Academic journal article Journal of Risk and Insurance

Do Property-Casualty Insurance Underwriting Margins Have Unit Roots?

Academic journal article Journal of Risk and Insurance

Do Property-Casualty Insurance Underwriting Margins Have Unit Roots?

Article excerpt

A growing literature analyzes determinants of insurance prices using time series data on insurer underwriting margins. If the variables analyzed are stationary, conventional regression models may be appropriately used to test hypotheses. Based on pretests for a unit root, several studies have instead used co-integration analysis to analyze the long-run relationship between purportedly nonstationary underwriting margins and macroeconomic variables. We apply a battery of unit root tests to investigate whether underwriting margins are stationary under different assumptions concerning deterministic components in the data generating process (DGP). When linear and/or quadratic trends are included in the assumed DGPs, the tests reject the null hypothesis of a unit root for loss ratios, expense ratios, combined ratios, and economic loss ratios from 1953 through 1998 for many of the individual lines examined and for all lines combined. Consistent with prior work on whether macroeconomic variables have unit roots, a simulation of test power for underwriting margins during the sample period demonstrates that nonrejections of the null hypothesis of a unit root could easily reflect low power. The overall findings suggest that conventional regression methods can be used appropriately to analyze underwriting margins after controlling for deterministic influences and transforming any nonstationary regressors.


A large literature examines time-series variation in property-casualty insurance underwriting margins, such as loss ratios and combined ratios (see Harrington and Niehaus, 2000, for a review). Many studies provide evidence that historical underwriting margins have been cyclical. A smaller but important literature estimates the relationship between underwriting margins, measures of insurance capacity, and macroeconomic variables to test theories of the determinants of insurance prices (e.g., Gron, 1994; Winter, 1994). Econometric modeling of underwriting margins may grow in importance as theoretical work on insurance price fluctuations progresses.

A critical issue in time series regression analyses is whether the underwriting margins and relevant explanatory variables are stationary. If underwriting margins or one or more regressors are nonstationary, then least squares regression results are essentially meaningless (see, e.g., Enders, 1995, pp. 216 ff., for detailed discussion). An exception to this distressing conclusion arises if the regression disturbance is nonetheless stationary, which requires that the regressand and regressors be co-integrated (integrated of the same order) and implies a linear long-run relationship among the variables (Engle and Granger, 1987). (1) Least squares regression thus provides meaningful inferences only when the regressand and regressors are either all stationary or co-integrated. In either case, whether underwriting margins have unit roots is of considerable importance in applied work.

Testing for unit roots, initially developed by Granger and Newbold (1974), exploded following Nelson and Plosser's (1982) evidence that many economic time series had unit roots. Such testing eventually became standard operating procedure in econometric studies using time series data. (2) Early time series analyses of underwriting results are often silent on stationarity (see, e.g., Venezian, 1985; Cummins and Outreville, 1987; Doherty and Kang, 1988). A few studies analyze first differences in underwriting margins, which is appropriate if margins are difference stationary. Several more recent studies employ co-integration analysis and error correction models to analyze short- and long-run relationships between underwriting margins, interest rates, and other macroeconomic variables (Haley, 1993, 1995; Grace and Hotchkiss, 1995; Choi and Thistle, 1997).

Haley (1993) reports that property-casualty insurer underwriting profit margins are co-integrated with interest rates with a negative long-run relationship. …

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