TY - JOUR
AU - Anelli,, Massimo
AB - Abstract I take advantage of a discontinuity in the probability of admission to a highly selective private university to estimate causal returns to investing in elite university education. I use a newly assembled data set that combines individual administrative records about high school attendance, university admission, university attendance, and tax returns. I find a discontinuity in income of 38 log points at the admission cutoff. The fuzzy regression discontinuity estimate for the elite enrollment effect is 58 log points. This should be interpreted as the average treatment effect for students applying to the elite university who are close to the cutoff and chose to enroll. When I take into account the evidence that students enrolling in the elite university tend to make different field choices, the net institutional enrollment premium is 41 log points. Cumulated over 15 years, the net-of-tuition elite premium is €246,991. I explore potential channels explaining the sizeable enrollment effects and I find that students just above the admission cutoff are 15 percentage points more likely to complete a university degree, they are 26 percentage points more likely to graduate on time and attend university with substantially higher quality peers. 1. Introduction Students pay substantially higher tuition fees to attend elite private universities. Expected returns to this education investment are a very important determinant of their university choice. Although it is clear in the data that students who attend elite universities earn more, the extent to which these higher earnings reflect a higher (gross) return to the education investment is less clear. For instance, to what extent do higher earnings reflect higher-skilled individuals selecting into elite institutions? What would be their earnings in the counterfactual scenario of attending a less selective university? Students indeed select into elite universities based on characteristics that may also be correlated with higher potential earnings. Although a similar selection issue has been analyzed by the literature on the returns to educational attainment (see Card 1999 handbook of labor economics chapter for a comprehensive review) and the one on returns to college quality (Black and Smith 2004), we have limited evidence on the causal returns to elite university education, most likely because selection is particularly strong in this context. Analyses that do not credibly account for this selection tend to overestimate returns to attendance at the most selective universities. Rankings based on graduates’ average or median earnings may overestimate returns to selective universities and thus give students incorrect information about relative returns to different education investment decisions. This fact can have a great impact on the university choice of students and lead them to suboptimal education investment decisions.1 In a period of rising college tuition fees and selectivity of elite universities (Hoxby 2009), understanding the magnitude of returns to elite university attendance is an important question. In this paper, I estimate causal returns to attending an elite, highly selective, more expensive, private university offering business, economics and law degrees relative to attending less selective universities in a large Italian city with a considerably large higher education market. I control for selection into the elite university by exploiting a sharp discontinuity in the probability of admission based on admission scores. I use self-collected administrative data that combine individual high school data, university admission data, university performance, and tax returns2 to estimate the early-career earnings premium to attending the private elite university. I am also able to link family and spatial background information. My quasi-experimental approach relies on the assumption that applicants obtaining a score close to the admission cutoff are locally randomly assigned to elite university attendance. Idiosyncratic shocks in admission test performance and relative academic quality of applicants in each round of admissions make admission close to the unknown cutoff seemingly random. Multiple falsification tests are consistent with this assumption. This paper offers several important contributions to the literature. First, I look at an unexplored and highly relevant dimension of university choice: the choice between attending a private, more expensive, elite university and less expensive, less selective public universities. This choice is highly relevant for the many students who are on the margin of trading-off quality for a more affordable university education. This is a fundamental difference to most prior work that looks at returns to university quality/selectivity within public university systems that do not imply substantial heterogeneity in cost of attendance: see Hoekstra (2009), Zimmerman (2014), Andrews et al. (2016) for the United States, Chevalier (2014) for the United Kingdom, Canaan, and Mouganie (2018) for France, Jia and Li (2018) for China.3 Second, the objective nature of the admission score in my empirical setting creates sharp discontinuities in the probability of admission. Admissions at the elite university under consideration are indeed based on a unidimensional numerical score. No subjective evaluations such as recommendation letters, essays, or athletic performance are considered for admission. Contrary to several other contexts, where admission depends on subjective evaluations unobservable to the researcher, this setting allows me to perfectly predict the admission outcome as a function of the admission score. This offers a very clean quasi-random assignment to elite admission. Third, the fact that I focus on a country with relatively low mobility for graduates allows for a proper comparison of income across individuals. Although I match income data for the entire country, a large share of the students graduating from the universities under analysis end up working in the metropolitan area around the city where the universities are located. This allows me to overcome concerns about regional earning heterogeneity. For instance, if elite university attendance causally increases the likelihood to move to a city with higher living costs, the elite premium would be overestimated. Finally, to my knowledge, this is the first paper providing empirical evidence of causal returns to elite university attendance in the higher education context of continental Europe, which is characterized by a rather bimodal quality offer, with a very large number of public nonselective universities and very few highly selective universities.4 In such higher education systems, the drop in selectivity and quality for students not admitted in the elite universities can be more abrupt than in other contexts such as the United States or central America. My work offers novel evidence about this relevant margin. My estimates show a causal income elite premium for students enrolling at the elite university under analysis ranging between 44 and 58 log points according to the bandwidth considered in the RD analysis. Results are very robust to different bandwidths and an alternative IV strategy exploiting the whole sample of applicants. These estimates are large with respect to the average Italian university-high school premium (35 log points) and are comparable to the values observed in the United States (56 log points). When interpreting the magnitude of the estimated enrollment premium, it is important to take into account that it reflects the average enrollment effect for students applying to the elite university who are close to the admission cutoff and choose to enroll. These students are likely to be more motivated and to have higher returns from attending the elite university. Therefore, the estimated enrolment effect should be considered an upper bound for the average treatment effect for the population of students applying to the elite university. Field of study choices also play an important role in determining the size of the enrollment effect in this institutional context. The elite university indeed offers degrees in economics, business, and law, whereas students not admitted to the elite universities tend to choose a broader range of degrees, some of which are in less remunerative fields of study. I estimate the enrolment effect on the field of study choice and find that students attending the elite university are 27 percentage points more likely to choose economics or business as their field. I take into account the effect of the different field choices on income and I find that the institutional quality effect of attending the elite university (“net of field of study returns”) ranges from 31 to 41 log points. These estimates are in-line with those previously estimated in countries such as Colombia (Saavedra 2014) and China (Jia and Li 2018) and slightly larger than those estimated in the United States (Hoekstra 2009). I develop a net-benefit analysis that takes into account tuition costs, the average time to graduation and a 3% discounting rate to translate the estimated annual income premium into discounted net returns to investment. Cumulated over the first 15 years on the labor market (the span of income data for my sample), net returns to attending the elite university amount to €246,991, equivalent to an implicit internal rate of return of 55%. To understand whether signaling and reputation play an important role in this context, I study the elite premium trajectory over the first 15 years on the labor market. The premium appears to have a high degree of persistence over graduates’ career. Although separating signaling from human capital effects is beyond the scope of this work, the fact that returns to quality conditional to ability are not shrinking with experience on the labor market suggests that the elite university adds to productivity and does not only signal ability (MacLeod et al. 2017). I thus explore the academic mechanisms that can explain a positive impact on human capital. I find that students attending the elite university are 15 percentage point more likely to complete a university degree and they are 26 percentage points more likely to graduate on time. This suggests that the educational environment of the elite university may motivate students more. Further empirical analysis shows that enrollment at the elite university determines a substantial increase in the average academic potential of university peers and points at peer quality playing a role in increasing the motivation of students enrolling at the elite university. Finally, a descriptive comparison of institutional characteristics shows that the elite university invests marginally more in faculty salaries, but substantially more in services and physical capital per student. 2. Literature Review Several studies have estimated returns to higher educational quality using a wide range of econometric techniques and focusing on different margins and countries. The first set of papers focused on selection on observables to estimate returns to college quality. Brewer et al. (1999) model high school students’ choice of university in the United States and estimate a 40% earnings premium for attending an elite private institution relative to attending public universities. Andrews et al. (2016) focus on quantile treatment effects and compare the wage distribution of graduates from a flagship state university to a counterfactual wage distribution of students from nonselective state institutions that assumes the same observable characteristics as for the selective university. They find an 11.5% average premium for attending the flagship state university and evidence of substantial heterogeneity in the returns to quality. For the United Kingdom, Chevalier (2014) exploits generalized propensity score methods and finds that moving from an institution in the |$3{\text{rd}}$| quality quartile of the college quality distribution to a top quality institution is associated with a 7% increase in earnings. Other studies have relied on the comparison of twins or students with very similar characteristics. Behrman et al. (1996) focus on female twins from Minnesota and find evidence of positive returns to attending private universities with well-paid senior faculty, whereas Lindahl and Regnér (2005) use Swedish sibling data and show that within-family estimates of the wage premium to college quality are half of the cross-sectional estimates. Dale and Krueger (2002, 2014) compare earnings of graduates from selective colleges to those of students admitted at equally selective universities, but chose to attend less selective institutions, and find positive returns only for low-income students. The availability of detailed individual-level administrative data has allowed the recent literature to focus on regression discontinuity design as the main approach to estimate returns to college quality. Using U.S. data, Hoekstra (2009) exploits a discontinuity in the admission rule of a U.S. flagship state university to estimate returns to education quality in a public higher education context. He estimates a 23 log point income premium in earnings for the graduates of the flagship state university. Saavedra (2014) also exploits a RD design with applicants data for Los Andes University, a top-ranked selective college in Colombia, to estimate the effects of enrollment on learning, employment and earnings one year after graduation. Earning returns in that context range from 30 to 50 log points. Zimmerman (2019) estimates the effect of elite college admission on students’ chances of attaining top-positions in the economy using data from Chile and finds that admission to elite programs raise the number of leadership positions students hold by 50% and the share with incomes in the top 0.1% of the distribution by 45%. Canaan and Mouganie (2018) estimate returns to college quality for low-skilled students using French data and show that students who marginally passed the final high school exam at the first attempt gain access to higher quality universities, are more likely to enroll in a STEM major and have a 12.5% increase in earnings between the ages of 27 and 29.5 Finally, Jia and Li (2018) use Chinese data and estimate returns to enrollment in first-tier Chinese universities between 33 and 47 log points. In terms of methodology, empirical setting and research question, my paper most closely relates to Hoekstra (2009) and Saavedra (2014). I improve on the work of Hoekstra (2009) by tracking the individual counterfactual university career of students not admitted to the elite university. This is an important contribution because it allows me to explore the academic mechanisms through which elite university education improves returns to education investment. Although Saavedra (2014) only observes earnings in the first year after graduation, I can estimate RD returns for up to 5 years in the labor market and I can study career trajectories using alternative empirical strategies for up to 15 years. This is useful to understand whether the elite premium is driven by signaling and reputation more than by human capital accumulation. When considering quality and price margins, the institutional setting under analysis is characterized by a larger drop of both selectivity and tuition between the elite university and the alternatives with respect to both Hoekstra (2009) and Saavedra (2014). Other papers relevant for this study use a regression discontinuity design to estimate returns to elite college education on the marriage market in Chile (Kaufmann et al. 2013), effects of admission to 4-year public colleges on college completion (Goodman et al. 2017), returns to college admission for students who are at the margin of attending university (Zimmerman 2014) and returns across degree programs (Hastings et al. 2013; Kirkeboen et al. 2017). Interestingly, Kirkeboen et al. (2017) exploits the Norwegian centralized college admission process to estimate the payoffs of different fields and finds that different fields have widely different payoffs, but estimates of returns to a major do not appear to be affected by institution quality. This suggests that, contrary to Italy and other studied contexts (United States, Chile, Colombia, France, China), returns to Norwegian post-secondary education quality might be more limited. 3. Data Collection, Analytical Sample, and Educational Setting The master sample for this paper consists of 30,000 individuals who graduated from college-preparatory high schools (in Italian, “Licei”) between 1985 and 2005 in a large Italian city.6 High school data for these individuals were collected from 11 different high schools (6 offering the scientific track and 5 offering the classical track) and contain information on high school exit tests, class peers, teachers and the location of their home. The Italian high school system can be classified in three main tracks: college-preparatory high schools (“licei”), technical high schools (“istituti tecnici”) and vocational schools (“formazione professionale”). Tracking is not strict since track choice is purely voluntarily and there are no enrollment caps nor selection processes. Moreover, university enrollment is open to students from all tracks. However, there is substantial segregation across tracks, with a vast majority of graduates from college-preparatory high schools enrolling in university and much lower shares for the other two tracks. The system is mostly public and private high schools tend to attract students with lower academic performance or dropouts of public schools. Within the college-preparatory track, there are several specializations. However, the majority of students planning to enroll in university attend one of the two traditional specializations, the “scientific” and the “classical” ones. My data collection effort was targeted at all public college-preparatory high schools specializing in either the scientific or the classical academic specialization in the city under analysis. This decision was driven by the goal of focusing on a homogeneous population of students with the highest propensity to attend college. In the city under analysis there are 15 of these schools (9 offering the scientific specialization and 6 offering the classical specialization).7 I have obtained permission to digitize hard-copy registries for 11 of these schools, whereas the principals of the other 4 schools did not agree to release the data. The 11 schools in my sample represent 71% of the target population.8 To give a sense of the selection of students in my sample, I can rely on the property value where the students previously live at the time of high school attendance. Students’ home addresses—where they lived during high school—were retrieved from the hard-copy registries, and matched to property market values.9 Although an average individual at high school age lived in a house that had a value of €2696 m|$^{-2}$|⁠, the average student attending one of the high schools in my sample lived in a house with a value of €3102 m|$^{-2}$|⁠. For comparison, consider that kids living in the 25% wealthiest neighborhoods lived in a house that had a value of €4174 per square meter and those from the 25% least wealthy neighborhoods lived in a house worth €2301 m|$^{-2}$|⁠. Hence, although my analytical sample of high school students is likely highly selective with respect to academic motivation, it is only marginally positively selective regarding students’ background. The high-school master data have been linked to multiple sources of administrative data as illustrated in Figure 1. They have been matched (using names, place and date of birth) to student records from the 5 universities present in the same city. Given that most public universities require only a very low “token fee” for enrollment, relocation and commuting costs are the most relevant factors influencing the decision of where to attend university. As a consequence, Italian high school graduates have little incentive to move away to attend university. This is especially true for the city under analysis since all fields of study are offered by at least one of these 5 universities. In my analytical sample, 83% of all high school graduates obtain a university degree and among all university graduates almost 90% of them are matched to the data of at least one of the 5 universities.10 For the students with a linked university record, I can reconstruct their university career: degree completion, year of graduation, field of study, change of degree and final graduation exit score. In a further step, the initial 30,000 records of the university preparatory high school graduates have been linked to internal revenue service data on personal gross income for year 2005, the only year for which tax returns data have been made available by the Ministry of Finance.11 It is important to keep in mind that, although earnings data are matched for all cohorts in the data set, they are available for one tax year only. Labor market conditions for 2005 in the part of the country where the universities are located were moderately good, but not exceptional: unemployment was 4.1% and GDP growth was 1.6%. Figure 1. Open in new tabDownload slide This diagram presents the different sources of administrative data I have assembled. High school administrative records are the master data set to which I have linked the other data sets. The dashed-line box highlights the subsample of individuals (those who applied to the elite university) on which the regression discontinuity analysis is run. Figure 1. Open in new tabDownload slide This diagram presents the different sources of administrative data I have assembled. High school administrative records are the master data set to which I have linked the other data sets. The dashed-line box highlights the subsample of individuals (those who applied to the elite university) on which the regression discontinuity analysis is run. For a stratified random 10% subsample of all high school graduates, more detailed information has been collected from telephone interviews conducted in June 2011.12 The additional information includes many variables such as family background, parental income, job and education, current employment and current family situation of the individual. Finally, I merged these data with records from the admission office of the private selective university under study. The admission office performed the match using the name, birth date, high school and year of high school graduation of each individual and returned the matched data after full anonymization. The admission office matched information for all high school students in the master data set (both admitted and not admitted) who applied to the private elite university between 1995 and 2012. The university has indeed kept digital databases only for the admission sessions from 1995 onward, which are a subset of the cohorts available in my data. Figure A.1 in the Online Appendix summarizes graphically the “time-line” of admission information availability: data on admission are available for the elite university for the high school cohorts enrolling in university between 1995 and 2000, whereas background information, high school, and university performance data, 2005 taxable income and 2011 phone survey data are available for all cohorts enrolling in 1985–2005. It is important to keep in mind that the admission process for the elite university is fully independent (for timing and rules) of the other universities. A practical consequence of this fact is that only a subsample of my initial set of high school graduates actually apply to the elite university.13 My regression discontinuity analysis thus focuses on this subsample of students. Collecting data for the remaining (large) number of high school graduates who did not apply to the elite university was still crucial to identify the counterfactual sample of students below the cutoff for admission to the elite university. Overall, this rather complicated and costly data collection design presents some limitations, but also some advantages. One limitation is due to the fact that my main regression discontinuity analysis is limited to high school graduates of the city under analysis applying to the elite university, instead of considering the complete sample of students applying to the elite university.14 Although this feature of the data limits the interpretation of my results to a geographically determined sample of students, the internal validity of the quasi-experiment is not affected by it. On the contrary, the focus on this very homogeneous sample of high school graduates allows me to exclude sample selection problems close to the admission cutoff that would otherwise be likely.15 3.1. The Institutional Context Table 1 summarizes relevant statistics for the elite university vis-a-vis the average characteristics of the other four universities in the city under analysis.16 The elite university is characterized by substantially different institutional characteristics, degrees of selectivity and outcomes. It is smaller in size (has around 11,000 students enrolled every year with respect to an average of 39,000 for the other universities), has 93% higher expenditures per student, 13% higher salaries per instructor, but does not have a better student-to-instructors ratio. Net of scholarships and tuition fee discounts, attending the elite university costs 3.7 times more on average than the other universities.17 Table 1. Summary statistics—Institutional and student background characteristics for elite and nonelite universities. . Elite . Other . . . . university . universities . Difference . Elite/Others . Institutional characteristicsa # Students 11841 39092 0.30 # Students/# Instructors 19.25 18.20 1.06 Total expenditures/# Students (€) 11545 5966 1.93 Avg. yearly expenditure per instructor (€) 75507 66567 1.13 Sticker price tuition (€) 11000 3370 3.3 Yearly tuition revenues/# Students (€) 4607 1245 3.70 Background characteristics of students Avg. high school exit score (on a scale of 0–100) 83 76 6.907 1.09 (0.325) Parents’ house value (€/|$\text{m}^2$|⁠) 3196 3088 111 1.04 (32) Parents’ monthly income (€) 2959 2593 366 1.14 (113) (Mother is college graduate = 1) 0.406 0.285 0.121 1.42 (0.047) . Elite . Other . . . . university . universities . Difference . Elite/Others . Institutional characteristicsa # Students 11841 39092 0.30 # Students/# Instructors 19.25 18.20 1.06 Total expenditures/# Students (€) 11545 5966 1.93 Avg. yearly expenditure per instructor (€) 75507 66567 1.13 Sticker price tuition (€) 11000 3370 3.3 Yearly tuition revenues/# Students (€) 4607 1245 3.70 Background characteristics of students Avg. high school exit score (on a scale of 0–100) 83 76 6.907 1.09 (0.325) Parents’ house value (€/|$\text{m}^2$|⁠) 3196 3088 111 1.04 (32) Parents’ monthly income (€) 2959 2593 366 1.14 (113) (Mother is college graduate = 1) 0.406 0.285 0.121 1.42 (0.047) Note: Standard error of difference in parentheses. a. Source for Institutional characteristics: Italian Ministry of Education (MIUR), 2001. Open in new tab Table 1. Summary statistics—Institutional and student background characteristics for elite and nonelite universities. . Elite . Other . . . . university . universities . Difference . Elite/Others . Institutional characteristicsa # Students 11841 39092 0.30 # Students/# Instructors 19.25 18.20 1.06 Total expenditures/# Students (€) 11545 5966 1.93 Avg. yearly expenditure per instructor (€) 75507 66567 1.13 Sticker price tuition (€) 11000 3370 3.3 Yearly tuition revenues/# Students (€) 4607 1245 3.70 Background characteristics of students Avg. high school exit score (on a scale of 0–100) 83 76 6.907 1.09 (0.325) Parents’ house value (€/|$\text{m}^2$|⁠) 3196 3088 111 1.04 (32) Parents’ monthly income (€) 2959 2593 366 1.14 (113) (Mother is college graduate = 1) 0.406 0.285 0.121 1.42 (0.047) . Elite . Other . . . . university . universities . Difference . Elite/Others . Institutional characteristicsa # Students 11841 39092 0.30 # Students/# Instructors 19.25 18.20 1.06 Total expenditures/# Students (€) 11545 5966 1.93 Avg. yearly expenditure per instructor (€) 75507 66567 1.13 Sticker price tuition (€) 11000 3370 3.3 Yearly tuition revenues/# Students (€) 4607 1245 3.70 Background characteristics of students Avg. high school exit score (on a scale of 0–100) 83 76 6.907 1.09 (0.325) Parents’ house value (€/|$\text{m}^2$|⁠) 3196 3088 111 1.04 (32) Parents’ monthly income (€) 2959 2593 366 1.14 (113) (Mother is college graduate = 1) 0.406 0.285 0.121 1.42 (0.047) Note: Standard error of difference in parentheses. a. Source for Institutional characteristics: Italian Ministry of Education (MIUR), 2001. Open in new tab Students attending the elite university are positively selected on their pre-university characteristics. Their high school exit scores18 are higher. Although the average student in my sample attending the elite university has on average a score of 83 out of 100, those attending the other universities have an average score of 76. When compared to the earliest available high school score distribution for the same Italian region, the 7-point difference between elite and nonelite corresponds to 65% of a standard deviation in the regional distribution.19 Alternatively, the average student in my sample is in the |$86{\text{th}}$| percentile of the regional high school exit score distribution, whereas the average student in the other 4 universities scores is in the |$76{\text{th}}$| percentile. Given that universities in this city offer different sets of degrees, this comparison might partly incorporate field selectivity.20 However, a comparison between the elite and the nonelite universities using my sample, holding field constant, shows that the average score for students attending nonelite universities is 74, only two points lower than the overall average. This is evidence that the bulk of selectivity happens across institutions in this context. Students at the elite university also come from slightly wealthier families (living in neighborhoods with 4% higher property values), have more educated mothers and their fathers are more likely to work in leadership occupations.21 Average differences in students’ outcomes are substantial. Table 2 shows several labor market outcomes for students in my sample and compares them to equivalent statistics estimated on nationally representative samples. Students graduating from the elite university had an average annual taxable income of €46,204 in 2005 (measured before taxes and after deductions between 1 and 15 years following graduation), which is 70% higher than the average income for graduates of the other four universities. When comparing tax return data, it is important to keep in mind that graduates of the elite university are marginally more likely to work abroad (the last row of Table 2 shows that graduates of the elite university are 9 percentage points more likely to live abroad in 2011). Assuming working abroad is associated with higher income, the higher propensity of elite university graduates to emigrate might cause underestimation of the elite income premium. However, for the interpretation of my RD estimates, I will show that the probability of having missing tax return data, which is strictly linked to living abroad, is continuous through the admission cutoff. I put my sample income statistics into the Italian context by comparing them to statistics estimated using an Italian nationally representative survey (the Bank of Italy Survey on Household Income and Wealth (2006)) and university graduate surveys for 45 universities (the Almalaurea consortium 2007). Although for my paper I use taxable income data after deductions22, both SHIW and Almalaurea data only provide data on net income. Thus, in Table 2, I also show descriptive statistics for after-tax income for my sample. Both SHIW and Almalaurea data are from 2006 surveys, the closest available data to the year for which I observe tax return data. Mean net income estimated with SHIW data for university graduates from the same part of the country in the same age bracket is lower but comparable in size to that estimated for the graduates of the nonelite universities in my sample for both men and women. The median for men of the nonelite universities is higher than that of Italian university graduates in the same part of the country and lower for women. I also compare my sample to the data from the Almalaurea consortium graduate survey. The estimates refer to individuals who, in 2006, graduated 5 years earlier from 45 public universities around the country. Mean income 5 years after graduation in my data is marginally higher than the one estimated by the Almalaurea survey but comparable. Average employment rates for my sample are estimated using data from the phone survey run in 2011 for a 10% subsample. Thus, they capture the employment opportunities for individuals who in 2011 had between 5 and 21 years of potential labor market experience (approximately between 30 and 46 years old). They are very high for both the elite and nonelite universities and the difference in the values is not statistically significant. When compared to university graduates in the same age range and geographical area of the SHIW survey, students from my sample have very similar employment rates. Almalaurea employment data are instead for students in the 25–30 age bracket (younger than in my sample), but their national estimates are not much lower than those of my sample. Around 65% of elite university graduates (between 30 and 46 years old) work in leadership occupations (managers, professionals, directors or business-owners) with respect to 40% of the other graduates in my sample. Also, with respect to this statistic, the graduates of nonelite universities in this city are similar to other university graduates in the same part of the country. Taken all together, the comparison with nationally representative data reassures the fact that my sample is not selected in special ways. This also suggests that, although the focus of my paper is only on students from one city, their labor market outcomes might not be that different from other university graduates in the same part of the country and my results might generalize to a broader context. Table 2. Summary statistics—Student outcomes for elite and nonelite universities compared to national averages. . All students . Women . Men . . Paper . SHIW . Almal. . Paper . SHIW . Almal. . Paper . SHIW . Almal. . . . . . Same . . . . . Same . . . . . Same . . . . . . Region . It. Coll. . . . . Region . It. Coll. . . . . Region . It. Coll. . . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . (13) . (14) . (15) . Taxable income Mean 46204 27009 41363 21081 48860 33758 Median 31380 18265 29664 14649 323738 23758 Net Income Mean 33102 20948 14890 17972 30494 16709 11972 15570 34532 25774 17218 20709 Median 24344 14589 14000 16500 22966 11816 12000 15000 25222 18805 15000 18350 Net income first 5 years after graduation Mean 26656 18242 15924 30494 16709 14112 26936 21408 18492 Employeda 0.95 0.92 0.75 0.92 0.9 0.96 0.90 0.63 0.89 0.87 0.94 0.94 0.89 0.97 0.94 Leadershipb 0.65 0.40 0.10 0.37 0.40 0.34 0.08 0.27 0.73 0.46 0.14 0.50 Work abroad 0.16 0.07 0.08 0.06 0.18 0.07 . All students . Women . Men . . Paper . SHIW . Almal. . Paper . SHIW . Almal. . Paper . SHIW . Almal. . . . . . Same . . . . . Same . . . . . Same . . . . . . Region . It. Coll. . . . . Region . It. Coll. . . . . Region . It. Coll. . . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . (13) . (14) . (15) . Taxable income Mean 46204 27009 41363 21081 48860 33758 Median 31380 18265 29664 14649 323738 23758 Net Income Mean 33102 20948 14890 17972 30494 16709 11972 15570 34532 25774 17218 20709 Median 24344 14589 14000 16500 22966 11816 12000 15000 25222 18805 15000 18350 Net income first 5 years after graduation Mean 26656 18242 15924 30494 16709 14112 26936 21408 18492 Employeda 0.95 0.92 0.75 0.92 0.9 0.96 0.90 0.63 0.89 0.87 0.94 0.94 0.89 0.97 0.94 Leadershipb 0.65 0.40 0.10 0.37 0.40 0.34 0.08 0.27 0.73 0.46 0.14 0.50 Work abroad 0.16 0.07 0.08 0.06 0.18 0.07 Notes: All income values are in €, observed in 2005 for my analytical sample (columns (1), (2), (6), (7), (11), (12)), in 2006 for the Survey on Household Income and Wealth Bank of Italy Data (columns (3), (4), (8), (9), (13), (14)) and in 2006 also for the Almalaurea college graduate survey data. Sample: in columns (1), (2), (6), (7), (11), (12) students that graduated from college-preparatory high schools enrolling in one of the five universities of the city under analysis from 1985 to 2000 high school graduating cohorts (aged 25–40 in 2005). In columns (3), (8), (13) all Italians aged 25–40, columns (4), (9), (14) Italian university graduates from the same region aged 25–40, columns (5), (10), (15) Italian university graduates 5 years after graduation. a. Employment rates for my sample are measured from the 2011 phone survey and thus cover individuals who are between 30 and 46 years old, SHIW employment rates are estimated on a comparable age range, whereas Almalaurea employment rates are available for individuals between 25 and 30 years old b. Leadership occupations defined as managers, professionals, directors, or business-owners. Open in new tab Table 2. Summary statistics—Student outcomes for elite and nonelite universities compared to national averages. . All students . Women . Men . . Paper . SHIW . Almal. . Paper . SHIW . Almal. . Paper . SHIW . Almal. . . . . . Same . . . . . Same . . . . . Same . . . . . . Region . It. Coll. . . . . Region . It. Coll. . . . . Region . It. Coll. . . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . (13) . (14) . (15) . Taxable income Mean 46204 27009 41363 21081 48860 33758 Median 31380 18265 29664 14649 323738 23758 Net Income Mean 33102 20948 14890 17972 30494 16709 11972 15570 34532 25774 17218 20709 Median 24344 14589 14000 16500 22966 11816 12000 15000 25222 18805 15000 18350 Net income first 5 years after graduation Mean 26656 18242 15924 30494 16709 14112 26936 21408 18492 Employeda 0.95 0.92 0.75 0.92 0.9 0.96 0.90 0.63 0.89 0.87 0.94 0.94 0.89 0.97 0.94 Leadershipb 0.65 0.40 0.10 0.37 0.40 0.34 0.08 0.27 0.73 0.46 0.14 0.50 Work abroad 0.16 0.07 0.08 0.06 0.18 0.07 . All students . Women . Men . . Paper . SHIW . Almal. . Paper . SHIW . Almal. . Paper . SHIW . Almal. . . . . . Same . . . . . Same . . . . . Same . . . . . . Region . It. Coll. . . . . Region . It. Coll. . . . . Region . It. Coll. . . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . Elite . Other . . Coll. . Grads . . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . univ. . univ. . Italy . Grads . Survey . . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . (9) . (10) . (11) . (12) . (13) . (14) . (15) . Taxable income Mean 46204 27009 41363 21081 48860 33758 Median 31380 18265 29664 14649 323738 23758 Net Income Mean 33102 20948 14890 17972 30494 16709 11972 15570 34532 25774 17218 20709 Median 24344 14589 14000 16500 22966 11816 12000 15000 25222 18805 15000 18350 Net income first 5 years after graduation Mean 26656 18242 15924 30494 16709 14112 26936 21408 18492 Employeda 0.95 0.92 0.75 0.92 0.9 0.96 0.90 0.63 0.89 0.87 0.94 0.94 0.89 0.97 0.94 Leadershipb 0.65 0.40 0.10 0.37 0.40 0.34 0.08 0.27 0.73 0.46 0.14 0.50 Work abroad 0.16 0.07 0.08 0.06 0.18 0.07 Notes: All income values are in €, observed in 2005 for my analytical sample (columns (1), (2), (6), (7), (11), (12)), in 2006 for the Survey on Household Income and Wealth Bank of Italy Data (columns (3), (4), (8), (9), (13), (14)) and in 2006 also for the Almalaurea college graduate survey data. Sample: in columns (1), (2), (6), (7), (11), (12) students that graduated from college-preparatory high schools enrolling in one of the five universities of the city under analysis from 1985 to 2000 high school graduating cohorts (aged 25–40 in 2005). In columns (3), (8), (13) all Italians aged 25–40, columns (4), (9), (14) Italian university graduates from the same region aged 25–40, columns (5), (10), (15) Italian university graduates 5 years after graduation. a. Employment rates for my sample are measured from the 2011 phone survey and thus cover individuals who are between 30 and 46 years old, SHIW employment rates are estimated on a comparable age range, whereas Almalaurea employment rates are available for individuals between 25 and 30 years old b. Leadership occupations defined as managers, professionals, directors, or business-owners. Open in new tab Two important features of Italian university education, which are features that are common to all other European countries, are relevant for this study. First, admission to Italian universities is degree-specific: students apply for a specific field of study at one or more universities. In order to change degree after enrollment, a student must wait for the following round of admissions (once a year) and make a new application. Where an admission test is required, it is administered by the single university itself. There is no centralized admission system. Second, not every university offers degrees in all fields of study. The elite university offers degrees in Business, Economics and Law with a wide range of specializations, from public management to marketing. Its mission emphasizes the preparation of managers and leaders with a strong economic background in a very wide range of fields. For this reason, the elite university attracts a large number of students with preferences for degrees different from Economics and Business as shown later on in this paper.23 Overall, the descriptive statistics show that students who attend the elite university tend to be selected on pre-university characteristics and have substantially better labor market outcomes. This suggests that selection bias might play an important role in determining the large gap in student outcomes. The quasi-experimental analysis presented in the next sections will shed light on the casual returns to elite university attendance, net of this selection bias. 3.2. The Admission Rule The admission procedure of the elite university is based on an objective uni-dimensional composite score that equally weights a combination of high school grades and an admission test score. The admission test is administered by the elite university simultaneously for all students, is multiple choice and is identical for all students. Applicants are ranked according to the composite admission score. The admission score has a 0–100 point original scale and in my regression discontinuity analysis is rescaled to be 0 at the admission cutoff. Every year, the number of admitted students is fixed at N before the admission test is taken and every year the N students with the highest admission score are offered admission.24 The admissions office of the elite university provided the exact admission score for the students in my sample and all the relevant admission cutoffs for 6 rounds of admission, all taking place at the beginning of September of each year between 1995 and 2000. In all those years, courses started at the beginning of October. Only a single admission test per year was administered. Given the multiple choice nature and the use of scanning machines, admitted students used to receive information on the test outcome a few days after the test date and then had time until the last week of September to decide whether to enroll or not. Applicants would receive a communication from the university containing the admission outcome, but the communication did not include information on their admission test score, nor about the admission score cutoff. Given the short time span between the test and the enrollment deadline, there was no waiting list: the university would admit a number of students slightly above its capacity based on previous years’ rates of enrollment of admitted students so that generally some degrees would end up marginally under-subscribed. For the first 4 rounds of admissions (1995–1998), the elite university admitted students on the basis of a single admission cutoff valid for all applicants, independently of preferred degrees. Assignment to degrees would take place after admission. Then, starting from the year 1999, admissions were determined taking individual preferences for specific degrees (e.g., business degree, economics degree, law degree, etc.) into account ex ante. In 1999 students listed and ranked two preferred degrees at the moment of their application (first choice compulsory, second optional). After the admission test, they were ranked according to the same admission score (as for the previous rounds of admissions). Following admission score priority, students are assigned their first choice until degrees reached their respective caps. Most degrees filled up in this first step. Some were not filled because fewer applicants were choosing them as first choice than slots available. Students who did not make the cut for their first choice, and had one of the unfilled degrees as second choice, are assigned to unfilled degrees within a broad degree group. Eventual remaining unfilled spots were not covered. In my data, 93% of all admitted students were admitted to their first choice and 7% to their second choice. For the September 2000 admission (the last round I observe), the process was structured in the same way, but with 7 possible degree preference choices (only first choice compulsory) instead of two to avoid leaving spots unfiled. Thus, for 1999 and 2000 admissions, I have taken this institutional feature into account by rescaling the admission cutoff to be 0 separately for each applicant and considering her/his degree preferences. In practice, for each student, I have considered the lowest admission score for each degree across the two steps25 as a relevant admission cutoff. Given the objective nature of admission scores and the institutional features described, admission cutoffs identify a sharp discontinuity in the probability of admission at the elite university for the year of the admission test. However, students can retake the test and eventually be admitted. The decision to reapply has the high cost of losing one or multiple years and is indeed observed infrequently in my data (only 23 students rejected in their first round application retook the admission test in following years). For the sake of the regression discontinuity analysis, I consider the very first observed admission test score as the running variable and ever-admitted/ever-enrolled as the relevant treatments. In Figure 2, panels A and B, I show the discontinuities in the probability of ever being admitted and ever enrolled at the threshold for my sample of applicants. Although having an admission score above the cutoff in this setting corresponds one-to-one with being admitted and captures the effect of admission on future income, I am most interested in estimating the effect of enrollment. Since not every admitted student decides to enroll at the elite university, the discontinuity in the probability of enrolling at the elite university is large but not sharp. About 71% of admitted students in my sample end up enrolling in the elite university. There are two possible reasons why students admitted to the elite university may decide not to enroll. Either the students prefer to enroll in a degree not offered by the elite university, for example, engineering, or they may expect the returns to attending the elite university to be lower than the higher tuition costs.26 Thus, in my regression discontinuity analysis, I focus on a fuzzy RD approach in which I instrument the probability of ever enrolling in the elite university with a dummy equal to one if the student has an admission score above the cutoff in her/his first observed admission test. Figure 2. Open in new tabDownload slide Treatment and predetermined covariates at the cutoff. Sample is all students applying to elite university between 1995 and 2000. Running variable is first observed admission score for each individual in deviation from the cutoff of that year. Dependent variables is admission (A), enrollment at the elite university in the year when the student first takes the admission test or in any following year (B), income predicted based on predetermined characteristics only (C), a female dummy (D), parental house value (E), and average high school exit score in own high school class (F). Bandwidth is mean square error (MSE)-optimal bandwidth for treatment probabilities in (A) and (B) and coverage error (CER)-optimal bandwidth for all predetermined characteristics in (C)–(F). Fitted local polynomial of degree 1. Bin selection mimicking variance evenly-spaced bin selection method. Figure 2. Open in new tabDownload slide Treatment and predetermined covariates at the cutoff. Sample is all students applying to elite university between 1995 and 2000. Running variable is first observed admission score for each individual in deviation from the cutoff of that year. Dependent variables is admission (A), enrollment at the elite university in the year when the student first takes the admission test or in any following year (B), income predicted based on predetermined characteristics only (C), a female dummy (D), parental house value (E), and average high school exit score in own high school class (F). Bandwidth is mean square error (MSE)-optimal bandwidth for treatment probabilities in (A) and (B) and coverage error (CER)-optimal bandwidth for all predetermined characteristics in (C)–(F). Fitted local polynomial of degree 1. Bin selection mimicking variance evenly-spaced bin selection method. 4. Identification Strategy My regression discontinuity analysis relies on a local linear polynomial approach with mean square error (MSE)-optimal bandwidth selection, triangular kernel and robust inference following Calonico et al. (2014). Conditional on the choice of the polynomial degree p and the weighting scheme |$K(\cdot )$|⁠, this approach is fully data-driven and does not leave room for estimate picking as in more global parametric specifications. The goal of the local approach is to approximate the regression functions underlying the raw data separately for treatment |$\mathbb {E}[Y_i(1)|X_i=x]$| and control group |$\mathbb {E}[Y_i(0)|X_i=x]$| using only observations that are sufficiently close to the cutoff, where “sufficiently” is defined by purely data-driven methods. Within the local bandwidth h, the triangular kernel assigns higher weights to the observations that have values of the running variable |$X_i$| closer to the cutoff c. Altogether, these methods aim to obtain reliable estimates of the expected outcomes for treatment |$\mathbb {E}[Y_i(1)|X_i=c]$| and control |$\mathbb {E}[Y_i(0)|X_i=c]$| at the cutoff c. Empirically, this amounts to estimate the intercepts |$\alpha ^{+}$| and |$\alpha _{-}$| of the treatment and control local regression functions at the cutoff. The discontinuity estimate |$\tau$| is then calculated as the vertical distance |$\alpha ^{+} - \alpha _{-}$| between these two intercepts. The advantages of this approach are that they are substantially less sensitive to outliers and observations further from the cutoff, and that their potential mis-specification can be modeled formally. In particular, the data-driven choice of the optimal bandwidth h relies on the idea that the narrower the bandwidth, the smaller the model mis-specification error for the underlying regression function (no matter the true underlying functional form, the regression function will get closer to the linear approximation for smaller and smaller bandwidths), but the larger the variance of the treatment effect estimate. The mean square error of the discontinuity estimate |${\textit{MSE}}(\tau )$| incorporates this bias-variance trade-off. Calculating the bandwidth |$\hat{h}$| that minimizes |${\textit{MSE}}(\tau )$| is thus the most straightforward approach to data-driven optimal bandwidth choice and the one I use for this paper. The sharp discontinuity design described allows me to estimate the income discontinuity at the admission score cutoff. I interpret this as the average intent-to-treat effect |$\tau _{\textit{ITT}}$| near the cutoff of being admitted to the elite university. Since I am ultimately interested in estimating the impact of attending the elite university, I rely also on a standard fuzzy regression discontinuity design. This design rescales the sharp estimate of the intent-to-treat effect |$\tau _{\textit{ITT}}$| by the sharp estimate of the treatment take-up at discontinuity |$\tau _{\textit{FirstStage}}$| (i.e., the discontinuity in enrollment at the cutoff). As a result, the treatment effect of admission for students near the cutoff who enroll in the elite university |$\tau _{\textit{Enr}}$| can be retrieved. As for every fuzzy regression discontinuity design, my estimates for the enrollment effect will thus be “local” with respect to two dimensions: local with respect to the cutoff and local with respect to being “compliers”, that is, individuals who choose to attend the elite university if their score is above the admission cutoff and do not attend it when the score is below. Although the fact that 70% of students near the cutoff are compliers in this setting implies that my estimate is “local” to a substantial part of individuals applying to the elite university, we must take into account that compliers will likely have stronger advantages or motivation for attending the elite university. Moreover, it is important to keep in mind that my estimates reflect the local average treatment effect for the population of students who actually choose to apply to the elite university in the first place, which is positively selected with respect to the whole population of university students. The estimated enrollment effect is thus to be considered an upper bound for the average treatment effect in the population. I bring this approach to my empirical setting by choosing a linear polynomial of degree zero. This choice was driven by two empirical facts. First, the regression function of income on the admission score using underlying raw data appears to have a very similar (and rather flat) slope both to the left and to the right of the cutoff. Second, the relatively small sample size implies that slopes of higher order polynomials are sensitive to a few observations in small bandwidths and as a consequence tend to deliver estimates that depend more on the chosen bandwidth. Importantly, it must be noticed that the choice of a zero-degree polynomial comes with substantially smaller bandwidths, since the MSE-optimal bandwidth selection procedure automatically takes into account that linear degree-polynomials of degree zero might have a larger mis-specification bias. This implies that there is no theoretical advantage in making this choice with respect to higher order degree polynomials. In this empirical case, results with a zero-degree polynomial tend to be the most conservative and the most demanding since they are estimated on rather small bandwidths.27 Standard errors are clustered at cohort high-school level in all specifications.28 Included controls are parental house value, a female dummy and fixed effects for the round of submission. For the latest cohorts, a small portion of individuals are still enrolled in university when their tax return is observed. Since the goal of the study is to estimate the effect of elite education on post-university employment outcomes using specifications with labor market outcomes on the left-hand side, I also include a dummy for whether the individual was still enrolled in university in 2005, that is, the year when income is observed. Although I am aware that including this control is problematic since enrollment in 2005 is a potential outcome in this framework, I believe it is important to take into account that some of the observed income might be coming from part-time work during university and therefore not reflect the real earning potential of each individual.29 When interpreting the results of my analysis, it is important to keep in mind that it is run only for the subsample of individuals applying to the elite university, which is positively selected and substantially more homogeneous with respect to the population of high school students. Figure 3 shows the distribution of high school exit scores for students applying to the elite university and those who did not apply. The distribution for students applying to the elite university is substantially shifted to the right. Hence, also students who are further away from the cutoff in my analytical sample are likely to have similar academic and earning potential. This fact allows me to also consider a simple 2SLS instrumental variable alternative approach in which I instrument enrollment in the elite university with a dummy for the admission score being above the cutoff. The advantages of this alternative approach are that it is fully independent of bandwidth choice and polynomial specification and provides information on the treatment effect for individuals far from the cutoff although the estimate remains local to the subgroup of compliers. Moreover, given the selected nature of the admission sample, the global span of student quality and earning potential is not substantially broader for the IV strategy than for the local approach of the RD data. In practice, we can consider this alternative strategy as a lottery setting in which all students are equally likely to be admitted, but only those who randomly receive a score above the admission cutoff win access to the elite university.30 I present estimates for this alternative IV strategy together with my RD analysis to reinforce the evidence of a large treatment effect that is independent of choices made for the RD design. Figure 3. Open in new tabDownload slide Distribution of high school exit scores for students who applied to the elite university (dotted line) and of those who did not apply (solid line). Figure 3. Open in new tabDownload slide Distribution of high school exit scores for students who applied to the elite university (dotted line) and of those who did not apply (solid line). 5. Validity of the Regression Discontinuity Analysis The main identification assumption for my empirical strategy is that the assignment around the cutoff determining treatment is locally random (Lee and Lemieux 2010). Before presenting my results, I test the validity of this assumption in several ways. The local randomness condition may be violated if the probability of treatment, that is, the probability of admission to the elite university, around the threshold depends on observable or unobservable characteristics that are correlated with the outcomes under study. In this context, this would manifest in the manipulation of admission outcomes around the threshold by individuals with specific characteristics, for example, if students with better potential outcomes can actively target a score right above the admission cutoff. In the institutional setting under analysis, given the fixed number of admitted students, the purely objective admission procedure, that is, no recommendation letters and no soft skill evaluations, and the idiosyncratic variation in ability of each year’s applying cohort, it is extremely hard for students, and for the admission office, to predict the cutoff score for admission. However, if there was any manipulation, we would observe a discontinuity in the density of applicants at the admission threshold (McCrary 2008). Figure 4 tests for the presence of manipulation of the admission score close to the threshold using the local polynomial density estimators proposed in Cattaneo, Jansson, and Ma (2017). Frequency discontinuity at the cutoff estimated using fully data-driven optimal bandwidth selection is |$-$|0.0685 with a p-value of 0.95. This is reassuring evidence that scores were not manipulated. A second test of local random assignment to the treatment verifies that pre-treatment characteristics are smooth across the threshold. This is analogous to a test for balance of background characteristics in an experimental study. Table 3 and the corresponding Figure 2, panels C–F, show that this “smoothness” condition is verified for several relevant background characteristics. Following Cattaneo et al. (2020), I use Coverage Error (CER)-Optimal Bandwidth to test discontinuity in all predetermined characteristics in panels C–F.31 I fit a local polynomial of degree 1 and a triangular kernel. For the graphical representation, I select bins by relying on data-driven methods: more specifically, I use the Mimicking Variance Evenly-Spaced bin selection method following Calonico, Cattaneo, and Titiunik (2015) to better illustrate the variability of these variables as functions of the admission score. In Table 3, I report robust p-values and confidence intervals using robust inference as developed in Calonico et al. (2014). For Figure 2C, I estimate predicted income based on all relevant predetermined characteristics (parental house value, high school exit score, school cohort fixed effect and gender) using the entire sample of students. This predicted outcome has the advantage of capturing potential discontinuities of all background characteristics at once. Figure 2C and Table 3, column (1) clearly show that there is no discontinuity for this outcome at the cutoff. In Figure 2D–F I, instead, focus on disaggregated predetermined characteristics: a female dummy in panel D, parental house value in panel E and average high school exit score in own high school class in panel F. All figures and their relative point estimates in Table 3 confirm that there is no evidence that predetermined covariates are discontinuous at the cutoff. Figure 4. Open in new tabDownload slide Density test around the admission threshold. Test for the presence of manipulation of admission score close to the threshold implemented using the local polynomial density estimators proposed in Cattaneo, Jansson, and Ma (2017), based on McCrary (2008). Frequency discontinuity at the threshold estimated using fully data-driven optimal bandwidth selection is |$-$|0.0685 with a p-value of 0.95. Sample is all students applying to elite university between 1995 and 2000. Running variable is admission score in deviation from the admission threshold on a 100-point scale. Figure 4. Open in new tabDownload slide Density test around the admission threshold. Test for the presence of manipulation of admission score close to the threshold implemented using the local polynomial density estimators proposed in Cattaneo, Jansson, and Ma (2017), based on McCrary (2008). Frequency discontinuity at the threshold estimated using fully data-driven optimal bandwidth selection is |$-$|0.0685 with a p-value of 0.95. Sample is all students applying to elite university between 1995 and 2000. Running variable is admission score in deviation from the admission threshold on a 100-point scale. Table 3. Discontinuity in predetermined characteristics. . . . . Class . . . . . mean . . Predicted . . . high . . log . House . . school . . income . value . Female . score . . (1) . (2) . (3) . (4) . Score |$> $| Cutoff 0.00530 −0.00254 −0.0767 0.142 Robust p-value 0.989 0.925 0.516 0.909 95% Rob. Conf. Int. [−0.156; 0.154] [−0.143; 0.157] [−0.369; 0.185] [−1.681; 1.890] Control N 129 150 134 153 Treatment N 265 367 289 404 Optimal bandwidth 7.023 9.886 7.697 10.65 Pol. degree 1 1 1 1 Mean Dep. Var. 9.782 8.071 0.458 76.27 S.D. Dep. Var 0.260 0.269 0.499 3.938 . . . . Class . . . . . mean . . Predicted . . . high . . log . House . . school . . income . value . Female . score . . (1) . (2) . (3) . (4) . Score |$> $| Cutoff 0.00530 −0.00254 −0.0767 0.142 Robust p-value 0.989 0.925 0.516 0.909 95% Rob. Conf. Int. [−0.156; 0.154] [−0.143; 0.157] [−0.369; 0.185] [−1.681; 1.890] Control N 129 150 134 153 Treatment N 265 367 289 404 Optimal bandwidth 7.023 9.886 7.697 10.65 Pol. degree 1 1 1 1 Mean Dep. Var. 9.782 8.071 0.458 76.27 S.D. Dep. Var 0.260 0.269 0.499 3.938 Notes: Specification: Regression discontinuity with polynomial of degree 1. Mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). Standard errors clustered at high school/cohort level. Running variable: First observed admission score for each individual in deviation from the cutoff of that year. Dependent Variables: In column (1), income predicted based on predetermined characteristics only. In column (2), a female dummy. In column (3), parental house value. In column (4), average high school exit score in own high school class. Sample|$:$| All students applying to elite university between 1995 and 2000. Open in new tab Table 3. Discontinuity in predetermined characteristics. . . . . Class . . . . . mean . . Predicted . . . high . . log . House . . school . . income . value . Female . score . . (1) . (2) . (3) . (4) . Score |$> $| Cutoff 0.00530 −0.00254 −0.0767 0.142 Robust p-value 0.989 0.925 0.516 0.909 95% Rob. Conf. Int. [−0.156; 0.154] [−0.143; 0.157] [−0.369; 0.185] [−1.681; 1.890] Control N 129 150 134 153 Treatment N 265 367 289 404 Optimal bandwidth 7.023 9.886 7.697 10.65 Pol. degree 1 1 1 1 Mean Dep. Var. 9.782 8.071 0.458 76.27 S.D. Dep. Var 0.260 0.269 0.499 3.938 . . . . Class . . . . . mean . . Predicted . . . high . . log . House . . school . . income . value . Female . score . . (1) . (2) . (3) . (4) . Score |$> $| Cutoff 0.00530 −0.00254 −0.0767 0.142 Robust p-value 0.989 0.925 0.516 0.909 95% Rob. Conf. Int. [−0.156; 0.154] [−0.143; 0.157] [−0.369; 0.185] [−1.681; 1.890] Control N 129 150 134 153 Treatment N 265 367 289 404 Optimal bandwidth 7.023 9.886 7.697 10.65 Pol. degree 1 1 1 1 Mean Dep. Var. 9.782 8.071 0.458 76.27 S.D. Dep. Var 0.260 0.269 0.499 3.938 Notes: Specification: Regression discontinuity with polynomial of degree 1. Mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). Standard errors clustered at high school/cohort level. Running variable: First observed admission score for each individual in deviation from the cutoff of that year. Dependent Variables: In column (1), income predicted based on predetermined characteristics only. In column (2), a female dummy. In column (3), parental house value. In column (4), average high school exit score in own high school class. Sample|$:$| All students applying to elite university between 1995 and 2000. Open in new tab A final concern about my analysis is related to records with a declared income of zero and those with missing tax return records. If students attending the elite university are less likely to declare zero income or to have missing tax return records (e.g., because they graduate faster), my estimates based on the logarithm of income as an outcome may be biased. In Online Appendix Figure A.2 I exploit all cohorts of data available in my sample to show how the elite premium evolves in the first 10 years on the labor market and test the sensitivity of the premium to the inclusion of zero and missing income values and to controlling for whether students had already graduated in 2005, when income is observed. The premium is estimated with an OLS specification of income (in levels) on a dummy variable for enrolling in the elite university. The specification also includes gender, high school exit score, parental house value, potential experience and its squared, high school teacher fixed effects32, high school/graduation year fixed effects and is estimated on 5-year windows centered at each given year on the labor market after university graduation. The solid blue line shows the premium trajectory estimated excluding zero income records, the long dashed line includes zero income records and the short dashed line includes both zero declared income and missing tax returns imputed as zeros. The elite premium estimates appear highly robust to the inclusion of zeroes, especially in the first years on the labor market (the years for which differences in time to graduation should be most relevant). The estimates of the elite premium including a dummy for whether students had already completed university in 2005 (dashed dotted black line) are also almost identical to those of the baseline specification (solid blue line), suggesting that differences in time to graduation are unlikely impacting the estimated elite premium. 6. Results Table 4 and Figure 5 present my main estimates for the returns to elite university attendance for the six cohorts applying to the elite university between 1995 and 2000. Before presenting results based on the RD analysis, it is useful to discuss baseline OLS and IV estimates for the attendance effect. Column (1), panel A of Table 4 presents OLS estimates for the elite university premium for all students graduating from high school in the city under analysis between 1995 and 2000. This sample has a substantially larger control group since it includes all students not applying to the elite university. The OLS specification controls for the same set of predetermined characteristics included for the RD analysis (parental house value, a dummy female and fixed effects for high school graduation year) with clustered standard errors at the same level (high school/cohort). The OLS elite university premium for the population of high school students attending the college-preparatory tracks in the city under analysis is 54 log points. Figure 5. Open in new tabDownload slide Returns to elite university education. Regression discontinuity with polynomial of degree 0, mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014) (A, C, and D) and twice the optimal bandwidth (B). Evenly spaced bin selection method following Calonico et al. (2015a). Sample is students applying to Elite University between 1995 and 2000. Running variable is first observed admission score for each individual in deviation from cutoff of that year. Dependent variable is logarithm of personal taxable income (A and B), probability that tax return has zero taxable income (C) and probability that tax return is missing (D). Figure 5. Open in new tabDownload slide Returns to elite university education. Regression discontinuity with polynomial of degree 0, mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014) (A, C, and D) and twice the optimal bandwidth (B). Evenly spaced bin selection method following Calonico et al. (2015a). Sample is students applying to Elite University between 1995 and 2000. Running variable is first observed admission score for each individual in deviation from cutoff of that year. Dependent variable is logarithm of personal taxable income (A and B), probability that tax return has zero taxable income (C) and probability that tax return is missing (D). Table 4. Returns to elite university education. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment Effect—Dep. Var.: Log(Income) Elite = 1 0.538 0.532 0.583 0.487 0.444 Robust p-value 0.000 0.022 0.044 0.045 0.023 95% Rob. Conf. Int. [0.379; 0.696] [0.076; 0.988] [0.021; 1.536] [0.019; 1.716] [0.112; 1.544] MSE-Opt. Bandwidth 3.849 7.698 11.55 Control N 3168 247 68 87 97 Treatment N 404 398 94 193 285 Mean Dep. Var. Contr. 8.889 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.469 1.358 1.694 1.607 1.591 Panel B: Intent to Treat.—Dep. Var.: Log(Income) Score |$> $| Cutoff 0.362 0.381 0.354 0.317 Robust p-value 0.017 0.046 0.051 0.025 95% Rob. Conf. Int. [0.064; 0.659] [0.008; 0.981] [−0.004; 1.181] [0.072; 1.097] MSE-Opt. Bandwidth 4.191 8.382 12.57 Control N 247 71 90 98 Treatment N 398 104 213 311 Mean Dep. Var. Contr. 9.168 9.087 9.188 9.133 S.D. Dep. Var. Contr. 1.358 1.671 1.609 1.590 Panel C: First Stage—Dep. Var.: Pr(Ever Enrolled at Elite University) Score |$> $| Cutoff 0.680 0.675 0.735 0.729 Robust p-value 0.000 0.000 0.000 0.000 95% Rob. Conf. Int. [0.578; 0.782] [0.465; 0.809] [0.455; 0.814] [0.564; 0.862] MSE-Opt. Bandwidth 4.062 8.125 12.19 Control N 247 70 89 98 Treatment N 398 100 208 299 Panel D: Dep. Var.: Pr(Income = 0) Score |$> $| Cutoff −0.114 −0.0399 −0.0252 −0.0229 −0.0161 Robust p-value 0.000 0.436 0.483 0.711 0.651 95% Rob. Conf. Int. [−0.143; |$-$|0.085] [−0.140; 0.060] [−0.154; 0.073] [−0.150; 0.102] [−0.137; 0.086] MSE-Opt. Bandwidth 5.415 10.83 16.25 Control N 4176 312 96 117 128 Treatment N 469 463 168 333 453 Mean Dep. Var. Contr. 0.241 0.208 0.188 0.179 0.188 S.D. Dep. Var. Contr. 0.428 0.407 0.392 0.385 0.392 Panel E: Dep. Var.: Pr(Income is Missing) Score |$> $| Cutoff −0.135 −0.0894 −0.00636 −0.0305 −0.0361 Robust p-value 0.000 0.067 0.784 0.838 0.986 95% Rob. Conf. Int. [−0.179; −0.091] [−0.185; 0.006] [−0.105; 0.140] [−0.116; 0.143] [−0.116; 0.114] MSE-Opt. Bandwidth 4.483 8.966 13.45 Control N 6188 444 112 145 162 Treatment N 557 549 172 336 483 Mean Dep. Var. Contr. 0.325 0.297 0.196 0.241 0.247 S.D. Dep. Var. Contr. 0.468 0.458 0.399 0.429 0.433 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment Effect—Dep. Var.: Log(Income) Elite = 1 0.538 0.532 0.583 0.487 0.444 Robust p-value 0.000 0.022 0.044 0.045 0.023 95% Rob. Conf. Int. [0.379; 0.696] [0.076; 0.988] [0.021; 1.536] [0.019; 1.716] [0.112; 1.544] MSE-Opt. Bandwidth 3.849 7.698 11.55 Control N 3168 247 68 87 97 Treatment N 404 398 94 193 285 Mean Dep. Var. Contr. 8.889 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.469 1.358 1.694 1.607 1.591 Panel B: Intent to Treat.—Dep. Var.: Log(Income) Score |$> $| Cutoff 0.362 0.381 0.354 0.317 Robust p-value 0.017 0.046 0.051 0.025 95% Rob. Conf. Int. [0.064; 0.659] [0.008; 0.981] [−0.004; 1.181] [0.072; 1.097] MSE-Opt. Bandwidth 4.191 8.382 12.57 Control N 247 71 90 98 Treatment N 398 104 213 311 Mean Dep. Var. Contr. 9.168 9.087 9.188 9.133 S.D. Dep. Var. Contr. 1.358 1.671 1.609 1.590 Panel C: First Stage—Dep. Var.: Pr(Ever Enrolled at Elite University) Score |$> $| Cutoff 0.680 0.675 0.735 0.729 Robust p-value 0.000 0.000 0.000 0.000 95% Rob. Conf. Int. [0.578; 0.782] [0.465; 0.809] [0.455; 0.814] [0.564; 0.862] MSE-Opt. Bandwidth 4.062 8.125 12.19 Control N 247 70 89 98 Treatment N 398 100 208 299 Panel D: Dep. Var.: Pr(Income = 0) Score |$> $| Cutoff −0.114 −0.0399 −0.0252 −0.0229 −0.0161 Robust p-value 0.000 0.436 0.483 0.711 0.651 95% Rob. Conf. Int. [−0.143; |$-$|0.085] [−0.140; 0.060] [−0.154; 0.073] [−0.150; 0.102] [−0.137; 0.086] MSE-Opt. Bandwidth 5.415 10.83 16.25 Control N 4176 312 96 117 128 Treatment N 469 463 168 333 453 Mean Dep. Var. Contr. 0.241 0.208 0.188 0.179 0.188 S.D. Dep. Var. Contr. 0.428 0.407 0.392 0.385 0.392 Panel E: Dep. Var.: Pr(Income is Missing) Score |$> $| Cutoff −0.135 −0.0894 −0.00636 −0.0305 −0.0361 Robust p-value 0.000 0.067 0.784 0.838 0.986 95% Rob. Conf. Int. [−0.179; −0.091] [−0.185; 0.006] [−0.105; 0.140] [−0.116; 0.143] [−0.116; 0.114] MSE-Opt. Bandwidth 4.483 8.966 13.45 Control N 6188 444 112 145 162 Treatment N 557 549 172 336 483 Mean Dep. Var. Contr. 0.325 0.297 0.196 0.241 0.247 S.D. Dep. Var. Contr. 0.468 0.458 0.399 0.429 0.433 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3) mean square error-optimal bandwidth selection and robust inference. In columns (4) and (5), twice and three times the optimal bandwidth. Standard errors clustered at high school/cohort level. Sample: In column (1), all students graduating from high school, in all other columns students applying to the Elite University. Running variable: Admission score in deviation from cutoff. Dependent variable: In panels A and B logarithm of personal taxable income. In panel C, probability of enrolling in the Elite University. In panel D, probability that the tax return has zero taxable income and in E probability that the tax return is missing. Controls: Dummy female, parents’ house value, dummy for students commuting, dummy for whether the individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. Open in new tab Table 4. Returns to elite university education. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment Effect—Dep. Var.: Log(Income) Elite = 1 0.538 0.532 0.583 0.487 0.444 Robust p-value 0.000 0.022 0.044 0.045 0.023 95% Rob. Conf. Int. [0.379; 0.696] [0.076; 0.988] [0.021; 1.536] [0.019; 1.716] [0.112; 1.544] MSE-Opt. Bandwidth 3.849 7.698 11.55 Control N 3168 247 68 87 97 Treatment N 404 398 94 193 285 Mean Dep. Var. Contr. 8.889 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.469 1.358 1.694 1.607 1.591 Panel B: Intent to Treat.—Dep. Var.: Log(Income) Score |$> $| Cutoff 0.362 0.381 0.354 0.317 Robust p-value 0.017 0.046 0.051 0.025 95% Rob. Conf. Int. [0.064; 0.659] [0.008; 0.981] [−0.004; 1.181] [0.072; 1.097] MSE-Opt. Bandwidth 4.191 8.382 12.57 Control N 247 71 90 98 Treatment N 398 104 213 311 Mean Dep. Var. Contr. 9.168 9.087 9.188 9.133 S.D. Dep. Var. Contr. 1.358 1.671 1.609 1.590 Panel C: First Stage—Dep. Var.: Pr(Ever Enrolled at Elite University) Score |$> $| Cutoff 0.680 0.675 0.735 0.729 Robust p-value 0.000 0.000 0.000 0.000 95% Rob. Conf. Int. [0.578; 0.782] [0.465; 0.809] [0.455; 0.814] [0.564; 0.862] MSE-Opt. Bandwidth 4.062 8.125 12.19 Control N 247 70 89 98 Treatment N 398 100 208 299 Panel D: Dep. Var.: Pr(Income = 0) Score |$> $| Cutoff −0.114 −0.0399 −0.0252 −0.0229 −0.0161 Robust p-value 0.000 0.436 0.483 0.711 0.651 95% Rob. Conf. Int. [−0.143; |$-$|0.085] [−0.140; 0.060] [−0.154; 0.073] [−0.150; 0.102] [−0.137; 0.086] MSE-Opt. Bandwidth 5.415 10.83 16.25 Control N 4176 312 96 117 128 Treatment N 469 463 168 333 453 Mean Dep. Var. Contr. 0.241 0.208 0.188 0.179 0.188 S.D. Dep. Var. Contr. 0.428 0.407 0.392 0.385 0.392 Panel E: Dep. Var.: Pr(Income is Missing) Score |$> $| Cutoff −0.135 −0.0894 −0.00636 −0.0305 −0.0361 Robust p-value 0.000 0.067 0.784 0.838 0.986 95% Rob. Conf. Int. [−0.179; −0.091] [−0.185; 0.006] [−0.105; 0.140] [−0.116; 0.143] [−0.116; 0.114] MSE-Opt. Bandwidth 4.483 8.966 13.45 Control N 6188 444 112 145 162 Treatment N 557 549 172 336 483 Mean Dep. Var. Contr. 0.325 0.297 0.196 0.241 0.247 S.D. Dep. Var. Contr. 0.468 0.458 0.399 0.429 0.433 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment Effect—Dep. Var.: Log(Income) Elite = 1 0.538 0.532 0.583 0.487 0.444 Robust p-value 0.000 0.022 0.044 0.045 0.023 95% Rob. Conf. Int. [0.379; 0.696] [0.076; 0.988] [0.021; 1.536] [0.019; 1.716] [0.112; 1.544] MSE-Opt. Bandwidth 3.849 7.698 11.55 Control N 3168 247 68 87 97 Treatment N 404 398 94 193 285 Mean Dep. Var. Contr. 8.889 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.469 1.358 1.694 1.607 1.591 Panel B: Intent to Treat.—Dep. Var.: Log(Income) Score |$> $| Cutoff 0.362 0.381 0.354 0.317 Robust p-value 0.017 0.046 0.051 0.025 95% Rob. Conf. Int. [0.064; 0.659] [0.008; 0.981] [−0.004; 1.181] [0.072; 1.097] MSE-Opt. Bandwidth 4.191 8.382 12.57 Control N 247 71 90 98 Treatment N 398 104 213 311 Mean Dep. Var. Contr. 9.168 9.087 9.188 9.133 S.D. Dep. Var. Contr. 1.358 1.671 1.609 1.590 Panel C: First Stage—Dep. Var.: Pr(Ever Enrolled at Elite University) Score |$> $| Cutoff 0.680 0.675 0.735 0.729 Robust p-value 0.000 0.000 0.000 0.000 95% Rob. Conf. Int. [0.578; 0.782] [0.465; 0.809] [0.455; 0.814] [0.564; 0.862] MSE-Opt. Bandwidth 4.062 8.125 12.19 Control N 247 70 89 98 Treatment N 398 100 208 299 Panel D: Dep. Var.: Pr(Income = 0) Score |$> $| Cutoff −0.114 −0.0399 −0.0252 −0.0229 −0.0161 Robust p-value 0.000 0.436 0.483 0.711 0.651 95% Rob. Conf. Int. [−0.143; |$-$|0.085] [−0.140; 0.060] [−0.154; 0.073] [−0.150; 0.102] [−0.137; 0.086] MSE-Opt. Bandwidth 5.415 10.83 16.25 Control N 4176 312 96 117 128 Treatment N 469 463 168 333 453 Mean Dep. Var. Contr. 0.241 0.208 0.188 0.179 0.188 S.D. Dep. Var. Contr. 0.428 0.407 0.392 0.385 0.392 Panel E: Dep. Var.: Pr(Income is Missing) Score |$> $| Cutoff −0.135 −0.0894 −0.00636 −0.0305 −0.0361 Robust p-value 0.000 0.067 0.784 0.838 0.986 95% Rob. Conf. Int. [−0.179; −0.091] [−0.185; 0.006] [−0.105; 0.140] [−0.116; 0.143] [−0.116; 0.114] MSE-Opt. Bandwidth 4.483 8.966 13.45 Control N 6188 444 112 145 162 Treatment N 557 549 172 336 483 Mean Dep. Var. Contr. 0.325 0.297 0.196 0.241 0.247 S.D. Dep. Var. Contr. 0.468 0.458 0.399 0.429 0.433 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3) mean square error-optimal bandwidth selection and robust inference. In columns (4) and (5), twice and three times the optimal bandwidth. Standard errors clustered at high school/cohort level. Sample: In column (1), all students graduating from high school, in all other columns students applying to the Elite University. Running variable: Admission score in deviation from cutoff. Dependent variable: In panels A and B logarithm of personal taxable income. In panel C, probability of enrolling in the Elite University. In panel D, probability that the tax return has zero taxable income and in E probability that the tax return is missing. Controls: Dummy female, parents’ house value, dummy for students commuting, dummy for whether the individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. Open in new tab Column (2) shows IV estimates (panel A) and reduced-form estimates (panel B) for the subsample of students who applied to the elite university. The reduced form effect estimated for students with an admission score above the cutoff is 36 log points (column (2), panel B), whereas the IV estimate for the effect of elite attendance is 53 log points, which amounts to rescaling the 36 log point reduced form effect by the first stage estimate of 68 percentage point increase in probability of enrolling in the university if the admission score is above the cutoff. Both estimates are precisely estimated. Table 4, columns (3)–(5) present my main RD estimates using a local linear degree-zero polynomial and data-driven bandwidth selection, as described in Section 4. The optimal selected bandwidth is less than 4 points to the right and the left of the cutoff (which corresponds to one-third of the standard deviation in the admission score) and identifies the discontinuity on a very small window around the cutoff.33 The estimated discontinuity for the logarithm of income is 0.38 (column (4), panel B) with a robust p-value of 0.05. Figure 5A represents the same discontinuity graphically over the same optimal bandwidth. When rescaled by the 68 percentage point “first-stage discontinuity” in a fuzzy RD setting, the effect of enrollment in the elite university raises to 58 log points with a robust p-value of 0.04. As a robustness check, I replicate my RD analysis using a bandwidth that is double (Table 4, column (4)) and three times (column (5)) the one estimated by the MSE-optimal procedure. The point estimates for the enrollment effects are slightly smaller (49 and 44 log points, respectively), but not statistically different from the ones obtained with the optimal bandwidth.34 Although these alternative estimates rely on a substantially larger number of observations, they do not appear to improve on precision. About 29% of students admitted to the elite university end up enrolling in other universities. Given this partial compliance, both IV and RD estimates for the effect of elite attendance must be interpreted as the local average treatment effect for compliers (i.e., individuals who choose to attend the elite university if their score is above the admission cutoff and do not attend it when the score is below) among the population of students applying to the elite university. There are several reasons to expect that returns to elite university attendance for compliers are higher than for admitted students deciding to attend other universities. For instance, admitted noncompliers may expect their returns to attending the elite university (net of the higher tuition fee) to be lower than at other universities. In this case, the estimated elite attendance premium might be an upper bound for the returns in the population of students applying to the elite university. To shed some light on what partial compliance implies in this context for my estimates, in Online Appendix Table A.3 I present descriptive statistics for compliers and noncompliers. Students admitted to the elite university but not enrolling appear to be positively selected on average with higher high school exit score and higher university admission score with respect to admitted students who decide to enroll. Top students might expect their returns to be high independently of whether they enroll at the elite university or not and are thus less likely to be willing to pay higher tuition fees to enroll in it. As a matter of fact, when I run a baseline OLS specification in Online Appendix Table A.4, column (2) restricting the analysis to the subsample of students applying to the elite university35, the estimated elite premium shrinks. This is the result of including the 217 high-performance and high-earning noncomplying students in the control group of the OLS specification and suggests that indeed the returns to elite university for noncomplying students are likely to be smaller than for the complying ones. An alternative reason for noncompliance in this institutional setting is students enrolling in a degree not offered by the elite university, (i.e., “hard sciences” such as engineering, physics, mathematics, etc.). They might prefer to do so for instance because they have a comparative advantage in these study fields not offered by the elite university. In Online Appendix Table A.3 I thus take advantage of the university field of study suggestion that high school teachers formalize and report in the (digitized) school registries to characterize noncompliers over this comparative advantage dimension: although admitted students who decide to enroll in the elite university have a probability of 9% to be suggested to enroll in a hard science degree, those who do not enroll have a substantially higher probability (18%). This second piece of evidence on compliers therefore reinforces the hypothesis that the IV/Fuzzy-RD estimates are likely to represent an upper bound for the elite premium in the population of students applying to the elite university. The RD estimate is not only local to the compliers. By construction, it is “local” also to individuals in the proximity of the cutoff. Given that this empirical setting has multiple cutoffs that vary idiosyncratically over the rounds of admission, this effect should be interpreted as a weighted average of RD treatment effects for each cutoff value underlying the original score variable. Given the idiosyncratic nature of the cutoff in each round of admissions, this should marginally extend the external validity of the local treatment effect to a larger set of individuals. A concern about my analysis is the presence of individuals with zero income values or missing tax returns. Given the focus on the log of income as my main outcome, these individuals are dropped from the analysis. This might be especially problematic in the first years on the labor market, for instance because enrollment at the elite university changes time to degree, as I show in Section 7.2. Thus, in Table 4, panels D and E, I estimate the discontinuity in the probability of observing zero income or having a missing tax return. Point estimates for these discontinuities (and the relative graphical representations in Figure 5C and D) are very small and not statistically different from zero (robust p-values range between 0.48 and 0.99 according to different specifications). To ensure that my results are not sensitive to these zero/missing values, in Table 5 I replicate my main specification including zero income in the analysis using the inverse hyperbolic sine of income instead of the log (panel A) and include missing income values as zero (panel B). Estimates are slightly larger, but less precise. This is not surprising since zero and missing income can be a sign of two very opposite academic outcomes: some individuals might have zero or missing income because they are late graduates, or have poor employability, whereas others might find a job abroad or be in graduate school. Although the former type of graduates are likely associated with relatively low potential earnings, the latter are likely the best students with very high potential earnings. Setting outcomes for both these types of individuals to zero will inevitably reduce precision. For this reason, in Table 5, panel C, I predict earnings for these individuals with missing or zero income based on pre-university characteristics and pre-university academic performance. Moreover, I condition the prediction to whether in 2005, that is, the year for which I observe income, the individual was still enrolled in university and to time to degree, which is observed for all students. I do not condition the prediction on any other university performance information, nor on the university attended. Results replacing zero and missing income with this predicted income are very similar in magnitude and precision to the main results obtained dropping individuals with missing and zero income (4 panel A). Table 5. Returns to elite university education—Sensitivity checks. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Inverse Hyperbolic Sine of Income including zero IHS(Income) 1.549 0.772 0.845 0.800 0.653 Robust p-value 0.000 0.139 0.194 0.287 0.204 95% Rob. Conf. Int. [1.255; 1.843] [−0.251; 1.796] [−0.602; 2.970] [−0.885; 2.988] [−0.615; 2.888] MSE-Opt. Bandwidth 3.784 7.569 11.35 Control N 4176 312 83 105 118 Treatment N 469 463 113 233 341 Mean Dep. Var. Contr. 7.269 7.806 7.980 8.140 8.065 S.D. Dep. Var. Contr. 4.296 4.189 4.070 3.997 4.035 Panel B: Inverse Hyperbolic Sine of Income with missing imputed as zero IHS(Inc. = treated as 0) 2.174 1.109 0.886 0.881 0.775 Robust p-value 0.000 0.059 0.289 0.348 0.291 95% Rob. Conf. Int. [1.815; 2.533] [−0.042; 2.259] [−0.815; 2.737] [−1.042; 2.956] [−0.814; 2.716] MSE-Opt. Bandwidth 5.336 10.67 16.01 Control N 6188 444 121 153 168 Treatment N 557 549 202 406 551 Mean Dep. Var. Contr. 4.906 5.486 6.314 6.165 6.078 S.D.Dep. Var. Contr. 4.904 5.008 4.887 4.930 4.934 Panel C: Log(Income) with missing imputed based on individual characteristics Imputed missing inc. 0.424 0.451 0.615 0.453 0.405 Robust p-value 0.000 0.007 0.013 0.017 0.007 95% Rob. Conf. Int. [0.306; 0.542] [0.122; 0.780] [0.165; 1.392] [0.145; 1.473] [0.201; 1.288] MSE-Opt. Bandwidth 3.776 7.552 11.33 Control N 6188 395 95 129 147 Treatment N 557 549 135 274 401 Mean Dep. Var. Contr. 8.747 8.919 8.934 8.964 8.947 S.D. Dep. Var. Contr. 1.151 1.191 1.472 1.377 1.350 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Inverse Hyperbolic Sine of Income including zero IHS(Income) 1.549 0.772 0.845 0.800 0.653 Robust p-value 0.000 0.139 0.194 0.287 0.204 95% Rob. Conf. Int. [1.255; 1.843] [−0.251; 1.796] [−0.602; 2.970] [−0.885; 2.988] [−0.615; 2.888] MSE-Opt. Bandwidth 3.784 7.569 11.35 Control N 4176 312 83 105 118 Treatment N 469 463 113 233 341 Mean Dep. Var. Contr. 7.269 7.806 7.980 8.140 8.065 S.D. Dep. Var. Contr. 4.296 4.189 4.070 3.997 4.035 Panel B: Inverse Hyperbolic Sine of Income with missing imputed as zero IHS(Inc. = treated as 0) 2.174 1.109 0.886 0.881 0.775 Robust p-value 0.000 0.059 0.289 0.348 0.291 95% Rob. Conf. Int. [1.815; 2.533] [−0.042; 2.259] [−0.815; 2.737] [−1.042; 2.956] [−0.814; 2.716] MSE-Opt. Bandwidth 5.336 10.67 16.01 Control N 6188 444 121 153 168 Treatment N 557 549 202 406 551 Mean Dep. Var. Contr. 4.906 5.486 6.314 6.165 6.078 S.D.Dep. Var. Contr. 4.904 5.008 4.887 4.930 4.934 Panel C: Log(Income) with missing imputed based on individual characteristics Imputed missing inc. 0.424 0.451 0.615 0.453 0.405 Robust p-value 0.000 0.007 0.013 0.017 0.007 95% Rob. Conf. Int. [0.306; 0.542] [0.122; 0.780] [0.165; 1.392] [0.145; 1.473] [0.201; 1.288] MSE-Opt. Bandwidth 3.776 7.552 11.33 Control N 6188 395 95 129 147 Treatment N 557 549 135 274 401 Mean Dep. Var. Contr. 8.747 8.919 8.934 8.964 8.947 S.D. Dep. Var. Contr. 1.151 1.191 1.472 1.377 1.350 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3) mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). In columns (4) and (5), bandwidth is respectively twice and three times the optimal bandwidth. Standard errors clustered at high school/cohort level. Sample: In column (1), all students graduating from high school between 1995 and 2000, in all other col. students applying to the elite university between 1995 and 2000. Running variable: First observed admission score for each individual in deviation from cutoff of that year. Dependent variable: In panel A, inverse hyperbolic sine of income including zero tax returns. In panel B, inverse hyperbolic sine of income including zero tax returns and missing tax returns imputed as zero. In panel C, log of income with zero tax returns and missing tax returns imputed based on predetermined characteristics. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, dummy for whether the individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. Open in new tab Table 5. Returns to elite university education—Sensitivity checks. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Inverse Hyperbolic Sine of Income including zero IHS(Income) 1.549 0.772 0.845 0.800 0.653 Robust p-value 0.000 0.139 0.194 0.287 0.204 95% Rob. Conf. Int. [1.255; 1.843] [−0.251; 1.796] [−0.602; 2.970] [−0.885; 2.988] [−0.615; 2.888] MSE-Opt. Bandwidth 3.784 7.569 11.35 Control N 4176 312 83 105 118 Treatment N 469 463 113 233 341 Mean Dep. Var. Contr. 7.269 7.806 7.980 8.140 8.065 S.D. Dep. Var. Contr. 4.296 4.189 4.070 3.997 4.035 Panel B: Inverse Hyperbolic Sine of Income with missing imputed as zero IHS(Inc. = treated as 0) 2.174 1.109 0.886 0.881 0.775 Robust p-value 0.000 0.059 0.289 0.348 0.291 95% Rob. Conf. Int. [1.815; 2.533] [−0.042; 2.259] [−0.815; 2.737] [−1.042; 2.956] [−0.814; 2.716] MSE-Opt. Bandwidth 5.336 10.67 16.01 Control N 6188 444 121 153 168 Treatment N 557 549 202 406 551 Mean Dep. Var. Contr. 4.906 5.486 6.314 6.165 6.078 S.D.Dep. Var. Contr. 4.904 5.008 4.887 4.930 4.934 Panel C: Log(Income) with missing imputed based on individual characteristics Imputed missing inc. 0.424 0.451 0.615 0.453 0.405 Robust p-value 0.000 0.007 0.013 0.017 0.007 95% Rob. Conf. Int. [0.306; 0.542] [0.122; 0.780] [0.165; 1.392] [0.145; 1.473] [0.201; 1.288] MSE-Opt. Bandwidth 3.776 7.552 11.33 Control N 6188 395 95 129 147 Treatment N 557 549 135 274 401 Mean Dep. Var. Contr. 8.747 8.919 8.934 8.964 8.947 S.D. Dep. Var. Contr. 1.151 1.191 1.472 1.377 1.350 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Inverse Hyperbolic Sine of Income including zero IHS(Income) 1.549 0.772 0.845 0.800 0.653 Robust p-value 0.000 0.139 0.194 0.287 0.204 95% Rob. Conf. Int. [1.255; 1.843] [−0.251; 1.796] [−0.602; 2.970] [−0.885; 2.988] [−0.615; 2.888] MSE-Opt. Bandwidth 3.784 7.569 11.35 Control N 4176 312 83 105 118 Treatment N 469 463 113 233 341 Mean Dep. Var. Contr. 7.269 7.806 7.980 8.140 8.065 S.D. Dep. Var. Contr. 4.296 4.189 4.070 3.997 4.035 Panel B: Inverse Hyperbolic Sine of Income with missing imputed as zero IHS(Inc. = treated as 0) 2.174 1.109 0.886 0.881 0.775 Robust p-value 0.000 0.059 0.289 0.348 0.291 95% Rob. Conf. Int. [1.815; 2.533] [−0.042; 2.259] [−0.815; 2.737] [−1.042; 2.956] [−0.814; 2.716] MSE-Opt. Bandwidth 5.336 10.67 16.01 Control N 6188 444 121 153 168 Treatment N 557 549 202 406 551 Mean Dep. Var. Contr. 4.906 5.486 6.314 6.165 6.078 S.D.Dep. Var. Contr. 4.904 5.008 4.887 4.930 4.934 Panel C: Log(Income) with missing imputed based on individual characteristics Imputed missing inc. 0.424 0.451 0.615 0.453 0.405 Robust p-value 0.000 0.007 0.013 0.017 0.007 95% Rob. Conf. Int. [0.306; 0.542] [0.122; 0.780] [0.165; 1.392] [0.145; 1.473] [0.201; 1.288] MSE-Opt. Bandwidth 3.776 7.552 11.33 Control N 6188 395 95 129 147 Treatment N 557 549 135 274 401 Mean Dep. Var. Contr. 8.747 8.919 8.934 8.964 8.947 S.D. Dep. Var. Contr. 1.151 1.191 1.472 1.377 1.350 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3) mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). In columns (4) and (5), bandwidth is respectively twice and three times the optimal bandwidth. Standard errors clustered at high school/cohort level. Sample: In column (1), all students graduating from high school between 1995 and 2000, in all other col. students applying to the elite university between 1995 and 2000. Running variable: First observed admission score for each individual in deviation from cutoff of that year. Dependent variable: In panel A, inverse hyperbolic sine of income including zero tax returns. In panel B, inverse hyperbolic sine of income including zero tax returns and missing tax returns imputed as zero. In panel C, log of income with zero tax returns and missing tax returns imputed based on predetermined characteristics. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, dummy for whether the individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. Open in new tab Finally, in Online Appendix Figure A.4 I perform a standard falsification test by replicating my main RD analysis based on placebo cutoff scores 1 or more points away from the true cutoff. The figure plots estimates for the true and the placebo cutoffs together with robust confidence intervals. It clearly confirms that the only significant income discontinuity present in the data is at the true cutoff, reassuring the causal interpretation of the estimated returns to admission at the elite university. 7. Discussion In this section, I contextualize the magnitude of my estimates and exploit earlier cohort data (those for which admission records are missing) to study the persistence of the elite premium along the labor market trajectory. This provides suggestive evidence about the role of signaling and value-added. I also explore the potential mechanisms underlying the elite value-added and use a simple cost–benefit analysis to provide estimates for the cumulative discounted net returns to elite university education. As shown in Table 4, I estimate sizeable enrollment returns at the elite university (between 44 and 58 log points). To put these returns into context, Oreopoulos and Petronijevic (2013) estimate that the U.S. college-high school premium was 56 log points using CPS data for the same year (2005). university premia in Europe tend to be lower than in the United States (Crivellaro 2014). For Italy, Depalo (2017) uses EU-SILC data for the years 2004–2012 and estimates a university premium of 33 log points for all individuals aged 25–65. To establish a more direct comparison, I have used data from the 2006 Bank of Italy Survey of Household Income and Wealth (SHIW) to estimate the university-high school income premium for individuals who, in 2006 (just a year after I observe income for my sample), had the same age as those in my sample.36 The average Italian university-high school premium is around 35 log points in the first years on the labor market (see the plotted black triangles in Figure 6). Hence my RD estimates for the elite university premium are slightly higher than the Italian university-high school wage premium and similar to the U.S. estimates. Figure 6. Open in new tabDownload slide Longterm elite premium trajectory and comparison with Italian university-high school premium. All trajectories estimated with OLS specification of log income on a dummy for enrolling in the Elite University that includes gender, high school exit score, parental house value, potential experience and its square, teacher team fixed effects, high school |$\times$| graduation year fixed effects. Each point on the graph is estimated on 5-year windows centered at each given year on the labor market after university graduation. Diamonds refer to the elite premium estimates for the baseline trajectory, crosses for the elite premium controlling for field fixed effects and triangles represent the Italian university-high school wage premium estimated using the 2006 Bank of Italy Survey of Household Income and Wealth (SHIW) with a basic mincerian OLS specification. Figure 6. Open in new tabDownload slide Longterm elite premium trajectory and comparison with Italian university-high school premium. All trajectories estimated with OLS specification of log income on a dummy for enrolling in the Elite University that includes gender, high school exit score, parental house value, potential experience and its square, teacher team fixed effects, high school |$\times$| graduation year fixed effects. Each point on the graph is estimated on 5-year windows centered at each given year on the labor market after university graduation. Diamonds refer to the elite premium estimates for the baseline trajectory, crosses for the elite premium controlling for field fixed effects and triangles represent the Italian university-high school wage premium estimated using the 2006 Bank of Italy Survey of Household Income and Wealth (SHIW) with a basic mincerian OLS specification. When comparing my results to other estimates from the literature, it is important to take institutional differences into account. In terms of selectiveness and outcomes, the difference between the elite university and the other universities in my setting could be compared to the case of U.S. private elite college versus moderately selective public universities. However, the higher education system of continental Europe is different and presents a rather bimodal offer with a very large number of public nonselective universities and very few highly selective (private or public) universities in each country.37 In such a higher education system, the drop in selectivity and quality between elite universities and other public universities is certainly more abrupt than in other institutional contexts. Thus, it is not surprising if the income premium estimated in this paper is larger than in other empirical contexts. Hoekstra (2009) finds that U.S. students attending a flagship state university earn 22 log points more than those who attend nonflagship state universities. Brewer et al. (1999) estimate a 42 log point earning premium to attending an elite private institution relative to attending a low quality public college. Using Chinese data, a recent working paper (Jia and Li 2018) estimates returns to enrollment in first-tier Chinese universities between 33 and 47 log points. Saavedra (2014) also exploits an RD design with applicants data for Los Andes University, a top-ranked selective college in Colombia. Although in a different continent, his empirical setting is the one that most closely resembles mine in terms of data and methodology. His fuzzy RD estimates for the effect of enrollment at Los Andes University on earnings one year after graduation range between 30 and 50 log points depending on the bandwidth used. Another institutional feature that is standard in most higher education markets, with the United States being a notable exception, and explains the magnitude of my estimates is the fact that at university enrollment, students choose simultaneously an institution and a field of study because most universities offer only a subset of degrees. This often bundles the decision to enroll at a selective university with the choice of a specific field of study as is the case for the universities under study. As I discuss in Section 7.2, there is a 23 percentage points discontinuity in the probability of enrolling in a major in Economics and Business at the admission cutoff. Since Economics and Business is the highest paying field in this empirical context, part of the large premium is explained by this fact. I developed multiple strategies to identify the role played by field of study choice in the empirical context under analysis. They can explain at most 17 log points so that, net of the preferences for field of study, the lower bound for the purely institutional elite premium component is between 41 (for the estimate with MSE-optima bandwidth) and 31 log points (for the estimate with 3 times the optimal bandwidth), overlapping with most estimates from the cited studies covering different countries and institutional contexts. 7.1. The Elite Premium Trajectory in Early- and Mid-stage Career The results of my analysis reflect labor market returns in early career stages defined as between 1 and 6 years after graduation. One might be concerned that income differentials between elite university graduates and graduates of the other universities in the first years on the labor market are a very noisy proxy of life-cycle returns. For instance, if early career differentials are due to the fact that graduates of the elite university complete their degree faster or they find employment faster after graduation, then differentials might fade away quickly later on in the career trajectory. To address this potential concern, I explore how the elite premium evolves over time. To do so, I proceed in two steps. I first provide suggestive evidence that the RD returns are not driven by the initial years after graduation. Then, I exploit the 10 earlier cohorts that completed high school between 1985 and 1994, which have no admission test scores available, to study longer income trajectories with a mincerian specification saturated with controls and relevant fixed effects. A crucial caveat to the following discussion is related to the fact that I observe income tax returns only for 2005. This implies that any consideration on trajectory relies simply on a comparison across cohorts. Interpreting this comparison as suggestive evidence for the trajectory in the labor market thus requires the strong assumption that the trajectories are similar across cohorts. In Figure 7, I focus on two rounds of admission at a time and plot estimated differences in mean log income between those who are above the cutoff and those who are below it, within a bandwidth around the cutoff equivalent to the optimal bandwidth of my main specification as shown in Table 4, panel A (3.85 points) to gauge the variability of the income discontinuity across cohorts.38 Conditional on the important caveat stated previously, these RD returns for separate cohorts provide some information on the trajectory of the elite premium over the early-stage career since later cohorts have been on the labor market for fewer years and vice-versa. Estimates appear quite stable over the first years on the labor market. I interpret this evidence as a suggestive indication that my main estimates are not driven by abnormal differentials in the very first years after graduation, nor by differences in time to completion across university.39 Figure 7. Open in new tabDownload slide RD elite admission effect—early career trajectory. Each point represents the estimated difference in average log income for those who are below and above the cutoff for 2 consecutive admission cohorts. Averages are calculated within the same optimal bandwidth for my main specification (3.85 points). By the time I observe tax returns for 2005, the two latest cohorts observed applying to the elite university have been on the labor market for 1 and 2 years, the previous two for 3 and 4 years and the earliest two for 5 and 6 years. Figure 7. Open in new tabDownload slide RD elite admission effect—early career trajectory. Each point represents the estimated difference in average log income for those who are below and above the cutoff for 2 consecutive admission cohorts. Averages are calculated within the same optimal bandwidth for my main specification (3.85 points). By the time I observe tax returns for 2005, the two latest cohorts observed applying to the elite university have been on the labor market for 1 and 2 years, the previous two for 3 and 4 years and the earliest two for 5 and 6 years. To study the persistence of the elite premium over a longer period of time, I rely on all available cohorts of data (cohorts graduating from high school between 1985 and 2000) and estimate returns to enrollment in the elite university for the first 10 years on the labor market. In Figure 6, I plot elite return coefficients in log points estimated with an OLS specification that includes gender, high school exit score, parental house value, potential experience and its square, teacher fixed effects, and school/year fixed effects. This specification, thus, controls for substantially more selection than a standard mincerian regression by comparing students graduating from the same high school class, sharing the same teachers, finishing in the same year with the same high school score, etc. In order to smooth the estimates, each coefficient is estimated on a 5-year window, that is, the first coefficient is estimated for students who are 0–4 years on the labor market, the second coefficient on students who are 1–5 years and so on and so forth. Returns to enrollment in the elite university are close to 60 log points in the first 5 years on the labor market, similar to my RD estimates, and slightly decrease to around 50 points later on at the midstage of their career. Overall, these two graphs present evidence that the elite premium has a substantial degree of persistence over the life-cycle. Under certain assumptions, the persistence of the premium over the career can also provide information about the role of ability signaling as potential determinant of the returns to elite university attendance. Following the work of Farber and Gibbons (1996) and Altonji and Pierret (2001), the literature makes a distinction between two different measures of returns to university reputation/quality: the unconditional return—the simple effect of a change in the reputation of the educational institution on earnings—and the conditional return—the effect of a change in the reputation on earnings for individuals with similar ability. Importantly, MacLeod et al. (2017) presents a competitive labor market model that has two different predictions about the correlation between wage trajectories and university reputation based on whether one considers conditional or unconditional returns. First, the unconditional return to reputation is expected to remain constant along the career trajectory. This prediction follows Farber and Gibbons (1996) according to whom the effect of characteristics observable to employers at the moment of first hire on earnings should not change with experience, whereas unobserved characteristics—for example, ability—should increase their correlation with wages the more the employer learn about them. In this framework, university reputation would be observed by employers at hiring and incorporated in the initial wage, therefore its effect should not change with experience. The second prediction of MacLeod et al. (2017) mirrors the intuition by Altonji and Pierret (2001) on “easily observed” variables and “hard-to-observe correlates of productivity” and states that the conditional return to university reputation should fall with experience, unless there are other university characteristics correlated to reputation—for example, value-added—that impact the wage of university graduates. The elite return coefficients in Figure 6 are estimated with a regression that includes, among others, high school exit score, parental house value and teacher fixed effects. These correlates of ability are to be reasonably considered as “hard-to-observe” at the time of hiring. My estimated university quality premia over the career trajectory should thus be viewed as conditional. Under this assumption, if graduation to the elite university under analysis were to only act as signal, we should expect a decline in the elite premium with labor market experience. The evidence that this decline is limited suggests that the elite university has attributes affecting wages beyond pure signaling. These attributes might include added skills, network quality, job placement in sectors or firms with higher wages, etc. Determining the relative importance of these potential attributes in affecting the elite premium goes beyond the empirical potential of this project. Nonetheless, the suggestive evidence on the limited role of ability signaling in explaining the university quality premium is important and mirrors the empirical results of MacLeod et al. (2017). They exploit Colombian college admission data and find that providing more information about students’ individual skills to employers does reduce conditional returns to reputation, however wages and wage growth of graduates remain positively correlated with reputation even after employers have learned about individual ability. MacLeod et al. interpret this as evidence that colleges add to skill and that value-added is correlated to college university reputation. 7.2. Academic Mechanisms If value-added appears to play a role in determining the elite premium, it is interesting to explore the possible academic mechanisms underlying the large “bundled” effect of attendance at the elite university on labor market returns presented in Table 4. In this section, I take advantage of the richness of my data set to explore how admission to the elite university affects academic decisions and performance. The potential channels I explore in my analysis are university completion, time to graduation, peer composition and choice of field of study. In Table 6, I exploit the entire sample of students applying to the elite university and the instrumental variable strategy—as in the main results Table 4, column (2)—to test potential mechanisms. In column (1), I focus on the probability of graduating from university. Students enrolling the elite university were 14.9 percentage points more likely to graduate than those just below, with respect to a 52% baseline probability of graduation for the control group. The estimate is marginally precise, with a p-value of 0.07, but is sizeable. Although the elite university is a more competitive and demanding academic environment, it causally increases chances of degree completion. This evidence is consistent with Cohodes and Goodman (2014), which exploits an RDD and shows that students ending up in lower quality higher education institutions have lower completion rates. Similarly, Bound, Lovenheim, and Turner (2010) find that the declining college completion rates have been most pronounced for individuals enrolling in less selective public universities and community colleges. Table 6. Academic mechanisms. . Pr. . Pr. . Univ. . Enrolled . . college . graduated . peer . Econ. & . . completion . within 6 . quality . Business . . IV . IV . IV . IV . Variables . (1) . (2) . (3) . (4) . Elite = 1 0.149 0.258 5.631 0.274 Robust p-value 0.054 0.000 0.000 0.000 95% Rob. Conf. Int. [−0.003; 0.300] [0.176; 0.341] [4.435; 6.827] [0.147; 0.401] Control N 444 309 309 444 Treatment N 549 549 549 549 Mean Dep. Var Contr. 0.520 0.472 76.68 0.273 S.D. Dep. Var. Contr. 0.500 0.500 2.744 0.446 . Pr. . Pr. . Univ. . Enrolled . . college . graduated . peer . Econ. & . . completion . within 6 . quality . Business . . IV . IV . IV . IV . Variables . (1) . (2) . (3) . (4) . Elite = 1 0.149 0.258 5.631 0.274 Robust p-value 0.054 0.000 0.000 0.000 95% Rob. Conf. Int. [−0.003; 0.300] [0.176; 0.341] [4.435; 6.827] [0.147; 0.401] Control N 444 309 309 444 Treatment N 549 549 549 549 Mean Dep. Var Contr. 0.520 0.472 76.68 0.273 S.D. Dep. Var. Contr. 0.500 0.500 2.744 0.446 Notes: Specifications: 2SLS using admission dummy as an instrumental variable for enrollment in the Elite University. Sample: Students applying to the Elite University between 1995 and 2000. Dependent variable: In column (1), probability of ever completing any university degree. In column (2), probability of completing the degree enrolled within 6 years (zeros also include students dropping the degree enrolled after the admission test). In column (3), average high school exit score of peers in own cohort in the university enrolled after the admission test. In column (4), probability of enrolling an Economics and Business degree after the admission test. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, admission test year fixed effects. Open in new tab Table 6. Academic mechanisms. . Pr. . Pr. . Univ. . Enrolled . . college . graduated . peer . Econ. & . . completion . within 6 . quality . Business . . IV . IV . IV . IV . Variables . (1) . (2) . (3) . (4) . Elite = 1 0.149 0.258 5.631 0.274 Robust p-value 0.054 0.000 0.000 0.000 95% Rob. Conf. Int. [−0.003; 0.300] [0.176; 0.341] [4.435; 6.827] [0.147; 0.401] Control N 444 309 309 444 Treatment N 549 549 549 549 Mean Dep. Var Contr. 0.520 0.472 76.68 0.273 S.D. Dep. Var. Contr. 0.500 0.500 2.744 0.446 . Pr. . Pr. . Univ. . Enrolled . . college . graduated . peer . Econ. & . . completion . within 6 . quality . Business . . IV . IV . IV . IV . Variables . (1) . (2) . (3) . (4) . Elite = 1 0.149 0.258 5.631 0.274 Robust p-value 0.054 0.000 0.000 0.000 95% Rob. Conf. Int. [−0.003; 0.300] [0.176; 0.341] [4.435; 6.827] [0.147; 0.401] Control N 444 309 309 444 Treatment N 549 549 549 549 Mean Dep. Var Contr. 0.520 0.472 76.68 0.273 S.D. Dep. Var. Contr. 0.500 0.500 2.744 0.446 Notes: Specifications: 2SLS using admission dummy as an instrumental variable for enrollment in the Elite University. Sample: Students applying to the Elite University between 1995 and 2000. Dependent variable: In column (1), probability of ever completing any university degree. In column (2), probability of completing the degree enrolled within 6 years (zeros also include students dropping the degree enrolled after the admission test). In column (3), average high school exit score of peers in own cohort in the university enrolled after the admission test. In column (4), probability of enrolling an Economics and Business degree after the admission test. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, admission test year fixed effects. Open in new tab Admission to the elite university may also have an impact on the time students take to complete a degree. Tuition fees at the elite university are three times higher than for the other universities. This might constitute a strong incentive to avoid delaying graduation or an incentive to perform better and obtain higher returns.40 Since I cannot observe time to graduation for dropout students and dropout is an outcome in this setting, in Table 6, column (2), I test whether enrollment at the elite university affects the probability of graduating within 6 years. Conditional on graduating, the average time to completion in the control group of students applying to the elite university but not enrolling is 5.7 years and only 47% of them complete the degree by the end of the |$5{\text{th}}$| year. The estimate shows a large and statistically significant 26 percentage points increase in this probability of enrolling in the elite university. This is clear evidence that university completion and time to degree are important channels in explaining the returns to attending the elite university. Although I cannot make causal statements on how the elite university might increase the probability of graduation, these results imply that some of the educational inputs of the elite university determine a substantial improvement in academic outcomes. For instance, the elite university may have better incentives in place to encourage students to complete their university education. A more intense instructor–student interaction or a more rewarding learning experience might play a role. Looking back at Table 1 might shed light on the institutional features affecting these academic outcomes. The level of expenditure per student is 93% higher at the elite university. However, only a small fraction of these higher expenditures appear to be invested in better-paid faculty (the elite university pays only 13% more per faculty member than other universities). The other dimensions, on which the elite university invests substantially more than the other universities, are infrastructure (e.g., buildings, computers, labs, student spaces, etc.), services to students (e.g., career service, international exchange programs, etc.) and services to faculty (e.g., administration, teaching, and research assistants, etc.). These dimensions might all contribute to the increase in the probability of completing university and to reducing time to degree. Another important factor that goes beyond teaching quality and infrastructure is the quality of peers. In column (3), I estimate a discontinuity in the average quality of peers. Since I only have data for the city under analysis, I define peers as students in my sample who enroll in the same university, degree and cohort. However, it is likely that students from the same city end up being the closest and most relevant peers in this context. Estimates show that admitted students close to the cutoff are exposed to peers that had a score in the high school exit exam 5.6 points higher on average (0.47 of a standard deviation in the high school exit score). Exposure to higher-skilled, more motivated peers might play a crucial role in explaining the improved academic performance for students admitted at the elite university. Although it remains challenging to identify the specific institutional features that positively affect these academic outcomes, my analysis suggests that higher university graduation probabilities and exposure to higher skilled peers are clearly relevant features incorporated in the bundled “value-added” of attending this elite university. In column (4) of Table 6, I test whether the choice of field is one of the relevant channels explaining the estimated returns to elite university attendance. More specifically, I focus on the probability of choosing an Economics or Business degree as an outcome in my specification. The elite university offers a broad range of degrees, but most of all formally listed under the “Business and Economics” label, which may lead admitted students to major in this field more than others. Column (4) of Table 6 shows that students enrolling the elite university are 27 percentage points less likely to major in Business or Economics. In Online Appendix Figure A.5, I show which field students not admitted to the elite university chose. Only 58% of them major in Business and Economics, whereas the remaining 42% majored in law (16%), humanities (5%), engineering (4%), social sciences (4%), or other majors. Students do not appear to rank institutions by a specific chosen field or choose a field conditional on university. On the contrary, they rank a bundle of institution and field choices and trade-off fields for which they might have an absolute advantage or strict preference with institutional quality. Baseline differences in income by field of study are large and the estimate in column (4) of Table 6 shows that admission to the elite university increases the probability to choose a degree in economics and business. The choice of field is clearly an important potential determinant of returns to attending the elite university under study. Although, ideally, one would need a second instrument for major choice to credibly disentangle institution from study field effects in Table 7, I present three alternative suggestive empirical strategies to gauge the importance of field-specific returns for the magnitude of my estimates.41 In panel A I replicate my main fuzzy RD specification (as in Table 4, panel A) including fixed effects for 4 broad fields of study (economics and business, law, STEM and humanities/other social sciences). When compared to Table 4, panel A, these estimates are marginally higher for both the IV (column (2)) and the RD specifications (columns (3)–(6)). Although I am aware that these fixed effects are to be considered as “bad controls”42 in this setting, as they are potential outcomes, and these estimates should be taken with caution, they indicate that differences in field choice are far from explaining the whole elite premium. In Table 7, panel B, I take advantage of earlier cohort data (the ones for which I do not have admission scores) to parcel out field fixed effects from the income variable. I regress the logarithm of income on 11 disaggregated fields of study fixed effects for all 16 cohorts completing high school between 1985 and 2000 and take residuals as my outcome of interest. This strategy has the advantage of being substantially more exogenous than the one in panel A since it relies on a much larger sample of individuals and cohorts with respect to the RD analytical sample. Moreover, it captures longer term differentials in the returns to field. The estimates with this alternative strategy are roughly 17 log points smaller (they are 42 log points for the optimal bandwidth RD specification in column (3)) with respect to the main results in Table 4, panel A, but are less precise. Finally, in Table 7, panel C, I follow a complementary strategy aimed at identifying the impact of different fields at the cutoff. I estimate the log of average income for each of the 11 fields of study using all 16 cohorts completing high school between 1985 and 2000 and impute the average value for each individual based on their field choice. I then replicate the fuzzy RD analysis using these values as outcomes.43 According to this empirical exercise, the impact of field of study effects on the magnitude of my elite premium estimates is around 17 log points. These results are very similar across all RD and IV specifications. This confirms that the choice of field plays an important role in determining the magnitude of the elite premium estimate, however, it can explain only up to about one-third of the overall effect. A simple back-of-the-envelope calculation shows that, net of the 17 field of study effects, the purely institutional component of the elite premium is between 41 (for the estimate with MSE-optima bandwidth) and 31 log points (for the estimate with 3 times the optimal bandwidth). When put into the Italian education context, a gap ranging between 31 and 41 log points is very close to the university-high school premium (35 log points). It is also close to those estimated by previous literature in similar contexts (e.g., Saavedra 2014). To test the robustness of the net-of-field estimate resulting from the RD analysis, I also took a different approach. I exploit the entire sample of high school students graduating from high school between 1985 and 2000 and, in Figure 6, I plot the elite premium trajectory in log points estimated with a specification that controls for gender, high school exit score, parental house value, potential experience and its square, teacher fixed effects and school/year fixed effects. The blue diamonds in Figure 6 represent the baseline elite premium, whereas the green crosses refer to the elite premium estimated by controlling for university field of study fixed effects. The estimates of the net-of-field elite premium are in the range of the log point gaps derived from the RD estimate. Interestingly, the trajectory of the net-of-field premium over the first years on the labor market has very similar values to the average Italian university premium (black triangles) estimated using the SHIW data. Table 7. Returns to elite university education—Field fixed effects. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment effect with field fixed effects—Dep. Var.: Log(Income) Elite = 1 0.339 0.510 0.607 0.527 0.474 Robust p-value 0.023 0.025 0.053 0.038 0.018 95% Rob. Conf. Int. [0.047; 0.630] [0.063; 0.957] [−0.011; 1.657] [0.055; 1.968] [0.166; 1.800] MSE-Opt. Bandwidth 3.817 7.633 11.45 Control N 247 247 68 87 97 Treatment N 398 398 92 192 283 Mean Dep. Var. Contr. 9.168 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.358 1.358 1.694 1.607 1.591 Panel B: Treatment Effect—Dep. Var.: Log(Income residualized with field fixed effects) Elite = 1 0.158 0.363 0.415 0.330 0.284 Robust p-value 0.049 0.145 0.124 0.073 0.066 95% Rob. Conf. Int. [0.001; 0.315] [−0.125; 0.851] [−0.151; 1.246] [−0.068; 1.544] [−0.044; 1.389] MSE-Opt. Bandwidth 4.243 8.487 12.73 Control N 3851 247 71 90 98 Treatment N 404 398 106 216 313 Mean Dep. Var. Contr. −0.787 −0.705 −0.856 −0.731 −0.793 S.D. Dep. Var. Contr. 1.456 1.387 1.673 1.637 1.615 Panel C: Treatment Effect—Dep. Var.: Imputed Log(field average income) Elite = 1 0.409 0.179 0.169 0.173 0.169 Robust p-value 0.000 0.244 0.298 0.306 0.358 95% Rob. Conf. Int. [0.235; 0.583] [−0.122; 0.480] [−0.138; 0.453] [−0.149; 0.476] [−0.186; 0.515] MSE-Opt. Bandwidth 5.073 10.15 15.22 Control N 3851 247 78 96 103 Treatment N 404 398 130 256 363 Mean Dep. Var. Contr. 10.12 10.31 10.38 10.38 10.38 S.D. Dep. Var. Contr. 0.336 0.276 0.329 0.329 0.328 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment effect with field fixed effects—Dep. Var.: Log(Income) Elite = 1 0.339 0.510 0.607 0.527 0.474 Robust p-value 0.023 0.025 0.053 0.038 0.018 95% Rob. Conf. Int. [0.047; 0.630] [0.063; 0.957] [−0.011; 1.657] [0.055; 1.968] [0.166; 1.800] MSE-Opt. Bandwidth 3.817 7.633 11.45 Control N 247 247 68 87 97 Treatment N 398 398 92 192 283 Mean Dep. Var. Contr. 9.168 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.358 1.358 1.694 1.607 1.591 Panel B: Treatment Effect—Dep. Var.: Log(Income residualized with field fixed effects) Elite = 1 0.158 0.363 0.415 0.330 0.284 Robust p-value 0.049 0.145 0.124 0.073 0.066 95% Rob. Conf. Int. [0.001; 0.315] [−0.125; 0.851] [−0.151; 1.246] [−0.068; 1.544] [−0.044; 1.389] MSE-Opt. Bandwidth 4.243 8.487 12.73 Control N 3851 247 71 90 98 Treatment N 404 398 106 216 313 Mean Dep. Var. Contr. −0.787 −0.705 −0.856 −0.731 −0.793 S.D. Dep. Var. Contr. 1.456 1.387 1.673 1.637 1.615 Panel C: Treatment Effect—Dep. Var.: Imputed Log(field average income) Elite = 1 0.409 0.179 0.169 0.173 0.169 Robust p-value 0.000 0.244 0.298 0.306 0.358 95% Rob. Conf. Int. [0.235; 0.583] [−0.122; 0.480] [−0.138; 0.453] [−0.149; 0.476] [−0.186; 0.515] MSE-Opt. Bandwidth 5.073 10.15 15.22 Control N 3851 247 78 96 103 Treatment N 404 398 130 256 363 Mean Dep. Var. Contr. 10.12 10.31 10.38 10.38 10.38 S.D. Dep. Var. Contr. 0.336 0.276 0.329 0.329 0.328 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3), mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). In columns (4) and (5), bandwidth is, respectively, twice and three times the optimal bandwidth. In panels A and B standard errors clustered at high school/cohort level. In panel C standard errors clustered at field of study level. Sample: In column (1), all students graduating from high school between 1995 and 2000, in all other col. students applying to Elite University between 1995 and 2000. Running variable: First observed admission score for each individual in deviation from cutoff of that year. Dependent variable: In panel A, logarithm of personal taxable income. In panel B, residual of logarithm of personal taxable income after regressing log(income) on 11 field of study fixed effects for all 16 cohorts in the data completing high school between 1985 and 2000. In panel C, log of average income for 11 fields of study estimated using all 16 cohorts in the data completing high school between 1985 and 2000 and imputed to each student based on the enrolled field of study. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, dummy for whether an individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. In panel A fixed effects for 4 fields of study (economics and business, law, STEM, or Humanities/other Social Sciences) are also included. Open in new tab Table 7. Returns to elite university education—Field fixed effects. . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment effect with field fixed effects—Dep. Var.: Log(Income) Elite = 1 0.339 0.510 0.607 0.527 0.474 Robust p-value 0.023 0.025 0.053 0.038 0.018 95% Rob. Conf. Int. [0.047; 0.630] [0.063; 0.957] [−0.011; 1.657] [0.055; 1.968] [0.166; 1.800] MSE-Opt. Bandwidth 3.817 7.633 11.45 Control N 247 247 68 87 97 Treatment N 398 398 92 192 283 Mean Dep. Var. Contr. 9.168 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.358 1.358 1.694 1.607 1.591 Panel B: Treatment Effect—Dep. Var.: Log(Income residualized with field fixed effects) Elite = 1 0.158 0.363 0.415 0.330 0.284 Robust p-value 0.049 0.145 0.124 0.073 0.066 95% Rob. Conf. Int. [0.001; 0.315] [−0.125; 0.851] [−0.151; 1.246] [−0.068; 1.544] [−0.044; 1.389] MSE-Opt. Bandwidth 4.243 8.487 12.73 Control N 3851 247 71 90 98 Treatment N 404 398 106 216 313 Mean Dep. Var. Contr. −0.787 −0.705 −0.856 −0.731 −0.793 S.D. Dep. Var. Contr. 1.456 1.387 1.673 1.637 1.615 Panel C: Treatment Effect—Dep. Var.: Imputed Log(field average income) Elite = 1 0.409 0.179 0.169 0.173 0.169 Robust p-value 0.000 0.244 0.298 0.306 0.358 95% Rob. Conf. Int. [0.235; 0.583] [−0.122; 0.480] [−0.138; 0.453] [−0.149; 0.476] [−0.186; 0.515] MSE-Opt. Bandwidth 5.073 10.15 15.22 Control N 3851 247 78 96 103 Treatment N 404 398 130 256 363 Mean Dep. Var. Contr. 10.12 10.31 10.38 10.38 10.38 S.D. Dep. Var. Contr. 0.336 0.276 0.329 0.329 0.328 . . Applied to elite university . . All students . . Opt. Bw. . 2 |$\times$| Opt. Bw. . 3 |$\times$| Opt. Bw. . . OLS . IV . RD . RD . RD . . (1) . (2) . (3) . (4) . (5) . Panel A: Treatment effect with field fixed effects—Dep. Var.: Log(Income) Elite = 1 0.339 0.510 0.607 0.527 0.474 Robust p-value 0.023 0.025 0.053 0.038 0.018 95% Rob. Conf. Int. [0.047; 0.630] [0.063; 0.957] [−0.011; 1.657] [0.055; 1.968] [0.166; 1.800] MSE-Opt. Bandwidth 3.817 7.633 11.45 Control N 247 247 68 87 97 Treatment N 398 398 92 192 283 Mean Dep. Var. Contr. 9.168 9.168 9.047 9.132 9.118 S.D. Dep. Var. Contr. 1.358 1.358 1.694 1.607 1.591 Panel B: Treatment Effect—Dep. Var.: Log(Income residualized with field fixed effects) Elite = 1 0.158 0.363 0.415 0.330 0.284 Robust p-value 0.049 0.145 0.124 0.073 0.066 95% Rob. Conf. Int. [0.001; 0.315] [−0.125; 0.851] [−0.151; 1.246] [−0.068; 1.544] [−0.044; 1.389] MSE-Opt. Bandwidth 4.243 8.487 12.73 Control N 3851 247 71 90 98 Treatment N 404 398 106 216 313 Mean Dep. Var. Contr. −0.787 −0.705 −0.856 −0.731 −0.793 S.D. Dep. Var. Contr. 1.456 1.387 1.673 1.637 1.615 Panel C: Treatment Effect—Dep. Var.: Imputed Log(field average income) Elite = 1 0.409 0.179 0.169 0.173 0.169 Robust p-value 0.000 0.244 0.298 0.306 0.358 95% Rob. Conf. Int. [0.235; 0.583] [−0.122; 0.480] [−0.138; 0.453] [−0.149; 0.476] [−0.186; 0.515] MSE-Opt. Bandwidth 5.073 10.15 15.22 Control N 3851 247 78 96 103 Treatment N 404 398 130 256 363 Mean Dep. Var. Contr. 10.12 10.31 10.38 10.38 10.38 S.D. Dep. Var. Contr. 0.336 0.276 0.329 0.329 0.328 Notes: Specifications: OLS in column (1), IV in column (2), regression discontinuity with polynomial of degree 0 in columns (3)–(5). In column (3), mean square error (MSE)-optimal bandwidth selection and robust inference following Calonico et al. (2014). In columns (4) and (5), bandwidth is, respectively, twice and three times the optimal bandwidth. In panels A and B standard errors clustered at high school/cohort level. In panel C standard errors clustered at field of study level. Sample: In column (1), all students graduating from high school between 1995 and 2000, in all other col. students applying to Elite University between 1995 and 2000. Running variable: First observed admission score for each individual in deviation from cutoff of that year. Dependent variable: In panel A, logarithm of personal taxable income. In panel B, residual of logarithm of personal taxable income after regressing log(income) on 11 field of study fixed effects for all 16 cohorts in the data completing high school between 1985 and 2000. In panel C, log of average income for 11 fields of study estimated using all 16 cohorts in the data completing high school between 1985 and 2000 and imputed to each student based on the enrolled field of study. Controls: Dummy female, parents’ house value, dummy for students commuting from outside the city, dummy for whether an individual is still enrolled in university in 2005 when income is observed, admission test year fixed effects. In panel A fixed effects for 4 fields of study (economics and business, law, STEM, or Humanities/other Social Sciences) are also included. Open in new tab 7.3. Net Discounted Returns Although the annual income premium of attending the elite university is large and significant, it is interesting to evaluate the net returns after taking into account the substantially higher tuition fees. In Figure 8, I present a “net-benefit” calculation that takes into account the trajectory of the premium over the first 15 year on the labor markets, yearly tuition sticker prices, a small difference in average time to graduation and a baseline 3% discount rate to translate the estimated annual income premium into the net returns to investment. I exploit the mincerian specification of Figure 6 with high school/year and instructor fixed effects for the first 15 years after university graduation to model the income trajectory. I rely on the RD 52 log point estimate from Table 4 panel A, column 4 for the first 6 years after university graduation and assume that the RD causal effect estimated has the same trajectory as the mincerian estimates in the following years up to the |$15{\text{th}}$|⁠.44 As Figure 6 shows, cumulative net returns are already positive in the fourth year after university graduation, steep in the first years and have decreasing marginal returns in the following years. After 15 years on the labor market, they cumulate to €246,991. For comparison, the college-high school lifetime expected net returns calculated by Avery and Turner (2012) using the same exact discount rate (3%) for a man at the median of the income distribution are €450,000 ($607,000) and €665,000 ($897,000) for a man at the 75th percentile of the income distribution. The implicit internal rate of return of elite university attendance 15 years after graduation is 55%. Following Hoxby (2017), I also consider the substantially higher expenditure per student of the elite university and estimate productivity for the marginal dollar as the ratio of the net present value of value-added over the net present value of the extra cost to society. I calculated a net present value for the higher expenditure per student of about €30,000, which, compared to the discounted marginal benefit over the first 15 years on the labor market (€285,295), determines a productivity for the marginal dollar of 9.6. Figure 8. Open in new tabDownload slide Net benefits of attending the elite university over the first 15 years on labor market. The figure shows the cumulated expected benefits of attending the elite university net of the differential tuition costs using a discounting rate of 3%. The returns underlying the net benefit calculation are based on the RD local linear estimate with a polynomial of degree zero and double the optimal bandwidth. For years on the labor market after the first five the progression of returns follows the same progression estimated for the full sample using a mincerian OLS specification. Figure 8. Open in new tabDownload slide Net benefits of attending the elite university over the first 15 years on labor market. The figure shows the cumulated expected benefits of attending the elite university net of the differential tuition costs using a discounting rate of 3%. The returns underlying the net benefit calculation are based on the RD local linear estimate with a polynomial of degree zero and double the optimal bandwidth. For years on the labor market after the first five the progression of returns follows the same progression estimated for the full sample using a mincerian OLS specification. 8. Conclusions I exploit a newly collected administrative Italian data set following students from high school through university and into the labor market to estimate returns to enrolling at an elite university in Italy. I take advantage of a sharp discontinuity in the probability of admission at the admission score cutoff to obtain quasi-experimental estimates of returns to enrollment. This regression discontinuity approach allows me to overcome concerns of selection bias due to students selecting into elite universities based on unobservable characteristics correlated with potential income. This study expands the literature about the returns to elite higher education by providing novel evidence for the institutional setting typical of higher education systems in continental Europe, which are characterized by a rather bimodal quality distribution with a very large number of public nonselective universities and very few, highly selective universities. I estimate a causal income elite premium for students enrolling at the elite university ranging between 44 and 58 log points according to the bandwidth considered in the RD analysis. Results are robust to different bandwidths and to an alternative IV strategy exploiting the whole sample of applicants. These estimates are large with respect to the average Italian university-high school premium (35 log points) and are comparable to the U.S. one (56 log points). The estimated enrolment effect should be interpreted as the average treatment effect for individuals close to the admission cutoff who choose to enroll, among the population of students applying to the elite university. I find that students obtaining an admission score just above the admission cutoff are 27 percentage points more likely to choose economics or business as their field of study. I show that net of field choice, the residual institutional quality effect of attending the elite university ranges between 31 and 41 log points. These estimates are in line with those previously estimated in Colombia (Saavedra 2014), China (Jia and Li 2018), and slightly larger than those estimated in the United States (Hoekstra 2009). I also present a net-benefit analysis that takes into account tuition costs, average time to graduation and a 3% discounting rate to translate the estimated annual income premium to discounted net returns to investment. This exercise shows that cumulative net returns to attending the elite university already are positive in the fourth year after graduation and are equal to €246,991 15 years after graduation. This is equivalent to an implicit internal rate of return of 55%. The estimates I obtain must be interpreted as the effect of the “bundled” value-added of the elite university. This might be a result of several educational inputs such as faculty, research, physical capital investments, career services, but also be potential effects of peer effects, networks, and signaling. To understand whether signaling play an important role in this context, I test whether the returns to attending the elite university are persistent over the course of one’s career, in a regression that controls—among other variables—for high school exit score, parental house value, and teacher fixed effects. Under the assumption that these correlates of ability are “hard-to-observe” for employers at the time of hiring, my estimated university quality premia can be viewed as conditional returns in the sense of MacLeod et al. (2017) and should be expected to fall with experience if university quality correlates with earnings only through ability signaling. The very limited decline of conditional returns to quality over the course of graduates’ career in my sample suggests that the elite university has attributes affecting wages beyond pure signaling, namely value-added. I thus explore the academic mechanisms that point at possible positive impacts on human capital. I find that students attending the elite university are 15 percentage point more likely to complete a university degree and they are 26 percentage points more likely to graduate on time. This suggests that the educational environment of the elite university may motivate students more. Competitive and motivated peers or more effective instruction might play a role in this. Attendance at the elite university indeed determines a considerable change in the average quality characteristics of university peers. Finally, a comparison of institutional characteristics shows that the elite university invests marginally more in the faculty salaries, but substantially more in services and physical capital per student. Acknowledgments I thank Silvia Barbareschi, Jack Melbourne, and Giulia Olivero for their great research assistantship. I am grateful to Paola Borsetto, Enrica Greggio, Erika Zancan for providing data that are crucial for the success of this project. I thank Tito Boeri, Michele Pellizzari, and Giovanni Peri for their support with data collection and their comments. I thank also David Autor, Gaetano Basso, Colin Cameron, Scott Carrell, Caroline Hoxby, Hilary Hoynes, Michal Kuerlander, Michael Lovenheim, Claudio Lucifora, Paco Martorell, Douglas Miller, Hessel Oosterbeek, Marianne Page, Na’ama Shenhav, Seth Zimmerman, the participants of the CESifo Area Conference on Employment and Social Protection, of the seminars at UC Davis, Stanford, Sonoma State University, LMU, Bocconi University, Bank of Italy, Copenhagen University, LISER, fondazione Rodolfo DeBenedetti and the NBER Education Program Meeting for important comments. The author is a CESifo Research Fellow and an IZA Research Affiliate. Footnotes 1. Alternative rankings, not based on earnings, have been proposed by scholars. Avery et al. (2013), for example, make use of college choices of high-achieving students to create a revealed preference ranking of American colleges and universities. 2. Importantly, for the validity of my research design, probability of matching tax return data is smooth across the admission cutoff, as shown in Table 4, panel E. 3. Saavedra (2014) and Zimmerman (2019) focus on Colombia and Chile and rely on an empirical settings with a mix of private and public (two-thirds of colleges are private in the Columbian setting) universities where the tuition-selectivity tradeoff is limited across alternatives. 4. Consider, for instance, Grandes écoles in France, Pompeu Fabra in Spain, LMU in Germany, the University of Zurich in Switzerland, and many others. 5. The empirical context of Canaan and Mouganie (2018) is not informative about the admission effect to “grandes écoles”, the French equivalent of the margin studied in my work. 6. The same high school data have also been used in Anelli and Peri (2019). 7. Data have been obtained from the website of the Ministry of Education at the following link http://dati.istruzione.it/opendata/opendata/catalogo/elements1/?area=Studenti. 8. These 11 schools were originally 13 but 4 of them were combined into 2 large schools in the 1990s. 9. Property value data have been provided by the governmental agency “Agenzia del Territorio”. The earliest possible available values for housing in each neighborhood is 2013. Although house prices have gone up overall, there have not been drastic changes in relative values across different neighborhoods. 10. Of the unmatched 10% of students graduating from university, 68% attended another Italian university outside the city under analysis, whereas the rest went abroad for their university studies. 11. The administrative file of reported income includes all individuals in the country and it is mandatory to report any income. If a person does not appear it is because he/she has no income or he/she lives outside the country. Self-employed are included in the sample. 12. The survey was conducted by “Carlo Erminero & Co.”, an Italian company specialized in surveys. 13. Nine hundred ninety-three students as shown in Figure 1. 14. Unfortunately, no digital data set with high school and university records is available for the cohorts under analysis. Tracking academic careers thus implied digitization of hard-copy registries, which was costly and time-consuming already for one city. 15. For instance, applicants to the elite universities coming from outside the city are often willing to move only if they are admitted to the elite university, but they otherwise enroll in universities that are geographically closer to their places of residence. Absent a coverage of university records for students attending university outside of this city, the analysis would be affected by a worrisome sample selection. 16. All cohorts of students in my analytical sample applied to university under the pre-Bologna reform process and thus attended 4-year degree programs under the old regime. 17. Of the other four universities, one is private with nominal tuition fees that are about half those of the elite university under analysis, whereas the other state universities require low token fees. 18. At the end of high school, all Italian students take an exit exam prepared by the Ministry of Education and graded by external committees. Scores are thus comparable across schools. 19. The mean score was 75 and the standard deviation is 10.9 on a 0–100 scale. 20. This is not an extraordinary institutional feature. Most related studies on college quality face a similar context in Europe, central America, and even Asia. 21. Defined as managers, professionals, directors or business-owners. 22. Most studies using tax return data focus on similar measures. For instance Chetty et al. (2014) focus and adjusted gross income. 23. Degrees in Economics and Business are also offered by the other private university in the sample and one of the public universities. 24. In the years under analysis there were, on average, around 3,300 students attempting the test with around 2,500 spots available (76% admission rate). 25. It is indeed frequent in the data to observe that the lowest admission score in the second step is higher than in the first step. 26. Tuition at the elite university is almost four times higher than tuition at the other universities. 27. In Online Appendix Figure A.3 and Table A.2 I also show the discontinuity estimated using a polynomial of degree 1. The discontinuity estimate is indeed larger. 28. This level captures correlation within the relevant high school network and is the most demanding specification, allowing for a number of clusters that is sufficient for correct inference and following Cameron and Miller (2015). 29. Since including this control is problematic, in Online Appendix Table A.1 I also present results for specifications that exclude this dummy. Results are very similar, but slightly larger, suggesting that when we do not take into consideration part-time work during university, a portion of the elite income differential around university graduation might be driven by a higher rate of part-time student jobs among the students of the nonelite universities. I have also tested a third alternative specification in which I restrict the analysis to students who are not enrolled in university in 2005. Results, available upon request, are very robust with respect to the inclusion of the dummy as a control. 30. Hoxby (2017) presents a similar argument. She compares the outcomes of students who apply to the same postsecondary institutions, thus demonstrating similar interests and motivation, but attended different ones for a “coin flip”. 31. Since in this case we want to test the null hypothesis of no effect, CER-optimal bandwidth selection is the most appropriate bandwidth selection method because it gives more weight to inference with respect to the bias. 32. For each high school class within a school, I can associate a specific team of teachers. I can thus track which students in different cohorts were taught by the same teachers during high school. 33. I have also considered asymmetric optimal bandwidths based on separate MSE to the right and to the left of the cutoff. The resulting bandwidths are very similar to the symmetric one. 34. Three times the optimal bandwidth roughly corresponds to one standard deviation in the admission score. 35. Table A.4, column (1) in the Online Appendix replicates, as a reference, the OLS estimates for the entire population of high school students as in Table 4, column (1). 36. Estimates were obtained from basic Mincerian OLS regression models controlling for age, experience, and regional fixed effects. 37. Consider, for instance, Grandes écoles in France, Pompeu Fabra in Spain, LMU in Germany, the University of Zurich in Switzerland, and many other examples. 38. Given the size of my analytical sample, I cannot use my main nonparametric RD specification. I take two cohorts at a time because it is the most disaggregate level at which I can estimate differences between averages in a small bandwidth with some precision. This is equivalent to estimate a fully parametric RD specification with a zero-degree polynomial. 39. I define years on the labor market in an “exogenous sense” by considering the fifth year since university enrollment to be the first year of potential labor market experience independently of effective graduation. 40. Using a regression discontinuity design, Garibaldi et al. (2012) find that an increase of €1,000 in tuition fees reduces the probability of late graduation by at least 6.1 percentage points with respect to a benchmark average probability of 80%. 41. To my knowledge, the only paper that causally identifies separate field and institution effects is Kirkeboen et al. (2017) in the context of Norwegian higher education. However, the scope for studying returns to university quality in their setting is very limited since cross-institution heterogeneity in Norway is very low in terms of quality and selectivity. Their analysis indeed shows a very limited role of institutional quality in determining earnings. 42. See Angrist and Pischke (2008). 43. For this specification, I cluster standard errors at the field of study level, however, the inference is likely not reliable in this setting. The objective of this exercise is solely to retrieve a point estimate. 44. 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TI - The Returns to Elite University Education: a Quasi-Experimental Analysis
JO - Journal of the European Economic Association
DO - 10.1093/jeea/jvz070
DA - 2020-03-20
UR - https://www.deepdyve.com/lp/oxford-university-press/the-returns-to-elite-university-education-a-quasi-experimental-iEoqSmsqTo
DP - DeepDyve
ER -