Bargaining with Heterogeneous Beliefs: A Structural Analysis of Florida Medical Malpractice Lawsuits. Abstract

Size: px
Start display at page:

Download "Bargaining with Heterogeneous Beliefs: A Structural Analysis of Florida Medical Malpractice Lawsuits. Abstract"

Transcription

1 Bargaining wih Heerogeneous Beliefs: A Srucural Analysis of Florida Medical Malpracice Lawsuis Anonio Merlo and Xun Tang 1 Deparmen of Economics Rice Universiy May 16, 2015 Absrac We propose a srucural bargaining model where players hold heerogeneous beliefs abou he nal resoluion if no selemen is reached ouside he cour. We show he disribuion of heir beliefs and he sochasic surplus are nonparamerically ideni ed from he probabiliy for reaching an selemen and he disribuion of nal ransfers beween players. We hen use a Simulaed Maximum Likelihood (SML) approach o esimae he beliefs of docors and paiens in medical malpracice lawsuis in Florida in he 1980s and 1990s. We nd srong evidence ha he beliefs for boh paries vary wih he severiy of he injury and he quali caion of he docors in he lawsuis, even hough hese characerisics are saisically insigni can in explaining wheher he cour rules in favor of he plaini or he defendan. Key words: Bargaining wih heerogeneous beliefs, nonparameric ideni caion, medical malpracice lawsuis 1 We hank paricipans a Brown, OSU and Economeric Sociey Norh America Summer Meeing 2014 for useful feedbacks. This research is funded by NSF Gran # xxxxxx. We hank Devin Reily and Michelle Tyler for capable research assisance. Errors (if any) are our own. 1

2 1 Inroducion A major heme in recen developmen of bargaining heory is o raionalize he delay in reaching an agreemen ha are prevalen in real-world bargaining episodes. (See, for example, Cho (1990), Merlo and Wilson (1995) and Yildiz (2004).) One explanaion for he delay is ha he paries involved in bargaining are oo opimisic abou heir respecive bargaining power in he absence of a common prior belief. Speci cally, consider a bilaeral bargaining episode where players could learn abou each oher s bargaining power hrough hisory of negoiaion. In he presence of opimism, a player i will decide o wai in hopes ha he oher player j will learn abou his (i s) self-perceived srong posiion and agree o his (i s) erms. As ime passes, he learning slows down, and i becomes no longer worhwhile o wai for he oher paries learning. Tha is when hey reach an agreemen. Yildiz (2004) inroduced his model and showed ha here is a deerminisic selemen dae, which is predeermined by he prior and he discoun facor of he players, such ha players will wai unil his dae o reach an agreemen. Since is inroducion, he model of bargaining wih opimism has been applied in a wide range of empirical conex, such as prerial negoiaions in medical malpracice lawsuis (Waanabe (2006)), negoiaion abou marke condiions (Thanassoulis 2010), and cross-license agreemens (Galasso (2006)). Despie he recen surge in he heory and he applicaion of bargaining wih opimism, we are no aware of any exising work which addresses he ideni caion quesion in such a model formally. Tha is, under wha condiions can he srucural elemens of he model be unambiguously recovered from he hisory of bargaining repored in he daa. One of he objecives of our paper is o ll in his gap beween heory and empirical work by inroducing a framework for he srucural esimaion of bargaining wihou a common prior. In paricular, we propose a model for bilaeral bargaining where players have opimism abou he sochasic nal oucome in case no agreemen is reached. The players have a one-ime opporuniy for reaching an agreemen a an exogenously scheduled dae during he bargaining process, and make decisions abou he selemen based on heir beliefs and ime discoun facors. We show ha all srucural elemens in his model are ideni ed nonparamerically from he probabiliy for reaching an agreemen and he disribuion of ransfer in he nal resoluion. The ideni caion sraegy does no rely on any paramerizaion of he srucural primiives such as players beliefs or he surplus disribuion. We hen propose a Simulaed Maximum Likelihood (SML) esimaor based on exible paramerizaion of he join beliefs. The model we inroduce is a simpli caion of he model of bargaining wihou a common prior in Yildiz (2004). We model a one-ime selemen opporuniy for he players o reach an agreemen. Consequenly here is no dynamic learning consideraion in players decisions, and he daes of he nal resoluion of he bargaining episodes are deermined by players opimism, heir paience and heir percepion of he surplus o be shared. 2

3 There are boh heoreical and empirical moivaion for such simpli caion and modi - caion. Firs o, in real-world bargaining episodes, daa limiaion prevens researchers from deriving robus (paramerizaion-free) argumens for he ideni caion of srucural elemens in a full- edged model of bargaining wih uncommon prior. For insance, he ideniy of proposers and he iming or he size of rejeced o ers in negoiaions are seldom repored in he daa available o researchers. By absracing away from he dynamic learning aspecs in Yildiz (2004), we adop a pragmaic approach o build a model ha is ideni able under less sringen daa requiremens and mild economeric assumpions. Despie his simpli caion, our model capures a key aspec of models wihou a common prior in ha he iming of he agreemen is deermined by he players opimism and heir paience. Thus our work provides a benchmark for undersanding wha addiional daa or economeric assumpions are needed o recover he primiives in more elaborae models of bargaining wihou common priors. Our modeling choices are also moivaed by he empirical quesion addressed in his paper: In medical malpracice lawsuis, wha do he selemen decisions by paiens and docors ell us abou heir respecive percepion of how likely he cour would rule in heir favor in case a cour hearing is necessary? The law of he Sae of Florida requires ha here should be a one-ime mandaory selemen conference beween he plaini and he defendan, which is scheduled by he couny cour someime prior o he hearing and is mediaed by cour-designaed legal professionals. Besides, unlike Yildiz (2004) where a player s bargaining power is modeled as his chance for being he proposer, we model bargaining power as a player s percepion of he probabiliy ha he will receive he favored oucome in he nal resoluion in case no agreemen is reached. This modi caion is mean o be a beer approximaion of he acual decision environmen in he legal conex. Our sraegy for idenifying his model builds on a couple of insighs: Firs o, if he lengh of ime beween he scheduled selemen conference and he cour hearing (a.k.a. he wai-ime ) were repored in he daa, we would be able o recover he disribuion of opimism by observing how he condiional selemen probabiliy varies wih he lengh of wai-ime. Second, he disribuion of he poenial surplus o be divided beween players can be recovered from he disribuion of oal compensaion awarded o he plaini by he cour decision, provided he surplus disribuion is orhogonal o he beliefs. Third, because he acceped selemen o ers re ecs a plaini s ime-discouned expecaion of his share of he oal surplus, we can idenify he disribuion of he plaini s belief condiional on selemen using he disribuion of acceped selemen o ers given he lengh of he wai-ime. This is done hrough a deconvoluion argumen using he disribuion of surplus recovered above. Las, since opimism is de ned as he sum of boh paries beliefs minus one, he objecs ideni ed from he preceding seps can be used o back ou he join disribuion of he beliefs hrough a sandard Jacobian ransformaion. 3

4 A key challenge for implemening he ideni caion sraegy in he environmen of malpracice lawsuis is ha he lengh of wai-ime is no direcly repored in he daa. In order o solve his issue of unobserved wai-ime, we ap ino a branch of recen lieraure ha uses an approach based on eigenvalue decomposiion o idenify nie mixure models or srucural models wih unobserved heerogeneiy. (See for example Hall and Zhou (2003), Hu and Schennach (2008), Kasahara and Shimosu (2009), An, Hu and Shum (2010) and Hu, McAdams and Shum (2013).) To do so, we rs exploi he insiuional deails in our environmen o group lawsuis ino smaller clusers (de ned by he couny and he monh in which a lawsui is o cially led) ha can be plausibly assumed o share he same (albei unobserved) lengh of wai-ime beween selemen conference and cour hearings. We hen use he cases in he same cluser as insrumens for each oher and apply an eigenvalue decomposiion o he join disribuion of selemen decisions and acceped o ers wihin he cluser. This allows us o recover he selemen probabiliy and he disribuion of acceped o ers condiional on he unobserved wai-ime. Then he argumens from he preceding paragraph applies o idenify he join disribuion of beliefs. The inference of docors and paiens beliefs in medical malpracice lawsuis is an ineresing empirical quesion in is own righ. In paricular, a cenral issue in he reform of U.S. healh care sysem is how o minimize he liigaion coss in medical malpracice lawsuis, which are known o consiue a large porion of he soaring insurance expenses. Knowing how selemen ouside he cour depends on paiens and docors opimism in he bargaining process could shed lighs on policy design. Using daa from medical malpracice lawsuis in Florida in he 1980s and 1990s, we nd clear evidence in our esimaes ha he beliefs of he docors and paiens vary wih observed characerisics of he lawsuis such as he severiy of he injury and he quali caion of he docors. This conrass wih he realiy ha he cour and jury decisions depend mosly on he naure and he cause of he malpracice and no so much on hese observed case characerisics (which is anoher fac revealed in our esimaes in he applicaion). Our esimaes can be used for answering fuure policy design quesions such as how he selemen probabiliy would change if he disribuion of he wai-ime is changed or some caps on pu on he poenial compensaion possible. The res of he paper is organized as follows: Secion 2 inroduces he model of bilaeral bargaining wih uncommon beliefs. Secion 3 esablishes he ideni caion of srucural elemens in he model. Secion 4 de nes he Simulaed Maximum Likelihood (SML) esimaor. Secion 5 describes he daa and he insiuional deails in he applicaion of medical malpracice lawsuis in Florida. Secion 6 presens and discusses he esimaion resuls. Proofs and a mone carlo sudy are presened in he appendices. 4

5 2 The Model Consider a lawsui following an incidence of medical malpracice involving a plaini (or paien) and a defendan (or docor). The oal amoun of poenial compensaion C is common knowledge among he plaini and he defendan. (I should be inerpreed as a sunk cos for he defendan, analogous o he money paid by he defendan for bailou.) Afer he ling of a lawsui, he plaini and he defendan are noi ed of a dae for a one-ime selemen conference, which is mandaory by he Sae Saues in Florida. The conference requires aendance by boh paries (and heir aorneys), as well as legal professionals designaed by he couny cour where he lawsui is led. Such selemen conferences ake place wihin 120 days afer he ling of he lawsui. 2 During he conference, he defendan has he opporuniy o make an selemen o er of S C o he plaini. If he plaini acceps i, hen he legal process ends wih plaini receiving S and he defendan reclaiming C S. Oherwise he case needs o go hrough a cour hearing process ha culminaes in jury decisions. Boh he defendan and he plaini are aware ha he cour hearing needs o be a leas hree weeks laer han he selemen conference; and he exac dae is deermined by he schedule and he backlogs of all judges available a he coun cour. Le T denoe he lengh of ime beween he selemen conference and he scheduled cour hearing dae. Le A 1 if a selemen is reached a he conference; and A 0 oherwise. In he laer case, a he end of he cour hearing process, he jury makes a binary decision D as o wheher he plaini ges compensaed wih he full amoun C (i.e. D = 1) or he defendan is acquied wih no compensaions o he plaini required (i.e. D = 0). The plaini and he defendan believe heir chances of winning are p and d 2 [0; 1] respecively. These beliefs are common knowledge beween he paries, bu are no repored in daa. The join suppor of beliefs is f( p ; d ) 2 (0; 1] 2 : 1 < p + d 2g. This means excessive opimism always occurs (i.e. p + d > 1 wih probabiliy 1). We mainain he following assumpion hroughou he paper. Assumpion 1 (i) ( p ; d ) and C are independen from he wai ime T ; and he disribuions of ( p ; d ) is coninuous wih posiive densiies over. (ii) Condiional on A = 0, he jury decision D is orhogonal o C and T. Assumpion 1 allows plaini s and defendans beliefs o be correlaed wih each oher and asymmeric wih di eren marginal disribuions. This is empirically relevan because he marginal disribuion of beliefs may well di er beween paiens and docors due o 2 See Secion 108 in Chaper 776 of Florida Saues Web link: hp:// www. senae. gov/ Laws/ Saues/ 2012/

6 facors such as informaional asymmeries (e.g. docors are beer informed abou he cause and severiy of he malpracice) or unobserved individual heerogeneiies. Beliefs of plaini s and defendans are also likely o be correlaed hrough unobserved heerogeneiy of he case of malpracice. For example, hey may boh observe aspecs relaed o severiy or cause of he malpracice ha are no recorded in daa. Such aspecs lead o correlaions beween paiens and plaini s beliefs from an ousider s perspecive. Assumpion 1 also accommodaes correlaion beween ( p ; d ) and C. The independence beween he wai ime T and he beliefs is a plausible condiion, because he wai ime T is mosly deermined by availabiliy of judges and juries in he couny cour during he lawsuis. This depends on he schedule and backlogs of judges, which are idiosyncraic and orhogonal o paries beliefs ( p ; d ). The orhogonaliy of C from D given T and A = 0 in condiion (ii) is also jusi ed. On he one hand, C is a moneary measure of he magniude of he damage in iced on he plaini regardless of is cause; on he oher hand, D capures he jury s judgemen abou he cause of damage based on cour hearings. I is likely ha he jury decision is correlaed wih speci c feaures of he lawsui ha are repored in daa and ha may also a ec he beliefs of boh paries. Neverheless, once condiional on such observable feaures, jury decisions are mos likely o be orhogonal o measure of damage capured by C. A he end of his secion, we discuss how o exend our model o accoun for heerogeneiies across lawsuis repored in daa. We now summarize how he disribuions ha are direcly ideni able from daa are linked o model primiives under he assumpion ha boh paries follow raional sraegies. A he selemen conference, he plaini acceps an o er if and only if S T p C, where is a consan ime discoun facor xed hroughou he daa-generaing process and available in daa. The defendan o ers he plaini S = T p C if he remainder of he poenial compensaion C S exceeds T d C. Hence a selemen occurs during he conference if and only if: C T p C T d C, d + p T. The resuled disribuion of selemens, condiional on he wai ime beween he selemen conference and scheduled cour hearing being T =, is: Pr (S s j A = 1; T = ) = Pr p C s j d + p. (1) where lower cases denoe realized values for random variables; and he equaliy follows from par (i) in Assumpion 1. Besides, he disribuion of poenial compensaion, condiional on he absence of selemen in he conference T = periods ahead of he cour hearing and condiional on he jury ruling in favor of he plaini, is: Pr(C c j A = 0; D = 1; T = ) = Pr(C c j d + p > ) (2) 6

7 where he equaliy follows from boh condiions in Assumpion 1. In pracice, he daa repors di erences in he characerisics of plaini s and defendans, such as he professional quali caion of he defendan or he demographics of he plaini. Besides, he daa also repors feaures relaed o he cause and he severiy of malpracice in quesion. Such informaion available in daa (denoed by a vecor X) are correlaed wih oal compensaion C and beliefs ( p ; d ). The simplisic model above can incorporae such observed case heerogeneiies by leing he primiives (i.e. disribuions of beliefs ( p ; d ), compensaions C, jury decisions D and he wai-ime T ) depend on X. If boh resricions in Assumpion 1 hold condiional on X, hen raional sraegies are characerized in he same way as (1) and (2) excep ha all disribuions needs o be condiioned on X. More imporanly, he ideni caion sraegy proposed in Secion 3 below are applicable when daa repors heerogeneiies across lawsuis. Formally, he resuls in Secion 3 (Lemma 1 and Proposiion 1) hold afer condiioning on X, provided he idenifying condiions (Assumpions 2, 3, 4 and 5) are formulaed as condiional on X. Noneheless, in order o simplify exposiion of he main idea for ideni caion, we choose o suppress dependence on observable case characerisics in Secion 3, and only incorporae hem explicily laer in he esimaion secion. 3 Ideni caion This secion shows how o recover he disribuion of boh paries beliefs from he probabiliy for reaching selemens and he disribuion of acceped selemen o ers. We consider an empirical environmen where for each lawsui he daa repors wheher a selemen occurs during he mandaory conference (A). For cases seled a he conference, he daa repors he amoun paid by he defendan o he plaini (S). For he oher cases ha underwen cour hearings, he daa repors jury decisions (D) and, if he cour rules in favor of he plaini, he amoun of oal compensaions paid by he defendan (C). However, exac daes of selemen conferences and scheduled daes for cour hearings (if necessary) are never repored in daa. 3 Thus he wai-ime T beween selemen conference and scheduled cour hearings, which is known o boh paries a he conference, is no available in daa. 3 For example, he daa we use in Secion 5 repors Daes of Final Disposiion for each case. However, for cases seled ouside he cour, hese daes are de ned no as he exac dae of he selemen conference, bu as he day when all o cial adminisraive paperwork are concluded. There is a subsanial lengh of ime beween he wo. For insance, for a large proporion of cases ha are caegorized as Seled wihin 90 days of he ling of lawsuis, he repored daes of nal disposiion are acually more han 150 days afer he iniial ling. Similar issues also exis for cases ha underwen cour hearings in ha he repored daes of nal disposiion are no idenical o he acual dae of cour hearings. 7

8 To address his issue wih unrepored wai-ime, we propose sequenial argumens ha exploi an implici panel srucure of he daa in he curren conex. In paricular, we noe ha lawsuis led wih he same couny cour during he same period (week) pracically share he same wai-ime T. The reason for such a paern is as follows: Firs, he daes for selemen conferences are mosly deermined by availabiliy of auhorized legal professionals a liaed wih he coun cour, and are assigned on a rs-come, rs served basis. Thus selemen conferences for cases led wih he same couny cour a he same ime are pracically scheduled for he period. Besides, he daes for poenial cour hearing are deermined by he schedule and backlog of judges a he couny cour. Hence cases led wih he same couny cour simulaneously can be expeced o be handled in cour in he same period in he fuure. This allows us o e ecively group lawsuis ino clusers wih he same T, despie unobservabiliy of T in daa. We formalize his implici panel srucure as follows. Assumpion 2 Researchers have su cien informaion o divide he daa ino clusers, each of which consiss of a leas hree lawsuis sharing he same wai-ime T. Across he cases wihin he same cluser, he beliefs ( p ; d ), he oal compensaion C and he poenial jury decision D (if necessary) are independen draws from he same disribuion. This implici panel srucure in our daa allows us o use acceped selemen o ers in he lawsuis wihin he same cluser as insrumens for each oher, and apply eigendecomposiion-based argumens in Hu and Schennach (2008) o recover he join selemen probabiliy and disribuions of acceped selemen o ers condiional on he unobserved T. We hen use hese quaniies o back ou he join disribuion of beliefs using exogenous variaions in T. For he res of his secion, we rs presen argumens for he case where T is discree (i.e. jt j < 1). A he end of his secion, we explain how o generalize hem for ideni caion when T is coninuously disribued. 3.1 Condiional disribuion of selemen o ers An inermediae sep for idenifying he join disribuion of beliefs is o recover he condiional selemen probabiliy and he disribuion of selemen o ers given he waiime before cour hearings T. Le S; T denoe he uncondiional suppors of S; T respecively. Assumpion 3 (i) The suppor of T is nie (jt j < 1) wih a known cardinaliy and inff : 2 T g 1=2. (ii) Given any ( p ; d ), he poenial compensaion C is coninuously disribued wih posiive densiy over a conneced suppor [0; c]. 8

9 We focus on he model wih nie T wih known cardinaliy because of is empirical relevance. Wihou loss of generaliy, denoe elemens in T by f1; 2; :; jt jg. Condiion (i) also rules ou unlikely cases where a cour hearing is scheduled so far in he fuure or he one-period discoun facor is so low ha he compounded discoun facor is less han one half. Condiion (i), ogeher wih he non-increasingness of E[A i j T = ] over 2 T due o Assumpion 1, pin down he index for eigenvalues and eigenvecors in he aforemenioned decomposiion. Par (ii) in Assumpion 3 is a mild condiion on he condiional suppor of poenial compensaion. A su cien condiion for his is ha C is orhogonal from ( p ; d ) wih a bounded suppor. 4 resul below. The role of par (ii) will become clear as we discuss he ideni caion Lemma 1 Under Assumpions 1, 2 and 3, E (A j T = ) and f S (s j A = 1; T = ) are joinly ideni ed for all and s. This inermediae resul uses argumens similar o ha in Hu, McAdams and Shum (2013) for idenifying rs-price sealed-bid aucions wih non-separable aucion heerogeneiies. I explois he panel srucure of he daa and he condiional independence of beliefs across lawsuis in Assumpion 2. These condiions allow us o break down he join disribuion of he incidence of selemen and he size of acceped selemen o ers across muliple lawsuis wihin one cluser ino he composiion of hree linear operaors. More speci cally, le f R1 (r 1, R 2 = r 2 j :) be a PrfR 1 ~r, R 2 = r 2 j :gj ~r=r1 for any discree random vecor R 2 and coninuous random vecor R 1. For any hree lawsuis i; j; k sharing he same wai-ime T, le A i;k = 1 be a shorhand for A i = A k = 1. By consrucion, f Si ;S k (s; s 0 ; A j = 1 j A i;k = 1) = P f Si (s j S k = s 0 ; A j = 1; T = ; A i;k = 1)E[A j j S k = s 0 ; T = ; A i;k = 1]f T;Sk (; s 0 j A i;k = 1) 2T = P 2T f Si (s j A i = 1; T = )E[A j j T = ]f T;Sk (; s 0 j A i;k = 1). (3) The second equaliies follow from Assumpion 1; from S = T p C whenever A = 1 and A = 1 if and only if p + d T ; and from he fac ha beliefs ( p ; d ) and poenial compensaion C are independen draws across he lawsuis i; j; k according o Assumpion 2. To illusrae he ideni caion argumen, i is useful o adop marix noaions. Le D M denoe a pariion of he uncondiional suppor of acceped selemen o ers S ino 4 I is worh noing ha our ideni caion argumen remains valid even wih c being unbounded, as long as he full-rank condiion in Lemma A1 holds for some pariions of S. 9

10 M inervals. Each of he inervals has a non-degenerae inerior and is denoed by d m. 5 For a given pariion D M, le L Si ;S k probabiliy ha S i 2 d m and S k 2 d m 0 be a M-by-M marix whose (m; m 0 )-h enry is he condiional on A i;k = 1 (selemens are reached in cases i and k); and le Si ;S k be a M-by-M marix wih is (m; m 0 )-h enry being f(s i 2 d m ; A j = 1; S k 2 d m 0 j A i;k = 1). Noe ha boh Si ;S k and L Si ;S k are direcly ideni able from daa. Thus a discreized version of (3) is : Si ;S k = L Si jt j L T;Sk (4) where L Si jt be a M-by-jT j marix wih (m; )-h enry being Pr(S i 2 d m j A i = 1; T = ); j be a jt j-by-jt j diagonal marix wih diagonal enries being [E(A j j T = )] =1;:;jT j ; and L T;Sk be a jt j-by-m marices wih is (; m)-h enry being Pr (T = ; S k 2 d m j A i;k = 1). Besides, due o condiional independence in Assumpion 2. L Si ;S k = L Si jt L T;Sk (5) Par (ii) in Assumpion 3 implies he supreme of he condiional suppor of acceped o ers given T = is c and hence decreases in. This, in urn, guaranees here exiss a pariion D jt j such ha L Si jt as well as L Si ;S k are non-singular (as proved in Lemma A1 in Appendix B). Then (4) and (5) imply Si ;S k (L Si ;S k ) 1 = L Si jt j L Si jt 1 (6) where he L.H.S. consiss of direcly ideni able quaniies. The R.H.S. of (6) akes he form of an eigen-decomposiion of a square marix, which is unique up o a scale normalizaion and unknown indexing of he columns in L Si jt and diagonal enries in j (i.e. i remains o pin down a speci c value of 2 T for each diagonal enry in j ). The scale in he eigen-decomposiion is implicily xed because he eigenvecors in L Si jt are condiional disribuions and needs o sum up o one. The quesion of unknown indices is solved because in our model E[A j j T = ] is monoonically decreasing in over T provided he paries follow raional sraegies described in Secion 2. This is again due o he independence beween iming and he beliefs in Assumpion 1 and he moderae compounded discouning in Assumpion 3. This esablishes he ideni caion of j and L Si jt, which are used for recovering L T;Sk and hen he condiional densiy of acceped selemen o ers over is full suppor (see proof of Lemma 1 in Appendix B). 3.2 The join belief disribuion We now explain how o idenify he join disribuion of beliefs ( p ; d ) from he quaniies recovered from Lemma 1 under he following orhogonaliy condiion. 5 Tha is, d m [s m ; s m+1 ] for 1 m M, wih (s m : 2 m M) being a vecor of ordered endpoins on S such ha s 1 < s 2 < :: < s M < s M+1 and s 1 inf S, s M+1 sup S. 10

11 Assumpion 4 The join disribuion of beliefs ( p ; d ) is independen from poenial compensaions C. This condiion requires he magniude of poenial compensaion o be independen from plaini and defendans beliefs. This condiion is plausible because C is mean o capure an objecive moneary measure of he severiy of damage in iced upon he paien. On he oher hand, he beliefs ( p ; d ) should depend on he evidence available as o wheher he defendan s neglec is he main cause of such damage. I hen follows from (2) ha he disribuion of C is direcly ideni ed as: Pr(C c) = Pr(C c j A = 0; D = 1). (7) Le S [0; c ] denoe he condiional suppor of acceped selemen o ers S = T p C given A = 1 and T = ; 6 and le ' (s) denoe he probabiliy ha a selemen is reached when he lengh of wai-ime beween he selemen conference and he dae for cour hearing is and ha he acceped selemen o er is no greaer han s. Tha is, for all (s; ), ' (s) Pr (S s; A = 1 j T = ) = Pr p C s= ; d + p 1= (8) where he equaliy is due o Assumpion 1. The non-negaiviy of C and ( p ; d ) and an applicaion of he law of oal probabiliy on he righ-hand side of (8) implies: ' (s) = Z c 0 1 Pr c p s 1 ; f(c)dc = d + p Z c 0 h (c=s) f C (c)dc (9) where f C (c) is he densiy of C and h (v) Prfp 1 v ; ( d + p ) 1 g; and he rs equaliy is due o orhogonaliy beween C and ( p ; d ). Changing variables beween C and V C=S for any xed and s, we can wrie (9) as: ' (s) = Z 1 0 h (v)(v; s)dv (10) where (v; s) sf C (vs)1fv c=sg. Wih he disribuion (and hence densiy) of C recovered from (7), he kernel funcion (v; s) is considered known for all (v; s) hereinafer for ideni caion purposes. Also noe for any s > 0, (:; s) is a well-de ned condiional densiy wih suppor [0; c=s]. 7 Le F V ja=1;t = denoe he disribuion of V given T = and A = 1 (or equivalenly d + p T ), whose suppor is denoed as V. Assumpion 5 For any and g(:) such ha E[g(V ) j A = 1; T = ] < 1, he saemen R 1 0 g(v)(v; s) = 0 for all s 2 S implies he saemen g(v) = 0 a.e. F V ja=1;t =. 6 In general, we could also allow suppors S;T and S o depend on observed heerogeneiies of lawsuis as well. Noneheless, hroughou his secion, we refrain from such generalizaion in order o simplify exposiion. 7 This is because (v; s) > 0 for any v 0, s > 0. Besides R 1 (v; s)dv = R c=s sf 0 0 C (vs)dv = 1 for any s. 11

12 This condiion, known as he compleeness of kernels in inegral operaors, was inroduced in Lehmann (1986) and used in Newey and Powell (2003) for ideni caion of nonparameric regressions wih insrumenal variables. Andrews (2011) and Hu and Shiu (2012) derived su cien condiions for various versions of such compleeness condiions when g(:) is resriced o belong o di erence classes. This condiion is analogous o a full-rank condiion on if he condiional suppors of S and V were nie. 8 Proposiion 1 Under Assumpions 1-5, Pr( p ; p + d ) is ideni ed for all 2 (0; 1] and 2 T. For he res of his secion, we discuss how o generalize resuls above when T is in nie (T is coninuously disribued over a known inerval). Firs o, he key idea of using eigendecomposiions in Secion 3.1 remains applicable, excep ha L Si jt and L T;Sk become linear inegral operaors, and heir inveribiliy needs o be saed as an assumpion as opposed o being derived from resricions on model primiives and implicaions of raional sraegies (as is he case when T is discree). Under he suppor condiion ha inff : 2 T g 1=2, he eigenvalues in he decomposiion E[A j j T = ] remains sricly monoonic over he inerval suppor T when T is coninuously disribued. On he oher hand, he argumen ha uses monooniciy of he eigenvalues over a nie suppor T o index hem is no longer applicable when T is coninuously disribued. However, raional sraegies in our model imply he supremum of he suppor of acceped selemen o ers given T = mus be c. Wih he supremum of he suppor of compensaions c ideni ed and known, his means can be expressed hrough a known funcional of he eigenvecors f Si (: j A i = 1; T = ) in he eigen-decomposiion ideni ed in he rs sep. Thus he issue wih indexing eigenvalues is also solved. The remaining sep of idenifying he join disribuion of ( p ; p + d ) from f S (: j A = 1; T = ) and E[A j T = ] follow from he same argumen above. I is worhy of noe ha an addiional sep based on Jacobian ransformaion leads o ideni caion of he join disribuion of ( p ; d ) when T is coninuously disribued. 8 If he suppor of poenial compensaion is unbounded, here are pleny of examples of parameric families of densiies ha saisfy he compleeness condiions. For example, suppose poenial compensaions follow a Gamma disribuion wih parameers ; > 0. Tha is, f C () = () 1 expf g. Then, wih s > 0, he kernel (v; s) sf C (vs) = [s] () v 1 expf v (s)g is a densiy of a Gamma disribuion wih a shape parameer > 0 and a scale parameer s > 0. Tha is, (v; s) remains a condiional densiy wihin he exponenial family, and sais es he su cien condiions for he compleeness condiion in Theorem 2.2 in Newey and Powell (2003). 12

13 4 Simulaed Maximum Likelihood Esimaion Our ideni caion resuls in Secion 3 lay he foundaion for nonparameric esimaion of he belief disribuion. However, a nonparameric esimaor based on hose argumens would require a large daa se, and he curse of dimensionaliy aggravaes if he daa also repor case-level variables ha may a ec boh paries beliefs (such as he severiy of injury in iced upon he plaini and he quali caion of he defendan) and herefore should be condiioned on in esimaion. To deal wih case-heerogeneiies in moderae-sized daa, we propose in his secion a Maximum Simulaed Likelihood esimaor based on a exible paramerizaion of he join belief disribuion. Consider a panel-srucure daa conain N clusers. Each cluser is indexed by n and consiss of m n 1 cases, each of which is indexed by i = 1; :::; m n. For each case i in cluser n, le A n;i = 1 when here is an agreemen for selemen ouside he cour and A n;i = 0 oherwise. De ne Z n;i S n;i if A n;i = 1; Z n;i C n;i if A n;i = 0 and D n;i = 1; and Z n;i 0 oherwise. Le T n denoe he wai-ime beween he selemen conference and he scheduled dae for cour decisions. We propose a Maximum Simulaed Likelihood esimaor for he join beliefs ( p ; d ) ha also explois variaion in he heerogeneiy of lawsuis repored in he daa. Throughou his secion, we assume he idenifying condiions also hold once condiional on such observed heerogeneiy of he lawsuis. Le x n;i denoe he vecor of case-level variables repored in he daa ha a ecs he disribuion of C. (We allow x n;i o conain a consan in he esimaion below.) These include he age, severiy, and couny average/median income (as well as heir ineracion erms). The oal poenial compensaion C in a lawsui wih observed feaures x n;i is drawn from an exponenial disribuion wih he rae parameer given by: (x n;i ; ) expfx n;i g for some unknown consan vecor of parameers. In he rs sep, we pool all observaions where he jury is observed rule in favor of he plaini o esimae : P ^ arg max n;i d n;i(1 a n;i ) [x n;i expfx n;i gc n;i ]. Nex, le w n;i denoe he vecor of case-level variables in he daa ha a ecs he join belief disribuion. (The wo vecors x n;i and w n;i are allowed o have overlapping elemens.) We suppress he subscrips n; i for simpliciy when here is no confusion. In he second sep, we esimae he belief disribuion condiional on such a vecor of case-level variables W using ^ above as an inpu in he likelihood. To do so, we adop a exible paramerizaion of he join disribuion of ( p ; d ) condiional on W as follows. For each realized w, le (Y 1 ; Y 2 ; 1 Y 1 Y 2 ) be drawn from a Dirichle disribuion wih concenraion parameers j expfw j g for j = 1; 2; 3 for some consan vecor ( 1 ; 2 ; 3 ). In wha follows, we suppress he dependence of j on w o simplify he noaion. 13

14 Le p = 1 Y 1 and d = Y 1 + Y 2. The suppor of ( p ; d ) is f(; 0 ) 2 [0; 1] 2 : g, which is consisen wih our model wih opimism. (Table C1 and Figure C1 in Appendix C show how exible such a speci caion of he join disribuion of ( p ; d ) is in erms of he range of momens and he locaion of he model i allows.) Also noe Y 2 = p + d 1 by consrucion, so i can be inerpreed as a measure of opimism. Under his speci caion, he marginal disribuion of Y 1 condiional on W = w is Bea( 1 ; ), where of course j s are funcions of w. The condiional disribuion Y 2 j Y 1 = ; W = w is he same as he disribuion of (1 )Bea( 2 ; 3 ). For any y and 2 (0; 1), we can wrie: Y2 PrfY 2 y j Y 1 = ; W = wg = Pr 1 y 1 Y 1 = ; W = w where he righ-hand side is he c.d.f. of a Bea( 2 ; 3 ) evaluaed a y=(1 Le q n;i Pr(D n;i = 1 j A n;i = 0; W n;i = w n;i ). Recall ha we mainain D is orhogonal o (T; C) once condiional on A = 0 and W. Hence q n;i does no depend on c n;i. This condiional probabiliy is direcly ideni able from he daa. Le h n (; ) denoe densiy of he wai-ime T n a T n = in cluser n. This densiy may depend on cluser-level variables repored in he daa, and is speci ed up o an unknown vecor of parameers. The log-likelihood of our model is: L N (; ; ) P N n=1 ln P 2T h n(; ) Q m n i=1 f n;i(; ; ) where f n;i (; ; ) is shorhand for he condiional densiy of Z n;i ; A n;i ; D n;i given T n =, W n;i = w n;i and wih parameer, evaluaed a (z n;i ; a n;i ; d n;i ). Speci cally, where f n;i (; ; ) [g 1;n;i (; ; )] a n;i fg 0;n;i (; ) [1 p n;i (; )] q n;i g (1 a n;i)d n;i f[1 p n;i (; )] (1 q n;i )g (1 a n;i)(1 d n;i ) p n;i (; ) Pr(A n;i = 1 j T n = ; W n;i = w n;i ; ) = Pr( p;n;i + d;n;i j w n;i ; ) = Pr(Y 2 1 = j w n;i ; ); g 0;n;i (; ) g 0 (z n;i ; x n;i ; ; Pr(C n;izja n;i =0;T n=;x n;i =x n;i ). = f C (z n;i j x n;i ;(11) ); Z=zn;i wih f C (: j x n;i ; ) being he condiional densiy of he poenial compensaion given X n;i = x n;i ; and g 1;n;i (; ; ) g 1 (z n;i ; w n;i ; x n;i ; ; ; Pr(S n;iz;a n;i =1jT n=;w n;i ;x n;i Z 0 Pr Y 1 1 Z=(c ); Y 2 1 wn;i ; 14 Z=zn;i f C (c j x n;i ; )dc (12). Z=zn;i

15 In he derivaions above, we have used he condiional independence beween C n;i and D n;i ; T n ; ( p;n;i ; d;n;i ) condiional on W n;i ; X n;i. Under mild regulariy condiions, he order of inegraion and di ereniaion in (12) can be exchanged. Tha is, g 1;n;i (; ; ) equals: Z 1 z n;i n Pr Y 2 1 Y1 = 1 z n;i =c; w n;i ; o f Y1 (1 z n;i =c j w n;i ; ) f C(c j x n;i ; ) c dc where he lower limi is z n;i because he inegrand is nonzero only when 1 z n;i =c 2 (0; 1), c 2 ( z n;i ; +1).Changing variables beween c and 1 z n;i =c for any i; n and xed, we can wrie g 1;n;i (; ; ) as: Z 1 0 Y2 Pr 1 1 (1 ) Y 1 = ; w n;i ; fy1 ( j w n;i ; )f C zn;i (1 (1 ) j x ) n;i; d 1 where he rs condiional probabiliy in he inegrand is a Bea c.d.f. evaluaed a (1 ) and parameers ( 2 (w n;i ; 2 ); 3 (w n;i ; 3 )) and he second erm f Y1 ( j w n;i ; ) is he Bea p.d.f. wih parameers ( 1 (w n;i ); 2 (w n;i ) + 3 (w n;i )). For each n, i, and a xed vecor of parameers (; ), le ^g 1;n;i (; ; ) be an esimaor for g 1;n;i (; ; ) using S > N simulaed draws of. (We experimen wih various forms of densiy for simulaed draws.) I follows from he Law of Large Numbers ha ^g 1;n;i (; ; ) is an unbiased esimaor for each n; i and (; ). sep is Our Maximum Simulaed Likelihood Esimaor for he belief parameers in he second (^; ^) arg max ; ^L N (; ; ^). (13) where ^L N (; ; ) is an esimaor for L N (; ; ) by replacing g 1;n;i (; ; ) wih ^g 1;n;i (; ; ) and replacing q n;i wih a parameric (logi or probi) esimae ^q n;i ; and ^ is he esimaes for he parameers in he disribuion of poenial compensaion in he rs sep. Under regulariy condiions, (^; ^) converge a a p N-rae o a zero-mean mulivariae normal disribuion wih some nie covariance as long as N! 1, S! 1 and p N=S! 1. The covariance marix can be consisenly esimaed using he analog principle, which involves he use of simulaed observaions. (See equaion (12.21) in Cameron and Trivedi (2005) for a deailed formula.) 5 Daa Descripion Since 1975 he Sae of Florida has required all medical malpracice insurers o le repors on heir resolved claims o he Florida Deparmen of Financial Services. Using his source, we consruc a sample ha consiss of 13,351 lawsuis led in Florida beween 1984 and Sieg (2000) and Waanabe (2009) also used he same source of daa. Our sample includes 15

16 he cases ha are eiher resolved hrough he mandaory selemen conference or by a jury decision ha followed he cour proceedings. For each lawsui, he daa repors he dae when i is led (Sui_Dae) and he couny cour wih which i is led (Couny_Code), he dae of he nal disposiion (Year_of_Disp) (when he claim was closed wih he insurer), and wheher he case is resolved hrough a selemen conference or by a jury decision in cour (A=1 if seled ouside he cour). The daa also repors he size of he ransfer from he defendan o he plaini upon he resoluion of he lawsui. This equals he amoun of acceped o er o he plaini (S) if a selemen is reached ouside he cour, or he oal compensaion awarded o he plaini according o he cour decision (C ) oherwise. In addiion we also observe case-level variables ha may be relevan o he disribuion of he join belief or ha of he poenial compensaion. These include he severiy of he injury due o negligence (Severiy), he age (Age) and gender of paiens and wheher he docors responsible are board-ceri ed (Board_Code). (Tha is, Board_Code = 1 if he docor is ceri ed by a leas one professional board and = 0 oherwise.) For he lawsuis seled ouside he cour, he daes for selemen conferences are no repored in he daa. The scheduled daes for cour hearings are no repored for he cases resolved by cour decisions eiher. Furhermore, he recorded daes for he nal disposiion only reveal when he claim is closed wih he insurer, which are ypically laer han he acual daes when an agreemen is reached in a selemen conference or when a decision is made by he judge in he cour. Therefore, he lenghs of he ime beween scheduled cour hearings and he selemen conferences are no direcly measured in he daa. Despie hese daa limiaions, we de ne clusers wihin which he cases could be reasonably assumed o share he same lengh of wai-ime. I is plausible ha he lawsuis led wih he same couny cour in he same monh would be scheduled for cour proceedings in he same monh. This is of course because he schedule for hearings in a couny cour is mosly deermined by he backlog of unresolved cases led wih ha cour, and by he availabiliy of judges and oher legal professional from he cour. By he same oken, he schedule for selemen conferences, which require he presence of cour o cials who have auhoriy o coordinae a selemen, are also mosly deermined by he backlog cases as well as he availabiliy of aorney represening boh paries. Due o hese empirical consideraions, we mainain ha he wai-ime beween selemen conferences and cour hearings are idenical for he cases led wih he same couny in he same monhs. As explained in Secion 3, he disribuion of selemen decisions and acceped o ers in lawsuis from hese clusers are su cien for recovering he join beliefs of plaini s and defendans. The daa consiss of 3,545 clusers de ned by monh-couny pairs. In oal here are 1,344 clusers which repor a leas hree medical malpracice lawsuis. Abou half of hese clusers (661 clusers) conain a leas six cases. Besides, among hese 1,344 clusers, 1,294 have a leas wo lawsuis ha were seled ouside he cour due o he mandaory conference. 16

17 These numbers con rm ha we can apply our ideni caion sraegy from Secion 3 o recover he join disribuion of paiens and docors beliefs. I is worh noing ha in our SML esimaion he likelihood includes all 3,545 clusers o improve he e ciency of he esimaor, even hough in heory ideni caion only requires he join disribuion of selemen decisions and acceped o ers from he subse of clusers ha have a leas wo selemens ou of hree or more cases. Table 1(a): Selemen probabiliy and acceped o ers Board Cer n Severiy # obs ^p sele s:e:(^p sele ) ^ SjA=1 ($1k) s:e:(^ SjA=1 ) ($1k) ceri ed low 1, medium 2, high 2, unceri ed low 1, medium 2, high 2, Nex, we repor some evidence from he daa ha he belief of he plaini s and he defendans are a eced by cerain observed characerisics in he lawsuis. Table 1(a) summarizes he selemen probabiliy and he average size of acceped o ers in he sample afer conrolling for he docors quali caion and he level of severiy. There is evidence ha boh he selemen probabiliy and he size of acceped selemen o ers di er sysemaically across he sub-groups. Table 1(b) repors he p-values of wo-sided -ess (using he unequal variance formula) for he equaliy of selemen probabiliies in sub-groups. We le (u,c) and (l,m,h) be shorhand for he realized values of (unceri ed, ceri ed) in Board_code and (low, medium, high) in Severiy respecively. Wih he excepion of hree pair-wise ess, he nulls in he oher ess are all rejeced a he 1% signi cance level. Among he hree excepions, he null for equal selemen probabiliy beween (u,l) and (u,h) is also rejeced a he 10% level. The only wo cases where he null can no be rejeced even a he 10% signi cance level are (u,l) versus (c,m) and (u,l) versus (c,h). This is somewha consisen wih he inuiion ha a plaini may end o be more opimisic ha he jury would rule in his favor when he injury in iced is more severe, or when he docor s quali caion is no suppored by board ceri caion. Our esimaes in he nex secion are also consisen wih his inuiion. The failure o rejec he null of equal selemen probabiliy beween he wo subgroups (u,l) and (c,h) for example may be due o he fac ha he impacs of severiy and of board ceri caion on he plaini s belief o se each oher. Pairwise -ess for he equaliy of 17

18 average acceped selemen o ers beween he sub-groups de ned severiy and docor quali caion also demonsrae similar paerns. Speci cally, he null of equal average selemen o ers is almos always rejeced a he 1% signi cance level for all pair-wise -ess using unequal variances, wih he only excepion being he ess comparing (u,l) versus (c,l). Table 1(b): p-values for -ess: selemen probabiliy u,l u,m u,h c,l c,m c,h u,l < < < u,m < < u,h < < < c,l < < c,m c,h The daa also conain some evidence ha he disribuion of oal compensaion may be parly deermined by he age of he plaini and he severiy of he injury. Ou of he oal 2,298 lawsuis which were no resolved hrough selemen, 359 were ruled in favor of he plaini by he cour. The observaions of he realized oal compensaion in hese cases are useful for inference of he disribuion of C. Figure 1(a) and 1(b) in Appendix A repor hisograms of he acceped o ers (S) from he cases seled ouside he cour and he oal compensaion (C ) from he cases where he cour ruled in favor of he plaini, condiioning on he informaion abou he plaini s. The variable Age is discreized ino hree caegories: young (Age < 33), older (Age > 54) and middle, wih he cuo s being he 33rd and he 66h perceniles in he daa. Figure 1(a) suggess he younger plaini s end o receive higher ransfers eiher hrough acceped o ers in selemen or hrough he oal compensaion paid by he defendan when he cour rules in favor of he plaini. Figure 1(b) shows he cases wih more severe injuries in general are associaed wih higher ransfers. Boh paerns are inuiive, and consisen wih our esimaes in he nex secion. To furher compare he disribuion of he acceped o ers wih ha of he oal compensaion ruled by he cour, we compare he perceniles of boh variables condiional on Age and Severiy. We nd ha he 10h, 25h, 50h, 75h and 90h condiional perceniles of he acceped o ers are consisenly lower han hose of he oal compensaion ruled by he cour. This is consisen wih he noion ha he acceped selemen o ers are he discouned expecaion of he oal compensaion o be ruled by he cour. The quali caion of he docors does no seem o have any noiceable e ec on he disribuion of he oal compensaion. Figure 1(c) repors he hisogram of he oal compensaion 18

19 for he cases where he cour ruled in favor of he plaini, condiioning on he board ceri caion of he docors. A -es for he equaliy of he average compensaion for he wo subgroups wih and wihou board ceri caion repors an asympoic p-value of (assuming unequal populaion variance). Besides, a one-sided Komolgorov-Simirnov es agains he alernaive ha he disribuion of C is sochasically lower when he defendan is board-ceri ed yields a es saisic of and an asympoic p-value of Thus in eiher es he null can no be rejeced even a he 15% signi cance level. On he oher hand, i is reasonable o posulae ha he oal poenial compensaion in a malpracice lawsui is posiively correlaed wih he conemporary income level in he couny where he lawsui is led. In order o conrol for such an income e ec, we collec daa on household income in all counies in Florida beween 1981 and We rs collec he daa on he median household income in each Florida couny in 1989, 93, 95, 97, 98 and 99 from he Small Area Income and Povery Esimaes (SAIPE) produced by he U.S. Census Bureau. 9 We also collec a ime series of sae-wide median household income in Florida each year beween 1984 and 1999 from U.S. Census Bureau s he Curren Populaion Survey. We hen combine his laer sae-wide informaion wih he couny-level informaion from SAIPE o exrapolae he median household income in each Florida couny in he years , 92, 94 and We hen incorporae his yearly daa on household income in each couny while esimaing he disribuion of oal compensaion nex year. 6 Esimaion Resuls As he rs sep in esimaion, we use a logi regression o he cour decisions in hose lawsuis ha are resolved hrough cour hearings. The goal is o provide some evidence abou wheher he jury decisions were a eced by case characerisics repored in he daa. Besides, he prediced probabiliy for D = 1 (he jury ruled in favor of he plaini ) from he logi regression will be used in he SML esimaion of he join beliefs of docors and paiens. 9 See hp://www.census.gov/did/www/saipe/daa/saecouny/daa/index.hml 10 The exrapolaion is done based on a mild assumpion ha a couny s growh rae relaive o he saewide growh rae remains seady in adjacen years. For example, if he raio beween he growh rae in Couny A beween 1993 and 1995 and he conemporary sae-wide growh rae is, hen we mainain he yearly growh raes in Couny A in (and ) are boh equal o p imes he sae-wide growh raes in (and respecively). Wih he yearly growh rae in Couny A beeen calculaed, we hen exrapolae he median household income in Couny A in 1994 using he daa from he SAIPE source. 19

20 Table 2. Logi Esimaes for Cour Decisions 11 (Response Variable: D. Toal # of observaions: 2,289 cases.) (1) (2) (3) Board_Code (0.120) (0.282) (0.288) Severiy ** (0.023) (0.033) (0.056) Age (0.003) (0.003) 0.021* (0.012) SeveriyBoard_Code (0.046) (0.046) Age (0.011) SeveriyAge (0.011) Consan *** (0.189) *** (0.228) *** (0.391) Log likelihood Pseudo-R p-value for L.R.T Noes: Sandard errors are repored in parenheses. (*** signi can a 1%; ** sig. a 5%; * sig. a 10%).Age 2 is repored in unis of 100 yr 2. Table 2 repors he logi regression esimaes under di eren speci caions, using 2,289 lawsuis from he daa ha were no seled ouside he cour and hus had o be resolved hrough scheduled cour hearings. The case heerogeneiy used in he logi regressions include Board_Code, Severiy and he age of he paiens Age. In all hree logi regressions, he consan erm is highly saisically signi can a he 1% level. The severiy is saisically insigni can in he laer wo speci caions. Besides, he age of he paien is only signi can a 10% level in he hird speci caion. The board ceri caion of docors and he ineracion erms in he logi regressions are all insigni can. The pseudo R-squares are low for all hree speci caions. This suggess ha he paien and case characerisics considered are raher insigni can in explaining he cour decisions. Furhermore he p-values for he likelihood raio ess of he join signi cance of all slope coe ciens are 0:1676, 0:2533 and 0:2557 in he hree speci caions respecively. Therefore we conclude from Table 2 ha he docor s board ceri caion, he severiy of he malpracice and he age of he plaini do no have signi can impac on jury decisions in he cour. Nex, we esimae he disribuion of oal poenial compensaion using a subse of he observaions of lawsuis above where he cour ruled in favor of he plaini s (A = 0 and D = 1). The descripive saisics in Secion 5 show ha he severiy of he injury and he age of he plaini s have a noiceable impac on he size of he oal poenial compensaion, while he docors board ceri caion does no. In one of he speci caions, we include he 11 Sandard errors are repored in he parenhesis. B.C. is shorhand for Board_Code, and Sev. for Severiy. The variable Age 2 is repored in unis of 100 yr 2. 20

Bargaining with Optimism: A Structural Analysis of Medical Malpractice Litigation. Abstract

Bargaining with Optimism: A Structural Analysis of Medical Malpractice Litigation. Abstract Bargaining wih Opimism: A Srucural Analysis of Medical Malpracice Liigaion Anonio Merlo and Xun Tang 1 Deparmen of Economics Rice Universiy Augus 3, 2015 Absrac We sudy ideni caion and esimaion of a srucural

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Appendix D Flexibility Factor/Margin of Choice Desktop Research

Appendix D Flexibility Factor/Margin of Choice Desktop Research Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Niche Market or Mass Market?

Niche Market or Mass Market? Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.

More information

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

Risk Modelling of Collateralised Lending

Risk Modelling of Collateralised Lending Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

Distributing Human Resources among Software Development Projects 1

Distributing Human Resources among Software Development Projects 1 Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

More information

Vector Autoregressions (VARs): Operational Perspectives

Vector Autoregressions (VARs): Operational Perspectives Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert

UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of Erlangen-Nuremberg Lange Gasse

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking? Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec Risk-Taking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

Option Put-Call Parity Relations When the Underlying Security Pays Dividends

Option Put-Call Parity Relations When the Underlying Security Pays Dividends Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of

More information

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

LIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b

LIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Dependent Interest and Transition Rates in Life Insurance

Dependent Interest and Transition Rates in Life Insurance Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies

More information

Relationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**

Relationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith** Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia

More information

Emergence of Fokker-Planck Dynamics within a Closed Finite Spin System

Emergence of Fokker-Planck Dynamics within a Closed Finite Spin System Emergence of Fokker-Planck Dynamics wihin a Closed Finie Spin Sysem H. Niemeyer(*), D. Schmidke(*), J. Gemmer(*), K. Michielsen(**), H. de Raed(**) (*)Universiy of Osnabrück, (**) Supercompuing Cener Juelich

More information

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are

More information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

WORKING P A P E R. Does Malpractice Liability Reform Attract High Risk Doctors? SETH A. SEABURY WR-674-ICJ. December 2009

WORKING P A P E R. Does Malpractice Liability Reform Attract High Risk Doctors? SETH A. SEABURY WR-674-ICJ. December 2009 WORKING P A P E R Does Malpracice Liabiliy Reform Arac High Risk Docors? SETH A. SEABURY WR-674-ICJ December 2009 This produc is par of he RAND Insiue for Civil Jusice working paper series. RAND working

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Graduate Macro Theory II: Notes on Neoclassical Growth Model

Graduate Macro Theory II: Notes on Neoclassical Growth Model Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.

More information

A Re-examination of the Joint Mortality Functions

A Re-examination of the Joint Mortality Functions Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

More information

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand Forecasing and Informaion Sharing in Supply Chains Under Quasi-ARMA Demand Avi Giloni, Clifford Hurvich, Sridhar Seshadri July 9, 2009 Absrac In his paper, we revisi he problem of demand propagaion in

More information

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by Song-Hee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 17-99

More information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 Introduction to Mathematical Finance Lesson 5 26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

More information

Factors Affecting Initial Enrollment Intensity: Part-Time versus Full-Time Enrollment

Factors Affecting Initial Enrollment Intensity: Part-Time versus Full-Time Enrollment acors Affecing Iniial Enrollmen Inensiy: ar-time versus ull-time Enrollmen By Leslie S. Sraon Associae rofessor Dennis M. O Toole Associae rofessor James N. Wezel rofessor Deparmen of Economics Virginia

More information

CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE

CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly

More information

Bid-ask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation

Bid-ask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation Bid-ask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Liang Ding* Deparmen of Economics, Macaleser College, 1600 Grand Avenue, S. Paul, MN55105, U.S.A. Shor Tile: Bid-ask

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

Hedging with Forwards and Futures

Hedging with Forwards and Futures Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

More information

Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds

Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds OPERATIONS RESEARCH Vol. 54, No. 6, November December 2006, pp. 1079 1097 issn 0030-364X eissn 1526-5463 06 5406 1079 informs doi 10.1287/opre.1060.0338 2006 INFORMS Invenory Planning wih Forecas Updaes:

More information

SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES

SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES Inernaional Journal of Accouning Research Vol., No. 7, 4 SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES Mohammad Ebrahimi Erdi, Dr. Azim Aslani,

More information

As widely accepted performance measures in supply chain management practice, frequency-based service

As widely accepted performance measures in supply chain management practice, frequency-based service MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 6, No., Winer 2004, pp. 53 72 issn 523-464 eissn 526-5498 04 060 0053 informs doi 0.287/msom.030.0029 2004 INFORMS On Measuring Supplier Performance Under

More information

Stochastic Optimal Control Problem for Life Insurance

Stochastic Optimal Control Problem for Life Insurance Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian

More information

NASDAQ-100 Futures Index SM Methodology

NASDAQ-100 Futures Index SM Methodology NASDAQ-100 Fuures Index SM Mehodology Index Descripion The NASDAQ-100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ-100 E-mini Index

More information

Child Protective Services. A Guide To Investigative Procedures

Child Protective Services. A Guide To Investigative Procedures Child Proecive Services A Guide To Invesigaive Procedures The purpose of his brochure is o help you undersand he Child Proecive Services (CPS) reporing and response process. Please conac your CPS worker

More information

Multiprocessor Systems-on-Chips

Multiprocessor Systems-on-Chips Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average

Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

Premium indexing in lifelong health insurance

Premium indexing in lifelong health insurance Premium indexing in lifelong healh insurance W. Vercruysse 1, J. Dhaene 1, M. Denui 2, E. Piacco 3, K. Anonio 4 1 KU Leuven, Belgium 2 U.C.L., Louvain-la-Neuve, Belgium 3 Universià di Triese, Triese, Ialy

More information

SPECULATIVE DYNAMICS IN THE TERM STRUCTURE OF INTEREST RATES. Abstract

SPECULATIVE DYNAMICS IN THE TERM STRUCTURE OF INTEREST RATES. Abstract SPECULATIVE DYNAMICS IN THE TERM STRUCTURE OF INTEREST RATES KRISTOFFER P. NIMARK Absrac When long mauriy bonds are raded frequenly and raional raders have non-nesed informaion ses, speculaive behavior

More information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

Chapter 4: Exponential and Logarithmic Functions

Chapter 4: Exponential and Logarithmic Functions Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

More information

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds

More information

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have

More information

Analysis of Tailored Base-Surge Policies in Dual Sourcing Inventory Systems

Analysis of Tailored Base-Surge Policies in Dual Sourcing Inventory Systems Analysis of Tailored Base-Surge Policies in Dual Sourcing Invenory Sysems Ganesh Janakiraman, 1 Sridhar Seshadri, 2, Anshul Sheopuri. 3 Absrac We sudy a model of a firm managing is invenory of a single

More information

Monetary Policy & Real Estate Investment Trusts *

Monetary Policy & Real Estate Investment Trusts * Moneary Policy & Real Esae Invesmen Truss * Don Bredin, Universiy College Dublin, Gerard O Reilly, Cenral Bank and Financial Services Auhoriy of Ireland & Simon Sevenson, Cass Business School, Ciy Universiy

More information

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.

More information

Information Theoretic Approaches for Predictive Models: Results and Analysis

Information Theoretic Approaches for Predictive Models: Results and Analysis Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven

More information

A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets

A Generalized Bivariate Ornstein-Uhlenbeck Model for Financial Assets A Generalized Bivariae Ornsein-Uhlenbeck Model for Financial Asses Romy Krämer, Mahias Richer Technische Universiä Chemniz, Fakulä für Mahemaik, 917 Chemniz, Germany Absrac In his paper, we sudy mahemaical

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? *

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? * Does Opion Trading Have a Pervasive Impac on Underlying Sock Prices? * Neil D. Pearson Universiy of Illinois a Urbana-Champaign Allen M. Poeshman Universiy of Illinois a Urbana-Champaign Joshua Whie Universiy

More information

SPECULATION AND THE TERM STRUCTURE OF INTEREST RATES. Abstract

SPECULATION AND THE TERM STRUCTURE OF INTEREST RATES. Abstract SPECULATION AND THE TERM STRUCTURE OF INTEREST RATES KRISTOFFER P. NIMARK Absrac A racable equilibrium erm srucure model populaed wih raional bu heerogeneously informed raders is developed and esimaed.

More information

Hiring as Investment Behavior

Hiring as Investment Behavior Review of Economic Dynamics 3, 486522 Ž 2000. doi:10.1006redy.1999.0084, available online a hp:www.idealibrary.com on Hiring as Invesmen Behavior Eran Yashiv 1 The Eian Berglas School of Economics, Tel

More information

Working Paper On the timing option in a futures contract. SSE/EFI Working Paper Series in Economics and Finance, No. 619

Working Paper On the timing option in a futures contract. SSE/EFI Working Paper Series in Economics and Finance, No. 619 econsor www.econsor.eu Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Biagini, Francesca;

More information

AP Calculus AB 2010 Scoring Guidelines

AP Calculus AB 2010 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College

More information

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1 Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces ime-series smoohing forecasing mehods. Various models are discussed,

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

3 Runge-Kutta Methods

3 Runge-Kutta Methods 3 Runge-Kua Mehods In conras o he mulisep mehods of he previous secion, Runge-Kua mehods are single-sep mehods however, muliple sages per sep. They are moivaed by he dependence of he Taylor mehods on he

More information

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. The Effecs of Unemploymen Benefis on Unemploymen and Labor Force Paricipaion:

More information

Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures

Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures w o r k i n g p a p e r 5 7 Recovering Marke Expecaions of FOMC Rae Changes wih Opions on Federal Funds Fuures by John B. Carlson, Ben R. Craig, and William R. Melick FEDERAL RESERVE BANK OF CLEVELAND

More information

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results: For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk

More information

Modeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling

Modeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se

More information

Economics Honors Exam 2008 Solutions Question 5

Economics Honors Exam 2008 Solutions Question 5 Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I

More information

Keldysh Formalism: Non-equilibrium Green s Function

Keldysh Formalism: Non-equilibrium Green s Function Keldysh Formalism: Non-equilibrium Green s Funcion Jinshan Wu Deparmen of Physics & Asronomy, Universiy of Briish Columbia, Vancouver, B.C. Canada, V6T 1Z1 (Daed: November 28, 2005) A review of Non-equilibrium

More information

A general decomposition formula for derivative prices in stochastic volatility models

A general decomposition formula for derivative prices in stochastic volatility models A general decomposiion formula for derivaive prices in sochasic volailiy models Elisa Alòs Universia Pompeu Fabra C/ Ramón rias Fargas, 5-7 85 Barcelona Absrac We see ha he price of an european call opion

More information