Methods & Data Appendix

Returns to Graduate Degrees in Michigan: Evidence from Administrative Wage Records, 2018–2025

1. Data Source and Provenance

1.1 The MiSchoolData Workforce Reports

We use the "Median Annual Wages by Field of Study" reports published by the Michigan Center for Educational Performance and Information (CEPI) on the MiSchoolData platform (mischooldata.org). These reports are produced annually as part of the Michigan Workforce Longitudinal Data System, a partnership among CEPI, the Michigan Department of Labor and Economic Opportunity (LEO), and the Unemployment Insurance Agency (UIA).

1.2 Underlying Data Systems

The wage reports are constructed by linking three administrative data systems:

• Student Transcript and Academic Record Repository (STARR): Contains enrollment, degree program (CIP code), and completion records for all students at Michigan public community colleges and universities.
• National Student Clearinghouse (NSC) StudentTracker: Supplements STARR with enrollment records from out-of-state and non-STARR-participating institutions, enabling tracking of Michigan high school graduates who attend college elsewhere.
• Unemployment Insurance (UI) Wage Records: Quarterly earnings records submitted by employers to the Michigan UIA. These cover virtually all wage and salary employment in Michigan but exclude self-employment, federal government employment, and out-of-state employment.

1.3 Report Construction by CEPI

CEPI matches education records to wage records to identify each individual's highest level of education and their post-completion earnings. Two cohorts are defined for each annual report:

• Wages After 1 Year: Graduates who completed their highest education credential approximately one year before the reporting period (four quarters of wage data).
• Wages After 5 Years: Graduates who completed approximately five years before the reporting period (four quarters of wage data).

Students who are still enrolled in education at the time of the wage observation are excluded. Individuals must have received their high school education in Michigan and must be currently employed in Michigan to appear in the data. The wage measure is the median annual wage within each cell, rounded to the nearest $100. Cells with fewer than 10 employed individuals are suppressed (wages not reported).

1.4 Years of Data

We use eight annual reports: 2018, 2019, 2020, 2021, 2022, 2023, 2024, and 2025. The 2018–2022 reports contain statewide aggregates only. The 2023–2025 reports additionally contain institution-level (IHE) data and demographic breakdowns by gender, age band, and race/ethnicity.

2. Sample Construction and Variable Definitions

2.1 Unit of Observation

Each observation in the raw data is a cell defined by the combination of: report year, location (statewide or specific institution), diversity type and category (if applicable), wage horizon (1 year or 5 years after completion), CIP code (field of study), and education level. The reported values for each cell are the median annual wage and the number of employed individuals.

2.2 Education Levels

The data classify individuals into four education levels based on their highest credential earned:

• Certificate: Sub-baccalaureate certificate or diploma
• Associate Degree: Two-year associate's degree
• Bachelor's Degree: Four-year baccalaureate degree
• Master's or Higher Degree: Master's degree, professional degree (JD, MD, PharmD, DDS, etc.), or doctoral degree

2.3 Field of Study Classification

Fields of study are identified by Classification of Instructional Programs (CIP) codes at three levels of granularity:

• 2-digit CIP: Broad field categories (e.g., CIP 14 = Engineering). We identify 43 unique 2-digit fields in the data; 27 have reportable master's-level wages.
• 4-digit CIP: Specific program areas (e.g., CIP 14.19 = Mechanical Engineering). We identify 316 unique 4-digit fields; approximately 136 have reportable master's-level wages.
• 6-digit CIP: Detailed program specializations. We identify 970 unique 6-digit fields, though many have small cell sizes.

Our primary analyses use 2-digit CIP codes for robustness and comparability across years. We supplement with 4-digit analyses to achieve closer correspondence with Altonji & Zhu's degree-specific estimates.

2.4 Deduplication

In some years, the data contain multiple rows for the same CIP code at a given level (with slightly different field name strings). We deduplicate by retaining the row with the largest number of employed individuals for each CIP × report year × education level × wage horizon cell. Post-deduplication, each cell is unique.

2.5 Demographic Categories (2023–2025 only)

The 2023–2025 reports provide statewide wage data broken down by three diversity dimensions:

• Gender: Male, Female, Unknown/Unreported
• Race/Ethnicity: American Indian or Alaska Native, Asian, Black or African American, Hispanic of Any Race, Native Hawaiian or Pacific Islander, Two or More Races, White, Unknown/Unreported
• Age Band: 18–24, 25–34, 35–44, 45–54, 55–64, >64

These breakdowns are reported separately from the overall statewide figures and cannot be cross-tabulated (e.g., we cannot observe wages for Black women specifically).

2.6 Institution-Level Data (2023–2025 only)

The 2023–2025 reports include wage data at the individual institution (IHE) level. We observe 43 institutions total, of which 14 report master's-level wage data: Central Michigan University, Eastern Michigan University, Ferris State University, Grand Valley State University, Michigan State University, Michigan Technological University, Northern Michigan University, Oakland University, Saginaw Valley State University, University of Michigan (Ann Arbor), University of Michigan–Dearborn, University of Michigan–Flint, Wayne State University, and Western Michigan University.

3. Estimation: Log Wage Premium

3.1 Core Estimand

For each field of study f, report year t, and wage horizon h ∈ {1, 5}, we compute the log wage premium of a graduate degree over a bachelor's degree:

where W̃ denotes the median annual wage for the indicated education level. This quantity approximates the proportional wage gap: for small values, Δ ≈ (W^MA+ − W^BA) / W^BA. We also report the exact percentage premium: %Δ = (W^MA+ − W^BA) / W^BA × 100.

3.2 Interpretation

The log wage premium is a descriptive measure. It captures the raw difference in median log earnings between graduate and bachelor's degree holders working in Michigan within the same broad field. It does not estimate the causal effect of obtaining a graduate degree, because:

• Individuals who pursue graduate degrees differ systematically from those who do not — in ability, motivation, prior academic performance, family background, and occupational preferences.
• The bachelor's median and master's-or-higher median within a field may reflect very different pools of workers, not the same people with and without a degree.
• We cannot control for undergraduate major, college GPA, demographics, or other confounders that affect both the graduate school decision and subsequent earnings.

The premium should generally be interpreted as an upper bound on the causal return, since positive selection into graduate programs (higher-ability individuals being more likely to pursue advanced degrees) biases the raw gap upward.

3.3 Pooling Across Years

For summary tables, we average the log premium across the three most recent report years (2023–2025) to reduce noise from year-to-year sampling variation while reflecting current labor market conditions. For trend analyses, we report year-by-year estimates.

3.4 Using Medians vs. Means

Our data report median wages, while Altonji & Zhu's regression estimates correspond to effects on the conditional mean of log earnings. In principle, if the earnings distribution is log-normal, the difference in log medians equals the difference in log means. In practice, skewness (particularly for high-earning fields like law and medicine) means our estimates may differ from what a regression on log earnings would produce. We cannot assess the magnitude of this discrepancy without access to the underlying microdata.

4. Synthetic Cohort Panel

4.1 Construction

The synthetic cohort panel exploits the fact that each annual report contains two wage horizons — 1 year and 5 years after completion — which correspond to different completion cohorts. Specifically:

• The "Wages After 1 Year" observation in report year t covers graduates who completed their highest credential in approximately year c = t − 1.
• The "Wages After 5 Years" observation in report year t covers completers from approximately c = t − 5.

A cohort completing in year c therefore appears as "1 year after" in report year c + 1 and as "5 years after" in report year c + 5. With reports spanning 2018–2025, we can link four cohorts at both horizons:

4.2 Within-Cohort Premium Growth

For each linked cohort, we compute the premium at both horizons and measure the change:

where ΔΔ is the within-cohort premium growth for field f and cohort c. This can be decomposed as:

That is, the premium grows if master's holders' wages grow faster than bachelor's holders' wages, and shrinks if the reverse is true. We report both the premium change and the separate wage growth components.

4.3 Assumptions and Caveats

The synthetic cohort approach assumes that the 1-year and 5-year observations within a cohort-field cell reflect approximately the same group of graduates. This assumption can fail due to:

• Differential out-migration: If higher-earning graduates are more likely to leave Michigan between years 1 and 5, the 5-year median will understate true wage growth. This concern is particularly acute for fields like law, business, and engineering where national labor markets may draw talent out of state.
• Selective labor force entry/exit: Individuals who were not employed at year 1 but are employed at year 5 (or vice versa) change the composition of the cell.
• Median sensitivity: Because we observe medians (not means), the addition or subtraction of a few individuals near the median can produce discrete jumps in measured wages that do not reflect actual wage dynamics for any individual.

4.4 COVID-Era Cohort Classification

For the COVID-era analysis, we classify the ~2017 and ~2018 completion cohorts as "pre-COVID" (they entered the labor market before the pandemic) and the ~2019 and ~2020 cohorts as "COVID-era" (they entered during or immediately after the pandemic's initial labor market disruptions). The ~2019 cohort is borderline — they entered the workforce approximately in 2020, at the pandemic's onset. We include them in the COVID-era group because their initial labor market experience was likely disrupted.

5. Relationship to Altonji & Zhu (2025)

5.1 What They Estimate

Altonji and Zhu (2025) estimate causal effects of 121 graduate degrees on log quarterly earnings using Texas Schools Project administrative data, which links individual-level records across high school, college, graduate school, and UI earnings. Their sample comprises approximately 31.5 million person-quarter observations. They employ six estimation strategies:

1. OLS with rich controls (college major × gender age profiles, race/ethnicity, college GPA, college credits, year dummies)
2. FEcg (their preferred): adds fixed effects for each undergraduate major × graduate field combination, absorbing permanent unobserved heterogeneity within these groups
3. FE (individual fixed effects): compares the same individual's earnings before and after graduate school
4. OLS-ps: propensity-score-reweighted OLS
5. FEcg-ps: propensity-score-reweighted FEcg
6. Dale-Krueger method: for institution-specific returns, controlling for application/admission sets

5.2 What We Estimate

Our log wage premium is conceptually most similar to a naïve OLS estimate without individual-level controls — a raw cross-sectional comparison of graduate vs. bachelor's median wages. The key differences are:

5.3 Interpreting the Gap Between Estimates

Our Michigan descriptive premium should systematically exceed Altonji & Zhu's FEcg estimates because our measure does not remove selection bias. The difference provides an informal gauge of selection severity by field. A large gap (e.g., Business: Michigan 5yr = 0.449 vs. AZ FEcg = 0.125) implies strong positive selection — MBA students would have earned substantially more than the average bachelor's holder even without the degree. A small gap (or a Michigan estimate below the AZ estimate) would suggest either negative selection, different field composition across states, or measurement differences.

5.4 Cross-State Comparability

Despite different data structures and methods, the cross-field ranking of graduate degree returns is broadly consistent between Michigan and Texas. This suggests the rank ordering of returns is driven by fundamental labor market forces (human capital accumulation, professional licensing requirements, occupational wage structures) rather than state-specific factors.

6. Heterogeneity Analyses (Phase 3)

6.1 Gender and Race/Ethnicity

Using the 2023–2025 demographic breakdowns, we compute the log wage premium separately by gender and by racial/ethnic group. The formula is the same as in Section 3.1, applied within each demographic cell. We average across the three available years to improve precision.

Because the demographic breakdowns cannot be cross-tabulated (we observe wages by gender or by race, not by gender × race), these analyses are necessarily univariate. We also cannot condition on other covariates (age, undergraduate major) within a demographic group.

6.2 Institution-Specific Returns

Using institution-level data from 2023–2025, we compute the log premium for each IHE that reports both bachelor's and master's-or-higher wages in a given field. We restrict attention to the 14 universities with master's-level data. For institution-specific returns by program rank, we correlate our institution-level premia with U.S. News & World Report program rankings, analogous to Altonji & Zhu's Figure 3.

Unlike Altonji & Zhu, we do not have application/admission data and therefore cannot implement the Dale-Krueger selection correction. Our institution-level estimates reflect both the causal effect of the institution and selection into institutions based on unobserved characteristics.

7. Approximate Internal Rate of Return (Phase 4)

7.1 Approach

We compute approximate internal rates of return (IRR) following the logic of Altonji & Zhu's Table 4. The IRR is the discount rate at which the present discounted value of the earnings stream with a graduate degree (net of tuition) equals the present discounted value of the counterfactual earnings stream without a graduate degree.

7.2 Inputs

• Post-degree earnings: Median wages from the Michigan data at the 1-year and 5-year horizons, interpolated and extrapolated as needed.
• Counterfactual earnings: Bachelor's median wages in the same field and year, serving as the proxy for what the graduate degree holder would have earned without the degree.
• Tuition: Sourced from IPEDS for Michigan institutions, by degree type and year. We use average tuition at public institutions.
• Program duration: Assumed from standard program lengths, calibrated to Altonji & Zhu's Table A2.1 where possible.

7.3 Limitations of the IRR Calculation

Our IRR estimates are rougher than Altonji & Zhu's because we lack individual-level earnings trajectories, data on earnings during enrollment, and the ability to condition on individual characteristics. The bachelor's median is an imperfect counterfactual. We report IRR estimates as indicative of the relative ranking of fields, not as precise point estimates of the financial return to any individual.

8. Limitations

8.1 No Causal Identification

This is the most fundamental limitation. Without individual-level data, we cannot implement any of the standard methods for addressing selection into graduate programs — individual fixed effects, FEcg, propensity score methods, instrumental variables, or regression discontinuity designs. Our estimates should be interpreted as descriptive wage premia, not causal returns.

8.2 Coarse Degree Classification

The "Master's or Higher Degree" category bundles master's degrees with professional degrees (JD, MD, PharmD, DDS, DVM) and research doctorates (PhD). Within a broad CIP category, this mixes programs with very different labor market returns. For example, at CIP 51 (Health Professions), our "Master's or Higher" category includes nursing master's students (moderate wages), physicians (very high wages), and public health master's students (moderate wages). The 4-digit CIP analysis mitigates this to some extent but does not fully resolve it.

8.3 Michigan Employment Only

The wage data only cover individuals employed in Michigan. Graduates who leave the state are excluded. If higher-earning graduates are more likely to move out of state (particularly from flagship programs in law, business, and medicine), our estimates understate the true returns for those fields. Altonji & Zhu note the same concern for Texas, citing Foote and Stange (2019), who find that individuals from flagship universities are more likely to move out of state.

8.4 Median vs. Mean

We observe medians, not means. Regression-based estimates (like Altonji & Zhu's) estimate effects on conditional means of log earnings. In fields with right-skewed earnings distributions (law, medicine, business), the mean and median of log earnings can differ, making direct comparison imprecise.

8.5 No Undergraduate Major Information

We cannot condition on undergraduate major, which Altonji & Zhu show is critical. Their Table 5 demonstrates that returns to an MBA vary from 0.066 for computer science majors to 0.326 for education majors. Our estimates average over all undergraduate backgrounds within a field.

8.6 Cross-Sectional Counterfactual

Our "counterfactual" — the bachelor's median in the same field — is the earnings of people who completed a bachelor's degree in that field, not the earnings that the graduate degree holder would have earned without the graduate degree. These can differ if graduate students come from different undergraduate majors than the bachelor's-only workers, or if they would have worked in different industries or occupations.

8.7 Suppression Bias

Cells with fewer than 10 employed individuals have suppressed wages. This may create bias if smaller programs have systematically different returns. We limit our analysis to non-suppressed cells, which tend to be larger and more established programs.

9. Robustness and Sensitivity

9.1 Stability Across Years

We assess robustness by examining whether cross-field rankings are stable across the eight years of data. For most fields, the rank ordering of premia is highly consistent year-to-year. The Spearman rank correlation of field-level premia between any two consecutive years exceeds 0.85 in most cases.

9.2 2-Digit vs. 4-Digit Estimates

Where both are available, 4-digit estimates sometimes diverge from the 2-digit aggregates, which is informative about within-field heterogeneity. For example, CIP 52 (Business) at 2-digit yields a 5-year premium of 0.449, while CIP 52.02 (MBA specifically) yields 0.525. The difference reflects that MBA students outperform the average business graduate degree holder, consistent with the MBA being the highest-return degree within business.

9.3 Cohort Consistency

We examine whether the synthetic cohort results are driven by any single cohort by comparing within-cohort premium growth across all four linkable cohorts. For most fields, the four cohorts produce qualitatively similar patterns, though individual cohort estimates can be noisy for smaller fields.

Appendix A: Data Inventory

A.2 CIP Code Coverage

A.3 Institutions with Master's-Level Wage Data

Central Michigan University, Eastern Michigan University, Ferris State University, Grand Valley State University, Michigan State University, Michigan Technological University, Northern Michigan University, Oakland University, Saginaw Valley State University, University of Michigan (Ann Arbor), University of Michigan–Dearborn, University of Michigan–Flint, Wayne State University, Western Michigan University.

A.4 Synthetic Cohort Panel Coverage

100 linkable cohort-field cells across 4 cohorts (~2017, ~2018, ~2019, ~2020) and 27 2-digit CIP fields.