The Economic Performance of the Canadian Insurance Business. Tarek Harchaoui

Transcription

1 CSLS Conference on Service Sector Productivity and the Productivity Paradox April 11-12, 1997 Chateau Laurier Hotel Ottawa, Canada The Economic Performance of the Canadian Inurance Buine Tarek Harchaoui (Indutrial Organization and Finance Diviion, Statitic Canada) Seion 4A Productivity in the Inurance Indutry April 12 8:30-10:00 AM

2 The Economic Performance of the Canadian Inurance Buine Scale, Scope and Productivity Meaurement * By Tarek M. Harchaoui Indutrial Organization and Finance Diviion Statitic Canada Jean Talon Bldg., 10-B6 Ottawa, Ontario K1A OT6 harctar@tatcan.ca April 1997 Abtract: Network effect have been hown in theory to have implication for a variety of activitie. Although previou attempt have introduced the network effect mainly in banking activitie, it application to the inurance buine where each firm ha acce to a wide network of agent and broker eem to be a natural extenion. Thi paper formulate a hort-run production framework that account for network externalitie. The application of thi framework to the modelling of total factor productivity allow for the ditinction between i) cale economie, ii) temporary equilibrium, iii) market tructure, and iv) technological change. Baed on an incomplete panel data et at the firm level for the period , the reult ugget that, with a 2.6 percent average annual growth rate of total factor productivity for life inurance companie and.8 percent for non-life inurance companie, the inurance buine outperformed both good-producing indutrie and non-financial ervice indutrie. Scale economie repreent the major component of thee TFP growth rate, followed by technological change, market tructure and the temporary equilibrium effect. In general, although total factor productivity growth tend to decline with the ize of firm, large firm till diplay productivity gain. JEL Claification Number: G2 and L8

3 * Paper to be preented at the CSLS Conference on Service Sector Productivity, April 11-12, 1997, Ottawa, Canada. The view expreed in thi paper are thoe of the author alone and hould not be attributed to Statitic Canada. 1

4 I. Introduction Much progre ha been made toward undertanding the production economic of manufacturing and non-financial ervice indutrie. Analyt, employing improved tatitical methodologie and meaurement technique, have produced an impreive body of reult about which there appear to be a growing conenu. Depite the impreive body of reult available on production in thee indutrie, it i only recently that tudie analying the tructure of production in financial ervice indutrie have appeared. Thi i omewhat urpriing, given the importance of financial ervice indutrie in the economic activity. Recent development of intermediarie and the increaing importance of financial ervice in the economic activity in advanced countrie have focued attention on the activitie of bank. Although bank may be the financial intitution we deal with mot often, they are not the only financial intermediarie houehold and buinee come in contact with. Non-bank financial intermediarie play a important a role in channeling fund from lender-aver to borrower-pender a bank do. In Canada for example, among thee financial intermediarie, inurance companie play a major role, ince they account for about 15 percent of the financial aet of all financial intitution, econd after chartered bank. In addition, the flow of revenue generated by the inurance buine through it role a a conduit for aving of all kind are conidered to be important enough to require ubtantial government protection and uperviion. Coniderable attention ha been given to the meaurement of variou economic performance indicator and the characterization of the underlying technology of the inurance firm. The literature ha been characterized by a teady progreion from imple invetigation of a monoproduct technology (Braeutigam and Pauly 1986) to the pecification of multiproduct cot function (Grace and Timme 1993; Suret 1990) and recently to the taking into account of the financial intermediation activity in the meaurement of inurance companie output (Berntein 1992). Depite the impreive nature of the reult obtained in 2

5 the literature to date on inurance firm cot tructure, everal important limitation till exit. Firt, virtually all tudie have ignored the importance of the network effect, which ha been hown to have an important impact on activitie uch a banking. It i particularly important to account for the network effect for firm in which ervice are provided over a network of patially ditributed point a cot per unit of output may vary among firm depending on the nature of their network erved. Depite the fact that the importance of a network i nowhere a obviou a in the inurance buine, it i urpriing that there have not been any attempt to meaure thee effect on firm performance. Previou attempt have introduced the network effect in the behaviour of the banking indutry (ee Saloner and Shephard 1995); the application of thi effect to inurance firm activitie eem to be a natural extenion. Second, except for tudie of economie of cale (and recently of cope), little attention ha been given to the general area of productivity analyi in the inurance buine a whole. 1 The primary focu of thi paper i on modelling and etimating the total factor productivity (TFP) of the growth of the inurance buine at the firm level. The meaurement and analyi of TFP growth i important, epecially given the recent trend that have taken place in thi indutry. For example, government tax policy ha had a profound effect on the demand for life inurance and on the product mix. Policie that have encouraged aving through tax-heltered regitered retirement aving plan (RRSP) have increaed demand for annuitie both for individual who initially regiter their RRSP with a life inurance company and for thoe who purchae an annuity upon maturity of an RRSP originally regitered with another financial intitution. In addition, the inurance indutry wa conidered a pioneer in the financial ervice indutrie becaue it wa the firt to ue financial ytem technologie uch a electronic data proceing (ee Globermann 1986). The invetment undertaken by inurance companie alo raie quetion regarding the effect of thee new technologie on 1 The exception i Daly et al. (1985), who meaured productivity in the Canadian life inurance indutry. 3

6 the efficiency of undertaking inurance activitie. There are alo reaon to believe that becaue of the very nature of inurance activity, a ignificant portion of the input are repreented by the ize of the retail activity network, a quai-fixed input in the hort run. When meauring cot change and productivity gain, thee factor mut be taken into account, including the poibility of a temporary equilibrium which may occur when unexpected demand hock lead to under- or over-utilization of capacity. Uing an incomplete panel data et, thi paper attempt to meet the challenge mentioned above in meauring TFP in the Canadian inurance buine during the period Thi incomplete panel data et reult from i) the ue in the ample of only multiproduct firm and ii) thee multiproduct firm diplayed a ubtantial turnover rate during the period under invetigation. Accordingly, to obtain unbiaed etimate of the cot tructure and the related economic performance indicator, the etimation technique need to account for electivity bia a the ued ample may not well repreent monoproduct firm excluded from the ample and the portion of multiproduct firm that are ubject to entry/exit. The econometric approach to the etimation of the cot tructure relie on the methodology developed by Baltagi and Griffin (1988) and extended by Dionne and Gagné (1992) to an incomplete panel data et. The TFP growth framework i broken down into it main component: 1) cale economie, 2) market tructure, 3) temporary equilibrium, and 4) technological change. It i applied to life and property and caualty (P&C) inurance companie operating in Canada a an illutration. The reult hown in thi paper ugget that the exitence of a network allow large inurance companie to exhibit return to cale that are higher than thoe of mall and medium-ized firm. In addition, cot-aving from joint 4

7 production and TFP growth are greater for mall and medium-ized firm, but they have a tendency to decline for larger one. Overall, for the period panned by the data, the TFP of life and non-life inurance buine grew, repectively, at an enviable average annual rate of growth of 2.6% and.81%, compared with a negative annual average rate of 0.39% for good-producing indutrie and 0.48% for non-financial ervice producing indutrie. Scale economie repreent the major component of thee TFP growth rate, followed by technological change, market tructure and the temporary equilibrium effect. The remainder of the paper i organized a follow: Section II outline the need for an alternative production framework for inurance firm and introduce the appropriate productivity framework. Section III dicue the data et and the meaurement of variable. Section IV preent the etimation technique. The parameter etimate of the retricted cot function and the TFP growth etimate are dicued in ection V. Section VI give a brief ummary of the paper. II. Theoretical Framework 1. Specification of the Technology The technology of an inurance company hare mot of the characteritic of the technology of any other activity in ervice indutrie. It ue tandard factor of production like capital Kt, () labour Lt (), and intermediate input Mt, () where t repreent time t =12,,..., T. Beide the primary and intermediate input that are ued in many other buinee, an inurance firm require the ue of a network of agent and broker N = N() t, a quai-fixed input, to provide retail ervice to policyholder (ell inurance policie, proviion of information, etc.). The quai-fixed nature of thi input follow from the ignificant adjutment cot and the time required to dimantle or ignificantly alter the ize of thi network. Inurance companie incur etup cot when etablihing their retail activitie. 5

8 A a reult of thee etup cot and the contractual arrangement with broker and agent, inurance companie are le likely to reduce the ize of the network during period when, at the margin, the network i not needed but i expected to be needed in the future. Factor other than adjutment cot may alo explain the quai-fixed nature of thi input. Regulatory retriction, inflexible organizational tructure and other intitutional rigiditie may all provoke hort-run fixitie. 2 The combination of thee input and the technological knowledge prevailing in the economy A = A() t allow the inurer to produce a vector of output Y = Y( t) under the following hort-run cot function: GwYN (,,, A), (1) where w ( w t w t w t ) ( KLM,, ). = (), (), () i a vector of the price of the variable input K L M A fundamental meaure identifying the network impact on productive performance i the hadow value of the network. Thi cot effect, expreed a a G variant of Shephard lemma (ee Diewert 1982), i ( ) = z. The hadow value, which how the cot-aving attributed to the availability of a network becaue of ubtitutability with other input, can be conidered a dual meaure of the marginal product of the network N. In thi cae, the return to the network are directly expreed in term of cot-aving given a particular output level rather than in term of the additional output poible given the available input. Thi meaure hould be poitive if the marginal product i poitive, and the ize of the meaure ugget how important the return to the network are to firm cot. N To explore the network contribution in more depth, thee meaure mut be further adapted to deal with additional iue uch a the cot and benefit of the network. The hadow value and market price of the network are ueful for evaluating the price when making deciion about network. Thee deciion 2 See Hunter and Timme (1993). 6

9 involve conidering how the benefit or return reflected by the hadow value relate to the aociated cot, taking into account the tock-flow nature of the network. Contructing the price of the flow of the network can be accomplihed imilarly to contructing a uer cot of capital. Optimal choice of a network require that z= u; z repreent the additional marginal benefit obtained by adding one more unit of N, and u meaure it marginal cot. Thu, the optimal tock level depend on both the cot-aving benefit and the cot of invetment. The cotbenefit comparion can be expreed either by contructing a hadow value ratio, or a meaure analogou to Tobin q, u z. If z exceed (fall hort of) u, the firm hould invet (diinvet) in the network to reach it cot-minimizing network ize. Thi implie that, in preent-value term, a meaure of the long-term return to a one-dollar invetment in the bae year dollar can be obtained by dividing z by u. That i, the one-year return on invetment in N i z, but the preent value of all return i u z. If thi ratio exceed 1, one more dollar of invetment (in contant bae-year price) hould be undertaken. Difference between the tranaction rental price u and z are uually thought to be due to the preence of increaing marginal cot of adjutment for the quai-fixed input. 2. The Total Factor Productivity Framework In the pat couple of decade, production theory model baed on duality theory have been hown to be a rich framework for analyi of firm technology and behaviour (ee Denny et al. 1981). The baic framework can be extended to conider a broad array of factor affecting firm deciion and performance in financial ervice indutrie. The dual approach to traditional TFP meaurement under the aumption of temporary equilibrium i derived from the exitence of a variable cot function G G( w Y N A) a =,,,. 3 Define the long-run implicit cot function 3 For the introduction of the temporary equilibrium effect in productivity meaurement, ee Berndt and Fu (1986). 7

10 ( ) C = G w, Y, N, A + zn. (2) The total differentiation of (2) with repect to time t, dividing throughout by C, uing the modified verion of Shephard lemma ( G G = X and = z), and rearranging term, yield C B Y wx i i wi zn z = + ε GY, + + (3) C B Y i C wi C z The total differentiation of C= wixi + zn with repect to time and rearranging i give C wx i i wi wx i i Xi zn z zn N = (4) C i C wi i C Xi C z C N Subtituting (4) into (3) give B Y = wx i i Xi zn N ε, GY, (5) B Y C X C N where G Y G Y GY,, ε ε 1 GY Y Y. i i w i i N Note that under the tandard aumption underlying the non-parametric TFP framework contant return to cale, perfect competition and no quai-fixed factor of production TFP growth i defined a TFP Y P wx X un N i i i = P ~ ~ TFP Y i C Xi C N Y where P Y P Y Y, P i the market price of the output, C ~ = wixi + ur PY PY deignate the total cot defined in term of market price, and u repreent the rental cot of the network N. Adding G Y Y G G G, P P Y Y P Y Y Y P Y and un N un N C ~ ~ on the N C N right-hand ide of (5) and uing the above definition of TFP growth give the following new meaurement framework of TFP growth: TFP B G P G Y Y Y zn un N = + 1 ε GY, + G P G + ~ (6) TFP B Y Y Y C C N i 8

11 Given the information on the growth rate of output, it cot elaticity, the input and their cot hare, one can ue (6) to etimate TFP growth and breakdown thi meaure into the factor contributing to TFP growth rate. Thee B factor include i) a hift in the cot function due to technical change ( B ), ii) a movement along the cot function due to cale economie Y departure from marginal cot pricing ( P G Y P G) Y Y zn un N effect ( C ~ ) N C 1 ε GY, Y G G Y, iii), and iii) the temporary equilibrium. Thi lat component deerve further explanation. It ha long been recognized that the exitence of temporary equilibrium, epecially that aociated with the buine cycle, can bia meaured productivity growth away from it long-run path. The productivity reidual i adjuted in a conitent manner to accommodate form of temporary equilibrium, uch a variation in the utilization rate of the network. Temporary equilibrium may occur when unexpected demand hock lead to under- or over-utilization of capacity, or when udden change in factor price reult in hort-run relative factor uage, which i inappropriate in the long-run. The above TFP framework doe not aume that producer are in the long-run equilibrium when in fact they may be in hort-run or temporary equilibrium. The propoed framework account for temporary equilibrium by altering the ervice price weight of the quai-fixed input, rather than directly altering their quantitie. III. Data Source and Meaurement Iue Thi tudy ue adminitrative data collected by the Office of the Superintendent of Financial Intitution (OSFI) on operation that inurance companie (life inurance and P&C inurance) booked in Canada during the period 1985 to The particular data et employed contain information on premium earned and claim incurred by product line, invetment income, and general expene. From thi data et, I retained only the companie operating under a multiproduct 9

12 technology: i.e., P&C inurance companie providing automobile inurance, property inurance, and liability inurance and life inurance companie providing life inurance and annuitie. By excluding monoproduct companie, I could avoid uing econometric technique, uch a the Box-Cox etimation method, which give reult that are not invariant to unit of meaure (ee Dagenai and Dufour 1992). The data on multiproduct firm wa linked to the data collected by Statitic Canada Survey of Employment, Payroll and Hour and to the data on capital tock and invetment from the Diviion of Invetment and Capital Stock in order to obtain the data on capital and labour. Variable cot, G, include labour compenation, capital ervice, and micellaneou expene. Labour expene are compried of alarie, wage, and benefit. Capital expene equal the um of the rental cot of building and equipment, and depreciation. Micellaneou expene include item uch a legal and accounting fee, travel, advertiing, and all other non-labour and non-capital expene. Hourly wage and capital ervice are etimated at the firm level from Statitic Canada ource. The ize of the network i etimated by the number of broker and agent affiliated with the inurance company; it rental cot i etimated a the ratio of commiion on premium and annuity conideration to the ize of the network. Nominal output, net of reinurance, i meaured a premium le claim plu invetment income. The latter ha been allocated by commodity line on the bai of the value of premium earned. The information on the number of policie and certificate of life inurance and annuitie collected from life inurance companie by OSFI allow the implicit price of thee two commodity line to be determined. The ame information for P&C inurance i not available from the ame ource. I therefore ued the inurance component of conumer price indice (automobile and property inurance) at the firm level. The combination of thee two component i ued a a ubtitute for the price of liability inurance a they both comprie a component of liability inurance. 10

13 I organized thee data into a time erie panel, thu making it poible not only to look at the tructure of firm in a given year, but alo to oberve their development over time. The final ample conited of 710 obervation of P&C companie and 580 obervation of life inurance companie, for which ummary tatitic are preented in Table I by type of buine (life v. non-life inurance). 4 Regardle of the product line, multiproduct firm generally have more than of 5 the market; however, thi proportion doe not eem to be contant over time from one product line to another with the important change occurring in the P&C inurance indutry. It i intereting to note that multiproduct firm increaed their market hare in the product line that had the greatet growth rate, uch a liability inurance and annuitie. The fact that the market hare of the monoproduct companie that were excluded from the ample changed from one period to the next and that there wa a relatively high turnover rate among the multiproduct firm retained in the ample jutifie taking electivity bia into account in the etimation of hort-run cot function parameter. [Inert Table I here] IV. Econometric Implementation 1. Econometric Iue The hort-run cot function GwYNA (,,, ) i ued to etimate the parameter underlying the technology and economic performance indicator of the inurance firm. The panel data et ued i in eence incomplete a a reult of the excluion of monoproduct firm from the ample. Specifically, ince I retained only multiproduct firm in the ample, the hort-run cot function for a ingle firm can be tated a (,,, ) + = (,,..., m) GwYN A ω iffy YY 1 2 Y G = 0 otherwie. (6) 11

14 An etimation that ignore thi ditinction by fitting equation GwYN (,,, A) by ordinary leat quare (OLS) technique uing population ubample that conit only of multiproduct firm reult in a non-random election of the error term ω, ince by (6), a firm will be included in the ample if and only if it operate under a multiproduct technology. Since obervation are ytematically elected into the etimation ubample according to the criterion ω > GwYN (,,, A), OLS parameter etimate baed on uch ubample do not provide conitent etimate of the hort-run cot tructure parameter. To correct for electivity bia, I ued a procedure developed by Heckman (1979) that involve an OLS etimation of an expanded hort-run cot function G. () The conditional expectation of multiproduct firm hort-run cot function can be written a * EG() = EG Y= Y, Y,..., Y = G + S ( ) () 1 2 m ( ) () ( ) f ( g) G() where S =σ h (with h F( g) ) i the conditional mean of ω; g σ, f() i the unit normal denity, and F () i the cumulative normal ditribution function. Since S in the equation above i eentially an omitted variable in the retricted cot function model G(), Heckman ha uggeted adding an etimate of h a a regreor to uch an equation and then etimating the expanded regreion equation by OLS while limiting the ample to multiproduct firm. He uggeted the etimation of h initially on the bai of a probit regreion uing data from all firm and how that when thi etimate of h i appended a a regreor to the hort-run cot function G, () OLS etimate are conitent. Since I am dealing with a pooled ample of firm, the iue of heterogeneity i an important one. Unoberved firm heterogeneity that perit over time may introduce erial correlation and, although OLS parameter etimate remain conitent in thi cae, they are inefficient, and the etimated tandard error may induce a fale ene of tatitical ignificance. In my ample, heterogeneity can arie from two main ource: i) life inurance and P&C inurance firm can be expected to operate under different technologie and ii) within any buine, firmpecific heterogeneity will exit becaue of difference in ownerhip and control. 12

15 Thee idioyncratic effect are accounted for by etimating eparately the hort-run cot function of life and non-life inurance firm. Difference in ownerhip and control are captured by the ue of the intercept dummy variable D W. D W = 1 if the firm i a mutual company; otherwie, D W = 0. Given the technology GwYNA (,,, ), a tranlog variable cot function i parametrized a a function of output Y, a meaure of the network ize ( N ), the price of variable input ( w i ), with i = K (capital), L (labour), and M (intermediate input), an index of indutry-wide technical change ( A ). Thi cot function ha an important ditinct feature from the one uually ued in the ene that the tandard time trend ha been replaced with an unoberved general index of technical change A (Baltagi and Griffin 1988). The parametrization of the hort-run cot function of k 12,,.., K i a multiproduct firm ( ) " ng = α + λ D + A( t) + α h + α " nw + γ " ny + φ (" nn ) kt o W W h i i i 1 2 ij i j i i i in A (" nw )(" nw ) (" nw )(" ny ) " nw A() t + α α + α i 1 1 (" nw )( ) ( ) ( ) i " nn 2, " ny " ny 2 RR " nn A()( t " ny ) A()( t " nn ) (" ny )(" nn ) AN N + α + γ + φ + γ + φ + β + ξ. However, (7) raie two major problem: Firt, t he panel data et of multiproduct firm ued i, in eence, incomplete a a reult of inurer turnover in term of entry/exit. The ue of a balanced panel raie the poibility of electivity bia ince new firm (thoe that opened during ) and unucceful firm (thoe that cloed during the ame period) are ytematically excluded from thi panel. A emphaized by Olley and Pake (1991), thi excluion may bia the etimate of the cot function parameter. The reult in term of economic performance indicator may alo be biaed. For example, technical change a meaured by a hift in the cot function may be erroneouly due to change in the ample of firm over time. Second, the etimation of (7) would be a imple matter if only At ( ) were obervable. However, uing time-pecific dummy 13 i R ia i 2 kt (7)

16 variable D t ( t =12 T),,..., and a pooled data et, I etimated (7) together with two of the correponding three hare equation (ee Baltagi and Griffin 1988; Dionne and Gagné 1992) * ( ) ( ) ( ) " ng = λ D + η D + α h + γ " ny D + φ " nn D + α " nw D kt W W t t h, t t t i j ij (" nw )(" nw ) (" nw )(" ny ) (" nw )(" nn ) 1 + α + α + α 2 i j i, i 1 2 (" ny )(" ny ) 2 (" nn ) (" ny )(" nn ) NN N i t Nt t it i t t i t 1 + γ + φ + β + ξ, 2 i iy i kt (8) and ( ) ( ) in ( ) * Si = α it Dt + αij " nw j + α i " ny + α " nn + µ kt. (9) t j Equation (8) and (9) are identical to the parameter in (7) if and only if () () () () () [ At () () tdet () () tdxt ()] [ At () () tdet () () tdxt ()] At () () tdet () () tdxt () ηt = α o + At+ π tdet + ψ tdxt * α = α + α + π + ψ it i ia γ = γ + γ + π + ψ t A [ ] φ = φ + φ + π + ψ Nt N AN where the dummy variable DE() t and DX () t capture the turnover that occur in the financial intermediation activity of inurance companie. DE()=1 t if the firm i not in the ample in t 1; otherwie, DE()=0. t DX ()=1 t if the firm unit i not in the ample in t + 1; otherwie, DX ()=0. t, (10) Etimate of At, ( ) the indutry-wide meaure of pure technical change, can be derived by impoing the retriction in (10) on the ytem of equation (8) and (9). Thi can be implemented by uing the non-linear iterated eemingly unrelated regreion procedure. Furthermore, taking the initial year a the bae year for At ( ) (i.e., A1 () = 0) and auming that entry/exit will not occur in the firt and lat π 1 = π T = ψ 1 = ψ T = 0, allow me to identify period, i.e. () ( ) () ( ) () () α o, αi, γ, φn, π t, ψ t a well a the index At. ( ) 14

17 2. Other Economic Performance Indicator By ubjecting the etimation of the parameter in (8) and (9) to (10), it i poible to compute the rate of technical change a T: B T = At ( ) At ( 1) + γ A" ny[ At ( ) At ( 1) ] B (10) + αia" nw j + φar" nn [ A() t A( t 1) ]. i The approach uggeted by (10) doe not impoe the retriction that pure technical change will change at a contant rate. Note that year-to-year change in the etimate of At ( ) may even provide a very erratic pattern of technical change, reflecting the effect of technological epoch. In turn, technical change can be broken down into the following three component: i) the effect of pure technical change [ At ( ) At ( 1 )], ii) the effect of cale augmentation γ AY [ At () At ( 1 )]" ny, and iii) the effect of non-neutral technical change α φ [ ( ) ( ) ja" nwj + AN" nn A t A t 1 ]. j The incluion of N along with the vector of output (and other variable) enable me to account for the network effect. It i particularly important to make thi ditinction for firm in which ervice are provided over a network of patially ditributed point a cot per unit of output may vary among firm depending on the nature of their network erved. Previou tudie introduced the network effect in the pecification of the banking indutry; the application of thi effect to the activity of inurance firm, which alo manage a ubtantial network of broker and agent, eem an obviou extenion. Return to cale ( RTS ) adjuted for the benefit generated by the exitence of a network are meaured a (ee Cave et al. 1981) 15

18 where and RTS = ( 1 εgn, ) εgy, { [ () () () () ()]} (" ) t αi( " nwi ) βn (" nn). εgy, = γ + γ A At+ π tdet + ψ tdxt Dt + γ ny + + t { [ () () () () ()]} t αin" nwi φnn" nn βn γ ( " ny) εgn, = φn+ φan At + π tdet + ψ tdxt Dt i where ε GN, capture the return to network expreed in term of cot-aving 16, (11a) (11b) elaticity, ε GY, i the output-pecific cot elaticity, and ε GY, i the overall cot elaticity of output. Return to cale are aid to be increaing, contant, or decreaing when RTS i greater than unity, equal to unity, or le than unity, repectively. Additional inight into the economic performance indicator are provided by examining economie of cope or interproduct complementaritie, which indicate whether it i more efficient to produce the output vector together or to produce it by eparate production unit. The degree of global economie of cope ( GES ) i meaured a GES = [ GY ( 1) + GY ( 2) + GY ( 3) GY ( )] GY ( ) where GES > 0, indicating that joint production i more efficient than otherwie and it magnitude meaure the cotaving from joint production. A cloer look at the cot complementarity may be obtained from product-pecific economie of cope ( PES j ) defined a PES 1 = [ GYY ( 1, 2) + GY ( 3) GY ( )] GY ( ), where PES 1 > 0 indicate the proportional increae in cot from eparating output 1 from the production of other ervice. V. Empirical Reult

19 1. Parameter Etimate and Retriction Tet With a data et coniting of 710 obervation on non-life inurance companie and 580 obervation on life inurance companie for the period , an iterative Zellner efficient etimation procedure wa ued on a ytem of a variable cot function and two cot hare (labour and material with the capital hare excluded). The parameter of both type of buinee were etimated eparately for the general model (equation (8) and (9)). The reult are diplayed in Table II. The tandard tet for a well-behaved cot function were upportive. The reult of ymmetry and concavity were not rejected. Homogeneity, however, wa rejected for P&C inurance only; nonethele, it wa impoed. A noted earlier, the excluion of multiproduct firm from the ample raie the iue of ample election bia, which occur if the excluded firm differed ytematically in their cot characteritic from the included one. Sample election bia wa therefore invetigated by teting that the invere Mill ratio α h wa ignificantly different from zero. A hown by Table II, the reult ugget that the variable h capture the otherwie miing information related to the excluded non-multiproduct firm. [Inert Table II here] The majority of the parameter in the etimated cot function are ignificant at conventional level and have the expected ign. The heterogeneity dummy control variable λ W i ignificant for both type of buinee and ugget that mutual life inurance companie are more efficient than the reference cae and vice vera for non-life inurance companie. Thi repreent a rejection in part of the main prediction of prevailing economic theorie of organization, which argue that becaue of impediment to monitoring manager activitie, mutual inurance companie may be le efficient than tock inurance companie (ee Fama and Jenen 1985; Mayer and Smith 1988). 17

20 The reult of the hypothei tet uing log-likelihood ratio are hown in Table III. Sample election bia related to the entry/exit of multiproduct firm wa invetigated by teting the hypothei π() t ψ() t = = 0 for t = 23,,..., T 1. The reult indicate that thi hypothei i readily rejected at le than one percent, which ugget that the electivity bia that may reult from entry / exit i an important iue in my ample. The likelihood ratio tet ugget a deciive rejection of the joint hypothei that the coefficient related to the network are zero, uggeting that thi variable i meaningful in explaining the cot tructure of inurance companie. Alo, the hypothei that inurance companie have not experienced technical progre of any kind wa deciively rejected. [Inert Table III here] A further decription of the production tructure i provided by the Allen- Uzawa partial elaticitie of ubtitution and elaticitie of demand. The entrie in Table IV indicate that for life and non-life inurance companie all own-price elaticitie are negative and tatitically ignificant, a neceary condition for the cot-minimizing factor-demand theory. The input can be ranked in the following order of declining (in abolute value) price elaticity of demand: intermediate input are by far more elatic than labour. With an elaticity of le than 0.05, labour i the input whoe own-price elaticity i the mot inelatic. With regard to the elaticitie of ubtitution, the entrie in Table IV indicate that labour and intermediate input are ubtitute and that both of them have a negative effect on the hadow price of the network. [Inert Table IV here] 2. Etimate of Economie of Scale and Scope A previouly dicued, in indutrie where firm ize ha two dimenion that of the ervice network and that of the magnitude of ervice the interpretation of 18

21 cale economie i different from the conventional meaure that ue the cot elaticity of output. In fact, the invere of the cot elaticity of output cannot be interpreted a a meaure of return to cale (RTS). Uing the parameter reported in Table II, RTS were etimated. To provide inight into the group cot characteritic over a reaonable range of the indutry cot manifold, etimate of RTS were alo derived for quartile ample output vector. The quartile ample mean output vector were formed by ranking each output by type of buine (life and non-life inurance). Thee etimate were compared with thoe of return to cale where network effect are contrained to be zero (CRTS). The reult in Table V indicate that, for the overall ample mean output vector, all type of buinee exhibit tatitically ignificant CRTS. The average CRTS for life inurance companie and P&C inurance companie are 1.08 and 1.02 repectively, which do not appear to be ignificantly different. Thi clearly ugget that, in the abence of network effect, both life inurance and non-life inurance buinee operate under contant RTS. But the reult how that the CRTS etimate vary ubtantially between the fourth output quartile and the firt quartile. For example, life and non-life inurance companie in the firt quartile exhibit relatively high and tatitically ignificant CRTS. By contrat, the hypothei of contant CRTS cannot be rejected for thee companie in the fourth quartile. With regard to interbuine comparion, the reult how that, in general, life inurance companie diplay higher CRTS than do their non-life counterpart. Thi ugget that, unlike their life inurance counterpart, non-life inurance companie incur higher incremental cot. [Inert Table V here ] By definition, the higher the cot-aving attributed to the availability of a network ( ε GN, <0), the higher the RTS. The reult in Table V how that, for the overall ample, mean output vector of large firm exhibit tatitically ignificant RTS economie. The average of the RTS for life inurance companie i 1.49, and 19

22 that of non-life inurance companie i However, there are ignificant difference in term of RTS between life and non-life inurance companie. Since they are ignificant RTS, thi implie that a non-parametric etimate of TFP may be a poor approximation of technical progre. Remarkably, although CRTS benefit motly firm in the firt and econd quartile, the cot-aving generated by the preence of the network allow large life and non-life inurance companie (thoe in the third and fourth quartile) to diplay important economie of cale. Analyi of economie of cope in the joint production of output provide inight into the cot-aving from jointly producing inurance ervice relative to producing each ervice individually. From the etimate in Table V, it appear that, on average, there are global economie of cope for both life and non-life inurance companie. Specifically, joint production i etimated to account for up to 20 percent of cot-aving. Interetingly, for both type of buinee, thee aving become maller a they move from the firt to the lat output quartile. In the cae of non-life inurance, however, the reult indicate that product-pecific economie of cope exit for each type of ervice but do not exceed 9.6 percent on average. Overall, the reult ugget that, for non-life inurance companie, greater aving can be achieved from the combination of all output a oppoed to the combination of one output with an exiting output. In ummary, the empirical evidence ugget that, while CRTS and cotaving complementaritie are generally exhauted for the larget inurance firm, the exitence of ubtantial cot-aving generated by a network effect allow large firm to diplay higher economie of cale. Thee reult hold for both life and nonlife inurance companie. In addition, cot-aving from jointly producing inurance ervice a oppoed to individually producing each ervice are larger for mall and medium-ized firm, but they have the tendency to be exhauted in the cae of larger firm. 3. Etimate of Total Factor Productivity 20

23 Firm etimate of productivity growth were developed and then weighted a a hare of indutry output to produce indutry-level etimate of TFP and it breakdown into technical change, cale economie, price-cot margin, and temporary equilibrium effect. In Table VI, life inurance companie TFP growth wa found to increae at an average annual rate of 2.6 percent for the period From 1985 to 1990, TFP grew at an average annual rate of roughly 3.4 percent. For the period, a light decline (only 2.1 percent) wa detected in the TFP growth, reflecting the effect of the buine cycle. A light recovery in the TFP growth rate wa noticeable during the ubequent recovery period (2.3 percent). [Inert Table VI here] It i of interet to ee whether there are identifiable pattern of TFP between life and non-life inurance companie. Inpection of entrie in Table VI indicate that, on average, life inurance companie enjoyed higher productivity growth than their non-life counterpart. With an average annual growth of TFP a low a 0.8 percent, non-life inurance companie diplayed an anemic productivity growth. A for life inurance companie, mot of the TFP growth took place during the period of economic growth. 4 During the period for which etimate of the productivity of good-producing indutrie and non-financial ervice indutrie are comparable, 5 that i , the TFP of life and non-life inurance buine grew, repectively, at an average annual rate of growth of 2.6% and.81%, compared with a negative annual average rate of 0.39% for good-producing indutrie and 0.48% for non-financial ervice producing indutrie. 4 Thi reult i in part due to the ue of inappropriate deflator of non-life inurance output. Since the value of inurance ervice conidered in the non-life inurance component of the CPI are contructed on the bai of the value of premium (intead of premium le claim plu invetment income), thi ha a tendency to overetimate the non-life inurance component of the CPI, which reult in an underetimation of my non-life inurance output. 5 See Statitic Canada (1996). 21

24 A noted in (10), the etimated technical change index can in turn be broken down into the effect caued by pure technical change, non-neutral technical change, and cale-augmenting technical change. Table VI provide the reult of thi breakdown for both life and non-life inurance companie for elected time interval. At 80 percent and 66 percent on average for life and non-life, repectively, cale-augmenting technical change wa the mot important component of technical change. It i followed well behind by non-neutral technical change (18 percent and 34 percent, repectively, for life and non-life inurance). The fact that life inurance companie cale-augmenting technical change contribution to technical change i higher than that of their non-life counterpart may be related to government policy and the product innovation that have taken place during the lat two decade in the life inurance buine. Government tax policy ha had a profound effect on life inurance companie product mix. Apart from a hift in product demand caued by tax change (ee Burbidge and Davie 1994), there ha been a pronounced trend away from whole life policie and toward term inurance. Policie that have encouraged aving through tax-heltered RRSP have increaed the demand for annuitie. A large portion of each dollar of whole life inurance premium (compared with term inurance premium for example) i retained for the acquiition of aet becaue whole life inurance, epecially in a policy early year, contain a ignificant aving component. Similarly, each dollar of deferred annuity premium goe almot entirely to acquire aet, which may be held for many year before liquidation. In thi ene, the change of life inurer product influence the growth of thi buine. The reult diplayed in Table VI how that cale economie have contributed to more than 60 percent of inurance companie TFP growth. However, thi contribution ha been lightly declining for both life and non-life inurance companie. The effect of market tructure repreent the third major component of TFP growth after economie of cale and technical change. However, the contribution of market tructure to TFP growth i twice a high for non-life 22

25 inurance a it i for life inurance. There i evidence of imperfect competition in the inurance buine, particularly in the non-life inurance indutry, a uggeted by a non-negligible contribution or price-cot margin to TFP growth. Problem of information aymmetry in favour of the buyer may force firm to charge higher price to high-rik individual. Although the network ize ha experienced a poitive, albeit mall, yearover-year growth rate, the effect of temporary equilibrium on TFP growth ha experienced three ditinct trend during the period. Although the effect of temporary equilibrium wa poitive during the ubperiod , it became negative in the ubequent period. The procyclical feature of the temporary equilibrium effect mainly ugget that the long-run hypothei underlying the non-parametric TFP framework ha been violated. A caual comparion of the etimated value of the hadow price of network z with it market price r ugget that, for the earlier year of the period , there wa a trong incentive for network invetment, which ultimately led the indutry to ue the network to full capacity. 6 Thi trend wa lightly revered during the ubperiod a the economy entered a receion, during which there wa an apparent exce capacity level of network. The incentive for additional network invetment fell during thi period, however it increaed lightly in the ubequent period a the economy entered a period of recovey. To provide inight on how company ize may effect TFP, etimate of TFP were alo derived for the quartile ample output of life and non-life inurance companie. Examination of the etimate of TFP growth for the quartile output reveal a conitent pattern with other economic performance indicator uch a the contrained return to cale and economie of cope. Chart 1, which plot TFP for life and non-life inurance firm, how a conitent pattern acro quartile. 6 During the period , the ratio q had an average annual growth rate of 18.3 percent for life inurance and 12.1 percent for non-life inurance companie. Thereafter, it tarted to decreae to 7.4 percent and 11.2 percent, repectively. 23

26 Although TFP growth tend to decline a the ize of the inurance firm, productivity gain do not appear to be fully exhauted for large life inurance firm. [Inert Chart 1 here] VI. Concluion With the proliferation of information technology over the pat everal decade, network have become increaingly important. Example include bank automated teller machine, airline reervation ytem, and the increaed ue of the Internet. Although network have been hown to have important implication on firm trategie for product announcement, technology adoption, and pricing (ee Katz and Shapiro 1985), there ha been no attempt to meaure the effect of network on firm cot tructure. In thi paper, a hort-run cot function defined over a vector of output and the ize of inurance companie network wa pecified and etimated for an incomplete panel data et of Canadian life and non-life inurance companie. RTS were found to be large and tatitically ignificant, particularly for large inurance companie, a cot-aving aociated with the exitence of a network of agent and broker allow large firm to exhibit increaing return to cale in the hort run. Failure to account for network effect ha led many previou tudie uing different national data to conclude that large firm operate under contant RTS. Change in TFP through time are hypotheized to be the reult of cale economie, technical change, market tructure, and the temporary equilibrium aociated with the exitence of a network with a given ize in the hort run. The finding indicate that although life inurance companie out perform their non-life counterpart in term of TFP growth, the bulk of thi growth for both type of firm i a reult of cale economie and technical change. There i evidence of imperfect 24

27 competition in the inurance buine, particularly in the non-life inurance indutry, a uggeted by a non-negligible contribution or price-cot margin to TFP growth. Problem of information aymmetry in favour of the buyer may force firm to charge higher price to high-rik individual. There i trong evidence that the long-run hypothei underlying the nonparametric TFP framework ha been violated. The reult ugget that, in general, the level of variou economic performance indicator decline with the firm ize. Thi indicate that, unlike medium-ized firm, large one have exhauted their potential for economic performance. Although there are variant acro buinee, thi reult hold for both life and non-life inurance companie. 25

28 Reference Baltagi B.H. and J. M. Griffin (1988); A General Index of Technical Change, Journal of Political Economy 96: Berndt, E.R. and M.A. Fu (1986); Productivity Meaurement with Adjutment for Variation in Capacity Utilization and Other Form of Temporary Equilibrium, Journal of Econometric. Berntein, J.I. (1992); Information Spillover, Margin, Scale and Scope: With an Application to Canadian Life Inurance, Scandinavian Journal of Economic 94 (Supplement): Braeutigam, R.R. and M.V. Pauly (1986); Cot-Function Etimation and Quality Bia: The Regulated Automobile Inurance Indutry, Rand Journal of Economic 17: Burbidge, J.B. and Davie, J.B. (1994); Government Incentive and Houehold Saving in Canada, in Poterba J. (Ed.): Public Policie and Houehold Saving, pp , Chicago Univerity Pre for the NBER, Chicago. Cave, D.W., L.T. Chritenen and J.A. Swanon (1981); Productivity Growth, Scale Economie, and Capacity Utilization in U.S. Railroad, , American Economic Review 71: Dagenai M.G. and J.-M. Dufour (1992); Invariance, Nonlinear Model, and Aymptotic Tet, Econometrica 89: Daly, M.J., P.S. Rao and R.R. Geehan (1985); Productivity, Scale Economie and Technical Progre in the Canadian Life Inurance Indutry, International Journal of International Organization 3: Denny, M., M. Fu, and L. Waverman (1981); The Meaurement and Interpretation of Total Factor Productivity in Regulated Indutrie, with an Application to Canadian Telecommunication in Cowing T.G. and R.E. Stevenon (ed.): Productivity Meaurement in Regulated Indutrie, Academic Pre. Diewert, E.W. (1982); Duality Approache to Microeconomic Theory, in Arrow, K. and M. Intriligator (ed.): Handbook of Mathematical Economic, Vol. II, Elevier Science Publiher, The Netherland. 26

29 Dionne, G. and R. Gagné (1992); Meauring Technical Change and Productivity Growth with Varying Output Qualitie and Incomplete Panel Data, Univerité de Montréal, Département de cience économique, cahier Fama, E.F. and M. Jenen (1985); Organizational Form and Invetment Deciion, Journal of Financial Economic, 14: Globerman, S. (1984); The Adoption of Computer Technology by Inurance Companie, Ottawa, Supply and Service Canada. Grace M.F. and S.G. Timme (1993); An Examination of Cot Economie in the United State Life Inurance Indutry, Journal of Rik and Inurance 93: Heckman (1979), J. Sample Selection Bia a a Specification Error, 47: Econometrica Hunter, W.C. and S.G. Timme (1993); Core Depoit and Phyical Capital: A Reexamination of Bank Scale Economie and Efficiency with Quai-Fixed Input, Federal Reerve Bank of Atlanta Working Paper Mayer, D. and C. Smith (1988); Ownerhip Structure Acro Line of Property and Caualty Inurance, Journal of Law Economic 31: Olley, S. and A. Pake (1991); The Dynamic of Productivity in the Telecommunication Equipment Indutry, Department of Economic, Yale Univerity, New Haven, CT. Saloner G. and A. Shephard (1995); Adoption of Technologie with Network Effect: An Emprical Examination of the Adoption of Automated Teller Machine, Rand Journal of Economic 26: Statitic Canada (1996); Aggregate Productivity Meaure (Annual), Catalogue XPE, Ottawa. Suret, J.-M. Scale and Scope Economie in the Canadian Property and Caualty Inurance Indutry, Geneva Paper of Rik and Inurance 89:

30 Table I. Summary Statitic Baed on Nominal Output (in $ million) Non-Life Inurance Property Auto Liability Property Auto Liability All firm (1) 1,819 2, ,892 4, Multiproduct firm (2) 1,624 2, ,383 3, (2) (1) in % Life Inurance Life inurance Annuitie Life inurance Annuitie All firm (1) 2,723 3,934 5,070 7,772 Multiproduct firm (2) 2,338 3,511 4,264 7,208 (2) (1) in % Life Inurance Non-Life Inurance Turnover Rate (in %) a ( ) Note: a Sum of abolute value of change in output over the period (output of entrant plu output of exiter) over the total output.

31 Table IIa. Parameter Etimate of Life Inurance Companie Short-Run Cot Function with a General Index of Technical Change Variable Etimate t tatitic Variable Etimate t tatitic α o π( 86) α L π( 87) α M π( 88) γ YL π( 89) γ YA π( 90) φ N π( 91) α LL π( 92) α MM π( 93) α LM π( 94) α LYL ψ( 86) α LYA ψ( 87) α MYL ψ( 88) α MYA ψ( 89) α LA ψ( 90) α MA ψ( 91) α LN ψ( 92) α MN ψ( 93) γ YY L L ψ( 94) γ YY γ YY A A A( 86) L A A( 87) φ NN A( 88) γ AYL A( 89) γ AYA A( 90) φ AN A( 90) β YLN A( 91) β Y N A A( 92) λ W A( 93) α h A( 94) A( 95) Equation Std. Error R 2 Cot Labour Share Intermediate Input Share Log of Likelihood 2,723