Influence of parties’ behavioural features on motor compensation disputes in insurance markets

Disputes between parties involved in motor insurance claims compensations are analysed. The decision to resolve the disagreement by either negotiation or trial may depend on how risk and confrontation adverse or pessimistic the claimant is. The extent to which these behavioural features of the claimant might influence the final compensation amount is examined. An empirical analysis, fitting a switching regression model to a Spanish database, is conducted in order to analyse whether the choice of the conflict resolution procedure is endogenous to the compensation outcomes. The results show that compensations awarded by courts are always higher, although 95% of cases are settled by negotiation. We show that this is because claimants are adverse to risk and confrontation, and are pessimistic about their chances at trial. By contrast, insurers are risk/confrontation neutral and more objective in relation to the expected trial compensation. During the negotiation insurers accept to pay the subjective compensation values of claimants, since these values are lower than their estimates of compensations at trial.


Introduction
Under fault-based systems injured victims involved in a motor collision are entitled to claim compensation for damages from the at-fault driver. When the driver is insured, and in the European Union motor liability insurance is compulsory, victims are compensated by insurance companies. The amount of financial compensation depends on numerous factors, such as the extent of the victim's bodily injury, the economic losses sustained as a consequence of the accident or whether the responsibility for the collision is shared with the insured driver. All these factors are derived from the accident, although the amount of compensation may also be influenced by external aspects such as the disputing skills of litigants or the resolution procedure followed, i.e. negotiation or trial.
A widely accepted belief is that compensations awarded by trial are greater than those settled by negotiation. However, if this is the case why do victims prefer a negotiation procedure when claiming compensation for damages caused by an automobile accident? In Spain most motor bodily injury claims are settled by negotiation, with fewer than 5% of cases going to court. Similar percentages are observed in other countries like the UK or the USA (Derrig and Rempala 2006;Lewis 2006). Given this apparent paradox we decided to conduct an empirical study, using a Spanish database, in order to investigate how the risk/confrontation behaviour of claimants might influence both the choice of conflict resolution procedure and the compensation outcomes achieved by motor injury victims.
The selection of a resolution mechanism for legal disputes has been broadly analysed in the economic and law literature (Cooter and Rubinfeld 1989;Daughety 2000;Shavell 2004;Sieg 2000). In the next section we will summarize the work of Cooter and Rubinfeld (1989), who define the litigation process as a bargaining model in which the cooperative and non-cooperative solutions correspond, respectively, to out-of-court and in-court settlements. In order to find a formal solution within the bargaining model, numerous studies assume that both parties are riskneutral (among others, Crocker and Tennyson 2002;Nalebuff 1987;P'ng 1983). However, it remains to be established whether the risk-neutral assumption is realistic, and how the game theory model might be affected when this assumption is relaxed.
To this end we investigate whether there are differences in compensation outcomes in Spain depending on the conflict resolution procedure followed, and in the event that such differences are observed we aim to identify their causes. Three alternative hypotheses are investigated: (i) differences in settlements arise because the two resolution mechanisms deal with claims with different levels of severity, with seriously injured victims tending towards judicial resolutions; (ii) differences are attributable to the resolution mechanism itself, with one mechanism being more generous than the other and (iii) differences are explained by the behaviour of claimants, with those victims who are more averse to risk and confrontation being compensated with lower amounts.
Let us briefly consider each of these hypotheses in more detail. Compensation differences between out-of-court and in-court settlements may arise because claims dealt with by the courts are more severe than those settled by negotiation. This hypothesis is consistent with empirical evidence showing that the higher legal costs associated with the judicial procedure act as a barrier which makes it unprofitable for litigants with low claims to pursue judicial resolutions (Browne and Puelz 1999;Hughes and Snyder 1995). Furthermore, claims involving seriously injured victims are normally more complex cases, and the literature suggests that greater complexity leads to an increased likelihood of litigation (Browne and Schmit 2008;Shavell 2004).
Another source of compensation differences could be the mechanism itself, such that one of the two mechanisms systematically awards greater compensation to claims and claimants with the same characteristics. Some studies point out that court settlements are increasingly large, and have grown well beyond inflation (de Castries 2005;Wright 1987). Actuaries have called this effect 'judicial inflation', and the Society of Actuaries (SOA 2008) defines it as the upward tendency of courts in interpreting the scope of liability. The National Health Service Litigation Authority (NHSLA 2010) estimates that judicial inflation in clinical negligence claims is now 10% per annum in the UK. One explanation for this is that injury litigation is seen by the courts as an unbalanced dispute between bodily injured victims and faceless insurers with an unlimited budget, a David vs. Goliath scenario.
Finally, and related to the main purpose of this paper, it may be that the attitude of claimants has an influence on the size of payouts. An aversion to risk and confrontation can also affect a claimant's willingness to reach a friendly settlement, with risk-adverse victims preferring negotiated (and more certain) settlements over the uncertainty of a court settlement. Similarly, the psychological costs of confrontation, as well as the time required by negotiation, can lead victims with greater conflict aversion to opt for friendly agreements reached in shorter negotiations. Preference for negotiated settlements is expected to influence negatively on the size of compensation. Indeed, previous studies suggest that uncertainty about the amount of financial compensation which might be awarded at trial results in risk-adverse individuals accepting lower negotiated settlements in exchange for certainty over payment (Doerpinghaus, Schmit, and Yeh 2008;Stuhlmacher and Walters 1999). Risk attitudes and perceptions also influence insurance coverage decisions (Austin and Fischhoff 2010;Hayakawa, Fischbeck, and Fischhoff 2000).
In order to investigate these three hypotheses the present paper applies a switching regression model to a Spanish database. A switching model is structured on two regression equations, which describe the compensation awarded under each one of the two conflict resolution procedures, and a criterion function that determines which conflict resolution procedure is followed. This structure allows for dependence between the choice of settlement mechanism and the compensation the individual receives once this mechanism is fixed. We can then analyse whether randomness of the settlement procedure for motor victims may be assumed. Non-randomness is due to self-selection of individuals, and would occur because litigants who decide to reach an agreement are systematically different from those who choose to go to court. Consequently, unobserved factors that influence the decision regarding the conflict resolution procedure also affect the financial compensation awarded for injuries.
It is important to note that model endogeneity may be generated by two different types of unobserved factors. The first concerns claim information that was not collected but may be observed a priori without a large cost. An example in our application would be the amount of compensation claimed by the plaintiff for economic losses. The second factor involves claim information which is almost never perfectly observed, such as the risk attitude and confrontation behaviour of claimants. A series of indicators are constructed to analyse how unobserved factors influence on the financial compensation payouts. The empirical results are interpreted by taking into account both these sources of endogeneity.
The structure of the paper is as follows. Section 2 describes the theoretical bargaining model, while Section 3 outlines the switching regression model. Section 4 presents the main characteristics of the Spanish compensation system, along with a description of the Spanish database used in the empirical application. This is followed in Section 5 by an interpretation of the results. A discussion of the implications of research findings is provided in Section 6.

The game theory model
The game theory model defined by Cooter and Rubinfeld (1989) is followed. In this basic model the cooperative and non-cooperative solutions correspond, respectively, to an out-of-court settlement and an in-court settlement. Both parties are assumed to have expectations regarding trial outcome. Variables defined in this model are related to the subjective value of the compensation (S), the associated cost to each resolution process (C), the subjective probability of success in trial (P) and the expected compensation in case of success (E). Subscripts are related to the resolution process: t for trial and n for negotiationand to the disputing partyc for claimant and d for defendant.
The claimant's subjective expected gain in bringing the suit to trial is S tc ÀC tc , where S tc is the subjective value to the claimant of the possible compensation awarded by court and C tc is the cost to the claimant if the case is settled by court. The magnitude of S tc depends on the claimant's estimate of the compensation that will be awarded at trial if he/she wins, E tc , as well as on his/her subjective view regarding the probability of victory at trial, P tc ; hence, S tc = f(P tc , E tc ). Similarly, the subjective expected loss of the defendant (in this case, the insurer) is S td + C td , where S td is defined as a function of the insurer's expectations about the compensation which will be awarded to the claimant at trial and his/her subjective view regarding the probability of the claimant's victory at trial, S td = f(P td , E td ).
For risk-neutral agents the subjective value of the court outcome is equal to the expected court compensation multiplied by the subjective probability of claimant victory, i.e. S tc = P tc Â E tc and S td = P td Â E td . However, risk aversion generates the following inequalities among agents: S tc < P tc Â E tc and S td > P td Â E td . The same effect can be derived for agent aversion to confrontation. Pessimism also influences an individual's expectations regarding the trial outcome. When parties are relatively pessimistic in this regard the claimant expects to win less than the insurer expects to pay, which is expressed as P tc Â E tc < P td Â E td . The opposite holds when parties are optimistic. For purposes of simplification, both court compensation expectations and subjective victory probabilities are characterized as scalars. However, they may be defined as vectors, to allow partial victories, or as functions of other variables, for instance, based on court costs in order to measure parties' efforts to win.
In game theory terms, the players' assessment of the value of the game is computed as the difference between their subjective values plus the associated costs. When a friendly compensation agreement is reached between parties their subjective values are equal, and thus the net transfer between them is zero. The cooperative value of the game (CV) is therefore determined by the transaction costs incurred by parties in the negotiation, CV = À(C nc + C nd ). In the non-cooperative game the net transfer is not necessarily equal and, therefore, the non-cooperative value is NCV = (S tc ÀS td )À(C tc + C td ). The difference between the values of these two games determines the surplus of the negotiated resolution, 1 SU = CVÀNCV = (C tc + C td )À (C nc + C nd ) + (S td ÀS tc ). We consider that parties show non-strategic behaviour. Disputes are then settled out of court if SU takes a positive value, while a negative value means that a judicial settlement is preferred. Both risk/confrontation aversion and pessimism of parties regarding court outcomes widen the gap between the parties' subjective values of trial outcomes, and it is therefore more likely that a friendly settlement is reached.

Hypothesis related to the behaviour of parties
We hypothesize that insurers have a systematic disputing behaviour that is based exclusively on their accurate expectation of the compensation payment which might be awarded at trial. It is presumed that courts systematically apply the same criteria to resolve disputes, these court criteria being defined by Priest and Klein (1984) as 'the decision standard'. However, insurer and claimant do not have the same information about possible trial outcomes, and we assume that the insurer has superior information in this regard. Indeed, insurance firms deal with legal disputes as part of their daily routine, and they typically call on experts from different disciplines (lawyers, medical experts, actuaries, etc.) to take part in legal proceedings. We therefore consider that this multidisciplinary team has better knowledge about how the legal system is likely to be interpretedand appliedby judges. Obviously, knowledge about how a court (or judge) may behave on average does not eliminate uncertainty about the amount of compensation that this court (or judge) will award in a particular case. As regards insurer behaviour, we assume that the insurer seeks to settle the claim at the minimum cost, regardless of the time of payment and the resolution procedure followed. Therefore, the insurer will prefer the resolution procedure associated with the lower expected compensation. This means that the insurer shows neither risk aversion nor confrontation aversion behaviour (Grochulski and Kareken 2004; Santolino 2010).
As already implied above, the decision to pursue a judicial resolution or to reach an agreement will mainly depend on the claimant. We consider throughout this paper that the judicial process and the negotiation process are separated. Although this does not have implications for our modelling, in practice the court verdict is observed when the negotiation process fails. The negotiation process consists of a round of bids/demands before an agreement is reached, but if such agreement proves impossible then the claim is resolved by judicial decision (Ayuso and Santolino 2011). The strategy followed by the risk-neutral insurer in the negotiation process would be to make relatively low initial bids to the victim. If these bids are rejected by the victim, the insurer would then progressively increase the amount of compensation offered in subsequent bids. The number of rounds before accepting the bid will depend on how risk and confrontation adverse or pessimistic the claimant is. The size of the maximum bid that the insurer is willing to pay will be based on his accurate expectation of the court compensation payment. In the event that the victim rejects this maximum bid, then the claim is settled by judicial decision. The judicial resolution is then pursued for those claimants with higher risk/confrontation preference and who are more optimistic regarding the compensation outcome at trial.
It is important to note that the analysis relies on a number of simplifying assumptions. We define the claimant as the victim and the insurer as the defendant, both of whom are usually represented by a lawyer. Furthermore, the defendant is the insured driver, even though he or she is covered by the insurance company. We therefore ignore incentive problems between the lawyer and the represented party, and between the insurer and the insured. The former are due to the moral hazard resulting from the superior information which the lawyer has compared to the claimant (Hay 1996). The latter are especially important when the insurance policy has coverage limits (Sykes 1994). The rules regarding the cost allocation of fees, where each party bears its own costs or where losers at trial pay the winner's legal fees, also have effects on the litigation decision (Hughes and Snyder 1995). An excellent review can be found in Shavell (2004).

Statistical methodology
Selection models can be used to model compensation payments when the selection of the resolution mechanism by parties is not random. In this section, we introduce an endogenous switching regression model to account for selection correction. The regression model with endogenous switching allows for dependence between the choice of the resolution mechanism and the compensation outcome. Based on the general framework described in Maddala (1983), let us consider the following model: In this model, I i is a dichotomous variable that takes value 1 if the ith claim is settled by judicial decision and 0 if the claim is settled by negotiation. y 1i and y 0i are the dependent variables that indicate the compensation (in natural logarithms) to the ith victim under the trial and the negotiation procedures, respectively. c, b 1 and b 0 are vectors of parameters subject to estimation. z i is a vector of characteristics that influence on the selection of the conflict resolution procedure; x 1i and x 0i are two vectors of characteristics that affect victims' compensation under each resolution mechanism. To facilitate the interpretation of results, we include the same regressors in both the trial and negotiation equations. The notation is then simplified as x 1i ¼ x 0i ¼ x i . Finally, u i , ɛ 1i and ɛ 0i are three random error terms that follow a trivariate normal distribution with mean vector zero and the covariance matrix where r 2 u is the variance of the error term in the criterion function and r 2 1 and r 2 0 are the variances of the error terms in the compensation equations. r 1u and r 0u are the covariances of u i and ɛ 1i and ɛ 0i , respectively. The covariance of ɛ 1i and ɛ 0i is not defined, as y 1i and y 0i are never observed simultaneously. Parameters may be estimated by maximum likelihood (for details, see Cameron and Trivedi 2005). Conditional expectations may be derived. Heckman (1979) showed that if the errors are jointly normal then E½e 1i ¼ r 1u u i and E½e 0i ¼ r 0u u i : Note that the truncated expected value of a standard normal random variable is equal to where /ðÁÞ is the standard normal density function, UðÁÞ is the standard normal distribution function and the division /ðc Z i Þ = Uðc Z i Þ is the inverse Mills ratio. Similarly, The conditional expectations are then: The expected value of compensation in trial when the claim is settled by trial: where q 1 ¼ r 1u = r u r 1 is the correlation coefficient between u i and ɛ 1i .
The expected value of compensation in negotiation when the claim is settled by negotiation: where q 0 ¼ r 0u = r u r 0 is the correlation coefficient between u i and ɛ 0i . Note that two additional conditional expectations may be computedalthough they can not be directly observed in the dataset: The expected value of compensation in trial when the claim is settled by negotiation: The expected value of compensation in negotiation when the claim is settled by trial: respectively. Three indicators can be introduced to compare the victims' compensation payments settled by courts with that obtained by means of negotiation, where a 1 is equal to the expected compensation of the ith victim when resolved in trial minus his/her expected compensation in negotiation. When the analysis is restricted to the trial sample or the negotiation sample, we obtain a 2 and a 3 , respectively. Indeed, a 2 computes the difference between the expected compensation in trial and the expected compensation in negotiation for claims settled by judicial decision. A similar interpretation applies to a 3 in case of negotiation.
Two additional indicators are computed to compare the level of compensation from different samples, k 1 compares the expected victim compensation in trial given the litigants pursued a judicial resolution with the expected compensation in trial whether litigants went to negotiation. For k 2 a similar deduction can be obtained for the negotiation case.

Empirical analysis: data
Motor injury compensations in Spain have to be assessed in compliance with a legislative compensation system. In fact, scheduled systems are used in most European countries to guide the assessment of compensation for bodily injuries result-ing from traffic collisions. The aim of these systems is to reduce uncertainty over the amount of awards and, consequently, to avoid litigation (Rogers 2001;Rothley 2003). The Spanish compensation system is relatively straightforward. A basic compensation is stipulated for non-economic damages, such as pain and suffering, and correction factors are then applied to account for economic damages. The amount of basic compensation depends on the duration and severity of injuries. Economic correction factors are based on the victim's annual income (Santolino 2010).
For the present analysis data were provided by one of the largest insurance companies operating in Spain. The database consists of a random sample of 24,938 non-fatal victims involved in traffic collisions in Spain, of which 23,816 claims were settled by a friendly agreement between the insurer and the claimant and 1122 were settled by judicial decision. All sample victims were compensated in the year 2007. The mean compensation awarded in claims settled by judicial decision was 18,385.34 Euros, with a standard deviation of 27,657.83 Euros. For negotiated settlements the mean compensation and standard deviation were 10,302.12 and 22,168.91 Euros, respectively.
The information included in the database was recorded by the insurer during the processing of claims in order to track them until settlement. The description of variables is shown in Table 1. Explanatory variables are classified as general factors or factors related to information about injuries. General factors include the age of the victim. In this regard, previous studies have analysed the risk and confrontation aversion as a function of age (Doerpinghaus, Schmit, and Yeh 2008;Halek and Eisenhauer 2001). The remaining general factors record information related to the type of victim (driver, passenger and pedestrian or cyclist) and information about the insured driver, such as his/her age and gender. The position of the victim influences the severity of injuries (Boucher and Santolino 2010). The type of the victim may also explain the attitude to conflict resolution (Derrig and Weisberg 2004;Doerpinghaus, Schmit, and Yeh 2003). The negotiation strategy depends on the relationship between agents and the conflict behaviour of the opposing party. Derrig and Weisberg (2004) suggested that passengers obtain lower settlements than do non-passengers due to the familiarity effect. Consistent with the hypothesis of different conflict behaviour in the insured driver, Doerpinghaus, Schmit, and Yeh (2003) found fault assessment differences as a function of the age and gender of the driver.
Injury factors provide a description of injuries resulting from the accident, such as the nature of injuries, their severity, evolution and the body region that was injured. The injury information recorded is based on medical assessments carried out by the insurer during the period in which victims are recovering from their injuries. There are three variables related to the period during which the victim is temporarily disabled; time in hospital, time out-of-hospital with inability to work and time out-of-hospital without inability to work. 2 Under the Spanish system these three types of temporary disabilities entitle the victim to a daily basic compensation.
The next two factors relate to permanent disability and aesthetic damage. Basic compensation for permanent disability depends on an injury score that ranges between 0 and 100 (from minimum to maximum severity). The score is derived from a medical scale that describes 475 injuries and provides severity scores for each one. Up to 50 points may be additionally awarded if the victim suffered aesthetic damage. A further four variables indicate whether variation occurred between the initial and final medical assessments as regards the temporary disability duration and the permanent disability severity. Variations across medical assessments may influence the settlement expectations of claimants and, consequently, their behaviour as regards conflict resolution. In addition to the duration and severity, other characteristics may also affect settlements. For instance, some types of injuries are associated with greater suspicion of fraud (Crocker and Tennyson 2002;Derrig and Weisberg 2004), while economic damages may vary in function of the injury type. Furthermore, information about the influence of injury type on settlements may have implications for the economic analysis of road safety policies. Injuries described in the legislative scale are classified according to their nature and the body location in order to reduce the number of injuries to a manageable number of diagnostic categories, this approach being inspired by the Barell diagnostic matrix (Barell et al. 2002). There are six factors that relate to the body location and seven to the nature of the injury. Victims may suffer more than one injury and, therefore, these factors are not mutually exclusive.

Empirical analysis: results
Parameters were estimated by maximum likelihood. Regressors that did not show significant coefficients were removed from equations, while the same covariates are used in both compensation regressions. The results for the selection equation of the conflict resolution procedure are reported in Table 2.
The results of the compensation regressions in the trial and negotiation procedures are reported in Table 3. It should first be noted that two factors from Table 1, x 3 (At-fault gender) and x 25 (Superficial), were dropped from the final regressions due to the lack of significance for parameters in all the equations of the switching regression model. Doerpinghaus, Schmit, and Yeh (2003) found a greater assessment of fault against females. In our application, compensation differences as a function of the driver's gender were not observed. The correlation coefficients q 0 and q 1 are both significantly different from zero (Table 3). Therefore, the choice of settlement mechanism is not independent of the compensation the individual receives once the settlement mechanism is fixed. This shows that the endogeneity assumption is realistic for these data, and therefore the use of an endogenous switching regression model is appropriate to account for the unobservable selection bias in deciding whether to go to court or negotiate with the insurance company. The same conclusion is obtained when the likelihood-ratio test is analysed where the hypothesis of joint independence of the three equations is rejected (LR test = 25.02 and p = 0.000).

Coefficient estimates of regressions
When we analyse which factors influence on the probability to choose each resolution via (Table 2), we observe that driver victims of middle ages who are involved in an accident caused by young or elder drivers of the other vehicle are more likely to go to court. The injury factors indicate that victims who are more seriously injured (with more disabled days or higher severity score) are more likely to go to court. Finally, victims for whom the number of hospital recovery days stated in the first medical examination is larger than in the last one, as well as victims with head injuries, are both more likely to go to court. However, victims are less likely to go to court if the insurance company recognizes that they suffered aesthetic damage.
The study of the factors that explain the compensation amount depends strongly on the resolution method that has been followed (Table 3). When the compensation    payout is the result of a negotiation procedure, pedestrian and cyclist victims of middle age are more likely to obtain a higher compensation. The age of the at-fault driver is not significant in this case. As was expected, victims with more hospital, disabled and non-disabled days and a higher severity score are more likely to obtain a higher compensation. Similarly, victims for whom the number of hospital recovery days or severity scores stated in the first medical examination is larger than those in the last one are more likely to obtain a higher compensation. By contrast, victims for whom the number of disabled or non-disabled days stated in the first medical examination is larger than in the last one, as well as victims with injuries to multiple regions or abrasion injuries, are more likely to obtain a lower compensation.
If the compensation is the result of a trial procedure, passengers in the at-fault vehicle, pedestrian and cyclist victims and victims from an accident caused by a middle-aged driver are more likely to obtain a higher compensation. However, the victim's age is not significant in this case. Regarding injury factors, victims with more disabled and non-disabled days and a higher severity score are more likely to obtain a higher compensation. Hospital days are not significant here. Victims with injuries in the upper or lower torso, sprain/strain or muscle injuries and victims with aesthetic damage are all more likely to obtain a higher compensation.

Indicator estimates
The mean and standard deviation of the indicators (2) and (3) for our data set are shown in Table 4.

Alpha indicators
The first group of indicators helps to compare expected compensation payouts under the trial and negotiation conditions, regardless of the resolution mechanism that is eventually followed by litigants. The fact that all alphas have a positive value means that in all cases court settlements produce, on average, larger compensation payouts than do friendly agreements with the insurance company. The first conclusion to be drawn is therefore that the judicial resolution mechanism is more generous than the one based on negotiation. This greater generosity of courts with respect to negotiation agreements is consistent with our hypothesis of risk-confrontation neutrality of insurers and a systematic disputing behaviour based on their deep knowledge of court performance. The maximum offer that insurers are willing to pay in the negotiation process is on average not larger than the compensation payment which is effectively awarded at trial. The alpha values also support our hypothesis that victims who accept a negotiated settlement have larger risk/confrontation aversion. Interpreting the negotiation process as a succession of bids/demands, insurers offer higher compensation amounts to victims with lower risk aversion and a stronger preference for confrontation. That means, these victims need more rounds before accepting the bid. The mean of a 1 measures the victim's average profitability from going to court irrespective of his/her choice of conflict resolution procedure. After correcting for selection bias, we observe that the victim's average profitability from going to court is much less for the trial sample (a 2 ) than for the negotiation sample (a 3 ).
The large value of a 3 may be explained by the high level of risk and confrontation aversion of those sample victims who were compensated through negotiation. On average, judges would have awarded them drastically higher compensation than was agreed in friendly negotiation. By contrast, victims compensated by courts would have obtained only a slightly lower compensation in negotiation, as indicated by the value of a 2 . Victims who seek a judicial resolution are less risk/confrontation adverse. And insurers are risk/confrontation neutral and make accurate estimates of trial outcomes. That means, during negotiation insurers would be willing to offer these victims a compensation payment close to the compensation finally awarded in trial.

Lambda indicators
The previous interpretation relies on the hypothesis that the source of unobserved claim characteristics that influences the compensation payout is related to the attitude of claimants regarding risk aversion and their confrontation preference. It is important to note that model endogeneity may be generated by other types of unobserved factors. For instance, although economic damages are partially captured by injury factors (Santolino 2010), information related to the financial losses incurred by claimants as a consequence of the accident is unobserved in our study. Different levels of compensation associated to each resolution route could be then because victims who settled by judicial decision sustained different economic damages, on average, than did victims who settled by negotiation. The lambda indicators are consistent with this hypothesis. In particular, lambda results suggest that the both sources of endogeneity act on opposite directions over the expected compensation payout.
The negative sign of k 1 indicates that victims who settled through negotiation are associated with a higher expected compensation payout by court than was actually obtained by those who were compensated by judicial decision. This result may be explained by taking into account the two sources of endogeneity. Firstly, victims who settle by negotiation show higher risk and conflict aversion in disputes, but these attitudinal characteristics play a minor role in the in-court assessment. Therefore, judges would award them higher compensation than was obtained through the negotiation procedure.
However, this interpretation is not sufficient to explain why these victims have larger expected compensations than do those who settled by judicial decision. We hypothesize that victims who settled by judicial decision sustained, on average, lower economic damages (or other types of unobserved recordable damages). Part of the explanation may be found in that victims who seek judicial resolutions are on average overly optimistic regarding the compensation that might be awarded by courts for sustained damages. Following the same reasoning of risk and confrontation neutrality and deeper knowledge of court behaviour, the insurance company accurately estimates the compensation payouts that might be awarded by courts for economic damages and includes them in the compensation bids made in the negotiation process. Therefore, victims who go to court are more likely to claim damages that are either legally not recoverable or not properly proven, or simply did not exist. An additional explanation of the lower damages may be that victims who seek a judicial resolution could be motivated by reasons that are not only financial. In Spain, most suits follow the criminal procedure and, therefore, injured victims with a stronger preference for a judicial resolution may seek not only financial compensation but also punishment of the criminal offence committed by the driver.
On the other hand, the positive k 2 indicates that victims who went to court would have obtained a higher compensation in negotiation than did those who actually reached a friendly agreement. As previously mentioned, victims who go to court have a lower level of risk/confrontation aversion. Therefore, they would obtain higher compensation in negotiation because they are most likely only willing to accept larger bids. To be consistent with the previous arguments made regarding k 1 , the positive sign of k 2 indicates that in the negotiation process the effect of risk/ confrontation aversion is higher than the effect of optimism regarding recoverable economic damages. Victims who settled by judicial decision are optimistic regarding their chances at trial, and this optimism influences the possibility of reaching an agreement with the insurer for a higher amount of compensation. If a trial finally takes place, however, these victims could receive relatively lower compensation amounts for the economic damages sustained. A similar interpretation holds when victims who settled by judicial decision seek punishment to the at-fault driver. To conclude, the lambda indicators strengthen the supposition that the risk/confrontation attitude of litigants is the main source of unobserved characteristics that explains compensation differences between resolution mechanisms. By contrast, the characteristics related to unobserved recoverable damages reduce these differences.

Discussion
Game models define the cooperative solution as the out-of-court settlement and the non-cooperative solution as the in-court settlement. Disputes are settled by negotiation when the difference between these two game values is positive, while a trial court settlement is preferred if the value is negative. Theoretical bargaining models often assume that parties are risk-neutral in order to find a formal solution to the game. However, the results of this empirical analysis with Spanish motor data lead us to conclude that the assumption of risk-neutral behaviour is barely fulfilled by claimants.
The analysis demonstrates that larger amounts of compensation are always awarded by judicial decision than by negotiation, regardless of the type of claims. However, most motor claims are settled by negotiation. We argue that claims are settled by negotiation because claimants are either risk/confrontation adverse or pessimistic about their chances at trial, or a combination of both. Risk/confrontation aversion and pessimism regarding court outcomes increase the gap between the subjective value of the trial outcome as perceived by claimants and by insurers. Consequently, the probability of the parties reaching a friendly settlement also increases.
Unlike in the case of claimants, the risk and confrontation neutrality of insurers is consistent with our results. The greater expertise of insurers makes them more objective than victims regarding the compensation payouts that might be awarded by courts. Insurers would start the negotiation process with relatively low initial compensation bids, and would increase these progressively as victims reject these offers. The judicial resolution route is only preferred by insurers when victims do not accept a maximum compensation offer that is close to the expected in-court compensation. Therefore, the point at which the negotiation process is successfully (or unsuccessfully) stopped will depend on how risk/confrontation adverse the victim is, and how optimistic he/she is regarding the compensation payout that might be awarded by court. As a consequence, risk and confrontation adverse victims obtain relatively lower amounts of compensation. By contrast, victims who are overly optimistic or who have a clear confrontation preference will eventually go to court, and in those cases the compensation awarded by courts will be lower than that for a random individual.
These results may have policy implications in terms of the characteristics that a motor compensation system should fulfil. In traditional motor compensation systems the settlement is the result of a negotiation between parties. In case the negotiation fails, then the compensation is awarded by judicial decision. However, we argue here that these systems could be favouring the characteristics of one of the involved parties. We demonstrate that the higher expertise of insurers enables them to have an advantageous position in the negotiation process, where more than 95% of claims are settled. The incorporation of elements of arbitrage in the negotiation stage may be useful to balance the position of parties in the dispute. In this regard, motor compensation systems in which an objective assessment of possible compensation is provided to both parties without increasing the courts' workload may be desirable. Examples such as the Irish system, which incorporates a non-partial intermediary agency that provides an objective assessment of motor compensation during the negotiation process, could be an interesting alternative.
To conclude, let us emphasize that reliability of results is based on distributional assumptions. Indeed, perturbation terms of the regression model are assumed to be multivariate normally distributed. Normality of errors is the most extended statistical assumption in empirical applications. Although testing for multivariate normality with continuous variables is a common practice, unfortunately these tests can not be applied in regression models with limited dependent variables. A deeper analysis of the influence on results of the assumptions regarding distributional properties of normality such as symmetry or tail shape is beyond the scope of our analysis.

Notes
1. Under Spanish motor law all injured victims must initiate a legal action in order to be eligible for injury compensation no matter what resolution procedure is finally followed. Consequently, differences in the associated costs of resolution mechanisms are not too large. 2. The period 'out-of hospital with inability to work' refers to the out-of-hospital recovery period during which the victim is on sick leave. The period 'out-of hospital without inability to work' relates to the out-of-hospital recovery period during which the victim is able to work but requires some form of therapy.