Unbundling returns to degrees and skills: Evidence from postsecondary education in Colombia

Busso, Matias; Muñoz, Juan Sebastián; Montaño, Sebastián Working Paper Unbundling returns to degrees and skills: Evidence from postsecondary education in Colombia IDB Working Paper Series, No. IDB-WP-01089 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Busso, Matias; Muñoz, Juan Sebastián; Montaño, Sebastián (2020) : Unbundling returns to degrees and skills: Evidence from postsecondary education in Colombia, IDB Working Paper Series, No. IDB-WP-01089, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0002121 This Version is available at: https://hdl.handle.net/10419/234678 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode Unbundling Returns to Degrees and Skills: Evidence from Postsecondary Education in Colombia Matías Busso Juan Sebastián Muñoz Sebastián Montaño IDB WORKING PAPER SERIES Nº IDB-WP-1089 January 2020 Department of Research and Chief Economist Inter-American Development Bank January 2020 Unbundling Returns to Degrees and Skills: Evidence from Postsecondary Education in Colombia Matías Busso* Juan Sebastián Muñoz** Sebastián Montaño*** * Inter-American Development Bank ** University of Illinois at Urbana Champaign *** University of Maryland at College Park Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Unbundling returns to degrees and skills: evidence from postsecondary education in Colombia / Matías Busso, Juan Sebastián Muñoz, Sebastián Montaño. p. cm. — (IDB Working Paper Series ; 1089) Includes bibliographic references. 1. Wages-Colombia. 2. Labor market-Colombia. 3. Vocational qualifications- Colombia. 4. Human capital-Colombia. I. Muñoz, Juan Sebastián. II. Montaño, Sebastián. III. Inter-American Development Bank. Department of Research and Chief Economist. IV. Title V. Series. IDB-WP-1089 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 Attribution- NonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. 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The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2020 Abstract1 This paper shows that returns to education are not enough to capture all the returns to human capital. Using longitudinal data of all college graduates in Colombia, we estimate labor market returns to postsecondary degrees and to various skills— including literacy, numeracy, foreign language, field-specific, and non-cognitive skills. Graduates of longer programs, of private institutions, and of schools with higher reputation earn higher wages. Even after controlling for all the characteristics of the degree, a one standard deviation increase in each skill predicts an average wage increase of two percent. Returns to skills vary along the wage distribution, with tenure, with the field of specialization and the type of job obtained immediately after graduation. JEL classifications: I20, I24, J24, J31 Keywords: Returns to skills, Returns to education, Numeracy, Literacy, Foreign language, Specific skills, Non-cognitive, Colombia 1 Matías Busso: Research Department, Inter-American Development Bank ([email protected]). Juan Sebastián Muñoz: Department of Economics, University of Illinois at Urbana Champaign ([email protected]). Sebastián Montaño: Department of Economics, University of Maryland ([email protected]). The data used in this research were provided by the Ministry of National Education through Agreement # 1465 (of 2017). We are especially grateful to the team of the Labor Observatory for Higher Education, which collects and manages the administrative records used in this project. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the University of Illinois, the University of Maryland, and the Inter-American Development Bank, its Board of Directors, or the countries they represent. 1 Introduction There is a long-standing tradition in economics of estimating returns to human capital by using the years of education with which the individual enters the labor market. This paper shows that returns to education are not enough to capture all the returns to human capital. We jointly estimate the labor market returns to various types of postsecondary degrees as well as to several types of skills (academic, specific and non-cognitive). We find that for individuals who graduated from similar programs, a one standard deviation increase in the measure of skills yields an average wage premium of 2 percent. Similarly, for students of comparable skills, the market valuation of postsecondary degrees is positive and varies widely with the length and quality of the program. We combine administrative records from a variety of sources to build a longitudinal data set that follows students from high school to college and into the labor market. Students in Colombia are evaluated after high school graduation by means of a mandatory standardized test (analogous to the SAT in the United States) on mathematics, language (Spanish), foreign language, and other subjects. We combine those data with information on students’ enrollment and graduation in postsecondary programs. For all college graduates we observe a rich set of characteristics including their field of study and the length of the program. Students who are about to graduate from two- and four-year colleges undergo evaluations on mathematics, literacy and foreign language, as well as on specific tests related to their field of studies (akin to the subject GRE). Furthermore, after graduation, Colombia’s Ministry of Education surveys a subgroup of recent graduates in a follow-up survey that contains measures of non-cognitive skills. We combine all these data with records from the Colombian Social Security Administration that contain information on wages and employment characteristics. We use an expanded Mincer earnings function to jointly estimate the labor market returns to different types of degrees and skills. We assuage concerns of an ability bias by controlling for a broad range of measures of both baseline and contemporaneous skills as well as quality measures of the different programs. A similar approach was taken recently, for instance, by Saiz and Zoido (2005), Hanushek et al. (2015), and Lindqvist and Vestman (2011). We first estimate returns to finishing different types of higher education degrees. We distinguish among four types: i) public two-year programs, ii) private two-year programs, iii) public four-year programs, and iv) private four-year programs. We find that the annual returns to graduating from a four-year private school (instead of a two-year public program) are 6 percent. Following MacLeod et al. (2017), we compute a measure of college reputation: for each individual the reputation of her college is calculated as the average of the high school exit exam among graduates in the same college. A one standard deviation in our measure of college reputation carries a wage premium of 3 percent. There is also a large heterogeneity in the returns by fields of study. Similarly to Kirkeboen et al. (2016), we find that the returns to certain fields are as large as the returns to completing a four-year college. We then estimate that, conditional on the degree, the program and its reputation, an 2 increase in one standard deviation in skills yields a wage return of 2 percent. Returns to education are not enough to capture all the returns to human capital. Returns to skills are fairly homogeneous. The returns to purely academic skills, numeracy and literacy, are 2 and 2.5 percent, respectively. Returns to foreign language are 1.6 percent. Returns to specific skills are 2.2 percent and the wage premia to non-cognitive skills are 2.3 percent.2Because tests scores are imperfect measures of a person’s skills, returns could be biased towards zero. We provide instrumental variables estimates that use high school exams as instruments to alleviate the attenuation bias potentially caused by measurement error. We explore different patterns of heterogeneity in the returns to skills. First, consistent with Farber and Gibbons (1996), we find that the returns to those skills that are less observable to the employer (numeracy and literacy), increase with tenure in the firm while returns to a more easily observable skill (such as foreign language) is constant. We assume that foreign language skills are easier to evaluate in an interview than skills in numeracy or literacy. Second, individuals realize what we term “returns to specialization.” For example, people who work or study in more math-oriented fields and industries have a higher return to numeracy, whereas individuals who graduate from social sciences have a larger return to literacy, and individuals who work in tourism have a higher return to foreign language skills. Third, returns to numeracy are higher for people graduating in most fields of study, and working in most economic sectors. Fourth, we find that women have more returns to foreign language skills than men. This study contributes to a large literature estimating returns to skills. Most of the previous literature provide estimates for developed countries. Our estimates for Colombia, a developing country with relatively low quality of education, fall within the range of estimates previously found in other studies. Returns to numeracy skills have been found to be on the order of 2 to 20 percent (Levine and Zimmerman,1995;Murnane et al.,1995;Tyler,2004; De Coulon et al.,2008;Song et al.,2008;Joensen and Nielsen,2009;James,2013;Hanushek et al.,2015). Returns to foreign language have been found to be around 2.5 to 60 percent (Bleakley and Chin,2004;Saiz and Zoido,2005;Christofides and Swidinsky,2010;Azam et al.,2013;Guo and Sun,2014;Budr´ıa and Swedberg,2015;Di Paolo and Tansel,2015; St¨ ohr,2015). Returns to literacy have been found to be as high as 20 percent (Ishikawa and Ryan,2002;De Coulon et al.,2008;Fasih et al.,2013;Hanushek et al.,2015;Sanders,2016). Several papers find that non-cognitive skills are valued in the labor market as much as cognitive skills (Bowles et al.,2001;Heckman et al.,2006;Lindqvist and Vestman,2011;Dasgupta et al.,2017). Similarly to this literature, we find that field-specific and non-cognitive skills are also as valued in the labor market as academic skills are.3To the best of our knowledge we are the first to estimate all these measures jointly. This paper also contributes to the literature analyzing the heterogeneity in the returns to different types of postsecondary degrees on two dimensions (Hastings et al.,2013;Rodr´ıguez 2The estimates of returns to one year of education were obtained using the Integrated Household Survey data (GEIH, according to the Spanish acronym) and are available upon request. 3Appendix Table 1summarizes the results, methodologies and samples used in previous studies. 3 et al.,2015;Kirkeboen et al.,2016;Busso et al.,2017b).4First, controlling for a wide range of measures of skills and for the quality of the college (as measured by its reputation), we find that the types of degrees as well as the field of study affects dramatically future income. Second, we estimate the returns to college reputation and find that this measure leads to sizable increases in wages. The rest of the paper is organized as follows. Section 2describes the Colombian education system and the data used. Section 3presents the results for the returns to skills and postsecondary degrees. Section 4analyzes the robustness and heterogeneity in the estimation of the returns to skills. Section 5then presents the robustness and heterogeneity in the estimation to different types of postsecondary degrees. Section 6concludes. 2 Background and Data Education in Colombia is divided into primary school (first to fifth year), middle school (sixth to ninth year), high school (tenth and eleventh), and postsecondary education. Programs in postsecondary education are divided into college degrees (equivalent to a U.S. bachelor’s degree, with a duration of four years) and two-year programs that offer vocational or technical instruction in different fields. We refer to all the institutions in postsecondary education as colleges, regardless of the duration of the program. During high school, students take classes in mathematics, language (Spanish), and foreign languages as part of the school curriculum. Around 95 percent of schools choose to teach English as a foreign language; therefore, we refer to English and foreign language interchangeably. During postsecondary education, the level and intensity of instruction in these areas depend on the student’s major, but most institutions require a minimum of foreign language knowledge as a graduation requirement. After graduation, students’ abilities and qualifications are extremely valuable in finding a job. Moreover, a mismatch of occupations and skills is more likely to happen among individuals with lower levels of abilities. A survey implemented in 2013 shows that 67 percent of the firms have employed at least one graduate with less than two years of experience and 73 percent, among these firms, consider that knowledge or specific abilities constitute the main selection criteria for hiring a graduate. Measures of Skills. Since 1980, all high school seniors in Colombia have been evaluated before graduation through a mandatory, high-stakes exit exam (Saber 11). The exam is a requirement for graduation, and its results are sometimes used by colleges to make decisions.5 The test resembles the SAT in the United States. It evaluates students in several subjects that, for convenience, we divide into two broad areas: i) general skills, which includes mathe- 4Several studies review the evidence of returns to education in Latin America. See for instance, Psacharopoulos and Ng (1994), Behrman et al. (2007), Bassi et al. (2012), and Lustig et al. (2012). 5Some colleges establish minimum scores that students must achieve to be considered for admission, while others apply their own admission exams and take Saber 11 only as an enrollment requirement. 4 matics, reading and language (in Spanish), and foreign language; and ii) subject skills, which includes biology, philosophy, physics, chemistry, and social sciences. The test is administered in two sessions, each of four hours and 30 minutes. It evaluates general knowledge of each subject with roughly 40 questions. The mathematics test measures basic knowledge in algebra, calculus, geometry, probability, and statistics; students must interpret information, design solutions to problems, follow procedures, and justify steps in problem-solving. The reading test evaluates the student’s ability to understand, interpret, and analyze critically written texts. The language exam tests the ability of the student to communicate in Spanish. The English test evaluates reading, grammar, and vocabulary. Since 2003, college students who completed at least 70 percent of their coursework have been also required to take a college exit exam (Saber Pro). This exam is a graduation requirement and resembles the GRE, both the general and subject tests. The exam provides a strong signal for students readiness to make the transition from college into the labor market. It is very common for schools to provide incentives (e.g., public recognition to the best-performing students within each school) to motivate students to aim for high scores because the results are used for calculating school quality indexes that are routinely published by the Ministry of Education. The college exit exam has two main components; one is general and the other is specific to the field of study from which the student is graduating.6The general section includes tests in numeracy, writing, reading, English, and citizenship abilities. Students have four hours and 40 minutes to complete the test, which includes a total of 161 questions (35 in numeracy, 35 in reading, 35 in citizenship abilities, 55 in English, and one in writing). The numeracy section evaluates basic mathematics knowledge needed to analyze and solve problems using quantitative methods and procedures. The reading section examines the capacity to read analytically by understanding the text and identifying different perspectives and value judgments. The writing section evaluates the ability to communicate ideas of a particular given topic. The English section focuses on testing the ability to communicate effectively in English. The specific section evaluates basic knowledge in the student’s field of study. There is a total of 40 specific exams, and students have 90 minutes to answer between 30 and 60 questions included in each of them. The questions, designed by experts in each of the different areas, follow specific standards that assure comparability of the exams. Economics majors, for instance, are advised to take an Economics Analysis test with micro, macro, and econometrics questions. In addition, since 2005, the Ministry of Education implemented a follow-up survey to recent college graduates that included measures of non-cognitive skills, with the purpose of tracking and evaluating professional performance. The survey was tested from 2005 to 2008 using a sub-sample of recent graduates that voluntarily completed an online form. Starting in 2011, and until 2014, the survey was implemented in person at the moment of graduation, 6Although the general part of the exam started in 2003, major-specific exams were introduced by a staggered roll out. By the second semester of 2011, all students were taking the general tests, while the specific exams have been applied since then to a large share of students. 5 However, controlling for potential pre-graduate sorting into fields recovers point estimates similar to those obtained in Table 1. These results as a whole imply that the measures of skills and the measures of types of degrees capture different information when estimating economic returns. In fact, it poses strong evidence suggesting that the returns to human capital cannot be exclusively attributed either to returns to education or returns to skills, but rather that a combination of both is important. Table 2: Returns to Different Types of Postsecondary Degrees Dependent Variable: log(Current Wage) (1) (2) (3) (4) (5) (6) (7) (8) Two-Years Private 0.046 0.078 [0.012] [0.014] Four-Years Public 0.127 0.175 [0.017] [0.011] Four-Years Private 0.235 0.243 [0.011] [0.020] Graduate Studies 0.163 0.160 [0.015] [0.017] College Reputation 0.042 0.042 [0.005] [0.006] Literacy 0.023 0.022 0.012 0.027 0.022 0.024 [0.002] [0.002] [0.007] [0.001] [0.002] [0.007] Numeracy 0.055 0.058 0.044 0.034 0.029 0.025 [0.005] [0.004] [0.012] [0.002] [0.003] [0.010] Foreign language 0.017 0.017 0.024 0.028 0.024 0.042 [0.003] [0.003] [0.008] [0.006] [0.006] [0.007] Field Specific -0.003 0.021 [0.003] [0.004] Non-Congnitive 0.030 0.023 [0.006] [0.005] Sample: Full Full Full Specific Survey Full Specific Survey Observations 363,330 363,330 363,330 155,939 2,401 363,330 155,939 2,401 R-squared 0.130 0.188 0.118 0.143 0.137 0.177 0.207 0.224 Controls: Individual Yes Yes Yes Yes Yes Yes Yes Yes Baseline Ability Yes Yes Yes Yes Yes Yes Yes Yes Field of Study Yes Yes Yes Yes Notes. Ordinary least squares estimations. The dependent variable is the log of the last observed wage for each individual from 2011 to 2016. 2-3 Years Private is a dummy variable for individuals graduated from technical or vocational tertiary programs taught by private universities, 4 >Years Public includes graduates from bachelor programs taught by public universities, and 4 >Years Private includes graduates from bachelor programs taught by private universities. The omitted category of postsecondary degrees is 2-3 Years Public, which identifies individuals graduated from technical or vocational tertiary programs taught by public universities. Columns (4) and (8) include measure of skills –literacy, numeracy and foreign language– computed from the college exit exam. Individual and field of study controls as described in the notes of Table 1. Standard errors clustered at the municipality level and in brackets. Skills Collinearity. The results in Table 1include simultaneously multiple test score 12 measures that are highly correlated. As previously discussed in Section 2, there is a high degree of skill complementarity: the level of skills of any given individual in a given subject is positively correlated with the skills of that individual in other subjects. This could be, for instance, because having better mathematics skills can allow a student to acquire science skills faster, or because having higher literacy skills, by better understanding the underlying structure of language, can affect the capacity of an individual to learn a foreign language. The simultaneous estimation of equation (1) will therefore yield a lower bound of the effect of skills on wages because the coefficient of one test score will bias the coefficient of the other test score. The separate inclusion of the test score measures, however, will estimate the upper bound of that effect (see (Lindqvist and Vestman,2011)). Table 3shows OLS estimates of equation (1) including every measure of skills simultaneously and separately (to save space, these point estimates are presented stacked).21 In columns (1) to (3) we present the same results as in Table 1, for comparison. Columns (4) to (6) show the point estimates of three and four separate regressions that use equation (1), but include each measure of skills separately. Using the full sample of workers, we again find that numeracy has the highest return (up to 4.4 percent), whereas literacy and foreign language have returns of 3.8 and 3 percent, respectively. Once again, we see that the return to numeracy decreases the most when considering the specific sample, although it remains the largest. Specific skills again show a point estimate among the highest (3.8 percent) when estimated in the same restricted sample. The coefficients on numeracy and literacy decrease, again suggesting that individuals who score high in generic skills also score high in specific skills. Regarding the estimations using the survey sample, we observe that the estimated returns to cognitive skills increase (compared to column (3)), while the return to non-cognitive skills remains stable (2.3 percent). Measurement Error Correction. Test scores are just a proxy variable of the true level of an individual’s skills. In other words, even though the exit exams are official and well established it is possible that test scores measure skills with error, biasing the estimated coefficients towards zero (attenuation bias). To account for this possibility, we assume a classical measurement error setting and instrument the college exit test scores with the high school exit test scores. We additionally control for initial ability. The identification of this model relies on the assumption that the level of a given skill in high school only affects wages through the skills level in college. Columns (7) to (11) of Table 3show the IV estimates. In column (7) we include all three measures of generic skills simultaneously and instrument them with the mathematics, language, and English result in the high school exit exam. The point estimates in the IV estimation increase considerably for literacy and numeracy, and they are similar in magnitude to those found by Lindqvist and Vestman (2011). The coefficient on literacy increases more than the others, and it becomes larger than the coefficient on numeracy. Notice as well 21Appendix Table 8presents the same results in Table 3, but including the point estimates for each type of degrees. 13 Table 3: Extensions: Estimates’ Ranges and Measurement Error Dependent Variable: log(Current Wage) OLS IV: Measurement Error Correction Simultaneous Stacked Simultaneous Stacked (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Literacy 0.027 0.020 0.017 0.038 0.036 0.026 0.075 -0.004 0.105 0.106 0.112 [0.001] [0.002] [0.007] [0.002] [0.002] [0.007] [0.011] [0.057] [0.012] [0.013] [0.046] Numeracy 0.035 0.025 0.019 0.044 0.041 0.027 0.045 0.154 0.087 0.083 0.140 [0.002] [0.003] [0.010] [0.003] [0.003] [0.010] [0.006] [0.046] [0.008] [0.010] [0.028] Foreign Language 0.016 0.016 0.026 0.030 0.031 0.035 -0.002 0.002 0.040 0.041 0.053 [0.006] [0.006] [0.006] [0.006] [0.006] [0.007] [0.004] [0.027] [0.006] [0.005] [0.022] Field Specific 0.022 0.038 0.123 [0.004] [0.003] [0.017] Socioemotional 0.023 0.023 0.026 0.022 [0.006] [0.006] [0.007] [0.006] Sample: Full Specific Survey Full Specific Survey Full Survey Full Specific Survey Observations 363,330 155,939 2,401 363,330 155,939 2,401 363,330 2,401 363,330 155,939 2,401 Controls: Individual & Field Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Types of Degrees Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Notes. The dependent variable and measures of skills are as described in the notes of Table 1. Estimations within the full sample use the same specification as column (4) of Table 1. Likewise, estimations within the specific and survey samples use, respectively, the specifications of columns (3) and (5) of Table 1. Stacked results refer to separate regressions for each ability measure. In columns (7) to (9), cognitive skills were instrumented using each time numeracy, literacy and foreign language standardized scores computed from the high school exit exam. Individual and types of degrees area as described in the notes of Table 1. Standard errors clustered by municipality and in brackets. that the returns to foreign language decrease and are negative, possibly because it estimates a lower bound when estimated jointly with the other measures of skills. In column (8) we restrict the sample to individuals from the follow-up survey of graduates. This column includes our three generic cognitive abilities and the measure of non-cognitive skills, which we instrument with the mentioned scores from the high school exit exam and a score computed from another set of non-cognitive related questions contained in the survey sample.22 We observe that the returns to non-cognitive skills are similar in magnitude to those found using OLS, while there is a remarkable change for the returns to cognitive skills. Observe that literacy and foreign language returns are close to zero, and the returns to numeracy are up to 15 percent. Column (9) includes each test score measure estimated separately but over-identified using the scores in mathematics, language, and English in the high school exam jointly as instruments.23 We find that all coefficients increase and are much larger than those estimated separately by OLS (in column (4) of Table 3) or estimated jointly (in column (7)). The point estimate on foreign language (4 percent) is now positive. Column (10) deals with the measurement error for workers who took the major specific test. Each point estimate 22Appendix Table 3shows the results from the factor model used to compute the instrument for the measure of non-cognitive skills. 23We also performed estimations using one instrument at a time. The results do not change. 14 corresponds to a separate regression. The results show that, as in the OLS case, the returns to literacy and foreign language do not change largely in this sample (compared to columns (9)), whereas the returns to numeracy decrease. All the coefficients increase compared to column (5), but the increase in specific skills and literacy is remarkable changing from 3.8 to 12.3 percent and from 3.6 to 10.6 percent, respectively. The last column in Table 3shows the results, adjusting for measurement error, for workers contained in the follow-up survey. Estimations are obtained from separate regressions for each measure of skills. We over-identified each measure using mathematics, language, and English from the high school exam, as well as a non-cognitive score computed from the questions contained in the survey of graduates. Literacy and foreign language returns increase (in comparison with column (8)) and are up to 11.2 percent and 5.3 percent, respectively. Returns to numeracy are around 14 percent, and returns to non-cognitive skills stay close to 2 percent.24 Taken together, these estimates indicate that numeracy skills have a return that ranges between 1.7 percent and 14 percent, literacy a return between 1.4 percent and 11.2 percent, foreign language skills between 1 percent and 12.6 percent, specific skills from 2.1 percent to 12.3 percent, and non-cognitive skills return around 1.2 percent and 2.6 percent. These ranges include upper (regressions with each test score alone) and lower bounds (regressions with all the measures simultaneously) accounting and not accounting for measurement error. 5 Beyond Average Returns We now focus on the heterogeneity of returns to degrees and skills. First, we explore heterogeneity across the wage distribution, then we present returns by tenure and, finally, we estimate the returns among fields of study, economic sectors, gender, and firm size. Returns Across Wage Distribution. We estimate conditional regression quantiles for each type of postsecondary degree and present the results in Figure 1. OLS point estimates are plotted to allow comparisons. We use the specification in column (4) of Table 1. Figure 1a shows the results for two-year private, figure 1b for four-year public, and 1c for four-year private. The results suggest an important degree of heterogeneity in the returns to postsecondary degrees. The three graphs show strictly increasing returns with wages, indicating that postsecondary degrees matter more among higher wage quantiles. Note that the lowest point estimate among four-year private degrees is around 0.8, which is comparable to the point estimates on returns to skills. It means that taking individuals from a two-year public program and placing them in a four-year private, keeping abilities constant, will increase the wage by at least 8 percent even if they get a job that pays in the first decile of the wage distribution. A similar increase in wage would be achieved if those same persons stayed in 24We additionally estimate a latent variable model that implements alternative estimation methods to deal with attenuation bias. The results are presented in Appendix D. 15 Figure 1: Returns to Types of Degrees at Conditional Quantiles of the Wage Distribution (a) Two-Year Private (b) Four-Year Public (c) Four-Year Private Notes. The solid lines represent the regression quantiles using Koenker and Bassett (1978) estimator. The dashed lines correspond to an OLS specification. Quantile and OLS estimations for 2-3 years private, 4-year public and 4-year private programs used specification (4) in Table 1. Figures 1a,1b, and 1c used the full sample of students who graduated from 2011 to 2016. OLS standard errors are clustered at the municipality level. Regression quantiles standard errors computed using 20 bootstrap replications. Confidence intervals of 95% are presented for all estimates. the two-year public program but increased their numeracy skills by one standard deviation. In Figure 2we present the results of conditional regression quantiles for each measure of skills.25 We use again the main specification as in column (4) of Table 1and contrast the quantile point estimates with the OLS.26 Figures 2a,2b, and 2c use the full sample of students who took the college exit exam between 2011 and 2016. Figure 2d uses the reduced 25We also estimate unconditional regression quantiles as in Firpo et al. (2009). Results are very similar and available upon request. 26For the case of specific and non-cognitive skills we use specifications (5) and (6) of Table 1, estimating the models in the corresponding restricted samples. 16 sample of students with information about field-specific tests scores. Figure 2e shows the results within the sample of surveyed workers with measures of non-cognitive skills. The returns to all the measures of skills are mostly positive along all deciles. They are lowest among people in the lowest percentiles and increase monotonically until roughly the 40th percentile. The returns to foreign language skills, however, are strictly increasing in the whole distribution, ranging from zero to 0.2. The returns to numeracy remain stagnant beyond the 40th percentile, although these are the highest returns we observe. The returns to literacy and major-specific skills decrease slightly beyond the 50th percentile, but that decrease is not statistically significant. The returns to non-cognitive skills are not precise because of the small sample size. However, they increase until the 20th percentile, remain steady until the 80th percentile and increase again for the top percentiles. One implication of these results is that inequality in the distribution of skills can explain part of the observed wage inequality in Colombia. 17 Figure 2: Returns to Skills at Conditional Quantiles of the Wage Distribution (a) Literacy (b) Numeracy (c) Foreign Language (d) Field Specific (e) Non-Cognitive Notes. The solid lines represent the regression quantiles using Koenker and Bassett (1978) estimator. The dashed lines correspond to an OLS specification. Quantile and OLS estimations for numeracy, literacy and foreign language used specification (6) in Table 1. Figures 2a,2b, and 2c used the full sample of students who graduated from 2011 to 2016. Figures 2d and fig:qregses used, respectively, the sample of students with major-specific test scores available and the sample of individuals in graduate follow-up survey. OLS standard errors are clustered at the municipality level. Regression quantiles standard errors computed using 20 bootstrap replications. Confidence intervals of 95% are presented for all estimates. 18 Returns Across Tenure. In some economics models, wages increase over time as a function of the capability of the employer to observe workers’ abilities (Farber and Gibbons,1996). Skills that are easily observable by the employer (such as foreign language) are predicted to have higher returns in the first year on the job, but then stay constant. The returns to less observable skills (such as numeracy or literacy), on the contrary, are expected to increase as the employer updates her beliefs about the worker.27 Notice that the worker’s type of postsecondary degree is very observable by employers and thus, following the previous argument, returns to degrees should not vary much with tenure. We test that hypotheses between tenure and returns by exploiting the longitudinal feature of the data. Estimations use the same specification as column (4) in Table 1, but among workers with one, two, three, and four years of tenure. Figures 3and 4present the results. In Figure 3we plot the returns to postsecondary degrees across years of tenure. Slight increases in the returns are observed, but the confidence intervals suggest that these slight increases are not in fact significant. We interpret this as evidence in favor of (Farber and Gibbons, 1996), suggesting that the returns to education degrees should not increase with tenure if they are observable for employers. Figure 3: Returns to Degrees by Years of Tenure Notes. The plotted circles, squares and triangles represent the point estimates of 2-3 year private programs, 4-year public programs and 4-year private programs, respectively. Separate regressions were run among workers with different years of tenure to the estimate simultaneously the returns to different types of degrees. Estimations used the same specification as in column (4) of Table 1. The dependent variable is the log(Wage) for each year of tenure. Confidence levels of 95% are presented for all point estimates. Returns across tenure for each measure of skills are presented in Figure 4. We additionally 27We assume that foreign language skills are more observable in a face-to-face interview (which is very common in a hiring process), whereas literacy and numeracy skills are more difficult to observe. 19 include the results among students with field-specific scores for comparability. Non-cognitive skills are not included because of the small sample size of workers who have available scores for this measure. The returns using the complete sample of students are plotted with circles, and the corresponding confidence intervals are represented with a dark area. These results show that numeracy and literacy are increasing with tenure. However, the returns to numeracy increase much more steeply, growing from 1.5 percent to 3.6 percent. The returns to foreign language, on the contrary, do not increase as much; they remain relatively steady across years of tenure. We interpret this as evidence in favor of the Farber and Gibbons (1996) model. We find similar patterns if we restrict the sample to students with available field-specific tests scores. Estimations within this sample use specification (5) in Table 1. Returns are plotted using squares, with whiskers representing confidence intervals. Using this sample, we are able to estimate returns to major-specific skills and observe that these do not change across years of tenure. We explain this by considering that during hiring processes employers may apply tests that allow them to know their applicants’ level of specific abilities. On the other hand, applicants could also reveal their specific skills during interviews in order to increase their probability of being hired. Thus, specific skills could be more observable for employers than other skills, at least in the labor market for college graduates. Returns to Specialization: Field of Study and Economic Sector. Returns to degrees and skills can in part reflect specialization. For instance, individuals with better mathematics skills can choose careers that place greater emphasis on those abilities. Then, they can find jobs that value their skills, receiving higher payments for greater levels. We explore whether the magnitude of returns varies with the person’s specialization (either in field of study or in economic sector). Estimations of returns across different areas of study use specifications (4) and (5) in Table 1without including field of study fixed effects. We exclude the estimation of returns to non-cognitive skills because of low sample sizes. In Table 4we present the returns to degrees and skills across groups of similar postsecondary programs or study areas. We estimate the returns for graduates of STEM, business and economics, social sciences and humanities, and health and education. 20 Figure 4: Returns to Skills by Years of Tenure (a) Literacy (b) Numeracy (c) Foreign Language (d) Field Specific Notes. The plotted circles and squares represent the point estimates for each measure of skills using, respectively, specifications (6) and (8) of 1. Separate regressions were run among workers with different years of tenure to estimate simultaneously numeracy, literacy, foreign language and major-specific skills. The dependent variable is the log(Wage) for each year of tenure. Confidence levels of 95% are presented for all point estimates. We find three main results. First, the positive gradient in the returns to degrees (by which four-year degrees pay more than two-year degrees and graduates from private school earn more than those of public schools) is observed in all fields of study. However, it is more pronounced in STEM, business and social sciences. Second, literacy and numeracy skills matter in all fields. In that sense, these basic skills are always remunerated, probably because they are highly transferable and ubiquitous across fields. Third, there is some evidence of positive returns to specialization in Table 4. Specific skills tend to be homogeneous across fields. Of course, different specific skills would be tested for each program. To shed some light on what those specific skills capture we estimate the model in the full sample without including specific skills (odd columns). Numeracy skills have the highest return in STEM, business and economics, but not in social sciences and humanities; for these individuals, the largest return is to literacy skills. Workers with STEM degrees have the lowest return to literacy skills (2.3 percent). Graduates from health and education degrees have similar returns across all skills. Furthermore, we see that including field-specific skills decreases remarkably the returns to numeracy for most fields, suggesting a large complementarity between specific 21 Dasgupta, U., Mani, S., Sharma, S., and Singhal, S. (2017). 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The Returns to Occupational Foreign Language Use: Evidence from Germany. Labour Economics, 32:86 – 98. Tyler, J. (2004). Basic skills and the earnings of dropouts. Economics of Education Review, 23:221–235. 30 A Appendix: Additional Tables 31 Appendix Table 1: Estimates of the Effect of Cognitive Skills from Previous Literature Skills Reference Country/ Population Identification Estimation Dependent Rangea City in Estimating Strategy Variable Lowest Highest Sample (log) Estimate Estimate Panel A: Numeracy Levine and Zimmerman (1995)USA 1980 HS graduates Selection on Observables OLS 1990 & 1986 weekly wage 0.028 0.030b Murnane et al. (1995)USA 1972 and 1980 HS graduates Selection on Observables OLS 1978 & 1986 hourly wage 0.026 0.069c Tyler (2004)Florida (USA) HS dropouts Selection on Observables OLS 1995-1999 quarterly earnings 0.063 0.074 Song et al. (2008)USA College graduates Selection on Observables IV 1993 earnings 0.181 0.210d Joensen and Nielsen (2009)Denmark 1986 and 1987 HS graduates Quasiexperiment IV 1999-2002 annual earnings 0.12 0.32e Hanushek et al. (2015)Several Adults aged 20 to 50 from 23 OECD countries Selection on Observables OLS 2011-2012 hourly earnings 0.079 0.178f Panel B: Literacy Ishikawa and Ryan (2002)USA Adults above 16 Selection on Observables OLS weekly wages 0.001 0.008g Fasih et al. (2013)Several Males aged 22 to 65 from 20 countries, mostly OECD Selection on Observables OLS hourly wage 0.021 0.210h Hanushek et al. (2015)Several Adults aged 20 to 50 from 23 OECD countries Selection on Observables OLS 1993 earnings 0.068 0.171 Sanders (2016)USA Populations represented in 5 longitudinal surveys Selection on Observables OLS real wages -0.056 -0.024 aEstimates points correspond to standardized test scores, unless another interpretation is suggested. bEstimations correspond to the number of mathematics classes taken during high school. cPoint estimates are given originally for levels of a mathematics score. Since a one standard deviation is 6.25, then coefficients are translated into this scale. Lower and upper bounds correspond, respectively, to 1972 and 1980 high school graduates. dThe mathematics score is estimated in levels. eNumeracy is a dummy valued 1 if individuals took a high-level mathematics course during high school. Reported bounds correspond to the pilot school sample. fNumeracy is also estimated using literacy as instrument and the coefficient found is 0.201. gLower and Upper bounds correspond to the point estimates for Black men’s and Hispanic men’s samples, which respectively are the lowest and highest point estimates. Literacy was estimated in levels. hLower and Upper bounds correspond to the point estimates for Denmark and Bermuda, which are respectively the lowest and largest estimates found. See the paper for more details. 32 Skills Reference Country/ Population Identification Estimation Dependent Range City in Estimating Strategy Variable Lowest Highest Sample (log) Estimate Estimate Panel C :Foreign Language Bleakley and Chin (2004)USA 1960-1974 Young immigrants Quasiexperiment IV 1990 annual wage 0.222 0.334i Saiz and Zoido (2005)USA College graduates Selection on Observables OLS 1997 hourly wage 0.025 0.028j Christofides and Swidinsky (2010)Quebec (CA) Fulltime native workers aged 15 to 64 Selection on Observables OLS 2000 earnings 0.109 0.139k Azam et al. (2013)India Male workers aged 18 to 65 Selection on Observables OLS 2005 earnings 0.345 0.603l Guo and Sun (2014)China College graduates Selection on Observables OLS 2010 monthly wage 0.033 0.131m Budr´ıa and Swedberg (2015)Spain Male immigrants aged 18 to 65 Quasiexperiment IV 2006-2007 hourly wages 0.049 0.204n Di Paolo and Tansel (2015)Turkey Male workers Selection on Observables OLS 2007 wage 0.107 0.072o St¨ ohr (2015)Germany Fulltime workers Selection on Observables OLS 2005-2006 gross monthly wage 0.033 0.093p iThe independent variable takes 1 as value if individual speaks English very well. jIV, Panel and PSM estimations are also considered. For instance, PSM point estimates ranged from 0.020 to 0.021. kPoint estimates correspond to a subsample of only men. The independent variable takes 1 as value if individual uses English in his/her workplace. Estimations are also carried for women and ranged from 0.068 to 0.076. lPoint estimates for a dummy variable that takes 1 as value if the individual is fluent in English. Estimations for knowing little English can be seen in the paper. mThe English score of CET-4 test is used to measure foreign language proficiency, check the paper for more details. nLower bound corresponds to OLS estimation and Upper bound corresponds to IV estimation using simultaneously the following instruments: 1(arrived before 12), 1(has a child proficient in spanish) and 1(willingness to stay in Spain). oThe independent variable takes 1 as value if the individual knows english. Other languages are estimated (French, German, Arabic and Russian), but those who know english account for 76%. pThe independent variable takes 1 as value if the individual’s occupation requires expertise in a foreign language. 33 Appendix Table 2: Non-Cognitive Skills in the Survey of Graduates Questionnaire item Factor Loadings Accept the difference and work under multicultural contexts 0.565 Learn and keep updated 0.593 Work under pressure 0.504 Adopt a coexistence culture 0.589 Work independently without permanent supervision 0.557 Convince and persuade others 0.532 Identify and use communication symbols 0.344 (i.e. non-verbal or iconic language) Abstraction capacity, analysis and synthesis 0.625 Identify, plan and solve problems 0.680 Notes. The answers for each item ranges from 1 to 4: (1) Very unsatisfied, (2) Unsatisfied, (3) Satisfied and (4) Very satisfied. The largest eigenvalue from a factor analysis model is 2.836, and the second largest is 0.109. For each item, the factor loadings in this table correspond to the factor with the largest eigenvalue. The scale reliability coefficient, α, is 0.80. Appendix Table 3: Non-Cognitive Skills Used As Instrumental Variable Questionnaire item Factor Loadings To be creative and innovative 0.5836 Look for, analyze, manage and share information 0.6014 Understand the surrounding reality 0.6350 Assume responsibilities and make decisions 0.6959 Plan and use time effectively to achieve the goals 0.6294 Formulate and execute projects 0.5479 Work in teams to achieve common goals 0.6575 Consider values and professional ethics to perform tasks 0.6479 Adapt to changes 0.6486 Take risks 0.6712 Identify opportunities and resources 0.6660 Notes. The answers for each item ranges from 1 to 4: (1) Very unsatisfied, (2) Unsatisfied, (3) Satisfied and (4) Very satisfied. The largest eigenvalue from a factor analysis model is 4.453, and the second largest is 0.109. For each item, the factor loadings in this table correspond to the factor with the largest eigenvalue. The scale reliability coefficient, α, is 0.88. 34 Appendix Table 4: Descriptive Statistics Estimation Sample Mean Difference Full Specific Survey (N = 363,330) (N = 155,939) (N = 2,401) Mean Std. dev. Mean Std. dev. Mean Std. dev. p-value (1) (2) (3) (1) - (2) (1) - (3) Panel A: Socioeconomic Statistics Age 26.93 3.44 26.86 3.5 28.74 4.57 0.00 0.00 Share female 0.61 0.49 0.63 0.48 0.59 0.49 0.00 0.08 Share living in big urban areas 0.73 0.45 0.71 0.45 0.80 0.40 0.00 0.00 Share living in low income households 0.45 0.50 0.43 0.50 0.46 0.50 0.00 0.40 Share graduate students 0.02 0.14 0.03 0.17 0.04 0.19 0.00 0.00 Panel B: Education Statistics Share graduated from: STEM 0.26 0.44 0.26 0.44 0.25 0.44 0.29 0.36 Business and Economics 0.31 0.46 0.27 0.45 0.27 0.44 0.00 0.00 Social Sc. and Humanities 0.16 0.36 0.15 0.36 0.12 0.33 0.00 0.00 Health and Education 0.22 0.41 0.28 0.45 0.22 0.41 0.00 0.66 Share postsecondary degrees: Two-Year Private 0.09 0.29 0.04 0.20 0.40 0.49 0.00 0.00 Two-Year Public 0.10 0.30 0.05 0.21 0.10 0.3 0.00 0.64 Four-Year Private 0.50 0.50 0.56 0.50 0.32 0.47 0.00 0.00 Four-Year Public 0.32 0.47 0.36 0.48 0.18 0.38 0.00 0.00 Panel C : Occupation Statistics Share working in: Manufacture 0.07 0.26 0.07 0.26 0.08 0.27 0.00 0.60 Commerce 0.03 0.18 0.03 0.17 0.04 0.19 0.00 0.27 Services 0.54 0.50 0.55 0.50 0.60 0.49 0.00 0.00 Turism 0.01 0.10 0.01 0.09 0.01 0.11 0.00 0.83 Retail 0.04 0.20 0.04 0.19 0.04 0.20 0.00 0.95 Share working as: Public Employee 0.03 0.18 0.04 0.21 0.04 0.19 0.00 0.12 Independent Workers 0.07 0.25 0.07 0.26 0.08 0.27 0.09 0.03 Share working in firms that are: [1 −10] 0.15 0.36 0.14 0.35 0.12 0.32 0.00 0.00 [11 −50] 0.18 0.39 0.18 0.39 0.16 0.37 0.97 0.02 [51 −100] 0.08 0.28 0.08 0.28 0.09 0.29 0.32 0.13 [101 −500] 0.21 0.40 0.21 0.41 0.21 0.41 0.15 0.50 [501 −1000] 0.10 0.30 0.10 0.30 0.09 0.29 0.02 0.26 [1001+] 0.28 0.45 0.28 0.45 0.33 0.47 0.01 0.00 Panel D: Labor Statistics Current Wage 16.86 11.24 17.48 11.59 19.75 10.79 0.00 0.00 First Wage 13.42 8.48 14.07 8.88 12.85 7.72 0.00 0.00 Average Wage 15.17 8.86 15.8 9.21 16.19 7.92 0.00 0.00 Current Tenure 1.77 1.02 1.78 1.11 2.28 1.3 0.00 0.00 Notes. Descriptive statistics of students who took the college exit exam from 2011 to 2015 for whom data were matched to earnings and college records. Big urban area refers to the largest 13 cities in Colombia. Low-income households refer to individuals in the first two income strata designated by place of residence. Wages are presented in nominal 2016 USD currency (1 USD = 3,050.98 COP). 35 Appendix Table 5: Correlation Matrix across Test Scores High School Exit Exams College Exit Exams Average Subject Literacy Numeracy Foreign Literacy Numeracy Foreign Panel A: Full Sample (N = 363,330) High School Exit Exams: Subject 0.941* Literacy 0.708*0.595* Numeracy 0.671*0.546*0.394* Foreign Language 0.726*0.571*0.460*0.428* College Exit Exams: Literacy 0.537* 0.497* 0.438* 0.314* 0.390* Numeracy 0.584* 0.553* 0.394* 0.487* 0.401* 0.449* Foreign Language 0.611* 0.515* 0.414* 0.393* 0.678* 0.458*0.464* Panel B: Specific Sample (N = 155,939) High School Exit Exams: Subject 0.941* Literacy 0.705*0.593* Numeracy 0.676*0.553*0.396* Foreign Language 0.727*0.573*0.459*0.431* College Exit Exams: Literacy 0.553* 0.513* 0.446* 0.331* 0.401* Numeracy 0.611* 0.579* 0.409* 0.509* 0.424* 0.470* Foreign Language 0.623* 0.526* 0.419* 0.405* 0.687* 0.472*0.490* Major-Specific 0.520* 0.496* 0.394* 0.344* 0.345* 0.519*0.511*0.413* Panel C : Survey Sample (N = 2,401) High School Exit Exams: Subject 0.933* Literacy 0.708*0.586* Numeracy 0.620*0.483*0.369* Foreign Language 0.668*0.508*0.420*0.347* College Exit Exams: Literacy 0.505* 0.461* 0.430* 0.278* 0.335* Numeracy 0.513* 0.483* 0.373* 0.417* 0.321* 0.395* Foreign Language 0.597* 0.500* 0.434* 0.352* 0.636* 0.463*0.400* Socioemotional: Factor Score 0.054* 0.053* 0.038†0.047* 0.039†0.026 0.025 0.058* Notes. Pairwise correlations are estimated using the Pearson’s formula. For both the college exit exam (Saber Pro) and the high school exit exam (Saber 11), individuals’ scores are standardized with respect to the corresponding average in each test edition. The specific scores from the college exit exam are standardized with respect to the average of the test edition and the corresponding group of related programs. The subject score from the high school exit exam is computed as the standardized average of biology, philosophy, physics, chemistry, and social science tests. The non-cognitive scores were computed as the predictions from a factor model considering categorical answers to nine questions (see Appendix Table 2). †p<0.1, * p<0.05. 36 Appendix Table 6: Other Outcomes Dependent Variable:Dependent Variable:Dependent Variable: log(First Wage After Graduation) log(Avg. Wage Since Graduation) log(Current Earnings) (1) (2) (3) (4) (5) (6) (7) (8) (9) Two-Year Private 0.068 0.061 0.144 0.078 0.077 0.137 0.080 0.084 0.130 [0.009] [0.010] [0.026] [0.011] [0.009] [0.036] [0.014] [0.013] [0.050] Four-Year Public 0.149 0.156 0.287 0.174 0.171 0.263 0.177 0.159 0.199 [0.010] [0.013] [0.029] [0.010] [0.012] [0.029] [0.011] [0.014] [0.041] Four-Year Private 0.211 0.221 0.216 0.244 0.244 0.225 0.251 0.239 0.218 [0.017] [0.019] [0.027] [0.018] [0.018] [0.025] [0.020] [0.022] [0.035] Literacy 0.016 0.010 0.008 0.023 0.016 0.017 0.027 0.020 0.015 [0.001] [0.002] [0.009] [0.001] [0.002] [0.006] [0.001] [0.002] [0.008] Numeracy 0.025 0.018 0.032 0.031 0.023 0.020 0.035 0.026 0.022 [0.001] [0.002] [0.011] [0.001] [0.002] [0.010] [0.002] [0.003] [0.010] Foreign language 0.011 0.013 0.047 0.015 0.016 0.032 0.015 0.015 0.025 [0.003] [0.003] [0.008] [0.004] [0.004] [0.006] [0.005] [0.005] [0.007] Field Specific 0.016 0.020 0.022 [0.003] [0.004] [0.004] Socioemotional 0.010 0.021 0.021 [0.011] [0.008] [0.006] College Reputation 0.026 0.029 0.030 0.031 0.032 0.050 0.032 0.031 0.059 [0.005] [0.005] [0.017] [0.004] [0.005] [0.020] [0.004] [0.005] [0.023] Sample: Full Specific Survey Full Specific Survey Full Specific Survey Observations 363,330 155,939 2,401 363,330 155,939 2,401 363,330 155,939 2,401 R-squared 0.196 0.237 0.244 0.233 0.264 0.324 0.195 0.220 0.244 Controls: Individual Yes Yes Yes Yes Yes Yes Yes Yes Yes Field of Study Yes Yes Yes Yes Yes Yes Yes Yes Yes Notes. Estimations in columns (1), (4) and (7) follow the specification of column (4) in Table 1. Estimations in columns (2), (5) and (8) follow the specification of column (5) in Table 1. Estimations in columns (3), (6) and (9) follow the specification of column (6) in Table 1. The dependent variable for columns (1) to (3) is the log of the first wage observed after the individual’s graduation year. The dependent variable for columns (4) to (6) is the log of the average wage from 2011 to 2016 for each individual, taking into account only wages after the year of graduation. The dependent variable for columns (7) to (9) is the log of the last observed annual earnings for each individual. Individual and field of study controls as described in the notes of Table 1. Standard errors are clustered at the municipality level and in brackets. 37 two cases, we are not able to link or merge them into our sample, explaining our merging results. Appendix Table 10: Results by Merging Technique with Saber Pro Dataset Dataset Identity Card Record Linkage High School Exit Exam (Saber 11) 281,861 905,748 (0.98) Undergraduate Enrollees (Spadies) 1,027,802 160,435 (0.97) Graduates Social Security Records (OLE) 922,684 12,844 (0.96) Notes. The numbers in this table correspond to individuals merged with a total of 1,448,395 Saber Pro test-takers. Record linkage merging method used names and birthdates to pair individuals. Average Jaccard index of similarity between names in parenthesis. A score of 1 is assigned to names with perfect similarity, a score of 0 is assigned to names without similarity. We required birth dates to be equal in order to merge individuals. After assembling the mentioned datasets with the Saber Pro population, we obtain a subset of 743,542 students who belong to the intersection of the three merging processes. However, we also make some selection of individuals in order to have more homogeneous samples. For instance, some individuals may have taken the college exit exam on different occasions. These could be individuals attending different undergraduate programs. For these, we keep the information from the first observed test scores, considering that those should reflect their level of skills at the time when they entered the labor market as graduates. It is also possible that some students took the high school exit exam more than once. In that case, we leave the information from the first observed results, keeping in mind that some individuals could have prepared after graduating from high school to apply for funding or a scholarship. It is also possible that students took the test more than once in order to get the minimum scores required to be admitted to some undergraduate programs. Also, we drop individuals who are under 19 or above the retirement age in Colombia (i.e. 57 years old for women and 62 for men). Individuals who graduated from other undergraduate programs before 2012 are dropped as well. We exclude observations with missing values in any of the independent variables commonly used in our regressions, remaining with a pool of 437,673 test-takers. We link them to individuals in a follow-up survey of graduates that contains information on non-cognitive abilities. The survey takes a stratified probabilistic sample from students who received their diplomas during the past year, three years ago and five years ago. Using the 2013 and 2014 surveys, we obtain information for a random sample of individuals whobelong to cohorts of graduates from 2011 to 2013. Notice that for the described sample, we observe values for gender, age, socioeconomic stratum, and also for literacy, numeracy and foreign language skills from both the college and high school exit exams. However, we may not have information about their high school, their specific skills, their non-cognitive skills or current wage. Thus, from this pool or complete sample (N= 437,673), we obtained three subsets: i) a full sample with formal workers for whom we observe high school and current wage (N= 363,330); ii) a specific sample with formal workers for whom we observe high school, current wage, and a measure of specific skill (N = 155,939); and iii) a survey sample with formal workers for whom we observe a 44 measure of non-cognitive skills and current wage, but for whom we may not observe their high school of graduation (N = 2,401). D Appendix: Alternative Robustness on Returns to Skills Following Heckman et al. (2006) and Acosta et al. (2015), we additionally address the potential attenuation bias by estimating the returns using a latent skills model. This model identifies the underlying latent parameters of a set of skills and estimates the associated economic returns. Assume the following model in which wages (W) are a function of latent skills (Θ) and other observables (XW). The reduced equation is given by: W=αWΘ + XWβW+eW(2) While the latent variable is unobservable, there are measures available in the data (i.e., test scores) that represent realizations of latent skills: T=αTΘ + XTβT+eT(3) where Tis an L×1 vector of test scores, and Lcorresponds to the number of associated test scores per latent skill. The identification assumption states that eT⊥eWconditional on (Θ, XW), and that L≥3.37. Parameters αW, αT, βWand βT, from equations (2) and (3), can be jointly estimated by maximizing the following likelihood function: L= N Y i=1 ZnfeW(XW, W, ζΘ)×feT1(XT1, T1, ζΘ)×... ×feTL(XTL, TL, ζΘ)odFΘ(ζΘ) (4) The results of this model (αW) should be interpreted as the economic return of a latent skill allowing for the presence of unobserved heterogeneity (Sarzosa and Urz´ua,2016; Carneiro et al.,2003). Since the return should be read in levels of the latent skill, we use the estimated distribution of the skill, c FΘ(ζΘ), to rescale αWso it can be read in terms of standard deviations. This way we can compare the results from this model with those previously obtained. Identification requires at least three test scores for each latent skill. Thus, to estimate the effect of latent literacy skills we use writing and reading scores from the college exit exam and the language (Spanish) test scores from the high school exit exam. To identify the latent effect of numeracy we use the numeracy measures from the college exams and the standardized mathematics and physics scores from the high school exit exams. For foreign language we use the test scores from the college and high school exit exams, and the social science score from the high school exit exam, since it is strongly correlated with the results on foreign language (0.46). Among the survey sample we replace the social sciences scores 37More details about these identification assumptions are given in Sarzosa and Urz´ua (2016). 45 with self-assessed information in the graduates’ follow-up survey about respondents’ abilities in listening, speaking, reading and writing in a foreign language.38 For major-specific skills we use different scores from the set of field-specific tests in the college exit exam, and a combination of scores from the high school exit exams. 39 For non-cognitive skills we divided the nine questions used to build the non-cognitive measure into three dimensions. We therefore exploit the full extent of the data and the large number of available tests scores to estimate the returns to latent literacy, numeracy, major-specific, and non-cognitive skills. This model is computationally demanding, and estimation times increase dramatically with sample size, controls, and the number of factors or latent skills to estimate (Sarzosa and Urz´ua,2016). Therefore, we respectively took two random samples of 36,403 and 15,585 individuals from both the complete set of test takers working formally and the set of formal workers with specific scores available.40 Notice as well that we use all the individuals in the survey sample to estimate the model. Appendix Table 11 presents the estimation of the latent skill model for each sample and, for comparison, it also presents OLS estimations. Again, simultaneous and stacked results could be interpreted as lower and upper bounds. Within the survey sample, the results suggest that latent numeracy skills have the largest returns (from 4.8 percent to 7.2 percent), followed by latent literacy skills (5.1 percent to 6 percent), foreign language skills (up to 1.8 percent) and, finally, non-cognitive skills (around 2 percent). On the other hand, using the random sample representing our complete set of students, we see that numeracy returns up to 6.4 percent, literacy latent skills returns from 3.7 percent to 7.1 percent, and foreign language returns up to 12 percent. The results from the sample representing the students with field-specific scores show that latent specific skills returns up to 6.7 percent. 38The follow-up survey includes a module in which respondents assess their own ability in listening, speaking, reading and writing in a foreign language. This information is only available for the sub-sample that was surveyed. 39Given the constraint on the number of test scores, we do this only for individuals who have taken only one or two specific tests and exclude those who took three. For students in health and agronomy, we use biology and chemistry test scores. For education, social sciences, humanities, and economics and business, we use history and geography tests scores. For students in arts, we use philosophy and history test scores. For engineering, mathematics and natural sciences we use chemistry and biology. 40We conducted a stratified probabilistic sampling within both sets of information: i) the set of workers who took the college exit exam between 2011 and 2015, and ii) the workers for whom specific test scores are available. Strata were defined using the nine test editions of the college exit exam, 18 groups of related majors, six cohorts of graduates, four groups or quartiles defined using the average score in the college exit exam, and quartiles defined by the current wage of individuals. Within each stratum, we applied a simple random sampling methodology to select 10 percent of test-takers. Expansion factors were computed as πkh =nh Nh, with nhas the number of sampled individuals in stratum h, and Nhas the original number of individuals in h. 46 Appendix Table 11: Structural Estimations: Measurement Error Correction Dependent Variable: log(Current Wage) OLS in Random Sample Unobserved Heterogeneity Simultaneous Stacked Simultaneous Stacked (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Literacy 0.029 0.013 0.040 0.030 0.037 0.035 0.051 0.071 0.070 0.060 [0.002] [0.007] [0.003] [0.006] [0.006] [0.009] [0.012] [0.004] [0.006] [0.011] Numeracy 0.032 0.033 0.042 0.047 -0.002 0.014 0.048 0.064 0.073 0.072 [0.004] [0.007] [0.005] [0.007] [0.007] [0.010] [0.020] [0.004] [0.006] [0.012] English 0.018 0.016 0.031 0.031 0.096 0.126 0.011 0.049 0.058 0.018 [0.007] [0.009] [0.008] [0.008] [0.011] [0.016] [0.011] [0.003] [0.005] [0.011] Field Specific 0.023 0.040 0.031 0.067 [0.005] [0.005] [0.007] [0.005] Socioemotional 0.023 0.022 [0.012] [0.011] Sample Full Specific Full Specific Full Specific Survey Full Specific Survey Observations 36,403 15,585 36,403 15,585 36,403 15,585 2,401 36,403 15,585 2,401 Controls: Individual & Field Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Types of Degrees Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Notes. The dependent variable is as described in the notes of Table 1. Columns (1) and (3) use the same specifications as columns (1) and (4) of Table 3, but within a stratified random sample. Columns (2) and (4) use the specifications of columns (2) and (5) of Table 3, within another random sample. Expansion factors for each random sample were used to estimate columns (1) to (4). The point estimates from the unobserved heterogeneity model are originally computed in levels of each latent skill. Using the standard deviation of these skills, we rescale the coefficients and the standard errors applying the “delta method.” From columns (5) to (10), to estimate literacy we used i) writing scores from the college exit exam, ii) reading scores from the college exam, and iii) language (Spanish) scores from the high school exit exam. Numeracy used i) quantitative reasoning scores from the college exam, ii) mathematics scores from the high school exam, and iii) physics scores from the high school exam. Foreign language used i) foreign language scores from the college exam, ii) foreign language scores from high school exam, and iii) a factor score predicted using self-reported ability in a foreign language for columns (7) and (10). For columns (5), (6), (8) and (9) we used the social science scores from the high school exam as the third score for foreign language. For non-cognitive estimations, we divided the nine categorical questions of Appendix Table 2into three scores, each time computed using a factor analysis model. Major-specific skills used the specific test scores from the college exit exam. When a student has only taken one or two specific tests in the college exam, we used the set of test scores from the high school exam, depending on the study area of the student (see footnote 26). Stacked results refer to separate regressions for each ability measure. Field of study and type of degrees controls as described in the notes of Table 1, however individual controls in columns (5) to (10) do not include high school fixed effects and the initial ability proxy. 47