Abstract Forensic economists strive to forecast a variety of economic variables (interest rates, wage growth rates, income tax rates, etc.) in personal injury and wrongful death cases. While stationarity of interest rates and wage growth rates have received considerable attention, forecasts of individual income tax rates have received little attention. This paper analyzes the time series properties of federal individual income tax rates using Internal Revenue Service (IRS) Statistics of Income (SOI) reports from 1954 to 2021. Tax rates each year are calculated in current year dollars and adjusted for inflation to 2021 dollars income groupings used in the SOI report. The stationarity properties of effective tax rates for an array of various adjusted gross income groupings (as delineated in the SOI reports) for singles and married couples filing jointly are studied. In general, income tax rates varied over time with a general decline over the 1954–2021 time frame. However, there is fairly strong evidence that effective tax rates are stationary in the 2001 to 2021 time period for most of the income groupings.
Traditional event study methodology can lead to erroneous conclusions—incorrect identification of an insignificant price change as statistically significant (and vice versa)—when there are volatility shifts, and the model is estimated from a prior low volatility period. Earlier studies have used the empirical distribution of the test statistic to adjust for the fatter tails created due to volatility shifts. We show that the empirical distribution approach (EDA) can only account for a shift in volatility and leads to biased results when there is a simultaneous shift in the beta. We propose using a regime switching (RS) model to estimate beta and volatility for different regimes. We show that using regime-specific beta and volatility removes the bias in excess returns caused by estimating the parameters from a prior period, with different beta and volatility. Our findings have practical implications for securities litigation, where event studies serve as key evidence. We highlight the need for re-evaluating excess return methodologies in high volatility environments and provide a framework for improving event study robustness in legal and regulatory contexts.
This note proposes a simplified approach to calculating the present value of future medical costs that eliminates the need for explicit inflation forecasting. Drawing on the stationarity-based framework of Rosenbaum and Mann (2024), we argue that when the growth in relative medical prices is stationary, the present value of life care plan costs can be reliably estimated using real interest rates and historical relative price trends. Applying Fisher’s equation, we demonstrate that projected inflation cancels out when it appears symmetrically in both cost escalation and discounting, making separate inflation forecasts unnecessary. This approach reduces complexity in forensic economic valuations and maintains logical coherence with economic theory. We illustrate the method using data on prescription drug costs and highlight its practical benefits, including transparency and ease of use, while acknowledging that other valuation frameworks may be appropriate in specific contexts.
Abstract Do single mothers work more throughout their lifetimes than married mothers? If so, do these differences vary by level of education? To answer, a two-state model is used to calculate worklives of mothers with a spouse present, in contrast to worklives of mothers without a spouse present. Worklives are generated for women of various education levels. Results show that married women with a spouse present have a shorter worklife than other marital status mothers. Regardless of marital status, less educated mothers have a shorter worklife than more educated mothers.
Abstract Litigation cases involving the expected earnings of minor children provide an ideal environment to examine the implications of public policies that attempt to mitigate racial, ethnic, and gender discrimination in the calculation of economic damages. This paper extends the existing literature on the implications of race, ethnicity, and gender neutral models by evaluating both educational attainment probabilities and estimated lifetime earnings within educational attainment categories. Recent related studies have focused on the educational attainment portion of the calculation only. We perform thousands of simulations of a child’s lifetime earnings using neutral estimations—a proxy for removing discrimination—and compare those estimates to ones in which race, ethnicity, and gender are taken into account. We find wide variation within racial and ethnic groups when earnings are incorporated into the analysis, consistent with prior research. Importantly, however, our findings pertain primarily to females, suggesting that interactions between gender and race and ethnicity are an added complexity. The practical implication of our findings is that neutral models can adversely impact individual members of protected groups. The results provide further guidance to policymakers who might be interested in the real-world outcomes associated with legislation that restricts how economists calculate economic damages.
Abstract Kurt V. Krueger’s seminal study used 2005-2009 Consumer Expenditure Survey (CEX) data to examine various measures of personal consumption rates for single persons. Given changes in survey methods, the impacts of inflation over the following decade, changes in tastes and other factors affecting consumer demand, we re-estimate Krueger’s measures using 2015-2019 survey data. The estimation of estate accumulation rates has expanded as well. Single person expenditures and consumption rates using the 2015-2019 data differ from the earlier results. They also differ from those acquired by deflating 2019 earnings to 2009 values and using the 2005-2009 consumption rates. Experts may find it useful to employ single-person expenditure rates using more recent data.
Abstract This paper updates and refines the estimates of age-earnings profiles provided in William E. Even and David A. Macpherson (2018). Relative to the earlier work, the estimates provided here use more recent data, improve the controls for the impact of the labor market on earnings, and provide both sex-specific and sex-neutral estimates of age-earnings profiles by education.
Abstract Forensic economists have used Healthy Life Expectancy: 2018 Tables (Kurt V. Krueger, 2020) in valuing the loss of household or personal care services due to injury or death of their supplier. The tables are used to decide how far into the future to project the loss. We focus on two easily avoided errors that may arise in that decision. First, the present value (PV) of a healthy life annuity (HLA ending when death occurs) falls short of the PV of an annuity certain for the healthy life expectancy (HLE), at any positive interest rate. Second, services are lost only during the combined healthy life of the supplier and life of the recipient. The expected PV of the supplier’s healthy life and the recipient’s whole life falls short of either. The paper illustrates the size of these potential errors for various ages of the two people and net interest rates of 0-3%; the errors can be significant. We provide an Excel workbook at the Journal of Forensic Economics website that allows the user to avoid both errors for calculating the PV of relevant (healthy) life annuities, for any of the demographic groups covered in the HLE tables. The paper gives formulas used for the present values of the life tables.
Kurt Krueger was a past Vice President and President of the National Association of Forensic Economics and a recipient of NAFE's Past Presidents Award. Kurt also was a vital member of the Journal of Forensic Economics' team in his role as Managing Editor and referee for papers submitted to the JFE.On his own and in collaboration with other researchers, Kurt's publications made significant contributions to the field of forensic economics. During his lifetime, Kurt had 33 peer reviewed publications in the JFE, as well as papers in Medical Economics, Medical Care, Earnings Analyst, Journal of Legal Economics, and Litigation Economics Review. Kurt's peer reviewed publications include work on Markov transitions for worklife expectancies, the use of the Consumer Expenditure Survey datasets to estimate personal consumption expenditures, laws governing damages calculations in personal injury and wrongful death cases in Kansas and Missouri, the whole-time concept, and measurement of healthy life expectancies. His published work also challenged the conventional wisdom in forensic economics concerning earnings growth and discounting to present value. In recognition of their work on using Markov models for measuring worklife expectancies, Kurt shared the JFE's Ward-Piette Outstanding Publication Award in 2018 with Gary Skoog and Jim Ciecka.Kurt created Expectancy Data, the publishing arm of John Ward Economics. Various editions of Expectancy Data's publications, including Dollar Value of a Day, Healthy Life Expectancy, and Full-Time Earnings in the United States are relied upon by damages expert witnesses nationally.Kurt was brilliant, but he did not suffer fools or pretentious behavior. However, he was also one of the kindest people in the field of forensic economics. He was more than willing to give his time to mentoring and answering questions from colleagues about data and theoretical issues related to forensic economics. Kurt was unparalleled in gathering, interpreting, and creating statistical information and garnering insights from large data sets for use in forensic economics.Kurt was one of a kind and had many interests other than forensic economics. We recall many delightful conversations with Kurt about politics, sports, music, electronics, and gadgets.Kurt loved his friends in forensic economics. His passing has left a huge hole in the field of forensic economics. He was our dear friend who we miss professionally and personally.
Abstract This article presents a guide for assessing economic damages in personal injury and wrongful death litigation in the state of Montana and is part of the Journal of Forensic Economics series of papers on this topic. The analysis provides experts with the information needed to produce opinions and give testimony on these subjects that is consistent common practice and Montana law.
A new method is proposed to project future costs for medical components of a life care plan. The technique estimates the historical link between inflation in medical components of the CPI and overall inflation. This linkage for each component can then be applied to a CPI forecast to project inflation in that underlying component. Estimates are made for 17 separate medical cost components of the CPI. Root mean square errors show that our proposed method for forecasting component inflation performs better than more commonly used forecast methods. Our method incorporates the best parts of both historical and forecasting methods; it utilizes information from the financial markets and professional surveys to form the baseline inflation forecast, then adjusts the value using historical data, thereby leveraging both expert opinion and empirical observation.
This paper examines medical inflation forecasting based on a two-step method proposed by Gilbert (2019), whereby the medical inflation rate is forecast via the sum of two terms: a broad inflation published forecast and a historical average of the inflation gap—this being the difference between medical inflation and broad inflation. In a simple forecasting experiment, the two-step method compares favorably to the one-step method of forecasting medical inflation based on its past values alone. Stationarity tests applied to the inflation gap mostly support stationarity, with a possible historical break. The econometric results generally support the use of the two-step method, with a limited historical window for inflation gap averaging, consistent with Gilbert (2019).
Event studies play a central role in class action securities fraud litigation. Event studies are used to assess market efficiency, price impact, loss causation, and damages, all of which are essential elements of a securities fraud claim. However, a substantial increase in market-wide volatility, such as what happened in 2020 with the COVID-19 pandemic, can render the standard event study methodology unreliable. In these periods, the usual distributional assumptions for t-tests of significance produce too many false positives. In this paper, we examine the extent of the problem and propose a solution that employs the empirical distribution of the t-statistic during the COVID period to adjust the critical test statistic value. We demonstrate this methodology with an application using the 19 constituents of the consumer durables index S5CODU in pre-COVID and COVID period samples, and with an evaluation of earnings announcement effects on stock prices. We show the methodology restores correct test size, eliminating excess spurious significance, while preserving substantial test power to correctly identify significant events in the COVID period.
After medical and medically-related insurance, the next most significant category of fringe benefits that employers voluntarily provide to employees is retirement and savings benefits, most often referred to as a pension plan or pension benefit program. According to the 2002 fringe benefit survey conducted by the U.S. Chamber of Commerce, a cost equal to 10.4% of payroll and pay for time not worked was incurred by the surveyed firms to provide medical and medically-related benefits to employees; 6.6% of payroll and pay for time not worked was spent providing retirement and savings benefit programs to employees.1 A roughly similar picture about the relative size of these two categories of fringe benefits is provided by data from the U.S. Department of Labor for September, 2002. Employer costs per hour worked for employee compensation were $19.09 for wages and salaries, paid leave, and supplemental pay (presumably comparable to “payroll” plus “pay for time not worked” in the U.S. Chamber of Commerce study), $1.67 for insurance benefits and $0.80 for retirement and savings plans; hence, insurance amounted to about 8.7% of hourly wages and salaries, while retirement and savings plans constituted about 4.2% of hourly wages and salaries.2The purpose of this paper is to discuss some issues that arise is carrying out the task of putting a value on losses of retirement and savings plans provided to employees. It is assumed in this paper that the reason such benefits are to be valued is due to a need to estimate damages from a wrongful termination, personal injury, or wrongful death that is the subject of litigation.3 Section II reviews some major types of retirement and savings plans. Section III describes the process of valuing the losses in this type of fringe benefit due to an event that causes a reduction in earnings.One of the most significant features of the retirement plans provided to workers by employers is that the plans are virtually always “qualified” retirement plans. According to one authority,4 a qualified retirement plan has two distinct elements. First, it is a retirement plan, meaning a plan that either provides retirement income to employees, or results in a deferral of income by employees for periods extending to the end of the employment period or beyond. Second, the plan is “qualified,” meaning that the plan is given special tax treatment for meeting a host of requirements for such a plan under the Internal Revenue Code. A “qualified” retirement plan provides workers with considerable tax-shelter benefits due to the fact that the contributions to the plan, whether by the worker or the employer, are sheltered from tax at the time they are made to the plan, and the interest, dividend and stock appreciation earned by money invested in the plan also is sheltered from tax until the time such earnings are withdrawn. Further, income taxes on certain types of distributions from the plan may be deferred by rolling over the distribution to an individual retirement account (IRA).Qualified retirement plans are classified as either defined contribution (DC) plans or defined benefit (DB) plans. A DC plan is a retirement plan that . . . .provides for an individual account for each participant and for benefits based solely upon the amount contributed to the participant’s account, and any income, expenses, gains or losses, and any forfeiture of accounts of other participants which may be allocated to such participant’s account. (Erisa § 3(34); IRC § 414 (i), as quoted from Krass, 2003, p. 2-1)With a defined contribution plan, there are three major consequences (Krass, 2003, p 2-2): plan contributions, but not retirement benefits, are defined by formula and not by actuarial requirements (except for target benefit plans, described below);plan earnings and losses are allocated to each participant’s account and do not affect the company’s retirement plan costs; andplan benefits are not insured by the Pension Benefit Guaranty Corporation (PBGC).A retirement plan that is not a DC plan is classified as a DB plan; under a DB plan annual retirement benefits must be definitely determinable, based on a formula contained in the plan. For example, in the Pennsylvania State Employees Retirement System, the annual retirement benefit for most employees reaching the normal retirement age of 60 is computed as the average of the three highest years of earnings x 2.5% x the number of years of state service. If a plan is categorized as a DB plan, then 1) plan formulas are geared to retirement benefits and not to contributions (except for cash balance plans); 2) the annual contribution is usually actuarially determined; 3) certain benefits may be insured by the PBGC; 4) early termination of the plan is subject to special rules; and 5) forfeitures (due to termination of employees not fully vested) reduce the company’s cost of providing retirement benefits.According to Ippolito (Table 1), over the period from 1980 to 1999, the percentage of the private labor force in the United States covered by an employer-sponsored pension plan remained very steady at about 46%. This steadiness in the overall percentage was accompanied, however, by a significant change in the mix of plans offered. The percentage of workers covered by a DB plan declined from about 38% of workers to about 20%, whereas the percentage of workers covered by a DC plan rose from about 8% to about 26%. Using data from the Survey of Income and Program Participation (SIPP), Copeland documents a similar dramatic shift for the decade ending in 1998, finding the proportion of workers covered in defined benefit plans shrank from approximately two-thirds of workers with pension coverage to one-third, with a corresponding increase in the proportion with defined contribution plans. Data from the Department of Labor indicates that 48% of workers were covered by at least one type of retirement plan in the year 2000, with 19% having coverage under a DB plan, 36% being covered by a DC plan, and with 7% of workers being covered by both types of plans.5Some major types of DC and DB plans and some plans that mix features of the two are briefly described below.6Over the past decade, a number of companies with traditional defined benefit plans have replaced these traditional plans with cash-balance plans. This conversion has been interpreted by Copeland and Coronado to be a response to competitive pressures in the labor market, rather than an effort to avoid penalty taxes (levied on firms that convert over-funded defined benefit plans to defined contribution plans), or surreptitiously reduce worker pension benefits. Cash-balance conversions have been more prevalent in industries with younger, more mobile workers and tighter labor markets. Copeland and Coronado conclude that such conversions reflect a desire to improve the pension plan offered to a mobile work force but at the same time preserve the benefits (reduced employee turnover, increased loyalty) of having some form of deferred compensation. Most cash-balance plans have five-year vesting requirements and increased employer contributions with tenure at the firm because contributions are a percentage of pay and pay typically rises with tenure.8The brief review of pension plans in the previous section reveals that a wide variety of plans exist, and the rules governing pension plans are complex, as a perusal of a book providing comprehensive coverage of pension plans, such as Krass, will quickly reveal. Valuing the loss of pension benefits in a particular case obviously requires knowledge of the specific plan. However, there are a number of issues and principles that arise in attempting to put a value on any retirement and savings plan. I begin with a discussion of some of these issues and principles and then turn to some examples of pension valuation in wrongful termination, personal injury and death cases.A substantial number of economic reports I have seen, and a sizable number that I have written myself, value the loss of fringe benefits as a percentage of lost earnings. Many of these reports rely for this purpose on the Chamber of Commerce or Department of Labor statistics cited at the beginning of this paper. The first issue that needs to be addressed is the question of when is it appropriate to value the loss of pension benefits as a percentage of lost earnings.If all employers offered defined contribution plans under which each employer contributed 3% of each employee’s gross earnings to a pension plan account in the employee’s name, the task of valuing pension plans would be easy. To each estimate of earnings loss one would just add 3% for the pension plan. But a substantial number of employers do not offer pension plans, and those that do offer a variety of plans, as described above. Hence, the duration of employment that a worker would have had with a particular employer and the type of pension plans offered by other employers for whom worker might have worked become matters of concern.The circumstance in which use of a percentage of earnings to value pension benefits seems most compelling is the case of an injury of a young person who has not yet entered the labor force. There is no employer and no track record of earnings. Use of U.S. Chamber of Commerce or U.S. Dept. of Labor statistics cited at the beginning of this paper to estimate the loss of pension benefits would seem to be the only recourse. These statistics include employers who have no employee pension plan and cover all types of employers. The future labor market experience very much a blank slate for this person and average statistics for a sample of employers spanning all industries and occupations in the labor force would seem to be the best way of obtaining a measure of the pension benefit loss.Another circumstance where the “percentage of earnings” approach might be the best procedure is where it is known that the person was employed at the time of the case-causing event but nothing is known about the fringe benefits. Use of a percentage to measure all relevant9 fringe benefits, including a pension plan, is a stop-gap, temporary solution that may be remedied at a later time if and when more information becomes available.Based on the discussion of pension plan trends presented above, it is clear that, while the chances of a randomly-selected worker being covered by any type of pension plan have stayed about the same, the chances are getting greater that, given coverage, the worker will be covered by a defined contribution plan, or by a cash balance plan. For both of these types of plan–in sharp contrast to defined benefit plans, as emphasized below–valuation of pension losses as a percentage of earnings is appropriate. Hence, to take yet another situation where use of a “percentage of earnings” may be a reasonable approach, if a worker randomly selected from the working-age population is unemployed at the time of the case-causing event, it is more likely today than in 1980 or 1990 that the next job the worker gets will be a job with a defined contribution pension plan.10If a worker is employed at the time of the case-causing event and is covered by a defined benefit plan, the details of which can be determined, it is inappropriate to use a percentage of the estimated loss of earnings to measure the worker’s loss of the pension benefits arising from the reduction in earnings. With a defined benefit plan, there is no separate account set aside for each specific worker. The amount the employer contributes to the defined benefit plan each year is determined by a variety of factors considered by the plan actuary, as described above, such as the age distribution of employees and their mortality, the amount of employee turnover which affects the percentage of employees who are vested in the plan, and the level of interest rates and the rate of return on other assets in which the funds of the plan are invested. When all of these factors influencing a firm’s contributions to its pension plan are considered, it become obvious that the link between the firm’s contributions to its pension plan per employee in any given year, or over the last X years, would bear only a very loose and uncertain relationship to the present value of the employee’s loss of pension benefits during the time of retirement.An argument that might be made for using the percentage of lost earnings approach to value the pension loss when a person is covered by a defined benefit pension benefits is based in the KISS (Keep it simple, stupid) principle. The use of the percentage of earnings approach simplifies a damage report in several ways. For one thing, it avoids making the loss period reach any further into the future than the end of the person’s working life. Valuing the pension losses by computing the present value of future pension benefits but for and given the case-causing event and deducting the latter from the former means extending the loss period out to the end of the worker’s life expectancy. This duration is virtually always longer than the projected age of retirement. As Gerald Martin (year?) has noted, “Most economists seem to claim the loss over the worklife as a loss of benefits because this avoids the need to push another 20 years or so further into the future” (p. 4–16.2). A simpler damage report and opinion is easier to present in testimony and it takes less time to prepare. It is therefore less expensive. The loss of wages itself may in many cases be sufficiently high to exceed the applicable insurance limits for the case. Incurring additional expert fees for the time to undertake a relatively elaborate computation of the pension loss may be an expense that fails the attorney’s cost-benefit test. If some cheaper proxy for all lost fringe benefits, including the pension loss, are available, well and good. Do it poorly and cheaply, or, in the alternative, don’t include an estimate of the pension loss at all.Given a world where nine in 10 cases settle without trial, using inappropriate methods to compute damages is a calculated risk. Use of inappropriate methods makes the using side vulnerable to an effective attack that exposes the error in the proffered estimate. Depending on the particular context, such an exposure could call into question the entire damage appraisal.With many, if not most, defined benefit plans workers covered by the plan are required to contribute some percentage of pay toward the cost of the plan. For the same level of pension benefits at retirement, a plan that requires contributions from the worker is worth less to the worker than would be the case if no contributions are required. When valuing the pension loss arising from a reduction in earnings, care must be taken, therefore, to reflect this obvious fact in the valuation of the pension loss. The most straightforward way of doing this is to deduct the worker’s pension contribution from the estimate of the pension loss or the estimate of lost earnings.It would clearly be inappropriate to value the loss of pension from a defined benefit plan as a percentage of earnings and also by computing the present value of the loss of future benefits. Such double counting may occur because of sloppy work: the pension loss is estimated as the present value of the loss of future pension benefits paid after retirement; a “percentage of earnings” approach is used to value the loss of all other fringe benefits except the pension loss, with the expert forgetting to remove the component of the fringe benefit percentage representing retirement plans before multiplying it by the loss of earnings.Having discussed some issues and ideas that apply to the valuation of pension losses in all kinds of cases, I provide some examples and discuss some additional issues that arise in the context of particular kinds of cases.Suppose that a person is wrongfully terminated and, for sake of concreteness, has lost 3 years of back pay and is expected to lose 2 additional years of front pay before retiring from the work force at age 65.First assume that the discharged employee had a DC savings plan wherein the employer matched 50% of the employee’s contribution up to 4% of pay. Suppose the employee had pay of $30,000 per year, and assume that pay would have increased by 3% per year over the 5-year loss period. Suppose further that the employee had a history of contributing the maximum of 4% of pay to the DC plan each year. Under these assumptions, and discounting of future losses to present worth at 5%, the mortality-adjusted present value of the pension loss would be $3,158, as shown in Part A of Table 1. The present value is computed as of 1/1/03. For simplicity, the assumption being made that pay is received at the end of the year. The mortality adjustment (based on mortality data for all persons in the U.S. in 2000) makes little difference: without the adjustment, the loss is $3,184, only $26 more. The adjustment is included for extension to the estimate of the loss with a DB plan, discussed below.Assume alternatively that the employee was covered under a DB plan. Assume that the plan’s benefit formula is such that annual retirement benefits equal to 1% of salary during the year before the date of retirement multiplied by years of service. The retirement age under the plan is age 65 with no provision for early retirement. Assume that the pension is solely funded by the firm with no contribution required of employees. Suppose at the time of the wrongful termination, the employee had 30 years of service and would have been eligible to retire at 65 with 35 years of service, but for the wrongful termination. Assume a salary of $30,000 per year and a 3% pay increase each year. But for the wrongful termination, the person would have had retirement benefits of 1% x $34,778 x 35 years = $12,172 per year. Given the wrongful termination, the person will be able to draw benefits, at the normal retirement age, of 1% x $30,000 x 30 years = $9,000 per year. The annual loss of pension, therefore, is $3,172 per year. Using the 2000 United States Life Tables, cited in Table 1, the life expectancy of a person exactly 60 years old is 21.6 years to age 81.6. Assuming a 16.6-year life expectancy beyond retirement at age 65, the present value of this loss using a 5% discount rate would be $31,185, as shown in Table 1. If, instead of using this “annuity certain” approach, the “life annuity” approach is used to compute the present value of the pension loss, that loss would be $29,599, also shown in Table 1.12Now consider a modification to this example wherein the employee is allowed to begin drawing a reduced pension immediately at the time of termination due to an “early retirement” provision that allows employees to retire as early as age 60, with at least 25 years of service. Suppose further that the penalty for “early retirement” is 5% for each year the employee is under age 65. The loss of pension due to wrongful termination is computed for this scenario in Table 2. The early retirement option reduces the size of the pension loss to $22,339 using the annuity certain approach and to $18,390 using the life annuity approach. More generally, the smaller the penalty for early retirement, the smaller the pension loss. If there was no penalty for retirement at age 60 or later, the pension loss from retiring at age 60 rather than age 65 would be negative, meaning that retiring with a pension of $9,000 at age 60 has a higher present value as of age 63 than waiting to age 65 and retiring with an annual pension of $12,172.Note that it would be difficult if not impossible to determine the value of the employee’s pension loss by computing the employer’s contribution to the plan on behalf of this particular employee. As noted above, with a DB plan the employer does not make contributions on behalf of particular employees. Even if the amount the employer contributed in the years after the termination could be determined and divided by the number of employees in the plan, the resulting average contribution per employee would have only a minuscule chance of measuring the employee’s pension loss. It is also worth noting that the average percentage of employee pay that employers spend on retirement and savings plans–6.6% using the U.S. Chamber of Commerce survey, and 4.2% using data from the U.S. Dept. of Labor in the year 2002–would provide poor estimates of the DB pension loss computed in Tables 1 and 2. For example, in Table 1, the life annuity pension loss of $29,599 is about 18.6% of the loss of earnings of $159,211. Using either of these employer cost percentages to estimate the pension loss as a multiple of lost earnings–either 6.6% or 4.2% of the loss of earnings of $159,211–significantly understates the loss of pension benefits. Similarly, in Table 2, the life annuity pension loss of $18,390 is about 11.6% of lost earnings of $159,211.Take the same scenario as that depicted in Part B of Table 1, with one change. Assume that employees are required to contribute 5% of earnings to the DB retirement plan. The correct valuation of the pension loss when the employee is required to make a contribution is to deduct the amount of that contribution from the loss. The contribution is a cost to the employee of participating in the plan and makes the plan less valuable than one with the same benefits that is totally financed by the employer. Hence, the pension loss would be the Table 1 loss of $29,599, as above, less 5% x $159,211 = $7,961. The pension loss is therefore $21,638 = $29,599 - $7,961.13As a final alternative, suppose the employer provides employees with a cash balance pension plan. Assume that at the time of the employee’s termination, the amount in the employee’s hypothetical account is $250,000. Suppose further that additional credits are added thereafter to the employee’s hypothetical cash balance through annual credits computed as 4% of employee pay. Furthermore, assume that employee balances grow based on interest credits that are not conditioned on continued employment. Under these assumptions the loss in the value of the cash balance plan is simply 4% of the loss of back and front pay. Continuing the above example, the loss would be 4% x $159,211 = $6,368. Because the interest credits are not conditioned on continued employment, those credits would not be part of the loss.Social Security provides a type of defined benefit pension plan under which retirement benefits depend on years spent working in covered employment and the amount of earnings in all those years. This record of earnings is summarized in the employee’s “average indexed monthly earnings” (AIME). As I have argued elsewhere (Rodgers, 2000), multiplying the employer’s FICA tax “contribution” 5.3% (the part of the FICA tax of 7.65% that funds the retirement portion of the Social Security program) by the lost earnings virtually always provides a poor estimate of the employee’s loss of Social Security benefits.To continue with the above example, the loss of the last five years of the terminated employee’s working life could have the effect of reducing the employee’s AIME, which would result in a loss of Social Security retirement benefits relative to what those benefits would have been but for the termination. The loss depends on the terminated worker’s earnings history in covered employment. The loss can be as low as zero if the earnings the worker would have received but for the wrongful termination would not have been used to compute the worker’s AIME–a situation that would arise if those earnings were not among the highest 35 years of indexed earnings used to compute AIME.The maximum loss that the worker could sustain would be the total loss of Social Security retirement benefits from being denied coverage because the loss of the five years of work was enough to keep the worker from being “fully insured.” This would be an unusual situation where the worker had attained less than 40 quarters (credits) of coverage up to the time of the wrongful termination at age 60. The situation where a worker begins working full-time after age 50 and has obtained no quarters of coverage prior to that date is probably very rare indeed. But in such an instance, the wrongful termination could render the person ineligible for any benefits. If this person was “on the cusp” of becoming fully insured and never became so due to the wrongful termination, then the loss of social security retirement benefits could be substantial.A somewhat more likely scenario where there could be a substantial loss of Social Security retirement benefits would be the situation where a person had worked for many years as a Federal civilian employee (being hired prior to 1984) and then took a job in the private sector in 1994 at age 54. Such a worker would have obtained 24 quarters of coverage by age 60–less than the 40 quarters of coverage required to be eligible for Social Security retirement benefits. But for the termination, the worker, using the assumptions above, would have obtained an additional 20 quarters of coverage over the five years of employment during the period 2000 through 2004, allowing the worker to be eligible for a Social Security pension.14Table 3 shows an example of the calculation of the loss of Social Security benefits in two scenarios. In the first, It is assumed that the terminated worker had earnings prior to 1999 that bore the same relationship to average covered earnings in those years as earnings of $30,000 in 1999 bore to average covered earnings in that year. The worker’s AIME based on the highest 35 years of indexed earnings from age 22 to age 64 is computed, but for, and given the termination. As can be seen, AIME is $2,652 but for the termination and $2,638, given the termination, so the effect of the termination on AIME is very small. The effect of the termination on the primary insurance amount (PIA) is therefore very small, reducing the amount from $1,192 to $1,188, or by $4 per month. The reduction is the same for the age 65 monthly benefit, from $1,152 to $1,148 per month.15 This reduced monthly benefit will have a smaller present value than the present value of the 5.3% OASI portion of the FICA tax paid by the employee on the lost earnings, which, from the example above, is 5.3% x $159,211 = $8,438. The net loss, as shown in Table 4, is a negative $7,860.16In the second scenario, it is assumed that the worker began working in covered employment in 1994 at the age of 54. Therefore, at the time of the termination, insufficient quarters of coverage (24) were held for being “fully insured and no Social Security benefits would be collectable, given the termination. But for the termination, the worker would have had sufficient quarters of coverage. Hence, the entire present value of benefits, but for the termination, would constitute the worker’s loss of benefits. Table 5 computes the present value of the gross loss of benefits as $44,359, and the net loss after OASI FICA taxes as $35,921.It is worth noting that multiplying the employer’s 5.3% tax “contribution” times the loss of earnings of $159,211 produces a number equal to $8,438. This number is a not a good estimate of the Social Security pension losses in either of the two scenarios depicted in Tables 4 and 5. This illustrates the point noted above that what might be termed the “FICA tax method” of estimating the employee’s loss of Social Security benefits does not accurately estimate such losses.The previous situations were couched in terms of an older employee close to retirement. Let us examine the loss of pension for a case of a younger employee, but otherwise in the same circumstances.For the DC Savings Plan with Employer Match scenario, the loss remains the same, namely, $3,184, as shown in Table 1. For the DB Plan Funded 100% by the Employer, there is a difference in the loss. To fix the difference, assume that the younger terminated employee was 40 years old with 10 years of service at the time of termination. Assume, as before, that there are three years of back pay losses and two years of front pay losses, with the same pay structure.17 But for the wrongful termination, the retirement benefits would have been computed as 1% x $34,778 x 15 years = $5,217 per year. Given the wrongful termination, the person will be able to draw benefits, at the normal retirement age, of 1% x $30,000 x 10 years = $3,000 per year. The annual loss of pension, therefore, is $2,217 per year. Assuming a 15-year life expectancy beyond retirement, the present value of this loss using a 5% discount rate would be $7,867, as shown in Table 6. The loss is much smaller due to the effect of discounting a loss occurring further in the future. In the scenario, DB Plan Funded Partly by the Employer and Partly by the Employee, a deduction of an employee contribution of 5% of lost earnings would result in no net loss of pension, as the present value of the employee contribution to the pension plan of $7,961 would exceed the present value of the pension loss of $7,867. In Valuing the Loss in a Cash Balance Plan, the loss would continue to be the same with the same credit of 4% of employee pay, and the loss would be the same as in the earlier example, namely, $6,368. Estimating the Loss of Social Security Benefits for a younger person would entail the same type of issues as for an older person, but with the added uncertainty created by the much longer time period for market work and earnings before retirement. The likelihood of a net loss of benefits arising would be smaller due to the nearness in time of the employee’s 5.3% “contribution,” compared to the possible loss of benefits is a distant, more heavily discounted future.Personal injury cases obviously differ from wrongful termination cases in a number of ways. In termination cases, the plaintiff has not been physically injured and a signifi
This note corrects errors in Table 3 of Edward Foster's article (2020, p. 107). The original paper was addressed to forensic economists who use, or contemplate using, healthy life expectancy (HLE) to estimate the period for future loss of household or personal services due to death or catastrophic injury of the service provider. The paper's purpose was to alert readers to some features of HLE, as originally defined by the United States Department of Health and Human Services (DHHS) and published by Kurt Krueger (2019), that could influence the way one might use HLE in that application.Table 3, “The Distribution of HLE Over the Lifespan,” addresses implications of assuming that but for the service provider's injury or death, he or she would have been able to provide services at the same level as before, to the end of the healthy life expectancy. Those with some actuarial education would know that the assumption is inaccurate because it front-loads healthy life years: HLE is calculated as the sum of annual increments to healthy life to the end of the table, that is to age 100 in Krueger's HLE tables. For integer age x ranging from 25 to 70, and age y = x + HLEx, column 4 of Table 3 gives the years of healthy life accumulated from age x up to age y; column 5 shows column 4 as a percentage of the total HLEx.Thus, for a male age 25 with HLE of 42.43 years to age 67.43, only 33.14 healthy life years, 78% of the total, will have been accumulated by that age; one must accumulate his healthy life years to age 100 to reach the full HLE of 42.43 years. To assume that the service provider at age 25 would have been able to continue providing services at his former level out to age 67.43 is to front-load those services, by assuming that he would have provided 42.43 years of healthy life in a period which would, on average, provide only 33.14 years.Columns 4 and 5 of the original Table 3 are accurate for males, but not for females. Table 3 in this note provides the correction; as column 5 shows, the correction shows the front-loading for females closely in line with that for males, with a range of 80% to 65% for females aged 25 to 70, compared to a range of 78% to 65% for males. An additional error occurs in column 8 for females at age 50; the correct value is 0.75 healthy life years after age 90, recorded in the original paper as 0.13 years, wrong on its face based on the values for other ages. Finally, the footnote to Table 3 in the original paper misstates the formula for calculating column 4 by writing column (3) in place of column (2).This note also acknowledges a change in assumptions in Krueger (2020) compared to those used in Krueger (2019 and earlier years). The population that the HLE tables are intended to represent includes those confined to institutions such as nursing homes, prisons, long-term care hospitals and other care facilities. Krueger (2020) applies healthy life years of zero to those residents, because they would be unable to provide household or personal services to unconfined care recipients. Earlier HLE tables had assumed positive values for those residents, appropriate for HLE as an index of public health for the population but not as an indicator of availability to provide household or personal services. (Foster, 2020, p. 106)
This note contains graphs of worklife expectancies by quarters from 2012Q2 through 2022Q2. Graphs show Covid-19 pandemic-related downward movements in worklife expectancies were most prominent from 2020Q2 to 2021Q1. However, worklife expectances returned to their pre-pandemic levels starting in 2021Q2.
Various studies estimate personal consumption expenditures from Consumer Expenditure (CEX) data. Early analysis relied on CEX data that was aggregated across expenditure categories and income groupings, while later studies used microdata containing disaggregated expenditures across individual items for each surveyed household. These newer studies allocated expenditures for each item to relevant household members, but analyzed results aggregated across income strata. We extend the microdata analysis by examining personal consumption expenditures at the household level. Our results indicate that at all but the lowest incomes, personal consumption rates generated using microdata-level observations differ only slightly from existing models using income-strata data. Forensic experts accounting for personal consumption may, thus, feel comfortable using either method of analysis.
Abstract This paper examines the impact of using a model that excludes race and ethnicity on predicted educational attainment and income of a child in a personal injury legal matter. We use the updated ordered probit models with and without race and ethnic variables from Spizman and Kane (2020) and compare the earning capacity losses of a minor child based on each one. We perform this calculation for more than 3,000 combinations of the right-hand side variables for males and females separately, with more than 1,000 combinations each for White, Black, and Hispanic individuals. We find wide variation within each racial and ethnic group, with some subgroups benefiting and others being adversely impacted. The results of our analyses provide guidance to policymakers who might be interested in the real-world outcomes associated with legislation requiring that race and ethnicity not be considered when estimating damages in personal injury cases.
Unlike for personal consumption of income, there is no literature for personal consumption of household services. Absent such a literature, some forensic economists use a variety of methods to estimate personal consumption of household services while others make no estimate. Using the American Time Use Survey (ATUS) data from 2003-2019, this study estimated the percentage of household services that are self-consumed based on the characteristics of the decedent and the decedent's household. The results show that the personal consumption percentage varies with the household size; number of household adults; age of the youngest child; and the decedent's sex, age, employment status, and (when applicable) the employment status of the decedent's spouse/partner. Generally, the personal consumption percentage is higher for men than women, decreases with the number of household children, increases with the age of the youngest child, is higher for respondents employed full-time compared to other employment statuses, and lower when the respondent's spouse/partner is employed full-time compared to other employment statuses. Note that in making these estimates, fungibility of time presents challenges when accounting for the contributions of various household members in the production of household services. These challenges are likely substantial between adults and minors in a household. To ignore the contribution of household members other than the decedent will underestimate the personal consumption of household services, just as ignoring fungibility issues by including the contributions of all household members will overestimate the personal consumption of household services. Accordingly, this study developed a model for the personal consumption of household services that considers only the contributions of household adults.
