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Institution, Major, and Firm-Specific Premia: Evidence from Administrative Data

We examine how a studentâ€™s major and the institution attended contribute to the labor market outcomes of young graduates. Administrative panel data that combine student transcripts with matched employer-employee records allow us to provide the first decomposition of premia into individual and firm-specific components. We find that both major and institutional premia are more strongly related to the firm-specific component of wages than the individual-specific component of wages. On average, a studentâ€™s major is a more important predictor of future wages than the selectivity of the institution attended, but major premia (and their relative ranking) can differ substantially across institutions, suggesting the importance of program-level data for prospective students and their parents.


Introduction
Though there is an extensive literature documenting the importance of firm-specific premia in the labor market, there is very limited research on how the returns to education operate through access to higher paying firms. In other words, are the earning gains associated with these treatments primarily because of high productivity skills that are portable across firms or access to top employer networks? Pan (2018) examines the impact of associate degrees on firm-level premia, and Engbom and Moser (2017) describe differences across education levels in firm premia. Our study contributes to this literature by providing the first descriptive evidence on how firm premia vary by a student's major and college. Describing the degree to which major and institutional premia operate through person-or firm-based channels is important because it provides a foundation for understanding why different majors and institutions yield such different returns.
In addition to providing the first evidence on how firm premia vary by major and institution, we provide a more detailed analysis of how earnings vary across majors and institutions. Specifically, we consider how major premia vary across different institutions and the relative importance of students' majors and which school they attended. This is important to students and parents as they make educational decisions. It also has implications for policy debates such as the allocation of taxpayer resources, the optimal design of institutional accountability policies, and the importance of different types of information provided to students (e.g., are school-level outcomes sufficient?).
We use rich administrative data from the state of Ohio to examine these questions. Our data consist of transcript-level data from every public postsecondary institution in Ohio, matched with linked employer-employee records, which cover nearly all employment outcomes in the state.
We find that, on average, a student's major is a more important predictor of future wages than the institution attended (at least among Ohio public schools). Major premia (and their relative ranking) can differ substantially across institutions, suggesting the importance of program-level data for prospective students and their parents.
Decomposing wages into individual and firm-specific components, we find several interesting relationships. First, despite large selectivity differences across schools, the individualspecific component of wages (which includes time-invariant ability) has a modest relationship to the institution attended, with relatively small differences between institutions. Second, the firmspecific component of wages is on average more strongly related to both major and institution attended than individual-specific factors. Across institutions, the firm-specific component accounts for roughly two-thirds of the entire institutional premium. Finally, STEM (24 percentage points) and Business (17 percentage points) graduates are the only students who receive a meaningful boost to the likelihood of finding work at a top-paying firm (defined as being in the top 10 percent of all firms in the state of Ohio).
The remainder of the paper is organized as follows. Section 2 surveys the recent literature on returns to majors and institutional quality. Sections 3 and 4, respectively, describe the data and empirical strategies employed in this study. Section 5 presents the results, and Section 6 concludes.

Literature Review
This paper contributes to three active literatures within the field of labor economics: the returns to college quality, the returns to different majors, and the wage decomposition into person-and firm-specific components.
College quality can be measured in many different ways. Differences based on the type of school (e.g., public/private/2-year/4-year) flagship status, student quality (typically proxied by test scores), or spending per student. Although a large literature examines how these college characteristics relate to academic outcomes, 1 a smaller literature examines the degree of heterogeneity across institutions in their labor market outcomes.
Most studies find positive labor market returns to their measure of college quality using a variety of different identification strategies (Brewer, Eide, and Ehrenberg, 1999;Black and Smith, 2004;Black and Smith, 2006;Hoekstra, 2009;Griffith and Rask, 2016;Andrews, Li, and Lovenheim, 2016;Goodman, Hurwitz, and Smith, 2017;Canaan and Mouganie, 2018). Notable exceptions to this general finding are Krueger, 2002, 2014), which find no returns on college quality on average but large returns only to students from low-income backgrounds.
The causes and consequences of major choice have been active in the literature in recent years; see Altonji, Arcidiacono, and Maurel (2016) for a recent summary of research in these fields. Recent work on major choice can be categorized into three distinct identification strategies: structural/discrete choice modeling (Arcidiacono, 2004;Arcidiacono, Hotz, and Kang, 2012), selection on detailed observable characteristics (Walker and Zhu, 2011;Webber, 2014Webber, , 2016, and identification based on cutoff rules for admission into certain majors (Hastings, Neilson, and Zimmerman, 2013;Kirkebøen, Leuven, and Mogstad, 2016;Andrews, Imberman, and Lovenheim, 2017). While each methodology has a unique set of benefits and drawbacks, there is remarkable consistency across approaches of large differences in the returns to various majors.
The current manuscript also adds to the large body of work aimed at decomposing wages into firm-and worker-specific components, pioneered by the seminal work of Abowd, Kramarz, and Margolis (1999). A large literature within labor economics has focused on the estimation of models with high-dimensional fixed effects and subsequently investigating the distributions of each set of effects and their correlation with important labor market features such as inequality, job referral networks, the gender wage gap, and compensating differentials (Card, Heining, and Kline, 2013;Schmutte, 2014;Card, Cardoso, and Kline, 2015;Lavetti and Schmutte, 2016). Pan (2018) examines the impact of an associate's degree on firm-level premia using a novel difference-in-differences identification strategy and finds a large firm premium for these graduates. Engbom and Moser (2017) document differences across multiple education levels in the importance of firm-level factors.
Relative to the above literature, we make several contributions. First and foremost, we are the pioneers in decomposing college major and institutional premia into firm-and individuallevel components. Second, we simultaneously estimate the returns to majors and institutions, which allows us to assess the importance of each dimension and avoids confounding institutional quality with variation in majors offered. Finally, we are the first to consider the intersection of institution and major premia, and we show that the rank ordering of major premia varies substantially across institutions.
Although we extend this literature on several dimensions, our study features several limitations. First, we measure outcomes for relatively young individuals so we cannot assess the effect of educational inputs on midcareer outcomes. Second, we only have data for public institutions from Ohio, so our data do not cover the very top of the college selectivity distribution. Finally, as with Engbom and Moser (2017), our analysis is descriptive in nature so it is not possible to make causal statements based on our results.

Data
We use administrative transcript-level data for every Ohio public university student linked to The earnings data come from the Ohio Department of Job and Family Services. The higher education data include the universe of two-and four-year public college enrollment figures in Ohio; however, in this study, we focus on four-year institutions. 3 The UI data cover the universe of workers in Ohio with the exception of federal workers and the self-employed.
The UI data allow us to follow both firms and workers over time, with quarterly observations on employment and earnings.
We restrict the UI earnings data to payments of at least $500 per quarter and focus on each worker's primary employer for each quarter as measured by total quarterly pay from each employer. This is done because the UI data include any payment from a firm to an individual, even in cases in which that payment would not constitute what we normally consider an employment relationship (e.g., legal payment). 4 Furthermore, since earnings are measured quarterly, we only examine employment spells that span at least three quarters, discarding the first and last quarters of a spell that would understate an employee's quarterly earnings if they began/ended their work at any time other than the first/last day of the quarter.
We are unable to observe enrollment at any private institutions or at public institutions outside of the state of Ohio. One comparison group that we examine is the set of individuals who started at an Ohio public institution but never graduated. In these analyses, our major and institutional premia are biased downward so that some of these students either transferred to a private college or completed their degree out of state and then returned to Ohio. We are able to track students if they transferred to any of the 38 two-or four-year colleges in the state of Ohio; these institutions represent more than 75% of students in the state. We are also not able to distinguish among unemployment, lack of labor force participation, federal employment, selfemployment, and leaving the state of Ohio. For this reason, we limit our analysis to earnings that are conditional on having a UI earnings record. Because the focus of this paper is on the return to undergraduate credentials, we remove any individual from the sample who attended any form of graduate school at a public institution within the state of Ohio.
Academic majors are only recorded in the data for conferred degrees and are identified by the Classification of Instructional Programs (CIP) code. To avoid small sample sizes for individual majors, all degrees are categorized into one of the following categories: arts/humanities, business, education, health, social sciences, STEM, or other. The "other" category encompasses the many majors that do not fit into a broader category and is included in regression models to make the set of major categories collectively exhaustive.
One major drawback inherent in many studies that use UI data to analyze labor market outcomes is that basic worker demographics are typically not available. However, in our data, we have demographic information for any individual who appears in the higher education portion of our data. For this reason, we restrict all analyses to only those individuals enrolled in an Ohio public institution at some point. This is a desirable restriction for two important reasons. First, knowing an individual's age is key to this study. Since our data window allows us to study roughly the first 10 years of earnings post-college, we would likely get a significantly downward-biased estimate of the returns to college if age were not included as a control and our comparison group included the entire working population (while the treatment group was limited to young workers). Furthermore, by including only workers who at some point enrolled in college, we partially deal with selection concerns inherent to any returns to college paper. We also restrict our sample to individuals who were under age 30 at the time they first appeared in the higher education sample. Only employment that occurs after a student left school are included in the final sample. Table 1 presents summary statistics for both the entire sample (workers who at some point enrolled in any Ohio postsecondary institution) and those with degrees from one of Ohio's 13 public four-year institutions.

Empirical Strategy
We first estimate a series of regression models that allow us to evaluate the degree to which major and institutional factors play a role in future labor market outcomes. We present various specifications of Equation (1): where Y denotes the log earnings of person i at firm j in quarter t; X is a vector of control variables that includes age, experience, gender, indicator variables for race, cumulative GPA (in models that include only college graduates); and year fixed effects. Major is a set of mutually exclusive and collectively exhaustive indicator variables for major categories (arts/humanities, business, education, health, social sciences, STEM, and other). Institution is a set of dummy variables comprising each of Ohio's 13 public four-year institutions.
The second set of analyses conducted in this paper concerns the impact of majors and institutions on person-and firm-specific components estimated using the Abowd, Kramarz, and Margolis (AKM; 1999) two-way fixed effects model. Figure 1 illustrates how we can conceptualize firm and worker components of the returns to education.
Specifically, we estimate Equation (2) where Y denotes the log earnings of person i at firm j in time t, X is a vector of time-varying control variables (e.g., quadratics of tenure and experience 5 ), along with a set of person and firm fixed effects. For the main set of analyses, the worker and firm effects are estimated from the full Ohio workforce data set, regardless of whether an individual appears in the higher education component of our data.
As a robustness check, we also estimate the AKM model using only workers who attended a public higher education institution within Ohio. A benefit of this approach is that we have information on workers' ages, but a significant drawback is that the interpretation of our results is limited to those who have only some postsecondary schooling experience. Although the results are similar, we focus on the outcomes from the full AKM estimation to maximize generalizability (e.g., firm effects apply to the entire worker population rather than just the college educated population) and precision of our estimates.
As noted in Abowd, Creecy, and Kramarz (2002), the magnitudes of worker and firm effects can only be compared with each other if they are part of the same connected set. We thus limit our analysis to the largest connected set of workers and firms of our sample. This restricted sample represents 99.8% of the worker-firm-quarters, 99.6% of the workers, and 95.2% of the firms from the full Ohio sample.
While the relationship between the person effects and major/institution indicators is not causal (e.g., higher-ability students sort into higher-quality schools), this type of wage decomposition is still inherently important. Regardless of the mechanism (e.g., human capital, innate ability), the person-specific component represents productivity, which is portable across the labor market. We examine how individual-specific premia differ across majors and institutions in a descriptive way, even if they cannot be interpreted causally.
Next, we lay out the specific identification conditions related to models with person and firm effects as dependent variables so the reader can assess the degree to which our results represent causal effects or noncausal associations. We can rewrite Equation (2) in the following form (which cannot be estimated simultaneously using a fixed-effect model): = + + + + + + . (3) As above, X represents time-varying characteristics of workers and firms. Now, we have separately written time-invariant observable (p and q, respectively, for person and firm) and time-invariant unobservable characteristics and . Hence, the estimates of the person and firm effects from our AKM estimation can instead be defined as = + (4) = + (5).
A regression of the person-specific effect on time-invariant personal characteristics (such as major or school attended) could only be interpreted as fully causal if these variables were uncorrelated with all other unobservables at the person level. This assumption is certainly violated. Regressions of firm-specific premia on person-level variables, however, would not suffer from any such bias as all individual-specific factors have been partialed out. An exception to this logic arises if the true data-generating process of wages includes not only additive worker and firm effects but also interactions between these two sets of variables. In other words, the quality of the match between workers and firms could be considered an omitted variable in our setting (Jackson, 2013). Table 2 presents major and institutional premia that college graduates receive relative to workers who attended but did not graduate from an Ohio public college. STEM and business majors each receive premia of roughly 55 log points (73%), and graduates with degrees in health fields receive only a slightly lower 60% earnings boost. Other fields have sharply lower rates of return:

Results
social sciences (23%), arts/humanities (11%), and education (17%). The institutional premia range from a low of 25% to a high of 60%, but they are mostly clustered together around a 35% premium.
Although suggestive, these results don't necessarily point to majors being a stronger predictor of future earnings than institutions. First, while Ohio does have a diverse collection of postsecondary institutions, the entire distribution of college quality in the nation is larger, particularly when low-performing, for-profit institutions are considered. In other words, the average graduate at each school in our data tends to perform well in the labor market, but this might not be the case if we had access to data comprising all postsecondary education. Second, major and institutional premia are not estimated in the same regression because a collectively exhaustive set of major categories is perfectly collinear with the full set of institutional fixed effects. Thus, some of the differences in institutional premia could be because some schools have a larger composition of certain majors. Table 3 sidesteps the latter concern by including a full set of major and institution variables while instead focusing on college graduates only, with the omitted categories being education majors from School 13. The same pattern from the above holds in this set of specifications, with majors seeming to account for a greater fraction of the variance in earnings across individuals than the institution attended.
Another important consideration for prospective students is the degree to which major premia vary across schools. Is knowing the average institutional outcomes (available for instance from the U.S. Department of Education's College Scorecard tool) and knowing the average returns to a given major sufficient to predict outcomes at the school-major level? Table 4 separately estimates major premia for each four-year public school in Ohio. The comparison group is constant across each model and represents the entire "some college" population from public Ohio institutions. Table 4 reveals that major and institution effects are clearly not additive/rank-preserving.
The top major premia at six schools is STEM, with business claiming the top spot at five schools and health graduates performing the best at the remaining two. At School 3, arts/humanities majors have a relative premium of 3.3 log points over social sciences graduates, while School 5 reflects a deficit of 22.6 log points with the same comparison. Figure 2 illustrates the results from These findings suggest a clear policy recommendation that program-level data on student outcomes (as opposed to the current institution-level averages) be made available to prospective students. Although we cannot evaluate what specifically makes the premia differ by institution (e.g., professor quality, career placement service), it is clear that labor market prospects depend heavily not just on major and institution but on the major-institution match. While this information is important in any context, the deepening struggles that many individuals face with student debt (Goldrick-Rab, 2016), especially across race/class boundaries (Addo, Houle, and Simon, 2016) makes this all the more crucial.
Tables 5 and 6 report on the decomposition of major/institutional premia into person- (Table 5) and firm-specific (Table 6) components. As before, the comparison group is composed of workers who attended, but did not graduate, from an Ohio public college. Similar to the overall wage premia, the person-specific component varies more across majors than institutions.
Coefficients range from lows of 0.02 (arts/humanities), and 0.04 (social sciences) to highs of 0.12 (health), 0.13 (STEM), 0.15 (education), and 0.19 (business). By contrast, there was a spread of 11 log points (0.06 to 0.17) between the coefficients on the top (School 7) and bottom (School 3) institutions.
As discussed previously, these estimates are not causal and instead represent a mix of sorting based on innate ability/family background and human capital accumulation. As we restrict our analyses to workers after they receive their bachelor's degree, it is not possible to disentangle these factors.
The relationship between majors and firm-specific premia is largely similar to that of the individual-specific wage component: -0.05 (education), 0.04 (arts/humanities), and 0.13 (social sciences) to highs of 0.36 (STEM), 0.25 (health), and 0.29 (business).
Interestingly, the firm-specific components of wages appear to account for a much larger share of the total wage premia among institutions. This likely points to something specific that institutions are providing their students in terms of job placement (simple name recognition by employers of a given school would be contained in the individual-specific component as it is carried by workers wherever they go). Potential mechanisms include alumni network effects, strong career/job preparation services offered by schools (e.g., interviewing or negotiation skills), or arrangements such as internships. Future research should explore this mechanism in greater detail, possibly estimating the degree to which programs such as internships contribute to the previous results.
Finally, since much of the literature on firm-specific wage premiums focuses on "superstar firms" (those near the top of the distribution), we examine the probability that a given individual finds work at a firm in the top 10% of the firm-specific premia distribution by major and institution. Relative to individuals with some college, a STEM graduate has a 24 percentage point greater likelihood of working at a top-paying firm, followed by business graduates with a arts/humanities, health, and education having 6, 4, -2, and -5 percentage point increases, respectively. The most notable contrast with our other results is that of health majors, which fared much better when examining average premia. This leads to the interesting (although certainly not surprising) conclusion that graduates of health-related majors enjoy high average wages, but there is a smaller variance in outcomes, so they are not more likely to be at a top firm.
One important caveat is that the populations being compared in the previous analyses are a subset of all workers. Namely, each premium is in comparison to workers who attended, but did not graduate, from an Ohio public institution. Setting aside that they may have transferred to a private or out-of-state school before returning to Ohio, many workers are still excluded. The dominant reason this comparison group was chosen is because we lack demographic information on any individual who never enrolled in an Ohio public school during our sample frame, most importantly, their age. Given that we only observe the first decade or so of college graduates' working lives, it would not be a fair comparison to have mid-or late-career workers in the comparison group in which we could not control for age/experience effects.

Conclusion
As the price of attending college has steadily risen in recent decades, it has become increasingly important for both policymakers and researchers to understand at a deeper level the mechanisms through which postsecondary education increases earnings. In this paper, we shed light on the relative importance of majors and the institution a student attends and examine the mechanisms through which they relate to future earnings.
We leverage rich administrative panel data from the state of Ohio that combines transcript-level student information with matched employer-employee records. We find that on average a student's major is a more important predictor of future wages than the selectivity of the institution attended among Ohio public institutions. Major premia (and their relative ranking) can differ substantially across institutions, suggesting the importance of program-level data when prospective students and their parents are making decisions about which school to attend and which major to pursue.
Decomposing wages into individual and firm-specific components, we find several interesting relationships. First, despite large selectivity differences across schools, the individual-specific component of wages (which includes time-invariant ability) has only a modest relationship to the institution attended, with relatively small differences between institutions.
Second, the firm-specific component of wages is on average more strongly related to both major and institution attended than individual-specific factors. Across institutions, the firm-specific component comprises roughly two-thirds of the entire institutional premium. Finally, STEM (23 percentage points) and business (16 percentage points) graduates are the only students who receive a meaningful boost to the likelihood of finding work at a top-paying firm (defined as being in the top 10% of all firms in the state of Ohio).  The full sample is composed of all individuals for whom we observe enrollment in a public Ohio institution and subsequent employment (subject to sample restrictions described in the Data section). The college graduate sample is composed of only those students who eventually graduate with a degree from an Ohio public institution.       Note: This table presents estimates from regressions of the firm-specific component from an AKM estimation on major and institution dummy variables. The omitted group in each panel represents students who attended an Ohio public college but never graduated. Controls refer to sex, race, age, experience, and year fixed effects. Standard errors are clustered at the individual level. AKM = Abowd, Kramarz, and Margolis two-way fixed effects model. * p<0.10, ** p<0.05, *** p<0.01 Note: This table presents estimates from linear probability model of the probability of an individual being employed at a firm with a firm-specific wage component in the top 10% of the empirical distribution. The omitted group in each panel represents students who attended an Ohio public college but never graduated. Controls refer to sex, race, age, experience, and year fixed effects. Standard errors are clustered at the individual level. * p<0.10, ** p<0.05, *** p<0.01