It may be thought that this is a peculiarity of the one-period models; it is not. In the general model which treats the probability of going insolvent in the infinite future, the effect of a change in price under the most favorable circumstances is, at most, a one-for-one effect; that is, the rise of price by 1% lowers the probability of insolvency over the infinite future by less than one percentage point.

The data on the relationship between the rate of insolvencies and the amount of unpaid losses indicates that the effect of a change in price on reduction of unpaid claims is even smaller. The little data available seems to indicate that the ratio of unpaid claims to total claims is approximately one-fifth of the rate of insolvency. If this is the case, then the 1% rise in price would lower the ratio of unpaid claims by a maximum of 0.2%; a more likely figure would be but one tenth of this.

The conclusions thus seem unambiguous on the relationship between price and the rate of insolvency or unpaid claims. Reasonable changes in the price of insurance would lead to changes of the rate of insolvency of a small magnitude; the effect on the unpaid claim ratio would be even smaller.

COMPETITION AND SOLVENCY

Having discussed the implications of the insolvency model for the price/solvency question, the second issue is the implication of the model for the competition/solvency question. More specifically, what does the insolvency model imply for the effect of a more competitive market structure on the rate of insolvency? This question would be easy to answer once we could predict the effect of competition on price and reserves. If price were to fall 5%, we could use the predictions given by the price/insolvency relation to show the deterioration of the rate of insolvency. A price change of this direction and magnitude would be consistent with economic theory, common sense, and some empirical findings. Unfortunately, however, it conflicts with empirical work done during the course of the present study. We have noted earlier the evidence that the average rate of return in the property and liability industry has been very significantly below the normal profit rate associated with a commensurate risk. While we cannot speculate on the reason for this phenomenon, it is very possible that a more competitive market structure would raise price and improve solvency. We conclude that the implications of our theoretical model on the competition/solvency question are ambiguous.

INVESTMENT INCOME AND SOLVENCY

A final application of the model is to the effect of a change in the treatment of investment income on the rate of insolvency. Investment income affects insolvency in two opposing directions. On the one hand, the rate of return (net of dividends to owners) positively affects solvency by improving the financial resources available to pay loss. On the other hand, if the rate of return is risky, there is an additional cause of variation, which in turn raises the probability of insolvency.

How important do these two effects seem to be, according to our models? It appears that there is little net effect on the rate of insolvency, although, as might be expected, the probability of insolvency rises slightly. The reason for the absence of effect is that both the rate of return and its variance are so low relative to the variance of the loss ratio that the latter dominates in the totality.

It appears, then, that the treatment of investment income has little direct effect upor, the rate of failure. It is further apparent that, for the purposes of determining this rate, the question of the ownership of investment income is irrelevant. If the income is available for payment of losses when unusually large loss experience occurs, then for the purposes of insolvency regulation, this is a factor reducing the probability of insolvency, regardless of its legal ownership.

Within the general conclusion that the treatment of investment income has little effect on the rate of insolvency, the present analysis suggests that some second-order effects of treatment of investment income may have unfavorable effects on failure of companies. First, as we have stated, the rate of return used in calculating the chance of failure is net of dividend payments and withdrawals of voluntary reserves. If it is true, as has been alleged, that the change in treatment of investment income would lead to different dividend payout ratios or to withdrawal of capital, the chance of failure would be raised. A withdrawal of 10% of the industry's reserves would raise the chance of failure to approximately 110% of its present level. While we do not have evidence that a movement of capital of this magnitude would follow a change in the treatment of investment income, this possibility seems of sufficient moment to consider. Other second-order effects are that a change in treatment will change the rate of return and riskiness of the investments and that entry or exit of firms will ensue. We have no evidence to guide quantitative calculations of the effect of these contingencies.

HISTORICAL EXPERIENCE

The third part of the examination of the adequacy of the price of insurance draws on all available evidence in order to test the validity of the conclusions drawn from the model. In addition, we have attempted to find other statistics relevant to the question of adequacy of price.

First, we have derived the rates of exit and insolvency for firms in the insurance industry. Since we felt that the life insurance industry might contribute to our informational base, we sought the rate of exit and insolvency for these companies as well. The rate of exit has been defined as the ratio of number of exits to total number of firms in the industry. Four different studies at different points during the last 60 years gave estimates for the life insurance industry. The annual rates of exit vary from a low of 1.4% to a high of 4.6%. Data for the property and liability industry indicate that its rate of exit was not dissimilar; three studies gave rate-of-exit estimates ranging from 0.5% to 4%.

Rates of insolvency were lower than rates of exit, since some firms leave the industry without becoming insolvent. Rates of insolvency were estimated at an average annual rate of slightly less than 1% in the postwar period. Two industry studies show that

the high-risk automobile industry had a rate of insolvency five times larger during the period 1960-1965. Surety and fidelity seems to have compiled the worst record, with nearly 20% of companies failing annually in the period 1930-1934. Indications are that the rate of insolvency of life insurance companies was similar to that for property and liability companies.

Although the evidence is by no means conclusive, the fact that rates of exit and insolvency are close to the level predicted by the model indicates that the validity of the model cannot be rejected on that ground.

A second essential bit of information was the measure of social loss due to insolvency. As was noted earlier, the best single measure of loss is probably the incidence of unpaid claims or, more precisely, the ratio of unpaid claims to total losses. This ratio gives the percentage of insured risks borne by individuals which the industry is unable to transfer because of insolvencies. The only two pieces of evidence on this are the data on the surety and fidelity lines and the data on the high-risk automobile line. The former shows a rate of unpaid claims of 3.5%, but this result is the most pessimistic imaginable figure, including both the great depressions and the single largest amount of unpaid claims recorded (Nationa Surety). The figures for high-risk automobile seem somewhat more complete and representative; they show that for a rate of insolvency of about 5% the ratio of unpaid to total claims is 0.8%. In general, one would expect that this kind of proportion is the usua rule, since the companies which fail will usually be smaller than average and some of the claims of these companies will be paid out of remaining assets. We will thus assume that the ratio of unpaid claims to total claims is about one-fifth of the insolvency rate.

The third area of empirical investigation was designed to test the effect of competitive regulatory environment on insolvency. To perform a controlled experiment o the relation, it is necessary to have an environment in which the amount of competitivenes and no other variables change. Probably the closest approximation to the ideal is the variation of regulation among the several states. Although the ideal data do not exist, we di find data of sufficient quality to test the competitiveness/insolvency relation and deriv meaningful results.

To measure the degree of competitiveness in a state, we have obtained data on th percentage of fire premiums written below bureau rates for 26 of the 51 jurisdictions in 1957. In addition, we have the Senate data on three measures of company failure: (a) on the number of domestic insurance companies which have left the industry voluntarily o involuntarily; (b) for dissolutions and insolvencies; and (c) for insolvencies alone. We can us these data to test the proposition that there is a relationship between competitiveness an insolvency; it further sheds light on the relation between a lower price and insolvency.

In the regression analysis, the following results were obtained. In no case di competitiveness explain as much as 1% of the variance or dispersion in failures among th states. The coefficients on the measure of competitiveness were statistically insignifican even at the 50% confidence level. Finally, all coefficients had the wrong signs.

How are we to interpret these technical statistical results for the purpose of th present study? First, we make the usual caveat about the shortcomings of the data and th

sks of making conclusions from limited statistical material. Nevertheless, the results indicate that there is no simple and significant relationship between competitiveness and olvency. Whatever relation exists seems to be swamped by other factors. The evidence does not indicate that an increase in the competitiveness of insurance markets would lead to an increase in the number of insolvencies. This is again repeating what we showed in application of the insolvency model: To regulate insolvency by price is expensive and Reffective

We have found that regulating, preventing, or alleviating insolvency by price is exceedingly expensive. Are there, then, more efficient ways of alleviating the social costs of solvency? The criterion of efficiency we use is how much it costs to lower the amount of unpaid losses by a dollar. This is an extremely complex question, which was only peripherally related to the main focus of the study, so we have only briefly examined the ssues. It should be stressed that thorough examination of the issues is necessary before a final decision is reached on the question of different remedies to prevent insolvency. A brief examination of these shows that while price has a cost/benefit ratio of about 100, several of the proposals have cost/benefit ratios of less than 10. It appears that regulating solvency by price is the most inefficient remedy of those for which estimates are available.

CONCLUSIONS

The major results of the investigation of adequacy of the price of insurance have been presented. The implications for the major question of the study are as follows.

First, to what extent is insolvency a major social ill and what particular aspects should be alleviated? We have found that, in spite of the volume of public outcry, the level of unpaid claims does not indicate that an epidemic of insolvencies is presently causing major social losses. If our estimate of the ratio of unpaid claims to total losses is accurate, then the total annual average amount of unpaid losses is about 0.2% ($25 million out of a total of $12 billion). Given the relative size of these magnitudes, we conclude that consumers can be insulated from losses of this magnitude without changing the structure of the market from its most efficient form.

Second, to what extent are price and price competition a major source of actual or potential insolvency in the property and liability industry? Our results on this all point in the same direction: Both the theoretical and the empirical analysis have shown that other variables beside price have been the major determinants of the current rate of insolvency. Moderate changes in price, which continue to allow profits of insurance companies, will not lead to a significant rise in the number of insolvencies. Moreoever, these data indicate that, to the extent that past experience can be extrapolated beyond the observed range, there is no reason to believe that significant changes in the direction of a less-regulated price structure will lead to a noticeable rise in the rate of insolvency.

Third, are there more efficient ways of preventing insolvency and alleviating its effects than raising the price of insurance? We have concluded that, even if the low level of unpaid claims is thought to be a social ill requiring action, the most efficient way to prevent or alleviate insolvency is not through an increase in the price of insurance.

We thus conclude the following regarding the adequacy of price. We stress that all the following conclusions are restricted to consideration of the adequacy of price solely from the point of view of lowering the social costs of insolvency, and not using any other performance variable as a criterion. Conclusions from the point of view of other performance variables have been given elsewhere.

First, under the above restriction, we have not found theoretical or empirical evidence to confirm the statement that the price of insurance is inadequate. The net gains from raising the price of insurance appear to be outweighed by the costs.

Second, still under the above restriction, the evidence we have examined would indicate that, for changes within the existing range of variation of price, the result of lowering the price of insurance will not be to raise significantly the rate or social cost of insolvency. From the point of view of solvency alone, and not taking into consideration rates of profit or other criteria, prevention of insolvency cannot be used as a justification of raising the price above the level which would be optimal from the point of view of these other criteria. Unless there are other reasons to maintain price at its present level, the prevention of insolvency cannot be used to justify the present price level.

Third, if by competitiveness we mean absence of rate regulation or absence of conformity to bureau rates, we have found no evidence that increased competitiveness has a significant effect on the rate of insolvency in either direction.

Finally, although there is evidence that the treatment of investment income may affect the rate of insolvency, we have uncovered no evidence to indicate the strength of this effect.