Do property-casualty insurance underwriting margins have unit roots?

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.