Pierre Lemaire, Doctoral Student
Wharton School of the University of Pennsylvania

Many studies have provided useful information on the structure and performance of the property and liability insurance industry. The following articles have been invaluable to this paper: Joskow (1973), Cummins and Weiss (1992), Mayers and Smith (1988), and Carroll (1993). Joskow generally reports that the property insurance industry possesses the characteristics of a competitive market. His analysis focuses on market concentration, economies of scale, and ease of entry. Joskow�s examination of the former is specifically applied to two individual lines of business: automobile and fire insurance. He also notes, however, that regulation and cartel pricing have discouraged price competition.

In their study, Cummins and Weiss appropriately extend the depth and breath of Joskow�s study to include most lines of insurance. The aim of their paper is to dispel the notion that insurance companies were responsible not only for premium inflation throughout the eighties but also the 1984-85 liability crisis. They echo Joskow�s conclusion that the property-liability insurance industry is competitively structured, yet thoroughly delineate the problems that have beleaguered the property-liability insurance industry. Some of these problems include: the availability and affordability of automobile insurance, the underwriting cycle, inappropriate profitability measures, rate regulation focus, and solvency requirements. While it could serve as an asset to the insurance industry, historically, regulation has focused on the wrong aspect of the industry.

Mayers and Smith use specialization and line of business concentration to examine the impact of major ownership structures of the property and casualty insurance industry. They report that Lloyds and reciprocals are more concentrated by line-of-business than stocks. When controlling for size, however, stocks are not only indistinguishable from mutuals, but appear also more concentrated than Lloyds. They mirror Joskow and Cummins and Weiss in that regulation may be an important determinant of variation.

The fourth study, by Carroll, provides a detailed analysis of the private workers� compensation market. While controlling for economic variables, she uses concentration (Herfindahl), regulation, and ease of entry to attempt to support her collusion and differential hypotheses. While she is not able to support either of these, she provides great insight in the use of her control variables.

The purpose of this paper is to provide an analysis of the Private and Commercial Auto Liability lines of business in the same spirit as the Carroll paper. A few additions have been included. First, the analysis to follow will scrutinize the choice of variable used to measure market concentration. Second, I include an intra-concentration index as an explanatory variable to the regression equation. The data is provided by BEST�s Aggregate Experience by State by Line from 1982 to 1992.

The compliment of the combined ratio, or the underwriting profit ratio, would present a better measure as it takes other expenses into account:

(Cummins and Tennyson 1992). Better still, would be the Overall Operating Ratio, one that also includes investment income. Ideally, however, profitability should include premiums, investment income, expenses, and the present value of losses. The stipulation of analysis and use of BEST�s Aggregate Data requires the allocation of investment income and expenses on a by-line basis (as insurers tend to write more than one line within a state). Rather than establishing the most suitable allocation measure, profitability is measured as follows:

and investments, expenses, and loss development is proxied (similarly to Carroll (1993)). The profit variable will simply be denoted as PROFIT.

First, to pick up the effect of investment income on profitability, the yearly Treasury bill return will be used to capture changes in interest rate (TBILL). These rates were obtained from The Center for Research in Security Prices (CRSP) asbbi file. Second, the ratio of unpaid losses to incurred losses will be used to capture the payout pattern (TAIL). By definition, the longer the payout tail, the greater the proportion of losses yet to be paid. Third, as suggested by Carroll, the direct writers� share of the market within each state serves as a proxy for expenses (DW). Cummins and VanDerhei (1978) reported that direct writers are more efficient than independent agency writers. Carroll�s main argument for the use of this variable is that it may capture the average demand for product quality.

In the industrial organization literature, many indexes have been utilized to summarize the concentration of market shares as a single index. The most popular ones are the Gini coefficient (for examples see Sastry and Kelkar (1994), Lerman and Yitzhaki (1984), Shalit (1985)), the m-firm concentration ratio (for an example see Golan and Judge (1996), Theil�s Entropy (for examples see Van Hove (1993), Nissan (1996)), and, of course, the Herfindahl Index.

The second market concentration variable, the m-firm concentration ratio, simply sums the m highest shares in the industry:

Golan and Judge (1996) find that if only one measure is used in estimating the distribution of the market shares, the Herfindahl Index provides a more effective method of estimation than the m-firm concentration ratio. Thus, the popular Herfindahl Index is the first concentration measure considered in this analysis. It is straightforwardly computed as the sum of the squares of the market shares:

Theil�s Entropy index is computed as the sum of the shares times their logarithm:

Hannah and Kay, using United Kingdom experience, have found the entropy index to be one of the most satisfactory (as the Herfindahl gives relatively too much weight to large size firms). As a result, the Herfindahl and Theil�s Entropy encompasses two of the three measures evaluated in this study. Figure One graphs the Herfindahl and Entropy measures on market share.

Koller and Weiss (1989) have also expressed the aforementioned premonition regarding the Herfindahl index in that it assigns a relatively great weight to large size companies. A Transformed Herfindahl is accordingly considered as the square root of the Herfindahl Index:

Theil�s Entropy, the Herfindahl, and the Transformed Herfindahl are computed on the basis of direct premiums written. These measures will be denoted as ENTROPY, HERF, and TRHERF respectively. Only firms with positive direct written premiums are considered in the computations of these variables. This is necessary not only to avoid violations of the logarithmic functions but also to render both Herfindahl measures sensible. Each will be compared in this framework.

The central focus of this paper is the intra-company concentration ratio. It is a Herfindahl-like concentration measure, simply computed as

As previously mentioned, Cummins and VanDerhei (1978) have found that direct writers have lower costs than independent writers. This finding, however, was coupled with the result that the inefficiencies of the independent agent seem not to be associated with loss adjustment factors, but rather from marketing and administrative expenses. Performing separate regressions for direct writers and agencies should make no difference as only premiums earned and losses incurred are taken into account in our profit measure.

While the impact of rate regulation is hard to predict, it must be included in my analysis. The variable measuring rate regulation in each state is a dummy variable that is given a value of one if rates are restrictively regulated, and zero if rates are not. This data is only available through 1992 and therefore disables us from using a more recent information base. Furthermore, no regulation information is available for Alabama, the District of Columbia, Georgia, and Nebraska.

 Auto Liability Insurance is divided into two branches: Private Auto and Commercial Auto. Figure 3 displays Private Auto Liability Market Concentration for 1982. As we stated in the introduction, traditional economic theory dictates that concentration facilitates collusion between firms and increases industry profitability. The Herfindahl Index was used to determine the degree of concentration of the auto liability insurance market. The states showing the highest market concentration are Washington, Oregon, New Mexico, Oklahoma, Kansas, Wisconsin, Ohio, Kentucky, Maine, Maryland and Missouri.

Figure 3: Private Auto Liability Concentration for 1982.

Figure 5: Private Auto Regulation and Market Concentration 1992.

As the number of firms in a market increases, so does competition. An increase in competition, in turn, may lead to a decrease in price and therefore to decrease profits. Figure 8 examines the Commercial Auto Liability Profit and Market Concentration for 1982. There were only two states displaying a profit: North Dakota and Kansas. The states with the highest concentration were Mississippi, Massachussets, Idaho, Montana, Nebraska, and West Virginia.

 Figure 8: Commercial Auto Liability Profit and Market Concentration for 1982.

In addition to market concentration, an intra-company concentration ratio is also included in the analysis. For more detail, please consult part two.

The states displaying the highest intra firm market concentration for 1992 are California, Texas, Illinois, and New York. The highest profits are observed in Washington, Oregon, New Mexico, Oklahoma, Kansas, Iowa, Missouri, Wisconsin, Kentucky, Maryland, and Maine. Texas and California stand out for the highest private auto liability profit in 1992.

The following regression equation is estimated for the Private and Commercial Auto Liability lines of

Business in SAS on transformed data (around state means):

The analysis covers 1982 through 1992 and includes 47 States. Table 2A summarizes the regression variables. Table 2B and 2C provide summary of the Herfindahl for the Private Auto and Commercial Auto lines respectively.

The results were tabulated into two segments. The first three provide analysis of variances and parameter estimates for the Herfindahl, Entropy, and Transformed Herfindahl respectively (using the aforementioned regression equation). The most striking aspect of the regression results in these tables is that the variable TAIL is significant at the 1% level in all but one regression. This is actually not surprising as direct losses incurred figures in both the profit and tail measures. The second three provide the same summary statistics when TAIL is not included in the regression equation. Only the tables with the Herfindahl Index (Commercial and Private) are included.

The second surprising result is the great disparity in not only R² measures, but also in parameter estimates when comparing the private and commercial Lines. First, in each equation, the model is notably more explanatory in the commercial lines, with R² reaching as high as .40. Second, while market concentration and regulation estimates carry the same, sign every other parameter contrast when comparing the two lines.

In the commercial line, the INTRA-concentration is negative and mostly insignificant. This would tend away from specialization. The TBILL coefficient is negative and highly significant. This is consistent with the Cummins and Harrington result that price-cost margins are inversely related to the level of interest rates. The negative DW can be interpreted as counter evidence that direct writers earn higher profits than independent agents. When TAIL is included in the model, the sign of DW switches, but is still insignificant. Regulation DUMMY is negative and significant at the 1% level indicating that the presence of regulation in the market is associated with a decrease in profits. The HERF and THERF coefficients, while insignificant, are surprisingly negative (ENT positive) suggesting that decreases in concentration are actually associated with reduction in profits. Carroll obtained similar results on concentration. Comparison of market concentration measures is difficult in this line, as all coefficients are insignificant. The Herfindahl performed generally better than the other two.

In private line, the INTRA-concentration is positive and significant at the 5% level for all but one of the equations. This tends to favor specialization opportunities in this line. The TBILL and DW are positive, but not significantly so. As in the commercial line, the market concentration variables are also negative (positive entropy). In comparing the market concentration measures, the Entropy Index performed notably better than its counterparts, with p-values close to the 1% rejection area without TAIL and 5% with TAIL.

Introducing the INTRA-concentration index provides an interesting twist to market performance and structure analysis. The difference in signs obtained when comparing the two auto liability lines may be inherent in the lines themselves. The negative (ENT significantly positive) market concentration in private auto liability may be partially explained by the ability of smaller companies to specialize in this line. Preliminary regressions involving an interaction of market and intra concentrations yielded positive and significant at the 5% level coefficients. This was not the case for the commercial line. Further research in this variable is needed.

Additional details could give rise to questions on the validity of the model: positive TBILL coefficient in the private line, negative DW in the commercial line, and relatively small private line R². It must be noted that when regressing on individual data points, the signs of the coefficients are mostly preserved. Care, however, must be used when interpreting these results for the profit variable is simply computed as one minus the loss ratio. Adding market and administrative expenses, as well as investment income would make the variable much more representative of a true profit measure. Additionally, an evaluation of the loss payment pattern would include the volatility of the tail into the model. The ability to obtain these values would allow the amelioration of the model to a by state by line analysis.