I. Introduction

Forensic economists frequently estimate the present value of lost earnings for personal injury or wrongful death litigation. A key ingredient to such calculations is a forecast of how earnings would have grown from the date of injury or death until the end of work life. In our earlier paper on the subject (Even and Macpherson 2018), we discussed various approaches forensic economists use for forecasting earnings growth. However, economic theory and empirical evidence suggest that the most accurate forecasting approach relies on age-earnings profile estimates. There is substantial evidence showing that wage growth is greatest when workers are young, but growth gradually declines with age (e.g., Jacob Mincer, 1974; Kevin M. Murphy and Finis Welch, 1990; and James J. Heckman, Lance J. Lochner, and Petra E. Todd, 2006). As shown in our earlier paper, a failure to account for changes in wage growth over the life cycle can lead to significant biases in estimating future earnings losses.

This paper updates our earlier estimates of wage growth over the life cycle in several ways. First, we use more recent data. Our earlier paper used a combination of Census and American Community Survey (ACS) data from 2000 through 2015. This study uses ACS data from 2002 through 2021. Second, in addition to providing sex-specific estimates of wage growth by education group, this study provides sex-neutral estimates in light of growing calls for ignoring sex in the estimation of earnings loss (see Lawrence M. Spizman and Steven J. Shapiro, 2020). Third, we adjust our earlier estimation process to improve the controls for labor market conditions to improve the identification of true age effects from cohort or year effects.

II. Background

Recent surveys show forensic economists use various methods for forecasting earnings growth (e.g., David I. Rosenbaum, David Schap and Michael R. Luthy, 2018 and David Schap, Michael R. Luthy and David I. Rosenbaum, 2020). Some examples mentioned in the surveys include average historical earnings growth; Congressional Budget Office (CBO) estimates of future growth in the Employment Cost Index; Social Security Administration estimates of future wage growth; or an age-earnings profile that allows wage growth to vary over the life cycle.

While forecasting earnings growth is simplified by assuming a constant wage growth rate over a person’s life, numerous studies show that such an assumption is invalid (e.g., Mincer, 1974; Murphy and Welch, 1990; Heckman, Lochner and Todd, 2006). The evidence indicates that earnings growth is highest when workers are young and gradually diminishes as a person ages.

The accuracy of an earnings forecast for an individual will be improved by allowing wage growth to vary with age. As noted in our earlier work, properly estimating an age-earnings profile requires separating age, period, and cohort effects with multiple years of cross-sectional data. For example, if workers of two different ages are compared in a given year, the earnings difference could be due to age effects or the fact that they are from different birth cohorts. Since the data is from the same year, the difference would not be due to period effects. On the other hand, if the data was from two different years and the earnings for people from the same birth cohort, the difference could be due to age or period effects.

To separate age, birth, and cohort effects, we try to control for period effects on earnings by including controls that would cause earnings changes independent of age effects (e.g., an unusually strong labor market). In our earlier work, we controlled for period effects by including controls for the state-specific unemployment rate and the coincident index of economic activity. In this study, we modify the earlier approach in two ways. First, rather than deflate earnings by the consumer price index (CPI), we deflate by the employment cost index (ECI) for wage and salary workers based on the worker’s broad occupation.¹ Earnings deflated by the ECI will reflect changes in the average cost of a given quality of labor and should remove period effects. That is, if the average cost of a given quality of service workers rises 10% between years, the period effect on earnings from one year to the next is 10%. Deflating by the ECI removes the period effect on the earnings measure, leaving only the true age effect when comparing workers from the same birth cohort across time.

While deflating by the ECI helps control for period effects, the ECI is a national measure of wage conditions. To better control for variation across the country in period-specific labor market conditions effects, we also include a control for state-specific deviations from the mean unemployment rate. Finally, we add state-specific fixed effects to allow for the possibility that wage levels consistently differ across states over time. We also include occupation-fixed effects to allow for the possibility that earnings levels differ across occupations.

III. Data and Estimates of Age-Earnings Profiles

The American Community Survey data for 2002 through 2021 are used for our analysis.² Following our earlier work and that in Expectancy Data (2019), our sample is restricted to civilian full-time, year-round wage and salary workers between the ages of 19 and 65 at the time of the survey.³ The sample excludes workers who report zero or negative earnings; those who report any income from self-employment, Social Security, or Supplemental Security Income; and those with a military occupation. All respondents with imputed values for earnings, age, sex, race, education, weeks worked in the past year, or usual weekly hours are excluded from the sample.⁴ Unlike our earlier analysis, this study excludes workers with imputed values of key variables and weights the regression to adjust for this to reduce any resulting bias, as recommended by Christopher R. Bollinger and Barry T. Hirsch (2009). Also, unlike our earlier work, we exclude workers who report attending school at any time in the three months before the survey. The effects of these changes on estimates of earnings growth will be discussed.

For our analysis, annual earnings are converted into 2021 dollars after deflating by the ECI or CPI. There are a few important points to consider with the data. The ACS is administered annually throughout the calendar year. For example, the 2010 survey was administered between January and December 2010. The ACS does not reveal the month that the ACS was administered. The person’s reported age is the person’s age as of their most recent birthday prior to the survey.

The ACS earnings measure used in this study is the person’s total pre-tax wage and salary income (wages, salaries, commissions, cash bonuses, tips, and other money income) received in the twelve months prior to the survey. Since the ACS reports the year (but not the month) the survey was administered, the precise 12 months over which earnings are measured is uncertain. For example, in the 2010 data, the survey could have been administered any time between January and December 2010. If the survey was administered in January 2010, the earnings period would be January through December 2009. If it was administered in December 2010, the earnings period would be December 2009 through November 2010. This is an important complication when matching the ECI or CPI to earnings data. Given the uncertainty of the appropriate time period for surveys administered in a given year, we calculate a weighted average of the index over the relevant time periods where the weights reflect the probability that each time period is relevant. For example, for surveys administered in 2010, there is a 1/12 chance that the survey was administered in each month of 2010. We then take a weighted average of the ECI over the relevant 12-month periods (e.g., 1/12 weight on January through December 2009, 1/12 weight on February 2009 through January 2010, etc.). This approach is used to calculate an appropriate average of the ECI/CPI when deflating earnings from a given year of ACS data.

Tables 1a–1c summarize some sample statistics for our sample for males, females, and both sexes combined. It lists the seven education groups considered, the mean of real earnings (in 2021 dollars after deflating by the CPI), and the sample sizes. In addition, the earnings growth between consecutive age groups is provided for each education group. Consistent with the fact that earnings growth varies over the life-cycle, for every education group and sex, the earnings growth between consecutive age groups is greatest at the earliest ages (e.g., comparing the growth between the group 25 and under versus the group 26-35) and diminishes (and sometimes turns negative) at older ages. It is important to emphasize that these estimates are not pure age effects since year and cohort effects have not been controlled for, workers are not uniformly distributed across individual years of age within the age groups, and no adjustment has been made for the inclusion of workers with imputed values for key variables. Also, the estimates are not an average annual growth rate between age groups since, for example, it compares the average earnings of 19-25-year-olds to 26-35-year-olds. Despite these shortcomings, the simple statistics are strong evidence that earnings growth is highest at the youngest ages and diminishes (and may turn negative) as workers age. For each of the seven education groups, the greatest earnings growth occurs between the youngest and second youngest age groups, and earnings growth diminishes as workers move into the older age groups.

Table 1aAverage Earnings by Age and Education: Males

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Table 1bAverage Earnings by Age and Education: Females

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Table 1cAverage Earnings by Age and Education: Both Sexes

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To identify age effects by year of age, we estimate regression models to remove period and cohort effects. We also estimate the regression separately by education and gender to allow earnings growth to differ in each subgroup. The regression model we estimate for a given education/gender sample is as follows: (1) $$y_{\mathit{ist}}={\beta }_0+{\beta }_{1}Ag{e}_{it}+{\beta }_{2}Ag{e}_{it}^2+{\beta }_{3}Ag{e}_{it}^3+{\beta }_{4}Ag{e}_{it}^4+U_{it}^{*}\theta +O_i+C_i+S_i+{\epsilon }_{it}$$

The subscript i indexes the person, and t indexes the year of the data; y is the natural log of real earnings in 2021 dollars after deflating by either the ECI or CPI; Age is the person’s age at the time of the survey; U* is the deviation of the relevant person’s state-specific unemployment rate from its state-specific mean over the sample period; O_i is an occupation-specific fixed effect for each of the nine occupations for which the ECI is calculated; C_i is a birth-cohort specific fixed effect (i.e., a set of dummy variables reflecting all possible birth years in our sample which range from 1937 to 2002); S_i is a state-specific fixed effect; and $\epsilon$ is an error term that is assumed to be independent across observations with zero mean. The regression includes a quartic in age, given the research by Murphy and Welch (1990) establishing that the quartic is the functional form that best fits the age-earnings profile.⁵ We follow the recommendation in Bollinger and Hirsch (2009) and estimate the earnings regression using inverse probability weights to adjust for the fact that observations with imputed values are excluded from the sample.⁶

The rationale for deflating earnings by the ECI (instead of CPI) is that it will do a better job of removing period effects from earnings. While deflating by the CPI would remove period effects on earnings due to inflation, the ECI captures a broader range of period effects affecting earnings. Not only would the ECI adjust for economy-wide changes in earnings for a given quality of worker caused by inflation, but it would also control for economy-wide changes in productivity or labor supply or demand changes. Moreover, unlike the CPI, deflating by the ECI removes period effects specific to a given occupation. To understand the impact of using the ECI instead of the CPI for deflating earnings, we first investigated the relationship between the two indexes over our sample period (2002-2021).⁷ Over this period, the average annual rate of change for the ECI was 2.5%, and that for the CPI was 2.2%. The raw correlation between the annual rate of change in the two indexes over the sample period is .58. Figure 1 plots the two time series and shows that the one-year change in the CPI has greater volatility than the one-year change in the ECI. The Congressional Budget Office (CBO) projections of future economic conditions generally predict that the ECI will grow faster than the CPI. For example, a review of CBO forecasts between 2010 and 2021 shows that the ECI was projected to grow faster than the CPI in all their 10-year forecasts. On average, the annual growth rate in the ECI was projected to exceed the growth in the CPI by 1.0 percentage points.

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We pursue the following approach to determine whether deflating by ECI or CPI better removes period effects. First, we estimate the earnings regression in equation (1) using the natural log of three different measures of normalized earnings: (1) nominal earnings without deflating; (2) nominal earnings deflated by the CPI; and (3) nominal earnings deflated by the person’s occupation-specific ECI.⁸ After estimating the three earnings regressions for the 21 education/gender samples (seven education groups and three gender groups), each group's mean forecast error is calculated by year. The mean forecast error should not vary over the years if period effects are completely removed. Comparing the standard deviation of the mean forecast error over the years for a given sub-sample reveals which method of deflating nominal earnings best purges earnings of period effects.

The results of this exercise are given in Table 2. Surprisingly, compared to the case where nominal earnings is used as the dependent variable, deflating by CPI actually worsens the removal of period effects in 16 of the 21 sub-samples. Across the 21 subsamples, the average standard deviation of the year effects is .029 with nominal earnings and .033 with earnings deflated by the CPI. Deflating by the CPI does not do a very good job of purging the year effects from the earnings measure. On the other hand, relative to the unadjusted series of earnings, deflating earnings by the occupation-specific measure of the ECI substantially reduces the standard deviation of the period effects for every sub-sample considered. Across the 21 subsamples, the standard deviation of the period effects is always lower when using earnings deflated by the ECI than either unadjusted earnings or earnings deflated by the CPI. Averaging across the 21 subsamples, the standard deviation of the period effects is .015 with earnings deflated by the ECI, .033 with earnings deflated by CPI, and .029 with unadjusted earnings. Hence, deflating by the ECI does a better job of removing period effects than either not deflating earnings at all or deflating by CPI. Consequently, we use this earnings measure to remove period effects and identify the age and cohort effects in our earnings regressions.

Table 2Standard Deviation of Mean Forecast Error Across Years forDifferent Earnings Measures

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Figure 2 provides the estimated earnings growth by age for the seven education groups and three different gender groupings using earnings deflated by the ECI.⁹ As expected, earnings growth is highest when a worker is young, gradually diminishes with age, and turns slightly negative at late ages for some sub-samples. Also, for a given age, earnings growth is generally the lowest for workers with the lowest levels of educational attainment. Finally, at most ages, male earnings growth is higher than female growth, particularly during the younger years. Not surprisingly, the sex-neutral estimates of earnings growth lie between those for men and women. Precise numerical values of the earnings growth estimates are provided by single year of age for each of the seven education groups in Table 3a for males, 3b for females, and 3c for both sexes combined.¹⁰ Due to the log-linear form of the estimated earnings regression, the estimated growth rates depend only upon a person’s age and not on any assumptions about other control variables in the regression (e.g., education, state of residence, birth year).¹¹

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Table 3aEarnings Growth by Age and Education: Males

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Table 3bEarnings Growth by Age and Education: Females

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Table 3cEarnings Growth by Age and Education: Both Sexes

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IV. Sensitivity of Estimates

A comparison of the earnings growth estimates with those in our earlier work reveals lower growth rates for most groups—particularly at younger ages. The changes could be due to the different data employed here (dropping 2000–2001 data and adding data for 2016–2021). Alternatively, it could be driven by the fact that this study's sample restrictions and methodology differ from our earlier work in three important ways. First, our earnings regressions are based on earnings deflated by the ECI instead of the CPI. Second, we employ weighted regressions to reduce the potential bias of excluding observations with imputed values for key variables. Finally, this study drops workers who report attending school in the three months prior to the administration of the survey. Below, we consider the effect of each of these modifications on the estimates of earnings growth.

In Table 4, we report the effect of each change on estimated wage growth for the seven education groups. The results are presented only for the sex-neutral groups and all ages combined and separately for those aged 30 and under and those aged 30–65. The top panel shows the effect of deflating by ECI instead of CPI. Across all age and education groups, deflating by ECI instead of CPI reduces the estimate of wage growth by .29 percentage points per year. While the effect differs across the education groups, the differences are relatively modest. Also, the reduction in estimated wage growth is slightly larger for those 30 and under than for those over 30.

Table 4Impact of Alternative Estimation Methods on Estimates of Earnings Growth for Both Sexes Combined

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The middle panel of Table 4 presents the effect of using inverse probability weights to adjust for deleting observations with imputed values. We have no strong priors on the direction of this bias but expect any bias to be greater among younger workers since they are more likely to have imputed values. Across all ages and education groups, average wage growth estimates are affected only slightly by weighting (a decrease of .03 percentage points). However, consistent with our priors, the effects are slightly larger (in absolute value) among younger workers. Moreover, the direction of the impact varies across the sub-samples.

The bottom panel of Table 4 shows the effect of excluding workers who reported attending school at any time in the three months before the survey. Keeping in mind that the sample is already restricted to full-time, full-year workers, we expect that workers who are also attending school will have lower earnings as it may place some restrictions on acceptable jobs or hours. Moreover, since the probability of attending school is highest when a worker is young, deleting workers attending school should decrease the measured earnings growth. Our prediction is consistent with the change in the estimates of earnings growth caused by dropping school attendees. Across all age and education groups, the average effect is to reduce the average estimate of annual earnings growth by .11 percentage points. Among workers 30 and under, the reduction is .49, whereas for those over age 30, it is only .03 percentage points. Examination of these effects by single year of age reveals particularly large effects (as large as a 1.0 percentage point reduction) at the earliest ages considered in our analysis.

V. Summary

This study provides updated estimates of earnings growth by age and educational attainment. The analysis makes three changes relative to our earlier work and others that we believe improve the validity of the estimated age-earnings profiles. Deflating by the ECI instead of the CPI slightly reduces estimates of earnings growth. Weighting the regressions to offset imputation bias has relatively small effects that differ across age and education groups. Finally, excluding workers who recently attended school reduces estimates of earnings growth by a fairly substantial amount—particularly among young workers.

To use the wage growth estimates, economists should be careful to adjust for the fact that the measure of earnings is deflated by the employment cost index. Hence, the earnings growth measures presented here should be increased by projections of the growth in the ECI, which are provided regularly by the CBO. While projections are available for growth in the ECI for all wage and salary workers, our measure of earnings was deflated by occupation-specific measures of the ECI to better account for the period effects unique to each occupation. To our knowledge, no forecasts of ECI growth by occupation are available. One option would be to use the projection for all occupations combined. An alternative would be to obtain an estimate of ECI growth for the specific occupation—though we know of no source for such projections at the time of writing.