Estimating the Degree of Expert s Agency Problem: The Case of Medical Malpractice Lawyers


 Arleen Russell
 1 years ago
 Views:
Transcription
1 Estimating the Degree of Exert s Agency Problem: The Case of Medical Malractice Lawyers Yasutora Watanabe Northwestern University March 2007 Very Preliminary and Incomlete  Comments Welcome! Abstract I emirically study the exert s agency roblem in the context of lawyers and their clients. Incentives of lawyers and clients are misaligned in disute resolution under contingency fee arrangement with which lawyers receive a fraction of recovered ayment as comensation while bearing the legal cost. Lawyers refer to ursue a case less than their clients refer as they incur all the legal costs and receive smaller fraction of ayment. In this aer, I measure the degree to which lawyers work in the interest of their clients. To do so, I construct a bargaining model of disute resolution that nests two secial cases as well as their convex combinations in which lawyers work in their clients best interests and in which they work in their own interests, and estimate the model using data of medical malractice disutes. The timing of droed cases identi es the nesting arameter because cases are droed more frequently and at earlier timings if lawyers work in their own interests. I nd that lawyers work almost erfectly in their own interest. Then, I comute the cost of agency roblem resulting from misaligned incentives by simulating the rstbest outcome using the estimated model. Finally, I evaluate the imact of tort reform on contingency fee, and show that limitation of contingency fee lower the joint surlus further. Deartment of Management and Strategy, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL
2 1 Introduction Exert agents can mislead their clients in their own interests due to lack of exertise on the side of their clients. Exerts such as lawyers, hysicians, auto reairers, and real estate agents are better informed of the services they rovide than their clients. Due to this asymmetry of information, clients make decision based on advices of exerts or even delegate their decision to the exerts, and clients may not know or nd it very costly to verify if the exerts worked in their best interests. As a result, exerts have incentive to work in their own interests instead of their clients interests. On the other hand, factors such as reutational concern, rofessional liability, caacity constraint, and/or rofessional ethics mitigates the exerts agency roblem to some extent. For examle, a dentist may suggest an exensive orcelain lling instead of a quick comosite resin lling to treat a simle dental cavity, but she may refrain from doing so because of reutational concern or due to caacity constraints (lack of time for another aointment to lace orcelain lling). The degree to which exerts work in the interest of their clients deends on relative strength of these factors and is an oen emirical question. Existing studies either con rms the existence of the exerts agency roblem or countering e ects of the mitigating factor, but have not measured the relative strength. In this aer I estimate the degree to which exerts work in their client s interest. Seci cally, I consider the exerts agency roblem for the case of lawyers and their clients in resolution of medical malractice disutes. A lainti in medical malractice disute signs contingency fee contract with a lawyer. The incentives of the lawyer and the client are misaligned in disute resolution under contingency fee arrangement with which the lawyer receives a fraction of recovered ayment as comensation while bearing all the costs of legal services. Since the client incur no cost of the lawyer s services, the lawyer refer to settle the case earlier than the client refers, and the lawyer has stronger incentive to dro a case. 1 Using data on timing of settlements and droing, I answer the rimary question of this aer: What is the degree to which a lawyer work in the interest of a client? Contingency fee is also an imortant olicy issue in tort reform discussion, esecially on medical malractice. Regulation on contingency fees are adoted by 15 states as of and are currently under consideration at the federal level. 3 In site of its olicy imortance, 1 In this aer, "dro" means that the side of the lainti stos ursuing the case, which includes voluntary dismissal, settlement with zero ayment without ling of a lawsuit, and settlement with zero ayment after ling of a lawsuit.. 2 See the database of state tort law reforms constructed by Avraham (2006). These regulations tyically imose a limit on the fraction lawyers can receive as contingency fee such as 40% and 33%. 3 The House of Reresentatives assed the Hel E cient, Accessible, LowCost, Timely Healthcare (HEALTH) Act of 2003 in the 108th Congress, while the Senate voted against it. The bill has been reintroduced in 2004 and 2005 and is currently ending. The Medical Care Access Protection Act of 2006 stalled in the Senate also includes regulation on contingency fee for lainti s attorneys on medical malractice 2
3 little is known emirically about how regulation on contingency fee a ects the outcomes of medical malractice disutes such as legal costs, settlement ayments, and robability of lawsuits, as well as how it a ects the agency roblem of lawyers and their clients. This is another question I ask in this aer. In order to answer these questions, I construct a bargaining model of disute resolution that nests two secial cases as well as their convex combinations; one in which lawyers work in the best interests of their clients, and one in which lawyers work for their own interests. I estimate the model using a unique microlevel data on medical malractice disutes. The nesting arameter measures the degree to which incentives are misalignement. Using the estimated model, I simulate the rstbest outcome and measure the cost of agency roblem resulting from the misaligned incentive. Finally, I conduct a counterfactual olicy exeriment of limiting contingency fees and assess the imact of the olicy on outcomes and welfare. A lainti (i.e. a atient) in a medical malractice disute retain a lawyer and adot contingency fee arrangement for vast majority of cases. 4 A claim by the side of lainti against a healthcare rovider initiates a medical malractice disute. The lainti s lawyer 5 and the defendant engage in negotiations over the terms of settlement in the shadow of court judgment. If the side of lainti les a lawsuit and the arties do not reach an agreement or the side of the lainti do not dro the case, they will face a judgment by the court, which determines whether the defendant is liable and, if so, the award to the lainti. The side of the lainti can dro a case at any time during the rocess. To study this rocess, I construct a dynamic bargaining model in which the lainti s lawyer and the defendant bargain over a settlement following Yildiz (2003, 2004) and Watanabe (2006). At any time during the negotiation, as long as the case has neither been settled nor droed, the lainti s lawyer has the otion of ling a lawsuit that would initiate the litigation hase. If the case is neither settle nor droed during the litigation hase, the case is resolved in court, where a jury verdict determines whether the defendant is liable and, if so the award to the side of the lainti. In any eriod rior to the termination of a disute, the lainti s lawyer and the defendant must ay the legal costs which I allow to di er across the sides of the lainti and the defendant and deending on whether or not a lawsuit is led. In articular, the legal costs are tyically higher during the litigation hase, which entails additional legal rocedures with resect to the relitigation hase. I do not consider exert s agency roblem for the side of the defendant because medical liacases. 4 For examle, Sloan et al (1993) reorts that lainti s retained lawyers in 99.4 ercent of the cases and that contingency fee arrangement was adoted in 99.4 ercent of the cases in Florida. 5 I assume throughout the aer that the lainti s lawyer is the decision maker for the side of the lainti. This is a common assumtion in the literature that is suorted by surveys for individual clients (see, e.g. Sloan et al (1993) and Kritzer (1998)). 3
4 bility insurance comanies who are wellinformed of the legal issues and rocedures makes desicions for the defendant. A arameter 2 [0; 1] in the model re ects the degree to which the lawyer work in the client s interest. Deending on the value of this arameter the model nests two secial cases and their convex combination; one in which the lainti s lawyer work in the best interest of the lainti ( = 0), and one in which the lawyer work in her own interest ( = 1). In the former case, the objective of the lainti s lawyer is to maxmize the ayment from the defendant ignoring any legal cost incurred by the side of the lainti. In the latter case, the objective of the lainti s lawyer is to maximize a contingency fee fraction of ayment from the defendant minus the sum of ereriod legal cost incurred by the side of the lainti. I characterize the unique subgameerfect equilibrium of this dynamic bargaining game. Equilibrium outcomes secify (i) the lawyer s decision of whether to le a lawsuit and (ii) if so the time to ling, (iii) whether or not the case is droed by the lainti s lawyer, (iv) whether or not the case is settled out of court, (v) the time to resolution by droing or by settlement, (v) the legal costs incurred, and (vi) the terms of settlement. Delaying agreement is costly because of the ereriod legal costs. However, the ossibility of learning new information makes delay valuable for both layers. This fundamental tradeo lays an imortant role in the equilibrium characterization and is a key determinant of the time to ling and the time to settlement. Furthermore, I nd that the more misaligned the incentives of the lainti and his or her lawyer are, the shorter the time to settlement as well as to droing and the higher the robability of droing a case. This is because the laini s lawyer takes her ereriod cost more fully if their incentives are misaligned. This roerty identi es the nesting arameter in estimation. I estimate the model using a unique data set on individual medical malractice disutes. The data set contains detailed information on the time, mode, cost, and terms of settlement as well as the time of ling lawsuit (if a lawsuit is led) and the time of droing (if a case is droed) for all medical malractice disutes in Florida over the eriod The estimate for the nesting aramater is , which imlies that the lawyers do not work very much in the best interest of their clients. I use the estimated structural model to comute the cost of agency roblem resulting from the incentive misalignment. To do so, I simulate the rstbest outcome which corresonds to the case that the lainti s lawyer maximize the ayment from the defendant minus the legal cost incurred. 6 I nd that the joint surlus for the side of the lainti is 6 Socially otimal outcome cannot be achieved in the model we estimate. In case the lainti s lawyer work in his/her interest, the lawyer only considers a fraction of the ayment from defendant minus the legal cost. In this case, the lawyer is giving too much weight for the legal cost. In case the lainti s lawyer work in the lainti s best interest, the lawyer ignores the legal cost she incurs. In this case, the legal cost is underweighted. 4
5 15% less comared to the rtbest outcome. Under the rstbest outcome, more cases are litigated and the time to resolution increases. The legal costs of the both side increases, but the increase in ayment to the side of the lainti from the side of the defendant is larger than the increase in cost. Finally, I conduct couterfactural olicy exeriments and evaluate how regulation on contingency fee arrangement a ects the outcomes of disute resolution as well as the cost of the agency roblem. Seci cally, I consider a limit on contingency fee at 25%. I nd that more cases are droed, frequency of ling of lawsuits decrease, and mean time to resolution decreases. This is because the lainti s lawyer receive less fraction of the ayment as comensation with such limit on fees while the ereriod legal cost remains the same. The exected joinsurlus decreases by about 13% re ecting a large decrease in exected ayment. 1.1 Literature A small but growing emirical literature studies agency roblem in exert services. 7 Levitt and Syverson (2006) comares home sales in which real estate agents are the owner of the house and in which they are not, and found that houses are sold at higher rice and stayed longer on market in the former case. Gruber and Owings (1996) analyzed hysicians likelihood of erforming cesarean section delivery, and show a strong correlation between decline in fertility and increase in cesarean, which they interret as hysician s inducing demand for cesarean by exloiting agency relationshi. Iizuka (2006) investigates Jaanese rescrition market in which hysician can sell drugs as well as rescribing it and nd that their rescritions are in uenced by the marku of the drugs. All these aers resents evidence that agency roblem exists in exert services. Hubbard (1998) studies auto reaireres s emission insection decision, and shows that auto reairers hel to ass by execting customers to return rather than maximizing short run ro ts by selling reairs. This aer shows an evidence of factors that mitigates agency roblem. None of the aer, however, directly estimates the degree of incentive misalignment and quantify the cost of the agency roblem. The aer also adds to the literature on emirical study of retrial bargaining. 8 Using data on the mode of resolution of civil disutes, Waldfogel (1995) estimates twoeriod bargaining model with heterogenous belief. Sieg (2000) estimates barganing model with 7 Theoretical models of exert sercises includes Dranove (1988), Wolinsky (1993), Emons (1997), and Fong (2005). 8 See the surveys by Kessler and Rubinfeld (2005) and Sier (2007). Theoretical literature on agency roblem regarding contingency fee contract includes Miller (1987), Rubinfeld and Scotchmer (1990), Dana and Sier (1993), Watts (1994), Hay (1996, 1997), Rickman (1999), Choi (2003), and Polinsky and Rubinfeld (2003). These aers emloys twoeriod models which abstracts from learning during rocedure. Hence, droing during retrial bargaining is not considered. 5
6 asymmetric information to study the mode, cost, and terms of settlement in medical malractice disute using the same data set I use in this aer. Watanabe (2006) further investigate the disute resolution rocess by constructing and estimating a multieriod dynamic barganing model to study the timing of settlement and litigation in addition to the mode, cost and terms of settlement. All of these aers, however, abstract from the droing decision and otential agency roblem bewteen lainti and lainti s lawyer, and do not utilize the data of droed cases. Danzon and Lillard (1983) uses data of droing in medical malractice disutes and nd that limits on contingency fees lowers likelihood of droing signi cantly. Helland and Tabarrok (2003) also uses data on medical malractice disutes and nd that limit on contingency fees both lowers likelihood of droing and increases time to settlement. These two aers, however, are not interested in agency roblem and timing of droing, which I address in this aer. The remainder of the aer is organized as follows. In Section 2, I resent the model and characterize the equilibrium. Section 3 describes the data and Section 4 resents the econometric seci cation. Section 5 will contains the results of the emirical analysis. 2 Model I consider a sequential bargaining model of legal disute resolution with erfectinformation and stochastic learning. The layers of the bargaining game are a lainti s lawyer () and a defendant (d). 9 The lainti s lawyer and the defendant bargain over the comensation ayment x 2 R + from the defendant to the lainti to resolve the disute. Each layer i 2 fd; g has linear vonneumannmorgenstern references over monetary transfer and legal costs. Both layers know the amount of the otential jury award V 2 R +, but the outcome of the judgement is uncertain, i.e. the layers do not know who will win the case in the event of a trial. 10 Hence, defendant ays V to the side of the lainti if the lainti wins the judgmen, while the defendant does not ay any amount otherwise. I denote the lainti s robability of revailing by. 9 Throughout the aer, I assume the decision maker for the side of the lainti as lainti s lawyer. Sloan et al. (1993) nds that lainti s "almost always followed their lawyer s advice regarding settlement (85)." They reort that lainti s setted 100% of the cases when lawyer s advice favored acceting and 4.8% when lawyer s advice favored rejecting. Another reason for this assumtion is due to the informational asymmetry between lainti s and his/her lawyers. Lawyers are exerienced exerts of the medical liability system, and the lainti s are less likely have better information than the lawyers. However, for the side of the defendant, I do not assume defendants lawyers as decision makers because the defendants are rimarily insurance comanies and are wellinformed and have exertise on disute resolution. 10 In the literature the uncertainty of the judgment is caused either (i) by the uncertainty of the winning arty (see e.g., Pries and Klein(1984)) or (ii) by the uncertainty of the award amount (see e.g. Sier (1992)). Imlications of the model do not di er between (i) and (ii) because the exected award is what matters. I take the former assumtion because I can better exlain the data in which a large roortion of cases concludes with no jury award at the court judgment. 6
7 Plainti s and his/her lawyers adot contingency fee arrangement for vast majority of the medical malractice cases in Florida 11, while defendants legal councils charge an hourly legal fee. The contingency fee arrangement entitles the lainti s lawyers to a fraction of the money received from the defendant only if a ositive ayment is received. I denote the fraction by ; hence a lainti s lawyer receives fraction of the defendant s ayment to the side of the lainti as comensation for the legal services they rovide, and the alinti receives the remaining fraction 1. Timing and Phases The bargaining game has two multieriod hases deending on whether the lainti s lawyer has led a lawsuit or not: the relitigation hase (Phase O) and the litigation hase (Phase L). The game starts with Phase O at eriod t = 0: Players bargain every eriod until they reach an agreement. Phase O has a nite number of eriods T < 1, due to the statute of limitation at eriod t = T + 1 < 1, after which the lainti s claim to recover is barred by law. The lainti has an otion of ling a lawsuit in Phase O as long as no agreement has been reached and the case has not been droed. The ling of a lawsuit moves the game to Phase L. Thus, in Phase O, a case may be either led (leading to Phase L), droed (without ling a lawsuit), settled (without ling a lawsuit), or terminated by the statute of limitations. The lainti s endogenous decision to le a lawsuit initiates Phase L. Let t L 2 f0; :::; T g denote the date of the ling of lawsuit. Once the lainti les a lawsuit, the case is rocessed in court towards the judgment scheduled T + 1 eriods after the date of ling, that is date t = t L + T + 1 < 1. While the case is rocessed in court, it can always be droed by the lainti or settled by both arties until t = t L + T: Failure to reach a settlement agreement by t = t L + T results in the resolution by the court judgment at t = t L + T + 1. Information and Beliefs The model is a game of erfect information. As described above, the layers can observe all the actions of the other layer. The information revealed is also commonly observed by both layers. Hence, there is no asymmetric information. The layers, however, do not have a common rior over the robability that the lainti will win the case (). This asymmetry in initial beliefs may be due for examle to di erences in each arty s ercetion of the relative ability of his or her lawyer or to di erences in oinion about the redisosition of otential juries. I assume that the layers beliefs of the robability of the lainti s revailing 2 [0; 1] follow beta distributions, a exible as well as tractable distribution with suort [0; 1] that is widely used in statistical learning models on Bernoulli trial rocess. Player i s initial 11 Sloan et al. (1993) reorts that 99.4% of the cases adoted contingency fee arrangement in their Survey of Medical Malractice Claimants conducted in Florida during
8 re litigation hase (length T ) filing lawsuit (tl ) statute of limitation (T+1 ) judgment (tl+t+1 ) litigation hase (length T ) Figure 1: Diagram of Model Structure. The lainti and the defendant start bargaining over a settlement in relitigation stage. At any time in relitigatioin stage, as long as the lainti has not droed the case or no agreement has been reached, the lainti has the otion of ling a lawsuit that endogenously determine t L and would initiate the litigation stage. If neither a lawsuit is led, the case is droed, nor a settlement is reached by T in relitigation hase, the case is no longer valid due to statute of limitation. If neither agreement is reached nor the case is droed during the litigation stage, the case is resolved by court judgment at t L + T + 1: belief, denoted by b i 0 ; are reresented by Beta( i; i ); where 0 < d < < : 12 A common arameter reresents the rmness of belief as exlained later. Thus, at the initial date, the layers have exected robability of lainti s revailing as E(b 0 ) = E(b d 0) = d for the lainti, and for the defendant. At the beginning of each eriod t in Phase J 2 fo; Lg, information related to winning robability (such as the result of a third arty medical examination or testimony by an exert witness) arrives with robability J. I denote an arrival of information at t by n t 2 f0; 1g, where n t = 1 means arrival of information while n t = 0 reresents no arrival. 12 See Yildiz (2003, 2004) for a similar learning mechanism. Arrival of information is deterministic in his model, while it is stochastic in my model. 8
9 The cumulated amount of information at eriod t is denoted by n t 2 f0; :::; tg, and therefore n t = n t 1 + n t : Information is either in favor of or against the lainti. I denote the content of the arrived information n t by m t 2 f0; 1g: The content is for the lainti if m t = 1;while m t = 0 means the arrived information is against the lainti, and ( m t 0 with robability 1 = 1 with robability ; where is not known to the layers. The cumulated information in favor of the lainti is denoted by m t 2 f0; :::; n t g, leading to m t = m t 1 + n t m t where m t is multilied by n t since the content of information matters only if information arrives. Players udate their beliefs according to Bayesian udating as follows: The beliefs at eriod t, denoted by b t and bd t, follow Beta( + m t ; + n t m t ) and Beta( d + m t ; d + n t m t ) resectively. Hence, at eriod t; the exectations on the robability of lainti s revailing on the judgement are and E(b t ) = + m t + n t E(b d t ) = d + m t + n t : The layers use these exectations as their estimates of. The rmer the beliefs (i.e., the higher the rmness of belief arameter ), the less is the imact of the information obtained in the legal rocess. By modelling beliefs this way, I can cature the relative imact of new learning on rior beliefs. The information environment I have described above is common knowledge to both layers. For notational convenience, I let k t = (n t ; m t ) 2 f0; tg f0; tg denote the information state. Stage Games In Phase O, layers lay the following stage game in every eriod t 2 f0; :::; T g. At the beginning of each eriod, information arrives with robability Ot and does not arrive with robability 1 Ot. The information is such that it a ects the outcome of the judgment (e.g., the result of thirdarty medical examination) and is commonly 9
10 observed by both layers. Then, the lainti s lawyer chooses whether to dro the case or continue it. If she chooses to dro the case, the case is resolved with no ayments being made from defendant to the side of the lainti. Otherwise, nature chooses the rooser, with robability for the lainti and 1 for the defendant. The chosen arty rooses the amount of comensation ayment x, which will be either acceted or rejected by the other arty. If acceted, the game concludes with the roosed amount of money x being transferred from the defendant to the side of the lainti, and the disute is resolved. In such a case, the lainti s lawyer receives x and the lainti receives (1 )x. If the roosal is rejected, the lainti chooses whether or not to le a lawsuit. The case moves to Phase L if the lainti les a lawsuit, while it remains in Phase O and the same stage game is reeated if the lainti chooses not to le. If the case is neither led nor settled during the T eriods, the statute of limitation renders the claim by the lainti to be ine ective. After the side of the lainti les a lawsuit, the arties lay the following stage game in every eriod t 2 ft L ; :::; t L + T g until the court judges on the case at t = t L + T + 1. At the beginning of each eriod, information that a ects the outcome of the judgment arrives with robability Lt and does not arrive with robability 1 Lt. Then, the lainti s lawyer chooses whether to dro the case or continue it. If she chooses to dro the case, the case is resolved with no ayments being made from defendant to the side of the lainti. Otherwise, nature again chooses the rooser, with robability for the lainti and 1 for the defendant. The chosen arty rooses the amount of comensation ayment x, which will be either acceted or rejected by the other arty. If acceted, the game terminates with the roosed amount of money being transferred from the defendant to the side of the lainti, and the disute is resolved. In such a case,, the lainti s lawyer receives x and the lainti receives (1 )x. If rejected, the case remains in Phase L and the same stage game is reeated until t = t L + T: I allow the rates of information arrival to di er across hases. One of the reasons for di ering rates stems from the discovery rocess. In this rocess, both arties can emloy a variety of legal devices to acquire information on the case that follows the ling of a lawsuit. I denote ereriod legal costs at eriod t in Phases O and L for layer 2 fd; g by COt i 2 R+ and CLt i 2 R+ resectively. I assume that these legal costs are drawn indeendently in each eriod t from identical distributions. I allow the distribution of ereriod costs to di er deending on whether or not the lainti has led a lawsuit. In articular, the legal costs of both sides are tyically higher in the litigation hase, which entails additional legal rocedures with resect to the relitigation hase. The distributions from which ereriod costs are drawn in Phases O and L are denoted by G CO () and G CL (). The realizations of the ereriod costs only a ect the total legal costs, 10
11 and they do not a ect the equilibrium stoing timing and settlement terms because layers make desicions based on exeted legal cost of the subsquent eriods. I consider a common timediscount factor denoted by 2 [0; 1]. A Parameter to Measure the Degree of Incentive Misalignment As discussed above, lainti s lawyers use a contingency fee arrangement, while defendants legal councils charge an hourly legal fee. The contingency fee arrangement entitles the lainti s lawyers to a fraction 2 [0; 0:5) 13 of the money received from the defendant only if a ositive ayment is received. Because of this deferment, the lainti incurs no additional legal cost by delaying agreement because the lainti s lawyer incurs the legal cost. Hence, the lainti and his/her lawyer s incentive are not aligned. The lainti refer to ursue a case much longer than her lawyer refer. The lainti s s objective is to maximize the exected ayment from the defendant, while the lawyer always considers the cost as well as the ayment. The main objective of this aer is to measure the degree to which lawyers and their clients incentives are misaligned, and I will measure this with the following arameter 2 [0; 1]: If a lawyer behaves erfectly in the interst of her lainti, she maximizes the exected ayment and does not consider ereriod legal cost. If ayment is x, such lawyer s ayo can be written as u 0 = (1 )x: If a laywer behaves in her best interest, she considers the legal cost and only fraction of the ayment. Hence, we can write it as u 1 = x C j : where j 2 fo; Lg. My interest is to measure what the true ayo system is for the lainti s lawyer, and these two cases are the secial cases in which the lawyer are erfectly working in the interest of her client and in which she work in her own interest. Since these two cases are the extreme ones, I can consider a convex combination of these two cases with a arameter, which can be written as u = u 1 + (1 ) u 0 (1) = (1 + 2)x C j Now, = 1 imlies that a lawyer behaves in her interest and = 0 imlies that a lawyer behaves in the lainti s interest. Hence, mesures the degree to which the incentive of 13 I imose this assumtion because contingency fee are below 50% for vast majority of cases. 11
12 the lawyers and the lainti are misaligned. For notational convenience, I de ne function A() as A() 1 + 2: 2.1 Equilibrium Characterization The model is a dynamic game with erfect information. Thus, I emloy subgameerfect equilibrium as the equilibrium concet. Because the model has a nite number of eriods, backward induction rovides us with a characterization of the unique subgameerfect equilibrium. I start the analysis from the last stage in Phase L, and move to Phase O Phase L (Litigation Phase) In order to characterize the unique subgame erfect equilibrium by backward induction, I start my analysis from the date of the judgment by the court at the end of Phase L. Recall that a Phase L subgame is reached only if the case is litigated at some eriod during Phase O. Let t L 2 f0; :::; T g denote the date of ling the lawsuit which is an endogenously determined. If the layers cannot settle by date t L + T, the judgement by the court at t = t L + T + 1 determines the outcome of the last stage. Since two decisions are made in each eriod in Phase L, we de ne two continuation values for each layer. Let V i t t L (k t ) denote the continuation value for layer i 2 f; dg at the beginning of date t in Phase L with information state k t, and V i t t L (k t ) the continuatoin value after droing decision by lainti s lawyer and before settlement decision at the end of the eriod t. Note that the subscrit is t t L, which is the number of eriods in Phase L so that V1 i(k t L ) corresonds to the continuation value at the rst eriod in Phase L that will be on the right hand side of the Bellman equation in Phase O. where A()V V T +1 (k t L +T +1) = V d T +1(k tl +T +1) = ( ( The continuation value of the judgment is A()V V 0 0 if the lainti revails otherwise. if the lainti revails otherwise. is the amount lainti s laywer obtains if she win the case and V is the amount aid the defendant to the side of the lainti. The lainti will have the di erence (1 A())V: Having above V i T +1 (k t L +T +1) as nal values, I can obtain V i t t L (k t ) and V i t t L (k t ) by alying backward induction. The equilibrium in Phase L subgame is characterized in the Proosition 1 below. 12
13 Proosition 1 In the unique subgame erfect equilibrium given k t and t L, 1. the ayo of the layers at t 2 ft L + 1; :::; t L + T g in Phase L are exressed as where V n V t t L (k t ) = max t t L (k t ) = max 0; V t t L (k t ) ( Vt d 0 if 0 > V t L (k t ) = V d t t L (k t ) t t L (k t ) otherwise. A()Et d +(1 )E t V (k t+1 ) CL ; h i V d V d t t L (k t ) = Et d (k t+1 ) CL d +(1 ) max h i Vt+1 d t L (k t+1 ) CL d ; E t V (k t+1 ) C o L 1 A() E t V (k t+1 ) C L ; E d t hvt+1 d t L (k t+1 ) CLi : 2. the lainti s lawyer dros the case at t 2 ft L + 1; :::; t L + T g in Phase L i 0 > V t t L (k t ) 3. the layers settle at t 2 ft L + 1; :::; t L + T g in Phase L i 0 E t [V (k t+1 ) C L ] + A()Ed t [V d (k t+1 ) C d L]: 4. given that layers settle at t 2 ft L + 1; :::; t L + T g in Phase L, the ayment is x t = ( Et d 1 A() E t Proof. See Aendix A V d t+1 tl (k ts +1) CL d V (k ts +1) C L if the lainti is a rooser if the defendant is a rooser, This roosition characterizes the subgame erfect equilibrium in Phase L: The exression for V t t L (k t ) in 1 is the continuation value at the beginning of the eriod when lainti s lawyer faces the droing decsion. As described in 2, lainti s lawyer dros a case if her interim continuation value V t t L (k t ) is below 0. In such a situation, both sides have 0 as their continuation value. Interim continuation value after droing decision and before settelment decision V i t t L (k t ) is obtained by solving for randomrooser barganing. Note that exectations are indexed by layer because two layers have di erent beliefs over the robability of winning at judgment. 13
14 The identify of the rooser do not a ect the settlement decision as can be seen in 3. The amount of ayment deends on the identify of the rooser as in 4. This arises because the layers choose to settle if the joint surlus of settlement today is larger than the joint surlus of continuing the case. The comensation ayment deends on the identity of the rooser because the recognized rooser obtains all of the surlus. This is true even in the extreme case that lainti s lawyer work in the interest of her client (i.e. A() = 1 ) and do not take ereriod legal costs into consideration. Delaying agreement is still costly for her because she misses the bene ts of the saving of the defendant s legal costs that indirectly increases comensation ayment. Therefore, delaying agreement is costly for both layers, and quick settlement is referable. However, the ossibility of learning new information makes delay valuable, since this information enhances the robability of a settlement, which in turn generates ositive surlus for both layers. This fundamental tradeo lays an imortant role in the equilibrium characterization and is a key determinant of the timing of settlement. Droing decision is simly an individual rationality constraint for the lainti s lawyer at each eriod. If there is no learning, the continuation values for the lainti s lawyer increases monotonically over time as can be seen from 1. This monotonicity imlies that if the value is negative at eriod t, the value is also negative for any eriod t 0 < t, i.e. if a case is to be droed at t, it must be droed at any earlier date t 0. Hence, all droing occurs only in the initial eriod if there is no learning. Therefore, droing in eriods other than the initial eriod only occurs with learning at arrival of new information against the lainti s side. In such case, continuation value stays ositive for rst several eriods, and it become negative at the arrival of unfavorable information. The roosition also shows that droing and settlement decisions are directly a ected by the degree of incentive misalignment. Increase in decreases the continuation value of the lainti s lawyer in two ways; through increase in ereriod cost and through decrease in A(). Decrease of A() lowers V t t L (k t ) because the exected award at judgement E t [A()V ] decreases corrsoding to change in A(). Thus, the larger is, the smaller V t t L (k t ) is, and the more likely tha the case is droed. In other words, lainti s lawyer refer to dro a case at earlier date if her incentives is less aligned. In the extreme case that the lawyer works erfectly in her client s interest ( = 0), the case is never droed. Similar intuition works for the e ect of incentive alignment and settlement decision. The exression in 3 can be rewritten as E t [C L + Cd L] E t [V (k t+1 )] + A()E d t [V d (k t+1 )]; where the lefthand side is exected ereriod legal cost which is not indexed by layer 14
15 because layers have common belief over the distribution of cost. The righthand side is the exected surlus from continuation. Increase in increase the value of the lefthand side, and decreases the value of the right hand side 14. Hence, the less aligned the incentives are (the larger is), the shorter it takes to reach a settlement on average. The lainti s lawyer who considers her own legal cost more seriously and focusing more on ayments to herself, which is much smaller than the ayment to the lainti, refer to settle at earlier dates Phase O (PreLitigation Phase) Let W i t (k t ) denote the continuation value for layer i 2 f; dg at the beginning of date t in Phase O with information state k t. Again, I start from the last stage of Phase O subgame. The maximum number of eriods in Phase O is T ; after which the claim by the lainti loses its value due to the statute of limitation. of 0 at date T + 1, i.e., W T +1 (k T +1 ) = W d T +1 (k T +1 ) = 0: Hence, each layer has continuation ayo I comute W i t (k t ) by alying backward induction and having the above as nal values. In Phase O, the lainti has an otion of litigating a case at any date t 2 f0; :::; T g. Solving the value function in Proosition 2 u to the rst eriod in Phase L, I can obtain the continuation value of the Phase L subgame, V i 1 (k t). Note that this continuation value of litigation does not deend on the date of litigation t L itself but does deend on the information state k t at eriod t. First, I will look at the ling decision by the lainti s lawyer because ling decision is the last decsion to be made in a eriod. The lainti s lawyer chooses to litigate at the end of date t if and only if E t V 1 (k t+1) C L Et W t+1 (k t+1) CO ; where the lefthand side is the ayo from ling a lawsuit and the righthand side is the ayo from stay in relitigation hase. Hence, the continuation value for the lainti at the end of date t is written as Y t (k t) = max E t V 1 (k t+1) C L ; Et W t+1 (k t+1) CO ; where Y t (k t) denotes an interim continuation value for the lainti s lawyer after the settlment decision and before the ling decision in eriod t in Phase O given state k t. The 14 Though A() increase in, A()Et d [Vt+1 d t L (k t+1)] decrease in because Et d [Vt+1 d t L (k t+1)] is always negative and decreases in : 15
16 defendant s continuation value deends on the ling decision of the lainti s lawyer described above, and is written as Y d t (k t ) = ( E t V d 1 (k t+1 ) CL d E t W d t+1 (k t+1 ) C O if E t V 1 (k t+1) C L otherwise, E t W t+1 (k t+1) C O where Y d t (k t ) denotes an interim continuation value for the lainti s lawyer after the settlment decision and before the ling decision in eriod t in Phase O given information state k t. I can then conduct the exact same analysis for settlement and droing decision as I did for Phase L; and the subgameerfect equilibrium for Phase O is characterized in Proosition 2. Proosition 2 In any subgame erfect equilibrium given k t ; 1. the ayo s of the layers at t 2 f0; :::; T g in Phase O are exressed as W t (k t) = max 0; W t (k t ) ( Wt d 0 if 0 > W (k t ) = W d t (k t ) t (k t ) otherwise. where n W t (k t ) = max W d t (k t ) = Y d t (k t ) + (1 o A()Yt d (k t ); Y t (k t) + (1 )Y t (k t); 1 ) max A() Y t (k t); Yt d (k t ) : 2. the layers settle at t 2 f0; :::; T g in Phase O i Y t (k t) + A()Y d t (k t ) 0: 3. the lainti litigates at t 2 f0; :::; T g in Phase O i E t [V 1 (k t L +1)] E t W t+1 (k t+1) : 4. given that layers settle at t 2 f0; :::; T g in Phase O, the ayment is x t = ( Y d t (k t ) Y t (k t) if the lainti is a rooser if the defendant is a rooser, 16
17 Proof. See Aendix B This roosition characterizes the subgame erfect equilibrium in Phase O: The mechanics of the settlement and droing decisions are exactly the same as for the characterization for Phase L. The only di erence is that the cost of delay and the ossibility of learning in the next eriod deend on the lainti s decision to le or not at the end of each eriod. The decision to le a lawsuit by the lainti is also derived from a tradeo between the cost of delay and the ossibility of learning. The cost of delaying ling has two comonents. One is the ereriod legal cost of the relitigation hase, because the total length of the underlying game becomes one eriod longer if ling is delayed by one eriod. Even though the lainti incurs no legal cost er eriod, this delay still imacts him because minimizing the defendant s legal cost may result in a higher comensation ayment to the lainti. The second comonent is the cost of delay due to discounting. The lainti refers to obtain the continuation value of the Phase L subgame earlier, since a oneeriod delay in ling costs him (1 )V 1 () when no information arrives. The bene t of delaying ling by one eriod is that the arties have one more eriod to obtain new information and hence reach an agreement. Thus, the lainti refers to stay in Phase O longer if CO i are small and is large, while low Ot rovides an incentive for the lainti to le early. 3 Data The Florida Deartment of Financial Services, an insurance regulator of the Florida state government, collects a detailed microlevel data set on medical malractice disutes in Florida. A statute on rofessional liability claims requires medical malractice insurers to le a reort to the Deartment on all of their closed claims once the claim is resolved. The reort contains detailed information on the disute resolution rocess, as well as individual case characteristics. The information on the disute resolution rocess includes imortant dates (calender date of occurrence, initial claim, ling of lawsuit, resolution either by droing, settlement, or by court judgement), settlement ayments (or award by the court in case of resolution by court judgment), and total legal costs incurred by the defendants. The information on case characteristics includes atient characteristics (e.g. age and sex), defendant characteristics (e.g. defendant tye, secialty, and insurance olicy), and the characteristics of injury (e.g. severity and lace of occurrence). Hence, this data set contains detailed information on all the variables of interest, i.e., if and when a lawsuit is led, whether or not the case is settled out of court or droed, the time to resolution, the legal costs incurred and the terms of settlement. My samle of observations consists of 5,379 claims against hysicians 15 which were 15 Claims against hositals, HMOs, dentists, ambulance surgical centers, and crisis stabilization units are 17
18 Droed without Lawsuit Droed after Lawsuit Settled without Lawsuit Settled after Lawsuit Resolved by Judgment with Positive Award Resolved by Judgment with No Award Number of Observations Resolution Probability , Total 5, Mean Comensation 0 (0) 0 (0) 314; 266 (303; 917) 303; 402 (379; 909) 541; 832 (620; 722) 0 (0) 203; 210 (343; 922) Mean Defense Legal Cost 7; 330 (23; 023) 40; 370 (44; 978) 9; 047 (15; 014) 53; 989 (88; 887) 127; 966 (113; 147) 83; 182 (87; 268) 45; 047 (77; 794) Comensation ayments and legal costs are measured in 2000 dollars. rovides standard deviations. Numbers in arentheses Table 1: Descritive Statistics I  Resolution Probability, Payments and Legal Costs resolved between October 1985 and July Following Sieg (2000), I restrict attention to cases with the defendant s legal cost exceeding $1,000 and which were not droed during the litigation rocess. 17 Because the timing and disosition of cases di er greatly deending on the severity of the injury, I restrict attention to the cases in which injuries resulted in ermanent major damage to or death of the atient. Tables 1 and 2 show the descritive statistics of all the variables I use for estimation. In my data, 28.6% of the cases are droed or settled with zero ayment, 62.5% of the cases were settled by arties, and the remaining 9.1% of the cases were resolved by judgement by the court. Regarding droed and settled cases, only one senveth of settled cases settled without ling a lawsuit and majority of settled cases are settled after ling a lawsuit, while the roortion of cases droed without ling a lawsuit and after ling a lawsuit are about the same around 14%. For the judged cases, the defendants were three times more likely to win the judgment (i.e., award was zero). Mean comensation ayments were similar for excluded from my samle to control for the heterogeneity of the lainti. 16 During this eriod, there were no major changes in state law retaining to resolution of medical malractice disutes. 17 This rocedure eliminates small cases. 18
19 Time to Filing Time to Resolution after Filing Total Time to Resolution Droed without Filing 4:81 (3:22) Droed after Filing 2:30 (2:31) 7:36 (4:51) 9:66 (5:09) Settled without Filing 3:23 (2:41) Settled after Filing 2:48 (2:26) 7:45 (4:55) 9:93 (5:16) Resolved by Judgment with Positive Award 2:69 (2:67) 11:41 (6:61) 14:10 (7:17) Resolved by Judgment with No Award 2:50 (3:21) 9:69 (5:17) 12:19 (6:24) Total 2:45 (2:38) 7:75 (4:76) 8:81 (5:57) Numbers are in quarters of a year. The numbers in arentheses rovide standard deviations. Table 2: Descritive Statistics II  Timings the cases that were settled after ling a lawsuit and those that were settled without ling a lawsuit (around $300,000). Legal costs for defendants substantially di ered across modes of resolution. Defense lawyers usually charge based on the amount of time they sent. It is not surrising to nd that the mean of the defense legal costs correlates strongly with the mean time to resolution as dislayed in Table 2. Mean of defence legal costs for cases settled without a lawsuit is about one fth of the cases settled after a lawsuit. This di erence correlates with the shorter mean time to resolution as in Table 2. The cases settled after ling a lawsuit have a signi cantly higher mean cost ($53,989) comared to the settled cases without a lawsuit ($9,047). Similary, the cases droed after ling a lawsuit have a signi cantly higher mean cost ($40,370) comared to the cases droed without a lawsuit ($7,330). Among the cases resolved by court judgement, mean defense costs are more than 50% higher for the cases won by the lainti s than the cases won by the defendants, which again corresonds to the longer time to resolution. Mean time to ling a lawsuit, which corresonds to the eriods sent in the relitigation hase, is similar across the droed cases, the settled cases, and the cases resolved by court 19
20 fraction Time to droing without a lawsuit Time to settlement without a lawsuit Time to filing a lawsuit quarters Figure 2: Histogram of Time to Droing, Settlement and Filing. Fractions of time to droing without a lawsuit, settlement without a lawsuit, and ling a lawsuit add u to one. This isbecause cases are either 1) droed without a lawsuit, 2) settled without a lawsuit, or 3) resolved after a lawsuit is led. judgment. The time to resolution di er between the cases settled after ling and the cases resolved by the judgment. This di erence results from the di erence in time to resolution after ling lawsuit. The cases settled without a lawsuit, which corresond to settlement in relitigation hase, send longer eriods in the relitigation hase than the led cases on average, and the cases droed without a lawsuit sends even longer time on average about 4.81 quarters. Figure 2 rovides the histogram of ling, droing, and settlement in relitigation hase. Note that the sum of the fractions for ling, droing, and settlement add u to one because each case is either led, droed without a lawsuit, or settled without a lawsuit. In Florida, the statute of limitation regarding a medical malractice cases is two years. Hence, more than 95% of the cases are led or settled without ling a lawsuit before the ninth quarter. 18 A fraction of cases ling lawsuits in relitigation hase and a fraction of cases settling 18 The remaining cases may be due, for examle, to invervening medical comlications that entail an automatic extension of the statute of limitations. 20
Estimating the Degree of Expert s Agency Problem: The Case of Medical Malpractice Lawyers
Estimating the Degree of Exert s Agency Problem: The Case of Medical Malractice Lawyers Yasutora Watanabe Northwestern University March 2007 Abstract I emirically study the exert s agency roblem in the
More informationLearning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation
Learning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation Yasutora Watanabe y Kellogg School of Management Northwestern University August, 2005 Abstract Lengthy
More informationLearning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation
Learning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation Yasutora Watanabe y Northwestern University May 2006 Abstract This paper studies the dispute resolution
More informationTHE WELFARE IMPLICATIONS OF COSTLY MONITORING IN THE CREDIT MARKET: A NOTE
The Economic Journal, 110 (Aril ), 576±580.. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 50 Main Street, Malden, MA 02148, USA. THE WELFARE IMPLICATIONS OF COSTLY MONITORING
More informationLearning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation
Learning and Bargaining in Dispute Resolution: Theory and Evidence from Medical Malpractice Litigation Yasutora Watanabe University of Pennsylvania (JOB MARKET PAPER) November, 2004 Abstract Lengthy legal
More informationPresales, Leverage Decisions and Risk Shifting
Presales, Leverage Decisions and Risk Shifting Su Han Chan Professor Carey Business School Johns Hokins University, USA schan@jhu.edu Fang Fang AssociateProfessor School of Public Economics and Administration
More informationRisk and Return. Sample chapter. e r t u i o p a s d f CHAPTER CONTENTS LEARNING OBJECTIVES. Chapter 7
Chater 7 Risk and Return LEARNING OBJECTIVES After studying this chater you should be able to: e r t u i o a s d f understand how return and risk are defined and measured understand the concet of risk
More informationTworesource stochastic capacity planning employing a Bayesian methodology
Journal of the Oerational Research Society (23) 54, 1198 128 r 23 Oerational Research Society Ltd. All rights reserved. 165682/3 $25. www.algravejournals.com/jors Tworesource stochastic caacity lanning
More informationA Simple Model of Pricing, Markups and Market. Power Under Demand Fluctuations
A Simle Model of Pricing, Markus and Market Power Under Demand Fluctuations Stanley S. Reynolds Deartment of Economics; University of Arizona; Tucson, AZ 85721 Bart J. Wilson Economic Science Laboratory;
More informationAn important observation in supply chain management, known as the bullwhip effect,
Quantifying the Bullwhi Effect in a Simle Suly Chain: The Imact of Forecasting, Lead Times, and Information Frank Chen Zvi Drezner Jennifer K. Ryan David SimchiLevi Decision Sciences Deartment, National
More informationMultiperiod Portfolio Optimization with General Transaction Costs
Multieriod Portfolio Otimization with General Transaction Costs Victor DeMiguel Deartment of Management Science and Oerations, London Business School, London NW1 4SA, UK, avmiguel@london.edu Xiaoling Mei
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More informationLarge firms and heterogeneity: the structure of trade and industry under oligopoly
Large firms and heterogeneity: the structure of trade and industry under oligooly Eddy Bekkers University of Linz Joseh Francois University of Linz & CEPR (London) ABSTRACT: We develo a model of trade
More informationManaging specific risk in property portfolios
Managing secific risk in roerty ortfolios Andrew Baum, PhD University of Reading, UK Peter Struemell OPC, London, UK Contact author: Andrew Baum Deartment of Real Estate and Planning University of Reading
More informationA joint initiative of LudwigMaximilians University s Center for Economic Studies and the Ifo Institute for Economic Research
A joint initiative of LudwigMaximilians University s Center for Economic Studies and the Ifo Institute for Economic Research Area Conference on Alied Microeconomics  2 March 20 CESifo Conference Centre,
More informationOn Software Piracy when Piracy is Costly
Deartment of Economics Working aer No. 0309 htt://nt.fas.nus.edu.sg/ecs/ub/w/w0309.df n Software iracy when iracy is Costly Sougata oddar August 003 Abstract: The ervasiveness of the illegal coying of
More informationRisk in Revenue Management and Dynamic Pricing
OPERATIONS RESEARCH Vol. 56, No. 2, March Aril 2008,. 326 343 issn 0030364X eissn 15265463 08 5602 0326 informs doi 10.1287/ore.1070.0438 2008 INFORMS Risk in Revenue Management and Dynamic Pricing Yuri
More informationF inding the optimal, or valuemaximizing, capital
Estimating RiskAdjusted Costs of Financial Distress by Heitor Almeida, University of Illinois at UrbanaChamaign, and Thomas Philion, New York University 1 F inding the otimal, or valuemaximizing, caital
More informationAsymmetric Information, Transaction Cost, and. Externalities in Competitive Insurance Markets *
Asymmetric Information, Transaction Cost, and Externalities in Cometitive Insurance Markets * Jerry W. iu Deartment of Finance, University of Notre Dame, Notre Dame, IN 465565646 wliu@nd.edu Mark J. Browne
More informationJoint Production and Financing Decisions: Modeling and Analysis
Joint Production and Financing Decisions: Modeling and Analysis Xiaodong Xu John R. Birge Deartment of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208,
More informationA MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
9 th ASCE Secialty Conference on Probabilistic Mechanics and Structural Reliability PMC2004 Abstract A MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
More informationOntheJob Search, Work Effort and Hyperbolic Discounting
OntheJob Search, Work Effort and Hyerbolic Discounting Thomas van Huizen March 2010  Preliminary draft  ABSTRACT This aer assesses theoretically and examines emirically the effects of time references
More informationCompensating Fund Managers for RiskAdjusted Performance
Comensating Fund Managers for RiskAdjusted Performance Thomas S. Coleman Æquilibrium Investments, Ltd. Laurence B. Siegel The Ford Foundation Journal of Alternative Investments Winter 1999 In contrast
More informationSupplemental material for: Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options
Sulemental material for: Dynamic jum intensities and risk remiums: evidence from S&P5 returns and otions Peter Christo ersen University of Toronto, CBS and CREATES Kris Jacobs University of Houston and
More informationThe Economics of Credence Goods: On the Role of Liability, Verifiability, Reputation and Competition
WORKING PAPERS IN ECONOMICS No 348 he Economics of Credence Goods: On the Role of Liability, Verifiability, Reutation and Cometition Uwe Delleck Rudolf Kerschbamer Matthias Sutter February 29 Institutionen
More information6.042/18.062J Mathematics for Computer Science December 12, 2006 Tom Leighton and Ronitt Rubinfeld. Random Walks
6.042/8.062J Mathematics for Comuter Science December 2, 2006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Random Walks Gambler s Ruin Today we re going to talk about onedimensional random walks. In
More information1 Gambler s Ruin Problem
Coyright c 2009 by Karl Sigman 1 Gambler s Ruin Problem Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial fortune of $i and then on each successive gamble either wins
More informationDynamics of Open Source Movements
Dynamics of Oen Source Movements Susan Athey y and Glenn Ellison z January 2006 Abstract This aer considers a dynamic model of the evolution of oen source software rojects, focusing on the evolution of
More informationIEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 2011 757. LoadBalancing Spectrum Decision for Cognitive Radio Networks
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 757 LoadBalancing Sectrum Decision for Cognitive Radio Networks LiChun Wang, Fellow, IEEE, ChungWei Wang, Student Member, IEEE,
More informationc 2009 Je rey A. Miron 3. Examples: Linear Demand Curves and Monopoly
Lecture 0: Monooly. c 009 Je rey A. Miron Outline. Introduction. Maximizing Pro ts. Examles: Linear Demand Curves and Monooly. The Ine ciency of Monooly. The Deadweight Loss of Monooly. Price Discrimination.
More informationPenalty Interest Rates, Universal Default, and the Common Pool Problem of Credit Card Debt
Penalty Interest Rates, Universal Default, and the Common Pool Problem of Credit Card Debt Lawrence M. Ausubel and Amanda E. Dawsey * February 2009 Preliminary and Incomlete Introduction It is now reasonably
More informationAn inventory control system for spare parts at a refinery: An empirical comparison of different reorder point methods
An inventory control system for sare arts at a refinery: An emirical comarison of different reorder oint methods Eric Porras a*, Rommert Dekker b a Instituto Tecnológico y de Estudios Sueriores de Monterrey,
More informationAn Empirical Analysis of the Effect of Credit Rating on Trade Credit
011 International Conference on Financial Management and Economics IPED vol.11 (011) (011) ICSIT Press, Singaore n Emirical nalysis of the Effect of Credit ating on Trade Credit JianHsin Chou¹ MeiChing
More informationThe fast Fourier transform method for the valuation of European style options inthemoney (ITM), atthemoney (ATM) and outofthemoney (OTM)
Comutational and Alied Mathematics Journal 15; 1(1: 16 Published online January, 15 (htt://www.aascit.org/ournal/cam he fast Fourier transform method for the valuation of Euroean style otions inthemoney
More informationEconomics 431 Fall 2003 2nd midterm Answer Key
Economics 431 Fall 2003 2nd midterm Answer Key 1) (20 oints) Big C cable comany has a local monooly in cable TV (good 1) and fast Internet (good 2). Assume that the marginal cost of roducing either good
More informationCRITICAL AVIATION INFRASTRUCTURES VULNERABILITY ASSESSMENT TO TERRORIST THREATS
Review of the Air Force Academy No (23) 203 CRITICAL AVIATION INFRASTRUCTURES VULNERABILITY ASSESSMENT TO TERRORIST THREATS Cătălin CIOACĂ Henri Coandă Air Force Academy, Braşov, Romania Abstract: The
More informationMethods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical Records
(Generating Evidence & Methods to imrove atient outcomes) Volume 1 Issue 3 Methods for CER, PCOR, and QI Using EHR Data in a Learning Health System Article 6 1212013 Methods for Estimating Kidney Disease
More informationLargeScale IP Traceback in HighSpeed Internet: Practical Techniques and Theoretical Foundation
LargeScale IP Traceback in HighSeed Internet: Practical Techniques and Theoretical Foundation Jun Li Minho Sung Jun (Jim) Xu College of Comuting Georgia Institute of Technology {junli,mhsung,jx}@cc.gatech.edu
More informationAutomatic Search for Correlated Alarms
Automatic Search for Correlated Alarms KlausDieter Tuchs, Peter Tondl, Markus Radimirsch, Klaus Jobmann Institut für Allgemeine Nachrichtentechnik, Universität Hannover Aelstraße 9a, 0167 Hanover, Germany
More informationDAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON
DAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON Rosario Esínola, Javier Contreras, Francisco J. Nogales and Antonio J. Conejo E.T.S. de Ingenieros Industriales, Universidad
More informationMachine Learning with Operational Costs
Journal of Machine Learning Research 14 (2013) 19892028 Submitted 12/11; Revised 8/12; Published 7/13 Machine Learning with Oerational Costs Theja Tulabandhula Deartment of Electrical Engineering and
More informationEffect Sizes Based on Means
CHAPTER 4 Effect Sizes Based on Means Introduction Raw (unstardized) mean difference D Stardized mean difference, d g Resonse ratios INTRODUCTION When the studies reort means stard deviations, the referred
More informationA Multivariate Statistical Analysis of Stock Trends. Abstract
A Multivariate Statistical Analysis of Stock Trends Aril Kerby Alma College Alma, MI James Lawrence Miami University Oxford, OH Abstract Is there a method to redict the stock market? What factors determine
More informationCashintheMarket Pricing and Optimal Bank Bailout Policy 1
CashintheMaret Pricing and Otimal Ban Bailout Policy 1 Viral V. Acharya 2 London Business School and CEPR Tanju Yorulmazer 3 Ban of England J.E.L. Classification: G21, G28, G38, E58, D62. Keywords:
More informationSeparating Trading and Banking: Consequences for Financial Stability
Searating Trading and Banking: Consequences for Financial Stability Hendrik Hakenes University of Bonn, Max Planck Institute Bonn, and CEPR Isabel Schnabel Johannes Gutenberg University Mainz, Max Planck
More informationPOISSON PROCESSES. Chapter 2. 2.1 Introduction. 2.1.1 Arrival processes
Chater 2 POISSON PROCESSES 2.1 Introduction A Poisson rocess is a simle and widely used stochastic rocess for modeling the times at which arrivals enter a system. It is in many ways the continuoustime
More informationOn the predictive content of the PPI on CPI inflation: the case of Mexico
On the redictive content of the PPI on inflation: the case of Mexico José Sidaoui, Carlos Caistrán, Daniel Chiquiar and Manuel RamosFrancia 1 1. Introduction It would be natural to exect that shocks to
More informationAn optimal batch size for a JIT manufacturing system
Comuters & Industrial Engineering 4 (00) 17±136 www.elsevier.com/locate/dsw n otimal batch size for a JIT manufacturing system Lutfar R. Khan a, *, Ruhul. Sarker b a School of Communications and Informatics,
More information401K Plan. Effective January 1, 2014
401K Plan Effective January 1, 2014 Summary Plan Descrition Particiation...2 Contributions...2 Disabled Particiants...4 Definition of Comensation...4 Legal Limits on Contributions...4 Enrollment...5 Investment
More informationThe Economics of the Cloud: Price Competition and Congestion
Submitted to Oerations Research manuscrit The Economics of the Cloud: Price Cometition and Congestion Jonatha Anselmi Basque Center for Alied Mathematics, jonatha.anselmi@gmail.com Danilo Ardagna Di. di
More informationTimeCost TradeOffs in ResourceConstraint Project Scheduling Problems with Overlapping Modes
TimeCost TradeOffs in ResourceConstraint Proect Scheduling Problems with Overlaing Modes François Berthaut Robert Pellerin Nathalie Perrier Adnène Hai February 2011 CIRRELT201110 Bureaux de Montréal
More informationInterbank Market and Central Bank Policy
Federal Reserve Bank of New York Staff Reorts Interbank Market and Central Bank Policy JungHyun Ahn Vincent Bignon Régis Breton Antoine Martin Staff Reort No. 763 January 206 This aer resents reliminary
More informationThe risk of using the Q heterogeneity estimator for software engineering experiments
Dieste, O., Fernández, E., GarcíaMartínez, R., Juristo, N. 11. The risk of using the Q heterogeneity estimator for software engineering exeriments. The risk of using the Q heterogeneity estimator for
More informationWhat is Adverse Selection. Economics of Information and Contracts Adverse Selection. Lemons Problem. Lemons Problem
What is Adverse Selection Economics of Information and Contracts Adverse Selection Levent Koçkesen Koç University In markets with erfect information all rofitable trades (those in which the value to the
More information6.4 The Basic Scheme when the Agent is Risk Averse
100 OPTIMAL COMPENSATION SCHEMES such that Further, effort is chosen so that ˆβ = ˆα = 0 e = δ The level of utility in equilibrium is strictly larger than the outside otion (which was normalized to zero
More informationPLEASE DO NOT QUOTE OR CIRCULATE VERY PRELIMINARY VERSION The Economics of Reverse Contingent Fees
PLEASE DO NOT QUOTE OR CIRCULATE VERY PRELIMINARY VERSION The Economics of Reverse Contingent Fees Albert CHOI University of Virginia Nuno GAROUPA Universidade Nova de Lisboa CEPR, London June 2005 Abstract
More informationSage HRMS I Planning Guide. The Complete Buyer s Guide for Payroll Software
I Planning Guide The Comlete Buyer s Guide for Payroll Software Table of Contents Introduction... 1 Recent Payroll Trends... 2 Payroll Automation With Emloyee SelfService... 2 Analyzing Your Current Payroll
More informationIEEM 101: Inventory control
IEEM 101: Inventory control Outline of this series of lectures: 1. Definition of inventory. Examles of where inventory can imrove things in a system 3. Deterministic Inventory Models 3.1. Continuous review:
More informationAmbiguity, Risk and Earthquake Insurance Premiums: An Empirical Analysis. Toshio FUJIMI, Hirokazu TATANO
京 都 大 学 防 災 研 究 所 年 報 第 49 号 C 平 成 8 年 4 月 Annuals 6 of Disas. Prev. Res. Inst., Kyoto Univ., No. 49 C, 6 Ambiguity, Risk and Earthquake Insurance Premiums: An Emirical Analysis Toshio FUJIMI, Hirokazu
More informationTitle: Stochastic models of resource allocation for services
Title: Stochastic models of resource allocation for services Author: Ralh Badinelli,Professor, Virginia Tech, Deartment of BIT (235), Virginia Tech, Blacksburg VA 2461, USA, ralhb@vt.edu Phone : (54) 2317688,
More informationSoftmax Model as Generalization upon Logistic Discrimination Suffers from Overfitting
Journal of Data Science 12(2014),563574 Softmax Model as Generalization uon Logistic Discrimination Suffers from Overfitting F. Mohammadi Basatini 1 and Rahim Chiniardaz 2 1 Deartment of Statistics, Shoushtar
More informationThe Behavioral Economics of Insurance
DEPARTMENT OF ECONOMICS The Behavioral Economics of Insurance Ali alnowaihi, University of Leicester, UK Sanjit Dhami, University of Leicester, UK Working Paer No. 0/2 Udated Aril 200 The Behavioral Economics
More informationPiracy and Network Externality An Analysis for the Monopolized Software Industry
Piracy and Network Externality An Analysis for the Monoolized Software Industry Ming Chung Chang Deartment of Economics and Graduate Institute of Industrial Economics mcchang@mgt.ncu.edu.tw Chiu Fen Lin
More informationOutsourcing and Technological Innovations: A FirmLevel Analysis
DISCUSSION PAPER SERIES IZA DP No. 3334 Outsourcing and Technological Innovations: A FirmLevel Analysis Ann Bartel Saul Lach Nachum Sicherman February 2008 Forschungsinstitut zur Zuunft der Arbeit Institute
More informationAn actuarial approach to pricing Mortgage Insurance considering simultaneously mortgage default and prepayment
An actuarial aroach to ricing Mortgage Insurance considering simultaneously mortgage default and reayment Jesús Alan Elizondo Flores Comisión Nacional Bancaria y de Valores aelizondo@cnbv.gob.mx Valeria
More informationJena Research Papers in Business and Economics
Jena Research Paers in Business and Economics A newsvendor model with service and loss constraints Werner Jammernegg und Peter Kischka 21/2008 Jenaer Schriften zur Wirtschaftswissenschaft Working and Discussion
More informationfor UK industrial and scientific companies managed by Business Marketing Online
for UK industrial and scientific comanies managed by Business Marketing Online This is a Google AdWords advertisement and so is this... and so is this......advertising with Google Adwords is now essential.
More informationThe impact of metadata implementation on webpage visibility in search engine results (Part II) q
Information Processing and Management 41 (2005) 691 715 www.elsevier.com/locate/inforoman The imact of metadata imlementation on webage visibility in search engine results (Part II) q Jin Zhang *, Alexandra
More informationWhy Plaintiffs Attorneys Use Contingent and Defense Attorneys Fixed Fee Contracts
Why Plaintiffs Attorneys Use Contingent and Defense Attorneys Fixed Fee Contracts Winand Emons 1 Claude Fluet 2 1 Department of Economics University of Bern, CEPR, CIRPEE 2 Université du Québec à Montréal,
More informationCredible Discovery, Settlement, and Negative Expected Value Suits
Credible iscovery, Settlement, and Negative Expected Value Suits Warren F. Schwartz Abraham L. Wickelgren Abstract: This paper introduces the option to conduct discovery into a model of settlement bargaining
More informationEstimating the Gains from Liberalizing Services Trade: The Case of Passenger Aviation *
Estimating the Gains from Liberalizing Services Trade: The Case of Passenger Aviation * Anca Cristea, University of Oregon avid Hummels, Purdue University & NBER Brian Roberson, Purdue University March
More informationTHE EFFECT OF SETTLEMENT IN KAPLOW S MULTISTAGE ADJUDICATION
THE EFFECT OF SETTLEMENT IN KAPLOW S MULTISTAGE ADJUDICATION Abraham L. Wickelgren Professor Louis Kaplow s article, Multistage Adjudication, presents an extremely useful framework for thinking about how
More informationProbabilistic models for mechanical properties of prestressing strands
Probabilistic models for mechanical roerties of restressing strands Luciano Jacinto a, Manuel Pia b, Luís Neves c, Luís Oliveira Santos b a Instituto Suerior de Engenharia de Lisboa, Rua Conselheiro Emídio
More informationCorporate Compliance Policy
Cororate Comliance Policy English Edition FOREWORD Dear Emloyees, The global nature of Bayer s oerations means that our activities are subject to a wide variety of statutory regulations and standards
More informationService Network Design with Asset Management: Formulations and Comparative Analyzes
Service Network Design with Asset Management: Formulations and Comarative Analyzes Jardar Andersen Teodor Gabriel Crainic Marielle Christiansen October 2007 CIRRELT200740 Service Network Design with
More informationCFRI 3,4. Zhengwei Wang PBC School of Finance, Tsinghua University, Beijing, China and SEBA, Beijing Normal University, Beijing, China
The current issue and full text archive of this journal is available at www.emeraldinsight.com/20441398.htm CFRI 3,4 322 constraints and cororate caital structure: a model Wuxiang Zhu School of Economics
More informationBeyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis
Psychological Methods 004, Vol. 9, No., 164 18 Coyright 004 by the American Psychological Association 108989X/04/$1.00 DOI: 10.1037/108989X.9..164 Beyond the F Test: Effect Size Confidence Intervals
More informationWeb Application Scalability: A ModelBased Approach
Coyright 24, Software Engineering Research and Performance Engineering Services. All rights reserved. Web Alication Scalability: A ModelBased Aroach Lloyd G. Williams, Ph.D. Software Engineering Research
More informationCapital, Systemic Risk, Insurance Prices and Regulation
Caital, Systemic Risk, Insurance Prices and Regulation Ajay Subramanian J. Mack Robinson College of Business Georgia State University asubramanian@gsu.edu Jinjing Wang J. Mack Robinson College of Business
More informationPoint Location. Preprocess a planar, polygonal subdivision for point location queries. p = (18, 11)
Point Location Prerocess a lanar, olygonal subdivision for oint location ueries. = (18, 11) Inut is a subdivision S of comlexity n, say, number of edges. uild a data structure on S so that for a uery oint
More informationOptimal pricing and capacity choice for a public service under risk of interruption
Otimal ricing and caacity choice for a ublic service under risk of interrution Fred Schroyen y Adekola Oyenuga z November 6, 2. We are grateful to Kåre Petter Hagen, Nicolas Treich and Louis Eeckhoudt
More informationLocal Connectivity Tests to Identify Wormholes in Wireless Networks
Local Connectivity Tests to Identify Wormholes in Wireless Networks Xiaomeng Ban Comuter Science Stony Brook University xban@cs.sunysb.edu Rik Sarkar Comuter Science Freie Universität Berlin sarkar@inf.fuberlin.de
More informationAn Introduction to Risk Parity Hossein Kazemi
An Introduction to Risk Parity Hossein Kazemi In the aftermath of the financial crisis, investors and asset allocators have started the usual ritual of rethinking the way they aroached asset allocation
More informationThe Changing Wage Return to an Undergraduate Education
DISCUSSION PAPER SERIES IZA DP No. 1549 The Changing Wage Return to an Undergraduate Education Nigel C. O'Leary Peter J. Sloane March 2005 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study
More informationComputational Finance The Martingale Measure and Pricing of Derivatives
1 The Martingale Measure 1 Comutational Finance The Martingale Measure and Pricing of Derivatives 1 The Martingale Measure The Martingale measure or the Risk Neutral robabilities are a fundamental concet
More informationSTATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND
STATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND Giorgio Sciascia *, Sandro Scalise *, Harald Ernst * and Rodolfo Mura + * DLR (German Aerosace Centre) Institute for Communications
More informationThe Economics of the Cloud: Price Competition and Congestion
Submitted to Oerations Research manuscrit (Please, rovide the manuscrit number!) Authors are encouraged to submit new aers to INFORMS journals by means of a style file temlate, which includes the journal
More informationApplications of Regret Theory to Asset Pricing
Alications of Regret Theory to Asset Pricing Anna Dodonova * Henry B. Tiie College of Business, University of Iowa Iowa City, Iowa 522421000 Tel.: +13193379958 Email address: annadodonova@uiowa.edu
More informationSecure Step Life Insurance gives you peace of mind and provides lifetime financial protection for your loved ones.
Secure Ste Life Insurance Alication Secure Ste Life Insurance Do you have enough life insurance? If not, you re not alone. Studies show that 93% of Americans say they need it, too. Grange makes it easy
More informationComparing Dissimilarity Measures for Symbolic Data Analysis
Comaring Dissimilarity Measures for Symbolic Data Analysis Donato MALERBA, Floriana ESPOSITO, Vincenzo GIOVIALE and Valentina TAMMA Diartimento di Informatica, University of Bari Via Orabona 4 76 Bari,
More informationReDispatch Approach for Congestion Relief in Deregulated Power Systems
ReDisatch Aroach for Congestion Relief in Deregulated ower Systems Ch. Naga Raja Kumari #1, M. Anitha 2 #1, 2 Assistant rofessor, Det. of Electrical Engineering RVR & JC College of Engineering, Guntur522019,
More informationStat 134 Fall 2011: Gambler s ruin
Stat 134 Fall 2011: Gambler s ruin Michael Lugo Setember 12, 2011 In class today I talked about the roblem of gambler s ruin but there wasn t enough time to do it roerly. I fear I may have confused some
More informationSage HRMS I Planning Guide. The HR Software Buyer s Guide and Checklist
I Planning Guide The HR Software Buyer s Guide and Checklist Table of Contents Introduction... 1 Recent Trends in HR Technology... 1 Return on Emloyee Investment Paerless HR Workflows Business Intelligence
More informationMethods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical Records
EDM Forum EDM Forum Community egems (Generating Evidence & Methods to imrove atient outcomes) Publish 122013 Methods for Estimating Kidney Disease Stage Transition Probabilities Using Electronic Medical
More informationPartialOrder Planning Algorithms todomainfeatures. Information Sciences Institute University ofwaterloo
Relating the Performance of PartialOrder Planning Algorithms todomainfeatures Craig A. Knoblock Qiang Yang Information Sciences Institute University ofwaterloo University of Southern California Comuter
More informationTHE HEBREW UNIVERSITY OF JERUSALEM
האוניברסיטה העברית בירושלים THE HEBREW UNIVERSITY OF JERUSALEM FIRM SPECIFIC AND MACRO HERDING BY PROFESSIONAL AND AMATEUR INVESTORS AND THEIR EFFECTS ON MARKET By ITZHAK VENEZIA, AMRUT NASHIKKAR, and
More informationFDA CFR PART 11 ELECTRONIC RECORDS, ELECTRONIC SIGNATURES
Document: MRM1004GAPCFR11 (0005) Page: 1 / 18 FDA CFR PART 11 ELECTRONIC RECORDS, ELECTRONIC SIGNATURES AUDIT TRAIL ECO # Version Change Descrition MATRIX 449 A Ga Analysis after adding controlled documents
More informationContingent Fees, Signaling and Settlement Authority
Contingent Fees, Signaling an Settlement Authority SHMUEL LESHEM USC Law School Conventional wisom suggests that uner contingent fee contracts, attorneys have an excessive incentive to settle the case;
More informationTOWARDS REALTIME METADATA FOR SENSORBASED NETWORKS AND GEOGRAPHIC DATABASES
TOWARDS REALTIME METADATA FOR SENSORBASED NETWORKS AND GEOGRAPHIC DATABASES C. Gutiérrez, S. Servigne, R. Laurini LIRIS, INSA Lyon, Bât. Blaise Pascal, 20 av. Albert Einstein 69621 Villeurbanne, France
More informationBUBBLES AND CRASHES. By Dilip Abreu and Markus K. Brunnermeier 1
Econometrica, Vol. 71, No. 1 (January, 23), 173 24 BUBBLES AND CRASHES By Dili Abreu and Markus K. Brunnermeier 1 We resent a model in which an asset bubble can ersist desite the resence of rational arbitrageurs.
More information