Tort Reforms and Performance of the Litigation System; Case of Medical Malpractice [Preliminary]

Transcription

1 Tort Reforms and Performance of the Litigation System; Case of Medica Mapractice [Preiminary] Hassan Faghani Dermi Department of Economics, Washington University in St.Louis June, 2011 Abstract This paper studies the effects of tort reforms on the performance of itigation system. We utiize a muti stage bargaining game between patient and physician s awyers. After case has been seected by patient s awyer, both sides bargain over the settement payment. If there is no agreement in a finite period of time then judge(jury) resoves the dispute. We estimate a structura mode which takes into account underying information structure of itigation system. In particuar, whether the case is mapractice or not affects the information strength which payers receive in each period. The measures of performance in the itigation system are type I and Type II errors. The resut of simuated counterfactua poicies indicates that putting non-economic cap woud decrease the performance of the itigation system. On the other hand, reducing contingency fee woud increase the performance of the system. Keywords:Medica Mapractice, Tort reform, Litigation system, Performance. JEL cassification:i11,i18,k13,k32. I am gratefu to Juan Pantano for his comments and suggestions aong deveoping the idea of this paper and aso on estimation of the mode. I am aso thankfu to Yasutora Watanabe for his hepfu comments about the mode. 1

2 1 Introduction Medica mapractice has been one of the most debated issues in heath care system since 1980 s in U.S. Many studies investigated different aspects of this phenomena by ooking at how it affects other important aspects of heath care or identifying the causes of medica mapractice. One of the aspects of heath care which got more attention is insurance premium of medica mapractice iabiity. Since 1980 the insurance market of medica mapractice experienced severa hard and soft market conditions. It has been a common perception in this iterature that high insurance premium is one of the factors which eads to rise of heath care costs in U.S. Defensive medicine, which is a precautionary reaction of heath service providers to avoid mapractice iabiity caim, is thought to be other contributor to rise in heath care costs. Since high amount and voatiity of medica mapractice payments from heath service providers to patients were recognized as the reason of increasing heath care costs, market intervention was justified with the hope to reduce the risks of medica mapractice caim payment. Tort reforms were the resut of that (e.g. Caps on payments, change of contingency fee,...). Different tort reforms were enacted in different states to contro crisis in medica mapractice iabiity insurance market. Numerous studies in this iterature investigated the effects of tort reforms from different aspects (Hyman,Siver(2006) provides an exceent iterature review). Adverse outcome is not unusua in medica care. Patient s conditions can get worse in the process of medica care. Medica mapractice, however, is not about a injuries. Medica mapractice is professiona negigence by act or omission by a heath care provider in which care provided deviates from accepted standards of practice in the medica community and causes injury or death to the patient. A heath provider is iabe to injuries if the injury was a resut of negigence. Negigence refers to a wrong performance which coud be preventabe under norma care conditions. For exampe, hospitas reported 19,885 incidents of medica negigence from 1996 to 1999 in Forida state. It does not mean that a of those cases fied awsuit. As a matter of fact ony 3,177 (16%) of new caim fied (which potentiay incude both cases with and without negigence) in that period in Forida state. Low ratio of fiing caim among cases with negigence is a we documented fact in this iterature 1. As it was noted in Forida state exampe above, not a cases brought to the ega 1 Other studies in Caifornia (1974), New York (1984), Utah and Coorado (1992) reported that amost 2% of the cases with negigence fied caim. 2

3 system are medica mapractice. This is the main source of debate on different reforms in medica mapractice. One of the objectives of tort reforms is to prevent frivoous cases to fie caim. Fairness and efficiency of medica mapractice itigation system is the other objective of tort reforms. The idea tort reform woud be the one which changes incentives of the payers in dispute resoution of medica mapractice such that any side receives what she/he deserves. Most of the patients who ook for payments as a resut of medica mapractice bring their case to ega system via a awyer. 98.5% of the caimants who got paid more than $10, 000 in Texas empoyed awyer during period of The type of contract between patient and awyer, which is a portion of vaue if he wins (contingency fee), usuay 30%, gives significant incentive to the awyer to choose seectivey among different cases. More than 85% of the cases are rejected by awyers (Kritzer, 1997). This makes awyers one of the important payers in this system. A awyer accepts a case to represent if the expected payoffs of the case are more than its expected costs. Physicians usuay empoy a awyer. Since we do not distinguish between patient (or paintiff as its ega term) and his awyer after the case has been accepted and aso physician (or defendant as its ega term) and her awyer, we use paintiff and defendant instead of them as we proceed in this paper. The separation wi be made whenever it woud resut in confusion. Third payer in the ega system, in addition to paintiff and defendant, is judge (or jury). One of the important aspect of dispute resoution(particuary in medica mapractice) is that payers do not know what is the exact state. Whether the case is mapractice or not is a binary phenomenon. Since payers do not know the true situation they have to assign a probabiity to any case which indicates the ikeihood of being mapractice. The probabiistic approach that payers choose may resut in errors in compensating each case. Severa studies have been done in different time periods to find how efficient is the performance of medica mapractice compensation system. Studdert et. a.(2006) investigated on 1452 cosed mapractice caims and found that among those cases which had injury 63% were resut of negigence and 73% of them got paid whie among those cases with no merit (remaining 37%) just 28% got paid. They aso reported that amount of payment in cases with no negigence were significanty ower than those with meritorious caims 2. The effects of tort reforms on medica mapractice insurance premiums and defensive 2 Faber and White (1991) wi be expained in next section. 3

4 medicine have been investigated in different states(viscusi, Born(1995)). However, the effects of tort reform on the performance of the medica mapractice itigation system is the area which has not been expored so far. We estimate the parameters of a bargaining mode (which wi be expained in a moment) and use estimated parameters to quantify the effect of different tort reforms on the performance of the system. Here, by performance we mean the magnitude of type I and type II errors. Let define P r(t ype I error) = α 0 and P r(t ype II error) = β 0. The idea itigation system woud perform if α 0 + β 0 = 0. However, this does not happen in reaity. We say a tort reform is stricty enhancing the performance of system if it decreases both type of errors. And it enhancing the performance of system if it decreases α 0 + β 3 0. We can essentiay ook at the effects of different tort reforms on the performance of system for both cases accepted by patient s awyer and cases which is ooking for awyer. We are interested to ook at ater measure of performance because as it is cear in the graph beow after 2003 in state of Forida, which was the time that cap on non-economic payments was enforced, the number of reported cases decined significanty 4. Figure 1: Number of reported cases in Forida state The question we are interested to see is what is the effect of such tort reform on 3 One coud ook at the cost saving under different tort reforms as a measure of efficiency. 4 One shoud be carefu that a of this decine is not because of tort reform. Since some of the cases are not reported so far that coud be another expanation for that. However, since more than 95% of the cases are reported in ess than 3 years we coud safey concude about the decine to 2007 as resut of tort reform in state of Forida. 4

5 the performance measure which we defined above. The intention of this paper is not to expain this graph though. We just brought this graph as a support to the egitimacy of our question. We essentiay are interested to see whether tort reforms give incentives to payers in the system to enhance performance of the system or they do opposite. In this paper we utiize a bargaining mode to expain the basic interactions in the system. Paintiff s awyer chooses whether to accept the case or not, if she accepts then an stochastic aternating bargaining game starts. In each period two sides receive information and person who was chosen to offer, offers the settement amount. If the offer is accepted by the other payer then the game is over and if it is rejected they wait one more period to get new information and one of them randomy wi be chosen to offer and game continues with same procedure. They can continue the bargaining without awsuit before statute of imitation, the maximum time periods which awsuit can be initiated after the time that injury happened. If paintiff decides to itigate then they move to the next phase of the game which is bargaining after awsuit. There is a finite time period in which if paintiff and defendant did not sette, the case is decided by judge. The beow time ine depicts the important timing of the mode Figure 2: Time-ine of events. The disputed injury happens at time 0, at period T the case is accepted by paintiff s awyer to be represented. Then from period T to T paintiff s awyer (henceforth paintiff) and defendant s awyer (henceforth defendant) bargain to reach settement. T indicates statue of imitation in our mode. That is if by that period two sides do not reach resoution or the case is not itigated then the case oses its ega face. Let t c [T, T ] represent the period in which paintiff s awyer itigates the case. After t c, they continue bargaining in the court unti reach to period T. At T + 1 judge(or jury) decides about the case. To estimated the mode I use a sighty modified structura estimation method which has been deveoped in (Watanabe 2010). And use the estimated parameter to simuate counterfactua poicies. 5

6 2 Literature Review This paper is reated to two different iteratures. We use a bargaining mode which aows deay in settement by Yidiz (2003) and the methods of estimation such a game by Watanabe(2009, 2010). The other part of iterature which the contribution of this paper is pertained to that is medica mapractice. Yidiz (2003) deveops a bargaining mode in which two sides start with different priors and in each period receive new information regarding to their beiefs. The use of different priors is deay in the settement. The observation that we see in the medica mapractice settement. We use a modified version of his mode in which in each period paintiff and defendant receive new information regarding to the strength of the case and aso ikeihood of getting noneconomic payment. One of the reason that we separate these two signas is that we want to ook at effect of tort reform on noneconomic payments. My mode, in particuar in the estimation part borrows a ot from Watanabe (2009, 2010). Despite the difference in the information structures and bargaining protoco in the modeing, I use estimation strategy used by Watanabe (2009,2010). Watanabe (2009) estimates a bargaining mode using data set of Forida state medica mapractice reports. His main contribution is to deveop an estimation strategy to estimate bargaining games. Watanabe (2010) uses the strategies deveoped in his previous paper to measure the agency probem between paintiff s awyer and paintiff 5. Hyman and Siver (2006) perform a iterature review on medica mapractice itigation and tort reform. In this paper they ask different questions and try to answer by ooking at empirica resuts in the iterature. Their focus is on the performance of the itigation system. Unfortunatey, they do not have any comparison of the overa performance of medica mapractice itigation under different tort reforms. Their concusion is that new tort reforms shoud take into account payers incentive to be effective. Kritzer (1997) studies the effect of contingency fee on the awyer s behavior. He brings evidence showing the roe of awyers as gatekeepers. In his data set more than 80% of patients who are ooking for awyer can not find a awyer since the case is weak and aso the expected vaue of the case is ow. Studdert et. a. (2000), study the frequency of negigent and non-negigent injuries which ead to caim in Utah and Coorado in They aso anayze the characteristic 5 He does not deveop a forma mora hazard mode to measure the agency probem. He essentiay estimates a parameter which measures how much weight awyer puts on his interest as opposed to patient interest. 6

7 of the injuries which were not compensated or coud not find awyer to represent them. They concude that the poor correation between medica negigence and mapractice caims which was present in New York in 1984 is present in Utah and Coorado too. They aso find that the edery and poor are more ikey not to sue despite suffering from negigent injuries. Studdert et. a. (2006), study the performance of medica mapractice system to measure how frequent are frivoous itigation. They concude that caims with no error are not uncommon. However, most of them do not get paid. Most of the expenditures in medica mapractice system are reated to the cases with errors and administrative costs of itigation is a significant part of itigation costs. 3 Mode Setup At every period paintiff and defendant receive information (signa) regarding to the dispute. We denote information in each period by I t = (x t, y t ) in which x t stands for the received information regarding to the case at period t. It indicates with which probabiity the case is mapractice (strength of the case) and 0 < x t < 1. The eve information y t contains the signa of the probabiity that the non-economic payment is going to be awarded to the paintiff and the vaue of eve signa is 0 < y t < 1}. Suppose portion of cases which are encountered by paintiff s awyer and decined is π 0. Now we expain the structure of beiefs of different payers. The difference of beiefs between paintiff and defendant is the source of deay in the bargaining mode that we utiize. Both paintiff and defendant assign initia beief that the case is mapractice. We assume that the initia beief of payers about whether the case is mapractice regarding to patients represented by patient s awyer is drawn from F Be. ( P atient Accepted) distribution function. So F Be. ( ) is the beief about whether the case is mapractice regarding to patients who were ooking for awyer and accepted by awyer. Both payers observe same information regarding to the case but of course with different interpretation since their initia beief is different. The reaization of case information foows a conditiona probabiity density which we denote by F 0 (x) = P r(x not Mapractice) and F 1 (x) = P r(x Mapractice). The structure of case signa is such that if the case is mapractice then on average payers get signa with more strength. The concusiveness of the signas depend on the informativeness of the signas structure. This issue wi be expained in detai when we go to the distributiona assumptions. The damage of a disputed injury incudes two parts. First, the economic oss of 7

8 disputed damage is E and it is drawn from F E ( ) distribution function. Second, the non-economic damage of disputed damage (NE) is drawn from F NE ( ) distribution function. Most part of the uncertainty and dispute regarding to the amount of payment stem from non-economic damage. The economic part of the damage is not the source of dispute because it is reativey easier to cacuate. The part which is more under dispute is non-economic damage. We mode the dispute regarding to the ikeihood of receiving non-economic payment as foows. Each payers draw initia beief regarding the noneconomic payment is going to be awarded. 6. So the initia beief of payers regarding to the probabiity of non-economic payment being awarded is drawn from G Be. ( ) distribution function 7. Payers receive information regarding to the ikeihood of non-economic payment is awarded at each period. The reaization of eve signa depends on whether non-economic damage is awardabe or not 8. We assume that the signa distributions are drawn from G 0 (y not Awardabe) if non-economic payment is not awardabe and G 1 (y Awardabw) otherwise. Payers incur cost in each period to bargain. We denote the per period cost of dispute resoution before and after itigation by C i 1 and C i 2, i {p, d}, respectivey. We argue that the difference between two sides stems from their interpretations (beiefs) about the information (signas) they receive in each period. One of the expanation for this difference coud originate from the difference of awyers ski. The intuition is that if a awyer is more experienced her perception of any signa is more coser to the underying distribution than ess experienced one. The other interpretation coud be each of payers get some private signas which capture the different initia beief. We denote the case probabiity attachment of payers by f p, f d and f J. We aso denote the individua probabiity attachment to the ikeihood of getting non-economic payment with g p, g d and g J. These differences refect how each side interprets the received information. The underying assumption that we carry aong this paper is that the non-economic payment (which is usuay reated to pain and suffering) is more reated to the severity of the injury independent of whether the case is mapractice or not. As a resut we assume that beief and signas of whether the case is mapractice or not and whether the non-economic 6 The other option is that they have different beief regarding to the vaue of noneconomic damage. We proceed by ooking at the probabiity that the noneconomic payment is awarded since it is more tractabe and easier to estimate. 7 We expain the distributiona assumptions in the estimation part. 8 As it wi be expained in foowing sections, the awardabe is more reated to the standards in judicia system. The interpretation is that if the judicia standards are vague then the new eve signas are not informative. 8

9 payment is going to be awarded or not are independent. Seection Decision by Paintiff s Lawyer Paintiff s awyer is the most important payers in the dispute resoution system. She encounters many cases caiming to be meritorious. Anticipating the structure of the game, which wi be expained in a moment, she decides to represent the case or not. The awyer decides to represent the case if expected payoff of the case is more than her outside option (which we normaized to zero). So from empirica point of view we just see the cases in the data which passes this criterion. So paintiff s awyer represents the paintiff at time T, given α, the contingency fee fraction, if E p [ W p (I T )] C p 1 0 where W p 1 ( ) is the continuation payoff of the paintiff s awyer. So we have F p Be. ( ) = F ( E p [ W p (I T )] C p 1 0) and [E p W p F 1 (I T ) C1) p 0] = 1 π 0. These two conditions make reation between the portion of cases which are accepted and underying assumption about probabiity of a case is mapractice. Timing of the Game The structure of the game and aso the bargaining protoco we are using is simiar to Yidiz(2003) and Watanabe(2009). Before starting the game, nature draws whether case is mapractice or not, non-economic payment is awardabe or not, and oss vaues (economic and non-economic). We assume that 0 f d < f p 1 and same reation for probabiity vaue of non-economic payment is being awarded. The information (signa) regarding to each dimension is reaized from F. (x) and G. (). Reca that in this mode the reaization of information regarding to case and eve are independent from each other. The interpretation is that the source of expanation of each signa is different. What we have in our mind is that the case signas are expained based on the medica standards whie judicia standards are used for eve signas. Payers update their beiefs by Bayes rue and compute their expected vaue based on that 9. In this mode payers bargain over the settement vaue. To do that they take into account both case and eve. Based on the statute of imitation, payers have to either decide before itigation or itigate before passing a known periods of time after injury happened. If they do not decide or itigate then the dispute oses its ega face. At the beginning of each period, nature decides who offers in that period. We assume with probabiity φ paintiff gets the chance to offer and with probabiity 1 φ defendant offers. Before observing who is going to offer in a period, paintiff can drop the case 9 In estimation section we expain how they do so. 9

10 and game is over. If paintiff offers then defendant either accepts which the game is over or rejects which they go to next period. Simiar procedure happens if defendant offers. However, before itigation paintiff has option to itigate at the end of each period and they move to the court 10 in next period. At the end of bargaining in the court judge decides about the case. Information structure and beief Given that whether the case is mapractice or not the case information vaues are drawn from F 1 ( ) or F 0 ( ). However, payers have different beiefs by observing the information as expained above. Based on these two different distribution density they construct their expectation of continuation vaue of the dispute. With simiar way of updating payers use new information to update their beief regarding to the probabiity that non-economic payment is being awarded. Judge s decision is based on the provided information from both sides. She decides based on her beief regarding to both case and eve. We divide support of signas into two parts such that if 0 < x t 0.5 then x t = x and if 0.5 < x t < 1 then x t = x h and simiary for y t. This type of information structure says that in each period the vaue of signa coud be ow or high depending on the absoute vaue of it. We denote the history of information with I t = (x t, y t ) where x t = (x 1, x 2,..., x t ) and y t = (y 1, y 2,..., y t ). This information structure in each period is the state space of the mode. That is depending on that in each period how many of signas avaiabe the expectation and continuation vaue are constructed. We can write information structure in each period as I t = (x nx n y + n y h = t 11., x nx h h ; yny, y ny h h ). Note that in each period (t), we have nx + n x h = t and simiary Payments have two components, economic and non-economic parts. Let V = E +N E, these two vaues are known to payers. The probabiity of getting, however, is not the same and differs depending on the initia beieves regarding to case and eve for each payer. Since both sides are not sure about whether case is mapractice or not and non-economic damage is awardabe or not, they use expected vaues to decide in each period. Given information I, et define E(V I) = E x I (E + E y I NE). Both expectation operators are defined over the signa structure expained above. Since the game is perfect information we proceed by soving the probem by subgame perfect equiibrium soution concept. We do it via backward induction. We start by the ast phase and sove the probem backward. 10 We use terms outside of court for before itigation and in the court for after itigation 11 As an exampe of information structure, et t = 2, a possibe signas avaiabe are {2, 0; 2, 0}, {2, 0, 1, 1}, {2, 0; 0, 2}, {1, 1; 2, 0}, {1, 1; 2, 0}, {1, 1; 1, 1}, {1, 1; 0, 2}, {0, 2; 2, 0}, {0, 2; 1, 1}and{0, 2; 0, 2}. 10

11 In the ast period of each phase we have V p T = V d T = 0 and V p T +1 = V d T +1 = βe(v j T I T ) where β is the discount factor. Payers pay cost of each period before entering to that period. In the foowings we divide the probem into two phases based on when they bargain; before or after itigation. 1-In the Court Suppose awsuit happens at period t C {T + 1,..., T 1}. In this situation the vaues of the paintiff s awyer and defendant at the period T + 1, when judge decides, are V p T t c+1 (I T +1) = α( V d T t c+1 (I T +1)) = α(e J (I T )) where the E( ) is the operator which gives the expected vaue by taking into account information of both case and eve for each payers. In the court payers either continue or sette in periods t c < t < T + 1. We argue that if E p t (V p (I t+1 ) C p 2) + αe d t (V d (I t+1 ) C d 2) > 0 then they continue and wait for next period s information otherwise they sette. Suppose not, et s t R + be the settement payment from defendant to paintiff at time t. Suppose paintiff gets chance to offer s t. If s t β[e d t (Vt+1 t d c (I t+1 )) C2] d then defendant accepts the offer. On the other hand, if defendant gets chance to offer she offers αs t β[e p t (Vt+1 t P c (I t+1 )) C2] p and paintiff wi accept it. That is defendant and paintiff wi sette if E p t (V p (I t+1 ) C2) p + αe d t (Vt+1 t d c (I t+1 ) C2) d 0. This condition contradicts with E p t (V p (I t+1 ) C2) p + αe d t (Vt+1 t d c (I t+1 ) C2) d > 0. So they continue under this condition. Hence at the end of period t we have { V p t t c (I t ) = β[e p t (V p (I t+1 ) C2)] p V d t t c (I t ) = β[e d t (V d (I t+1 ) C d 2)] So at the beginning of period t, before nature chooses who is going to offer the continuation vaue of paintiff and defendant are as foows; V p t t c (I t ) = φβ[ α(e d t (V d (I t+1 )) C d 2)] + (1 φ)β[e p t (V p (I t+1 ) C p 2)] V d t t c (I t ) = φβ[e d t (V d (I t+1 )) C d 2] + (1 φ)β[ 1 α (Ep t (V p (I t+1 ) C p 2))] This gives us the payoffs of paintiff and defendant at each period t c < t T as foows; V p t t c (I t ) = φβ max { α(e d t (V d (I t+1 ) C d 2 )), E p t (V p (I t+1 ) C p 2 )}+(1 φ)β[ep t (V p (I t+1 ) C p 2 )] V d t t c (I t ) = φβ[e d t (V d (I t+1 ) C d 2 )]+(1 φ)β max {E d t (V d (I t+1 ) C d 2 ), 1 α (Ep t (V P (I t+1 ) C p 2 ))} The foowing proposition summarizes the above resuts 12 ; 12 Simiar arguments of this and next proposition can be found in Watanabe(2010) as we. 11

12 Proposition 1 Given I t and t c, the unique subgame-perfect equiibrium is; 1. The payoff for the payers at t {t c + 1,..., t c + T } in the court is V p t t c (I t ) = φβ max{ α(e d t (V d (I t+1 ) C d 2 )), E p t (V p (I t+1 ) C p 2 )}+(1 φ)β[ep t (V p (I t+1 ) C p 2 )] V d t t c (I t ) = φβ[e d t (V d (I t+1 ) C d 2 )]+(1 φ)β max{e d t (V d (I t+1 ) C d 2 ), 1 α (Ep t (V P (I t+1 ) C p 2 ))} 2. The payers sette at t {t c + 1,..., t c + T } in the court iff E p t (V p (I t+1 ) C p 2) + αe d t (V d (I t+1 ) C d 2) 0 3. Given payers sette at t {t c + 1,..., t c + T } in the court the payment is s t = { β[e d t (Vt+1 t d c (I t+1 ) C2)] d if paintiff offers 1 α β[ep t (V p (I t+1 ) C2)] p if defendant offers 4. The paintiff s awyer drops the case at the beginning of period t if 2-Outside of the Court V p t t c (I t ) 0. In this situation we expain when they sette and under what condition paintiff itigates. We use simiar arguments ike above. At period T, time of statue of imitation, the continuation vaue of paintiff and defendant are W p T (I T ) = W d T (I T ) = 0. In each period T < t < T, if E p t (W p t+1(i t+1 ) C p 1) < E p t (V P 1 (I t+1 ) C p 2) then paintiff itigates. So his continuation vaue at the end of period t is and R d t (I t ) = R p t (I t ) = β max {E p t (W p t+1(i t+1 ) C p 1), E p t (V P 1 (I t+1 ) C p 2)} { β[e d t (V1 d (I t+1 ) C2)] d if E p t (Wt+1(I p t+1 ) C1) p < E p t (V1 P (I t+1 ) C2) p β[e d t (Wt+1(I d t+1 ) C1)] d if E p t (Wt+1(I p t+1 ) C1) p E p t (V1 P (I t+1 ) C2) p Now we argue that if αr d t (I t ) > R p t (I t ) then they continue and wait for new information. Let denote payment from defendant to the paintiff at period t as s t R +. Suppose not, if paintiff offers s t R d t (I t ) then defendant accepts it and if defendant offers αs t R p t (I t ) paintiff accepts it immediatey. So we have αr d t (I t ) R p t (I t ). That is if αr d t (I t ) > R p t (I t ) then they wait one more period and continue. The continuation vaue at the beginning of period t, before nature chooses the proposer, is W p t (I t ) = φ[ αr d t (I t )] + (1 φ)r p t (I t ) 12

13 W d t (I t ) = φr d t (I t ) + (1 φ)[ 1 α Rp t (I t )] so the payoffs of paintiff and defendant can be written as W p t (I t ) = φ max { αr d t (I t ), R p t (I t )} + (1 φ)βr p t (I t ) W d t (I t ) = φr d t (I t ) + (1 φ) max { 1 α Rp t (I t ), R d t (I t )} The foowing proposition summarizes the stated arguments. Proposition 2 Given I t, the unique subgame-perfect equiibrium has the foowing properties; 1. The payoff for the payers at t {T, T + 1,..., T } outside of the court is W p t (I t ) = φ max { αr d t (I t ), R p t (I t )} + (1 φ)βr p t (I t ) W d t (I t ) = φr d t (I t ) + (1 φ) max { 1 α Rp t (I t ), R d t (I t )} 2. The payers sette at t {T, T + 1,..., T } outside of the court iff αr d t (I t ) R p t (I t ) 3. The paintiff s awyer itigates at t {T, T + 1,..., T } outside of the court iff E p t (W p t+1(i t+1 ) C p 1) < E p t (V P 1 (I t+1 ) C p 2) is 4. Given that payers sette at t {T, T + 1,..., T } outside of the court the payment s t = { R d t (I t ) if paintiff offers 1 α Rp t (I t ) if defendant offers 5.The paintiff s awyer drops the case at the beginning of period t if W p t t c (I t ) 0. 13

14 4 Data The data set we are using is from Forida Office of Insurance Reguation, Medica Professiona Liabiity (MPL) cosed caims. A fied medica mapractice are reported to that office. The data sets contains case ID, date of injury, date of report, type of insurance, name of insured, date of itigation (if any), date of fina decision, stage of settement (i.e. before or after tria), county where injury happened, county where suit happened, severity of injury, accumuated ega costs, noneconomic payment (if any), and noneconomic payment (if any). The data set contains a cosed caim from The important tort aw in these period was cap on non-economic damages which was expained in figure 1. We use data set from since we do not want to take probabe tort reform effects in the mode and this subset of data has been used by other studies previousy. Then it makes easier to compare resuts. It contains 7500 cosed caims. Majority of cases (86%) fied awsuit against defendant. Ony 5% of the a cases are resoved by judge(or jury 13 ). 7.5% of the caims are dropped after seected by paintiff s awyers. 81% of the caims are compensated, 43% of the caims are paid just for noneconomic 14 damages and 26% of them are paid for just economic oss. Ony 13% of payments incude both economic and non-economic payments. Tabe 1 shows some of the variabes in the data set which are in our interest. We present them taking into account whether awsuit happened or not. The vaues in the parenthesis are standard deviation. 15 Drop ratio is much ower if awsuit happens. 25% of the caims which did not fie awsuit dropped the case whie this ratio is 4.6% among cases which fied awsuit. 54% of cases are paid for noneconomic damage. 37% of cases are paid for economic oss. Ony 14% of cases are paid for both of them. The figures in appendix (Sec.9.5) depicts distribution of paid economic, noneconomic, and tota payments.the time distributions of cases which resoved before and after tria are aso depicted in figure 3 and Figure 4. The important point of these figures is that cases which fie awsuit tends to spend more time in the itigation system. 13 In the data set we just observe that case is resoved in the court. We do not observe whether it was by jury or judge. 14 In the data set there is no separation between economic and non-economic payments. Since we have tota payment and aso non-economic payments, we just get economic payments by subtracting non-economic payments from tota payments. 15 We drop cases with payments higher than Those are just 2% of the observation. 14

15 Variabe Without Lawsuit With Lawsuit Tota Tota Payments (341.7) (516.7) (494.0) Non-economic Payments (190.8) (346.7) (327.5) Economic Payments 80.2C (282.6) (372.8) (360.1) Cost (28.4) (101.8) (95.1) Report Time (1.6) (1.6) (1.57) Litigation Time (1.67) (1.54) Settement Time (2.6) (4.3) (4.3) Tabe 1: Summary statistics. ( ) 10 3 $, and ( ) 6 Months is the unit of a time period. Figure 3: Time distribution of events for cases which resoved before itigation. 15

16 Figure 4: Time distribution of events for cases which resoved after itigation. 5 Estimation and Identification 5.1 Estimation The estimation method which we use originay was deveoped by Watanabe(2009). We take some observed decisions in data and use proposition 1 and 2 conditions for different decisions to buid the ikeihood contribution of each observation 16. Before going to introducing ikeihood contribution we expain the underying assumptions regarding to different distribution used in the mode. One of the crucia part of the estimation is that we consider unobserved heterogeneity in some of the parameters. The strategies for identification come afterward. We denote the portion of patients with injury who are decined by patients awyer by π 0. That is among the patients with injury(either mapractice or not) and who are ooking for awyer ony 1 π 0 portion of them are accepted by awyer 17. Note that vaue of π 0 captures decined portion of cases among who are ooking for awyer. As it is a fact in this iterature around 10% of patients with medica mapractice ook for awyer. So with imperfect screening of the cases, there are both meritorious and frivoous caims. We use π 0 = 85%. So we do not estimate this parameter in the mode. Difference in the priors of paintiff and defendant come from different attachment of initia probabiity that the injury is the resut of mapractice. We denote the probabiity distribution of initia beief of payers with F Be ( d AC = 1) Beta(α Be, β Be ). We assume that the distributions that payers draw initia beiefs are symmetric. That is α p Be = βd Be and βp Be = αd Be. This 16 The steps which we perform for estimation is expained in detai in the appendix. 17 We do not observe this information from the data set which we are using. We use this information from other studies from state of Wisconsin and Texas with the assumption that the average behavior of awyers are not different in different state. 16

17 wi save us two parameters. As it is important in our mode the difference of the initia beief is important to have deay in the bargaining game. This symmetric distribution assumption aso do another favor to us as the initia beief of paintiff is higher than defendant. That is paintiff is more certain that the case is mapractice than defendant. Payers aso draw a prior regarding to the probabiity that court wi award noneconomic payment. We assume that probabiity distribution of the initia beief of payers foows as G Be ( d AC = 1) Beta(α GBe, β GBe ). Simiar assumption regarding to the symmetry of beiefs are imposed for these case as we. The judge prior regarding to both of these draws are assumed to have a uniform distribution with support of f j 0 [f 0 d, f p 0 ] and gj 0 [gd 0, gp 0 ], respectivey. We denote the distribution of economic and non-economic damage by F E ( ) Lognorm(µ E, σe 2 ) and F NE ( ) Lognorm(µ NE, σne 2 ), respectivey. In each period payers receive new information (signa) regarding to strength of the case and ikeihood of whether non-economic payment is being awarded. We argue that the interpretation of different signas are different depending on how concusive they are. In other words, upon receiving new signa, interpretation about the ikeihood of the case being mapractice depends on how distinctive are the medica service procedures. If the procedures of performing a medica service are we defined it is expected to have more informative signas than when the procedures or standards are vague. The beow picture iustrates this idea. It shows two different signa generating distributions which signas of outer distribution (with parameter c) is more concusive than the inner one (with parameter d) 18. Figure 5: Distribution of case (eve) signas with different parameters. Having the above idea in mind we try to capture that in a concise and parsimonious way. We assume that case signas are drawn (depending on whether the case is mapractice or not) from 18 Note that for each parameter two distributions are symmetric. 17

18 F 0 ( not Mapractice) T rianguar(0, 1, γ H ) where 0 < γ H 1 2 and F 1( Mapractice) T rianguar(0, 1, 1 γ H ). We simiary argue that judicia standards or procedures of courts coud be concusive or vague. We proceed by assuming simiar probabiity distribution of signas about the ikeihood of noneconomic payment is being awarded. We assume that eve signas are drawn from G 0 ( not Awardabe) T rianguar(0, 1, γ J ) where 0 < γ J 1 2 and G 1( Awardabe) T rianguar(0, 1, 1 γ J ). Both of γ M and γ J show how concusive are the medica and judicia standards, respectivey. The coser to 0.5 the more vague are the procedures. Statute of imitation is 2 years in state of Forida. However, in the data set we observe cases which are reported after 2 years of when injury occurred. We use T = 7 which is 3.5 years given that our unit of time is six month in this study. Under this assumption we can use more than 95% of the cases in the data set since the reporting time of them is ess than 7. Different cases not ony have different payment schedues but they aso have different time schedues. We denote the probabiity distribution of period in which judge decide about the dispute with F T. We assume it foows negative binomia distribution. F T ( ) Negbino(ς 0T, ς 1T ). We do not estimated the parameters of F T in the mode, we just use the distribution of time period of cases which are resoved by judge. Per period cost of payers are drawn independenty from F c i ( ) and F 1 c i ( ), outside and in the 2 court where i {p, d}. In a competitive market there shoud not be any difference between wage of defendant and paintiff. That is per period cost of operation for both paintiff and defendant s awyers are drawn from same distribution function.we assume that F C ( ) (µ c, σc 2 ). The other fact in the itigation system is that cost of operation after itigation is higher than before that. We take into account this fact by assuming that C i 2 = (1 + η)ci 1 where η foows og-norma distribution with µ η and σ 2 η. The in the court cost not ony is higher for each case but aso the ratio is not fixed. That is why η is not fix. This gives us a heterogeneity of cost among different cases. 5.2 Identification In this section we expain how we identify parameters given the assumptions regarding to the probabiity distributions. We use raw data to estimate distribution function of T, F T ( ). This essentiay means that there is no systematic difference between T of cases which are decided by judge and ones which resoved before being decided by judge. Distribution function of noneconomic payment is identified by noneconomic payment same as economic payment. We use the tota payment to identify φ. Since we know the vaue offered by either side from proposition 1 and 2 the amount of the settement in the observed data can 18

19 be used to identify the φ parameter. Given that both awyers work in a competitive market, we assume that their per period cost shoud not differ systematicay. So we use same cost distribution functions with different draws for paintiff and defendant s awyers outside and inside of court in each period. We do not observe the cost of paintiff s awyer, however, this assumption heps us to draw per period cost for paintiff s awyer from same distribution as defendant. The observed tota cost of defendant in the data set is used to identify cost parameters. There is conceptua difference between beief of payers and judge regarding to whether case is mapractice or not and beief of payers regarding to ikeihood of non-economic payment being awarded. In the former a agents assign initia beief to the strength of case and update their beief using standards of medica services (namey via F 0 ( ), F 1 ( )). For the ater, however, payers initia beief and their updating depend on judicia standards (namey via G 0 ( ), G 1 ( )). We use ratio of paid non-economic payment in the raw data to estimate the beief of judge. For estimating the vagueness of judicia standards or procedures we appy same strategy as for medica service standards. Other parameters of the mode can be jointy identified with timing of acceptance, itigation, dropping, and settement before and after tria. That is we have enough variation in the data which can hep us to identify those parameters. We use α = 0.33 as previous studies (Soan (1993), Seig(2000), Watanabe(2009,2010)) for ratio of contingency fee and β = 0.98 for time discount factor. The parameters we estimate can be summarized in Θ = {µ c, σ 2 c, µ η, σ 2 η, µ E, σ 2 E, µ NE, σ 2 NE, α Be, β Be, α GBe, β GBe, γ H, γ J, φ}. Unobserved Heterogeneity We assume unobserved heterogeneity among different cases in different dimensions. We can summarize the distributions of parameters with unobserved heterogeneity as ψ = {F c, F η, F E, F NE, F T, F Be, F GBe }. Based on stated assumptions we wi estimate the ikeihood contribution of each observation as foows; L(Θ T, r, v, t s, s, t C, f) =... P r(t, r, v, t s, s, t C, f ψ; θ)df c df η df T df E df NE df Be df GBe We use Monte Caro simuation to integrate out these integras and use the simuated ikeihood contribution of each observation to find the parameters which maximize the observed patterns in the data. 19

20 6 Resuts The estimated parameters are presented in Tabe 2. Since in the data set which we are using it is not specified whether the case is mapractice or not we use the resut of paper by Studdert, et a (2006). We use the portion of medica mapractice from that study. That is to find the simuated ikeihood contribution of each observation we assume each case is medica mapractice with probabiity of 0.63% 19. Parameter Vaue(S.E.) Parameter Vaue(S.E.) µ c (0.581) γ H (0.005) σ c (0.024) γ J (0.008) µ η (0.019) α GBe (0.046) σ η (0.083) β GBe (0.005) µ E (0.294) α Be (0.027) σ E (0.016) β Be (0.004) µ NE (0.085) φ (0.007) σ NE (0.003) Tabe 2: Estimated parameters and standard errors. We aso use the resut of other studies(kritzer(1997), Greenberg and Garber (2009)) for portion of cases which are decined by the paintiff s awyers. This assumption indicates that we approximatey 15% of injured patients get their case represented by a awyer. The foowing figures show the mode fit. The eft(bue) figure is the data and the right(red) is the resut of the mode. Figure 6: Distribution of the positive tota payments, Data(eft) and Mode(right). 19 This is the ratio of cases with negigent error in Studdert, et. a.(2006). 20

21 Figure 7: Distribution of the positive economics payments, Data(eft) and Mode(right). Figure 8: Distribution of tota costs, Data(eft) and Mode(right). Mode is capturing the pattern of the payments and costs. Despite that high vaues are not fitted we enough but the most important range of vaues are fitted quite good. The other part of the data which are used for identification of the distribution of signas and beiefs are patterns of timing. The foowing figures depict the mode fit for time patterns of acceptance, itigation, and settement. Figure 9: Distribution of acceptance time, Data(eft) and Mode(right). 21

22 Figure 10: Distribution of itigation time, Data(eft) and Mode(right). 7 Poicy Experiment In this section we expain the effects of two different tort reforms. Cap on non-economic payments is the tort reform which most states (incuding state of Forida) have chosen in different years with different amounts as cap. The other tort reform which was intended to change the incentive of paintiff s awyer not to accept frivoous cases is reducing contingency fees. To find two types of errors in the basic mode, we randomy draw some observation from data set and assume that a of them are meritorious cases. Next we cacuate the probabiity of settement by simuating the mode with estimated parameters. Then we compute the probabiity of rejection of case which is medica mapractice. We proceed with simiar approach to find probabiity of accepting a case which is not medica mapractice. In the basic mode the estimated error α 0 = 0.36 and β 0 = These two estimated errors are not far from Studdert, Et. a.(2006) study. There is no other criterion which coud be used to see how good is the fit of the mode. However, the point of this paper is about effect of tort reform on these errors. In the foowing we expain how we perform counterfactua poicies. 7.1 Cap on Non-economic Payments Cap on non-economic payments is one of the more debated tort reform in medica mapractice. To see the effect of this poicy we fix the maximum achievabe non-economic vaue as $250, 000. After that we do exact same procedure as above to find the errors. The estimated error indicates that cap on non-economic payments increases type I error 62% and it aso increases type II error 39%. Given our definition of the effect of a tort reform, cap on non-economic payments is worsening performance of itigation system. The intuition for this resut is that putting cap on non-economic payment woud make cases with no merit a good substitute of meritorious cases. 22

23 The empirica finding of this iterature indicates that average payments to cases with no merit are ess than meritorious cases. This anaysis shows that cap on non-economic payments hurts more cases with medica mapractice. 7.2 Reducing Contingency Fee To perform this counterfactua poicy we change basic mode such that contingency fee α = 0.33 α = 0.2. That is we decrease share of awyer from the tota payments(if any). We proceed exact procedure to find errors in this case. The simuated errors indicate that reducing contingency fee increases type I error 15% and decreasing type II error 69%. One of the expanation of this resut is that reducing contingency fee reduces the payment to the awyer even if the case is mapractice so it potentiay increases type I error. Decrease in type II error comes from the fact that cases with no merit are ess vauabe and reducing awyer s share of tota vaue woud make bargaining more costy and that woud increase bargaining position of defendant not to sette. By the measure which we defined this tort reform enhance the performance of itigation system. This anaysis is not concusive regarding to the question that which contingency rate is optima. This resut just says that reducing the contingency fee enhance the defined performance measure. 8 Concusion The aim of any tort reforms reated to medica mapractice shoud be enhancing the performance of the itigation system. In the iterature the main focus was to ook at the effect of different tort reforms on the cost of and payments in the itigation system. One of the important factor which we investigate in this paper is the effect of tort reforms on the performance of itigation system. One of the important area which needs to be studied more cosey is the effect of different tort reform on the accessabiity of itigation system to whom have meritorious case. One of the probem in this regard is the avaiabiity of a unified data set. There is no data set which tracks injured patients and ooks whether they caim their case or not. The most important probem, however, is whether the case is mapractice or not. Since any payers in the itigation system can make mistake, the resut of any resoution coud potentiay be miseading to decide whether the case was mapractice or not. The importance of buiding mode and simuating such scenarios is that we can ook at the effect of hypothetica tort reforms on the performance of the system. Since we do not have a unified data set about tracking a patients, this paper suffers from ack of some part of data set. We borrowed different vaues from other studies in the iterature and used them as far as our 23

24 mode suggested. Since some of those numbers are from different states and different situation one shoud be carefu about interpretation of the resuts of our mode. 9 Appendices 9.1 Computation of Conditiona Choice Probabiity 20 We expained the rationae of how a awyer chooses a case and aso the bargaining between paintiff s awyer and defendant. Since a choices in the mode depend on the information state (i.e. I t = (x t, y t )), so it is a critica component of decisions. Unfortunatey, this part is not observabe for us as econometricians. We need to compute conditiona choice probabiity of any observabe decisions. Since both case and eve have continues support, we spit each of them into two equa bin s as it was expained in the text. Hence I t = (x nx that x is reaized n x times by period t. d DO t Let d AC t, x nx h h ; yny, y ny h h ) shows (I t ) denote the decision of accepting (d AC t (I t ) = 1) the case by patient s awyer, (I t, T ) decision of dropping (d DO t (I t, T ) = 1) the case outside of the court given that the case is accepted by the paintiff s awyer at period T, d SO t (I t, T ) decision of settement (d SO t (I t, T ) = 1) outside of the court given period of representing the case T, d F t I (I t, T ) decision of fiing awsuit (d F I t (I t, T ) = 1) given the period of representing the case, T,d DC t (I t, t c, T ) decision of dropping in the court(d DC t (I t, t c, T ) = 1) given t c and T and d SC t (I t, t c, T ) decision of settement in the court(d SC t (I t, t c, T ) = 1) given t c and T. We derived the condition for each of above expained indicators in proposition 1 and 2. So we can write d AC t (I t ) = I{E p t (W p 1 (I t+1) C p 1 ) 0} d DO t (I t, T ) = I{ W p t (I t) < 0} d SO t (I t, T ) = I{R p t (I t) + αrt d (I t ) 0} d F t I (I t, T ) = I{E p t (W p t+1 (I t+1) C p 1 ) < Ep t (V p 1 (I t+1) C p 2 )} d DC t (I t, t L, T ) = I{ V p t t c (I t ) < 0} d SL t (I t, t L, T ) = I{E p t (V p (I t+1 ) C p 2 ) + αed t (Vt+1 t d c (I t+2 ) C2 d) 0} Denote zt P S (x nx, x nx h h ; yny, y ny h h ) as the probabiity of being in state I t = (x nx, x nx h h ; yny h, T ) ) out- period t before the case has been seected by the paintiff s awyer. Denote aso zt O (x nx and zt C (x nx, x nx h h ; yn, y ny h h, t c, T ) as the probabiity of being in state I t = (x nx, x nx h h ; yny side the court and in the court, given T and t c, respectivey. We can drive probabiity of reaching to any feasibe state foowing beow procedure; z P S 0 (x 0, y 0 ) = 1 20 The estimation method deveoped here foows cosey Watanabe(2010), y ny h h ) at, x nx h h ; yny 1, yny h, y ny h h 24

25 zt P S (x nx, x nx h h ; yny, y ny h h ) = 2 2 k=1 i=1 f(x k)g(y i )zt 1 P S (xn k 1 k, x k ; y n i 1 i, ȳ i ) 21 So we can write the initia condition of zt O (, ) as zt O(x T, y T ) = zt P S(x T, y T ) and the probabiity of being in specific state given the patient is represented by awyer at time T z O t (x nx [1 d DO t, x nx h h ; yny 1, yny h h, T ) = 2 k=1 2 i=1 (x n k 1 k ( f(x k )g(y i )z O t 1 (xn k 1 k, x k ; y n i 1 i, ȳ i, T ), x k ; y n i 1 i, ȳ i ) d SO t, x k ; y n i 1 i, ȳ i )] [1 d F t I i, ȳ i )] Simiary, we can drive initia condition (zt O c (x tc, y tc ) = zt C c (x tc, y tc )) and probabiity of being (x n k 1 k (x n k 1 k, x k ; y n i 1 in any specific state in the court. So we have zt C (x nx, x nx h h ; yn, y ny h h, t c, T ) = 2 ( 2 k=1 i=1 f(x k )g(y i )zt 1 C (xn k 1 k, x k ; y n i 1 i, ȳ i, t c, T ) ) [1 d DC t (x n k 1 k, x k ; y n i 1 i, ȳ i ) d SC t (x n k 1 k, x k ; y n i 1 i, ȳ i )] Now we expain the situations that can happen. Let r={accept, Reject} which r=accept means that patient can find a awyer to represent his/her case and r=reject means otherwise. Let f={fie, NoFie} denote that case is itigated {f=fie} or not {f=nofie}. ) Denote aso s={drop, Sette, Judge} such that the case is resoved either by drop {s=drop}, sette {Sette}, or Judge {s=judge}. 1) If a case is rejected then we do not see any other decisions regarding to that case. But if a case is accepted by a awyer to be represented then five different situations which are mutua excusive can happen. 2) (f,s)={fie, Drop} which means that dispute is itigated and it is dropped in the court. 3) (f,s)={fie,sette} which means that the dispute is itigated and setted in the court. 4) (f,s)={fie, Judge} which means that the dispute is itigated and finay decided by judge (or jury). 5) (f,s)={nofie,drop} which means that the case is dropped outside of the court. 6) (f,s)={nofie, Sette} which means that the case is setted outside of the court. Before going to describe the conditiona probabiity that any observabe event occurs, we introduce some other notations. Let N x (t) be the coection of a possibe combination of case signas in period t. And simiary, et N (t) with same feature for eve signas. Having these notations expained, we describe conditiona probabiity of seeing any specific events. The probabiity that we see a awyer accepts (reports) the case P r(accept, T ) = N x(t ) N y(t ) zt P S (N x, N y )d AC T (N x, N y ) 22 in words the expression says that the probabiity of case being accepted is equa to summing over the probabiity of dispute reaches specific state (zt P S(N x, N y )) mutipied by the decision indicator function in that state d AC T (N x, N y ). The probabiity that we see a case is itigated 21 x k indicates a x s except x k remain fix and same as for ȳ i. 22 The term zt P S(N x, N y ) essentiay contains a possibe combination of N x case signas and N y eve signas. 25

26 given the period of acceptance (report),t, can be written as P r(f ie, t c T, Accept) = N x(t c) N y(t c) z O t L (N x, N y, T )d F I t c (N x, N y, T ) Dropping, settement, and decision by judge in the court happens if a case is seected and aso itigated. So we can write the probabiity of seeing a dispute dropped and setted in the court at period t s as P r(t s, Drop T, t c, Accept, F ie) = P r(t s, Sette T, t c, Accept, F ie) = N x(t s) N y(t s) N x(t s) N y(t s) z C t s (N x, N y, T, t c )d DC t s (N x, N y, T, t c ) zt C s (N x, N y, T, t c )[1 d DC t s (N x, N y, T, t c )][d SC t s (N x, N y, T, t c )] If dispute is not resoved in the court by two paintiff s awyer and defendant then it is decided by the judge. The probabiity that we see such an event can be represented as P r(judge T, t c, Accept, F ie) = N x(t ) N y(t ) zt C (N x, N y, T, t c )[1 d DC T (N x, N y, T, t c ) d SC T (N x, N y, T, t c )] For some disputes which are dropped or setted outside of the court, we can write the probabiity of reaching these events at period t s as P r(t s, Drop T, Accept, NoF ie) = N x(t s) N y(t s) z O t s (N x, N y, T )d DO t s (N x, N y, T ) P r(t s, Sette T, Accept, NoF ie) = N x(t s) N y(t s) zt O s (N x, N y, T )[1 d DO t s (N x, N y, T )]d SO t s (N x, N y, T ) the interpretation of the components of these probabiities is the same as previous ones. To compute the probabiity of observing specific amount of payment and cost we divide the support of payment and cost distributions into bins of v k and C k, respectivey. By proposition 1 and 2, we know that the amount of settement is different depending on who is offering. To capture this idea we use indicator functions d p and d d as foow; d p (I t, v k, T, t s, t c, F ie) = I{ β[e d t (V d t s t c+1 (I t+1) C d 2 )] = v v k} d d (I t, v k, T, t s, t c, F ie) = I{ 1 α β[ep t (V p t s t c+1 (I t+1) C p 2 )] = v v k} d p (I t, v k, T, t s, NoF ie) = I{ R d t (I t ) = v v k } d d (I t, v k, T, t s, NoF ie) = I{R p t (I t) = v v k } Since at the beginning of each period, nature chooses paintiff s awyer with probabiity φ to offer and defendant with probabiity 1 φ then the probabiity of seeing a specific amount of payment v 23 in the court can be written as 23 Since we differentiate between economic and non-economic costs, this payment essentiay contains both of them. 26

27 P r(v v k T, t s, Sette, t c, F ie) = φzt C s (N x, N y, T, t C )d p (N x, N y, v k, T, t s, t C, F ie) N x(t s) N y(t s) + (1 φ)zt C s (N x, N y, T, t c )d d (N x, N y, v k, T, t s, t c, F ie) N x(t s) N y(t s) We can use simiar procedure to find the probabiity that payment is in bin v k and happens outside of court. That is P r(v v k T, t s, Sette, NoF ie) = + N x(t s) N y(t s) N x(t s) N y(t s) φz O t s (N x, N y, T )d p (N x, N y, v k, T, t s, NoF ie) (1 φ)z O t s (N x, N y, T )d d (N x, N y, v k, T, t s, NoF ie) If the payment is decided by judge then the beief and expectation of judge pay roe. The probabiity of observing payment in bin v k decided by judge is P r(v v k T, t s, Judge, t c, F ie) = P r( N x(t ) N y(t ) zt C (N x, N y, T, t c )E J (V ) = v v k ) When a dispute is dropped there is no payment. This is equivaent to say that P r(v = 0 T, t s, Drop, t c, F ie) = 1 P r(v = 0 T, t s, Drop, NoF ie) = 1 We can foow same procedure to find the probabiity of observing defense cost, C, to fa in bin C k. For disputes which are setted after itigation, the probabiity of observing cost of defense fas in bin C k at period t s is P r(c C k T, t s, Sette, t c, F ie) = for disputes without itigation we can write { 1, if C = t=tc t=t r C1 d(t) + t=t s t=t c+1 Cd 2 (t) C k 0, if C = t=t c t=t r C1 d(t) + t=t s t=t c+1 Cd 2 (t) C k as P r(c C k T, t s, Sette, NoF ie) = { 1, if C = t=ts t=t r C d 1 (t) C k 0, if C = t=t s t=t r C d 1 (t) C k we can aso compute the probabiity of observing cost of disputes which are resoved by judge P r(c C k T, t s, Judge, t c, F ie) = { 1, if C = t=tc t=t r C1 d(t) + t=t s t=t c C2 d(t) C k 0, if C = t=t c t=t r C1 d(t) + t=t s t=t c C2 d(t) C k We can use simiar procedure to compute the probabiity of observing specific amount of defense cost for disputes which are dropped. For disputes which are dropped in the court we have 27

28 P r(c C k T, t s, Drop, t c, F ie) = and for disputes which are dropped outside of the court { 1, if C = t=tc t=t r C1 d(t) + t=t s t=t c C2 d(t) C k 0, if t=t c t=t r C1 d(t) + t=t s t=t c C2 d(t) C k P r(c C k T, t s, Drop, NoF ie) = 9.2 Likeihood Function { 1, if C = t=ts t=t r C d 1 (t) C k 0, if C = t=t s t=t r C d 1 (t) C k We summarize the distributions of parameters with unobserved heterogeneity as ψ = {F c, F η, F E, F NE, F T, F Be, F GBe }. The ikeihood contribution function of each observation is as foows L(Θ T, r, v, t s, s, t C, f) =... P r(t, r, v, t s, s, t C, f ψ; θ)df c df η df T df E df NE df Be df GBe We use Monte Caro integration to integrate out the unobserved heterogeneity based on the assumed distributions. We can compute P r(t, r, v, t s, s, t C, f ψ; Θ) as foow 1) For cases which are rejected by paintiff s awyer; P r(t, r, v, t s, s, t c, f ψ; Θ) = P r(reject ψ; Θ) 2) For disputes which are accepted by paintiff s and dropped without itigation; P r(t, c, v, t s, s, t c, f ψ; Θ) = {P r(accept, T ψ, Θ)} {P r(t s, Drop T, ψ, Θ)} {P r(v v k T, t s, Drop, ψ, Θ)} {P r(c C k T, t s, Drop, ψ, Θ)} 3) For disputes which are setted without itigation we have; P r(t, c, v, t s, s, t c, f ψ; Θ) = {P r(accept, T ψ, Θ)} {P r(t s, sette T, ψ, Θ)} {P r(v v k T, t s, Sette, ψ, Θ)} {P r(c C k T, t s, Sette, ψ, Θ)} 4) For disputes which are dropped after itigation; P r(t, c, v, t s, s, t c, f ψ; Θ) = {P r(accept, T ψ, Θ)} {P r(f ie, t c T, ψ, Θ)} {P r(drop, ts T, t c, F ie, ψ, Θ)} {P r(v v k T, t s, Drop, t L, F ie, ψ, Θ)} {P r(c C k T, t s, Drop, t L, F ie, ψ, Θ)} 5) For disputes which are setted after itigation we have; P r(t, c, v, t s, s, t c, f ψ; Θ) = {P r(accept, T ψ, Θ)} {P r(f ie, t c T, ψ, Θ)} {P r(sette, t s T, t c, F ie, ψ, Θ)} {P r(v v k T, t s, 28

29 Sette, t L, F ie, ψ, Θ)} {P r(c C k T, t s, Sette, t L, F ie, ψ, Θ)} 6) For disputes which are resoved by the Judge; P r(t, c, v, t s, s, t c, f ψ; Θ) = {P r(accept, T ψ, Θ)} {P r(f ie, t c T, ψ, Θ)} {P r(judge, t s T, t c, F ie, ψ, Θ)} {P r(v v k T, t s, Judge, t L, F ie, ψ, Θ)} {P r(c C k T, t s, Judge, t L, F ie, ψ, Θ)} 9.3 Steps of Estimation 1- Fix θ Θ, 2- Draw from specified distributions in ψ, 3- Cacuate expected vaue at time T and T, 4- Cacuate other periods vaues backward, having forward vaues using proposition 1 and 2 5- Check conditions of {Accepting, Dropping, Litigating, Setting, Judging }, given the vaues in each periods, 6- Cacuate the probabiity of being in different states given the conditions, 7- Cacuate ikeihood contribution of an observation, 8- Repeat steps 5-7 for other observations, 9- Sum over a ikeihood contributions, 10- Repeat steps 2-9, 11- Divide the ikeihood vaue over number of observations and number of draws for monte caro integration, 10- Change θ and repeat steps 2-11, 11- Choose θ such that maximize ikeihood. 9.4 Computing Empirica Posterior Probabiities To compute posterior probabiity of case being mapractice, f i, i {p, d, j}. We use a simpe Bayesian updating. Given that a case signas are reaized based on whether the case is mapractice or not via f 0 ( ) = P r( Not Mapractice) and f 1 ( ) = P r( Mapractice), the posterior probabiity of case being mapractice given observed signas (x nx f(x nx, x nx h h ) = f 0 2 k=1 [f 1(x k )] nx k f 0 2 k=1 [f 1(x k )] nx k + (1 f 0 ) 2 k=1 [f 0(x k )] nx k, x nx h h ) is where f 0 is the initia beief of case being mapractice. Given the structure of information we have, for exampe, f(x ) = f 0 (v)dv as the probabiity that the strength of signa is ow if the case is not-mapractice. Ceary the posterior probabiity of case being mapractice among payers are different depending on the initia beief of case being mapractice. 29

30 We use same procedure to compute the posterior probabiity of noneconomic payment awarded. Let g i (y k ), i {0, 1} be the probabiity of observing signa y k depending on whether non-economic payment is going to be awarded, 1, or not,0. eve signas is (y ny can be computed by g(y ny And aso suppose the observed, y ny h h ). So the posterior probabiity of noneconomic payment is awarded, y ny h h ) = g 2 0 k=1 [g 1(y k )] n y k g 2 0 k=1 [g 1(y k )] ny k + (1 g 0 ) 2 k=1 [g 0(y k )] ny k where g 0 is the initia beief of non-economic payment is awardabe. Note that different payers use their initia beief to update the new information. Now we can expain the meaning of E( ) by using above notations. is computed by taking into account both case and eve information. I t = (x nx, x nx h h ; yny The eve of expected payment So given state of, y ny h h ) at period t the expected payment of the dispute can be expressed as E(v(I t )) = f(x nx, x nx h h ) [E + g(yny, y ny h h ) NE] Different payers have different expectation based on their updated posteriors. 9.5 Figures Figure 11: Distribution of economic payment. 30

31 Figure 12: Distribution of noneconomic payment. Figure 13: Distribution of tota payment. 31

32 10 References 1-Baker, T., 2005; Medica Mapractice and the Insurance Underwriting Cyce, Working Paper. 2-Danie, S.; Martin, J., 2006; Paintiffs Lawyers, Speciaization, and Medica Mapractice, Vanderbit Law Review. 3-Greenberg, M.; Garber, S., 2009; Patterns of Speciaization in Medica Mapractice Among Contingency Fee Attorneys, RAND working paper. 4-Hyman, D.; Siver, C., 2006; Medica Mapractice Litigation and Tort Reform: It s the Incentives, Stupid, Vanderbit Law Review. 5-Kritzer, H., 1997; Hoding Back the Foodtide: The Roe of Contingent Fee Lawyers, Wisconsin Lawyer. 6-Pheps, C., 2010; Heath Economics, Addison-Wesey pubication. 7- Sieg, H., 2000; Estimating a Bargaining Mode with Asymmetric Informa-tion: Evidence from Medica Mapractice Disputes, Journa of Poitica Economy. 8-Studdert, D.; et. a., 2006; Caims, Errors, and Compensation Payments in Medica Mapractice Litigation, The New Engand Journa of Medicine. 9-Studdert, D.; et. a., 2000; Negigent Care and Mapractice Caiming Behavior in Utah and Coorado, Medica Care. 10-Viscusi, W.; Born, P., 1995; Medica Mapractice Insurance in the Wake of Liabiity Reform, The Journa of Lega Studies. 11-Watanabe, Y., 2009; Learning and Bargaining in Dispute Resoution: Theory and Evidence from Medica Mapractice Litigation, Working Paper. 12-Watanabe, Y., 2010; Estimating the Degree of Experts Agency Probem: The Case of Medica Mapractice Lawyers, Working Paper. 13-Woodridge, J., 2002; Econometric Anaysis of Cross Section and Pane Data, The MIT Press. 14-Yidiz, M., 2003; Bargaining Without a Common Prior - An Immediate Agreement Theorem, Econometrica. 15-Yidiz, M., 2004; Waiting to Persuade, Quartery Journa of Economics. 32