From Snapshots to Earnings Histories
The subject of this chapter is the matched ACS–LEHD design used to study college-major earnings profiles. Its focus is practical: what does each dataset know, what crosses the boundary between them, and why does a long earnings history provide different evidence from a one-year comparison of workers at different ages? By the end, readers should be able to judge the strength of the design without confusing more observations with automatically better identification.
Four pieces of the matched design
The study works because the two data systems contribute different pieces of the same person’s record. The American Community Survey supplies information that is essential to the question: a respondent’s college major and other characteristics reported around the time of the survey. The Longitudinal Employer–Household Dynamics data supply something the ACS does not: earnings observed repeatedly through employment records. Neither source, by itself, provides the full comparison the paper needs.
The ACS is the label-bearing side of the design. For the main comparable sample, the researchers use 2009–2017 respondents between ages 23 and 50 who have at least a four-year college degree, a valid major, nonmissing earnings and occupation, and no military occupation. The major is grouped into broad categories so that engineering and computer science can be compared with business, life and physical science, social science, and the large “other” category. Those categories are not interchangeable: the last includes humanities, education, health, vocational fields, and related degrees.
The LEHD is the history-bearing side. It is built from linked employer–employee records and provides annual earnings histories from quarterly observations. The paper has access to records from 27 states, representing approximately 65 percent of the U.S. workforce, and uses earnings before 2020 to avoid complications associated with the COVID-19 period. The LEHD infrastructure covers more than 95 percent of U.S. employment, but the study’s usable sample is narrower than that national infrastructure because the researchers work with the states and linked ACS respondents available to them.
The boundary between the two systems is the linkage. The LEHD does not carry the college-major field needed for the analysis. The authors therefore use unique person identifiers to connect someone appearing in the ACS to the person’s earnings records in the LEHD. In the resulting record, the major comes from the survey side and the earnings history comes from the employment side. This is the crucial interface: information about educational field crosses into a database whose strength is labor-market continuity.
After the match, the authors construct one observation per person per year. Annual earnings are formed by adding earnings across the quarters, jobs, and states in which a person appears during that year. They also retain the number of quarters with positive earnings. That second measure matters because a lower annual total can result from earning less while working, working fewer quarters, or both. The data design does not solve that distinction by itself, but it makes the distinction observable enough to examine later.
This aggregation is a substantive choice, not just a formatting step. A worker can have more than one job in a year, move between covered states, or have a year with employment in only some quarters. Summing the records produces a yearly labor-market outcome that is closer to the question about annual earnings, but it also combines several events into one total. The quarters-worked count preserves one additional signal about those events. It cannot say exactly how many hours a person worked or what their wage was in every job, so later interpretations must not call every change in the total a change in skill value.
The scale of the resulting system illustrates the trade-off. The ACS sample contains about 2.8 million people with, on average, one survey observation each. The linked baseline LEHD sample contains about 2.4 million people but roughly 38 million person-years; each individual is observed for an average of 18.3 years. The panel has fewer people because the geographic and matching requirements are stricter, yet it has far more information about how earnings change over time for those who remain in the linked sample.
The matching does not appear to create a completely different major distribution. Engineering and computer science account for roughly 13 percent of people in both the ACS and baseline LEHD samples, business for about 20 percent, and the broad other group for about half. That similarity helps the comparison, because the dramatic change in the estimates cannot be dismissed simply as the linked sample containing no comparable fields. It still does not establish that every subgroup is equally represented: a similar overall composition can conceal differences in location, age coverage, or the kinds of people whose records can be linked.
The interface also determines what travels with a worker and what does not. The ACS contributes a major label and survey characteristics at the time of observation; it does not turn the LEHD into a complete educational biography. The LEHD contributes a repeated earnings record; it does not independently tell the analyst which degree field to assign. Treating the combined record as if one source measured everything would hide the dependency that makes the design possible.
The sequence is not a claim that one database governs the other. Each side retains a different kind of state. The ACS preserves the educational field and the survey context; the LEHD preserves repeated labor-market observations. The linkage creates a combined analytical record, but it also creates a dependency: the major-specific result applies only where the survey label and the employment history can be connected reliably.
It also explains why the authors run a matched cross-section before exploiting the full history. If the pattern changed immediately after restricting the ACS to people who can be linked, the selection or geography of the linked sample would be a plausible explanation. If the pattern changed only after adding earlier and later LEHD observations, time depth would carry more of the explanation. If it changed again after worker fixed effects, persistent person-level differences would matter as well. The design is strongest when these interfaces are tested in sequence instead of treated as one indivisible data merge.
What the design can see—and what it cannot
It helps to distinguish four comparisons that can be made after the linkage. The first is the original ACS comparison: each person contributes the survey-year earnings and major information observed at one point. The second uses the same people who can be matched to LEHD, but still uses only the earnings measure from their ACS survey year. This checks whether geography or the selected linked sample alone explains the result.
The third uses those same workers’ LEHD earnings in all available years. Now a person who appears in the ACS at one age can contribute observations from other ages, and the analysis no longer relies as heavily on placing different cohorts at different points on the profile. The fourth adds worker fixed effects. This does not create a new observation; it changes the comparison by accounting for permanent, unobserved differences in a worker’s earnings level. The sequence therefore changes two things separately: time depth first, then the treatment of persistent individual heterogeneity.
That separation is important. If the estimate changes when the analysis moves from the ACS survey year to the full LEHD history, the additional years are doing meaningful work. If it changes again when worker fixed effects are included, the result is also sensitive to stable differences among people. A reader who sees only the final coefficient cannot tell which of those transitions mattered. A reader who follows the nested design can.
The time span is what makes the first transition valuable. LEHD earnings are available from 1985 to 2022 in the underlying data, although the paper restricts its main analysis to pre-2020 earnings and the initial year varies by state. The ACS observations used to assign majors are concentrated in the recent period from 2009 to 2019, while the linked employment histories extend much farther back. As a result, young workers can be observed in earlier calendar years and older workers in later years. This gives the model more within-person and within-cohort information than a short recent survey alone.
More time does not mean unlimited visibility. The baseline analysis still restricts workers to ages 23–50 when estimating the profiles, and the major label must come from an ACS observation. The 27-state coverage means that the linked sample is not a complete national panel. Matching can also affect who enters the analysis: a person must be observed in the relevant ACS sample and have a usable link to the employment records. These are design boundaries, not footnotes to be dropped once the panel looks persuasive.
The earnings measure creates another boundary. ACS earnings are self-reported annual amounts, while LEHD earnings are derived from unemployment-insurance records. The paper compares them and finds that switching from the ACS measure to the LEHD measure in the matched survey-year sample has little impact on the estimated major-specific profiles. That is reassuring for the central comparison, but it does not make the measures identical in every respect. Administrative continuity and survey context are different sources of information, with different possible errors.
That comparison functions as a measurement check. It asks whether the cross-sectional pattern is mainly an artifact of respondents reporting earnings differently from the employment records used in the panel. The answer in the paper is largely no: the age-profile estimates are similar when the outcome changes but the matched people and regressors stay fixed. The remaining discrepancy between the short cross-section and the full panel therefore cannot be assigned automatically to a reporting difference. It points back toward the information gained from observing histories and modeling who those histories belong to.
Nor does annual earnings equal an hourly wage. Summing quarterly earnings across jobs and states captures the amount recorded over a year, not only the price of an hour of labor. The number of quarters with positive earnings supplies a rough indicator of labor-market attachment, but it does not fully measure hours, occupation, or the intensity of work within a quarter. This is why the panel’s labor-supply variable is useful as a diagnostic rather than a complete decomposition of pay.
The design also does not turn major choice into an experiment. People with different majors can differ in preparation, preferences, location, institutions attended, occupation, and other characteristics. Worker fixed effects remove permanent individual components of earnings that are stable enough to be captured in the model, but they do not recreate the earnings path a person would have had under a different major. The result is best understood as a more disciplined relative profile, not as the causal payoff to switching fields of study.
This limitation is compatible with the design’s value. A better comparison need not answer every possible question to answer one important one more credibly. Here, the relevant improvement is moving closer to the question “how do earnings profiles evolve for linked workers with different majors?” It is not answering “what would this exact worker have earned after changing majors?” Keeping those questions separate prevents the panel from being oversold and preserves the reason to use it.
There is a final trade-off between breadth and continuity. A one-time ACS sample can include many people and offer broad population information, but it sees each person briefly. The linked LEHD sample follows fewer states and depends on a successful match, but it records many more person-years. The paper chooses continuity because the question is about lifecycle growth. That choice improves the age comparison while narrowing the population to which the estimate can be applied.
The data design therefore changes the question in stages. At the first stage, the analyst sees the distribution of earnings by major among people observed at different ages. At the second, the analyst sees a longer sequence for the same linked workers. At the third, the analyst asks whether the profile remains after stable worker differences are taken out. Each transition preserves some information and exposes a different limitation. The strength of the final conclusion depends on keeping those transitions visible rather than describing the entire process as simply “using better data.”
The next issue is how those nested comparisons alter the actual estimates. The key question is whether the apparent technical-major penalty disappears because the panel adds years, because fixed effects change the comparison, or because both changes work together.