UBC Theses and Dissertations

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UBC Theses and Dissertations

Analysis of the marginal cost of writing automobile insurance Janssen, Hubertus Anna Nicholas 1967

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AN ANALYSIS OF THE MARGINAL COST OF WRITING AUTOMOBILE INSURANCE by HUBERTUS ANNA NICHOLAAS JANSSEN B. Sc., University or B r i t i s h Columbia, 1 9 6 5 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n the Faculty or Graduate Studies We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 6 7 In presenting t h i s thesis In p a r t i a l f u l f i l m e n t of the re-quirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l -able f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis f o r scholarly purposes may be granted by- the Head of my Department or by h i s repre-sentatives. I t i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of r.nmme-rce and Business Administration The University of B r i t i s h Columbia Vancouver b, Canada ABSTRACT The Royal Commission oh Automobile Insurance of B r i t i s h Columbia was established i n I 9 6 6 to enquire, among other things, into the cost of providing automobile insurance by insurers to the public. This thesis Is concerned with evaluating the cost of w r i t i n g automobile insurance i n Canada, and how t h i s cost a f f e c t s the rate making p o l i c i e s of the Canadian Underwriters' Association, and f i n a l l y , as to the influence of the cost factor i n establishing a centralized agency. In establishing a gross premium, the insurer must cover expected losses a r i s i n g out of claims and cover adminis-t r a t i v e costs. Detailed accounts are kept of claims incurred by l i n e of Insurance. However, f o r the expense portion only d i r e c t claims expenses are allocated, by l i n e of insur-ance; no accounts by l i n e of insurance are kept f o r the rest of the administrative expenses. Expense accounts are submitted annually to the Super-intendent of Insurance, but are not broken down by l i n e of insurance. By using multiple regression analysis on cross sectional data f o r one calendar year, one can estimate the marginal costs of w r i t i n g d i f f e r e n t l i n e s of insurance. The hypothesis w i l l be that expenses can be expressed as a l i n e a r function of premiums written by l i n e of Insurance. In addition, i t w i l l be possible to determine whether any economies of scale are present i n wri t i n g automobile insurance. The r e s u l t s of the s t a t i s t i c a l study indicated that the marginal cost or w r i t i n g automobile insurance was be-tween 28 and 30 percent or the gross premium, which i s lower than the 33 percent expense fa c t o r currently used by the Canadian Underwriters' Association. In addition no economies of scale were found i n w r i t i n g automobile insurance i n Canada. TABLE OP CONTENTS CHAPTEE PAGE I INTRODUCTION....................... 1 Ob j ective s of Study 1 Method of Analysis................ 3 Sources of Data and Constraints... 3 Organization of the Study... 5 I I THE EXPENSE FACTOR: HISTORY, COMPOSI-TION, AND EFFECT ON RATES. 7 Introduction 7 The Loss Cost Ratio. 9 The Trend Factor. 14 The Problem of A l l o c a t i o n . . . . . . . . . 21 Summary........................... 24 I I I THE STATISTICAL STUDY: THE MODEL.... 26 The Multiple Regression Model..... 27 Eliminating M u l t i c o l l l n e a r i t y . . . . . 3<+ The Stepwise Regression........... 35 Summary 36 IV THE STATISTICAL STUDY: THE RESULTS.. 37 Net Adjustment Expenses Incurred.. 41 Net Commissions Incurred.. 42 Net P r o f i t Commissions Incurred... 47 Taxe s Incurred 4b General Expenses Incurred......... 50 Bad Debts........................... 50 CHAPTER PAGE IV Total Expenses Incurred 51 Comparison of S t a t i s t i c a l Results with C.U.A, Expense Factor..... 51 Implications or Study ror Manage-ment Control 54 V ECONOMIES OF SCALE 55 Economies of Scale i n Automobile Insurance....................... 55 Comparison or American Expense Ratios with the Canadian S t a t i s t i c a l Results............ 62 Summary........................... 6 7 VI SUMMARY AND CONCLUSIONS 68 BIBLIOGRAPHY.., .. , ........... 75 APPENDICES APPENDIX A. Tables or Variables In-cluded i n Regression Study 76 APPENDIX B , S t a t i s t i c a l Results or Multiple Regression...... 81 APPENDIX C, Results of Simple Regres-sion on American Data.... 117 APPENDIX D, L i s t or Companies by Agency Structure......... 120 LIST OP TABLES TABLE PAGE I Percent Increase In Countrywide Loss-cost.. 12 I I Private Passenger Automobile Loss-cost Ratio and Expense Factor Breakdown, 1930 to 196b...,,..-..*.. 1** I I I Calculation of Weighted Average Commission Rate................, .. 4-5 IV Comparison of Canadian and U.S.A. Expense Ratios..... •.. 63 LIST GP FIGURES FIGURE PAGE 1 Least Squares Trend Line of Loss-costs f o r Countrywide Experience lb 2 Expense Relationship with a Single-line Company........................... 3 0 3 Expense Relationship of a Two-line Company 3 0 4 Total Costs f o r a Single-line Company with Major Economies of Scale 5 7 5 Total Costs f o r Single-line Company with Major Diseconomies of Scale....... 5 7 6 Unit Costs of a Single-line Company.. 5b 7 Total Costs of a Single-line Company. 5 b CHAPTER I INTRODUCTION Objectives of Study In the recent past the automobile insurance industry-has come under close scrutiny by the public at large, or-ganizations and governmental agencies. Automobile Insur-ance rates have increased at such a pace that I t was Inevit-able that the industry would be c a l l e d to task. For example, tor B r i t i s h Columbia t e r r i t o r y 1, Vancouver r a t i n g d i s t r i c t , private passenger automobile t h i r d party l i a b i l i t y rates were increased 29 per cent on January 1st 1 9 6 5 , an addi-t i o n a l 5 per cent on July 1st, 1 9 6 5 i and an additional 11 per cent on January 1st, 1966.^ " This Is equivalent to a f i f t y per cent increase i n rates In one year. In the spring of 1966 a Royal Commission on Automobile Insurance was established to inquire, among other things, I n t o : 2 "...the cost to Insurers, to persons who pay insurance premiums and to the public generally of providing pre-sent forms of automobile insurance determined on the Icanadlan Underwriters' Association B r i e f (presented to the Royal Commission on Automobile Insurance, June I966, hereinafter C.U.A. B r i e f ) , p. 18. 2 Transcript, Royal Commission on Automobile Insurance of B r i t i s h Columbia (hereinafter Transcript R.C.A.I.), Volume 1, pp. 6-7. 2 basis of past and current experience and whether the cost i s i n proper relationship to the ef f e c t i v e protection obtained,.., the j u s t i f i c a t i o n f o r recent variations In automobile insurance premium rates, whether the public of t h i s Province w i l l be better served by the continuation of present procedures f o r the re-covery of damages a r i s i n g out of motor-vehicle accidents and by the preservation of present forms of insurance coverage or by some v a r i a t i o n or variations thereof,.., whether such a v a r i a t i o n or a plan f o r compensation or such a combination, i f recommended, should be administered p r i v a t e l y or by or through a governmental department or a governmental agency or a combination t h e r e o f , H This thesis i s concerned with evaluating the "cost to insurers" of w r i t i n g automobile insurance i n Canada, and how t h i s cost a f f e c t s the rate-making p o l i c i e s of the insurers, and f i n a l l y , as to the influence of the cost factor i n establishing a centralized agency. 3 In establishing a rate or gross premium the insuring company must cover expected losses a r i s i n g out of claims and cover administrative expenses required to write auto-mobile insurance. No s t a t i s t i c s are kept by l i n e s of i n -surance as to what proportion of overhead costs pertain to automobile Insurance. This study w i l l thus attempt to evalu-ate the v a l i d i t y of the 33 percent expense factor currently being used by the Canadian Underwriters* Association S t a t i s t i -c a l Agency. The procedure used In t h i s study w i l l also 3Gross premium i s that amount that the Insured pays, f o r a s p e c i f i e d amount of coverage. 3 enable us to d i s t i n g u i s h among economies and diseconomies or no economies of s c a l e i n the w r i t i n g of automobile I n s u r -ance i n Canada* The r e s u l t s w i l l i n d i c a t e whether any reduc-t i o n In a d m i n i s t r a t i v e expenses would occur i f automobile insurance b u s i n e s s were c e n t r a l i z e d . Method of A n a l y s i s The procedure t h a t w i l l be f o l l o w e d r e q u i r e s the use of m u l t i p l e r e g r e s s i o n a n a l y s i s . The h y p o t h e s i s w i l l be t h a t expenses can be expressed as a l i n e a r f u n c t i o n of l i n e s of Insurance. Through s t a t i s t i c a l c r i t e r i a i t w i l l be pos-s i b l e t o determine the m a r g i n a l c o s t s of w r i t i n g a p a r t i -c u l a r l i n e of insurance f o r each expense category I n c l u d e d In the study. The r e s u l t s w i l l be analyzed s t a t i s t i c a l l y to determine whether they are s i g n i f i c a n t l y d i f f e r e n t from zero and the confidence t h a t can be p l a c e d i n t h e i r p r e d i c -t i v e v alue f o r d e t e r m i n i n g the expense f a c t o r l o a d i n g of the gross premium. Sources of Data and C o n s t r a i n t s , The main source of d a t a i s contained i n the Annual Reports of the F e d e r a l Superintendent of Insurance.^ The ^Report of the Superintendent of Insurance f o r Canada. Annual Statements - F i r e arid C a s u a l t y Insurance, Queens' P r i n t e r , Ottawa 1965, Volumes I and I I ( h e r e i n a f t e r Blue Books). 4 automobile Insurance companies report annually on a standard reporting form to each of the P r o v i n c i a l Superintendents and to the Federal Superintendent t h e i r automobile experience! The information collected i s based upon the calendar year's experience f o r 1964, and f o r the purposes of t h i s study con-s i s t s of net premiums written, net premiums earned and net claims incurred.^ Premiums written consists of a l l of the insurance a company wrote i n Canada during the calendar year. Premiums earned consists of that portion of the premium that if: written on July 1st, f i f t y percent of the premium i s earned i n the year i n which i t was written. The unearned portion, the other f i f t y per cent of the premium, i s applied to the following calendar year's earned premium. Net claims incurred includes the losses a r i s i n g out of claims and bodily i n j u r y , property damage, and c o l l l s s l o n claim expenses that aris e out of a p a r t i c u l a r claim and can be traced to a p a r t i c u l a r l i n e of insurance, ^Transcript B.C.A,I., Volume 1, p. 25^ . See also Canadian and B r i t i s h Insurance Companies Act. 1932, C.46, 569,?0. &"Net" means a f t e r deduction of a l l reinsurance f o r Canadian companies but only registered or licensed reinsur-ance f o r B r i t i s h and foreign companies, ?This should not be confused with the "earned premiums" rigures used to calculate rates. On the latt e r , subject see the Report of the Royal Commission on Automobile In-surance. Nova Scotia, 1957, Volume I , pp. 35-6. (Nova Scotia R.C.A.I, hereafter). 5 In addition to the above, the Blue Book also con-tains the underwriting account f o r each Insurance company which l i s t s the t o t a l expenses Incurred and a breakdown of general expenses. The Superintendent of Insurance, or a duly q u a l i f i e d s t a f f member, must v i s i t each company to check the annual Q statements submitted at lea s t every three years. Thus i t may be concluded that the data to be used w i l l be uni-form and v a l i d . Organization of the Study Chapter I presents the objectives and method of the study Including sources of data, constraints and organiza-t i o n of the study. Chapter I I w i l l serve as an introduction to the h i s -tory of the expense factor loading, the components of the expense factor, and the ef f e c t of the trend f a c t o r on the expense factor as i t influences rate making by the s t a t i s t i c a l agency. Chapter I I I w i l l present a description of the model i n i t s o r i g i n a l form, and the subsequent refinements to provide meaningful r e s u l t s . BCanadian and B r i t i s h Insurance Companies Act. 1 9 3 2 , C.4-6, S . ? 2 , 7 3 , 7 4 . 6 Chapters IV and V include the results of the study and implications as to the effects of these results on pre-sent practice in the industry. Chapter IV is a detailed analysis of the individual expense items included in the study which are then compared with the current expense ratio of 33 percent. Chapter V includes an analysis of the ques-tion of economies of scale and a comparison between Canadian expense factors and American expense factors. Chapter VI will present the summary and conclusions based on the results of Chapters IV and V including recommenda' tlons based upon the statistical results. CHAPTER I I THE EXPENSE FACTOR: HISTORY, COMPOSITION, AND EFFECT ON RATES Introduction The Canadian Underwriters 1 Association S t a t i s t i c a l Agency produces s t a t i s t i c s on behalf of the Superintendents of Insurance of each Province (except Saskatchewan). The information to be provided upon which the s t a t i s t i c s are based i s a statutory requirement of each province f o r a l l companies. These s t a t i s t i c s are gathered according to the "Automobile S t a t i s t i c a l Plan" as l a i d down by the Super-intendents of Insurance. The "Green Book" i s the p r a c t i c a l r e s u l t culminating i n a comprehensive r a t i n g plan f o r the 1 many categories of r i s k . The Insurance industry i s then able to use these resul t s to establish t h e i r own rates i f they f e e l that t h e i r experience warrants a d i f f e r e n t rate, or accept the rates as published. Since underwriting judg-ment i s involved In setting rates, the Canadian Underwriters' Association's influence on r a t i n g practices i n in e v i t a b l e . In A p r i l of 1Q64-, the Insurance Bureau of Canada was •^C.U.A. Br i e f p. 2 . 2 formed. I t s members consist of independent companies, companies that are members of the Independent Insurance Conference, and companies that are members of the Canadian Underwriters' Association. The IBC's main purpose was to obtain the representation of most insurers so that informa-t i o n could be disseminated quickly and common problems of the industry discussed. The usefulness of the IBC appears to l i e i n general policy considerations of the Insurance Industry as a whole as opposed to a q u a l i f i e d organization f o r solving technical r a t i n g problems. The l a t t e r conclu-sion Is based on the b u l l e t i n s Issued by the IBC contained i n t h e i r Submission. Even though the assistance of the actuary f o r the S t a t i s t i c a l Agency i s available f o r consulta-t i o n , i t i s not known whether a l l technical matters receive his attention. S p e c i f i c a l l y on page 109 of the Document Bri e f i t i s stated that the l a s t two years of the l e a s t square loss-cost projections are weighted 60 per cent f o r the l a t e s t year's experience and 40 per cent f o r the pre-ceding year's. This weighting applies only to the evaluation as do whether the rates currently i n existence would have been adequate had they been i n e f f e c t during the l a s t two year's experience. Thus i t i s separate from the trend factor projection, and no weighting i s applied to the trend factor Submission of the Insurance Bureau of Canada to the Royal Commission on Automobile Insurance, November 1966 (I.B.C. Submission hereinafter) p. 3. 9 3 perse& present. There i s no doubt i n the writers opinion, that the I,B.C. serves a useful function In attempting to create an organization that represents a l l groups, associations and federations of insurance companies In Canada, i n order to discuss common problems. But u n t i l an Independent s t a f f of competent personnel i s acquired, t h e i r use as a rat i n g body w i l l remain l i m i t e d , i f not harmful, to the industry i t s e l f . Although I t Is possible that the mistake referred to above i s an is o l a t e d incident, any r e p e t i t i o n can only lead to the demoralization of the membership and hence the cooperation of i t s members, upon which i t depends, w i l l be l o s t . The Loss Cost Ratio When an Insurance company establishes a premium i t i s expected that over time the gross premiums collected w i l l cover the expected loss cost, the administrative expenses involved and provide some allowance f o r p r o f i t . The premium may thus be regarded as consisting of two separate factors: a c t u a r i a l losses plus an expense fa c t o r (including p r o f i t ) . The actual d i v i s i o n In practice, as u t i l i z e d i n the rate ^The trend factor i s used to weight the loss cost fac t o r , but the data used i n developing the trend factor i t s e l f i s not weighted. 10 making process of the Canadian Underwriters* Association, i s s l i g h t l y d i f f e r e n t . The a c t u a r i a l l y determined losses also include allocated claims expenses which can he traced d i r e c t l y to a p a r t i c u l a r l i n e of Insurance. Such allocated claims expenses may include a l l adjustment fees and other immediate out-of-pocket expenses such as medical expenses, towing fees and any other costs d i r e c t l y a r i s i n g out of a p a r t i c u l a r claim. The remaining portion of the premium consists of a l l unallocated claim and general overhead ex-penses and t y p i c a l l y Include commissions, premium taxes, rent and ah allowance f o r p r o f i t . The development of a gross premium based on expected losses and an allowance f o r expenses would i n i t i a l l y prove d i f f i c u l t i f no data existed to determine what proportion of the gross premium should be devoted to expenses. Once set, competitive factors might indicate the true nature of the expense factor. The e a r l i e s t loss-cost r a t i o 4 , i n Canada was developed on February 1, 1929 by the Canadian Automobile Underwriters* Association (a forerunner of the C.U.A.). The provision was f i f t y percent f o r losses and f i f t y percent f o r expenses; that I s , a loss-cost r a t i o of 50/50. At about the same time an Ontario Royal Commission ^Loss-cost r a t i o represents the r a t i o of the a c t u a r i a l losses and allocated claims expense as a percent of gross premium to the unallocated expense factor as a percent of gross premium. was established to evaluate the reasonableness of the then present loss-cost r a t i o . ^ The resultant findings of the Hodglns Report indicated that the r a t i o was too heavily-loaded with the expense factor and recommended that the expense fa c t o r should not exceed f o r t y - f i v e percent of the gross premium.b The industry subsequently adjusted the loss-cost r a t i o to 55/M-5 which was i n effect u n t i l 194-2 when a two percent federal premium tax changed the loss-cost r a t i o to 5 3 A 7 . In, I949 the board (.C.U.A. member) companies reduced the maximum commission on new automobile insurance business from 25 percent to 20 percent. The loss-cost r a t i o remained at the previous 53/47 l e v e l since the f i v e percent reduction i n commission was balanced by a f i v e percent increase i n the allowance f o r company expenses. In 1951, the loss r a t i o had Increased rapidly and premium rates were raised accordingly In 1952. However, the increase i n gross premium had also been applied to the expense fa c t o r , which the companies f e l t they might have d i f f i c u l t y i n j u s t i f y i n g . ? Hence i n 1953 the board com-panies changed the loss-cost r a t i o to 63 /37. The ten ^Report on Automobile Insuranbe Premium Rates, King•s Pr i n t e r s (Ontario), I930. „ ^ R e s t r i c t i v e Trade Practices Commission: Concerning^ The Business or Automobile Insurance i n Canada, Ottawa I90O. p. 158. ^Transcript R.C.A.I., Volume 27, p. 3I47. 12 percent change resulted m a f i v e percent reduction i n the factor f o r company expenses and a f i v e percent reduction i n commissions. Similar events preceding 1965 led to further adjust-ments i n the loss-cost r a t i o . Table I below i l l u s t r a t e s the r e l a t i v e l y constant l e v e l of claim frequency, accompanied by an ever increasing average cost per claim. In I965 the I.B.C. suggested that the commission rate could be reduced since TABLE I PERCENT INCREASE IN COUNTRYWIDE LOSS-COST POR BODILY INJURY AND PROPERTY DAMAGE, 1961 TO 1965. YEAR CLAIM FREQUENCY AVERAGE COST OF CLAIM AVERAGE LOSS-COST PERCENT . INCREASE 1961 9.6 361 3^.7 -1962 10.1 385 38.9 12.1 1963 10.2- 414 42.2 8.4 1964 10.2 4 4 4 45.3 7.3 1965 9.6 . 501 48.1 6.1 Source: Green Books of S t a t i s t i c a l Agency, I965. 13 the premiums had r i s e n sharply. I t also recognized that previous c r i t i c i s m s on t h i s problem had been voiced by the Combines Commission and the Nova Scotia Royal Commission. In August of I965 the Automobile Insurance S t a t i s t i c a l Com-mittee directed that the expense factor be reduced to 33 percent.^ The loss-cost r a t i o was thus changed to 67/33» achieved by reducing the agents' commission by 2f percent and company expenses by 1^  percent. A summary of the adjustments made i n the loss-cost r a t i o Viover the past t h i r t y - s i x years i s shown i n Table I I . The d i v i s i o n of the expense factor assumes the C.U.A, rates of commission, the other expense factors actual percent i s hypothetical. The C.U.A. B r i e f shows the 1966 d i v i s i o n of the expense factor a l i t t l e d i f f e r e n t l y than i n Table I I , and r e f l e c t s largely the d i f f i c u l t y of the Industry i n 10 a l l o c a t i n g a l l expenses by l i n e of insurance. I.B.C. Submission, B u l l e t i n No. 65-3, pp. 461-46j. I b i d . , p. 68. °0p. c i t . , p. 34, TABLE I I 14 PRIVATE PASSENGER AUTOMOBILE LOSS-COST RATIO AND EXPENSE FACTOR BREAKDOWN, 1930 TO 1966. DIVISION OF EXPENSE FACTOR PERIOD LOSS EXPENSE UNALLO- PROFIT FACTOR FACTOR COMMISSION CATED COMPANY LOSS EXPENSE EXPENSE (percent) 1930-41 55 45 • — — - — 1942-4-8 53 47 25.0 6 2.5 13.5 1949-52 53 47 20.0 6 2.5 16.5 1953-65 63 37 15.0 6 2.5 13.5 1966 67 33 12,5 6 2.5 12.0 Sources R e s t r i c t i v e Trade Practices Commission, l o c . c i t . The Trend Factor The rate making procedure of the C.U.A. s t a t i s t i c a l agency i n order to ensure that the Industry w i l l receive enough i n terms of gross premiums, consists of two steps. The f i r s t step consists of the formula guide to determine whether the rates that are now In effe c t would have been adequate f o r the losses Incurred during the l a s t f i v e years. The percentage differences are calculated, and the l a s t two years percentage change weighted: 60 percent f o r the most 15 recent year, and 40 percent f o r the preceding year's change.'1'1 The second step Involves the setting of a premium l e v e l by determining the probable future l e v e l of losses. In order to achieve t h i s e>.nd, the loss-cost f o r the pre-vious years i s determined by multiplying the average cost per claim by claim frequency. From these figures a trend i s established upon which a projection i s made as to the future expected loss-costs. Not u n t i l 1951 did the C.U.A. s t a t i s t i c a l agency 12 introduce the trend f a c t o r . U n t i l 1951, the average loss 13 cost per insured vehicle was r e l a t i v e l y constant. Since the average loss-cost figure consists of a combination of frequency of accidents, and average cost per claim, i t may be f e l t that separate trend factors should be developed f o r each. However, the data available suggested that the f r e -quency factor by I t s e l f was not a stable i n d i c a t i o n and seemed to fluctuate widely. The average cost per claim was, however, more useful In predicting future costs, as H C . U . A . B r i e f , pp. 14-15. l 2 T r a n s c r l p t R.C.A.I,, Volume 25, p. 2967. 13The average loss cost per insured vehicle represents a l l claims and allocated claim expenses a r i s i n g out of claims Incurred by the p o l i c i e s written i n a calendar year divided by the t o t a l number of equivalent car years insured ( i n -sured vehicles' i n text above). Car years insured means that two cars Insured f o r 6 months each constitute one car year. 16 I t reflected the r i s i n g costs of repairing automobiles, hospital and medical costs, l e v e l of court awards, and cost 14 of adjustment. In response to the r i s i n g average l o s s -cost per Insured vehicle i n both I95I and I96I, the C.U.A. s t a t i s t i c a l agency decided that some provision had to be made i n the rate making calculations to r e r l e c t t h i s trend. The concept i s equivalent to allowing f o r i n f l a t i o n i n c a l c u l a t i n g the future worth of an Investment. I n i t i a l l y the s t a t i s t i c a l agency used the experience of the preceding f i v e years i n analyzing the d i r e c t i o n and amount of the trend. In 1965 the number of years used to establish the loss-cost trend was reduced to three years because the minimum l i m i t s f o r coverage had been increased by P r o v i n c i a l statutes i n the d i f f e r e n t provinces. 1^ Thus I t was f e l t that the series used before would lack continuity i n establishing the expected projection of trend. This reduction i n the number of years used f o r establishing the trend factor severely increases the p r o b a b i l i t y of error, i n that the degrees of freedom have been decreased from 16 three to one. Thus any estimates based on these r e s u l t s would have a high expected error, and the r e s u l t i n g c o n f l -cons ^ T r a n s c r i p t R.C.A.I., Volume 2 5 , pp. 2 9 8 9 - 9 1 . 1 5 i b l d . , Volume 2 7 , pp. 3 2 1 7 - I 0 . 16rpne t o t a l number of observations, l e s s the estimating tants equals the number or degrees of freedom. 17 dence greatly reduced. I t would thus have been better i f the e x i s t i n g data used i n establishing the trend were adjusted to allow f o r the effects of Increasing the minimum l i m i t s . The procedure used to develop the expected loss-cost per insured vehicle fellows below. The actual loss-cost per insured vehicle i s plotted as a time series f o r countrywide experience, and f o r provin?-c i a l experience. An example of such a graph Is shown i n Figure 1 f o r countrywide loss-costs. The purpose of p l o t t i n g the chart i s to f i t a curve to the points that most closely represents a function expressed i n mathematical terms. Through f i r s t difference analysis, the analyst can establish whether the h i s t o r i c a l data may best be described by a f i r s t , second or t h i r d degree curve, or perhaps through a combina-t i o n of logarithmic manipulation to a r r i v e at an accurate description of the data. However, even a f t e r such a mathe-matical description has been achieved, the equation holds true only f o r the area described by the h i s t o r i c a l data. The use of the equation as a forecasting technique rests solely on the continuity of the underlying factors which produced the equation In the f i r s t place. Figure 1 i l l u s t r a t e s the r e s u l t of the C.U.A. actuaries' analysis. The trend l i n e has been f i t t e d by the least squares technique. In addition to the above constraint i n using t h i s curve f o r forecasting i s the problem of the length of time F I G U R E t L E A S T S Q U A R E S T R E N D L I N E VQF L O S S - C O S T S F O R C O U N T R Y W I D E E X P E R I E N C E 1959 I960 1961 1962 1963 1964 1965 1966 YEARS L e a s t s q u a r e s t r e n d l i n e T r e n d p r o j e c t i o n G o m p e r t z C u r v e Source : Green Books 1959 - 1965 19 over which observations are made. Clearly I f the 195P to 195a data Indicates fluctuations around a loss-cost of $ 3 2 , then the trend l i n e w i l l be l e v e l l e d to a greater extent. There i s also the p o s s i b i l i t y that the data from I 9 5 9 to 1964 represents more nearly the mirror image of a Gompertz curve m which case there w i l l be a maximum loss-cost esta-blished i n the near future. This may not be too wild a conclusion I f one sees that there i s a growing concern by auto-manufacturers that we have reached the point where there i s only replacement production, so that we have reached a maximum density of cars on the road. I f we couple t h i s with a declining b i r t h rate, and moderate i n f l a t i o n , the re s u l t s are not untenable. The actual choice of the f i n a l description of the observations by a mathematical formula thus w i l l depend not only on the time period chosen, but also on the continuity of the underlying factors that determine these observations. These factors w i l l includes the density of motor vehicle t r a f f i c , increased costs per claim due to r i s i n g labour costs, raw materials costs, and other i n f l a t i o n a r y pressures that are not as readi l y measured, such as higher court awards and increased claim consciousness. The industry has apparently recognized that at various points In the past, these under-l y i n g factors have created conditions so that i t was neces-20 sary to est a b l i s h a new trend l i n e i n order to predict with greater accuracy the expected loss-coBts. In 1961, 1962 and I963 the trend factor equalled 4.0 percent.; In 1964, 3.8 percent and i n 1965, 9.0 percent f o r the countrywide l o s s - c o s t . 1 ? Up to I964 a one-year projection of trend was u t i l i z e d , which was increased to a 1.5 year trend projection f o r 1965 and i n 1966 the planned forecast was to cover 2.4 18 years, equal.to a f u l l p o l i c y year. In 1966 the C.U.A, developed trend factors f o r regions at which time the 2.4 year loss cost projection amounted to 22.0 percent f o r B r i t i s h Columbia. In the introduction to t h i s thesis the proposition was put forward that the expenses Incurred In w r i t i n g auto-mobile insurance were d i r e c t l y or l i n e a r l y . r e l a t e d to volume of business written. Thus, applic a t i o n of the trend factor to both the loss-cost and the expense factor would appear l o g i c a l . However, the industry decreased the proportion allowed f o r expenses, Indicating that either expenses had been too large a proportion of the gross premium, or our hypothesis i s Incorrect. The actual analysis of the.data w i l l indicate a possible answer i n Chapter IV. 17C,U,A. B r i e f , p. 22, 1 8 I b l d . , p. 2 3 . The Problem of A l l o c a t i o n 21 The above review suggests the importance of e s t a b l i -shing uniform c r i t e r i a f o r developing an accurate expense loading f a c t o r . The method that the C.U.A, employs In esta-b l i s h i n g gross automobile premiums may be stated by the f o l -lowing equation: Pp where: Pp = loss-cost per vehicle (pure premium) e = expense factor (In percent) Pg = gross premium The two variables that enter into equation one are thus pure premium and the expense fact o r . Present a c t u a r i a l techniques u t i l i z i n g the countrywide data to develop loss experience and hence pure premiums are accepted as 'good p r a c t i c e 1 at pre s e n t . ^ The same cannot be said f o r the ex-pense factor M e n however. Here no data i s collected, analyzed and disseminated by the S t a t i s t i c a l Agency, Hence the size of the loading factor has been l e f t largely to chance. As !9with perhaps the exceptions noted under the trend f a c t o r (Chapter I I 14). 22 stated previously, the Hodglns Report found 45 percent ade-quate In 1930. In 1957 the Nova Scotia Report found that "...a provision i n the rates of 37 percent of the premium d o l l a r f o r expenses and p r o f i t i s not unreasonable In the l a t t e r case an attempt was made to allow f o r d i f f e r -ences i n commission rates; however, the r e s u l t s were con-fined to the study of board companies only, and lacked s t a t l s t l -21 c a l v a l i d i t y . I t may thus be apparent that l i t t l e success has been achieved to date i n determining an unambiguous expense factor f o r rate-making purposes. The expense factor w i l l t y p i c a l l y consist of two items. The f i r s t consists of d i r e c t costs which are those costs that can be d i r e c t l y traced as the cost of w r i t i n g a p a r t i -cular l i n e of insurance. The second cost consists of i n d i r e c t or overhead expenses which cannot be d i r e c t l y traced to an i n d i v i d u a l l i n e of insurance. The former costs, d i r e c t costs, may be allocated and e a s i l y determined through standard cost accounting procedures. However, when attempting to al l o c a t e overhead costs that are not associated with any p a r t i c u l a r l i n e of Insurance, the r e s u l t may w e l l be a r b i t -rary. This l a t t e r type of a l l o c a t i o n may be based upon net premiums written or as a percentage of d i r e c t costs Incurred 20Nova Scotia R.CUA.I., Volume I, p. 51, 2 1 I b l d . , p. 49. 23 or any other method. None of these methods has any more th e o r e t i c a l merit than any other. But once a method has been adopted, i t i s maintained so as to achieve continuity and comparability of expense data. At the present time, company expenses are collected by the Federal Superintendent of Insurance and published In the "Blue Book". The expenses shown are f o r the company as a whole, f o r a l l the l i n e s of Insurance i t i s engaged In. There has been no attempt to c o l l e c t d i r e c t costs by l i n e of Insurance and show separately unallocated costs. There would be two alternatives ror determining the costs applicable to a p a r t i c u l a r l i n e or Insurance. The f i r s t has already been described and would require the cor-porations to keep records or t h e i r d i r e c t expenses by l i n e or insurance. Thus we would then obtain the d i r e c t portion or the expense factor. However, t h i s s t i l l leaves us with the unsatisfactory method of a l l o c a t i n g f i x e d costs, some-what a r b i t r a r i l y . The method chosen w i l l have a d i s t i n c t bearing on the r e s u l t i n g expense r a t i o of any p a r t i c u l a r l i n e of insurance. The other method Involves the varying or the size of a l i n e of business, and observing the relationship with unallocable overhead factors. I f t h i s could be done f o r each item of expense, and every combination of l i n e s of insurance, we would be able to determine what proportion of an i n d i r e c t expense i s related to the volume of business 24 transacted In a l i n e of insurance. The second method outlined above i s more useful and the technique r e s u l t s In the a b i l i t y to determine the mar-g i n a l cost of w r i t i n g an a d d i t i o n a l premium d o l l a r f o r a p a r t i c u l a r l i n e of insurance. A s i m i l a r problem of a l l o c a t i n g overhead costs has been solved f o r carrying d i f f e r e n t kinds of f r e i g h t by r a i l i n the United S t a t e s . 2 2 In order f o r the technique to be successful, the accounting data must be uniformly prescribed and recorded, the number or observations or companies reporting large so the r e s u l t s w i l l have s t a t i -s t i c a l v a l i d i t y . The Federal Superintendent requires the reporting of expenses f o r a l l companies on a calendar year basis i n standard form, thus the f i r s t requirement Is met. Since there are over three hundred companies w r i t i n g insur-ance i n Canada, the second c r i t e r i a i s also f u l f i l l e d . Summary The expense factor used i n setting automobile rates has been traced over a period or time and has been reduced from an i n i t i a l r i f t y percent loading to the present t h i r t y -three percent of gross premium. The introduction of a trend fa c t o r rate i n 1951 has Increased the doubt as to the under-l y i n g relationships between expenses, and losses and gross premiums. The appli c a t i o n of standard cost accounting tech-2 2J,R. Meyer et a l , Economics of Competition In Trans- portation Industries. Harvard University Press, Cambridge, Mass., I964. 25 niques would not r e s u l t i n any more information as the l o s s -costs developed by the C.U.A. already Include allocated claim costs. Unallocated costs would s t i l l present an insurmoun-table problem as to the j u s t i f i a b i l i t y of one method as opposed to another. Hence, the problem of the determina-t i o n of the marginal cost of w r i t i n g automobile Insurance w i l l be the main subject of the following chapters. CHAPTER I I I THE STATISTICAL STUDY: THE MODEL The preceding chapter served as a b r i e f Introduction to the expense factor as I t influenced the rate-making pro-cedure. I t was seen that the actual expense loading factor "e" used In the rate-making rormula, was ar b i t r a r y i n that no s t a t i s t i c a l data had been collected to substantiate a s p e c i f i c expense r a t i o . I t was also argued that standard cost accounting techniques would not be of any greater benefit i n deciding upon an appropriate a l l o c a t i o n of overhead by l i n e of insurance. Similar problems face any multlproduct f i r m where many j o i n t costs are impossible to a l l o c a t e . * The f i r s t successful treatment of the determination of mar-gi n a l costs was achieved i n r a i l r o a d costing i n the United 2 States. The success of ."the technique, used In the United States, depends on the a v a i l a b i l i t y or uniformly reported s t a t i s t i c s and a large number or companies or observations. In Canada the Superintendent or Insurance requires the c o l -l e c t i o n or such data from a l l insurance companies doing lHen&erson and Quandt, Mlcroeoonomlc Theory: A Mathe-matical Approach. McGraw-Hill, New York, 1958, pp. 67-?2. 2J.R. Meyer, et a l . Competition i n the Transportation  Industry. Harvard University Press, Cambridge, Mass., 1964. 27 business, and publishes a summary annually i n the "Blue 3 Book", There are approximately three hundred and rour com-panies w r i t i n g d i f f e r e n t combinations of l i n e s of insurance. Thus there e x i s t s u f f i c i e n t companies and uniformly reported data to make the technique f e a s i b l e . The Multiple Regression Model The technique of multiple regression analysis i s by no means a new concept. The technique may be applied to time series analysis and used as a forecasting technique, as i t Is presently employed by the C.U.A. S t a t i s t i c a l Agency In projecting loss-costs. Or, the technique may be applied to a large sample of cross sectional data which does not have the Inherent problem or t r y i n g to predict beyond the observed values, as i s necessary ror the time series tech-nique. Since uniformly reported data i s available f o r the cross sectional analysis, i t w i l l be used to develop a model to determine the marginal costs of w r i t i n g a p a r t i c u l a r l i n e of insurance. The data covers the calendar year I964 and i s taken from the "Blue Book", Multiple regression analysis i s an extension of the f a m i l i a r l e a s t squares technique such that there are up to ^Report of the Superintendent of Insurance f o r Canada. Queen's P r i n t e r , Ottawa, 1965, Volume I I Annual Statements -F i r e and Casualty Insurance, 28 H n n independent variables entering into the equation. The same conditions apply, however, so that the sum of the d i f f e r -ence of the observed and actual dependent observations are zero, and the sum of the difference of the observed and actual values squared i s minimized. These conditions i n -sure that the resultant curve f i t s the observed data In a best possible manner, and may be stated as the best unbiased estimator of the underlying true population. The relationship between expenses incurred (Yi) and volume of net premiums written (X ), f o r a company w r i t i n g only one l i n e of Insurance, may be desorlbed by the following l i n e a r equation: Y l = A Q + b ^ (1) and i s represented In Figure 1. The f i x e d cost f o r the i t h expense category i s given by A 0, which i s incurred re-gardless of the volume of d o l l a r s of premiums written by the company. The above equation Is the end r e s u l t of the re-gression analysis, so that i f a company writes X^* d o l l a r s ^For a description of multiple regression analysis, see: Croxton & Cowden, Applied General S t a t i s t i c s . Prentloe-H a l l , New York, 1939; and Ezeklel & Fox, Methods of Cor-r e l a t i o n and Regression Analysis. John Wiley & Sons, Inc., New York, 1963, 3rd e d i t i o n . ' 5The assumption of l i n e a r i t y i s not inherent i n the data, and must be proven by the r e s u l t s . I f non-linearity r e s u l t s , techniques are available to convert the r e l a t i o n -ship to a l i n e a r function. 29 of premiums, the corresponding expenses may he determined by constructing a perpendicular l i n e from X^* u n t i l i t meets the derived l i n e , and then move p a r a l l e l to the X^ axis u n t i l I t Intersects the Y i axis at Y i * . In Figure I, I f X i equals one unit (In d o l l a r s ) , then Y i Is regarded as the marginal cost of w r i t i n g each add i t i o n a l d o l l a r of premium. As long as X±* i s within the observed range of data used i n deriving equation ( 1 ) , then the resultant expense factor prediction w i l l be accurate within the l i m i t a t i o n s of s i g -nlflgance and confidence present i n the o r i g i n a l data. Figure 2 i l l u s t r a t e s the case where an Insurance com-pany i s engaged i n two l i n e s of Insurance X^and X 2. The equation that describes t h i s s i t u a t i o n Is Y i = Ao + b j X i + b 2 x 2 ( 2 ) and describes a plane i n three dimensions. The f i x e d cost factor Involved In w r i t i n g both l i n e s of insurance i s AQ. The marginal cost of w r i t i n g an addi t i o n a l d o l l a r of Insurance of l i n e X i i s Y i , and the marginal cost of l i n e X2 i s Y 2. The o v e r a l l or t o t a l expense of category YI f o r X i * and X 2* do l l a r s of premiums written i s found by constructing per-pendiculars i n the X i and X 2 plane, and projecting a per-pendicular from t h e i r point of in t e r s e c t i o n u n t i l i t cuts the AoBCD plane. The height of t h i s point E from the X i X 2 plane determines the t o t a l expense factor YI*. FIGURE 2 EXPENSE R E L A T I O N S H I P OF A S I N G L E - L I N E COMPANY Expense Y; Category Net Premiums Written FIGURE 3 EXPENSE RELATIONSHIP OF A T W O - L I N E COMPANY Expense Category y . » / (Net Premiums Written, line 2 ) Equotion of plane a0BCD: Yi ; o0r b,X i + b2 X2 (Net Premiums Written, line I) 31 I f a company i s engaged i n more than two l i n e s of Insurance, a geometric representation or the expense r e l a t i o n -ship i s Impossible. The expense plane becomes a hyperplane In M n w dimensions, where n represents the number or l i n e s of insurance a company Is engaged i n . Thus i n order to obtain the needed information of the constant factor A 0, and the marginal costs of w r i t i n g a d d i t i o n a l d o l l a r s of Insurance, the technique of multiple regression analysis w i l l r e s u l t i n an algebraic representation of the r e l a t i o n -ship between expenses and volume of insurance written. Thus regression analysis Involves the derivation of an equation by which the dependent variable may be estimated rrom the independent variables. Closely related to regres-sion analysis i s c o r r e l a t i o n analysis which measures the closeness or the relationship described In the regression equation. For the purpose or t h i s study we have assumed that there e x i s t s a l i n e a r relationship between the dependent variables and the independent variables. The general equa-t i o n r or determining the amount of expense incurred f o r a p a r t i c u l a r company Is given by: Y = A Q + b i X l + b2 X2 + ....+ b n X n + e where: Y = the dependent variable representing a p a r t i c u l a r ex-pense category such as commissions, premium taxes, e t c . 0 6See Appendix A, Table I ror a complete l i s t i n g of a l l expense categories. 3 2 X l , 2 « ' . » » n ^ t n e independent variable denoting a l i n e of ' insurance where there are n such l i n e s . AQ = the constant f a c t o r and represents the f i x e d cost f o r being engaged i n the n l i n e s of insurance. b i 2---n = the regression c o e f f i c i e n t that determines which ' portion of the premium d o l l a r goes toward meeting the expenses of the corresponding l i n e of insurance. e = the residual error of the estimating equation, and - represents the difference between values estimated from the equation and actual Observed values. Thus the above equation states that the p a r t i c u l a r expense category Is equal to a constant term plus propor-t i o n a l amounts f o r each l i n e of insurance that a company i s engaged i n , . The error term indicates to what extent the equation over- or under- estimates the actual value f o r the dependent variable. There are three c l a s s i f i c a t i o n s f o r the data that may be used to describe the independent variables. These Include net premiums written, net premiums earned and net Q claims incurred. I t i s i n t u i t i v e l y apparent that a certain c l a s s i f i c a t i o n of independent variables i s more meaningful f o r estimating the value of a p a r t i c u l a r expense category. Hence net premiums written are probably best f o r estimating the rate of commissions paid f o r w r i t i n g a p a r t i c u l a r l i n e ^See Appendix A, Table I I f o r the i n i t i a l Independent variables included i n the model. ^Figures I and I I used the net premiums written c l a s -s i f i c a t i o n ; however, net premiums earned, on net claims In-curred could have been used also f o r i l l u s t r a t i v e purposes. 33 of insurance; whereas net claims incurred are a better e s t i -mator f o r allocated claims expenses which vary more d i r e c t l y with the loss costs incurred; and net premiums earned w i l l be more appropriate f o r expenses which are related to the length of the l i f e of a po l i c y . The f i n a l choice as to which set of explanatory variables or class of insurance to be used w i l l usually be made according to the highest B 2 value,the c o e f f i c i e n t of determination which Is the per-cent of the o r i g i n a l v a r i a t i o n i n the mean of the dependent variable that has been explained by the independent variables. The c o e f f i c i e n t of determination i s at the same time a mea-sure of the goodness of f i t achieved f o r the equation under study and i s thus an indi c a t o r of the r e l i a b i l i t y of any predictions made using the equation. The regression c o e f f i c i e n t s calculated are equivalent to the marginal or incremental cost Incurred In w r i t i n g a p a r t i c u l a r l i n e of insurance. The actual v a l i d i t y of the regression c o e f f i c i e n t can be determined by comparing the estimated value with the size of i t s standard error of e s t i -mate. The sample size and the absolute size of the standard error of estimate w i l l enable us to determine the confidence that we have i n the predictive value of the p a r t i c u l a r re-gression c o e f f i c i e n t . More s p e c i f i c a l l y the computer p r i n t -out supplies the corresponding F - r a t i o , which allows one to treat the observations as a normal p r o b a b i l i t y d i s t r l b u -3^ t i o n with a standard deviation and a corresponding measure as the expected confidence l i m i t s . Eliminating M u l t i c o l l l n e a r l t y After a l l the data had been coded, and the i n i t i a l o printout from the Trip Program^ reviewed, I t was found that many of the independent variables were highly correlated amongst each other. This r e s u l t s i n the i n a b i l i t y of the method to d i s t i n g u i s h whether a p a r t i c u l a r v a r i a t i o n i n expenses was due to a p a r t i c u l a r Independent v a r i a b l e s o correlated, or a combination of them. Thus the regression c o e f f i c i e n t s and the standard error of estimate w i l l not be meaningful. The only way to obtain s t a t i s t i c a l l y meaning-f u l r e s u l t s i s to aggregate those independent variables that are highly correlated. An a r b i t r a r y cutoff figure f o r the c o r r e l a t i o n c o e f f i c i e n t of O . 6 5 was used to combine the i n -dependent variables. This meant that 5 5 percent of the multi-c o l l l n e a r l t y i n the o r i g i n a l work had been reduced. Unfor-tunately t h i s r e s u l t s In the i n a b i l i t y to d i s t i n g u i s h between various independent variables, as they have now been aggregated In into a new composite variable. u The loss i s however small, since we could not d i s t i n g u i s h between the independent v a r i -ables by s t a t i s t i c a l means anyway. Hence the new r e s u l t s ?Trip: Triangular Regression Package, U.B.C. Computing Centre. l QSee Appendix A, Table I I I f o r the composition and designation of the new independent variables. 35 w i l l be more s t a t i s t i c a l l y meaningful than the i n i t i a l re-s u l t s . The Stepwise Regression A further refinement i n the analysis of the data may be achieved through the use of stepwise regression. I f In a p a r t i c u l a r equation the independent variables represent a spurious relationship with the dependent variables under consideration, then a l l the other Independent variables which are s i g n i f i c a n t may be affected so that the r e s u l t i n g re-2 gresslon c o e f f i c i e n t s are less accurate and the R value f o r the whole equation reduced. In other words we would l i k e to remove those Independent variables that do not con-tribute s i g n i f i c a n t l y to the reduction of the o r i g i n a l v a r i -ance observed i n the mean of the dependent variable. The technique i s such that each independent variable i s tested to see whether i t contributes s i g n i f i c a n t l y to the reduction of the variance of the dependent variable, and i f i t does, i t i s entered into the equation. The s t a t i s t i c used f o r the accept or reject decision i s c a l l e d an P - r a t i o . Thus I f the independent variable has an F - r a t i o greater than 11 the cut-off r a t i o , the variable w i l l be entered. I f how-ever at a l a t e r stage the F - r a t i o drops below the cut-1 : LAn F - r a t i o of 4.0 was used at the 5 percent l e v e l of signif i c a n c e . 3 6 off r a t i o due to the entry of other variables, i t w i l l be dropped from further consideration. The independent v a r i -ables are brought one at a time Into the regression equation, i n order of decreasing contribution to the reduction of variance or the dependent variable under consideration. The tests of significance used (F tests) are based on the r a t i o of the dependent variables variance contributed by the independent variables i n question; to the residual variance of the dependent variable a r t e r the i n c l u s i o n or the indepen-dent variable. Summary The multiple regression model developed above was r i r s t adjusted ror m u l t l c o l l l n e a r l t y and f i n a l l y the i n s i g -n i f i c a n t variables were removed from the equation to permit more meaningful r e s u l t s to be obtained. In the following chapter the r e s u l t s w i l l be analysed as they apply to the expense factor loading. Ah analysis or the economies or scale and r e l a t i v e perrormance or the Canadian insurance industry and the American insurance Industry w i l l be treated separately i n Chapter V. CHAPTER IV STATISTICAL STUDY: THE RESULTS The analysis of the s t a t i s t i c a l study that Is to follow w i l l indicate the r e s u l t s of the model developed i n Chapter I I I . A comparison between the C.U.A. breakdown of expenses with those of t h i s study w i l l be made a f t e r a de-t a i l e d discussion of the v a l i d i t y of each factor included i n the f i n a l r e s u l t s . The data i s drawn from Tables I to XXXV i n Appendix B. The t i t l e of each table designates the dependent variable or expense category. Tables I to VII are the r e s u l t of the stepwise regression and represent the major expense categories that w i l l be used, to evaluate the C.U.A. breakdown of the expense factor. Tables VIII to XXXV represent a detailed breakdown of Table V, the re-i gresslon analysis. I t w i l l f i r s t prove prudent to determine the v a l i d i t y of the assumption of l i n e a r i t y of the model, such that the marginal cost of wr i t i n g an addi t i o n a l d o l l a r of insurance premium i s constant. Reference to the data indicates that the residual error or standard error of estimate i s larger than the constant value f o r each and every equation derived. I f the data could not be represented by a l i n e a r equation, ^As opposed to stepwise regression which eliminates a l l s t a t i s t i c a l l y l n s l g n l f i g a n t Independent variables, hence the blank spaces In Tables I to VII of Appendix B. 38 then we would have obtained d i f f e r e n t r e s u l t s . I f the data would have been better described by a c u r v i l i n e a r function, then the assumption as to l i n e a r i t y would have resulted In a l i n e a r approximation to the curve at i t s most densely populated area, such that a large negative or positive con-stant would have resulted* Since there are no large values f o r the constant the assumption of l i n e a r i t y Is correct and w i l l be useful i n estimating the marginal costs of w r i t i n g d i f f e r e n t l i n e s of insurance. This conclusion i s v a l i d f o r a l l l i n e s of insurance including automobile insurance. In the discussion to follow, certain features w i l l be common throughout the analysis or each expense ractor. Although regression analysis can be u t i l i z e d to determine, from given values of the independent variables, an absolute value f o r the dependent variable, t h i s discussion w i l l mainly be concerned with the marginal costs involved i n w r i t i n g a p a r t i c u l a r l i n e of insurance. In t h i s manner the problem of t r y i n g to attach any s p e c i f i c meaning to the value ;" of the constant can be ignored. In general i t represents the cost of being engaged In the business of wr i t i n g insurance. How-ever since the standard error of estimate i s r e l a t i v e l y large i n a l l cases with respect to the "a" value, exact numerical conclusions would be hard to j u s t i f y . The only general state-ment to be made i s that some firms w i l l f i n d themselves with higher f i x e d costs than others, but that i n general no economies of scale e x i s t , as w i l l be developed more f u l l y In Chapter V. 39 The concept of the d i f f e r e n t c l a s s i f i c a t i o n s of i n -dependent variables into net premiums written, net premiums earned and net claims incurred was Introduced i n the preceding chapter. The choice as to which c l a s s i f i c a t i o n best s u i t s the Independent variable i n estimating a corresponding value f o r the dependent variable w i l l be based l a r g e l y on the value of the c o e f f i c i e n t of determination. The c o e f f i c i e n t of determination shows the percent of the t o t a l o r i g i n a l variance i n the mean of the dependent variable that has been explained by the Independent variables considered In the general equation. However, at times I t w i l l be neces-sary to forego a higher explanation of t o t a l variance i n favour of I n t u i t i v e reasonableness of the r e s u l t s , especially i f the c o e f f i c i e n t s of determination are not s i g n i f i c a n t l y d i f f e r e n t from each other. The. emphasis f o r the purposes of t h i s study w i l l be to u t i l i z e the regression c o e f f i c i e n t s of the Independent variables to determine the marginal cost of w r i t i n g auto-mobile insurance. Each regression c o e f f i c i e n t i s accompanied by i t s standard error, so that we can express the conclusions drawn i n the form of confidence l i m i t s and at the f i v e and one percent l e v e l of significance. The usefulness of t h i s approach hinges on the assumption that marginal cost i s the factor to be used i n the expense loading of the rate making formula. Since the volume of Insurance written i s to a large extent by e x i s t i n g insurance companies, then i t Is 40 the marginal costs of w r i t i n g insurance that are s i g n i f i c a n t from the companies* points or view, and a l l past costs with respect to expenses and investments are sunk costs. The present d i f f i c u l t y that the industry has i n a l l o c a -t i n g overhead costs, whether these are f i x e d or variable, when w r i t i n g primarily f i r e and automobile Insurances, i l l u -strates the usefulness of the marginal cost concept when no economies of scale are present. The industry recognizes that i t i s r e l a t i v e l y more expensive to write f i r e insurance 2 than I t i s to write automobile Insurance. I t Is also sus-pected that automobile Insurance to some extent subsidizes f i r e insurance by taking on a larger share of overhead, than would have occurred had:.the "company been w r i t i n g automobile 3 Insurance only.- I t Is impossible to t e l l what the marginal cost of w r i t i n g f i r e insurance I s , as i t i s aggregated with 4 t h e f t , personal property, plate glass and public l i a b i l i t y . However i t i s estimated that as much as 2# percent of the automobile expense factor i s an overloading from f i r e i n -surance.^ Thus i f there are no s i g n i f i c a n t economies or scale present, the marginal cost factor w i l l a l locate over-2Transcrlpt R.C.A.I., Volume 54, pp. 6391-92. 3ibld,, Volume 56 pp. 6582-83, ^Appendix A, Table I I I . 5Loc. C i t . , p, 6583, 41 head expenses equitably among the kinds of insurance that t h i s study i s able to d i s t i n g u i s h among. The determination of the marginal cost of w r i t i n g automobile Insurance w i l l be broken down into seven cate-gories as shown, by the headings of Tables I to VII, and the l i m i t a t i o n s of conclusions drawn w i l l be described i n the sections that follow. Net Adjustment Expenses Incurred 0 Net adjustment expenses incurred are those expenses a r i s i n g out of c o l l i s i o n claims and i n general represent the fees paid to claim adjusters. "Net" refers to the amount the company paid out a f t e r recovery of any adjustment ex-penses from the other parties involved. This expense f a c t o r i s included i n the loss portion of the expense f a c t o r f o r rate making purposes by the C.U.A, s t a t i s t i c a l agency, and thus does not represent part of the 33 percent expense loading presently used. Turning now to the data, the c o e f f i c i e n t of deter-mination i s largest (o . 8 7 7 4 ) f o r net claims incurred and i n -dicates that the expense factor should be derived from t h i s column. This r e s u l t i s also i n t u i t i v e l y appealing since i t i s expected that claims expenses are d i r e c t l y related to the frequency and size of claims Incurred, The regression c o e f f i c i e n t of 3 , 2 6 percent represents the marginal cost i n -volved i n servicing every net d o l l a r of claim incurred. Since the °Source or data; Appendix B, Table I, 42 standard error or the regression c o e f f i c i e n t i s small, the resultant P - r a t i o indicates that t h i s r e s u l t Is s i g n i f i -cantly d i f f e r e n t from zero at the one percent l e v e l of s i g -n i f i c a n c e . At the same time the standard error of the re-gression c o e f f i c i e n t indicates that 68 percent of the time a company w i l l have claims expenses f o r c o l l i s i o n claims of 3.2b percent plus or minus 0.19 percent of t o t a l claims Incurred. Net Commissions Incurred? Net commissions Incurred are the commissions paid to the agents who s e l l insurance, whether i t he as an employee of a single firm or as a licensed agent who does business with more than one firm. The c o e f f i c i e n t of determination explained 89.75 percent of the o r i g i n a l v a r i a t i o n i n net commissions incurred with respect to net premiums written. Again t h i s value f o r the c o e f f i c i e n t of determination was larger than f o r net premiums earned and net claims incurred. This re s u l t would be expected as remuneration Is t y p i c a l l y based on the volume of net premiums written. The net regression c o e f f i c i e n t i s 7.58 percent, s i g -n i r l e a n t at the one percent l e v e l and with a standard error of 0.66 percent. This figure i s r e l a t i v e l y low i n comparison 7Appendix B, Table I I . 4 3 with the quoted. C.U.A. rate of commission of 1 2 . 5 percent 8 and needs further explanation. Board companies write only 3 1 . 1 percent of the t o t a l business of automobile insurance i n the province of B r i t i s h Columbia and about 3 3 percent 9 of the t o t a l business i n Canada. Thus i t may be concluded that the C.U.A, rates are not representative of the com-missions paid i n terms of volume of insurance written. In order to determine the reason f o r a lower commission rate than might at f i r s t be expected, i t i s necessary to compare the competitive differences with respect to the market-ing of insurance premiums. Members of the Canadian Underwriters' Association, Independent Insurance Conference, and two-thirds of the Independent independents operate through the Indepen-dent agency s t r u c t u r e , 1 0 Licensed agents establish t h e i r own o f f i c e s , and may write and remit automobile insurance premiums to any members of the above. The remuneration received by the agents consists s t r i c t l y of commissions paid by the companies. The remainder of insurers not i n -cluded i n the above consist of independent independents 11 who are d i r e c t w r iters. These companies employ t h e i r ^commission rate on private passenger automobile > insurance, C.U.A. B r i e f p. 3 4 . 9 I b l d . , p. 1 - 2 . *°See Appendix D, Table I f o r companies w r i t i n g under the independent agency structure. Usee Appendix D, Table I I f o r companies who are di r e c t w r i t e r s . 44 own agents as employees, and pay them commissions, plus providing o f f i c e space and related supporting o f f i c e per-sonnel. I f i t could he established what premium volume i s written by each of the groupings above, and t h e i r respective commission rates, a weighted average may be derived to compare with the 7,58 percent factor obtained from the s t a t i s t i c a l r e s u l t s . At the same time I t would be necessary to deter-mine what percentage of the t o t a l automobile insurance written consists of private passenger automobile Insurance. The Nova Scotia Report found that 25.7 percent of the t o t a l re-presented private passenger, 26.3 percent of the t o t a l was commercial, and the remaining 46 percent f a l l i n g into four-teen other c l a s s i f i c a t i o n s f o r Nova Scotia experience i n 1 2 1955. However f o r Ontario the private passenger Insurance accounted f o r 45 percent of the t o t a l i n 1953, 67 percent i n 1954, and 72 percent of the t o t a l i n 1955. Unfortunately no Canada-wide s t a t i s t i c s were available then, or, at the present time. Even though precise data i s lacking, i t i s possible to I l l u s t r a t e the method that could be used i n estimating a hypothetical commission rate f o r t o t a l automobile insur-ance written i n order to compare the r e s u l t with the 7.58 £%ova Scotia R.C.A.I., Volume I, p. 30, footnote 15. 13lbld., Volume I I , Table XLII, p. 263. 45 percent factor. The following table shows the weighted aver-age commission rate expected on private passenger automobile insurance written. TABLE I I I CALCULATION OF WEIGHTED AVERAGE COMMISSION BATE PERCENT OF COMMISSIONS TOTAL PAID WEIGHTED VOLUME (MAX.) . AVERAGE (1) Canadian Underwriters Association* 33 12.5 4.1 ( i i ) Independent Insurance Conference* 23 15 3.5 (ill)Independent Independents* 36 14 5»0 (lv) Independent Independents** 18 6 1.1 13.7 * w r i t i n g through an independent agency structure ** d i r e c t writers Source of data: ( i ) C.U.A. Bri e f p. 1 and p. 34. ( l i ) Transcript, R.C.A.I., Volume 31, p. 3490 and p. 3521. ( i i i ) d e r i v e d (lv) calculated from Appendix D, Table I I companies f o r volume written, commission rate i s that of A l l s t a t e . The weighted average commission rate of 13.7 percent repre-sents the expected figure i f a l l automobile Insurance written were private passenger only. However as i s mentioned above, 46 private passenger business represents only some f r a c t i o n of the t o t a l . Thus i f we were to assume that 60 percent of the t o t a l was private passenger Insurance, then the expected commission rate f o r t h i s study would be 60 percent of 13.7 plus 40 percent of the weighted average of the remaining types of automobile coverage commissions. Private passenger automobile Insurance carries the highest commission rate i n terms of percent, because the 14 average actual d o l l a r s per premium i s low.- Por commercial and other classes of automobile Insurance, the commissions as a percent of t o t a l d o l l a r s per premium i s lower because of the higher value per premium written. Thus i f the actual volume of premiums written Is r e l a t i v e l y high f o r c l a s s i f i c a -tions other than private passenger, the r e s u l t i n g average commission rate would be expected to be considerably lower than that presently u t i l i z e d i n establishing ah expense fac t o r loading f o r the t o t a l Industry experience, which i s what t h i s study i s attempting to do. Lower commission rates are also paid on premiums written under the assigned r i s k plan. For private passenger i t Is 10 percent, whereas f o r commercial insurance i t varies between 5 and 7§ percent lowerithan normal rates.15 However, l4Transcrlpt, R.C.A.I., Volume 18, p. 2178. 15iranscript, R.C.A.I., Volume 18, pp. 2177-8. 47 In 1964 the t o t a l volume written represented only one half of one percent of a l l business written, t h i s figure had doubled by 1965.1^ Thus at t h i s time i t did not af f e c t the average commission rate expected. In addition to the foregoing comments, there i s one addi t i o n a l reason to accept the 7«5a percent figure as pro-bably a r e l i a b l e measure of the t o t a l commissions Incurred. Commission rates obtained i n other l i n e s of insurance were within one per cent of those expected i n industry. 1? Por these reasons i t i s possible that the 7.58 percent factor i s a r e a l i s t i c weighted average commission rate. Net P r o f i t Commissions Incurred 1^ Net p r o f i t commissions may be considered a bonus on top of net commissions incurred. Usually a contract exists between an agent and an insurance company so that i f an agent remits good r i s k s to the insurer, the insurer rewards the agent by paying him a premium on top of the normal com-Ib i b i d . , p. 2192. ^Conversation with insurance agent, name witheld on request. 1 8Appendix B, Table I I I . The Independent Insurance Conference c a l l s these 'contingent p r o f i t commissions 1. The maximum rate being •§ to 1 % of earned premiums. The actual number of agreements of t h i s nature i s small and Is usually extended by a company who wishes to eith e r increase the market share, or penetrate a market not formerly engaged i n . Transcript H.C.A.I., Volume 31, pp. 3492-97. 46 mission paid. The idea i s to allow the agent to share i n the net p r o f i t s f o r having selected good r i s k s . This method of additional remuneration applies only to the board-member companies who use the Independent agency system, but does not apply to the Independents.^9 The c o e f f i c i e n t or determination i s largest f o r the net premiums earned c l a s s i f i c a t i o n which would be expected since t h i s remuneration Is based on earned premiums to a large extent. The net regression c o e f r i c i e n t f o r automobile Insurance i s 0.13 percent, which i s s i g n i f i c a n t at the one percent l e v e l , and the standard error equals 0.04 percent. This expense should only apply to the board-member companies, and not the various independents. 20 Taxes Incurred The taxes Incurred are p r o v i n c i a l taxes l e v i e d on the premiums written by an insurance company. A This p a r t i c u l a r category or expenses does not Include income taxes, but does Include property taxes and other minor miscellaneous tax items that do not f a l l under the rederal taxation a u t h o r i t i e s . l9Transcrlpt, R.C.A.I., Volume 31, pp. 3492-97, 20Appendix B, Table IV. ^Premium taxes equal 2% of net premiums written ror automobile insurance. 49 The c o e f f i c i e n t of determination Is largest f o r the net claims Incurred at 0.9624; whereas f o r net premiums written i t i s a l i t t l e less at 0 .9307. Since the taxes are collected on the basis of net premiums written, and the actual d i f f e r -ence between the determination c o e f f i c i e n t s i s small, the net regression c o e f f i c i e n t chosen was based on net premiums written. Thus automobile premium taxes account f o r 1.97 percent of net premiums written with a standard error of 0.07 percent, the regression c o e f f i c i e n t being s i g n i f i c a n t at the one percent l e v e l . i . T h i s figure Is lower than expected since premium taxes are a minimum of 2.0 percent. However, t h i s year's taxes are based on l a s t year's net premiums writ-ten. The amount of automobile Insurance net premiums written increased from 336 to 407 m i l l i o n d o l l a r s from I963 to I964, This represents a 20 percent Increase i n d o l l a r volume In one year. Thus by adding 20 percent to the 1.97 percent f i g u r e , the taxes Incurred equal 2.4 percent of net premiums 22 written f o r the previous year. For the purposes of t h i s study the 2.4 percent figure w i l l be used as i t r e f l e c t s the current expense l i a b i l i t y . The 2 .4$ figure agrees exactly with that quoted i n the Report of the Superintendent of Insurance I964, Volume I, p. x l v . 50 General Expenses Incurred 2^ The general expenses Incurred category includes general administrative expenses such as s a l a r i e s , rent, various fees f o r d i f f e r e n t reports, and other Items of expense Incurred while engaged i n the insurance business. The c o e f f i c i e n t s of determination are about equal f o r both net premiums written and net claims incurred, and the choice between the two Is e s s e n t i a l l y a r b i t r a r y and w i l l on, give the same results i n either case. The choice f a l l s on net premiums written by convention and p r a c t i c a l reasons f o r l a t e r comparison. The net regression c o e r r i c i e n t equals 15.98 percent with a standard error of only O.69 percent, and i s s i g n i f i c a n t at the one percent l e v e l . Bad Debts 2^ Bad debts expenses occur through non-payment of pre-miums. For automobile Insurance the regression c o e f f i c i e n t was not brought into the f i n a l regression and i s thus i n -s i g n i f i c a n t . The reason f o r the n e g l i g i b l e amount of bad debts appearing i n the corporate accounts is; that a l l indepen-dent agents submit the t o t a l premium written to the p a r t i c u l a r 2 3Appendix B, Table V. 2 i , ,This r e s u l t follows i f one allows f o r volume d i f -ferences between net premiums written and net claims Incurred. 25Appendix B, Table VI. 51 insurance company i t wrote the policy r o r , so that i f the account proves uricollectable, the agent suffers the lo s s , not the company. Bad debts w i l l be incurred however, by companies that write under the d i r e c t agency system. Total Expenses Incurred ° The t o t a l expense Item i s the summation of a l l the expense categories discussed so f a r . The R 2 value i s 0.9512 hence the equation has accounted f o r 95-12 percent of the t o t a l variance of the o r i g i n a l expense category i n terms of net premiums written. The resultant regression c o e f f i c i e n t i s 27.70 percent of net premiums written, with a standard error of 0.99 percent, which i s s i g n i f i c a n t at the one percent l e v e l . This figure should not be compared d i r e c t l y with the C.U.A, expense r a t i o , as the expense factors upon which the respective figures are based are not d i r e c t l y comparable. Comparison of S t a t i s t i c a l Results with  C.U.A. Expense Factor In order ror the comparison between the two sets of data to be v a l i d , i t i s important to ensure that the items of expense are based on the same c l a s s i f i c a t i o n of insurance. I f we ignore the net adjustment expenses Incurred category, since i t i s r e f l e c t e d i n the loss portion of the s t a t i s t i c a l 2 oAppendlx B, Table VII. 52 agencies rate making formula, then the re s u l t s obtained rrom the study Indicate the following marginal costs as based on net premiums written: Net Commissions Incurred..... 7«58 % Net P r o f i t Commissions Incurred.... 0.09 Taxes Incurred........................... 2.40 General Expenses Incurred................ 15«96' 26.05 In addition to the t o t a l shown above, I f we add 2.5 percent as an allowance f o r p r o f i t , then the t o t a l expense factor equals 2b,55 percent of net premiums written. Another way of c a l c u l a t i n g the same t o t a l expense factor Is to r e c a l l that t o t a l expenses Incurred was calculated i n Table VII. 2? The marginal cost was found to be equal to 27,70 percent of net premiums written. By subtracting the net adjustment expenses i n c u r r e d 2 0 of 2.12 percent and adding the 2.5 percent allowance f o r p r o f i t , the resultant expense factor equals 29 28.51 percent. 7 The confidence l i m i t s of t h i s figure may be obtained by taking the standard errors of both the t o t a l expenses and the net adjustment expense which equals 1.15 27Appendix B. 2 t JBased on net premiums written, Table I, Appendix B. ^In c l u d e s the tax adjustment from 1.97$ to 2.4$ of net premiums written. 53 percent. Thus ninety three percent of the time we expect to f i n d that companies w i l l have expenses that are between 25.7*5 ana 30.38 percent of net premiums written. The expense factor breakdown as published by the C.U.A, s t a t i s t i c a l agency i s as follows:30 Premium and other Taxes.................. 2.4 % Commission to Agents..................... 12.5 Insurance Association Fees............... 0.6 Unallocated Claims Adjustment Expense.... 4.0 Administrative Expense (Including 2.5 % P r o f i t ) 13.5 33.0 In order to compare the s t a t i s t i c a l r e s u l t s of t h i s study with the above table, insurance association fees, unallocated claims, adjustment expenses and administrative expenses are the equivalent of the general expenses Incurred plus the 2.5$ allowance f o r p r o f i t . The s t a t i s t i c a l r e s u l t s can be used to i l l u s t r a t e what the expense fa c t o r breakdown would be i f the commissions paid were 12.5$. I t Is only necessary to add 4.92 percent to the net commissions Incurred and sub-t r a c t 4.92 from the general expenses Incurred. This r e s u l t follows from the observation that there i s no advantage with respect to t o t a l expenses as to whether a company Is a d i r e c t w r i t e r or uses the agency system.3* The s t a t i s t i c a l r e s u l t s 30c.U.A, B r i e f , p. 34. 3lTranscrlpt H.C.A.I., Volume 20, pp. 2326,2329,2377. 54 thus Just show what the t o t a l average industry expenses are l i k e l y to he f o r a p a r t i c u l a r firm with the confidence l i m i t s establishing bounds on the predictive value of the r e s u l t s . Implications of Study f o r  Management Control The manager of an Insurance corporation may w e l l know the general Industry average f o r the expense categories l i s t e d and compare his company's results with those of the s t a t i s t i c a l study. He may be above the allowed expense r a t i o or below and s t i l l not know where the i n e f f i c i e n c i e s a r i s e . The breakdown of the general expenses incurred however would allow a more detailed comparison of his company to the i n -dustry average, and thus concentrate his attention on those areas or expense by l i n e or insurance that appear to be the trouble spots. Thus Tables VIII to XXXV I l l u s t r a t e the measuring rods that the entrepreneur can use i n employing the p r i n c i p l e or management by exception.3 2 As an example i n determining management remuneration one can look at the industry average and compare t h i s with the p r o f i t p o s i t i o n of the p a r t i c u l a r f i r m . Thus i f claims adjusters are more e f f i c i e n t and operating expenses are down, an increased p r o f i t i s l i k e l y to accrue to the company, and salaries, may be increased accordingly, 32Appendix B. CHAPTER V ECONOMIES OP SCALE Economies of Scale In Automobile Insurance The s t a t i s t i c a l r e s u l t s of the study can also be u t i l i z e d to determine whether or not there are s i g n i f i c a n t economies of scale involved i n the w r i t i n g of automobile insurance. I f there are s i g n i f i c a n t economies of scale, they would most l i k e l y be r e f l e c t e d i n the f i x e d expense portion of the gross premium, and perhaps also i n the allocated claims costs. Thus H operations are such that one large ent i t y could administer the Insurance volume more e f f i c i e n t l y or economically than a large number of smaller e n t i t i e s , a natural monopoly would e x i s t . In order to determine whether there are economies, diseconomies or no economies of scale, the underlying reason-ing behind each p o s s i b i l i t y w i l l be b r i e f l y examined. I f the marginal costs of a fir m are f a l l i n g , economic theory t e l l s us that there w i l l be economies of scale present. Since there are usually also some f i x e d costs involved, average cost w i l l f a l l as output (that i s , volume of premiums written) r i s e s , as long as the f i x e d costs are not exceedingly large. From the above I t i s apparent that the t o t a l cost curve 2 w i l l rise. at. a diminishing rate. And since the l i n e a r 2-Economles of scale may occur due to decreasing marginal costs. 2See Figure 4. FIGURE 4 T O T A L COSTS FOR A S I N G L E - L I N E C O M P A N Y W I T H M A J O R E C O N O M I E S OF S C A L E Y Total Expenses O o Net Premiums Written FIGURE 5 T O T A L C O S T S FOR A S I N G L E - L I N E COMPANY W I T H M A J O R D I S E C O N O M I E S OF S C A L E 56 equations used i n the study represent t o t a l cost, we would expect t h i s equation to he tangent to the curve at i t s highest point, since t h i s i s where major economies would r e s u l t . Extrapolation of the straight l i n e to the I - axis would then indicate a large "a" value. I f , on the other hand, marginal costs increase as the volume of premiums written Is increased, then the t o t a l cost curve w i l l r i s e at an increasing rate.3 The straight l i n e equation produced by the multiple regression study drawn tangent to t h i s curve and extrapolated to the Y-axis would indicate that diseconomies of scale were present through a large negative "a" value. The t h i r d a l t e r n a t i v e , that there are neither economies nor diseconomies of scale present, assumes that marginal costs u, are constant throughout the observed range. Average f i x e d costs w i l l f a l l , and i f the t o t a l f i x e d costs are not large, no economies of scale would be foundlas r e f l e c t e d by a very low M a " value f o r the l i n e a r equation."' I t may be useful to r e c a l l b r i e f l y what i s meant by the standard error of estimate. Por a simple regression, i t i s merely the square root of the sum of the squares of the v e r t i c a l deviations of Y divided by the number of observations. The standard error of estimate i s s i m i l a r to the r e l a t i o n the standard deviation of a frequency d i s t r i b u t i o n bears 3See Figure 5. ^See Figure 6. 5see Figure 7. FIGURE 6 UNIT COSTS OF A S I N G L E - L I N E COMPANY Expenses per dollar of Net Premiums Written -Average Cost Marginal Cost Net Premiums Written FIGURE 7 TOTAL COSTS OF A S I N G L E - L I N E COMPANY Total Expenses Total Cost o *1 Net Premiums Written 57 to the arithmetic mean. Thus i f the deviations are normally d i s t r i b u t e d , sixty-eight percent of the deviations w i l l l i e within a distance of one standard error of estimate from the l i n e . Por a multiple regression s i t u a t i o n , i f the addi-t i o n a l independent variables contribute any information about the dependent variable, the standard error of estimate com-puted from the multiple regression equation w i l l be smaller than that obtained from the simple regression equation. The s t a t i s t i c a l r e s u l t s as reriected i n Tables I to VII In Appendix B, indicate that there are no economies of scale f o r the l i n e s of insurance f o r which s t a t i s t i c a l l y s i g n i f i c a n t regression c o e f f i c i e n t s are l i s t e d . The fore-going conclusion i s based on the f a c t that the standard error of estimate f o r the l i n e a r equation i s s i g n i f i c a n t l y larger than the constant value H a M . This same observation held f o r each operation performed during the stepwise re-gression. I t may at t h i s point be objected that the economies i n one l i n e of insurance may be o f f s e t by the diseconomies of another, while a t h i r d may have constant marginal costs, but a high f i x e d cost. However, the stepwise regression computer printout shows the same res u l t s as i n Tables I to VII as each Independent variable i s brought into the equa-ti o n . Thus the standard error of estimate r e a l l y represents a confidence i n t e r v a l , such that i f we draw two p a r a l l e l 58 l i n e s one standard error of estimate away from our calculated straight l i n e , we would expect any one fi r m w r i t i n g a p a r t i -cular volume of a l i n e of insurance to have a corresponding expense f a c t o r as read from the I - axis s i x t y eight out 6 of a hundred times. I f we take two standard errors of e s t i -mate, we expect that ninety-three times out of one hundred that the departure of t h i s observation from the true value w i l l not be larger than the confidence Interval just c a l -culated. Returning b r i e f l y to the concept that the standard error of estimate was s i g n i f i c a n t l y larger than the "a" values calculated from the p a r t i c u l a r regression equations, the following statements Indicate the lack of any economies or diseconomies of scale. Since bur confidence i n the ab-solute value of the constant i s determined largely by the r e l a t i v e size of the standard error of estimate; and the standard error of estimate i s from four to twenty times greater than the constant f o r a l l expense categories, there i s therefore no more reason to suspect that there i s either a consistent upward or downward bias of the standard error of estimate i n expressing confidence l i m i t s f o r "a" at the Y - a x i s . Hence the only conclusion that appears tenable i s that, there are no major, economies or diseconomies of scale. °This applies to a company w r i t i n g one l i n e of insur-ance, however, an extension into n dimensions i s possible by the use of algebra. 59 I t i s Important to r e a l i z e that the foregoing con-clusion shows the long run s i t u a t i o n . Thus the equations that describe the relationship between t o t a l expenses and premium volume picture a firm on the long run marginal cost curve. I t i s recognized that a p a r t i c u l a r firm may at some time not be on the long run marginal cost curve. A new firm entering into the business w i l l Incur costs i n i t s early years, that could exceed the Industry average. For instance, i n order f o r a firm to break into the market and obtain a large enough share, i t may have to o f f e r commission rates f a r above the Industry •norm1.-' Even e x i s t i n g firms may f i n d themselves temporarily incurring costs that are higher than expected. This may occur when mechanization of pro-cedures could reduce the overhead expenses now incurred through manual labour. Another area where economies or diseconomies might occur i s In ' t i e - i n ' business. Certain l i n e s of i n -surance are cheaper to underwrite and administrate i f com-bined, so that t o t a l costs would be much greater i f these l i n e s were written separately. Such a grouping Is Indicated i n t h i s study f o r certain l i n e s of insurance, but not f o r automobile. This grouping appears to have significance f o r 5Transerlpt, R.C.A.I., Volume 33, pp. 364-6-47. ^Recall that some of the I n i t i a l independent variables included i n the study tabulated In Appendix A, Table I I , were aggregated i n Table I I I , Appendix A. 60 those Insurance companies who write l i n e s of insurance that are included i n the aggregations. The actual benefits derived from w r i t i n g these aggregated l i n e s of Insurance as opposed to w r i t i n g each l i n e separately i s impossible to establish from t h i s study. However a company that writes only auto-mobile insurance does not appear to be at a p a r t i c u l a r ad-vantage or disadvantage i n terms of such t i e - i n underwriting with other l i n e s of insurance.? The argument has been advanced that the use of auto-mation, s p e c i f i c a l l y computerized, operations, would r e s u l t Q i n s i g n i f i c a n t cost savings. This r e s u l t would only occur i f computers came i n only a few sizes and involved a high c a p i t a l expenditure. However, the combination of various computer sizes and costs probably allow f l e x i b i l i t y i n deter-mining whether mechanization would be cheaper at a p a r t i c u l a r volume of business than manual labour. Rental of machine time on a part-time basis plus pooled arrangements also allow the use of more e f f i c i e n t data processing at a l l levels of o operations regardless of the size of the corporation.' One area which may y i e l d s i g n i f i c a n t economies of scale f o r a very large f i r m could r e s u l t through horizontal integration. Automobile insurers could, f o r example, esta-?Even i f the industry were unaware of such cost savings by t i e - i n underwriting, the s t a t i s t i c a l r e s u l t s would have shown a high c o r r e l a t i o n c o e f f i c i e n t between automobile Insurance and any other l i n e of insurance. No such correla-t i o n was found. 8 T r a n s c r l p t R.C.A.I., Volume 33 pp. 3852-53. 9lbid., Volume 48, pp. 5597, 5612. 6 1 b l l s h t h e i r own repair shops f o r automobiles. 1 0 A possible cost saving might occur through the elimination of at least one claims adjuster from either the repair shop or rrom the company. Other areas f o r cost savings may arise i n terms of further d i v e r s i f i c a t i o n i n the future when the volume of business written becomes large enough to support the additional f a c i l i t i e s on an economical basis. In t h i s respect i t i s expected that these horizontal integration movements would appear f i r s t In the United States where both volume and 11 market concentration are s i g n i f i c a n t l y higher than i n Canada. The r e s u l t s or t h i s study are based on Canada-wide expense experience and insurance volume. Thus the extent to which economies of scale e x i s t at the p r o v i n c i a l l e v e l i s a matter of argument. I t appears that due to the f l e x i -b i l i t y i n the methods employed to market the product that no economies of scale would r e s u l t In these operations. 1 2 A l l data and information i s e a s i l y transported to a central headquarter established anywhere i n the country where normal business concentrates. Market size and concentration may be a l i m i t i n g factor when w r i t i n g on a p r o v i n c i a l basis, so that the market i s only large enough to support the opera-t i o n of one insurer. I f a second insurer entered, both would l 0 I b l d . , Volume 33, pp. 2850-51 1 : L I b l d . , Volume 7, pp. 776-79$ Volume 4b. pp. 5 6 I 3 , 1 2 I b i d . , Volume 16, pp. 1983-84; Volume 48, p. 5597, Volume 5b, p. 6587. 62 Incur a higher expense r a t i o . Thus a case ror a regional monopoly regulated by the province -co Insure appropriate rates may he made. In general, however, i f a market i s not large, chances of claims w i l l be reduced accordingly and claim expenses r e l a t i v e l y low. Thus I t i s not expected that any economies of scale e x i s t at the p r o v i n c i a l l e v e l . Thims, the conclusion that there are no economies of scale follows from the lack of i n d i v i s i b i l i t i e s of scale, with no major outlays required to operate an insurance busi-ness other than the minimum required to obtain a large enough and d i v e r s i f i e d experience so that one bad loss w i l l not bankrupt the c o r p o r a t i o n . ^ Although some firms w i l l reach a size where mechanization of procedures becomes f e a s i b l e , t h i s i s neither a handicap to small operations nor an ad-vantage to large ones. 1 4 . In the above discussion, i t must be remembered that this i s the long run s i t u a t i o n that the study measures, so that i t i s possible ror any one r i r i a to temporarily have r i s i n g or f a l l i n g marginal costs. Comparison of American Expense Ratios  with the Canadian S t a t i s t i c a l  Results The remainder of t h i s chapter w i l l be devoted to a substantiation of the conclusion based upon Canadian data 13Transcript R.C.A.I. Volume 4b", pp. 5594-96. 1 4 I b i d . , p. 5597. 63 that there are no economies of scale i n the operation of automobile insurance. A comparison of the American auto-mobile expense factors with the Canadian counterparts suggests that the American commission rates are double those or Canada, while t h e i r general expense factor i s s i g n i f i c a n t l y lower. The argument has been proposed that the explanation resides i n the economies of scale of the American experience. The argument suggests that because the volume written by American companies i s so large, economies i n automation must be re-f l e c t e d i n lower t o t a l expense r a t i o s f or the very large f i r m s , 1 5 The following table i l l u s t r a t e s the comparison between Canadian expense r a t i o s and American expense r a t i o s . TABLE IV COMPARISON OF CANADIAN AND U.S.A. EXPENSE RATIOS . • '• " U.S. Stock Companies F i r e , Expense Item Canadian B.I. P.D. Other Thert A i l Coverage L l a b l l i t y L i a b l l i t y & Compre-" hensive Taxes (W) .0197 .033 .031 .127 .12b Commissions (W) .075« .150 .156 .183 .177 Other Acqulsltions(E) ,0013 .049 .051 .048 .051 General Expenses (E) .l?9b ±251 .063 .•0.^8 .061 • 2966 ai21 .301 .316 .317 Source of U.S. Data: I965 Loss and Expense Ratios, New York Insurance Department. 1 5 l b i d ., Volume 16, pp. 1983-B^ 64 The above expense r a t i o s should only be used to com-pare r e l a t i v e magnitudes since the American values are supplied through standard a l l o c a t i o n procedures, and may not r e f l e c t actual experience i f the same s t a t i s t i c a l procedures outlined i n Chapter I I I were used. The reader should be aware of t h i s shortcoming. However, i t i s f e l t that the conclusions w i l l not be affected. The data contained i n the above table shows the expense r a t i o s f o r bodily injury l i a b i l i t y ; property damage l i a b i l i t y ; other coverage; and f i r e , t h e f t , and compre-hensive f o r the U.S. stock companies, which are roughly com-parable to the majority of corporations w r i t i n g automobile insurance i n Canada. The expense items l i s t e d include taxes and commission expense r a t i o s as a percent of net premiums written ( W ) and other acquisitions and general expenses as a percent of net premiums earned (E). The Canadian figures are drawn from Tables I I , I I I , IV and V, where net p r o f i t commissions are roughly the equivalent of other a c q u i s i t i o n s . 1 0 Ignoring the d i f f e r e n t tax effect s , I t Is seen that the four categories of coverage l i s t e d i n the American r a t i o s can now be compared with the Canadian r a t i o s . Although t o t a l expense r a t i o s are roughly s i m i l a r , the d i s p a r i t y appears i n commissions paid to the American agents as compared with the Canadian counterpart. The l a t t e r obtaining approximately half of the former In commissions. Even i f we allow that 1 6Appendix B. 65 some of the other a c q u i s i t i o n costs included i n the American experience Is probably r e f l e c t e d i n the Canadian general expense r a t i o , s t i l l the results show that the general expense r a t i o f o r the Canadian corporations i s about double that of t h e i r American counterpart. The conclusion reached i s that the Canadian companies are le s s e f f i c i e n t i n the administration of automobile i n -surance i n Canada. There i s of course the p o s s i b i l i t y that there are economies of scale involved i n w r i t i n g automobile insurance i n the United States because of the tremendous volume written. To test t h i s l a t t e r hypothesis, a simple regression study was designed to test the p o s s i b i l i t y of the inverse relationship between size of automobile Insurance premiums earned and the expense r a t i o s incurred. The results are found i n Appendix C, Table I to IV. Por each class of Insurance, bodily injury l i a b i l i t y , property damage l i a b i l i t y , c o l l i s i o n and f i r e , theft and comprehensive, net premiums earned was designated the 'de-pendent variable', r e f l e c t i n g the absolute size of the firm. Within each class the 'independent variable' was i n turn: general expenses, other a c q u i s i t i o n s , the sum of these two, and the sum of the two plus commissions and brokerage. The resul t s f o r a l l of the simple regressions calculated from 125 stock companies based on countrywide experience indicated that there were no major economies or diseconomies of scale present. In every instance the standard error of 66 estimate was from twenty to one hundred percent larger than the corresponding value f o r the constant. Further proof that there was l i t t l e or no relationship between the v a r i -ables measured i s indicated by the F - r a t i o s calculated f o r each simple regression. None of the "b H values were s i g n i f i c a n t l y d i f f e r e n t from zero at the f i v e percent l e v e l of confidence. A word of caution i s necessary with respect to Inter - r pretation of the data contained i n Tables I to IV of Appendix C. I f an absolute i n t e r p r e t a t i o n of the simple equation Y = a + vX^ i s required, then a l l the figures of the columns headed by the "standard error" and the "constant" should be m u l t i p l i e d by one thousand, and the figures under the column headed by "regression c o e f f i c i e n t " divided by one hundred. These changes do not af f e c t the conclusions reached and were only recorded i n t h i s manner to f a c i l i t a t e easier coding f o r the computer. Recall also that none of the regression c o e f f i c i e n t s were s i g n i f i c a n t at the f i v e percent l e v e l ; hence, the equations represented are not of predictive value at a l e v e l of confidence high enough to warrant further attention. 67 Summary Two s e p a r a t e s t u d i e s have been used t o d e t e r m i n e w h e t h e r any economies o f s c a l e a r e p r e s e n t i n w r i t i n g a u t o -m o b i l e i n s u r a n c e . N e i t h e r t h e Canadian d a t a n o r t h e Amer i can d a t a s u g g e s t s t h a t any economic advan tage w o u l d be d e r i v e d f r o m p l a c i n g a l l t h e a u t o m o b i l e I n s u r a n c e b u s i n e s s i n t h e hands o f a s i n g l e c o r p o r a t i o n . T h i s does n o t mean t h a t c e r t a i n s o c i a l b e n e f i t s w o u l d n o t a c c r u e t o s o c i e t y , i t o n l y answers t h e q u e s t i o n t h a t i f t he I n s u r a n c e was p l a c e d w i t h a s i n g l e c a r r i e r , no r e d u c t i o n i n t h e t o t a l e x p e n d i t u r e s o f b o t h a d -m i n i s t r a t i v e and a l l o c a t e d c l a i m s c o s t s w o u l d r e s u l t . Thus b a r r i n g non-economic t e r m s o f r e f e r e n c e , t h e p r e s e n t m i x o f many i n d e p e n d e n t i n s u r a n c e companies i s as e x p e n s i v e as a s i n g l e l a r g e o p e r a t i o n . CHAPTER VI SUMMARY AND CONCLUSIONS In chapter I I the appropriateness of applying the trend f a c t o r to both the loss cost and expense fa c t o r In developing new rates was questioned. The successive reduc-tions i n the expense factor loading as a percent of gross premiums meant either that expenses did not vary d i r e c t l y with the size of premium or i t was already too large and any further increase would be d i f f i c u l t to j u s t i f y . The reductions were probably as much a re s u l t of an i n t u i t i v e f e e l i n g by the ra t i n g agency that the expense factor may have been too high, as much as competitive pressures by the i n -dependents, even though the l a t t e r depended heavily f o r t h e i r rate making procedures on the rating agency of the C.U.A. The r e s u l t s of Chapters IV and V indicated that the general equation used i n estimating the expense loading factor was l i n e a r . Thus the marginal costs of wr i t i n g i n -surance are constant, and w i l l also represent a constant factor of gross premiums. This r e s u l t , although obtained from a single year's data, does represent the underlying relationship between the expense factor and gross premiums. Hence the trend factor can be applied to both the loss cost and expense component of gross premium, provided the current expense loading i s v a l i d . This i s not to say that the ex-pense factor of 28 percent developed from the I964 data b9 should remain at that l e v e l forever. I f at any time changes occur In some of the basic cost expense relationships such as Increased cost of stationery or unionization of c l e r i c a l help, these allowances must be made i n subsequent rate making' decisions as I t applies to the expense factor. Comparison or the expense factor loading used by the C.U.A. s t a t i s t i c a l agency and that derived from t h i s study using 1964- data I l l u s t r a t e s that the decrease i n the expense factor from 37 to 33 was In effect j u s t i f i e d , and that a further reduction to 30 percent could be achieved. Hence a 70/30 loss-cost r a t i o would not appear to provide undue hardships f o r companies engaged i n automobile insurance. The actual breakdown of the expenses depends to a large extent on the commission remuneration structure employed, which b a s i c a l l y represents the d i f f e r e n t methods of marketing the product. The study Indicated what the industry average commission was, and how to adjust the general expense factor to allow f o r d i f f e r e n t rates of commission. Knowing what the expense factor i s has the added benefit of being able to determine how any one p a r t i c u l a r firm compares with the rest of the Industry. The conclusions reached i n Chapter V indicated that there were no s i g n i f i c a n t economies of scale present In wri t i n g any l i n e of Insurance, i n p a r t i c u l a r automobile i n -70 surance. Thus the implication i s that no one c a r r i e r would he able to achieve a lower o v e r a l l expense factor because of the structure of technology required. There are no i n d i v i s i -b i l i t i e s of scale, no large input factors of a scarce nature required. Thus the expense factors can be used as standards to determine whether the firm i s on the long run marginal cost curve. Hence management w i l l be able to determine the optimum point of e f f i c i e n c y and scale of manpower Inputs as opposed to c a p i t a l Intensity. In order to f a c i l i t a t e future expense factor loading calculations as a percent of gross premiums, the submission of industry expense and premium data should be on standard punch cards so that they may be used f o r both the publishing of the data, as i s now required f o r the annual reports, and also allow the c a l c u l a t i o n of up to date marginal expenses f o r a l l l i n e s of insurance, and not just automobile insurance. Once the computer programme has been written, the information that r e s u l t s w i l l be obtainable annually at very l i t t l e cost. In addition to the study of the Canadian data presented i n t h i s t h e s i s , i t would appear f r u i t f u l i f the American data were subjected to the same type of analysis to determine whether there i s any difference i n experience or whether i t substantiates the data presented here with respect to expense fa c t o r loading. A crude comparison was presented i n Chapter V; however, a detailed comparison would require further 71 refinements. In t h i s study the data u t i l i z e d covered only the period of the one year 1964 hence the allowance f o r underlying changes over time with respect to the expense factor In the past may provide ad d i t i o n a l information to base future rate making decisions on. In t h i s sense the study may be l i m i t e d In i t s usefulness to provide predictive information f o r the future as productivity Increases may accure to the industry over time. The extent to which the foregoing comments i n -fluence the v a l i d i t y of the conclusions i s at t h i s time not f e l t to be severe as the difference between the s t a t i s t i c a l r e s u l t s of t h i s study and the present expense factor loading are s i g n i f i c a n t l y d i f f e r e n t from each other as shown by the l e v e l of significance and confidence l i m i t s presented i n Chapter IV. This thesis has mainly been concerned with evaluating phe adequacy or the expense factor used by the C.U.A, i n developing automobile insurance premiums. Through analysis or industry-wide data, an industry average expense loading or approximately 2b to 30 percent was round to be adequate to write automobile insurance business. Although such an expense loading would be adequate f o r the Industry i n aggregate, i t may not r e f l e c t accurately the expense experience or In-d i v i d u a l companies. Thus f o r some the expense loading would be adequate, while ror others they might be wholly inadequate. 72 These differences could a r i s e out of marketing procedures employed, breadth of market engaged In, and length of time the company had been i n the business. In addition to the short-coming of t h i s Industry average approach Is the continued problem of deciding at which point gradation of expense factors i s warrented. 1 At present studies have indicated that a f i x e d expense percentage as opposed to a f i x e d d o l l a r amount of premiums written i s appropriate f o r r i s k s up to $1,000. Since automobile premiums f o r private passenger business Is nowhere near t h i s at present, the percent loading or v a r i a -t i o n appears appropriate. I t may thus be f e l t that Instead of producing a com-prehensive loss-cost formula f o r developing rates, expenses be determined by each company separately. Thus expected losses could be developed according to the i n d i v i d u a l company's experience, and the expense fa c t o r would be wholly determined by competitive factors e x i s t i n g at any time i n the industry. This l a t t e r method allows i n d i v i d u a l corporate judgment.to e x i s t , perhaps even at the branch l e v e l of large integrated corporations, to meet the current and l o c a l conditions e x i s t i n g i n the market. The r e s u l t i n g competition would probably Increase the e f f i c i e n c y of the industry as a whole, and l.This. comment, and those, that follow i s developed i n the Commonwealth of Vlrglnnla Report of Aotvarles by Woodward and F o n d i l l e r , Inc., August 1966, pp. 8,10,13»l4,16*,ia,27, 28,51-55; Appendix pp. 3,9,19,20,22-26. 73 place an added premium on expense reducing innovations. This l a t t e r method thus would probably be more equitable to a l l companies w r i t i n g automobile Insurance since they would not be r e s t r i c t e d by a perhaps a r t i f i c i a l expense formula. In conclusion then i t may be stated with confidence that i f the formula approach to rate making was continued, the loss-cost r a t i o could be reduced to 70/30 thus decreasing the expense loading factor another three per cent from i t s 1966 l e v e l . I t Is also f e l t that no reduction In t o t a l expenses Incurred could be effected by l e t t i n g a single c a r r i e r or agency operate automobile insurance i n Canada. If the automobile insurance business i s to be taken over by public administration, the reasons w i l l be other than a reduction i n operating expenses. BIBLIOGRAPHY 75 BIBLIOGRAPHY Canadian Underwriters* B r i e f , presented to the Royal Commission on Automobile Insurance, June 1966. Commonwealth of Vlrglnnia Report of Actuaries, A Report Prepared by Woodward and F o n d i l l e r , Inc., August l9bb. Croxton, F.E., and Cowden D.J. Applied General S t a t i s t i c s . New York: Prentice-Hall, 1939. E z e k i e l , M., and Fox, K. Methods of Correlation and Regression Analysis. New York: John Wiley & Sons Inc., 1963, 3rd e d i t i o n . Henderson,. J.M., and Quandt, R.E., Mlcroeconomlc Theory; A Mathematical Approach. New York: McGraw-Hill,195b, Meyer, J.R., Peck M.J., Stenason, J , , and Zwi.ck,. C. Economics  of Competition i n the Transportation Industries; Cambridge, Mass.: Harvard University Press, 1964. Report of the Royal Commission on Automobile Insurance. Nova Scotia, 1957. Report of the Superintendent or Insurance ror Canada, Annual Statements - F i r e and Casualty Insurance, Ottawa: Queen's P r i n t e r , 1965. Report on Automobile Insurance Premium Rates, Ontario: King's P r i n t e r , 1930. R e s t r i c t i v e Trade Practices Commission: Concerning the Business or Automobile Insurance In Canada, Ottawa: Queen's Pr i n t e r , i960. Richmond, S.B,, S t a t i s t i c a l Analysis. New York: Ronald Press Co., 1964. 2nd e d i t i o n . Submission of the Insurance Bureau or Canada to the Royal Commission on Automobile Insurance, November I966. Transcript, Royal Commission on Automobile Insurance or B r i t i s h Columbia 1966-67. APPENDIX A 7 7 TABLE I Name DEPENDENT VARIABLES ( - EXPENSE CATEGORIES) Y l Net adjustment expenses Incurred Y2 Net commissions incurred Y 3 Net p r o f i t commissions Incurred \ Taxes incurred (other than on income and r e a l estate) h General expenses incurred Y6 Bad debts J 7 Salaries Y8 Agents' allowance s Y 9 Contributions to s t a f f pensions and insurance plans Y10 Unemployment and other s o c i a l insurance contributions Y l l Directors' fees Y12 Auditors' fees Y 1 3 Management remuneration Y14 Advertising Y 1 5 Books and periodicals Y16 Bureau and Association dues Y 1 7 -j Y18 Charitable donations Y 1 9 Inspections and Surveys Y20 Insurance other than insurance on r e a l estate Y21 Legal expense Y22 Maps and plans Y 2 3 Medical examiners' fees Y24 Mercantile agencies' reports DEPENDENT VARIABLES ( - EXPENSE CATEGORIES) Office furniture and equipment Postage, telegrams, telephones and express P r i n t i n g and stationery-Rents S t a t i s t i c a l bureau expenses Tra v e l l i n g expenses Other Expense allowance assumed (+) Expense allowance ceded (-) Expense allowance to company Miscellaneous expense ( i . e . those not covered above) 79 TABLE I I Name INDEPENDENT VARIABLES ( - CLASS OF INSURANCE) X i FJire X 2 Personal Property X3 Real Property X ^ Inland Transportation X5 Theft X$ B o i l e r - h o l l e r Xr? B o i l e r - machinery Xg Plate glass X Q Credit X ^ Q Guarantee - f i d e l i t y X±l Guarantee - surety X 1 2 L i a b i l i t y - public l i a b i l i t y X13 L i a b i l i t y - employers' l i a b i l i t y Xi4 Personal accident and sickness - Group X ^ Personal accident and sickness - Individual -cancellable X16 Personal accident and sickness - Individual -non-cancellable X ^ Automobile - l i a b i l i t y X^g Automobile - other X 1 Q A i r c r a f t - l i a b i l i t y X 2 0 A i r c r a f t - other 20 X 2 i Miscellaneous category = (Total Insurance - ^jT x , ) 1=1 1 bo TABLE I I I NEW CLASS CLASS OP INSURANCE ORIGINAL INDEPEN-DENT VARIABLES X, ' 4 Xb Xo X 1 0 X l l F i r e ; Personal Property; Theft; Plate Glass; Public l i a b i l i t y . B o i l e r - b o i l e r ; B o i l e r - machinery Real property Inland Transportation Credit Guarantee-fidelity; Guarantee-surety Empl o y e r s - l i a b i l i t y Personal Accident/sickness - group Personal Accident/sickness -in d i v i d u a l Cancellable; Non-cancellable Auto - l i a b i l i t y : Auto - other A i r c r a f t - l i a b i l i t y ; A i r c r a f t - other Xi+X 2+X5*X5+X 1 2 x6+x7 A 4 *9 X 1 0 + X 1 1 x 1 3 1 4 x 1 5 + x 1 6 x 1 7 + x 1 8 x l 9+x 2 0 12 Miscellaneous "21 APPENDIX B 82 TABLE I NET ADJUSTMENT EXPENSES INCURRED REGRESSION COEFFICIENT LINE OF INSURANCE N p w N P E N C I F i r e ; Theft; Personal Property; 0.0363** 0 .0309 ' * 0.0736** Plate glass; Public l i a b i l i t y (0.0028) (0,0029) (0.0047) B o i l e r - b o i l e r ; Boilers-machinery Real property Inland transportation Credit -0 .0117** l . l i o l * * (0.0020) (0.3020) Guarantee-fidelity 0.0378* 0,0384* 0.0807** Guarantee-surety (0.0153) (0.0172) (0.0301) E m p l o y e r s * - l i a b i l i t y Personal Accident/sickness 0.0101** O.OllO** 0.015b -group (0 .0032) (0.0033) (0 .0036) Personal Accident/sickness Individual-cancellable " -non-cancellable A u t o m o b i l e - l i a b i l i t y 0.0212** 0.0269** 0.0326** " -other (0,0016) (0.0018) (0 .0019) A i r c r a f t - l i a b i l i t y -0 .0937* " -other (0.0456) Miscellaneous R 2 0,7709 0.7^ -55 0.8237 a 13.4407 13.2317 9.0353 SY 52.7151 52.4602 46.4012 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l notes figures i n brackets represent standard error of re-gression c o e f f i c i e n t 63 NET COMMISSIONS INCURRED LINE OF INSURANCE TABLE I I REGRESSION COEFFICIENT F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y B o i l e r - b o i l e r ; Bo i1er-machlnery Real Property Inland transportation Credit Guarantee-fidelity Guarantee-sure ty Em p l o y e r s ' - l i a b i l i t y Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable A u t o m o b i l e - l i a b i l i t y -other A i r c r a f t - l i a b i l i t y -other Miscellaneous R* a SY NPW 0 . 3 2 7 2 " (0 . 0 1 2 0 ) 0.1695** (0.0633) 0.2856** (0,0643) 0.0647«* (0.0147) 0.1745** ( 0 . 0 1 3 3 ) 0.0758** (0.0066) 0.8975 5.4467 221.9650 NPE 0,2761 (0.0152) 0.2841** (0.0532) 0.1884** (0.0493) 0.3153** (0.0924) 0.1852* (0.080b) 0.0603** (0.0183) 0.2063** (0.0247) 0.1057** (0.0094) 0.4249** (0.1443) 0.1?99** (0.0281) 0.6224 14.9955 277.4401 NCI 0.5579** (O.0254) O.4.760 * (O.2296) 3.9&04* (1.6488) -3.9432* (1.58bl) 0.5614** (0.1&55) 0.0694** (0.0202) 0 . 3 H 6 * * 0.0257 0.1464** (0.0102) 0.6774 -0.3303 243.5902 • Denotes sfignlfigant at 5$ l e v e l • • Denotes s i g n l f i g a n t at 1% l e v e l note: figures in, brackets represent standard error of regression c o e f f i c i e n t 84 TABLE I I I NET PROFIT COMMISSIONS INCURRED LINE OF INSURANCE REGRESSION COEFFICIENT NPW NPE NCI F i r e ; Theft; Personal Property; 0.0070** 0.0085** 0.0116** Plate glass; Public l i a b i l i t y (0.0007) (0.0006) (0.0012) B o i l e r - b o i l e r ; -0.0059* Boiler-machinery (0.0023) Real Property Inland Transportation Credit Guarantee-fidelity -0.0179* Guarantee-surety (0.0076) Empl o y e r s - l i a b i l i t y 0.0265* 0.0492** (0.0130) (0.0157) Personal Accident/siclmess 0.001b* 0.0020-* 0.0019* -group (0.0007) (0.0007) (0.0009) Personal Accident/sickness Individual-cancellable -non-cancellable A u t o m o b i l e - l i a b i l i t y 0.0009* 0.0013** 0.0025** -other (0.0003) (0.0004) (0.0005) A i r c r a f t - l i a b i l i t y 0.03^ 4** -other (0.0116) Miscellaneous 0.0010** (0.0002) R 2 0.5356 0.5896 0.5549 a 0.5115 -0.2621 -O.0274 SY 11.7378 10.9016 11.5332 • Denotes s l g n i f l g a n t at 5% l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE IV 85 TAXES INCUREED LINE OP INSURANCE F i r e ; Theft; Personal Property-Plate glass; Public l i a b i l i t y B o i l e r - b o i l e r ; Boiler-machinery Real Property Inland transportation Credit Guarant e e - f i d e l l t y Guarant e e-sure ty Emp l o y e r s - l i a b i l i t y Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable A u t o m o b i l e - l i a b i l i t y -other A i r c r a f t - l i a b i l i t y -other Miscellaneous E 2 a S I REGRESSION COEFFICIENT NPW 0.0278** (0.0013) 0.0276 (0.0071) 0.0357** (0.0072) 0.0224** (0.0017) 0.0225** (0.0015) 0.0197** (0.0007) 0.9307 3 . 3 W 25.0103 NPE 0.0224** (0.001b) 0.0184* (0.0072) 0.0267** (0.00b2) 0.027b** (0.0040) 0.0326** (0.0092) 0.0195* (0.0060) 0.0207** (0.0018) 0.0224** (0.0025) 0.0257** (0.0009) 0.0222** (0.0021) ' 0.9037 3.b207 27.8748 NCI 0.0466** (0 .0019) 0.0877** (0.0174) 0.0636** (0.012b) 0.0286** (0 .0015) 0.0427** (0 .0019) 0.0333** (0.0008) 0.079b** (0.0283) 0.9624 1.8013 18.4554 • Denotes s i g n i f l g a h t at 5% l e v e l ••Denotes s i g n i f l g a n t at 1% l e v e l Note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE V GENERAL EXPENSES INCURRED LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y B o i l e r - b o i l e r ; Boiler-machinery Real property Inland transportation Credit Guarantee-fidelity Guarantee-surety E m p l o y e r s 1 - l i a b i l i t y Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable A u t o m o b i l e - l i a b i l i t y -other A i r c r a f t - l i a b i l i t y -other Miscellaneous R 2 a SY REGRESSION COEFFICIENT NPW 0.1160" (0.0139) 0.4465" (0.0665) 0. 14-05* (0.0676) 0.9868** (0.2608) 0.0945** (0.0153) 0.2083** (0.0139) 0.1598** (0,0069) 0.8824 29.0285 231.6124 NPE 0.1031** (0.0169) 0.37&5** (0.0802) 0.3382** (0.0689) 0.1210** (0,0443) 0.7316** (0,0892) 0.0874** (0.0205) 0.2067** (0.0277) 0,1998** (0.0105) 0.1526** (0.0236) 0.7665 26.8998 311.0469 NCI 0.2323" (0.0228) 1.5434-* (0.2076) 1.3393** (0.3099) 0.1198** (0.0190) 0.3770** (0.0241) 0.2470** (0.0094) 0.8846 20.8148 229.2430 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE VI 8 7 BAD DEBTS LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y B o i l e r - b o i l e r ; Boiler-machinery Real property Inland transportation Credit Guarantee-fidelity Guarantee-surety Em p l o y e r s - l i a b i l i t y Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable A u t o m o b i l e - l i a b i l i t y -other A i r c r a f t - l i a b i l i t y -other Miscellaneous R 2 a SY REGRESSION COEFFICIENT NPW 0 . 0 0 5 7 * * (0.0008) 0 . 0 0 7 8 * * ( 0 . 0 0 2 6 ) 0.0014 (0.0002) 0 . 3 5 2 1 0 . 1 3 8 7 2 . 7 9 9 7 NPE 0 . 2 6 2 5 ( 0 . 0 2 9 9 ) 0 . 2 0 3 7 -1.8049 113.2626 NCI 0.0006* ( 0 . 0 0 0 3 ) 0.0146** (0.0041) 0 . 0 0 2 3 # * ( 0 . 0 0 0 3 ) 0 . 2 1 0 9 0.2140 3 . 0 8 9 7 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note; figures In brackets represent standard error of regression c o e f f i c i e n t TABLE VII TOTAL EXPENSES INCURRED LINE OP INSURANCE REGRESSION COEFFICIENT NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.5032** (0.0200) 0,4340#* (0.0295) 0.9011** (O.O369) B o i l e r - b o i l e r ; Boiler-machinery 0.6194** (0.0953) 0.4187** (0,1356) 2.0605** (O.3252) Real Property 6.3204** (2.3431) Inland transportation 0.6241** (0.1166) Credit 0.2475" (0.0750) Guarantee-fidelity Guarante e-sure ty 0.4-9 26" (0.0969) 0.554-3** (0,1728) 0.6612** (0,2368) E m p l o y e r s ' - l i a b i l i t y 1.5630 (0.3736) 1.2032** (0.1508) 1.9657** (0.4732) Personal Accident/sickness -group 0* I.925 •* (0.0220) 0.1665** (0.03^7) 0.2530 •• (0.0286) Personal Accident/sickness Individual-cancellable -non-cancellable 0.4-0 50 (O.OI99) 0.4396** (0.0469) 0.7335** (0.03&3) A u t o m o b i l e - l i a b i l i t y -other 0,2770** (0.0099) 0.3590** (0.0179) 0,4596** (0,0l42) A i r c r a f t - l i a b i l i t y -other Miscellaneous 0.3090** (0.0399) R 2 0.9512 0.8698 0.9477 a 55.71B1 63.6666 30.2802 SI 332,1161 525.9969 344.4602 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t 89 TABLE VIII SALARIES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0749" (0.0124) 0.0838** (0.0108) 0.1505** (0.0197) B o i l e r - b o i l e r ; Bo11er-machinery 0.2925** (0.0423) 0.2945** (0.0370) 1.0233** (0.1412) Real property -0.1b61 (0.8413) -0.9913 (0.6686) 1.2780 (1.0256) Inland Transportation 0.032b (0.1857) 0.0575 (0.1619) -0.4752* (0.1984) Credit 0.460l (0.24b?) 0.3512 (0.2007) 1.3543 (O.9749) Guarantee-fidelity Guarante e-sure ty 0.0665 (0.0430) 0.0848 (0.0425) -0.0578 (0.1038) E m p l o y e r s - l i a b i l i t y 0.7536** (0.1688) 0.6216** (0.1508) 0.8941** (0.2083) Personal Accident/sickness -group 0.0612** (0.0097) 0.0579** (0.0086) 0.0779** (0.0124) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0958** (0.0088) 0.1007** (0.0079) 0.1716** (0.0157) A u t o m o b i l e - l i a b i l i t y -other 0.0840** (0.0047) 0.1023** (0.0045) 0,1321** (0.0063) A i r c r a f t - l i a b i l i t y -other -0.0693 (0.1287) -0.0471 (0.1141) 0.0117 (O.I532) Miscellaneous 0.0408 (0.1277) 0,0576 (0,1189) 0.1730 (0.2342) R 2 0.858 0,691 0.853 a 0.238 -13.409 -4,965 SY 146.943 128.315 149.414 • Denotes s l g n l f l g a n t at % l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE IX AGENTS' ALLOWANCES REGRESSION COEFFICIENT. LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0009 (0.0013) 0,0011 (0,0013) 0.0001 (0.0020) B o i l e r - b o i l e r ; Bo1ler-machlnery -0.0004 (0.0046) -0.0004 (0.0046) 0.0000 (0.0146) Real property -0.0528 (0.0914) -0.0520 (0.0828) -0.0449 (0,1060) Inland Transportation -0.016? (0.0202) -O.OI78 (0,0200) -0.0110 (0.0205) Credit -O.OO57 (0.0268) -0.0057 (0.0248) -0.0886 (0,1008) Guarantee-fidelity Guarantee-surety -O.OOI3 (0.0047) -0.0018 (0.0053) -O.OO5O (0,010?) Emp l o y e r s - l i a b i l i t y -O.O250 (0.0183) -0,0286 (0.018?) -0,0217 (0.0215) Personal Accident/sickness -group -0,0001 (0.0011) -0,0004 (0,0011) -0,0011 (0,0013) Personal Accident/sickness Individual-cancellable -non-cancellable 0,008?»« (0.0010) 0.-009-1** (0.0010) 0.0172-' (0.0016) Au t o m o b i l e - l i a b i l i t y -other 0.0006 0,0005 0.0011 (0.0006) 0,0017* (0.0007) A l r c r a f t r - l l a b i l l t y -other -0.0086 (0.0140) -0.0084 0.0141 -0,011? (0,0158) Miscellaneous -O.OOI3 (0.0139) ^0.0023 (0.0147) -0.0067 (0.0242) R 2 0.258 0.266 0.306 a 0.506 0.271 0.423 SY 15.972 15.665 I5.444 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE X CONTRIBUTIONS TO PENSION AND INSURANCE PLANS LINE OP INSURANCE REGRESSION COEFFICIENT NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y -0.0019 (0.0014) -0.0021 (0.0014) -0.0033 (0.0021) B o i l e r - b o i l e r ; Bo i l e r-machlnery 0.0 2?7" (0.0049) 0.0282** (0.0048) 0.0798** (0.0147) Real property -O.ObbS (0,0983) -0.0477 (0.0665) -0.1450 (0.1067) Inland Transportation -0.0032 (0.0217) -0.0053 (0.0209) 0.0142 (0.0206) Credit 0.0688* (0.0288) 0.0568* (0.0260) o,4l95 , # (0.1014) Guarantee-fidelity Guarantee-surety 0.0187** (0.0050) 0,0195** (0.0055) 0.0449•• (0.0108) E m p l o y e r s ' - l i a b i l i t y 0.0469• (0.0197) 0.0390 (0.0195) 0.103b*• (0.0217) Personal Accldent/slclmess -group O.OO27 (0.0011) 0.0024 (0.0011) 0.0032 (0.0013) Personal Accldent/slclmess Individual-cancellable -non-cancellable 0.0057* (0,0010) 0.0061* (O.OOlO) 0.0105* (0.0016) A u t o m o b i l e - l i a b i l i t y -other 0.0063** (0.0005) 0.0076** (0.0006) 0.0088** (0.0007) A i r c r a f t - l i a b i l i t y -other -0.0250 (0.0150) -O.0250 (0.0148) -0.0349* (0.0159) Miscellaneous 0.0521** (0,0149) 0.0572** (0.0154) 0.0669** (0.0244) R 2 0.590 0.617 0.bb4 a 0.235 -0.369 0,782 SY 17.172 16.596 15.540 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l notes figures i n brackets represent standard error of regression Coefficient TABLE XI UNEMPLOYMENT AND OTHER SOCIAL INSURANCE CONTRIBUTIONS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Inert; Personal Property; Plate glass; Public l i a b i l i t y 0.0006** (0.0001) 0.0008** (0.0001) 0.0014** (0.0002) B o i l e r - b o i l e r ; Boiler-machinery 0.0010 • (0,0004) 0.0010** (0.0003) 0.0033## (0.0012) Real property 0.0027 (0,0076) -0.0067 (0.0060) 0.0031 (0.0086) Inland Transportation -o.oool (0.001?) -0,0004 (0,0015) -0.0042* (O.OOI7) Credit 0.0041 (0.0023) 0.0030 (0.0018) 0.0172 (0.0061) Guarantee-fidelity Guaran t e e-surety 0.0003 (0,0004) 0.0004 (0.0004) -0.0007 (0.0009) Emp l o y e r s - l i a b i l i t y 0,0039* (0,00lb) 0.0027 (0.0014) 0.0046 * (0.0017) Personal Accident/sickness -group 0,0003** (0,0001) 0.0003** (0.0001) 0.0004** (0.0001) Personal Accident/sickness Individual-cancellable -non-cancellable 0,0009** (0.0001) 0.0009** (0.0001) 0,0016** (0,0001) A u t o m o b i l e - l i a b i l i t y -other 0.0008** (0,0000) o.ooo9** (0,0000) 0.0012** (0,0001) A i r c r a f t - l i a b i l i t y -other -0.0015 (0,0012) -0.0016 (0,0010) -0.0018 (0,0013) Miscellaneous -0.0007 (0,0012) -0.0006 (0,0011) -0.0004 (0.0020) R 2 0.827 0,874 0.853 a -0.115 -0 . 244 -0.187 SY 1.35* 1.156 1.248 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e r r i c l e n t TABLE XII DIRECTORS1 FEES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0 . 0 0 0 8 * * ( 0 . 0 0 0 2 ) 0 . 0 0 0 8 * * ( 0 . 0 0 0 2 ) 0 . 0 0 1 0 * ( 0 . 0 0 0 4 ) B o i l e r - b o i l e r Boiler-machinery 0 . 0 0 0 7 ( 0 . 0 0 0 8 ) 0.0007 ( 0 . 0 0 0 8 ) 0.0025 (0.0027) Real property 0 . 0 0 0 8 ( 0 . 0 1 6 9 ) -0.0137 (O.OI50) 0.0110 ( 0 . 0 1 9 8 ) Inland Transportation - 0 , 0 1 0 8 * * ( 0 . 0 0 3 7 ) - 0 . 0 0 9 9 * * ( 0 . 0 0 3 6 ) -0.0130** ( 0 . 0 0 3 8 ) Credit O . O O I B ( 0 . 0 0 4 9 ) 0 . 0 0 0 9 ( 0 . 0 0 4 5 ) 0 . 0 1 2 4 ( 0 . 0 1 8 9 ) Guarantee-fidelity Guarantee-surety 0 . 0 0 0 7 (0.0009) 0 . 0 0 1 2 ( 0 . 0 0 1 0 ) - 0 . 0 0 1 6 ( 0 . 0 0 2 0 ) E m p l o y e r s - l i a b i l i t y - 0 . 0 0 0 9 (0.0034) - 0 . 0 0 1 0 ( 0 . 0 0 3 4 ) 0 . 0 0 1 6 ( 0 . 0 0 4 0 ) Personal Accident/sickness -group -0.0005* ( 0 . 0 0 0 2 ) -0.0005** ( 0 . 0 0 0 2 ) - 0 . 0 0 0 6 * ( 0 . 0 0 0 2 ) Personal Accident/sickness Individual-cancellable ; -non-cancellable 0.0001 ( 0 . 0 0 0 2 ) 0 . 0 0 0 1 ( 0 . 0 0 0 2 ) 0 . 0 0 0 2 (0.0003) A u t o m o b i l e - l i a b i l i t y -Other 0.0007** ( 0 . 0 0 0 1 ) 0 . 0 0 0 6 * * ( 0 . 0 0 0 1 ) 0 . 0 0 1 2 * * ( 0 . 0 0 0 1 ) A i r c r a f t - l i a b i l i t y -other -0.0035 ( 0 . 0 0 2 6 ) -0.0033 ( 0 . 0 0 2 6 ) - 0 . 0 0 2 1 (0.0030) Miscellaneous -0.0050 ( 0 . 0 0 2 6 ) -0.0050 ( 0 . 0 0 2 ? ) - 0 . 0 0 9 1 * ( 0 . 0 0 4 5 ) R 2 0 . 3 7 3 0 . 4 0 0 0 . 3 9 6 a 0.521 0 . 4 2 5 0 . 4 6 8 SY 2 . 9 4 3 2 . 8 7 8 2 . 8 8 9 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XIII 94 AUDITORS* FEES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0006** (0.0002) 0.0007** (0.0002) o.ooo?** (0,0003) B o i l e r - b o i l e r Boiler-machinery 0.0007 (0.0006) 0.0007 (0.0006) 0.0033 (0,0018) Real property 0.0145 (0,0112) 0.0151 (0.0102) 0.0457** (0.0131) Inland transportation -0.0031 (0.0025) -0.0029 (0.0025) -0.0059* (0.0025) Credit 0.0008 (0,0033) 0.0003 (0,0031) 0.0058 (0.0125) Guarantee-fidelity Guarant e e-sure ty -0.0011 (0.0006) -0.0009 (0.0006) -0.0045•• (0.0013) E m p l o y e r s ' - l i a b i l i t y -0.0009 (0.0023) -0.0019 (0.0023) 0,0009 (0.0027) Personal Accident/sickness -group -0.0001 (0.0001) -0.0001 (0.0001) -0.0000 (0.0002) Personal Accident/sickness Individual-cancellable -non-caneellable 0.0001 (0.0001) 0.0001 (0.0001) 0.0002 (0,0002) A u t o m o b i l e - l i a b i l i t y -other 0.0006** (0.0001) 0*0007** (0.0001) o.opio** (0.0001) A i r c r a f P l i a b i l i t y -other -0.0009 (0,0017) -0.0016 (0.0017) -0.0015 (0,0020) Miscellaneous -0.0042* (0,0017) -0.0051** (0.0018) -0.0026 (0,0030) R 2 0.514 0.514 0.536 a 0,297 0.203 0.249 SY 1.961 1.961 1.915 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t MANAGEMENT REMUNERATION TABLE XIV REGRESSION COEFFICIENT 95 LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0043 (0.0084) 0.0021 (0.0084) 0.0198 (0.0128) B o i l e r - b o i l e r Bo iler-machinery -0.0032 (0.0288) -0.0035 (0.0287) -0.0202 (0.0920) Real Property 1.2970* (0.5736) 1.5120** (O.5I9O) -O.2399 (0.6661) Inland Transportation -0.0052 (0,1266) 0.0433 (0,1257) 0.4503** (0.1292) Credit -0.0490 (0,1682) -0.0501 (0,1558) -O.3636 (0.6351) Guarantee-fidelity Guarantee-surety -O.0229 (0.0293) -0,0246 (0,0330) -0.0714 (0.0676) E m p l o y e r s - l i a b i l i t y -0.0990 (0,1151) -0.0825 (O.II7I) -0.0880 (0.1357) Personal Accident/sickness r-group -0.0042 (0,0066) •^0.0046 (0.0067) -0.0036 (0.0081) Personal Accident/sickness Individual-cancellable -0,0012 (O.OObQ) -0.0011 (0.0061) -O.OOI9 (0,0103) -non-canee1lable A u t o m o b i l e - l i a b i l i t y -other 0 . 0 0 0 6 ( 0 . 0 0 3 2 ) 0 . 0 0 1 2 ( 0 . 0 0 3 5 ) - 0 . 0 0 1 2 (0.0041) A i r c r a f t - l i a b i l i t y -other 0.0434 ( 0 , 0 6 7 7 ) 0 . 0 1 7 3 (0.0886) -O . I O 5 I ( 0 . 0 9 9 8 ) Miscellaneous -0.1826* (0,0871) - 0 . 2 1 5 3 * ( 0 . 0 9 2 3 ) - 0 . 3 6 9 6 * ( 0 . 1 5 2 6 ) R 2 0.035 0.046 0 . 0 8 9 a I8.997 18.204 17.600 SY 1 0 0 . 1 7 3 99.608 97.332 • Denotes s l g n i f l g a n t at 5% l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XV 9b ADVERTISING REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y - 0 . 0 0 2 ? ( 0 . 0 0 2 2 ) -0.0024 ( 0 , 0 0 2 2 ) -0.0107** (0,0032) B o i l e r - b o i l e r Boiler-machinery 0.0025 (0.0075) 0.0019 (0.0074) O.OI96 (0.0230) Real property -0,14-91 (0.1485) -O.I303 ( O . I 3 4 I ) 0.1293 ( 0 . 1 6 7 2 ) Inland Transportation -0.0108 ( 0 , 0 3 2 8 ) - 0 . 0 2 1 3 ( 0 . 0 3 2 5 ) -0.0090 (0.0323) Credit 0.0414 (0,0435) 0,0290 (0,0402) 0 , 2 7 0 3 ( 0 . 1 5 6 9 ) Guarantee-fidelity Guarantee-surety - 0 . 0 0 6 5 (0.0076) -0.0104 (0.0065) -0.0184 (0,0169) E m p l o y e r s * - l i a b i l i t y - 0 . 0 7 6 1 * ( 0 . 0 2 9 6 ) - 0 . 0 8 7 7 * * (0.0302) -O.O456 (0.0340) Personal Accident/sickness -group -0.0036* (0.0017) -o.oo4o* (0.0017) -0.0056** ( 0 , 0 0 2 0 ) Personal Accident/sickness Individual-cancellable -non-cance1lable 0 . 0 2 2 2 • * (0.0016) 0 . 0 2 3 1 * * (0.0016) 0,0428** (0.0026) A u t o m o b i l e - l i a b i l i t y -other 0.0119** (0,0006) 0.0136** (0.0009) 0.0169** ( 0 . 0 0 1 0 ) A i r cr af t- 1 1 ab 1 1 1 ty -other 0.0057 (0.0227) 0 . 0 1 2 5 (O.O229) 0 . 0 2 5 1 (0.0250)-Miscellaneous 0.0046 (0.0225) -0.0039 ( 0 . 0 2 3 9 ) -0.0099 ( 0 . 0 3 6 2 ) R 2 .626 0.634 0.672 a -3.I56 -3.792 - 2 . 8 2 5 SY 25.93* 25.734 24.357 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XVI 9 7 BOOKS AND PERIODICALS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0002** (0.0001) 0.0002** (0.0000) 0.0003** (0.0001) B o i l e r - b o i l e r ; Boiler-machinery 0.0001 (0.0002) 0.0001 (0.0002) 0.0003 (0.0005) Real property 0.0003 (0.0035) 0.0016 (O.OO29) 0.0004 (0.0038) Inland transportation -0.0006 (0.0008) -0.0008 (0.0007) -0.0018* (0.0007) Credit 0.0010 (0.0010) 0.0007 (0.0009) 0.0055 (0.0036) Guarantee-fidelity Guarantee-surety -0.0001 (0.0002) -0.0001 (0.0002) -0.0001 (0.0004) E m p l o y e r s ' - l i a b i l i t y 0.0012 (0.0007) 0.0005 (0.0006) 0.0010 (0.0008) Personal Accident/sickness -group 0.0001* (0.0000) 0.0001 (0.0000) 0.0001* (0.0000) Personal Accldent/slclmess Individual-cancellable -non-cancellable 0.0003** (o.oooo) 0.0003** (0.0000) 0.0005** (0.0001) A u t o m o b i l e - l i a b i l i t y -other 0.0002** (0.0000) 0.0002** (0.0000) 0.0003** (0.0000) A i r c r a f t - l i a b i l i t y -other 0.0002 (0.0005) 0.0004 (0.0005) 0.0009 (0.0006) Miscellaneous -0.0000 (0.0005) -0.0003 (0.0005) -0.0001 (0.0009) R 2 0.566 0.650 0.640 a -0.036 -0.06b -0.062 SY 0.612 0.551 0.559 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XVII BUREAU AND ASSOCIATION DUES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0094** (0.0015) 0.0107** 0.0015 0.0197** (0.0023) B o i l e r - b o i l e r Boiler-machinery 0.0071 (0.0051) 0.0064 (0.0050) 0.1275 (0.0162) Real property 0.2466* (0.1014) 0.1766 (0.0905) 0.6254** (0.1178) Inland transportation 0.0487* (0.0224) 0.0572** (0.0219) -0.0153 (0.0228) Credit 0.0003 (0.0297) -0.0012 (0.0272) 0.0021 (0.1119) Guarantee-fidelity Guarantee-surety 0.0067 (0.0052) 0.0094 (0.0057) 0.0187 (0.0119) E m p l o y e r s 1 - l i a b i l i t y 0.1101** (0.0203) 0.0985** (0.0204) 0.1172** (0.0239) Personal Accldent/slclmess -group 0.0001 (0.0012) -0.0001 (0.0012) 0.0005 (0.0014) Personal Accldent/slclmess Individual-cancellable -non-cancellable 0.0009 (0.0011) 0.0010 (0.0011) 0.0017 (0.0018) Aut o m o b i l e - l i a b i l i t y -other 0.0002 (0.0006) 0.0004 (0.0006) 0.0008 (0.0007) A i r c r a f t - l i a b i l i t y -other -0.0011 (0.0155) -0.0150 (0.0154) 0.0136 (0.0176) Miscellaneous 0.0340* (0.0154) 0.0386* (0.0161) 0.1086** (0.0269) H 2 0.655 0.668 0.676 a 0.198 -O.52I -O.35I SY 17.705 17.363 17.158 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t 99 TABLE XVIII CHARITABLE DONATIONS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0,0001 (0,0001) 0.0001 (0.0001) 0.0002 (0.0002) B o i l e r - b o i l e r ; Boiler-machinery 0.0003 (0.0004) 0.0003 (0.0004) 0.0012 (0.0014) Real property 0.0015 (0.0081) -0.0043 (0.0074) -0.0061 (0.0099) Inland transportation -0.0039* (0.0018) -0.0036* (0.0018) -0.0042* (0.0019) Credit 0.0019 (0.0024) 0.0015 (0.0022) 0.0014 (0.0094) Guarantee-fidelity Guarante e-sure ty 0.0008 (0.0004) 0.0010* (0.0005) -0.0018 (0.0010) E m p l o y e r s 1 - l i a b i l i t y -0.0004 (0.0016) -0.0002 (0.0017) 0.0012 (0.0020) Personal Accident/sickness -group -0.0000 (0.0001) -0.0000 (0.0001) -0.0000 (0.0001) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0002* (0.0001) 0.0002* (0.0001) 0.0003* (0.0002) A u t o m o b i l e - l i a b i l i t y -other 0.0005" (0.0000) 0.0005** (0.0000) 0.0007* (0.0001) A l r craf t-11 ab i 11 ty -other -0.0010 (0.0012) -0.0009 (0.0013) -0.0014 (0.0015) Miscellaneous -0.0011 (0.0012) -0.0009 (0.0013) -0.0023 (0.0023) E ? 0.453 0.454 0.427 a -0.091 -0.114 -0.053 SY 1.412 1.411 1.445 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XIX INSPECTION AND SURVEYS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0028** (0.0007) 0.0026*# (0.0007) 0.0027* (0.0012) B o i l e r - b o i l e r ; Boiler-machinery -0.0005 (0.0025) -0.0007 (0.0025) 0.0022 (0.0082) Real property -0.0891 (0.0490) -0.0787 (0.0447) -0.0522 (0.0598) Inland transportation -0.0209 (0.0108) -0.0162 (0.0108) -0.0023 (0.0116) Credit -0.0041 (0.0144) -0.0036 (0.0134) -0.0279 (0.0566) Guarantee-fidelity Guarantee-sure ty 0.0037 (0.0025) 0.0046 (0.0026) 0.0005 (0.0061) E m p l o y e r s 1 - l i a b i l i t y -0.0068 (0.0098) -0.0062 (0.0101) -0.0025 (0.0i21) Personal Accldent/slcimess -group -0.0000 (0.0006) -0.0000 (0.0006) -0.0001 (0.0007) Personal Accident/sickness Individual-cancellable -non-cancellable -0.0002 (0.0005) -0.0002 (0.0005) -0.0002 (0.0009) A u t o m o b i l e - l i a b i l i t y -other -0.0004 (0.0003) -0.0003 (0.0003) -0.0000 (0.0004) A i r c r a f t - l i a b i l i t y -other -0.0029 (0.0075) 0.0016 (0.0076) 0.0105 (0.0069) Miscellaneous -0.0058 (0.0074) -0.0061 (0.0080) -0.0135 (0.0137) R 2 0.083 0.077 0.050 a 1.519 1.419 1.437 SY 8.560 6.587 8.712 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XX 101 INSURANCE OTHER THAN INSURANCE ON REAL ESTATE REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0001 (0.0001) 0.0001 (0.0001) o.ooo5* (0.0002) B o i l e r - b o i l e r Boiler-machinery 0.0029** (0.0004) 0.0029** (0.0004) 0.0098** (0.0014) Real property 0.0218** (0.0081) 0.0102 (0.0074) -0.0152 (0.0098) Inland transportation 0.0027 (0.0018) 0.0025 (0.0018) -0.0006 (0.0019) Credit 0.0019 (0.0024) 0.0015 (0.0022) 0.0068 (0.0093) Guarantee-fldellty Guarantee-surety 0.0006 (0.0004) 0.0008 (0.0005) -0.0036** (0.0020) Emp l o y e r s - l i a b i l i t y -0.0034* (0.0016) -0.0030 (0.0017) -0.0007 (0.0020) Personal Accident/sickness -group 0.0004** (0.0001) 0.0004** (0.0001) 0.0005** (0.0001) Personal Accident/sickness Individual-cancellable -non-cancellable -0.0000 (0.0001) 40.0000 (0.0001) -0.0001 (0.0002) Au t o m o b i l e - l i a b i l i t y -other 0.0003** (0.0000) 0.0003** (0.0000) 0.0004** (0.0001) A i r c r a f t - l i a b i l i t y -other 0.0006 (0.0012) 0.0002 (0.0013) 0.0001 (0.0015) Miscellaneous 0.0004 (0.0012) 0.0005 (0.0013) 0.0044 (0.0022) H 2 0.417 0.418 0.405 a -0.002 -0.023 0.042 SY 1.418 1.417 1.432 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l notes figures In brackets represent standard error of regression c o e f f i c i e n t 102 TABLE XXI LEGAL EXPENSE REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0002* (0,0001) 0.0002** (0.0001) 0.0003** (0.0001) B o i l e r - b o i l e r ; Boiler-machinery 0.0002 (0.0003) 0.0003 (0.0003) 0.0003 (0.0009) Real property -0.0080 (0.0050) -0.0069 (0.0046) -0.0044 (0.0064) Inland transportation -0,0030** (0.0011) -0.0023* (0,0011) -0.0032* (0.0012) Credit 0.0129** (0.0015) 0.0120** (0.0014) 0.0343** (0.0061) Guarantee-fidelity Guarantee-surety 0.0004 (0.0003) 0.0005 (0.0003) 0.0014* (0,0007) Employers * - l i a b i l i t y 0.0000 (0.0010) -0.0004 (0.0010) -0.0009 (0.0013) Personal Accident/sickness -group -0.0000 (0.0001) -0.0000 (0.0001) -0.0000 (o.oooi) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0002** (0.0001) 0.0002** (0.0001) 0.0004*' (0.0001) A u t o m o b i l e - l i a b i l i t y -other 0.0000 (0.0000) 0.0001* (0.0000) 0.0001 (0.0000) A i r c r a f t - l i a b i l i t y -other -0.0012 (0,0008) -0.0011 (0.0006) -0.0012 (0.0010) Miscellaneous 0.0025** (0.00C8) 0.0009 (0.0008) -0.0005 (0.0015) R 2 0,336 0.329 0.231 a 0.157 0.138 0.173 SY 0.873 0,677 0.939 • Denotes s l g n i f l g a n t at 5% l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXII MAPS AND PLANS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE * NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0001 (0.0000) 0.0001* (0.0000) 0.0002** (O.oooi) B o i l e r - b o i l e r Boiler-machinery -0.0001 (o.oooi) -0.0001 (0.0001) -0.0000 (0.0004) Real property -0.0022 (0.0026) -0.0011 (0,0024) -0.0035 (0.0032) Inland transportation 0.0026** (0.0006) 0.0016** (0.0006) 0.0016* (0.0006) Credit -0.0001 (0.0006) -0.0001 (0.000?) -0.0005 (0.0030) Guarantee-fidelity Guarantee-surety -0.0002 (0.0001) -0.0002 (0.0002) -0.0005 (0.0003) E m p l o y e r s 1 - l i a b i l i t y 0.0003 (0.0005) 0.0001 (0.0005) 0.0006 (0.0006) Personal Accident/sickness -group -0.0000 (0.0000) -0.0000 (0.0000) -0.0000 (0,0000) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0000 (0.0000) 0.0000 (0.0000) 0.0000 (0.0000) A u t o m o b i l e - l i a b i l i t y -other -0.0000 (0.0000) -0.0000 (0,0000) -0.0000 (0.0000) A i r c r a f t - l i a b i l i t y -other -0.0003 (0.0004) -0.0004 (0.0004) -O.OOOl (0,0005) Miscellaneous -0.0006 (0.0004) -0.0006 (0.0004) 0.0000 (0.0007) R2 0.162 o - . u a 0.120 a 0.014 0,004 -0,010 SY 0.446 0.460 0.459 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t 104 TABLE XXIII MEDICAL EXAMINERS' FEES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e : Thert: Personal Property; Plate glass; Public l i a b i l i t y 0.0000 (o.oool) 0.0001 (o.oool) 0.0002 (0.0001) B o i l e r - b o i l e r Boiler-machinery 0.0001 (0.0002) 0.0001 (0.0002) 0 . 0 0 0 6 (0.0009) Real property 0.0 io6* (0.0049) 0.0047 ( 0 . 0 0 4 5 ) 0.0006 (O.OO65) Inland transportation 0.0007 (0.0011) 0.0002 (0.0011) -0.0005 (0.0013) Credit 0.0005 (0.0014) 0.0004 (0.0013) 0.0044 (0.0062) Guarantee-fidelity Guarante e-sure ty -o.oool (0.0003) -0.0002 (0.0003) -0.0008 (0.0007) E m p l o y e r s ' - l i a b i l i t y o.oool (0.0010) -0.0000 (0.0010) 0.0004 (0.0013) Personal Accident/sicimess -group 0.0001* (0.0001) 0.0001 (o.oool) 0.0002* (0.0001) Personal Accident/sickness Individual-cancellable -non-cancellable o.ooi7** (0.0001) 0.0017** (o.oool) 0.0029*' (0.0001) A u t o m o b i l e - l i a b i l i t y -other 0.0000 (0.0000) 0.0000 (0.0000) 0.0000 (0.0000) A i r c r a f t - l i a b i l i t y -other -0.0009 (0.0006) -0.0015 (0.0008) -0.0014 (0.0010) Miscellaneous 0.U009 (0.0007) 0.0011 (0.0008) 0.0025 (0.0015) R 2 0.819 0.820 0.760 a -0.051 -0.062 -0.025 SY 0.858 0 . 8 5 6 0.946 • Denotes s l g n l f l g a n t at 5$ l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXIV MERCANTILE AGENCIES* REPORTS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y -0.000b (0.0011) -0.0004 (0.0009) 0.0021 (0,0016) B o l i e r - b o i l e r Boiler-machinery -0.0010 (0.003b) -0.0009 (0 . 0 0 3 2 ) -0 . 0 0 1 3 (0,0112) Real property 0.0655 (0.0719) 0.0210 (0 . 0 5 7 1 ) 0.0154 (O.OO16) Inland transportation 0.0074 (0 . 0 1 5 9 ) 0.0037 (0 . 0 1 3 b ) -0 . 0 2 8 3 (0 . 0 1 5 b ) Credit o.o3«b (0.0211) 0 . 0 2 9 1 (0.0171) 0.1899* (0.0776) Guarantee-fidelity Guarantee-surety 0 . 0 0 4 5 (0.003?) 0.0044 ( 0 , 0 0 3 b ) 0.0106 (0 . 0 0 8 3 ) E m p l o y e r s ' - l i a b i l i t y 0.0552** (0.0144) 0.0466** (0 . 0 1 2 9 ) O . O 6 3 8 " (0.0166) Personal Accident/sickness -group -0.0000 ( 0 . 0 0 0 b ) -0.0004 (0.0007) 0.0002 (0.0010) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0031** ( 0 . 0 0 0 8 ) 0.0033** (0.000?) 0.0050** (0 . 0 0 1 3 ) A u t o m o b i l e - l i a b i l i t y -other 0 . 0 0 5 8 * * (0.0004) 0 . 0 0 7 3 * * (0.0004) 0 . 0 0 6 3 * * (0.0005) A i r c r a f t - l i a b i l i t y -other -O.OOttO ( 0 . 0 1 1 0 ) -0.0098 (0.0087) -0.0165 (0.0122) Miscellaneous 0.018? ( 0 . 0 1 0 9 ) 0 . 0 2 2 5 * (0.0102) 0 .0326 (0.0186) E 2 0. 641 0.727 0.678 a 0 . 9 4 5 0.14? 0.787 SY 12.564 10.95^ 11.891 • Denotes s l g n l f l g a n t at 5% l e v e l Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error /of regression c o e f f i c i e n t TABLE XXV OFFICE FURNITURE AND EQUIPMENT REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0015 (0,-0011) 0.0021 (0.0011) 0.0062** (0,0016) B o i l e r - b o i l e r Boiler-machinery 0.0026 (0.0039) 0.0027 (0.0037) 0.0082 (0.0128) Real property 0.0244 (0.0?68) -O.O388 (0.0665) 0.1056 (0.0933) Inland transportation 0.0034 (0.0169) 0.0007 (0.0161) -0.0438* (0,0181) Credit -0,0116 (0.0225) -0.0143 (0.0199) -0.1926* (O.Obo?) Guarantee-fidelity Guarantee-surety 0.0165** (0.0039) 0,0190** (0.0042) 0.021?* (0.0094) Emp l o y e r s ' - l i a b i l i t y 0.0294 (0.0154) 0.0206 (0.0150) 0.0090 (0.0190) Personal accident/sickness -group 0.0035** (0.0009) 0.0033** (0.0009) 0.0042%* (0.0011) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0104 (0.0006) O.OlOb** (0.0008) 0.0192** (0.0014) Au t o m o b i l e - l i a b i l i t y -other 0,oo6o%* (0.0004) 0.0071** (0.0004) 0.0066** (0.0006) A i r c r a f t - l i a b i l i t y -other -0.0024 (O.OII7) -0,0039 (0.0113) -0.0086 (0.0.139) Miscellaneous 0.0021 (O.OII7) 0.0030 (0.0118) 0.0043 (0.0213) B 2 0.741 0.765 0.733 a -O.934 -1.59* -1.005 SY 13.411 12.755 13.596 • Denotes s l g n i f l g a n t at 5$ l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t 10? TABLE XXVI POSTAGE REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0016 (0.0013) 0,0020 (0.0011) 0.0050* (0.0020) B o i l e r - b o i l e r ; Boiler-machinery 0.0102* (0.00*3) 0.0101*' (0.0038) 0.0378* (0.0145) Real property -0.0*05 (0.0657) -0.0669 (0.0687) 0.0467 (0.1053) Inland transportation 0.0169 (0.0169) 0.0105 (0.0166) -0.0255 (0.0204) Credit 0,055** (0.0251) 0.0427* (0.0206) 0.2835** (0.0101) Guarantees-fidelity Guarantee-surety 0.0105* (0.004*) 0.0107* (0,0044) 0.0077 (0.0107) E m p l o y e r s * - l i a b i l i t y 0.0234 (0,0172) 0.0124 (0.0155) 0.0304 (0.0214) Personal Accident/sickness -group 0.0022* (0.0010) 0.0019* (0.0009) 0,0035** (0.0013) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0099** (0,0009) 0,0103** (0.0008) 0,0163** (0.0016) Aut o m o b i l e - l i a b i l i t y -other 0.0090** (0.0005) 0,0109** (0.0005) 0.0128** (0.0007) A i r c r a f t - l i a b i l i t y -other -0.0013 (0,0131) 0,0029 0.0117 0.0051 (0.0157) Miscellaneous 0.0051 (0.0130) 0,0070 (0.0122) 0.0068 (0,0241) E 2 0.779 0.629 0.768 a 0.703 -0.406 0,5*3 SY 14.976 13.169 15.3*7 • Denotes s l g n i f l g a n t at 5$ l e v e l • • Denotes s l g n i f l g a n t at 1% l e v e l note; figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XXVII 10b PRINTING AND STATIONERY REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0*00 3«>** (0.0013) 0.0038** (0,0012) 0.0064*" (0.0020) B o i l e r - b o i l e r Boiler-machinery 0.013B" (0.0043) 0.0139** (0.0040) 0.0436** (0.0143) Real property -0,0Ibb (•0 .-08.5b) -0,0463 (0.0717) 0.1189 (0.1037) Inland transportation -0.0046 (0,0169) -0.0005 (0,0174) -0.0092 (0,0200) Credit 0.0162 (0,0251) 0.0072 (0,0215) 0.0376 (0.09b5) Guarantee-fidelity Guaran t e e-sur e ty 0.0113* (0,0044) 0.0128** (0.0046) 0.0252* (0.0105) E m p l o y e r s ' - l i a b i l i t y 0.0320 (0.0172) 0.0209 (0,0162) 0.0407 (0.0211) Personal Accident/sickness -group 0.0049** (0.0010) 0.0045#» (0.0009) 0.0060** (0,0013) Personal Accident/sickness Individual-cancellable -noncanceliable 0.0165** (0,0009) 0.0172** (0.0008) 0.0306** (0.0016) A u t o m o b i l e - l i a b i l i t y -other 0.0092** (0,0005) 0.0110** (0.0122) 0.0135** (0.0005) A i r c r a f t - l i a b i l i t y -other -0,0144 (0,0133) -0.0138 (0.0.122) -0.0135 (0.0155) Miscellaneous 0.0179 (0.0130) 0.0163 (0.012b) 0.0252 (0,0237) E 2 0.844 0.868 0.641 a 1.006 -0.022 I.I52 SY 14,947 13.759 15.101 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t 109 TABLE XXVIII RENTS REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0097** (0.0019) 0.0106** (0.0017) 0.0162** (0.0030) B o i l e r - b o i l e r Bo1ler-machlnery 0.0192** (0.0065) 0.0189** (0,0060) 0.0620** (0,0215) Real property -0.0787 (0.1290) -0.1689 (0,1080) 0.1581 (0.1560) Inland transportation 0.0106 (0.0165) 0.0139 (0.0261) -0.0599 (O.0302) Credit 0.0663 (0.0378) 0.0503 (0,0324) 0.3049* (0.1483) Guarantee-fidelity Guarantee-sure ty 0.0223** (0.0066) 0,0 246 ** (0,0069) 0,0b63** (O.OI58) E m p l o y e r s ' - l i a b i l i t y 0.064-5 •• (0.0259) 0.0623* (0,0244) 0.0936** (0.0317) Personal Accident/sickness -group 0,0090** (0.0015) 0.0086** (0.0014) 0.0120** (0.0019) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0157** (0,0004) 0,0165** (0.0013) 0.0278** (0,0024) Aut o m o b i l e - l i a b i l i t y -other 0,0116* * (0.0007)" 0.0141** (0.0007)' O.OI74** (0.0010) A i r c r a f p l i a b i l i t y -other 0.0022 (0,0197) 0,0106 (0.0184) 0.0251 (0.0233) Miscellaneous 0.0321 (0.0196) 0.0391* (0.0192) 0.0702 (0.0356) R 2 0.631 0.857 0.828 a -1.702 -3.377 -1.666 SY 22,525 20,719 22.725 • Denotes s l g n i f l g a n t at 5% l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXIX STATISTICAL BUREAU EXPENSES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0 . 0 0 2 0 # * (0.0006) 0 . 0 0 2 2 * * (0.0006) 0.0035* ( 0 . 0 0 1 0 ) B o i l e r - b o i l e r Boiler-machinery 0 . 0 0 0 1 ( 0 . 0 0 2 2 ) - 0 . 0 0 0 1 ( 0 . 0 0 2 2 ) 0 . 0 0 2 0 ( O . O O 6 9 ) Real property 0.0270 (0.0441) 0.0199 (0.0398) 0.0927 (0.0502) Inland Transportation -0.0109 (0.0097) -0.0106 ( 0 . 0 0 9 6 ) T0.0241* (0.0097) Credit 0.0243 (0.0129) 0.0204 (0.0119) 0 . 2 2 1 0 * * (0.0477) Guarantee-fidelity Guarante e-sure ty -0.0016 (0.0023) - 0 . 0 0 2 0 (0.0025) -0.0032 (0.0051) E m p l o y e r s 1 - l i a b i l i t y -0.0043 (0.0088) -0.0052 (0.0090) 0 . 0 0 1 0 ( 0 . 0 1 0 2 ) Personal Accident/sickness -group -0.0007 (0.0005) -0.0008 (0.0005) -0.0008 (0.0006) Personal Accident/sickness Individual-cancellable -non-cancellable 0 . 0 0 0 1 (0.0005) 0 . 0 0 0 1 (0.0005) 0 . 0 0 0 2 (0.0008) A u t o m o b i l e - l i a b i l i t y -other 0.0004 ( 0 . 0 0 0 2 ) 0.0005 (0.0003) 0.0006 (0.0003) A i r c r a f t - l i a b i l i t y -other -0.0003 (0.0067) -0.0004 ( 0 . 0 0 6 8 ) 0.0081 (0.0075) Miscellaneous - 0 . 0 0 7 4 ( 0 . 0 0 6 7 ) -0.0090 (0.0071) - O . O I 7 3 (0.0115) R 2 0.136 0.150 0 . 2 2 0 a 0.940 0 . 7 1 8 0 . 6 0 5 SY 7.694 7.630 7.307 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l notes figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXX 111 TRAVELLING EXPENSES REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0051** (0.0016) 0.005b** (0.0015) 0.0129** (0.0025) B o i l e r - b o i l e r Boiler-machinery 0.0606** (0 .0055) 0.0612** (0 .0050) 0.2095** (0.0177) Real property 0.0272 (0.1066) -0.0308 (0.0903) -0.0311 (0.1287) Inland transportation 0.0157 (0.0240) 0.019b (0.0219) -0.0195 (0.0249) Credit 0.0565 (0.0319) 0.0462 (0.0271) 0.2603* (0.1223) Guarant e e - f l d e l l t y Guarantee-surety 0.0045 (0.005b) 0.0058 (0.0057) -0.0489** (O.OI30) E m p l o y e r s 1 - l i a b i l i t y 0.0713** (0.021a) 0.0611** (0.0204) 0.1060** (0.0261) Personal Accident/sickness -group 0.0057** (0.0013) 0.0051** (0.0012) 0.0068** (0.0016) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0129** (0.0011) 0.013b** (0,0011) O.O227" (0.0020) A u t o m o b i l e - l i a b i l i t y -other 0.00b0** (0.0006) 0.0076** (0,0006) 0.0097** (0.0008) A i r c r a f t - l i a b i l i t y -other -0.0190 0.0166 -0 .0099 (0.0154) -0.0168 (0.0192) Miscellaneous 0.0046 (0.0165) 0 .0003 (0.0161) 0.0067 (0.0294) R 2 0.7*5 0.788 0.752 a 2.815 1.469 2.283 SY 18.994 I7.326 18,744 • Denotes s l g n i f l g a n t at 5% l e v e l ; ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXXI OTHEH REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y -0.0005 (0.0020) 0.0004 (0.0009) 0.0022 (0.0015) B o i l e r - b o i l e r Boiler-machinery 0.0078* (0.0033) 0.0080* (O.OO3I) 0.0312** (0.0106) Real property -0.0716 (0.0654) -0.1045 (0.0554) -0.0379 (0.0767) Inland transportation 0.0355* (0.0144) 0.0308* (0.0134) -0.0059* (0.0148) Credit 0.0299 (0.0192) 0.0222 (0.0166) 0.2263** (0.0729) Guarantee-fidelity Guarant e e-sure ty 0.0040 (0.0033) 0^ 0038 (6.0035) -0.0048 (0.0078) E m p l o y e r s - l i a b i l i t y -0.0049 (0.0131) -0.0158 (0.0125) -0.0117 (0.015b) Personal Accident/sickness -group -0.0008 (0.0006) -0.0009 (0.0007) -0.0006 (0.0009) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0061** (6.0007) 0.0084** (0.0007) 0.0138** (0.0012) A u t o m o b i l e - l i a b i l i t y -other O.OObO** (0.0004) 0.0070** (0.0004) 0.0083** (0.0005) A i r c r a f t - l i a b i l i t y -other -0.0081 (0.0100) -0.0096 (0.0095) -0.0179 (0.0115) Miscellaneous -0.0152 .(0.0099) -0.0197 (0.0099) -0.0417* (0.0175) R 2 0.666 0.727 0.699 a 0.448 -0.308 0.039 SY 11.417 10.638 11.179 • Denotes s i g n i f i g a n t at l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXXII n 3 EXPENSE ALLOWANCE ASSUMED (+) REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0019 ( 0 . 0 0 3 2 ) 0 . 0 0 1 1 ( 0 . 0 0 3 2 ) 0 . 0 0 1 0 ( 0 . 0 0 5 1 ) B o i l e r - b o i l e r Boiler-machinery -O .OOO5 ( 0 . 0 1 1 0 ) - 0 . 0 0 0 3 ( 0 . 0 1 1 0 ) -0.0042 (0.03b2) Real property - 0 . 1 0 9 3 ( 0 . 2 1 8 9 ) - 0 . 0 4 5 0 ( 0 . 1 9 9 5 ) 0.0440 (0.2633) Inland transportation - 0 . 0 2 2 5 ( 0 . 0 4 6 3 ) - 0 . 0 1 6 9 (0.0483) - 0 . 0 1 2 9 ( 0 . 0 5 0 9 ) Credit - 0 . 0 0 1 0 (0.0642) TO.0008 ( 0 . 0 5 9 9 ) 0 . 0 0 9 2 ( 0 . 2 5 0 2 ) Guarantee-fidelity Guarantee-surety 0 . 0 0 2 0 ( 0 . 0 1 1 2 ) 0 . 0 0 3 5 ( 0 . 0 1 2 7 ) O . O O 8 9 (0.0266) E m p l o y e r s ' - l i a b i l i t y -0.0026 (0.0439) -O.OO9O ( O . O 4 5 0 ) -0.0249 ( 0 . 0 5 3 5 ) Personal Accident/sickness -group 0 . 0 1 5 3 * * ( 0 . 0 0 2 5 ) 0 . 0 1 5 2 * * (0.0026) 0.018?* ( 0 . 0 0 3 2 ) Personal Accident/sickness Individual-cancellable -non-cancellable -0.0054* ( 0 . 0 0 2 3 ) - 0 . 0 0 5 3 * (0.0024) - 0 . 0 0 7 9 (0.0040) A u t o m o b i l e - l i a b i l i t y -other - 0 . 0 0 1 1 ( 0 . 0 0 1 2 ) - 0 . 0 0 1 0 ( 0 . 0 0 1 3 ) -0.0008 (0.0016) A i r c r a f t - l i a b i l i t y -other -O . O O 8 7 ( 0 . 0 3 3 5 ) - 0 . 0 0 3 8 ( 0 . 0341) -O.OO3I ( 0.0393) Miscellaneous 0 . 0 0 1 2 ( 0 . 0 3 3 2 ) 0.0014 ( 0 . 0 3 5 5 ) - 0 . 0 0 9 6 (0.0601) R2 0 . 1 1 3 0 . 1 1 0 0 . 1 0 7 a 2.141 2 . 1 5 5 1 . 8 9 6 SY 36.234 36.286 3 6 . 3 5 3 • Denotes s l g n i f l g a n t at 5 $ l e v e l ••Denotes s l g n i f l g a n t az .1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXXIII EXPENSE ALLOWANCE CEDED (-) BEGBESSION COEFFICIENT LINE OF INSUBANCE NPW NPE NCI Fire;; Theft; Personal Property; Plate glass; Public l i a b i l i t y 0.0005 (0.0015) 0.0006 (0.0015) 0.0010 (0.0024) B o i l e r - b o i l e r Boiler-machinery 0.0006 (0.0052) 0.0006 (0.0052) 0.0017 (0.0171) Real property 0.0115 (0.1038) -0.0004 (0.0945) 0.0089 (0.1244) Inland transportation -0.0006 (0.0229) -0.0007 (0.0229) -0.0014 (0.0241) Credit 0.0034 (0.0304) 0.0031 (0.0283) 0.0104 (0.1183) Guarantee-fidelity Guarantee-surety 0.0002 (0.0053) 0.0003 (0.0060) -0.0006 (0.0126) Emp l o y e r s ' - l i a b i l i t y -0.0027 (0.0208) -0.0032 (0.0213) -0.0019 (0.0253) Personal Accident/sickness -group 0.0000 (0.0012) 0.0001 (0.0012) 0.0001 (0.0015) Personal Accldent/slclmess Individual-cancellable -non-cancellable 0.0002 (0.0011) 0.0002 (0.0011) 0.0003 (0,0019) A u t o m o b i l e - l i a b i l i t y -other 0.0000 (0.0006) 0.0000 (0.0006) 0.0000 (0.0008) A i r c r a f P l i a b i l i t y -other 0.0014 (0.0159) 0.0008 (0.0161) 0.0006 (0.0186) Miscellaneous 0.0006 (0.0158) 0.0004 (0.0168) 0.0017 (0.0284) H 2 0.002 0.002 0.002 a -1.689 -1.717 -I.703 SY 18.130 18.129 18.129 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures In brackets represent standard error of regression c o e f f i c i e n t TABLE XXXIV 115 EXPENSE ALLOWANCE TO COMPANY REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y -0.0004 (0.0002) -0.0003 (0.0002) -0.0000 (0.0003) B o l l e r - b o l l e r Boiler-machinery 0.0002 (0.0007) 0.0001 (0.0007) -0.0003 (0.0025) Real property 0.0706** (0.0145) 0.0550** (0.0133) 0.0128 (0.0180) Inland transportation 0.0014 (0.0032) 0.0016 (0.0032) -0.0001 (0.0035) Credit 0.0000 (0.0042) -0.0002 (0.0040) -0.0000 (0.0172) Guarantee-fidelity Guarant e e-surety -0.0002 (0.0007) -0.0002 (0.0008) 0.0002 (0.0016) E m p l o y e r s - l i a b i l i t y -0.0015 (0.0029) -0.0009 (0.0030) -0.0006 (0.0037) Personal Accident/sickness -group -0.0001 (0.0002) -0.0000 (0.0002) -0.0000 (0.0002) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0000 (0.0002) 0.0000 (0.0002) -0.0000 (0.0003) A u t o m o b i l e - l i a b i l i t y -other 0.0000 (O.OOOl) 0.0000 (0.0001) -0.0000 (0.0001) A i r c r a f t - l i a b i l i t y -other 0.0018 (0.0022) 0.0000 (0.0023) -0.0006 (0.0027) Miscellaneous -0.0028 (0.0022) -0.0028 (0.0024) -0.0014 (0.0041) R 2 0.078 0.057 0.003 a 0.083 0.124 0.196 SY 2.529 2.557 2.629 • Denotes s l g n i f l g a n t at 5% l e v e l ••Denotes s l g n i f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t TABLE XXXV 116 MISCELLANEOUS EXPENSE REGRESSION COEFFICIENT LINE OF INSURANCE NPW NPE NCI F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y -0.0013 (0.0008) -0,0012 (0.0008) -0.0013 (0.0014) B o i l e r - b o i l e r Boiler-machinery 0 .0047 (0.0029) 0.0045 0.0029 0.0157 (0.0100) Real property 0.0312 (0.0575) 0.0275 (0.0518) -0.0047 (0.0728) Inland transportation 0.0047 (0.0127) 0.0042 (0.0125) 0.0031 (0.0141) Credit -0.1307** (0.0169) -0.1242** (0.0155) -0.3384** (0.0692) Guarantee-fidelity Guarantee-surety -0.007 (0.0029) -0,0013 (0,0033) -0.0061 (0.007*0 Empl o y e r s • - l i a b i l i t y -0.0053 (0.0115) -0,0090 (0.0117) -0.0063 (0.0148) Personal Accident/sickness -group -0.0003 (0.0007) -0.0005 (0.0007) -0.0005 (0,0009) Personal Accident/sickness Individual-cancellable -non-cancellable 0.0000 (0.0006) 0.0001 (O.0006) 0.0001 (o.ooii) A u t o m o b i l e - l i a b i l i t y -other 0.0008* 0,0003 0.0012** (0,0003) 0.0013** (0.0005) A i r c r a f t - l i a b l l l t y -other 0.0086 (0.0088) 0.0070 (0.0086) 0.0026 (0.0109) Miscellaneous 0.0033 (0.0087) -0.0031 (0.0092) -0.0035 (0.0166) R 2 0.188 0.207 0.096 a 0.942 0.686 0,580 SY 10,048 9.932 10.602 • Denotes s l g n l f l g a n t at 5% l e v e l ••Denotes s l g n l f l g a n t at 1% l e v e l note: figures i n brackets represent standard error of regression c o e f f i c i e n t APPENDIX C TABLE I NET PREMIUMS EARNED POR AUTO BODILY INJURY LIABILITY INDEPENDENT VARIABLE STANDARD CONSTANT REGRESSION ERROR COEFFICIENT GENERAL EXPENSES (G.E.)39159.74 I6989.76 -38.5676 (40.7769) OTHER ACQUISITIONS (O.A.) 39287.99 16815.57 -15.6358 (64.4612) G.E. + O.A. 39212.54 18635.67 -20.4010 (27.6499) G.E. +. O.A. + 38815.24 30562.58 -47.3096 COMMISSION AND BROKER- (2b.6636) AGE - . TABLE I I NET PREMIUMS EARNED FOR AUTO PROPERTY DAMAGE LIABILITY. INDEPENDENT VARIABLE STANDARD CONSTANT REGRESSION ERROR COEFFICIENT GENERAL EXPENSES (G.E.)14748.87 7390.79 -13.313b (16.1452) OTHER ACQUISITIONS 14785.31 6732.63 - 6.8697 (O.A.) (24.1276) G.E. + O.A, 14762.74 7304.75 - 7.1869 (10.6964) G.E, + O.A. + COMMIS- 14651.74 11019.22 -14.8553 SION AND BROKERAGE ( 9.7982) 119 TABLE I I I NET PREMIUMS EARNED POR AUTO COLLISION INDEPENDENT VARIABLE STANDARD ERROR CONSTANT REGRESSION .COEFFICIENT GENERAL EXPENSES (G.E.) 13739.29 7762.52 -21.5016 (16.5104) OTHER ACQUISITIONS (O.A.) 13829.55 6434,55 - 6,0895 (24.6962) G.E, + O.A. 13765.06 7873.72 -13.6653 (12.4156) G.E. + O.A. + COMMISSION AND BROKERAGE 13666.61 11309.27 -I5.6627 ( 9.5998) TABLE IV NET PREMIUMS ! EARNED POR AUTO THEFT., FIRE AND COMPREHENSIVE INDEPENDENT VARIABLE STANDARD ERROR CONSTANT REGRESSION COEFFICIENT GENERAL EXPENSES (G.E.) 7722.02 4185.16 -10.0838 (10.5901) OTHER ACQUISITIONS (O.A.) 77*2.44 3061.24 - 8.2465 (16.7131) G.E. + O.A. 7742.84 3911.80 - 3.8487 ( 8.0155) G.E, + O.A. + COMMISSION AND BROKERAGE 77I3.89 4707.69 - 3.7867 ( 3.4972) APPENDIX D TABLE I 121 COMPANIES THAT OPERATE THROUGH THE INDEPENDENT AGENCY SYSTEM Acadia Insurance Co. Adanac General Insurance Co. A d r i a t i c Insurance Co. Aetna Casualty & Surety Co. Aetna Insurance Co. Albion Insurance Co. of Canada Al l i a n c e Assurance Co. Ltd. American Insurance Co. American Mutual L i a b i l i t y Insurance Co. American National F i r e Insurance Co. American Road Insurance Co. Anglo-Scottish Insurance Co. Ltd. Atlas Assurance Co. Ltd. Banters & Traders Insurance Co. Ltd. Beaver Insurance Co. Bee Insurance Co. Boston Insurance Co. B r i t i s h America Assurance Co. B r i t i s h Canadian Insurance Co. B r i t i s h Empire Assurance Co. B r i t i s h Northwestern Insurance Co. Calvert F i r e Insurance Co. Canada Accident & Fi r e Assurance Co. Canada Security Assurance Co. Canadian Commerce Insurance Co. Canadian General Insurance Co. Canadian Home Assurance Co. Canadian Indemnity Co. (Canadian National Insurance Co.) Canadian Mercantile Insurance Co. Canadian Pioneer Insurance Co. Canadian P r o v i n c i a l Insurance Co. Canadian Surety Co. Casualty Co. of Canada (Citadel Insurance Co. 6 f Canada) Century Insurance Co. Ltd. Commerce General Insurance Co. Commercial Union Assurance Co. Ltd. Continental Casualty Co. Continental Insurance Co. C o r n h l l l Insurance Co. Ltd. Dominion Insurance Corporation Dominion of Canada General Insurance Co. Economical Mutual Insurance Co. 1 2 2 E l i t e Insurance Co. Employers' L i a b i l i t y Assur. Corp. Ltd. Employers Mutual L i a b i l i t y Insurance Co. of Wisconsin English & American Insurance Co. Ltd. Federal F i r e Insurance Co, of Canada Federal Insurance Co. Federation Insurance Co. of Canada F i d e l i t y & Casualty Co. of New York F i d e l i t y Insurance Co. of Canada Fldelity-Phenlx Insurance Co. Fi r e Insurance Co. of Canada Fireman's Fund Insurance Co. Firemen's Insurance Co. of Newark F i r s t National Insurance Co. of America General Accident Assurance Co. of Canada General Accident F i r e & L i f e Assurance Corporation Ltd. General Insurance Co. of America General Security Insurance Co. of Canada Glens F a l l s Insurance Co. (Global General Insurance Co.) Globe Indemnity Co. of Canada Gore Mutual Insurance Co. Granite State Insurance Co. Great American Insurance Co. Great Eastern Insurance Co. Guarantee Co. of North America Guardian Assurance Co. Ltd. Guardian Insurance Co. of Canada Guil d h a l l Insurance Co. Ltd. Gui l d h a l l Insurance Co. of Canada Halifax Insurance Co. Hardware Mutual Casualty Co. Hartford Accident & Indemnity Co. Hartford F i r e Insurance Co. Helvetia Swiss F i r e Insurance Co. Home Insurance Co. Hudson Bay Insurance Co. Imperial Guarantee & Accident Insurance Co. of Canada Imperial Insurance Office Insurance Co. of North America Insurance Corporation of Ireland Ltd. Law, Union & Eock Insurance Co. Ltd. Legal & General Assurance Society Ltd. Liverpool & London & Globe Insurance Co. Ltd. London & Edinburgh Insurance Co. Ltd. London & Lancashire Guarantee & Accident Co. of Canada London & Lancashire Insurance Co. Ltd. London & Midland General Insurance Co. London & Scottish Assurance Corp. Ltd. London Assurance 123 London-Canada Insurance Co, London Guarantee & Accident Co, Ltd, Lumbermens Mutual Casualty Co. Maryland Casualty Co. Merchants Marine Insurance Co. Ltd. Milwaukee Insurance Co. of Milwaukee, Wis. Missiquoi & Rouville Insurance Co. National Employers Mutual General Insurance Assn. Ltd. New Hampshire Insurance Co, New India Assurance Co. Ltd. New Zealand Insurance Co. Ltd.(Non-Marine Underwriters, Member of Lloyds, London, Eng.) Niagara F i r e Insurance Cd. North B r i t i s h & Mercantile Insurance Co, Ltd, Northern Assurance Co. Ltd, Northwestern Mutual Insurance Co. Norwich Union F i r e Insurance Society Ltd. Ocean Accident & Guarantee Corp. Ltd. Old Colony Insurance Co, Old Republic Insurance Co. Olympic Insurance Co. ( P a c i f i c Automobile & F i r e Insurance Co.) ( p a c i f i c Indemnity Co.) Orion Insurance Co. Ltd. P a c i f i c Coast F i r e Insurance Co. P a c i f i c Insurance Co. pf New York Pea r l Assurance Go. Ltd. Perth Mutual F i r e Insurance Co. Phoenix Assurance Co. Ltd, (Provident Assurance Co.) Phoenix Insurance Go. P r o v i n c i a l Insurance Co. Ltd. Prudential Assurance Co. Ltd. Quebec Assurance Co, Queensland Insurance Co, Ltd. Railway Passengers Assurance Co. Reliance Insurance Go. of Canada Reliance Insurance Co. of Philadelphia Royal Exchange Assurance Royal Insurance Co. Ltd. St. Paul F i r e & Marine Insurance Co. St. Paul Mercury Insurance Co. Safeco Insurance Co. of America Saskatchewan Mutual Insurance Co. Scottish Canadian Assurance Corporation Scottish Metropolitan Assurance Co. Ltd. Scottish Union & National Insurance Co. Sea Insurance Co. Ltd. Security National Insurance Co. Service F i r e Insurance Co. New York Skandinavia Insurance Co. Ltd. Stanstead & Sherbrooke Insurance Co. 1 2 4 Storebrand Insurance Co. Ltd. Sun Insurance Office Ltd. Switzerland General Insurance Co. Ltd. Toronto General Insurance Co. Traders General Insurance Co. Transport Indemnity Co. Travelers Indemnity Co. Travelers Insurance Co. Union Assurance Society Ltd. Union Insurance Society of Canton Ltd. United Canada Insurance Co. United States F i d e l i t y & Guarantee Co. United States F i r e Insurance Co. Unity F i r e & General Insurance Co. V i c t o r i a Insurance Co. of Canada Victory insurance Co, Ltd. Wawanesa Mutual Insurance Co. Wellington F i r e Insurance Co. (Western Union Insurance Co.) Western Assurance Co. Westminster F i r e Office World A u x i l i a r y Insurance Corp. Ltd. World Marine & General Insurance Co. Yorkshire Insurance Co. Ltd, Zurich Insurance Co. Source: Insurance Agents* Association of B r i t i s h Columbia, 1 2 5 TABLE I I COMPANIES OPERATING AS DIRECT WRITERS A l l s t a t e Insurance Co. A l l s t a t e Insurance Co. of Canada Co-operative F i r e & Casualty Co. Emmco Insurance Co. Employers Mutual Casualty Co. ( F r u i t Growers Mutual Insurance Co.) Federated Mutual Implement & Hardware Insurance Co. Liberty Mutual Fire Insurance Co. Liberty Mutual Insurance Co. Merit Insurance Co. Motors Insurance Corporation .Security Mutual Casualty Co. State Farm F i r e & Casualty Co. State Farm Mutual Automobile Insurance Co. Source: Insurance Agents' Association of B r i t i s h Columbia. 

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