When Age Is Standing In for Cohort
The subject here is the age–earnings profile attached to a college major, and the specific problem is that a short survey can make birth-cohort differences look like aging. For engineering and computer science, the key question is whether a lower relative advantage among older observed workers reflects slower earnings growth or simply the fact that those workers entered the labor market with a smaller premium. Understanding that distinction gives readers a way to judge cohort-major and year-major evidence without treating either adjustment as a magic answer.
Three clocks in one data window
An age–earnings profile seems to have one obvious clock: age. A worker is 25, then 35, then 45, and earnings change along the way. But a dataset that observes many people once contains at least three clocks at the same time. Age measures position in the working life. Birth cohort identifies the group born around the same period. Calendar year identifies the labor market in which an observation is recorded. Those dimensions can be related, but they do not mean the same thing.
A repeated cross-section is a set of snapshots, not a set of home movies. The American Community Survey observes different respondents in different survey years. In a short window, an older respondent is generally from an earlier birth cohort than a younger respondent. The older respondent is not the younger respondent after several decades; they are people who began their education and work under different conditions. When the data move from one age group to another, the observed population changes as well as the age label.
That distinction is easy to miss because age is visible in every record while cohort history is not. A table can list earnings by age and major, and a line can connect those averages, without showing that the line is being supported by different generations at different points. The line may still be a useful description of the sample. What it cannot automatically provide is a within-person or within-cohort trajectory.
Consider a hypothetical survey in 2017. A 25-year-old may have been born around 1992, while a 50-year-old may have been born around 1967. The survey records both as observations in the same labor market, but they did not enter college or work at the same time. If the value of computer science rose sharply between their entry periods, the younger person’s higher relative earnings could be a cohort difference. Calling the gap “the effect of being 25 rather than 50” would mix that difference with whatever happens as either person gains experience.
This also shows why the comparison can survive ordinary controls and still be misleading. Adjusting for gender, race, citizenship, education, or calendar year can make people more comparable on measured characteristics. It does not automatically recover the unobserved starting position of a cohort or the selection process that placed different students into different majors. A profile can therefore be carefully estimated and still answer a narrower question than the reader assumes.
The problem is especially important when the value of a major changes across generations. Imagine two groups of engineering graduates. The older group entered the labor market when engineering carried a modest premium over the comparison fields. The younger group entered when demand for their particular training was stronger, or when a more selective set of students was choosing the field. If both groups are surveyed at the same time, the younger group is concentrated at the low-age end of the chart and the older group at the high-age end. A difference in starting levels is then placed on an axis labeled age.
The same issue applies to computer science even if the underlying skills of each worker become more valuable with experience. If recent computer-science cohorts begin higher than earlier cohorts, a short cross-section compares newer high-premium entrants with older lower-premium workers. The resulting decline can be produced by the movement between cohorts rather than by a decline inside either cohort. The observed curve has entered a misleading state: it looks like a lifecycle path, but part of the information that would identify the path has been lost at the snapshot stage.
Calendar year supplies a third clock. A 30-year-old surveyed in 2010 and a 30-year-old surveyed in 2020 are the same age but face different labor markets. Conversely, a 50-year-old and a 30-year-old observed in 2010 necessarily belong to different birth cohorts. In a simple identity, birth year equals survey year minus age. Once two of those quantities are known, the third is fixed. This is why a model cannot freely assign an independent effect to every age, cohort, and year combination without imposing additional structure.
The consequence is not that researchers must choose one clock and discard the rest. It is that each design makes a different claim easier to see. A short ACS window has broad coverage and useful information about major, but it leans heavily on comparisons across cohorts. A long earnings history supplies more observations for the same people, but it also introduces calendar-time variation that must be considered. The question is which source of variation is doing the work of the estimate.
In lifecycle terms, the snapshot state preserves a worker’s age and reported major but loses most of the path that produced the observation. Moving to a panel state preserves repeated earnings for a person, yet it does not automatically preserve a clean separation between aging and the calendar. Moving again to a model with cohort-by-major terms preserves a more explicit account of changing starting premiums, but it still depends on how the terms are specified. Each transition recovers some information and leaves another ambiguity behind. That is why the paper’s evidence has to be read as a sequence of comparisons rather than as one final number.
From a changing premium to an apparent slope
The paper formalizes the issue with a simplified model in which earnings depend on a major-specific starting level, an age slope, and a cohort-specific premium. Suppose the return to a technical major is higher for workers born after 1980. In the ACS window, those newer workers tend to be younger. The indicator for being in the newer cohort is therefore negatively related to age. If the indicator is omitted, the estimated age slope absorbs some of the cohort premium and is biased downward.
In plain language, the curve is asked to explain two things at once: how earnings change as people age and how the economic value of the major changed for the generation entering later. If the model has only one place to put both movements, it can report the second movement as part of the first. This is not a flaw unique to technical degrees. It becomes consequential here because the paper finds evidence that recent engineering and computer-science cohorts have a larger relative premium.
The direction of the bias is what matters most. When the newer, higher-premium group is concentrated among younger observations, omitting its cohort term makes the age coefficient too low for that major. The estimate does not need to be numerically large in every age bin for the accumulated profile to look like a pronounced decline by mid-career. Nor does a cohort correction need to produce a positive coefficient to be useful: it can show that the negative cross-sectional estimate was partly carrying a comparison between generations.
The paper’s reported cohort effects make the possibility concrete. Relative to the pre-1961 base group, the cohort-by-major estimates for engineering and computer science rise to about 0.134 log points for people born in 1991 or later. The authors also report especially strong increases for cohorts born after 1981. These figures are not themselves age slopes. They describe differences in the level of the major premium across cohorts. But when those cohorts occupy different age positions in a short survey, their level differences can bend the estimated age profile.
This gives us an important distinction between a level shift and a slope change. A level shift means that one cohort starts from a different place: at comparable ages, its members may have a higher or lower premium than an earlier cohort. A slope change means that the premium grows or shrinks at a different rate as that cohort ages. The first can generate a misleading cross-sectional decline even when the second is absent. Establishing the first does not establish the second.
A useful mental experiment is to imagine a chart with two parallel lines. The newer technical cohort’s line sits above the older cohort’s line because its entry premium is larger, but both lines rise at the same rate with age. If a short survey sees the newer line mostly at ages 25–35 and the older line mostly at ages 45–55, connecting all observations produces a downward pattern across age even though neither line slopes downward. The visual chart is not fabricated; it is answering a different question from the one a reader may assume.
The paper tests the cohort explanation against a calendar-time explanation. Returns to a major might change over time because technology changes, employers alter demand, or the economy rewards some skills more than others in particular years. In the long LEHD history, researchers can allow the return to a major to vary by calendar year. If major-by-year changes were the main reason the cross-sectional and panel estimates diverged, adding those interactions should pull the panel profile back toward the short-cross-section result.
It does not do so in the paper’s comparison. The estimates with major-by-year effects are similar to the panel estimates without them and remain different from the cross-sectional estimates. The authors therefore judge calendar-time changes not to be the key driver of the discrepancy, while still finding that technical-major returns rose mildly over time. That is a comparative result, not a claim that calendar time has no economic role. It says that the observed movement between designs is more consistent with cohort-major differences than with a simple common-time shock to technical fields.
This comparison also identifies what new evidence would matter. If allowing major-by-year effects had moved the long-panel profile close to the ACS profile, a period-specific explanation would deserve more weight. If cohort-specific slopes had differed sharply, the claim would need to become “the trajectory varies by generation,” rather than “the cross-section is mainly distorted by different starting levels.” The reported results do neither strongly: calendar-time adjustments leave the main gap, and the two birth-cohort slope estimates are close.
The distinction between a cohort level and a cohort slope is tested separately. The authors split the long panel into workers born by 1970 and workers born after 1970 and estimate profiles with worker fixed effects. At ages 47–48, the engineering-and-computer-science coefficients are 0.039 for the earlier group and 0.040 for the later group. The estimates across the two groups are generally similar. That pattern offers little evidence of a large difference in technical age slopes, even though the level of the technical premium changed across cohorts.
There is a practical reason to keep these tests separate. If newer technical graduates are more positively selected, or if their education contains skills with a higher market value, a short cross-section may exaggerate the appearance of decline. A cohort adjustment can account for the changed starting position in the comparison. It cannot tell us whether the newer graduates learn faster, switch occupations differently, or become exposed to different technology as they age. Those are additional mechanisms requiring additional evidence.
This diagram captures the transition from the snapshot state to the interpretation state. At the snapshot, age is visible but the cohort-specific starting position is partly hidden. Once cohort-major variation is modeled, the observed profile can be decomposed into a level difference and a slope question. Calendar-time variation remains a competing explanation, but it cannot be assumed to be the same as either cohort change or aging.
The important comparison is therefore not simply “cross-section bad, panel good.” A cross-section can be the right tool for describing the earnings distribution at a given moment. A panel can be the right tool for asking how linked workers’ earnings evolve. The two answers can differ without one being an error, because they condition on different information. The paper’s contribution is to show that the strong language of technical skill decay requires the second kind of evidence, or at least a repeated-cross-section design long enough to model changing returns by cohort.
The paper’s evidence favors a disciplined conclusion. In the short ACS data, the technical-major profile is downward relative to the broad comparison group. In the longer panel, recent cohort premiums and additional within-worker information make that profile much less negative or positive. The likely problem is not that age is meaningless; it is that age is standing in for several transitions at once: a worker’s career stage, a generation’s starting position, and the labor market’s calendar.
That conclusion also explains why the correction has a boundary. A study cannot identify every age, period, and cohort effect without assumptions, and the paper’s cohort and year tests are separate approximations. The evidence supports cohort composition as the more plausible explanation for the particular cross-section/panel discrepancy. It does not prove that all technical cohorts have identical careers, or that rapidly changing skills never affect earnings.
The next step is to examine the data transition that makes this comparison possible. The key issue is no longer only which clock matters, but how the study obtains repeated earnings observations for the same workers while retaining their college-major information.