This paper considers one of the intangible aspect of human capital: the university knowledge accumulation. It is relevant both for academic management and for recruitment world. In the former case it can be an useful guide to identify the characteristics of clever students, while in the latter case it can be applied to worker selection. Because of the velocity of credit acquisition is not sign of cleverness, it becomes important to analyze different aspects of university human capital accumulation. We will investigate it through latent growth modeling on administrative data come from an Italian university

Simonetto, Anna

Zavarrone, Emma

SIMONETTO, Anna

Archivio istituzionale della ricerca - Università di Brescia

Evaluation of Human Capital in anEducation-Based PerspectiveEmma Zavarrone and Anna SimonettoAbstract This paper considers one of the intangible aspect of human capital: theuniversity knowledge accumulation. It is relevant both for academic managementand for recruitment world. In the former case it can be an useful guide to identifythe characteristics of clever students, while in the latter case it can be applied toworker selection. Because of the velocity of credit acquisition is not sign of clever-ness, it becomes important to analyze different aspects of university human capitalaccumulation. We will investigate it through latent growth modeling on administra-tive data come from an Italian university.Key words: University human capital, Latent growth model, Gompertz curve1 IntroductionSince the beginning of modern economic thought, the human capital (hereafter HC)and its implication on growth process have been widely analyzed. The HC defini-tion can be considered an expression of its time, so it has undergone several exten-sions and adjustments from its first appearance. Currently, OECD [10] introduces,in the HC definition, the non-market activities, outlining a set of “knowledge, skills,competencies and attributes embodied in individuals that facilitate the creation ofpersonal, social and economic well-being”. The OECD definition appears the mostcomplete one and it would seem to indicate the successful completion of the HCtheory both in terms of national accountability and individual analysis. Howeversome methodological problems are still unresolved, i.e. which kind of metric has toEmma ZavarroneDepartment of Communication, Behaviour and Consumption “Giampaolo Fabris”, IULM Univer-sity, e-mail: emma.zavarrone@iulm.itAnna SimonettoDepartment of Economics and Management, University of Brescia, e-mail: simonett@eco.unibs.it12 Emma Zavarrone and Anna Simonettobe adopted for HC investments. This absence can be justified by the nature of HCmeasurement: HC is formed by intangible and tangible aspects so a unique measureleads to the underestimation of some components. Several types of measurementmodels have been proposed, based on different approaches.We adopt the education-based approach, in order to quantify the training or ed-ucational paths pursued. In details, we analyzed the process of accumulation of in-tangible aspects of HC during the university using latent models. We configure asub-dimension of HC given by the difference between students’ HC before enter-ing university and the HC held at graduation. We refer to the definition proposedby Civardi and Zavarrone [3] (hereafter CZ), where this sub-dimension of Uni-versity HC, called UHC, can be defined as the improvement of knowledge, skillsand attitudes attained thanks to the educational activities, the use of didactic struc-tures, passed exams and social interaction with fellow students. In CZ, UHC hasbeen measured through exams, considering their marks and ECTs (European Uni-versity Credits). These proxies, adequately multiplied and normalized, have beencumulated for each slice of time. CZ applied this measure at five courses of Eco-nomics at the Bicocca University in Milan, and they observed that the growth ofUHC was nonlinear. The use of variance component model has highlighted that theaccumulation process of knowledge was characterized by different velocity accord-ing to discipline courses analyzed. On the same data, analogous results have beenachieved using the three way analysis [6]. Bianconcini and Cagnone [1] estimatedthe students’ performances over time using a multivariate latent growth approach.They linked some students’ covariates (as gender, type and degree of Bachelor) tothe characteristics of the achieved exams (number and mark),and used as manifestindicators of student performances. Their results show the effective presence of sig-nificant differences in the latent variable of performance: lowest mark at bachelorlevel imply worse performance in University.We want to extend the analysis of UHC considering different ways in which thestudents acquire knowledge during the time they spent at university. Since the latenttrajectory of UHC is not linear, it becomes important to quantify the knowledgeaccumulation velocity. We use a set of variables to explain these different velocities,thus constituting different clusters of characteristics of students.Section 2.1 is devoted to the methodology, in Section 2.2 we explain the useddata and report the results in Section 2.3. The conclusions and further developmentsare in the last section.2 Analysis2.1 MethodologyIn social and behavioral sciences, the change over time can be studied through thegrowth curves approach on repeated observations. It allows to explain the changesEvaluation of Human Capital in an Education-Based Perspective 3inter-individuals through linear and/or nonlinear functions. The literature disentan-gles growth curves models via multilevel and via latent variable methodologies. Inthe multilevel approach, a simple way to study the change over time is a two-levelmodel in which level-1 refers to the individual growth and level-2 to the variationof growth parameters as random effects [11]. In the latent variables methodologies,the manifested change is the consequence of a latent variable change, expressed interms of latent intercept and latent slope. The confirmatory factor analysis repre-sents the starting point for these estimates [7]. Y is the vector of repeated measures,Λ is the matrix of factor loadings, η is the vector of latent factors and ε is the vectorof residuals: Y = Λη + ε. In linear cases, the latent factors (η) are intercepts (αi)and slopes (βi):η = µη +ζ[αiβi]=[µαµβ]+[ζαiζβi]In this study, we will focus on the latent growth curves. These two parallel sta-tistical perspectives, under restrictive hypothesis, lead to the same results [8]. Wemodel the latent change in UHC from one time to another and we use the person-parameter of the accumulation curve to identify a set of covariates that can help usto pinpoint students who accumulate knowledge more quickly and with better per-formances. We divide the analysis process in two stages: in the first one we estimatethe latent Gompertz curve that models the acquisition of UHC over time by indi-vidual students. In the second stage we use the UHC estimates to cluster students.Following Grimm and Ram [4], we implemented the following model in Mplus 6.12[9]:Ti= 1∗g0 +Li∗g1 + εi i= 1,2, ..., t (1)Li= e(−e(−α∗(i−λ ))) i= 1,2, ..., t.Ti (i = 1,2, ..., t) are the t temporal splits, α is the rate of change, λ represents thetime at which maximum growth rate occurs, g0 is the lower asymptote, and (g0+g1)is the upper asymptotic value of the function. α e λ are phantom variables, so theyare unrelated to all other variables in the model, and have no variance. Their role isto constrain the slope loadings (Li) to follow the prespecified Gompertz functions.2.2 DataData come from the statistical office of IULM University. The demo-social aspects(identification number, gender, date of birth, secondary school’s type and mark) anduniversity characteristics (enrollment year, course enrollment, marks, credits andtime of examinations, types and marks of bachelor degree) are investigated for twocohorts of enrolled students at the five faculties of IULM. The first cohort refers tothe students enrolled in 2006 (N1 = 864); the second one to the students enrolled in4 Emma Zavarrone and Anna Simonettothe 2007 (N2 = 803). In this application we analyze only students who have gradu-ated by the end of 2012 (i.e. 67% and 63% of 2006 and 2007 cohort, respectively).Tab. 1 contains some statistical insights on demo-social structures of the cohorts.Table 1 Descriptive statistics for graduate students in the cohort 2006 and 2007aCohort 2006 Cohort 2007Type of Bachelor degree (%)Lyceum 66.60 67.97Technical 23.01 19.33Others 10.38 12.70Mark of Bachelor degree 79.61 (12.35) 77.85 (11.84)Age at degree 23.46 (1.54) 23.36 (2.11)Degree’s grade 96.54 (8.80) 96.49 (8.91)a In the brackets standard deviation valuesIn order to quantify the university knowledge accumulation, we use the UHCmeasure based on the product between mark and credits for each examination [3]:mc j(i) =∑jmark j(i)∗ credit j(i)UHC j(T ) =∑Ti=1mc j(i)maxmc.mc j(i) is the UHC acquired in the i-th time split by the j-th student, maxmc equals30 (maximum grade without considering the possible “laude”) per 174 (numberof formative credits to be achieved in order to access the degree, which is worth6 credits), and UHC j(T ) is the normalized cumulated UHC acquired till the T-thtime split. The observed trajectories of the UHC j(T ) in the two cohorts suggest toanalyze the knowledge accumulation using a nonlinear approach (see Fig. 1 andTab.2). Following the CZ research, we use a Gompertz function to estimate the rateof accumulation.2.3 ResultsIn the first phase of the analysis we estimated the latent Gompertz curve that modelsthe acquisition of UHC over time by individual students. To identify the time in-stants of interest, we conducted an Exploratory Factor Analysis (EFA) on the examsessions. As results of the EFA, for the cohort 2006 we used as splits: January, April,June, September from 2007 to 2009 and January 2010. We implemented a Gompertzmodel (see Eq. 1) with 13 temporal splits (henceforth defined “Long-time Gom-pertz model”). For the “Long-time Gompertz model”, we obtain χ2 = 3616.417,RMSEA = 0.290, CFI = 0.761, and TLI = 0.745. As these fit statistics are decid-Evaluation of Human Capital in an Education-Based Perspective 5Fig. 1 Observed trajectories for 2006 and 2007 cohortsTable 2 Mean of UHC measures from 2007 to 2011Months Cohort 2006 Cohort 2007 Months Cohort 2006 Cohort 20072007 January 0.04 (0.03) – 2010 January 0.74 (0.16) 0.50 (0.14)April 0.06 (0.04) – April 0.76 (0.15) 0.54 (0.15)June 0.16 (0.07) – June 0.79 (0.13) 0.67 (0.18)September 0.23 (0.07) – September 0.80(0.12) 0.73(0.17)2008 January 0.29 (0.10) 0.04 (0.03) 2011 January 0.80 (0.11) 0.75 (0.15)April 0.30 (0.10) 0.04 (0.03) April 0.81 (0.10) 0.78 (0.14)June 0.42 (0.14) 0.15 (0.03) June 0.82 (0.09) 0.80 (0.12)September 0.48 (0.14) 0.21 (0.07) September 0.82 (0.08) 0.81 (0.10)2009 January 0.54 (0.15) 0.25 (0.09)April 0.55 (0.15) 0.27 (0.09)June 0.65 (0.18) 0.39 (0.13)September 0.72 (0.17) 0.46 (0.14)a In the brackets the standard deviation valuesedly unpleasant, we decided to continue the investigation by testing new models. Aswell known, the significance of χ2 can be misleading if sample size is large or theassumption of multivariate normality has been violated. Both cases characterize ourapplication then we can neglect the information come from this class of indexes.We can neglect RMSEA too: the index assumes high values when residual vari-ances are quite small [2], as in our application. Hu and Bentler [5] suggestested touse alternative indexes as IFI, CFI, and SRMR for fit evaluating.Focusing on these indices, we chose the model that considers a shorter period,ie the last 7 splits (2008: June, September; 2009: January, April, June, September;2010: January, see Fig. 2). We summarized the parameters’ estimates and the fitstatistics of the “Short-time Gompertz model” in Tab. 3. Obviously for the cohort2007, split times have been shifted to a year.The average growth rate is not constantbetween the two cohorts and it indicates that the cohort of 2007 performs better .This is reflected in a mean time-to-degree lower than the 2006’s cohort. Obviously itis a partial comparison due to the fact that the observation time is different between6 Emma Zavarrone and Anna Simonettothe two cohorts. For both cohorts, starting at L4 (April 2009, see Fig. 2) we noticea change in the individual trajectories, embodied in the allocation of a predominantrole to the disciplines addressed in the final phase. Among these exams, there areobviously those belonging to the third year of the curriculum, but also those that arefaced as last because they are perceived as difficult.The objective of the second phase of the analysis is to identify homogenousgroups of students according to their ability to accumulate UHC. Our interest is todefine the characteristics of these groups. Using Gompertz growth curve model pa-rameters and graduation marks, we perform a hierchical cluster analysis with Ward1linkage. We divided the graduates into three clusters, indicating 3 different levels ofUHC: “A-fast and good students”; “B- good but not fast students”; “C- neither goodnor fast”. Tab. 4 summarizes the characteristics of these groups.Looking at the cohort of 2006, the 3 clusters are sorted with respect to the es-timates of UHC. For ease of reading, we reported only the average grade in eachcluster and the corresponding standard deviation. With reference to the geographi-cal residence, passing from the group of the fastest and good to that of less clever,lower the percentage of students from the northeast Italy, while increasing thosecoming from northwest and middle Italy. The percentage of students coming fromsouthern Italy and abroad remains fairly constant. The distribution of the bachelordegree mark is similar to that of graduation mark, so we can say that students whoenter the university with the best grades are those who have a vote of degree higher.Similarly, students with a lower degree mark, they also have a low-grade diploma. Itis interesting to note that even the distribution of Bachelor degree varies in the dif-ferent clusters. We find more students graduated at lyceum in the groups of the beststudents. In the third cluster we have a bit of technical graduates. Also the weight ofthe residual category (masterly, professional, foreign) considerably increases in thegroup of students with the lowest UHC.Regarding the cohort of 2007, the considerations are entirely analogous. The onlydifference concerns the distribution of geographical residence, with a peak in clusterB of students from northwest and southern Italy.Fig. 2 The SEM Short-time Gompertz model latent curves model1 The objective of this method is to minimize the total within-cluster variance. In general, it isregarded as very efficient, however, it tends to create clusters of small size.Evaluation of Human Capital in an Education-Based Perspective 7Table 3 Parameter’s estimates and fit statistics for the “Short-time Gompertz model”Cohort 2006 2007g0: mean (SE) 0.000 (0.012) 0.000 (0.014)g1: mean (SE) 0.000 (0.027) 0.000 (0.026)α 1.442 1.829λ 4.602 4.305T1: intercept - L1 0.416 - 0.000 0.391 - 0.000L2: intercept - L2 0.479 - 0.000 0.460 - 0.000L3: intercept - L3 0.538 - 0.000 0.497 - 0.000L4: intercept - L4 0.552 - 0.092 0.538 - 0.174L5: intercept - L5 0.654 - 0.569 0.675 - 0.755L6: intercept - L6 0.729 - 0.875 0.739 - 0.956L7: intercept - L7 0.768 - 0.969 0.781 - 0.993χ2 479.225 273.082RMSEA 0.224 0.177CFI 0.947 0.963TLI 0.931 0.951IFI 0.947 0.965SRMR 0.099 0.091Table 4 Cluster analysis aCohort 2006 2007Cluster A B C A B C# of students 154 147 277 176 152 183graduation mark 108.01 99.12 88.80 106.65 96.36 86.84(2.92) (2.03) (4.31) (11.54) (10.95) (8.71)Area of residenceNorthwest Italy 58% 63% 67% 66% 64% 68%Northeast Italy 25% 16% 13% 19% 18% 11%Middle Italy 3% 6% 4% 4% 1% 5%Southern Italy 13% 12% 14% 10% 16% 13%Abroad 1% 3% 2% 1% 1% 3%Bachelor degree’s mark 89.67 80.23 73.56 85.41 76.98 70.97(10.10) (11.52) (10.51) (11.54) (10.95) (8.71)Type of Bachelor degreeLyceum 70% 61% 53% 74% 61% 48%Technical 20% 22% 26% 12% 20% 25%Other 10% 17% 21% 14% 19% 27%a In the brackets the standard deviation values8 Emma Zavarrone and Anna Simonetto3 Discussion and future directionsThe HC can be studied under several perspectives; in this application we have cho-sen to analyze theHC accumulated by students for achieving a degree. Following thedefinition proposed by CZ [3], we focused on University Human Capital (UHC) andwe tested the velocity (or rate) of knowledge accumulation through a latent growthcurve model. This model has been applied on two cohorts of students. Given thenon-linear nature of these trajectories, we estimated a latent type Gompertz curve.In the second stage of analysis, we used estimates of the UHC to divide studentsaccording to different modes of knowledge accumulation. We have thus obtainedthree different clusters: “A- good and fast students”, “B- good but not fast students”and “C-not clever students”. This information can be very useful in the processof university orientation. These results highlight that lyceum’s students with highBachelor degree’s marks are the best and fastest ones. A hints for university man-agement could be to orient their activity in upper schools in order to capture thesetypologies of students. Finally, the model can be used profitably by job placementsupport, providing information about the different capabilities of students. It is inter-esting to note that this analysis represents one of the first cases of application of theUHC analysis in humanistic faculties. The cited studies, in fact, refer to scientificfaculties. Despite this important difference, the results found are in line with thosereported in the literature.References1. Bianconcini S., Cagnone S.: A general multivariate latent growth model with applications tostudent achievement. Journal of Educational and Behavioral Statistics, 37, 339-364 (2012)2. Browne M.W., MacCallum, R.C., Kim, C., Andersen, B.L., and Glaser, R.: When fit indicesand residuals are incompatible. Psychological Methods7,403-21(2002)3. Civardi M., Zavarrone E.: Estimating University Human Capital through Education Evalua-tion In: Fabbris L. (eds.) Effectiveness of University Education in Italy. Physica-Verlag, NewYork, 369-380 (2006)4. Grimm, K. J., Ram, N.: Nonlinear growth models in Mplus and SAS. Structural EquationModeling.6, 676-701(2009)5. Hu, L.T. Bentler, P.M.: Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Con-ventional Criteria Versus New Alternatives. Structural Equation Modeling.6(1),1-55 (1999)6. Mariani, P., Mussini M., Zavarrone E.: Measuring Dissimilarity In Learning Capital UsingTime Trajectories. accepted for publication by Stat. Appl. (2013)7. McArdle J.J. and Epstein D:B: Latent growth curves within developmental structural equationmodels. Child Development, 58(1)110-133(1987)8. Muthe´n, B: Latent variable growth modeling with multilevel data. In M. Berkane (Ed.), LatentVariable Modeling with Applications to Causality, 149-161. Springer Verlag (1997)9. Muthe´n, L. K., Muthe´n, B. O.: Mplus user’s guide (6th ed.) [Computer software manual]. LosAngeles, CA: (1998-2010)10. OECD: Social Capital,Human Capital and Health What is the Evidence? OECD-IRDES(2001) http://www.oecd.org/edu/research/45760738.pdf11. Singer, J.: Using SAS Proc Mixed to fit multilevel models, hierarchical models, and individualgrowth curves. Journal of Educational and Behavioral Statistics. 24, 4, 323-355(1998)

Evaluation of human capital in education-based perspective

This paper considers one of the intangible aspect of human capital: the university knowledge accumulation. It is relevant both for academic management and for recruitment world. In the former case it can be an useful guide to identify the characteristics of clever students, while in the latter case it can be applied to worker selection. Because of the velocity of credit acquisition is not sign of clever- ness, it becomes important to analyze different aspects of university human capital accumulation. We will investigate it through latent growth modeling on administra- tive data come from an Italian universit

Evaluation of human capital in education-based perspective

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