Total factor productivity growth in the Canadian life insurance industry:

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1 Toal facor produciviy growh in he Canadian life insurance indusry: J E F F R E Y I. B E R N S T E I N Carleon Universiy and Naional Bureau of Economic Research 1. Inroducion Produciviy growh is an imporan indicaor of indusry performance, in general, and producion efficiency, in paricular. There have been few aemps o direcly measure oal facor produciviy growh (TFPG) for service indusries, and specifically for he Canadian life insurance indusry. Indeed, since services are wo-hirds of Canada's gross domesic produc, a careful underaking of oupu and inpu measuremen for services can yield a clearer picure of Canada's produciviy performance and hereby, is compeiive posiion. Measured produciviy growh raes for services are generally lower han he raes obained for manufacuring indusries. However, his finding is suspec because of he difficulies in using official saisics o measure oupu of service indusries. The purpose of his paper is o compue oupu, inpu, and produciviy growh raes for he Canadian life insurance indusry based on firm-level daa obained from he Office of he Superinenden of Financial Insiuions (OSFI). In addiion, he rae of TFPG is decomposed in order o deermine he relaive conribuion of reurns o scale and raes of echnological change o produciviy growh. This paper is organized in he following way. Secion 2 discusses he posiion of he life insurance indusry in he Canadian economy. Secion 3 perains o he measuremen of oupu prices and quaniies in he life insurance indusry. Secions 4, 5, and 6 discuss labour, capial and inermediae inpu prices and quaniies. Secion 7 conains he discussion of he rae of TFPG. Secion 8 presens he analysis of he decomposiion of TFPG. The las secion is he conclusion. 2. Life insurance in he Canadian economy The larges secoral conribuor o Canadian gross domesic produc (GDP) is services. Indeed, he proporion of GDP conribued by he manufacuring secor Canadian Journal of Economics Revue canadienne d Economique, Vol. 32, No. 2 April / avril Prined in Canada Imprimé au Canada / 99 / $1.50 Canadian Economics Associaion

2 Toal facor produciviy growh 501 during he las hree decades has been abou 19.0 percen while he service secor 1 has coninued o grow, reaching 67.0 percen by Along wih services in general, he finance, insurance and real esae (FIRE) secor has grown over he 1980 s from 14.6 percen in 1981 o 16.7 percen in Throughou his period, he insurance indusry (ha is, boh life and propery and casualy insurance) has kep pace wih he service secor as a whole and he FIRE subsecor. Insurance accouns for abou 0.70 percen of GDP. The GDP conribuion of life insurers from 1981 o 1992 increased from 0.30 o 0.42 percen. Manufacuring indusries ha are of comparable size o life insurance (in erms of GDP proporions) include indusrial chemicals (0.43 percen), elecommunicaion broadcasing (0.43 percen), and air ransporaion and incidenal services (0.51 percen). In 1991, 79.0 percen of premiums wrien by life insurers were for life insurance policies and annuiies wih he remainder coming from acciden and sickness insurance. Of hese premiums, federally regisered firms wroe 92.2 percen, and he remainder were wrien by provincial insurers. In 1991, here were 175 federally regisered life insurance companies in Canada, of which 69 (39.4 percen) were domesically owned and 106 were foreign firms or subsidiaries of foreign paren firms operaing in Canada. The life insurance indusry is one of he few Canadian indusries in which he companies ha dominae he indusry are of Canadian naionaliy (in erms of ownership or regisraion). Despie being markedly ounumbered by foreign compeiors, Canadian-owned firms accouned for 70.1 percen of premiums. Wih respec o financial asses, in 1991 life insurers held 13.8 percen, or $153.2 billion. In comparison o oher major financial inermediaries, charered banks held 43.2 percen, credi unions and caisse populaires held 8.0 percen, rus and morgage loan companies held 11.5 percen, ruseed pension plans held 20.3 percen, and propery/casualy insurers held 3.2 percen. Alhough he percenage of financial asses held by life insurers has fallen over he pos World War II period (in 1961 he percenage was 26.5), by he middle 1980's he rae 2 sabilized. In his paper, oupu, inpu and produciviy growh raes are measured for he welve major firms (as an aggregae or as a whole) ha operae in he life insurance indusry. These welve firms accoun for 76 percen of all he premiums and 81 percen of all asses over he period from 1978 o A lis of he companies sudied, showing heir sales as a percen of he oal sales of all life insurance companies and heir asses as a percen of he oal asses of all life insurance companies is presened in able 1. Sales are measured by oal premium revenue in all lines of life insurance and annuiies. Asses include 3 socks and bonds, morgages, real esae, shor-erm paper, and cash. All welve firms offered life insurance lines ha ranged from individual life insurance o group annuiies. These companies were federally regisered companies. The marke share of he larges, he Manufacurers Life Insurance

3 502 Jeffrey I. Bernsein Company was on average 20.5 percen over he period from 1978 o 1989, whereas he marke share of he smalles company, Naional Life Assurance was approximaely 1.0 percen over he same period. As we can see from able 1, he ranking of firms by premium revenue is quie similar o he ranking by asses. TABLE 1 Life Insurance Companies Asses and Premium Revenue as a % of Toal Asses and Premium Revenue (Average ) Toal Asses Premium Revenue Company (% of oal) (% of oal) 1 Manufacurers Life Insurance Grea Wes Life Insurance Sun Life Insurance Canada Life Insurance Muual Life Insurance London Life Insurance Norh American Life Insurance Imperial Life Insurance Excelsior Life Insurance Mariime Life Insurance Assurance-Vie Desjardins Naional Life Assurance Toal Oupu measuremen Insurance oupu has been measured generally as premiums paid, or premiums ne of claims (see Bernsein and Geehan 1988 for a discussion and references concerning he differen measures of insurance oupu). However, hese variables do no represen oupu quaniy. They are alernaive measures of revenues ha are defined in erms of curren dollars, and hereby conain he influence of prices. Suppose ha a uni of insurance is purchased his year for $100 (a his poin we will no concern ourselves wih he definiion of a uni of insurance). Nex year, he price of his uni becomes $110. Alhough premiums increased, insurance oupu has remained consan. In order o measure he growh rae of oal facor produciviy (ha is oupu growh ne of inpu growh) i is necessary 4 o decompose insurance revenue ino price and quaniy componens. Consideraions of he naure of he produc or producs sold by insurers are imporan in he measuremen of insurance oupu quaniy. Purchasers of insurance are buying fuure financial proecion when a paricular even occurs. An insurance firm is able o offer his proecion because i has creaed he faciliies o pool risks. Indeed insurance policies specify he erms of agreemen beween insurers and insurees. Wih respec o life insurance, hese erms relae o such elemens as he premium, he dollar value of insurance (i.e. he face

4 Toal facor produciviy growh 503 value), he even ha is being insured agains, and he ime period over which he policy is in force. Clearly, hen, a policy, wih is deailed characerizaion of he life insurance conrac, delimis oupu quaniy. For example, he number of policies defined for individuals, wih face values of $100,000, for en years, represens oupu quaniy for his paricular ype of life insurance. This view of life insurance oupu quaniy recognizes ha insurers produce muliple oupus. Wih he availabiliy of sufficienly deailed firm-level daa, i is possible o define muliple policy ypes. Aggregaing over policy ypes (by using he prices and quaniies associaed wih each policy) leads o an aggregae measure of life insurance oupu quaniy. The adopion of his approach o oupu measuremen highlighs he difficulies in using official saisics. These daa relae o (1) aggregae daa, and (2) revenue (or curren dollar) measures. Specifically, policy numbers are no available for a variey of policy ypes. The inference here is ha aemps o measure oupu quaniies of life insurers using official saisics are problemaic. There are a number of oher aspecs in he calculaion of revenue, oupu price and oupu quaniy of life insurance ha mus be considered. Firs, in he life insurance indusry here are acive reinsurance markes. In hese markes insurers sell pars of a policy o oher insurers in order o diversify risk. In his paper all premiums are included in revenue, and any premium revenue ha has been sold or ceded o oher insurers is included in inermediae inpus. When an insurer cedes par of a policy in reinsurance markes, i is purchasing services from anoher insurer. A second consideraion in oupu measuremen perains o claims. Premiums for a policy are se on an acuarial basis. Premiums reflec an expeced ineremporal income flow aking ino consideraion he expeced claims ha will arise from he policy. Life insurers mus se aside, or reserve, a porion of he premium in order o pay for he increase in expeced claims ha may arise from he policies in force. Changes in reserves represen he annual changes o expeced claims associaed wih he annual premium paid on a policy. This means ha changes in reserves mus be subraced from premiums o calculae annual revenue. Third, life insurers inves par of he funds hey obain hrough premiums. The reurns from hese invesmens help diversify he risk and defray he coss of financial inermediaion. Thus, gross reurns from invesmen are added o premiums and he cos of obaining hese reurns are refleced in he labour, 5 inermediae inpus, and capial coss of he insurance firm. Oupus of life insurers have a number of differen feaures or characerisics. There are hree main ones. Firs, here is he insured even: for example, deah or reiremen. The second characerisic perains o he face amoun of he policy. This is he value received by he insured if he insured agains even occurs. The hird characerisic concerns he policyholder. I is eiher an individual or group, and groups can consis of various numbers of individuals. There are many lines

5 504 Jeffrey I. Bernsein (i.e. differen ypes of oupu) of insurance and any adjusmens o premiums o obain revenue mus be carried ou for each line. Once he revenue per line has been calculaed, hen dividing i by he number of policies per line, which is oupu quaniy, yields o he price of a policy per line of insurance. In his paper, insurance oupu is divided ino four caegories. These are individual insurance, group insurance, individual annuiies and group annuiies. Individual and group insurance oupu includes whole life, erm life and endowmen insurance wrien as boh paricipaing and non-paricipaing policies. The erm of a whole life policy is he lifeime of he insured. Term insurance covers he life of he insured for a specific period only. Endowmen polices provide a cash paymen when he policy is ceased. Paricipaing policies pay dividends o policyholders, as hey are also equiyholders. Individual and group annuiies include pensions wih and wihou las survivor and disabiliy feaures. All he oupu-relaed annual daa for he welve firms over he period from 1978 o 1989 are obained from he Office of he Superinenden of Financial Insiuions (OSFI). The oupu price measure for he ih line of insurance or annuiy is P i ' [(pd i % pa i )% giv i & Äpr i ]/N i where P i is he oupu price, pd i is he premium revenue earned from direc sales, pa is he premium revenue earned by assuming reinsurance from anoher i insurance firm, giv i is he gross invesmen income, Äpr i is he annual change in policy reserves, and N is he number of polices or group cerificaes, all in he i ih line of insurance or annuiy. The change in policy reserves reflecs he expeced change in fuure claims associaed wih he annual premiums. In he case of group insurance, or annuiies, individuals do no own he policies. However, hey are issued a cerificae ha esablishes he life insurer s liabiliy o hem hrough he policy owned by he group. The oupu price of he ih line of insurance is he price per policy charged for he financial inermediary services provided by he life insurance firm. This price is normalized o 1.00 in Nex, he oupu quaniy of a line, given by he number of policies in ha line, is muliplied by he normalized price. The produc of he normalized oupu price and quaniy is he revenue earned by he company for financial inermediaion services in he respecive line of insurance or annuiy. This is P N, or he per i i policy price muliplied by he number of policies in he ih line of insurance or annuiy. Oupu prices are defined wih respec o produc characerisics: in his case, individual or group, and insurance or annuiy. As previously noed, here are a number of oher oupu characerisics. One specific characerisic is he face value of an insurance policy or annuiy conrac. Alhough daa on face values (ne of ceded insurance) are unavailable from OSFI, he oupu price index ha is developed in his paper is consisen wih a consan face value index. This (1)

6 Toal facor produciviy growh resul is presened in he appendix. The nex sep is o aggregae over he welve firms o obain growh raes for each of he four oupus. The ih oupu quaniy is aggregaed in he following way. Firs, a Tornquis aggregae (over firms) price index is formed for each oupu. The aggregae price formed in his way is hen normalized o 1.00 in Second, oupu quaniy (for he aggregaion of he welve firms) for each line is consruced by dividing revenue for a specific line by is price index. Growh raes for each of he oupu lines aggregaed over all welve firms are presened in able 2. The four oupus are individual insurance, individual annuiies, group insurance, and group annuiies. TABLE 2 Growh Raes of Oupus (Percen) Period Individual Individual Group Group Insurance Annuiy Insurance Annuiy This able shows ha over he period from 1979 o 1989 annuiies grew significanly faser han insurance. In addiion, he annual raes of growh for individual and group annuiies were abou equal wih raes a around 10.0 percen. Individual insurance grew a around 3.25 percen over he period, while here was virually no growh for group insurance. Oupu growh was greaer in he laer half of he 1980's for each caegory. In fac, he posiive growh in group insurance over his period jus overcame he negaive growh in he firs half of he decade. 4. Labour inpu The number of persons employed by he life insurance indusry in Canada increased from 50,400 in 1978 o 65,100 in In 1978, 38 percen of all company employees were engaged in sales and 62 percen were engaged in

7 506 Jeffrey I. Bernsein adminisraive work. In 1989, hese percenages were 35 percen and 65 percen respecively. Adminisraive labour inpu includes clerical, daa processing, invesmen, and acuarial personnel. Sales labour inpu includes capive agens and sales managers. Capive agens are agens who represen only one company. In reurn, a life insurance company provides he capive agens heir office space and equipmen. The majoriy of life insurance sales are obained hrough capive agens. Independen agens may work for more han one company and provide heir own office faciliies and equipmen. There are few independen agens in life insurance. The welve major life insurance companies ha are considered in his paper paid an average of 70 percen of all wages and benefis earned in he life insurance indusry over he period Wages include head office employee wages, branch office employee wages, sales manager salaries, agen salaries, commissions and allowances, and direcor fees. Benefis include conribuions o company pension plans for employees and agens, he employer's conribuions o governmen pension plans and unemploymen insurance, hospialisaion and medical insurance for employees, and cafeeria expenses. Labour inpu quaniy is calculaed in he following way. Curren annual wages and benefis for each firm are divided by a labour price index consruced for he life insurance indusry. This labour price index is consruced by firs dividing oal annual life insurance indusry wages and benefis by oal annual life insurance indusry hours o obain a series of annual hourly wage raes specific o his indusry. This series of hourly wage raes is indexed o 1.00 in Toal annual life insurance wages and benefis are obained from he Canadian Life and Healh Insurance Associaion. Toal life insurance indusry hours are obained by muliplying oal annual hours for he FIRE secor by he percenage of life insurance employmen o FIRE employmen. Employmen and hours daa are obained from Saisics Canada. The labour quaniy for each of he welve firms is hen curren annual wages and benefis for each firm divided by his labour price index. Nex, he labour quaniies for each firm are aggregaed o obain a labour quaniy for all welve life insurance firms. Since he labour price index is idenical for all firms, labour quaniy for all firms is he sum of all firms curren labour coss divided by he indusry labour price index. Table 3 presens he raes of growh of labour quaniy. From his able we see ha labour quaniy grew a around 2.5 percen annually over he period. Moreover, unlike oupu quaniy growh, he labour quaniy growh rae was quie sable over he whole decade. TABLE 3 Growh Raes of Inpus (Percen) Period Labour Building Machinery Inermediae Capial Capial Inpus

8 Toal facor produciviy growh Capial inpu Two ypes of capial inpu are used in he life insurance indusry: machinery and buildings. Buildings for own use are hose buildings used by he life insurance firm for all of is insurance and invesmen aciviies. Machinery used in he life insurance indusry consiss of office furniure, elecronic daa processing equipmen of all ypes, and compuer sofware. The measure of building capial is consruced from real esae expenses provided by firms o OSFI. Real esae expenses include impued and acual rens on buildings for own use, mainenance expenses, and oher real esae expenses. Acual and impued rens include rens on head, and branch offices used for insurance and invesmen purposes. Building capial for a firm is measured as real esae expenses divided by he renal rae on building capial. This rae is defined as, w = p (ä + r)(1 - u ) (2) b b b p where w b is he renal rae on buildings, p b is he acquisiion price index of building capial, ä is he depreciaion rae on buildings, r is he long-erm b governmen bond ineres rae, and u p is he propery ax rae. The acquisiion price index relaes o he FIRE secor. This price is published by Saisics 7 Canada, and is indexed o 1.00 in The depreciaion rae is he annual depreciaion on buildings divided by he value of buildings. These daa are provided by OSFI. The propery ax rae is he annual amoun of propery axes paid as repored o OSFI divided by he value of buildings. Nex, he building capial socks for each firm are aggregaed in order o measure he buildings capial inpu quaniy for all welve life insurance firms. Since he building capial acquisiion price index is idenical for all firms, he building capial quaniy for all firms is he sum of annual coss of buildings

9 508 Jeffrey I. Bernsein capial for all he firms divided by he building capial price index. Turning o machinery capial, i is eiher owned or leased. Renal paymens for leased machinery are obained from general and miscellaneous expenses in he OSFI daa. Many smaller insurance firms no only lease heir office space bu also lease equipmen. This equipmen usually includes elecronic daa processing equipmen. Impued ren on owned equipmen for each of he welve firms is calculaed by muliplying he quaniy of owned equipmen by he renal rae for equipmen. The quaniy of owned equipmen is he curren value of owned equipmen repored as an asse in he OSFI daa divided by he acquisiion price for machinery capial. This price is obained from Saisics Canada for he FIRE secor, and is indexed o 1.00 in The renal rae for machinery and equipmen capial is, w = p (ä + r) (3) m m m where w m is he renal rae on machinery, p m is he acquisiion price index of machinery capial, and ä m is he depreciaion rae on machinery. The depreciaion rae is he annual depreciaion on owned machinery divided by he value of machinery. These daa are provided by OSFI. For each of he welve firms, summing he impued ren on owned machinery wih he renal paymens on leased machinery resuls in he oal ren on machinery. Dividing his sum by he renal rae yields he machinery capial inpu 8 quaniy. Nex he machine capial inpu quaniies for each firm are aggregaed o give machinery capial quaniy relaing o he welve life insurance firms, as a whole. Since he price index is idenical for all firms, aggregae machinery capial quaniy is he sum of all welve firms annual cos of machinery capial divided by he price index. Table 3 presens he capial inpu growh raes for building and machinery capial respecively. This able shows ha he average annual growh rae of building capial was 8 percen. In addiion, growh was significanly greaer in he las half of he decade. Table 3 also shows he enormous growh in machinery capial over he 1980's. The average annual rae of around 32 percen reflecs he imporance of new equipmen associaed wih informaion processing echnologies. In fac, he growh rae of equipmen was greaer in he firs half of he decade. Recall ha his was a period of slower oupu growh. 6. Inermediae inpus Inermediae inpus consis of maerials, supplies, and hired or purchased services. Reinsurance services are a componen of purchased services. They are purchased from oher insurance companies. In addiion, hired services consis of professional services purchased from medical praciioners, lawyers, accounans,

10 Toal facor produciviy growh 509 and invesigaors. For each of he welve firms, he curren value of maerials and supplies expenses is added o he curren value of professional service expenses o form he curren cos of maerials, supplies, and professional services. The quaniy of maerials, supplies and professional services is obained by dividing he curren cos by he inermediae inpu price deflaor published by Saisics Canada for he FIRE secor. This index is 1.00 in The quaniy of ceded reinsurance for each of he welve firms is consruced 9 in he following way. The number of ceded policies, conracs or cerificaes in any one line of insurance or annuiy is calculaed as he proporion of ceded reinsurance premiums o direc insurance and assumed reinsurance premiums, muliplied by he number of direc and assumed policies or cerificaes in ha line of insurance or annuiy. The oal quaniy of ceded insurance or annuiies for each firm is he sum of quaniies across he four lines of insurance and annuiies. Nex, he price of ceded insurance is obained by dividing he oal curren value of ceded insurance by he oal quaniy of ceded insurance. The value of reinsurance ceded over all four caegories of oupu is colleced from he OSFI daa. This value is he premiums ne of he change in policy reserves associaed wih reinsurance ceded. The price of ceded insurance is normalized o 1.00 in The measure of he quaniy of inermediae inpus for each of he welve firms is he aggregaion of he quaniies of maerials, supplies, and professional services relaing o insurance and invesmen aciviy, and he quaniy of reinsurance ceded. Price indices of maerials, supplies, and professional services, and reinsurance ceded are combined as a weighed-sum o form he price index of inermediae inpus. The weighs used in his summaion are he conemporaneous cos shares of maerials, supplies, professional services, and ceded insurance. This aggregae price is normalized o 1.00 in The quaniy of inermediae inpus, for each firm, is he curren cos of inermediae inpus divided by he price index of inermediae inpus. Nex inermediae inpu quaniies for each of he welve firms mus be aggregaed across firms. An aggregae inermediae inpu price index is consruced using he weighed-sum of individual firm price indices. The weighs are firm inermediae inpu cos as a proporion of aggregae (across firms) inermediae inpu cos. This price index is normalized o 1.00 in Aggregae inermediae inpu quaniy is measured as aggregae inermediae inpu cos divided by he aggregae inermediae inpu price index. The las column in able 3 presens he growh raes for inermediae inpu quaniy. This able shows ha he average annual growh for inermediae inpus was 5.1 percen. This growh rae was quie sable over he decade. 7. Toal facor produciviy growh

11 510 Jeffrey I. Bernsein The rae of oal facor produciviy growh (TFPG), for all welve firms combined as an aggregae, is he rae of oupu growh minus he rae of inpu growh. The rae of growh of oupu in period is given by 4 ÄlnY() ' '[(s yj (%1)%s yj ())/2]ln(y j (%1)/y j ()), (4) j'1 where s () is he jh oupu revenue share in period, and y () is he jh oupu for yj j period. Recall ha he four oupus are individual insurance, individual annuiies, group insurance, and group annuiies. The annual growh raes of oupu, for he welve firms as an aggregae, are shown in able 4. This average growh rae was 4.5 percen in he firs half of he decade and abou 7.0 percen in he second half. Over he whole decade oupu growh averaged 5.5 percen. In a similar fashion o oupu growh, inpu growh, for all welve firms as a whole, can be measured as, 4 ÄlnV() ' ' [(s vj (%1)% s vj ())/2]ln(v j (%1)/v j ()) j'1 where s () is he cos share of he jh inpu in period, and v () is he quaniy of vj j he jh inpu in period. There are four inpus: labour, building capial, machinery capial and inermediae inpus. Table 4 shows ha inpu growh averaged around 4.5 percen over he decade and his was quie sable. The rae of TFPG in period is, 10 TFPG = ÄlnY() - ÄlnV() (6) The las column in able 4 presens TFPG. Table 4 shows ha oal facor produciviy growh in he life insurance indusry is higher during he period , relaive o he firs half of he decade. The average annual rae of TFPG for life insurance was abou 1 percen over he decade. The life insurance indusry, as refleced by he welve major firms, experienced a slowdown in produciviy growh similar o ha experienced in Canadian manufacuring indusries during he firs half of he 1980's (see Denny, Bernsein, Fuss, Nakamura and Waverman (DBFNW) 1992). The average TFPG (5)

12 Toal facor produciviy growh 511 TABLE 4 Growh Raes of Oupu, Inpu and Produciviy (Percen) Period Oupu Growh Inpu Growh TFPG rae for he life insurance indusry over he period ouperformed welve of he eigheen manufacuring indusries (calculaed by DBFNW) over he period Moreover, over he depressed period he rae of TFPG for life insurance was greaer han he rae for seven of eigheen manufacuring indusries. During he period from 1980 o 1985 only five Canadian manufacuring indusries had a beer TFPG performance han he life insurance indusry during he period from 1979 o These indusries were rubber, leaher, lumber, primary meals, and elecrical machinery. The period from 1979 o 1985 in Norh America covers a rough o peak period. Such a period is accompanied by large changes in capial uilizaion and good TFPG performance is experienced by indusries characerized by a large quaniy of fixed asses. The life insurance indusry does no have a large sock of fixed asses when compared o such indusries as lumber and elecrical machinery indusries, and hus is more likely o show poor TFPG during such a period. Produciviy growh sudies peraining o he banking indusry also show low TFPG raes in he period from 1967 o Huner and Timme (1991) used aggregae oupu and inpu daa and found TFPG in he U.S. commercial banking indusry o range from o 0.60 percen a year during he period from 1977 o Humphrey (1991) also found lower posiive and less negaive annual raes of produciviy growh over he period from 1967 o 1987 compared o Huner and Timme. Parsons, Golieb, and Denny (1990) calculaed TFPG raes for Canadian commercial banking. They found an average annual TFPG rae of 1.9 percen from May 1974 o Ocober Thus we find ha over he 1980's he rae of TFPG for life insurance is comparable o he rae found for

13 512 Jeffrey I. Bernsein commercial banking. 8. Decomposiion of oal facor produciviy growh TFPG raes can be decomposed ino wo pars. One par relaes o he degree of reurns o scale and he oher perains o he rae of echnological change. The decomposiion can be wrien as (see Diewer 1988 and Bernsein 1996) TFPG ' (1& ñ &1 y )ÄlnY()%z c ()%å, (7) where ñ y is he measure of scale economies, z is c he (inpu-based) rae of echnological change, and å is he residual due o oher facors. From equaion (7), if here are consan reurns o scale hen here is no scale effec on TFPG. If here are increasing reurns o scale along wih posiive raes of oupu growh hen scale conribues o TFPG. In addiion, posiive raes of echnological change conribue o TFPG. Equaion (7) shows us how o decompose measured TFPG raes ino scale, echnology, and residual componens. In his paper we do no esimae he degree of reurns o scale or he rae of echnological change. We obain hese esimaes from he exising lieraure. The esimaes of scale economies (ñ ) are aken from y Bernsein (1992). The esimaes of scale are: 1.40 for he period from 1978 o 1981, 1.17 for he period from 1982 o 1984, 1.31 for he period from 1985 o 1987, and 1.13 for he period from 1987 o As equaion (7) shows, hese esimaes of reurns o scale are muliplied by he oupu growh raes ha perain o he welve firms as a whole, and found in able 4. The esimae of he rae of echnological change (z ) is from Daly, Rao and Geehan (1985). The annual rae c is 1.5 percen. The resuls on he decomposiion of TFPG are presened in able 5. On average he main elemen conribuing o TFPG for life insurance is echnological change. This resul is similar o ha found for banking. In addiion, he rae of echnological change used in he decomposiion is similar o raes esimaed for banking. In he U.S. banking indusry he rae of echnological change has been esimaed o be 0.96 percen per year for he period from 1980 o This esimae relaes o a panel of 219 U.S. banks (see Huner and Timme 1991), alhough Humphrey (1991) esimaed he rae o be percen for he period from 1977 o 1988 for a panel of 683 banks accouning for wo hirds of all U.S. bank asses. This finding is consisen wih Parsons, Golieb and Denny (1990), who find an average rae of echnological change in Canadian banking of 1.0 percen over he period from 1980 o These raes of echnological change compare wih 1.5 percen for he Canadian life insurance indusry found by Daly e al. (1985) for he period from 1974 o TABLE 5 Decomposiion of Toal Facor Produciviy Growh

14 Toal facor produciviy growh 513 (Percen for seleced periods) Period TFPG Scale Technological Change Residual Bernsein (1992) finds evidence of slighly increasing reurns o scale in he life insurance indusry. Indeed, scale economies, on average, accoun for a slighly smaller effec on TFPG han he rae of echnological change. Moreover, in comparison o banking, Huner and Timme (1991), and Humphrey (1991) find ha reurns o scale are almos consan in U.S. commercial banking, while Parsons, Golieb and Denny (1990) find consan reurns o scale in Canadian banking. Thus here appears o be a somewha greaer degree of reurns o scale in life insurance and hese scale economies conribue o he rae of TFPG. The residual erm in he decomposiion represens a number of elemens. Firs, i represens measuremen errors in he rae of TFPG. For example, if oupu or inpu prices are no measured correcly hen errors will appear in he measured TFPG raes. Indeed, he significan growh of machinery capial has caused measured TFPG o decline because he subsanial decline in compuer prices is no fully capured by Saisics Canada price indexes. Second, he residual can reflec oupu prices ha are no equal o marginal coss of producion. This means ha he measured rae of TFPG reflecs more han jus echnological efficiency. In his case, he residual encompasses price-cos margins which are no refleced in measures of he degree of reurns o scale and raes of echnological change. Third, he exisence of a residual can mean ha esimaes of he degree of reurns o scale or he rae of echnological change need o be improved. Indeed, his may be he case for he rae of echnological change. There is lile conemporaneous evidence on he rae of echnological change in he Canadian life insurance indusry. This omission is especially imporan in ligh of he imporance of developmens in informaion echnologies in he delivery of life insurance services. Fourh, he residual capures elemens ha conribue o TFPG oher han scale and echnological change. One such elemen perains o capial adjusmen. For example, here may be significan coss associaed wih he implemenaion of informaion echnology (such as raining coss) ha have no been capured in he decomposiion of he rae of TFPG. Clearly, given he annual variaions and size of he residual, furher work is needed in deermining he decomposiion of TFPG for he Canadian life insurance indusry.

15 514 Jeffrey I. Bernsein 9. Conclusion In his paper, for he firs ime, comprehensive esimaes of oal facor produciviy growh for he Canadian life insurance indusry have been developed. We find ha over he period from 1979 o 1989 he average annual rae of produciviy growh was abou 1 percen. Based on he exising empirical evidence, produciviy growh in he life insurance indusry was generally higher han he raes esimaed for wo-hirds of Canadian manufacuring indusries over he comparable period from 1973 o The major source of oupu growh in he calculaion of TFPG was he significan growh in annuiies, as individual and group annuiies had average annual growh raes of around 10 percen. Informaion echnologies were an imporan source of inpu growh. Average annual growh for machinery capial, which reflecs informaion echnology, was an asounding 32 percen over he decade. The rae of echnological change and he degree of scale economies are wo imporan elemens ha conribue o produciviy growh. Curren esimaes sugges ha echnological change is relaively more significan as a source of produciviy growh. However, we found a large residual elemen in he decomposiion of produciviy growh. Alhough his residual can arise from numerous sources, we believe ha wo main deficiencies accoun for he residual. Firs, here are only a few, and daed esimaes of he rae of echnological change for he life insurance indusry. Second, he decomposiion analysis did no accoun for he rapid, significan and cosly adjusmen associaed wih implemenaion of informaion processing echnologies in he delivery of life insurance services. Furher research is needed o provide a more comprehensive decomposiion of TFPG raes. Neverheless, nowihsanding improvemens in our undersanding of he decomposiion of produciviy growh, we have clearly shown ha he produciviy performance of he Canadian life insurance indusry is comparable o manufacuring indusries.

16 Appendix Oupu Price Aggregaion and Face Amouns p i FI i P i ' (p i b i N i )/N i FI i Q i ' b i /b i &1 ' p i FI i ' p i b i N i /[b i &1N i ], Toal facor produciviy growh 515 When measuring oupu over ime, i is necessary o accoun for all oupu characerisics. Wih respec o insurance, oupu measures mus reflec a consan face value for a given policy. This consan face value reflecs he quaniy of risk insured. In he case of life insurance his quaniy of risk is a single life valued in consan dollars. Wih respec o annuiies, he quaniy of risk associaed wih a single life or annuian is refleced by a consan dollar annual annuiy paymen. This appendix shows ha he Tornquis oupu price indexes are consisen wih consan face amouns of insurance and annuiies. The premium per policy (or in oher words he price) of line i in period is, (A.1) where is he price of insurance per uni face amoun or he price of an annuiy of one dollar in period, b i is he face amoun of insurance or he annuiy paymen in period, and N i is he number of policies of line i insurance or he number of annuiy conracs in he case of an annuiy. The value p i b i N i is he premium revenue of line i of insurance or annuiy in period. We can consruc an index of consan face amouns of insurance as (A.2) where is he index of individual face amouns or annual annuiy paymens, having a value of 1.0 in period -1. The price of insuring a base year uni face or he price of a consan dollar annuiy of $1 is (A.3) where b i &1 N i is he period face amoun of insurance in unis of period -1 face amouns, or he consan period -1 dollar paymens of annuiies. The Tornquis price index of he prices of consan face amouns of insurance or a consan dollar annuiy is Ð n i'1 [Q i /Q i i &1 ]s ' Ð n i'1 [p i b i N i /[b i &1 N i ]b i &1 N i &1 /[p i &1 b i &1 N i i &1 ]]s 'Ð n i'1 [P i /P i i &1 ]s (A.4) where s i ' (p i &1 b i &1 N i &1 /'n j'1 p j &1 b j &1 N j &1 % p i b i N i /' n j'1 p j b j N j )0.5 P i /P i &1 ' p i b i /p i &1 b i &1. The Tornquis price index of he prices of consan face amouns of insurance or a consan dollar annuiy is equivalen o he Tornquis price index of he per policy price of insurance or an annuiy. and

17 516 Jeffrey I. Bernsein Noes The auhor would like o hank Graham Corke and Jason Morrison for heir research assisance. Michael Denny, Alice Nakamura, and an anonymous referee, provided valuable commens. This paper is an abbreviaed version of a paper presened a he CSLS Conference on Service Secor Produciviy, held in April 1997, in Oawa, Canada. 1. This paper relaes o he measuremen of produciviy growh for life insurance over he period Thus we wan o characerize he life insurance indusry wihin he economy during his ime period. 2. The relaive decline in life insurers holdings of financial asses compared o oher financial insiuions was due o he 1967 revision of he bank ac. This revision made i profiable for charered banks o ener he morgage marke (see Bernsein and Geehan 1988 for a discussion). 3. In 1991 oal premiums for he life insurance indusry were $35.5 billion, and oal asses were $166.6 billion. 4. If life insurers produced a single oupu, under consan reurns o scale in compeiive produc and facor markes, hen TFPG could be measured as he weighed average of inpu price growh raes ne of he oupu price growh. In his case oupu growh raes would no be needed o calculae TFPG. Unforunaely, life insurers produce muliple producs, under join cos condiions. In addiion, here is evidence of increasing reurns o scale (see Bernsein and Geehan 1988, and Bernsein 1992). 5. An alernaive approach is o rea invesmen aciviy as disinc from insurance and annuiies. In oher words an addiional disinc class of oupu could be defined. However, he presen approach permis us o ake advanage of he deailed manner ha he daa are provided by life insurers o OSFI. 6. In he appendix, we are assuming ha here is no change in he disribuion of face values across produc lines over ime. 7. Capial acquisiion prices for he life insurance are unavailable from Saisics Canada. 8. Alernaively, renal paymens could be divided by he renal rae on owned machinery and equipmen, and hen he implied rened machinery and equipmen capial and owned socks could be added o obain machinery and equipmen capial. 9. There were some large percenage changes in inermediae inpus in 1981 and 1985 (see he las column in able 3) due o ceded insurance. However, average annual growh remained sable over he decade. In addiion, from able 4, we shall see ha inpu growh, and hereby TFPG, was no affeced by hese large changes in inermediae inpus. 10. Noice ha TFPG is measured as he difference in growh raes beween oupus and inpus. I is an index number, or growh accouning, calculaion. There is no esimaion of producion or cos funcions. References Bernsein, J.I. (1992) Informaion spillovers, margins, scale and scope: wih an applicaion o Canadian life insurance, Scandinavian Journal of Economics S94, ))) (1996) The Canadian communicaion equipmen indusry as a source of R&D spillovers and produciviy growh, in The Implicaions of Knowledge-Based Growh

18 Toal facor produciviy growh 517 for Micro-Economic Policies, ed. P. Howi (Calgary: Universiy of Calgary Press) Bernsein, J.I., and R.R. Geehan (1988) The Insurance Indusry in Canada (Torono: The Fraser Insiue) Daly, M., P. Rao, and R. Geehan (1985) Produciviy, scale economies and echnical progress in he Canadian life insurance indusry, Inernaional Journal of Indusrial Organizaion 3, Denny, M., J. Bernsein, M. Fuss, S. Nakamura, and L. Waverman (1992) Produciviy in manufacuring indusries, Canada, Japan and he Unied Saes, : Was he produciviy slowdown reversed? Canadian Journal of Economics 3, Diewer, W.E. (1989) The measuremen of produciviy, U.B.C. Discussion Paper No Halpern P.J., and G.F. Mahewson (1975) Economies of scale in financial insiuions: a general model applied o insurance, Journal of Moneary Economics 2, Humphrey, D.B. (1991) Produciviy in banking and effecs from deregulaion, Economic Review, Federal Reserve Bank, Richmond, Virginia 77(2), Huner, W.C., and S.G. Timme (1991) Technological change and producion economies in large U.S. commercial banking, Journal of Business 64, Kim, M. (1986) Banking echnology and he exisence of a consan oupu aggregae, Journal of Moneary Economics 18, Parsons, D.J., C.C. Golieb, and M. Denny (1990) Produciviy and compuers in Canadian banking, Working paper no. 9012, Deparmen of Economics, Universiy of Torono, Canada

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