ASYMMETRIC INFORMATION AND THE SETTLEMENT

Transcription

1 The Journal of Risk and Insurance, 2001, Vol. 68, No. 4, ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS Paul Fenn Neil Rickman INTRODUCTION ABSTRACT The authors present a version of Spier s (1992) dynamic model of litigation and use it to derive predictions about the duration of legal claims against motor insurers. Those predictions are tested against a unique set of case data collected from an English motor insurer. The main predictions are supported, with one exception. The authors results suggest that information plays a key role in such cases and indicate that insurers may be able to speed cases by taking steps to collect information at early stages in a case. They also suggest that different forms of plaintiff finance (including insurance) can affect case duration. Finally, the results suggest a role for signaling models of litigation. Delay in litigation concerns liability insurers for several reasons. Because it is costly to both sides, it inevitably affects expected claim costs and therefore premiums. Moreover, increased delay typically implies increased uncertainty about the eventual settlement, and there are plausible arguments why insurers may themselves be risk- or ambiguity-averse. Despite these concerns, little research has been performed on the causes of delay in the settlement of insurance claims. The aim of this article is to contribute to such work by testing predictions, derived from a theoretical model, about the factors that might affect the timing of claim disposition. In particular, the authors are interested in the effect of information asymmetries between insurers and plaintiffs ( third parties in insurance terminology) on the timing of settlement. The theoretical analysis of litigation has evolved from an initial stage in which information asymmetries were recognized as being a factor behind the failure to settle, towards an attempt to use the strategic removal of information asymmetries over time as an explanation for delay. 1 In this article, the authors build upon that theoretical Paul Fenn is with the Centre for Risk and Insurance Studies, Nottingham University Business School. Neil Rickman is with the Department of Economics, University of Surrey. 1 See Cooter and Rubinfeld (1989) and Hay and Spier (1998) for valuable surveys of the literature on the economics of out-of-court settlement. 615

2 616 THE JOURNAL OF RISK AND INSURANCE foundation and present evidence from an insurer s motor vehicle claims department in order to test key hypotheses. 2 Following Rickman (1998), the authors can identify three broad phases of theoretical work by economists on litigation. The phases have been: Non-strategic models: Dating from the initial work of Posner (1973) and Gould (1973), these focus on the conditions necessary for a case to be filed and to settle or go to trial. They are non-strategic in the sense that they do not attempt to model the process of litigation itself or the strategic decisions of litigants as the case progresses. The crucial result to emerge from these models is that, for a case to reach trial, it is necessary that both parties are sufficiently optimistic about the result of trial that they are willing to risk trial costs: future costs are seen as a disincentive to prolonging the case. Accordingly, assessments of liability and quantum, as well as estimated costs, are important to the likely outcome of a case. One-shot models: It is apparent that cases go to trial even though the necessary conditions from non-strategic models are not fulfilled: e.g., even when the facts of the case appear not to justify the costs of trial. Initial work by P ng (1983), Bebchuk (1984), and Reinganum and Wilde (1986) rationalized this observation by allowing for the fact that litigants have private information when bargaining about their case. 3 This can make it difficult for the less well-informed party to make an appropriate offer. The authors refer to these models as one-shot models because they presume that one party is allowed to a make a single offer to the other, with trial commencing if the offer is rejected. This explicitly captures the role of private information in affecting the prospects of trial. Dynamic models: One-shot models may not help us understand why some cases settle earlier than others. For this, we need to allow litigants to make sequential offers, with trial only occurring after a series of these. Spier (1992) was the first paper to examine this. In dynamic models, the role of private information is richer than in the one-shot counterparts: in addition to generating trials, it also accounts for delay in reaching settlement, as the parties use the negotiations to elicit information from their opponents. However, even in such models simplifying assumptions are typically made to preclude the possession of private information by both sides. 4 2 Other empirical studies have used claim-level data from automobile liability insurers to explore factors determining claim severity (Browne and Puelz, 1996; Harrington, 1994) and settlement delay (Kessler, 1996). Fournier and Zuelke (1996) also examine settlement delay using data on a wider set of civil disputes. 3 Private information may arise in a case for several reasons: perhaps the plaintiff has private information about the damages he or she has suffered, or the defendant has more detailed knowledge about his or her liability for the damages in question. Available models allow for each of these and also for signaling or screening of this information during settlement negotiations. For example, Bebchuk assumes that the party making settlement offers is uninformed relative to the opponent (a screening model), while Reinganum and Wilde assume that the offeror is privately informed so that offers can signal this information. 4 For example, superior knowledge about the likelihood of liability by the defendant at the same time as the plaintiff is more aware about his or her losses.

3 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 617 In the Theory section of the article, following Fenn and Rickman (1999), the authors have extended Spier s model to take account of English cost rules and defendant beliefs about case value, liability, and legal costs. The section titled Empirical Modeling outlines the authors estimation methodology, by which the settlement hazard is modeled as a function of both time and defendant beliefs, and where defendant beliefs are permitted to change over time. The Data and Results section describes the insurer s data and presents results. The final section concludes and discusses some implications of the authors findings. THEORY To model delay in settlement, the authors require a model of bargaining with several pretrial periods; this admits the prospect of settlement at early stages, or later ones in a case. One suitable model here is Spier (1992), which assumes that pretrial bargaining takes place over a finite period of time, so that a finite number of settlement offers can be made. Spier s model concentrates on American litigation in the sense that it assumes both parties bear their own costs, regardless of case outcome. As the authors data are from English litigation, it is important to examine predictions from a model adapted for English cost rules (in which the loser pays the winner s costs). 5 Fenn and Rickman (1999) therefore adapt Spier s model to generate predictions about settlement delay from a model with English cost rules. This requires the introduction of an assessment of defendant liability. In what follows, the authors summarize this version of Spier s model. Assume that an accident has occurred and that the plaintiff has brought charges against the alleged defendant. The plaintiff is aware of her level of damages, but the defendant is not. Denoting damages by x, the defendant knows that x [ gx, gx], x > x > 0, and his priors over this are assumed to be uniformly distributed. Here, g > 0 is a severity parameter : as g rises, the mean and variance of the defendant s priors increase, as might be expected with a more severe injury. Damages are assumed to be the only source of asymmetric information in the model. As we will see, this is sufficient to generate settlement delay (as the defendant struggles to find an appropriate settlement offer). However, it also means that all other features of the litigation are common knowledge, including, importantly, the defendant s liability for the damages claimed. The authors assume that this liability is captured by p ( 0,1), with higher values of implying a more liable defendant. Settlement bargaining takes place over a finite T > 0 periods. The model is a screening one since, in each of these periods the defendant makes an offer St, t = 1,, T, to the plaintiff to settle the case. Acceptance of the offer ends the case, while rejection induces the next offer. If S T is rejected, the case goes to trial, in which the judge awards the correct damages to the plaintiff with probability p. While asymmetric information gives the defendant a reason for delaying settlement, bargaining costs give him the opposite incentive. The authors assume that the parties both incur per period costs of c p and c d and, for notational convenience, these also represent trial d 0,1. costs. The authors also assume that they discount the future at common rate ( ) 5 In fact, comparison of the authors results with Spier (1992) confirms that cost allocation rules do not influence the comparative statics that the authors present. The reason is that liability for the damages is common knowledge (see Reinganum and Wilde, 1986).

4 618 THE JOURNAL OF RISK AND INSURANCE This stylized model of litigation is sufficient to generate a distribution of settlement probabilities across the length of the case. To do this, the authors solve for the Perfect Bayesian Equilibrium of the model. This requires that, at each stage, the defendant s settlement offer and the plaintiff s acceptance decision are optimal given the defendant s beliefs, which are generated by Bayes s rule. Intuitively, the defendant makes settlement offers that work along the distribution of plaintiff-types. If the defendant enters period t knowing that the lower bound on the distribution is x t, each offer is designed to minimize her expected payout given the number of periods remaining and the fact that plaintiffs of type xt g x will have accepted that earlier settlement offers. Thus, the defendant prepares a set of T settlement offers that partition the distribution of plaintiff types. In turn, this partitioning determines the probability of settlement in each period. Following Spier (1992), and defining C cp + cd, Fenn and Rickman (1999) show that the equilibrium partitions are as follows: 6 x1 = g x ; t 1 1 T i xt = gx + d d C, t = 2,, T; (1) p x i= 1 x C p T+ 1 = T +. To understand these results, first note that higher costs (C) increase the partitions. The reason for this is that these costs represent savings available through settlement and, therefore, induce the defendant to make an offer based on higher damages. Simi- g also increases the partition values. However, a more larly, a more severe case ( ) liable defendant ( ) p lowers the partitions. The reason for this is that the more liable defendant receives a smaller share of the savings associated with settlement (recall that the plaintiff is assumed to be aware of the defendant s liability), which reduces his willingness to make a high-damage offer. The authors use these results to generate predictions about the probability of settlement over time. In particular, the authors concentrate on the conditional probability of settlement (the hazard rate), which, substituting from Equation (1), Fenn and Rickman (1999) find to be ( pg ) ( 1 ) t T tc d d l,,, =, t = 1,, T 1 T t ( 1 d) b d ( d d ) for x x and b pg /C. It is easy to confirm the following, where 1 ( 1 ) Ω d b + d T : 6 In solving for the equilibrium, one must derive the optimal settlement offers as well as these partition values. As the authors focus is on settlement timing in this article, they present only the latter.

5 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 619 l l l l 0 Ω 0; > 0; < 0; < 0; t C g p l t-t l l 0 Ω d ;, 0 Ω d tc t g t p Interpreting these results, the authors expect a monotonic hazard (upward or downward), which shifts up as costs rise and shifts down as liability and severity rise. The effects of costs and liability follow from the authors discussion of Equation (1). As far as severity is concerned, it should be noted that this is now captured by g, which represents the range of potential damages as severity rises. An increase here worsens the defendant s adverse selection problem and, therefore, lowers the settlement probability. Because the authors results hold for any t, this suggests that the model may accommodate an exogenous change in the variables at any date. Consequently, the predictions set out above hold both in relation to differences between individual claims and in relation to differences for a given claim over time. In addition, the model can also generate predictions about how changing variables affect the slope of the hazard over time that is, the effect of a change in the variables as we move away from t. Although these are generally ambiguous, it can be seen that, conditional on an l l l upward-sloping (and positive) hazard, > 0,, < 0. tc t g t p With these predictions in mind, the authors can now describe their data and the techniques they use to test the model. t T 7 EMPIRICAL MODELING The previous section has presented a model suggesting some key factors that might be expected to influence delay in litigation. Table 1 summarizes these predictions. 1. When the plaintiff is assumed to know his or her loss with certainty, the defendant s uncertainty over quantum can generally be predicted to reduce the settlement hazard and therefore increase claim duration. 2. When an insurer believes it is wholly liable for the plaintiff s losses, it will reduce the settlement hazard (and thus increase settlement delay) relative to cases in which it believes it is only partially liable. The reason is that the model assumes both plaintiff and defendant share information about the defendant s liability. In such circumstances, the plaintiff knows when the defendant thinks it s liable and is subsequently strengthened. 7 It is interesting to note that these intertemporal results particularly distinguish the current model from Bebchuk s (1984) static version. While it is easily checked that the impact effects described in the previous paragraph can be derived from his model, those relating to behavior over time cannot be. As a result, the dynamic predictions provide insight into the (potentially) complex behavior over time of the hazard. This is of empirical as well as theoretical value as it influences the authors choice of a flexible form hazard in the empirical estimates below.

6 620 THE JOURNAL OF RISK AND INSURANCE TABLE 1 Model Predictions Variable Impact on Duration to Settlement Uncertainty over quantum + Estimate of liability + Defendant costs - Plaintiff costs - Time? 3. Higher legal costs for both sides are predicted to increase the settlement hazard (reduce delay in settling) because they weaken bargaining positions. 4. The settlement hazard is monotonic: it either rises or falls over time but never does both. Modeling these predictions empirically requires that the hazard rate is defined as a function of observed characteristics of the individual claim as well as of elapsed time. Moreover, the authors wish to augment these predictions in the empirical specification to take account of data they have on changes in the insurer s beliefs over time. Given the prediction of monotonicity, the authors initially rely on a Weibull specification for the hazard in order to test their hypotheses. Assuming a conventional loglinear form for the effect of covariates, the empirical Weibull hazard function can be written as: l( t) = a e t b1 g { x x } + b ( ) 2 p + ( t) b 3 c + dt ( ) b 4 c p t a 1, (2) where the covariates are as defined in the theoretical section above, b 1,2,3,4 are associated parameters, and t is elapsed time since the claim was initiated. The Weibull shape parameter a determines the time dependence of the baseline hazard: the latter increases or decreases monotonically according to whether a > 1 or a < 1. 8 This reflects the ambiguity in the intertemporal results presented earlier. By explicitly writing the covariates as a function of time, the authors allow for the possibility that beliefs held by the insurer will vary as the claim is delayed. The parameters b 1,2,3,4 and a can be estimated through maximization of the following log likelihood function: N ( ti)[ x x] ( ti) cd( ti) cp( ti) L = lna e t i i= 1 t bg 1 + bp 2 + b3 + b4 a 1 i a 1 e b a 1g ( t)[ x x] + bpt 2 ( ) + b3cd( ti) + b4cp( t) t dt 0 (3) A potential bias arises if the covariate vector is not a complete specification of all of 8. If a = 1, the hazard is a simple exponential that is constant over time.

7 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 621 the sources of heterogeneity in the sample, and this is potentially serious where the hazard is constrained to have a specific distribution. If the unobservable influences on the hazard are captured multiplicatively by a random variable v, then the modified Weibull hazard can be written as: 1g ( t)[ x x] p ( t) 3cd( t) 4cp( t) l( t) = va e t b + b + b + b 2 a 1. (4) To consistently estimate the parameters, one must eliminate v from the log likelihood function. A way of doing this is by forming the joint distribution of the data and the individual effect, v, and then integrating out the latter. 9 Both nonparametric and parametric estimators for this distribution have been suggested in the literature. 10 The authors choose to adopt a conventional assumption that v has a gamma distribution with mean one and variance q. The latter therefore represents a further parameter to be estimated, and this is presented along with the other parameter estimates in the authors Weibull results. In addition, as the prediction of monotonicity obtained above is based on certain potentially restrictive modeling assumptions, the authors prefer to estimate a second specification for the hazard function that does not imply any particular functional form for the settlement hazard over time. A partial likelihood approach suggested by Cox (1972) can be used to estimate a proportional hazard model in which the settlement hazard is separated into an unspecified baseline hazard and a loglinear function of the covariates: bg 1 ( t)[ x x] + b ( ) 3 ( ) 4 ( ) 2 p t + b cd t + b cp t l( t) = l0 ( t) e. (5) Given the proportionality assumption, and a ranking of observed settlement times defined as t 1,, t N, then the conditional probability that the i th claim is settled at t i, given that any of the claims still open could have settled at t i, is ( t )[ x x] + ( t ) + c ( t ) + c ( t ) 1 i 2 p i 3 d i 4 p i e N bg 1 ( tj)[ x x] + bp 2 ( tj) + b3cd( tj) + b4cp( tj e ). (6) j= i bg b b b This is the contribution to the likelihood from the i th observation on delay. Again, the covariates are permitted to change across claims and over time, allowing the authors to test for the effect of variations in insurer beliefs about the claim s value and costs. The product of the individual contributions forms a partial likelihood function that can be estimated by standard techniques. Clearly, only the rank order of delays is used in this procedure, because the baseline hazard l 0 ( t) cancels out of the ratios. l and that infer- This means that there is no need to specify a functional form for ( ) 0 t 9 See Lancaster (1990), p Fournier and Zuelke (1996) adopt a nonparametric estimator for the unobserved heterogeneity. Meyer (1990), while estimating semi-parametrically a piecewise linear hazard function, chose to model unobserved heterogeneity with a gamma distribution.

8 622 THE JOURNAL OF RISK AND INSURANCE ences about the b parameters can be made without any constraints of this kind. In the following section, the authors estimate values for the parameters using both methods. DATA AND RESULTS The authors have collected data from a major motor vehicle insurer in relation to a sample of 301 closed personal injury claims against its own policyholders in 1998 and Information was collected in relation to the payments made at various stages in the settlement process, and these were categorized under the headings personal injury damages; medical expenses; third-party costs; own costs. In addition, data were collected in relation to the estimates made by the claims managers about the likely costs and damages at regular intervals after the claim was initiated, the severity of the plaintiff s injury, and procedural events such as the serving of a writ or a payment into court. Finally, the senior solicitor in the insurer s claims department was asked to make a judgment in the light of evidence in the claim file about the likely source of the plaintiff s finance for the claim (i.e., legal aid, legal expenses insurance, trade union, etc.). Table 2 shows the descripive statistics for the principal variables. TABLE 2 Descriptive Statistics N Minimum Maximum Mean Std. Deviation Delay from incident to closure (days) Initial estimate of claim value ( ) Initial estimate of own costs ( ) Initial estimate of third-party costs ( ) Initial estimate of liability (%) Severe injury Legal aid Legal expenses insurance Trade union The mean delay for all claims from incident to closure was just over two years. The insurer s claims have an initial expected value of 7238 and an initial expected combined cost of 1272, where the latter consists mainly of anticipated third-party (plaintiff) costs. The insurer s own costs are expected to be low, principally because much of the work is done in-house and is not therefore costed. Given the nature of the personal injury claims arising out of road traffic accidents, the majority are believed to be a straightforward case of the policyholder s being liable for the third party s losses. Hence, on average, the insurer rates its percentage responsibility at over 95 percent. Most of the cases involve fairly homogeneous injuries, typically referred

9 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 623 to as whiplash. Consequently, the proportion of severe injuries (that is, those involving major or permanent disabilities) in the sample is quite low at 17 percent. Finally, the source of plaintiff finance recorded shows that the predominant means by which the plaintiff s legal costs are met is legal expenses insurance cover (49 percent), followed by legal aid (20 percent) and trade union funding (3 percent). To capture the way that the insurer s beliefs change over time as the litigation proceeds, one must control for the fact that cases that last longer may be in some respects different from those that settle earlier. Consequently, Figures 1 and 2 show the change in beliefs about case value and third-party costs separately for claims that settled in Years 1 to 4, respectively. These figures repay close inspection. While in both charts the final mean estimates in the year of settlement increase for cases with longer delays, this is not true for the initial mean estimates (i.e., those in Year 1). Indeed, what seems to happen is that claims that settle in Years 2 and 3 are associated with a fall from the initial estimate over time, whereas claims that settle in Year 4 are associated with a distinct rise from the initial estimate over time. One rationalization of this evidence is that it demonstrates the combined effect of screening behavior and the arrival of exogenous information over time: cases that settle early are more likely to be those in which new information arrived that caused insurers to revise downwards their initial estimate of claim value and cost; cases that settle late are more likely to reflect the upward revisions in estimates that occur as a consequence of the information yielded through the bargaining process. The authors now attempt to use the methodology of the Empirical Modeling section to explain these dynamics empirically within a multivariate analysis. FIGURE 1 Insurer s Claim Value Estimates Over Time Year of estimate Year of settlement 4.00

10 624 THE JOURNAL OF RISK AND INSURANCE FIGURE 2 Insurer s Cost Estimates Over Time Year of settlement Tables 3 and 4 show the results of the Weibull and Cox proportional hazard regressions, respectively. Baseline parameters are associated with regressors defined as follows: EST1 = insurer s initial estimate of claim value, in units of 10,000 ( g ) OWN1D = insurer s initial estimate of total own (defendant) costs per day (c d ) TP1D = insurer s initial estimate of total third-party (plaintiff) costs per day (c p ) RESP_1 = insurer s initial assessment about its percentage responsibility for the plaintiff s loss ( p ) INJ = binary variable taking the value 1 if severe injury, 0 otherwise Year of estimate LADUM = binary variable taking the value 1 if plaintiff legally aided, 0 otherwise LEDUM = binary variable taking the value 1 if plaintiff s legal costs met by legal expenses insurance, 0 otherwise TUDUM = binary variable taking the value 1 if plaintiff s legal costs met by trade union, 0 otherwise DESTDAM = time-varying covariate measuring the change in insurer s beliefs about case value over time DOWN1D = time-varying covariate measuring the change in insurer s beliefs about own costs over time DTP1D = time-varying covariate measuring the change in insurer s beliefs about thirdparty costs over time

11 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 625 Additional parameters estimated are: Sigma = the reciprocal of the Weibull shape parameter (i.e. 1 a ) and Theta = the variance of the Gamma distribution for the heterogeneity. TABLE 3 Weibull Regression Parameter Estimates I. Without time-varying covariates Variable Coeff. Std. Error t-stat. p-value Constant EST OWN1D TP1D RESP LADUM LEDUM TUDUM INJ Theta Sigma Log likelihood function II. With time-varying covariates Variable Coeff. Std. Error t-stat. p-value Constant EST OWN1D TP1D RESP LADUM LEDUM TUDUM INJ DESTDAM DOWN1D DTP1D Theta Sigma Log likelihood function

12 626 THE JOURNAL OF RISK AND INSURANCE TABLE 4 Cox Proportional Hazard Regression Parameter Estimates I. Without time-varying covariates Variable Coeff. Std. Error t-stat. p-value EST OWN1D TP1D RESP LADUM LEDUM TUDUM INJ Log likelihood II. With time-varying covariates Variable Coeff. Std. Error t-stat. p-value EST OWN1D TP1D RESP LADUM LEDUM TUDUM INJ DESTDAM DOWN1D DTP1D Log likelihood In each table, models are estimated with and without the time-varying covariates. 11 The Weibull parameters presented in Table 3 are consistent with a monotonically increasing settlement hazard over time. 12 In both tables, the estimated effects of the 11 The Weibull parameter estimates are interpreted as marginal effects on duration to settlement, whereas the Cox parameter estimates are interpreted as marginal effects on the settlement hazard. Consequently, similar effects will have opposite signs in Tables 3 and Moreover, the estimated value of q is significant for the version of the model without timevarying covariates, indicating the presence of unobserved heterogeneity, presumably due to case-specific factors that were missing from the data set. However, q becomes insignificant once time-varying covariates are added to the model, indicating that some of the missing heterogeneity is captured by these variables.

13 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 627 insurer s initial beliefs about case value and plaintiff costs are broadly in accordance with the predictions of the authors model for g and c p, respectively. 13 Holding other things constant, more severe cases, with higher expected values ex ante, result in lower settlement hazards and consequently longer delays. 14 Cases believed by the insurer to be more costly for the plaintiff are associated with higher settlement hazards and consequently shorter delays. These findings have a high degree of statistical significance in both models. The results are quite intuitive: the parties seek to settle earlier the more costly it becomes to prolong the case, but they are less willing to settle the more uncertain is the appropriate settlement offer. Moreover, the dynamic adjustment of the settlement decision to changes in beliefs over the course of the litigation is strongly supported by the authors results on the time-varying covariates in both models. When the insurer s perception of case value increases relative to the initial estimate, the settlement hazard falls, and delay therefore increases. By contrast, when the insurer s perception of the plaintiff s legal costs per day increases relative to the initial estimate, the settlement hazard rises, and delay is therefore reduced. These results are consistent with some process of information exchange over time in relation to g and c p, which are, of course, assumed to be common knowledge in the model of the Theory section. In relation to the insurer s ex ante beliefs about its own liability, i.e., the plaintiff s likelihood of prevailing in court, ( p ), the model s predictions are not supported: the insurer s belief about its own legal responsibility for the plaintiff s losses is significantly related to a higher conditional probability of settlement, and therefore a lower delay. It appears that a case in which the insurer believes its policyholder is fully responsible in law will, other things being equal, be associated with shorter delays. This conflicts with the prediction obtained from bargaining theory and questions the appropriateness of the model in this regard (see Fenn and Rickman, 1999). One possible reason for this conflict relates to the defendant s views about his or her liability. In the current theory of litigation delay, as we have seen, the assessment of liability is assumed to be common (and exogenous) across the parties. In fact, the authors empirical liability variable (RESP_1) represents the insurer s prior view of its likely liability in the case. Whether the plaintiff can reach a similar view, and whether both sides are aware of this, can be doubted. To the extent that this is so, the authors p (and the assumption of a one-sided informational asymmetry) does not sufficiently reflect the informational structure of the litigation process. Instead, it would be more appropriate to model pretrial bargaining as involving two-sided informational asymmetries, where the defendant has private information about the extent of his or her liability and the plaintiff has priors over this. Several articles have modeled uncertainty over liability, as opposed to uncertainty over damages (e.g., Bebchuk, 1984), but only Schweizer (1989) and Daughety and Reinganum (1994) model two-sided private information in litigation game. Those models assume only one period of pre- 13 As explained above, the insurer s own costs, c d, cannot be observed in full: only those costs that are incurred outside the company are recorded. Unsurprisingly, therefore, the coefficients on the variables reflecting estimates of these costs were always insignificant. 14 Interestingly, Kessler (1996) argues that Spier-type models of litigation are unsatisfactory because they fail to predict this effect. This objection holds, however, only for a variancepreserving increase in the average damage level and not, as the authors have seen, if increased severity is accompanied by increased uncertainty.

14 628 THE JOURNAL OF RISK AND INSURANCE trial bargaining, leaving the extension to a more dynamic framework as important future research. 15 Finally, in relation to plaintiff finance, in both tables the authors use binary variables reflecting the identified source (legal aid, legal expenses insurance, trade union funding). While these are generally not significant on their own, the results suggest a difference between the settlement hazard for legally aided claims by comparison with those backed by legal expenses insurance (in some cases a Wald test of the null that the coefficients were equal was rejected at the 10 percent level). The implication is that there may be tentative evidence of longer delays when claims are legally aided, and hence relatively immune to cost pressures, controlling for the size of the claim and the likely plaintiff costs. CONCLUSIONS The authors have presented a strategic model of English pretrial bargaining and tested its predictions regarding settlement timing by insurers using data relating to personal injury claims closed by a major motor vehicle insurer in England. The authors believe that this article has moved forward the understanding of the way litigation delay is determined at present by liability insurers and third-party plaintiffs, and at the same time has raised some general issues in relation to the theoretical modeling of delay. In particular, the authors have looked at the effects of the insurer s beliefs over claim value, plaintiff and defendant costs, and liability on the conditional probability of settlement over time. The authors results suggest that settlement delay is increased when the insurer perceives the case to be of potentially high value, when litigants face low costs of bargaining, and when the defendant believes he or she is less responsible in law for the damages being claimed. The occasions when the model s predictions are not supported empirically can, the authors believe, be attributed to the stylized informational structure assumed. In particular, and certainly when English cost rules are employed, the authors believe that there is a need for two-sided informational asymmetries to be modeled in a dynamic pretrial context. Moreover, the authors empirical findings have strongly indicated that changes in the information holdings of the insurer over the course of the litigation is a significant factor explaining litigation delay. From the insurer s perspective, the message is clear: better estimates, obtained earlier, shorten delay and therefore presumably reduce expected claims costs and premiums. Finally, tentative evidence suggests that the source of plaintiff finance influences litigants behavior. In effect, the nature of legal aid funding in England during the period this study covers meant that neither plaintiffs nor their lawyers were under sig- 15 Another possibility here is that the relationship between liability and delay is nonlinear as suggested, for example, by Ross s (1980) observation that delay ought to be least where liability is clear-cut. Posner s (1973) optimism model of litigation might generate such a result given its prediction that divergent expectations across the parties (which may correspond to liability not being clear-cut ) are required to force a case to trial. Differentiating between this explanation and the one based on asymmetric information that the authors have presented is beyond the scope of this article; see Waldfogel (1998) and Osborn (1999).

15 ASYMMETRIC INFORMATION AND THE SETTLEMENT OF INSURANCE CLAIMS 629 nificant cost pressure to settle. 16 Again, the possible implications for policy are evident: when plaintiff litigation is funded through lawyers, such as is typical in the United States, the cost of continuing litigation is a constant factor in the decision to settle. When plaintiff litigation is funded through third parties such as legal expense insurers or a government agency, as is often the case in Europe, emphasis is placed on the extent to which the third parties monitor the settlement decisions of their appointed lawyers. REFERENCES Bebchuk, L., 1984, Litigation and Settlement Under Imperfect Information, RAND Journal of Economics, 15: Browne, M., and R. Puelz, 1996, Statutory Rules, Attorney Involvement, and Automobile Liability Claims, Journal of Risk and Insurance, 63(1): Cooter, R., and D. Rubinfeld, 1989, Economic Analysis of Legal Disputes and Their Resolution, Journal of Economic Literature, 27(3): Cox, D., 1972, Regression Models and Life Tables, Journal of the Royal Statistical Society, B, 34: Daughety, A., and J. Reinganum, 1994, Settlement Negotiations With Two-Sided Asymmetric Information: Model Duality, Information Distribution, and Efficiency, International Review of Law and Economics, 14: Fenn, P., and N. Rickman, 1999, Delay and Settlement in Litigation, Economic Journal, 109: Fournier, G., and T. Zuelke, 1996, The Timing of Out-of Court Settlements, RAND Journal of Economics, 27(2): Gould, J., 1973, The Economics of Legal Conflicts, Journal of Legal Studies, 2(2). Harrington, S., 1994, State Decisions To Limit Tort Liability: An Empirical Analysis of No-Fault Automobile Insurance Laws, Journal of Risk and Insurance, 61: Hay, B., and K. Spier, 1998, Settlement of Litigation, in P. Newman (ed.) The New Palgrave Dictionary of Law and Economics (London: Macmillan). Kessler, D., 1996 Institutional Causes of Delay in the Settlement of Legal Disputes, Journal of Law Economics and Organization, 12: Kritzer, H., 1990, The Justice Broker: Lawyers and Ordinary Litigation (Oxford: Oxford University Press). Meyer, B., 1990, Unemployment Insurance and Unemployment Spells, Econometrica, 58(4): Osborn, E., 1999, Who Should be Worried About Asymmetric Information in Litigation?, International Review of Law and Economics, 19: However, in recent years the legal aid system in the United Kingdom has changed significantly. Most personal injury litigation is now funded either through lawyers themselves on what is known as a conditional fee basis or through various forms of legal expense insurance (see Rickman, Fenn, and Gray, 1999).

16 630 THE JOURNAL OF RISK AND INSURANCE P ng, I., 1983, Strategic Behaviour of Suit, Settlement and Trial, Bell Journal of Economics, 14: Posner, R., 1973, An Economic Approach to Legal Procedure and Judicial Administration, Journal of Legal Studies, 2: Reinganum, J., and L. Wilde, 1986, Settlement, Litigation and the Allocation of Legal Costs, RAND Journal of Economics, 17: Rickman N., 1998, The Empirical Analysis of Litigation: A Survey of the Economics Literature, Lord Chancellor s Department Research Paper. Rickman, N., P. Fenn, and A. Gray, 1999, The Reform of Legal Aid in England and Wales, Fiscal Studies, 20(3): Ross, S., 1980, Settled Out of Court: The Social Process of Insurance Claims Adjustment (New York: Aldine). Schweizer, U., 1989, Litigation and Settlement Under Two-Sided Incomplete Information, Review of Economic Studies, 56: Spier, K., 1992, The Dynamics of Pre-Trial Negotiation, Review of Economic Studies, 59: Waldfogel, J., 1998, Reconciling Asymmetric Information and Divergent Expectations Theories of Litigation, Journal of Law and Economics: