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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., U n i v e r s i t y 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 F a c u l t y or Graduate Studies  We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 1 9 6 7  In presenting  t h i s t h e s i s In p a r t i a l f u l f i l m e n t of the r e -  quirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y able f o r reference and study. f o r extensive may  avail-  I f u r t h e r agree that permission  copying of t h i s t h e s i s f o r s c h o l a r l y purposes  be granted by- the Head of my Department or by h i s repre-  sentatives.  I t i s understood that copying or p u b l i c a t i o n  of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Department of  r.nmme-rce  and Business  The U n i v e r s i t y of B r i t i s h Columbia Vancouver b, Canada  Administration  ABSTRACT The Royal Commission oh Automobile Insurance of B r i t i s h Columbia was e s t a b l i s h e d i n I 9 6 6 to enquire, among other t h i n g s , i n t o the cost of p r o v i d i n g automobile insurance by i n s u r e r s to the p u b l i c .  This t h e s i s I s concerned with  e v a l u a t i n g 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 r a t e making p o l i c i e s of the Canadian Underwriters'  A s s o c i a t i o n , and f i n a l l y , as t o the  i n f l u e n c e of the cost f a c t o r i n e s t a b l i s h i n g a c e n t r a l i z e d agency. In e s t a b l i s h i n g a gross premium, the i n s u r e r must cover expected losses a r i s i n g out of claims and cover administ r a t i v e costs.  D e t a i l e d accounts are kept of claims  by l i n e of Insurance.  incurred  However, f o r the expense p o r t i o n  only d i r e c t claims expenses are allocated, by l i n e of i n s u r ance; no accounts by l i n e of insurance are kept f o r the r e s t of the a d m i n i s t r a t i v e expenses. Expense accounts are submitted annually to the Superintendent of Insurance, but are not broken down by l i n e of insurance.  By using 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 on cross  s e c t i o n a l 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 f u n c t i o n of premiums w r i t t e n by l i n e of Insurance. In a d d i t i o n , i t w i l l be p o s s i b l e to determine whether any economies of scale are present i n w r i 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 i n d i c a t e d 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 f a c t o r c u r r e n t l y used by the Canadian Underwriters' A s s o c i a t i o n .  In a d d i t i o n no economies  of scale were found i n w r i t i n g automobile insurance i n Canada.  TABLE OP CONTENTS CHAPTEE I  II  PAGE INTRODUCTION....................... Ob j e c t i v e s of Study  1  Method of A n a l y s i s . . . . . . . . . . . . . . . .  3  Sources of Data and C o n s t r a i n t s . . .  3  Organization of the Study...  5  THE EXPENSE FACTOR: HISTORY, COMPOSITION, AND EFFECT ON RATES.  III  IV  1  7  Introduction  7  The Loss Cost R a t i o .  9  The Trend Factor.  14  The Problem of A l l o c a t i o n . . . . . . . . .  21  Summary...........................  24  THE STATISTICAL STUDY:  THE MODEL....  26  The M u l t i p l e Regression Model.....  27  Eliminating Multicolllnearity.....  3<+  The Stepwise Regression...........  35  Summary  36  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  V  VI  T o t a l Expenses Incurred  51  Comparison of S t a t i s t i c a l Results with C.U.A, Expense Factor.....  51  I m p l i c a t i o n s or Study r o r Management Control  54  ECONOMIES OF SCALE  55  Economies of Scale i n Automobile Insurance.......................  55  Comparison or American Expense Ratios w i t h the Canadian S t a t i s t i c a l Results............  62  Summary...........................  67  SUMMARY AND CONCLUSIONS  BIBLIOGRAPHY.., .. , ...........  68 75  APPENDICES APPENDIX A. Tables or V a r i a b l e s I n cluded i n Regression Study  76  APPENDIX B , S t a t i s t i c a l Results or M u l t i p l e Regression......  81  APPENDIX C, Results of Simple Regress i o n on American Data....  117  APPENDIX D, L i s t or Companies by Agency S t r u c t u r e . . . . . . . . .  120  LIST OP TABLES TABLE I II  III IV  PAGE Percent Increase I n Countrywide Loss-cost.. P r i v a t e Passenger Automobile Losscost Ratio and Expense Factor Breakdown, 1930 t o 196b...,,..-..*.. C a l c u l a t i o n of Weighted Average Commission Rate................, .. Comparison of Canadian and U.S.A. Expense R a t i o s . . . . .  •..  12  1** 4-5 63  LIST GP FIGURES FIGURE  PAGE  1  Least Squares Trend Line of Loss-costs f o r Countrywide Experience  lb  2  Expense R e l a t i o n s h i p w i t h a S i n g l e - l i n e Company...........................  30  3  Expense R e l a t i o n s h i p of a Two-line Company  30  4  T o t a l Costs f o r a S i n g l e - l i n e Company w i t h Major Economies of Scale  57  5  T o t a l Costs f o r S i n g l e - l i n e Company w i t h Major Diseconomies of Scale.......  57  6  Unit Costs of a S i n g l e - l i n e Company..  5b  7  T o t a l Costs of a S i n g l e - l i n e Company.  5b  CHAPTER I INTRODUCTION Objectives of Study In the recent past the automobile insurance  industry-  has come under close s c r u t i n y by the p u b l i c a t l a r g e , o r ganizations and governmental agencies.  Automobile Insur-  ance r a t e s have increased a t such a pace that I t was I n e v i t able that the i n d u s t r y would be c a l l e d to task.  For example,  t o r 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 , p r i v a t e 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 additional  5  per cent on J u l y 1st,  1965i  per cent on January 1st, 1966.^"  and an a d d i t i o n a l 11  This I s equivalent to a  f i f t y per cent increase i n rates I n one year. In the s p r i n g of 1966 a Royal Commission on Automobile Insurance was e s t a b l i s h e d to i n q u i r e , among other t h i n g s , Into:  2  "...the cost to Insurers, to persons who pay insurance premiums and to the p u b l i c g e n e r a l l y of p r o v i d i n g present forms of automobile insurance determined on the Icanadlan Underwriters' A s s o c i a t i o n B r i e f (presented to the Royal Commission on Automobile Insurance, June I966, h e r e i n a f t e r C.U.A. B r i e f ) , p. 18. 2  T r a n s c r i p t , Royal Commission on Automobile Insurance of B r i t i s h Columbia ( h e r e i n a f t e r T r a n s c r i p t R.C.A.I.), Volume 1, pp. 6-7.  2  b a s i s of past and current experience and whether the cost i s i n proper r e l a t i o n s h i p to the e f f e c t i v e p r o t e c t i o n obtained,.., the j u s t i f i c a t i o n f o r recent v a r i a t i o n s In automobile insurance premium r a t e s , whether the p u b l i c of t h i s Province w i l l be b e t t e r served by the c o n t i n u a t i o n of present procedures f o r the r e covery of damages a r i s i n g out of motor-vehicle accidents and by the p r e s e r v a t i o n of present forms of insurance coverage or by some v a r i a t i o n or v a r i a t i o n s thereof,.., whether such a v a r i a t i o n or a p l a n 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 t h e s i s i s concerned w i t h e v a l u a t i n g the "cost to i n s u r e r s " 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 i n s u r e r s , and f i n a l l y , as to the i n f l u e n c e of the cost f a c t o r i n e s t a b l i s h i n g a c e n t r a l i z e d agency. 3  I n e s t a b l i s h i n g a rate or gross premium  the i n s u r i n g  company must cover expected l o s s e s a r i s i n g out of claims and cover a d m i n i s t r a t i v e expenses r e q u i r e d to w r i t e automobile 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 p r o p o r t i o n of overhead costs p e r t a i n 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 f a c t o r c u r r e n t l y being used by the Canadian Underwriters* A s s o c i a t i o n S t a t i s t i c a l Agency.  The procedure used I n t h i s study w i l l a l s o  3 G r o s s 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 e n a b l e u s t o d i s t i n g u i s h among e c o n o m i e s and or  no  economies o f s c a l e  ance i n Canada*  The  i n the w r i t i n g  results will  t i o n In administrative i n s u r a n c e b u s i n e s s were  of  multiple  that of  procedure  Insurance.  sible  cular line the  to  determine  tive  Analysis  t h a t w i l l be  followed requires The  the  hypothesis w i l l  expressed as a l i n e a r f u n c t i o n of criteria  i t w i l l be  the m a r g i n a l c o s t s of w r i t i n g a  use  be lines pos-  parti-  o f i n s u r a n c e f o r each expense c a t e g o r y I n c l u d e d  In  study.  z e r o and  reduc-  centralized.  Through s t a t i s t i c a l  to determine  Insur-  i n d i c a t e w h e t h e r any  regression analysis.  e x p e n s e s c a n be  of automobile  expenses would o c c u r i f automobile  Method o f The  diseconomies  The  r e s u l t s w i l l be  analyzed  whether they are s i g n i f i c a n t l y  the c o n f i d e n c e t h a t  c a n be  statistically different  placed i n their  from  predic-  v a l u e 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 o f  the  g r o s s premium.  Sources The Reports  o f D a t a and  Constraints ,  main source of d a t a i s c o n t a i n e d i n the  Annual  of the F e d e r a l Superintendent of Insurance.^  The  ^ R e p o r t o f t h e S u p e r i n t e n d e n t o f I n s u r a n c e f o r Canada. A n n u a l S t a t e m e n t s - F i r e arid C a s u a l t y I n s u r a n c e , Queens' P r i n t e r , O t t a w a 1965, Volumes I and I I ( h e r e i n a f t e r B l u e Books).  4 automobile Insurance companies report annually on a standard r e p o r t i n g 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 c o l l e c t e d 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 cons i s t s of net premiums w r i t t e n , net premiums earned and net claims i n c u r r e d . ^  Premiums w r i t t e n c o n s i s t s of a l l of the  insurance a company wrote i n Canada during the calendar year. Premiums earned c o n s i s t s of that p o r t i o n of the premium that i f : w r i t t e n on J u l y 1st, f i f t y percent of the premium i s earned i n the year i n which i t was w r i t t e n .  The unearned  p o r t i o n , the other f i f t y per cent of the premium, i s a p p l i e d to the f o l l o w i n g calendar year's earned premium.  Net claims  i n c u r r e d includes the l o s s e s a r i s i n g out of claims and b o d i l y i n j u r y , property damage, and c o l l l s s l o n claim expenses that a r i s 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, ^ T r a n s c r i p t B.C.A,I., Volume 1, p. 25^. Canadian and B r i t i s h Insurance Companies Act.  569,?0.  See a l s o 1932, C.46,  "Net" means a f t e r deduction of a l l reinsurance f o r Canadian companies but only r e g i s t e r e d or l i c e n s e d r e i n s u r ance f o r B r i t i s h and f o r e i g n companies, &  ?This should not be confused with the "earned premiums" r i g u r e s used to c a l c u l a t e r a t e s . On the l a t t e r , subject see the Report of the Royal Commission on Automobile I n surance. Nova S c o t i a , 1957, Volume I , pp. 35-6. (Nova S c o t i a R.C.A.I, h e r e a f t e r ) .  5  In a d d i t i o n to the above, the Blue Book a l s o cont a i n s the u n d e r w r i t i n g 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 a t l e a s t every three years.  Thus  i t may be concluded that the data to be used w i l l be u n i form and v a l i d . Organization of the Study Chapter I presents the o b j e c t i v e s and method of the study I n c l u d i n g sources of data, c o n s t r a i n t s and organizat i o n of the study. Chapter I I w i l l serve as an i n t r o d u c t i o n to the h i s tory of the expense f a c t o r l o a d i n g , the components of the expense f a c t o r , and the e f f e c t of the trend f a c t o r on the expense f a c t o r as i t i n f l u e n c e s r a t e 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 d e s c r i p t i o n 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 . B  Canadian and B r i t i s h Insurance Companies Act.  C.4-6, S . ? 2 ,  73,  74.  1932,  6  Chapters IV and V include the results of the study and implications as to the effects of these results on present 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 question 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 s t a t u t o r y 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 P l a n " as l a i d down by the Superintendents 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 p l a n f o r the 1  many categories of r i s k .  The Insurance industry i s then  able to use these r e s u l t s to e s t a b l i s h 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 r a t e , or accept the rates as published.  Since underwriting  ment i s involved I n s e t t i n g r a t e s , the Canadian  judg-  Underwriters'  A s s o c i a t i o n ' s i n f l u e n c e on r a t i n g p r a c t i c e s i n i n 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. B r i e f p. 2 .  formed.  2  I t s members c o n s i s t 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  obtain the representation of most i n s u r e r s so that t i o n could be disseminated the i n d u s t r y discussed.  to  informa-  q u i c k l y and common problems of The usefulness of the IBC appears  to l i e i n general p o l i c y considerations of the Insurance Industry as a whole as opposed to a q u a l i f i e d o r g a n i z a t i o n f o r s o l v i n g t e c h n i c a l r a t i n g problems.  The l a t t e r conclu-  s i o n I s based on the b u l l e t i n s Issued by the IBC i n t h e i r Submission.  contained  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 a v a i l a b l e f o r consultat i o n , i t i s not known whether a l l t e c h n i c a l matters r e c e i v e his attention.  S p e c i f i c a l l y on page 109  of the Document  B r i e f i t i s stated that the l a s t two years of the l e a s t square l o s s - c o s t p r o j e c t i o n s 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 preceding year's.  This weighting a p p l i e s only to the evaluation  as do whether the rates c u r r e n t l y i n existence would have been adequate had they been i n e f f e c t during the l a s t year's experience.  two  Thus i t i s separate from the trend f a c t o r  p r o j e c t i o n , and no weighting i s a p p l i e d to the trend f a c t o r  Submission of the Insurance Bureau of Canada to the Royal Commission on Automobile Insurance, November (I.B.C. Submission h e r e i n a f t e r ) p. 3.  1966  9 3  perse& There present. i s no doubt i n the w r i t e r s opinion, that the I,B.C. serves a u s e f u l f u n c t i o n I n attempting  t o create  an o r g a n i z a t i o n that represents a l l groups, a s s o c i a t i o n s and f e d e r a t i o n s of insurance  companies I n Canada, i n order  to d i s c u s s 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 r a t i n g body w i l l remain l i m i t e d , i f not harmful, to the industry itself.  Although I t I s p o s s i b l e that the mistake r e f e r r e d  to above i s an i s o l a t e d i n c i d e n t , any r e p e t i t i o n can only lead t o 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 e s t a b l i s h e s a premium i t i s expected that over time the gross premiums c o l l e c t e d w i l l cover the expected l o s s cost, the a d m i n i s t r a t i v e expenses involved and provide some allowance f o r p r o f i t .  The premium  may thus be regarded as c o n s i s t i n g of two separate f a c t o r s : a c t u a r i a l losses plus an expense f a c t o r ( i n c l u d i n g p r o f i t ) . The a c t u a l d i v i s i o n I n p r a c t i c e , as u t i l i z e d i n the rate ^The trend f a c t o r i s used to weight the l o s s cost f a c t o r , but the data used i n developing the trend f a c t o r i t s e l f i s not weighted.  10 making process of the Canadian Underwriters* A s s o c i a t i o n , is slightly different.  The a c t u a r i a l l y determined l o s s e s  a l s o i n c l u d e a l l o c a t e d 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 a l l o c a t e d  claims expenses may i n c l u d e 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 p o r t i o n of the premium  c o n s i s t s of a l l u n a l l o c a t e d c l a i m 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 l o s s e s 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 e x i s t e d to determine what p r o p o r t i o n of the gross premium should be devoted to expenses. set,  Once  competitive f a c t o r s might i n d i c a t e the t r u e nature  of the expense f a c t o r .  The e a r l i e s t l o s s - c o s t r a t i o  Canada was developed on February 1,  1929  4 ,  in  by the Canadian  Automobile Underwriters* A s s o c i a t i o n (a forerunner of the C.U.A.).  The p r o v i s i o n was f i f t y percent f o r l o s s e s and  f i f t y percent f o r expenses; that I s , a l o s s - c o s t 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 l o s s e s and a l l o c a t e d claims expense as a percent of gross premium to the u n a l l o c a t e d expense f a c t o r as a percent of gross premium.  was e s t a b l i s h e d to evaluate the reasonableness of the then present l o s s - c o s t r a t i o . ^  The r e s u l t a n t f i n d i n g s of the  Hodglns Report i n d i c a t e d that the r a t i o was too heavilyloaded with the expense f a c t o r and recommended that the expense f a 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 l o s s -  cost r a t i o t o 55/M-5 which was i n e f f e c t u n t i l 194-2 when a two percent f e d e r a l premium tax changed the l o s s - c o s t 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 l o s s - c o s t r a t i o  remained  a t 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 l o s s r a t i o had Increased r a p i d l y and premium r a t e s were r a i s e d accordingly I n 1952. However, the increase i n gross premium had a l s o been applied to the expense f a 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 companies changed the l o s s - c o s t r a t i o to 6 3 / 3 7 .  The t e n  ^Report on Automobile Insuranbe Premium Rates, King•s P r i n t e r s (Ontario), I930. „ ^ R e s t r i c t i v e Trade P r a c t i c e s Commission: Concerning^ The Business or Automobile Insurance i n Canada, Ottawa I90O. p. 158. ^ T r a n s c r i p t R.C.A.I., Volume 27, p. 3I47.  12 percent change r e s u l t e d m a f i v e percent reduction i n the f a c t o r f o r company expenses and a f i v e percent reduction in  commissions. S i m i l a r events preceding 1965 l e d to f u r t h e r adjust-  ments i n the l o s s - c o s t 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 i n c r e a s i n g average cost per claim.  I n I965 the I.B.C.  suggested that the commission r a t e could be reduced since TABLE I PERCENT INCREASE IN COUNTRYWIDE LOSS-COST POR BODILY INJURY AND PROPERTY DAMAGE, 1961 TO 1965. YEAR  CLAIM FREQUENCY  1961  9.6  361  3^.7  1962  10.1  385  38.9  1963  10.2-  414  42.2  8.4  1964  10.2  444  45.3  7.3  501  48.1  6.1  1965 Source:  9.6 .  AVERAGE COST OF CLAIM  AVERAGE PERCENT LOSS-COST . INCREASE  Green Books of S t a t i s t i c a l Agency, I965.  12.1  13 the premiums had r i s e n sharply.  I t a l s o 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 S c o t i a Royal Commission. I n August of  I965  the Automobile Insurance S t a t i s t i c a l Com-  mittee d i r e c t e d that the expense f a c t o r be reduced t o 33 percent.^  The l o s s - c o s t r a t i o was thus changed t o  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 l o s s - c o s t ratio  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 f a c t o r assumes the C.U.A, r a t e s of commission, the other expense f a c t o r s a c t u a l 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 f a c t o r 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 l a r g e l y the d i f f i c u l t y of the Industry i n 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. I b i d . , p. 68. °0p. c i t . , p.  34,  65-3,  10  pp.  461-46j.  14 TABLE I I PRIVATE PASSENGER AUTOMOBILE LOSS-COST RATIO AND EXPENSE FACTOR BREAKDOWN, 1930  TO 1966. DIVISION OF EXPENSE FACTOR  PERIOD  LOSS FACTOR  EXPENSE UNALLO- PROFIT FACTOR COMMISSION CATED COMPANY LOSS EXPENSE EXPENSE (percent)  1930-41 1942-4-8 1949-52 1953-65 1966 Sources  55 53 53 63 67  45 47 47 37 33  •  —  25.0 20.0 15.0 12,5  —  6 6 6 6  -  2.5 2.5 2.5 2.5  —  13.5 16.5  13.5 12.0  R e s t r i c t i v e Trade P r a c t i c e s 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 t h a t the Industry w i l l receive enough i n terms of gross premiums, c o n s i s t s of two steps. The f i r s t step c o n s i s t s of the formula guide t o determine whether the rates that are now I n e f f e c t would have been adequate f o r the l o s s e s Incurred during the l a s t f i v e years. The percentage d i f f e r e n c e s are c a l c u l a t e d , 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 s e t t i n g of a premium l e v e l by determining the probable f u t u r e l e v e l of l o s s e s . In order to achieve t h i s e>.nd, the l o s s - c o s t f o r the previous years i s determined by m u l t i p l y i n g the average cost per claim by c l a i m frequency.  From these f i g u r e s a trend  i s e s t a b l i s h e d upon which a p r o j e c t i o n i s made as t o the f u t u r e expected l o s s - c o s t s . Not u n t i l 1951 d i d 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 l o s s  13 cost per insured v e h i c l e was r e l a t i v e l y constant.  Since  the average l o s s - c o s t f i g u r e c o n s i s t s of a combination of frequency of a c c i d e n t s , and average cost per c l a i m , i t may be f e l t t h a t separate trend f a c t o r s should be developed f o r each.  However, the data a v a i l a b l e suggested that the f r e -  quency f a c t o r by I t s e l f was not a stable i n d i c a t i o n and seemed t o f l u c t u a t e widely. was,  The average cost per claim  however, more u s e f u l I n p r e d i c t i n g f u t u r e c o s t s , as  B r i e f , pp. 1 4 - 1 5 . l T r a n s c r l p t R.C.A.I,, Volume 25, p. 2967. 13The average l o s s cost p e r insured v e h i c l e represents a l l claims and a l l o c a t e d claim expenses a r i s i n g out of claims Incurred by the p o l i c i e s w r i t t e n i n a calendar year d i v i d e d by the t o t a l number of equivalent car years insured ( i n sured v e h i c l e s ' i n t e x t above). Car years insured means t h a t two cars Insured f o r 6 months each c o n s t i t u t e one c a r year. HC.U.A. 2  16  I t r e f l e c t e d the r i s i n g costs of r e p a i r i n g automobiles, h o s p i t a l and medical c o s t s , 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 v e h i c l e 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 p r o v i s i o n had to be made i n the r a t e making c a l c u l a t i o n s to r e r l e c t t h i s trend. The concept i s equivalent to a l l o w i n g 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 a n a l y z i n g the d i r e c t i o n and amount of the trend.  In 1965  the number of years used to  e s t a b l i s h the l o s s - c o s t 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 p r o v i n c e s . ^ 1  Thus  I t was f e l t that the s e r i e s used before would l a c k c o n t i n u i t y i n e s t a b l i s h i n g the expected p r o j e c t i o n of trend.  This  reduction i n the number of years used f o r e s t a b l i s h i n g the trend f a c t o r severely increases the p r o b a b i l i t y of e r r o r , 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 e r r o r , and the r e s u l t i n g c o n f l ^ 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  27,  pp.  3217-I0.  16rp t o t a l number of observations, l e s s the estimating cons tants equals the number or degrees of freedom. ne  17  dence g r e a t l y reduced.  I t would thus have been b e t t e r i f  the e x i s t i n g data used i n e s t a b l i s h i n g the trend were adjusted to allow f o r the e f f e c t s of Increasing the minimum l i m i t s . The procedure used to develop the expected l o s s - c o s t per insured v e h i c l e f e l l o w s below. The a c t u a l l o s s - c o s t per insured v e h i c l e i s p l o t t e d as a time s e r i e s 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 l o s s - c o s t s .  The purpose of p l o t t i n g  the chart i s to f i t a curve to the p o i n t s that most c l o s e l y represents  a f u n c t i o n expressed i n mathematical terms.  Through f i r s t d i f f e r e n c e a n a l y s i s , the a n a l y s t can e s t a b l i s h 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 combinat i o n of l o g a r i t h m i c manipulation to a r r i v e at an accurate d e s c r i p t i o n of the data.  However, even a f t e r such a mathe-  m a t i c a l d e s c r i p t i o n 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 f o r e c a s t i n g technique r e s t s s o l e l y on the c o n t i n u i t y of the underlying f a c t o r s 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. a c t u a r i e s ' analysis. technique.  The trend l i n e has been f i t t e d by the l e a s t squares In a d d i t i o n to the above c o n s t r a i n t i n using t h i s  curve f o r f o r e c a s t i n g i s the problem of the length of time  FIGURE  LEAST  SQUARES  TREND  1959  LINE  I960  V  QF  t  LOSS-COSTS  1961  1962  FOR  COUNTRYWIDE  1963  1964  YEARS  Least  squares  Trend  projection  Gompertz  Source  :  Green  Books  1959  trend  Curve  -  1965  line  EXPERIENCE  1965  1966  19  over which observations are made.  C l e a r l y I f the 195P to  195a data I n d i c a t e s f l u c t u a t i o n s around a l o s s - c o s t 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 a l s o the p o s s i b i l i t y t h a t the data from  I959  to  1964 represents more nearly the m i r r o r image of a Gompertz curve m which case there w i l l be a maximum l o s s - c o s t estab l i s h e d i n the near f u t u r e .  This may not be too w i l d 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  w i t h a d e c l i n i n g b i r t h r a t e , and moderate i n f l a t i o n , the r e s u l t s are not untenable. The a c t u a l choice of the f i n a l d e s c r i p t i o n of the observations by a mathematical formula thus w i l l depend not only on the time p e r i o d chosen, but a l s o on the c o n t i n u i t y of the underlying f a c t o r s that determine these observations. These f a c t o r s w i l l includes  the density of motor v e h i c l e  t r a f f i c , increased costs p e r claim due to r i s i n g labour c o s t s , raw m a t e r i a l s c o s t s , and other i n f l a t i o n a r y pressures  that  are not as r e a d i l y measured, such as higher court awards and increased claim consciousness.  The industry has apparently  recognized that a t various p o i n t s I n the past, these underl y i n g f a c t o r s have created conditions so that i t was neces-  20 sary to e s t a b l i s h a new trend l i n e i n order t o p r e d i c t with greater accuracy the expected l o s s - c o B t s . and  I963  the trend f a c t o r equalled  I n 1961, 1962  4.0 percent.;  In  1964,  3.8 percent and i n 1965, 9.0 percent f o r the countrywide loss-cost. ? 1  Up t o  I964  a one-year p r o j e c t i o n of trend was  u t i l i z e d , which was increased to a 1.5 year trend p r o j e c t i o n f o r 1965 and i n 1966 the planned f o r e c a s t was to cover 2.4 18 years, equal.to a f u l l p o l i c y year.  I n 1966 the C.U.A,  developed trend f a c t o r s f o r regions a t which time the 2.4 year l o s s cost p r o j e c t i o n amounted t o 22.0 percent f o r B r i t i s h Columbia. In the i n t r o d u c t i o n t o t h i s t h e s i s the p r o p o s i t i o n was put forward t h a t the expenses Incurred I n w r i t i n g automobile insurance were d i r e c t l y o r l i n e a r l y . r e l a t e d t o volume of business w r i t t e n .  Thus, a p p l i c a t i o n of the trend f a c t o r  to both the l o s s - c o s t and the expense f a c t o r would appear logical.  However, the industry decreased the  proportion  allowed f o r expenses, I n d i c a t i n g that e i t h e r expenses had been too l a r g e a p r o p o r t i o n of the gross premium, o r our hypothesis i s I n c o r r e c t .  The a c t u a l a n a l y s i s of the.data  w i l l i n d i c a t e a p o s s i b l e answer i n Chapter IV.  17C,U,A. B r i e f , p. 22, 1 8  I b l d . , p. 2 3 .  21 The Problem of A l l o c a t i o n 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 factor.  The method t h a t the C.U.A, employs I n e s t a -  b l i s h i n g gross automobile premiums may be stated by the f o l lowing equation: Pp  where: Pp = l o s s - c o s t per v e h i c l e (pure premium) e  = expense f a c t o r ( I n percent)  Pg = gross premium The two v a r i a b l e s that enter i n t o equation one are thus pure premium and the expense f a c t 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 l o s s experience and hence pure premiums are accepted as 'good practice  1  at present.^  pense f a c t o r e M  n  however.  The same cannot be s a i d f o r the exHere no data i s c o l l e c t e d , analyzed  and disseminated by the S t a t i s t i c a l Agency,  Hence the s i z e  of the l o a d i n g f a c t o r has been l e f t l a r g e l y to chance. As !9with perhaps the exceptions noted under the trend f a c t o r (Chapter I I 14).  22 stated p r e v i o u s l y , the Hodglns Report found 45 percent adequate In 1930.  In 1957  the Nova S c o t i a Report found that  "...a p r o v i s i o n i n the r a t e s 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 r a t e s ; however, the r e s u l t s were conf i n e d to the study of board companies only, and lacked s t a t l s t l -  21 cal 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 f a c t o r f o r rate-making purposes. The expense f a c t o r w i l l t y p i c a l l y c o n s i s t of two items. The f i r s t c o n s i s t s 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 c u l a r l i n e of insurance. The second cost c o n s i s t s 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 c o s t s , may be a l l o c a t e d and e a s i l y determined through standard cost accounting procedures.  However, when attempting to  a l 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 w r i t t e n or as a percentage of d i r e c t costs Incurred  20Nova S c o t i a 2 1  I b l d . , p.  R.CUA.I., Volume I , p.  49.  51,  23 or any other method.  None of these methods has any more  t h 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 by the Federal Superintendent In the "Blue Book".  collected  of Insurance and published  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 u n a l l o c a t e d c o s t s . There would be two a l t e r n a t i v e s r o r determining the costs a p p l i c a b l e 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 r e q u i r e the corporations 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 o b t a i n the d i r e c t p o r t i o n  or the expense f a c t o r .  However, t h i s s t i l l leaves us w i t h  the u n s a t i s f a c t o r y method of a l l o c a t i n g f i x e d c o s t s , somewhat 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 v a r y i n g or the  s i z e of a l i n e of business, and observing the w i t h u n a l l o c a b l e overhead f a c t o r s .  relationship  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 p r o p o r t i o n of an i n d i r e c t expense i s r e l a t e d to the volume of business  24  transacted In a l i n e of insurance. The second method o u t l i n e d above i s more u s e f u l and the technique r e s u l t s In the a b i l i t y to determine the marg 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 c a r r y i n g 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 s u c c e s s f u l , the accounting data must be uniformly p r e s c r i b e d and recorded, the number or observations or companies r e p o r t i n g l a r g e so the r e s u l t s w i l l have s t a t i stical validity.  The Federal Superintendent r e q u i r e s the  r e p o r t i n g of expenses f o r a l l companies on a calendar year b a s i s i n standard form, thus the f i r s t requirement I s met. Since there are over three hundred companies w r i t i n g i n s u r ance i n Canada, the second c r i t e r i a i s a l s o f u l f i l l e d . Summary The expense f a c t o r used i n s e t t i n g automobile r a t e s has been traced over a p e r i o d or time and has been reduced from an i n i t i a l r i f t y percent l o a d i n g to the present three percent of gross premium.  thirty-  The i n t r o d u c t i o n of a trend  f a c t o r r a t e i n 1951 has Increased the doubt as to the underl y i n g r e l a t i o n s h i p s between expenses, and l o s s e s and gross premiums.  The a p p l i c a t i o n of standard cost accounting tech-  J , R . Meyer et a l , Economics of Competition I n Transp o r t a t i o n I n d u s t r i e s . Harvard U n i v e r s i t y Press, Cambridge, Mass., I964. 22  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 a l l o c a t e d claim costs.  Unallocated costs would s t i l l present an insurmoun-  t a b l e problem as to the j u s t i f i a b i l i t y opposed to another.  of one method as  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 f o l l o w i n g chapters.  CHAPTER I I I THE STATISTICAL STUDY:  THE MODEL  The preceding chapter served as a b r i e f I n t r o d u c t i o n to the expense f a c t o r as I t i n f l u e n c e d the rate-making procedure.  I t was seen that the a c t u a l expense l o a d i n g f a c t o r  "e" used I n the rate-making rormula, was a r 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 c o l l e c t e d t o s u b s t a n t i a t e a s p e c i f i c expense r a t i o .  I t was a l s o argued that standard  cost accounting techniques would not be of any greater b e n e f i t i n d e c i d i n g upon an appropriate a l l o c a t i o n of overhead by l i n e of insurance.  S i m i l a r 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 s u c c e s s f u l treatment of the determination of marg i n a l c o s t s was achieved i n r a i l r o a d c o s t i n g i n the United 2 States.  The success of ."the technique, used I n the United  S t a t e s , 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 o r observations. In Canada the Superintendent or Insurance r e q u i r e s 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 Mathem a t i c a l Approach. McGraw-Hill, New York, 1958, pp. 67-?2. J.R. Meyer, et a l . Competition i n the Transportation Industry. Harvard U n i v e r s i t y P r e s s , Cambridge, Mass., 1964. 2  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 M u l t i p l e Regression Model The technique 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 i s by no means a new concept.  The technique may be a p p l i e d to  time s e r i e s a n a l y s i s and used as a f o r e c a s t i n g technique, as i t I s p r e s e n t l y 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 a p p l i e d  to a large sample of cross s e c t i o n a l data which does not have the Inherent problem or t r y i n g to p r e d i c t beyond the observed values, as i s necessary r o r the time s e r i e s technique.  Since uniformly reported data i s a v a i l a b l e f o r the  cross s e c t i o n a l a n a l y s i s , 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", 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 i s an extension of the f a m i l i a r l e a s t squares technique such t h a t 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 v a r i a b l e s entering i n t o the equation.  The  same conditions apply, however, so that the sum of the d i f f e r ence of the observed and a c t u a l dependent observations  are  zero, and the sum of the d i f f e r e n c e of the observed and a c t u a l values squared i s minimized.  These conditions i n -  sure that the r e s u l t a n t curve f i t s the observed data In a best p o s s i b l e manner, and may  be stated as the best unbiased  estimator of the underlying true  population.  The r e l a t i o n s h i p between expenses i n c u r r e d (Yi) and volume of net premiums w r i t t e n (X ), f o r a company w r i t i n g only one l i n e of Insurance, may linear  be desorlbed by the f o l l o w i n g  equation: Yl = A  Q  (1)  + b ^  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 r e -  gardless of the volume of d o l l a r s of premiums w r i t t e n by company.  the  The above equation Is the end r e s u l t of the r e -  gression a n a l y s i s , so t h a t i f a company w r i t e s X^* d o l l a r s ^For a d e s c r i p t i o n of m u l t i p l e regression a n a l y s i s , see: Croxton & Cowden, Applied General S t a t i s t i c s . PrentloeH a l l , New York, 1939; and E z e k l e l & Fox, Methods of Corr e l a t i o n and Regression A n a l y s i s . 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 n o n - l i n e a r i t y r e s u l t s , techniques are a v a i l a b l e to convert the r e l a t i o n ship to a l i n e a r f u n c t i o n .  29  of premiums, the corresponding expenses may he determined by c o n s t r u c t i n g 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^ a x i s u n t i l I t I n t e r s e c t s the Y i a x i s a t Y i * .  I n Figure I , I f  X i equals one u n i t ( I n d o l l a r s ) , then Y i I s regarded as the marginal cost of w r i t i n g each a d d i t i o n a l d o l l a r of premium. As long as X±* i s w i t h i n the observed range of data used i n d e r i v i n g equation ( 1 ) , then the r e s u l t a n t expense f a c t o r p r e d i c t i o n w i l l be accurate w i t h i n the l i m i t a t i o n s of s i g n l f l g a n c e 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 company i s engaged i n two l i n e s of Insurance X^and X . 2  The  equation t h a t describes t h i s s i t u a t i o n I s 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  f a c t o r Involved I n 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 a d d i 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 X 2 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  d o l l a r s of premiums w r i t t e n i s found by c o n s t r u c t i n g perpendiculars i n the X i and X  2  plane, and p r o j e c t i n g a per-  p e n d i c u l a r from t h e i r p o i n t of i n t e r s e c t i o n u n t i l i t cuts the AoBCD plane. X  2  The height of t h i s p o i n t E from the X i  plane determines the t o t a l expense f a c t o r YI*.  FIGURE EXPENSE  Expense Category  RELATIONSHIP  OF  2  A  SINGLE-LINE  COMPANY  Y;  Net  RELATIONSHIP  OF  Written  3  FIGURE  EXPENSE  Premiums  A  TWO-LINE  COMPANY  /  (Net  Expense Category  Premiums  Written,  line 2 )  y.»  Equotion  of plane  Yi ; o r b,X i + b X 2  0  (Net  Premiums  a BCD: 0  2  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 r e p r e s e n t a t i o n or the expense r e l a t i o n ship i s Impossible. In n M  The expense plane becomes a hyperplane  dimensions, where n represents the number or l i n e s  w  of insurance a company I s engaged i n . Thus i n order to o b t a i n the needed i n f o r m a t i o n of the constant f a c t o r  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 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 w i l l r e s u l t i n an a l g e b r a i c r e p r e s e n t a t i o n of the r e l a t i o n ship between expenses and volume of insurance w r i t t e n . Thus r e g r e s s i o n a n a l y s i s Involves the d e r i v a t i o n of an equation by which the dependent v a r i a b l e may be estimated rrom the independent v a r i a b l e s .  C l o s e l y r e l a t e d to regres-  s i o n a n a l y s i s i s c o r r e l a t i o n a n a l y s i s which measures the closeness or the r e l a t i o n s h i p described In the r e g r e s s i o n equation.  For the purpose or t h i s study we have assumed  t h a t there e x i s t s a l i n e a r r e l a t i o n s h i p between the dependent v a r i a b l e s and the independent v a r i a b l e s .  The general equa-  t i o n r o r determining the amount of expense i n c u r r e d f o r a p a r t i c u l a r company I s given by: Y = A  Q  + b i X l + b2 X2 + ....+  b  n  X  n  + e  where: Y =  the dependent v a r i a b l e representing a p a r t i c u l a r expense category such as commissions, premium taxes, etc. 0  See Appendix A, Table I r o r a complete l i s t i n g of a l l expense c a t e g o r i e s . 6  32  Xl,2«'.»»  '  AQ =  ^ independent v a r i a b l e denoting a l i n e of insurance where there are n such l i n e s . n  t n e  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 r e g r e s s i o n c o e f f i c i e n t t h a t determines which ' p o r t i o n 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 r e s i d u a l e r r o r of the estimating equation, and - represents the d i f f e r e n c e between values estimated from the equation and a c t u a l Observed values. Thus the above equation s t a t e s t h a t the p a r t i c u l a r  expense category I s equal to a constant term p l u s proport 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 e r r o r term i n d i c a t e s to what extent the equation over- or under- estimates the a c t u a l value f o r the dependent v a r i a b l e . 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 v a r i a b l e s .  These  Include net premiums w r i t t e n , net premiums earned and net Q  claims i n c u r r e d .  I t i s i n t u i t i v e l y apparent that a c e r t a i n  c l a s s i f i c a t i o n of independent v a r i a b l e s i s more meaningful f o r e s t i m a t i n g the value of a p a r t i c u l a r expense category. Hence net premiums w r i t t e n are probably best f o r estimating the r a t e of commissions p a i d 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 v a r i a b l e s included i n the model. ^Figures I and I I used the net premiums w r i t t e n c l a s s i f i c a t i o n ; however, net premiums earned, on net claims I n curred could have been used a l s o f o r i l l u s t r a t i v e purposes.  33 of insurance; whereas net claims i n c u r r e d a r e a b e t t e r e s t i mator f o r a l l o c a t e d claims expenses which vary more d i r e c t l y w i t h the l o s s costs i n c u r r e d ; and net premiums earned  will  be more appropriate f o r expenses which are r e l a t e d to the l e n g t h of the l i f e of a p o l i c y .  The f i n a l choice as t o  which set of explanatory v a r i a b l e s or c l a s s of insurance to be used w i l l u s u a l l y be made according t o the highest B  2  value,the c o e f f i c i e n t of determination which I s 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 v a r i a b l e that has been explained by the independent v a r i a b l e s . The c o e f f i c i e n t of determination i s a t the same time a measure of the goodness of f i t achieved f o r the equation under study and i s thus an i n d i c a t o r of the r e l i a b i l i t y of any p r e d i c t i o n s made u s i n g the equation. The r e g r e s s i o n c o e f f i c i e n t s c a l c u l a t e d are equivalent to the marginal or incremental cost Incurred 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.  The a c t u a l v a l i d i t y of the  r e g r e s s i o n c o e f f i c i e n t can be determined by comparing the estimated value w i t h the s i z e of i t s standard e r r o r of e s t i mate.  The sample s i z e and the absolute s i z e of the standard  e r r o r of estimate w i l l enable us to determine the confidence that we have i n the p r e d i c t i v e value of the p a r t i c u l a r r e 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 s u p p l i e s the corresponding F - r a t i o , which allows one to t r e a t 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 d e v i a t i o n 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 A f t e r a l l the data had been coded, and the  initial  o  p r i n t o u t from the T r i p Program^ reviewed, I t was found that many of the independent v a r i a b l e s were h i g h l y amongst each other.  correlated  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  c o r r e l a t e d , or a combination of them.  variableso  Thus the  regression  c o e f f i c i e n t s and the standard e r r o r of estimate w i l l be meaningful.  The only way  not  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 v a r i a b l e s are highly c o r r e l a t e d .  that  An a r b i t r a r y c u t o f f f i g u r e 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 v a r i a b l e s .  This meant that 5 5 percent of the m u l t i -  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 v a r i a b l e s , as they have now been aggregated In  i n t o a new  composite v a r i a b l e .  u  The l o s s 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 ? T r i p : Triangular Regression Package, U.B.C. Computing Centre. S e e Appendix A, Table I I I f o r the composition and designation of the new independent v a r i a b l e s . lQ  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 r e sults. The Stepwise Regression A f u r t h e r refinement i n the a n a l y s i s of the data may be achieved through the use of stepwise r e g r e s s i o n . I f I n a p a r t i c u l a r equation the independent v a r i a b l e s represent a spurious r e l a t i o n s h i p w i t h the dependent v a r i a b l e s under c o n s i d e r a t i o n , then a l l the other Independent v a r i a b l e s which are s i g n i f i c a n t may be a f f e c t e d so that the r e s u l t i n g r e 2  gresslon c o e f f i c i e n t s are l e s s accurate and the R f o r the whole equation reduced.  value  I n other words we would  l i k e t o remove those Independent v a r i a b l e s that do not cont r i b u t e s i g n i f i c a n t l y to the r e d u c t i o n of the o r i g i n a l v a r i ance observed i n the mean of the dependent v a r i a b l e .  The  technique i s such that each independent v a r i a b l e i s t e s t e d to see whether i t c o n t r i b u t e s s i g n i f i c a n t l y to the r e d u c t i o n of the variance of the dependent v a r i a b l e , and i f i t does, i t i s entered i n t o the equation.  The s t a t i s t i c used f o r  the accept o r r e j e c t d e c i s i o n i s c a l l e d an P - r a t i o .  Thus  I f the independent v a r i a b l e has an F - r a t i o greater than 11  the c u t - o f f r a t i o , the v a r i a b l e w i l l be entered.  I f how-  ever a t a l a t e r stage the F - r a t i o drops below the cutAn F - r a t i o of 4.0 was used a t the 5 percent l e v e l of s i g n i f i c a n c e . 1:L  36  off r a t i o due to the entry of other v a r i a b l e s , i t w i l l dropped from f u r t h e r consideration.  be  The independent v a r i -  ables are brought one at a time Into the regression equation, i n order of decreasing c o n t r i b u t i o n to the reduction variance  of  or the dependent v a r i a b l e under consideration.  The t e s t s of s i g n i f i c a n c e used (F t e s t s ) are based on  the  r a t i o of the dependent v a r i a b l e s variance contributed by independent v a r i a b l e s i n question; to the r e s i d u a l  the  variance  of the dependent v a r i a b l e a r t e r the i n c l u s i o n or the independent v a r i a b l e . Summary The m u l t i p l e regression model developed above was r i r s t adjusted r o r 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 v a r i a b l e s were removed from the equation to permit more meaningful r e s u l t s to be obtained.  In the f o l l o w i n g  chapter the r e s u l t s w i l l be analysed as they apply to the expense f a c t o r loading.  Ah a n a l y s i s 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 separately  i n Chapter V.  treated  CHAPTER IV STATISTICAL STUDY:  THE RESULTS  The a n a l y s i s of the s t a t i s t i c a l  study that I s to  f o l l o w w i l l i n d i c a t e 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 w i t h those of t h i s study w i l l be made a f t e r a det a i l e d d i s c u s s i o n of the v a l i d i t y of each f a c t o r included i n the f i n a l r e s u l t s .  The data i s drawn from Tables I t o  XXXV i n Appendix B. The t i t l e of each t a b l e designates the dependent v a r i a b l e o r expense category.  Tables I t o V I I  are the r e s u l t of the stepwise r e g r e s s i o n and represent the major expense categories t h a t w i l l be used, to evaluate the C.U.A. breakdown of the expense f a c t o r .  Tables V I I I  to XXXV represent a d e t a i l e d breakdown of Table V, the r e 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 w r i t i n g an a d d i t i o n a l d o l l a r of insurance premium i s constant.  Reference t o the data i n d i c a t e s that  the r e s i d u a l e r r o r o r standard e r r o r of estimate i s l a r g e r than the constant value f o r each and every equation d e r i v e d . I f the data could not be represented by a l i n e a r equation, ^As opposed t o stepwise r e g r e s s i o n which e l i m i n a t e s 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 v a r i a b l e s , hence the blank spaces I n Tables I t o 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 b e t t e r described by a c u r v i l i n e a r f u n c t i o n , then the assumption as to l i n e a r i t y would have r e s u l t e d I n a l i n e a r approximation to the curve a t i t s most densely populated area, such t h a t a large negative o r p o s i t i v e constant would have r e s u l t e d * for  Since there are no large values  the constant the assumption of l i n e a r i t y I s c o r r e c t and  w i l l be u s e f u l i n e s t i m a t i n g 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 i n c l u d i n g automobile  insurance.  In the d i s c u s s i o n to f o l l o w , c e r t a i n features w i l l be common throughout the a n a l y s i s or each expense r a c t o r . Although r e g r e s s i o n a n a l y s i s can be u t i l i z e d t o determine, from given values of the independent v a r i a b l e s , an absolute value f o r the dependent v a r i a b l e , t h i s d i s c u s s i o n w i l l mainly be concerned w i t h the marginal costs i n v o l v e d 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.  I n t h i s manner the problem  of t r y i n g to a t t a c h any s p e c i f i c meaning t o the value ;;" of the constant can be ignored.  I n general i t represents the cost  of being engaged I n the business of w r i t i n g insurance.  How-  ever since the standard e r r o r of estimate i s r e l a t i v e l y large i n a l l cases w i t h respect to the "a" value, exact numerical conclusions would be hard t o j u s t i f y .  The only general s t a t e -  ment to be made i s that some f i r m s w i l l f i n d themselves w i t h 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 I n 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 v a r i a b l e s i n t o net premiums w r i t t e n , net premiums earned and net claims i n c u r r e d 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 v a r i a b l e i n e s t i m a t i n g a corresponding value f o r the dependent v a r i a b l e 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  coefficient  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 v a r i a b l e that has been explained by the Independent v a r i a b l e s 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 , e s p e c i a l l y 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 r e g r e s s i o n c o e f f i c i e n t s of the Independent v a r i a b l e s to determine the marginal cost of w r i t i n g automobile insurance.  Each r e g r e s s i o n c o e f f i c i e n t i s accompanied  by i t s standard e r r o r , so t h a t 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 s i g n i f i c a n c e .  The usefulness of t h i s  approach hinges on the assumption t h a t marginal cost i s the f a c t o r to be used i n the expense l o a d i n g of the r a t e making formula.  Since the volume of Insurance w r i t t e n i s to a  large extent by e x i s t i n g insurance companies, then i t I s  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* p o i n t s or view, and a l l past costs w i t h respect to expenses and investments are sunk c o s t s . The present d i f f i c u l t y that the i n d u s t r y has i n a l l o c a t i n g overhead c o s t s , whether these are f i x e d or v a r i a b l e , when w r i t i n g p r i m a r i l y f i r e and automobile Insurances, i l l u s t r a t e s the usefulness of the marginal cost concept when no economies of scale are present.  The i n d u s t r y recognizes  that i t i s r e l a t i v e l y more expensive to w r i t e f i r e insurance  2 than I t i s to w r i t e automobile Insurance.  I t I s a l s o sus-  pected that automobile Insurance to some extent s u b s i d i z e s f i r e insurance by t a k i n g on a l a r g e r share of overhead, than would have occurred had:.the "company been w r i t i n g automobile 3 Insurance only.I t I s 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 w i t h  4 t h e f t , personal property, p l a t e g l a s s and p u b l i c l i a b i l i t y . However i t i s estimated t h a t as much as 2# percent of the automobile expense f a c t o r 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 f a c t o r w i l l a l l o c a t e over2  54, 6582-83,  T r a n s c r l p t R.C.A.I., Volume  3ibld,,  Volume  56  pp.  ^Appendix A, Table I I I . 5  L o c . C i t . , p,  6583,  pp.  6391-92.  41 head expenses e q u i t a b l y 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 i n t o seven cate-  g o r i e s as shown, by the headings of Tables I to V I I , 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 f o l l o w . Net Adjustment Expenses I n c u r r e d  0  Net adjustment expenses i n c u r r e d 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 a d j u s t e r s .  "Net" r e f e r s to the amount  the company p a i d out a f t e r recovery of any adjustment expenses from the other p a r t i e s i n v o l v e d .  This expense f a c t o r i s  included i n the l o s s p o r t i o n of the expense f a c t o r f o r r a t e 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 l o a d i n g p r e s e n t l y used. Turning now to the data, the c o e f f i c i e n t of determination i s l a r g e s t ( o . 8 7 7 4 ) f o r net claims i n c u r r e d and i n d i c a t e s that the expense f a c t o r should be d e r i v e d from t h i s column.  This r e s u l t i s a l s o 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 r e l a t e d to the frequency and s i z e of claims Incurred,  The r e g r e s s i o n  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 s e r v i c i n g every net d o l l a r of c l a i m i n c u r r e d . Since the °Source or data;  Appendix B, Table I ,  42 standard e r r o r or the r e g r e s s i o n c o e f f i c i e n t i s s m a l l , the r e s u l t a n t P - r a t i o i n d i c a t e s that t h i s r e s u l t I s s i g n i f i c a n t l y d i f f e r e n t from zero a t the one percent l e v e l of s i g nificance.  At the same time the standard e r r o r of the r e -  g r e s s i o n c o e f f i c i e n t i n d i c a t e s t h a t 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 p l u s or minus 0.19  percent of t o t a l claims  Incurred. Net Commissions Incurred? Net commissions Incurred are the commissions p a i d to the agents who  s e l l insurance, whether i t he as an employee  of a s i n g l e f i r m or as a l i c e n s e d agent who does business w i t h more than one f i r m . explained  89.75 percent  The c o e f f i c i e n t of determination of the o r i g i n a l v a r i a t i o n i n net  commissions i n c u r r e d w i t h respect to net premiums w r i t t e n . Again t h i s value f o r the c o e f f i c i e n t of determination was l a r g e r than f o r net premiums earned and net claims i n c u r r e d . T h i s r e 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 w r i t t e n . The net r e g r e s s i o n 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 a t the one percent l e v e l and w i t h a standard e r r o r of 0.66  percent.  This f i g u r e i s r e l a t i v e l y low i n comparison  7Appendix B, Table I I .  43  w i t h the quoted. C.U.A. rate of commission of 1 2 . 5 percent 8  and needs f u r t h e r explanation.  Board companies w r i t e 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 r e p r e s e n t a t i v e of the commissions p a i d i n terms of volume of insurance w r i t t e n . In order to determine the reason f o r a lower commission r a t e than might a t f i r s t be expected, i t i s necessary t o compare the competitive d i f f e r e n c e s with respect to the marketi n g of insurance premiums.  Members of the Canadian Underwriters'  A s s o c i a t i o n , Independent Insurance Conference, and two-thirds of the Independent independents operate through the Independent agency s t r u c t u r e ,  Licensed agents e s t a b l i s h t h e i r  1 0  own o f f i c e s , and may w r i t e and remit automobile insurance premiums to any members of the above.  The remuneration  received by the agents c o n s i s t s s t r i c t l y of commissions p a i d by the companies.  The remainder of i n s u r e r s not i n -  cluded i n the above c o n s i s t of independent independents 11  who are d i r e c t w r i t e r s . These companies employ t h e i r ^commission r a t e on p r i v a t e passenger automobile > insurance, C.U.A. B r i e f p. 3 4 . I b l d . , p. 1 - 2 . 9  *°See Appendix D, Table I f o r companies w r i t i n g under the independent agency s t r u c t u r e . U s e e Appendix D, Table I I f o r companies who are d i r e c t writers.  44 own agents as employees, and pay them commissions, plus p r o v i d i n g o f f i c e space and r e l a t e d supporting o f f i c e personnel. I f i t could he e s t a b l i s h e d what premium volume i s w r i t t e n by each of the groupings above, and t h e i r r e s p e c t i v e commission r a t e s , a weighted average may be d e r i v e d t o compare with the 7,58 results.  percent f a c t o r obtained from the s t a t i s t i c a l  At the same time I t would be necessary to deter-  mine what percentage of the t o t a l automobile insurance w r i t t e n c o n s i s t s of p r i v a t e passenger automobile Insurance.  The  Nova S c o t i a Report found that 25.7 percent of the t o t a l r e presented p r i v a t e 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 i n t o f o u r teen other c l a s s i f i c a t i o n s f o r Nova S c o t i a experience i n 12  1955.  However f o r Ontario the p r i v a t e passenger  accounted f o r 45 percent of the t o t a l i n 1953, 1954, and 72 percent of the t o t a l i n 1955.  Insurance  67 percent i n  Unfortunately  no Canada-wide s t a t i s t i c s were a v a i l a b l e then, or, a t the present time. Even though p r e c i s e data i s l a c k i n g , i t i s p o s s i b l e to I l l u s t r a t e the method t h a t could be used i n e s t i m a t i n g a h y p o t h e t i c a l commission r a t e f o r t o t a l automobile i n s u r ance w r i t t e n i n order to compare the r e s u l t w i t h the 7.58 £%ova S c o t i a R.C.A.I., Volume I , p. 30, footnote 15.  13lbld.,  Volume I I , Table X L I I , p.  263.  45  percent f a c t o r .  The f o l l o w i n g t a b l e shows the weighted aver-  age commission rate expected on p r i v a t e passenger automobile insurance w r i t t e n . TABLE I I I CALCULATION OF WEIGHTED AVERAGE COMMISSION BATE  PERCENT OF TOTAL VOLUME Canadian Underwriters Association* ( i i ) Independent Insurance  COMMISSIONS PAID WEIGHTED (MAX.) . AVERAGE  (1)  33  12.5  23  15  3.5  ( i l l ) I n d e p e n d e n t Independents*  36  14  5»0  ( l v ) Independent Independents**  18  6  1.1 13.7  Conference*  * w r i t i n g through an independent agency s t r u c t u r e ** d i r e c t w r i t e r s  4.1  Source of data: ( i ) C.U.A. B r i e f p. 1 and p. 34. ( l i ) T r a n s c r i p t , R.C.A.I., Volume 31,  p. 3490 and p. 3521.  (iii)derived ( l v ) c a l c u l a t e d from Appendix D, Table I I companies f o r volume w r i t t e n , commission rate i s that of A l l s t a t e . The weighted average commission rate of 13.7 percent represents the expected f i g u r e i f a l l automobile Insurance w r i t t e n were p r i v a t e passenger only.  However as i s mentioned above,  46 p r i v a t e 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 t h a t 60 percent of  the t o t a l was p r i v a t e passenger Insurance, then the expected commission r a t e f o r t h i s study would be 60 percent of 13.7 p l u s 40 percent of the weighted average of the remaining types of automobile coverage  commissions.  P r i v a t e passenger automobile Insurance c a r r i e s the highest commission r a t e i n terms of percent, because the 14 average a c t u a l d o l l a r s per premium i s low.-  Por commercial  and other c l a s s e s 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 w r i t t e n .  Thus i f the a c t u a l  volume of premiums w r i t t e n I s r e l a t i v e l y high f o r c l a s s i f i c a t i o n s other than p r i v a t e passenger, the r e s u l t i n g average commission r a t e would be expected to be considerably lower than t h a t p r e s e n t l y u t i l i z e d i n e s t a b l i s h i n g ah expense f a c t o r l o a d i n g 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 r a t e s are a l s o paid on premiums w r i t t e n under the assigned r i s k p l a n .  For p r i v a t e passenger  i t I s 10 percent, whereas f o r commercial insurance i t v a r i e s between 5 and 7§ percent lowerithan normal rates.15 l 4 T r a n s c r l p t , R.C.A.I., Volume 18, p. 2178. 15iranscript, R.C.A.I., Volume 18, pp. 2177-8.  However,  47 In 1964 the t o t a l volume w r i t t e n represented only one h a l f of one percent of a l l business w r i t t e n , doubled by  1965. ^ 1  t h i s f i g u r e had  Thus a t t h i s time i t d i d not a f f e c t the  average commission r a t e expected. In a d d i t i o n to the foregoing comments, there i s one a d d i t i o n a l reason to accept the 7«5 percent f i g u r e as proa  bably a r e l i a b l e measure of the t o t a l commissions Incurred. Commission r a t e s obtained i n other l i n e s of insurance were w i t h i n one per cent of those expected i n i n d u s t r y . ? Por 1  these reasons i t i s p o s s i b l e t h a t the 7.58 percent f a c t o r i s a r e a l i s t i c weighted average commission r a t e . Net P r o f i t Commissions I n c u r r e d ^ 1  Net p r o f i t commissions may be considered a bonus on top of net commissions i n c u r r e d . Usually a contract e x i s t s between an agent and an insurance company so that i f an agent remits good r i s k s to the i n s u r e r , the i n s u r e r rewards the agent by paying him a premium on top of the normal comI b i b i d . , p. 2192. ^ C o n v e r s a t i o n w i t h insurance agent, name w i t h e l d on request. A p p e n d i x B, Table I I I . The Independent Insurance Conference c a l l s these 'contingent p r o f i t commissions . The maximum r a t e being •§ to 1 % of earned premiums. The a c t u a l number of agreements of t h i s nature i s small and I s u s u a l l y extended by a company who wishes to e i t h e r increase the market share, o r penetrate a market not formerly engaged i n . T r a n s c r i p t H.C.A.I., Volume 31, pp. 3492-97. 18  1  46 mission p a i d .  The idea i s to a l l o w the agent to share i n  the net p r o f i t s f o r having s e l e c t e d good r i s k s .  This method  of a d d i t i o n a l remuneration a p p l i e s 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 l a r g e s t 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 I s based on earned premiums to a l a r g e extent.  The net r e g r e s s i o n 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 a t the one  percent l e v e l , and the standard e r r o r equals 0.04  percent.  This expense should only apply to the board-member companies, and not the various independents. Taxes Incurred  20  The taxes Incurred are p r o v i n c i a l taxes l e v i e d on the premiums w r i t t e n 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 t h a t do not f a l l under the r e d e r a l t a x a t i o n 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 w r i t t e n r o r automobile insurance.  49 The c o e f f i c i e n t of determination I s l a r g e s t f o r the net claims Incurred a t 0.9624; whereas f o r net premiums w r i t t e n i t i s a l i t t l e less at 0.9307.  Since the taxes are c o l l e c t e d  on the b a s i s of net premiums w r i t t e n , and the a c t u a l d i f f e r ence between the determination c o e f f i c i e n t s i s s m a l l , the net r e g r e s s i o n 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 w r i t t e n w i t h a standard e r r o r of 0.07 percent, the r e g r e s s i o n c o e f f i c i e n t being s i g n i f i c a n t a t the one percent l e v e l . i . T h i s f i g u r e I s 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 w r i t ten.  The amount of automobile Insurance net premiums w r i t t e n  increased from 336 to 407 m i l l i o n d o l l a r s from I963 to I 9 6 4 , This represents a 20 percent Increase i n d o l l a r volume I n 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  w r i t t e n f o r the previous year.  For the purposes of t h i s  study the 2.4 percent f i g u r e 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 $ f i g u r e agrees e x a c t l y w i t h that quoted i n the Report of the Superintendent of Insurance I964, Volume I , p. x l v .  50 General Expenses I n c u r r e d ^ 2  The general expenses Incurred category i n c l u d e s general a d m i n i s t r a t i v e expenses such as s a l a r i e s , r e n t , various fees f o r d i f f e r e n t r e p o r t s , 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 w r i t t e n and net claims i n c u r r e d , 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 r e s u l t s i n e i t h e r case.  The choice f a l l s  on net premiums w r i t t e n by convention and p r a c t i c a l reasons f o r l a t e r comparison. 15.98  The net r e g r e s s i o n c o e r r i c i e n t equals  percent w i t h a standard e r r o r 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 premiums.  For automobile Insurance the r e g r e s s i o n c o e f f i c i e n t  was not brought i n t o the f i n a l r e g r e s s i o n and i s thus i n significant.  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 w r i t t e n to the p a r t i c u l a r 23  A p p e n d i x B, Table V.  This r e s u l t f o l l o w s i f one allows f o r volume d i f ferences between net premiums w r i t t e n and net claims Incurred. 2i,,  2  5Appendix B, Table VI.  51 insurance company i t wrote the p o l i c y r o r , so that i f the account proves u r i c o l l e c t a b l e , the agent s u f f e r s the l o s s , not the company.  Bad debts w i l l be i n c u r r e d however, by  companies that w r i t e under the d i r e c t agency system. T o t a l 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 w r i t t e n .  27.70 percent  The r e s u l t a n t r e g r e s s i o n c o e f f i c i e n t i s  of net premiums w r i t t e n , w i t h a standard e r r o r  of 0.99 percent, which i s s i g n i f i c a n t a t the one percent level.  This f i g u r e 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 f a c t o r s upon which the r e s p e c t i v e f i g u r e s 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 F a c t o r In order r o r 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 l o s s p o r t i o n of the s t a t i s t i c a l 2o  A p p e n d l x B, Table V I I .  5  2  agencies r a t e making formula, then the r e s u l t s obtained rrom the study I n d i c a t e the f o l l o w i n g marginal costs as based on net premiums w r i t t e n : 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 a d d i t i o n 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 f a c t o r equals 2b,55 percent of net premiums w r i t t e n .  Another way  of c a l c u l a t i n g the same t o t a l expense f a c t o r I s t o r e c a l l that t o t a l expenses Incurred was c a l c u l a t e d i n Table V I I . ? 2  The marginal cost was found to be equal to of net premiums w r i t t e n . expenses i n c u r r e d  2 0  27,70  percent  By s u b t r a c t i n g the net adjustment  of 2.12  percent and adding the 2.5 percent  allowance f o r p r o f i t , the r e s u l t a n t expense f a c t o r equals 29 28.51 percent.  7  The confidence l i m i t s of t h i s f i g u r e may  be obtained by t a k i n g the standard e r r o r s of both the t o t a l expenses and the net adjustment expense which equals  1.15  27Appendix B. 2tJ  Based on net premiums w r i t t e n , Table I , Appendix B.  ^ I n c l u d e s the tax adjustment from 1.97$ premiums w r i t t e n .  to 2.4$ of net  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 w r i t t e n . The expense f a c t o r 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 A s s o c i a t i o n Fees...............  0.6  Unallocated Claims Adjustment Expense....  4.0  A d m i n i s t r a t i v e Expense ( I n c l u d i n g 2.5 Profit)  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 t a b l e , insurance a s s o c i a t i o n fees, unallocated claims, adjustment expenses and a d m i n i s t r a t i v e expenses are the 2.5$  equivalent of the general expenses Incurred p l u s the 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 f a c t o r breakdown would be i f the commissions paid were  12.5$.  I t I s only necessary  to add 4.92 percent to the net commissions Incurred and subt r a c t 4.92  from the general expenses Incurred.  This r e s u l t  f o l l o w s from the observation that there i s no advantage w i t h respect to t o t a l expenses as to whether a company I s 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 f i r m w i t h the  confidence  l i m i t s e s t a b l i s h i n g bounds on the p r e d i c t i v e value of the results. I m p l i c a t i o n s 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 h i s company's r e s u l t s w i t h 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 i n c u r r e d however would a l l o w a more d e t a i l e d comparison of h i s company to the i n dustry average, and thus concentrate h i s a t t e n t i o n on those areas or expense by l i n e or insurance that appear to be the trouble spots.  Thus Tables V I I I 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  a d j u s t e r s 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 a c c o r d i n g l y , 3 Appendix B. 2  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 a l s o be u t i l i z e d to determine whether o r 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 s c a l e ,  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 p o r t i o n of the gross premium, and perhaps a l s o i n the a l l o c a t e d claims c o s t s .  Thus H  operations are such that one l a r g e  e n t i t y could administer the Insurance volume more e f f i c i e n t l y or economically than a l a r g e number of smaller e n t i t i e s , a n a t u r a l monopoly would e x i s t . In order to determine whether there are economies, diseconomies or no economies of s c a l e , the underlying reasoni n g 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. marginal costs of a f i r m are f a l l i n g , economic theory us that there w i l l be economies of scale present.  I f the tells  Since  there are u s u a l l y a l s o some f i x e d costs i n v o l v e d , average cost w i l l f a l l as output (that i s , volume of premiums w r i t t e n ) r i s e s , as long as the f i x e d costs are not exceedingly l a r g e . From the above I t i s apparent that the w i l l rise. at. a d i m i n i s h i n g r a t e . costs.  2  t o t a l cost curve  And since the l i n e a r  2-Economles of scale may occur due to decreasing 2  See Figure 4.  marginal  FIGURE TOTAL  COSTS  WITH  4  FOR A S I N G L E - L I N E  MAJOR  ECONOMIES  OF  COMPANY SCALE  Y  Total Expenses  O o  Net  FIGURE TOTAL  COSTS  WITH  MAJOR  FOR A  Premiums  5  SINGLE-LINE  DISECONOMIES  COMPANY  OF SCALE  Written  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 a t i t s highest p o i n t , since t h i s i s where major economies would r e s u l t . E x t r a p o l a t i o n of the s t r a i g h t l i n e to the I - a x i s would then i n d i c a t e a l a r g e "a" value. I f , on the other hand, marginal costs increase as the volume of premiums w r i t t e n I s increased, then the t o t a l cost curve w i l l r i s e a t an i n c r e a s i n g rate.3  The s t r a i g h t l i n e  equation produced by the m u l t i p l e r e g r e s s i o n study drawn tangent to t h i s curve and extrapolated to the Y-axis would i n d i c a t e that diseconomies of scale were present through a l a r g e negative "a" value. The t h i r d a l t e r n a t i v e , t h a t there are n e i t h e r economies nor diseconomies  of scale present, assumes t h a t 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 l a r g e , no economies of scale would be foundlas r e f l e c t e d by a very low a " value f o r the l i n e a r equation."' M  I t may be u s e f u l to r e c a l l b r i e f l y what i s meant by the standard e r r o r of estimate.  Por a simple r e g r e s s i o n ,  i t i s merely the square r o o t of the sum of the squares of the v e r t i c a l d e v i a t i o n s of Y d i v i d e d by the number of observations. The standard e r r o r of estimate i s s i m i l a r to the r e l a t i o n the standard d e v i a t i o n of a frequency d i s t r i b u t i o n bears 3 ee Figure 5. S  ^See Figure 6.  5see Figure 7.  FIGURE  UNIT  Expenses dollar  COSTS  of  SINGLE-LINE  -Average  per  Premiums  OF A  6  COMPANY  Cost  Net Written Marginal  Net  FIGURE  TOTAL  COSTS  OF A  Cost  Premiums  Written  7  SINGLE-LINE  COMPANY  Total Expenses  Total  o  Cost  *1 Net  Premiums  Written  57 to the a r i t h m e t i c mean.  Thus i f the d e v i a t i o n s are normally  d i s t r i b u t e d , s i x t y - e i g h t percent of the d e v i a t i o n s w i l l l i e w i t h i n a distance of one standard e r r o r of estimate from the l i n e .  Por a m u l t i p l e r e g r e s s i o n s i t u a t i o n , i f the a d d i -  t i o n a l independent v a r i a b l e s c o n t r i b u t e any information about the dependent v a r i a b l e , the standard e r r o r of estimate computed from the m u l t i p l e r e g r e s s i o n equation w i l l be smaller than that obtained from the simple r e g r e s s i o n equation. The s t a t i s t i c a l r e s u l t s as r e r i e c t e d i n Tables I to VII I n Appendix B, i n d i c a t e that there are no economies of scale f o r the l i n e s of insurance f o r which  statistically  s i g n i f i c a n t r e g r e s s i o n c o e f f i c i e n t s are l i s t e d .  The f o r e -  going conclusion i s based on the f a c t that the standard e r r o r 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 l a r g e r than the constant value a . This same observation H  M  held f o r each operation performed during the stepwise r e gression.  I t may a t t h i s p o i n t be objected t h a t 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 c o s t s , but a high f i x e d cost.  However, the stepwise r e g r e s s i o n  computer p r i n t o u t shows the same r e s u l t s as i n Tables I to VII as each Independent v a r i a b l e i s brought i n t o the equation. Thus the standard e r r o r of estimate r e a l l y represents a confidence i n t e r v a l , such t h a t i f we draw two p a r a l l e l  58 l i n e s one standard e r r o r of estimate away from our c a l c u l a t e d s t r a i g h t l i n e , we would expect any one f i r m w r i t i n g a p a r t i c u l a r 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 - a x i s s i x t y eight out  6 of a hundred times.  I f we take two standard e r r o r s 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 l a r g e r than the confidence I n t e r v a l j u s t c a l culated. Returning b r i e f l y to the concept that the standard e r r o r of estimate was s i g n i f i c a n t l y l a r g e r than the "a" values c a l c u l a t e d from the p a r t i c u l a r r e g r e s s i o n equations, the f o l l o w i n g statements I n d i c a t e the l a c k of any economies or diseconomies  of s c a l e .  Since bur confidence i n the ab-  solute value of the constant i s determined l a r g e l y by the r e l a t i v e s i z e of the standard e r r o r of estimate; and the standard e r r o r of estimate i s from f o u r to twenty times g r e a t e r than the constant f o r a l l expense c a t e g o r i e s , there i s therefore no more reason to suspect that there i s e i t h e r a c o n s i s t e n t upward or downward b i a s of the standard e r r o r of estimate i n expressing confidence l i m i t s f o r "a" a t the Y - axis.  Hence the only conclusion that appears tenable i s  that, there are no major, economies or diseconomies  of s c a l e .  °This a p p l i e s to a company w r i t i n g one l i n e of i n s u r ance, however, an extension i n t o n dimensions i s p o s s i b l e by the use of algebra.  59  I t i s Important to r e a l i z e that the foregoing conc l u s i o n shows the long run s i t u a t i o n .  Thus the equations  that describe the r e l a t i o n s h i p between t o t a l expenses and premium volume p i c t u r e a f i r m on the long run marginal cost curve.  I t i s recognized that a p a r t i c u l a r f i r m may a t some  time not be on the long run marginal cost curve.  A new f i r m  entering i n t o the business w i l l Incur costs i n i t s e a r l y years, that could exceed the Industry average.  For instance,  i n order f o r a f i r m to break i n t o the market and obtain a large enough share, i t may have to o f f e r commission r a t e s f a r above the Industry •norm .-' Even e x i s t i n g f i r m s may 1  f i n d themselves temporarily i n c u r r i n g costs that are higher than expected.  This may occur when mechanization  of pro-  cedures could reduce the overhead expenses now i n c u r r e d through manual labour.  Another area where economies or diseconomies  might occur i s I n ' t i e - i n ' business.  C e r t a i n l i n e s of i n -  surance are cheaper to underwrite and administrate i f combined, so that t o t a l costs would be much greater i f these l i n e s were w r i t t e n separately.  Such a grouping I s Indicated  i n t h i s study f o r c e r t a i n l i n e s of insurance, but not f o r automobile.  This grouping appears to have s i g n i f i c a n c e f o r  5Transerlpt,  R.C.A.I., Volume  33,  pp. 364-6-47.  ^ R e c a l l that some of the I n i t i a l independent v a r i a b l e s i n c l u d e d i n the study tabulated I n Appendix A, Table I I , were aggregated i n Table I I I , Appendix A.  60  those Insurance companies who w r i t e l i n e s of insurance t h a t are included i n the aggregations.  The a c t u a l b e n e f i t s 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 e s t a b l i s h from t h i s study.  However a company that w r i t e s only auto-  mobile insurance does not appear to be at a p a r t i c u l a r advantage 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 automation, 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 s i z e s and i n v o l v e d a high c a p i t a l expenditure.  However, the combination  of v a r i o u s  computer s i z e s and costs probably a l l o w f l e x i b i l i t y i n determining 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 b a s i s p l u s pooled arrangements a l s o allow the use of more e f f i c i e n t data processing at a l l l e v e l s of o operations regardless of the s i z e of the c o r p o r a t i o n . ' 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 l a r g e f i r m could r e s u l t through h o r i z o n t a l i n t e g r a t i o n . Automobile i n s u r e r s could, f o r example, e s t a ?Even i f the i n d u s t r y 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 c o r r e l a t i o n was found. 8  33 pp. 3852-53. 5597, 5612.  T r a n s c r l p t R.C.A.I., Volume  9lbid.,  Volume 48, pp.  61  b l l s h t h e i r own r e p a i r shops f o r a u t o m o b i l e s .  10  A possible  cost saving might occur through the e l i m i n a t i o n of at l e a s t one claims a d j u s t e r from e i t h e r the r e p a i r shop or rrom the company.  Other areas f o r cost savings may a r i s e i n terms  of f u r t h e r d i v e r s i f i c a t i o n i n the future when the volume of business w r i t t e n becomes large enough to support the a d d i t i o n a l f a c i l i t i e s on an economical b a s i s .  I n t h i s respect i t i s  expected that these h o r i z o n t a l i n t e g r a t i o n movements would appear f i r s t In the United States where both volume and 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 a t 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 o p e r a t i o n s .  1 2  A l l data and i n f o r m a t i o n i s e a s i l y transported to a c e n t r a l headquarter e s t a b l i s h e d anywhere i n the country where normal business concentrates. Market s i z e and concentration may be a l i m i t i n g f a c t o r when w r i t i n g on a p r o v i n c i a l b a s i s , so that the market i s only large enough to support the operat i o n of one i n s u r e r . l 0  I f a second i n s u r e r entered, both would  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 ,  I b i d . , Volume 16, pp. 1983-84; Volume 48, p. Volume 5b, p. 6587. 1 2  5597,  11  62  Incur a higher expense r a t i o .  Thus a case r o r a r e g i o n a l  monopoly regulated by the province -co Insure r a t e s may he made.  appropriate  I n general, however, i f a market i s not  l a r g e , 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 a t 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 f o l l o w s from the l a c k of i n d i v i s i b i l i t i e s  of s c a l e ,  w i t h no major outlays r e q u i r e d to operate an insurance b u s i ness other than the minimum required to o b t a i n a large enough and d i v e r s i f i e d experience  so that one bad l o s s w i l l not  bankrupt the c o r p o r a t i o n . ^  Although some f i r m s w i l l  reach  a s i z e where mechanization of procedures becomes f e a s i b l e , t h i s i s n e i t h e r a handicap to small operations nor an advantage to l a r g e ones.  14.  I n the above d i s c u s s i o n , i t must  be remembered that t h i s i s the long run s i t u a t i o n that the study measures, so that i t i s p o s s i b l e r o r 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 c o s t s . Comparison of American Expense Ratios w i t h 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 s u b s t a n t i a t i o n 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 t h a t there are no economies of s c a l e i n the operation of automobile insurance.  A comparison of the American auto-  mobile expense f a c t o r s w i t h the Canadian counterparts suggests t h a t the American commission r a t e s are double those or Canada, while t h e i r general expense f a c t o r i s s i g n i f i c a n t l y lower. The argument has been proposed that the explanation r e s i d e s i n the economies of scale of the American experience.  The  argument suggests that because the volume w r i t t e n by American companies i s so l a r g e , economies i n automation must be r e f l e c t e d i n lower t o t a l expense r a t i o s f o r the very l a r g e firms,  1 5  The f o l l o w i n g t a b l e 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 . • Expense Item  '• "  U.S. Stock Companies  Fire, 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) Commissions (W) Other A c q u l s l t i o n s ( E ) General Expenses (E)  .0197 .075« ,0013  .033 .150  .l?9b  ±251 ai21  • 966 2  Source of U.S. Data:  .049  I965 Loss  .031 .156 .051  .127  .063  .183 .048 .•0.^8  .301  .316  .12b .177 .051  .061 .317  and Expense R a t i o s , 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 compare r e l a t i v e magnitudes since the American values are s u p p l i e d through standard a l l o c a t i o n procedures, and may not r e f l e c t a c t u a l experience i f the same s t a t i s t i c a l procedures i n Chapter I I I were used. shortcoming.  outlined  The reader should be aware of t h i s  However, i t i s f e l t that the conclusions w i l l  not be a f f e c t e d . The data contained i n the above t a b l e shows the expense r a t i o s f o r b o d i l y i n j u r y 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 comprehensive f o r the U.S. stock companies, which are roughly comparable to the majority of corporations w r i t i n g insurance i n Canada.  automobile  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 w r i t t e n ( W ) and other a c q u i s i t i o n s and general expenses as a percent of net premiums earned ( E ) .  The Canadian f i g u r e s  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 . Ignoring the d i f f e r e n t t a x e f f e c t s , I t I s seen t h a t the f o u r categories of coverage l i s t e d i n the American r a t i o s can now be compared w i t h 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 w i t h the Canadian counterpart.  The l a t t e r o b t a i n i n g approximately  h a l f of the former I n commissions. 16  A p p e n d i x B.  Even i f we allow that  1 0  65 some of the other a c q u i s i t i o n costs included i n the American experience I s 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 r e s u l t s show that the general expense r a t i o f o r the Canadian corporations i s about double t h a t of t h e i r American counterpart. The conclusion reached i s t h a t the Canadian companies are l e s s e f f i c i e n t i n the a d m i n i s t r a t i o n 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 i n v o l v e d i n w r i t i n g  automobile  insurance i n the United States because of the tremendous volume w r i t t e n .  To t e s t t h i s l a t t e r hypothesis, a simple  r e g r e s s i o n study was designed to t e s t the p o s s i b i l i t y of the inverse r e l a t i o n s h i p between s i z e of automobile  Insurance  premiums earned and the expense r a t i o s i n c u r r e d .  The r e s u l t s  are found i n Appendix C, Table I t o IV. Por each c l a s s of Insurance, b o d i l y i n j u r y  liability,  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 , t h e f t and comprehensive, net premiums earned was designated the 'dependent v a r i a b l e ' , r e f l e c t i n g the absolute s i z e of the f i r m . Within each c l a s s the 'independent v a r i a b l e ' was i n t u r n : 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 p l u s commissions and brokerage. The r e s u l t s f o r a l l of the simple regressions c a l c u l a t e d from 125 stock companies based on countrywide  experience  i n d i c a t e d t h a t there were no major economies or diseconomies of scale present.  I n every instance the standard e r r o r of  66  estimate was from twenty to one hundred percent l a r g e r than the corresponding value f o r the constant.  Further proof  that there was l i t t l e or no r e l a t i o n s h i p between the v a r i ables measured i s i n d i c a t e d by the F - r a t i o s c a l c u l a t e d f o r each simple r e g r e s s i o n . 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 c a u t i o n i s necessary w i t h respect to Inter-r p r e t a t i o n 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 r e q u i r e d , then a l l the f i g u r e s of the columns headed by the "standard e r r o r " and the "constant" should be m u l t i p l i e d by one thousand, and the f i g u r e s under the column headed by "regression c o e f f i c i e n t " d i v i d e d by one hundred. These changes do not a f 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 e a s i e r coding f o r the computer.  R e c a l l a l s o t h a t none of the r e g r e s s i o n  c o e f f i c i e n t s were s i g n i f i c a n t a t the f i v e percent l e v e l ; hence, the equations represented are not of p r e d i c t i v e value at a l e v e l of confidence high enough to warrant f u r t h e r attention.  67 Summary Two s e p a r a t e  s t u d i e s have been used t o  w h e t h e r any e c o n o m i e s o f mobile insurance.  determine  scale are present i n w r i t i n g  N e i t h e r the Canadian d a t a n o r the  d a t a s u g g e s t s t h a t any e c o n o m i c a d v a n t a g e w o u l d be from placing a l l hands o f a s i n g l e  the automobile corporation.  carrier,  if  it  only  t h e I n s u r a n c e was p l a c e d w i t h a  o f many i n d e p e n d e n t large  insurance  single  of both ad-  operation.  the present  c o m p a n i e s i s as  certain  answers  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 .  b a r r i n g non-economic terms of r e f e r e n c e ,  as a s i n g l e  the  T h i s d o e s n o t mean t h a t  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  ministrative  American  derived  Insurance business i n  s o c i a l b e n e f i t s would not accrue to s o c i e t y , the question t h a t  auto-  Thus mix  expensive  CHAPTER VI SUMMARY AND CONCLUSIONS In chapter I I the appropriateness of applying the trend f a c t o r to both the l o s s cost and expense f a c t o r I n developing new r a t e s was questioned.  The successive reduc-  t i o n s i n the expense f a c t o r l o a d i n g as a percent of gross premiums meant e i t h e r that expenses d i d not vary d i r e c t l y w i t h the s i z e of premium o r i t was already too l a r g e and any f u r t h e r 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 r e s u l t of an i n t u i t i v e f e e l i n g by the r a t i n g agency t h a t the expense f a c t o r 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 h e a v i l y f o r t h e i r rate making procedures on the r a t i n g agency of the C.U.A. The r e s u l t s of Chapters IV and V i n d i c a t e d that the general equation used i n e s t i m a t i n g the expense l o a d i n g f a c t o r was l i n e a r .  Thus the marginal costs of w r i t i n g i n -  surance are constant, and w i l l a l s o represent a constant f a c t o r of gross premiums.  This r e s u l t , although obtained  from a s i n g l e year's data, does represent the underlying r e l a t i o n s h i p between the expense f a c t o r and gross premiums. Hence the trend f a c t o r can be a p p l i e d to both the l o s s cost and expense component of gross premium, provided the current expense l o a d i n g i s v a l i d .  This i s not to say t h a t the ex-  pense f a c t o r of 28 percent developed from the I964 data  b9  should remain a t that l e v e l f o r e v e r .  I f a t any time changes  occur I n some of the b a s i c cost expense r e l a t i o n s h i p s such as Increased  cost of s t a t i o n e r y o r u n i o n i z a t i o n of c l e r i c a l  help, these allowances must be made i n subsequent rate making' d e c i s i o n s as I t a p p l i e s to the expense f a c t o r . Comparison or the expense f a c t o r 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 f a c t o r from 37 to 33 was I n e f f e c t j u s t i f i e d , and that a f u r t h e r reduction t o  30  percent could be achieved.  Hence a  70/30  l o s s - c o s t r a t i o would not appear to provide undue hardships f o r companies engaged i n automobile insurance.  The a c t u a l  breakdown of the expenses depends to a large extent on the commission remuneration s t r u c t u r e 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 t o adjust the general expense f a c t o r to a l l o w f o r d i f f e r e n t rates of commission.  Knowing what the expense  f a c t o r i s has the added b e n e f i t of being able to determine how any one p a r t i c u l a r f i r m compares w i t h the r e s t of the Industry. The conclusions reached i n Chapter V i n d i c a t e d that there were no s i g n i f i c a n t economies of scale present I n w r i 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 i m p l i c a t i o n i s t h a t no one c a r r i e r would  he able to achieve a lower o v e r a l l expense f a c t o r because of the s t r u c t u r e of technology r e q u i r e d . There are no  indivisi-  b i l i t i e s of s c a l e , no l a r g e input f a c t o r s of a scarce nature required.  Thus the expense f a c t o r s can be used as standards  to determine whether the f i r m i s on the long run marginal cost curve.  Hence management w i l l be able to determine  the  optimum p o i n t 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 I n t e n s i t y . In order to f a c i l i t a t e  f u t u r e expense f a c t o r l o a d i n g  c a l c u l a t i o n s as a percent of gross premiums, the submission of i n d u s t r y expense and premium data should be on standard punch cards so that they may be used f o r both the p u b l i s h i n g of the data, as i s now r e q u i r e d f o r the annual r e p o r t s , and a l s o a l l o w 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 j u s t automobile insurance. Once the computer programme has been w r i t t e n , the information t h a t r e s u l t s w i l l be obtainable annually a t very l i t t l e cost. In a d d i t i o n 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 a n a l y s i s to determine whether there i s any d i f f e r e n c e i n experience or whether i t s u b s t a n t i a t e s the data presented here w i t h respect to expense f a c t o r l o a d i n g . A crude comparison was presented i n Chapter V; however, a d e t a i l e d comparison would r e q u i r e f u r t h e r  71 refinements. In t h i s study the data u t i l i z e d covered only the p e r i o d of the one year 1964 hence the allowance f o r underlying changes over time w i t h respect to the expense f a c t o r In the past may provide a d d i t i o n a l i n f o r m a t i o n to base f u t u r e rate making d e c i s i o n s 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 p r e d i c t i v e information f o r the f u t u r e as p r o d u c t i v i t y 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 d i f f e r e n c e 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 f a c t o r l o a d i n g 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 s i g n i f i c a n c e and confidence l i m i t s presented i n Chapter IV. This t h e s i s has mainly been concerned w i t h e v a l u a t i n g phe adequacy or the expense f a c t o r used by the C.U.A, i n developing automobile insurance premiums.  Through a n a l y s i s  or industry-wide data, an i n d u s t r y average expense l o a d i n g or approximately 2b to 30 percent was round to be adequate to w r i t e automobile insurance business.  Although such an  expense l o a d i n g would be adequate f o r the Industry i n aggregate, i t may not r e f l e c t a c c u r a t e l y the expense experience or I n d i v i d u a l companies.  Thus f o r some the expense l o a d i n g would  be adequate, while r o r others they might be wholly  inadequate.  72 These d i f f e r e n c e s could a r i s e out of marketing procedures employed, breadth of market engaged I n , and l e n g t h of time the company had been i n the business.  In a d d i t i o n to the  short-coming of t h i s Industry average approach Is the  continued  problem of d e c i d i n g at which point gradation of expense f a c t o r s i s warrented.  1  At present studies have i n d i c a t e d 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 w r i t t e n i s appropriate f o r r i s k s up to $1,000. Since automobile premiums f o r p r i v a t e passenger business Is nowhere near t h i s at present, the percent l o a d i n g or v a r i a t i o n appears appropriate. I t may prehensive  thus be f e l t t h a t Instead of producing a com-  l o s s - c o s t formula f o r developing r a t e s , expenses  be determined by each company separately.  Thus expected l o s s e s  could be developed according to the i n d i v i d u a l company's experience, and the expense f a c t o r would be wholly determined by competitive f a c t o r s e x i s t i n g at any time i n the i n d u s t r y . 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 a t the branch l e v e l of large i n t e g r a t e d 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 f o l l o w i s developed i n the Commonwealth of V l r g l n n l a 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 c o n c l u s i o n then i t may be stated w i t h confidence that i f the formula approach to r a t e making was continued, the l o s s - c o s t r a t i o could be reduced to 70/30 thus decreasing the expense l o a d i n g f a c t o r another three per cent from i t s 1966  level.  I t I s a l s o f e l t that no r e d u c t i o n In t o t a l  expenses Incurred could be e f f e c t e d by l e t t i n g a s i n g l e c a r r i e r or agency operate automobile insurance i n Canada. I f the automobile insurance business i s to be taken over by p u b l i c a d m i n i s t r a t i o n , 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 V l r g l n n i a Report of A c t u a r i e s , 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. A p p l i e d General S t a t i s t i c s . New York: P r e n t i c e - H a l l , 1939. E z e k i e l , M., and Fox, K. Methods of C o r r e l a t i o n 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 I n d u s t r i e s ; Cambridge, Mass.: Harvard U n i v e r s i t y Press, 1964. Report of the Royal Commission on Automobile Insurance. Nova S c o t i a , 1957. Report of the Superintendent or Insurance r o r 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 Printer, 1930. R e s t r i c t i v e Trade P r a c t i c e s Commission: Concerning the Business or Automobile Insurance In Canada, Ottawa: Queen's P r i n t e r , i960. Richmond, S.B,, S t a t i s t i c a l A n a l y s i s . Co., 1964. 2nd e d i t i o n .  New York: Ronald Press  Submission of the Insurance Bureau or Canada to the Royal Commission on Automobile Insurance, November I966. T r a n s c r i p t , Royal Commission on Automobile Insurance or B r i t i s h Columbia 1 9 6 6 - 6 7 .  APPENDIX  A  77  TABLE I DEPENDENT VARIABLES ( - EXPENSE CATEGORIES)  Name Y  l  Y  2  Net adjustment expenses Incurred Net commissions i n c u r r e d Net p r o f i t commissions Incurred  3  Y  \  Taxes i n c u r r e d (other than on income and r e a l estate)  h  General expenses i n c u r r e d  Y  Bad  6  Salaries  7  J  Y  Y  debts  Agents' allowance s  8  Contributions to s t a f f pensions and insurance plans  9  Y  10  Unemployment and other s o c i a l insurance c o n t r i b u t i o n s  Y  ll  D i r e c t o r s ' fees  12  A u d i t o r s ' fees  Y  Y  Y  Y  Y  Y  Management remuneration  1 3  Advertising  14  Books and p e r i o d i c a l s  1 5  Bureau and A s s o c i a t i o n dues  16 17  -  j Y  Y  18 19  C h a r i t a b l e donations Inspections and Surveys  Y  20  Insurance other than insurance on r e a l estate  Y  21  Legal expense  Y  22  Maps and plans  2 3  Medical examiners'  Y  Y  24  fees  Mercantile agencies' r e p o r t s  DEPENDENT VARIABLES ( - EXPENSE CATEGORIES) O f f i c e f u r n i t u r e and equipment Postage, telegrams, telephones and express P r i n t i n g and stationeryRents S t a t i s t i c a l bureau expenses T r a 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)  Xi X  FJire Personal Property  X3  Real Property  X^  Inland Transportation  X5  Theft  X$  Boiler - holler  Xr?  B o i l e r - machinery  Xg  P l a t e glass  X  Credit  2  Q  X^Q  Guarantee - f i d e l i t y  X±l  Guarantee - surety  X  L i a b i l i t y - public l i a b i l i t y  1 2  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 - I n d i v i d u a l cancellable  16  Personal accident and sickness - I n d i v i d u a l non-cancellable  X^  Automobile - l i a b i l i t y  X^g  Automobile - other  X  Aircraft - l i a b i l i t y  X  X  1 Q  2 0  X i 2  A i r c r a f t - other 20 Miscellaneous category = ( T o t a l Insurance - ^jT  1=1  x,) 1  bo  TABLE I I I NEW CLASS  CLASS OP INSURANCE  ORIGINAL INDEPENDENT VARIABLES  F i r e ; Personal Property; Theft; P l a t e Glass; P u b l i c l i a b i l i t y .  Xi+X +X5*X5+X  B o i l e r - b o i l e r ; B o i l e r - machinery  x +x  2  6  7  Real property X,' 4  Inland Transportation Credit Guarantee-fidelity; Guarantee-surety Employers-liability  b  Personal Accident/sickness - group  Xo  Personal Accident/sickness i n d i v i d u a l C a n c e l l a b l e ; Noncancellable  X  X  10  Auto - l i a b i l i t y : Auto - other  X  ll  Aircraft - l i a b i l i t y ; A i r c r a f t - other  12  Miscellaneous  A  4  *9 X  10  x  13  + X  11  1 4  x  15  + x  16  x  17  + x  18  x +x l9  "21  20  12  APPENDIX B  82  TABLE I NET ADJUSTMENT EXPENSES INCURRED LINE OF INSURANCE  REGRESSION COEFFICIENT N p w  F i r e ; Theft; Personal Property; 0.0363** Plate glass; Public l i a b i l i t y (0.0028)  N P E  N C I  0.0309'* (0,0029)  0.0736** (0.0047)  -0.0117** (0.0020)  l.liol** (0.3020)  0.0378* (0.0153)  0,0384* (0.0172)  0.0807** (0.0301)  0.0101** (0.0032)  O.OllO** (0.0033)  0.015b (0.0036)  0.0212** (0,0016)  0.0269** (0.0018)  0.0326** (0.0019)  Boiler-boiler; Boilers-machinery Real property Inland  transportation  Credit Guarantee-fidelity Guarantee-surety Employers*-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable " -non-cancellable Automobile-liability " -other Aircraft-liability " -other  -0.0937* (0.0456)  Miscellaneous R  0,7709  0.7^-55  0.8237  a  13.4407  13.2317  9.0353  SY  52.7151  52.4602  46.4012  2  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l notes f i g u r e s i n brackets represent standard e r r o r of r e gression c o e f f i c i e n t  63 TABLE I I NET COMMISSIONS INCURRED  REGRESSION COEFFICIENT  LINE OF INSURANCE  NPW  F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y  0.3272" (0.0120)  Boiler-boiler; Bo i1er-machlnery  0.1695** (0.0633)  NPE 0,2761 (0.0152)  NCI 0.5579** (O.0254) O.4.760 * (O.2296)  3.9&04*  Real Property 0.2841**  Inland t r a n s p o r t a t i o n  (1.6488)  (0.0532)  0.1884** (0.0493)  Credit Guarantee-fidelity Guarantee-sure ty  0.2856** (0,0643)  Employers'-liability Personal Accident/sickness -group  0.0647«*  0.3153**  (0.0924) 0.1852* (0.080b)  -3.9432*  (1.58bl) 0.5614** (0.1&55)  0.0694**  (0.0147)  0.0603** (0.0183)  Personal Accident/sickness Individual-cancellable -non-cancellable  0.1745** (0.0133)  0.2063** (0.0247)  0.3H6** 0.0257  Automobile-liability -other  0.0758** (0.0066)  0.1057** (0.0094)  0.1464** (0.0102)  Aircraft-liability -other  0.4249** (0.1443)  Miscellaneous  0.1?99** (0.0281)  R*  0.8975  a  5.4467  SY  221.9650  (0.0202)  0.6224  0.6774  14.9955  -0.3303  277.4401  243.5902  • Denotes sfignlfigant a t 5$ l e v e l • • Denotes s i g n l f i g a n t a t 1% l e v e l note:  f i g u r e s in, brackets represent standard e r r o r of r e g r e s s i o n coefficient  84  TABLE I I I NET PROFIT COMMISSIONS INCURRED LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery  REGRESSION COEFFICIENT NPW NPE NCI 0.0070** 0.0085** 0.0116**  (0.0007) (0.0006) (0.0012) -0.0059* (0.0023)  Real Property Inland Transportation Credit  -0.0179*  Guarantee-fidelity Guarantee-surety Employers-liability Personal Accident/siclmess -group  (0.0076)  0.0265* 0.0492** (0.0130) (0.0157) 0.001b* 0.0020* 0.0019* (0.0007) (0.0007) (0.0009) -  Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other  0.0009* 0.0013** 0.0025** (0.0003) (0.0004) (0.0005) 0.03^4** (0.0116)  Miscellaneous  R  2  a  SY  0.5356 0.5115 11.7378  0.0010** (0.0002) 0.5896  0.5549  -0.2621  -O.0274  10.9016  11.5332  • Denotes s l g n i f l g a n t a t 5% l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  85  TABLE IV TAXES INCUREED LINE OP INSURANCE  REGRESSION COEFFICIENT NCI NPE NPW  F i r e ; Theft; Personal PropertyPlate glass; Public l i a b i l i t y  0.0278** (0.0013)  0.0224** (0.001b)  0.0466** (0.0019)  Boiler-boiler; Boiler-machinery  0.0276 (0.0071)  0.0184* (0.0072)  0.0877** (0.0174)  Real Property Inland  0.0267** (0.00b2)  transportation  0.027b** (0.0040)  Credit Guarant e e - f i d e l l t y Guarant e e-sure ty  0.0357** (0.0072)  Employers-liability  0.0326** (0.0092)  0.0636** (0.012b)  0.0195* (0.0060)  Personal Accident/sickness -group  0.0224** (0.0017)  0.0207** (0.0018)  0.0286** (0.0015)  Personal Accident/sickness Individual-cancellable -non-cancellable  0.0225** (0.0015)  0.0224** (0.0025)  0.0427** (0.0019)  Automobile-liability -other  0.0197** (0.0007)  0.0257** (0.0009)  0.0333** (0.0008)  0.0222** (0.0021)'  0.079b** (0.0283)  0.9307  0.9037  0.9624  a  3.3W  3.b207  1.8013  SI  25.0103  27.8748  18.4554  Aircraft-liability -other Miscellaneous E  2  • Denotes s i g n i f l g a h t a t 5% l e v e l ••Denotes s i g n i f l g a n t a t 1% l e v e l Note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE V GENERAL EXPENSES INCURRED LINE OF INSURANCE  REGRESSION COEFFICIENT NCI NPE NPW  F i r e ; Theft; Personal Property; 0.1160" Plate glass; Public l i a b i l i t y (0.0139) Boiler-boiler; Boiler-machinery  0.4465"  (0.0665)  0.1031**  (0.0169)  0.37&5**  (0.0802)  0.2323"  (0.0228)  1.5434 * (0.2076) -  Real property Inland t r a n s p o r t a t i o n  0.3382** (0.0689)  Credit  0.1210** (0,0443)  Guarantee-fidelity Guarantee-surety Employers -liability 1  0. 14-05* (0.0676) 0.9868** (0.2608)  Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other  0.0945** (0.0153) 0.2083** (0.0139) 0.1598** (0,0069)  (0.0205)  1.3393** (0.3099) 0.1198** (0.0190)  0.2067**  0.3770**  0.7316** (0,0892) 0.0874**  (0.0277) 0,1998** (0.0105)  (0.0241) 0.2470** (0.0094)  Aircraft-liability -other  0.1526**  Miscellaneous R  2  0.8824  a  29.0285  SY  231.6124  • Denotes s l g n i f l g a n t a t 5$ l e v e l  (0.0236) 0.7665 26.8998 311.0469  0.8846 20.8148  229.2430  ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  87  TABLE VI BAD DEBTS LINE OF INSURANCE  REGRESSION COEFFICIENT NCI NPE NPW  F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y  0.0006* (0.0003)  Boiler-boiler; Boiler-machinery Real property Inland  transportation  Credit Guarantee-fidelity Guarantee-surety Employers-liability  0.0057**  (0.0008) 0.0078** (0.0026)  0.2625 (0.0299)  0.0146** (0.0041)  Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable  0.0014 (0.0002)  0.0023 * #  (0.0003)  Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  0.3521  0.2037  a  0.1387  -1.8049  SY  2.7997  113.2626  0.2109  0.2140 3.0897  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note; f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE V I I TOTAL EXPENSES INCURRED LINE OP INSURANCE  REGRESSION COEFFICIENT NPE NCI NPW 0,4340 *  F i r e ; Theft; Personal Property; 0.5032** Plate glass; Public l i a b i l i t y (0.0200)  (0.0295)  0.6194**  0.4187**  Boiler-boiler; Boiler-machinery  (0.0953)  #  (0,1356)  0.9011**  (O.O369) 2.0605** (O.3252)  6.3204** (2.3431)  Real Property 0.6241** (0.1166)  Inland t r a n s p o r t a t i o n  0.2475"  Credit Guarantee-fidelity Guarante e-sure ty Employers'-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other  0.4-9 2 6 " (0.0969) 1.5630  (0.3736) 0* I.925 •* (0.0220)  2  a SI  (0,1728)  1.2032**  (0.1508) 0.1665**  (0.03^7)  0.6612**  (0,2368) 1.9657**  (0.4732) 0.2530 •• (0.0286)  0.4396** 0.7335** 0.4-0 50 (O.OI99) (0.0469) (0.03&3) 0,2770** 0.3590** 0,4596** (0.0099) (0.0179) (0,0l42)  Miscellaneous R  (0.0750) 0.554-3**  0.9512 55.71B1 332,1161  0.3090** (0.0399) 0.8698 0.9477 63.6666 30.2802 525.9969  344.4602  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  SALARIES  TABLE V I I I REGRESSION COEFFICIENT NPW NPE NCI  LINE OF INSURANCE  F i r e ; Theft; Personal Property; 0.0749" (0.0124) Plate glass; Public l i a b i l i t y Boiler-boiler; Bo11er-machinery Real property Inland Transportation Credit Guarantee-fidelity Guarante e-sure ty Employers-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  0.1505** (0.0197) 0.2925** 0.2945** 1.0233** (0.0370) (0.1412) (0.0423) 1.2780 -0.1b61 -0.9913 (0.6686) (1.0256) (0.8413) 0.032b 0.0575 -0.4752* (0.1619) (0.1857) (0.1984) 0.460l 0.3512 1.3543 (0.24b?) (0.2007) (O.9749) 0.0848 0.0665 -0.0578 (0.0425) (0.0430) (0.1038) 0.7536** 0.6216** 0.8941** 0.0838** (0.0108)  (0.1688) 0.0612**  (0.1508)  (0.2083)  (0.0097)  (0.0086)  (0.0124) 0.1716**  (0.0045) -0.0471 (0.1141)  (0.0063)  0.0958** (0.0088) 0.0840** (0.0047) -0.0693 (0.1287) 0.0408  (0.1277) 0.858  a SY  89  0.238 146.943  • Denotes s l g n l f l g a n t a t %  0.0579**  0.0779**  0.1007** (0.0079) (0.0157) 0.1023** 0,1321**  0,0576  (0,1189)  0,691 -13.409 128.315  0.0117  (O.I532) 0.1730 (0.2342)  0.853 -4,965 149.414  level  ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE IX AGENTS' ALLOWANCES LINE OF INSURANCE  REGRESSION COEFFICIENT. NPW NPE NCI  F i r e ; Theft; Personal Property; 0.0009 Plate glass; Public l i a b i l i t y (0.0013)  0,0011 (0,0013)  0.0001 (0.0020)  Boiler-boiler; 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  Credit  -O.OO57  (0.0268)  -0.0057 (0.0248)  -0.0886 (0,1008)  Guarantee-fidelity Guarantee-surety  -O.OOI3  -0.0018 (0.0053)  -O.OO5O  Employers-liability  -O.O250  -0,0286 (0.018?)  -0,0217 (0.0215)  Personal Accident/sickness -group  -0,0001 (0.0011)  -0,0004  -0,0011 (0,0013)  Personal Accident/sickness Individual-cancellable -non-cancellable  0,008?»« (0.0010)  (0.0047) (0.0183)  (0,0011) 0.-009-1**  (0.0010)  (0.0205)  (0,010?)  0.0172 ' -  (0.0016)  0.0006  0.0011  Alrcraftr-llabillty -other  -0.0086 (0.0140)  (0.0006) -0.0084 0.0141  Miscellaneous  -O.OOI3  ^0.0023 (0.0147)  -0.0067 (0.0242)  R  0.258  0.266  0.306  a  0.506  0.271  0.423  SY  15.972  15.665  I5.444  Automobile-liability -other  2  0,0005  (0.0139)  0,0017*  (0.0007) -0,011? (0,0158)  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE X CONTRIBUTIONS TO PENSION AND INSURANCE PLANS LINE OP INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; -0.0019 (0.0014) Plate glass; Public l i a b i l i t y  -0.0021 (0.0014)  Boiler-boiler; Bo i l e r-machlnery  0.0 2?7" (0.0049)  0.0282** (0.0048)  Real property  -O.ObbS  -0.0477 (0.0665)  Inland Transportation Credit  (0,0983) -0.0032 (0.0217) 0.0688* (0.0288)  -0.0033  (0.0021) 0.0798**  (0.0147) -0.1450 (0.1067)  -0.0053 (0.0209)  (0.0206)  0.0568* (0.0260)  o,4l95 (0.1014)  0.0142 ,#  (0.0197)  0,0195** 0.0449•• (0.0108) (0.0055) 0.0390 0.103b*• (0.0195) (0.0217)  Personal Accldent/slclmess -group  O.OO27 (0.0011)  0.0024 (0.0011)  (0.0013)  Personal Accldent/slclmess Individual-cancellable -non-cancellable  0.0057*  0.0061* (O.OOlO)  0.0105* (0.0016)  Guarantee-fidelity Guarantee-surety Employers'-liability  Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY  0.0187**  (0.0050) 0.0469•  0.0032  (0,0010) 0.0063** 0.0076** 0.0088** (0.0005) (0.0006) (0.0007) -0.0250 -O.0250 -0.0349* (0.0150) (0.0148) (0.0159) 0.0521** 0.0572** 0.0669** (0,0149) (0.0154) (0.0244) 0.bb4 0.590 0.617 0,782 0.235 -0.369 17.172 16.596 15.540  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l notes f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n Coefficient  TABLE XI UNEMPLOYMENT AND OTHER SOCIAL INSURANCE CONTRIBUTIONS LINE OF INSURANCE F i r e ; I n e r t ; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery Real property Inland Transportation Credit Guarantee-fidelity Guaran t e e-surety Employers-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY  REGRESSION COEFFICIENT NPW NPE NCI  0.0006** 0.0008** (0.0001) (0.0001) 0.0010 • 0.0010** (0,0004) (0.0003) 0.0027 -0.0067 (0,0076) (0.0060) -0,0004 -o.oool (0.001?) (0,0015) 0.0041 0.0030 (0.0023) (0.0018) 0.0004 0.0003 (0,0004)  0,0039* (0,00lb)  (0.0004)  0.0027  (0.0014)  0.0014**  (0.0002) 0.0033 (0.0012) 0.0031  ##  (0.0086)  -0.0042*  (O.OOI7)  0.0172  (0.0061)  -0.0007  (0.0009) 0.0046 *  (0.0017)  0,0003** 0.0003** 0.0004** (0,0001) (0.0001) (0.0001) 0,0009**  0.0009**  0,0016**  (0.0001) (0,0001) o.ooo9** 0.0012** (0,0000) (0,0000) (0,0001) -0.0018 -0.0015 -0.0016 (0,0012) (0,0010) (0,0013) -0.0007 -0.0006 -0.0004 (0,0012) (0,0011) (0.0020) 0.827 0,874 0.853 -0 . 244 -0.115 -0.187 1.35* 1.248 1.156 (0.0001) 0.0008**  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coerriclent  TABLE X I I DIRECTORS FEES 1  REGRESSION COEFFICIENT NPW NPE NCI  LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y  ( 0 . 0 0 0 2 )  ( 0 . 0 0 0 2 )  Boiler-boiler Boiler-machinery  0 . 0 0 0 7 ( 0 . 0 0 0 8 )  ( 0 . 0 0 0 8 )  0.0025 (0.0027)  0 . 0 0 0 8  -0.0137  0.0110  Real property  0 . 0 0 0 8 * *  ( 0 . 0 1 6 9 )  Inland Transportation  - 0 , 0 1 0 8 * * ( 0 . 0 0 3 7 )  Credit  O.OOIB ( 0 . 0 0 4 9 )  Guarantee-fidelity Guarantee-surety  0 . 0 0 0 7  Employers-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable ;  Automobile-liability -Other  0 . 0 0 0 8 * *  0.0007 (O.OI50)  - 0 . 0 0 9 9 * * ( 0 . 0 0 3 6 ) 0 . 0 0 0 9 ( 0 . 0 0 4 5 ) 0 . 0 0 1 2  0 . 0 0 1 0 * ( 0 . 0 0 0 4 )  ( 0 . 0 1 9 8 )  -0.0130** ( 0 . 0 0 3 8 ) 0 . 0 1 2 4 ( 0 . 0 1 8 9 ) - 0 . 0 0 1 6  (0.0009)  ( 0 . 0 0 1 0 )  - 0 . 0 0 0 9  - 0 . 0 0 1 0  (0.0034)  ( 0 . 0 0 3 4 )  ( 0 . 0 0 4 0 )  -0.0005*  -0.0005**  - 0 . 0 0 0 6 *  ( 0 . 0 0 0 2 )  ( 0 . 0 0 0 2 )  ( 0 . 0 0 0 2 )  0 . 0 0 0 1  0 . 0 0 0 2  0.0001 ( 0 . 0 0 0 2 )  0.0007**  ( 0 . 0 0 0 2 ) 0 . 0 0 0 6 * *  ( 0 . 0 0 2 0 ) 0 . 0 0 1 6  (0.0003) 0 . 0 0 1 2 * *  ( 0 . 0 0 0 1 )  ( 0 . 0 0 0 1 )  ( 0 . 0 0 0 1 )  Aircraft-liability -other  -0.0035  -0.0033  - 0 . 0 0 2 1  ( 0 . 0 0 2 6 )  ( 0 . 0 0 2 6 )  Miscellaneous  -0.0050  -0.0050  ( 0 . 0 0 2 6 )  R  2  ( 0 . 0 0 2 ? ) . 4 0 0  (0.0030)  - 0 . 0 0 9 1 * ( 0 . 0 0 4 5 )  0 . 3 7 3  0  a  0.521  0 . 4 2 5  0 . 4 6 8  SY  2 . 9 4 3  2 . 8 7 8  2 . 8 8 9  0 . 3 9 6  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE X I I I AUDITORS* FEES LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI 0.0006**  (0.0002) 0.0007 (0.0006) 0.0145  (0,0112) -0.0031 (0.0025) 0.0008  Credit Guarantee-fidelity Guarant e e-sure ty Employers'-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-caneellable Automobile-liability -other Aircraf P l i a b i l i t y -other Miscellaneous R  2  a SY  94  (0,0033) -0.0011 (0.0006) -0.0009 (0.0023) -0.0001 (0.0001)  0.0007** (0.0002) 0.0007 (0.0006) 0.0151 (0.0102) -0.0029 (0.0025) 0.0003 (0,0031) -0.0009 (0.0006) -0.0019 (0.0023) -0.0001 (0.0001)  o.ooo?**  (0,0003) 0.0033 (0,0018)  0.0457** (0.0131) -0.0059* (0.0025) 0.0058 (0.0125) -0.0045•• (0.0013) 0,0009 (0.0027) -0.0000 (0.0002)  0.0002 0.0001 (0,0002) (0.0001) 0.0006** 0*0007** o.opio** (0.0001) (0.0001) (0.0001) -0.0009 -0.0016 -0.0015 (0,0017) (0.0017) (0,0020) -0.0042* -0.0051** -0.0026 (0,0017) (0.0018) (0,0030) 0.514 0.536 0.514 0,297 0.249 0.203 1.961 1.961 1.915 0.0001 (0.0001)  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  95  TABLE XIV MANAGEMENT REMUNERATION LINE OF INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; 0.0043 (0.0084) Plate glass; Public l i a b i l i t y Boiler-boiler Bo iler-machinery  -0.0032  Real Property  1.2970* (0.5736) -0.0052  Inland T r a n s p o r t a t i o n  (0.0288)  0.0021  (0.0084)  0.0198 (0.0128)  -0.0035 -0.0202 (0.0287) (0.0920) 1.5120** -O.2399 (O.5I9O) 0.0433  (0.6661)  0.4503** (0.1292)  (0,1257) -0.0501  -O.3636  (0,0066)  (0.0067)  (0.0081)  Personal A c c i d e n t / s i c k n e s s Individual-cancellable -non-canee1lable  -0,0012  -0.0011  -O.OOI9  Automobile-liability -other  0.0006 (0.0032)  0.0012 (0.0035)  -0.0012  Aircraft-liability -other  (0,0677)  (0.0886)  0.0173  -O.IO5I  -0.1826* (0,0871)  -0.2153* (0.0923)  -0.3696* (0.1526)  0.035  0.046  0.089  I8.997  18.204  17.600  99.608  97.332  (0,1266)  -0.0490 (0,1682)  Credit Guarantee-fidelity Guarantee-surety Employers-liability Personal Accident/sickness r-group  Miscellaneous R2  a SY  (0.6351) -O.0229 -0,0246 -0.0714 (0.0676) (0,0330) (0.0293) -0.0825 -0.0880 -0.0990 (0,1151) (O.II7I) (0.1357) -0.0042 ^•0.0046 -0.0036 (O.OObQ)  0.0434  100.173  (0,1558)  (0.0061)  (0,0103) (0.0041)  (0.0998)  • Denotes s l g n i f l g a n t a t 5% l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XV ADVERTISING LINE OF INSURANCE  9b  REGRESSION COEFFICIENT NPW NPE NCI -0.0024  -0.0107** (0,0032)  F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y  -0.002? (0.0022)  Boiler-boiler Boiler-machinery  0.0025 (0.0075)  (0.0074)  Real property  -0,14-91  -O.I303  (0.0230) 0.1293  Inland Transportation  -0.0108  (0,0328)  -0.0213 (0.0325)  -0.0090 (0.0323)  Credit  0.0414 (0,0435)  (0,0402)  Guarantee-fidelity Guarantee-surety  -0.0065  -0.0104  (0.0065)  -0.0184 (0,0169)  Employers*-liability  -0.0761* (0.0296)  -0.0877**  -O.O456  Personal Accident/sickness -group  -0.0036* (0.0017)  -o.oo4o*  -0.0056**  (0.0017)  (0,0020)  Personal Accident/sickness Individual-cancellable -non-cance1lable  (0.1485)  (0.0076)  0.0222•*  (0.0016)  0.0119**  Automobile-liability -other  (0,0006)  A i r cr af t - 1 1 ab 1 1 1 ty -other  0.0057 (0.0227)  (0,0022)  0.0019  (O.I34I)  0,0290  (0.0302)  0.0231**  (0.0016)  0.0136**  (0.0009) 0.0125  O.OI96  (0.1672)  0,2703 (0.1569)  (0.0340)  0,0428** (0.0026) 0.0169** (0.0010) 0.0251  (O.O229)  (0.0250)-  -0.0039  -0.0099  .626  0.634  0.672  a  -3.I56  -3.792  SY  25.93*  25.734  Miscellaneous R  2  0.0046  (0.0225)  (0.0239)  (0.0362)  -2.825  24.357  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  97  TABLE XVI BOOKS AND PERIODICALS LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery Real property Inland t r a n s p o r t a t i o n Credit Guarantee-fidelity Guarantee-surety Employers'-liability Personal Accident/sickness -group Personal Accldent/slclmess Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY  REGRESSION COEFFICIENT NPW NPE NCI  0.0002** 0.0002** 0.0003** (0.0001) (0.0000) (0.0001) 0.0001 0.0001 0.0003 (0.0002) (0.0002) (0.0005) 0.0016 0.0004 0.0003 (0.0035) (O.OO29) (0.0038)  -0.0006 (0.0008)  -0.0008 (0.0007)  -0.0018*  (0.0007) 0.0055  0.0010 0.0007 (0.0010) (0.0009) (0.0036) -0.0001 -0.0001 -0.0001 (0.0002) (0.0002) (0.0004) 0.0012 0.0010 0.0005 (0.0007) (0.0006) (0.0008) 0.0001* 0.0001 0.0001* (0.0000) (0.0000) (0.0000) 0.0003**  0.0003** 0.0005** (o.oooo) (0.0000) (0.0001) 0.0002** 0.0002** 0.0003** (0.0000) (0.0000) (0.0000) 0.0002 0.0004 0.0009 (0.0005) (0.0005) (0.0006) -0.0000 -0.0003 -0.0001 (0.0005) (0.0005) (0.0009) 0.566 0.650 0.640 -0.06b -0.036 -0.062 0.612 0.551 0.559  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XVII BUREAU AND ASSOCIATION DUES LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI 0.0094**  (0.0015) 0.0071 (0.0051) 0.2466* (0.1014) 0.0487* (0.0224)  Credit Guarantee-fidelity Guarantee-surety Employers -liability 1  Personal Accldent/slclmess -group Personal Accldent/slclmess Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous H  2  a SY  0.0003 (0.0297) 0.0067 (0.0052) 0.1101** (0.0203) 0.0001 (0.0012) 0.0009 (0.0011) 0.0002 (0.0006)  0.0107** 0.0197** 0.0015 (0.0023) 0.0064 0.1275 (0.0050) (0.0162) 0.6254** 0.1766 (0.0905) (0.1178) 0.0572** -0.0153 (0.0228) (0.0219) 0.0021 -0.0012 (0.0272) (0.1119) 0.0187 0.0094 (0.0119) (0.0057) 0.0985** 0.1172** (0.0239) (0.0204) -0.0001 0.0005 (0.0014) (0.0012) 0.0010 (0.0011) 0.0004 (0.0006)  -0.0011 -0.0150 (0.0155) (0.0154) 0.0340* 0.0386* (0.0154) (0.0161) 0.668 0.655 0.198 -O.52I 17.705 17.363  0.0017  (0.0018) 0.0008  (0.0007) 0.0136 (0.0176) 0.1086** (0.0269) 0.676 -O.35I 17.158  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  CHARITABLE DONATIONS  TABLE XVIII  LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI  0,0001 (0,0001) 0.0003 (0.0004)  0.0015 (0.0081)  -0.0039* (0.0018)  0.0019  Credit Guarantee-fidelity Guarante e-sure ty  (0.0024)  0.0008  (0.0004)  Employers -liability  -0.0004 (0.0016)  Personal Accident/sickness -group  -0.0000 (0.0001)  1  Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other A l r craf t-11 ab i 11 ty -other Miscellaneous E?  a SY  99  0.0002* (0.0001) 0.0005" (0.0000) -0.0010 (0.0012) -0.0011 (0.0012) 0.453 -0.091 1.412  0.0001 (0.0001) 0.0003  0.0002 (0.0002) 0.0012  -0.0043  -0.0061  (0.0074) -0.0036*  -0.0042*  (0.0004)  (0.0018)  0.0015 (0.0022) 0.0010* (0.0005) -0.0002 (0.0017) -0.0000 (0.0001) 0.0002* (0.0001) 0.0005** (0.0000) -0.0009 (0.0013) -0.0009 (0.0013)  (0.0014)  (0.0099) (0.0019) 0.0014 (0.0094)  -0.0018  (0.0010) 0.0012 (0.0020) -0.0000 (0.0001) 0.0003* (0.0002) 0.0007* (0.0001)  -0.0014  (0.0015) -0.0023 (0.0023)  0.454  0.427  -0.114  -0.053 1.445  1.411  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XIX INSPECTION AND SURVEYS LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y  REGRESSION COEFFICIENT NPW NPE NCI 0.0028**  0.0026*  #  Real property  (0.0007) (0.0007) -0.0005 -0.0007 (0.0025) (0.0025) -0.0891 -0.0787 (0.0490)  (0.0447)  Inland t r a n s p o r t a t i o n  -0.0209  (0.0108)  -0.0162 (0.0108)  Credit  -0.0041 (0.0144)  -0.0036 (0.0134)  Guarantee-fidelity Guarantee-sure ty  0.0037 (0.0025)  0.0046 (0.0026)  Employers -liability  -0.0068  Boiler-boiler; Boiler-machinery  1  Personal Accldent/slcimess -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY  0.0027* (0.0012) 0.0022 (0.0082)  -0.0522 (0.0598) -0.0023 (0.0116)  -0.0279 (0.0566) 0.0005 (0.0061)  -0.0062 -0.0025 (0.0098) (0.0101) (0.0i21) -0.0000 -0.0000 -0.0001 (0.0006) (0.0006) (0.0007) -0.0002 -0.0002 -0.0002 (0.0005) (0.0005) (0.0009) -0.0004  (0.0003) -0.0029 (0.0075) -0.0058 (0.0074)  0.083 1.519 8.560  -0.0003 -0.0000 (0.0003) (0.0004) 0.0016 0.0105 (0.0076) (0.0069) -0.0061 -0.0135 (0.0080) (0.0137) 0.050 0.077 1.419 1.437 8.712 6.587  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  101  TABLE XX INSURANCE OTHER THAN INSURANCE ON REAL ESTATE LINE OF INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; 0.0001 (0.0001) Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n Credit Guarantee-fldellty Guarantee-surety  0.0029** 0.0218** (0.0081)  0.0102 (0.0074)  -0.0152 (0.0098)  0.0027  (0.0018)  0.0019  0.0015  (0.0024) 0.0006 (0.0004)  Personal Accident/sickness Individual-cancellable -non-cancellable  -0.0000 (0.0001)  2  a SY  0.0025  (0.0018)  0.0004** (0.0001)  H  0.0098**  (0.0014)  Personal Accident/sickness -group  Miscellaneous  (0.0002)  (0.0004)  -0.0034* (0.0016)  Aircraft-liability -other  0.0029**  o.ooo5*  (0.0004)  Employers-liability  Automobile-liability -other  0.0001 (0.0001)  0.0003** (0.0000) 0.0006 (0.0012) 0.0004 (0.0012) 0.417  (0.0022) 0.0008  -0.0006  (0.0019) 0.0068  (0.0093) -0.0036** (0.0020)  (0.0005) -0.0030 -0.0007 (0.0020) (0.0017) 0.0004** 0.0005** (0.0001)  (0.0001)  40.0000 (0.0001)  -0.0001 (0.0002)  0.0003** (0.0000) 0.0002  (0.0013) 0.0005 (0.0013)  0.0004** (0.0001) 0.0001  (0.0015)  0.0044 (0.0022)  0.418  0.405  -0.002  -0.023  0.042  1.418  1.417  1.432  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l notes f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  102  TABLE XXI LEGAL EXPENSE LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery Real property Inland t r a n s p o r t a t i o n Credit Guarantee-fidelity Guarantee-surety Employers * - l i a b i l i t y Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY  REGRESSION COEFFICIENT NPW NPE NCI  0.0002* (0,0001) 0.0002 (0.0003) -0.0080 (0.0050) -0,0030** (0.0011) 0.0129** (0.0015) 0.0004  0.0002** 0.0003** (0.0001) (0.0001) 0.0003 0.0003 (0.0003) (0.0009) -0.0069 -0.0044 (0.0046)  (0.0064)  -0.0023* -0.0032* (0,0011) (0.0012) 0.0120** 0.0343** (0.0014)  0.0005 (0.0003)  (0.0061) 0.0014*  (0.0003) (0,0007) -0.0004 0.0000 -0.0009 (0.0010) (0.0010) (0.0013) -0.0000 -0.0000 -0.0000 (0.0001) (0.0001) (o.oooi) 0.0002** 0.0002** 0.0004*' (0.0001) (0.0001) (0.0001) 0.0000 0.0001* 0.0001 (0.0000) (0.0000) (0.0000) -0.0012 -0.0011 -0.0012 (0,0008) (0.0010) (0.0006) 0.0025** 0.0009 -0.0005 (0.0008) (0.0015) (0.00C8) 0.231 0,336 0.329 0.138 0.157 0.173 0,677 0.873 0.939  • Denotes s l g n i f l g a n t a t 5% l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXII MAPS AND PLANS LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPE * NCI NPW  0.0002** 0.0001 0.0001* (0.0000) (0.0000) (O.oooi) -0.0001 -0.0001 -0.0000 (0.0001) (0.0004) (o.oooi) -0.0022 -0.0011 -0.0035 (0,0024) (0.0026) (0.0032) 0.0026**  (0.0006)  Credit  -0.0001  Guarantee-fidelity Guarantee-surety  -0.0002 (0.0001) 0.0003 (0.0005) -0.0000 (0.0000) 0.0000 (0.0000)  (0.0006)  Employers -liability 1  Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous  R2 a SY  0.0016**  (0.0006)  -0.0001 (0.000?) -0.0002 (0.0002) 0.0001 (0.0005) -0.0000 (0.0000) 0.0000 (0.0000)  0.0016*  (0.0006)  -0.0005 (0.0030) -0.0005 (0.0003) 0.0006 (0.0006)  -0.0000 (0,0000) 0.0000 (0.0000)  -0.0000 -0.0000 -0.0000 (0.0000) (0,0000) (0.0000) -O.OOOl -0.0003 -0.0004 (0.0004) (0.0004) (0,0005) -0.0006 -0.0006 0.0000 (0.0004) (0.0004) (0.0007) 0.162 o-.ua 0.120 0.014 0,004 -0,010 0.446 0.460 0.459  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  104  TABLE XXIII MEDICAL EXAMINERS' FEES LINE OF INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e : Thert: Personal Property; 0.0000 Plate glass; Public l i a b i l i t y (o.oool)  0.0001 (o.oool)  0.0002 (0.0001)  Boiler-boiler Boiler-machinery  0.0001 (0.0002)  0.0001 (0.0002)  (0.0009)  0.0io6*  0.0047  Real property  0.0006  0.0006  (0.0049)  (0.0045)  (O.OO65)  Inland t r a n s p o r t a t i o n  0.0007 (0.0011)  0.0002 (0.0011)  -0.0005 (0.0013)  Credit  0.0005 (0.0014)  0.0044 (0.0062)  Guarantee-fidelity Guarante e-sure ty  -o.oool (0.0003) o.oool (0.0010) 0.0001* (0.0001)  0.0004 (0.0013) -0.0002 (0.0003) -0.0000 (0.0010)  Employers'-liability Personal Accident/sicimess -group  -0.0008 (0.0007) 0.0004 (0.0013)  0.0001  0.0002* (0.0001)  0.0017** (o.oool) 0.0000 (0.0000)  0.0029*' (0.0001)  Automobile-liability -other  o.ooi7** (0.0001) 0.0000 (0.0000)  Aircraft-liability -other  -0.0009 (0.0006)  -0.0015 (0.0008)  0.U009  0.0011 (0.0008)  Personal Accident/sickness Individual-cancellable -non-cancellable  Miscellaneous R  2  a SY  (0.0007)  (o.oool)  0.0000 (0.0000) -0.0014 (0.0010) 0.0025 (0.0015)  0.819  0.820  0.760  -0.051  -0.062  -0.025  0.858  0.856  0.946  • Denotes s l g n l f l g a n t a t 5$ l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXIV MERCANTILE AGENCIES* REPORTS LINE OF INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; -0.000b Plate glass; Public l i a b i l i t y (0.0011)  -0.0004 (0.0009)  Bolier-boiler Boiler-machinery  -0.0010  -0.0009  Real property  0.0655 (0.0719)  Inland t r a n s p o r t a t i o n Credit Guarantee-fidelity Guarantee-surety Employers'-liability Personal Accident/sickness -group  (0.003b)  0.0074  (0.0032)  0.0021 (0,0016) -0.0013 (0,0112)  0.0210  0.0154 (O.OO16)  (0.0571)  (0.0159)  (0.013b)  0.0037  -0.0283 (0.015b)  o.o3«b (0.0211)  0.0291  (0.0171)  0.1899* (0.0776)  0.0044 (0,003b)  (0.0083)  0.0045  (0.003?) 0.0552**  0.0466**  0.0106  O.O638"  (0.0144)  (0.0129)  (0.0166)  -0.0000  -0.0004  0.0002 (0.0010)  (0.000b)  (0.0007)  Personal Accident/sickness Individual-cancellable -non-cancellable  (0.0008)  Automobile-liability -other  (0.0004)  (0.0004)  (0.0005)  -O.OOttO  -0.0098 (0.0087)  -0.0165 (0.0122)  Aircraft-liability -other Miscellaneous E  2  a SY  0.0031** 0.0058**  (0.0110)  0.018?  0.0033**  (0.000?)  0.0073**  0.0225*  0.0050** (0.0013) 0.0063**  0.0326  (0.0109)  (0.0102)  (0.0186)  0. 641  0.727  0.678  0.945  0.14?  0.787  12.564  10.95^  11.891  • Denotes s l g n l f l g a n t a t 5% l e v e l Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r /of r e g r e s s i o n coefficient  TABLE XXV OFFICE FURNITURE AND EQUIPMENT LINE OF 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  0.0015 (0,-0011)  Boiler-boiler Boiler-machinery  (0.0039)  Real property Inland t r a n s p o r t a t i o n  0.0026  0.0244  (0.0?68) 0.0034  (0.0169) -0,0116  Credit  (0.0225)  Guarantee-fidelity Guarantee-surety Employers'-liability Personal accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous  B  2  0.0165**  (0.0039) 0.0294 (0.0154) 0.0035**  (0.0009) 0.0104  (0.0006) 0,oo6o* %  (0.0004) -0.0024  (O.OII7) 0.0021 (O.OII7) 0.741  a  -O.934  SY  13.411  0.0021 (0.0011) 0.0027 (0.0037) -O.O388  (0.0665) 0.0007 (0.0161)  -0.0143  (0.0199) 0,0190** (0.0042)  0.0062** (0,0016) 0.0082 (0.0128) 0.1056  (0.0933) -0.0438* (0,0181)  -0.1926* (O.Obo?)  0.021?* (0.0094)  0.0206 0.0090 (0.0150) (0.0190) 0.0033** 0.0042 * (0.0009) (0.0011) %  O.OlOb** (0.0008)  0.0071** (0.0004)  -0,0039 (0.0113) 0.0030 (0.0118)  0.765 -1.59* 12.755  0.0192** (0.0014) 0.0066** (0.0006) -0.0086  (0.0.139) 0.0043 (0.0213) 0.733 -1.005 13.596  • Denotes s l g n i f l g a n t a t 5$ l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  10?  TABLE XXVI POSTAGE LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler; Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI 0.0016  (0.0013) 0.0102*  (0.00*3) -0.0*05 (0.0657)  0.0169  (0.0169) Credit Guarantees-fidelity Guarantee-surety Employers*-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous E  2  a SY  0,055** (0.0251) 0.0105* (0.004*)  0.0234 (0,0172) 0.0022* (0.0010)  0,0020 0.0050* (0.0011) (0.0020) 0.0101*' 0.0378* (0.0038) -0.0669 (0.0687)  (0.0145) 0.0467 (0.1053)  0.0105  -0.0255  (0.0166) 0.0427* (0.0206)  0.0107*  (0,0044) 0.0124  (0.0155) 0.0019* (0.0009)  (0.0204)  0.2835** (0.0101)  0.0077 (0.0107) 0.0304 (0.0214)  0,0035** (0.0013)  0.0099** 0,0103** 0,0163** (0,0009) (0.0008) (0.0016) 0.0090** 0,0109** 0.0128** (0.0005) (0.0005) (0.0007) 0,0029 -0.0013 0.0051 (0,0131) 0.0117 (0.0157) 0.0068 0,0070 0.0051 (0.0130) (0.0122) (0,0241) 0.629 0.768 0.779 -0.406 0.703 0,5*3 14.976 13.169 15.3*7  • Denotes s l g n i f l g a n t a t 5$ l e v e l • • Denotes s l g n i f l g a n t a t 1% l e v e l note; f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXVII PRINTING AND STATIONERY  10b  LINE OF 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*00 3«>**  Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n Credit Guarantee-fidelity Guaran t e e-sur e ty Employers'-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -noncanceliable Automobile-liability -other Aircraft-liability -other Miscellaneous E  2  a SY  (0.0013)  0.013B" (0.0043)  -0,0Ibb  (•0 .-08.5b)  0.0038**  (0,0012)  0.0139**  (0.0040) -0,0463  0.0064*"  (0.0020) 0.0436**  (0.0143) 0.1189 (0.1037)  (0.0717) -0.0046 -0.0005 -0.0092 (0,0169) (0,0174) (0,0200) 0.0162 0.0072 0.0376 (0,0215) (0,0251) (0.09b5) 0.0113* 0.0128** 0.0252* (0,0044) 0.0320  (0.0172) 0.0049**  (0.0010) 0.0165**  (0.0046)  0.0209  (0,0162) 0.0045 » #  (0.0009)  0.0172**  (0.0105) 0.0407 (0.0211) 0.0060**  (0,0013) 0.0306**  (0,0009)  (0.0008)  -0,0144  (0.0122) -0.0138  -0.0135  (0.0130)  0.0163 (0.012b)  0.0252 (0,0237)  0.844  0.868  0.641  1.006  -0.022  I.I52  14,947  13.759  15.101  0.0092** (0,0005) (0,0133) 0.0179  0.0110**  (0.0.122)  (0.0016)  0.0135**  (0.0005) (0.0155)  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  109  TABLE XXVIII RENTS LINE OF 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  0.0097**  Boiler-boiler Bo1ler-machlnery Real property Inland  transportation  Credit  (0.0019) (0.0017) 0.0192** 0.0189** (0.0065) -0.0787 (0.1290) 0.0106  (0.0165) 0.0663  Guarantee-fidelity Guarantee-sure ty Employers'-liability Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraf p l i a b i l i t y -other Miscellaneous R  2  a SY  0.0106**  (0.0378) 0.0223**  (0,0060) -0.1689 (0,1080)  (0,0324)  (0.0066)  (0.0259) 0,0090** (0.0015)  0.0623* (0,0244) 0.0086** (0.0014)  0.0157** (0,0004)  0,0116* *  (0.0007)"  0.0022 (0,0197) 0.0321 (0.0196) 0.631 -1.702 22,525  0.0620** (0,0215) 0.1581 (0.1560)  0.0139 -0.0599 (0.0261) (O.0302) 0.3049* 0.0503 0,0 246 ** (0,0069)  0.064-5 ••  0.0162** (0.0030)  0,0165** (0.0013) 0.0141** (0.0007)'  0,0106  (0.0184) 0.0391*  (0.0192) 0.857 -3.377  20,719  (0.1483) 0,0b63**  (O.OI58)  0.0936** (0.0317)  0.0120** (0.0019) 0.0278** (0,0024)  O.OI74** (0.0010) 0.0251 (0.0233) 0.0702 (0.0356) 0.828  -1.666 22.725  • Denotes s l g n i f l g a n t a t 5% l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXIX STATISTICAL BUREAU EXPENSES LINE OF INSURANCE  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; 0 . 0 0 2 0 * Plate glass; Public l i a b i l i t y (0.0006) #  Boiler-boiler Boiler-machinery  0 . 0 0 0 1  0 . 0 0 2 2 * *  (0.0006) - 0 . 0 0 0 1  0.0035* ( 0 . 0 0 1 0 ) 0 . 0 0 2 0  (O.OO69)  ( 0 . 0 0 2 2 )  ( 0 . 0 0 2 2 )  Real property  0.0270 (0.0441)  (0.0398)  (0.0502)  Inland Transportation  -0.0109 (0.0097)  -0.0106  T0.0241* (0.0097)  0.0243  Credit  0.0199  ( 0 . 0 0 9 6 )  0.0204  0.0927  0 . 2 2 1 0 * *  (0.0129)  (0.0119)  Guarantee-fidelity Guarante e-sure ty  -0.0016  - 0 . 0 0 2 0  Employers -liability  -0.0043 (0.0088)  -0.0052  (0.0090)  ( 0 . 0 1 0 2 )  -0.0007  -0.0008 (0.0005)  -0.0008 (0.0006)  1  Personal Accident/sickness -group  (0.0023)  (0.0005)  Personal Accident/sickness Individual-cancellable -non-cancellable  (0.0005)  Automobile-liability -other  ( 0 . 0 0 0 2 )  Aircraft-liability -other  -0.0003 (0.0067)  Miscellaneous  - 0 . 0 0 7 4  0 . 0 0 0 1  0.0004  ( 0 . 0 0 6 7 )  (0.0025)  0 . 0 0 0 1  (0.0477)  -0.0032 (0.0051) 0 . 0 0 1 0  0 . 0 0 0 2  (0.0005)  (0.0008)  0.0005  0.0006  (0.0003)  (0.0003)  -0.0004  0.0081 (0.0075)  ( 0 . 0 0 6 8 )  -0.0090 (0.0071)  -O.OI73  (0.0115)  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  R  2  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l notes f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXX TRAVELLING EXPENSES LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI  0.005b** 0.0129** (0.0015) (0.0025) (0.0016) 0.0606** 0.0612** 0.2095** (0.0050) (0.0055) (0.0177) 0.0272 -0.0308 -0.0311 0.0051**  (0.1066)  0.0157  (0.0240)  0.0565 (0.0319)  Credit Guarant e e - f l d e l l t y Guarantee-surety Employers -liability 1  Personal Accident/sickness -group Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other  111  0.0045  (0.0903)  0.019b (0.0219) 0.0462  (0.0271) 0.0058  (0.1287)  -0.0195  (0.0249) 0.2603*  (0.1223)  -0.0489**  (0.005b) (0.0057) (O.OI30) 0.0713** 0.0611** 0.1060** (0.021a) (0.0204) (0.0261) 0.0057** 0.0051** 0.0068** (0.0013) (0.0012) (0.0016) 0.0129** 0.013b** O.O227" (0.0011) (0,0011) (0.0020) 0.00b0** 0.0076** 0.0097** (0.0006) -0.0190 0.0166  -0.0099  Miscellaneous  0.0046 (0.0165)  (0.0161)  0.0003  0.0067 (0.0294)  R  0.7*5  0.788  0.752  2.815  1.469  2.283  18.994  I7.326  18,744  Aircraft-liability -other  2  a SY  (0,0006) (0.0154)  (0.0008) -0.0168  (0.0192)  • Denotes s l g n i f l g a n t a t 5% l e v e l ; ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXXI OTHEH LINE OF INSURANCE F i r e ; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery Real property Inland t r a n s p o r t a t i o n  REGRESSION COEFFICIENT NPW NPE NCI  -0.0005 (0.0020) 0.0078* (0.0033) 0.0355*  0.0308* (0.0134) 0.0222  0.0040  Guarantee-fidelity Guarant e e-sure ty  (0.0033)  Employers-liability  -0.0049  Personal Accident/sickness Individual-cancellable -non-cancellable Automobile-liability -other Aircraft-liability -other Miscellaneous R  2  a SY • Denotes s i g n i f i g a n t a t  (0.0106)  -0.1045 (0.0554)  0.0299 (0.0192)  Personal Accident/sickness -group  (O.OO3I)  -0.0716 (0.0654)  (0.0144)  Credit  0.0080*  0.0022 (0.0015) 0.0312**  0.0004 (0.0009)  (0.0166)  0^0038  (6.0035)  -0.0379 (0.0767) -0.0059* (0.0148)  0.2263** (0.0729)  -0.0048 (0.0078)  -0.0158 -0.0117 (0.0131) (0.0125) (0.015b) -0.0008 -0.0009 -0.0006 (0.0006) (0.0007) (0.0009) 0.0138** (6.0007) (0.0007) (0.0012) O.OObO** 0.0070** 0.0083** (0.0004) (0.0005) (0.0004) -0.0081 -0.0096 -0.0179 (0.0100) (0.0095) (0.0115) -0.0152 -0.0197 -0.0417* .(0.0099) (0.0099) (0.0175) 0.666 0.699 0.727 0.448 -0.308 0.039 10.638 11.417 11.179 0.0061**  0.0084**  level  ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXXII  n  3  EXPENSE ALLOWANCE ASSUMED (+) LINE OF 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  (0.0032)  Boiler-boiler Boiler-machinery  -O.OOO5 (0.0110)  Real property  -0.1093  Inland  transportation  0.0019  (0.2189) -0.0225 (0.0463)  0.0011  (0.0032) -0.0003 (0.0110)  -0.0450 (0.1995) -0.0169  0.0010  (0.0051) -0.0042 (0.03b2) 0.0440 (0.2633) -0.0129  (0.0509)  Credit  -0.0010  (0.0483) TO.0008  Guarantee-fidelity Guarantee-surety  0.0020 (0.0112)  (0.0127)  (0.0266)  Employers'-liability  -0.0026 (0.0439)  -O.OO9O  -0.0249  (0.0642)  Personal Accident/sickness -group  0.0153**  (0.0599)  0.0035  (O.O450) 0.0152**  0.0092  (0.2502) O.OO89  (0.0535)  0.018?*  Personal Accident/sickness Individual-cancellable -non-cancellable  (0.0025)  (0.0026)  -0.0054*  -0.0053*  Automobile-liability -other  -0.0011 (0.0012)  -0.0010  (0.0013)  -0.0008 (0.0016)  Aircraft-liability -other  -O.OO87  -0.0038  -O.OO3I  Miscellaneous R2 a SY  (0.0023) (0.0335) 0.0012  (0.0024)  (0.0341) 0.0014  (0.0032) -0.0079  (0.0040)  (0.0393)  -0.0096  (0.0332) 0.113  (0.0355) 0.110  0.107  2.141  2.155  1.896  36.234  36.286  36.353  (0.0601)  • Denotes s l g n i f l g a n t a t 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: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXXIII EXPENSE ALLOWANCE CEDED (-) LINE OF INSUBANCE Fire;; Theft; Personal Property; Plate glass; Public l i a b i l i t y Boiler-boiler Boiler-machinery  BEGBESSION COEFFICIENT NPW NPE NCI  0.0005 (0.0015) 0.0006  0.0006  (0.0015)  0.0010 (0.0024)  (0.0052)  0.0006  0.0017 (0.0171)  Real property  (0.0052) 0.0115 (0.1038)  -0.0004 (0.0945)  0.0089 (0.1244)  Inland t r a n s p o r t a t i o n  -0.0006  (0.0229)  -0.0007 (0.0229)  -0.0014 (0.0241)  Credit  0.0034 (0.0304)  (0.0283)  0.0031  0.0104 (0.1183)  (0.0060)  0.0003  -0.0006 (0.0126)  (0.0208)  -0.0032 (0.0213)  -0.0019 (0.0253)  Personal Accident/sickness -group  0.0000 (0.0012)  0.0001 (0.0012)  (0.0015)  Personal Accldent/slclmess Individual-cancellable -non-cancellable  0.0002 (0.0011)  0.0002 (0.0011)  (0,0019)  Automobile-liability -other  0.0000 (0.0006)  0.0000 (0.0006)  0.0000 (0.0008)  0.0014  (0.0159)  0.0008 (0.0161)  0.0006 (0.0186)  0.0006 (0.0158)  0.0004 (0.0168)  (0.0284)  Guarantee-fidelity Guarantee-surety Employers'-liability  Aircraf P l i a b i l i t y -other Miscellaneous  0.0002  (0.0053) -0.0027  0.0001  0.0003  0.0017  0.002  0.002  0.002  a  -1.689  SY  18.130  -1.717 18.129  -I.703 18.129  H  2  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s I n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXXIV EXPENSE ALLOWANCE TO COMPANY LINE OF INSURANCE  115  REGRESSION COEFFICIENT NPW NPE NCI  -0.0003 (0.0002) 0.0002 0.0001 (0.0007) (0.0007) 0.0706** 0.0550** (0.0145) (0.0133) 0.0014 0.0016 (0.0032) (0.0032) 0.0000 -0.0002  F i r e ; Theft; Personal Property; -0.0004 (0.0002) Plate glass; Public l i a b i l i t y Boller-boller Boiler-machinery Real property  -0.0000 (0.0003) -0.0003 (0.0025) 0.0128  (0.0042)  (0.0040)  -0.0002  Employers-liability  -0.0002 (0.0007) -0.0015  (0.0180) -0.0001 (0.0035) -0.0000 (0.0172) 0.0002  Personal Accident/sickness -group  -0.0001 (0.0002)  -0.0009 (0.0030) -0.0000 (0.0002)  -0.0006 (0.0037) -0.0000 (0.0002)  0.0000 (0.0002) 0.0000 (0.0001) 0.0000 (0.0023)  -0.0000 (0.0003) -0.0000 (0.0001)  Inland t r a n s p o r t a t i o n Credit Guarantee-fidelity Guarant e e-surety  Personal Accident/sickness Individual-cancellable -non-cancellable  (0.0029)  0.0000 (0.0002) 0.0000  Automobile-liability -other  (O.OOOl)  Aircraft-liability -other  (0.0022)  Miscellaneous  -0.0028  R  2  a SY  0.0018  (0.0022) 0.078 0.083 2.529  (0.0008)  (0.0016)  -0.0006  (0.0027)  -0.0028 (0.0024)  -0.0014 (0.0041)  0.057  0.003 0.196 2.629  0.124  2.557  • Denotes s l g n i f l g a n t a t 5% l e v e l ••Denotes s l g n i f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  TABLE XXXV MISCELLANEOUS EXPENSE LINE OF INSURANCE  116  REGRESSION COEFFICIENT NPW NPE NCI  F i r e ; Theft; Personal Property; -0.0013 (0.0008) Plate glass; Public l i a b i l i t y  -0,0012 (0.0008)  -0.0013 (0.0014)  Boiler-boiler Boiler-machinery  (0.0029)  0.0047  0.0045 0.0029  0.0157 (0.0100)  Real property  0.0312 (0.0575)  0.0275 (0.0518)  -0.0047 (0.0728)  Inland t r a n s p o r t a t i o n  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  Employers•-liability  -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  0.0008* 0,0003  0.0012** (0,0003)  Ai rcraf t - l i a b l l l t y -other  0.0086 (0.0088)  0.0070 (0.0086)  Miscellaneous  0.0033 (0.0087)  -0.0031 (0.0092)  R  0.188  0.207  0.942  0.686  0,580  10,048  9.932  10.602  Automobile-liability -other  2  a SY  (o.ooii)  0.0013** (0.0005) 0.0026 (0.0109) -0.0035 (0.0166) 0.096  • Denotes s l g n l f l g a n t a t 5% l e v e l ••Denotes s l g n l f l g a n t a t 1% l e v e l note: f i g u r e s i n brackets represent standard e r r o r of r e g r e s s i o n coefficient  APPENDIX C  TABLE I NET PREMIUMS EARNED POR AUTO BODILY INJURY LIABILITY INDEPENDENT VARIABLE  STANDARD ERROR  CONSTANT  REGRESSION COEFFICIENT  GENERAL EXPENSES (G.E.)39159.74  I6989.76  -38.5676  OTHER ACQUISITIONS (O.A.)  39287.99  16815.57  -15.6358 (64.4612)  G.E. + O.A.  39212.54  18635.67  -20.4010  G.E. +. O.A. + 38815.24 COMMISSION AND BROKERAGE  30562.58  (40.7769)  (27.6499) -47.3096 (2b.6636)  -  .  TABLE I I NET PREMIUMS EARNED FOR AUTO PROPERTY DAMAGE LIABILITY. INDEPENDENT VARIABLE  STANDARD ERROR  CONSTANT  GENERAL EXPENSES (G.E.)14748.87  7390.79  OTHER ACQUISITIONS (O.A.)  14785.31  6732.63  (16.1452) - 6.8697  G.E. + O.A,  14762.74  7304.75  - 7.1869  G.E, + O.A. + COMMIS- 14651.74 11019.22  -14.8553  SION AND BROKERAGE  REGRESSION COEFFICIENT  -13.313b  (24.1276) (10.6964)  ( 9.7982)  119 TABLE I I I NET PREMIUMS EARNED POR AUTO COLLISION REGRESSION .COEFFICIENT  INDEPENDENT VARIABLE  STANDARD CONSTANT ERROR  GENERAL EXPENSES (G.E.)  13739.29 7762.52  -21.5016  OTHER ACQUISITIONS (O.A.)  13829.55  6434,55  - 6,0895  G.E, + O.A.  13765.06 7873.72  -13.6653  G.E. + O.A. + COMMISSION AND BROKERAGE  13666.61  11309.27  -I5.6627  (16.5104) (24.6962) (12.4156)  ( 9.5998)  TABLE IV NET PREMIUMS !EARNED POR AUTO THEFT., FIRE AND COMPREHENSIVE INDEPENDENT VARIABLE  STANDARD CONSTANT ERROR  REGRESSION COEFFICIENT  GENERAL EXPENSES (G.E.)  7722.02  4185.16  -10.0838  OTHER ACQUISITIONS (O.A.)  77*2.44 3061.24  - 8.2465  G.E. + O.A.  7742.84  3911.80  - 3.8487  G.E, + O.A. + COMMISSION AND BROKERAGE  77I3.89 4707.69  (10.5901) (16.7131)  ( 8.0155) - 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. A l b i o n Insurance Co. of Canada A l l i a n c e Assurance Co. L t d . American Insurance Co. American Mutual L i a b i l i t y Insurance Co. American N a t i o n a l F i r e Insurance Co. American Road Insurance Co. A n g l o - S c o t t i s h Insurance Co. L t d . A t l a s Assurance Co. L t d . Banters & Traders Insurance Co. L t d . 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. C a l v e r t F i r e Insurance Co. Canada Accident & F i r e Assurance Co. Canada Security Assurance Co. Canadian Commerce Insurance Co. Canadian General Insurance Co. Canadian Home Assurance Co. Canadian Indemnity Co. (Canadian N a t i o n a l 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 ( C i t a d e l Insurance Co. 6 f Canada) Century Insurance Co. L t d . Commerce General Insurance Co. Commercial Union Assurance Co. L t d . Continental Casualty Co. Continental Insurance Co. C o r n h l l l Insurance Co. L t d . Dominion Insurance Corporation Dominion of Canada General Insurance Co. Economical Mutual Insurance Co.  122  E l i t e Insurance Co. Employers' L i a b i l i t y Assur. Corp. L t d . Employers Mutual L i a b i l i t y Insurance Co. of Wisconsin E n g l i s h & American Insurance Co. L t d . 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 F l d e l i t y - P h e n l x Insurance Co. F i r e Insurance Co. of Canada Fireman's Fund Insurance Co. Firemen's Insurance Co. of Newark F i r s t N a t i o n a l Insurance Co. of America General Accident Assurance Co. of Canada General Accident F i r e & L i f e Assurance Corporation L t d . General Insurance Co. of America General S e c u r i t y 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. L t d . Guardian Insurance Co. of Canada G u i l d h a l l Insurance Co. L t d . G u i l d h a l l Insurance Co. of Canada H a l i f a x Insurance Co. Hardware Mutual Casualty Co. Hartford Accident & Indemnity Co. Hartford F i r e Insurance Co. H e l v e t i a Swiss F i r e Insurance Co. Home Insurance Co. Hudson Bay Insurance Co. Imperial Guarantee & Accident Insurance Co. of Canada Imperial Insurance O f f i c e Insurance Co. of North America Insurance Corporation of I r e l a n d L t d . Law, Union & Eock Insurance Co. L t d . Legal & General Assurance Society L t d . L i v e r p o o l & London & Globe Insurance Co. L t d . London & Edinburgh Insurance Co. L t d . London & Lancashire Guarantee & Accident Co. of Canada London & Lancashire Insurance Co. L t d . London & Midland General Insurance Co. London & S c o t t i s h Assurance Corp. L t d . London Assurance  123  London-Canada Insurance Co, London Guarantee & Accident Co, L t d , Lumbermens Mutual Casualty Co. Maryland Casualty Co. Merchants Marine Insurance Co. L t d . Milwaukee Insurance Co. of Milwaukee, Wis. M i s s i q u o i & R o u v i l l e Insurance Co. N a t i o n a l Employers Mutual General Insurance Assn. L t d . New Hampshire Insurance Co, New I n d i a Assurance Co. L t d . 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, L t d , Northern Assurance Co. L t d , Northwestern Mutual Insurance Co. Norwich Union F i r e Insurance Society L t d . Ocean Accident & Guarantee Corp. L t d . 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. L t d . 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 P e a r l Assurance Go. L t d . P e r t h Mutual F i r e Insurance Co. Phoenix Assurance Co. L t d , (Provident Assurance Co.) Phoenix Insurance Go. P r o v i n c i a l Insurance Co. L t d . P r u d e n t i a l Assurance Co. L t d . Quebec Assurance Co, Queensland Insurance Co, L t d . Railway Passengers Assurance Co. Reliance Insurance Go. of Canada Reliance Insurance Co. of P h i l a d e l p h i a Royal Exchange Assurance Royal Insurance Co. L t d . St. Paul F i r e & Marine Insurance Co. St. P a u l Mercury Insurance Co. Safeco Insurance Co. of America Saskatchewan Mutual Insurance Co. S c o t t i s h Canadian Assurance Corporation S c o t t i s h Metropolitan Assurance Co. L t d . S c o t t i s h Union & N a t i o n a l Insurance Co. Sea Insurance Co. L t d . S e c u r i t y N a t i o n a l Insurance Co. Service F i r e Insurance Co. New York Skandinavia Insurance Co. L t d . Stanstead & Sherbrooke Insurance Co.  124  Storebrand Insurance Co. L t d . Sun Insurance O f f i c e L t d . Switzerland General Insurance Co. L t d . Toronto General Insurance Co. Traders General Insurance Co. Transport Indemnity Co. Travelers Indemnity Co. Travelers Insurance Co. Union Assurance Society L t d . Union Insurance Society of Canton L t d . 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 V i c t o r y insurance Co, L t d . Wawanesa Mutual Insurance Co. Wellington F i r e Insurance Co. (Western Union Insurance Co.) Western Assurance Co. Westminster F i r e O f f i c e World A u x i l i a r y Insurance Corp. L t d . World Marine & General Insurance Co. Yorkshire Insurance Co. L t d , Z u r i c h Insurance Co.  Source:  Insurance Agents* A s s o c i a t i o n of B r i t i s h Columbia,  125  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. L i b e r t y Mutual F i r e Insurance Co. L i b e r t y Mutual Insurance Co. M e r i t 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' A s s o c i a t i o n of B r i t i s h Columbia.  

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