The transition from university to work: a multilevel approach to the analysis of the time to obtain the rst job

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1 J. R. Statist. Soc. A 2001) 164, Part 2, pp. 293±305 The transition from university to work: a multilevel approach to the analysis of the time to obtain the rst job L. Biggeri, M. Bini and L. Grilli UniversitaÁ degli Studi di Firenze, Italy [Received November Revised August 2000] Summary. The aim of the paper is to characterize the factors that determine the transition from university to work as well as to evaluate the effectiveness of universities and course programmes with respect to the labour market outcomes of their graduates. The study is focused on the analysis of the time to obtain the rst job, taking into account the graduates' characteristics and the effects pertaining to course programmes and universities. For this a three-level discrete time survival model is used, where the logit of the hazard Ð conditionally on the random effects at course programme and university level Ð is a linear function of the covariates. The analysis is accomplished by using a large data set from a survey on job opportunities for the 1992 Italian graduates. Keywords: Discrete time survival model; Effectiveness; Job opportunities; Multilevel model 1. Introduction Owing to the high unemployment rates for young people in most European countries, studying the transition from university to work has received increasing attention in recent years. The aim of this paper is to characterize the factors that determine the transition from university to work as well as to evaluate the e ectiveness of universities and course programmes with respect to the labour market outcomes of their graduates. Speci cally, the analysis includes two aspects: a) a study of the in uence of graduates' characteristics, such as gender, age, socioeconomic status and educational history on the time to obtain their rst job; b) an assessment of the di erences between course programmes and universities with respect to the time to obtain the rst job for the corresponding graduates, taking also into account the possibility that the relationships between individual level variables vary according to course programmes and universities. In particular, the paper tackles the problem in Italy, analysing a large data set individuals) from a survey on job opportunities for the 1992 Italian graduates conducted by the Italian National Statistical Institute INSI) in 1995 Italian National Statistical Institute, 1996). This data set allows us to determine, for each graduate, the time needed to obtain their rst job in months) or the censored time for those still unemployed at the date of the interview. The graduates are nested in course programmes which are grouped into universities, so the data set has a hierarchical three-level structure. Address for correspondence: L. Biggeri, Dipartimento di Statistica ``G. Parenti'', UniversitaÁ degli Studi di Firenze, Viale Morgagni 59, Firenze, Italy. biggeri@ds.uni.it & 2001 Royal Statistical Society 0964±1998/01/164293

2 294 L. Biggeri, M. Bini and L. Grilli The problem of the transition from the educational system to work has been studied mainly by using descriptive statistical methods e.g. Centre for Educational Research and Innovation 1997) and Tronti and Mariani 1994)). Simple regression models have also been used to study the probability of being employed e.g. Lynch 1987)), but the problem of the time needed to obtain a job seems to have been overlooked. Apart from the econometric literature, the few exceptions are the works of Layder et al. 1991), Dolton et al. 1993) and Santoro and Pisati 1996), which are all based on the continuous time Cox model. Recently, a discrete time survival model has been used by Firth et al. 1999), and an alternative approach has been proposed by Mealli and Pudney 1999) with a transition model. In contrast, the multilevel approach Goldstein, 1995) has been widely used to study various aspects of the educational process, but not to evaluate the e ectiveness of educational institutions with respect to job opportunities. The present paper is a contribution to the study of the transition from university to work by using for the rst time a multilevel discrete time survival model. The choice of a discrete time approach is motivated by the large number of ties in the recorded times, which make the use of a continuous time model inappropriate. The INSI survey on job opportunities for the 1992 Italian graduates will be described in Section 2. Discrete time survival models will be presented in Section 3, along with their multilevel versions. A model with a logit link will be used in the analysis of the INSI data set: Section 4 concerns the implementation of the model, whereas Section 5 presents the main results. Finally, Section 6 is devoted to some concluding remarks. 2. The Italian National Statistical Institute's survey on job opportunities for Italian graduates The INSI survey on job opportunities for the 1992 Italian graduates was based on two distinct strati ed samples for males and females, where the strata were de ned as intersections between course programmes and universities. The planned sample size was 21173, which is about 24% of the population graduates). However, because of the response rate of about 64% which is quite a high percentage for a postal questionnaire), the resulting sample size was As a consequence the sample used in the present analysis is not properly representative of the total population although the INSI used a weighting system for post-strati cation to reduce the bias due to the non-response); so, the results presented in the following sections should be considered with caution. For the present analysis, the sample of records has been reduced to records by eliminating the graduates who, at the date of the interview, had the same job as before receiving their degree or who declared that they were not interested in nding a job. The sample employed in the analysis has 64 universities and 766 course programmes a course programme is characterized by a subject and a university combination, so that, for example, a course in economics in Florence is distinguished from a course in economics in Pisa). The number of graduates per course programme varies considerably, from 1 to 156, with a median of 10. In the present paper, the object of interest is the time to obtain the rst job. Here, it is not possible to distinguish between temporary and permanent jobs, or part-time and full-time jobs: in fact, the questionnaire allows us to make this classi cation only with respect to the job held at the date of the interview, which is not necessarily the rst job. The graduates in 1992 were interviewed in December 1995, so the observed time to obtain their rst job ranges from 1 to 48 months. The time for the graduates who were still unemployed at the date of the

3 Transition from University to Work 295 Fig. 1. Frequency distribution of uncensored * ) and censored & ) times Fig. 2. Empirical hazard function interview is right censored and assumes a value between 37 and 48 depending on the month in which the individuals received their degree. Fig. 1 displays the frequency distribution of the uncensored and censored times, whereas Fig. 2 shows the corresponding empirical hazard function, which is clearly decreasing. The de nitions of the covariates used in the analysis are reported in Table 1 along with their sample means. As regards the covariates the following points should be stressed. a) All the variables are measured at the individual level, so there are no contextual covariates that can explain the possible di erences between course programmes and between universities. b) Time-varying covariates are not present in the data set though they are included in the model de ned in Section 4 as interactions between xed time covariates and time). c) In Italy military service, which is compulsory, was 1 year long in 1992, with the possible call to perform it occurring within 1 year after graduation. Since the starting date of military service is unknown, the dichotomous variable military service simply indicates whether the service was done after the degree as opposed to either being done before the degree or that the student was exempted from it. d) In Italian universities the nal mark ranges from 66 to 110 with a highly skewed distribution: the lower quartile, median and upper quartile for the sample are

4 296 L. Biggeri, M. Bini and L. Grilli Table 1. De nitions of the covariates and sample averages Name and definition Average Time in months, from 1 to 48) Gender 0, male; 1, female) 0.49 Military service 0, done before degree or exempted from; 1, done after degree) 0.17 School leaving certi cate 1, the graduate received the school leaving certi cate 0.76 in a technical college; 0, otherwise) Final mark integers from 66 to 110) First-class Honours degree 1, the graduate received a rst-class Honours degree; , otherwise) Institutional time 1, the graduate received the degree in the institutional time 0.16 established for the course programme he or she attended; 0, otherwise) Course programme change 1, the graduate moved from one course 0.11 programme to another during his or her university studies; 0, otherwise) Residence 1, the graduate was not resident in the city of the university; , otherwise) Occupational status of the parents 1, at least one of the parents was working at the 0.69 date of the degree; 0, other conditions) Professional status of the parents 1, at least one of the parents was a non-manual 0.66 worker; 0, otherwise) Educational level of the parents 1, at least one of the parents had a secondary 0.59 school certi cate or a degree; 0, other conditions) Age at the date of the degree 0, less than or equal to 30 years; 1, over 30 years) 0.07 Occupational status while attending university 1, the graduate held at least one 0.47 job during university studies; 0, otherwise) respectively 100, 106 and 110 to simplify the interpretation of the results, the covariate nal mark has been centred at the value 100). Such a distribution would suggest that there is a `ceiling e ect' which reduces the appropriateness of the nal mark as an indicator of academic ability. e) To compensate partially for the previously mentioned de ciencies of the nal mark, a covariate named institutional time is used which takes the value 1 if and only if the graduate received their degree in the institutional time established for the course programme that he or she attended Ð since such a case is rather rare, this covariate should pick up some good students. f) The covariates which seem to be more strongly associated with the job status are gender and military service Table 2). 3. Multilevel discrete time survival models In a discrete time survival analysis context, let t ˆ 1, 2,...index a sequence of time intervals and i ˆ 1, 2,..., n a sample of individuals. The observation for individual i is the couple Table 2. Gender and military service by job status Ð absolute and row percentage values Unemployed Employed Total Males who did military service before their degree or 692 were exempted from it 19.6% Males who did military service after their degree % Females % Total % % % % % % % % %

5 Transition from University to Work 297 t i, i, where t i is the last observed time interval and i is an indicator which takes the value 1 if and only if the non-recursive event of interest occurred in t i, i.e. the observation is uncensored. Indicating by T the discrete random variable which represents the underlying waiting time, the hazard function can be de ned as t ˆP T ˆ tjt 5 t, t ˆ 1, 2,..., 1 i.e. t is the probability that the event of interest takes place at time interval t given that it has not yet occurred. The corresponding unconditional probability can be written in terms of the hazard function as follows: P T ˆ t ˆ t Qt 1 f1 s g. sˆ1 2 A general approach to the analysis of discrete time survival data is to model a transformation g. of the hazard as a linear function of the covariates; for individual i at time interval t we have Allison, 1982) gf tjx it ;, g ˆ Pr sˆ0 s t s x 0 it, 3 where. is the discrete time hazard function, x it is a vector of possibly time-varying covariates, r is the order of the polynomial which models the base-line hazard function and 0 ˆ 0,..., r and 0 ˆ 1,..., p are vectors of parameters to be estimated. In particular represents the e ect on the scale induced by g. ) of the covariates on the baseline hazard. Two common choices for the link function g. are the logit link Cox, 1972) and the complementary log±log-link Prentice and Gloeckler, 1978), which is a grouped time version of the continuous time proportional hazards model. The logit model is computationally convenient and has an easy interpretation in terms of odds ratios; on the contrary, the complementary log±log-model might be preferred because of the invariance of the coe cient vector with respect to the length of the time intervals. However, in most cases the two link functions yield very similar results. The likelihood function of a discrete time survival model can be expressed for individual i as Allison, 1982) L i ˆ t i jx iti ;, tq i i 1 Q t 1 i i f1 sjx is ;, g f1 sjx is ;, g sˆ1 sˆ1 ˆ t i jx iti ;, i f1 t i jx iti ;, g 1 i tq i 1 sˆ1 f1 sjx is ;, g, assuming that the censoring always takes place at the end of the time interval. An alternative form of the likelihood, which is useful for computational purposes, can be written using the following criterion, due to Brown 1975). Let y is be an indicator which takes the value 1 if and only if the event of interest occurs to individual i at time interval s s ˆ 1, 2,..., t i : so the couple t i, i can be replaced by the vector y i1, y i2,...,y iti, which is 0, 0,..., 0 if i ˆ 0or 0, 0,..., 1 if i ˆ 1. This transformation allows the likelihood to be rewritten as

6 298 L. Biggeri, M. Bini and L. Grilli L i ˆ Qt i sjx is ;, y is f1 sjx is ;, g 1 y is, sˆ1 which is exactly the likelihood of t i independent Bernoulli random variables y i1, y i2,...,y iti with E y is jx is ;, ˆ sjx is ;,. Thus the discrete time survival model 3) is equivalent to a binary response model based on the extended data set that can be obtained by replacing, for each individual, the couple t i, i with the vector y i1, y i2,...,y iti. This equivalence is useful because standard software for the estimation of generalized linear models can then be used. A multilevel version of the discrete time survival model 3) can be obtained by introducing random e ects at course programme and university level. Speci cally, for graduate i of course programme j at university k, model 3) becomes gf tjx ijkt ;,, u jk, v k g ˆ Pr sˆ0 s t s x 0 ijkt v k u jk, where v k is the random e ect for university k and u jk is the random e ect for course programme j at university k. The former expressions for the likelihood are still valid, conditionally on the random e ects. Therefore model 4) is formally equivalent to a multilevel binary response model based on an extended data set in which every graduate's record is replicated as many times as the observed number of time intervals before obtaining a job or being censored. A model like equation 4) with a logit link has recently been used by Firth et al. 1999) for an evaluation of two UK Government programmes for long-term unemployed people in Great Britain. However, their model included only a random e ect at the individual level to capture unobserved heterogeneity, so it is not a multilevel model Implementation of the model The INSI data set on job opportunities for the 1992 Italian graduates, presented in Section 2, has been extended to exploit the equivalence between model 4) and a three-level binary response model, as described in Section 3; this equivalence allows model 4) to be calibrated with standard multilevel software, which in the present case is MLwiN Goldstein et al., 1998). However, to limit the dimension of the extended data set, it was necessary to group months into quarters, so that the time ranges from 1 to 16. This clustering of months causes little loss of information since, on the basis of a number of randomly selected subsamples, tting both the model with time in quarters and the model with time in months gives similar results in terms of covariates e ects. The resulting structure of the extended data set is given in Table 3. The graduates do not constitute a level in this structure. This is not a compulsory choice, because the model might also be based on a four-level structure in which the graduates are Table 3. Structure of the extended data set Level Index Number of units Type of unit 3 k 64 University 2 j 766 Course programme 1 i Observation on a single time interval for a single graduate

7 the level 2 units see Firth et al. 1999) for an application to non-hierarchical data). Such a structure would allow us to take into account a possible unobserved heterogeneity between graduates; however, it was not supported by the data. In fact, tting the model discussed below with a four-level structure instead of a three-level structure yields a zero estimate for the variance component at the graduate level. Hence, in the present case there is no important unobserved heterogeneity between individuals. This result may be due to the large amount of information that is available on each graduate, concerning not only their individual characteristics but also family background, educational history and work experience. Both the logit and the complementary log±log-models have been considered in the analysis and yield similar results. For the present work, the invariance property of the complementary log±log-model is not particularly relevant, so the results shown in the next section refer only to the three-level logit model y ijk jv k, u jk binomial 1, ijk, logit ijk ˆP h x ijkh v k u jk, h v k N 0, 2 v, u jk N 0, 2 u. Transition from University to Work 299 The nal model has been selected through a sort of backward elimination procedure based on the Wald test at the 95% con dence level. The estimation method which was adopted was the second-order penalized quasi-likelihood method Goldstein and Rasbash, 1996), which always converged in a few iterations eight iterations for the nal model). 5. Results 5.1. Parameter estimates Table 4 reports the estimates of the xed and random parameters with corresponding standard errors. As regards the random parameters, the estimates are both signi cant and the level 2 component is twice the level 3 component. Thus the variability in the success rate of the job search depends more on di erences between course programmes than between universities. The model selection procedure also tested the hypothesis that some covariates had di erent e ects according to the course programme or university by allowing their coe cients to be random at level 2 or 3: however, such a hypothesis was not supported by the data. The polynomial which models the base-line hazard has order r ˆ 3 and interacts only with two other covariates, namely military service and gender. The most relevant interaction is certainly that which involves the military service covariate; Fig. 3 shows that the pattern for males who did their service after their degree is clearly di erent from that for males who did it before their degree or were exempted from military service. Actually, the starting date of military service is unknown, but this lack of information is not a serious problem since, as mentioned in Section 2, military service was 1 year long, with the possible call occurring within 1 year after graduation; hence, a military service covariate equal to 1 indicates except for about 5% of the cases) that the service started and ended within the observation period of the survey, thus controlling for a de nitely prior event. However, the military service covariate does not complicate the interpretation of the results too much, since, apart from the interactions with the polynomial which models the base-line

8 300 L. Biggeri, M. Bini and L. Grilli Table 4. Estimates of xed and random parameters Estimate Standard error Fixed parameters Constant Time in quarters, from 0 to 15) Time Time Gender Gender*time Gender*time Military service Military service*time Military service*time Military service*time Final mark integers from 34 to 10) Final mark*gender Institutional time Occupational status of the parents Educational level of the parents Age at the date of the degree Occupational status while attending university Random parameters Level 3 2 v) Level 2 2 u) Fig. 3. Estimated hazard functions: *, males who did military service before their degrees or were exempted from it; &, females; ~, males who did military service after their degrees the other covariates and the random effects were set to 0) hazard, it has no statistically signi cant interaction with other covariates i.e. institutional time, age at the date of the degree and occupational status while attending university). With regard to gender di erences, we can see that the estimated hazard functions for females and males without military service have similar shapes, but with males having larger values for all quarters see again Fig. 3).

9 Transition from University to Work 301 Table 5. Estimated hazards and unconditional probabilities of obtaining the rst job{ Quarter Hazard %) Unconditional probability %) Final mark 100 Final mark 110 Final mark 100 Final mark 110 m f s m f s m f s m f s Total {m, males who did military service before their degree or were exempted from it; f, females; s, males who did military service after their degree; the other covariates and the random e ects are set to 0. Considering the covariates related to academic ability, the nal mark has a slightly positive e ect on the probability of obtaining a job, and the low in uence of the nal mark, which can be appreciated from Table 5 discussed later), might be explained by the previously mentioned ceiling e ect. Moreover, the estimates show a signi cant interaction between the nal mark and the gender of the graduate Ð speci cally, a good mark is more important for a female than for a male. This nding seems to con rm that males still bene t to some extent from ascriptive selection see Reskin and McBrier 2000) for a recent study on this topic). Still concerning academic ability, the covariate institutional time has a signi cant and positive coe cient, which suggests that the students who can complete their degree in the time formally established for the course programme seem to have some good skills that are also useful to obtain a job. As regards the social background covariates, the occupational status and educational level of the parents at the date of the degree are both signi cant Ð this means that a graduate has a higher probability of obtaining a job if at least one of their parents is currently working though no signi cant e ect was found for the type of work) or if at least one of their parents has a secondary school certi cate or a degree. Among the other covariates the most in uential is the occupational status while attending university, which suggests that the graduates who have previous working experience are more likely to obtain a job. Finally, the mature graduates over 30 years of age at the date of the degree) seem to be at a disadvantage with respect to the young graduates. A further interesting nding is that tting the model to two di erent subsets of the data, one restricted to females and males with the military service covariate equal to 0 and the other restricted only to females, yields results which are consistent with the present analysis. In fact, the model tted to the rst subset yields results that are very similar to those of Table 4; the main di erence concerns the e ect of institutional time, which increases from to

10 302 L. Biggeri, M. Bini and L. Grilli Fig. 4. Simultaneous con dence intervals for level 3 residuals: *, North Italy; &, Central Italy; ~, South Italy Moreover, tting the model only to females yields estimates of covariate e ects and variance components which are all higher, in absolute value, than the corresponding estimates obtained in the presence of the males; this result is probably because males have an advantage in nding a job with respect to females, thus con rming the presence of the earliermentioned ascriptive selection. Table 5 reports the estimated hazards and unconditional probabilities derived according to the previous formula 2)) of obtaining a job for the 16 quarters for some types of graduates, who attended a `mean' course programme in a `mean' university. This amounts to setting the random e ects to their mean values, i.e. v k ˆ u jk ˆ 0 note, however, that, owing to the non-linear link function, the resulting values of the hazards are to be interpreted as median values). Summing the unconditional probabilities for a certain type of graduate yields the probability of obtaining a job within December 1995 for that type of graduate, so the totals of Table 5 can be compared with the sample proportions that are reported in Table 2. The di erences are due to the fact that the estimated probabilities of Table 5 are obtained by setting the remaining covariates, as well as the random e ects, to 0. Interestingly, the estimated probabilities reveal that the e ect of the military service covariate is greater than what the sample proportions would suggest Residual estimates An analysis of the residuals allows us to evaluate the e ectiveness of course programmes and universities with respect to job opportunities. Fig. 4 shows a simultaneous con dence interval plot which compares couples of level 3 residuals: two residuals are statistically di erent at a 95% con dence level if and only if their intervals are disjoint Goldstein and Healy, 1995). It is apparent that in most cases the couples are not statistically di erent, which means that we should be very careful when trying to rank universities. The only incontrovertible fact is that all the largest residuals refer to universities

11 Transition from University to Work 303 Fig. 5. Estimated hazards for the rst quarter for two types of course programmes: *, biology; &, economics that are in the north of Italy, which means that those are the best with respect to the time to obtain the rst job. These results can be interpreted as type A relative e ectiveness Willms, 1992), since the model does not control for the e ects of social and economic factors e.g. local unemployment rates), nor for the characteristics of the universities e.g. available resources). The residuals can also be used to estimate the probabilities of obtaining the rst job for a graduate who attended a speci c course programme in a speci c university. This allows us to study the performance of a certain type of course programme in all the Italian universities in which it is held. As an example, Fig. 5 compares the course programmes in economics and biology by plotting the estimated probabilities for the rst quarter for the base-line graduate i.e. the graduate for whom all the covariates are set to 0). It is apparent that the performance of the course programme in economics is better and presents greater variability between the universities. This feature might be explained by the fact that the graduates in economics and biology predominantly direct their job search towards respectively the private and the public sector: of course, the chances of employment in the private sector strongly depend on the local labour market conditions which, in Italy, di er greatly from region to region. 6. Conclusions The analysis of the INSI data set on Italian graduates shows that the transition from university to work is a complex phenomenon, with many intervening factors. The main points which emerged from the analysis are the following: a) the hazard of obtaining the rst job is monotonically decreasing in time; b) there are substantial di erences between course programmes, but also between universities; in particular the universities in the north of Italy are the most e ective with respect to job opportunities; c) military service delays the job search and causes a gap which is only partially closed 3 years after the degree; d) there is an important gender di erence in favour of males which is more pronounced for graduates with low nal marks; e) the nal mark, as expected, has a positive e ect, but of low magnitude.

12 304 L. Biggeri, M. Bini and L. Grilli As for the methodological approach that was used in the present analysis, it combines discrete time survival methods and multilevel modelling in a simple and e ective manner. Some interesting features of the resulting model are a) an easy implementation, b) an easy interpretation of the results, c) the hazard function for di erent categories of graduates can be modelled in a exible way and d) the course programmes and universities can be compared through an analysis of the residuals. As regards the last point, it should be noted that pairwise comparisons between course programmes or universities often show no statistically signi cant di erence. However, an informal analysis of the residuals clearly reveals some patterns of substantive interest, like systematic regional di erences between universities. Additional information on the conditions of the local labour markets and on the characteristics of the universities and course programmes e.g. class sizes) would permit the evaluation of type B relative e ectiveness Willms, 1992) of educational institutions with respect to job opportunities. Acknowledgements The data set that was used in the present work has kindly been made available by the Comitato Nazionale per la Valutazione del Sistema Universitario±Ministero dell'universitaá e della Ricerca Scienti ca e Tecnologica, for which Dr M. Bini carried out a research project. Moreover, the authors wish to thank the referees for their valuable suggestions. References Allison, P. D. 1982) Discrete-time methods for the analysis of event histories. In Sociological Methodology ed. S. Leindhart), pp. 61±98. San Francisco: Jossey-Bass. Brown, C. C. 1975) On the use of indicator variables for studying the time dependence of parameters in a responsetime model. Biometrics, 31, 863±872. Centre for Educational Research and Innovation 1997) Education at a Glance: OECD Indicators. Paris: Organization for Economic Co-operation and Development. Cox, D. R. 1972) Regression models and life-tables with discussion). J. R. Statist. Soc. B, 34, 187±220. Dolton, P. J., Makepeace, G. H. and Treble, J. G. 1993) The youth training scheme and the school to work transition. ResearchPaper 93/22. University of Wales, Bangor. Firth, D., Payne, C. and Payne, J. 1999) E cacy of programmes for the unemployed: discrete time modelling of duration data from a matched comparison study. J. R. Statist. Soc. A, 162, 111±120. Goldstein, H. 1995) Multilevel Statistical Models. London: Arnold. Goldstein, H. and Healy, M. J. R. 1995) The graphical presentation of a collection of means. J. R. Statist. Soc. A, 158, 175±177. Goldstein, H. and Rasbash, J. 1996) Improved approximations for multilevel models with binary responses. J. R. Statist. Soc. A, 159, 505±513. Goldstein, H., Rasbash, J., Plewis, I., Draper, D., Browne, W., Yang, M., Woodhouse, G. and Healy, M. J. R. 1998) A User's Guide to MLwiN. London: Institute of Education. Italian National Statistical Institute 1996) Inserimento professionale dei laureati: indagine Informazioni 10. Italian National Statistical Institute, Rome. Layder, D., Ashton, D. and Sung, J. 1991) The empirical correlates of action and structure: the transition from school to work. Sociology, 25, 447±464. Lynch, L. M. 1987) Individual di erences in the youth labour market: a cross-section analysis of London youths. In From School to Unemployment?: the Labour Market for Young People ed. P. N. Junakar), pp. 185±211. London: Macmillan.

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