Legal expenses insurance and legal fees: Some recent developments

Transcription

1 Legal expenses insurance and legal fees: Some recent developments Yue Qiao Shandong University Neil Rickman University of Surrey and CEPR Abstract We present a simple one-shot model of litigation that allows for recent developments in the funding of civil litigation in England and Wales. This involves a form of contingency payment (the conditional fee ) along with insurance that ca be purchased after an accident has taken place. We analyse the effects of these arrangements on settlement probabilities, settlement amounts, care levels and the plaintiff s welfare. We also show how the model can be amended to include risk averse plaintiffs and recoverable element of the conditional fee. Our results exhibit some ambiguity. The paper is intended as an early attempt to model this innovative method of funding legal services. As such, we suggest useful developments in the Conclusion. JEL number: K41; K13; D74 Keywords: Litigation, fees, insurance.

2 1 Introduction It is well known that litigation can expose the parties involved to considerable risk. Not only does trial leave the loser bearing whatever financial loss is the object of the case, but some jurisdictions also require the loser to meet all the costs of litigation, including those of the winner (the British indemnity rule). The presence of such risks has encouraged several market responses. In the US, it is common for individual plaintiffs to retain lawyers on a contingent basis, thereby shifting some risk on costs to their agent. Alternatively, the majority of European jurisdictions have well developed insurance markets where protection against the risk of legal expense can be purchased. In England and Wales, although the market for such legal expenses insurance (LEI) has developed slowly, this position is changing as policy makers look to substitute private insurance for the increasingly expensive social insurance against legal expense provided by legal aid. One mechanism for achieving this has been conditional fee agreements (CFAs). These introduce a specific kind of contingency payment into the lawyer-client contract, whereby the lawyer receives hourly fees plus a prespecified mark-up on these to compensate for the fact that there is no payment if the case is lost. There is also an interesting interesting insurance dimension: in order to insure the client against the opponent s costs if the case is lost, an insurance policy can be bought. The interesting feature of this policy is that it is bought after the event (ATE), i.e. after the case has materialized, as opposed to more traditional before the event (BTE) legal expenses insurance, which is purchased in anticipation of a possible claim. The overall effect of this development is to introduce elements of US-style contingency payment and European-style insurance into UK litigation so this is a topic with potentially broad appeal. The purpose of our paper is to consider the effects of this new development on the decision to settle or take a case to trial. A number of other authors have looked at various aspects of the problem we study. Thus, the role of fees in litigation have been considered, as has the role of CFAs (without the added insurance dimension), while legal expenses insurance has also been analysed. Furthermore, empirical work is increasingly confirming the role of fees in litigation and recent work has established several important effects of CFAs in this respect. 1 None of this work, however, looks at the combined effect of conditional fees and insurance. In itself, this means that there is a gap in terms of the institutional detail that has been researched. Perhaps more importantly, however, it means that the after-the-event innovation has received no attention. The paper is structured as follows. Section 2 looks at the role of insurance in the settlement of a one-shot litigation game with asymmetric information. This follows the model in Gravelle & Waterson (1993). By and large, we assume that insurance is purchased by a risk neutral plaintiff so we, effectively, view this as a strategic decision (Kirstein 2000). 2 Having set out the model, Section 1 See Yarrow & Abrams (2000): Nothing to Lose? Clients Experiences of Using Conditional Fees and Society of Advanced Legal Studies (2001): Ethics of Conditional Fee Arrangement. 2 Heyes, Rickman & Tzavara (2004) consider the purchase of LEI by a risk averse plaintiff 2

3 3 compares settlement probabilities, accident probabilities and welfare between before-the-event insurance (with hourly fees) and after-the-event policies (with CFAs) these appear to be the market leaders in high-street litigation in England and Wales (see Fenn, Gray, Rickman & Mansur (2006)). In Section 4, we discuss risk aversion and, then, unrecoverable success fees and ATE premiums. In Section 5, we extend our basic model to a dynamic one to analyse the timing of settlement. Finally, Section 6 offers our concluding remarks. 2 The litigation model We follow the model of litigation popularised by Gravelle in a number of papers, most particularly for our purposes in Gravelle & Waterson (1993). An accident may take place with probability π which, in turn is dependent on a (potential) defendant s care level x: π (x) < 0, π (x) > 0. Accidents cause damage L drawn from the cumulative distribution Q(L), with density q(l) on [L 0, L 1 ]. Only the plaintiff (P) knows the true value of L; the defendant (D) knows its distribution. The defendant can make a single settlement offer (S) to P, who then decides whether to accept this or reject it in favour of trial, where his probability of winning is w (which is commonly known). He takes legal advice on this though we generally assume this advice to be unbiased. Settlement costs P s lawyer c 0 while trial costs him c 1. In return, P pays the lawyer a fee of f S if the case settles, f w if the case wins at trial and f 0 if the case loses at trial. The defendant pays her lawyer f D at trial. All parties are risk neutral (effectively, insurance is a strategic purchase, as defined by Kirstein (2000); see Heyes et al. (2004) for an alternative set-up). Since cost shifting rules exist, the loser has to pay the winner a proportion k of the total legal fees. Thus, the expected legal fees transfer from the defendant to the plaintiff is t = k[pf w (1 p)f D ]. Unlike most other models in this literature (see Heyes et al. (2004)), we allow the plaintiff to buy legal expenses insurance (LEI) against legal costs in particular, against trial costs. Later on, we shall distinguish different types of insurance but, for now, we simply compare the effects of an insured plaintiff (PI) and a self-funded plaintiff (PS). Consider the offers that the plaintiff would accept. A well informed selffunded plaintiff would accept the settlement offer S if 3 S f S w(l f w ) (1 w)f 0 + t, where t = k[wf w (1 w)f D ], 0 k 1. The expected gain from acceptance compared with trial for him is: G P S = S wl + wf w + (1 w)f 0 f S t (1) The plaintiff would accept an offer S iff G P S 0. Since G P S is decreasing in L, if there exists l [L 0, L 1 ] such that G = 0 then l is the unique acceptance level. in a similar model. Baik & Kimb (2007) compare contingent fees with LEI. However, none of them consider CFAs. 3 Like (Gravelle & Waterson 1993), we could consider the plaintiff s decision when he receives self-interested and impartial advice from his lawyer. In fact, because insurance does not affect the fees paid to the lawyer (only the identity of the payer), little, apart from complication, is gained from such a generalisation when comparing PI and PS. 3

4 Equivalently, when S is given, P would accept an offer whenever l P S (S, ) L where l P S is the self-funded plaintiff s acceptance level defined by G P S 0. Now we consider a well informed insured plaintiff. The settlement offer normally includes two parts: the compensation of loss and the reimbursement of legal costs. We assume P meets his own legal costs if accepting settlement. The plaintiff s receipt is only the compensation of the loss. He would accept the settlement offer S iff his expected gain from settlement is S f S wl, G P I = S wl f S (2) As before, we define this acceptance level as l P I (S, ). We note (as is standard; see (Gravelle 1993)) that these acceptance levels increase with S (at a rate of 1/w) and are sensitive to the fee regime in operation. Insurance and acceptance levels The difference in the gains from settlement between the self-funded and insured plaintiff is: G = G P S G P I = wf w + (1 w)f 0 t Equivalently, this can be written: l = l P S l P I = wf w + (1 w)f 0 t w Substituting t = k[wf w (1 w)f D ] into this, l = (1 k)wf w + (1 w)f 0 + k(1 w)f D w Since 0 k 1 and w < 1, l is always positive. (3) Result 1. Given the defendant s settlement offer, if the plaintiff purchases insurance, his acceptance level becomes lower. The probability of a given offer S being accepted is Q(l) and the higher the acceptance level, the greater the probability of acceptance. Thus, holding S fixed, insurance toughens P s bargaining stance by making less offers acceptable to him. The defendant s settlement offer The defendant chooses the settlement offer S to minimize his expected post-accident costs (H): L1 H = Q(l)S + [1 Q(l)](f D + t) + w LdQ l The first-order condition defining the optimal (interior) settlement offer S is: dh ds = Q(l) + q(l) w (S wl f D t) = 0 (4) 4

5 Rearranging equation (4), the settlement offer becomes: S = S(l, ) = wl + f D + t w Q(l) q(l) [ = f D + t wl 1 1 ] η(l) (5) where η = Q l/q: the elasticity of settlement probability with respect to P s acceptance level. Since D s offer is a function of the acceptance level l, we have ds dl = q (l)w Q(l) q(l) 2 Thus, the effect of insurance on D s settlement offer is given by: S = S P S S P I = l P S l P I q (l)w Q(l) q(l) 2 dl. Result 2. The defendant will reduce (increase) the settlement offer to the insured plaintiff if q (l) is greater (less) than 0. The effect of insurance on the settlement offer is driven by the distribution of plaintiff losses. In particular, when the distribution contains a high proportion of low-damage plaintiffs (i.e. q < 0), insurance raises the offer. The reasons is straightforward: insured plaintiffs bargain harder and accept fewer offers c.p. Result 1 so D s marginal benefit from raising the offer is limited unless enough low-damage plaintiffs are present to make its acceptance likely. Settlement probability Since insurance influences the settlement offer, it affects the plaintiff s equilibrium acceptance level as well call these l P S and l P I. Straightforward substitution of S P S and S P I into (2) and (1) gives: l = l P S l P I = S w + l This adjusts l from (3) to take account of the effects of the settlement offer on P s acceptance decision. It is clear that the settlement probability Q[l (S, ), ] is affected by the acceptance level directly and the settlement offer indirectly. Result 3. The effect of insurance on settlement probability is ambiguous. If insurance reduces the settlement offer, this decreases the settlement probability. This result is easily explained because of the direct and indirect effects mentioned above: we cannot rule out the possibility that these work in opposite directions. The second part of the Result simply observes that lowering the settlement offer will do nothing to offset the insured P s naturally tougher bargaining stance. 5

6 Accident probability The defendant chooses his care expenditure x to minimise his ex ante welfare, which is given by: W D = [1 π(x)](y D x) + π(x)(y D x H ). Assuming his optimal care x is positive, it satisfies 1 π (x)h = 0 and is obviously increasing in H. The effect of insurance on the ex post cost H is given by: dh dl = q(l)(s wl f D t). From (5), we know that S wl f D t < 0, therefore dh dl < 0. Now it is clear that x is decreasing in l: it is the fear of trial that induces care from D. Since the insured plaintiff and self-funded plaintiff may have different settlement offers and different acceptance levels, we have: Result 4. Insurance increases the defendant s care level if and only if it reduces the plaintiff s acceptance level. Thus, Result 2 tells us that when insurance reduces the settlement offer, it reduces care and increases the accident probability. 3 BTE hourly fee contracts vs ATE conditional fee contract Specification of the contracts and funding methods We now focus more specifically on the principal current funding/insurance options in England and Wales: hourly fee contracts with LEI purchased before the accident occurs (this is known as before-the-event insurance) and the conditional fee contracts with insurance purchased after the accident has occurred ( after-the-event insurance). In an hourly fee contract the lawyer is paid a fee equal to his actual costs whatever the result of the case: f S = c 0 and f w = f 0 = c 1. In a conditional fee contract the lawyer is paid a fee equal to his costs plus a success fee which is a proportionate mark-up of µ if the plaintiff wins or settles. If the plaintiff loses, the lawyer gets nothing: f S = (1 + µ)c 0, f w = (1 + µ)c 1 and f 0 = 0. Under the UK cost shifting rule the losing party has to pay the winning party s success fee: i.e. t = w(1 + µ)c 1 (1 w)f D. If the plaintiff purchased legal expenses insurance before the accident (BTE insurance), all his legal expenses at trial are covered by the insurance policy whatever which fee agreement he signed with his lawyer. If the plaintiff was not insured before the event, he can choose to pay all legal expenses by himself or purchase an after-the-event (ATE) insurance policy before the lawsuit starts. We assume both insurance premiums are actuarially fair. Under BTE insurance, the plaintiff pays a premium α B to the insurer. Under ATE insurance, the plaintiff pays a premium α A to the insurer, but it may be recovered from the losing party if he wins. 4 4 Technically, we model a situation where the success fee and the ATE premium are recov- 6

7 Acceptance levels Given a settlement offer from the defendant, by substituting fees settings into (1) and (2), we can compare the plaintiff s acceptance levels. A well-informed BTE insured plaintiff, under the hourly fee contract (denoted Bh), would accept D s settlement offer S iff S c 0 wl the expected gain from acceptance compared with trial for him is: G Bh = S c 0 wl The plaintiff would accept the offer S iff G Bh 0. Hence, his acceptance level is l Bh = 1 w (S c 0) For a well-informed ATE insured plaintiff, under the conditional fee contract (denoted Aµ), when the insurance premium is recoverable he would accept D s settlement offer S iff S (1 + µ)c 0 wl + wα A so his expected gain from settlement is Similarly, his acceptance level is G Aµ = S (1 + µ)c 0 wl wα A l Aµ = 1 w [S (1 + µ)c 0 wα A ] (6) Rearranging the acceptance levels of the above two situations, we find where l Aµ = l Bh, = 1 w (µc 0 + wα A ) > 0 Essentially, measures the additional revenue that P expects to receive under the ATE/CFA arrangement with recoverability. He recovers µc 0 if he settles and wα A if he goes to trial. The positive value of tells us that these extra gains make P relatively more belligerent than under the BTE/hourly arrangement. Thus, P is less willing to accept the offer S under the ATE conditional fee contract: Result 5. Given the defendant s settlement offer, compared with the BTE hourly fee contract, the ATE conditional fee contract lowers the plaintiff s acceptance level. erable. This became the case following legislation in It created a problem in that many defendants (especially insurers in road traffic cases) argued that success fees were unwarranted in cases where liability was immediately admitted. As such, they refused to pay and significant amounts of satellite litigation ensued, culminating in the House of Lords hearing Callery vs Gray. 7

8 Settlement offers Working as we did in Section 3 (in advance of Result 2), it is straightforward to establish that: S Bh S Aµ = l Bh l Aµ q (l)w Q(l) q 2 (l) dl Since l Bh l Aµ = > 0, the sign of S Bh S Aµ depends on the sign of q (l). Result 6. The ATE conditional fee contract increases (decreases) the defendant s settlement offer compared with the BTE hourly fee contract as q (l) is negative or positive. Note that the distribution of losses plays the same role here as in Result 2. Settlement and accident probability As concluded earlier, changes in D s settlement offer directly affect P s acceptance level. Substituting D s reactions (i.e. offers) into the acceptance levels, we obtain: l Bh l Aµ = 1 w (SBh S Aµ ) + Since is positive, when q (l) 0, the BTE hourly fee contract increases the settlement probability compared with ATE conditional fee contract. When q (l) < 0, ambiguity arises: Result 6 tells us that S Aµ > S Bh so that ATE may now have the higher settlement probability if this difference is large enough to offset > 0. Now, for ATE/CFA to increase the settlement probability, D requires a sufficiently large differential in the settlement offer to make him give up his extra revenue (represented by ) under ATE/CFA. From Result 4, we know that D s expenditure on care x is decreasing in l. So, when q (l) 0, l Bh l Aµ > 0, and the BTE hourly fee contract increases the accident probability compared with ATE conditional fee contract. When q (l) < 0, the situation is more complicated since now l P S l P I. Only when 1 w (SBh S Aµ ) > does the ATE conditional fee contract increase the accident probability compared with the BTE hourly fee contract. 3.1 Welfare analysis We start from the defendant. The defendant s ex ante welfare is: W D = [1 π(x)](y D x) + π(x)(y D x H ) = y D x π(x)h Since dh/dl < 0, it is clear that D s ex ante welfare is increased if a given settlement offer is accepted. Next, consider P s welfare. The ex post welfare of the ATE insured conditional fee plaintiff is: W p Aµ = y P L α A + Q(l Aµ )[S Aµ (1 + µ)c 0 ] +w LdQ + [1 Q(l Aµ )]wα A l Aµ = y P L (1 w)α A + Q(l Aµ )[S Aµ c 0 ] Q(l Aµ )w + w LdQ. l Aµ 8

9 The ex post welfare of BTE insured hourly plaintiff is: W p Bh = y P L α B + Q(l Bh )(S Bh c 0 ) + w LdQ l Bh The ex post welfare change between these two situations is: l Aµ W p Bh W p Aµ = (1 w)α A α B + w LdQ + Q(l Aµ )w l Bh +Q(l Bh )[S Bh c 0 ] Q(l Aµ )[S Aµ c 0 ] Three factors contribute to the welfare change. The first is the gain from settlement: Q(l Bh )[S Bh c 0 ] Q(l Aµ )[S Aµ c 0 ] + Q(l Aµ )w ; the second is the gain from trial: w l Aµ LdQ; and the last is the gain from different levels l Bh of the insurance premium: (1 w)α A α B. Table 1 shows how the distribution of damages influences the sign of this welfare change. (The last three columns relate to the sign of each of the effects we have identified on the welfare change. For example, Not clear in the first line of the Settlement column says that the combination of settlement offers and equilibrium acceptance levels generated by q induces an ambiguous welfare change.) Table 1: BTE hourly fee vs ATE conditional fee Distribution Settlement offer Acceptance level Settlement Trial Premium q > 0 S Bh < S Aµ l Bh > l Aµ Not clear < 0 Not clear q = 0 S Bh = S Aµ l Bh > l Aµ > 0 < 0 Not clear q < 0 S Bh > S Aµ l Bh > l Aµ > 0 < 0 Not clear q < 0 S Bh > S Aµ l Bh = l Aµ > 0 = 0 Not clear q < 0 S Bh > S Aµ l Bh < l Aµ Not clear > 0 Not clear Discussion: Uniform distribution Given the ambiguous welfare effects summarised in Table 1, we now consider the effects of a specific loss distribution: the uniform distribution. 5 If the loss distribution is uniform, assuming L 0 = 0, we can write the loss distribution as Q = L, q = 1. L 1 L 1 Since q = 0, S Bh = S Aµ (Result 6). Hence, the difference between the acceptance levels is given by l Bh l Aµ = = 1 w (µc 0 + wα A ). Note that 5 The uniform distribution is tractable as opposed to being entirely plausible. (Gravelle 1993) also look at a logarithmic distribution, where the majority of damages are collected in the lower tail. 9

10 l Bh = (S c 0 )/w. Substitute Q into the welfare functions to obtain: l Aµ W p Bh W p Aµ = (1 w)α A α B + w LdQ + Q(l Aµ )w l Bh +Q(l Bh )[S Bh c 0 ] Q(l Aµ )[S Aµ c 0 ] = (1 w)α A α B w (l Bh + l Aµ ) + laµ w + wl Bh 2L 1 L 1 = (1 w)α A α B w 2L 1 (l Bh + l Aµ ) + w L 1 (l Bh + l Aµ ) L 1 = (1 w)α A α B + w 2L 1 (l Bh + l Aµ ) Since w 2L 1 (l Bh +l Aµ ) > 0, if (1 w)α A α B 0, the ex post welfare under BTE hourly fee is absolutely greater than the ex post welfare under ATE conditional fee. TO gain some further insight into this expression, assume that the insurance premiums are actuarially fair: α A = [1 Q(l Aµ )](1 w)f D α B = π(l Bh )[1 Q(l Bh )(1 w)(c 1 + f D )]. and substitute these into (1 w)α A α B. Rearrangement now tells us that BTE generates higher welfare if w α A α B = 1 π(l Bh ) (L 1 l Bh ) α A (L 1 l Aµ ) (c 1 + f D ) f D (7) Substitute l Bh = (S c 0 )/w and l Aµ = (S c 0 )/w into (7) to give: w 1 π(l Bh (wl 1 S c 0 )(c 1 + f D ) ) [w(l 1 α A ) S (1 + µ)c 0 ]f D (8) Even now, whether this expression is satisfied is somewhat unclear. We can, however, inspect the right-hand side to gain some insights into the factors that influence the welfare comparison. We use Z to denote the right-hand side of (8). First, since Z/ f D > 0, Z/ c 1 < 0 and Z/ c 0 < 0, the condition is more likely to be hold when D s legal cost f D increases or P s legal costs c 1 and c 0 decrease, which means P is more likely to be better off post-accident under the BTE hourly fee contract rather than under the ATE conditional fee contract when the D s legal cost is very high or his own legal costs are very low. Second, since Z/ w < 0 and Z/ µ > 0, the condition in (8) is more likely to hold if the probability of winning w is lower or the proportion of fee mark-up µ is higher. Third, since Z/ L 1 < 0 and Z/ S > 0, (8) is more likely to hold when the defendant s settlement offer S is higher or the maximum loss L 1 is lower. Finally, since dπ/dl > 0 and Z/ π < 0, the condition is more likely to hold when π is more inelastic with respect to l Discussion: Risk aversion Until now, we have assumed a risk neutral plaintiff, effectively implying the strategic purchase of insurance. We now indicate how the model can be amended 10

11 to allow for plaintiff risk aversion. 6 Under BTE hourly fee and ATE conditional fee, the ex ante certainty equivalents of the risky prospects of trial (y T are: y Aµ T = y p (1 w)l (1 w)α 1 A r Aµ y Bh T = y p (1 w)l α 1 B r Bh where r Bh and r Aµ are the risk premiums for BTE and ATE respectively and αa 1 and αb 1 both recognise that actuarially fir insurance premiums may be sensitive to any changes in acceptance levels brought about by insurance. Note also that the expected judgements depend on the realised accident loss. The acceptance levels are given by: therefore, y p l Aµ r α 1 A + S (1 + µ)c 0 = y Aµ T y p l Bh r α 1 B + S c 0 = y Bh T l Bh r l Aµ r = 1 w (rbh r Aµ ) + 1 w (µc 0 + wα 1 A) = 1 w (rbh r Aµ ) + 1 (9) where 1 reflects the role of risk aversion in setting insurance premiums. Since trial generally reflects a riskier prospect under ATE/CFA, we know that r Bh < r Aµ. We also know from (Heyes et al. 2004) that acceptance levels are higher under risk aversion so αa 1 < α A, so that 1 <. As a result (9) tells us that risk aversion reduces the gap between acceptance levels under BTE and ATE and, indeed, could cause their signs to be reversed. Welfare effects are still ambiguous Discussion: Unrecoverable ATE premium and success fee We now return to risk neutrality and move to a situation where neither the ATE premium α A nor the plaintiff s success fee µ are recoverable by the defendant if the plaintiff wins at trial: P must now pay them himself. 7 This was the position in England and Wales prior to The plaintiff will now accept D s settlement offer only when: His acceptance level becomes S (1 + µ)c 0 w(l µc 1 ) l A = 1 w (S c 0) + µ w (wc 1 c 0 ) Comparing this with the acceptance level under the BTE hourly fee contract, we have: l A = l Bh + µ w (wc 1 c 0 ) (10) Interestingly, this difference is now ambiguous: it depends on wc 1 and c 0. Clearly, the unrecoverable ATE conditional fee contract imposes more costs 6 Unlike (Heyes et al. 2004), we assume that P s (constant) level risk aversion is known to D. 7 In fact, some insurance policies allowed variation son this theme but, broadly, the situation we consider reflects the position prior to the change of policy in

12 on the plaintiff, especially when the case is more likely to win at trial. Since l A l Bh = µ w (wc 1 c 0 ), the plaintiff is more likely ro accept a given settlement offer S under the unrecoverable ATE conditional fee contract when w is higher. Given the ambiguity in (10) analysis analogous to that preceding Result 2 tells us that S Bh S A so that equilibrium acceptance levels are given by l Bh l A = 1 w (SBh S A ) µ w (wc 1 c 0 ) (11) The sign of (11) remains ambiguous so we can no longer be sure that acceptance levels, settlement probabilities and ex ante care levels are ranked as in the unrecoverable case. However, if µ w (wc 1 c 0 ) is negative, when q (l) 0, the BTE hourly fee contract increases the settlement probability compared with unrecoverable ATE conditional fee contract; this occurs when w < c 0 /c 1 i.e. when the prospects at trial are sufficiently low. When q (l) < 0, the outcome (as earlier) depends on the relative size of the settlement amounts. With a uniform loss distribution, the plaintiff s ex post welfare gain under Bh can be shown to be: W p Bh W p A = α A α B + wµc 1 + (µc 0 µwc 1 ) 2L 1 (l Bh + l Aµ ) Given that the ATE premium is higher than the BTE one, the sign of this effect is again related to c 0 wc 1. When this is positive (i.e. small w), the BTE policy generates more ex post welfare for the plaintiff than the unrecoverable ATE/CFA policy. 4 Conclusion We have presented the first analysis of an important development in civil litigation in England and Wales. As in other papers on fees and litigation, a number of our results imply ambiguity in the comparisons. Of course, this reflects a fundamental complexity in the underlying relationships we model but, for this reason, such ambiguity should not be ignored: policy needs to be carefully considered, with suitable opportunities or empirical evaluation (and, ideally, prior empirical analysis how existing policies are working. We appreciate that our model is basic in a number of respects. The one-shot extensive form is restrictive while it would be desirable to examine the role of risk aversion more fully than we have done. In addition, we have not considered the actual choice of inurance arrangement. Other authors have modelled lawyer effort and taken more notice of the principal-agent relationship between lawyer and plaintiff. We have, of course, shown that our model can accommodate extensions so there is scope for additional complexity along these lines. The fact that our simple setting yields ambiguous results, however, suggests that more complicated ones will do so as well. Even so, our model can highlight the influences on the outcomes that might be expected under different fee arrangements and suggest fruitful areas for empirical work. In this way, we hope that the paper contributes to a potential, and valuable, research agenda. 12

13 References Baik, K. H. & Kimb, I.-G. (2007), Contingent fees versus legal expenses insurance, International Review of Law and Economics 27, Fenn, P., Gray, A., Rickman, N. & Mansur, Y. (2006), The funding of personal injury litigation: Comparisons over time and across jurisdictions, Technical report, Department of Constitutional Affair Research Series, London. Gravelle, H. S. E. (1993), The efficiency implications of cost-shifting rules, International Review of Law and Economics 13, Gravelle, H. S. E. & Waterson, M. (1993), No win, no fee: Some economics of contingent legal fees, The Economic Journal 103(420), Heyes, A., Rickman, N. & Tzavara, D. (2004), Legal expenses insurance, risk aversion and litigation, International Review of Law and Economics 24, Kirstein, R. (2000), Risk-neutrality and strategic insurance, The Geneva Papers on Risk and Insurance. Issues and Practice 25(2), Yarrow, S. & Abrams, P. (2000), Nothing to Lose? Clients Experiences of Using Conditional Fees, University of Westminster, London. 13