The Unexpected Effect of Tort Reform Do Caps Delay Settlements

The Unexpected Effect of Tort Reform: Do Caps Delay Settlements? Ronen Avraham 1 and Alvaro Bustos 2 February 2007 Preliminary Version. Do not circulate Abstract: Conventional economic analysis of tort reform suggests that caps on noneconomic damages reduce the time to settlement and consequently save litigation expenses. What the conventional analysis ignores is the real life fact that many of the caps are struck down by state supreme courts within a few years of enactment. We develop a simple screening and asymmetric information model which accounts for parties’ symmetrical expectations for a striking down of the reform. The model predicts that caps on non-economic damages not only tend to increase the fraction of cases that settle (which reduces litigation expenses) but also tend to increase the time required to resolve the conflict (which increases litigation expenses). We show that in states in which the expectation of a strike down is small (we call them states with solid caps) the first effect dominates and litigation expenses would decrease, whereas in states in which that expectation is high (we call them states with non-solid caps) the second effect may dominate, in which case litigation expenses would increase. In addition, the model predicts that while plaintiff's with high claims always receive lower recoveries in states with caps, plaintiffs with low claims may receive lower or higher recoveries. Using almost 200,000 medical malpractice settlement payments between 1991 and 2005 we show that many of our model’s predictions are confirmed in practice. Importantly, we show that cases which were subject to solid caps were resolved faster (between .59 to 1.74 years faster) and, for plaintiffs with high claims, were resolved at a lower amount (10%-13% lower) compared with cases not subject to caps. In contrast, cases subject to non solid caps were resolved 1/3 of a year more slowly compared to states with no caps and their recovery was not lower than recoveries in cases not subject to caps. Thus, caps seem to hit plaintiffs either by reducing the recoveries of plaintiffs with large claims, if caps are not struck-down, or by causing plaintiffs to get their damages at a later date, if caps are struck down. Implications for the pending federal medical malpractice bill are discussed. 1 2 Northwestern University School of Law: r-avraham@law.northwestern.edu Northwestern University School of Law and Kellogg School of Management: abustos@law.northwestern.edu 1 In the last few decades, dozens of different tort and medical malpractice reforms have been enacted, struck down or reenacted. 3 Indeed, tort reform is perhaps the foremost legal item on state legislative agendas. Interest groups regularly spend hundreds of millions of dollars pursuing or fighting against reform. 4 Pressure for tort reform is building on the federal level as well. No fewer than sixteen bills to federalize various aspects of medical malpractice law have been debated in the Congress since Republican control. 5 The most recent bill passed in the Senate in 2006. 6 One of the most popular reforms is caps on non-economic (pain-and-suffering) damages. In 2005 twenty-four states had caps on non-economic damages. From 1991 alone caps on non-economic damages were enacted in 12 states and struck down in 4 states. 7 In some states, such as Illinois and Ohio, they were struck down and reenacted more than once. Proponents of caps on non-economic damages argue that these caps will lower recoveries, shorten the time to settlement and save overall litigation expenses. 8 The reason is not only that the uncertainty associated with unlimited jury awards for noneconomic damages is reduced, therefore facilitating faster negotiation, but also because the limited recoveries provide plaintiffs with weaker incentives to resolve disputes through a costly trial instead of through a less costly settlement. Indeed, various law and economic models with asymmetric information predict that caps will shorten the time to settlement. 9 In contrast, opponents of caps highlight the fact that caps lower recoveries for the most severely injured plaintiffs. 10 However, what proponents and opponents of caps on non-economic damages and the law and economic models of settlement negotiation fail to account for is the fact that the 3 See Ronen Avraham, Database of State http://papers.ssrn.com/sol3/papers.cfm?abstract_id=902711 Tort law Reforms, available at 4 5 The data is available at: http://www.publicintegrity.org/lobby/top.aspx?act=topcompanies 104 H.R. 3103 (1996), 104 H.R. 956 (1996), 105 H.R. 1091 (1997), 106 H.R. 2242 (1999), 107 H.R. 2563, 107 S. 812, 107 H.R. 4600 (2002), 108 H.R. 5 (2003),108 S.2061, 108 S. 11 (2003), 108 S. 2207, 108 H.R. 4280 (2004), 109 H.R. 534 (2005), 109 S. 366, 367, 354, 109 H.R. 5, 109 S. 22 S.22, 109th Cong. (2006). See Table 5. Cite ATRA. Look at my NU piece. See for example Watanabe (2006). PUT HERE MORE REFERENCES. Cite ATLA. Viscusi. Look at my NU piece. 6 7 8 9 10 2 constitutionality of more than half of the caps on non-economic damages will be challenged first in lower courts and later in state supreme courts within a few years of enactment. The uncertainty about the constitutionality of the reforms might provide incentives to parties to delay settlement until after the reform’s constitutionality status is resolved by the state’s Supreme Court. If caps are struck down, recoveries might not decrease at all. In section II we develop an asymmetric information screening model which accounts for plaintiff’s idiosyncratic non-economic harm and parties’ (symmetrical) expectations for a striking down of the reform. We show that caps on non-economic damages have two effects: 1) they decrease total litigation expenses by increasing the fraction of cases that settle instead of being litigated due to the fact that settlements become, relative to trials, even more attractive to defendants than under the no-cap regime, and 2) they increase total litigation expenses by increasing the time required to resolve the conflict due to the expectation for a strike-down. Our model implies that in states where the expectation for a strike down is low (we call these states: solid caps states) the first effect dominates and total litigation expenses decrease whereas in states where the expectation for a strike down is high (we call these states: non-solid caps states) the second effect, in general although not always, dominates and time to settlement as well as total litigation expenses increase. The intuition is that stronger the expectations are that caps will be struck down in the future the higher the incentives are for plaintiffs to wait and resolve their disputes also in the future and the higher their incentives are to go to trial instead of to settle. In addition, our model predicts that plaintiffs with high claims are always worse-off in states with caps (whether or not they are solid) either because they recover less or they recover the same amount but later in time. The model also predicts, counterintuitively, that plaintiffs with low value claims may end up better off as well as worse off in states with caps, relative to states with no caps. Low value plaintiffs may be worse off in states with caps when the proportion of plaintiffs with low value claims is low enough. In that case, just as is the case in states with no caps, low value plaintiffs obtain the same recoveries as plaintiffs with high claims because defendants are unable to distinguish among them. In other words, both in states with no caps, and states with caps there is a 3 pooling equilibrium where low value plaintiffs recover whatever high value plaintiffs recover. And, as was just explained, because high value plaintiffs are always worse off in states with caps relative to states with no-caps, so do low value plaintiffs. On the other hand, low value plaintiffs may be better off in states with caps when the proportion of plaintiffs with low claims is neither too low nor too high. In that case, the equilibrium in states with no cap, is a separating equilibrium so that low value plaintiffs recover their real (low) value whereas in states with caps, the equilibrium is a pooling equilibrium and low value plaintiffs recover whatever the high value plaintiffs recover, which is higher than their real low value. In Section III, using almost 200,000 medical malpractice settlement payments from 1991 to 2005 we show that many of our model’s predictions are confirmed in practice. In a previous study Avraham (2007) showed that when caps on non-economic damages are solid (ex-post, i.e. not struck down) they lower average recoveries by 65 to 72 percent. 11 Yet, Avraham (2007) did not distinguish between high claims victims and low claims victims. This paper explores the effect of caps on non-economic damages on the time to settlement using difference-in-differences techniques. The large number of enactments, in addition to the fact that a few reforms were struck down, makes difference-indifference techniques a particularly attractive avenue to explore. In general, we find that when caps on non-economic damages are solid they decrease the time to settlement by 0.59 to 1.74 years, whereas non-solid caps increase time to settlement by 1/3 of a year, both relative to a regime with no caps. Additionally, we find that high-value claims subject to solid caps resolved at a lower amount (10%-13% lower) compared with cases not subject to caps. In contrast, recoveries of cases subject to non solid caps were not lower than cases not subject to caps. We conclude that caps seem to hit plaintiffs either by reducing the recoveries of plaintiffs with large claims, if caps are not struck-down, or by causing plaintiffs to get their damages at a later date, if caps are struck down. Implications for the federal medical malpractice bill and the role of litigants' expectations about the life of the legislation for its effectiveness are discussed. 11 Ronen Avraham, The Impact of Tort Reforms on Medical Malpractice Settlement Payments. 4 The rest of this paper is organized as follows. Section I reviews the relevant literature. Section II discusses the theoretical model which we developed. Section III discusses the methodology, Section IV presents the data, Section IV presents the results, and Section V concludes. I. Tort Reform- Literature Review. Despite the attention it attracts, there is little academic consensus about the actual impact of tort reform. Early studies on tort reform focused mainly on the impact of tort reform on litigation outcomes and on various insurance variables. Studies that explored the effect of tort reform on litigation outcomes focused on the effect of tort reforms on average awards, frequency of lawsuits, and total payments. These studies often found mixed results and are plagued with selection issues. 12 More recent nationally representative studies of tort reform and litigation variables have found an effect. Avraham (2007) found that caps on pain-and-suffering damages reduced the number of annual payments, and that caps on pain-and-suffering damages and limitation on the collateral source rule reduced average awards. The other reforms had no statistically significant effect on the total annual payments. Using a different dating scheme, Currie & MacLeod (2006) found that caps on non-economic damages and modification of the collateral source rule reduce the number of payments, while joint and several liability reform increases the number of payments. Caps on non-economic damages also reduced total payments while joint and several liability increased total payments. There are almost no empirical studies that explore the impact of tort reform on time to settlement. The only exception is a 1996 study by Daniel Kessler which explored the causes of delay in settling automobile accident disputes. [describe study. He did not account for strike downs] For reviews of previous literature see Stephen Zuckerman, Christopher F. Koller and Randall R. Bovbjerg, Information on Malpractice: A Review of Empirical Research on Major Policy Issues, 49 Law and Contemporary Problems 85, 101-03 (1986); U.S. Congress, Office of the Technology Assessment, Impact of Legal Reforms on Medical Malpractice Costs, at 57-75, 105-111 (1993); U.S. Congress, Congressional Budget Office, The Effects of Torts Reform: Evidence from the States (2004). 12 5 There are very few law and economics models of tort reform. These models usually deal with the impact of tort reform on plaintiffs’ recoveries or physicians’ initial behavior. None of the models take into account the possibility that the tort reform will be struck down. [describe papers: McLeod, Yas, Spier, etc] Our work is a contribution to the normative and the positive lines of studies. Indeed, this study is the first study to systematically model and empirically explore the impact of the most prevalent tort reform- caps on non-economic damages- on the time to settlement of medical malpractice disputes. II. The Theoretical Model A risk neutral medical malpractice victim (Plaintiff) has a valid claim X against a risk neutral negligent physician (Defendant). The claim X= xo + xi has two components: an observable component, xo, which represents the economic harm, such as medical bills, loss of income, etc, and an idiosyncratic unobservable component, xi which represents the non-economic harm such as pain and suffering, mental anguish, etc. For simplicity we normalize the observable components, xo, to equal zero and focus on the idiosyncratic component, xi and denote it as x. Whereas the liability of the physician is not disputed, there is some uncertainty about the victim’s non-economic harm. There are two possible types of victims: A victim with a high non-economic harm, xH and a victim with a low non-economic harm, xL where xH > xL. The defendant cannot observe x, instead, based on the observable economic harm, he can only estimate the probability π that the plaintiff is a low type victim. In order to capture the possibility of delay, the screening model has two periods (see diagram 1). In the first period the defendant makes a settlement offer (S1) that the plaintiff can either accept or reject. If the plaintiff accepts (S1), the game ends there. If the plaintiff rejects it, he either goes to court which would award damages (xH or xL) according to the true type of the victim (still in period 1), or instead the plaintiff can wait 6 for a new settlement offer in the second period. 13 In the second period, the defendant makes a new settlement offer (S2) and once again the plaintiff can either accept or reject it. If he rejects the offer, parties go to court which would award damages (xH or xL) according to the true type of the victim. In order to simplify the exposition of the results we consider that in the case where the plaintiff is indifferent between settlement and trial during the same period he prefers settlement. 14 Diagram 1 presents the game. [Diagram 1 here] Settlement negotiations and litigation are of course costly to both parties. Following the literature and for simplicity’s sake we normalize the plaintiff costs to be zero. Hence, we assume that the defendant faces a fixed cost c for each period of pretrial negotiation (so that if the plaintiff accepts (S1) the defendant incurs c, but if the plaintiff rejects (S1) and waits for a new offer the defendant incurs 2c). In addition we assume that the defendant incurs a fix cost k if the case goes to court (either in period 1 or period 2) with k > c. We also follow the literature and assume that the parties have the same discount factor δ. We compare the negotiation behavior and recoveries of the low type plaintiff and the high type plaintiff in a regime with and without caps on non-economic damages. We therefore denote xc ∈ [xL,xH] as the cap on non-economic damages. 15 As was explained in the introduction, caps are routinely struck down by state supreme courts’. Parties’ expectations about caps’ strike downs is a key factor in understanding their decisions regarding solving the dispute. In order to capture these 13 That courts can correctly observe plaintiff’s true harm is not a strong assumption once we realize that it is enough for our model that courts are not systematically biased and get it right, on average. This is the same assumption used by Spier (92) or Watanabe (06). The main results don’t depend on this assumption. In practical terms it allows us to rule out equilibriums in which the plaintiff randomizes between settlement and trial in the same period when he receives an offer equal to his harm 15 The comparison between the low and high type plaintiffs is interesting only if the size of the cap is smaller than xH. If the cap is too high then it is irrelevant in the decisions of the agents. To simplify the algebra we consider that the cap is larger than xL although the qualitative results don’t change if we obviate that condition. 14 7 expectations we assume that both parties share the same beliefs that the cap may get struck down at period 2 with probability α. 16 We define x = αx H + (1 − α ) x c as the expected payment obtained by a high type plaintiff if he goes to trial in the second period when caps are in place: if the caps are struck down the high type plaintiff receives his true valuation xH, whereas if the caps are upheld he gets the caps, x c . Diagram 2 presents the time line in the second period. [Diagram 2 here] Equilibrium A complete proof of the equilibriums reached in the regimes (with and without caps) as well as a detailed numerical example which demonstrates the main results are relegated to appendix B and A, respectively. Here we summarize the most important characteristics and implications of the equilibriums. A common property in the solutions is that for every type of regime there exists a cut-off probability that the plaintiff is a low type victim such that for any probability smaller than this cut-off value, the solution defines a pooling equilibrium (where the defendant ends up paying the same amount of money to both types of plaintiffs). For any probability higher than this cut-off the solution defines a separating equilibrium (where, in general, the defendant ends up paying different amounts of money to the high and the low type victims). As will be explained in more detail below, there are different cut-off probabilities for the no-caps regime ( π NC ), for the regime with relatively solid caps ( π SC ), and for the regime with relatively non-solid caps ( π NSC ). In Appendix C we show that π NC < π SC , which entails that, ceteris paribus, there are more pooling equilibriums under Regime SC than under Regime NC. In the appendix we also show that if the ratio The assumption that both sides have the same beliefs about the probability of a strike down significantly simplifies the model. In addition, that assumption describes reality more accurately as we do not think that, in general, it is true that one side has more (or less) information than the other side regarding the possibility of a strike-down. 16 8 between the settlement costs, c, and litigation costs, k, is large enough then, ceteris paribus, there are more pooling equilibriums under Regime NSC than under Regime SC, i.e. π NSC > π SC . If c/k is small enough then, ceteris paribus, there are less pooling equilibriums under Regime NSC than under Regime NC, i.e. π NSC < π NC and for intermediate values of c/k, we show that π SC > π NSC > π NC . The intuition for the association between c/k and the order relation among the cut-offs will become clear once we comment on Proposition 3 below. Figure 1 summarizes the most important characteristics of the solutions for the regimes with and without caps. [Figure 1 here] A Regime With No Caps (Regime NC)- When the parties face no caps there exists a unique Sub-game Perfect (SP) equilibrium (which turns to be a pure strategies equilibrium) in which both types of victims resolve their dispute in the first period. Specifically, when there is a low probability that the defendant faces a low type victim, i.e. when π < π NC , the defendant’s offers is xH and both types of plaintiffs accept it. In that case of pooling equilibrium the low type plaintiff benefits (by obtaining more than his true claim, xL) from defendant’s unwillingness to offer xL. 17 Conversely, when there is a high probability that the defendant faces a low type victim, i.e. when π > π NC , the defendant offers xL. In that case of separating equilibrium, the low type settles immediately and the high type goes to court in this same time-period, obtaining a higher recovery of xH. The high type victim does not benefit from waiting an extra period, as all that it would yield him is a recovery of δxH. The defendants does not want to incur a second round of negotiations costs, c, and possibly legal costs, k, if the case goes to trial. 17 9 A Regime With Caps- When the parties face caps there still exists a unique SP equilibrium but with two differences relative to the regime of no caps. First, the equilibrium may be a mixed strategy equilibrium, and second, the parties may end up resolving their dispute in the second period. As Figure 1 shows in the regime with caps we distinguish between two cases: 18 A Regime With Relatively Solid Caps (Regime SC)- When the caps are larger than the discounted expected payment that the plaintiff can obtain at a trial during the second period, i.e. when xc > δ x which is equivalent to saying that the probability of a strike down is smaller than the bound x c (1 − δ ) / δ ( x H − x c ) , the results that we obtained in the regime without caps are replicated here only that xc replaces xH. Specifically, when there is a low probability that the defendant faces a low type victim, i.e. when π < π SC , there is a pooling equilibrium in which both types of victims receive xc in the first period. Otherwise, when there is a high probability that the defendant faces a low type victim, i.e. when π > π SC , there is a separating equilibrium where the low type victim receives xL and the high type receives xc. Thus, wherever the high type plaintiff got his true harm, xH , in the regime with no caps, he could get only the caps, xc , in the regime of relatively solid caps. The intuition is simple: since the caps are relatively solid, the high type plaintiff prefers to settle immediately for xc as his hope to get his true harm in the next period xH is not big enough. A Regime With Relatively Non-Solid Caps (Regime NSC)- When the caps are smaller than the discounted expected payment that the plaintiff can obtain at a trial during the second period, i.e. when xc < δ x which is equivalent to say that the probability of a strike down is larger than the bound x c (1 − δ ) / δ ( x H − x c ) , then the analysis becomes more nuanced. As was in the case of Regime SC, when there is a low probability that the defendant faces a low type victim, i.e. when π < π NSC (observe the difference between π NSC in this case and π SC in the previous case), there is a pooling equilibrium in which 18 The case where xc = δ x is discussed in Appendix B. 10 both types of victims receive δ x in the first period. However, when there is a high probability that the defendant faces a low type victim, i.e. when π > π NSC things change in three ways compared to Regime SC. First, the high type victim always waits for a second period settlement offer (S2). Second, the settlement offer (S2) is the following: with probability p D the defendant offers xL in which case the high type plaintiff goes to court and receives x 19 , or, alternatively, with probability 1 − p D , the defendant offers x in which case the high type plaintiff accepts it. That is, the defendant mixes between xL and x . Third, the low type plaintiff also follows a mixed strategy. He settles in the first period for xL with probability 1 − p LP or settles in the second period for (S2) with probability p LP . The exact expressions for the probabilities of the defendant’s and the low type plaintiff’s mixed strategies, p D and p LP , respectively, are derived in appendix B. Observe that the high type victim never settles in the first period because in the second period he can do better than xL. The low type victim also has incentives to wait as he may end up better-off in the second period by getting x . Yet, as was just explained, the low type victim will sometimes settle in the first period. 20 Main Results The former analysis allows us to uncover two important effects induced by caps when the parties in conflict believe that they may get struck down in the future. The first effect is that caps may increase the time required to resolve a dispute because plaintiffs believe that they will get higher recoveries in the future. The second effect is that, in general (there is one exception), caps tend to increase the fraction of disputes that are resolved through settlement instead of through trial. The reason is that caps make trials less attractive to plaintiffs because they reduce the amount of recoveries that plaintiffs 19 The offer xL is an option given that the defendant knows that the low type may have mimicked the high type. As usual in these cases, there is no pure strategy equilibrium for the low type plaintiff because if he always waits then he only gets δx L as the defendant induces the high type to settle in the first period by offering him δ x . In the same way, if the low type plaintiff never waits he only gets xL. 20 11 can get at trial in both nominal terms (actual recoveries are smaller) and real terms (recoveries are obtained in the future). We summarize these effects in the next two propositions. Proposition 1: (Time of dispute resolution) Part (a): On average, the time of dispute resolution is the same in a Regime SC and in a Regime NC. Part (b): On average, the time of dispute resolution is longer in a Regime NSC than in a Regime NC. Proof: Part (a) For all values of π both types of plaintiffs resolve their disputes in one period both under regimes NC and Regime SC. Part (b) Under Regime NSC, when π < π NSC both types of plaintiffs resolve their disputes in one period. When π > π NSC the high type plaintiff resolves his dispute in two periods while the low type plaintiff resolves his dispute in two periods with probability p LP . In contrast, both types of plaintiff always resolve their disputes in one period under regimen NC. End Proof. Proposition 2 (Proportion of Settlements): Part (a): On average, there is a higher proportion of settlements in Regime SC than in Regime NC. Part (b): On average, unless c/k is small enough and δ is big enough, there is a higher proportion of settlements in Regime NSC than in Regime NC. Proof: 12 Part (a) Under Regime NC, trials take place only when the plaintiff is high type and π > π NC . Under Regime SC, trials take place only when the plaintiff is high type and π > π SC . As π SC > π NC , ceteris paribus, the set of pairs of defendants and plaintiffs that resolve their disputes through settlement is higher under Regime SC than under Regime NC. Part (b) Under Regime NSC, trials take place with probability (1 − π ) p D only when π > π NSC . We distinguish two cases: a) If c k > δ x − x L δ (x H − x L ) − p D δ 1− π * δ where π * = k /(k + x − x L ) then it is true (( ) )( ) that π NSC > π NC (see appendix C for details). In that situation it is straightforward to observe that there are more trials under Regime NC than under Regime NSC (see Figure 1). b) If c k < ((δ x − x L ) δ (x H − x L ) − p D δ )(1− π * ) δ then it is true that π NSC < π NC . In that situation, under Regime NSC the fraction of settlements decreases by (1 − π ) p D in region [π , NSC π NC ], while it increases by (1 − π )(1 − p D ) in region [π , NC 1]. Then, ceteris paribus, the set of pairs of defendants and plaintiffs that resolve their disputes through settlement is higher in Regime NSC than under Regime NC if and only if δ x − xL δ x − xL 1 pD = ( ) < π NC 1 ∫ (1 − π ) f (π )dπ NSC = A(δ ) (P2) π ∫ (1 − π ) f (π )dπ where f (π ) is a general density function for the probability π . Which is equivalent to saying that δ must be smaller than (1 − x L x )A(δ ) + x L x but as this last expression is always smaller than 1 and A(δ ) is decreasing in δ we conclude that for each set of parameters (c, k , x L , x H , x c , α ) there exists δ such that for all δ ∈ δ ,1 (P2) is not satisfied. [ ] End Proof. 13 Interestingly, the two effects uncovered by propositions 1 and 2 affect the litigation expenses in opposite directions. While the first effect increases them, the second one decreases them. Hence, taken together we obtain the counterintuitive result that caps may actually increase and not reduce litigation expenses. The next proposition addresses this point and compares the litigation expenses incurred by a party in dispute under regime NC with the litigation expenses that it would have incurred under Regimes SC and NSC. Proposition 3: (Litigation expenses) Part (a): For all values of π litigation expenses are equal or smaller under Regime SC than under Regime NC. Part (b): For all values of π litigation expenses may be bigger under Regime NSC than under Regime NC. Proof: Part (a) We compare the value of litigation expenses under Regimens SC and NC for all values of π . Comparing cases 1 and 2 in Figure 1 reveals that for all π < π NC and for all π > π SC the litigation expenses in Regime SC are equal to the litigation expenses in Regime NC. Specifically, if π < π NC then in both legal regimes, both types of victims settle in the first period and the total litigation expenses are c. If π > π SC then in both legal regimes the low type victim settles in the first period and the high type victim goes to court in the first period. Thus, the total litigation expenses are πc + (1-π)(c + k). However, if π ∈ [π NC , π SC ] then the litigation expenses are smaller in Regime SC than in Regime NC. Specifically, in the no caps regime the litigation expenses are equal to πc + (1-π)(c + k) whereas in the legal regime with solid caps they are equal to c. Part (b) As we already know π NSC may be bigger or smaller than π NC depending on the ratio of negotiation costs to litigation costs, i.e. c/k. When comparing cases 1 and 3 in Figure 1 we distinguish between three possibilities: 14 Case 1) If c k < ((δ x − x L ) δ (x H − x L ) − p D δ )(1− π * ) δ then we get that π NSC < π NC , in which case for all π < π NSC the litigation expenses are equal to c in both legal regimes. For all π ∈ [π NSC , π NC ] the litigation expenses are smaller in Regime NC, where they are equal to c, than in Regime NSC, where they are equal to c + πp PL δc + (1 − π )( p D δk + δc). And, for all π > π NC litigation expenses are larger under Regime NC because that we are in the case in which c + (1 − π )k > c + πp PL δc + (1 − π )( p D δk + δc) given c k < 1 − p D δ 1 − π * δ = (c k ) . ( )( ) The intuition for the last expression is as follows: Unlike in Regime NC where all disputes are resolved in the first period, in Regime NSC there is always the risk of a second round of negotiations; this effect increases the total litigation expenses expected in Regime NSC. On the other hand, in Regime NSC there are fewer (second-period) trials than in Regime NC (where first-period trials sometimes occur); this effect decreases the litigation expenses in Regime NSC. Thus, caps reduce litigation expenses if the second effect outweighs the first effect which happens if and only if c + (1 − π )k > c + πp PL δc + (1 − π )( p D δk + δc) or equivalently (1 − δp D )(1 − π )k > πp LP + (1 − π ) δc, ( ) (1) The right-hand-side of expression (1) represents the increase in the negotiation costs, whereas the left-hand-side represents the reduction of litigation expenses due to trials. Expression (1) can be finally rewritten as c ⎛ c ⎞ 1 − p Dδ 1 − π * <⎜ ⎟= k ⎝k⎠ δ ( )( ) That is, litigation expenses are lower under Regime NSC if the relation between the costs of negotiation and the costs of trial are small enough. 15 Case 2) If c k ∈ ((δ x − x L ) δ (x H − x L ) − p D δ )(1 − π * ) δ , (c k ) then we get that π NSC > π NC , in which case for all π < π NC the litigation expenses are equal to c in [ ] both legal regimes, for all π ∈ [π NC , π NSC ] the litigation expenses are smaller in Regime NSC, where they are equal to c, than in Regime NC, where they are equal to c + (1 − π )k . And, for all π > π NSC litigation expenses are still smaller under Regime NSC because c + (1 − π )k > c + πp PLδc + (1 − π )( p D δk + δc) . Case 3) If c k > (c k ) then we get that π NSC > π NC , and for all π < π NC the litigation expenses are equal to c in both legal regimes, for all π ∈ [π NC , π NSC ] the litigation expenses are still smaller under Regime NSC, where they are equal to c, than under Regime NC, where they are equal to c + (1 − π )k . However, this time, for all π > π NSC the litigation expenses are larger under Regime NSC because c + (1 − π )k < c + πp LP δc + (1 − π )( p D δk + δc) . After characterizing all possible comparisons, we end the proof by showing that for all values of π there always exist sets of parameters in which Regime NSC increases the litigation expenses. To do that, we first fix the value of π NC and then we analyze the situations in which π is larger or smaller than that bound. 1) For any value of π > π NC we fix a ratio of c/k big enough to belong to the interval (c k ), ((δ x − x L )π k (1 − π ) − p D δ )(1 − π * ) δ . That assures that we are in the region of separating equilibrium in both regimens ( π > π NSC > π NC ) and effect 1 dominates effect 2 which means that the litigation expenses under Regime NSC are higher than the litigation expenses under Regime NC. In the same way, 2) for any value of π < π NC we fix a ratio of c/k small enough to belong to the interval c k ∈ 0, δ x − x L min π (1 − π ) k , 1 δ (x H − x L ) − p D δ 1 − π * / δ . That assures that we are [ ] [ (( ) { })( ) ] in the region of a separating equilibrium under Regime NSC but in a region of a pooling equilibrium under Regime NC ( π NSC < π < π NC ) and effect 1 dominates effect 2 which means that the litigation expenses under Regime NSC are higher than the litigation expenses under Regime NC. 16 End Proof. Proposition 3 tells us that a priori we do not know whether caps save litigation expenses (settlement and trial costs). The proposition shows that if the expectation of a strike down is small enough or equivalently, if the caps are big enough (a solid regime) then caps reduce litigation expenses. However if the expectation of a strike down is large enough or equivalently, if the caps are small enough (a non-solid regime) then caps may actually increase litigation expenses! When would that happen? The proposition distinguishes two cases. First, if the fraction of low type victims is large then caps increase litigation expense if the ratio c/k is big enough. The reason being that the bigger that ratio is the more likely it is that the effect uncovered by proposition 1 (increase in litigation expenses due to a delay in the time of resolution of the conflict) will dominate the effect uncovered by proposition 2 (decrease in litigation expenses due to a reduction in the fraction of trials) and generate an aggregate increase in litigation expenses. Second, if the fraction of low types is small, then caps increase litigation expenses if the ratio c/k is small enough. The reason this time is that the smaller that ratio is, the more likely it is that the defendant will make an offer that generates a separating equilibrium (which brings with it a delay in the resolution of the conflict) while in the case in which there are no caps, ceteris paribus, the defendant makes an offer that generates a pooling equilibrium (a situation with no trials). Proposition 3 above shows that caps reduce litigation expenses only under certain conditions. But even if these conditions are met, caps are not necessary Pareto efficient because in most cases they make the plaintiff worse off (at the expense of the defendant) compared to a no-cap regime. Proposition 4 provides more details about this point. Proposition 4: (Recoveries) Part (a): For all values of π high type victims receive lower recoveries in regimes with caps (whether SC or NSC) than in a regime without caps. 17 Part (b): For all values of π < π NC low type victims receive smaller recoveries in regimes with caps (whether SC or NSC) than in a regime without caps. For all values of π ∈ π NC , max(π SC , π NSC ) low type victims receive bigger or equal (expected) recoveries in regimes with caps (whether SC or NSC) than in a regime without caps. For all values of π > max(π SC , π NSC ) low type victims receive equal (expected) recoveries in regimes with caps (whether SC or NSC) and without caps. Proof: Part (a): We compare the recoveries obtained by the high type plaintiff under regimes with and without caps for all values of π . Comparing cases 1, 2 and 3 in Figure 1 reveals that in Regime NC high type victim get xH for all values of π whereas in the regime with caps the maximum that the high types victims get, for any value of π , is xc (in Regime SC) and δ x (in Regime NSC), which are smaller than xH. Part (b): We compare the recoveries obtained by the low type plaintiff under regimes with and without caps for all values of π . (We distinguish between Regime SC and Regime NSC for each value of π ). For all π < π NC low type plaintiffs are worse off in both Regime SC and NSC compared to Regime NC as they get xc in Regime SC and δ x in Regime NSC, both which are smaller than the xH they gets in Regime NC. For all π ∈ π NC , max(π SC , π NSC ) low type plaintiffs are better-off in Regime SC compared to Regime NC as they receive xc instead of xL. In addition, low type plaintiffs are also better-off in Regime NSC compared to Regime NC if max(π SC , π NSC ) = π NSC [ ] [ ] as they receive δx instead of xL. However, if max(π SC , π NSC ) = π SC then we have to distinguish between two cases. Case 1) If π NSC < π NC then in the interval π NC , π SC low plaintiffs are indifferent between [ ] regimes as they expect to recover xL in both cases (it is true that they receive δ x with probability 1 − p D when the caps are non-solid but in expected value they receive xL); Case 2) If π NSC > π NC then in the interval [π NC , π NSC ] low type 18 plaintiffs are better-off in a solid cap regime compared to a no-caps regime as they receive δ x instead of xL but in the interval [π NSC , π SC ] low plaintiffs are indifferent between regimes as they expect to recover xL. For all π > max(π SC , π NSC ) low types plaintiffs are indifferent between the two legal regimes (caps and no-caps) as they expect to get xL in both scenarios. End Proof. The intuition for Part (a) of Proposition 4 is straightforward. High type victims are always worse off with caps. They are worse off if they go to court in the first period (in Regime SC) because they would only get xc ; they are worse off if they settle in the first period because they would get either xc in Regime SC or δ x in Regime NSC. Lastly, they are worse off if they wait until the second period (in Regime NSC) because the maximum they could there is δ x . 21 The intuition for Part (b) of Proposition 4 is more subtle. One would expect that low type victims would be indifferent between legal regimes with and without caps, because for low type victims the caps are “not binding”, they are higher than the “true harm” of the low type victims. This intuition is wrong however. Part (b) shows that the low type victims may be worse off, indifferent, or better off in a regime with caps (whether Regime SC or Regime NSC) compared to the regime without caps. The reason why the low type victims may be worse off under a regime with caps is as follows: when there is a pooling equilibrium (π is low enough), low type victims receive whatever high type victims recover. As we saw in Part (a), the high type victims’ recovery is always smaller under a regime with caps (whether SC or NSC) than their recovery under a regime without caps. Thus, it follows that the recovery of the low type victims is smaller under a regime with caps (whether SC or NSC) compared to the no-caps regime. The reason why the low type victims may be better off is the following: when for the same values of π there is a separating equilibrium under Regime NC but a pooling equilibrium under Regimen SC or NSC (π is intermediate), low type victims receive xL under Regime If the uncertainty is resolved at the beginning of the period then the high type victims are still worse-off as they he may get only δxH. 21 19 NC but xc and δ x under Regimes SC and NSC, respectively. The low type benefits from the defendant’s willingness to make a high offer more frequently in a regime with caps because the high offer is larger than in the regime without caps. 22 We derive from Proposition 4 a simple corollary Corollary 1: (Recoveries) Part (a): On average, high type victims receive lower recoveries in Regime SC than in Regime NC. On average, low type victims may receive higher or lower recoveries in Regime SC than in Regime NC. Part (b): On average, high type victims receive lower recoveries in Regime NSC than in Regime NC. On average, low type victims may receive higher or lower recoveries in Regime NSC than in Regime NC. Testable Predictions The model generates several testable predictions (TP) which we will attempt to confirm in the next section. TP1 follows from Proposition 1, TP2 follows from Proposition 2 and TP3 follows from a direct Corollary 1 to Proposition 4. Length of Dispute Resolution (Proposition 1): TP1a. On average, the time of dispute resolution is the same in Regime SC and in Regime NC. TP1b. On average, the time of dispute resolution is longer in Regime NSC than in Regime NC. Notice that it can also be argued that, if we care about the ex-post recovery, low types may end up being better-off when π is big enough. The reason is that under Regime NSC low type victims may get a settlement offer of x (which the defendant makes with probability 1-pD) if they decide to wait for the second period. However in that case there is also the possibility that low types may end up being worse-off as they may get xL in the second period. 22 20 Proportion of Settlements (Proposition 2): TP2a. On average, there is a higher proportion of settlements in Regime SC than in Regime NC. TP2b. On average, the proportion of settlements in Regime NSC may be higher or smaller compared to Regime NC. Recoveries (Corollary to Proposition 4): TP4a. On average, high type victims receive lower recoveries in Regime SC than in Regime NC. On average, low type victims may receive higher or lower recoveries in Regime SC than in Regime NC. TP4b. On average, high type victims receive lower recoveries in Regime NSC than in Regime NC. On average, low type victims may receive higher or lower recoveries in Regime NSC than in Regime NC. III. The Empirical Investigation- Methodology. A. Tort Reforms Dating and Reform Definitions We date tort reforms using the Database of State Tort Law Reforms (DSTLR, 2nd). This is a new dataset compiled by Avraham and discussed at length in Avraham (2006). 23 The database was assembled by cross referencing his own review of the laws and court cases of the 50 states (and Washington DC) from 1980 to 2005 to existing 23 The dataset is available for free download at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=902711 21 compilations. 24 The process discovered that commonly used dating schemes suffer from missed reforms, missing or erroneously coded effective dates of reforms, and missing or incorrectly coded Supreme Courts' decisions striking down or upholding reforms. We believe the DSTLR 2nd to be the most comprehensive legal dataset on tort reform to date. There are ten common tort reforms, which include a variety of damage caps, damage payment reforms, and reforms of joint and several liability. However, we have sufficient variation in the years of our study to analyze only six of them. Fortunately, these six reforms also constitute the main portion of federal tort reform proposals. 25 For a detailed compilation of state adoption and invalidation of all major reforms, see Table 6A in the appendix. Joint and Several. The most common reform passed in state legislatures in recent decades is the limitation of joint and several liability for malpractice defendants (variable name “Joint and Several”). Forty-two states had some variant of this reform in 2004. The common law doctrine of joint-and-several liability allows the plaintiff to collect full damages from any of the defendants irrespective of the defendant's proportional fault, should one defendant be insolvent. This means that plaintiff can go after “deep pocket” defendants, like hospitals, and collect all their damages even if the doctor is the main party at fault. The reforms adopted by states limit this possibility by either imposing liability based on fault, or by allowing for joint-and-several liability only if the defendant is responsible for a significant proportion of the harm, usually at least 50%. Periodic Payment. Periodic payment of large future damage awards is now allowed or required in thirty-one states (“Periodic Payment”). The reform allows or requires courts to award future damages that are above some threshold, usually $200,000, in periodic The compilations include: The American Tort Reform Association State and Federal Reforms compilation (available at http://www.atra.org/reforms/); A compilation by the National Conference of State Legislators, available at: http://www.ncsl.org/standcomm/sclaw/medmaloverview.htm; American Medical Liability Association's Comparison of State Medical Liability Laws; Westlaw's compilation of 50 State Surveys, Medical Malpractice-Tort Reform; CRS Report for Congress; Medical Malpractice Liability Reform: Legal Issues and Fifty-State Survey of Caps on Punitive damages and Non economic Damages (February 2005), available at: http://shelby.senate.gov/legislation/MedicalMalpractice.pdf. 25 24 In the recently proposed federal legislation, there are eight legal reforms in addition to limiting liability for drug manufacturers. We examine six of the eight. We lack the variation to consider the other two (statute of limitations and contingent fee reforms). 22 installments. This reform eases the burden on the defendant who can purchase a taxadvantaged annuity for that purpose, and can potentially relieve a defendant of a portion of her due damages if the plaintiff dies before the damages are fully awarded. Collateral Source. Discretionary or mandatory consideration of collateral sources of payment for medical costs is another common reform established in thirty-five states by 2004. The collateral source rule was developed by common law courts in the 19th century when insurance became more popular. The rule says that the damages that the defendant needs to pay will not be offset by plaintiff's insurance coverage. An implication of this rule is that the plaintiff may get more than his full harm in case of an accident. The reforms adopted by states either require or allow courts to offset plaintiff's private and or public insurance benefits from the awarded damages. Damage Caps. Some of the more controversial reforms involve ceiling caps on damage awards. These caps most commonly apply to non-economic damages (“Caps – Noneconomic”, in twenty-three states) or punitive damages (“Caps – Punitive”, in twenty-six states), but can also apply to total damages (“Caps – Total”, in seven states, which we do not include in the study). Caps come in many flavors. Some impose a cap of fix dollar amount, indexed or not to inflation, while others use a multiplier of the economic damages. Many states also implemented heightened pleading, evidentiary, or other procedural standards for punitive damages (“Punitive Evidence”, in 32 states). For example, some states now require punitive damages to be proven with “clear and convincing evidence” rather than merely the traditional “preponderance of the evidence.” Other states require proof that defendant acted with “deliberate disregard” or “willful indifference” towards plaintiff’s potential injury. Less Frequent Reforms. There are three other reforms that are not considered in the regressions, in part because so few states changed the rules in the time period examined (see Table 6a above). In 2004, six states required the plaintiff to share with the state a portion of the punitive damages (“Split-Recovery”). The rationale usually provided for such reforms is that plaintiff was already made whole with the compensatory damages, so the punitive damages are a windfall which should therefore be shared with the state. Fifteen states limited contingency fee agreements between lawyers and their clients, capping plaintiffs’ lawyers’ recoveries (“Contingency Fee”). While, historically contracts 23 between lawyers and their clients were left for the market to determine, the Contingency Fee reforms impose caps on the percentage of the damages that lawyers can collect. Lastly, eleven states had compensation funds from which patients can collect their recoveries (“Patient Compensation Fund”). The patient compensation fund is a state fund which usually pays the medical malpractice victims monies if the damages awarded are above some threshold, such as $400,000. The rationale given for such arrangement is that it lower physician's premiums and spread the risk of risky medical specialties across the entire population of doctors and tax payer. B. Exogeneity of Reforms An important concern is that our results could be biased because reforms were driven in part by malpractice payments and the time it takes to settle them. For example, long time-to-settlement may have been important in creating the necessary political environment for tort reform. This scenario while somewhat unlikely is not entirely implausible. While definitely a possibility, there are several reasons to believe that endogeniety should either not be a factor or work against a positive finding. First, insofar as some of our findings suggest a decrease in time to settlement due to tort reform, it is unlikely that lower time to settlement motivated legislatures to adopt medical malpractice reforms. Second, a significant portion of the reforms enacted in the period of the study are not specific to medical malpractice, but rather apply torts generally. Thus, even if medical malpractice reforms were enacted in reaction to long time to settlement of medical malpractice cases, the more general tort reforms were most probably not. Third, in some states reforms were adopted by courts rather than by legislatures. Higher evidentiary requirements for punitive damages is an example of such a judicial reform. For these reforms, the endogeneity story described above does not neatly apply. Finally, unlike most difference-in-differences studies, some of the variation in our tort reform dataset arises from states switching back to the old law after the state’s supreme court strikes down the reform. Thus, the reverse causality theory becomes even less plausible; it is 24 simply hard to believe that states' supreme courts strike down tort reforms in reaction to long time to settlement of medical malpractice cases. 26 In some specifications, we control for state specific linear time trends, helping to deal with the possible biasing effects of state-specific trends and serial correlation. In addition, we are less concerned about spikes or dips in pre-reforms variables, caused by a reversion to the mean, because we have a relatively long time frame which should average out such dips. C. Matching Reforms to Payments After identifying the pertinent datasets, analyzing them together required accurately matching the malpractice payments to tort reforms. There are several important legal substantive and related methodological issues associated to effective date of the reform carefully addressed in this study which enhances the reliability of the results. First, in many cases there is a lag between enactment date and effective date. For example, a reform might be passed in July 1st, with an effective date of January 1st the following year. Second, for the purposes of matching a case to the applicable legal regime, the relevant date in most cases is the injury date as opposed to the complaint filing date. Previous studies have (mistakenly in our view) assumed that the relevant date is the filing date. 27 Third, legislative creation of reforms has only (subject to some qualifications presented make below) prospective application unless expressly made 26 One might argue that plaintiffs' lawyers experiencing low fees (as result of tort reform) mobilized the strike down by the court by searching for an appropriate case, litigating it in lower courts, etc. It seems to us most probable that lawyers attempts to strike down the reform are motivated primarily by the constitutional environment in that state. For example, Patricia Danzon seems to have used the filing date as the relevant date for whether or not the reform applies to specific cases. See Patricia Danzon, The Frequency and Severity of Medical Malpractice Claims, Journal of Law and Economics, Vol 27 (1984) 115-158, 139. Thus it seems that many of the claims she used in her dataset, which were closed between 1975 and 1978, should not have been coded as subject to reforms which were enacted in 1975 and 1976. First, claims closed in these years were most likely for injuries that occurred before 1975. Second, those claims that did occur after 1975-6 and closed before 1978 were likely only the small claims, a fact which creates selection bias in the analysis. The same problem appears in her 1986 study, where she argues that “tort reforms are likely to affect the filing and disposition of claims during the calendar years in which the laws are in effect.” See Patricia M. Danzon, The Frequency and Severity of Medical Malpractice Claims: New Evidence, Law and Contemporary Problems, Vol 49(2) (1986) 57-84, 80. Catherine Sharkey also seems to use filing dates in her analysis of punitive damages. See Catherine Sharkey, Unintended Consequences of Medical Malpractice Damages Caps, 80 NYU Law Rev 391 (2005) at Table 1 (using filing dates for Ohio and Illinois reforms instead of using injury dates). 27 25 retroactive, whereas striking down of reforms has retrospective applicability, because striking down of a law declares it to never have been constitutional. 28 The retroactive applicability of striking down a reform implies that malpractice cases initiated after a reform was enacted, yet pending at the time the reform was struck down, should be treated as subject to the pre-reform regime. To illustrate this point, consider the following example. Illinois passed caps on non-economic damages which applied to "causes of action accruing on or after" March 9, 1995. The reform was struck down in December 18, 1997. 29 If one just counts the number of payments for injuries that occurred after the effective date but before the striking down date, the number is about 1155. Yet, if one counts the number of these cases that were actually paid before the strike down date (and were therefore really subject to the reform) the number is only about 80, less then 7% of the cases. This becomes critical when using a difference-in-differences approach that uses state fixed effects, because in difference-in-differences models the estimation of the effect of tort reforms is done based only on changes in the reforms. Put differently, under difference-in-differences approach, only the states that enacted or struck down a reform during the years in question are relevant for the accurate estimation of the impact of the reforms. Other states, which either had or did not have the reforms all the way through the years in question are not as important. 30 Thus, ignoring the strikedown dates and their impact on individual payments, as shown below, might yield enormous errors. Accounting for strike down dates to properly link cases to applicable law is not exceedingly difficult when analyzing individual level data, doing so with statelevel data is less straightforward. 31 We suspect that previous research has not done it all. 28 29 An extensive discussion of these points could be found in Ronen Avraham, The Impact of Tort Reform. See 735 ILCS 5/2-1115.1 for enactment and Best v. Taylor Machine Works, Inc., 689 N.E.2d 1057 (Ill. 1997) for striking down. Jeffrey Wooldridge, Introductory Econometrics: A modern Approach (2005) 30 31 In the interest of full disclosure, it should be mentioned that the NPDB does not allow us to perfectly cure this problem. Because parties can report the case up to 30 days after the payment was executed, payment done in December of a given year might be reported in January of the following year. As the public records provide the payment year only (and not the exact date) there could be some glitches in our coding for reforms that were struck down in December. 26 D. The Econometric Specifications We use micro level data where the dependent variables are time to settlement and recoveries. In addition, at the state level we use proportion of settlement as a dependent variable. The individual data allow us to employ a rich set of control variables to remove heterogeneity. The basic specification takes the form: TimeToSettlementist = αConstant + λYeart + ψStates + τDemographicst + θControlsit + δ1SolidTort Reformst +δ2 NonSolidTort Reformsp + E st where the subscript i indicates the case, subscript s the state at which the case occurred, subscript p indicates the time of the payment, and the subscript t indicates the time of the injury. SolidTortReform is a dummy variable which is equal to 1 when a case was subject to a tort reform in time t was not struck down in time p. NonSolidTortReform is a dummy variable which is equal to 1 when a case was subject to a reform in time t which was eventually struck down in time p. Thus, the omitted group is for states which never had tort reform. Observe that δ1 and δ2 are the variables of interest. δ1 measures the average increase in time to settlement (compared with state which never enacted caps) after the adoption of caps on non-economic damages which was not struck-down as of time p. δ2 measures the average increase in time to settlements after the adoption of caps on noneconomic damages which was struck-down as of time p. Year is a matrix of year effects, State is a matrix of state fixed effects. Demographic control variables at the state level are percent with college degree, percent with high school diploma, percent in labor force, percent government employed, percent private employment, percent self-employed, percent union members, and percent black. In addition we use some individual level control variables such as doctor’s field of practice, age and age-squared. 27 Recall that our model generates different predictions for the recoveries of high-type and low-type victims. Since we do not have victims’ original claims, nor do we have victims’ characteristics, we defined claims as being high or low based on the fields of the physicians. Unfortunately, the coding of physicians’ fields in the NPDB is not that good. Eighty-nine codes distinguish between doctors, nurses, dentists, pharmacists and other types of health care practitioners. We simplified these codes into fourteen consolidated codes. We then regressed (log of) victims’ recoveries on the fourteen fields (with controls) and based on the results, grouped the fourteen fields into three categories: low, medium and high claims field. 32 Lastly, we interacted this new Field variable with the reform and the strike-down variables. The specification takes the form: Log(Recoveries)ist = αConstant + λYeart + ψStates + τDemographicst + θControlsit + δ1SolidTort Reformst +δ2 NonSolidTort Reformst + δ3SolidTortReformst* HighClaim +δ4 NonSolidTortReformst *HighClaim +E st Where δ3 and δ4 a are the new variables of interest: δ1 measures the impact of solid tort reform on low-type claims, δ2 measures the impact of non-solid caps on low-type claims, δ3 measures the impact of solid reform on high-type claims and δ4 measures the impact of non-solid reforms on high-type claims. The excluded group is no-caps claims. IV. The Data We obtained medical malpractice payment information from the National Practitioner Data Bank Public Use Data File, dated December 2005 (the “NPDB Database”). 33 This file is published quarterly by the U.S. Department of Health and Under the Low Type category one can find: chiropractors, dentists, physical therapy and accidents related to drugs. Under the Medium Type one can find: counselors, foot doctors, psychiatrists and psychologists, and radiologists. Under High Type category, one can find physicians, eye doctors, emergency room doctors and nurses. National Practitioner Data Bank Public Use File, September 30, 2003, U.S. Dept. of Health and Human Services, Health Resources & Services Administration, Bureau of Health Professions, Division of Practitioner Databanks, available at http://www.npdb-hipdb.com (hereinafter “NPDB Database”). 33 32 28 Human Services in accordance with the Health Care Quality Improvement Act of 1986 34 and its implementing regulations at 45 CFR 60, et seq. Beginning on September 1, 1990, these laws require that (with some exceptions) all medical malpractice payments to be reported to the Department of Health within 30 days of payment. 35 We limited our analysis to settlements in all 50 states (excluding court awards, and payments in the District of Columbia, and U.S. territories) thus using about 200,000 cases which were paid between 1991 and 2005. Like any other database, the NPDB is not perfect. The problems it suffers from are: lack of reporting of cases where no payments were made, reporting of only closed claims, under-reporting of payments, duplicate reporting of cases, inaccurate reporting of structured settlements, lack of individual characteristics in all the reported cases, lack of the exact day and month of the medical malpractice injury date and settlement payment. The NPDB’s deficiencies and the way to handle them were discussed at length elsewhere. 36 The important point is that, as I showed elsewhere, despite the NPDB’s limitations, it is still a much better data set to work with then alternative available datasets that have been used by other scholars. 37 V. Results Time to Resolving the Dispute. We start with our predictions regarding the time length for resolving disputes. Recall our TP1 which states that time to settlement is increased in Regime NSC relative to Regime NC. While the model does not allow us to generate different predictions about 34 35 42 U.S.C. §§ 11101-11152 (1986). Self-insured practitioners originally reported their malpractice payments. However, on August 27, 1993, the U.S. Court of Appeals for the D.C. Circuit reversed the December 12, 1991, Federal District Court ruling in American Dental Association, et al., v. Donna E. Shalala, No. 92-5038, and held that self-insured individuals were not “entities” under the HCQIA and did not have to report payments made from personal funds. All such reports have been removed from the NPDB. See National Practitioner Data Bank 2003 Annual Report, at 9. 36 37 See Ronen Avraham, The Impact of Tort Reform Id 29 the time to settlement in Regime NC versus Regime SC, intuition suggests that solid caps will decrease the time to settlement. Thus it is hypothesized that time to settlement is ordered in the following way: Regime NSC>RegimeNC>RegimeSC. We first present some simple summary statistics that show the average time to settlement for cases not subject to caps, cases subject to solid caps and cases subject to non-solid caps. The left two bars in Table 1 presents that average time to settlement for cases in states with and without caps. For cases in states that never had caps the average time-tosettlement is 4.08 years. For cases in states that have caps the average time to settlement is 3.33 years. The right two bars in Table 1 separates cases in states that have caps into two subgroups: states with reforms that were not struck down (which are our proxy for states with solid caps 38 ) and states with reforms that were struck down (which are our proxy for states with non-solid caps.) In states with solid caps the average time-tosettlement is 3.26 years whereas in states with non-solid caps the average time-tosettlement is 4.4 years. Thus, Table 1 suggests that caps in general reduce the time-tosettlement by roughly ¾ of a year. This effect seems to be driven by the impact of states with solid caps. States with non-solid caps increase time-to-settlement by roughly 1/3 of a year (compared to states without caps) and by more than a year (compared with state with solid-caps). All differences are significant at 1% or less. Thus, Table 1 confirms the predictions that time to settlement in Regime NSC>RegimeNC>RegimeSC. At this point we cannot tell whether these differences in case length are robust to more rigorous regression analysis to which we now turn. Table 2 presents results only for the main reform and strike-down effects. Three variables are presented: “Caps Non-Economic” which represents the impact of caps on non-economic damages on time-to-settlement when caps are not separated into solid and non-solid caps; “Solid Caps” which represents the impact of caps that were not struck Our current strategy which equates non-solid caps and solid caps (which is a theoretical property about parties’ ex-ante expectations) with states that did and did not strike down the reform, respectively, (which is an empirical finding about states’ ex-post actions) assumes parties have perfect expectations. In future drafts we plan to try and capture parties’ expectations about the strike down in different ways. For example, we can look at the voting margin in cases that struck-down and up-held the reform, at the political composition of the state supreme court in those times, and more generally at the reversal history of the supreme courts’ strike-down as a proxy for activism. 38 30 down, and lastly “Non-Solid Caps” which represents the impact of caps that were struck down. All regressions cluster by state. Model 1 includes no controls except the reform dummies and year dummies, Model 2 includes no controls except the reform dummies, year dummies, and state fixed effects. Model 3 adds state and individual level controls, while Model 4 adds state-specific time trends. Table 2 shows that when caps on non-economic damages are not separated into those that were struck down and those that were not, there is no significant impact on time-tosettlement. 39 Table 2 also shows that solid caps had a negative impact on the time-tosettlement of between 0.59 to 1.74 years (significant at the 5% level) compared to having no caps. Non solid caps had positive impact on the time-to-settlement of about 1/3 of a year (significant at the 5% level) compared to states with no caps. 40 Thus, the time it takes parties to settle a dispute is ranked as follows: Regime NSC>Regime NC> Regime SC, as we predicted above. In sum, the results of the regression analysis confirm by-and-large the results presented in Table 1: States with solid reforms experienced a much shorter time to settlement compared with states without caps. States with non-solid reforms experienced a longer time to settlement compared with states without caps. The only difference between the two tables is that whereas in Table 1 caps not separated into solid and nonsolid were associated with a ¾ of a year reduction in time-to-settlement, in the regressions analysis of Table 2 this effect disappears once control variables were accounted for in the regressions. 41 These results are not only robust to the specifications reported in Table 2 but also to other specifications not reported, such as specifications which control for the individual level control variables only, and more importantly, specifications which control for other tort reforms which exist in the state s in time t or p. The only salient exception is Model 1 in which caps seem to reduce time to settlement by 0.7 years. The results in Model 1where there are no controls except for year dummies are indeed similar to the results in Table 1. 40 41 39 The only salient exception is Model 1 in which there are no controls except for year dummies. Moreover, in non-reported results we tested whether the model’s more subtle predictions about time-tosettlements for high type victims versus low type victims are also confirmed in the data. We defined lowtype and high-type victims in different ways (see below for more details). In all permutations the model’s more subtle predictions were supported. 31 Lastly, in non reported regressions we ran the same analysis for trials rather than for settlements. Our very preliminary results show that solid caps significantly reduce the time to settlement whereas non-solid caps do not. Thus, the time-length of resolving litigated disputes is ranked as follows: (Regime NC/Regime NSC)>Regime SC. The reason that, in contrast to our prediction, the time to resolving the dispute in Regime NSC is no longer than in Regime NC might be that parties have less flexibility with delaying the dispute resolution in on-going trials than when privately negotiating towards a settlement. Proportion of Settlements. [Still under construction. This is a state level variable and I am having a hard time coming up with an estimate given that I have only 4 states and 9 (out of 650) state-years] Recoveries. We now turn to testing the predictions about recoveries for cases subject to no caps versus cases subject to solid or non-solid caps. Recall that for high-type victims our TP4 was that the recoveries in Regime NC are larger than in regimes with caps, whether solid or not. For low-type victims our model did not generate definite predictions. Importantly, low-type victims can be better off or worse off under regimes with caps (solid or non-solid). As before, we first present some simple summary statistics that show the average payments of for cases subject to no-caps, to solid caps and to non-solid caps. The left two triple-bars in Table 3 present the average payment for cases with and without caps broken down by type of the victim’s claim. Cases subject to caps had lower recoveries than cases not subject to caps, across all victims’ types. The right two triple-bars breaks down the impact of caps to solid and non-solid caps. In cases subject to solid caps, the average payment was lower than in cases subject to non-solid caps, again across victims’ types. Most of the differences are significant at the 1% or less except for low type victims for which the impact of caps was not significant. In sum, Table 3 shows that the recoveries are ranked as follows: Regime NSC>Regime NC> Regime SC (for high-type) and 32 (Regime NSC/Regime NC)> Regime SC (for low-type). Table 3 only partially supports our predictions in that it does not show that non-solid caps have negative impact on hightype victims. We now turn to our regressions analysis. Table 4 presents results only for the main reform and strike-down effects. Three variables are presented: “Caps Non-Economic” which represents the impact of caps on non-economic damages on recoveries when caps are not separated into solid and non-solid caps; “Solid Caps” which represents the impact of caps that were not struck down, and lastly “Non-Solid Caps” which represents the impact of caps that were struck down. All regressions cluster by state. Model 1 includes no controls except the reform dummies and year dummies, Model 2 includes no controls except the reform dummies, year dummies, and state fixed effects. Model 3 adds state and individual level controls, while Model 4 adds state-specific time trends. The excluded group is no-caps regime. Table 4 shows that solid caps have negative impact on recoveries, yet this impact is (weakly) significant primarily for high-type claims. Specifically, solid caps reduce hightype claims by 10-13 percent, depending on the specification. 42 Non-solid caps had a positive impact on victims’ recoveries (about 10% on low-types and 2% on high-types) yet this impact was not significant at any reasonable level. The results in Table 4 are similar to those presented in Table 3 in that solid caps had a significant negative impact on high-type victims and a non-significant negative impact on low type victims. The results in Table 4 differ from the results presented in Table 3 in that non-solid caps positive impact on high-type claims was not found to be a significant at the 10%. The results in Table 4 are consistent with the models’ predictions except that nonsolid caps were not found to have a negative impact on high-type victims. The reason could be related to the fact that we proxied states with non-solid caps through states that ended up striking down the caps. These states might have had an especially large α , (which is the ex-ante probability of a strike-down). Indeed, as α is closer to 1, the model predicts that there will be no significance difference between Regime NC and NSC. 42 The 11% reduction in model 3, almost made it to the 10% significance level. 33 These results are not only robust to the specifications reported in Table 2 but also to other specifications not reported such as specifications which control for the individual level control variables only, and more importantly, specifications which control for other tort reforms which exist in the state s in time t or p. 34 Conclusions. From an efficiency perspective, one of the most important corollaries of the theoretical model we presented in this paper is that solid caps (i.e. caps that are likely to not be struck down) decrease legal expenditures whereas non-solid caps may increase them. Indeed, our empirical findings show that cases which were subject to solid caps resolved faster (between .59 to 1.74 years faster) and, for high-type victims, resolved at a lower amount (10%-13% lower) compared with cases not subject to caps. In contrast, cases subject to non solid caps resolved 1/3 of a year more slowly compared to states with no caps and their recovery was at best not lower than cases not subject to caps. Moving away from pure efficiency considerations, our model and empirical findings suggest that caps hit plaintiffs with large claims the hardest. These plaintiffs either receive lower recoveries if the caps are solid, or delayed settlements, if the caps are not. Interestingly, the model predicts that in some circumstances, non-solid caps may make plaintiffs with small claims (perhaps plaintiffs with frivolous lawsuits) better off as it enables them to sometimes receive the same settlement offer that plaintiffs with high claims receive, which is higher than what they could get in regime with no caps. Our empirical findings provide weak support for this prediction. We do find that non-solid caps increased the recovery of victims with low claims by 10%, yet this increase was not found to be significant. The implications for the pending federal medical malpractice bill are clear. Whether or not the bill is constitutional is a question for constitutional law scholars. However, it is worth noting that there has almost never been a case in which caps were struck down by a state Supreme Court for violating the federal constitution. Rather, almost all the strikedowns of caps on non-economic damages were for violating the State’s own constitution. Therefore, to the extent that this fact reflects the notion that caps on non-economic damages do not in fact violate the federal constitution, then there are reasons to believe that federal caps on non-economic damages may not be struck down by the US Supreme Court. If our analysis is correct, then the federal bill should be analogized to solid caps. Consequently, it is anticipated that these (solid) caps will reduce legal costs (due to 35 increased fraction of settlements), reduce the recovery of plaintiffs with large claims and reduce the time to settlement. Future research should focus on the robustness of our theoretical and empirical results to various changes. On the theoretical side we wonder whether changing the model from a screening to a signaling model would significantly change the predictions. Similarly, it should be interesting to explore whether a model with more periods will generate different results. On the empirical side we are interested to know whether the theoretical predictions will survive more sophisticated approaches such as semi-parametric hazard model. 36 References Avraham, Ronen (2007) "The Impact of Tort Reforms on Medical Malpractice Settlement Payment" (under review). Currie, Janet & MacLeod W. Bentley, First Do No Harm? Tort Reform And Birth Outcomes (working paper) Spier, Kathryn (1992) “The Dynamics of Pretrial Negotiations” Review of Economic Studies 59 (1) 93-108. Watanabe, Yasutora (2006) “Learning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation, working paper, Kellogg School of Management. Stephen Zuckerman, Christopher F. Koller and Randall R. Bovbjerg, Information on Malpractice: A Review of Empirical Research on Major Policy Issues, 49 Law and Contemporary Problems 85, 101-03 (1986); U.S. Congress, Office of the Technology Assessment, Impact of Legal Reforms on Medical Malpractice Costs, at 57-75, 105-111 (1993); U.S. Congress, Congressional Budget Office, The Effects of Torts Reform: Evidence from the States (2004). 37 Diagram 1- The Game Period 1 Plaintiff accepts the offer and the dispute ends there Defendant makes settlement offer S1 Plaintiff rejects the offer Plaintiff initiates a trial and the dispute ends there Plaintiff waits for the second period Period 2 Plaintiff accepts the offer and the dispute ends there Defendant makes settlement offer S2 Plaintiff rejects the offer, there is a trial and the dispute ends there 38 Diagram 2- Resolution of Uncertainty In States With Caps Period 2 Settlement negotiations Trial begins if negotiations fail Supreme Court decides whether to strike down the caps Trial ends and payoffs are realized 39 Figure 1: Equilibriums For State With and Without Caps ( π SC > π NSC > π NC ) Case 1- States w/o caps L-T: settle for xH at t = 1 H-T: settle for xH at t = 1 L-T: settle for xL at t = 1 H-T: Go to court for xH at t = 1 k − xL + k π NC = xH L-T: settle for xc at t = 1 H-T: settle for xc at t = 1 L-T: settle for xL at t = 1 H-T: Go to court for xc at t = 1 Case 2- States w/Caps & δ x < x c π SC = k x − xL + k c Case 3- States w/Caps & δ x > x c L-T: settle for x at t = 1 H-T: settle for x at t = 1 L-T: with 1- pLP settle for xL at t = 1 and With pLP settle for S2 at t = 2. H-T: with pD go to court for x at t = 2 and with 1- pD settle for x at t = 2. π NSC 40 Table 1 Time-To-Settlement 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 No Caps Caps Solid Caps Non-Solid Caps N=196,129 settlements. The Time Period is 1991-2005.The bars represent the average time-to-settlement. All differences between any two bars are significant at less than 1%. Years 41 Table 2- Time to Settlement 1 2 3 4 No Controls, No Fixed-Effects Add State Fixed-Effects Add Controls Add State Trends Cap Non-Economic -.70** .02 .02 .06* (.32) (.07) (.05) (.32) Solid Cap -.74** -.59* -.75** -1.40** (.32) (.30) (.36) (.59) Non-Solid Caps .08 .36** .31** .32** (.42) (.17) (.15) (.08) N=196,129 settlements. The Time Period is 1991-2005.Dependent variable is the time-to-settlement (in years). Not reported: Year dummies, State Dummies, Percentage of Population over 65,Percentage with Bachelor degrees, Car Fatalities Per Million People, Per Capita Healthcare Expenditures, Income per Capita, Lawyers per Capita, Life expectancy for Newborns, Consumer Price Index for medical goods, Metropolitan Percentage, Percentage of new Residents, Unemployment Rate, HMO penetration, Age of physician at event, Year of graduation, State Fund Paid, Fields of Physicians. All regressions include year fixed-effects. Regressions 2-4 include state fixed-effects.* significant at 10% or less. ** significant at 5% or less. *** significant at 1% or less. Excluded group is No-Caps. 42 Table 3-Recoveries by Type Recoveries (by type) 500,000 400,000 300,000 200,000 100,000 0 NC Caps Low Type Med Type SC High Type NSC N=196,129 settlements. The Time Period is 1991-2005.The bars represent the average payment for High-Type, Medium-Type and Low-Type victims as determined by physician’s field. Most differences between bars are significant at less than 1%. 43 Table 4- Recoveries by Type. 1 2 3 4 No Controls, No Fixed-Effects Add State Fixed-Effects Add Controls Add State Trends Type Low High Low High Low High Low High Cap Non-Economic -.38** -.08 .20 -.13* .17 -.11 .19* -.11 (.16) (.08) (.12) (.07) (.11) (.07) (.10) (.07) Solid Cap -.41** -.10 -.01 -.13* -.06 -.11 -.07 -.12* (.15) (.08) (.13) (.07) (.12) (.07) (.18) (.07) Non-Solid Caps .16 .02 .15 -.02 .09 .01 .06 .02 (.20) (.05) (.11) (.04) (.11) (.03) (.11) (.04) N=195,938 settlements. The Time Period is 1991-2005.Dependent variable is log of recoveries. Not reported: Year dummies, State Dummies, Percentage of Population over 65,Percentage with Bachelor degrees, Car Fatalities Per Million People, Per Capita Healthcare Expenditures, Income per Capita, Lawyers per Capita, Life expectancy for Newborns, Consumer Price Index for medical goods, Metropolitan Percentage, Percentage of new Residents, Unemployment Rate, HMO penetration, Age of physician at event, Year of graduation, State Fund Paid, Fields of Physicians. All regressions include year fixed-effects. Regressions 2-4 include state fixedeffects.* significant at 10% or less. ** significant at 5% or less. *** significant at 1% or less. Excluded group is No-Caps 44 Table 5- Caps enacted or struck down between 1991-2005 Cap Enacted StruckState Size Down √ AL 400 √ √ IL 500 √ √ OH 500 √ OR 500 MT ND SD ME MS OK TX FL TN NV 250 500 500 400 500 300 250 450 250 350 √ √ √ √ √ √ √ √ √ √ 45 0 0 .2 Density .4 .6 .8 5 Case_Length 10 15 46 0 0 1.0e-06 Density 2.0e-06 3.0e-06 5000000 10000000 15000000 Payment 20000000 25000000 0 5 .05 .1 Density .15 .2 .25 10 15 Log_Payment 20 25 47 Appendix A: Numerical Example In the following numerical example we compare the regimes with no-caps to the regimes with solid and non-solid caps. We show that non-solid caps lead to increased litigation expenses whereas solid caps lead to decreased litigation expenses. We also show that the high type plaintiff always ends up worse-off in a regimen with caps but the low type plaintiff may end up equal, better or worse. Regime with no-caps The Set-up Suppose that a plaintiff has a non-economic claim that can be either for the amount of $10,000 or for $100,000 (we call the former a low-type and the latter a high-type). Suppose also that the plaintiff knows the amount of his claim but the defendant only knows that it is either $10,000 with probability 0.9 or $100,000 with probability 0.1. In other words, unlike the plaintiff, the defendant has incomplete information and his best guess is that there is a 90% chance that the plaintiff is a low type plaintiff. In addition, suppose that the parties resolve their dispute in two periods in the following way: In the first period, the defendant makes a settlement offer. Next, still in the first period, the plaintiff may respond to the offer in three ways. 1) He can accept the offer, in which case the conflict is resolved; 2) He can reject the offer and demand a trial immediately (in the first period) or 3) he can reject the offer and wait for the second period. If the plaintiff opted for the last option then the parties move on to a second period. In the second period, the defendant makes a new settlement offer, but now the plaintiff may respond in two and not three ways. 1) He can accept the offer in which case the conflict is resolved or 2) he can reject the offer and demand a trial immediately (in the second period). The game ends here. In the case of a settlement, the plaintiff gets whatever the defendant offered him, while in the case of a trial, a court compensates the plaintiff for the value of his true claim. For example, if the claim of the plaintiff is $100,000 but the defendant offered him $10,000, then at settlement the plaintiff gets $10,000 while at a trial he would get $100,000. We assume that both parties have a discount factor of 0.9. Finally, there are only two sources of litigation expenses, both faced by the defendant. Each round of negotiation costs the defendant $50 whereas a trial costs her $1,000. Solving the game The only equilibrium in this game is that the defendant offers the plaintiff $10,000 in the first period. The low-type plaintiff accepts the offer but the high-type plaintiff rejects it and demands a trial immediately in which case he recovers $100,000. 48 The defendant offers $10,000 in the first period. 43 In that case she gets disutility of – $10,150: there is a round of negotiations ($50), the low type settles immediately (0.9*$10,000) because if he waits until the next period he would get the same recovery only discounted. The high type rejects the offer and goes to trial in that same first period (0.1*($100,000+$1,000)). If the defendant offered $100,000, then she would have gotten a disutility of -$100,050: both types of plaintiffs settle immediately. In sum, in this unique equilibrium, the expected litigation expenses are $150. The reason is that regardless of the type of the plaintiff there is a negotiation in the first period ($50). In addition, a trial takes place in the first period with certainty if the plaintiff is high-type (0.1*$1000)). Regime with Non-Solid Caps The Set-up Now, suppose that there is a cap of $20,000 on non-economic damages in the state in which the parties resolve their dispute. Suppose also that the cap is in place during the first period, nevertheless, during the second period there is a probability 0.8 that the caps will be struck down by the state supreme court. 44 Thus, if the high type goes to trial in the first period he can only recover $20,000 but if he goes to a trial in the second period his expected recovery is $84,000 (0.8*$100,000+ 0.2*$20,000). In contrast, the low type expects to recover $10,000 at a trial regardless of whether it happens in the first or the second period. Solving the game The only equilibrium is that the defendant’s pure strategy in the first period is to offer the plaintiff $10,000 whereas his mixed strategy in the second period is to offer $10,000 with probability 0.985 or $84,000 with probability 0.115. The low-type plaintiff accepts the $10,000 offer in the first period with probability 0.9985 and rejects it and settles in the second period (for whatever amount the defendant would offer him) with probability 0.0015. The high-type plaintiff always rejects the first period settlement offer and accepts To see that this is the only equilibrium we need to notice two points. First, the defendant only offers settlements of $10,000 or $100,000. She doesn’t offer less than $10,000 because no plaintiff accepts it, she doesn’t offer more than $100,000 because it is more than the maximum that a plaintiff can possibly demand and she doesn’t offer something between these two values because with that offer only the low-type plaintiff settles and that outcome can be achieved by offering just $10,000. Second, in the hypothetical case that the plaintiff doesn’t accept the first offer the defendant makes a second period offer of $10,000. The reason is that, in that case, her expected disutility is -19.150 (50 + 0.1 *(100.000+1000) + 0.9*($10,000)), the high-type plaintiff rejects the offer and goes to trial in which she gets $100,000 while the low-type plaintiff accepts the offer) whereas in the case that she offers $100,000 her expected disutility is -100.050 (both types accept the offer). Consequently the defendant is better offering the low amount. 44 43 We assume that the uncertainty is resolved after the settlement negotiations but before a trial is resolved. 49 the second period offer when it is $84,000 but rejects it and demands a trial when it is $10,000 in which case his expected recovery in court is $84,000. 45 In sum, as in the solution without caps, the expected litigation expenses are $183.59. Regardless of the plaintiff type there is a negotiation in the first period ($50), and in addition, if the plaintiff is low type then there is some probability that he would wait and settle in the second period, generating a second round of negotiations (0.9*0.0015*0.9*$50) and if the plaintiff is high type then he would always wait, hence there is a second round of negotiations, but in addition there is a probability that he would go to trial (0.1*0.9*($50+0.985*$1000)). Comparison of litigation expenses between the Regimes. The central point of the example is that non-solid caps may increase the litigation expenses. In the example, the expected litigation expenses are $183.59 in a regime with caps, while only $150 in a regime without them. The next table identifies the components that determine these expenses Component Negotiation First Period Trial First Period Negotiation Second Period Trial Second Period Without Caps $50 0.1*$1,000 $150 With Non-Solid Caps 50 (0.1+0.9*0.0015)*$50 0.1*0.985*$1,000 $183.59 To see that this is the only equilibrium, we need to notice two points. First, the high type always waits for the second period because the defendant is never willing to offer $75,600 in the first period (that is what the high type gets in the second period). The reason is that the defendant is better off if she offers something smaller than $10,000 in the first period and then $10,000 in the second period (in that case her disutility is 0.9*(0.9*$10,000+0.l*($84,000+$1000)) = $15,050) hence, offering $75,600 cannot be her optimal strategy. Second, there is no pure strategies equilibrium. As the high type always waits, it is never the case that the low type always settles in the first period (he knows that by waiting he could get more) or always waits for a second period (he knows that if he does that then it would induce the defendant to always offer $10,000, but if sometimes he accepts the first period offer he may make her believe that in the second period she is facing the high type with a probability high enough to induce her to make a higher settlement offer.) Consequently: in the first period the defendant offers $10,000 knowing that if the plaintiff is low type there is a probability that he will settle immediately and in the second period she offers $10,000 with probability 0.985 and $84,000 with probability 0.115. That strategy is the one that makes the low type indifferent between settling in the first period ($10,000) or waiting for the second period (0.9*($10,000*0.985 + $84,000*0.115 = $10,000). Under the same logic (of a mix strategies equilibrium), the low type accepts the first period offer only with probability 0.9985. That probability leaves the defendant indifferent between offering $10,000 (the low type settles (0.013*$10,000) while the high type goes to trial (0.987*($84,000 + $1000)) = $84,000) or offering $84,000 (both types settle giving a total of $84,000) at the second period. 45 50 Observe the following. First, all the conflicts in the no-caps regime are resolved in the first period while some of the conflicts in regimens with non-solid caps are resolved in the second period. Second, while in the no-caps regime, trials may take place in the first period in the regime with non-solid caps that may take place in the second period. Third, there are fewer trials in the regime with non-solid caps than in the no-caps regime. Hence, we conclude that in this example, the total litigation expenses are smaller in the no-caps regime because the savings, due to the fact that all the conflicts that are resolved in the first period are larger than the extra expenditures, due to the fact that there are more trials in the no-caps regime. We now turn to a regime with solid caps. Regime with Solid Caps The Set-up Suppose that the former setup is still valid but the probability that the plaintiff is low type is 0.0105. In a regime with no caps, the unique solution is that the defendant offers $10,000 in the first period, the low type victim settles immediately but the high type goes to trial where he gets $100,000. Thus, the expected litigation expenses are $1,039.5 (first round of negotiations ($50) plus the cost of a trial if the plaintiff is high type (0.9895*$1,000)). Suppose now that the cap is $90,000. Solving the game The unique solution is that the defendant offers $90,000 in the first period and the plaintiff always accepts it (regardless of his type). Thus, the expected litigation expenses are $50. In this example caps decreased the litigation expenses because they induced the parties to settle in the first period without any trials involved. The plaintiff is not willing to wait for a second period because the cap is bigger than the expected payoffs in the second period i.e. $90,000 > $76,000 > $9,000. In addition, the high type plaintiff ends worse-off in a regime with caps as he gets $90,000 and not $100,000 but the low type plaintiff ends better-off as also he gets $90,000 and not $10,000. 51 Appendix B Solution For State Without Caps At t = 2. We denote π2 as the Bayesian update of the probability that the plaintiff is of low type in the second period. The cost faced by the defendant C conditional on the second period settlement offer S2 is given by If S2 < xL then C = π2xL + (1-π2) xH + k + c If S2 ∈ [xL,xH) then C = π2S2 + (1-π2)( xH + k) + c If S2 ≥ xH then C = S2 + c In the calculation of C we used the fact that no plaintiff accepts a settlement offer lower than his harm. That structure of settlement offers implies that S2 = xL if and only if π2 > k /( x H − x L + k ) , otherwise S2 = xH. In the first case, the low type plaintiff settles while the high type goes to trial, in the second case, both settle. The negotiation costs are irrelevant. At t = 1. It is clear that the high type plaintiff accepts all settlement offers higher or equal than xH while he litigates all inferior offers, that is, he never waits for the second period. Knowing that, the low type plaintiff accepts all settlement offers higher or equal than xL while he litigates all inferior offers, that is, he doesn’t wait for the second period either (he doesn’t benefit by waiting because he cannot mimic the high type). Consequently, the defendant only offers xL or xH and she prefers the first one when πxL + (1-π)( xH + k) + c < xH + c. Hence: If π > k /( x H − x L + k ) = π NC then S1 = xL. While the low type plaintiff settles the first period, the high type plaintiff litigates and gets xH. Neither of them wants to wait because in that case they only get δxL and δxH respectively. Notice that the defendant knows that the high type never waits and consequently the low type cannot get δxH if he waits. 52 If π < k /( x H − x L + k ) = π NC then S1 = xH. Both types settle in the first period. Solution For State With Caps Unlike in the solution for states without caps here we distinguish three cases If δ x < xc then At t = 2. The solution is the same as in the case without caps but instead of offering xL and xH the defendant offers xL and x . At t = 1. The strategies of the defendant and the plaintiffs are the same as in the case without caps with the following exceptions. First, instead of offering xL and xH the defendant offers xL or xc and second, the high type plaintiff accepts all settlement offers higher or equal than xc (not xH) while litigate all inferior offers. As in the solution for states without caps, the settlement offer in the first period depends on the probability that the plaintiff is a low type. If π > k /( x c − xL + k ) = π SC then S1 = xL. While the low type plaintiff settles, the high type gets more going to trial. Both actions take place in the first period. If π < k /( x c − xL + k ) = π SC then S1 = xc. Both types settle in the first period. If δ x > xc then At t = 2. The strategies of the defendant and the plaintiffs are the same as in the case without caps with the following exception. Instead of offering xL and xH the defendant offers xL and x . In addition, this time we have to consider the option that the defendant randomizes between these two strategies. The defendant may randomize because the plaintiff may decide to wait for the second period. The high type has incentives to wait because he expects to get more in the second than in the first period (regardless whether he settles or litigates in the first period) and the low type has incentives to wait because in 53 the second period he can get more than in the first if he manages to mimic the high type. We define the probabilities that need to be determined to characterize the equilibrium. We call p D the probability that the defendant offers xL in the second period, p LP the probability that the low type plaintiff waits for the second period and p HP the probability that the high type plaintiff waits for the second period. At t = 1. The defendant chooses between offering xL and δ x . If the offer is δ x then both plaintiffs accept it right away as they cannot get more if they wait. Instead, if the offer is xL then both plaintiffs may decide to wait in order to get δ x . Consequently, p LP and p HP correspond to the probabilities that the respective plaintiffs wait when S1 = xL. As in the former cases, the offer made by the defendant depends on the probability that the plaintiff is a low type. More specifically, she offers xL if and only if π 1 − p LP x L + p LP δ p D x L + (1 − p D ) x + c +c <δx+c + (1 − π ) (1 − p HP )( x + k ) + p HP δ ( p D ( x + k ) + (1 − p D ) x + c) [ [( ) ( )] ] (B1) In order to determine the values of p D , p LP and p HP we notice that the defendant randomizes at the second period if and only if π2 =π* = k (x − xL + k) , and by Bayes rule π2 = p LP π p LP π+p HP (1 − π ) = π *, Hence we have that p LP = π * 1 − π HP p 1− π * π But we know that the low type must be indifferent between waiting and settling when he is offered xL and that happens if and only if x L = δ ( p D x L + (1 − p D ) x) . In addition, we know that the high type always waits if he is offered xL because in the second period he always gets δ x . That is, 54 p LP = pD = π * 1− π 1− π * π δ x − xL δ (x − xL ) If we replace the value of these expressions in (B1) we get that the defendant offers xL if and only if ⎡ ⎢ ⎣ ⎡ ⎤ δ x − xL π * 1−π ⎤ δc ⎥ + (1 − π )δ ⎢ x + k + c⎥ < δ x * π 1−π ⎥ ⎢ δ (x − xL ) ⎥ ⎦ ⎣ ⎦ π ⎢xL + which leads us to conclude that: π *δc +δ pDk + c * 1− π If π < [ ] π *δc + δ p D k + c + (δ x − x L ) 1− π * [ ] = π NSC then S1 = δ x . Both types settle in the first period. π *δc +δ pDk + c * 1− π If π > ⎧ x with p D ⎪ = π NSC then S1 = x L and S2 = ⎨ L . The π *δc ⎪ x with 1 − p D D ⎩ + δ p k + c + (δ x − x L ) 1− π * [ ] [ ] high type plaintiff always wait for the second period in which case he settles when he receives offer x but goes to trial when receives offer xL. The low type settles in the first period with probability p LP = π * 1− π otherwise he settles in the 1− π * π second period, that is, with probability 1 − p LP . If δ x = xc then At t = 2. The defendant and plaintiffs strategies are the same as in the case with δ x > xc. The difference is that now, the defendant may face a plaintiff that in the first period rejected the offer δ x . That is possible because the high type plaintiff randomizes 55 strategies. As before, at this point we define the probabilities that need to be determined to characterize the equilibrium. We call p 2 D the probability that the defendant offers xL in the second period, p1 D the probability that the defendant offers xL in the first period p LP the probability that the low type plaintiff waits for the second period when he faces offer xL and p HP the probability that the high type plaintiff waits for the second period when he faces offer δ x . At t = 1. The defendant chooses between offering xL and δ x . Unlike before, the defendant randomizes between these two strategies. That is, it is true that π 1 − p LP x L + p LP δ p 2 D x L + (1 − p 2 D ) x + c + c = πx c + (1 − π ) (1 − p HP ) x c + p HP δ x + c + p 2 D k + c D D + (1 − π ) δ ( p 2 ( x + k ) + (1 − p 2 ) x + c) [( ) [ ( ] )] [ ( )] which simplifies to π x c − x L + p LP δc = (1 − π )(1 − p HP ) c + p 2 D k [ ] [ ] (B2) As before, the low type must be indifferent between waiting and settling when he is offered xL and that happens if and only if x L = δ ( p 2 D x L + (1 − p 2 D ) x) which implies that it is D still true that p 2 = (δ x − x L ) δ (x − x L ) and as before the defendant randomizes at the second period if and only if π2 =π* = k (x − xL + k) , Which implies p LP = π * 1 − π HP p 1− π * π (B3) But now it is not true that the high type always waits if he is offered xL. That is, p LP and p HP are determined by (B2) and (B3). Finally, we notice that the equilibrium is sustained for any value of p1D 56 We conclude then that for all values of π S1 = ⎪ ⎨ ⎧ x L with p1 D ⎪x c with 1 − p1 D ⎩ ⎧ x with p 2 D and S2 = ⎪ L . ⎨ D ⎪ x with 1 − p 2 ⎩ The low type plaintiff always accepts offer S1 = x c but offer S1 = x c only with probability 1 − p LP . The high type plaintiff always rejects offer S 2 = x L but offer S 2 = x c only with probability p HP . 57 Appendix C In this appendix we briefly explain the order relation among the cut-off probabilities in each of the regimes. It is straightforward to realize that π NC < π SC . This reflects the fact that the pooling equilibrium is more attractive to the defendant (compared to the separating equilibrium) under Regime SC than under Regime NC, because it involves lower costs. To see that we compare the expressions that determine these cut-off probabilities: πx L + (1 − π ) x H + (1 − π )k + c = x H + c (1) in the case of π NC and πx L + (1 − π ) x c + (1 − π )k + c = x c + c (2) in the case of π SC . By subtracting (2) from (1) we get that for each π the separating equilibrium is more attractive than the pooling equilibrium under Regime NC than Regime SC exactly by π ( x H − x c ) . Consequently, the set of values of π for which the defendant generates a pooling equilibrium is larger under Regime SC than under Regime NC. The comparison of π NSC with the other cut-offs probabilities requires more effort. Observe that the expression which determines the value of π NSC is ⎡ δc ⎤ + p D δk ⎥ + c = δ x + c ⎣1 − π ⎦ * πx L + (1 − π )δ x + (1 − π ) ⎢ (3) where π * = k /(k + x − x L ) . Thus, in the expression that determines the cut-off probability one can find changes (compared to the regimens NC and SC) not only in the expected recovery of the high type victim but also in the expected litigation costs faced by the defendant when she offers S1 = x L . In Regimens NC and SC the expected litigation 58 expenses were (1 − π )k + c whereas under Regime NSC they are (1 − π ) ⎡ ⎢ δc ⎤ + p D δk ⎥ + c . * ⎣1 − π ⎦ The first expression in the square bracket represents the defendant’s negotiation costs in the second period. The second expression in the brackets represents the costs associated with trials that might take in Regime NSC (although less frequently compared to the other regimes). Intuitively then, the higher the value is of the ratio c/k, the less attractive it is for the defendant to offer xL (which would have generated the separating equilibrium) under regime NSC relative to the other regimes. Consequently, if c/k is large enough then π NSC is larger than π SC , if c/k is small enough then π NSC is smaller than π NC and for intermediate values of c/k, π NSC locates between these two cut-offs. The exact characterization of each case is as follows: ⎞ 1− π * c ⎛ δ x − xL >⎜ − δp D ⎟ then π NSC > π SC c ⎟ δ k ⎜ δ x − xL ⎝ ⎠ If If ( ) ⎞ 1− π * c ⎡⎛ δ x − x L ∈ ⎢⎜ − δp D ⎟ ⎟ δ k ⎢⎜ δ (x H − x L ) ⎠ ⎣⎝ ⎛ δ x − xL ⎞ 1− π * ⎤ ⎥ − δp D ⎟ ,⎜ ⎜ δ xc − x ⎟ δ ⎥ L ⎝ ⎠ ⎦ ( ) then π NSC ∈ [π NC , π SC ] If ⎞ 1− π * c ⎛ δ x − xL <⎜ − δp D ⎟ then π NSC < π NC ⎟ δ k ⎜ δ (x H − x L ) ⎝ ⎠ 59