Mean Reversion in Net Discount Ratios: A Study in the Context of Fractionally Integrated Models

Summary

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This article introduces a new alternative to the ongoing debate about stationarity and mean reversion of the net discount ratio. Modeling the net discount ratio as a fractionally integrated (I(d)) process, we apply recently developed frequency domain estimation procedures and find evidence that the net discount ratio is an I(d) process with 1/2 ≤ d < 1. Although nonstationary, such series behave like stationary processes in one interesting respect; they are mean-reverting. We present results from a simulation experiment suggesting that the finding of a nonstationary, but mean-reverting net discount ratio generally supports the validity of current practice in estimating economic damages in personal injury litigation. Moreover, if recognized and accounted for, the presence of long memory in the net discount ratio even offers the potential to significantly improve forecasts of the present value of future earnings.

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Mean Reversion in Net Discount Ratios: A Study in the Context of Fractionally Integrated Models

INTRODUCTION

There has been a long-running and, at times, heated debate in the literature on the estimation of damages in negligent injury and wrongful death/survivor claims. In these cases the injured party loses all or part of his or her ability to earn future wages. The objective of tort law is to place the injured party and dependents, if applicable, in the financial position they were in prior to the negligent injury. As a result, the amount of damages, both economic and noneconomic, that a person incurs as a result of a catastrophic injury can be substantial. The ability to accurately estimate such damages is more important than ever due to trends including increases in the cost of medical care, expansion of the types of damages claimed, and implementation of caps on noneconomic damages in healthcare professional liability insurance.

In this study, we are primarily concerned with the accurate estimation of lost future wages. In particular, we focus on the time series properties of the net discount ratio which is of central importance due to the need to factor in the time value of money and expected future wage growth when awarding damages. In practice, most courts award the amount of earnings that the injured pe...

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