TESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET by Oksana Lyashuk A thess submtted n partal fulfllment of the requrements for the degree of Master of Arts n Economcs Natonal Unversty Kyv-Mohyla Academy Economcs Educaton and Research Consortum Master s Program n Economcs 2007 Approved by Mr. Serhy Korabln (Head of the State Examnaton Commttee) Program Authorzed to Offer Degree Master s Program n Economcs, NaUKMA Date
Natonal Unversty Kyv-Mohyla Academy Abstract TESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET by Oksana Lyashuk Head of the State Examnaton Commttee: Mr. Serhy Korabln, Economst, Natonal Bank of Ukrane In the paper I nvestgate the evdence of adverse selecton n Kyv automoble nsurance market, whch can be dentfed as a developng nsurance market. For separaton of adverse selecton from moral hazard, as a cause of asymmetrc nformaton problem, I employ the unused observables test, proposed by Fnkelsten and Poterba (2006), whch allows for the presence of heterogenety n rsk preferences. I fnd that ndvdual rskness nfluences the choce of coverage and the occurrence of accdents, whch gves the opportunty to state about the evdence of adverse selecton problem n the market. Usng dfferent specfcaton of the polcyholder s rskness, I check obtaned results for the robustness. Investgatng the relatonshp between the ndvdual loss rato and choce of coverage, I do not fnd presence of cross subsdzaton n the nsurance market. Thus, I conclude that Kyv automoble nsurance market s affected by adverse selecton, but, on the other hand, t s not serously nfected by cross subsdzaton problem between polcyholders. It supports prevous fndngs suggestng that problem of asymmetrc nformaton s mmanent manly for undeveloped and developng nsurance markets.
TABLE OF CONTENTS LIST OF TABLES..... ACKNOWLEDGMENTS... GLOSSARY. v Chapter 1: INTRODUCTION...1 Chapter 2: LITERATURE REVIEW..6 2.1. Dfferent Approaches for Separatng Adverse Selecton from Moral Hazard. 6 2.2. Emprcal Studes concernng the Problem of Adverse Selecton and Cross Subsdzaton n Automoble Insurance Market...9 Chapter 3: METHODOLOGY 13 3.1. The Postve Correlaton Test for Asymmetrc Informaton.... 13 3.2. Testng for Asymmetrc Informaton and Adverse Selecton n the Presence of Heterogenety n Rsk Preferences... 16 3.3. Testng for Cross Subsdzaton.....18 Chapter 4: DATA DESCRIPTION.. 20 4.1. Voluntary Automoble Insurance Market n Ukrane......20 4.2. Descrptve Statstcs..... 22 Chapter 5: EVIDENCE FOR ADVERSE SELECTION..... 29 5.1. Testng for Asymmetrc Informaton......29 5.2. Testng for Adverse Selecton caused by Unobservable Varables... 32 5.3. Testng for Cross Subsdzaton.....37 Chapter 6: CONCLUSIONS.....39 BIBLIOGRAPHY 41 APPENDICES.....43
LIST OF TABLES Number Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Appendx A Appendx B Appendx C Appendx D Page Lst of Varables 23 Descrptve Statstcs. 26 Estmaton Results for Coverage-Clam Correlaton 30 Condtonal Correlaton between Coverage and Clam 31 Testng for Adverse Selecton...34 Estmaton Results for Loss Rato Determnaton.. 37 Estmaton Results for Premum Determnaton Testng for Asymmetrc Informaton Dstrbuton of Accdents, Deaths, and Injures across the Kyv Cty Dstrcts Estmaton Results for Coverage-Past Clam Correlaton
ACKNOWLEDGMENTS I would lke to express sncere grattude and mmense acknowledgment to Professor Roy Gardner for nvaluable gudance, useful correcton, and mmedate comments upon my thess. Hs professonal and moral support was uncommonly large and helpful durng thess wrtng and especally at the tme of ts completon. I want to thank Professor Olena Nzalova for the valuable advce and for assstance n choosng the topc for research. Specal thanks to Professor Tom Coupe for the careful readng of my thess drafts and for the precous suggestons. I also deeply apprecate feedbacks on my work provded by Pavlo Prokopovych, Serhy Malar and other professors who shared wth ther thoughts about the nvestgatng topc. Many thanks to my EERC colleagues and frends: Dans Rozhn for hs openness to dscussons and econometrc ssues, and Dmytro Blodd for the moral support and great works concernng data sortng.
GLOSSARY Adverse selecton problem problem, whch s present when, before the sgnng of a contract, the party that establshes the condtons of the contract has less nformaton than the other party on some mportant characterstcs affectng the value of the contract. Asymmetrc nformaton occurs when one party to a transacton has more or better nformaton than the other party. Cross subsdzaton s market stuaton, where one group pays a relatvely hgh prce and thus enables another group to pay a relatvely low prce. Insurance a form of rsk management prmarly used to hedge aganst the rsk of a contngent loss. Moral hazard problem problem, whch appears when the agent receves prvate nformaton after the relatonshp has been ntated; t refers to the possblty that the redstrbuton of rsk (such as nsurance whch transfers rsk from the nsured to the nsurer) changes people s behavor. v
Chapter 1 INTRODUCTION Durng the past decades, the problem of asymmetrc nformaton has receved ncreasng attenton among nsurance and economc theores. Snce Rothschld and Stgltz (1976) frst nvestgated the ssues of adverse selecton n nsurance markets, theoretcal analyss on the markets wth asymmetrc nformaton and adverse selecton n partcular was provded by many other researchers; among them were Myazak (1977), Spence (1978), Rley (1979), and Arnott and Stgltz (1988). Accordng to Rothschld and Stgltz (1976) adverse selecton n nsurance markets refers to the theoretcal tendency for low rsk ndvduals to avod or drop out of voluntary nsurance wth the result that nsurance pool can be expected to contan too many hgh rsk ndvduals. In other words, adverse selecton problem appears n the case when the nsurer has no nformaton about the rsk profles; the cover and premum level are set somewhere between what s requred by the low and hgh rsk users, so that the company can at least break even. In ths stuaton, the low rsk polcyholders feel that they are payng too much for the nsurance relatve to ther rsk-profle and drop out of the rsk pool, whch leads to the average rsk n the pool to rse, causng premums to rse, and more people to drop nsurance pool. A number of recent papers are devoted to the emprcal applcaton of the theory n order to determne whether asymmetrc nformaton exsts n partcular nsurance markets. To fnd the evdence of asymmetrc nformaton, a correlaton test s used. Accordng to t, the null hypothess of symmetrc nformaton s
rejected f there s postve correlaton between the choce of contract purchased and the occurrence or severty of an accdent, condtonal on the polcyholder s characterstcs whch are used n determnaton of the nsurance premum. Under adverse selecton as a cause of asymmetrc nformaton, t s consdered that hghrsk agents most lkely choose full coverage of the nsurance contract and typcally get an accdent n the perod under nsurance. Whle nvestgatng the problem of asymmetrc nformaton and adverse selecton n partcular, researches came to dfferent conclusons about ts exstence. Rothschld and Stgltz (1976) strongly predct that adverse selecton exsts because of exstence of postve correlaton between nsurance clams and the level of nsurance. Puelz and Snow (1994) prove ths emprcally showng that there s adverse selecton n the contractual relatonshp between an Amercan nsurer and ts polcyholders. However, Donne et al. (2001) argue that the Puelz s and Snow s results can not be robust because of ncomplete specfcaton n the econometrc model tested. Donne et al. (2001) conclude that there s no evdence of asymmetrc nformaton usng a model based on smlar data from a Canadan nsurance company and the test for non-lneartes n nsurance prcng. Cohen (2005) argues that adverse selecton problem n automoble nsurance market s present snce polcyholders wth relatvely large drvng experence get to know ther type of rsk. Based on ths knowledge, they take a decson about the type of contract coverage, causng coverage-accdent correlaton. Fnkelsten and Poterba (2006) dentfy the presence of adverse selecton n the U.K. annuty market by presentng ther own unused observables test for adverse selecton. Huang et al. (2005) also fnd the emprcal evdence of asymmetrc nformaton n Tawan s automoble nsurance market. However, they use data n the early stage of the developng nsurance market, and t s possble that asymmetrc nformaton s present especally n the early stage of the nsurance market. 2
However, many more emprcal studes have faled to fnd evdence for asymmetrc nformaton and adverse selecton n partcular. Among them are van de Ven and van Vlet (1995), who studed Netherlands health nsurance (1995); Cawley and Phlpson (1999), who analyzed the Amercan lfe nsurance market; Chappor and Salane (2000), who studed French automoble nsurance market; Cardon and Hendel (2001), who researched the Amercan health nsurance market; Sato (2003), who nvestgated Japanese automoble nsurance market; Fnkelsten and McGarry (2004), who analyzed the Amercan long-term lfe nsurance market, and others. Although the researchers can descrbe possble problems assocated wth adverse selecton and suggest polcy to allevate these problems, the emprcal evdence of nsurance market sufferng from adverse selecton occurs rarely. Ths phenomenon mght be explaned by the fact that nsurer n the case of usng approprate rsk classfcaton, experence ratng, and deductbles can elmnate adverse selecton n the nsurance market (Donne et al. (2000)). Asymmetrc nformaton matters n less developed nsurance markets because nsurance companes experence lack of statstcal data on traffc accdents, undeveloped relatonshps between frms, and legslaton regulaton of bad qualty. All these factors cause dffcultes when wrtng optmal contracts. Moreover, companes operatng on developng nsurance market have less experence detectng the nsurance fraud and managng nsurance agents. Snce these mechansms help reduce the problem of adverse selecton and/or moral hazard, nformatonal problems matter more n developng nsurance markets than n the developed ones. Takng nto account that organzaton and realzaton of auto nsurance n Ukrane do not fully confrm to the world standards and meet a lot of legal, socal, economc, and organzatonal problems, whch can be manly explaned by 3
the lack of nsurance market development, I consder that the Kyv automoble nsurance market s a good approxmaton of developng nsurance market. Thus, the am of my research s to nvestgate the evdence of adverse selecton n developng automoble nsurance market. More specfcally, I ask the emprcal questons: () whether developng automoble nsurance market s characterzed wth adverse selecton problem and () whether hgh rsk polcyholders are crosssubsdzed by low rsk polcyholders n t. To the best of my knowledge, I am the frst to do such a research n Ukrane. Separaton of adverse selecton from moral hazard s one of the most mportant emprcal ssues n ths feld. That s why, n my research I wll concentrate on the queston whether the evdence of adverse selecton (not just asymmetrc nformaton) really exsts n the developng automoble nsurance market. For determnaton of evdence for adverse selecton, I wll employ the unused observables test, proposed by Fnkelsten and Poterba (2006), who have used ths test for long-term lfe nsurance market. Accordng to ths test, f t s found that unused observable characterstc s correlated wth polcyholder s rsk type and hs choce of nsurance coverage, then the presence of adverse selecton s ndcated. In order to nvestgate the presence of cross subsdzaton on the automoble nsurance market, I mplement the test for cross subsdzaton to determne whether the equlbrum causes the cross subsdzaton of hgh rsks by low rsks wthn a gven rsk category as predcted by Myazak s theory of adverse selecton (1977). To provde evdence for the cross subsdzaton hypothess, I wll test f the loss rato s postvely related to the choce of nsurance coverage. I wll check whether low rsk polcyholders pay a relatvely hgh prce and thus enable hgh rsk ndvduals to pay a relatvely low prce for the nsurance coverage. In my research I wll use the data set whch contans nformaton about the automoble nsurance polces and clam hstory provded by a Ukranan 4
nsurance company. Rsk classfcaton used by nsurance company s based on drver s characterstcs (gender, company experence, and type of use) and on vehcle s characterstcs (age, model and value of the car, country, where the car was manufactured, cylnder capacty of engne, and type of car body). The company also has collected other nformaton about polcyholder, such as place of resdence, but does not use t n settng prces, whch gve us opportunty to test for adverse selecton usng unused observables test, where ths varable s consdered as unused observable characterstc. The observatons for the research are avalable from more than 2000 polcyholders durng the 2004 year: snce January 2004 tll December 2004. The remander of ths paper s organzed as follows. In chapter 2 I brefly show the lterature revew concernng the problem of adverse selecton. Emprcal hypothess and methodology are presented n chapter 3. Data descrptons are shown n chapter 4 and estmaton of results are descrbed n chapter 5. Fnally, n chapter 6 I present concludng remarks. 5
Chapter 2 LITERATURE REVIEW 2.1. Dfferent Approaches for Separatng Adverse Selecton from Moral Hazard Asymmetrc nformaton can prevent the effcent operaton of nsurance markets. However, the ssue about exstence of asymmetrc nformaton n partcular market s controversal. Most of the current researches have tested for the evdence of asymmetrc nformaton usng postve correlaton test proposed by Chappor et al. (2000). Accordng to the test, f a postve correlaton between the amount of nsurance purchased and rsk occurrence, condtonal on the polcyholder characterstcs whch are used n premum determnaton, exsts, the null hypothess of symmetrc nformaton s rejected. Accordng to Chappor et al. (2006), the condtonal correlaton approach s very robust and smple. In the Rothschld s and Stgltz s (1976) model of competton under adverse selecton, the exstence of correlaton s explaned by the proposton that hgh rsk agents prefer to pay more than low rsk for addtonal coverage. Thus, hgh rsk agents choose nsurance contract wth hgher coverage. Accordng to Arnott and Stgltz (1988), under moral hazard the opposte reason causes the same correlaton. An agent swtches to a contract wth greater coverage becomes more rsky because he makes less effort beng careful. Tryng to separate adverse selecton and moral hazard n the nsurance market s not easy. Chappor and Salane (2000) consder ths problem and state that both cause the postve correlaton between the choce of nsurance coverage and the 6
occurrence of the clam. Therefore, under the test they proposed, t s not possble to dentfy whether the asymmetry n nformaton s caused by adverse selecton or moral hazard. Donne and Gagne (2002) separate moral hazard from adverse selecton usng the analyss of the effect of the replacement cost endorsement. The test they proposed can not always be used, snce the dependent varable characterzes the exstence or absence of replacement cost endorsement. Ths specal endorsement gves the opportunty to the polcyholder to get a new car n case of ts total damage or theft. However, n practce, such endorsement s rare. Fnkelsten and Poterba (2004), as well as Donne and Gagne (2002), separate moral hazard from adverse selecton usng a partcularty of a sample set. Fnkelsten and Poterba (2004) use data of annuty market n order to provde a drect test for adverse selecton, assumng that moral hazard problem s lmted n the market. They study the mortalty experence of people who buys annutes and fnd support for adverse selecton effects n the annuty market. After a robustness check, the authors conclude that no adverse selecton exsts on ntal amount of annuty payment. Chappor and Heckman (2000) propose employng dynamc data to verfy the moral hazard problem. Accordng to ther research, under moral hazard, the hazard rate of an accdent ncreases before an accdents and falls afterwards. In case of the absence of moral hazard problem, the hazard rate should not change after an accdent occurs, whch s tested n parametrc and non parametrc way. Abbrng et al. (2003) also show that dynamc nsurance data allow to separate moral hazard and adverse selecton. Testng for adverse selecton (and partcularly asymmetrc learnng) requres analyzng the jont process followed by accdents and contractual choce. 7
Sato (2003) examnes whether adverse selecton could be nferred when regulaton prohbts nsurance companes from usng some of the drvers characterstcs. If regon classfcaton s not used and adverse selecton problem exsts, polcyholders from rsker regons wll purchase more nsurance coverage. He tests for ths wth a bvarate probt model and χ 2 test proposed by Chappor and Salane (2000) and checks obtaned results for the robustness usng dfferent defntons of rsk. Huang et al. (2005) propose to test for adverse selecton usng data on polcy renewal. By adoptng clam records as a proxy of the nsured s rsk type, they allege that only adverse selecton, not moral hazard, can explan the relatonshp between the choce of coverage and the prevous-year clam records for the contnung renewal contracts. They argue that the ndvdual losses wll be postvely correlated to choce of coverage, f both adverse selecton and cross subsdzaton exst on the marker. Fnkelsten and Poterba (2006) propose ther own test for adverse selecton n nsurance markets whch take nto account heterogenety n polcyholders preferences. Ths test uses any observable characterstc of polcyholder that s not used n settng nsurance rates. If that characterstc s correlated wth polcyholder s rsk type and hs choce of nsurance coverage, then adverse selecton exsts. Chappor et al. (2006) propose the test for asymmetrc nformaton complemented to unused observable test proposed by Fnkelsten and Poterba (2006). For ther test dstngushng between two types of the contract proposed by nsurer s needed. Accordng to ther test whether polcyholder, who choose not full nsurance coverage (contracts whch covers not all but selected rsk occurrence) nstead full nsurance coverage (contracts whch cover all possble nsurance rsk), get hgher premum for the contract and net losses can be 8
determned. Test for asymmetrc nformaton proposed by Chappor et al. requres an assumpton about the nsurer s cost structure. The unused observables test proposed by Fnkelsten and Poterba does not need ths restrcton. Moreover, test for asymmetrc nformaton can be used only n the case when nsurer propose two types of nsurance products, whle the unused observables test can be used regardless lmtaton n nsurance products offered by nsurer. On the other hand, the dsadvantage of the unused observables test s that t requres dstngushng among ndvdual characterstcs those attrbutes whch are not used n prce determnaton, but whch are correlated wth demand for nsurance polcy and rsk of accdent. Unused observables test, unlke the test for asymmetrc nformaton proposed by Chappor et al. (2006), gves opportunty to determne the evdence of adverse selecton (not just for asymmetrc nformaton). Quotng Fnkelsten and Poterba (2006), observng that a characterstc that nsurance companes do not use n prcng s postvely correlated wth nsurance quantty purchased and wth ex post rsk occurrence [and] when there s external nformaton that certan characterstcs are correlated wth rsk occurrence for reasons other than nsurance coverage then the unused observables test can dentfy the presence of adverse selecton and rule out moral hazard as the exclusve source of the observed correlaton between ndvdual attrbutes, nsurance quantty, and rsk of loss. 2.2. Emprcal Studes concernng the Problem of Adverse Selecton and Cross Subsdzaton n Automoble Insurance Market After consderng the man emprcal tests used to detect adverse selecton, I turn to the emprcal evdence. Snce I am nterested n the behavor of dfferent agents n automoble nsurance market, n ths secton I am gong to consder the man results and weaknesses of the prncpal studes concernng the evdence of 9
adverse selecton n automoble nsurance market. I dvde these studes nto those whch fnd adverse selecton and those whch do not. The strongest evdence for adverse selecton s n Cohen (2005). She uses Israel data on a 5-year panel of drvers. She tests for correlaton between low deductbles and more accdents usng OLS, Posson and Negatve Bnomal specfcatons. In order to defne the evdence for adverse selecton she also uses bvarate probt recommended by Chappor and Salane (2000). Cohen (2005) fnds that polcyholder who chooses low-deductble cost the nsurer approxmately 20% more than a regular-deductble. Thus, she fnds that Israel nsurance market s spoled by the adverse selecton problem. She also shows the evdence of learnng n ths panel. For polcyholders wth low drvng experence, choosng low-deductble contract s not assocated wth a hgher accdent rate and more clams. Such assocaton exsts only wth more experenced drvers. The author also concludes that polcyholders who change nsurers have hgher probablty of accdent and hgher nsurance rate, whch s defned on the base of all characterstcs observed to the nsurer. Despte fndng the strongest evdence for adverse selecton n automoble nsurance market, Cohen (2005) rases several unanswered questons. Snce tests for the evdence of adverse selecton can be consdered as tests of the jont hypothess that nsurers maxmze ther proft, the presence of asymmetrc nformaton s nconsstent wth the proft-maxmzng nsurers behavor. The nsurers, who want to operate wth profts, should recognze the hgher accdent rsks by low-deductble polcyholder s choce, and establsh a hgher premum to them, overcomng the problem of dshonest behavor of polcyholders. Huang et al. (2005), followng Chappor and Salane (2000), study Tawan s automoble nsurance market. They fnd adverse selecton showng the postve 10
correlaton between the choce of nsurance coverage and the prevous-year clam records, and the postve correlaton relatonshp between loss rato and the choce of coverage. They use data n the early stage of the developng nsurance market. It s lkely that asymmetrc nformaton exsts especally n the early stage of the nsurance market. Chappor and Salane (2000) test for asymmetrc nformaton n France examnng a large dataset from a sngle nsurer. Ther data represent the nsured polces of a homogeneous group of drvers wth three year drvng experence. They conclude that n the process of choosng automoble nsurance contract polcyholders behave lke they have not better nformaton then the nsurer about ther rsk type. Therefore, the man fndng of Chappor and Salane (2000) s that there s no evdence for asymmetrc nformaton and adverse selecton n partcular n the automoble nsurance market. The absence of evdence for adverse selecton suggests that ths problem exsts only to a very lmted extent or not at all n the automoble French nsurance market. The absence of adverse selecton n the nsurance market of low experence drvers s not extremely surprsng result. However, t s even more worth defnng, whether nsured drvers wth much experence allow learnng about ther rskness faster than the nsurance company. Donne et al. (2001) test for adverse selecton n the Quebec auto nsurance market usng a more lmted dataset. They crtcze the econometrc methods and dataset used by Puelz and Snow (1994), concludng that hgh-rsk drvers would not choose small deductbles wthn rsk classes n the market under ther research. They also show that rsk classfcaton used by nsurer fxes the problem of adverse selecton. Sato (2003) nvestgates f adverse selecton could be made worse by rate regulaton whch prohbts nsurance company from usng some of the drver s 11
characterstcs. He tests data from the automoble nsurance polces of the large nsurance company, assumed representatve n Japan. He fnds no evdence of adverse selecton. Instead, he fnds negatve correlaton between rsk and coverage, whch s reverse to the adverse selecton hypothess. He explans the absence of a sgn of adverse selecton by the fact that ths phenomenon exsts only to a very lmted extent n the Japanese market. Emprcal support of the asymmetrc nformaton theory ndcates that nsurance customers rarely act through an adverse selecton mechansm, and does not provde evdence on the cross subsdzaton hypothess that hgh rsk polcyholders are subsdzed by low rsk ones. For these reasons, t s also essental for my research to nvestgate not only the evdence for adverse selecton n the undeveloped nsurance market, but also the evdence for cross subsdzaton of hgh rsk polcyholders by low rsk ones. Only a few researchers fnd evdence of cross subsdzaton n nsurance markets. Among the recent research the evdence for cross subsdzaton has been found only by Makk and Somwaru (2001), who show that hgh rsks are undercharged and low rsks are overcharged n the U.S. crop nsurance market, and by Huang et al. (2005), who fnd that the loss rato s postvely correlated to the choce of nsurance coverage n Tawan s automoble nsurance market. 12
Chapter 3 METHODOLOGY 3.1. The Postve Correlaton Test for Asymmetrc Informaton Accordng to asymmetrc nformaton theory, n nsurance market polcyholders who purchase more coverage are more lkely to experence accdent. Under moral hazard problem, drvers under nsurance lower ther cost when the accdents occur and thus ncrease the expected losses of the nsurer. Under adverse selecton problem, polcyholders before sgnng the contract have better knowledge about ther rskness than nsurer and thus hgh rsk polcyholders wll purchase more nsurance coverage. The most common test for asymmetrc nformaton s the postve correlaton test, proposed by Chappor and Salane (2000). Accordng to ths test correlaton between the amount of polcyholder s nsurance and hs ex-post rsk experence, condtonal on the observable characterstcs that are used n prcng nsurance polces, s determned. In order to mplement ths test I need the followng assumpton. Let = 1,, n denote polcyholders. X s the set of exogenous varables for polcyholder. Let suppose exstence of two 0-1 endogenous varables: (1) C = 1 f buys nsurance wth full coverage; C = 0 f buys nsurance product accordng to whch only selected rsk s nsured; (2) A = 1 f occurs at least one accdent n whch he was at fault; otherwse A = 0. 13
Although nsurance company offers dfferent possble terms of contract wth, for nstance, dfferent level of deductbles, I treat them dentcally snce other non standard contracts are proposed rarely and are defned accordng to the specal agreement wth company. I also separate accdents n whch polcyholders are at fault and those n whch they are not. I do ths because n the case when the nsured has an accdent n whch another drver s blamed, nformaton about polcyholder s rsk type can not be determned defntely. Fnally, snce few drvers have more than one accdent, I do not dstngush them ether. Followng Chappor and Salane (2000), I set up two probts models: one for the choce of coverage ( C ) and one for the occurrence of an accdent ( A ). The estmatng equatons are: C = 1 f C = βx + ε > 0 0, otherwse (1a) and A = 1 f A = γx + η > 0 0, otherwse (1b) Under the null hypothess of symmetrc nformaton, the resduals n these equatons, ε andη, should be uncorrelated. Otherwse, a statstcal sgnfcant postve correlaton between them mples rejecton of the null hypothess. In order to determne the exstence of correlaton between resduals, I frst estmate these probts ndependently, and then compute the generalzed resduals ε andη : φ( X β ) φ( X β ) ε = E( ε C ) = C (1 C ) (2a) Ф( X β ) Ф( X β ) 14
φ( X β ) φ( X β ) η = E( η A ) = A (1 A ) (2b) Ф( X β ) Ф( X β ) Where φ and Ф specfy the densty and the cumulatve dstrbuton functon of N(0,1). Test statstcs s defned as W ( n = 1 = n = 1 ε η ) 2 ε η 2 2 (3) Under the null of condtonal ndependence between the choce of coverage and the occurrence of an accdent, cov( ε, ) = 0, W s dstrbuted asymptotcally η 2 as χ (1), whch gve us possblty to test for the exstence of symmetrc nformaton. However, n order to use ths methodology, I need to choose what exogenous varables should be ncluded n X. From a theoretcal pont of vew, the most relevant exogenous varables are varables whch nsurer uses n the process of ratemakng. For ths reason I nclude n X vehcle s, polcyholder s, and contract characterstcs whch are known for the nsurer and recorded n the polcy. Takng nto account that estmatng two probts ndependently s approprate only under the absence of condtonal ndependence between dependent varables, I also estmate a bvarate probt wth ε and η dstrbuted as N (0,1) and correlaton coeffcent ρ between them. Estmaton of ths coeffcent wll allow to test for the evdence of asymmetrc nformaton under the null hypothess for symmetrc nformaton ρ = 0. 15
3.2. Testng for Asymmetrc Informaton and Adverse Selecton n the Presence of Heterogenety n Rsk Preferences The postve correlaton test can gve approprate nformaton about asymmetrc nformaton only n the case of polcyholders homogenety n rsk preferences. If ndvduals have dfferent preferences for nsurance, the absence of correlaton between ε andη may not mply symmetrc nformaton n nsurance market. To see ths, suppose that ndvduals have prvate nformaton about ther rsk type ( Z 1) and dfferent rsk averson ( Z 2 ). Then ε andη, the resduals from the coverage equaton (1а ) and the rsk of accdent occurrence (1b ) respectvely, can be defned as: ε * + ω (4a) = Z1, π 1 + Z 2, * π 2 and η Z + v (4b) = 1, * θ1 + Z 2, * θ 2 Under postve correlaton test, rsk type ( Z 1) wll be postvely correlated wth nsurance coverage and the rsk of accdent occurrence f there s prvate nformaton about rsk type so that π > 1 0 andθ > 0 1. However, n the case when rsk averson ( Z 2 ) s also postvely correlated wth coverage but negatvely correlated wth rsk of loss ( π > 2 0 butθ < 0), the correlaton between 2 ε and η may be zero or even negatve. Therefore, even n the presence of asymmetrc nformaton n the case that polcyholders rsk heterogenety exsts the postve correlaton test can fal to reject the null hypothess of symmetrc nformaton. So, usng the postve correlaton test n the presence of heterogenety n ndvdual preferences can lead to Type II error. 16
Also, more rsk-averse polcyholders or polcyholders wth hgh volatlty n ncome wll be more lkely to purchase nsurance coverage. At the same tme, a postve relatonshp between nsurance coverage and rsk occurrence can be generated f such ndvduals also have a hgher rsk of loss. Agan, t does not necessarly mean the presence of asymmetrc nformaton n the market. In ths case, usng the postve correlaton test n the presence of heterogenety n ndvdual preferences can reject the null hypothess about symmetrc nformaton leadng to Type I error. To deal wth these complcatons, I follow Fnkelsten and Poterba (2006). Accordng to them, n order to determne the evdence of asymmetrc nformaton even n the presence of heterogenety n preferences test for asymmetrc nformaton usng unused observables can be employed. The authors argue that when there s symmetrc nformaton, condtonal on the rsk class n whch the nsurance company places a buyer, there should not be any buyer characterstcs that can be observed by the econometrcan and that are correlated wth both nsurance coverage and rsk of loss. The exstence of such a characterstc, known to the potental polcyholder, but not to the nsurer, and correlated wth coverage and ex-post rsk of loss, provdes evdence of asymmetrc nformaton. In order to mplement the unused varables test I ntroduce the followng notatons. Let X denotes the attrbutes that are used by an nsurer n order to refer a potental polcyholder to a rsk class. ndvdual, and C s nsurance coverage of A s hs accdent occurrence. An element of ether polcyholder s rsk type ( Z 1) or hs rsk preference ( Z 2 ) s denoted by varable W, whch represent the unused observable varable. Estmatng the followng regresson by bvarate probt gve us opportunty to apply the unused varables test for the automoble nsurance market. 17
C = 1 f C = + + βx αw > 0 ε 0 otherwse (5a) and A = 1 f A = + + γx δw > 0 η 0 otherwse (5b) Regardless of the sgn of α andδ, rejectng the jont null hypothess that α = 0 and δ = 0 s equvalent to rejectng the null hypothess of symmetrc nformaton. In order to mplement the unused observables test I requre the followng nformaton about nsured: () polcyholder s characterstcs known by nsurance companes, () nsurance coverage, () ex-post rsk experence, and (v) ndvdual characterstc, whch s not used for prcng the contract. In my case, nsurer has the nformaton about ndvdual place of resdence, whch s not used n nsurance prce determnaton, but should be correlated wth demand for nsurance and polcyholder s rsk type. Moreover, polcyholder s place of resdence as unobservable characterstc gves us opportunty to determne the evdence for adverse selecton. Accordng to the Fnkelsten and Poterba (2006), such an unobservable characterstc, correlated wth possble rsk occurrence but not taken nto account by nsurer, allows to elmnate moral hazard as a source of the correlaton. 3.3. Testng for Cross Subsdzaton In my research I also want to test for cross subsdzaton. To provde evdence for ths, I test whether the loss rato (LR ), clam amount dvded by premum, s related to the choce of coverage. Accordng to Huang at al. (2006), n the presence of cross subsdzaton, the loss rato should be postvely correlated wth the polcyholder s choce of rsk coverage. Thus, assumng that LR s the total 18
clam amount dvded by the premum for each ndvdual, X and C have the same determnaton as prevously; I can defne the exstence of cross subsdzaton by testng the followng Tobt regresson: LR = β 1 X + β 2C + ϖ (6) The selecton of usng Tobt regresson n determnng the relatonshp between loss rato and choce of coverage can be explaned by the fact that dependent varable LR has a mass on zero. Ths happens because most polcyholders do not experence a clam. I run a Tobt regresson of (6), estmate parameters, and test the null hypothess that β > 2 0. Rejectng the null hypothess s equvalent to rejectng the null hypothess of cross subsdzaton. 19
Chapter 4 DATA DESCRIPTION 4.1. Voluntary Automoble Insurance Market n Ukrane I apply the postve correlaton test and unused observables test for the determnaton of asymmetrc nformaton and adverse selecton, and test for the cross subsdzaton to the voluntary automoble nsurance market n Kyv. To do ths, I frst descrbe the nsttutonal settng pecular to Ukrane and Kyv n partcular. Automoble nsurance n Ukrane conssts of oblgatory automoble lablty nsurance and voluntary nsurance. Oblgatory nsurance only covers cvl lablty for bodly njury and property damage lablty. All the other damages are covered by voluntary nsurance. Types of coverage of voluntary automoble nsurance n Ukrane correspond to the types of nsurance coverage usng n developed automoble nsurance markets. Among the man types of nsurance coverage used n Ukrane are Collson, Comprehensve, Unnsured, Loss of Use, and Car Towng coverage. Man characterstc of these types of nsurance coverage are descrbed below, followng Wkpeda (www.wkpeda.org.ua): Collson coverage provdes coverage for an nsured's vehcle that s nvolved n an accdent, subject to a deductble. Ths coverage s desgned to provde payments to repar the damaged vehcle, or payment of the cash value of the vehcle f t s not reparable. Comprehensve (a.k.a. - Other Than Collson) coverage provdes coverage, subject to a deductble, for an polcyholder s vehcle that s damaged by ncdents that are not consdered by Collsons. For example, fre, theft (or attempted theft), vandalsm, weather, or mpacts wth anmals are some types of 20
Comprehensve losses. Unnsured coverage provdes coverage f another at-fault party ether does not have nsurance or does not have enough nsurance. In effect, nsurance company acts as at fault party's nsurance company. Loss of Use coverage, also known as rental coverage, provdes rembursement for rental expenses assocated wth havng an nsured vehcle repared due to a covered loss. Car Towng coverage s also known as Roadsde Assstance coverage. Tradtonally, automoble nsurance companes have agreed only to pay for the cost of a tow that s related to an accdent that s covered under the automoble polcy of nsurance. Ths had left a gap n coverage for tows that are related to mechancal breakdowns, flat tres and runnng out of gas. To fll that vod, nsurance companes started to offer the Car Towng coverage, whch pays for non-accdent related tows. Insurance companes n Ukrane also propose for ther potental customers Lablty coverage can have hgher lmt of lablty than under oblgatory cvl lablty coverage. Lablty coverage n the case of oblgaton and opton provdes payment for loss of health for thrd person or hs damaged vehcle wthn a lmt defned n contract. Law of Ukrane concernng automoble nsurance confrms to the common features of nternatonal market of nsurance. In Ukrane the potental nsured can freely choose the nsurance company n whch he wants to nsure hs vehcle. However, the nsurer can not force the polcyholder to renew hs nsurance contract n the next perod or even to dsrupt the contract n the perod of nsurance. At the same tme, there s requrement accordng to whch polcyholder could not nsure the same rsk several tme by usng servces of dfferent nsurers. Insurance market of Ukrane s not well developed n comparson wth other markets, prmarly because of the lack of development n rate makng. Experence ratng, where the polcyholder s nsurance premum for the next year s defned on the base of the prevous drver s clam hstory, s commonly used n the countres of EU. In Ukrane, ths methodology s not common, manly because non-publcty of nsurance nformaton. There s no database n Ukrane, whch s accessble for all nsurers and whch has nformaton about the drvers and ther clam hstory. Hence, the bonus-malus system of ratemakng, where postve (clam-free) hstory of drvng experence leads to decrease n the premum, s not present. Snce experence ratng s one of the methods to elmnate possble 21
problems of asymmetrc nformaton, t s wse to expect that n the absence of approprate rate makng system t s more probable to observe problems of asymmetrc nformaton, because of the hgher attractveness of nsurance to the bad drvers and drvers wthout experence. 4.2. Descrptve Statstcs For my research I use data obtaned from a large nsurance company that operates n the market for automoble nsurance n Ukrane. Snce most of data observatons come from Kyv regon, I lmt the sample to the polces that were sold n Kyv n order to nvestgate the evdence of adverse selecton n ths regon. For smplcty, I also exclude the polcyholders who purchased contracts wth contractual perods not equal to one year, snce ths excluson nfluences my sample by less than one percent. My fnal sample for the perod from the 1 st of January 2004 to the 31 st of December 2004 conssts of more than 2000 voluntary nsurance polces undertaken. Ths data should be representatve for the automoble nsurance market n Kyv, snce t comes from a top 10 (by sales) nsurance company, out of more than 100 n Ukrane. Data corresponds to the man features of automoble nsurance market n Ukrane, and Kev n partcular: the man peculartes, whch are typcal for the entre market (that I am gong to dscuss below), are also typcal for the company from whch I obtan nformaton for research. Data for the research contans all nformaton that the nsurance company has about polcyholders. In partcular, I have the nformaton about the polcy ssued n the year polcyholder joned the nsurer and for those who stayed for more than one year. The nformaton about the clam hstory s also avalable. Thus, I have both quanttatve and qualtatve nformaton about the contracts and clams occurred (see Table 1). 22
Value of car Weght of vehcle Sze of engne Type of body Sedan Estate car Off-road vehcle Mnvan Mnbus Truck Country of the car Asa Eastern Europe West Europe USA Age of the car Company experence Gender Type of vehcle s use Place of resdence Type of coverage Premum pad Amount of clams Clam occurrence Table 1: Lst of Varables Vehcle s characterstcs The value of the car (n UAH) The weght of the car (n klograms) The sze of engne (n square centmeters) Equal to 1 f the car s sedan Equal to 1 f the car s estate car Equal to 1 f the car s off-road vehcle Equal to 1 f the car s mnvan Equal to 1 f the car s mnbus Equal to 1 f the car s truck or wagon Equal to 1 f the car s made n Asa Equal to 1 f the car s made n Eastern Europe Equal to 1 f the car s made n West Europe Equal to 1 f the car s made n USA Age of the car (n years) Polcyholder s characterstcs Equal to the number of years that the polcyholder has been wth the nsurer Equal to 1 f polcyholder s male Equal to 1 f car s used n prvate needs and equal to 0 f t s used n commercal needs Equal from 1 to 10 dependng on the cty dstrct were polcyholder s regstered Contract s characterstcs Equal to 1 f all rsks are nsured Yearly premum All payments resultng from the from the nsurance of the polcy Equal to 1 f clam concernng the nsurance contract appears I have the followng nformaton about polcyholders, ther cars, and clam occurrences. Polcyholder s car characterstcs: sze of engne, type of fuel, model year, car weght, type of car body, value of car, country of car n whch t was made; Polcyholder s characterstcs: place of resdence whch s used for bllng purposes, gender, company experence, whch show how many years polcyholder had 23
nsurance wth ths nsurer n the past, and type of vehcle s use (commercal or prvate). Contract s characterstcs: type of contract (new polcy or renewal), type of coverage (full or not full), premum pad. Perod covered: the length of the perod covered by the purchased polcy. Realzaton of rsk covered by the polcy: descrpton of the clam occurred, ncludng the amount of damages reported and the amount whch the nsurer pad or was expected to pay. The nsurer offers for ts potental customers a menu of contract choces after obtanng the above nformaton. Voluntary motor nsurance, under whch polcyholder nsures possble rsks and whch are not contrary to Ukranan legslaton, are connected wth the followng rsks: 1) rsk of loosng the possesson, usng and dsposng of vehcle, ncludng rsk of vehcle s damage and theft (Comprehensve Coverage); 2) rsk of rembursement by nsured a property damage or personal njury to thrd partes n the case of nsured s fault (Cvl lablty: Death / Bodly Injury and Damage to Property); 3) rsk of loosng lfe, health and ablty to work for persons whch was n nsured vehcle durng the rsk occurrence (Personal Injury Protecton). The company proposes three types of nsurance coverage that are typcal for automoble nsurance n Ukrane and some achevable combnatons of the three. In order to support the methodology, whch I am gong to use, I dvde all polces ssued nto two types: contract, whch covers all rsk (full coverage) 24
aganst the one, whch covers only selected rsks (not full coverage). I assume that more ndvduals, who are not confdent n ther drvng capablty, wll demand full coverage n the presence of adverse selecton. As shown n Table 2, from the data obtaned, I can state that about 43% of all customers choose to nsure all type of rsks. However, the clam frequency s qute large and equals to 22% wth average clam amountng UAH 3042.30. Lkewse, the average premum that polcyholder pad equals UAH 4267.47. On average, more than 90% of polcyholders are men and only about 26% of the polcyholders use vehcles for prvate needs. These numbers are typcal for the entre automoble nsurance market n Ukrane. Accordng to Annual Insurance Market Overvews whch were done by the League of Insurance Companes n Ukrane (www.uansur.com) and other ndependent researchers (www.fornsurer.com), voluntary automoble nsurance and other types of nsurance, are relatvely expensve for a drver wth mddle ncome. For ths reason, most of the nsured are legal enttes. Ukranan nsurance statstcs also shows that females n Ukrane, lke n the rest of the world, have lower probablty to get nto an accdent. So, I can state that those descrptve statstcs are representatve for the automoble nsurance n Ukrane and Kyv n partcular. The average length of the nsurance of the vehcle amounts to 2.5 years, whch gves us the sense that mostly new cars are nsured wth the average sze of engne about 2055 square centmeters. The average value of a car nsured amounts to UAH 92967. On average, expensve cars are mostly nsured wth the mn value of UAH 5100 and the maxmum value of UAH 988006. Insurer also dvdes vehcles by the type of body (sedan, estate car, off-road vehcle, mnvan, mnbus, truck) and accordng to the country where the cars were made (Eastern Europe, Western Europe, Asa, and USA). From the data descrptve statstcs I can see that the common car nsured s sedan (63%), and as a rule, the car nsured comes 25
from Western Europe (57%) or Eastern Europe (21%). Prevous statstcs also corresponds to the man features of the entre nsurance market n Ukrane, snce demand for new cars, especally for not bg daly used cars, ncreases whch nfluences the automoble nsurance contracts. At the same tme, the most popular cars come to Ukrane from Germany, France, England, and countres of Far East. Table 2: Descrptve Statstcs Varable Mean Std. Dev. Mn Max Vehcle characterstcs Value of car 92966.71 89437.91 5100 988006 Weght of vehcle 1471.353 1418.117 720 19700 Sze of engne 2054.764 1522.52 796 14566 Age of the car 2.45118 2.66763 0 25 Type of body Sedan 0.633966 0.481831 0 1 Estate car 0.118001 0.322684 0 1 Off-road vehcle 0.088385 0.28392 0 1 Mnvan 0.050902 0.219849 0 1 Mnbus 0.026377 0.16029 0 1 Truck 0.082369 0.27499 0 1 Country of the car Asa 0.178158 0.382735 0 1 Eastern Europe 0.206386 0.404804 0 1 West Europe 0.568718 0.49537 0 1 USA 0.046738 0.211125 0 1 Polcyholder s characterstcs Company experence 1.030541 1.445617 0 6 Gender 0.910227 0.285923 0 1 Type of vehcle s use 0.256826 0.436984 0 1 Contract characterstcs Type of coverage 0.434058 0.495747 0 1 Premum pad 4267.468 4602.167 94 82305.5 Amount of clams 3042.304 13290.83 0 250000 Clams occurrence 0.223508 0.416692 0 1 26
In settng the prce (premum) of the contract for each potental polcyholder, the nsurance company uses the nformaton descrbed above, whch s obtaned from ts customers. Not havng an access to the nsurer s formula, I try to defne how the nsurance company determned premum to the polcyholders. I regress for all ndvduals the premum pad by each polcyholder on all characterstcs that the company has as shown n Appendx 1 by regresson (1). At 5% level of sgnfcance, most of coeffcents of ordnary least square are sgnfcant and ft the model well (R 2 =0.69). Moreover, after ncludng squares of the major varables and ther ntercepton as shown n Appendx 1 by regressons (2) - (4), I fnd that they are nsgnfcant, suggestng that the company s formula for premum determnaton s pretty much lnear. The model for premum gves us reasonable explanaton of how polcyholder s and hs car s characterstcs nfluence the premum. Thus, wthn 90% confdence nterval, n the case of full coverage the premum should ncreased by UAH 1378 aganst the case of not full nsurance coverage. In the case when a car s used for prvate needs, the premum should ncrease by UAH 667 and the male should pay approxmately by UAH 541 more than female. The last dependence s commonly used not only by Ukranan nsurance companes, but also n the world practces because t s proved that women are more careful drvers. The value of a car s also a reasonable factor n defnng the premum level. Value s ncrease by UAH 1 causes the ncrease n premum by UAH 0.045. However, a type of body s not always sgnfcant n determnaton of value of premum. Nevertheless, at 10% level of sgnfcance for the nsurance of off-road vehcle and estate car the premum ncreases by UAH 848 and UAH 400 correspondngly, and for the nsurance of truck premum of nsurance contract s premum decreases by UAH 804 n comparson wth the premum for sedan s 27
nsurance. If car s made n the USA, Asa, or Eastern Europe, the premum should ncrease by UAH 992, UAH 402, and UAH 424 accordngly n comparson to the car made n Western Europe. However, from the regresson I also observe that every addtonal year of nsurance experence n the same company ncreases the amount of premum by UAH 360. Ths suggests that t s not common for the Ukranan company to use drver s experence n order to encourage safe drvng. However, t s more usual that the polcyholder who renews hs polcy has not good clam hstory. The last statement s supported by fndng that, wth 95% confdence nterval, there s a sgnfcant postve nfluence of polcyholder s experence relatve to hs loss rato (see Table 6.). Thus, I fnd that every addtonal year of polcyholder s experence n the same company ncreases loss rato by 0.664. Ths suggests that nsurance company mostly nsures bad drvers, who have hgh probablty of havng accdents. Ths fact s confrmed by the fndng that the loss rate s qute large. 28
Chapter 5 EVIDENCE FOR ADVERSE SELECTION 5.1. Testng for Asymmetrc Informaton My emprcal analyss begns wth testng the exstence of asymmetrc nformaton n Kyv automoble nsurance market. I start by comparng polcyholders wth full and not full coverage n terms of the clams submtted. I frst test for a correlaton between contracts wth full coverage and clam amount usng ordnary OLS and a correlaton between contracts wth full coverage and occurrence of an accdent usng bprobt and logt specfcatons. For the set of all customers choosng ether full or not full coverage n a contract, I regress the amount of clam n monetary unts (for the probt and logt, occurrence of at least one clam) on all polcyholder s and vehcle s characterstcs and on a dummy varable representng whether a full or non-full coverage was chosen. The results, whch are shown n Table 3, ndcate that even at 10% level of sgnfcance the amount of clams s not statstcally sgnfcantly nfluenced by the type of polcyholder s contracts. In other words, f a polcyholder chooses contract whch covers all rsk or only selected ones, n general, ths does not nfluence the amount of clams whch ndvdual requres f an accdent occurs. Smlar concluson follows from the bnary equatons. Snce type of contract s coverage does not nfluence the occurrence of an accdent, polcyholder s choce of contract does not nfluence the probablty of accdent occurrence, whch gves the possblty to reject the hypothess of evdence for asymmetrc nformaton n the Kyv automoble market. 29
Table 3: Estmaton Results for Coverage-Clam Correlaton (asymmetrc nformaton determnaton) COEFFICIENT OLS Probt Logt Amount of clams Clam occurrence Clam occurrence Full coverage 166.7 0.0999 0.167 (604) (0.066) (0.11) Company experence 478.1** 0.132*** 0.225*** (212) (0.022) (0.037) Prvate use 1332 0.277*** 0.472*** (828) (0.089) (0.15) Male -719.2-0.169-0.279 (1156) (0.12) (0.20) Age of car -130.3-0.0620*** -0.112*** (121) (0.015) (0.027) Sze of engne -3.53e-05-1.07e-04-2.89e-05 (2.90e-05) (2.80e-05) (2.90e-05) Value of car 1.03e-06*** 3.68e-07** 9.64e-07** (4.50e-07) (4.40e-07) (4.40e-07) Off-road vehcle 502.6-0.243** -0.417** (1140) (0.12) (0.21) Mnbus 1081-0.336-0.632 (1814) (0.23) (0.42) Mnvan 1054-0.101-0.190 (1325) (0.15) (0.26) Estate car 877.4-0.112-0.207 (911) (0.10) (0.18) Truck -780.0-0.109-0.212 (1216) (0.14) (0.26) USA 4.464-0.1000-0.160 (1404) (0.16) (0.29) Asa 573.3 0.323*** 0.540*** (888) (0.092) (0.16) Eastern Europe 643.2 0.145* 0.247* (786) (0.086) (0.15) Constant 778.8-0.807*** -1.321*** (1335) (0.14) (0.24) Observatons 2161 2161 2161 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely. I also use postve correlaton test for determnng the evdence of asymmetrc nformaton suggested by Chappor and Salane (2000), n whch a par of probts 30
models are used n order to test the condtonal dependence between the choce of coverage and the occurrence of clam. These two equatons are the choce of the contract s coverage (full or not full) on the polcyholder s and vehcle s characterstcs and the occurrence of at least one clam on the polcyholder s and vehcle s characterstcs. To test the condtonal dependence of models resduals I use a test statstc W usng formula (3) descrbed n chapter 3. W s dstrbuted asymptotcally as χ 2 (1). Under the null hypothess of cov( ε, ) = 0 there s no asymmetrc nformaton. If asymmetrc nformaton exsts n automoble nsurance market, the condtonal dependence between the choce of coverage and the occurrence of the clam should be sgnfcantly postve. However, n nsurance market under consderaton the statstcs W dsplayed n Table 4 shows that the correlatons between the choce of coverage and the occurrence of a clam are not sgnfcantly dfferent from zero. Thus, I can reject null hypothess about exstence of asymmetrc nformaton n the market. η Table 4: The Condtonal Correlaton between Coverage and Clam W~ χ 2 (1) ρ 2.288281 0.0600413 Prob > χ 2 (1) = 0.1304 Prob > z = 0.134 Do not reject H 0 : cov( ε, ) = 0 Do not reject H 0 : ρ = cov( ε, ) = 0 η No evdence for asymmetrc nformaton No evdence for asymmetrc nformaton η In order to test the same condtonal dependence between the choce of coverage and the occurrence of the clam, I also estmate these regressons usng bvarate probt. The bvarate probt estmates the correlaton ρ between the errors terms of two bnary equatons. If the error terms of the two equatons are ndependent, then ρ wll be equal to zero. The results of ths regresson are dsplayed n Appendx 2. An estmate for ρ s postve, but statstcally nsgnfcant even at 31
10% confdence level. Thus, test statstc W and correlaton coeffcent ρ between the errors terms of two bnary equatons, whch are reported n Table 4, show that the emprcal evdence mples that asymmetrc nformaton problems do not exst n Kyv automoble nsurance market. 5.2. Testng for Adverse Selecton caused by Unobservable Varables The frst look at the data from the Kyv State Vehcle Inspectorate, dsplayng n Appendx 3, suggests that probablty of accdents, njures, and death from car accdents vary among the cty dstrcts: the probabltes of crash accdents are hgher n non-central dstrct, snce they mostly occur n the case of hgh-speed drvng. Thus, f premums are not dscrmnated by regon and f dsposton for adverse selecton exsts, drvers n more rsk regon are more lkely to purchase nsurance wth hgh coverage than n lower rsk regon. However, accordng to Fnkelsten and Poterba (2006) n order to prove that adverse selecton exsts n the automoble nsurance market, place of resdence, as a polcyholder s characterstc that s unused by the nsurance company, should be correlated wth both nsurance coverage and ex-post rsk of loss. I assume that place of resdence as geographc nformaton s correlated wth ndvdual characterstcs that affect both demand for nsurance and polcyholder s rsk type and thus cause the problem of adverse selecton. Drvers, who lve n rsk regon, where t s hgh possblty to get an accdent, and where they are probably drve n mornng and evenng rush hours or around the place of resdence durng the day, are more lkely to demand nsurance contract compared to the drvers who are regstered n safer cty regons. On the other hand, I suppose that drvers regstered n more rsky cty regons should be more rsky, snce they are not able to avod bad road nfrastructure (for nstance dangerous 32
turnng), to lmt speed for other drvers and to avod other traffc dsadvantages of a dstrct. For ths reason drvers who lve n more rsk regon become more senstve to get crash accdents. In order to test for adverse selecton usng test wth unused varables proposed by Fnkelsten and Poterba (2006), I estmate bvarate probt model as shown n Table 5 by regresson (1), regressng clam occurrence and then type of contract s coverage on all polcyholder s and vehcle s characterstcs and varable whch approxmates rskness of polcyholder by representng number of car accdents n prevous to nsurance year n the dstrct where polcyholder s regstered. Thus, f adverse selecton as a source of asymmetrc nformaton exsts, coeffcent whch determnes rskness of regon (number of car accdents n prevous to nsurance year) should sgnfcantly nfluence on the type of coverage polcyholder chose and the probablty of accdent. At 5% level of sgnfcance I fnd that n Kyv automoble nsurance market place of polcyholder s resdence nfluences on the polcyholder s choce of coverage and on the occurrence of accdents; hence, I can reject the null hypothess of symmetrc nformaton statng that I fnd evdence for adverse selecton. Moreover, n order to prove that obtaned results are robust I use the same model but approxmate rskness of drvers by representng number of car accdents per sq km n prevous to nsurance year n the dstrct where polcyholder s regstered. I use ths approxmaton snce n smaller dstrct fewer accdents can be regstered and the wrong decson about dstrct danger and thus polcyholder s rskness can be taken. For ths reason, I consder that t s also valuable to consder densty of accdents occurrence n all dstrcts as ndvdual rskness. 33
Table 5: Estmaton Results for Adverse Selecton Determnaton COEFFICIENT Bprobt (1) Bprobt (2) Clam occurrence Full coverage Clam occurrence Full coverage Company experence 0.133*** 0.183*** 0.133*** 0.179*** (0.022) (0.021) (0.022) (0.022) Prvate use 0.232*** -0.469*** 0.277*** -0.361*** (0.090) (0.085) (0.089) (0.085) Male -0.173 0.161-0.165 0.175 (0.12) (0.12) (0.12) (0.12) Age of car -0.0635*** -0.0440*** -0.0602*** -0.0326** (0.015) (0.013) (0.015) (0.013) Sze of engne -3.53e-05-1.07e-04*** -2.89e-05-9.08e-05*** (2.90e-05) (2.80e-05) (2.90e-05) (2.80e-05) Value of car 1.03e-06** 3.68e-07 9.64e-07** 1.96e-07 (4.50e-07) (4.40e-07) (4.40e-07) (4.40e-07) Off-road vehcle -0.240** -0.0972-0.254** -0.143 (0.12) (0.11) (0.12) (0.11) Mnbus -0.346-0.242-0.304-0.102 (0.23) (0.19) (0.23) (0.19) Mnvan -0.103-0.0778-0.0898-0.0220 (0.15) (0.13) (0.15) (0.13) Estate car -0.101 0.326*** -0.100 0.337*** (0.10) (0.091) (0.10) (0.091) Truck -0.0798 0.139-0.0851 0.167 (0.14) (0.12) (0.14) (0.12) USA -0.119 0.328** -0.109 0.304** (0.16) (0.14) (0.16) (0.14) Asa 0.317*** 0.269*** 0.336*** 0.312*** (0.092) (0.089) (0.091) (0.090) Eastern Europe 0.124 0.261*** 0.150* 0.299*** (0.087) (0.080) (0.086) (0.079) Accdents 0.000848** 0.00151*** (0.00043) (0.00041) Accdents per area 0.00159* 0.00562*** (0.00095) (0.00090) Constant -0.945*** -0.632*** -0.888*** -0.760*** (0.17) (0.16) (0.16) (0.16) athrho 0.0553 0.0557 (0.040) (0.040) Observatons 2161 2161 2161 2161 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely. 34
I estmate bvarate probt model agan as shown n Table 5 by regresson (2), regressng clam occurrence and then type of contract s coverage on all polcyholder s and vehcle s characterstcs and varable whch approxmates rskness of polcyholder s by representng number of car accdents per sq km n prevous to nsurance year n the dstrct where polcyholder s regstered. There I observed smlar results (however wth a smaller level of sgnfcance): at 10% level of sgnfcance, place of polcyholder s resdence nfluences on the polcyholder s choce of coverage and on the occurrence of accdents. Therefore, I can reject the null hypothess of symmetrc nformaton statng that I fnd evdence for adverse selecton. Thus, I obtan that postve correlaton test proposed by Chappor and Salane (2000) ndcates for the absence of asymmetrc nformaton n Kyv automoble nsurance market, whle unused observables test ndcates for the exstence of asymmetrc nformaton caused by adverse selecton due to dfferent rskness of the cty dstrcts. However, these results are not surprsng: Fnkelsten and Poterba (2006) and Chappor at al. (2006) affrmed that prmary postve correlaton test and just correlaton between type of contract coverage and accdence occurrence n the same nvestgaton perod can lead to type I and type II errors (whch I descrbe n chapter 3) due to neglectng polcyholder s rsk heterogenety. Therefore, under pure theoretcal assumpton that all polcyholders are homogeneous n rsk tolerance, the postve correlaton test reflects the absence for asymmetrc nformaton and adverse selecton n partcular. However, takng nto account unobserved heterogenety n ndvdual preferences, and thus elmnatng type II error, unused observables test shows that at 10% level of sgnfcance I can reject the null hypothess of symmetrc nformaton. At the same tme, I can state that I found the evdence for adverse selecton (not just for asymmetrc nformaton). Ths can be explaned by the fact that usng polcyholder s place of resdence as unused varable n the model corresponds to 35
condton of determnaton for the evdence of adverse selecton. Accordng to Fnlelsten and Poterba (2006), observng that a characterstc that nsurance companes do not use n prcng s postvely correlated wth nsurance quantty purchased and wth ex post rsk occurrence [and] when there s external nformaton that certan characterstcs are correlated wth rsk occurrence for reasons other than nsurance coverage [such case as I have ] then the unused observables test can dentfy the presence of adverse selecton and rule out moral hazard as the exclusve source of the observed correlaton between ndvdual attrbutes, nsurance quantty, and rsk of loss. Thus, I can conclude that takng nto account heterogenety n ndvdual rsk preferences, there s evdence for adverse selecton as a source of asymmetrc nformaton n the Kyv automoble nsurance market. I go even further n order to check for the robustness of my conclusons. Snce most of the researchers, among whch there are Chappor and Heckman (2000), Abbrng et al. (2003), Huang et al. (2005), have used dynamc data n order to defne the evdence for adverse selecton, I also use clam hstory of polcyholders n order to approxmate ther rskness. I use a sub-sample wth polcyholders who were nsured wth ths nsurance company n prevous years. The record of accdent n prevous to nvestgaton perod could be a proxy of drver s rsk type. To test whether a hgh rsk type wll choose hgh coverage, causng problem of adverse selecton, I regress type of contract s coverage chosen by nsured on all hs characterstcs, characterstcs of hs car and varable whch approxmates rskness of polcyholder s by representng hs clam (or accdent occurrence) n prevous to nsurance year. The results, whch are shown n Appendx 4, ndcate that at 1% level of sgnfcance the type of contract s coverage chosen by nsured s statstcally sgnfcantly nfluenced by hs rsk type, whch gve us possblty to state that I 36
cannot reject the hypothess of evdence for adverse selecton. In other words, more rsky drvers (n my case drvers who had accdent n prevous to nsurance year) choose contract wth full coverage nsurng all possble rsks, thus causng the problem of adverse selecton n the market. 5.3. Testng for Cross subsdzaton Fnally, to trace the exstence of cross subsdzaton as a problem whch accompanes problems of asymmetrc nformaton n Kyv automoble nsurance market, I check whether the choce of contract s type nfluences the polcyholder s loss-rato. Table 6: Estmaton Results for the Loss Rato Determnaton COEFFICIENT Tobt Tobt COEFFICIENT Loss rato Loss rato Full coverage 0.572 Mnbus 0.0685 (0.41) (1.32) Company experence 0.664*** Mnvan -0.00197 (0.14) (0.92) Prvate use 1.783*** Estate car -0.330 (0.56) (0.64) Male -0.591 Truck -0.772 (0.73) (0.91) Age of car -0.360*** USA -0.473 (0.093) (1.01) Sze of engne 0.000109 Asa 1.816*** (0.00017) (0.57) Value of car 0.00000114 Eastern Europe 0.864 (0.0000027) (0.54) Off-road vehcle -1.118 Constant -6.131*** (0.76) (0.91) sgma 6.579*** (0.24) Observatons 2161 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely. 37
I regress loss rato on all the polcyholder s and vehcle s characterstcs and type of coverage they chose as shown n Table 6. Usng ths methodology, I want to check whether polcyholders who buy contract wth full coverage are more rsky and have hgher loss rato and thus are cross-subsdzed by low rsk polcyholders, whose prce for the contracts are overcharged n ths case. Fndng that coeffcent near the varable type of nsurance coverage s nsgnfcant, gve opportunty to state that loss rato does not depend on the type of coverage nsured chose, and therefore there s no evdence for cross subsdzaton n the Kyv automoble nsurance market. From the regresson above I also come to concluson that company experence, type of vehcle s use and the age of car are the varables whch at 1% level of sgnfcance nfluence the loss rato. Thus, addtonal year of prevous nsurance wthn the same nsurer ncreases loss rato by around 0.664 tmes, f polcyholder s prvate agent hs loss rato ncrease by 1.783 tmes compared to the polcyholder, who represent legal entty. If an nsured has a newer car hs loss rato decreases. Thus, the ssues from ths and prevous models mply that the developng voluntary automoble nsurance market under consderaton s spolt by the asymmetrc nformaton problem caused by adverse selecton and free from cross subsdzaton problems. Although I fnd that there s no problem of cross subsdzaton, I am not nsstng that ths problem does not exst n the market. My study ndcates that the Kyv automoble nsurance market s affected by adverse selecton but s not serously nfected by cross subsdzaton problem between polcyholders. 38
Chapter 6 CONCLUSIONS The emprcal applcaton of the theory concernng dentfyng the evdence of asymmetrc nformaton has receved ncreasng attenton. Specal concern n the lterature s devoted to determnaton of the source of asymmetrc nformaton n the nsurance market. In my research, for separaton of adverse selecton from moral hazard I employ the unused observables test, proposed by Fnkelsten and Poterba (2006). Accordng to ths test, I nvestgate whether place of resdence as unused observable characterstc s correlated wth polcyholder s rsk type and hs choce of nsurance coverage. For determnng the cross subsdzaton problem, whch accompanes to the problem of adverse selecton, I test whether ndvdual loss rato s postvely related to the choce of nsurance coverage. I start wth nvestgatng whether the problem of asymmetrc nformaton s typcal for Kyv voluntary automoble nsurance market, whch can be dentfed as a developng nsurance market. I use ordnary OLS, bprobt and logt specfcatons to test for a correlaton between contracts wth full coverage and clam occurrence. I fnd that whether a polcyholder chooses contract whch covers all rsks or only selected ones, n general, ths does not nfluence the amount of clams whch an ndvdual requres f an accdent occurs. Postve correlaton test for the asymmetrc nformaton proposed by Chappor and Salane (2000) gves us the same concluson supportng the evdence of symmetrc nformaton n the market. Takng nto account that prmary postve correlaton test and just correlaton between type of contract coverage and accdence occurrence n the same 39
nvestgaton perod need an assumpton about ndvdual homogenety n rsk preferences, I also test for the evdence of asymmetrc nformaton usng unused observables test, whch relaxes ths assumpton. Usng dfferent specfcatons of the polcyholder s rskness based on hs place of resdence, I come to the concluson that there s problem of adverse selecton n the market under consderaton. In order to check whether obtaned results are robust, I also employ dynamc data, approxmatng polcyholder s rskness by accdent occurrence n a prevous to nsurance year. I fnd that more rsky drvers choose contracts wth full coverage nsurng all possble rsks, thus causng the problem of adverse selecton n the market. Investgatng the relatonshp between ndvdual loss raton and choce of coverage, I do not fnd presence of cross subsdzaton n nsurance market. Thus, I conclude that Kyv automoble nsurance market s affected by adverse selecton, but s not serously nfluenced by cross subsdzaton problem between polcyholders. My fndng does not contradct the papers n whch the evdence for adverse selecton s not found, snce n most of them developed nsurance markets are examned. My nvestgaton supports fndngs that asymmetrc nformaton problem s more common to the developng markets snce exstng mechansms n developed nsurance market tend to allevate the problem of adverse selecton and/or moral hazard. My study suggests that further research of asymmetrc nformaton and adverse selecton n partcular should concern the nvestgaton of nsurance market over larger perod of tme or across countres wth nsurance markets n dfferent stages of development, n order to determne how the mprovement n market performance nfluences on the asymmetrc problem. 40
BIBLIOGRAPHY Abbrng, Jaap, Perre-Andre Chappor, and Jean Pnquet. 2003. Moral hazard and dynamc nsurance data, Journal of the European Economc Assocaton, 1, pp. 767-820. Arnott, Rchard and Joseph Stgltz. 1988. The basc analytcs of moral hazard, Scandnavan Journal of Economcs, 90, pp. 383-413. Cardon, James and Igal Hendel. 2001. Asymmetrc nformaton n Health Insurance: Evdence from the Natonal Medcal Expendture Survey, Rand Journal of Economcs, 32, pp. 408-427. Cawley, John and Tomas Phlpson. 1999. An emprcal examnaton of nformaton barrers to trade n nsurance, Amercan Economc Revew, 89, pp. 827-846. Chappor, Perre-Andre and James Heckman. 2000. Testng for moral hazard on dynamc nsurance data: theory and econometrc tests, mmeo, Unversty of Chcago, accessed at http://home.uchcago.edu/~pch appo/wp/pacjhfn.pdf Chappor, Perre-Andre and Bernard Salane. 2000. Testng for Asymmetrc Informaton n Insurance Markets, Journal of Poltcal Economy, 108, pp. 56-78. Chappor, Perre-Andre, Bruno Jullen, Bernard Salane, and Francos Salane. 2006. Asymmetrc Informaton n Insurance: General Testable Implcatons, Rand Journal of Economcs. Cohen, Alma. 2005. Asymmetrc Informaton and Learnng n the Automoble Insurance Market, Revew of Economcs and Statstcs, 87, pp. 197-207. Donne, Georges and Robert Gagné. 2002. Replacement Cost Endorsement and Opportunstc Fraud n Automoble Insurance, Journal of Rsk and Uncertanty, 24 (3), pp. 213-230. Donne, Georges, Chrstan Goureroux and Charles Vanasse. 2001. Testng for evdence of adverse selecton n the automoble nsurance market: a comment, Journal of Poltcal Economy, 109(2), pp. 444-451. Donne, Georges, Nel A. Doherty, and Nathale Fombaron. 2000. Adverse selecton n nsurance markets, In Georges Donne, ed. Handbook of Insurance Economcs, pp. 185-244. Fnkelsten, Amy and James Poterba. 2004. Adverse Selecton n Insurance Markets: Polcyholder Evdence from the U.K. Annuty Market, Journal of Poltcal Economy, 112, 183-208. Fnkelsten, Amy and James Poterba. 2006. Testng for Adverse Selecton wth Unused Observables, NBER Workng Paper No. W12112 avalable at 41
SSRN: http://ssrn.com/abstract=89376 7. Fnkelsten, Amy and Kathleen McGarry. 2004. Multple Dmensons of Prvate Informaton: Evdence from the Long-Term Care Insurance Market, Amercan Economc Revew. Huang Rachel J., Larry Y. Tzeng, Jennfer L. Wang and Kl C. Wang. 2005. Evdence for Adverse Selecton n the Automoble Insurance Market, mmeo, Mng Chuan Unversty, accessed at http://www.ara.org/meetngs/2 006papers/HuangTzengWangWa ng.pdf Makk, Shva S. and Agap Somwaru. 2001. Evdence of Adverse Selecton n Crop Insurance Market, Journal of Rsk and Insurance, 68, pp. 685-708. Myazak, Hajme. 1977. The Rat Race and Internal Labor Markets, The Bell Journal of Economcs, 8, pp. 394-418. Puelz, Robert and Arthur Snow. 1994. Evdence on Adverse: Equlbrum Sgnalng and Cross Subsdzaton n the Insurance, Journal of Poltcal Economy, 102 (2), pp. 236-257. Rley, John G. 1979. Informatonal equlbrum, Econometrca, 47, pp. 331-359. Rothschld, Mchael and Joseph Stgltz. 1976. An Essay on the Economcs of Imperfect Informaton, Quarterly Journal of Economcs, 90, pp. 629-649. Sato, Kunyosh. 2003. Does Less Rsk Classfcaton Induce More Adverse Selecton? Evdence from Automoble Insurance Market, mmeo, Unversty of Tokyo, accessed at http://www.e.utokyo.ac.jp/crje/research/works hops/mcro/mcropaper03/ksat o.pdf Spence, Mchael A. 1978. Product Dfferentaton and Performance n Insurance Markets, Journal of Publc Economcs, 10, pp. 427-447. van de Ven, Wynand and Rene van Vet. 1995. Consumer Informaton Surplus and Adverse Selecton n Compettve Health Insurance Markets: An Emprcal Study, Health Economcs, 14, pp. 149-161. www.fornsurer.com www.uansur.com www.wkpeda.org.ua 42
APPENDIX A Estmaton Results for the Premum Determnaton Dependent varable: Premum for the contract pad COEFFICIENT OLS (1) OLS (2) OLS (3) OLS (4) Premum pad Premum pad Premum pad Premum pad Company experence 359.7*** 353.7*** 359.9*** 361.4*** (41.7) (41.9) (42.7) (42.2) Full coverage 1378*** 1374*** 1378*** 1289*** (119) (118) (118) (133) Prvate use 667.4*** 635.1*** 1326 1511* (163) (162) (904) (901) Male 540.8** 533.2** 1193 1336 (227) (226) (879) (870) Age of car 5.601-36.49-39.87-100.1* (23.7) (60.3) (60.4) (60.5) Sze of engne -0.356*** -0.329*** -0.329*** 0.714*** (0.048) (0.048) (0.048) (0.16) Value of car 0.0445*** 0.0378*** 0.0378*** 0.0327*** (0.00082) (0.0020) (0.0020) (0.0022) Off-road vehcle 847.7*** 952.4*** 947.2*** 754.9*** (224) (225) (225) (225) Mnbus 298.9 369.0 372.1-338.6 (356) (355) (355) (367) Mnvan -137.2-145.2-149.3-240.1 (260) (259) (259) (257) Estate car 400.1** 336.3* 330.5* 205.3 (179) (179) (179) (179) Truck -804.1*** -888.7*** -889.8*** -990.3*** (239) (239) (239) (237) USA 992.4*** 984.9*** 981.5*** 821.3*** (276) (275) (275) (273) Asa 401.7** 428.1** 430.2** 277.8 (174) (175) (175) (175) Eastern Europe 424.1*** 255.6 251.9 78.57 (154) (161) (161) (161) Age of car^2 1.662 1.861 3.210 (3.68) (3.69) (3.67) Value of car^2 1.18e-08 1.19e-08 1.57e-08 (2.99e-09) (3.00e-09) (3.02e-09) Value of car*age of car -0.000107-0.000104-0.000357 (0.00036) (0.00036) (0.00035)
COEFFICIENT OLS (1) OLS (2) OLS (3) OLS (4) Premum pad Premum pad Premum pad Premum pad Prvate use*male -705.2-976.7 (908) (900) Prvate use*full coverage 120.3 (279) Sze of engne^2-7.59e-05-1.10e-05 Constant -1044*** -518.4* -1175-2216** (262) (309) (900) (906) Observatons 2161 2161 2161 2161 R-squared 0.69 0.69 0.69 0.70 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely.
Appendx B Estmaton Results for Asymmetrc Informaton COEFFICIENT Bprobt Clam occurrence Full coverage Company experence 0.139*** 0.198*** (0.022) (0.021) Prvate use 0.261*** -0.415*** (0.088) (0.084) Male -0.162 0.175 (0.12) (0.12) Age of car -0.0634*** -0.0442*** (0.015) (0.013) Sze of engne -0.0000301-0.0000983*** (0.000029) (0.000028) Value of car 0.000000989** 0.000000315 (0.00000044) (0.00000044) Off-road vehcle -0.246** -0.111 (0.12) (0.11) Mnbus -0.345-0.244 (0.23) (0.19) Mnvan -0.104-0.0779 (0.15) (0.13) Estate car -0.100 0.324*** (0.10) (0.091) Truck -0.106 0.0971 (0.14) (0.12) USA -0.0851 0.390*** (0.16) (0.14) Asa 0.333*** 0.304*** (0.091) (0.089) Eastern Europe 0.157* 0.326*** (0.086) (0.078) Constant -0.769*** -0.325** (0.14) (0.14) athrho 0.0600 (0.040) Observatons 2161 2161 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely.
APPENDIX C Dstrbuton of Accdents, Deaths, and Injures across the Kyv Cty Dstrcts Dstrcts Accdent Death Injury 2003 2004 2003 2004 2003 2004 Holosvsky 261 279 41 38 266 318 Darnytsky 193 205 26 26 213 238 Desnyansky 304 441 33 48 333 515 Dnprovsky 371 330 36 39 396 373 Obolonsky 250 283 37 34 284 319 Pechersky 174 170 13 10 208 197 Podlsky 215 204 28 26 234 257 Svyatoshynsky 322 385 38 36 344 461 Solomyansky 350 318 32 27 384 339 Shevchenkvsky 351 437 23 25 388 508
APPENDIX D Estmaton Results for Coverage-Past Clam Correlaton (adverse selecton determnaton) COEFFICIENT Probt Logt Type of coverage Type of coverage Clam occurrence n prevous year 0.308*** 0.514*** (0.11) (0.17) Company experence 0.0787** 0.127** (0.038) (0.062) Prvate use -0.545*** -0.906*** (0.13) (0.22) Male 0.0581 0.0991 (0.18) (0.30) Age of car -0.0357** -0.0589** (0.017) (0.028) Sze of engne -0.0000826* -0.000134* (0.000043) (0.000069) Value of car -0.00000110-0.00000192 (0.00000076) (0.0000013) Off-road vehcle -0.0612-0.126 (0.15) (0.25) Mnbus -0.259-0.407 (0.24) (0.39) Mnvan 0.0416 0.0691 (0.20) (0.33) Estate car 0.367*** 0.603*** (0.13) (0.22) Truck 0.487 0.783 (0.31) (0.51) USA -0.579*** -1.004*** (0.21) (0.36) Asa -0.230* -0.370* (0.13) (0.22) Eastern Europe -0.314*** -0.525*** (0.11) (0.19) Constant 0.426* 0.709* (0.25) (0.41) Observatons 936 936 Standard errors are shown n parentheses. ***, **, * ndcate statstcal sgnfcance at 1%, 5%, and 10% levels respectvely.