Perceived skill outcomes among coursework and research graduates and evolution over time

ABSTRACT

This study explores perceived skill outcomes among graduates of 39 Australian higher education institutions in the short- to medium-term after course completion. While acknowledging important dimensions of graduate employability beyond the skills-based approach, we investigated graduate perspectives on their industry-relevant skill outcomes from university, in preparation for employment. Using national data, we build on earlier research by examining the viewpoints of 24,044 research and coursework graduates, at all levels, at six months and three years post-graduation. We found that as graduates progressed in their careers, perceived skill outcomes from university became less favourable, particularly among coursework graduates. Further, we observed differing perceptions among student groups, emphasising the potential learning gain for non-traditional student groups participating in skill-related interventions, such as work-integrated learning, and the need to design activities which cater to differing needs and are accessible by all. The study highlights how exploring graduate perspectives into the longer term can develop our understanding of the value of university education for enhancing skills and identifying potential areas for curriculum review.

KEYWORDS:

• Human capital
• skills
• employability
• graduate outcomes

1. Introduction

Higher education (HE) is widely considered to be responsible for developing graduates that can contribute to the knowledge economy and are appropriately skilled to enhance organisational and national prosperity (Sin and Neave 2016). In today’s rapidly evolving work context, this means educating students to meet fluid labour market demands and producing new-age workers that can innovate in sustainability, digitalisation and artificial intelligence. According to human capital theory (Becker 1964), skills and knowledge acquired through education lead to superior workplace productivity and more favourable employment outcomes. However, evidence of rising graduate underemployment and graduate labour market inequalities, particularly weaker employment outcomes for students of lower socioeconomic status (SES) (Green and Henseke 2021; Morrison 2019), suggest that developed human capital may not always initiate labour market rewards (see Marginson 2019), due to soft labour markets and expansionary HE policies in many countries. Considerable attention, however, continues to be given to skill demands in different industries, and HE’s success in instilling these skills in new graduates.

While industry-relevant skills are strongly linked to graduate employability (Oliver and Jorre de St Jorre 2018), other factors empower graduates in realising their career and life goals. Career self-management, networks, professional identity development, work experience and self-perceived employability are known to contribute in varying ways (Dacre-Pool and Sewell 2007; Tomlinson 2017). Withstanding the complexities of employability, this study focuses on graduate perceptions of their industry-relevant skills from university, given the positive association between notions of one’s skills and capabilities and self-perceived employability, leading to greater career success (Berntson and Marklund 2007; De Vos, De Hauw, and Van der Heijden 2011). Studies have shown (e.g. Moreau and Leathwood 2006) that graduates place considerable emphasis on skill outcomes from university and how this enables, or inhibits, their labour market achievements. We recognise skill perceptions can vary and explore differing perspectives across graduates by personal, degree-related and employment characteristics.

We group industry-relevant skills into foundation (e.g. communication/numeracy), adaptive (e.g. problem-solving/independent working/innovation) and collaborative skills (e.g. working with diverse others) (Social Research Centre 2020). Collectively, employers prioritise these over discipline-related skills as they enable graduates to adapt to work contexts and meaningfully contribute to complex, cross-cultural and collaborative environments (see Succi and Canovi 2020). Although Tight (2021) asserts that developing skilled graduates is integral to HE curriculum, others argue these skills need to be consciously and explicitly embedded (Griffiths et al. 2018), guided by targeted outcomes and measures of success. Despite significant attention to the development of industry-relevant skills (e.g. Smith et al. 2018), graduate skill deficits persist and the HE sector is not keeping pace with industry expectations (Clarke 2018; Pennington and Stanford 2019).

Drawing on national, longitudinal data, our study explores the perspectives of 24,044 research and coursework graduates and addresses three research questions. RQ1: How do graduates perceive their industry-relevant skill outcomes from HE? RQ2: How do perceptions of skill outcomes change over time? RQ3: Do graduates’ perceptions on skill development vary by personal, degree-related and employment characteristics? We build on extant literature in three ways. First, we focus on perceptions of industry-relevant skills at all course levels, beyond Bachelor graduates. There is notably less consideration of how postgraduate skills fare against industry standards, particularly among Higher-Degree-by-Research (HDR) (e.g. Doctoral/Masters-by-research) students (Spronken-Smith et al. 2018), problematic given increasing numbers enter industry rather than academic roles (Escardíbul and Afcha 2017). Second, we investigate if and how perceptions of skill outcomes change over time, extending typical analysis beyond transition to work to three years post-graduation. Finally, we explore how perceptions of skills vary across diverse groups.

2. Background

2.1. Industry-relevant skills and employability

Some recognise commonalities across industry-relevant skill frameworks (Tight 2021), while others highlight differences (Griffiths et al. 2018) and disparity among academic and industry stakeholders is observed (Succi and Canovi 2020). Our study uses the Graduate Attributes Scale (GAS), comprising three skill domains (foundation/adaptive/collaborative) which HE is expected to develop (Social Research Centre 2016a). Foundation skills are fundamental for graduates’ transition to work (e.g. literacy/communication/numeracy/solving problems/ability to develop and integrate skills and knowledge) (see Oliver and Jorre de St Jorre 2018). Synonymous with enterprise capabilities, adaptive skills span working independently, adapting and applying skills and knowledge across different contexts and being innovative. Graduates must navigate complex work arrangements (e.g. portfolio/gig/remote working) (FYA 2020), and demonstrate skill transferability, agility and a mindset that embraces change (AIG 2016; FYA 2016). Collaborative skills are critical for effective work performance (World Economic Forum 2020) in increasingly heterogeneous workplaces (Clark and Polesello 2017). They are prioritised in graduate selection criteria worldwide (AAGE 2019; Tomlinson 2021), including in HDR graduates (Brown 2019).

Human capital theory asserts that well-developed skills signal an ability to perform effectively at work to prospective employers and instil greater confidence in one’s marketability, purportedly leading to more favourable employment prospects (see Clarke 2018). It postulates that HE participation will enhance labour market outcomes irrespective of personal characteristics (see Tomaszewski et al. 2021) and does not account for how external, structural factors (e.g. labour market policy) can impact the return from skills development (Marginson 2019).

Perceived skill outcomes may, however, vary among diverse graduate cohorts. Students from less advantaged backgrounds often have lower perceptions of their own employability (Clarke 2018), or develop these perceptions through challenges with accessing skilled work (Morrison 2019), along with ethnic minority groups, females and individuals with disability (Magrin, Marini, and Nicolotti 2019; Qenani, MacDougall, and Sexton 2014). This could be from lower levels of self-efficacy which may manifest as weaker confidence in their developed capabilities. Alternatively, limited access to professional networks and career support could mean a relative lack of understanding of industry skill expectations and standards which may adversely affect confidence in skill development at university and notions of their preparedness for employment. Further, graduate experiences at work – such as management feedback, internal career progression and success in external recruitment – may influence perceptions of the quality of degree-related skill development, and their broader employability. Moreau and Leathwood (2006) illuminate the complexities around graduates recognising direct and indirect discrimination in the workplace and non-traditional graduates may not only ‘have fewer opportunities within the labour market, but they are also likely to blame themselves for any failure to succeed’ (p.320).

2.2. HE response to skill demands

There is increasing stakeholder focus on the outcomes of HE, with job attainment a popular measure of success (Jackson and Bridgstock 2018). The widely held belief that skill development is positively associated with employment has meant considerable investment in authentic learning activities to foster industry-relevant skills among HE students (e.g. Smith et al. 2018). Partnering with industry as part of formal learning and assessment to help prepare students for future work, termed Work-Integrated Learning (WIL), is gathering momentum, including internships, client-based projects and consulting. Evidence suggests WIL is highly effective for developing students’ skills, alongside other aspects of employability (Jackson and Dean 2022a), and fosters human capital for improved graduate outcomes (e.g. Bolli, Caves, and Oswald-Egg 2021).

Despite ongoing efforts to develop future-capable graduates, employers lament skill deficits among Bachelor (see Griffiths et al. 2018) and doctoral graduates (De Grande et al. 2014), questioning their ability to add value and enhance organisational productivity and performance (Pennington and Stanford 2019) and the return of public investment in HE (Tomlinson 2021). Skill development may be hampered by resource limitations (see Young, Kelder, and Crawford 2020), academic resistance to the discourse of employability (Osborne and Grant-Smith 2017), difficulties with crowded curriculum (Oliver 2013) or Faculty not prioritising industry’s evolving skill demands (e.g. Moore 2020), particularly if they vary in diverse work contexts (Moore and Morton 2017). Preparing HDR graduates for industry roles is particularly complex with less transparent labour market needs that vary by field (see Young, Kelder, and Crawford 2020).

Importantly, widening participation policies have meant increasing proportions of non-traditional students (e.g. lower SES, ethnic minority groups) are entering HE with comparably less developed foundation skills (Productivity Commission 2019). It is incumbent on HE institutions to recognise these differences and ensure that skill development initiatives are accessible and inclusive in design.

2.3. Graduate perceptions of skill outcomes

Some studies have found Bachelor graduates largely perceive their skills as well-developed, albeit less so for team-working (Crebert et al. 2004; Jackson 2016), echoed among doctoral graduates (Jackson and Michelson 2016). Other studies, however, have observed Bachelor graduates feeling inadequately prepared for work with underdeveloped skills following university (e.g. Gedye, Fender, and Chalkley 2004), along with doctoral students (Beasy et al. 2022). Tomlinson (2021) acknowledges how UK-based employer perspectives on graduate skills can vary by survey type, how skills are classified and perceptions on what constitutes a skills deficit. There are notable differences in observations on skill outcomes by personal and degree-related characteristics, such as gender, age, study mode and discipline (e.g. Jackson, 2016), the latter perhaps reflecting alternative approaches to skill development across disciplines (Sin et al., 2019).

Graduates’ work context may also influence the perceived usefulness of their degree, such as the extent to which their role utilises their degree education (e.g. they are not overqualified) (Vaatstra and De Vries 2007). Jackson and Michelson (2016) also found that doctoral graduates in non-academic roles held less favourable perceptions on skill development at university, perhaps attributed to a greater pressure to demonstrate these skills in industry settings. Some (Bryan and Guccione 2018; Kalafatis and Ledden 2013) found the perceived value from the degree increased as time lapsed post-graduation, the benefits of their learning not being immediately apparent upon graduation. Meanwhile, Tuononen Parpala, and Lindblom-Ylänne (2019) found Bachelor graduates’ assessment of the development of collaboration and communication skills worsened between graduation and three years’ later, attributed to metacognition (more accurate recall of skill development at graduation) or graduates progressing into more demanding roles and concluding that degree-related skill development was weaker than initially perceived.

3. Methodology

3.1. Participants

Participants were domestic graduates of Bachelor (n = 13,855), postgraduate coursework (n = 8,745) and HDR (n = 1,444) degrees in 39 Australian universities who completed the Graduate Outcomes Survey (GOS) in 2016 and 2017 and then the Graduate Outcomes Survey – Longitudinal (GOS-L) in 2019 and 2020. The graduate samples were employed when completing the surveys, their characteristics summarised in Table 1.

Table 1. Graduate characteristics.

		Bachelor (n = 13,855)		P/grad(coursework) (n = 8,745)		P/grad (research) (n = 1,444)
Variable	Sub-groups	Count	%	Count	%	Count	%
Age	0–24	5,966	43.1	787	9.0	16	1.1
	25–29	4,299	31.0	1,860	21.3	301	20.8
	30–39	1,987	14.3	2,943	33.7	605	41.9
	40+	1,603	11.6	3,155	36.1	522	36.2
Gender	Male	4,556	32.9	3,124	35.7	597	41.3
	Female	9,299	67.1	5,621	64.3	847	58.7
Indigenous	Indigenous	185	1.3	77	0.9	4	0.3
	Non-Indigenous	13,670	98.7	8,452	96.7	1,440	99.7
Disability	Disabled	753	5.4	293	3.4	46	3.2
	Not disabled	13,102	94.6	8,452	96.6	1,398	96.8
SES	Low	2,418	17.5	1,056	12.1	113	7.8
	Not low	11,437	82.5	7,689	87.9	1,331	92.2
Birth status	Local-born	11,957	86.3	6,837	78.2	985	68.2
	Not local-born	1,898	13.7	1,908	21.8	459	31.8
First-in-Family to attend university	First-in-Family	266	1.9	678	7.8	21	1.5
	Not First-in-Family	13,589	98.1	8,067	92.3	1,423	98.5
Non-English-Speaking Background (NESB)	NESB	214	1.5	207	2.4	92	6.4
	ESB	13,641	98.5	8,538	97.6	1,352	93.6
Postgraduate coursework	Graduate Certificate			1,460	16.7
	Graduate Diploma			1,524	17.4
	Master’s degree			5,761	65.9
Postgraduate research	Master-by-Research					119	8.2
	Doctor of Philosophy					1,325	91.8
Honours completion	Honours degree	2,078	15.0
	Non-Honours degree	11,777	85.0
Study mode	On-campus	9,459	68.3	4,971	56.8	1,317	91.2
	Off-campus	1,705	12.3	2,780	31.8	84	5.8
	Mixed-mode	2,691	19.4	994	11.4	43	3.0
Attendance status	Full-time	2,935	21.2	3,860	44.1	829	57.4
	Part-time	10,920	78.8	4,885	55.9	615	42.6
Discipline	Natural/Physical Science	1,220	8.8	178	2.0	313	21.7
	Information Technology	381	2.8	171	2.0	38	2.6
	Engineering/related	1,037	7.5	308	3.5	136	9.4
	Architecture/Building	279	2.0	190	2.2	13	0.9
	Agriculture/Environment	271	2.0	123	1.4	67	4.6
	Health/related	3,936	28.4	1,900	21.7	337	23.3
	Education/related	1,582	11.4	2,142	24.5	78	5.4
	Management/Commerce	1,897	13.7	2,110	24.1	84	5.8
	Society/Culture	2,614	18.9	1,456	16.7	317	22.0
	Creative Arts/Other	638	4.6	167	1.9	61	4.2

3.2. Procedures

The GOS/GOS-L are national, online surveys coordinated by the SRC for the Australian Government. The GOS is administered bi-annually, at four to six months post-graduation, with a 2016 response rate of 39.7% and 2017 rate of 45.0% (Social Research Centre 2016a, 2017). The GOS-L is administered annually to graduates who completed the GOS at three years post-graduation. Response rates for 2019 and 2020 were 55.9% and 50.0% respectively (Social Research Centre 2019, 2020).

3.3. Measures

The GOS questions gather data on satisfaction among recent graduates and their employment outcomes, and are replicated in the GOS-L. Our study focused on the development of industry-relevant skills as outcome variables, measured by eight items on foundation skills, six items on adaptive skills, and five items on collaborative skills. Graduates used a five-point Likert scale (‘strong disagree’[1],‘strongly agree’[5]) to indicate their level of agreement with that skill item preparing them for their current job. Item scales have been used over time and are considered valid measures (see Social Research Centre 2016b). Predictor variables included personal, degree-related and employment characteristics (see Table 1). Graduates’ attended institution was classified into Group-of-Eight (Go8), or not (the Go8 being a research-intensive group of universities akin with the UK’s Russell Group). SES was determined by residential postcode. Employment characteristics included sector (public/private/not-for-profit) and whether in a professional role (Manager/Professional), or not. Further, graduates were classified as perceiving themselves as overqualified (or not), a belief that their current role is not utilising the skills and knowledge acquired from their degree education. This classification is derived by the SRC using an eight-item scale.

3.4. Analysis

Descriptive analyses examined trends in perceived skill outcomes in the short- and medium-term post-graduation among graduates of all course levels. Paired ‘t’-tests evaluated changes in perceptions of skills over time. The relationships between perceived skill outcomes and personal, degree-related (see breakdown in Table 1) and employment characteristics (sector/occupation/industry) were examined with multivariate linear regression models. A three-level hierarchical linear modelling approach was adopted as opposed to standard linear models which ignore the inherent clustering in the data, violating assumptions such as independence of observations which could lead to inaccurate estimates (Niehaus, Campbell, and Inkelas 2014). Specifically, these models account for students (level one) clustering in ten study fields (level two, and based on the broad fields in the Australian Standard Classification of Education) which are in turn nested within the 39 HE institutions (level three), thus accounting for potential effects from institutional culture and practices, and in turn field of study-specific practices. Likelihood-ratio tests assessing the validity of fitting hierarchical linear regression models were all statistically significant, validating our modelling approach. The three-level hierarchical linear modelling comprised two steps: (i) an intercept-only model examining the proportion of variance for each hierarchical level, and (ii) a random intercept model with graduate-level explanatory variables. The dependent value for both was graduates’ perceived skill value in the study field in their attended institution (see Appendix for model expressions).

4. Findings

4.1. Perceptions on skill outcomes over time

Table 2 presents the means and standard deviations at item level for the foundation, adaptive and collaborative skill constructs, and results from the paired ‘t’-tests of mean differences between graduates’ perceived skill outcomes at six months and three years. Cronbach’s alpha scores for the skill constructs at six months and three years ranged from α = 0.89 to 0.92, indicating good internal consistency among survey item measures.

Table 2. Means and ‘t’-tests of mean differences for skill outcomes.

	Bachelor					Postgraduate coursework					HDR
	Six months		Three years			Six months		Three years			Six months		Three years
Variable	Mean	SD	Mean	SD	Diff	Mean	SD	Mean	SD	Diff	Mean	SD	Mean	SD	Diff
Oral communication	4.02	0.98	3.94	0.97	−0.08***	3.75	1.10	3.76	1.04	0.01	4.27	0.94	4.27	0.90	0.00
Written communication	4.21	0.89	4.15	0.88	−0.07***	4.10	0.96	4.06	0.94	−0.04***	4.59	0.73	4.58	0.68	−0.01
Numeracy	3.60	1.13	3.57	1.09	−0.02***	3.21	1.18	3.25	1.13	0.04***	3.75	1.14	3.76	1.11	0.01
Ability to develop relevant knowledge	4.28	0.80	4.21	0.79	−0.07***	4.31	0.80	4.26	0.79	−0.06***	4.56	0.74	4.57	0.65	0.01
Ability to develop relevant skills	4.21	0.84	4.13	0.82	−0.08***	4.22	0.83	4.16	0.82	−0.06***	4.45	0.78	4.43	0.74	0.01
Ability to solve problems	4.20	0.85	4.12	0.85	−0.08***	4.07	0.92	4.05	0.90	−0.02**	4.50	0.78	4.53	0.71	0.02
Ability to integrate knowledge	4.26	0.79	4.20	0.78	−0.07***	4.28	0.81	4.22	0.81	−0.07***	4.59	0.70	4.61	0.65	0.02
Ability to think independently about problems	4.23	0.85	4.16	0.85	−0.08***	4.17	0.90	4.14	0.88	−0.03***	4.60	0.73	4.61	0.66	0.01
Foundation skills average	4.13	0.67	4.06	0.66	−0.07***	4.02	0.71	3.99	0.70	−0.03***	4.42	0.65	4.42	0.57	0.00
Broad general knowledge	4.03	0.91	3.95	0.91	−0.08***	4.07	0.92	4.02	0.91	−0.05***	3.92	1.03	3.92	1.00	0.00
Ability to develop innovative ideas	3.84	0.97	3.75	0.96	−0.09***	3.93	0.96	3.85	0.94	−0.08***	4.28	0.86	4.26	0.84	−0.02
Ability to identify new opportunities	3.91	0.93	3.79	0.93	−0.12***	3.97	0.93	3.88	0.93	−0.09***	4.15	0.91	4.11	0.91	−0.05**
Ability to adapt knowledge in different contexts	4.15	0.81	4.08	0.79	−0.08***	4.20	0.81	4.13	0.80	−0.07***	4.40	0.75	4.40	0.76	−0.01
Ability to apply skills in different contexts	4.12	0.83	4.04	0.81	−0.08***	4.16	0.84	4.10	0.82	−0.06***	4.32	0.83	4.33	0.78	0.01
Capacity to work independently	4.20	0.88	4.15	0.84	−0.05***	4.04	0.97	4.01	0.93	−0.02**	4.58	0.76	4.57	0.71	−0.01
Adaptive skills average	4.04	0.71	3.96	0.69	−0.08***	4.06	0.73	4.00	0.73	−0.06***	4.28	0.68	4.26	0.66	−0.01
Working well in a team	4.04	0.95	3.95	0.93	−0.08***	3.74	1.06	3.74	0.99	−0.00	3.74	1.12	3.72	1.10	−0.02
Getting on well with others in workplace	3.92	0.98	3.84	0.95	−0.09***	3.65	1.05	3.64	1.00	−0.01	3.78	1.05	3.78	1.03	0.00
Working collaboratively with colleagues to complete tasks	4.09	0.92	4.00	0.90	−0.09***	3.85	1.04	3.83	0.97	−0.02**	3.91	1.08	3.86	1.06	−0.05**
Understanding of different points of view	4.12	0.86	4.03	0.85	−0.09***	4.06	0.90	3.99	0.89	−0.07***	4.15	0.89	4.12	0.88	−0.03
Ability to interact with co-workers from different/multicultural backgrounds	4.04	0.96	3.95	0.95	−0.09***	3.74	1.06	3.70	1.01	−0.04***	3.89	1.06	3.89	1.04	0.01
Collaborative skills average	4.03	0.82	3.95	0.79	−0.09***	3.80	0.90	3.78	0.86	−0.03***	3.89	0.89	3.87	0.88	−0.02

***p < .001,**p < .05,*p < .01.

At both Bachelor and postgraduate coursework levels, average ratings for foundation and adaptive skills largely hovered around the ‘agree’ (4) rating, indicating most were developed during courses to prepare them for employment. Relatively lower ratings were reported in both cohorts for numeracy and developing innovative ideas and identifying new opportunities. Master graduates also reported relatively lower oral communication skills. HDR graduates rated their skills far higher than coursework graduates for both foundation and adaptive skills, except in numeracy which – again – was notably lower. While Bachelor graduates’ collaborative skills were on par with the two other skill sets, this was not the case for postgraduate cohorts. Their average ratings consistently fell below ‘agree’ apart from understanding different viewpoints where averages of above four were recorded.

Regarding changes over time, significant differences in skill ratings are emboldened in Table 2, the significant level recorded as a footnote. Skill ratings were significantly lower across the board among Bachelor graduates and for all but three of the 19 skills for postgraduate coursework graduates. Although significant, changes in the mean ratings between the six months and three-year time points were not large, with most approximating to 0.10. Ratings among HDR graduates changed little over time, with significant results reported only for a perceived lessened ability to identify opportunities and improved ability to work collaboratively with colleagues.

4.2. Determinants of perceived skill outcomes

Results from the hierarchical linear regression models of skills outcomes for Bachelor, postgraduate coursework and HDR samples are presented in Tables 3, 4 and 5, respectively. Again, significant results are emboldened and the significance level indicated as a table footnote.

Table 3. Hierarchical linear regression model of skills outcomes (Bachelor, n = 13,855).

	Six months			Three years
Variables	Foundation	Adaptive	Collaborative	Foundation	Adaptive	Collaborative
Female	0.035***	0.073***	0.109***	0.016	0.039***	0.082***
	(3.137)	(6.374)	(8.023)	(1.598)	(2.896)	(5.263)
25–29 years	−0.051***	−0.060***	−0.083***	−0.014	−0.014	−0.071***
	(−4.252)	(−4.159)	(−5.693)	(−0.963)	(−0.834)	(−5.439)
30–39 years	−0.070***	−0.127***	−0.268***	0.007	0.001	−0.161***
	(−4.239)	(−7.011)	(−10.364)	(0.337)	(0.063)	(−6.821)
40+ years	−0.004	−0.069***	−0.236***	0.064***	0.004	−0.163***
	(−0.211)	(−3.043)	(−10.049)	(3.022)	(0.175)	(−5.485)
Indigenous	0.065	0.132***	0.047	0.123**	0.122**	0.089
	(1.239)	(2.697)	(0.751)	(2.117)	(2.291)	(1.405)
Disability	−0.047	−0.020	−0.083**	0.037	−0.010	−0.024
	(−1.366)	(−0.657)	(−2.146)	(1.535)	(−0.402)	(−0.818)
Local-born	−0.036**	−0.047***	−0.071***	−0.037**	−0.037**	−0.069***
	(−1.978)	(−2.644)	(−3.329)	(−2.047)	(−2.102)	(−3.382)
Low-SES	0.028*	0.037**	0.058***	0.020	0.023*	0.042**
	(1.775)	(2.094)	(3.099)	(1.383)	(1.808)	(2.231)
First-in-Family	−0.059*	−0.020	−0.061	−0.046	−0.014	−0.046
	(−1.764)	(−0.444)	(−1.240)	(−1.302)	(−0.443)	(−1.308)
NESB	0.201***	0.171***	0.202***	0.139**	0.106*	0.196***
	(4.665)	(3.615)	(3.323)	(2.308)	(1.751)	(3.099)
Honours	0.134***	0.088***	−0.013	0.143***	0.089***	−0.020
	(8.538)	(6.080)	(−0.666)	(9.198)	(4.428)	(−1.040)
Off-campus	−0.016	0.079**	−0.180***	−0.006	0.069***	−0.149***
	(−0.639)	(2.570)	(−5.208)	(−0.314)	(3.470)	(−4.580)
Mixed-mode	0.024	0.031*	−0.013	−0.004	0.000	−0.039*
	(1.333)	(1.874)	(−0.481)	(−0.239)	(0.014)	(−1.909)
Part-time study	−0.039*	−0.018	−0.078***	−0.023	−0.032**	−0.076***
	(−1.809)	(−0.771)	(−3.374)	(−1.440)	(−2.078)	(−3.837)
Private sector employment	−0.035***	−0.019	−0.048***	−0.036***	−0.016	−0.036***
	(−2.946)	(−1.386)	(−3.318)	(−3.082)	(−1.252)	(−3.252)
Not-for-profit employment	0.019	0.068***	−0.010	−0.018	0.027	−0.045**
	(0.921)	(2.830)	(−0.413)	(−0.926)	(1.149)	(−1.985)
Professional occupation	0.044***	−0.006	0.003	0.027*	−0.026	−0.001
	(3.753)	(−0.413)	(0.149)	(1.671)	(−1.469)	(−0.033)
Perceived overqualification	−0.060***	−0.048***	−0.040**	−0.080***	−0.058***	−0.079***
	(−4.935)	(−3.320)	(−2.373)	(−4.559)	(−3.181)	(−4.111)
Constant	4.142***	4.076***	4.187***	4.064***	3.993***	4.094***
	(179.939)	(153.894)	(135.846)	(148.103)	(131.822)	(133.165)
Prob > χ^2	0.000	0.000	0.000	0.000	0.000	0.000

() = Robust standard errors.

***p < .001, **p < .05, *p < .0.01.

Table 4. Hierarchical linear regression model of skills outcomes (postgraduate coursework, n = 8745).

	Six months			Three years
Variables	Foundation	Adaptive	Collaborative	Foundation	Adaptive	Collaborative
Female	−0.036**	−0.016	−0.006	−0.030*	−0.032	−0.017
	(−2.115)	(−1.023)	(−0.285)	(−1.817)	(−1.576)	(−0.911)
25–29 years	−0.135***	−0.111***	−0.172***	−0.021	−0.007	−0.036
	(−5.531)	(−4.500)	(−5.078)	(−0.797)	(−0.307)	(−1.344)
30–39 years	−0.141***	−0.094***	−0.272***	−0.039	0.012	−0.099***
	(−5.205)	(−3.143)	(−6.582)	(−1.423)	(0.351)	(−3.575)
40+ years	−0.074***	−0.036	−0.199***	0.039	0.074***	−0.020
	(−2.666)	(−1.244)	(−5.305)	(1.475)	(2.959)	(−0.645)
Indigenous	0.067	0.097	0.079	0.137	0.155*	0.083
	(0.768)	(0.925)	(0.670)	(1.618)	(1.795)	(0.735)
Disability	0.041	0.031	0.078	0.044	0.019	0.007
	(0.891)	(0.671)	(1.241)	(0.978)	(0.493)	(0.135)
Local-born	−0.072***	−0.053**	−0.124***	−0.038	−0.010	−0.073***
	(−3.544)	(−2.461)	(−4.946)	(−1.559)	(−0.426)	(−3.118)
Low-SES	0.077***	0.044*	0.082***	0.071***	0.070***	0.091***
	(3.734)	(1.655)	(4.046)	(3.484)	(3.268)	(3.900)
First-in-Family	−0.006	0.045*	0.040	−0.019	0.011	0.008
	(−0.212)	(1.689)	(1.193)	(−0.662)	(0.449)	(0.228)
NESB	0.146***	0.082	0.241***	0.112**	0.111**	0.242***
	(2.691)	(1.241)	(3.597)	(2.086)	(2.263)	(4.103)
Graduate Certificate	−0.196***	−0.155***	−0.134***	−0.160***	−0.142***	−0.127***
	(−8.336)	(−6.298)	(−4.043)	(−7.441)	(−5.801)	(−3.838)
Graduate Diploma	−0.129***	−0.184***	−0.111***	−0.157***	−0.204***	−0.110***
	(−4.691)	(−5.528)	(−3.862)	(−5.089)	(−6.625)	(−3.890)
Off-campus	−0.033	0.045*	−0.223***	−0.036*	0.019	−0.194***
	(−1.276)	(1.699)	(−5.571)	(−1.887)	(0.799)	(−6.201)
Mixed-mode	−0.023	0.015	−0.057**	−0.019	−0.007	−0.071**
	(−0.702)	(0.470)	(−2.296)	(−0.661)	(−0.205)	(−2.059)
Part-time study	0.005	0.062***	−0.077**	−0.005	0.042**	−0.073***
	(0.229)	(2.920)	(−2.463)	(−0.269)	(2.537)	(−2.998)
Private sector employment	0.003	−0.002	0.029	−0.017	−0.013	0.009
	(0.173)	(−0.077)	(1.063)	(−0.970)	(−0.746)	(0.491)
Not-for-profit employment	−0.028	0.013	−0.005	0.016	0.028	−0.017
	(−0.905)	(0.505)	(−0.112)	(0.814)	(1.335)	(−0.496)
Professional occupation	0.024	−0.011	0.005	−0.034**	−0.060***	−0.032*
	(1.611)	(−0.577)	(0.210)	(−2.363)	(−4.275)	(−1.692)
Perceived overqualification	−0.052**	−0.058***	−0.038	−0.140***	−0.109***	−0.129***
	(−2.508)	(−2.694)	(−1.407)	(−7.926)	(−4.795)	(−5.843)
Constant	4.245***	4.193***	4.234***	4.156***	4.081***	4.069***
	(129.852)	(113.195)	(93.849)	(93.057)	(88.332)	(83.120)
Prob > χ^2	0.000	0.000	0.000	0.000	0.000	0.000

() = Robust standard errors.

***p < .001, **p < .05, *p < .0.01.

Table 5. Hierarchical linear regression model of skills outcomes (HDR, n = 1444).

	Six months			Three years
Variables	Foundation	Adaptive	Collaborative	Foundation	Adaptive	Collaborative
Female	0.002	0.013	0.004	0.027	0.024	0.041
	(0.047)	(0.367)	(0.103)	(1.055)	(0.926)	(0.895)
25–29 years	0.036	0.019	0.055	−0.016	0.078	0.466**
	(0.528)	(0.139)	(0.242)	(−0.113)	(0.514)	(2.201)
30–39 years	0.037	0.071	−0.000	−0.031	0.130	0.340*
	(0.632)	(0.477)	(−0.001)	(−0.239)	(0.873)	(1.648)
40+ years	−0.183**	−0.037	−0.283	−0.195	0.022	0.075
	(−2.137)	(−0.250)	(−1.310)	(−1.458)	(0.160)	(0.372)
Disability	0.109*	−0.053	−0.041	−0.041	−0.086	0.058
	(1.751)	(−0.590)	(−0.338)	(−0.373)	(−0.964)	(0.471)
Local-born	0.008	0.010	−0.024	0.003	0.028	−0.024
	(0.236)	(0.241)	(−0.563)	(0.099)	(0.785)	(−0.441)
Low SES	0.019	0.069	0.161*	−0.058	−0.011	−0.010
	(0.299)	(1.055)	(1.940)	(−0.894)	(−0.164)	(−0.105)
First-in-Family	0.149*	0.139**	0.155***	0.109***	0.129***	0.254***
	(1.894)	(2.320)	(2.738)	(3.221)	(2.830)	(3.794)
NESB	−0.064	0.003	0.221*	−0.041	−0.015	0.224***
	(−0.873)	(0.047)	(1.837)	(−0.621)	(−0.180)	(2.652)
Master-by-research	−0.208***	−0.125*	−0.111	−0.259***	−0.185**	−0.221***
	(−3.656)	(−1.953)	(−1.392)	(−3.378)	(−2.090)	(−2.944)
Off-campus	−0.028	0.082	−0.012	−0.061	0.027	−0.043
	(−0.385)	(1.000)	(−0.103)	(−0.792)	(0.309)	(−0.399)
Mixed-mode	0.003	0.068	0.263***	0.005	0.018	0.030
	(0.065)	(0.920)	(3.467)	(0.039)	(0.148)	(0.220)
Part-time study	0.025	0.051	0.006	0.034	0.064	−0.032
	(0.756)	(1.470)	(0.138)	(0.907)	(1.587)	(−0.702)
Private sector employment	−0.137***	−0.071*	−0.151***	−0.040	−0.064*	−0.152***
	(−2.976)	(−1.686)	(−2.955)	(−1.318)	(−1.942)	(−3.158)
Not-for-profit employment	−0.101**	−0.124**	−0.208***	−0.092	−0.128**	−0.110
	(−1.967)	(−2.283)	(−2.823)	(−1.592)	(−2.196)	(−1.180)
Professional occupation	0.088	0.038	0.123	0.071*	−0.040	0.059
	(1.629)	(0.611)	(1.534)	(1.806)	(−0.879)	(0.812)
University academic	0.142**	0.084	0.030	0.099*	0.030	0.050
	(2.299)	(1.250)	(0.292)	(1.775)	(0.445)	(0.631)
Perceived overqualification	−0.153***	−0.201***	−0.224***	−0.137***	−0.142***	−0.230***
	(−2.679)	(−3.277)	(−3.134)	(−3.302)	(−2.737)	(−4.968)
Constant	4.460***	4.264***	4.002***	4.491***	4.223***	3.667***
	(51.022)	(26.622)	(16.564)	(30.265)	(23.786)	(14.901)
Prob > χ^2	0.000	0.000	0.000	0.000	0.000	0.000

() = Robust standard errors.

***p < .001, **p < .05, *p < .0.01.

4.2.1. Bachelor graduates

As shown in Table 3, female Bachelor graduates reported higher perceived skill outcomes (between 0.03 and 0.1 of a standard deviation in magnitude) at six months across all three domains, relative to males. This held into the longer-term, for adaptive and collaborative skills. There were varying results across time by age. At six months, the youngest age group (24 years/below) reported the highest levels of perceived skill outcomes in all three domains. At three years, the same effect was apparent for collaborative skills. These estimated differences no longer existed for foundation and adaptive skills, although graduates in the oldest group (40 years/plus) perceived higher levels of foundation skill outcomes compared to the youngest.

Indigenous graduates reported higher levels of adaptive skills of approximately 0.12 of a standard deviation at both six months and three years, and stronger foundation skill outcomes at three years compared to their non-Indigenous counterparts. There were no statistically distinguishable effects for perceived skills outcomes by disability status. Local-born graduates observed marginally weaker skill outcomes across all three domains, in the short and longer-term, compared to foreign-born domestic graduates. Also relatively small in magnitude, low SES graduates reported higher skill outcomes at six months and, to a lesser extent, at three years, relative to more advantaged peers. First-in-family graduates reported a statistically significant lower result only for foundation skills at six months, although dissipated at three years. There were higher skill outcomes for graduates from non-English-speaking-background (NESB) in all three domains at approximately one fifth of a standard deviation compared with ESB graduates at six months, and slightly reduced differences at three years.

For degree-related characteristics, completing an honours’ degree was associated with statistically significant positive effects for foundation and adaptive skills, although not collaborative skills, at both time periods. There were mixed results for study mode with off-campus graduates reporting superior outcomes for adaptive skills and considerably weaker ratings for collaborative skills in the short and longer-term. Graduates who combined on and off-campus study (mixed-mode) also observed lower levels of collaborative skills relative to on-campus graduates in both time periods, although weaker in magnitude than those studying off-campus and not statistically significant at six months. Marginally weaker skill outcomes were detected for part-time graduates, compared with those who had studied full-time.

There were also observed differences in skill outcomes by graduates’ type of employment, although not exceeding 0.08 of a standard deviation. Relative to the reference category of working in the public sector, private sector graduates had significantly lower levels of foundation and collaborative skill outcomes, across time. For those in not-for-profit organisations, significantly higher adaptive skill outcomes were evident at six months, and lower collaborative skill outcomes at three years. Graduates employed in a professional occupation, relative to those in non-professional roles, were estimated to have significantly higher perceived foundation skills outcomes in the short-and longer-term. Finally, graduates who perceived themselves to be overqualified for their jobs also perceived lower levels of skills outcomes for all three skill domains, consistent across time.

4.2.2. Postgraduate coursework graduates

Table 4 shows that gender influenced perceived foundation skill outcomes with female coursework postgraduates reporting marginally lower levels at six months and three years. Gender effects were not observed for adaptive and collaborative skills. Age observed similar effects on skill outcomes to Bachelor graduates, more mature graduates generally self-assessing their skill outcomes lower in the short and longer-term, although a positive effect for adaptive skills was observed for the oldest group at three years. The age effects were stronger for collaborative skills (ranging from 0.17–0.27 of a standard deviation) and reduced over time for all skills. Skill outcomes did not vary by Indigenous status, except for a weakly significant, positive result for adaptive skills among Indigenous students in the longer term. As for Bachelor graduates, local-born coursework postgraduates observed lower levels of skill outcomes across the three domains at six months, persisting into the longer-term for collaborative skills only. Higher levels of perceived skill outcomes were reported across all skills among lower SES graduates, consistent across time yet of less than 0.1 of a standard deviation in size. As with Bachelor graduates, NESB postgraduates reported markedly higher levels of skills relative to ESB graduates in all three skills domains, consistent across time although not statistically significant for adaptive skills at six months.

Differences were observed by degree type/level within the postgraduate coursework cohort, ranging between 0.1 and 0.2 of a standard deviation. Relative to Master graduates, those who completed a graduate certificate/diploma had lower levels of self-assessed skills outcomes across the board and over time. As at Bachelor level, those who studied off-campus reported significantly lower perceived collaborative skill outcomes of about one fifth of a standard deviation, consistent across time, and marginally lower foundation skills at three years. Off-campus graduates, however, were estimated to have higher (albeit weakly significant) perceptions of adaptive skills at six months, although not in the longer term. Although of less magnitude than those enrolled off-campus, graduates who studied mixed-mode similarly reported weaker perceived collaborative skills relative to on-campus graduates, in the short- and longer-term. Graduates who studied part-time had marginally stronger adaptive skills and weaker collaborative skill outcomes, consistent across time, compared with full-time graduates.

Employment sector did not determine perceptions of skill outcomes while graduates in professional occupations had significantly, albeit marginally, lower perceptions of skill outcomes across all three domains at three years, not in the short term. Graduates who perceived themselves to be overqualified for their jobs had lower self-assessments of skill outcomes for all three skill domains, with differences strengthening across time, except for collaborative skills which was only statistically significant at three years.

4.2.3. HDR graduates

HDR graduate results (see Table 5¹), indicated no gender effects and some differences by age, with the oldest age group associated with lower levels of foundational skills at six months and the 25–29 year and 30–39 year groups reporting stronger perceived collaborative skill outcomes at three years, around 0.5 and 0.35 of a standard deviation respectively. Graduates with disability perceived higher levels of foundation skill outcomes at six months, albeit weakly significant and not into the longer-term. There were no statistical differences by birth status and SES, other than a weakly significant positive estimate for collaborative skills in the short term for the latter. First-in-family status, however, was associated with higher levels of perceived skill outcomes across the board and time, ranging from 0.1 to one quarter of a standard deviation. NESB graduates reported more than one fifth of a standard deviation higher ratings of collaborative skill outcomes across time, compared with ESB graduates.

Study mode and attendance status did not appear influential, other than mixed-mode study reporting a one quarter of a standard deviation higher level of collaborative skills compared to on-campus. Relative to PhDs, Master’s graduates perceived considerably lower levels of all skills at six months and three years, except for collaborative skills at six months. HDR graduates employed in private or not-for-profit sectors generally perceived lower levels of skills across all domains and more so at six months, compared with those in public organisations with reported differences greatest for collaborative skills (0.15 to 0.2 of a standard deviation). There were scant meaningful effects by employment in professional occupations. Importantly, the professional occupation category for this cohort excluded university academics, which were entered into the regression models as a separate variable. University academics perceived higher levels of foundation skill outcomes across time compared with those not employed in academia. Finally, as with coursework graduates, HDR graduates who considered themselves as overqualified perceived lower skill outcomes at six months and three years, ranging from 0.13 to 0.23 of a standard deviation across all skills domains.

For ease, the significant differences for personal/degree-related/employment characteristics and perceived overqualification for Bachelor, postgraduate coursework and research graduates are summarised in Table 6. Asterisked results indicate significant differences of greater magnitude (e.g. one fifth of a standard deviation or higher). The summary broadly affirms the important role of personal and study characteristics on perceived skill outcomes while graduates’ current employment context had less influence, although feeling overqualified in their role was impactful, especially for research graduates.

Table 6. Summary of key results.

	Bachelor		Postgraduate		Research
	Short-term	Longer-term	Short-term	Longer-term	Short-term	Longer-term
Gender	✔	✔	✔	✔
Age	✔*	✔	✔*	✔	✔	✔*
Indigenous	✔	✔		✔
Disability	✔				✔
Local-born	✔	✔	✔	✔
Low-SES	✔	✔	✔	✔	✔
First-in-family	✔		✔		✔	✔*
NESB	✔*	✔	✔*	✔*	✔*	✔*
Study characteristics	✔	✔	✔*	✔*	✔*	✔*
Employment characteristics	✔	✔		✔	✔*	✔
Overqualification	✔	✔	✔	✔	✔*	✔*

*Standard deviation > 0.2.

5. Discussion

In terms of lesser-developed skills, weak results for numeracy align with reported skill gaps among graduates (Hack-Polay 2020) and highlight the need for curriculum renewal in earlier schooling years. Otherwise, foundational skills were considered by each graduate cohort to be reasonably well developed in HE. For adaptive skills, coursework graduates’ lower self-assessments of generating innovative ideas and identifying new opportunities could be contributing to Australia’s comparably weak performance in innovation (OECD 2017), and support curriculum review in fostering creativity and change mindsets. The stronger results for postgraduate research graduates suggest that HDR offerings are fostering innovation, entrepreneurialism and autonomy, potentially refuting concerns that courses are struggling to meet labour market demands (e.g. Cuthbert and Molla 2015). Weak postgraduate (coursework and research) collaborative skills are, however, concerning and may reflect an overall lack of group activities and assessments, and explicit guidance on how to work well with diverse others. Given their criticality across professions, greater consideration to embedding these skills in postgraduate offerings is important.

Skill ratings falling over time among coursework graduates supports Tuononen et al.’s (2019) assertion that ‘some graduates are not able to identify and evaluate their competences before they can use them in real working-life situations’ (p. 590). This aligns with the Dunning-Kruger effect (Kruger and Dunning 1999) where new graduates are less exposed to skill demands (‘don’t know what they don’t know’) whereas three years post-course completion, they may be in more challenging roles with greater clarity on skill requirements, which they believe exceed their own capabilities (Teichler 2007). The lack of change over time for HDR graduates may be due to greater consistency in their roles over the six-month to three-year period, reducing their exposure to markedly increased skill demands.

Perceived skill outcomes among coursework graduates, both Bachelor and postgraduate, varied according to certain personal characteristics. Females completing Bachelor degrees were generally more favourable in their evaluation of skill development while coursework postgraduates less so compared to males. While one might tentatively conclude that female Bachelor graduates may respond more positively to skills-related interventions to prepare for employment, interventions can be crafted to optimise learning by gender (see O’Leary 2021) and further investigation is warranted. There was more congruence for age with younger graduates seeming to garner more from their courses, most likely due to their lesser exposure to diverse skill development opportunities in work/other activities during their lifespan. Similar thinking may be applied to low SES graduates whose consistently stronger perceived skill outcomes could reflect a greater appreciation of and gain from curriculum, given their less developed cultural and social capital (APPG 2017) and elevated commitments and personal pressures (Jackson and Dean 2022b) can mean fewer opportunities to engage in professional socialisation, network building and skill building activities outside university, such as self-organised internships. Those born overseas or from non-English background also seemed to gain more than their counterpart groups, the skills provision perhaps providing key insights on capabilities specific to cultural competence, communication and collaboration practices and which are important for local labour market success yet not accessible beyond curriculum.

Notable gains among certain groups were more evident in coursework degrees, possibly due to explicit embedding of targeted skills initiatives. This highlights the potential value of university courses for advancing human capital, perhaps more so for students who have less exposure to relevant developmental opportunities. Broadly, findings highlight the importance of ensuring in-curricular skill-related initiatives can be leveraged by all students, and educators recognising the need for tailoring interventions to diverse student needs (Monteiro et al. 2020; Scott and Willison 2021) when developing student employability. An example is internships which are often more easily accessed by domestic students, the academic elite, those able to draw on networks to source industry partners and students able to bear associated costs, such as clothing, travel and childcare (Peach et al. 2016). Once in industry, WIL students’ experience can vary by their cultural capital and capacity to communicate effectively (Jackson 2017), highlighting the critical importance of recognising heterogeneity and adapting skill-related initiatives accordingly. There is emergent evidence of the value of HDR-level internships for developing professional skills (e.g. Stamati and Willmott 2023).

Degree-related characteristics appeared to be more associated with skill outcomes among coursework graduates. The value of a Bachelor honours degree was clear, the focus on data analysis, thesis writing and knowledge creation leading to perceptions of superior foundation and adaptive skills. Industry stakeholder support of honours programmes, such as scholarships, may help to provide them with a suitably skilled graduate talent pipeline. Similarly, postgraduate coursework at Master level appears to better equip graduates with the requisite skills for employment. Although evident, the gain in skills between Master and doctoral research graduates appeared relatively smaller.

Findings support extant literature that online learning can pose challenges for developing collaborative skills, the environment limiting peer interaction and meaningfully connection with others (see Gillett-Swan 2017). Off-campus study was associated with superior adaptive skills in the short term, perhaps presenting better opportunities for innovation and working independently. These findings have ramifications for any rise in online learning. Reported differences for attendance may reflect age and study mode patterns, for example, part-time Bachelor graduates’ lower perceived skill outcomes indicating an older cohort that largely studies off-campus.

Regarding associations between employment context and perceived skill outcomes, the weaker perceptions among Bachelor and HDR graduates in private organisations could indicate greater exposure to skill demands in their roles, compared with publicly funded organisations. Interestingly, across all three samples and over time, those who considered themselves as overqualified in their roles had lower perceived skill outcomes than those who did not feel overqualified. This suggests disillusionment with their course’s development of skills and preparedness for work, given their employment is at a level below what they aspired to/expected. This aligns with Semeijn et al. (2006) who found a positive association between graduates’ match between role and education, and their assessment of skill outcomes.

6. Conclusion

This study advances our understanding of perceived skill gaps, from the graduate perspective and at all course levels, to identify areas for curriculum review and renewal. Further, it provides insights on how perceived skill outcomes from university, in terms of preparedness for employment, change over time. We found that self-assessments become less favourable as time lapsed post-graduation, attributed to progression into more challenging roles which pose greater skill demands. We highlight the value of exploring graduate perspectives into the longer-term to gain a better sense of the value of university education for enhancing skills and potential areas for curriculum review. Varying perceived skill outcomes by course level signal the value of reviewing skill-related initiatives in all degree offerings, not just in Bachelor programmes.

Clearly, perceived skill outcomes vary by background characteristics, particularly in coursework degrees which traditionally incorporate more explicit, skill-related interventions and activities. Some graduate groups felt more positive about skill development and how their course prepared them for employment, with variance possibly explained by their lesser exposure to professional networks, work and life experiences which allow for skill development. These perceived gains highlight HE’s important role in providing opportunities for the development of industry-relevant skills and embedding skill-related pedagogy and practice (such as WIL) that is accessible and inclusive for all. The evidenced richness of face-to-face learning for fostering collaborative skills also provides a cautionary message to universities on online delivery.

The study has limitations, largely related to the GOS which uses self-report data on perceived skill outcomes, rather than objective measures. Further, the survey’s defined skill constructs may not encompass all industry-relevant skills, such as digital literacy. The sizeable samples and analysis at different course levels, however, carve important pathways for future research. For example, a mixed-methods design could more deeply investigate perceptions of the same student groups, and others (e.g. by type of disability), on their skill development and outcomes and how these may be improved. This would enhance our understanding of nuances among diverse cohorts, and even fields of study, and help to identify strategies to better support students with particular needs, such as those from less privileged backgrounds or who have mental health concerns.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. HDR models did not include Indigenous status due to low numbers.

Appendix

– Three-level hierarchical linear modelling

The three-level hierarchical linear modelling comprised two steps. First, estimation of an intercept-only model with no predictor variables, examining the proportion of variance for each hierarchical level:

$Y_{\mathit{ijk}}={\beta }_0+v_k+u_{\mathit{jk}}+e_{\mathit{ijk}}$

$v_k{}_{}\mathit{N}(0,{\sigma }_v^2)$

$u_{\mathit{jk}}{}_{}\mathit{N}(0,{\sigma }_u^2)$

(1) $e_{\mathit{ijk}}{}_{}\mathit{N}(0,{\sigma }_e^2)$(1)

where $Y_{\mathit{ijk}}$ denotes the perceived skill value of student i in the j^th field of education in the k^th university, ${\beta }_0$ is the mean across all universities, $v_k$ is the effect of university k, $u_{\mathit{jk}}$ is the effect of field of education j, and $e_{\mathit{ijk}}$ is the graduate level residual term. Variance in the outcomes attributed to the hierarchical levels in this first stage are used to estimate the variance partition coefficients and intra-class correlations, which are then used to assess the relative magnitude of the variance components in the outcome variables.

The second stage of modelling is a random intercept model with graduate level explanatory variables, expressed as:

$Y_{\mathit{ijk}}={\beta }_0+\mathit{\beta }{X}_{\mathit{ijk}}+v_k+u_{\mathit{jk}}+e_{\mathit{ijk}}$

$v_k{}_{}\mathit{N}(0,{\sigma }_v^2)$

$u_{\mathit{jk}}{}_{}\mathit{N}(0,{\sigma }_u^2)$

(2) $e_{\mathit{ijk}}{}_{}\mathit{N}(0,{\sigma }_e^2)$(2)

In equation (2)(2) $e_{\mathit{ijk}}{}_{}\mathit{N}(0,{\sigma }_e^2)$(2) , X represents a vector of graduate characteristics that are hypothesised to influence skill outcomes, including personal, degree-related and employment characteristics. While fields of study and institutions were specified as hierarchical levels (second and third levels) in the first modelling phase, the second stage only had graduate (first) level explanatory variables entered, and hence is a three-level hierarchical model with random intercepts.