A Multinomial Logit Based Evaluation of the Behavior of the Life Insureds in Romania

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1 Amercan Journal of Appled Scences 6 (1): , 2009 ISSN Scence Publcatons A Multnomal Logt Based Evaluaton of the Behavor of the Lfe Insureds n Romana 1 Crstan Dragos and 2 Smona Dragos 1 Teodor Mhal Street, Nr , S.231, , Clu Napoca, Romana 2 Teodor Mhal Street, Nr , S.239, , Clu Napoca, Romana Abstract: The Romanan lfe nsurance market s n full expanson. There exsts competton between nsurance companes as well as between dfferent products of the same company. In ths artcle we descrbe a study usng data that we collected from clents of a Romanan nsurance company. We have observed two types of varables: attrbutes of the nsurance products (e.g., proftablty, rsk), as well as characterstcs of the ndvduals (e.g., sex, age, ncome). Usng elements of economc theory and a multnomal logt model we explan the behavor of the lfe nsureds. We estmate the varatons n the market shares of lfe nsurance products usng margnal effects. The varatons are due to possble changes n the values of some attrbutes or characterstcs. Key words: Lfe nsurance demand, multnomal logt INTRODUCTION The study of the lfe nsured s behavor has attracted the nterest of a number of researchers n the past. Theoretcal models on lfe nsurance demand have been developed and emprcal studes also have been conducted extensvely to examne the nfluence of specfc factors on the demand for lfe nsurance. Ths research proceeds to revew the lterature related to lfe nsurance demand, to present the Romanan lfe nsurance market, to descrbe the data and estmaton model, to present and dscuss the emprcal results and to conclude wth the fndngs of ths study. Economc theory predcts that households wll save and nsure n order to enoy the same lvng standard over tme and n the event of the death of a household head or spouse. Economc theory n ths case accords wth common sense and every day observaton. We save to be able to mantan our lfe styles n retrement. And we buy lfe nsurance to make sure our survvors can contnue to lve at the same standard to whch they have become accustomed [1]. There s no unque theory for lfe nsurance demand. Yaary [2] was the frst to develop a theoretcal framework to study the uncertanty of lfetme and the demand for lfe nsurance. He predcted that nvestors make asset allocatons decsons and lfe nsurance purchase to maxmze ther lfetme utltes of wealth and consumpton. Almost all of the theoretcal works whch study the mpact of wealth and bequest motves on lfe nsurance demand developed later have expanded ther models based on the study of Yaary [2]. There are a number of emprcal studes of lfe nsurance demand that have been developed n the past. Bernhem [3] uses estmates of the demand for lfe nsurance to assess the strength of bequest motves. He fnds that a sgnfcant fracton of total savng s motvated by the desre to leave bequests. Browne and Km [4] present evdence on lfe nsurance demand across 45 countres. They fnd that the man determnants of country varatons n the demand for lfe nsurance are the dependency rato (the number of dependents per potental lfe nsurance consumer), ncome, nflaton and prce of nsurance. The fndngs of Browne and Km [4] and Outrevlle [5] confrm that the ncome level affects sgnfcantly the lfe nsurance demand. Lfe nsurance becomes more affordable when ncome ncreases. Hwang and Greenford [6] examne some of the key factors affectng lfe nsurance consumpton n Chna, Hong Kong and Tawan. Income and lfe nsurance consumpton are found to be strongly correlated, whch s consstent wth prevous studes. In a comparatve study, Truett and Truett [7] examne the varables affectng lfe nsurance demand n Mexco and n U.S. The results have shown that age, educaton and ncome mpact the demand for lfe nsurance. Correspondng Author: Crstan Dragos, Teodor Mhal Street, No , S.231, , Clu Napoca, Romana Tel:

2 Am. J. Appled Sc., 6 (1): , 2009 Over tme, the lfe nsurance decsons and the asset allocaton have been analyzed separately, both n theory and practce. However, results from Headen and Lee [8] ndcate that the demand for nsurance s a functon of varables such as savngs, consumer sentment and condtons f the fnancal market. Mayers and Smth [9] do not agree that wealther consumers demand less nsurance and fnd that the benefts of an nsurance polcy are dentfed wth the returns of other fnancal assets. These results mply that decsons to purchase nsurance are not ndependent of decsons to make other nvestments. The human captal s the factor that makes the lnkng between nsurance and nvestments decsons, because t affects both the optmal asset allocaton and the demand for lfe nsurance - Ibbotson & all [10]. They defned the human captal as the present value of an nvestor s future labor ncome. An nvestor s human captal contans a unque mortalty rsk, whch s the loss of all future ncome and wages n the unfortunate event of premature death. Lfe nsurance has been used for long tme to hedge aganst mortalty rsk. The greater the value of human captal s, the more lfe nsurance the famly demands. Younger nvestors have far more human captal than fnancal captal. Ths s because younger nvestors have more years to work and they have had few years to save and accumulate fnancal wealth. On the other hand, young nvestors tend to have more fnancal captal than human captal, snce they have fewer years ahead to work but have accumulated fnancal captal over a long career. The allocaton of captal n rsky asset decreases as the nvestor ages. Ths result [11] s due to the dynamc between human captal and fnancal wealth over tme. When an nvestor s young, the nvestor s total wealth s domnated by the human captal. Snce human captal n ths case s less rsky than the fnancal rsky asset, young nvestors wll nvest more fnancal wealth nto rsky assets to offset the mpact of human captal on the overall asset allocaton. As the nvestor gets older, the allocaton to rsky assets s reduced, as human captal gets smaller. The volume of lterature on lfe nsurance demand ndcates the mportance of the consumer demand for lfe nsurance n the fnancal servces ndustry. Wth the growng mportance of nsurance companes as maor partcpants n fnancal markets, as well as ncreasng competton for nvestment from nontradtonal nsttutons, ths topc s lkely to contnue to be a popular research topc for the developed and for the developng countres. MATERIALS AND METHODS Our applcaton nvolves clents of a Romanan nsurance company, whose name wll reman unrevealed, out of competton reasons. In July-August 2005, we consdered a sample consstng of 203 subects who possess nsurance polces at that company. Three nsurance products have been taken nto consderaton [12], [13] : term lfe nsurance, endowment lfe nsurance and unt lnked nsurance, whch altogether represent 80% of the turnover of the company. We menton that the applcaton s based on a mddle sze sample, so the conclusons must be regarded wth precauton. Our target s to realze a prospectve study concernng the behavor of the nsured persons. The ndvduals from the sample have been questoned about two knds of varables: attrbutes that characterse the nsurance products and characterstcs of the ndvdual that characterse the nsured person [14]. The Model: Supposng that each one of the ndvduals of the sample chooses only one type of lfe nsurance, the decson of choosng the product s dscreet. Consequently, the model chosen for explanng the choce of an nsurance product s a dscreet one, so the estmaton s made usng the econometrcs of qualtatve varables. The model s a multnomal one because the qualtatve dependent varable y has more than two values, y =, = 0,1,, m, respectvely. In our applcaton, the values of y represent the nsurance products. The Multnomal Logt Model. The multnomal Logt s actually an extenson of the bnary Logt model, havng more than two values for the dependent varable. Let (p 0, p 1,, p m ) be the probabltes of m+1 alternatves of choce. The probablty of an ndvdual to choose the alternatve s gven by: exp(x b ) p = P(y = ) = = 1,2,...,m m + 1 exp(x b ) = 1 (1) where, x s the vector of the ndependent varables assocated to the ndvdual and b s the vector of parameters assocated to the alternatve. 125

3 Am. J. Appled Sc., 6 (1): , 2009 The Condtonal Multnomal Logt Model. The generalzaton of the Logt model for the multnomal case s made by takng dfferent parameters b dependng on the alternatves of choce (products), such that the dependent varables x reman constants dependng on the products. Stll, there s another possblty: the McFadden condtonal Logt model whch consders a constant vector of parameters b and allows the ndependent varables x to depend on the alternatves (McFadden [15],[16] ). The probablty of an ndvdual to choose the product s gven by: exp(x b) exp(x b) = = = = m m exp(xkb) 1+ exp(xkb) (2) k= 1 k= 1 p P(y ) = 1,2,...,m where, x = x x0 and the rato of the probabltes s: exp(x b + x b ) p = P(y = ) =,k = 0,1,2,...,m m k= 1 exp(x b + x b ) k k (6) Once the parameters have been estmated, by replacng the values of the explcatve varables wth the mean values from the sample, we can obtan an estmaton of the probablty p that a randomly chosen ndvdual (average ndvdual) wll choose the product. By multplyng ths number by the total number of consumers N, an estmaton of the demand (or of the market share) for the product can be obtaned: D = p N (7) We can also obtan smulated market shares for products, computed for other values of the explcatve varables, thus facltatng the foundaton of some product polces. P(y ) exp(x b) exp(x b) = = = exp[(x x l)b] P(y l) exp(x b) exp(x b) = = l l,l = 1,2,...,m (3) whch, as n the case of the multnomal Logt s ndependent of the other alternatves of choce. When computng the margnal effects, we are nterested n the estmated varaton of the probablty of an ndvdual to choose the product, when the ndependent varable k assocated to a product vares. We have: K exp xkbk k = 1 p = (4) m K 1+ exp xhkbk h= 1 k = 1 the margnal effect p x lk beng: bkp (1 p ) f = l bkp (1 p l) f l (5) The General Multnomal Logt Model. Due to the fact that our applcaton nvolves both attrbutes of the products and characterstcs of the ndvdual, we use a more general model, whch contans both the multnomal and the condtonal logt models [15],[17], ],[18]. The probablty for an ndvdual to choose the alternatve s gven by: 126 The varables: Proftablty-values from 1 to 10 Rsk-values from 1 to 10 Age-years Sex-0 f the ndvdual s a woman, 1 f t s a man Income-RON/month Term-dummy varable. Equal to 1 f the term lfe nsurance product s chosen, 0 otherwse Endowment-dummy varable. Equal to 1 f the endowment nsurance product s chosen, 0 otherwse Unt lnked-dummy varable. Equal to 1 f the unt lnked nsurance product s chosen, 0 otherwse Age_term = Age Term Age_endowment = Age Endowment Age_unt lnked = Age Unt lnked Sex_term = Sex Term Sex_endowment = Sex Endowment Sex_unt lnked = Sex Unt lnked Income_unt lnked = Income Unt lnked Income_endowment = Income Endowment Income_unt lnked = Income Unt lnked RESULTS AND DISCUSSION Before estmatng the parameters of the model, we present some descrptve statstcs regardng the data from the sample (Table 1). The estmaton of the model: For estmatng the parameters we use the econometrc software LIMDEP

4 Am. J. Appled Sc., 6 (1): , and the Newton-Raphson method lke estmaton algorthm (Table 2). The values of the parameters are accordng to expectatons. The postve sgn for proftablty shows an ncreased probablty of choosng the product when the value of the varable ncreases. The negatve sgn for rsk shows a decrease of probablty. The negatve sgns for age_endowment and age_unt lnked show that when age ncreases, t decreases the probablty of choosng the endowment nsurance and unt lnked nsurance products, wth respect to the reference product, the term nsurance. The parameter of the sex_ endowment varable s not statstcally sgnfcant. The postve sgn for sex_unt lnked shows that t s more lkely for men to choose unt lnked nsurances than women. The negatve sgns for ncome_endowment and ncome_unt lnked show that when ncome ncreases, t ncreases the probablty of choosng the endowment nsurance and unt lnked nsurance products, wth respect to the reference product, the term nsurance. Table 1: The average values of varables n the sample Varables Sex (% Income Proftablty Rsk Age of males) (RON/month) Term Endowment Unt lnked Table 4: The margnal effects (%) for the varable proftablty The margnal effect over the Product Term Unt nsurance Endowment lnked The product Term for whch Endowment proftablty vares Unt lnked For each ndvdual, we can compute accordng to the formula (6) the probablty of choosng each of the three nsurance products (Table 3). A study of the estmated probabltes shows that the model s a pertnent one from the pont of vew of predctons, the percentage of correct predctons n the sample beng 72.9%. The applcablty of the model: We may consder the case when the values of the explcatve varables change. We compute the margnal effects, the percentage varatons of the share markets of the products respectvely, when the proftablty and rsk varables are ncreased by 1 (Table 4). The results obtaned are accordng to expectatons: the ncrease of the proftablty for a product determnes the ncrease of ts market share and the decrease of the market shares for the other products, but of dfferent values. For nstance, the ncrease of proftablty for the Table 2: Parameters estmates. Dscrete choce (multnomal logt) model Varable Coeffcent Standard dev. t-statstc Proftablty*** Rsk*** Age_term Fxed parameter - Age_endowment*** Age_unt lnked*** Sex_term Fxed parameter - Sex_endowment Sex_unt lnked** Income_term Fxed parameter - Income_endowment** Income_unt lnked*** N = 203 R 2 = ***: p<0.01, **: p<0.05, *:p<0.10 Table 3: Predcted probabltes Indv. Term Endowment Unt_lnked * * * * * * * * *: Marks chosen,+: Marks predcton 127 Table 5: The margnal effects (%) for the varable rsk The margnal effect over the product Term Unt nsurance Endowment lnked The product Term For whch Endowment rsk vares Unt Lnked Table 6: Estmated market shares for the nsurance products (group age: years) Income (RON/month) Term Endowment Unt Lnked Table 7: Estmated market shares for the nsurance products (ncome = RON/month) Age Term Endowment Unt Lnked

5 Percentage Term nsurance Endowment Unt lnked Income Fg. 1: The evoluton of the nsurance products wth respect to the ncome (55 years old person) term nsurances wll have a greater mpact on the endowment nsurances than on the unt lnked ones (Table 5). For the rsk varable, the results are very smlar, but of opposte sgn: when the rsk of a product ncreases ts market share decreases and the market share for the other products ncrease (Table 6, Fg. 1). The model can be also used for buldng some product strateges (advertsng, promoton). Consderng ths, we estmate the markets shares of the three nsurance products, for dfferent values of the varables ncome and age. The varables proftablty and rsk keep ther average values from the sample (Table 7, Fg. 2). Percentage Term nsurance Endowment Unt lnked Age Fg. 2: The evoluton of the nsurance products wth respect to the age (ncome = 1000 RON/month) CONCLUSION All n all, we have succeeded to explan through multnomal logt model dfferent aspects of the behavor of the lfe nsureds n a company from the Romanan nsurance market. The results obtaned n the applcaton match perfectly to the theory presented Am. J. Appled Sc., 6 (1): , prevously. The demand for products wth lower rsk level ncreases, as a person s gettng older, to the detrment of the products of hgher rsk level. Moreover, the ncome s a maor factor that nfluences the choce of a specfc nsurance product: as ncome ncreases, there exsts an ncreased affordablty for the hgher rsk products. The demand for each product s well predcted as well as the attrbutes of the products (and characterstcs of the ndvduals) that determne the choce. The model can be used by modfyng the characterstcs of the lfe nsurance products, n order to obtan among these a relaton that would maxmze the proft of the company. One nsurance product may be more proftable than another, whle the achevement of a demand structure, as proftable as possble for the company, can be determned based on the estmatons of the margnal effects of the rsk and of the proftablty of nsurance products. Ths study s a prospectve one; the sample s not hghly sgnfcant. Although, the model can explan the behavour of the lfe nsured and can be a base for further studes capable to estmate more precsely the demand for dfferent types of nsurances. REFERENCES 1. Kotlkoff, J., Gokhale, M., The Adequacy of Lfe Insurance, Taa-Cref Insttute Research Dalogue, no Yaary, M.E., On Consumer s Lfetme Allocaton Process, Internatonal Economc Revew, 5 (3): Bernhem, B., How Strong are Bequest Motves? Evdence Based on Estmates of the Demand for Lfe Insurance and Annutes, Journal of Poltcal Economy, 99: Browne, M., Km, K., An Internatonal Analyss of Lfe Insurance Demand, Journal of Rsk and Insurance, 60 (4): Outrevlle, J.F., Lfe Insurance Markets n Developng Countres, Journal of Rsk and Insurance, 63 (1): Hwang, T., Greenford, B., A Cross-Secton Analyss of the Determnants of Lfe Insurance Companes n Manland Chna, Hong Kong and Tawan, Rsk Management and Insurance Revew, 8 (1): Truett D.B., Truett L.J., The Demand for Lfe Insurance n Mexco and the Unted States: A Comparatve Study, Journal of Rsk and Insurance, 57:

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