How We Calculated the Return on Investment of a Graduate Degree

Our paper Is Graduate School Worth It? A Comprehensive Return on Investment Analysis calculates the net financial gains (increase in earnings minus education costs) that students can expect from nearly 14,000 advanced degree programs across the United States. This page describes the methodology underlying the return on investment (ROI) calculation for graduate programs.

Much of the strategy is similar to the methodology for our bachelor’s degree ROI analysis, but there are important differences. The data sources that inform the ROI calculation for graduate programs differ in key ways from the data sources for bachelor’s degree programs.

Like the ROI of a bachelor’s degree, the ROI of a graduate degree incorporates three main elements:

• Estimated earnings: The amount that a student who earns a particular advanced degree can expect to earn over the course of her career.
• Counterfactual earnings: The amount that the same student would have earned over the course of her career had she finished her bachelor’s degree but not attended graduate school. This includes foregone income while the student is earning her graduate degree.
• Graduate school costs: The amount that the student spends on tuition and required fees.

ROI is equivalent to estimated earnings minus the sum of counterfactual earnings and graduate school costs. In the following sections, I describe how I calculated each of these components individually. All cash flows are discounted at a real 3 percent rate to the year in which the student begins graduate school (which varies by degree type, as discussed further on), unless otherwise noted. I adjust all figures to 2020 dollars.

Estimated earnings

The earnings calculation combines two sources of data: the U.S. Department of Education’s College Scorecard by Field of Study and the U.S. Census Bureau’s American Community Survey (ACS). The Scorecard provides information on the median earnings of advanced degree recipients after completion for over 14,000 different programs.

Scorecard earnings are defined as the sum of wage and salary (Form W-2) income and positive self-employment income for individuals who received federal Title IV financial aid. Median earnings are currently reported for program graduates during the first two years after degree completion. Individuals who are not employed are excluded from the earnings cohorts. Graduate programs with small cohort sizes are excluded from the data for reasons of privacy, though the vast majority of federally aided students are in programs with reportable earnings data. According to Scorecard documentation, 90 percent of federally aided master’s degree recipients were in programs with reportable data, along with 99 percent of recipients of first-professional degrees. Only 58 percent of doctoral degrees recipients had reportable earnings data.

The generally high coverage rate is encouraging. However, the Scorecard’s central limitation is that it only reports earnings for the first two years after degree completion. Looking beyond two years requires the use of an additional data source, the American Community Survey. These data are provided by the IPUMS USA database at the University of Minnesota. ACS data allow the extrapolation of Scorecard earnings for each program over the course of graduates’ careers.

The Census Bureau surveys a 1 percent random sample of the U.S. population every year, collecting basic demographic data along with information on individuals’ earnings. Since 2009, the ACS has asked bachelor’s degree holders about their undergraduate college major, though it does not ask respondents where they attended college. More critically, the ACS does not ask individuals about the field of study of their graduate degree — only the level of the highest graduate degree ever obtained (master’s, doctoral, or professional).

Using ACS to estimate the earnings associated with each graduate degree requires knowing each ACS respondent’s graduate field of study, or at least imputing it. It is possible to impute each respondent’s graduate field of study by looking at their undergraduate field of study, which ACS does record. Certain undergraduate majors are more likely to lead to specific graduate degrees. If we observe an individual in ACS with a bachelor’s degree in psychology who also has a master’s degree, we can infer the likelihood that her master’s degree is also in psychology. But this strategy requires the use of a dataset which records both undergraduate and graduate fields of study.

Fortunately, such a dataset exists: the National Survey of College Graduates (NSCG). A project of the National Science Foundation, NSCG is a stratified random sample of individuals with a bachelor’s degree or higher. Recent waves of NSCG take their sample of individuals directly from ACS. For the purposes of this analysis, I use a combined sample of respondents from the 2010, 2013, 2015, 2017, and 2019 waves of NSCG. Some respondents were sampled repeatedly across different waves; I use only each individual’s first survey response and drop subsequent ones.

This yields a sample of 89,963 individuals with some graduate education. There are 285 uniquely identifiable graduate degrees in NSCG: 136 master’s degrees, 135 doctoral degrees, and 14 first-professional degrees. For each of these 285 graduate degree categories, I calculate the distribution of undergraduate fields of study. I drop graduate degrees for which there are fewer than 15 observations in NSCG due to the unreliability of small sample sizes. (Fortunately, 95 percent of enrollment-weighted degrees in the College Scorecard have at least 100 corresponding observations in NSCG.)

I save the results as a matrix with 285 rows and 129 columns. Each row corresponds to a graduate degree and each column corresponds to a bachelor’s degree. The cells record the percentage of individuals with each college major, for each of the 285 unique graduate degrees. Rows sum to 100 percent; columns do not.

The example of my own graduate degree, a PhD in economics from George Mason University, may help to illustrate the procedure. Among NSCG respondents with a doctoral degree in economics, 69 percent have an undergraduate degree in economics, 6 percent have an undergraduate degree in mathematics, 4 percent have an undergraduate degree in business administration and management, 3 percent have an undergraduate degree in financial management, and the remainder have undergraduate degrees in other fields. All these percentages are recorded in the row corresponding to doctoral degrees in economics.

With this matrix in hand, I turn back to ACS. I use a subsample of ACS datasets for the years 2009 through 2019. The combined subsample includes individuals with any graduate education between the ages of 26 and 65. (Earnings are reported for the previous year, so this effectively gives me a sample of incomes for people between 25 and 64.) To align with the cohort definition in the Scorecard, I exclude those currently enrolled in school or college, people who are unemployed or not in the labor force, and anyone with real earnings below $10,000 per year (as this may signal nonemployment in the previous year, when earnings were measured). This yields a sample of approximately 1.7 million observations.

I divide the ACS sample into eight groups of five years each, starting with ages 26 to 30 (corresponding to earnings at ages 25 to 29). I then calculate the mean and standard deviation of the natural log of personal income for each of the 285 unique graduate degrees in NSCG, within each age group. In order to estimate these statistics for each graduate degree, I limit the ACS sample to those with the applicable graduate degree level and reweight observations in ACS such that the distribution of undergraduate majors in ACS matches the distribution of undergraduate majors from NSCG.

For example, in calculating earnings for people who hold a doctoral degree in economics, I first limit the ACS sample to individuals with a doctoral degree. I then adjust the weights of these individuals such that individuals with an undergraduate degree in economics account for 69 percent of the weighted sample, since NSCG tells us that 69 percent of people with a doctorate in economics have also a bachelor’s degree in economics. Individuals with an undergraduate degree in mathematics account for 6 percent of the weighted sample, as they account for 6 percent of economics doctorates, and so on. When reweighting the sample in this way, I preserve the relative ACS weights among individuals with the same undergraduate major.

I use results for the age bands to interpolate the mean and standard deviation of log individual earnings for each graduate degree at each age, 25 to 64. These figures are merged to their corresponding graduate degrees in the Scorecard.

Recall that the Scorecard contains data on earnings for graduates of individual programs one and two years after degree completion. It is therefore possible to compare Scorecard earnings to the mean earnings for the applicable graduate degree group from ACS. This will tell us whether an individual graduate program is above or below average for its degree group, which in turn allows an extrapolation of earnings over the career.

The National Postsecondary Student Aid Study (NPSAS) collects data on the median age of graduation for individuals who complete various advanced degrees. Those ages are reported in the table below. I use the median age of graduation to determine which ACS age category I should compare Scorecard earnings to. For instance, the median age of graduation for a doctoral degree in the social sciences is 32. I therefore compare doctorates in economics in the College Scorecard to mean ACS earnings at ages 33 and 34.

Specifically, I calculate a Z-score for each program in the Scorecard. The Z-score is equivalent to the log difference between Scorecard earnings and ACS earnings for the corresponding graduate degree and age group, divided by the ACS standard deviation for that graduate degree and age group. In simpler terms, the Z-score is a measure of how high or low a Scorecard observation is relative to the average of its degree group.

Consider the following example, again using the doctoral degree in economics at George Mason University.

The Scorecard reports that average earnings in the two years after graduation are $79,623 (11.29 in log terms). ACS mean earnings for economics doctorates are $95,803 (11.47) at age 33 and $99,460 (11.51) at age 34, for a log average of 11.49. GMU economics doctorates are therefore 0.21 log points below the estimated average for economics doctorates. The average ACS log standard deviation is 0.68. Dividing the mean absolute deviation (0.21) by the standard deviation (0.68) yields a Z-score of -0.31.

I repeat this process for all 14,000 graduate degrees with data in the Scorecard. The weighted average Z-score for all programs is -0.076, suggesting that Scorecard earnings undershoot ACS earnings by a small margin. The likely explanation is that individuals who did not use federal financial aid are excluded from the Scorecard earnings cohorts, while ACS earnings data includes everyone. Individuals with higher salaries are, all else being equal, less likely to use federal financial aid for graduate school, since they may be able to finance tuition out of savings. This speaks to a larger caveat the reader should bear in mind: the methodology in this report can only estimate ROI for individuals who use federal financial aid.

Having calculated Z-scores for all Scorecard observations, I use the ACS means and standard deviations for subsequent age groups to generate earnings estimates for each Scorecard program at all points during graduates’ careers. The key assumption is that median earnings for each program retain the same Z-score (relative to ACS earnings for that major) at all ages throughout the life-cycle. I also smooth the Scorecard’s earnings estimates for the first two years after graduation using the same methodology.

For instance, at age 45, ACS mean earnings for economics doctorates are $128,177 (11.76 in log terms) and the ACS standard deviation is 0.75. Assuming that graduates of George Mason University’s doctoral economics program retain the same Z-score at age 45 (-0.31), I can estimate their log earnings by calculating 11.76 + (-0.31*0.75) = 11.53. Log earnings of 11.53 translate to absolute estimated earnings of $101,390.

The calculations yield estimates of average earnings for every year from graduation until retirement (assuming age 65). I discount all earnings estimates at a 3 percent rate to the year before the student begins her graduate degree. I also assume that earnings are zero while the student is enrolled in graduate school.

Counterfactual earnings

With earnings estimates in hand, I now turn to the calculation of counterfactual earnings — what graduates of each advanced degree program would have earned had they never attended graduate school. As different graduate degree programs attract students with different types of undergraduate education, counterfactual earnings will vary considerably. An advanced degree program that attracts engineering majors will have much higher counterfactual earnings than a program which attracts philosophy majors.

To estimate counterfactual earnings, I return to the ACS. I take a subsample of individuals with exactly a bachelor’s degree (meaning I exclude those with any graduate education). I drop individuals younger than 24 or older than 65, which gives me a sample of earnings for people aged 23 to 64. I also drop people who are unemployed, people who are enrolled in school or college, and people whose prior year income was less than $10,000. These exclusions yield a sample of 2.7 million individuals.

I use this sample to build an Ordinary Least-Squares (OLS) regression model that predicts log personal income based on age, sex, race, ethnicity, state, metropolitan area, and undergraduate major. I then use the results of this regression to predict counterfactual earnings for each graduate degree based on the characteristics of each program’s students.

I then collect data on the gender and racial makeup of each program’s graduates from the Integrated Postsecondary Education Data System (IPEDS). My model adjusts counterfactual earnings based on these demographic characteristics. For instance, women tend to have lower earnings than men, so programs with more women have lower counterfactual earnings, all else being equal. The model also adjusts counterfactual earnings based on the location of the school. College graduates in New York tend to have higher earnings than college graduates in Mississippi, so graduate programs at institutions in New York have higher counterfactual earnings than programs at institutions in Mississippi.

There is another tool available to help us estimate counterfactual earnings for graduate degrees: each individual’s undergraduate major. Using the matrix of the distribution of undergraduate majors for each graduate program derived from NSCG, I also adjust counterfactual earnings based on undergraduate major composition. Programs that attract more students from high-earning majors like engineering or economics will have higher counterfactual earnings. It follows that such programs will need to “work harder” in order to supply their graduates with earnings that exceed the counterfactual.

The GMU economics doctorate example helps illustrate how the model predicts counterfactual earnings. For this program, the hypothetical counterfactual individual is a college graduate living in the state of Virginia and the Washington, D.C. metropolitan area. This fictional individual’s earnings are weighted based on gender (the doctoral program is 25 percent female), race/ethnicity (the program is 74 percent non-Hispanic white) and undergraduate major (recipients of a doctoral degree in economics have economics as an undergraduate major 69 percent of the time).

The regression model provides an estimate of counterfactual earnings after adjusting for basic demographics, geographic location, and undergraduate degrees. But other factors may influence counterfactual earnings, such as unobserved ability and motivation. The choice to pursue a graduate degree may be correlated with such unobservable factors, meaning an adjustment for those factors is necessary.

Using data from NSCG, Altonji and Zhong (2021) (hereafter AZ) have produced estimates of the appropriate adjustment factor. AZ run several regressions on a longitudinal sample of college graduates from NSCG, using log income as a dependent variable and including binary variables for each of 19 different graduate degree categories. An OLS model, which accounts for demographics and undergraduate major but not for unobservable factors, estimates the raw, unadjusted earnings premium associated with a graduate degree. AZ also estimate specifications which include person-level fixed effects (FE), which allow them to compare individual earnings before and after going to graduate school. By effectively using each student as her own control, this provides a reasonably unbiased estimate of the true earnings premium attributable to the graduate degree.

For each of the 19 graduate degree categories, I subtract the coefficients in the FE specification (averaged across AZ’s two FE estimates) from the coefficients in the OLS specification. The result is the portion of the graduate degree earnings premium, expressed in log points, that is attributable to unobservable individual characteristics. The result, known as the adjustment factor, is reported in the table below.

The adjustment factor is high for some graduate degrees, such as the MBA, which suggests that individuals who select into MBA programs have higher preexisting earnings potential than their peers with similar demographics and undergraduate education. But the adjustment factor is lower and even negative for other degrees, such as the master’s in biology, which suggests that individuals who select into a master’s in biology have lower preexisting earnings potential than their peers.

Note that AZ do not estimate coefficients for doctoral degrees. To determine the adjustment factor for these degrees, I turn to the National Longitudinal Survey of Youth (NLSY), using a strategy similar to the one I used to calculate the adjustment factor for bachelor’s degrees (see this page for details). The resulting adjustment factor for doctoral degrees is 0.06 log points.

I add the adjustment factor to my estimated counterfactual earnings for each major. For instance, estimated counterfactual earnings for GMU economics doctorates are $90,770 (11.41 in log points) at age 33, before making the selection bias adjustment. I add 0.06 to the log value to make the adjustment. My final estimate of counterfactual earnings for this program at age 33 is $96,382 (11.47 in log points). Note that I must assume that the appropriate adjustment factor remains constant throughout the year.

I discount counterfactual earnings at a 3 percent rate to the year before the student begins her graduate degree. This year is equal to the median age of graduation minus the typical program length. Master’s degrees are assumed to last one or two years, law degrees last three years, medical and other professional health degrees last four years, while PhDs and equivalent doctoral degrees last five years. For GMU’s economics doctorate, the median age of graduation is 32, and the typical program length for a PhD is five years, so the base year for the present value calculations is the year in which the student is age 27.

The chart below shows estimated vs. counterfactual earnings for GMU economics doctorates at all stages of the career. Earnings while enrolled are assumed to be zero, and earnings and counterfactual earnings before the program begins do not contribute to the calculation (since those occurred before the decision to attend graduate school). The present discounted value of lifetime earnings for GMU economics doctorates is $1.7 million, while the value of counterfactual earnings is $2.2 million, including foregone earnings during the five years that students are enrolled in school. The doctorate is therefore projected to reduce lifetime earnings by over $500,000.

Costs of graduate school

The final step in the ROI calculation is graduate school costs. There are two main components of college costs: tuition and required fees, and the opportunity cost of foregone income while enrolled in school. Foregone income is already accounted for in the counterfactual earnings calculation, so this section will focus on tuition and fees. I do not count living expenses as a cost of graduate school, as individuals must pay for the basic costs of living regardless of whether they pursue a graduate degree. While living expenses may present a financial barrier for some students, they are not a cost that arise because of the decision to attend graduate school.

The Integrated Postsecondary Education Data System (IPEDS) provides data on “sticker-price” tuition and required fees at the institution level for graduate programs. Tuition rates for law and medical programs are reported separately; I use these figures for law and medical programs in the Scorecard dataset. Otherwise, I use the headline graduate tuition number. I use in-state tuition for public universities that charge differential tuition by residency. About 200 programs in the dataset do not match to tuition data from IPEDS; I drop these.

The central challenge in estimating the tuition costs of graduate school is that IPEDS does not report data on the net price paid by students in graduate programs. Generous financial aid is less common at the graduate level than the undergraduate, but it is still an important feature of the graduate education system. While there is no way to systematically collect data on net price at the institution level, data does exist at higher levels of aggregation.

I turn back to NPSAS for this data. NPSAS, an official survey of stratified random sample of graduate students, collects information on both the published and net tuition that graduate students pay. Dividing net tuition by published tuition yields a “discount factor” which can be applied to IPEDS data on published tuition. The sample size of NPSAS is too small to provide reliable estimates at the institution level, so I analyze the data at the sector-program level. For instance, while I cannot estimate a discount factor for GMU’s economics doctorate, NPSAS can provide an estimate of discount factors for all doctoral programs in the social sciences at public universities.

The following table provides the NPSAS estimates of discount factors that I use in the analysis. Each number is equal to the average net price paid by students in that sector-program group, divided by the average sticker price. I use these factors to discount the IPEDS estimates of sticker prices.

For instance, the estimates imply that students in social science doctoral programs at public institutions pay 49 percent of the sticker price, on average. IPEDS reports that GMU charged its in-state graduate students a sticker price of $14,436 while the Scorecard cohort was enrolled. I multiply $14,436 by the discount factor of 49 percent for this sector-program category to arrive at an estimate of the annual net price for students of GMU’s economics doctoral program, which is $7,131.

I discount tuition cash flows at a rate of 3 percent to the year in which the student begins their graduate program. Master’s students are assumed to be responsible for one to two years of tuition, law students three years, medical and other professional health students four years, and PhD students five years. I subtract the present value of these tuition payments from the estimated lifetime earnings boost. For GMU doctoral economics students, this reduces the estimated lifetime payoff from negative $528,000 to negative $561,000.

Adjustment for completion outcomes and full cost of education

The ROI calculation described above provides a “clean” measure of the financial value of a graduate degree — it assumes that the student has a 100 percent chance of completing the degree and is responsible for only the costs of tuition, not the full underlying cost of the education. But even at the graduate level, completion is not a certainty, and most students receive a subsidy on their education. A more comprehensive measure of ROI would take these facts into account.

Unlike at the undergraduate level, institution-level data on completion rates for graduate programs does not exist. I therefore rely on completion rates at higher levels of aggregation. Another Department of Education survey, the Baccalaureate and Beyond survey of 2008–2018 (B&B), may be used to provide reasonable estimates of completion rates at the sector-credential level.

B&B is a random sample of individuals who earned a bachelor’s degree in the 2007–08 academic year. I use a subsample of B&B respondents who enrolled in a graduate degree program by 2012, and then record the proportion of this sample who had finished their degree program by 2018. This may be interpreted as the share of students who complete their degree programs within 6 to 10 years of enrollment; I assume that individuals who do not finish within this window do not finish at all.

For instance, I estimate a completion rate of 65.2 percent for students in doctoral degree programs at public universities. Completion rates for other credentials are higher, averaging 80 percent for master’s degrees and 88 percent for professional degrees. These figures align with other sources of data on graduate completion rates — for instance, the Association of American Medical Colleges estimates that the completion rate for medical students in four-year programs is around 84 percent.

Lacking any more comprehensive data on graduate school completion rates, I assume that completion rates are constant across all programs in the same level and sector. This assumption is almost certainly wrong — there is tremendous variation in dropout rates among law students at different schools, for example. The assumption will cause better-quality programs with higher completion rates to look worse in the ROI calculation, though the results should be unbiased when examined in the aggregate.

I assume that the completion rate reflects the likelihood of finishing the degree on time and therefore securing the associated earnings gains. For students who fail to complete their programs, I assume they drop out halfway through and therefore are responsible for half the tuition costs and half the foregone earnings. Non-completers enjoy none of the earnings gains associated with the degree. I combine these probabilities and compute a weighted-average ROI across the two possible completion outcomes.

In addition, most graduate students do not bear the full cost of their education, especially those at public universities who can pay in-state tuition subsidized by taxpayers. While students should be most interested in “private” ROI — the boost in earnings compared to net tuition costs, other stakeholders may want to consider “social” ROI — the boost in earnings compared to underlying spending per student.

In the “social” ROI calculation, I replace net tuition with the college’s education-related spending per full-time equivalent student. Education-related spending is the sum of spending on instruction, academic support, student services, and institutional support (administration). It excludes spending on research and public services, as well as spending on auxiliary enterprises such as dormitories and independent operations such as hospitals.

Most programs in the Scorecard dataset have lower net tuition than per-student spending. However, around 1,000 programs — mostly at expensive private nonprofit schools — have lower per-student spending than tuition, suggesting graduate students cross-subsidize undergraduates. In these cases, adjusting for underlying spending raises my estimates of ROI rather than lowering them.

ROI of lifetime learning

The ROI of lifetime learning calculation in the main paper computes the combined ROI of 20 popular combinations of bachelor’s and graduate degrees. Together, the 20 combinations listed account for 20 percent of all graduate degrees conferred. As many students begin their undergraduate education with the intention of earning a graduate degree, it is worthwhile to consider the “lifetime ROI” of their educational plans.

I compute ROI of lifetime learning as follows: I total estimated lifetime earnings with the graduate degree, adding any income that students may earn during the intermediate period after they finish college but before they begin graduate school. I then subtract the lifetime counterfactual earnings associated with the bachelor’s degree, since the appropriate counterfactual scenario to a bachelor’s-graduate combination is not going to college at all. I also subtract tuition and required fees for the student’s undergraduate and graduate education. I use medians to compute each of these statistics across individual Scorecard observations. By construction, the lifetime-learning ROI figures assume a 100 percent chance of degree completion.

I discount all cash flows at a rate of 3 percent to the year in which the student turns 18. This allows for consistency between my estimates of cash flows associated with undergraduate and graduate degrees. Note that because the base year for discounting differs between the undergraduate and graduate levels (undergraduate ROI is discounted to the year when the student turns 18, while graduate ROI is discounted to the year before the student enrolls in graduate school), it is not possible to simply add my estimates of undergraduate and graduate ROI together to calculate lifetime ROI.

For more details on the calculation of ROI for bachelor’s degrees, see the methodology for that report.

Caveats

This report endeavors to provide the best possible estimates of the returns to graduate degrees, but the calculations still require utilizing imperfect datasets and making several assumptions that may not hold in reality. Below are the most important caveats that the reader should bear in mind, organized by their implications for my estimates of ROI.

Caveats that should generally lead to overestimates of ROI:

• Earnings for individuals with a bachelor’s degree drop off in the late career, more so than earnings for individuals with a graduate degree. People with only a bachelor’s degree are more likely to work part time for non-economic reasons in their late career, according to the Current Population Survey. This may result in an understatement of counterfactual earnings, if individuals with a graduate degree are inherently more likely to choose full-time work regardless of educational attainment.
• The adjustment factors derived from Altonji and Zhong (2021) compare student earnings before and after attending graduate school to estimate the causal impact of the graduate degree on income — in effect, using each student as her own control group. But some students may choose to attend graduate school after a transitory negative shock to their earnings, a phenomenon known as the Ashenfelter dip. In other words, earnings before enrollment would understate students’ true earnings potential in the absence of a graduate degree. This may lead AZ to overestimate the graduate degree’s impact on earnings, which would in turn lead to an underestimate of the selection bias adjustment factors, an underestimate of counterfactual earnings, and an overestimate of ROI.
• The adjustment for completion rates assumes that all students who complete their degrees finish on time. But some students who do eventually complete their programs undoubtedly take longer than the standard time to do so, meaning they would bear a higher opportunity cost, potentially higher tuition, and enjoy one fewer year of earnings gains during their career. All these factors would tend to reduce ROI relative to my estimates.

Caveats that should generally lead to underestimates of ROI:

• The College Scorecard by Field of Study data only capture individuals who are working. For consistency, I exclude unemployed people from my ACS-derived estimates of earnings and counterfactual earnings. However, unemployment rates are lower for people with advanced degrees, though it is unclear how much of this is due to selection effects. Since the ROI calculations don’t take account of the lower probability of unemployment, the lifetime financial returns to a graduate degree may be understated.
• Only students who used federal Title IV financial aid are captured in the Scorecard earnings figures. As explained above, it is likely that these students have lower earnings potential than their peers who don’t use financial aid. However, since the counterfactual earnings calculation is based on all individuals with bachelor’s degrees — not just those who would use Title IV aid if they were to attend graduate school — the estimates of counterfactual earnings are probably slightly too high.

Caveats that could lead to an overestimate or underestimate of ROI:

• I assume that the Z-score for each program relative to average earnings for that degree remains constant throughout graduates’ careers. In reality, many graduates will move around on the earnings distribution during their lives. This is most true for those with professional degrees (especially in medicine) who temporarily work in lower-paid residencies and other entry-level roles after degree completion. For this reason, extrapolated earnings and estimated ROI for professional degrees are probably less reliable than for other degrees.
• I must assume that several factors calculated in the aggregate for broad categories of programs, such as median age of graduation, completion rate, and selection bias adjustment factors, are similar across all programs in that category. In reality, there are likely considerable differences across programs — these differences would lead me to underestimate ROI for a program with an above-average completion rate, for instance.
• I assume that students pay cash to finance their tuition. But many students use federal or private student loans to pay for graduate school. Since federal graduate student loans have interest rates above my chosen discount rate, students who finance tuition with loans will have higher realized tuition costs (and lower ROI) than I assume. However, some graduate students who use loans will get their loans canceled through Public Service Loan Forgiveness and other debt-relief programs, which could result in lower realized tuition costs, and higher private ROI. (Future research will examine the relationship between student debt and ROI further.)
• My calculation of counterfactual earnings relies on a weighted average of different undergraduate majors. But there is considerable variation in earnings within undergraduate majors, and this variation may correlate with choice of program. For instance, the top MBA programs may attract undergraduate business majors with the highest earnings potential, while lower-ranked MBA programs may attract business majors with lower earnings potential. But there is no way to disaggregate which business majors in ACS should constitute the appropriate counterfactual for each MBA program , so I must rely on weighted averages. Thus, it is possible that I overestimate ROI for top MBA programs and underestimate them for lower-ranked programs.
• I do not account for the social benefits or social costs of graduate school. Workers with higher levels of education may produce positive externalities, a social benefit. But there are also social costs to graduate school, since increasing educational attainment without commensurate gains in productivity will result in credential inflation, which closes off job opportunities to workers without graduate degrees. The net effect of these externalities may raise or lower social ROI relative to private ROI.

Given the available data, there is no perfect way to calculate the return on investment of a graduate degree. But the imperfect datasets and tools at our disposal allow a reasonable estimation of ROI, with caveats. As data collection on higher education outcomes improves, we should be able to assemble some of the missing puzzle pieces and provide even more accurate estimates of ROI.