Efficiency Test on Taiwan s Life Insurance Industry- Using X-Efficiency Approach

Transcription

1 Informaton and Management Scences Volume 18, Number 1, pp , 2007 Effcency Test on Tawan s Lfe Insurance Industry- Usng X-Effcency Approach James C. Hao Tamkang Unversty R.O.C. Abstract Usng twenty-three years of data, , I was estmatng translog cost functon for 26 lfe nsurance companes. Dstrbuton free analyss (DFA) was appled to determne the relatve effcency of nsurers n the sample. I then tested the constants to see f they were related to so-called X-effcences because of market share, dversfcaton products strategy, scale effcency and market growth rato. Results show that frms wth large market share tend to be cost effcent. Ths result concde the current polcy whch encourages merge and acquston. Keywords: Lfe Insurance Industry, X-Effcency, Economes of Scale, Dversfcaton Products Strategy, Market Power Theory. 1. Introducton The compettve envronment faced by Tawan lfe nsurers has undergone a myrad of changes durng the past decade. Such changes were facltated, n part, by fnancal servces deregulaton, entry by non-tawan lfe nsurance companes nto the Tawan market, nterest rate s volatlty, and technologcal advances n nformaton processng. The lfe nsurance companes responses nclude nnovatons n products desgn and nsolvences problem. Researchers are examnng nsurer cost structure and ndustry performance (Doherty [12], Skogh [33], Grace and Tmme [18], Geehan [17] and Wess [36]). Tradtonal research focuses on economes of scale and scope, but some research examned the effcency of the ndustry (Yuengert [37], Cummns and Z [10] and Hao and Chou [20]). Hao and Chou [20] employng Schmdt and Sckles [30] dstrbuton free approach (DFA) to estmate 8 Receved November 2004; Revsed February 2005; Accepted October Supported n part by the Natonal Scence Councl, Tawan, R.O.C. under NSC H

2 38 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 frms effcency, and fnd the effcency relates to some optmal scale and dversfcaton products strategy may be occurrng. Many research express that lfe nsurance average neffcency around 30% to 50% (Fecher et al. [14], Yuengert [37], Gardner and Grace [16], Hardwck [19] and Hao and Chou [20]). I am beng by Schmdt and Sckles [30] estmate Tawan 26-lfe nsurance companes effcency, and analyss the market share, optmal scale and dversfcaton products strategy mplcatons for effcent frm operatons n the lfe nsurance ndustry. Frst, a bref revew of effcency s present, secton 3 explans varable defntons and presents the relatonshps to be examned. Secton 4 descrbes models. Secton 5 descrbes the estmaton and results. Secton 6 dscuss the results and s followed by a concluson. 2. Background Producton theory dentfes several types of neffcences, ncludng allocatve, techncal, scale, scope, and X-effcency. Allocatve neffcency arses when company use the costly combnaton of nputs n producng output. Techncal neffcency occurs when the company fals to produce on effcent producton fronter. Scale neffcences arse when the frm cannot lower average costs by ncreasng or decreasng ts output levels. At last, scope effcences exst the frm can lower average costs by changng ts output mx. Lebensten [25] dentfed a ffth approach of examnng effcency, and called the term X-effcency to descrbe the resultng dfference between actual and mnmum cost. After Lebensten [25] defne X-effcency, Agner and Chu [1] follow Farrell [13] and Lebensten [25] development methodologcal n fronter producton functon estmaton. Today there exsts a multtude of approaches, about Schmdt and Sckles [30] measures effcency relatve to dstrbuton free approach (DFA), Agner, Lovell and Schmdt [2] measures effcency relatve to stochastc fronter approach (SFA) and Banker et al. [3] measures effcency relatve to data envelopment analyss (DEA). Schmdt and Sckles [30] expressed the Jondrow et al. [23] use cross-sectonal data estmate effcency has three problems. Frst, the techncal effcency of a partcular from (observaton) can be estmated but not consstently. Second, the estmaton of model and the separaton of techncal neffcency from statstcal nose requre specfc assumptons about the dstrbuton of techncal neffcency and statstcal nose. It s not clear how robust one s results are to these assumptons. Thrd, t may be ncorrect to assume that neffcency s ndependent of the regress.

3 Effcency Test on Tawan s Lfe Insurance Industry - Usng X-Effcency Approach 39 So I am beng by Schmdt and Sckles [30] dstrbuton free approach (DFA) to analyss Tawan 26 frms effcency, and analyss the market share, optmal scale and dversfcaton products strategy mplcatons for effcent frm operatons n the lfe nsurance ndustry. 3. Methodology 3.1. Data source Ths Study employ unbalance panel data gathered for 26 frms operatng n the Tawan lfe nsurance market durng I obtaned data from the Lfe Insurance Assocaton of the Republc of Chna Varable defntons Outputs Dffcultes assocated wth the defnton of output and the approprate levels of aggregaton of outputs are encountered n all nsurance cost studes. Geehan [17], for example, provdes a useful dscusson of the ssues nvolved and presents a comparson of major studes usng dfferent output measures. In ths study, a defnton of output based upon premums and annuty consderatons s employed. Ths s consstent wth the approach used by numerous authors (Wess [36], Grance and Tmme [18], Fecher et al. [14], Ra [28], Meador et al. [26], Hardwck [19] and Hao and Chou [20]). In addton, the dollar value of nvestments s also defned as an output. Includng nvestments s approprate for lfe nsurers snce they represent a major actvty for most frms. It s also consstent wth varous prevous costs of fnancal ntermedares (Mester [27], Berger et al. [5], and Cummns et al. [11]). and some authors beleved that the costs of fnancal ntermedares are reserves level (Yuengert [37] and Cummns and Z [10]). I was beleved that the busness lne s frm s outputs, and the costs of fnancal ntermedares are nvestments. So we follow conventon and defne outputs as the dollar amounts of: (1) ordnary lfe nsurance (Y1), (2) accdent and health premum (Y2), (3) Group lfe nsurance premum (Y3), (4) nvestments (Y4) Input prces Outputs are produced usng three nputs: (1) labor, (2) physcal captal, and (3) clam. The prce of labor (P1) s computed by multplyng the average salary of nsurance

4 40 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 workers reported by the lfe nsurance assocaton of the Republc of Chna. The prce of physcal captal (P2) equals physcal captal expenses dvdend by the value of physcal captal assets. The prce of clam (P3) equals ordnary lfe nsurance clam dvdend by busness n force of lfe nsurance numbers Costs Total cost s defned as operatng cost and should vary wth nput prces and the factors of producton. Operatng costs of the nsurer nclude all costs assocated wth operaton of company. Thus, total operatng costs are the sum of labor, physcal captal, and clam Envronmental nfluences Market share In Tawan, the largest frm s Cathay Company, and hold 35% market share n today. In research, the market power theory was mproved on lfe nsurance ndustry operaton (Shepherd ([31], [32]), Rhoades [29] and Kurtz and Rhoades [24]), and some authors beleved that more and more market share could brng more and more proft. So as to assume the neffcency s decreasng follow market share expand n ths paper Products focus Meador et al. [26] tested product focus was related to X-effcency, and they were beleved that product focus ncrease cause to neffcency rsng. Ths result can speak that dversfcaton products strategy wll mprove the frm s operaton effcency. The products focus formula s (1). F OCUS = Y Y Y Y 4 2 (Y 1 + Y 2 + Y 3 + Y 4 ) 2. (1) Y 1 s ordnary lfe nsurance premum, Y 2 s accdent and health premum, Y 3 s Group lfe nsurance premum, Y 4 s nvestments Total assets Gardner and Grace [16] beleved that the total assets ncrease, the neffcency would arse. They expressed ths pont cause from no-admt assets. But some authors dd not beleve ths result, and they were proved the total assets ncrease can cause to frm operaton have more effcency, t was so-called Scale effcency (Berger [4], Yuengert [37], Gardner and Grace [16] and Hao and Chou [20]). And some authors beleved that

5 Effcency Test on Tawan s Lfe Insurance Industry - Usng X-Effcency Approach 41 larger scale would brng more market share and proft (Gale and Branch [15], Smrlock et al. [34] and Stevens [35]). 4. Models Usng twenty-three years of unbalance panel data, , I was estmatng translog cost functon for 26 lfe companes. The translog cost functon s (2). ln T C t = α t + A ln Y t + B ln P ot + 1 C ln Y t ln Y j 2 j + 1 D ln P ot ln P kt + E ln Y t ln P ot + ε. (2) 2 o k o Y s output, P s prce of nputs, ε s error term. Outputs nclude ordnary lfe nsurance premum, accdent and health premum, Group lfe nsurance premum and nvestments. Inputs are labor, physcal captal, and clam, s stand for frm, t s stand for t year. α s stand for constant, A, B, C, D, and E s coeffcent. I am beng by Schmdt and Sckles [30] dstrbuton free approach (DFA) to examne Tawan 26 frms effcency. The functon s (3). U t = max(α t ) α t. (3) α stand for constant of formula (2), U stand for neffcency. I am beng by two factors model to analyss the market share, optmal scale and dversfcaton products strategy mplcatons for effcent frm operatons n the lfe nsurance ndustry, because the frm () and year (t) mpact of results. And we chose our model s fxed effect or random effect by Hausman approach [21]. The LM test can tell us that the model constant s random or fxed. The random effect model s (4), and fxed effect model s (5). U t = α t + β 1 T A t + β 2 MSHR t + β 3 F OCUS t + ε t. (4) U s neffcency, D s ndvdual effect dummy term, α s constant, α = α + µ, α s random of constant, µ s error of constant. T A s total assets, MSHR s market share rato, and Focus s products focus. U t = δd t + β 1 T A t + β 2 MSHR t + β 3 F OCUS t + ε t. (5)

6 42 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 I chose my model s fxed effect or random effect by Hausman approach [21], the Hausman Test null assumpton s: H0 : E(µ t x t ) = 0, random effects model s rght. H1 : E(µ t x t ) 0, fxed effects model s rght. The statstcs s (6) H = (b 0 b 1 ) [Var (b 0 ) Var (b 1 )] 1 (b 0 b 1 ). (6) The H s followng ch-square, b 0 s denote estmated coeffcent by GLS, and b 1 s stand for estmated coeffcent by LSDV. Ths statstc s sgnfcant that tell me the null assumpton s rejected, and I am estmatng by fxed model. In addton, I am testng heteroscedastcty by LM test, and the null assumpton s σ = σ t = 0. If null assumpton s accepted, I am estmatng by LS (Least Squares Regresson). On the contrary, I am estmatng by random effect model (Breusch and Pagan [7]). 5. Estmaton and Results Usng twenty-three years of unbalance panel data, , I was estmatng translog cost functon for 26 lfe companes. I obtaned data from the Lfe Insurance Assocaton of the Republc of Chna. In Table 1, the ordnary lfe nsurance relates to group lfe nsurance s substtutes, and t relates to nvestments s complement. So the frm wll ncrease hs ordnary lfe nsurance premum revenue, the frm must be mprovng hs nvestments. The prce of captal wll arse follow ordnary lfe nsurance ncrease, because the frm s facng to nterest rsk from revenue ncreasng and t wll mprove prce of captal arsng at same tme. The accdent and health nsurance relates to nvestments s substtutes. Because accdent and health nsurance are belongng to short-term polcy, and the clam never depend on nvestment revenue. The ordnary lfe nsurance relates to prce of clam s complement; because prce of clam wll arse follow ordnary lfe nsurance premum revenue ncrease. The nvestment revenue ncrease can download prce of captal. In Table 2, the translog cost functon accept null assumpton s addng-up restrctons and the homothetc functon or homogeneous functon restrctons, but the translog cost functon never s constant returns to scale functon or Cobb-Douglas functon n ths paper. So equaton (2) must be added to addng-up restrctons, and tested results s Table 2 (Berndt [6]).

7 Effcency Test on Tawan s Lfe Insurance Industry - Usng X-Effcency Approach 43 ln T C = α 0 + A ln Y + Table 1. Translog cost functon. B ln Po j C j ln Y ln Y j o k D ok lno ln Po ln P k + o E o ln Y ln Po + ε Varable Coeffcent P Value Varable Coeffcent P Value Constant *** E ** A C A *** C *** A *** E *** A E *** B ** E B C B *** E C E C *** E C E C *** E *** D *** E D *** D D D *** C D C ** C *** R-squared= E Adjusted R-squared=0.930 E *** Log-L= Y 1 s ordnary lfe nsurance premum, Y 2 s accdent and health premum, Y 3 s group lfe nsurance premum, Y 4 s nvestments, P 1 s prce of labor, P 2 s prce of captal, P 3 s prce of clam. 2. * Sgnfcant at the 10% level, ** sgnfcant at the 5% level, *** sgnfcant at the 10% level. Table 2. Model test. Sgnfcant at the H0 1% level value Wald Test Results (Ch-square value) B = 1 (Addng-up restrctons) D = E = 0 (Homothetc Functon or Homogeneous Functon) C = 1 and D = E = 0 (Constant Returns to Scale Functon) C = 1 and D = 0 Cobb-Douglas Data source: n ths paper Accepts H Accepts H Rejects H Rejects H0

8 44 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 In Table 3, the Tawan lfe nsurance ndustry average neffcency s 33.98%, the best frm s Shn Kong lfe, next s Cathay. We beleve above that about the value of total assets and market share large than others, but we should deep-gong mprove that relaton. In ths result, we fnd the chna lfe and Nan Shn lfe s very neffcency, because the chna frm s economes of scale are too small and Nan Shn frm s nvestment revenue s less than other ncumbent company n early stage ( ). The ING lfe s frst foregn frm and hs operaton effcency s thrd n Tawan. The CTC s publcly operated and economes of scale are too small, so the neffcency s hgh than others. Table 3. Frm s neffcency. U t = max(α t ) α t NO. Frm s Name Ineffcency Name lst NO. Frm s Name Ineffcency Name lst 1 CTC 46.86% ING lfe 23.26% 3 2 Tawan 25.38% 5 18 Georga 37.37% 16 4 Cathay 23.19% 2 19 Metropoltan 41.14% 23 5 Chna 40.77% Prudental lfe 37.66% 17 6 Nan Shan 39.55% Connectcut 41.09% 22 General 7 Kuo Hua 29.52% 8 22 Amercan lfe 42.69% 24 8 Shn Kong 22.23% 1 23 The Manufacturers 30.82% 10 9 Fubon 27.08% 7 24 Transamerca 38.18% 18 Occdental 10 Global 29.91% 9 25 New York 38.54% Mass Mutual 36.86% Wnterthur 25.63% 6 Mercures 12 Snon 37.31% The Natonal 35.49% 13 Mutual lfe Assocaton of Australasan 13 Sngfor 42.93% Aegon Levensverzekerng 25.00% 4 16 Allanz Presdent 32.33% Zurch 32.59% 12 Average neffcency 33.98% No.3 s stand for Prudental lfe assurance, no.14 s stand for Far Glory lfe, and no 15 s stand for Honta lfe, because these frms are change leadershp n perod, so we are delete these sample n data. It should be noted that my result s somewhat dfferent from ratng company s report. The possble explanaton s that our sample spans two decades and wll not exactly reflect the current fnancal report. For example, the ratng for the Tawan lfe nsurance company s better than my study. Also, the emergency of fnancal holdng company may have a bg mpact on the performance of the lfe nsurance company. I beleved that random effects model s rght, because Hausman test s not sgnfcant at the 5%. And LM test s explaned that constant term has random effect, so we are

9 Effcency Test on Tawan s Lfe Insurance Industry - Usng X-Effcency Approach 45 estmatng by random effects model (Breusch and Pagan [7]). To provde some evdence on the relatonshp between the total assets, market share, and dversfcaton products strategy, the above result s showed on Table 4. The result tells us non-admtted assets wll mpact of frm s effcency, and ths suggests that these assets exclude for solvency regulaton are potentally productve to the frm. Of the control varables employed n the effcency regresson only sze as measured by total assets was sgnfcantly related to effcency. Ths s consstent wth Yuengert [37], Gardner and Grace [16] fndng of Heteroscedastcty related to sze n the lfe nsurance ndustry. Table 4. Random effects model of Tawan lfe nsurance ndustry. U t = α t + β 1 T A t + β 2 MSHR t + β 3 F OCUS t + ε t Test Statstcs for the Classcal Model Model Log-Lkelhood R 2 Result (1) Constant term only (2) Group effects only (3) X - varables only (4) X and group effects (5) X, group and tme effects We employ ths equaton Hypothess Tests Dfference model Ch-squared P-Value Result (2) vs (1) ** (3) vs (1) *** (4) vs (1) *** (4) vs (2) *** (4) vs (3) *** (5) vs (4) *** (5) s the best model (5) vs (3) *** (5) s the best model Coeffcent T statstcal P-value Result TA ** No-admt assets cause to result MSHR ** Accept market power theory FOCUS The dversfcaton products strategy s not help mprove effcency. Constant *** Log-L R LM Test 173 P-Value 0.000*** Hausman Test 7.42 P-Value *** 1. TA s Total Assets, MSHR s market share rato, and Focus s products focus. 2. * Sgnfcant at the 10% level, ** sgnfcant at the 5% level, *** sgnfcant at the 10% level. In addton, from ths regresson the varable sgnfcantly related to proftablty was

10 46 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 market share (market power theory), t does suggest that frms wth larger market share are more proftable. The dversfcaton products strategy can t help frm to mprove hs operaton effcency (no sgnfcant), because the Tawan lfe nsurance frms always observe the standardzed polcy regulaton. 6. Concluson Ths paper estmated cost functons for the years 1981 to 2003 for 26 frms representng approxmately 90% of the ndustry s premums wrtten over the perod. The cost functon constants were then employed to construct a measure of frm effcency. We hypotheszed these constants should be a functon of market share, total assets, and products focus. I use Schmdt and Sckles [30] dstrbuton free approach (DFA) to calculate our effcency. The results of ths research provde us wth a number of polcy suggestons. Frst, I suggest that frms wth larger market share are cost effcent. Recently, the goal for reorganzng fnancal market s to ncrease effcency by merge and acquston. From my study, ths polcy does have a good mpact on lfe nsurance company performance. In addton, f the frm wants to ncrease hs ordnary lfe nsurance premum revenue; t must mprove ts nvestments ablty. It means that government should pay more attenton to fnancal solvency for the lfe nsurance company. Rght now, the emergency of fnancal holdng company and bancassurance do have a bg mpact on lfe nsurance company behavor. I suggest that future study should pay attenton to these two areas. References [1] D. J. Agner and S. F. Chu, On estmatng the ndustry producton functon, Amercan Economc Revew Vol.58, pp , [2] D. J. Agner, C. A. Lovell, and P. Schmdt, Formulaton and Estmaton of Stochastc Fronter Producton Functon Models, Journal of Econometrcs Vol.6, No.1, (July), pp.21-37, [3] R. D. Banker, A. Charnes and W. W. Cooper, Some models for estmatng techncal and scale neffcences n data envelopment analyss, Management Scence Vol.30, pp , [4] A. N. Berger, D. Hancock and D. B. Humphrey, Bank effcency derved from the Proft functon, Journal of Bankng and Fnance, Vol.17, pp , [5] A. N. Berger, J. D. Cummns and M. A. Wess, The coexstence of multple dstrbuton system for fnancal servces: The case of property-lablty nsurance. Workng Paper, Wharton Fnancal Insttutons Centers, Unversty of Pennsylvana, 1996.

11 Effcency Test on Tawan s Lfe Insurance Industry - Usng X-Effcency Approach 47 [6] E. R. Berndt, The Practce of Econometrcs: Classc and Contemporary. Frst Edton, Addson- Wesley Publshng Company, 474, [7] T. Breusch and P. Pagan, A smple test for heteroscedastcty and random coeffcent varaton, Econometrca, Vol.47, pp , [8] L. R. Chrstensen, D. W. Jorgenson and L. J. Lau, Transcendental Logarthmc Producton Fronters, The Revew of Economcs and Statstcs, 28-45, [9] J. D. Cummns and M.A. Wess, Measurng Cost effcency n the Property-lablty nsurance ndustry, Journal of Bankng and Fnance, Vol.17, pp , [10] J. D. Cummns and H. Z, Measurng cost effcency n the U.S. lfe nsurance ndustry: Econometrc and mathematcal programmng approaches. Workng Paper, Wharton Fnancal Insttutons Centers, Unversty of Pennsylvana, [11] J. D. Cummns, M. A. Wess and H. Z, Organzatonal from and effcency: An analyss of stock and mutual property-lablty nsurers. Workng Paper, Wharton Fnancal Insttutons Centers, Unversty of Pennsylvana, [12] N. A. Doherty, The measurement of output and economcs of scale n property-lablty nsurance, Journal of Rsk and Insurance, Vol.48, pp , [13] M. J. Farrell, The Measurement of Productve Effcency, Journal of Royal Statstcal Socety, Vol.120, pp , [14] F. Fecher, D. Kessler, S. Perelman and P. Pesteau, Productve Performance of the French Insurance Industry, The Journal of Productvty Analyss, Vol.4, pp.77-93, [15] B. T. Gale and B. S. Branch, Concentraton Versus Market Share: Whch Determnes Performance and Why Does It Matter, Anttrust Bulletn, Vol.27, pp , [16] L. A. Gardner and M. F. Grace, X-Effcency n the US lfe nsurance ndustry, Journal of Bankng and Fnance, Vol.17, pp , [17] R. Geehan, Economcs of scale n nsurance: Implcatons for regulaton, In B. Wasow (Ed.), The Insurance Industry n Economc Development Columba Unversty Press, New Yowk, [18] M. F. Grace and S. G. Tmme, An examnaton of cost economcs n the Unted States lfe nsurance ndustry, Journal of Rsk and Insurance, Vol.59, pp , [19] P. Hardwck, Measurng Cost neffcency n the UK lfe nsurance ndustry, Appled Fnancal Economcs, Vol.7, pp.37-44, [20] C. J. Hao and L. Y. Chou, The Impact of the Open Market Polcy on the Effcency of the Incumbent Insurance Companes, Insurance Monograph, Vol.18, No.2, pp , [21] J. Hausman, Specfcaton tests n econometrcs, Econometrca, Vol.46, pp , [22] A. Heshmat, Estmatng Techncal Effcency. Productvty Growth and Selectvty Bas Usng Rotatng Panel Data: An Applcaton to Swedsh Agrculture, Ph. D. Thess, Department of Economcs, Unversty of Goteborg, [23] J. Jondrow, C. A. Knox Lovell, I. S. Materov and P. Schmdt, On The Estmaton of Techncal Ineffcency In the Stochastc Fronter Producton Functon Model, Journal of Econometrcs, Vol.19, pp , [24] S. Kurtz and S. A. Rhoades, A Note on Market Share-Proftablty Relatonshp. Workng Paper, Board of Governors of Federal Reserve System, [25] H. Lebensten, Allocatve effcency vs. X-Effcency, Amercan Economc Revew, Vol.56, pp , [26] J. W. Meador, H. E. Ryan and C. D. Schellhorn, Products focus versus dversfcaton: Estmate of X-effcency for the US lfe nsurance ndustry. Workng Paper, Wharton Fnancal Insttutons Centers, Unversty of Pennsylvana, [27] Loretta J. Mester, A multproduct cost study of savngs and loans, Journal of Fnance, Vol.24, pp , 1987.

12 48 Informaton and Management Scences, Vol. 18, No. 1, March, 2007 [28] A. Ra, Cost effcency of nternatonal nsurance ndustry, Journal of Fnancal Servces Research, Vol.10, pp , [29] S. A. Rhoades, Market Share as a Source of Market Power: Implcatons and Some Evdence, Journal of economcs and Busness, Vol.37, pp , [30] P. Schmdt and R. C. Sckles, Producton Fronter and Panel Data, Journal of Busness and Economc Statstcs, Vol.2, pp , [31] W. G. Shepherd, Economcs of Scale and Monopoly Profts. In Industral Organzaton, Anttrust, and Publc Polcy, Edted by J. V. Craven Boston: Kluwer Njhoff, [32] W. G. Shepherd, Tobn s q and the Structure Performance Relatonshp Comment, Amercan Economc Revew, Vol.76, pp , [33] G. Skogh, Return of Scale n the Swedsh property-lablty nsurance ndustry, Journal of Rsk and Insurance, Vol.49, pp , [34] M. Smrlock, T. Gllgan and W. Marshall, Tobn s q and the Structure-Performance Relatonshp: Reply, Amercan Economc Revew, Vol.74, pp , [35] J. L. Stevens, Tobn s q and the Structure-Performance Relatonshp: Comment, Amercan Economc Revew, Vol.80, pp , [36] M. A. Wess, Analyss of Producton at frm level: An applcaton to lfe nsurers, Journal of Rsk and Insurance, Vol.53, pp.49-83, [37] A. M. Yuengert, The measurement of effcency n Lfe nsurance: Estmates of a mxed normal- Gamma error Model, Journal of Bankng and Fnance, Vol.17, pp , Author s Informaton James C. Hao s currently an assocate professor n the Department of Insurance, Tamkang Unversty, Tawan, R.O.C. He receved hs Ph.D. n Economcs from Unversty of Illnos. Hs research nterests are effcency, penson system, and bancassurance. Department of nsurance, Tamkang Unversty, Tamsu, Tape, Tawan 251, R.O.C. E-mal: cjhao@mal.tku.edu.tw TEL : ext