Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang Peng * Department of Rsk Management and Insurance, Feng Cha Unversty, Tawan Key words: rsk averson; lablty nsurance; automoble nsurance JEL classfcaton: D12; D82 1. Introducton In the last decade, extensve lterature has been devoted to analyzng the asymmetrc nformaton problem rased by Rothschld and Stgltz (1976) to test f there s a postve relaton between nsurance coverage and rsk. Among the assumptons requred under ther framework, homogenety n all dmensons s the fundamental one. However, rsk averson, although well acknowledged to be unobservable, s an mportant factor nfluencng the results of ther model. For example, Smart (2000) and Snow (2009) provde theoretcal proof to show that when rsk averson s taken nto account, the tradtonal argument of the postve relaton between rsk and coverage mght not exst. Therefore, the emprcal models wthout a rsk averson factor are not robust. In practce, the measurement of rsk averson, provded by Arrow (1970) and Pratt (1964), requres ndvdual wealth data for calculaton, but ths nformaton s sometmes dffcult to obtan. In the emprcal research assocated wth nsurance markets, there are two common approaches to measure rsk averson. One s a rsky behavor questonnare. Usng rsky behavor as proxes of rsk averson, the relatonshps between rsk averson and rsk occurrence or nsurance coverage are tested. The other approach, as used by Dreze (1981), Cohen and Enav (2007), and Sato (2006), uses deductbles to make nferences about rsk averson. However, both approaches requre sophstcated procedures or smplfed assumptons. In two semnal works, Puelz and Snow (1994) and Donne et al. (2001) use lablty nsurance as a proxy varable of wealth, representng rsk averson to test asymmetrc nformaton. Snce lablty nsurance s usually sold together wth other automoble nsurance as a bundle, the data s readly avalable and easly appled. * Correspondence to: Department of Rsk Management and Insurance, Feng Cha Unversty, Tachung, Tawan. E-mal: scpeng@fcu.edu.tw. We would lke to thank the edtors of ths journal for ther helpful comments.
160 Internatonal Journal of Busness and Economcs Whle feasble, the hypothess of whether automoble lablty nsurance purchases can sgnal rsk atttude has not been formally tested. The purpose of ths study s to examne f lablty nsurance contans nformaton of rsk averson and f t s correlated wth nsurance rsk. We focus on the relatonshp between comprehensve vehcle physcal damage nsurance (VDI) and voluntary thrd-party lablty nsurance (VLI) n the Tawanese automoble nsurance market. 2. Data and Emprcal Approach Our data from the Tawan Insurance Insttute s ndvdual-level nformaton that conssts of VDI and VLI polces sold by all Tawanese nonlfe nsurers n 2003. Our sample ncludes 212,481 VDI polces. Table 1. Descrptve Statstcs of Vehcle Clam Varables Vehcle coverage level t-statstc for Hgh vehcle coverage Low vehcle coverage Varable dfference Wth vehcle clam 0.54 (0.50) 0.48 (0.50) 21.65 Vehcle clam payment 15.14 (31.22) 13.86 (34.54) 6.91 Vehcle clam count 0.76 (0.86) 0.59 (0.70) 43.17 Observatons 170,964 (80.46%) 41,517 (19.54%) Lablty nsurance status Varable Wth lablty nsurance polcy Wthout lablty nsurance polcy t-statstc for dfference Wth vehcle clam 0.53 (0.50) 0.51 (0.50) 4.16 Vehcle clam payment 14.85 (31.74) 15.58 (34.74) 2.29 Vehcle clam count 0.73 (0.83) 0.71 (0.85) 1.51 Observatons 201,644 (94.90%) 10,837 (5.10%) Lablty coverage level t-statstc for Hgh lablty coverage Low lablty coverage Varable dfference Wth vehcle clam 0.55 (0.50) 0.53 (0.50) 6.76 Vehcle clam payment 16.43 (37.39) 14.39 (29.83) 12.17 Vehcle clam count 0.74 (0.85) 0.72 (0.83) 5.39 Observatons 46,278 (21.78%) 155,366 (77.05%) Notes: Standard devatons are n parentheses. The unt of vehcle clam payment s NTD 1,000. Table 1 provdes descrptve statstcs. We focus on the correlatons of both vehcle coverage and lablty coverage on vehcle rsk. For VDI polces, we defne those wth a deductble as low coverage and those wthout a deductble as hgh coverage. To correct for the problem of nconsstency n coverage and clams, we subtract the deductble from those clams wthout a deductble. Our sample shows that polcyholders wth hgh VDI have hgher vehcle rsk than those wth low VDI,
Chu-Shu L and Sheng-Chang Peng 161 whch s consstent wth the postve coverage-rsk correlaton. For the rsk averson role of lablty coverage, we also show vehcle rsk dfferences between polcyholders who purchase VLI polces and those who do not. Snce the average VLI coverage per person s NTD 1.92 mllon, and around 32% of polces are concentrated around NTD 2 mllon (not shown), we defne hgh lablty coverage as a covered amount over NTD 2 mllon. Polcyholders wth hgh lablty coverage have hgher vehcle rsk than those wth low lablty coverage. Ths s not consstent wth the hypothess that lablty coverage s a proxy of rsk averson. However, these results are prelmnary. Further study s needed to control for addtonal nformaton assocated wth the characterstcs of both polcyholders and vehcles. To nvestgate whether VLI coverage s an approprate proxy of rsk averson for VDI, we employ the Heckman model to estmate the correlaton between vehcle rsk and lablty coverage. There s potental endogenety n purchasng both types of polces, and the Heckman model can correct the problem of selecton bas. Therefore, we frst specfy a selecton functon for purchasng lablty coverage status, estmatng parameters by a probt model to compute the nverse Mlls rato for correctng endogenety bas. The model can be wrtten as: Prob(Wth lablty coverage = 1) = Φ( γ ), (1) Z where Wth lablty coverage s a bnary varable that equals 1 f ndvdual purchases VDI wth VLI and 0 otherwse, Z s a vector of control varables that ncludes demographc characterstcs of the polcyholder (age, gender, and martal status) and characterstcs of the vehcle (car age, car model, and exhaust class), γ s a vector of parameters, and Φ s the standard normal cumulatve dstrbuton. The nverse Mlls rato s ncluded n the clam behavor model and the followng equaton s estmated: Y = δ X + δ Hgh vehcle coverage + δ Wth lablty coverage 1 2 3 + δ Lablty amount + δλ+ ε, 4 5 (2) where X s a vector of control varables, Hgh vehcle coverage s a dummy varable that equals 1 f ndvdual purchases a VDI polcy wthout deductble and 0 otherwse, Lablty amount s the covered amount of VLI polcy, λ s the nverse Mlls rato, and ε s an error term. We employ three response varables ( Y ): Wth vehcle clam (.e., at least one clam s fled), Vehcle clam payment, and Vehcle clam count. 3. Emprcal Results Table 2 shows the estmated results of VDI and VLI on vehcle rsk. Models 1 and 2 examne the coverage-rsk correlaton wthout ncludng the nverse Mlls rato. To correct selecton bas, Models 3 5 explore the sutablty of VLI coverage as a measure of rsk averson. The sgnfcant coeffcent of λ shows the presence of
162 Internatonal Journal of Busness and Economcs endogenety bas for both types of polces. Table 2. Estmated Results of Vehcle Coverage and Lablty Coverage on Vehcle Rsk Model 1 Model 2 Model 3 Model 4 Model 5 Panel A: Response varable s whether at least one vehcle physcal damage clam s fled Hgh vehcle coverage 0.095*** 0.095*** 0.095*** 0.095*** 0.095*** (0.008) (0.008) (0.008) (0.008) (0.008) Wth lablty coverage 0.071*** 0.867*** 0.871*** 0.832*** (0.013) (0.214) (0.214) (0.215) Lablty amount 0.002 0.017** (0.003) (0.006) Lablty amount Hgh lablty coverage 0.012*** (0.005) λ 0.438*** 0.441*** 0.433*** (0.100) (0.100) (0.100) Observatons 212,481 212,481 212,481 212,481 212,481 Panel B: Response varable s vehcle clam payment Hgh vehcle coverage 5.371*** 5.372*** 5.372** 5.315*** 5.338*** (0.333) (0.333) (0.333) (0.333) (0.333) Wth lablty coverage 0.926* 18.296** 17.366* 15.185* (0.548) (8.858) (8.863) (8.886) Lablty amount 0.369*** 0.435* (0.118) (0.262) Lablty amount Hgh lablty coverage 0.643*** (0.187) λ 8.978** 8.212** 7.721* (4.130) (4.138) (4.140) Observatons 212,481 212,481 212,481 212,481 212,481 Panel C: Response varable s vehcle clam count Hgh vehcle coverage 0.189*** 0.189*** 0.189*** 0.190*** 0.191*** (0.009) (0.009) (0.009) (0.009) (0.009) Wth lablty coverage 0.060*** 0.711*** 0.727*** 0.677*** (0.014) (0.233) (0.233) (0.233) Lablty amount 0.006** 0.025*** (0.003) (0.007) Lablty amount Hgh lablty coverage 0.015*** (0.005) λ 0.361*** 0.373*** 0.362*** (0.108) (0.109) (0.109) Observatons 212,481 212,481 212,481 212,481 212,481 Notes: Standard errors are n parentheses. ***, **, and * denote statstcal sgnfcance at the 1%, 5%, and 10% levels, respectvely. The results are estmated by probt n Panel A and tobt n Panels B and C. The lablty amount s n NTD 1 mllon.
Chu-Shu L and Sheng-Chang Peng 163 Model 1 s one of the standard tests of asymmetrc nformaton on automoble nsurance. We obtan consstent results-postve coverage-rsk correlaton-for three measures of vehcle rsk condtonal on all nformaton used by nsurers for rsk classfcaton, whch dsplays the presence of asymmetrc nformaton. Relable results are shown for other models when we correct for selecton bas. We nvestgate the effect of VLI coverage on vehcle rsk by observng whether polcyholders concurrently purchase VDI and VLI. In Panel A, Model 2 shows that polcyholders wth VLI coverage have hgher vehcle rsk wthout consderng endogenety bas; however, a negatve correlaton s shown n Model 3 when the endogenety bas s corrected. Panels B and C have robust fndngs. Ths s consstent wth the effect of rsk averson. Model 4 n Panel A shows that polcyholders who purchase more VLI coverage have a lower tendency to fle a vehcle clam; however, ths s not statstcally sgnfcant. When vehcle rsk s measured by clam count, the effect of the lablty amount n Panel C s sgnfcantly negatve. However, n Panel B, vehcle clam payment and the lablty amount are sgnfcantly and postvely correlated. These estmated results are mxed n Model 4. We therefore further dentfy whether the effect of the lablty amount changes under dfferent extents of lablty coverage. We separate samples nto two groups based on VLI amount. The dummy varable, Hgh lablty coverage, equals 1 f an ndvdual purchases VLI wth an amount greater than 2 mllon and 0 otherwse. Usng the nteracton term between Lablty amount and Hgh lablty coverage, Model 5 n Panel A shows a sgnfcantly negatve correlaton between the lablty amount and the possblty of flng a vehcle clam when the lablty amount s equal to or less than NTD 2 mllon. Due to the postve effect of the nteracton term, the negatve correlaton s offset when the lablty amount s greater than NTD 2 mllon. 1 However, we fnd a sgnfcantly negatve correlaton n Panel C for two extents of lablty coverage. 2 Dependent on three rsk measure varables, there are consstently negatve correlatons under low lablty coverage. As polcyholders purchase relatvely low lablty coverage, the covered lablty amount seems to be approprate to measure rsk averson n the Tawanese automoble nsurance market. Those polcyholders who purchase hgh lablty coverage have fewer small vehcle clams but hgher clam payments. They mght actually be hgh rsk, and thus the rsk averson hypothess cannot be appled. 4. Conclusons Based on the emprcal results, we fnd that the role of voluntary thrd-party lablty nsurance n automoble nsurance can be presented n varous dmensons. In terms of purchasng or not purchasng VLI, the former contans rsk averson nformaton. However, when the amount of VLI s consdered, a hgher VLI amount may not be able to provde a postve sgnal of rsk averson.
164 Internatonal Journal of Busness and Economcs Notes 1. The coeffcent assocated wth Lablty amount when the covered lablty amount s greater than NTD 2 mllon s 0.017+0.012 = 0.005 wth a standard error of 0.003. 2. The coeffcent assocated wth Lablty amount when the covered lablty amount s greater than NTD 2 mllon s 0.025+0.015 = 0.010 wth a standard error of 0.003. References Arrow, K. J., (1970), Essays n the Theory of Rsk Bearng, Amsterdam: North-Holland. Cohen, A. and L. Enav, (2007), Estmatng Rsk Preferences from Deductble Choce, Amercan Economc Revew, 97(3), 745-788. Donne, G., C. Gouréroux, and C. Vanasse, (2001), Testng for Evdence of Adverse Selecton n the Automoble Insurance Market: A Comment, Journal of Poltcal Economy, 109(2), 444-453. Dreze, J. H., (1981), Inferrng Rsk Tolerance from Deductbles n Insurance Contracts, Geneva Papers on Rsk and Insurance, 20(1), 48-52. Pratt, J. W., (1964), Rsk Averson n the Small and n the Large, Econometrca, 32(1-2), 122-136. Puelz, R. and A. Snow, (1994), Evdence on Adverse Selecton: Equlbrum Sgnalng and Cross-Subsdzaton n the Insurance Market, Journal of Poltcal Economy, 102(2), 236-257. Rothschld, M. and J. E. Stgltz, (1976), Equlbrum n Compettve Insurance Markets: An Essay on the Economcs of Imperfect Informaton, Quarterly Journal of Economcs, 90(4), 629-649. Sato, K., (2006), An Emprcal Analyss of the Roles of Rsk Averson n the Automoble Insurance Market, Paper presented at Amercan Rsk and Insurance Assocaton 2006 Annual Meetng, Washngton D.C. Smart, M., (2000), Compettve Insurance Markets wth Two Unobservables, Internatonal Economc Revew, 41(1), 153-169. Snow, A., (2009), On the Possblty of Proftable Self-Selecton Contracts n Compettve Insurance Markets, Journal of Rsk and Insurance, 76(2), 249-259.