Workers Compensation Reserve Uncertainty

The increased emphasis on solvency monitoring of insurance companies, along with the American Academy of Actuaries’ vision of an expanded role for the Appointed Actuary, have stimulated reserving specialists to quantify the uncertainty in their estimates. This paper measures the uncertainty in workers compensation loss reserve indications, compares it to the “implicit interest margin” in statutory (undiscounted) reserves, and examines the implications for capital requirements. The paper uses a stochastic simulation analysis to model the loss reserving process, with separate but inter-linked components for the process risk of loss development, the parameter risk of estimating future age-to-age link ratios, and autocorrelated future interest rates. In addition, the past monetary inflation implicit in paid loss development link ratios is replaced with stochastically generated future inflation rates that are linked to both the concurrent interest rates and the previous year’s differential between the inflation rate and the interest rate. Separate simulations are performed for each accident year, and loss development fail factors are generated by an inverse power curve fit to extend the development from 23 years to ultimate. An “expected policyholder deficit ratio” procedure is used to calibrate the capital needed to guard against reserve uncertainty. Because of the statutory benefits in workers compensation, the steady payment patterns, and the long average duration of compensation reserves, the implicit interest margin in statutory reserves exceeds the capital required to guard against the variability in the reserve estimates at a 1% expected policyholder deficit level. The appendices to the paper contain descriptions of the simulation procedures, as well as a comparison of the paper’s conclusions with those of the NAIC’s risk-based capital formula.