A note on the relative efficiency of property-liability insurance distribution systems J. David Cummins* and Jack VanDerhei**

Property-liability insurance is distributed through two major marketing channels-the independent and the exclusive agency systems. Independent agents place business with several companies, while exclusive agents write insurance for only one company. W e jind that the independent agency system is less efficient than the exclusive agency system. The efjiciency differential did not change significantly during the period 1968 through 1976. When we used the total rather than the underwriting costs to measure expenses, we found that the relative but not the absolute expense differential was reduced. This suggests that the inefjiciencies of the independent agency companies stem from marketing and administrative rather than loss adjustment procedures. The findings imply that regulators should play a more active role in the dissemination of information on property-liability insurance prices.

1. Introduction H Property-liability insurance in the United States is distributed through

two major channels-the independent (American) agency system and the exclusive agency system.' Independent agents maintain contracts with several insurance companies and are not obligated to place business with any one of them. Most exclusive agents, on the other hand, are contractually bound to place their business with a single company. The independent agency system is the traditional method for distributing property-liability insurance and for many years was dominant in all types of coverage. During the past 25 years, exclusive agency companies, led by State Farm and Allstate, have captured a substantial share of the market for automobile and homeowners' insurance and have begun to challenge the independent agency firms for the business of commercial clients. * Associate Professor of Insurance, The Wharton School, University of Pennsylvania. * * Ph.D, candidate, Department of Insurance, The Wharton School, University of Pennsylvania. Property-liability insurance also is distributed by mail. In spite of the success of several of the direct mail companies, only a relatively small proportion of total premium volume is written in this way.

710 / THE BELL JOURNAL O F ECONOMICS

In his classic study of property-liability insurance markets, Joskow (1973) presented evidence that the exclusive agency system is substantially more efficient than the independent agency system. Based on regression results, Joskow (1973, p. 400) found that "the expense ratios of [exclusive agency companies] average 10.82 percentage points less than the agency companies ceteris paribus. For the auto companies themselves the figure is 11.48."2 He recommended that attempts be made "to speed up the transition from agency production of customers to direct writing wherever possible" (p. 425). Joskow's findings have received widespread attention both from the insurance industry and from regulators (MacAvoy, 1977). The defenders of the independent agency system have relied on three major arguments: (1) independent agents provide better, more personalized service than exclusive agents; (2) independent agency companies recently have introduced several costcutting innovations which may have narrowed the gap between their expense ratios and those of the exclusive agency firms;3 and (3) Joskow's results were biased because they focused only on underwriting costs.4 According to this argument, independent agency companies rely heavily on their agents to settle losses, while exclusive agency companies perform this service primarily through company personnel. Hence, if one considers total costs (for underwriting and loss adjustment services), the efficiency difference between the two systems should be less pronounced. Recent evidence presented by Etgar (1976) and by Cummins and Weisbart (1977) indicates that the first argument is not valid, i.e., there is no systematic difference in quality of service between independent and exclusive agents. The purpose of this note is to investigate the latter two points to determine whether Joskow's conclusion should be modified in any way.

2. Hypotheses and methodology Stated more formally, the hypotheses to be tested in this article are as follows: Hypothesis 1 : Exclusive agency companies are more efficient than independent agency companies, but the discrepancy has been declining. Hypothesis 2 : Exclusive agency companies are more efficient than independent agency companies, but the difference is smaller when one considers total costs rather than underwriting costs. The hypotheses were tested by estimating several different regression equations utilizing pooled cross section and time series data. Before presenting the equations, we discuss the sample selection procedure. The source of information on the distribution systems of insurance comThe expense ratio is the ratio of expenses to premiums written. It is usually expressed as a percentage. Qmong the innovations are automated accounting systems and direct billing, whereby the policyholder is billed by the company rather than by the agent (Florida Association of Insurance Agents, 1973). Because some agents have been reluctant to adopt direct billing and other innovations, it is doubtful that these techniques have been fully effective in reducing agency costs. * Insurance company underwriting costs are defined as any expenses (including marketing, overhead, etc.) not associated with the loss settlement process.

CUMMINS AND VANDERHEI

1 711

panies was a list that appears in Best's Executive Data S e r ~ i c eFrom . ~ this list, we focused on companies and groups that also appear in the automobile insurance sections of Best's Aggregates and Averages, thereby eliminating companies that are not active in the automobile insurance market.6 We used the automobile insurance criterion because of the importance of this insurance line in terms of overall premium volume and because expense ratios differ significantly among lines of insurance. As explained below, we designed the equation specifications to control for other differences among companies in business mix. The sample consists of 34 companies and groups-9 exclusive and 25 independent agency firms. We collected annual data on the sample for the period 1968 through 1976.' The firms vary widely in size (total premiums written in 1976 ranged from $71 million to $4.3 billion) and include both regional and national firms. In 1976 the companies and groups in the sample accounted for approximately 40 percent of the total net premiums written by propertyliability insurance companies in the United States. A list of the companies and groups in the sample is presented in the Appendix. We conducted the initial tests of the hypotheses by estimating the following equation, which is based on Joskow's specification:

where

+ a3,DPWjtDlt + a 4 , D l t + aStD2, + a6,Sjt + Eijt,

(1)

t = 1 , . . . , 9; j = l , 2 , . . . , 34; EIjt = the ith expense ratio of company j in year t ; the subscript i = 1 denotes the underwriting expense ratio, while i = 2 denotes the underwriting and loss adjustment expense ratio; DPW,, = total direct premiums written by company j in year t; NPW,, = total net premiums written by company j in year t, where net premiums written = direct premiums written + reinsurance assumed - reinsurance ceded; D l , = 1 in year t if company j is an exclusive agency company, 0 in other years and for independent agency companies; 0 2 , = 1 in year t if company j is a stock company, 0 in other years and for mutual companies; and S,, = a specialization variable, e.g., WCP W,,IDP W,,, where WCP W,, = workers' compensation direct premiums written by company j in year t .

This list is compiled by Best's on the basis of a survey of the largest 100 to 150 groups (depending on the year) in the United States. Slightly fewer than 100 groups usually respond to the survey. V n Joskow's study, companies were selected which were classified as predominantly auto and predominantly fire by Best's. Joskow categorized these firms by type of marketing system by using information provided in Best's Insurance Reports-PropertylLiability Edition (Joskow, 1973, p. 38511). Because the marketing information in Best's Insurance Reports-Property1 Liability Edition is sketchy, the authors' procedure should reduce the likelihood of misclassification. The data were obtained from Best's Aggregates and Averages and from Best's Insurance Reports-PropertyiLiability Edition. Several companies which otherwise met the sample criteria were eliminated because they sell insurance primarily through the mail, because they specialize in reinsurance, or because of the unavailability of continuous data for the nine-year sample period.

712 / THE BELL JOURNAL OF ECONOMICS

Estimation of equation (1) yielded a separate coefficient for each independent variable in each year. To obtain more precise parameter estimates, constraints were then imposed sequentially on various sets of coefficients and the equation was reestimated. The null hypothesis that each restriction was valid was tested by using an F- tati is tic.^ We tested the effect of the distribution system on the dependent variable by using the dummy variables Dl,, t = 1, 2, . . . , 9, separately and in interaction terms. If independent agency firms are less efficient than exclusive agency companies, the coefficients of the intercept dummies should be negative and significantly different from zero. If the efficiency differential has declined over time, a downward trend should be present in the coefficients. The hypothesis that the efficiency differential in total costs is less than that in underwriting costs (Hypothesis 2) was tested by estimating the equation for each of two dependent variables. Elj, is the underwriting expense ratio, while EZjt is the total (underwriting plus loss adjustment) expense ratio.g If Hypothesis 2 is correct, the coefficients of the D l , terms should be smaller in absolute value when E,,, is the dependent variable. In accordance with the usual procedure in insurance cost function research, premiums written are used as a proxy for output.1° The interaction terms DPWj,Dlt, are designed to determine whether economies of scale are more or less pronounced for exclusive agency companies. An alternative output measure, losses incurred, also was tested, on the basis of the rationale that the ultimate goal of insurance is loss redistribution and hence that the economic contribution of the industry can be measured in terms of loss disbursements. The equations in which losses appear as the output measure are reported where they provide a better fit to the data. The variables constructed as the ratios of net to direct premiums are designed to control for the effects of reinsurance. Net premiums are defined as direct premiums plus reinsurance assumed less reinsurance ceded. Companies that accept reinsurance generally pay ceding commissions to the reinsuring companies to recognize the direct acquisition and administrative costs incurred by the latter. Thus, the ratio of net to direct premiums should be positively related to the expense ratio. The dummy variables 0 2 , are designed to test for expense ratio differences between stock and mutual companies. There is no clear a priori rationale for expecting a positive or negative sign on these terms. The specialization terms Sj,are intended to control for differences in business mix among companies. Tests were run in the pooled cross sectionttime series models by using specialization variables for auto and workers' compensation insurance. The hypothesis is that these lines have different expense characteristics and hence that a concentration in one of them would affect the company's overall expense ratio. Equation (1) may not be the best specification for testing efficiency differences among insurance companies. Cost function specifications incorporate All hypothesis tests reported in this article are at the 5-percent level of significance. The total expense ratio is defined as (underwriting expenses/premiums written) plus (loss adjustment expenses incurred/premiums earned). Different denominators are used to recognize the fact that property-liability insurance company underwriting expenses are reported on a cash basis, while loss adjustment expenses are on an accrual basis (Strain, 1976, p. 295). l o See, for example, Houston and Simon (1970) and Allen (1974). The theoretically correct output measure would be the companies' physical production, that is, the number of policies issued, the number of claims paid, and s o on. Data of this type are not readily available.

CUMMINS AND VANDERHEI 1 713

implicit assumptions about the underlying production processes, and an accurate representation of these processes requires that the cost function be "consistent with the organization of production at the firm."" The recent tendency in insurance cost function research has been to hypothesize a CobbDouglas type production function and to estimate the cost equation in log-linear form (Houston and Simon, 1970; Allen, 1974; Cummins, 1977). Thus, we also tested the relative efficiency of the two distribution systems by estimating the following equation:

+ a d t D l t + a,tD2t + a,,ln(l

-

S,,)

+ . . . + eijt,

(2)

where j = 1, 2,

. . . , 34; t

= 1,

. . . , 9; and

Cijt = the expenses of the jth firm in year t . The subscript i = 1 denotes underwriting expenses, while i = 2 denotes underwriting and loss adjustment expenses. The major difference between Joskow's regressions and equation (1) is the necessity for specialization variables in the latter due to the method of sample selection. To control for the possibility that the specialization variables may not be fully effective, we also estimated an equation for auto physical damage insurance costs.12 This equation utilized a log-linear specification similar to equation (2).

3. Empirical findings The regression results for equation (1) appear in Table l.13 For each dependent variable-the underwriting expense ratio and the underwriting plus loss adjustment expense ratio-two equations are shown. One of them includes a separate distribution system dummy variable for each year of the sample period, while the other includes a single distribution system dummy applicable to all years. The equations with the underwriting expense ratio as the dependent variable are labelled (la) and (lb), and the equations in which the underwriting plus loss adjustment expense ratio is the dependent variable are denoted (lc) and (Id). The annual coefficients for direct premiums written are negative and most are significant (equations (la) and (lc)). The pooled estimates of this variable in equations (lb) and (Id) also are negative and significant. These results provide evidence of economies of scale, a finding at variance with Joskow (1973), whose equations showed no consistent evidence of scale economies. The interaction variables were eliminated from the final versions of the equations l 1 Schweitzer (1972, p. 159). The relationship between production and cost functions also is discussed in Shephard (1970). l 2 We chose automobile insurance because it is the line in which the exclusive agency companies have been most successful. We used automobile physical damage rather than liability insurance because the time to settlement is longer in the latter line, so that reported expense figures depend heavily o n estimates. l 3 We estimated the equations by using the AVETRAN program, developed by Robert B. Avery of Carnegie-Mellon University.

714 / THE BELL JOURNAL OF ECONOMICS TABLE 1 REGRESSION RESULTS FOR PROPERTY-LIABILITY SPECIFICATION INDEPENDENT

UNDERWRITING EXPENSE RATIO EQUATION ( l a ) *

DPW68 DPW69 DPW70 DPW71 DPW72 DPW73 DPW74 DPW75 DPW76

-1.353 (-1.176) -2.327 (-2.249) -3.062 (-3.347) -2.838 (-3.439) -2.246 (-2.974) -2.040 (-2.902) -1.542 (-2.328) -2.233 (-3.671) -2.282 (-4.672)

DPW NPWIDPW S D2

6.781 (3.948) -15.876 (-10.750) 1.868 (4.305)

D1 D l -68

INSURANCE COMPANY EXPENSE RATIOS: LINEAR

-8.069 (-7.189)

EQUATION (1b)

x 10-6

x

lo-6

x 10-6 x

EQUATION ( 1 ~ ) " -.853 (-687) -1.574 (-1.409) -1.964 (-1.988) -1.973 (-2.213) -1.595 (-1.956) -1.415 (-1.864) -.553 (-,773) -1.343 (-2.045) -1.450 (-2.750)

x

x

UNDERWRITING AND LOSS ADJ. EXPENSE RATIO

lo-6

x 10-~ x 10-~ x

-2.075 x (-7.041) 6.598 (3.882) -15.603 (-10.622) 1.79 1 (4.203) -6.725 (-13.937)

7.117 (3.837) -13.715 (-8.599) 1.132 (2.416)

EQUATION ( I d )

x IO-~ x IO-~ x x 10-~ x 10-~ x 10-~ x IO-~ x

lo-6

x IO-~

-1.373 x (-4.370) 7.157 (3.949) -13.580 (-8.668) 1.116 (2.456) -6.550 (-12.728)

-6.45 1 1-5.323)

because their coefficients were not significantly different from zero. This suggests that scale economies are no more pronounced for exclusive than for independent agency firms. The reinsurance variables, denoted NPWIDPW, are significant and have the expected positive signs in all four equations. The stock-mutual dummy variables also are positive and significant, providing evidence that stock companies have higher expense ratios than mutuals.14 The specialization term for workers' compensation proved to be significant and negative as expected, while the automobile insurance specialization terms were not significant and were eliminated from the final versions of the equation.15 l4 This finding does not necessarily indicate that mutual companies are more efficient, however, because they traditionally have been more likely to pay dividends than stock companies. Since the relevant variables cannot easily be measured net of dividends, the denominators of the mutual company expense ratios may be artificially inflated. The impact of dividends is ambiguous because stock companies also pay dividends, especially to large commercial clients. l5 Specialization variables for fire, allied lines, commercial multiple peril, and homeowners insurance were tested in annual equations for 1976. Only the commercial multiple peril variable was close to significance, with a t-ratio of 1.55. Although we did not deem this variable sufficiently important to be included in the pooled regressions, it is worth noting that the absolute value of the coefficient of the distribution system dummy was reduced somewhat when the commercial multiple peril term was present in the equation.

CUMMINS AND VANDERHEI I 715 TABLE 1 (CONTINUED) INDEPENDENT VARIABLE

Dl-69 D 1-70 Dl-71 Dl-72 Dl-73 D 1-74 Dl-75 Dl-76 CONSTANT -2

R

S. E.

UNDERWRITING EXPENSE RATIO EQUATION ( l a ) " -7.41 1 (-6.538) -7.321 (-6.421) -6.992 (-6.134) -6.960 (-6.122) -6.012 (-5.300) -5.408 (-4.763) -5.233 (-4.576) -6.299 (-5.489) 25.863 (15.411)

EQUATION (1b)

26.004 (15.656)

UNDERWRITING AND LOSS ADJ. EXPENSE RATIO EQUATION ( l c ) * -6.716 (-5.487) -6.661 (-5.410) -6.936 (-5.634) -6.693 (-5.452) -6.336 (-5.172) -5.978 (-4.875) -5.692 (-4.610) -7.285 (-5.879) 34.608 (19.096)

EQUATION ( I d )

34.552 (19.505)

,693

595

,597

,609

2.837

2.828

3.064

3.016

"AN F-TEST INDICATES THAT THE COEFFICIENTS OF D l - 6 8 THROUGH D l - 7 6 ARE NOT SIGNIFICANTLY DIFFERENT FROM ONE ANOTHER A T THE 5-PERCENT LEVEL OF SIGNIFICANCE. A SIMILAR RESULT WAS OBTAINED FOR THE COEFFICIENTS OF DPW68 THROUGH DPW76. N 0 T E : T H E EQUATIONS WERE ESTIMATED BY USING A N N U A L D A T A ON 34 INSURANCE COMPANIES

AND GROUPS OVER THE PERIOD 1968 TO 1976, INCLUSIVE. THE ESTIMATES WERE OBTAINED

THROUGH ORDINARY LEAST SQUARES. THE FIGURES IN PARENTHESES ARE t-STATISTICS.

KEY: DPW = DIRECT PREMIUMS WRITTEN; DPWxx = DIRECT PREMIUMS WRITTEN FOR YEAR xx I N YEAR xx, 0 IN OTHER YEARS, WHERE xx RANGES FROM 68 = 1968 THROUGH 76 = 1976; NPW = NET PREMIUMS WRITTEN; D l = 1 IF THE COMPANY UTILIZES THE EXCLUSIVE AGENCY SYSTEM, 0 OTHERWISE; D2 = 1 IF THE COMPANY IS A STOCK COMPANY, 0 OTHERWISE; S = (WORKERS' COMPENSATION DIRECT PREMIUMS WRITTEN)/(TOTAL DIRECT PREMIUMS WRITTEN); D l - x x = 1 IN YEAR xx IF THE COMPANY UTILIZES THE EXCLUSIVE AGENCY SYSTEM, 0 OTHERWISE, WHERE xx RANGES FROM 6 8 = 1968 THROUGH 76 = 1976.

The intercept dummies for the type of distribution system have the expected signs and are always significant. While a slight downward trend in the coefficients of the annual intercept dummies appears to be present in equation (la), an F-test indicates that these coefficients are not significantly different from one another. We obtained a similar result for equation (lc). The difference between the pooled estimates of the distributional system coefficients in equations (lb) and (Id) is not statistically significant. The results reported in Table 1 suggest the following conclusions:

( I ) Exclusive agency companies are significantly more efficient than independent agency companies, and this efficiency advantage did not decline appreciably from 1968 through 1976. The point estimate of the expense ratio differential is 6.72 percentage points for underwriting expenses and 6.55 percentage points for total expenses.16 If the premiums written in 1976 by the independent agency companies in the sample had been written at the expense l e The differences are less than those reported by Joskow (1973, p. 400), who found an efficiency differential of approximately 1 I percentage points. This discrepancy probably stems from differences in sampling procedures.

716 / THE BELL JOURNAL O F ECONOMICS

ratio of the exclusive agency companies, the savings would have been approximately $1 billion, ceteris paribus. (2) The relative but not the absolute value of the efficiency differential is reduced when the total expense ratio rather than the underwriting expense ratio is the dependent variable. At average values for the entire sample period, the underwriting expense ratios of exclusive agency companies are approximately 23 percent lower than those of the independent agency companies, while the differential for the underwriting plus loss adjustment expense ratios is about 17 percent. The regression results for the log-linear specifications appear in Table 2. Again, there are two equations for each dependent variable, one with annual TABLE 2 T O T A L COST FUNCTIONS FOR PROPERTY-LIABILITY INDEPENDENT

I n (DPW) I n (NPWJDPW) D2 I n (1-S)

I n (UNDERWRITING EXPENSES)

D 1-69 Dl-70 Dl-71 Dl-72 Dl-73 D 1-74 Dl-75 Dl-76 CONSTANT -2

R S.E.

SPECIFICATION

I n (UNDERWRITING + LOSS ADJUSTMENT EXPENSES)

EQUATION 2(a)*

EQUATION 2(b)

EQUATION 2 ( c ) *

EQUATION 2(d)

,957 (92.647) 1.039 (27.543) ,094 (2.215) ,264 (3.595)

,964 (85.062) 1.009 (26.065) ,085 (1.9631 ,250 (3.287) -.257 (-5.456)

,970 (120.6931 ,918 (25.524) ,058 (1.9451 ,127 (2.106)

,967 (109.422) ,916 (25.333)

.06 1

(1.978)

,144

(2.331) -.I64

(-4.984)

Dl D l -68

INSURANCE COMPANIES: LOG-LINEAR

-.290 (-6.0731 -.270 (-5.654) -.280 (-5,844) -.266 (-5.540) -.258 (-5.3761 -.228 (-4.730) -.202 (-4.1881

-.I62

(-4.7701

-.I68

(-4.937)

-.I72

(-5.021)

-.I78

(-5.186)

-.I63

(-4.739)

-.I55

(-4.493)

-.I40

(-4.053)

-.208 (-4.316) -.253 (-5.213) -680 (-5.492) ,990 ,1161

-.I58 (-4.566) -.212 (-6.051 1 -.578 (-6.091) ,994 ,0929

-0.760 (-5.6211 ,990 ,1164

-.548 (-5.260) ,994 ,0925

" A N F-TEST INDICATES T H A T THE COEFFICIENTS OF D l - 6 8 THROUGH D l - 7 6 ARE NOT SIGNIFICANTLY DIFFERENT FROM ONE ANOTHER AT THE 5-PERCENT LEVEL OF SIGNIFICANCE. N 0 T E : T H E EQUATIONS WERE ESTIMATED BY USING A N N U A L D A T A ON 34 INSURANCE COMPANIES AND GROUPS OVER THE PERIOD 1968 TO 1976, INCLUSIVE. A N ERROR COMPONENTS MODEL WAS EMPLOYED WITH BOTH TIME AND UNIT COMPONENTS. THE FIGURES IN PARENTHESES ARE t-STATISTICS. KEY: DPW = DIRECT PREMIUMS WRITTEN; NPW = NET PREMIUMS WRITTEN; D l = 1 IF THE COMPANY UTILIZES THE EXCLUSIVE AGENCY SYSTEM, 0 OTHERWISE; D2 = 1 IF THE COMPANY IS A STOCK COMPANY, 0 OTHERWISE; S = (WORKERS' COMPENSATION DIRECT PREMIUMS WRITTEN)/(TOTAL DIRECT PREMIUMS WRITTEN); D l - x x = 1 IN YEAR xx IF THE COMPANY UTILIZES THE EXCLUSIVE AGENCY SYSTEM, 0 OTHERWISE, WHERE xx RANGES FROM 68 = 1968 THROUGH 76 = 1976.

CUMMINS AND VANDERHEI 1 717

estimates of the coefficients of the distribution system intercept dummies and the other with a pooled estimate of this effect. In all four equations, the coefficient in ln(DPW) is significantly different from 1.O, which provides additional evidence that moderate scale economies are present in the sample group. We eliminated the interaction terms from the equations because they were insignificant. The findings with respect to the reinsurance, the stock-mutual, and the specialization variables are consistent with those reported for the linear specification. The coefficients of the annual distribution system dummy variables in equation (2a) are negative and significant. However, neither these coefficients nor their counterparts in equation (2c) are significantly different from one another. Hence, there is no evidence of a downward trend in the efficiency advantage. As in the linear specification, the relative efficiency advantage is smaller when loss adjustment expenses are included in the dependent variable (15 percent rather than 23 percent). In the log-linear equations, the absolute differential also is smaller, but this difference is not statistically significant, The cost functions for auto physical damage insurance, which are presented in Table 3, are noteworthy in several respects. First, a better fit resulted when losses rather than premiums were used as the output proxy. Second, all but one of the coefficients of the output variables are significantly different from 1.0, suggesting the existence of scale economies in automobile physical damage insurance.17 Third, the hypothesis that the coefficients of the independent-exclusive agency dummy variables declined during the sample period is again rejected both for underwriting and for underwriting plus loss adjustment expenses. For this reason, we show only the equations with pooled estimates of this effect in Table 3. Finally, the estimated expense advantage of the exclusive agency companies is less in both absolute and relative terms when loss adjustment expenses are included in the dependent variable. Other things equal, underwriting expenses are estimated to be 21.5 percent less for exclusive than for independent agency companies. For total expenses, the figure is 15.2 percent. This difference, however, is not statistically significant.

4. Summary and conclusions The results reported in this article clearly indicate that Joskow was correct in concluding that exclusive agency companies are more efficient than independent agency companies. Ceteris paribus, the expenses of exclusive agency companies are estimated to be from 15 to 23 percent less than those of independent agency companies, depending on the specification and the dependent variable. Significance tests indicate that Hypothesis 1 should be rejected, i.e., the efficiency advantage of the exclusive agency companies did not decline during the period 1968 through 1976. Tests of Hypothesis 2 reveal that the relative but not the absolute efficiency differential is reduced when loss adjustment expenses are included in the dependent variable. This suggests that the inefficiencies of the independent agency companies stem from administrative and marketing rather than from loss adjustment procedures. Additional research would be needed to determine the regulatory implications of the findings. At a minimum, however, the results l 7 The coefficients of the annual In(AL0SS) variables also differ significantly from one another, thereby accounting for their presence in the final version of the automobile insurance equations.

718 / THE BELL JOURNAL O F ECONOMICS TABLE 3 COST FUNCTIONS FOR AUTO PHYSICAL DAMAGE INSURANCE: LOG-LINEAR

SPECIFICATION

INDEPENDENT VARIABLES

I n (AUTO UNDERWRITING EXPENSES ) *

I n (AUTO UNDERWRITING A N D LOSS ADJUSTMENT EXPENSES)"

I n ( A LOSS68)

.977 (76.110) .973 (76.709) ,972 (77.239) ,979 (77.438) ,983 (78.414) ,978 (78.769) ,973 (79.146) .96 1 (79.366) ,967 (80.142) -.242 (-6.280) ,194 (5.927) -.466 (-2.775)

,979 (103.426)

,974

(104.182)

,974

(104.991)

,983

(105.416)

,984

(106.397)

,979

(106.909)

,975

(107.529)

,965

(107.977)

,970

(108.980)

-.I65

(-5.820)

,142

(5.865) -.240

(-1.942)

In (ALOSS69) I n (ALOSS70) In (ALOSS71) In (ALOSS72) I n (ALOSS73) In (ALOSS74) l n (ALOSS75) I n (ALOSS76) D1 D2 CONSTANT -2

R S.E.

.98 1 ,162

,966 ,220

"THE VARIABLES, D l - 6 8 THROUGH D l - 7 6 WERE ELIMINATED FROM THE F I N A L VERSION OF THE

EQUATIONS BECAUSE F-TESTS INDICATED T H A T THEIR COEFFICIENTS WERE NOT SIGNIFICANTLY

DIFFERENT FROM ONE ANOTHER. HOWEVER, THE HYPOTHESIS THAT THE COEFFICIENTS OF

In(ALOSS68) THROUGH In (ALOSS76) ARE EQUAL WAS REJECTED WITH A N F-TEST A T THE 5PERCENT LEVEL OF SIGNIFICANCE. NOTE: THE EQUATIONS WERE ESTIMATED BY USING A N N U A L D A T A ON 34 INSURANCE COMPANIES AND GROUPS OVER THE PERIOD 1968 TO 1976, INCLUSIVE. THE ESTIMATES WERE OBTAINED THROUGH ORDINARY LEAST SQUARES. THE FIGURES IN PARENTHESES ARE t-STATISTICS. KEY: ALOSSxx = LOSSES INCURRED FOR AUTO PHYSICAL DAMAGE INSURANCE FOR YEAR xx IN YEAR xx, 0 IN OTHER YEARS, WHERE xx RANGES FROM 6 8 = 1968 THROUGH 76 = 1976; D l = 1 IF THE COMPANY UTILIZES THE EXCLUSIVE AGENCY SYSTEM, 0 OTHERWISE: AND D2 = 1 IF THE COMPANY IS A STOCK COMPANY, 0 OTHERWISE.

imply that regulators should take a more active role in disseminating information on the prices of property-liability insurance policies issued by different companies. Appendix

Companies and groups included in the sample H The nine exclusive agency companies and the 25 independent agency companies are as follows:

Exclusive Agency Companies:

Allstate Insurance Company American Family Mutual American Mutual Liability Group Country Mutual Insurance

Federated Mutual Insurance Liberty Mutual Group MFA Mutual Insurance Company Nationwide Mutual Insurance Group State Farm Group

CUMMINS AND VANDERHEI 1 719

Independent Agency Companies: American General Group Atlantic Mutual Insurance Group Auto-Owners Insurance Company Central Mutual Insurance Company Chubb Corporation Cincinnati Insurance Company CNA Insurance Group Crum & Forster Group Fireman's Fund American Group General Accident Group Home Insurance Group Indiana Insurance Company Insurance Company of North America

Merchants Mutual Insurance Group Michigan Mutual Insurance Company National Grange Mutual NN Corporation Ohio Casualty Insurance Group Royal Globe Insurance Group St. Paul Companies Security Corporation Transamerica Insurance Company Travelers IndemnityIPhoenix Group Unigard Mutual Insurance Group United States Fidelity & Guarantee Insurance Group

References ALLEN,R.F. "Cross Sectional Estimates of Cost Economies in Stock Property-Liability Companies." Review of Economics and Statistics, Vol. 56 (1974), pp. 100- 103. Best's Aggregates and Averages. Oldwick, N.J.: annually. A.M. BEST COMPANY. -. Best's Executive Data Service. Oldwick, N.J.: annually. -. Best's Insurance Reports-PropertylLiability Edition. Oldwick, N.J.: annually. CUMMINS, J.D. "Economies of Scale in Independent Insurance Agencies." Journal of Risk and Insurance, Vol. 44, No. 4 (December 1977), pp. 539-553. -A N D WEISBART, S.N. The Impact of Consumer Services on Independent Insurance Agency Performance. Glenmont, N . Y . : IMA Education & Research Foundation, 1977. ETGAR,M. "Service Performance of Insurance Distributors." Journal of Risk and Insurance, Vol. 43, No. 3 (September 1976), pp. 487-499. OF INSURANCE A GENTS.The Florida Agents' Manifesto-Objective: FLORIDAASSOCIATION Survival. Tallahassee: 1973. H I L L , R.D. "Capital Market Equilibrium and the Regulation of PropertylLiability Insurance." Ph.D. dissertation, Massachusetts Institute of Technology, 1978. , "Economies of Scale in Financial Institutions: A Study in Life HOUSTON,D.B. A N D S I M O NR.M. Insurance." Econometrica, Vol. 38 (1970), pp. 856-864. JOSKOW, P.L. "Cartels, Competition, and Regulation in the Property-Liability Insurance Industry." The Bell Journal of Economics and Management Science, Vol. 4, No. 2 (Autumn 1973), pp. 375-427. MACAVOY,P.W., ED. Federal-State Regulation of the Pricing and Marketing of Insurance. Washington, D.C.: American Enterprise Institute for Public Policy Research, 1977. SCHWEITZER, S.A. "Economies of Scale and Holding Company Affiliations in Banking." Southern Economic Journal, Vol. 38 (1972), pp. 258-266. SHEPHARD,R.W. Theory of Cost and Production Functions. Princeton: Princeton University Press, 1970. STRAIN,R.W. Property-Liability Insurance Accounting. Santa Monica: The Merritt Company, 1976.