A Cointegration Analysis of the Relationship between Underwriting Margins and Interest Rates: 1930-1989

By Haley. Joseph D. | Journal of Risk and Insurance, September 1993 | Go to article overview

A Cointegration Analysis of the Relationship between Underwriting Margins and Interest Rates: 1930-1989


Haley. Joseph D., Journal of Risk and Insurance


Introduction

The property-liability insurance industry has long been characterized by profit cycles. The severe downturn in insurer profitability and coverage availability which began in 1983 and continued into 1985 increased the attention that the underwriting cycle has received in the literature. A portion of the literature has focused on measurement of the cycle (Venezian, 1985; Fields and Venezian, 1989; Doherty and Kang, 1988; Berger, 1988; and Cummins and Outreville, 1987). The prevailing opinion of this literature is that the cycle has an approximate length of six years. Another portion of the literature has focused on determining a fair underwriting margin for insurers (Hill, 1979; Fairley, 1979; Kraus and Ross, 1982; Doherty and Garven, 1986; Myers and Cohn, 1987; and Cummins, 1990, 1991). This literature provides a theoretical base from which an equilibrium premium rate is derived. All of the models developed in this literature are extensions of financial asset pricing models. The three most well-known models are the insurance capital asset pricing model (CAPM), the discounted cash flow model (DCF), and the option pricing model (OPT).(1) A general result of these financial pricing models is that the equilibrium price of insurance is negatively affected by the movement of interest rates.

The objective of this article is to empirically verify the relationship between premiums and interest rates and also to determine whether this relationship possesses the characteristics of equilibrium behavior. Doherty and Kang (1988) and Smith (1989) analyzed the effect interest rates have on underwriting margins and premium rates. Doherty and Kang used a traditional supply and demand construct to evaluate whether the underwriting cycle is the result of the industry making rational adjustments toward equilibrium. They conclude that the behavior of capital market rates provides a continuing series of exogenous shocks to which the industry is unable to make instantaneous adjustments. The slow adjustments manifest themselves as a cycle. Smith shows that, from 1950 through 1982, property-liability premium rates reflected taxable bond yields, and he thereby concludes that such a result is indicative of competitive behavior.

The purpose of this article is to enhance the results of Doherty and Kang and Smith by providing more robust estimations using the cointegration methodology. The Doherty and Kang analysis used only differenced data, so, at best, it captures only short-term dynamics. Cointegration captures long- and short-term dynamics. Smith's conclusion that the reflection of taxable bond yields in premium rates is indicative of competitive behavior is made more substantial with cointegration analysis, because cointegration analysis explicitly determines whether the short-term behavior of the underwriting margin is stationary. Stationarity is of significance because a stationary variable possesses the tendency to return to a particular value, and such a tendency is a characteristic of equilibrium behavior.

Verification of equilibrium dynamics has two important implications. First, the existence of equilibrium dynamics suggests that the persistence of the underwriting cycle is not due to irrationality on the part of insurers, a finding that would be consistent with Cummins and Outreville (1987). Second, an industry that responds to market conditions by moving toward competitive equilibrium requires different types of regulatory attention than an industry that does not.

The time period of analysis--1930 through 1989--encompasses many changes in the property-liability insurance industry. Cointegration analysis is robust enough to permeate these changes because cointegration separates long-term and short-term phenomena. Any structural changes that took place in the industry from 1930 to 1989 were long-term adjustments.(2) Hakkio and Rush (1991) conclude that the length of a data set in a cointegration study is of greater importance than the number of observations. …

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