exclusive vs. independent agencies: a comparison of performance

22
The Geneva Papers on Risk and Insurance Theory, Vol. 15, No. 2 (September 1990), 171-192 Exclusive vs. Independent Agencies: A Comparison of Performance* by Peter Zweifel and Peter Ghermi** Abstract A peculiar feature of insurance is its marketing through a variety of channels about whose performance rather little is known. This paper examines two of the more important variants prevailing in Continental Europe, exclusive and independent agencies (the latter typically having contractual relationships with several companies). Two types of contract governing their behavior are examined for their incentives in terms of growth and cost con- trol. Data covering insurance agencies of both types operating in the Swiss market are used to test for differences while holding constant contract provisions operating on the revenue side. The hypothesis that exclusive agents are less concerned about cost control than inde- pendent agencies receives a large measure of confirmation, while no evidence of better per- formance both in terms of growth and loss ratio can be found. 1. Introduction Insurance is sold to customers in quite different ways : At the one end of the spectrum, the insurance company advertises its product in the media and processes applications by mail ; at the other end of the spectrum, an insurance broker puts together a package possibly consisting of products from many companies for his clients in a taylor-made fashion. This spectrum has undergone major structural change in U.S. (see Webb et al. [1984]), with mail-order systems expanding and direct writer systems shrinking. In most Continental European countries, however, exclusive agencies and direct writers are still prominent, i. e. the company markets its products through its own employed sales force. With the exception of the Netherlands and Belgium (and Great Britain outside the continent) insurance brokers are very few. But a similar function is performed by the independent agency that has contractual relationships with more than one insurance company. * Thanks are due to J. A. Blanco (University of Zurich) for a thorough checking of the mathema- tical derivations. Helpful comments where provided by B. Berliner (Swiss Re), M: Hellwig (University of Basel), and H. Miiller (University of Zurich), participants at the 14th Seminar of the European Group of Risk and Insurance Economists, Geneva, September 21-23, 1987, and - last but not least - two anonymous referees. ** Institute for Empirical Economics, University of Zurich. 171

Upload: peter-zweifel

Post on 14-Aug-2016

216 views

Category:

Documents


4 download

TRANSCRIPT

Page 1: Exclusive vs. Independent agencies: A comparison of performance

The Geneva Papers on Risk and Insurance Theory, Vol. 15, No. 2 (September 1990), 171-192

Exclusive vs. Independent Agencies: A Comparison of Performance*

by Peter Zweifel and Peter Ghermi**

Abstract

A peculiar feature of insurance is its marketing through a variety of channels about whose performance rather little is known. This paper examines two of the more important variants prevailing in Continental Europe, exclusive and independent agencies (the latter typically having contractual relationships with several companies). Two types of contract governing their behavior are examined for their incentives in terms of growth and cost con- trol. Data covering insurance agencies of both types operating in the Swiss market are used to test for differences while holding constant contract provisions operating on the revenue side. The hypothesis that exclusive agents are less concerned about cost control than inde- pendent agencies receives a large measure of confirmation, while no evidence of better per- formance both in terms of growth and loss ratio can be found.

1. Introduction

Insurance is sold to customers in quite different ways : At the one end of the spectrum, the insurance company advertises its product in the media and processes applications by mail ; at the other end of the spectrum, an insurance broker puts together a package possibly consisting of products from many companies for his clients in a taylor-made fashion. This spectrum has undergone major structural change in U.S. (see Webb et al. [1984]), with mail-order systems expanding and direct writer systems shrinking. In most Continental European countries, however, exclusive agencies and direct writers are still prominent, i. e. the company markets its products through its own employed sales force. With the exception of the Netherlands and Belgium (and Great Britain outside the continent) insurance brokers are very few. But a similar function is performed by the independent agency that has contractual relationships with more than one insurance company.

* Thanks are due to J. A. Blanco (University of Zurich) for a thorough checking of the mathema- tical derivations. Helpful comments where provided by B. Berliner (Swiss Re), M: Hellwig (University of Basel), and H. Miiller (University of Zurich), participants at the 14th Seminar of the European Group of Risk and Insurance Economists, Geneva, September 21-23, 1987, and - last but not least - two anonymous referees.

** Institute for Empirical Economics, University of Zurich.

171

Page 2: Exclusive vs. Independent agencies: A comparison of performance

Casual observation across countries suggests that the more strongly regulated national markets are characterized by employed sales force or agencies working exclusively for one insurance company. Typical examples are Austria and Western Germany. More open markets, on the other hand, appear to offer good opportunities for insurance brokers, pre- sumably because product variety and premium differentials are greater, creating a market for intermediation. Belgium, Great Britain, and the Netherlands are examples of such markets; see Finsinger and Pauly [1986] for more details and Harrington [1984] for similar conjectures regarding the U.S.

A major reshuffling of marketing channels in insurance can be expected if the Eco- nomic Community realizes plans to liberalize trade in services by 1992 (Orluc [1988]). Some national regulations protecting inefficient companies will have to be demised, and price will become a more important argument in competition. But building up and maintaining one's own sales force is believed to be a rather expensive alternative of marketing. Other aspects of performance, in particular growth of premiums and low loss ratios, may weigh in favor of exclusive agents and direct writer systems. However, little is known about the relative performance of marketing channels. Against this backdrop, it may be worthwhile to examine growth, expense ratios and loss ratios as performance indi- cators of two marketing systems operating in a small national market belonging to the regulated camp, Switzerland. The two systems compared are exclusive and independent agents, the latter having contractual relationships with more than one company. In its theoretical part, the paper contains two behavioral models. The first deals with the incen- tives and constraints faced by an exclusive agent given a typical contract with his insurance company. For the sake of comparison, another model is developed, mirroring the decision situation of an independent agency. The theoretical part concludes with a comparison of optimal solutions for the two types of agencies, from which some empirically testable hypotheses concerning their conduct of business can be derived. The novelty of this approach lies in the fact that contractual incentives are explicitly modeled, admitting of an analysis of agency performance proper.

The empirical testing of these predictions constitutes the second part of the paper. A sample coming from agencies of both types operating in the Swiss market are used to measure agency performance while holding constant contractual incentives. Performance aspects measured are growth of gross premiums written, the underwriting expense ratio, and the loss ratio. While the sample of agencies is small in each single year, comprising less than sixty observations, it covers the period of 1980 to 1985, thus admitting of several independent estimates of hypothesized relationships. In fact, exclusive agents do not appear to be significantly more growth oriented than their independent counterparts, whereas the independents do seem to control underwriting expenses more successfully, ceteris paribus. The ceteris paribus clause is quite important in this context because pre- vious studies suggesting superior performance of direct writers and exclusive agents in the U.S. (Joskow [1973]; Etgar [1977]; Johnson et al. [1981]; Braeutigam and Pauly [1986]; but also see Harrington [1982]) fail to control for contract provisions that may differ among agency types, resulting e.g. in a favorable growth performance that has nothing to do with the choice of marketing channel.

The final section of this paper contains a few conclusions concerning the future of different marketing channels in insurance and some suggestions for future work in this area.

172

Page 3: Exclusive vs. Independent agencies: A comparison of performance

2. M o d e l o f an exclusive agency

In this section, a behavioral model of an agency is developed that writes insurance exclusively for one company. In keeping with the categorization introduced by Johnson et al. [1981], the term "exclusive agent" will be used for the decisionmaker concerned, although according to Swiss contract law, he is an employee of the company. But compared to an employed direct writer in the U.S., he operates under a contract providing him with incentives and a degree of flexibility that are typical of exclusive writers. For this reason, an explicit modeling of contractual provisions seems particularly important for analyzing agency behavior. Admittedly, some details of the description may be peculiar to the Swiss market (Gyr [1979]), but crucial features of the scheme are similar across national borders, as shown below.

For simplicity, the agent is assumed to have a two-period planning horizon only, over which he tries to maximize the present value of his income. This is sufficient to represent the dynamics of his income :

ye (1) ~ e = y ~ + l + r

= c"[P]" P + s ~ [ ( L + C ) / P , i ' l ' P + F[/ ' I

' [ 1 + ~ c" [P+, l - P+, + s ' [ ", ~b+, l �9 P+, + F[/b+,] - -max .

c": Commission, expressed as a percentage of gross premiums written. Decreases with premiums, i. e. 5c e / ~ P < 0

C: Underwriting expense

F: Fixed income. Depends on (previous) relative growth, with 5 F~ 5 ~b > 0

L : Losses incurred

P: Gross premiums written (stock)

b : Percentage growth of premiums written, = ( P - P - t ) / P-t

~ b + t : Percentage growth of premiums written in the following year, = (P+t - P) / P

r: Real rate of interest

s" : Bonus component, decreases with the combined ratio [3 s" / ~ ( L + C) / P < 0], (locally) increases with growth [as" / ~P -- 0], see text below

ye: Exclusive agent's income.

Thus, the exclusive agent's income consists of three parts. The first component of his income is the regular commission (c e) on the stock of premiums written, with c" differing between lines but amounting to about 1 percent on average. The lower the premium stock, the larger this commission. The second component has the characteristics of a bonus. While it is expressed again as a percentage of gross premiums written, the factor s" itself depends on two things: On the one hand, both the loss ratio and the loading with underwriting expense are considered; on the other hand, growth above a certain threshold (12 percent annually for most agents in the sample) gives rise to a bonus surcharge. Finally, the exclu- sive agent receives a fixed income, which however depends on growth performance in

173

Page 4: Exclusive vs. Independent agencies: A comparison of performance

previous years. These are features shared by e.g. French insurance companies (cf. Fabre [1982]; Peylet [1980], pp. 375-381). For simplicity the premium growth rate of the current year is entered in order to remain in the two-period framework.

The structure of the contract specified in equation (1) bears a certain resemblance with that predicted by principal-agent-theory. If the insurance company (the principal) aims both at profits and premium growth, which seems evident from equation (1), then efforts in both dimensions should be honored by a conditional fee policy. According to Shavell [ 1979] only a small fixed amount should be paid when measured performance is below a certain standard, while a complicated schedule should come into force above standard. This struc- ture is mirrored to some extent by the bonus s e which does depend on growth and combined ratio (an indicator of the contribution to gross profit). But the bonus is triggered only by growth and not by cost performance. Moreover, the "fixed" income component too depends on growth performance.

However, the main departure from principal-agent theory concerns the formulation of the objective function in equation (1) which fails to display risk aversion. A risk neutral agent, on the other hand, would opt for a fixed royalty to be paid to the principal, as pointed out by Shavell [1979]. Risk neutrality may therefore be justified only as a simplifying assumption.

Neither the combined ratio nor premium growth constitute the ultimate decision variables under the agent's control. Rather, it is through his employment decisions in terms of sales and administrative personnel that the agent influences these performance variables. On closer inspection, a "production relationship" holds between premiums, losses incurred through the settlement of claims, and customer satisfaction, as described by the following three equations:

(2) P= P (S, Z) ] (3) L = L (P, Z) I (all first-order partial derivatives positive) (4) Z--- Z ( L , A)

A: Employment of administrative personnel (decision variable) L: Incurred losses, net of change in claims reserve S: Employment of sales personnel (decision variable) Z: Customer satisfaction.

The last two of these three equations constitute a simultaneous submodel. According to equation (3), the greater the stock of premiums (P) and the level of customer satisfaction (Z) aimed at, the higher the losses (L) due to claims to be settled on account of this parti- cular agent. On the other hand, as shown by equation (4), high claims paid out (L), together with quick settlement made possible by ample employment of administrative per- sonnel (A), are conducive to high customer satisfaction (Z). In the sequel, full relationships between these variables, taking their simultaneity into due account, will be needed. These (partial) total differentials (e. g. dPIdS, with A held constant are derived in Appendix A, together with their likely signs.

Equations (2) to (4) show that the employment of administrative and sales personnel constitute the ultimate decision variables of the agent. Differentiating partially equation (1) with respect to S to derive necessary conditions for an optimum, one obtains

174

Page 5: Exclusive vs. Independent agencies: A comparison of performance

(5) OZ ~ Oc e dP d P ds" dP

= ~ . p + c e ~ + . p + s e ~ + OS ~P dS dS dS dS

OF aP+t d P ] Fds~'l P+I + - - 1

+ l + " r U dS Off+, OP " ~

O.

~F ok aP ok oP as

Detailed expressions for the total differentials d P / d S and d L / d S (together with their likely signs) can be found in appendix A, while the signs of dse/dS and ds~v/dS are derived in appendix B.

As it stands, equation (5) is difficult to interpret. For a simplification and as a first step towards equations (14) and (16) below, which lend themselves to empirical testing, it is assumed that the relationships between s e and the combined ratio (L + C ) / P and premium growth k as well as between fixed income F and premium growth P remain constant over time. Next, in order to avoid leading and lagging values of P,.note that by the definitions of P and P+t jn equation (1), O P / O P = P-t / P':I ~ 1 / P (1 - P) and OP+t / ~ P = - P+t / p2 ~- - (1 + P) / P. Then, the first-order optimum condition with respect to sales personnel (S) can be written

(6) e(sq S) OF 1 d P

c , [ l + e ( c ~ , P ) ] + s , [ l + ~ ] + . e(P,S) oP PO-P) dS

(+) (+)

1 r ds$t OF (I+P) d P q l + r I - - ' ~ -P+t -~ O~ P YJ I

L In this equation, elasticities are defined as usual, e.g. e(c', P) = (Oc'/OP)/(c'IP).

Differentiating the objective function (1) with respect to administrative personnel (A), one obtains

(7) OX e ac �9 dP dP ds �9 dP dP - - = ~ . ~ p + c e ~ + ~ ~ p + s e + OA OP dA dA dP dA dA

1 ids~. , dP P+,+ OF+, ok+, dP ] + l +---r dP dA dP +~ OP dA

= O.

OF oi a dP

ok oP dA

Again assuming OF//OP to remain constant over time, one obtains

0F I (8) c ' [1 + e(c e, V)] + se[1 + e (s e, e)] +

(+) ok P(1-P)

1 ds~l P+t § l + r dP OP

(-) (+)

175

Page 6: Exclusive vs. Independent agencies: A comparison of performance

3. Model of an independent agency

This section is devoted to the development of a second model, designed to mirror the specifics of a typical contract between an independent agency and one of the insurance com- panies it writes business for. Its income dynamics over two periods is given by

(9) ~:+ = Y+ + l + r

= c" [ e l . P + gi . ( e _ e_t) + s" [ (L + C) I P, P]" P - C [A, S]

+ - - ci [P+II �9 P+I + g~" (P+~ - P) + si [.,/'§ e+~ - C+/[A,+~, S . . l + r

Net income in a given period consists of four terms. First, there is the basic commission on the stock of premiums written (c9, which however is somewhat higher than in the case of the exclusive agent, i.e. c i > c +. Moreover, the commission decreases at a much slower pace, i.e. aci/aP > ac,/aP. The second term is a growth incentive in that the agency receives a fixed payment (g9 per Swiss franc of new business acquired, honoring absolute premium growth. Next, there is a bonus surcharge (s9 depending (negatively) on the combined ratio and (positively) on the percentage growth of premium volume in the same way as for the exclusive agent. The last term of equation (9) emphasizes the fact that the independent agency must cover its underwriting expense out of its income. In the main, these expenses are a function of administrative personnel (A) and sales force ($). Of course, the same rela- tionships hold in the second period although discounted by the real interest rate (r).

Partial differentiation of equation (9) with respect to the current sales force (S) yields

a~ i ac i dP dP dP ds i dP aC (10) a--~ = aP dS e + ci'-72"~ + gi + - e + s' dS dS dS aS ab

1 [ _ g ~ a t ' ds i , e ] + l + r dS + dS +t] = 0 .

After some rearrangement, this results in

(it) I e(si 'S) I dP ci[1 + e (c i, P)] + s i [ l + - - ] "l" g i (+) e (P, S) dS-

(+)

ac 1 [ aP] + - P+' + g"- l aS l +r dS

(+) (-) (+) J

For the sign of dP/dS, see appendix A ; for the signs of dsi/dS and dsj, l /dS, see the ana- logous expressions in equations (B.2) and (B.3) of appendix B. Partial differentiation of equation (9) with respect to administrative personnel (A) results in

176

Page 7: Exclusive vs. Independent agencies: A comparison of performance

O~i ~C i dP dP dP ds i dP (12) = ~ _ _ p + c i +gi + - - - - p

oA 8P dA dA dA dP dA

dP ~C l l dP ds i t dp ] + s i ~ _ ~ + _gi " + - P+I

dA ~A 1 + r dA dP dA

= 0 .

After some rearrangement, and using the fact that dsi/dP and ds i l /dP must have the same signs as dse/dP and ds~,t/dP, respectively (owing to the common functional form of s e [.] and s i [.], one obtains

(13) ci [ l+e(c i , p ) ]+s i [ l+e ( s i , p ) ] + g ' (+) (+) (+)

3C / dP 1 I dsi+l ] = ~ ~ + - P + I + g i .

3A dA 1 + r dP (+) (-) (+) J

4. Derivation of testable implications In this section, necessary conditions for an optimum are compared among exclusive

agents and independent agencies. First, employment of sales personnel (S) as an indicator of sales effort is considered ; the second subsection will be devoted to the employment of administrative personnel (A), which has implications for the underwriting expense ratio and possibly the loss ratio. In both instances, it is checked whether differences between the two marketing channels originating from the revenue side are likely to outweigh those due to the cost side. In act, incentives influencing the revenue side will be shown to be of comparable magnitude (despite quite different formulations at first sight), lending support to the working hypothesis that observable performance differentials are attributable to the cost side effects emphasized in this paper.

4.1. Sales effort: Exclusive and independent agencies compared Equation (6) of the second section contains an exclusive agent's optimum with regard

to sales personnel, which is reproduced here after division by dP/dS, using 1/e (P,S) 1/ [ d P / dS �9 (if+t/S)] and the approximation 1 + P ~ 1/(1 - P ) , which holds for small growth rates P:

(14) c e l + e ( c e , P) +s" 1+ e(P, S)

(+)

r a F / F F +1+--7 aP 7 (I+p)

1 I e(s~t'S) 1 l + r e (P, S) s~'l " (-)

177

Page 8: Exclusive vs. Independent agencies: A comparison of performance

As for the independent agency, equation (11) can be written as

I e(si, S) 1 r (15) c i [ l + e ( c i ,P, )] + si 1 + ~ e(P,S) + T~--; g'

e(C,S) C + 1 I e(s~t,S) si+tl " e(P,S) P l + r e(P,S)

The left-hand side of both optimum conditions reflects net marginal revenue associated with increasing sales personnel by one unit. While the structure of the two left-hand sides is fully analogous, the fact that the commission for the independent agency is greater (c i > c ~) and decreases much slower with premiums written [ 1 + e(c i, P) > 1 + e(c e, P) ] will make its marginal revenue larger, ceteris paribus, Next, the growth incentive gi, amounting to a few percentage points according to contracts as written, approximately equals the growth adjustment of the fixed income component in equation (14) (which amounts to a few per- centage points of premium volume on average). For each percentage point of growth, F is stepped up. by less than 10 percent (again according to the contracts of the sample) ; thus, (OF/F)/3P ~ O. 10 whereas the ratio of fixed income to premiums F~ P ~- 0.02. The product of these two terms is in the neighborhood of 0.2 percent, somewhat less than gL

The marginal cost associated with stepping up sales effort appears on the right-hand side. It is here that the two distribution channels differ greatly. In the case of the exclusive agent, marginal cost consists only of the effect increased sales today will have on tomor- row's benchmarks for growth performance. Accordingly, this cost is discounted. The independent agency, on the other hand, is fully affected by marginal cost because it bears the underw..riting expense out of its own income, The ratio of the two elasticities should be about unity, whereas the expense ratio amounts to some 0.3. Thus, marginal costs are far apart, much more than marginal revenues. These considerations can be summed up in

Prediction I: Growth orientation of exclusive agents should be stronger than of inde- pendent agencies. While their marginal revenue associated with increased sales effort is somewhat smaller, they are relieved to an important extent from bearing the full marginal cost of growth.

4.2. Administrative personnel: Another comparison In this subsection, conditions regarding employment of administrative personnel (A)

are compared between exclusive and independent agencies. To facilitate this comparison, equations (8) and (13) are reproduced below, written in slightly different form. For the exclusive agent, one has, using (ds~.JdP) �9 (P+l/s~.t) ~- e(s e, P),

I1 1 r aF/F F (l + fi) (16) c" +e(c' ,P) +s ' [ l+e ( s , ,P ) ] - t l+~ r ak P

1 [--e(se, P). S~A. = I + r

178

Page 9: Exclusive vs. Independent agencies: A comparison of performance

For the independent agency, equation (13) becomes

I 1 r g i (17) c i l + e(ci, P) + si[l + e(si, p)] +-~- 7

e(C'A) C l l 1 . . . . + - e ( s i, P)'si+l . e (P, A) P 1 § r

Once more, the director of an independent agency will consider that he has to bear the entire marginal cost of an additional administrative person employed. The elasticity e (C, A) probably lies around one, whereas e(P, A) should have a rather low value (0.1, say) because administrative expediency would not seem to contribute too decisively to premium volume. Multiplied by C/P ~ 1/3, this term could lie between 2 and 3, much greater than the common element of marginal cost involving e (s e, P) and e (s i, P) respectively. Thus, one has

Prediction 2: The independent agency will stop short employing administrative personnel at a point where exclusive agents would still consider marginal revenue associated with hiring additional personnel higher than marginal cost. Thus, administrative employ- ment - and along with it, underwriting expense - is predicted to be higher with exclu- sive agents than with independent agencies, ceteris paribus.

5. Empirical evidence

The data base used in the regression analysis below comes from a company working with exclusive as well as independent agents. For reasons of confidentiality, it cannot be described in any detail except stating that exclusive agents constitute the majority of obser- vations.

5.1. Growth performance The dependent variable is percentage growth of gross premiums written rather than the

ultimate decision variable itself, sales effort (S). This does not preclude an indirect test of Prediction 1, however. Given previous year's premium volume, growth can be related to current sales effort, see equation (A. 12) and accompanying text. Sales effort should in turn be set according to optimum conditions (14) and (15). While the elasticity of underwriting expense with regard to sales effort e (C, S) constitutes the principal (but unmeasured) diffe- rence between the two types of agency, other incentive parameters differ too. Thus, those other terms (operating on the revenue side) should be controlled for statistically in order to relate differences in growth performance to the cost term e (C, S). Accordingly, all incentive parameters influencing marginal revenue [c_" v ci-t," s~-v sit; git, F-l; see equations (14) and (15)] originally were included in the regression, assuming a lag adjustment of one year. Some of them had to be dropped in the sequel due to severe multicollinearity.

Since there was evidence of heteroscedasticity using the test developed by White [1980], the regression shown in Table 1 below are all heteroscedasticity-consistent as proposed by Messer and White [1984]. Elasticities are calculated on the basis of grand means throughout. Not one of the incentive variables listed above proved statistically significant (judged at the 5 percent confidence level), the significant coefficient of the growth bonus for independents in 1982/83 probably reflecting a coincidence. Of the remaining regressors, the dummy variable for the independent agencies (Independent = 1) merits special attention.

179

Page 10: Exclusive vs. Independent agencies: A comparison of performance

Tabl

e 1

:

Exp

lana

tory

Var

iabl

e M

odel

V

aria

ble t

)

Dum

my:

Inde

pend

ent =

1

(-)

i Gro

wth

Bon

us

g'-'l (

+)

Fixe

d Inc

ome

F a (

-)

Prev

ious

Yea

r

Reg

ular

Com

miss

ion

c~a (

7)

Prop

erty

Lin

e, Pr

evio

us Y

ear

Reg

ular

Com

miss

ion

c_~l (

?)

i LA

H2)

, Pre

viou

s Yea

r

i Dum

my:

Age

ncy S

tartu

p (+

)

Dum

my:

Age

ncy S

tartu

p (+

)

Dum

my:

Out

lier

(?)

Con

stan

t

Cor

rect

ed R

2

Prob

(F>

Fr

Det

erm

inat

ion

of P

rem

ium

Gro

wth

~

P-

P-t

. lO

O1

�9 19

80/8

1 -

1984

/85,

H

eter

osce

dast

icit

y-C

onsi

sten

t E

stim

atio

n L

P-,

3 19

81/8

2 19

82/8

3 19

8318

4 19

8418

5

Sign

ifica

nce a

t the

5 %

leve

l Si

gnifi

canc

e at

the

1% le

vel

Sign

ifica

nce

at th

e 0.

1% le

vel

1980

/81

Coeff

icien

t ]

Elas

ticity

--6.2

9 -0

.07

0.10

0.

01

-0.0

4 -0

.06

-0.3

9 -0

.42

0,42

0,

38

177.

4'**

159.

2'**

13.0

0.%

0.0

(two-

taile

d te

st)

(two-

taile

d te

st)

(two-

taile

d te

st)

Coe

~den

t El

astic

ity C

oeffi

cient

[ El

astic

ity

Coef

fcien

t [ El

astid

ty

Coef

fudc

at E

lastic

ity

-13.

50'

-0.2

4 --

8.98

-0

,20

8,02

0.

29

-1.0

0 -0

.00

-0.0

1 0.

00

0.33

***

0.11

-0

.08

-0.0

3 0.

24

0.02

-0.2

0 -0

.53

-0.0

7 -0

.28

0.17

0.

53

0.14

0.

09

-0.0

5 -0

.09

-0.0

1 -0

.02

0.64

1.

63

--0.3

3 -0

.19

0.09

0.

13

-0.0

7 -0

.16

-0.8

5 -1

.97

0.55

0.

30

87.8

***

45.5

***

--47.

6'**

21.1

'*

11.8

' 3.

0

0.11

0.

58

0.67

0.13

0.

0 0.

0

Not

es:

1)

2)

706.

7***

286.

6***

0.6

0.99

0.0

Theo

retic

ally

pre

dict

ed s

ign

of re

gres

sion

coe

ffic

ient

in

pare

nthe

ses

LA

H:

Liab

ility

, Acc

iden

t, H

ealth

Page 11: Exclusive vs. Independent agencies: A comparison of performance

In the previous section, Prediction 1 was derived, stating that independent agencies should have a weaker growth orientation than exclusive agents. But it is only in the period 1981/82 that the respective regression coefficient is significantly negative. Therefore, there is little basis for a claim that exclusive agents generally outperform independents in terms of premium growth. Apparently, the growth target setting procedure (common for both types of agency) does not allow such a differential to materialize.

In order to control for start-up agencies that necessarily display very high growth rates, dummy variables were introduced. This outlier correction contributes to the high coefficients of determination shown in Table 1, which range from 0.11 in 1981/82 to 0.99 in 1984/85. These results yield

Conclusion 1: Exclusive agents cannot be claimed to produce a higher growth of premiums written ceteris paribus, contrary to Prediction 1. More generally, incentive effects for premium growth in contracts as presently in force cannot be ascertained.

5.2. Underwriting expense performance

At this time, no data concerning the employment of administrative personnel in agencies are available. Again, this does not preclude an indirect test of Prediction 2. After all, the underwriting expense ratio is largely determined by administrative employment since C depends strongly on A in equation (9) whereas P varies mainly with S, not A, see equation (A.12) and accompanying text. Thus, C/P can serve as a substitute dependent variable. The variable appearing in Table 2 is the ratio of underwriting expense to premiums written, covering the years 198{) to 1985. The hcteroscedasticity-consistent estimation method proposed by Messer and White [1984] was used again.

First of all, Prediction 2 derived from the model stated that independent agencies should invest less in administrative personnel than do exclusive agents with a concomitant differential in terms of the underwriting expense ratio. This prediction is fully borne out in the last three of the six years considered, with the ceteris paribus cost differential increasing from 7 to 11 percentage points. Prior to 1983, the estimated differential is smaller, not quite attaining statistical significance in 1982 and 1981. This finding should be contrasted with the lack of a clear advantage of exclusive agents in terms of growth performance that was noted in the discussion of Table 1 (see the previous paragraph). Moreover, according to Cummins and Weisbart [1977], such cost differentials need not go along with lower quality of customer service.

But cost differentials easily flow from differences in portfolio composition. In particular, there is a presumption that life, accident, and health (LAH) business entails more administrative cost per unit premium written than does property insurance, a point emphasized by Johnson et al. [1981]. Due to data limitations, the respective volume shares are not available prior to 1983. As a substitute, the commission paid c', which differs between these two business lines, appears in the regression. While lacking influence on the overall growth rate, these incentives may still influence portfolio composition, which in turn would impact on the expense ratio of the agency. This expectation is confirmed to some extent in that in recent years, an increase in the property commission seems to have lowered the expense ratio. Conversely, creating an incentive in favor of LAH business would boost the expense ratio through a restructuring of the portfolio.

181

Page 12: Exclusive vs. Independent agencies: A comparison of performance

Tabl

e 2:

D

eter

min

atio

n of

Und

erw

ritin

g E

xpen

se R

atio

--

~ �9

I00

; 19

80-1

985,

Het

eros

ceda

stic

ity-C

onsi

sten

t E

stim

atio

n

Expl

anat

ory

Var

iabl

e M

odel

19

80

1981

19

82

1983

19

84

1985

V

at.I)

Co

effic

ient E

lastic

ity C

oeffi

cient [

Elas

ticity

Coe

[ficie

nl E

lasti

dly

Coef

ficien

t Ela

slidt

y Co

effici

ent [

Elas

ticity

Coe

fficie

nt E

lastic

ity

Dum

my:

Inde

pend

ent =

1

(-)

--6.

28

-0.0

4 [ -

-8.8

2 -0

.06

-7.2

4 -0

.06

7.37

* -0

.09

-11.

12'

-0.1

2 -1

1.41

' -0

.12

i

Regu

lar C

omm

Lssio

n:

Prop

erty

Lin

e

Regu

lar C

omm

issio

n:

LAH

2)

Prem

ium

s Writ

ten

Dum

my:

Age

ncy S

tartu

p

Dum

my:

Age

ncy S

tartu

p

~ Dum

my:

Out

lier

Dum

my:

Out

lier

I Con

stant

Corre

cted

R 2

~ob

Or> r

3

c'(-

) -0

.68

-0.3

8 I-

0.35

-0

.21

-0.6

2 -0

.45

-0.4

9 -0

.36

-0.8

3**

-0.5

8 -0

.80*

-0

.57

cr

1.23

0.

60

0.72

0.

38

0.89

* 0.

57

0.48

0'

.32

0.93

**

0.60

0.

75

'0.4

9

P(-)

-0

.001

3 -0

.08

-0.0

010

-0.0

8 -0

.001

0 -0

.10

-0.0

008

-0.1

0 -0

.001

0 -0

.11

-0.0

007

-0.0

8

(+)

69.2

***

42.6

***

23.7

***

(+)

26.4

***

(?)

52.7

***

-21.

3'**

23.7

'**

20.0

'**

13.1

'* 31

.1'**

29

.5'**

30

.1'**

29

.6**

* 31

.6'**

(7)

* Si

gnifi

canc

e at

the

5 % l

evel

**

Si

gnifi

canc

e at

the

1% le

vel

***

Sign

ifica

nce

at th

e 0.

1% l

evel

(tw

o-ta

iled

test

)

0.67

0.0

(two-

taile

d te

st)

(two-

taile

d te

st)

0.58

0.

54

0.14

0.

62

0.42

0.0

0.0

0.04

4 0.

0 0.

0001

5

Not

es:

1)

Theo

retic

ally

pre

dict

ed s

ign

of r

egre

ssio

n co

effic

ient

in

pare

nthe

ses

2)

LAH

: Li

abili

ty,

Acc

iden

t, H

ealth

Page 13: Exclusive vs. Independent agencies: A comparison of performance

It is interesting to see that the underwriting expense ratio tends to decrease with in- creasing volumes of premiums written, suggesting increasing returns to scale, as have been found in other studies (see e. g. Cummins and VanDerhei [1979] for the U.S., Skogh [1982] for Sweden). Unfortunately, coefficients, while attaining a 90 percent confidence level three times, never are fully significant. As pointed out by Skogh [1982], bookkeeping identities link premiums to operating costs, introducing simultaneity bias into OLS estimates. Moreover, the model states in equations (2) - (4), that administrative effort (A) has a payoff in terms of premiums written (P), which adds potential for simultaneity bias in these estimates. Lacking exogenous instruments for two-stage estimation, all one can say is that the case for increasing returns to scale should not be overstated. The estimated elasticity of the expense ratio with respect to premiums is indeed on the high side with values around -0.08, the value implied by the estimates of Cummins and VanDerhei [1979] being about -0.03 (see their Table 2).

Again, it was necessary to correct for outliers, mainly due to agencies entering business in the years 1980, 1984, and 1985. These agencies naturally have expense ratios that are extremely high and even exceed unity at times. Adjusted coefficients of determination range around 0.5, with the important exception of t983 (when it drops to 0.14). This discussion can be summed up in

Conclusion 2: Statistical evidence based on a sample taken from the Swiss insurance market suggests that independent agencies do attain a lower expense ratio, ceteris paribus. Moreover, there are preliminary indications of increasing returns to scale.

5.3. A trade-off between loss ratio and expense ratio ? In the previous paragraph, evidence was presented suggesting that independent agencies

enjoy an advantage in terms of underwriting expense. However, this advantage could be offset by two factors : On the one hand, independent agencies might be less growth oriented (which does not seem to hold true in this sample, see the discussion of Table 1), or they could have a higher loss ratio, e.g. because they skimp on trained claims processing person- nel.

Thus, an additional regression was run with the loss ratio (L/P) as the dependent variable, covering the years 1983 to 1985. Prior to 1983, the data do not permit distinction of actually paid claims from loss reserving. There is evidence to the effect that loss reserving follows a pattern of its own over time, mainly due to smoothing (Weiss [1985]). The buildup of loss reserves relative to premiums written serves as a quality indicator of the portfolio. ! n an attempt to control for other characteristics of the portfolio that might influence the loss ratio, the shares of LAH (Liability, Accident, Health) and Maritime/Goods in Transit lines in total premiums written were entered as well (see Table 3). Finally, since the loss ratio may be interpreted as an intermediate policy variable for attaining premium growth, the same incentives influencing premium growth may impact on the loss ratio as well. In particular, the special growth bonus awarded to independent agencies should be distin- guished as much as possible from the status of the agency as such. But once more, incentive parameters fail to exhibit a systematic pattern. The results for 1984 appear to stand out for their statistical significance. Much of this may be due to the introduction of higher deduc- tibles in nonlife insurance. This change shifted the distribution of expected future claims towards higher values, calling for an increased emphasis on loss reserving. As they tried to build up reserves, agencies seem to have put pressure on their loss ratios.

183

Page 14: Exclusive vs. Independent agencies: A comparison of performance

Table3: DeterminationofSettledClaimsRatioI-~.lO01; 1983-1985, Heteroscedasticity-Consistent Estimation

Explanatory Variable Model Var.t)

Dummy: Independent = I

Growth Bonus gi

Fixed Income F

Regular Commission c e Property Line

Regular Commission c' LAH

Loss Reserves/Premiums Property Line

Loss Reserves/Premiums LAH z)

Loss Reserves/Premiums Goods in Transit

LAH Premiums/ Total Premiums

Goods in Transit Preminmsrrotal

Constant

Corrected R 2

Prob (F>,~c)

Significance at the 5 % level Significance at the 1% level Significance at the 0.1% level

Notes: 1) 2)

1983 1984 Coefficient Elastici~ Coefficient [ Elasticity

-10.73 -0.05 6.91 0.03

-0.18 -0.01 -0.76** -0.04

-0.07 -0.03 0.25 0.09

-0.84 -0.26 -2.53*** -0.79

1985 Coefficient I Elasticity

-4.27 -0.02

0.41 0.02

0.10 0.04

0.63 0.22

0.46 0.13 2.21'* 0.63 -0.66 -0.21

0.61'* 0.07 -0.12 -0.00 -0.35 -0.00

0.46 0.03 -0.52*" -0.02 -0.35 -0.00

1.93'* 0.05 -1.23'** -0.00 0.29 0.00

0.66** 0.34 -0.07 -0.04 0.06 0.04

-0.10 -0.02 -0.61'** -0.14 -0.28 -0.08

184

No theoretically derived signs of regression coefficients in this relationship LAH: Liability, Accident, Health

(two-tailed test) (two-tailed test) (two-tailed test)

42.3'* 72.6'** 50.8***

0.26 0.49 0.15

0.026 0.00024 0.11

Page 15: Exclusive vs. Independent agencies: A comparison of performance

But the crucial finding of Table 3 is that independent agencies do not appear to differ from exclusive agents in terms of their loss ratio. The importance of this result lies in the suspicion that independents might achieve their cost advantage simply by selecting risks that require little in the way of claims processing. Such a filtering would tend to show in the loss ratio. The fact that no difference can be found in this variable tends to speak against an explanation of the cost differential in terms of risk selection. In all, the empirical analysis suggests the following

Conclusion 3: Independent agencies do not differ in a statistically recognizable way from exclusive agents in terms of their loss ratio. Thus, there is no indication to the effect that they achieve their advantage in terms of underwriting expense through a selection of risks.

6. Conclusion and outlook

This paper is about a challenge that will have to be faced by European insurance com- panies in the next few years, viz., finding the least cost mix of marketing channels for their products. Out of a whole spectrum of solutions, the two most popular ones in Europe are analyzed here, exclusive agents and the independent agencies. Little specific theoretical work seems to have been done, with empirical studies guided by some general notions surrounding principal-agent relationships. Moreover, empirical evidence so far has been rather mixed, with some U.S. studies suggesting lower underwriting expense ratios for exclusive agents (Etgar [1977]), others roughly equal ones (Johnson et al. [1981]) compared to independent agencies.

The novelty of this work therefore may be seen in its combination of theoretical argument and empirical test. On the theoretical side, it finds some reasons to expect a possibly stronger growth orientation of exclusive agents on the one hand but less concern for cost control on the other. These predictions are subjected to an empirical test using individual agency data concerning the Swiss market. No statistically significant difference in growth orientation (given the incentive structure inherent in contracts struck between companies and both types of agencies) was found. But exclusive agents do seem to have significantly higher expense ratios than do independent agencies, the difference amounting to 7 - 11 percentage points (cf. also Eugster [1981], p. 303). This difference cannot be attributed to risk selection by independents because loss ratios seem to be the same across the two types of agencies, ceteris paribus.

In future work, the sample should be extended, including companies that provide their agencies with possibly somewhat different incentives and testing for the impact of these incentives. More investigation is also needed into the structural breaks that seem to have occurred during the observation period. In this context, it may also pay to introduce some refinement of econometric technique, e.g. in the way of controlling for simultaneity bias and autocorrelation over time when tracing agencies over a sequence of years.

Over time, some contract provisions were changed. This gives rise to a second open question: Can these changes be explained on the basis of economic theory ? One possi- bility would be to invoke principal-agent theory, which would tend to result in a Cournot- Nash game evolving over time in a quasi-dynamic fashion. In the first period, the company might require a minimum contribution to profit, to which exclusive and independent agencies would adjust by finding optimal values for their sales effort and employment of

185

Page 16: Exclusive vs. Independent agencies: A comparison of performance

administrative personnel. Given these actions by agencies, the company would in turn search for newly optimal parameters for its contracts, e.g. a new benchmark value for premium growth that would entitle to extra bonuses or a new relationship between the regular commission and premiums written according to size. In the following period, the agencies would again adjust to the new situation, etc.

This view of an adjustment process suggests a final point. Given that the company's objectives are profit and growth, say, can the contracts concluded between them and their agencies be claimed to belong to an "optimal class"? The theoretical analysis contained in this paper showed actual contracts to be rather complicated, but maybe this level of intri- cacy is necessary to attain the company's objectives while preserving incentives of the individuals running their exclusive or independent agencies.

In all, comparing the performance of different insurance marketing channels seems to be a promising field for research, whose relevance for companies can only increase in the future.

Appendix A

In this appendix, total derivatives and their likely signs are determined for the simul- taneous subsystem given by equations (2) to (4) in the text. For convenience, these equations are repeated below:

(A.1) P = e ( S , Z ) (A.2) L = L (e, Z ) (A.3) Z = Z (L, A ) , with all first-order partial derivatives positive.

Total differentiation of this system yields, written in matrix notation,

E ,I [ o l (A.4) dL = a L OP 0 a L I 3 Z dL d Z 8 Z l a L 0 d Z

+

Upon solution for the left-hand side vector, this yields

(A.5) --0 ~P 1 .-.O ~ Z dL -.= 0 . - -OZI~L d Z a Z / ~ A �9 dA

186

Page 17: Exclusive vs. Independent agencies: A comparison of performance

When Cramer's rule is applied to this linear system, the solution takes on the following general form :

(A.6) idol Exl dL = -~ Y . dZ M

The elements of the right-hand side vector are given as follows:

(A.7) X = 3P / 3S . dS 0 - 3 P / 3 Z [

1 0 1 - -3L/3Z 3Z/OA �9 dA --3Z/3L l

= - - d S 1 0 - ~ O- dA 3S 3Z 3Z 3A

.ff_~] 8P 3Z 3P 1 3L 3Z dS+ dA, 3S 3Z 3Z 3A

(A.8) y = 1 3 P / 3 S . dS - 3 P / 3 Z

- 3 L / S P 0 - -3L/3Z 0 3 Z / a A �9 dA 1

3L 3Z

3Z 3A

3L 3P dA + ~ ~ d S - ~ - -

3P 3S

3L 3P 3Z

3P 3Z 3A m d A ,

and

(A.9) M = 1

--SL/aP 0

0 1

- -3Z/3L

8 P / 3 S . dS 0

3Z /3A �9 dA

3Z 3Z = 3-- A dA 4 3L

3L 8P

8P 3S r o d S .

187

Page 18: Exclusive vs. Independent agencies: A comparison of performance

The determinant is given by:

(A.IO) d = l 1 ~L ~ .] -a-'zaL aI_ ~ oLDZ Ol

8L aZ ~L ~P aZ - 1

3Z ~L OP ~Z aL

where it should be noted that L = L (., Z ) is a function different from Z = Z (., L). This determinant can be expressed in terms of elasticities as:

(A.U) A = 1 - e (L, Z ) �9 e (Z, L) - e (L, P) �9 e (P, Z) �9 e (Z, L)

>0 as a rule.

The positive sign of the determinant can be justified as follows. According to the pro- duction submodel, an increased target value in terms of customer satisfaction requires more generous loss settlement [see equation (A.2)]. The corresponding elasticity e (L, Z) cannot exceed 1 for the company to remain financially viable. In fact, attempts are made to limit the size of this elasticity by controlling the moral hazard effects involved through association-wide upper limits on coverage, detailed risk audits of large objects in property/ liability etc. Moreover, in view of the inconveniences associated with filing a claim, consumer satisfaction depends on paid-out loss with a rather small elasticity e (Z, L). As regards e (P, Z) , the impact of consumer satisfaction on premiums written is small due to long contract duration in Switzerland that keeps mobility at a low level. As a final point, A > 0 is necessary to preclude counterintuitive results in equations (A. 13), (A. 14), and (A.17).

On the basis of equations (A.6) - (A.11), the (partial) total differential of premiums with regard to sales force is given by:

(A.12) ~ = ,~ = ~ ' - - T a z - -

(+1 (+) (+)

with the positive sign of the expression in brackets implied by equation (A.10) as soon as A is positive.

Likewise, premiums are related to administrative personnel by total differentials given by:

dP X I d S = O 1 ~P ~ Z (A.13) dA -- zl A aZ aA > 0,

(+) (+) (+)

with e (P, S) > e (P, A ) likely because sales effort has an immediate impact on premiums whereas administrative employment affects premiums only indirectly, preventing cancella- tion of policies.

188

Page 19: Exclusive vs. Independent agencies: A comparison of performance

Next, losses incurred depend on the two decision variables as follows:

dL Y I dA = O 1 OL aP (A.14) dS A A aP aS > O,

(+) (+) (+)

and

(A.15) dL Y l dS = O 1 ['aL aL aP-] aZ = = - - . ~ + ~ ] >0. dA A A ~Z aP ~Z

(+) (+) (+) (+)

Finally, customer satisfaction also depends on sales force and administrative personnel :

dZ M [ dA = O 1 ~Z aL aP (A.16) dS A A aL aP aS >0,

(+) (+)

and

dZ M IdS=O 1 aZ (A.17) - = �9 - - > 0.

dA A A aA (+) (+)

Appendix B

In this appendix., the signs of ds,/dS and ds~l/dS as well as dse/dP and ds~q/dP are determined, using 5P/aP ~ 1/P and aP+t/aP ~ - 1 / P as in the main text.

dse ~s" ~ (L+C) /P as" aP dP

(B.1) d-"-S "= a (L+C) / t ; " ~S t -aP aP dS

aC dP P-(L+C)

as" aS dS ~s" 1 dP

a (L+C) /P pe aP P dS

(+) (+) as" dP

aP dS as" P a ( L + C ) / P

(-)

s (L+O dP S

~ C C d$ P

P (-/+)

> 0 as a rule.

C

S

189

Page 20: Exclusive vs. Independent agencies: A comparison of performance

The sign restriction can be justified as follows. The first term in the numerator of the bracket is the elasticity of underwriting expenses with respect to sales personnel, which might be somewhat less than one. On the other hand, the ratio (L+C)/C typically exceeds two, while the elasticity of premiums with respect to sales personnel should not lie very much below one. On balance, the term in brackets tends to be negative, resulting in a positive value for equation (B.2).

In analogous manner, one has

(B.2) ds~. 1 = as~ . a(L+C)/P +--ase aP+l dP dS a(L+C)/P aS aP+t aP dS

aC dP - - P - ( L + C )

as e aS dS as, 1 dP

= a ( L + c ) / e " p2 - D---if-"-fi- d"-ff

(+) (+) as* dP S

aP as e + as �9

s a(L+C)/P (+) (-)

[-(+) (+) [ ~ S ( L + O

C C

S (-/+)

1 ( M'" ~ - ~ - e (P,S) �9 +

s

as" C ) e ( C , S ) �9

a(L+C) le --fi- (-)

(+) dP S

dS P C

P

as �9 C 1 a(L+C)IP P (-)

< 0 as a rule.

e (.) : elasticity.

This time, the first term is rewritten to contain the elasticity of premiums with respect to sales personnel. This elasticity is multiplied by as, laP which is zero only'when the agency cannot hope to attain the bonus threshold (at i b -- 12 percent in most cases). But when it is effective, the bonus mechanism is much more geared to premium growth than to the combined ratio, which makes the sum in brackets positive and the full first term negative.

190

Page 21: Exclusive vs. Independent agencies: A comparison of performance

Finally, the evaluation of a Z , / a A in the text is based upon

(B.3) ds ~ as" O ( L + C ) / P as ~ aP

q , - - - . - - r - - -

dP a ( L + C ) / P aP aP aP

a L L + C

as" 1 as" a P P

= aP P + 8 ( L + C ) / P P

i E 1 as e as ~ = - - �9 + e (L ,P) . - -

P aP 8 ( L + C ) / P (+) (-)

> 0 as a rule.

P (-/+)

The sum in brackets, amounting roughly to a comparison between the loss ratio and the combined ratio, could conceivably turn the entire expression into negative. However, for this to become possible, the elasticity of losses with respect to premium volume would have to exceed (L + C ) / L or about 1.5.

Since the bonus component of the following year does not depend on the combined ratio of the current year, the last expression simplifies to

ds ~ l Os e a P + l Os" 1 (B.4) 0 4 - - - - = - < 0 .

de aP+, ae aP e (+)

191

Page 22: Exclusive vs. Independent agencies: A comparison of performance

REFERENCES

BRAEUTIGAM, R. R. and PAULY, M. V. [1986]: "Cost Function Estimation and Quality Bias: The Regulated Automobile Insurance Industry," Rand Journal of Economics, 17 (Winter 1986), 606-617.

CUMMINS, J. D. and WEISBART, S. N. [1977]: "The Impact of Consumer Services on Independent Insurance Agency Performance," IMA Education & Research Foundation, Glenmont NY.

CUMMINS, J. D. and VanDERHEI, J. [1979]: "A Note on the Relative Efficiency of Property- Liability Insurance Distribution Systems ," Bell Journal of Economics, 10 ( Autumn 1979), 709-719.

CUMM1NS, J. D. and HARRINGTON, S. E. [1987]: "The Impact of Rate Regulation in U.S. Pro- petty-Liability Insurance Markets: A Cross-Sectional Analysis of Individual Firm Loss Ratios," Geneva Papers on Risk and Insurance, 12 (January 1987), 50-62.

ETGAR, M. [1977]: "Cost Effectiveness in Insurance Distribution," Journal of Risk and Insurance, 44 (June 1977), 211-222.

EUGSTER, I. [1981]: "Vom Unternehmer zum Regieagenten, Kritische Gedanken zum Regie- vertrag" (From Independent to Exclusive Agent: Some Critical Remarks about the Contractual Relationship between Exclusive Agent and Insurance Company), Schweizerische Versicherungs- Zeitschrift, 302-305.

FABRE C. [1982]: "L'Art et les Mani~res d'Intrresser les Agents Grnrraux" (How to give exclusive agents the right incentives), L'Argus 31 (12), 2945-2947.

FINSINGER, J. [1983]: Versicherungsmiirkte (Insurance Markets), Campus Verlag, Frankfurt, New York.

FINSINGER, J. and PAULY, M. (Ed.) [1986l: The Economics of Insurance Regulation: A Cross- National Study, Mac Millan, London/New York.

GYR, W. [1979]: "Das schweizerische Provisionierungssystem'" (The Swiss System of Provisions), i)er Generalagent, 41 ( I ), 10-14.

HARRINGTON, S. E. [1982]: "Operating Expenses for Agency and Nonagency Life Insurers: Further Evidence," Journal of Risk and Insurance, 49 (June 1982), 229-255.

HARRINGTON, S. E. [1984]: "The Impact of Rate Regulation on Prices and Underwriting Results in the Property-Liability Insurance Industry: A Survey," Journal of Risk and Insurance, 51 (De- cember 1984), 577-623.

JOHNSON, J. E. et al. [1981]: "Return to Scale in the Property and Liability Insurance Industry," Journal of Risk and Insurance, 48 (March 1981), 18-45.

JOSKOW, P. [1973]: "Cartels, Competition, and Regulation in the Property-Liability Insurance Industry," Bell Journal of Economics 4 (Fall 1973), 375-427.

MESSER, K. and WHITE, H. [1984]: "A Note on Computing the Heteroscedasticity Consistent Co- variance Matrix Using Instrumental Variable Techniques," Oxford Bulletin of Economics and Statistics, 46(2), 181-184.

ORLUC, D. [1988]: "Franchissons les Obstacles en Commun," L'Argus No. 6052 (25.3.88), 854-857.

PEYLET, P. [1980]: Le Courtage d'Assurances, L'Argus, Paris. SHAVELL, S. [1979]: "Risk Sharing and Incentives in the Principal and Agent Relationship," Bell

Journal of Economics, 10 (Spring 1979), 55-73. SKOGH, G. [1982]: "Returns to Scale in the Swedish Property-Liability Insurance Industry," Journal

of Risk and Insurance, 49 (June 1982), 218-228. WEBB, B. L., LAUNIE, J. J., ROKES, W. P. and BAGLINI, N. A. [1984]: Insurance Company

Operations, 3rd ed., American Institute for Property and Liability Underwriters, Malvern, PA. WEISS, M. [1985]: "A Multivariate Analysis of Loss Reserving Estimates in Property-Liability

Insurers," Journal of Risk and Insurance, 52 (June 1985), 199-221.

WHITE, H. [1980]: "A Heteroscedasticity-Consistent Covariance Estimator and a Direct Test for Heteroseedasticity," Econometrica, 48 (July 1980), 817-838.

192