

case, faces a cost of C to pursue the claim.13 We normalize the cost to the claimant of pursing the

claim without the attorney to be 0. The attorney is paid a fraction � of the recovery M but only

if the claim is successful.

Let L be the amount that the claimant receives from collateral sources. Let’s first consider the

case where this amount is irrelevant because the amount owed by a liable defendant is not o↵set

by payments from collateral sources. This applies to cases or accidents that occurred in states that

did not modify the CS rule. In such cases, the potential client receives P1(1� �)M if they hire an

attorney and P0M if they do not. Therefore they will hire an attorney if P1(1� �)M > P0M or if

(1� �)P1 > P0. The attorney will take the case if �P1M > C.

Suppose that the state has modified the CS rule such that o↵sets are required. There are

two cases to consider. In Florida and Minnesota, state law requires attorneys to receive contingent

payments based onM�L. In other states, their law allows attorneys to receive contingent payments

based on M .

In the first case, under the modified CS rule, the claimant receives P1(1 � �)(M � L) if they

hire an attorney and P0(M�L) if they do not (assuming that the potential defendant’s insurer will

reduce any settlement o↵er by the expected o↵sets at trial). So the condition to hire an attorney is

still (1� �)P1 > P0. While the modification reduces the payment for claimants, it does not reduce

13This is generally assumed to be the opportunity cost of the attorney’s time plus expenses. In reality expensesare divided between the attorney and client and, as discussed below, attorney’s fees are often based on recovery netof expenses such as court costs and expert witness fees. In the model we follow the convention in the literature anassume the client pays none of the expenses.

7

their demand for an attorney since their decision rule remains the same.14 The attorney, however,

is less willing to take the claim. Their decision rule shifts to �P1(M � L) > C, which means they

are less likely to take the case for any given expected recovery and cost.

In the second case, under the modified CS rule, the claimant receives P1(M � L � �M) if

they hire an attorney and P0(M � L) if they do not, so the condition to hire an attorney is

(1 � �)P1 � P1�L

M�L > P0. There is a negative demand e↵ect since the client would recover less

after fees under a modified CS rule. The attorney will take the case if �P1M > C, so there would

be no supply e↵ect.

In summary, when lawyer’s contingent payments are based on M � L, the modification of the

CS rule has no demand e↵ect for attorneys but reduce their supply. When contingent fees are

based on M , the modification would lower the demand but has no e↵ect on supply. In both cases

claimants are less likely to hire an attorney when the collateral source rule is modified.

3 Identification with Invalid IV

3.1 Concepts and Notations

Let the subscript i denote the i-th individual (claimant) in our sample. The outcome variable Yi is

the payment he/she receives.15 The treatment variable Di is his/her decision to hire an attorney:

D1 = 1 if the claimant hired an attorney and Di = 0 if the claimant did not. The instrumental

variable Zi = 1 indicates that a claimant’s accident occurred in a state and year in which a modified

CS rule requiring o↵sets was in e↵ect and and Zi = 0 indicates an unmodified rule in which the

claimant can recover from both sources.14This is because they do not bear any cost of litigation under a contingent fee arrangement. If they did, they

would certainly be less likely to pursue litigation.15We consider two types of payments: our narrow measure is defined as the direct payment from the injurer’s

insurance, which includes compensations for medical or other expenses, settlement amounts, if any, or trial awards, ifany. We consider this narrow measure because attorneys in our sample are not negotiating with the claimant’s firstparty insurer meaning that this is the narrowest definition the value added by an attorney. It is also important tonote that the client and attorney’s recovery is typically net of expenses. Thus any cost of litigation other than theattorney’s time would be deducted from recovery before calculating fees. A broader measure includes all forms ofpayment from the claimant’s own health and auto insurance, government insurance such as the Medicare, Medicaid,disability insurance, other passenger’s insurance, and the injurer’s insurance. We consider this broader measurebecause the payments from first party insurance and third party insurance may be substitutes. We also consider bothmeasures net of lawyer’s fees payments.

8

We restrict our attention to claims occurred in states that modified the CS rule during the

sample period. Any claims occurred in states that did not modify the CS rule during the sample

period are excluded. What di↵erentiates the two groups in terms of the instrument is whether the

state applied the modification to all insurance claims or only medical malpractice claims: Zi = 1

indicates the the claim i was in a state that applied the modification to all insurance claims

and Zi = 0 indicates the claim was in a state that applied the CS modification only to medical

malpractice claims. The instrument is not the modification itself, but its scope.

Since the collateral source rule can a↵ect the decision to hire an attorney, we combine Di and Zi

and define potential treatment variables Di(Zi) (Imbens and Angrist (1994)). Since Zi takes two

values, {0, 1}, we have two potential treatment variables; Di(1) stands for the subject’s decision

to hire an attorney when Zi = 1 and Di(0) is the decision when Zi = 0. Thus if Di(1) = 0 and

Di(0) = 1, the subject i would hire an attorney only when his case was under the unmodified

collateral source rule.

The value of the outcome depends on the treatment (decision) and the instrument, so we define

potential outcome variables Yi(Zi, Di). Depending on Zi and Di, we have four potential outcome

variables. For example, Yi(1, 1) is payments the claimant would receive if he decided to hire an

attorney while his case was under a modified state, and Yi(1, 0) is the payment if he did not hire

an attorney in a modified state. Likewise, Y (0, 1) (or Y (0, 0)) are payments if he hired (or did

not hire) an attorney in a non-modified state. We observe n iid samples of triples (Yi, Di, Zi).

The observed variables and potential variables are related by Di = ZiDi(1) + (1 � Zi)Di(0) and

Yi = DiYi(Zi, 1) + (1�Di)Yi(Zi, 0).

One crucial assumption that makes the conventional instrumental variable method work is the

exclusion restriction. Following Angrist, Imbens and Rubin (1996) we write it as

Yi(1, Di) = Yi(0, Di) for Di 2 {0, 1}. (1)

This equation states that, givenDi, the value of Zi is irrelevant to outcomes. The only possible e↵ect

of Zi on Yi is through its e↵ect on Di. Except for this indirect channel, the exclusion restriction

9

says that there is no other channel through which the instrument can a↵ect the outcome. If this is

the case, potential outcomes can be simplified to Yi(Di).

In our setup, however, the instrumental variable (modification of the collateral source rule) has

a clear direct e↵ect on the outcome (payments) in addition to its indirect e↵ect through treatment

(hiring an attorney). The modification of the CS rule a↵ects the awards at trial directly because in

states which modify the CS rule to require o↵sets, the law change mechanically reduces the award

at trial by the amount the claimant has received from first party insurance sources prior to the

judgment. This impact is also expected to reduce the amount at stake in settlement negotiations

since these are constructed in expectation of the award at trial.

Although our instrument has both direct and indirect e↵ects on outcomes, it is the direct e↵ect

that causes a problem since it violates the exclusion restriction. For want of a better term we refer

to our instrument, modification of the CS rule to require o↵sets, as an invalid instrument.16

We solve this invalid instrumental variable problem by combing two facts that are inherent in

modifications to the CS rule requiring o↵sets. First, we introduce a potential outcome variable that

blocks the direct e↵ect of the instrument on outcome. Second, the potential outcome variable can

be linked to observed quantities and therefore its e↵ect can be learned from data. More precisely,

the potential variable we introduce has by design an upper and a lower bound and these bounds

can be constructed from observed quantities.

To do so, we consider a potential outcome Yi(0, Di(1)), the payments the subject i would receive

if the value of the instrument is allowed to a↵ect his decision to hire an attorney (through Di(1))

but not allowed to have a direct e↵ect since the value of the first argument is fixed at 0. The direct

e↵ect of Z on Y is suppressed since we fix the first argument.

Consider two scenarios. If one could assume an exclusion restriction, the individual e↵ect of Zi

on Yi can be written as

TEi = Yi(1, Di(1))� Yi(0, Di(0))

16It may appear to be oxymoronic to call an instrument that violates a crucial requirement of IV but we follow theliterature’s terminology and call it an invalid instrument.

10

We call this value the total e↵ect for the individual i. If the exclusion restriction is violated, the

expression Yi(1, Di(1)) is problematic because it includes both direct and indirect e↵ects of Zi on

Yi. To remove this direct e↵ect, we use Yi(0, Di(1)) as a way to measure the changes in outcomes

and define the indirect e↵ect (IE)17 of Zi on Yi as

IEi = Yi(0, Di(1))� Yi(0, Di(0)).

Individual e↵ects (TEi or IEi) cannot be measured. What we can measure instead is their

average values. The average total treatment e↵ect of lawyers would be given by

E[TEi] = E[Y (1, D(1))� Y (0, D(0))].

This e↵ect is not casual because modifications to the CS rule impact payments directly through

the required o↵sets. Therefore we use the average indirect treatment e↵ect, which does not allow

the direct e↵ect,

E[IEi] = E[Y (0, D(1))� Y (0, D(0))]. (2)

Since the direct e↵ect is blocked the modification to the CS rule impacts payment only through

the decision to hire a lawyer or not. This would have a causal interpretation.

3.2 Assumptions

We make the following assumptions.

Assumption 1 (Existence of (invalid) instruments) Let Zi be a binary random variable such

that

(i) P (z) = E[Di|Zi = z] is a non-trivial function of z,

17To understand the indirect e↵ect, consider the following thought experiment. Imagine that we allow the treatmentvariable to be changed from the value that would occur if the claimant’s case was in a modified state, Di(1), to thevalue that would occur if his case was in a non-modified state, Di(0). But we hold the direct e↵ect of the modificationat 0. What would be the change in outcomes? This counter-factual change is captured by IEi.

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(ii) {Yi(1, 1), Yi(1, 0), Yi(0, 1), Yi(0, 0), Di(1), Di(0)} are independent of Zi.

The first part of the assumption implies that the instrument Z has a non-zero e↵ect on the

treatment D, i.e. P (1)� P (0) = E[D(1)�D(0)] 6= 0. The second part of the assumption implies

the existence of a randomly assigned instrument but it also has a larger meaning. A random

assignment of Z does not guarante (ii); if Z is randomly assigned, it implies that the potential

treatment variables (Di(1), Di(0)) are independent of the instrument Z, but it does not imply that

the potential outcomes are independent of Z. In fact, the assumption (ii) means a particular type

of exclusion-like restriction in addition to independence of instrument.

To illustrate this, let’s consider a linear latent index model18

Yi = �0 + �1Di + �2Zi + "i (3)

D

⇤i = ↵0 + ↵1Zi + vi (4)

and

Di =

⇢

1 if D

⇤i � 0,

0 if D

⇤i < 0. (5)

In this simple, stylized model, Yi is the outcome, D⇤i is a continuous latent variable that can be

interpreted as the net utility from hiring an attorney, and Di is the observed decision variable. Here

the causal e↵ect of an attorney is captured by �1. The assumption (i) means that Cov(Zi, Di) 6= 0,

which can be interpreted as a requirement ↵1 6= 0. If �2 = 0, we have a conventional instrumental

variables model: the instrument Z has no direct e↵ect on the outcome but can have an indirect

e↵ect through its e↵ect on D. If �2 6= 0, Z has the direct e↵ect as well, a violation of the exclusion

restriction (1), so we have an invalid instrument problem. Given this background, what assumption

(ii) means is that

E[Zi"i] = 0 , E[Zivi] = 0.

18Note that we do not need to assume a linear functional form and/or constant treatment e↵ect that are inherentin this particular model. We use this simplified model only for the expositional purpose.

12

The zero correlation between Zi and "i summarises the idea that except for the direct e↵ect,

any other e↵ect of Z on Y must be due to the e↵ect of Z on D, i.e. the only possible indirect

channel is through D. The zero correlation between Zi and "i is guaranteed if the instrument is

random. Since "i and vi can be correlated, the zero correlation between Zi and vi guarantees that

there is no other indirect channel through the selection equation. So the key assumption we make

through (ii) is that we only allow two channels of e↵ect of Z on Y , a direct e↵ect (as captured by

a possibly non-zero �2) and an indirect e↵ect through D, but nothing else.

This assumption can be violated if there is a second indirect channel through which our instru-

mental variable may influence outcomes. One potential channel is that the modification of the CS

rule may change market environments for attorneys and change their approach to litigating the

case. For example, a modified CS rule may make attorneys exert more e↵ort in each case regardless

of the terms of the contract. Another possibility is that given new market conditions, attorneys

may change the fee structures in contracts with their client essentially increasing the fees rather

than simply refusing more cases. This will a↵ect net benefits of their customers. By assumption

(ii) we are essentially assuming that there is no such ‘second indirect’ channel. We are assuming

that attorneys are operating in a competitive market and behaving as price-takers.

The next assumption is the individual level monotonicity.

Assumption 2 (Monotonicity)

Di(1) Di(0) for all i.

This is a fundamentally untestable condition. In our case, the simple supply-demand analysis

in Section 2 predicts the assumption.

Under the monotonicity, there are only three distinct groups: ‘never-takers’ is a group of subjects

who never hire lawyers (Di(0) = Di(1) = 0), ‘compliers’ is those whose decision is a↵ected by

the law change in the sense that he would hire only when he was under a non-modified state

(Di(1) = 0, Di(0) = 1), and ‘always-takers’ is who always hire lawyers (Di(0) = Di(1) = 1). What

is not allowed under the monotonicity assumption is the existence of the so-called ‘defiers’, a set

13

of subjects who would hire attorneys only when he was in a modified state (Di(1) = 1, Di(0) = 0).

We will see that the e↵ect we can identify under the given assumptions and data is the e↵ect on

compliers.

4 Estimation Method

This section extends Imbens and Angrist (1994) and obtains a local average treatment e↵ect (LATE)

type estimator when instrumental variable is invalid.

Proposition 3 The local average indirect e↵ect (on compliers) can be identified by

E [Y (0, D(1))� Y (0, D(0))|D(1)�D(0) = �1] =E[Y (0, D(1))|Z = 1]� E[Y (0, D(0))|Z = 0]

E[D|Z = 1]� E[D|Z = 0].

(6)

Proof. By the independence assumption, the numerator of the right hand side of (6) is equal to

E[Y (0, D(1))� Y (0, D(0))]. By the law of iterated expectation,

E[Y (0, D(1))� Y (0, D(0))] = Pr(D(1)�D(0) = �1)E[Y (0, D(1))� Y (0, D(0))|D(1)�D(0) = �1]

+ Pr(D(1)�D(0) = 0)E[Y (0, D(1))� Y (0, D(0))|D(1)�D(0) = 0].

Here we use the non-existence of defiers due to the monotonicity. The second term on the right hand

side includes two types; never-takers, D(1) = D(0) = 0, and always-takers, D(1) = D(0) = 1. For

either type, we argue that Y (0, D(1))�Y (0, D(0)) = 0. To see this, consider never-takers. Because

Di(1) = Di(1) = 0, the e↵ect becomes Y (0, 0)�Y (0, 0) = 0. The same reasoning applies to always-

takers. So we conclude that E[Y (0, D1)�Y (0, D0)|D(1)�D(0) = 0] = 0. The second term vanishes.

The independence assumption means that Pr(D(1)�D(0) = �1) = E[D|Z = 1]�E[D|Z = 0], so

we get the expression (6).

To understand the expression (6), compare it to the LATE estimator with exclusion restriction.

In such a case, because E[Y |Z = 1] = E[Y D + Y (1 � D)|Z = 1] = E[Y (1, D(1))|Z = 1] and

E[Y |Z = 0] = E[Y D + Y (1 � D)|Z = 0] = E[Y (1, D(0))|Z = 0], the average total e↵ect for the

14

compliers can be written as

E[Y (1, D(1))� Y (0, D(0))|D(0)�D(1) = �1] =E[Y |Z = 1]� E[Y |Z = 0]

E[D|Z = 1]� E[D|Z = 0]

=E[Y (1, D(1))|Z = 1]� E[Y (0, D(0))|Z = 0]

E[D|Z = 1]� E[D|Z = 0].

(7)

The di↵erence is that we use indirect e↵ect IEi in (6) but use total e↵ect TEi in (7). The aver-

age indirect e↵ect in (6) is what we can estimate when we cannot assume the typical exclusion

restriction.

What remains uncertain in (6) is that Yi(0, Di(1)) is not observed. We need to link this potential

outcome to an observable quality; ideally Yi(1, Di(1)). For this purpose, let Wi be the maximum

that can be deducted from claimant’s settlement or trial awards under the modified CS rule. Note

that the exact nature of Wi depends on the year and state in which the accident occurred, because

state laws specify what types of insurance payments claimants have received (or will receive) should

be deducted from settlements or awards. In our sample the 23 states that have modified the

collateral source rule to require the trial court to deduct payments from the claimant’s judgment all

require o↵sets for first party health and auto insurance and the majority for workers compensation

and government provided health insurance.19 For more information on state specific rules, see

Table 4. The maximum Wi can take is when the possible judgment includes all sorts of payments

from all first party insurance sources available to the victim. We call this value the claimant’s ‘own’

insurance for simplicity, but it may includes payments from disability insurance, health insurance

including Medicare, Medicaid, and worker’s compensation plans. For all intents and purposes Wi

includes all source of insurance payments that are not from injurer’s insurance.20 Again depending

on what a state’s CS rule modification specifies, the actual Wi can di↵er from this maximum

amount.19Our sample predates strict enforcement of the Medicare Secondary Payer Act which requires repayment of all

expenses paid by Medicare. See Helland and Kipperman (2011)20In contrast, recall that the observed outcome Yi includes the payment from injurer’s insurance.

15

We assume that Wi is not a↵ected by Di or Zi because payments from ‘own’ insurance are

mostly mechanically determined by the reimbursements of medical bills or other damages. These

payments depend on characteristics of accidents and not on the decision to retain a lawyer or the

modification of the CS rule.

For the relationship between the unobserved quantity, Yi(0, Di(1)), and observed quantities,

Yi(1, Di(1)) and Wi, we assume the following.

Assumption 4 (Bounds on potential outcomes)

Yi(1, Di(1)) Yi(0, Di(1)) Yi(1, Di(1)) +Wi for all i.

In many ways this is not an assumption. It simply describes the mechanical way that the

modifications to the collateral source rule requiring o↵sets work. The first inequality, Yi(1, Di(1))

Yi(0, Di(1)) follows from how o↵sets under a modified collateral source rule work. The plainti↵ may

be paid twice for the same damage under the CS rule (captured by Y (0, d)) but may not under the

modification of the CS rule (as captured by Y (1, d)). So the former must be always greater than

or equal to the latter. The second inequality Yi(0, Di(1)) Yi(1, Di(1)) +Wi simply says that the

maximum that can be deducted from awards or settlements is Wi, the sum of all payments from

other collateral sources.

When the assumption holds, we have an interval identification of the average indirect e↵ect.

We state it as a proposition.

Proposition 5 Under Assumptions 1, 2, 4, the average partial e↵ect E [Y (0, D1)� Y (0, D0)|D1 �D0 = �1]

must lies in an interval [AIEL,AIEU ] where

AIEU =E[Yi|Zi = 1]� E[Yi|Zi = 0]

E[Di|Zi = 1]� E[Di|Zi = 0],

AIEL =E[Yi +Wi|Zi = 1]� E[Yi|Zi = 0]

E[Di|Zi = 1]� E[Di|Zi = 0].

And this bound is sharp in the sense that it is the narrowest bound that can be determined from

16

data and is still consistent with the given assumptions.

Note that this bound can be uniquely determined from observed quantities. In Section 7, we

present estimates of this bound to measure the value of an attorney.

So far, we focus exclusively on the average e↵ect. However, as is common in this type of

analysis, the data has a non-trivial right tail caused by several large payments. Most claims in our

dataset are relatively minor and therefore lead to small insurance payments and settlements/awards.

There are, however, occasional but infrequent large outliers in the sample. These outliers have a

significant influence on the average treatment e↵ect. Common approaches to outliers, such as

winsorized means or trimmed means, are not desirable considering that much of the policy debate

about lawyer values in the recovery process arises in the context of cases with serious stakes and

potentially large payments. These infrequent large payments may have valuable information so we

are reluctant to drop them.

For this reason we extend our analysis and consider the quantile indirect treatment e↵ects.

The median indirect treatment e↵ect is a special case of quantile indirect e↵ects. It is useful

because quantiles are less (or even not) a↵ected by outliers. Following Abadie (2002), we define

potential outcome distribution functions. We then invert them and obtain potential outcome

quantile functions. The ⌧ -th quantile e↵ects will be defined as the di↵erence in two such quantile

functions.

Let QY (0,D(1))(⌧ |D(1) �D(0) = �1) denote the ⌧ -th quantile of Y (0, D(1)) for compliers and

let QY (0,D(0))(⌧ |D(1) � D(0) = �1) be the ⌧ -th quantile of Y (0, D(1)) for compliers. The ⌧ -th

quantile indirect e↵ect is defined by

QY (0,D(1))(⌧ |D(1)�D(0) = �1)�QY (0,D(0))(⌧ |D(1)�D(0) = �1).

The next proposition states its sharp bound.

Proposition 6 Under Assumptions 1, 2, 4, the sharp bound of the quantile indirect e↵ect is given

as [QIEL,QIEU ] where

17

QIEU = Q

U(1) (⌧ |D(1)�D(0) = �1)�Q(0) (⌧ |D(1)�D(0) = �1) ,

QIEL = Q

L(1) (⌧ |D(1)�D(0) = �1)�Q(0) (⌧ |D(1)�D(0) = �1) ,

where we define potential quantile functions as

Q

U(1) (⌧ |D(1)�D(0) = �1) = inf

n

y|FU(1) (y|D(1)�D(0) = �1) � ⌧

o

,

Q

L(1) (⌧ |D(1)�D(0) = �1) = inf

n

y|FL(1) (y|D(1)�D(0) = �1) � ⌧

o

,

Q(0) (⌧ |D(1)�D(0) = �1) = inf�

y|F(0) (y|D(1)�D(0) = �1) � ⌧

.

The corresponding potential distribution functions are defined as

F

U(1) (y|D(1)�D(0) = �1) =

E[1{Y y}D|Z = 1]� E[1{Y y}D|Z = 0]

E[D|Z = 1]� E[D|Z = 0],

F

L(1) (y|D(1)�D(0) = �1) =

E[1{Y +W y}D|Z = 1]� E[1{Y +W y}D|Z = 0]

E[D|Z = 1]� E[D|Z = 0],

F(0) (y|D(1)�D(0) = �1) =E[1{Y y}(1�D)|Z = 1]� E[1{Y y}(1�D)|Z = 0]

E[1�D|Z = 1]� E[1�D|Z = 0].

The bounds on the potential distribution functions, therefore, the potential quantile functions,

only depend on observed quantities and can be estimated consistently.

5 Data and Variable Construction

5.1 Survey of Auto Injury Claims

The data for this study comes from the Insurance Research Council (IRC)’s Consumer Panel Study

of Auto Injury Claims. Because the data surveys accident victims it has several advantages for our

research over more traditional closed claim data. Most importantly for our purposes the Consumer

Panel contains data on payments from both first party insurance and third party sources. Under

a first party insurance contract the injured party is paid by his or her insurer in the event of an

injury regardless of whether the injury was caused by a third party or whether that 3rd party was

18

at fault. Health and auto insurance are the most common first party insurance in the data with

Medicare and Medicaid being the third and fourth most common insurance. Under third party (or

liability) insurance, the insured is protected against claims by a third party who alleges a negligent

action. Thus in our context third party payments are payments either from a liable or potentially

liable driver of another vehicle involved in the accident.

A “claimant” in our data who was involved in an accident and does not retain an attorney

might receive compensation from their own insurance (private health or auto insurance, Medicare,

Medicaid, worker’s compensation, or other sources), a third party insurer (even if they did not hire

an attorney or file a legal claim) or no compensation for the accident. This is also true of a claimant

who retained an attorney.21 The IRC Consumer Panel only contains data on the use of a lawyer in

a third party claim so we are certain that the lawyer in question did not help the claimant recover

from their own insurance.

The data covers the years 1982 to 2002 and all 50 states and the District of Columbia. The

Distribution of accidents by year is shown in Table 1 and the distribution by state is shown in

Table 2. The data contains information the age and gender of the claimant. We include these

variables to proxy both for potential di↵erences in bargaining strategy across age and gender but

also as a control for the potential scope of damage.22 We also include data on the scope of the

accident in terms of whether the accident was a collision with another moving vehicle, whether the

accident was a single vehicle accident, and the number of injured parties in the accident. The data

also contain information on the size of the claimant’s alleged injuries such as the number of days

of work lost, the amount of the claimants (alleged) medical bills and the total amount of alleged

damages. We also include whether the state has capped noneconomic damages at the time of the

accident, whether the state has no fault insurance laws and/or mandatory insurance policy. The

noneconomic damages indicator is derived from Ronen Avraham’s Database of State Tort Law

21The terminology for the accident victim becomes somewhat problematic in that we would typically refer to anaccident victim who sues another party as the plainti↵. However, since we are comparing the accident victim in thestate in which they retain a lawyer to assist them in receiving a payment from a third party to states in which theydo not, we choose to refer to the accident victims as claimants in both situations and askew the use of the wordplainti↵.

22Retired individuals, for example, cannot claim lost wages making their claims somewhat less lucrative to attorneysregardless of whether the collateral source role has been modified.

19

Reforms (DSTLR 5.1), however, we examined state statutes to determine if the cap applied to auto

injury cases as well as medical malpractice.23

We also include the real state per capita income and state population. The first party insurance

payments are largely determined by medical expenses and damages which would be tied to lost

income. So the former controls for any state-wide di↵erences in expenses or damages. The number

of accidents and therefore the number of claims is widely di↵erent across states, so the latter controls

for the relative representation of states in our sample. The summary statistics of our variables,

overall and broken down by whether the claimant hired a lawyer, talked to a lawyer or did not hire

or talk to a lawyer are given in Table 3.

Several patterns are clear from the summary statistics. First, cases involving more injured

parties, with more days of lost work and with significantly higher alleged medical costs and damages,

talk to or hire attorneys.24 This is not surprising since attorney are paid on a contingent fee in

these cases and are hence more likely to take larger cases. Since both victims and lawyers are

selective, however, simply regressing the presence of an attorney on compensation will be biased.

We construct four measures of the claimants total payment received as a result of their injury.

The broadest measure we label Total Payment and it captures compensation from all sources

inclusive of both first party health, government provided insurance, private auto insurance and

workers compensation and third party payments from the defendant’s auto insurance or personal

assets. Given the nature of the survey these are final payments and thus in states that have modified

their collateral source rule to require o↵sets for payments from first party insurers, the payments

at trial would reflect the required reductions. Our assumption is that payment in settlements are

negotiated based on the expected outcome at trial and thus would represent a bargain struck in

the shadow of the o↵set. One reason for estimating attorney’s impact on total payments is that the

proceeds of litigation, once they are secured either through litigation, or the threat of litigation,

must be used to pay for treatment of injuries resulting from the accident. In this way payments

from litigation preempt payments, at least in part, from first party insurance after the litigation is

23During out sample period 31 states have caps on non-economic damages for medical malpractice cases while only13 states have non-economic damage caps that apply to auto accidents.

24This maybe because these cases are inherently more complex. Shavell (2004) finds that the more complex thecase, the more likely an individual is to pursue litigation.

20

complete. This means that lawyers, at least indirectly, impact payments from first party insurance

over the course of the patients long term treatment in claims that involve litigation.

Our second measure is Direct Payments, which represents only payments from third parties. It

is common to receive compensation for injuries from a third party insurer even when the claimant

has not hired a lawyer so this measure is a more direct measure of attorneys value to their clients

relative to what the client would have been able to secure from third parties absent the presence

of the attorney. Our final two outcome measures take our Total and Direct payments and net out

attorney’s fees. These are typically one third of the total amount received in litigation although

the data contains some fees as high as 50% if the case went to trial and some fee contracts that

include fixed payments to the attorney, hourly rates and expenses (in the event that the client does

not recovery anything from the defendant).

5.2 Construction of the Instrument

In Table 4 we provide a state by state breakdown of our instrument. The status of the collateral

source rule, the year it was modified, and the statute modifying the rule are provided. The data

on the modifications to the CS rule also come from Roen Avraham’s DSTLR 5.1 but again we

examine the specific state statute to determine if it applies only to medical malpractice cases or

also includes auto cases. The entry ‘None’ in the ‘Statute’ column means that the state has never

modified the CS rule. In the ‘Types of claims’ column, ‘Medical only’ means that the modifications

only applies to Medical Malpractice cases and ‘All’ means that it applies to any cases. In some

cases the modification of the CS rule has been overturned by the state supreme court (e.g. Georgia

and Illinois). In those cases, the ‘E↵ective Date’ have both starting and ending dates.25

In Tables 5 and 6 we provide the breakdown of the sample by whether the state has modified

its collateral source rule. Table 5 includes all accidents while Table 6 only includes collisions with

another vehicles that report positive damages. The tables provide summary statistics of three

subgroups and the whole sample. Column (1) includes claims in state that modified the CS rule

and applied it to all types of claims, after the modification. Column (2) includes claims in states

25Note that if the law was enjoined, we use only the years for which it was in e↵ect.

21

that modified the rule but restricted its application to medical malpractice claims. Column (3)

includes claims in states that did not modify the CS rule. Column (4) is the whole sample. Our

identification strategy regards the claims in column (1) as the group with Z = 1 and claims in

column (2), plus claims in the states in (1) but occurred outside years in which the CS modification

was in e↵ect, as the group with Z = 0. A single vehicle accident or an accident with zero damage

rarely gets any third party insurance payment. So from now on we focus on the restricted sample

in Table 6.

The averages of the claimant demographics are similar across both modified and unmodified

states. By contrast claims in modified states appear to be more severe when judged from medical

costs or damages. This is interesting because modified states have slightly lower number of work

days lost. The probability of hiring lawyers is lower in modified states, which is consistent with

the theoretical prediction in Section 2. We provide additional statistical evidences supporting

the prediction shortly. The direct payment, payments from the third party insurance and trial

awards, is slightly lower in modified states, while the total payment, including victim’s own auto

and health insurance, is slightly higher. One possible explanation of the overall pattern is that

victims eventually get more from their own insurance when they lose by not hiring a lawyer. Put

di↵erently if a victim is dissuaded from hiring a lawyer by the modified CS rule, then he may claim

more of his injuries on his own insurance.

In Table 7 we present the probability of an accident victim hiring an attorney. We apply the

same sampling restriction as in Table 6, that is, we use collisions with non-zero damages. Group

1 are the treatment states which modified the collateral source rule for all case types. Before the

modification a claim had a 37.75% chance of being represented by an attorney. The likelihood of

being represented by an attorney falls to 34.49% after these states modify the collateral source rule.

This di↵erence is statistically significant with a t-value of 2.178 (p-value of 0.029). Group 2 are the

states which modified the collateral source rule only for medical malpractice cases, and hence had

the same political pressures to modify the collateral source rule but decided not modify it for all

cases. In this group, after the modification, a claim had a 38.36% chance of being represented by an

attorney. Between two groups, the di↵erence after the modification is statistically significant with

22

a t-value of -3.188 (p-value of 0.001). These two cases (Before vs. After in Group 1 and Group 1

vs. Group 2 after the modification) are the only significant changes in hiring probabilities and the

di↵erence is due to the prevalence of the CS rule change. Any other di↵erences are not statistically

significant. This is what we should expect if the theoretical prediction is correct.

In Table 8 we test the di↵erences between the probability of hiring a lawyer in states that

modified the collateral source rule before the modification was enacted against the same probability

in states that either modified the rule only for medical malpractice cases or for states which did

not modify the rule at all. As would be expected if the collateral source rule is causal in change the

probability of hiring a lawyer in auto claims, none of these groups show a statistically significant

di↵erence (because none of three groups were a↵ected by the CS rule change). This is consistent

with the theory.

6 Other Tort Reforms and Controlling for Covariates

There were other tort reforms in some states besides the modification of the collateral source rule

during the sample period. If other reforms have significant e↵ects on the payments that claimants

would receive, it will be important to control for these confounding factors. If states passed cluster

of these reforms, for example, the cap on noneconomic damages and the changes in the CS rule,

together, or if the changes in the collateral source rule triggered other reforms, the failure to control

for other factors can cause biases even if the instrument is as good as random.

This section discuss a simple method to control for the e↵ects of covariates including the passage

of other tort reforms. Allowing the e↵ects from covariates can be useful in two ways. It helps us

to refine the identification assumption, making the independence assumption (Assumption 1(ii))

conditional on covariates. This expands the plausibility of the assumption. We can also allow the

size of treatment e↵ects di↵erent for individual claims. By using covariates we can express the

idea that the e↵ects for claims can be distinct if claims can be di↵erentiated by means of their

covariates. We then use the reweighing method such as in Abadie (2005) to estimate the overall

treatment e↵ects, using covariate-dependent weights.

23

Our data includes the following tort reforms. Compulsory insurance is that state requires drivers

to have auto insurance. Noneconomic damage cap is that state caps noneconomic damages at the

time of the accident. No fault is that state has no fault insurance laws. Caps on attorney fees is

that state impose a cap on the lawyer’s fees. In addition, punitive damage cap is a cap on punitive

damages. Total damage cap is a cap on total damages. Joint liability is a limitation on joint and

several liability which means that in a multiple car accident one can recover all his damages from

di↵erent one’s party if another party can pay due to bankruptcy. Periodic payments is a payment

schedule for awards that means the plainti↵ doesn’t get a lump sum but gets periodic payments on

an agreed schedule set by the state. Punitive evidence sets a higher standard of proof for punitive

damages.

We also have a rich set of covariates other than tort reforms. They can be grouped into two

categories. The first group includes accidents specific variables. They include age and gender of

the claimant, number of persons injured in the accident, whether the accident was a collision with

another vehicle, whether the accident involved only a single vehicle, whether the accident involves

a pedestrian, the number of days lost, whether the victim has any insurance, medical expenses, and

(alleged) damages. The second groups are state specific variables that show the size and economics

conditions of each state. They include state real per capita income and state population. Let Xi

be the collection of covariates and Di is the decision to hire an attorney.

We use a simple method in Athey and Imbens (2006). The first stage is the following predictive

regression (without the overall intercept)

Yi = �1Di + �2(1�Di) +Xi� + ui (8)

Then construct the residuals with the group-specific e↵ects left in:

b

Yi = Yi �Xi� = �1Di + �2(1�Di) + ui. (9)

Finally, we use b

Yi as the outcome variable to estimate the average and quantile indirect treat-

24

ment e↵ects. 26

7 Empirical Findings

In the theoretical literature, discussed above, the value of an attorney is ambiguous. There is no

a priori reason to believe that lawyers will not systematically charge more than the surplus they

generate net of fees or that their presence will not systematically result in a lower payment than the

client would have received without them due to expenses. Yet there is also no reason to suppose

the reverse. The typical approach to this problem is to run the following regression,

paymenti = �0 + �1lawyeri + �2xi + ✏i (10)

where paymenti is one of our four measures of the claimants recovery, lawyeri is a discrete variable

equal to one if the claimant hires an attorney, xi is a set of control variables, and ✏i is the error

terms.

The results of this regression are shown in Tables 9 and 10. As shown in the regression the

impact of hiring an attorney on the direct payment is $ 18,266 or $18,343 depending on whether

the state and year fixed e↵ects are included in the regression model. This number rises to $33,614

or $ 31,349 when we include only payments from first party sources. When we net attorney’s fees

from our two measures of payments, the size of e↵ect falls to the range from $12,414 to $24,785.

The estimated e↵ects are always significantly di↵erent from zero. In all four cases, lawyers appear

to generate considerable value. This is even true holding constant a number of factors that could

plausibly impact the value of the claim.

The di�culty is that the decision to retain an attorney is likely to be endogenous. As noted

above our instrument, modifications to the collateral source rule that mandates o↵sets, certainly

impacts the likelihood of hiring an attorney, as shown in Table 11. In the linear probability model

the reduction in the likelihood of hiring an attorney is 6.4% when a state modifies its CS rule. The

impact is similar when we estimate the model with a logit or probit and continues to be negative

26We apply the above procedure for Yi and Wi separately.

25

in the fixed e↵ects logit although it is not significant.

In Table 12 we present the results of our alternative approach. Our estimate of the bounds

on the average indirect e↵ect of an attorney on claim value finds the causal impact is between a

$51,407 reduction to as much as a $230,879 reduction for total payments. Thus relative to simply

taking the payment on o↵er from the first party insurance sources and any payments from third

party insurers, lawyers actually reduce the amount recovered. Taken at face value this suggests that

potential clients are, on average, better o↵ without an attorney’s assistance. The impact on direct

payments for the injurer’s insurance is larger: $185,793 reduction to $9,980 increase suggesting that

this e↵ect is at least in part driven by the some substitutability between first party and third party

insurance.

In our two ‘after fees’ measures, the measures are $219,557 reduction to $40,085 reduction

for total payments and $174,471 reduction to $15,430 increase for direct payments. The negative

impact, even before we account for fees, is likely caused by expenses the claimant must incur to use

the tort system such as court costs and expert witness fees. Under the US system each side pays its

own expenses. In losing claims attorneys pay these costs but when the plainti↵ winds the expenses

are deducted from gross recovery. Particularly large claims involving more complex litigation these

expenses would be paid before the contingent fee was applied and the clients recovery would be net

of these expenses.27 For example in Helland et al.’s (2017) examination of expenses in New York

contingent fee litigation the typical expense is about 4% of gross recovery reflecting primarily filing

fees and medical records. These expenses can rise dramatically when expert witnesses and more

expensive forms of discovery are required, as they typically are in larger and more complex cases.

Since these costs are born by the claimant when they purse a successful claim, it is possible for

them to receive less, particularly in large claims, than they would have absent hiring an attorney.

These numbers might appear too large, however, the issue is likely some very large outliers

in the claims payments. Although the average payment is $17,210 the median payment is $4,369

suggesting a large right tail. It is possible, as Hammitt (1985) finds using the 1986 sample of the

data, that for very large claims the damages are so large and injuries so obvious that hiring an

27Our survey does not include these expenses and only identifies how much the attorney was paid and how muchwas received by the client.

26

attorney reduces the total payments received by the claimant both through the lawyer’s fees and

because the adversarial system’s expenses actually consumes more of the payment than the surplus

generated by the attorney.

If the negative value of attorneys in auto claims is driven by expenses, which are not observable

in our data, then the negative impact of attorneys should be driven by larger cases. In the remainder

of Table 12 we examine the impact broken down by quantile. At the lowest quantile (⌧ = .25) the

bounds on the impact of an attorney on all four of our measures includes zero, although for direct

payments the upper bound is zero. When we examine the median (⌧ = .50) the bounds continue

to include zero indicating that we cannot say whether attorneys create value for their clients. Even

at the 75th percentile (⌧ = .75) we continue to find no discernible impact on total recovery from

hiring an attorney. This changes when we examine the highest quantiles (⌧ = .95). Here we find

that for all four measures the upper and lower bounds are both negative. This suggests that our

negative upper and lower bounds on the average e↵ect are driven by large outliers.

The results of our quantile bounds are graphed in Figure 1 and 2. In both cases the bounds

suggest a negative impact only at the top portion of the distribution. One open question is why

hiring an attorney has such a large impact, even before fees, in large cases. These cases are much

more complex suggesting that the clients recover, what we are measuring, will be reduced by expert

witness fees, deposition fees and other costs that represent a sizable portion of the payment in any

complex case. Since attorneys fees do not include these costs, triggering them may well be extremely

costly and appears to actually reduce total compensation.

Table 13 reports results allowing for covariates. Overall, the estimated average and quantile

indirect e↵ects lead to the same conclusions that we reported in Table 12. One discernible di↵erence

is the magnitude of the average e↵ects, they are smaller now for the direct payments but not so

much for the total payments. This is because the covariates mainly help to explain the variation in

the first party payments (which is a bigger part of the total payment), but does not really explain

the variation in the third party insurance or litigation outcomes.

27

8 Conclusion

In this paper we examine the value added by hiring an attorney. A simple comparison of recoveries

in cases with and without attorneys will be uninformative given the endogenous nature of retaining

a lawyer. We utilize modifications to the collateral source rule that require payments from first

party insurance sources to be deducted from any award as an instrument for retaining an attorney.

The instrument is problematic in the sense that it impacts both the likelihood of retaining an

attorney and the eventual recovery. We exploit the mechanical nature of modification to the CS’s

o↵sets to produce bounds on the impact of attorneys on claim value.

Overall the results are consistent with the di↵erence between hiring an attorney and merely

accepted the payments o↵ered from first party and third party insurers without representation as,

on average, having the same return. That is for the average case lawyers do not add, or subtract

value from the case. This would suggest that the selection process of cases for representation works

well and that there are di↵erent levels of investment by attorneys in the case to make di↵erent

recoveries profitable. Evidence that at least part of this e↵ect is driven by market segmentation

is found in Engstrom’s (2009, 2011) studies which find that a large number of low value auto

case claimants seeking a lawyer will handled by “settlement mills” rahter than by more traditional

attorneys.28 In a competitive market plainti↵ firms would make investments in the case up to

the point where the potential client was just indi↵erent between the payment on o↵er from the

relevant insurers and fees charged by the attorney. Thus market pressures induce some segment of

the market, either “settlement mills” or traditional attorneys, to provide representation for most

clients seeking a lawyer. This e↵ect mitigates against positive returns to retaining a lawyer since

some attorney will pick up almost any case for which the contingent fee exceeds the cost of the

lawyers time.

Kritzer (2004) argues that the reputational constraints deter self-dealing by lawyers. Reputa-

tional penalties keep attorneys from pushing the returns into negative territory and simply taking

28Engstrom (2009, 2011) distinguishes “settlement mills” from more traditional firms in that the receive the majorityof their clients from advertising, invest relatively little time and e↵ort in the claim an settle a large volume of cases.By contrast traditional firms o↵er more case screening but invest more in each claim and thus require a higher returnto be competitive.

28

a one third cut of the payment the client would have received without representation. The com-

bination of market pressures to settle cases quickly and with minimum investment combined with

reputational penalties for settling cases too cheaply would produce exactly the phenomenon we

observer for the bottom 90% of our cases. Specifically an average return over the amount o↵ered

by insurers in the absence of legal representation of zero.

The question remains why these two limiting factors pushing the return above opportunity cost

to zero break down for larger cases. Engstrom (2011) argues that larger claims involving more

serious injuries simply require greater investment of attorney time and greater expenses. Assuming

that the value of the claimants injury is fairly consistent it is perhaps not surprising that on average

once expert witness fees and other expenses are deducted from any settlement amount the premium

earned by a lawyer over the amount paid to claimants is negative.

29

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31

Table 1: Distribution of Accidents, by year

Accident Year Frequency Percentage

1982 162 0.9

1983 839 4.7

1984 1229 6.9

1985 1350 7.6

1986 198 1.1

1989 1471 8.2

1990 1693 9.5

1991 2045 11.5

1992 155 0.9

1995 1327 7.4

1996 1728 9.7

1997 2132 12.0

1998 218 1.2

1999 955 5.4

2000 952 5.3

2001 1190 6.7

2002 187 1.0

Total 17831 100.0

Number of accidents by year.

Table 2: Distribution of Accidents, by state

Accident State Frequency Percentage Accident State Frequency Percentage

AK 4 0.02 MT 59 0.33

AL 273 1.53 NC 551 3.09

AR 266 1.49 ND 30 0.17

AZ 331 1.86 NE 121 0.68

CA 2061 11.56 NH 109 0.61

CO 250 1.4 NJ 568 3.19

CT 184 1.03 NM 95 0.53

DC 40 0.22 NV 107 0.6

DE 73 0.41 NY 1075 6.03

FL 877 4.92 OH 774 4.34

GA 470 2.64 OK 285 1.6

HI 2 0.01 OR 302 1.69

IA 211 1.18 PA 834 4.68

ID 82 0.46 RI 93 0.52

IL 725 4.07 SC 302 1.69

IN 430 2.41 SD 46 0.26

KS 131 0.73 TN 365 2.05

KY 319 1.79 TX 1178 6.61

LA 335 1.88 UT 143 0.8

MA 392 2.2 VA 384 2.15

MD 416 2.33 VT 36 0.2

ME 92 0.52 WA 475 2.66

MI 574 3.22 WI 351 1.97

MN 232 1.3 WV 147 0.82

MO 419 2.35 WY 33 0.19

MS 179 1.0 Total 17831 100.0

Number of accidents by state.

Table 3: Characteristics of Claims, by decision to hire lawyers

Variables Hired LawyerTalked to but

not hired LawyerNot hiredLawyer Whole Sample

Mean Median Mean Median Mean Median Mean Median

Age of Claimant 37.40 36.00 36.08 34.00 36.51 34.00 36.81 35.00

Claimant was Male 0.42 0.00 0.40 0.00 0.40 0.00 0.41 0.00

Number Injured 1.41 1.00 1.30 1.00 1.33 1.00 1.36 1.00

Number of Work Days Lost 29.10 1.00 10.85 0.00 7.29 0.00 14.58 0.00

Accident was a Collision 0.89 1.00 0.88 1.00 0.78 1.00 0.82 1.00

Accident was a Single Vehicle 0.05 0.00 0.07 0.00 0.19 0.00 0.14 0.00

No Fault 0.24 0.00 0.22 0.00 0.24 0.00 0.24 0.00

Modified CS Rule 0.23 0.00 0.25 0.00 0.27 0.00 0.25 0.00

Non-economic Damages Cap 0.08 0.00 0.06 0.00 0.08 0.00 0.08 0.00

State per-capita Income 33,120 32,960 32,670 32,610 32,670 32,520 32,820 32,770

Amount Claimed in Medical Cost 18,760 5,096 8,653 1,717 5,579 931 10,070 1,720

Amount Claimed in Damages 18,550 4,489 9,001 1,585 5,258 688 9,700 1,239

Total Amount Recovered 43,540 11,470 10,110 3,967 6,760 2,244 18,680 3,830

Total Recovered after fees 34,350 9,186 10,100 3,967 6,759 2,244 15,700 3,578

Direct Payment 19,100 0.00 4,124 227 2,229 0.00 9,755 0.00

Direct Payment after fees 13,620 0.00 4,117 224 2,227 0.00 7,308 0.00

All dollar amounts are measured in 2002 constant dollars.

Table 4: Collateral Source Rule Modifications Requiring O↵sets of 1st Party Insurance Payments

State Statute Year Types of Claims E↵ective Date

Alabama §12-21-45 1987 All June, 1987

Alaska §09.17.070 1986 All 1986 (amended Apr, 2008)

Arizona §12-565 1976 Medical only 1976

Arkansas None

California §3333.1 1975 Medical only Dec, 1975

Colorado §13-21-111.6 1986 All July, 1986

Connecticut §52-225a 1987 All Oct, 1987

Delaware §6862 1976 Medical only Apr, 1976

DC None

Florida §768.76 1986 All July, 1986

Georgia §51-12-1 1987-1991 All July, 1987- Mar, 1991

Hawaii §663-10 1986 All Aug, 1986

Idaho §6-1606 1990 All Mar, 1990

Illinois 5/2-1201 and 5/2-1205.1 1986-1997 All Nov, 1986-Dec, 1997

Indiana §34-44-1-2 (now 34-4-36-1) 1986 All Sep, 1986

Iowa §668.14 1987 All July, 1987

Kansas §60-3802 1988-1993 All July, 1988-Apr, 1993

Kentucky §411.188 1988-1995 All July, 1988-Jan, 1995

Louisiana None

Maine §2906 1990 Medical only Apr, 1990

Maryland None

Massachusetts 231 §60G 1986 Medical only Nov, 1986

Michigan §600.6303 1986 All Oct, 1986

Minnesota §548.251 1986 All Mar, 1986

Mississippi None

Missouri None

Montana §27-1-308 1987 All Oct, 1987

Nebraska §44-2819 1976 Medical only Apr, 1976

Nevada §42.021 2004 Medical only Nov, 2004

New Hampshire §507-C:7 1977-1980 All Sep, 1977-Dec, 1980

New Jersey §2A:15-97 1987 All Dec, 1987

New Mexico None

New York §4545 1984 Medical only Aug, 1984

North Carolina None

North Dakota §32-03.2-02 1987 All July, 1987

Ohio §2317.45 1997-1998 All Jan, 1997-Feb, 1998

Oklahoma §1-1708.1D 2003 Medical only July, 2003

Oregon §31.580 1987 All July, 1987

Pennsylvania §1303.508 2002 Medical only Mar, 2002

Rhode Island §9-19-34.1 1976 All 1976

South Carolina None

South Dakota §21-3-12 1977 Medical only Apr, 1977

Tennessee §29-26-119 1975 Medical only July, 1975

Texas None

Utah §78-14-4.5 1986 Medical only July, 1986

Vermont None

Virginia None

Washington §7.70.080 1975 Medical only June, 1975

West Virginia §55-7b-9a 2003 Medical only Mar, 2003

Wisconsin §893.55(7) 1995 Medical only May, 1995

Wyoming None

Source: Database of State Tort Law Reforms 5th edition and State Statutes.‘Medical only’ means that the modifications only applies to Medical Malpractice cases.

Table 5: Characteristics of Claims, by the modification of CS rule (include all claims)

Variables(1) CS Rule Modified

(applied to any)(2) CS Rule Modified

(medical only)(3) CS RuleNot Modified (4) Overall

Mean Median Mean Median Mean Median Mean Median

Age of Claimant 38.02 36.00 36.84 35.00 35.84 34.00 36.81 35.00

Claimant was Male 0.40 0.00 0.40 0.00 0.41 0.00 0.41 0.00

Number Injured 1.38 1.00 1.38 1.00 1.38 1.00 1.36 1.00

Number of Work Days Lost 12.62 0.00 13.91 0.00 13.68 0.00 14.58 0.00

Accident was a Collision 0.82 1.00 0.83 1.00 0.83 1.00 0.82 1.00

Accident was a Single Vehicle 0.14 0.00 0.12 0.00 0.14 0.00 0.14 0.00

No Fault 0.43 0.00 0.26 0.00 0.00 0.00 0.24 0.00

Hired Lawyer 0.30 0.00 0.35 0.00 0.34 0.00 0.33 0.00

Non-economic Damages Cap 0.22 0.00 0.00 0.00 0.00 0.00 0.08 0.00

State per-capita Income 34,270 33,590 35,390 35,410 29,900 28,980 32,820 32,770

Amount Claimed in Medical Cost 11,350 1,898 9,148 1,950 9,327 1,620 10,070 1,720

Amount Claimed in Damages 10,440 1,147 8,460 1,250 9,542 1,254 9,700 1,239

Total Amount Recovered 17,280 3,266 15,330 3,962 16,490 3,739 18,680 3,830

Total Recovered after fees 14,750 3,150 13,130 3,650 14,350 3,500 15,700 3,578

Direct Payment 7,075 0.00 7,359 0.00 8,183 0.00 9,755 0.00

Direct Payment after fees 5,126 0.00 5,637 0.00 6,390 0.00 7,308 0.00

All dollar amounts are measured in 2002 constant dollars. We show summary statistics of four groups. The group (1)includes claims in state that modified the CS rule and applied it to all types of claims, after modified. The group (2)includes claims in states that modified the rule but restricted its application to medic an malpractice only. The group(3) includes claims in states that did not modify the CS rule.

Table 6: Characteristics of Claims, by the modification of CS rule (only include collisions with positive damages)

Variables(1) CS Rule Modified

(applied to any)(2) CS Rule Modified

(medical only)(3) CS RuleNot Modified (4) Overall

Mean Median Mean Median Mean Median Mean Median

Age of Claimant 38.05 36.00 37.18 35.00 36.49 34.00 37.16 35.00

Claimant was Male 0.39 0.00 0.38 0.00 0.39 0.00 0.38 0.00

Number Injured 1.36 1.00 1.38 1.00 1.37 1.00 1.35 1.00

Number of Work Days Lost 13.79 0.00 15.38 0.00 14.65 0.00 15.83 0.00

Accident was a Collision 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Accident was a Single Vehicle 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

No Fault 0.42 0.00 0.23 0.00 0.00 0.00 0.23 0.00

Hired Lawyer 0.34 0.00 0.38 0.00 0.39 0.00 0.38 0.00

Non-economic Damages Cap 0.21 0.00 0.00 0.00 0.00 0.00 0.08 0.00

State per-capita Income 34,170 33,590 35,130 35,370 29,830 28,840 32,690 32,550

Amount Claimed in Medical Cost 11,140 2,032 8,509 2,160 8,861 1,727 9,418 1,981

Amount Claimed in Damages 12,710 2,244 9,688 2,364 10,460 2,109 10,870 2,244

Total Amount Recovered 18,320 3,573 15,600 4,587 17,510 4,327 17,210 4,369

Total Recovered after fees 15,300 3,452 13,200 4,321 15,050 4,016 14,550 4,096

Direct Payment 8,645 0.00 8,484 0.00 9,590 449 9,188 0.00

Direct Payment after fees 6,216 0.00 6,498 0.00 7,473 418 6,934 0.00

All dollar amounts are measured in 2002 constant dollars. We show summary statistics of four groups. The group (1)includes claims in state that modified the CS rule and applied it to all types of claims, after modified. The group (2)includes claims in states that modified the rule but restricted its application to medic an malpractice only. The group(3) includes claims in states that did not modify the CS rule.

Table 7: Probabilities of Hiring Attorneys

Group 1 Group 2 t-value

Before 0.3775 0.4104 -1.721 (0.085)

After 0.3449 0.3836 -3.188 (0.001)

t-value 2.178 1.578

(0.029) (0.115)

Probabilities (sample proportions) of hiring attorneys. At the bottomand in the left, we have t statistics and p-values (in parentheses) of thedi↵erences in probabilities. ‘Before’ means before the modification and‘After’ means after the modification. Group 1 is states that modifiedthe CS rule and applied it to all cases. Group 2 is states that modifiedthe CS rule but applied it only to medical malpractice.

Table 8: Probabilities of Hiring Attorneys - continued

Group 1 Group 2 Group 3

Probability 0.3775 0.3903 0.3885

Group 1 vs. Group 2 Group 2 vs. Group 3 Group 3 vs. Group 1

t-value -0.903 (0.366) 0.144 (0.885) 0.717 (0.473)

Probabilities (sample proportions) of hiring attorneys. Numbers inparentheses are p-values. Group 1 is states that modified the CS ruleand applied it to all cases (before modification). Group 2 is states thatmodified the CS rule but applied it only to medical malpractice (beforeand after modifications). Group 3 is states that did not modify the CSrule.

Table 9: Results of (plausible but misleading) regression models

Dependent variable:

Direct payments Total payments

(1) (2) (3) (4)

Age of claimant �76.1 �85.1 �25.0 �39.8

(91.1) (91.9) (114.9) (115.8)

Number injured �1, 989.4 �1, 443.5 �1, 169.1 �974.6

(2, 264.7) (2, 292.8) (3, 009.8) (3, 048.9)

Accident was a collision 653.9 3, 213.1 �5, 116.7 �4, 231.8

(11, 378.1) (11, 465.0) (13, 852.4) (13, 984.2)

Accident was a single vehicle 12, 038.7 14, 257.9 9, 716.6 10, 590.6

(12, 111.4) (12, 183.6) (14, 671.9) (14, 786.7)

Accident involved pedestrian 27, 752.5⇤ 30, 249.1⇤⇤ 38, 902.8⇤⇤ 40, 397.4⇤⇤

(14, 502.9) (14, 576.6) (18, 592.9) (18, 702.4)

Number of work days lost 66.5⇤⇤⇤ 60.3⇤⇤ 144.5⇤⇤⇤ 143.0⇤⇤⇤

(24.1) (24.2) (31.1) (31.2)

Hired attorney 18, 266.2⇤⇤⇤ 18, 343.4⇤⇤⇤ 33, 614.5⇤⇤⇤ 31, 349.5⇤⇤⇤

(3, 228.8) (3, 315.1) (4, 231.0) (4, 334.6)

Non-economic damage cap in place �6, 907.0 2, 415.9 �8, 086.9 285.1

(6, 226.0) (9, 385.1) (8, 014.9) (11, 430.6)

Cap on attorney fees 10, 121.8⇤⇤ 6, 920.1 13, 459.6⇤⇤ 8, 722.3

(4, 852.0) (11, 710.6) (6, 047.3) (13, 980.6)

Claimant has no insurance 14, 276.5⇤⇤⇤ 14, 882.7⇤⇤⇤ �704.7 336.8

(3, 470.3) (3, 571.3) (4, 114.6) (4, 298.9)

No fault state 15, 398.9 11, 006.2 14, 067.4 14, 224.4

(11, 121.6) (23, 157.6) (13, 138.4) (26, 787.1)

Compulsory insurance state 1, 755.8 2, 443.1 202.3 3, 100.2

(3, 849.9) (6, 149.7) (4, 793.2) (7, 550.8)

State and year fixed e↵ects No Y es No Y es

Observations 12,784 12,784 10,484 10,484

In addition to the listed independent variables, we include in regression models ‘claimant wasmale’, ‘no fault monetary’, ‘no fault verbal’, ‘state per capita real income’, ‘state population’,and the constant term. The standard errors are in parentheses. The stars indicate ⇤p<0.1;⇤⇤p<0.05; ⇤⇤⇤p<0.01.

Table 10: Results of (plausible but misleading) regression models - continued

Dependent variable:

Direct paymentsafter fees

Total paymentsafter fees

(1) (2) (3) (4)

Age of claimant �47.2 �51.9 10.5 0.3

(66.9) (67.4) (85.7) (86.4)

Number injured �1, 312.6 �882.5 �548.3 �382.3

(1, 662.0) (1, 682.7) (2, 245.2) (2, 274.2)

Accident was a collision 974.4 2, 842.6 �5, 239.3 �4, 533.8

(8, 350.1) (8, 414.0) (10, 333.5) (10, 430.7)

Accident was a single vehicle 9, 262.6 10, 908.6 6, 370.6 7, 136.3

(8, 888.3) (8, 941.4) (10, 944.8) (11, 029.3)

Accident involved pedestrian 19, 156.2⇤ 20, 944.9⇤ 24, 730.5⇤ 26, 004.0⇤

(10, 643.3) (10, 697.7) (13, 869.8) (13, 950.0)

Number of work days lost 51.2⇤⇤⇤ 46.7⇤⇤⇤ 129.1⇤⇤⇤ 128.0⇤⇤⇤

(17.7) (17.8) (23.2) (23.3)

Hired attorney 12, 414.2⇤⇤⇤ 12, 429.1⇤⇤⇤ 24, 785.0⇤⇤⇤ 22, 963.6⇤⇤⇤

(2, 369.5) (2, 432.9) (3, 156.2) (3, 233.1)

Non-economic damage cap in place �5, 227.7 1, 427.1 �6, 213.6 �343.8

(4, 569.1) (6, 887.7) (5, 978.9) (8, 526.0)

Cap on attorney fees 7, 679.5⇤⇤ 4, 905.3 10, 716.2⇤⇤ 7, 233.8

(3, 560.8) (8, 594.3) (4, 511.1) (10, 428.0)

Claimant has no insurance 10, 643.3⇤⇤⇤ 11, 160.6⇤⇤⇤�2, 688.0 �1, 801.9

(2, 546.7) (2, 620.9) (3, 069.3) (3, 206.5)

No fault state 11, 626.9 8, 817.4 10, 902.7 11, 786.7

(8, 161.9) (16, 995.2) (9, 800.9) (19, 980.3)

Compulsory insurance state 1, 493.9 2, 099.6 187.3 2, 967.6

(2, 825.4) (4, 513.2) (3, 575.6) (5, 632.1)

State and year fixed e↵ects No Y es No Y es

Observations 12,784 12,784 10,484 10,484

In addition to the listed independent variables, we include in regression models ‘claimant wasmale’, ‘no fault monetary’, ‘no fault verbal’, ‘state per capita real income’, ‘state population’,and the constant term. The standard errors are in parentheses. The stars indicate ⇤p<0.1;⇤⇤p<0.05; ⇤⇤⇤p<0.01.

Table 11: Determinants of hiring an attorney

Models:

Linear probability Logit Probit Fixed e↵ects logit

(1) (2) (3) (4)

Age of claimant0.0004⇤⇤ 0.001⇤⇤ 0.002⇤⇤ 0.002⇤⇤

(0.0002) (0.001) (0.001) (0.001)

Number injured0.041⇤⇤⇤ 0.116⇤⇤⇤ 0.196⇤⇤⇤ 0.214⇤⇤⇤

(0.005) (0.014) (0.024) (0.024)

Accident wasa collision

�0.003 �0.007 0.023 0.010

(0.028) (0.079) (0.130) (0.133)

Single vehicle accident�0.248⇤⇤⇤ �0.873⇤⇤⇤ �1.524⇤⇤⇤ �1.546⇤⇤⇤

(0.029) (0.085) (0.145) (0.148)

Accident involvedpedestrian

0.147⇤⇤⇤ 0.383⇤⇤⇤ 0.656⇤⇤⇤ 0.679⇤⇤⇤

(0.035) (0.098) (0.161) (0.165)

Number of work days lost0.001⇤⇤⇤ 0.005⇤⇤⇤ 0.010⇤⇤⇤ 0.010⇤⇤⇤

(0.0001) (0.0003) (0.001) (0.001)

CS rule modified�0.064⇤⇤⇤ �0.190⇤⇤⇤ �0.313⇤⇤⇤ �0.084

(0.010) (0.028) (0.047) (0.091)

Non-economic damagecap in place

0.022 0.067 0.107 0.202⇤

(0.015) (0.043) (0.071) (0.114)

Cap on attorney fees0.047⇤⇤⇤ 0.138⇤⇤⇤ 0.226⇤⇤⇤ �0.170

(0.012) (0.034) (0.056) (0.143)

Claimant hasno insurance

0.013 0.040 0.072⇤ 0.054

(0.009) (0.025) (0.041) (0.043)

No fault state0.073⇤⇤⇤ 0.233⇤⇤⇤ 0.413⇤⇤⇤ 0.004

(0.026) (0.079) (0.136) (0.287)

Compulsory insurance0.007 0.019 0.027 0.025

(0.009) (0.026) (0.043) (0.073)

Observations 16,908 16,908 16,908 16,908

Dependent variable is the decision to hire attorneies. (4) includes both state and year fixede↵ects. The standard errors are in parentheses. The stars indicate ⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01.

Table 12: Average and Quantile E↵ects of Hiring an Attorney

Outcomes Quantile E↵ects Average E↵ects

⌧ = 0.25 ⌧ = 0.5 ⌧ = 0.75 ⌧ = 0.9 ⌧ = 0.95

Direct Payment (-20,038, 0) (-63,931, 0) (-69,667, 76,405) (-231,294, 88,491) (-805,015, -72,233) (-185,793, 9,980)

Total Payment (-5,234, 4,147) (-17,218, 26,883) (-90,805, 60,270) (-320,712, 7,788) (-899,957, -403,085) (-230,879, -51,407)

Direct Payment after fees (-19,904, 0) (-62,827, 0) (-79,346, 67,872) (-227,559, 80,064) (-711,995, -42,095) (-174,471, 15,430)

Total Payment after fees (-5,375, 3,992) (-19,470, 22,748) (-79,352, 39,003) (-276,675, 470) (-975,622, -342,416) (-219,557, -40,085)

Bounds of the average and the ⌧ -th quantile e↵ects of hiring attorneys. All e↵ects are measured in 2002 constant dollars. Directpayment includes payments from injurer’s insurance plus settlement or trial awards (if there is any). Total payment is the sum ofall payments: direct payment plus payments from the first party (claimant’s own) insurance. The first two outcome variables arebefore deducting attorney’s fees and the last two outcome variables are after attorney’s fees.

Table 13: Average and Quantile E↵ects of Hiring an Attorney, Allowing for Covariates

Outcomes Quantile E↵ects Average E↵ects

⌧ = 0.25 ⌧ = 0.5 ⌧ = 0.75 ⌧ = 0.9 ⌧ = 0.95

Direct Payment (-174,742, 0) (-168,456, 0) (-100,064, 78,758) (-132,581, 120,829) (-290,095, 49,877) (-157,575, 30,057)

Total Payment (-86,073 -13,824) (-193,082, 8,049) (-153,913, 66,923) (-165,759, 114,363) (-323,783, 6,220) (-185,838, -12,788)

Direct Payment after fees (-165,445,0) (-166,307, 0) (-147,370, 46,452) (-165,241, 69,699) (-300,067, 60,129) (-153,632, 28,421)

Total Payment after fees (-79,256, -12,467) (-192,346, 2,335) (-183,982, 44,506) (-212,098, 65,222) (-347,976, -62,550) (-179,833, -6,782)

Bounds of the average and the ⌧ -th quantile e↵ects of hiring attorneys. All e↵ects are measured in 2002 constant dollars. Directpayment includes payments from injurer’s insurance plus settlement or trial awards (if there is any). Total payment is the sum ofall payments: direct payment plus payments from the first party (claimant’s own) insurance. The first two outcome variables arebefore deducting attorney’s fees and the last two outcome variables are after attorney’s fees.

Figure 1: Quantile E↵ects of Hiring Attorneys. Before Attorney’s Fees

(a) Direct Payment

0.0 0.2 0.4 0.6 0.8 1.0

−150

0−1

000

−500

0

Probability Index

$1,00

0

(b) Total Payments

0.0 0.2 0.4 0.6 0.8 1.0

−250

0−1

500

−500

0

Probability Index

$1,00

0

Bounds of Quantile E↵ects of hiring attorney’s at the level ⌧ 2 {0.02, 0.04, . . . , 0.96, 0.98}. All e↵ects (iny-axis) are in $1,000 (in 2002 constant dollars).

Figure 2: Quantile E↵ects of Hiring Attorneys. After Attorney’s Fees

(a) Direct Payment after attorney’s fees

0.0 0.2 0.4 0.6 0.8 1.0

−150

0−1

000

−500

0

Probability Index

$1,00

0

(b) Total Payments after attorney’s fees

0.0 0.2 0.4 0.6 0.8 1.0−250

0−2

000

−150

0−1

000

−500

0

Probability Index

$1,00

0

Bounds of Quantile E↵ects of hiring attorney’s at the level ⌧ 2 {0.02, 0.04, . . . , 0.96, 0.98}. All e↵ects (iny-axis) are in $1,000 (in 2002 constant dollars).