The Use of Event History Analysis to Examine Insurer Insolvencies

Introduction Insolvencies in the U.S. insurance industry have recently received increased attention. Both the number and magnitude of insolvencies have been significantly increasing relative to historical trends. In the 1980s, 258 insolvencies of property-liability insurers occurred, compared to 108 insolvencies during the 1970s. While the insolvencies of the 1970s occurred almost exclusively in small insurers, the more recent cases involved large property-liability insurers such as the Mission Insurance Group, Integrity Insurance Company, and Transit Casualty Company. Traditionally, life insurers have experienced considerably fewer insolvencies than property-liability insurers. From 1975 through 1990, 140 life insurer insolvencies have occurred, over half of which occurred from 1987 to 1990; in 1989 alone, 27 insurers became insolvent. The two major statistical models that have been used for insolvency studies are multivariate discriminant analysis and binary response regression models. Both of these methods use a sample of solvent and insolvent firms studied over a short time interval. One limitation of this type of analysis is that the output is a classification of companies into a set of distressed companies and the complimentary set. In contrast to classification methodologies, the principal purpose of this study is to employ a dynamic statistical methodology to the financial data of property-liability and life insurer insolvencies. Various potential factors associated with insolvencies are empirically modeled for a sample of insolvent and solvent insurers from 1984 through 1990 for property-liability insurers, and from 1987 through 1990 for life insurers. Because a superb review of earlier work on the use of statistical methods to identify financial distress in the insurance industry has been provided by BarNiv and McDonald (1992), we forego a review of the literature. Methodology Event History Analysis This study employs a dynamic statistical methodology called event history analysis to examine property-liability and life insurer insolvencies. The event history approach is not unique to the social sciences; similar methods have developed independently in such diverse areas as actuarial science, biostatistics, demography, and engineering (Amburgey, 1986; Barnett, 1990; Carroll, 1983; Freeman, Carroll, and Hannan, 1983; Stinchcombe, 1965; Tuma, 1979; and Yamaguchi, 1991). Event history analysis explicitly considers the dynamics of the factors influencing the probability of insolvency over an interval of time. In case of major fluctuations, the snapshot methodology of classification analysis, which considers a shorter interval, may provide an incomplete picture of the situation. Event history analysis explicitly incorporates information on prior history for improving the explanatory capacity of the model. Finally, since a static model can be viewed as a special case of a dynamic model, dynamic models have more implications, thereby expanding the ability to test hypotheses. This study focuses on the events of insurer insolvencies and factors associated with these insolvencies. Because events can be defined in terms of change over time, an effective way to study events and their causes is to collect event history data that record the exact time and sequence of particular kinds of changes. Thus, the problem is to specify how the occurrence of the event (in this case, insolvency) depends on explanatory variables. The most common approach is to define a variable called a hazard rate (also referred to as a force of mortality and a failure rate) that measures the conditional probability density of the occurrence of the event as a function of time and selected explanatory variables. The method allows for the examination of the causal factors possibly related to insolvency by finding whether the explanatory variables significantly affect the hazard rate. In a study of the duration of insurer insolvencies, the two states "solvent" and "insolvent" are distinguished. …