An Elon Musk generalist or a specialist? The impacts of interdisciplinary learning on post-graduation outcomes

ABSTRACT Interdisciplinary education has become increasingly prominent as a core instrument to prepare the next generation workforce. Yet, little is known about the impacts of long-term degree-oriented interdisciplinary education on post-graduation outcomes. This paper aims to investigate the influence of long-term degree-oriented interdisciplinary education on graduates’ post-graduation plan choices and labour market outcomes using unique administrative micro-data and career-tracking data from a comprehensive research university. Our results indicate that higher levels of engagement in interdisciplinary learning increase the probability of pursuing future study and employment in a field that differs from a graduate’s college degree, and are also associated with a higher probability to enter the workforce. Yet, this positive association between interdisciplinary learning and the probability of entering the workforce is specific to graduates from traditional disciplinary programmes. Additionally, our findings suggest that the impact of long-term degree-oriented interdisciplinary education on early labour market outcomes is overall beneficial but varies across degree fields. The findings of our study provided partial evidence in support of the influence of long-term degree-oriented interdisciplinary education on post-graduation plan choices and early labour market outcomes. We suggest that given resource constraints, higher education institutions could consider relaxing module choice restrictions in traditional disciplinary programmes to promote interdisciplinary education. However, it is important to note that higher education institutions should carefully consider the potential trade-off between the breadth of interdisciplinary content and the depth of specialist content, in order to strike a balance.


Background
As globalisation and the complexity of labour markets increase, interdisciplinary learning is becoming a pivotal instrument to enhance graduates' employability (Pattison et al. 2022;Power and Handley 2019).Often understood as learning knowledge and skills across different disciplines, interdisciplinary learning is argued to benefit learners in developing skills, such as critical thinking, communication, and integrating knowledge effectively to solve complex problems (Hains-Wesson and Ji 2020; Lattuca, Voigt, and Fath 2004).Interdisciplinary learning is described as adding to the list of desirable college experiences that current employers require from newly graduated college students.This is in addition to studying abroad and learning communities, all of which have been shown to positively affect students' post-graduation career outcomes (Miller, Rocconi, and Dumford 2018;Oswald-Egg and Renold 2021).
In view of the potential benefits of interdisciplinary learning, Higher Education Institutions (HEIs) have developed interdisciplinary programmes in various formats.The most prevalent form has been around interdisciplinary modules which may be carried out by a team-taught or drawing students from a broad selection of disciplinary backgrounds.The second type is collaborative projects involving actors from different modules.Students from different modules are put together and formed groups to work on a unique project.Both interdisciplinary modules and interdisciplinary collaborative projects are short-term interdisciplinary learning opportunities that undergraduates can choose to participate while studying.The third format is specialised interdisciplinary Bachelor degree programmes which allow students to select dual specialities from traditional disciplinary degree programmes.A fourth interdisciplinary learning option is to allow students from traditional disciplinary degree programmes to freely choose their modules from different disciplines and schools.Traditionally, the core educational idea of traditional disciplinary programmes is to train professional leaders.Under the backdrop, module credits that students can choose are limited to their own programmes and schools.Recent trends in interdisciplinary learning have propelled traditional disciplinary programmes to introduce more options on modules chosen and allow students to select module credits of their own interests in other fields of study.Yet the majority of credits remain in the field of study of their registered programme.Both specialised interdisciplinary degree programmes and flexible module-based interdisciplinary learning within traditional disciplinary programmes are long-term degree-type interdisciplinary learning mechanisms.High-school students need to apply for the programme before entering universities.
Existing research recognises the critical role played by short-term interdisciplinary learning opportunities in undergraduate academic performance and skills while studying (Burkholder et al. 2017;Hains-Wesson and Ji 2020).Burkholder et al. (2017), for example, investigated the impact of a three-course curriculum that combined environmental science, ethics, and integrative course on students' skills.The pre-and post-comparison suggested that the interdisciplinary curriculum improved students' interdisciplinary thinking, self-confidence, and public speaking skills.Yet, little is known about the effects of interdisciplinary learning on post-graduation plan choices and labour market outcomes.This is despite the fact that a key argument for the design of interdisciplinary education is to enhance graduate employability (Costa et al. 2019;Lattuca, Voigt, and Fath 2004).
Previous research on graduates' labour market outcomes has particularly focused on the effect of high-impact practices, such as internships, learning communities, study abroad, and research with faculty on labour market outcomes (Miller, Rocconi, and Dumford 2018;Silva et al. 2018).It has been demonstrated that high-impact practice participation enhances employability and leads to higher wages and reduced job search time.These high-impact practice experiences provide students with an opportunity to apply theoretical knowledge in a real-world setting, develop skills to approach complex circumstances, and build a professional network of contacts (Miller, Rocconi, and Dumford 2018).Learning interdisciplinarily is argued to gain similar benefits in employability as participating in high-impact practices but seems to take less extra time.Students can gain interdisciplinary experience by being enrolled in a specialised interdisciplinary degree programme or taking module credits outside their own traditional degree programmes.Therefore, understanding the association between interdisciplinary learning and labour market outcomes is of importance to provide students with a guideline to prepare for the workforce in an efficient way.
Moreover, the evidence discussed above on the positive relationship between interdisciplinary education and skill development is limited to short-term interdisciplinary projects (Burkholder et al. 2017;Khandakar et al. 2020) or specialised interdisciplinary degree programmes (Lattuca et al. 2017;Mansilla et al. 2009).The impact of interdisciplinary learning on graduates from traditional disciplinary degree programmes is limited.Most research on interdisciplinary learning often treats students in specialised interdisciplinary programmes as the only interdisciplinary learners.For example, Lattuca et al. (2017) used data from various interdisciplinary and traditional disciplinary majors from 17 institutions.They treated students in traditional disciplinary majors as non-interdisciplinary learners and thus compared the learning outcomes of students majoring in interdisciplinary programmes and those of students in traditional disciplinary majors.The recent trend in interdisciplinarity also makes module choices flexible gradually in traditional disciplinary programmes.Traditional disciplinary students can be exposed to interdisciplinary learning by registering for modules offered outside their disciplines.Research on interdisciplinary learning in traditional disciplinary degree programmes is needed to inform the design of effective interdisciplinary education programmes.
To address these limitations, we aim to examine the influence of two long-term degree-type interdisciplinary learning pathways on individual post-graduation plan choices and early labour market outcomes.To this end, we use a two-stage analysis.Drawing on unique administrative and survey data from the Taiwanese National Tsing Hua University (NTHU), we first use a set of logistic regression models to assess the effect of the two structures of interdisciplinary learning (i.e.traditional disciplinary and specialised interdisciplinary degree programmes) on post-graduation plan choices.Secondly, we combine individual records with programme-level career-tracking data from the Taiwanese Ministry of Education (MoE) and examine the impact of interdisciplinary learning on programme-mean salary and employment rate over time and across programmes using a set of cross-classified multilevel models.

Conceptual links between interdisciplinary learning and post-graduation plan choices and labour market outcomes
Multiple theories and perspectives can be used to understand and hypothesise about the associations between interdisciplinary learning and post-graduation plan choices and labour market outcomes.In this section, we elaborate on the associations between these theories and interdisciplinary learning and develop four main hypotheses about these associations.
First, interdisciplinary learning is believed to have a positive effect on students' employability skills such as critical thinking skills (Hains-Wesson and Ji 2020).Graduates who are confident in demonstrating employability skills, tend to be confident about applying for a job immediately after graduation (Miller, Rocconi, and Dumford 2018;Oswald-Egg and Renold 2021).Conversely, graduates who may perceive themselves as less prepared for workforce engagement might opt for an extended transition period to secure employment or exhibit a heightened inclination towards pursuing further studies in pursuit of a deeper knowledge foundation.Research on highimpact practices reveals that participation in high-impact practices, such as internships, capstones, or service learning, makes a positive contribution to students' employability skills (Miller, Rocconi, and Dumford 2018;Silva et al. 2018) and has a positive effect on students' plans to seek employment after graduation (Miller, Rocconi, and Dumford 2018).Similarly, interdisciplinary experience, which has been shown to equip students with employability skills, may also have a positive association with students' intention to seek employment immediately after graduation.We therefore hypothesise that: graduates learning through interdisciplinary training are more likely to seek employment immediately after graduation.
Hypothesis 1. 1 Second, interdisciplinary learning exposes learners to a wide range of disciplines and people from different backgrounds.Acquiring knowledge in a much wider pool of subjects empowers students to acquire knowledge not only from their primary discipline but also from diverse fields of study.This expands the scope of learners' knowledge, enhancing their versatility when making career choices.Research on diversity suggests that diversity may benefit organisations in improving organisational flexibility (Milem 2003).Similarly, diversity of disciplinary knowledge may increase learners' flexibility in career choices and the possibility to choose further studies or a job in a field that differs from their college degree.Engaging with people from different backgrounds is associated with greater openness to diversity and challenge (Milem 2003).Interacting with diverse peers in the learning environment during college shapes the way students think about their competencies in working with different types of people and how to work effectively with others (Milem 2003;Umbach and Kuh 2006).Such experience enables learners to have a greater openness to diversity and challenge after college, encouraging learners to experience a wide range of things away from their comfort zone (Milem 2003;Umbach and Kuh 2006).Similarly, exposure to diverse peers in the interdisciplinary learning context may make graduates confident in embracing a diverse working field (Bettencourt et al. 2023).We therefore hypothesise that: graduates learning through interdisciplinary training are more likely to pursue a further degree/job that is unrelated to their college degree.
Hypothesis 2. Third, human capital theory leads to the expectation that graduates with interdisciplinary experience have a higher probability to find a job immediately after graduation and higher starting salaries than those without interdisciplinary experience.According to human capital theory, there are two types of human capitalgeneric and specific human capital (Becker 1962).Generic human capital refers to skills, knowledge, and abilities that are broadly transferable and not specific to a particular job or industry.Specific human capital, on the other hand, refers to skills, knowledge, and experience that are specific to a particular job, industry, or company.A broader interpretation of specific human capital suggests that a particular configuration of general skills also constitutes a form of specific human capital (Lazear 2009).Organisations place considerable value on specific human capital, often demonstrating willingness to remunerate employees with elevated levels of such expertise (Slaughter, Ang, and Fong Boh 2007).Interdisciplinary learning facilitates the acquisition of knowledge from diverse academic domains, thereby augmenting the likelihood of individuals possessing the specific human capital sought after by organisations.As interdisciplinary experience serves as an indicator of specific human capital, employers may use it as a screening device by looking at new graduates' academic transcripts or degree certificates.Consequently, employers demonstrate keen interest in recruiting and providing elevated compensation to individuals with a background in interdisciplinary education.We thus hypothesise that: graduates learning through interdisciplinary training are more likely to achieve higher starting salaries and the likelihood of securing a job immediately after graduation.
Hypothesis 3. Fourth, human capital theory also predicts that interdisciplinary learning experience is associated with higher labour market outcomes such as salaries, but the influence may not appear immediately after graduation (Tomaszewski et al. 2021).Existing literature has documented the effects of interdisciplinary learning on mastering a series of skills, such as critical thinking, communication, and integrating knowledge effectively to solve complex problems (Hains-Wesson and Ji 2020; Lattuca, Voigt, and Fath 2004).According to human capital theory, these enhancements in generic human capital are usually compensated in the labour market through higher earnings (Becker 2009).Yet, human capital is an intangible asset embodied in individuals and unable to observe at first glance.Thus, new graduates' productivity may gain the recognition of employers and be rewarded in salaries gradually after they contribute to a company's productivity.We thus hypothesise that: the predicted benefits of interdisciplinary learning in labour market outcomes will grow over time.

Case study
The National Tsing Hua University represents our case study.Currently, the university consists of 10 schools, 26 Bachelor degree programmes, 27 graduate institutes as well as 10 independent master's and doctoral programmes.It offers a full range of degree programmes in Science, Engineering, Management, Humanities and Social Sciences.Each undergraduate requires to take a total of 128-132 credits, which is made up of university credits, school credits, programme credits, elective courses and free elective courses. 2 The difference in the graduation requirement of credits between programmes appears principally in school credits, programme credits and elective credits.Broadly, 24 Bachelor degree programmes can be categorised into two types of programmes -7 specialised interdisciplinary degree programmes and 17 traditional disciplinary degree programmes.
The first group comprises seven specialised interdisciplinary degree programmes.The key feature of interdisciplinary degree programmes is that original programme credits are divided into two specialities and school credits are added to the graduation requirement of credits.Students enrolled in interdisciplinary degree programmes need to take a general knowledge of their registered school during the first two years.After, students can choose one speciality in their school and choose a second speciality at any other school.The second group consists of 17 traditional disciplinary programmes.Traditionally, the educational goal of HEIs in Taiwan is to help students acquire a single, professional disciplinary knowledge.Students enrolled in a disciplinary programme are required to register for most of the module credits within their programmes.Because of the advocacy of interdisciplinary learning in recent years, NTHU provides students in traditional disciplinary programmes with an opportunity to learn interdisciplinarily by allowing them to register for module credits from different schools-fields.Free elective credits allow students to choose modules that suit their own interests, rather than those required by their main disciplinary programme.
The application methods for high-school students to enrol in a specialised interdisciplinary degree programme or a traditional disciplinary programme are the same.High-school students can apply to university degree programmes through two main routes -(1) application and recommendation or (2) examination and placement.Under the examination and placement route, high-school students are required to take the Advanced Subjects Test (AST).After obtaining their test results, students reference the average exam scores accepted by universities in the previous year and submit a list of preferred university programmes, with a maximum of 100 selections, ranked by preference.Subsequently, the College Entrance Examination Center allocates students to specific university programmes based on their AST scores and preference list.This process underscores that students are not able to secure enrolment in specific programmes based solely on their preferences.
The theoretical maximum extent of interdisciplinary exposure for interdisciplinary degree students (representing as First Speciality and Second Speciality in Table A1 in Appendix A) may arguably be well-defined and more than those for traditional disciplinary students (representing as Free Selective Credits in Table A1 in Appendix A).Comparing the effect of interdisciplinary learning of graduates from traditional disciplinary and specialised interdisciplinary programmes therefore may be inappropriate.As such, we conduct analyses on graduates from traditional disciplinary programmes and graduates from specialised interdisciplinary degree programmes separately.To examine the effect on labour market outcomes, we include an interaction term identifying the type of graduate programme and the extent of interdisciplinary learning (which is defined as the proportion of credits that were offered by other schools or by a different field).This helps distinguish graduates from the two types of programmes.The detailed methodology is described in Section 5.

Defining interdisciplinary learning
The term 'Interdisciplinary Learning' in this context is used literally to mean the process of learning knowledge and skills from different disciplines (Karlqvist 1999).In this scenario, the essence of 'Interdisciplinary Learning' manifests through the acquisition of knowledge and skills spanning multiple disciplines.We used two metrics to quantify the extent of interdisciplinary learninga school-level and a discipline-field-level metric.The first captures the share of module credits taken outside a student's school of enrolment.The second refers to the share of module credits taken in a disciplinary field that differs from the field of a student's school of enrolment.Equations 1 and 2 represent the mathematical form of these measures.To more easily understand these Equations, Figure 1 displays the generic structure of a student's module profile.Broadly, total credits registered by a student can be divided into three categories with module credits offered by: (1) their own programme, (2) other programmes in their own school, and (3) other schools.The latter can be further divided into three subgroups with module credits: (1) within the same disciplinary field, (2) from a similar field, and (3) from a different field.
school − level interdisciplinarity i = sum (credits student i took from other schools) total credits student i took (1) field − level interdisciplinarity i = sum (credits student i took from different field) total credits student i took (2) We categorised module credits offered by other schools into three subgroups in two steps.First, wclassified the seven schools at NTHU into three disciplinary fields: humanity, society, and technology according to the Taiwanese Ministry of Education's disciplinary classification.The School of Humanities and Social Sciences (HSS) belongs to the humanity field, School of Technology Management (CTM) belongs to the society field, and other five schools, including Science (SCI), Life Science (LS), Nuclear Science (NS), Electrical Engineering and Computer Science (EECS) and Engineering (ENGI), belong to the technology field.Next, we compared the similarity between the three fields based on Biglan's taxonomy of academic disciplines (Biglan 1973;Kolb 1981).According to Biglan's taxonomy of academic disciplines, humanity (consisting of Chinese Literature and Foreign Languages at NTHU) and society fields (consisting of Economics and Finance) are more similar to each other than any of these fields with technology fields (consisting of Science and Engineering).On the other hand, technology fields are more similar to society fields than to humanity fields.Therefore, if a humanity-field student took module credits offered in a technology field, the module credits would be classified as module credits offered by a different field.The extent of interdisciplinary learning can thus be captured by the share of module credits registered and completed at different schools or disciplinary fields over the duration of an undergraduate programme.

Data and methods
We used data from three sources: (1) NTHU administrative data, (2) NTHU Graduation Survey (GS) data, and (3) career-tracking data integrated by the Taiwanese Ministry of Education.Administrative data from different sections across NTHU provides information on students' backgrounds and module profiles.The Center for Institutional Research of NTHU distributes a Graduation Survey to collect information about students' learning experiences during their studies.This survey has been running annually since 2012 and collects data on students' individual and family background information and graduation plans.The response rate is high providing a return rate of, for example, 98.2% in 2015.Career-tracking data integrated by MoE collects post-graduation records, such as monthly salary, employment status and further education of all graduates in Taiwan since 2010 and tracks them annually up to five years after graduation.However, Taiwanese privacy and personal data protection laws prevented us from obtaining individual records for our analysis.We only had access to programme-level career-tracking data.While this constrains our analysis to examine programme-level aggregate labour market outcomes, such analysis still provides a valuable insight into the relationship between interdisciplinary learning and labour market outcomes.

Data
To analyse the influence of interdisciplinary learning on post-graduation plan choices, we linked the university administrative data and GS data to construct an individual-level dataset.The individuallevel dataset comprises 5922 observations who graduated between 2012 and 2017, with 14.51% of graduates enrolled in specialised interdisciplinary degree programmes.

Variables
We considered four outcomes for post-graduation plan choices: (1) planning to continue studies, (2) planning to enter the workforce, (3) the degree of alignment between a graduate's Bachelor degree field and planned future field of study, and (4) the degree of alignment between a graduate's Bachelor degree field and planned future field of job.Data were obtained from the GS.Panel A Table 1 lists and describes the data to measure these outcomes.
To isolate the relationship between interdisciplinary learning and post-graduate plan choices, we controlled for individual and household attributes which are known to influence these choices and outcomes (Miller, Rocconi, and Dumford 2018;Oswald-Egg and Renold 2021;Tomaszewski et al. 2021).Description of independent variables used in our analysis and their summary statistics across our sample are presented in Table B1 in Appendix B.

Modelling
We adopted two types of logistic regression models to analyse the influence of interdisciplinary learning on individual post-graduation plan choices.Binary logistic regression models were used to analyse two dichotomous choices; that is, (1) the plan to continue studies, and (2) the plan to enter the workforce after graduation.Ordered logistic regression models were used to examine ordinal outcomes; that is, (1) the degree of alignment between a graduate's Bachelor degree field and planned future field of study, and (2) a graduate's Bachelor degree field and planned future field of job. 3  We accounted for potential correlated plan choices from students within the same school.Students from the same schools may be more likely to make similar choices.To account for this potential effect, we added school dummy variables to control for school-level fixed effects and also clustered standard errors by schools to allow for systematic heteroskedasticity across clusters of observations.The detailed formulas of models are presented in Appendix C.1.
The sample was split into two sub-groups, graduates from traditional disciplinary degree programmes and graduates from specialised interdisciplinary degree programmes, because of the difference in programme design (Newswander and Borrego 2009).The structure of required credits varies across the two types of programmes (see Table A1 in Appendix A).Besides, the potential variance in content between traditional disciplinary and specialised interdisciplinary programmes may potentially introduce disparate effects of other independent variables on students' outcomes across these distinct programme categories.Embracing the sample split approach facilitates the introduction of coefficients that can vary across groups while maintaining a coherent analytical framework.Therefore, we performed separate regression models for the two subgroups to investigate the impact of interdisciplinary learning on individual post-graduation plans. 4

Data
Given the lack of individual information on labour markets, we transformed our individual-level data set into a programme level and assembled it with the programme-level career-tracking data to capture labour market outcomes.This programme-level data set comprises a total of 720 programme records from 2012 to 2017, including 24 programmes, six cohorts, and one to five years after graduation.

Variables
We used information on: (1) the average monthly nominal salary and (2) the employment rate to capture programme-level labour market outcomes.The average monthly nominal salary was transformed into the real value to adjust for inflation and took a logarithm to measure percent changes in salary.The employment rate is the percentage of employed graduates in relation to the total graduates in each programme.Panel B Table 1 lists and describes the data to measure these outcomes.To isolate the relationship between interdisciplinary learning and labour market outcomes, in addition to individual and household attributes, we also considered two macroeconomic factors -GDP deflators and unemployment ratesto capture potential employment differentials during business cycles (McQuaid 2017;Oreopoulos, Von Wachter, and Heisz 2012).

Modelling
We adopted cross-classified multilevel modelling to examine the effect of interdisciplinary learning on programme-level labour market outcomes and used random intercepts and slopes to capture variations in labour market outcomes across programmes and over the span of years subsequent to graduation.Particular disciplines are believed to benefit more significantly than others from interdisciplinary learning.The benefits of interdisciplinary learning are also expected to change over time; though the shape of these effects is unclearwhether they stabilise after an initial positive impact or accumulate over time.Figure 2 offers a visual representation of the cross-classified structure of our programme-level data.In our cross-classified multilevel structure, level 1 refers to programme-cohort observations.Level 2 comprises programme-level observations and years after graduation.We used varying intercepts to capture variations across programmes and the span of years subsequent to graduation, and varying slopes to capture the variability in the effect of interdisciplinary learning on labour market outcomes.The formulas of the cross-classified multilevel models are presented in Appendix C.2.

Phase 1: Varying effects of interdisciplinary learning on post-graduation plan choices
Table 2 presents the results of our logistic regression analysis modelling the plan of graduates' postgraduation choices.Specifically, it reports the marginal effect between our two measures of interdisciplinary learning and four post-graduation plan choices holding all other covariates fixed at their sample means.The results of ordered logistic regression analysis in Panel C and Panel D are shown for each of the three categories of our outcome variables (i.e.disagree, neutral and agree).Separate logistic regression models were estimated for traditional disciplinary graduates and specialised interdisciplinary graduates.
Panel A Table 2 shows the estimates for the probability to engage in further studies post-graduation.For graduates from traditional disciplinary programmes, results indicate that getting one more percent credit outside the school of their Bachelor degree reduced the probability of seeking to continue studies by .409%.Consistently, Panel B shows that traditional disciplinary graduates were .079%more likely to be willing to enter the workforce after graduation given one percent increase in school-level interdisciplinary learning.Together, these results suggest that traditional disciplinary graduates with a higher extent of interdisciplinary learning across schools tend to seek employment immediately after graduation.No significant estimates are observed for our field-level models, indicating graduates taking credits from a different field while studying did not affect their intention to study further or seek employment.By contrast, for graduates from specialised interdisciplinary programmes, a negative association was estimated between the extent of interdisciplinary learning and the likelihood of planning a transition into the workforce.Specialised interdisciplinary graduates with a higher extent of interdisciplinary learning had a lower intention to seek employment immediately after graduation, compared to those with a lower extent of interdisciplinary learning.
Panel C and D show the estimates for the degree of alignment between graduates' Bachelor degree field and their planned future field of study and job.The results indicate that graduates with interdisciplinary learning experience had a lower tendency to take up further studies and jobs related to their college degree whether they graduated from traditional disciplinary or specialised interdisciplinary degree programmes.For example, the coefficient on 'agree' of 'school-level interdisciplinarity' for traditional disciplinary graduates in Panel C and D indicate that, traditional disciplinary graduates with one more percent credits taken from other schools are associated with a decline of .684%and .575% in the probability of agreeing to pursue studies or a job aligned with their Bachelor degree field.The results were consistent for our two metrics of interdisciplinary learning.Similarly, for graduates from specialised interdisciplinary programmes, increasing one percent of credits outside their schools decreased .170%and .200%probability of agreeing that they would pursue studies or a job aligned with their Bachelor degree field.However, no significant effects were found under the field-level measure.

Phase 2: Varying effects of interdisciplinary learning on programme-level labour market outcomes
Table 3 presents the results of our multilevel models.Results for two outcome models are reported based on (1) our school-level measure and (2) field-level measure of interdisciplinary learning.Table 3 provides a summary of the estimated fixed-effect coefficients relating to interdisciplinary learning.The results indicate no statistically significant relationship between interdisciplinary learning and post-graduation programme-average salary and employment rate.Interdisciplinary learning seems to have no effect on post-graduation labour market outcomes.This relationship appears to be consistent for both graduates from traditional disciplinary and specialised interdisciplinary programmes, and our two metrics of interdisciplinary learning.These fixed-effect estimates however seem to conceal significant differences across programmes and over time.Figures 3 and 4 depict estimated random slopes capturing variations in the effect of interdisciplinary learning on labour market outcomes across programmes and over time.It is important to bear in mind that a positive random-effect estimate does not necessarily mean a positive relationship between interdisciplinary learning and labour market outcomes.A positive random effect in a particular programme indicates that the effect of interdisciplinary learning is greater in size for the programmecompared to the university average.The overall effects of interdisciplinary learning in each programme should combine the fixed and random effects estimates.We present the overall effects in Figures D3-D7 in Appendix D.3.
Figure 3 shows that interdisciplinary learning has a negative impact on programme-level salary within one and two years after graduationcompared to the average across all years (deviations from the fixed effect estimate).However, the impact of interdisciplinary learning turns positive on salary four years after graduation.An increase of one percent in credits outside a graduate's school is associated with a rise in programme-level salary in the fourth year after graduation by around .16% (see the top left figure of Figure 3).Our results indicate that the potential benefits of interdisciplinary learning on salary might appear after graduation for four years.
Turning to variations in the impact of interdisciplinary learning on salary across programmes, Figure 3 reveals significant variability in the relationship between interdisciplinary learning and salary across programmes.The plot shows that the effects of interdisciplinary learning on five out of 24 programmes differ significantly from the average effects of interdisciplinary learning in university.Among 24 programmes, the association between interdisciplinary learning and salary is the highest at the Department of Materials Science and Engineering (MS), followed by Interdisciplinary Programme of Electrical Engineering and Computer Science (IPEECS).The overall effects of interdisciplinary learning on salary at MS and IPEECS are also positive and indicate that interdisciplinarity benefits MS and IPEECS graduates in salary (see Figures D3 and D4 in Appendix D.3).In contrast, the effect of interdisciplinary learning on salary is the poorest at the School of Life Science, including the Department of Medical Science (DMS), Department of Life Science (LS), and Interdisciplinary Programme of Life Science (IPLS).The overall effects of interdisciplinary learning on salary are also consistently negative at the School of Life Science and indicate that interdisciplinary learning may have a negative effect on salary at that school (see Figures D3 and D4 in Appendix D.3). Figure 4 presents the random-effect estimates for the employment rate.The results indicate a negative relationship between interdisciplinary learning and the employment rate within the first and second year after graduation.This relationship is reversed to a positive correlation in the third to fifth years after graduation.This result is similar to the time variation in the effects of interdisciplinary learning on salary and indicates that the potential benefits of interdisciplinary learning on employment might appear after graduation for three years.
Figure 4 also displays variations in the impact of field-level interdisciplinary learning across programmes, whereas there is no variation across programmes in the impact of school-level interdisciplinary learning.The apparent absence of programme-level variation in the effect of the school-level interdisciplinary index on employment rates may be attributed to the nuances of how the extent of interdisciplinary learning is measured.The field-level interdisciplinary index could conceivably offer a more precise gauge of interdisciplinary learning compared to the school-level interdisciplinary index, mainly due to its consideration of the extent of divergence between students' disciplinary field and the field of the registered modules.
Our results show that four out of 24 programmes had statistically significant differences in the effect of field-level interdisciplinary learning from the university average.Department of Computer Science (CS) is the only programme whose correlation between field-level interdisciplinarity and the employment rate is significantly higher than the university average.Interdisciplinary learning seems to enhance the employment possibility of CS graduates.On the contrary, the effect of interdisciplinary learning on the employment rate is the poorest at PHYS, followed by DMS and LS.Learning interdisciplinarity seems to reduce the employment possibility of Department of Physics (PHYS), DMS, and LS graduates.

Discussion and conclusion
Interdisciplinary learning is increasingly recognised as a critical instrument to prepare the future workforce.As such, HEIs have established four types of interdisciplinary learning opportunities to allow students to be exposed to areas of knowledge outside their field of study.Yet, the effects of long-term, degree-oriented interdisciplinary learning pathways have not been closely examined.This paper sought to empirically assess the impact of long-term degree-oriented interdisciplinary learning on graduates' post-graduation plan choices (continuing studies, entering the workforce, the degree of alignment between a graduate's Bachelor degree field and planned future field of study/job) and programme-level labour market outcomes (salary and the employment rate) under traditional disciplinary and specialised interdisciplinary degree programmes drawing unique individual data from NTHU, Taiwan.We tested four hypotheses.First, we hypothesised that graduates learning through interdisciplinary training are more likely to seek employment immediately after graduation.Our evidence is mixed and indicates that the effects of interdisciplinary learning on seeking employment immediately after graduation vary across traditional disciplinary and specialised interdisciplinary graduates.Our results revealed that interdisciplinary learning increased the probability of the intention to seek employment for traditional disciplinary graduates, which is consistent with our hypothesis.However, the effects of interdisciplinary learning on specialised interdisciplinary degree graduates are opposite to those on traditional disciplinary graduates and inconsistent with our hypothesis.This result may be explained by the fact that specialised interdisciplinary graduates on average have higher levels of interdisciplinarity than traditional disciplinary graduates and thus may encounter the trade-off between breadth of general knowledge and depth in specialist content gained through interdisciplinary learning (Costa et al. 2019;Millar 2016).Generally, students with higher levels of interdisciplinary learning engagement stretch their time across multiple disciplines to gain a breadth of knowledge.They may gain an overview of the respective disciplines but lack a depth of discipline-specific knowledge.As a result, students with higher levels of interdisciplinarity may feel less prepared for the workforce and seek to pursue further study to gain sufficient disciplinespecific knowledge.At NTHU, the theoretical maximum extent of interdisciplinary exposure for interdisciplinary degree students is more than that for traditional disciplinary students because of the design of the total required credits.Therefore, specialised interdisciplinary graduates may have greater difficulties in acquiring specific knowledge and have a higher intention to pursue further study.
A second hypothesis concerns the idea that graduates learning through interdisciplinary training are more likely to pursue a further degree/job that is unrelated to their college degree.We posit that interdisciplinary learning can contribute to learners' increased flexibility in selecting career paths.Consistent with this statement, our results revealed that interdisciplinary learning increases the transition to study fields and jobs which differ from their college degree.This evidence is consistent across both traditional disciplinary and specialised interdisciplinary graduates, though the degree of association differs, with the probability of transitioning to a different field being smaller for the latter.Such difference may be due to the design of specialised interdisciplinary degree programmes.Graduates from specialised interdisciplinary degree programmes can choose two specialities (two study fields) across disciplines, while those from traditional disciplinary degree programmes specialise in a single discipline.Thus, specialised interdisciplinary graduates with two study fields are more likely to pursue a further job that is related to their college degree than traditional disciplinary graduates.
We also presented evidence in relation to two hypotheses relating to early labour market outcomes.We hypothesised that graduates learning through interdisciplinary training are more likely to achieve higher starting salaries and the likelihood of securing a job immediately after graduation (Hypothesis 3), and that the predicted benefits of interdisciplinary learning in labour market outcomes will grow over time (Hypothesis 4).Our evidence did not support Hypothesis 3. We found that interdisciplinary learning is negatively associated with programme-level monthly salary and employment rate in the first and second years after graduation.A possible explanation is that early career outcomes can quickly change as graduates secure their first full-time jobs and identify career development options.The potential benefits of interdisciplinary learning may be realised later.Also, some graduates seek to pursue further studies after graduation from their undergraduate programme.Normally, it takes two years to get a Master degree in Taiwan and this has become the normal route before transitioning to the labour market.Therefore, the salary and employment rate after graduation for three years may provide a more accurate representation of the actual entry-level employment outcomes for graduates.In relation to hypothesis 4, we showed that the effects of interdisciplinary learning on salary and employment rate were positive after graduation for three years growing during the following years.Our results provide support for Hypothesis 4.
This study has found that generally long-term degree-oriented interdisciplinary learning benefits graduates in preparing for the workforce and gains in salary and employment.Our results offered some support for the impact of long-term degree-oriented interdisciplinary education on postgraduation plan choices and early labour market outcomes.Yet, long-term degree-oriented interdisciplinary education in higher education needs to address the potential trade-off between the breadth and depth of specialist content.Greater efforts are needed to ensure students engage and acquire a 'deep' degree of specialist knowledge.Providing an overview understanding of a subject will probably not be enough to consolidate knowledge in an area.It is essential to recognise that these findings pertain specifically to the effects of long-term degree-oriented interdisciplinary learning and cannot be generalised to all forms of interdisciplinary education, particularly those involving short-term interdisciplinary modules or projects.
This study examined data capturing graduate labour market outcomes over the first five years immediately after graduation from their undergraduate programme.Our study thus provided evidence on the immediate, short-term effects of long-term degree-oriented interdisciplinary learning on career outcomes.Future research should expand this work by analysing the medium-and longterm impacts of interdisciplinary learning analysing the extent to which short-term differences between graduates from traditional disciplinary and specialised interdisciplinary degree programmes are exacerbated and reduced as graduates gain working experience.
Our results revealed wide variations in salary and employment outcomes associated with interdisciplinary learning across study programmes.Future work should seek to understand the causes of such large differences.It should aim to study the extent to which differences in labour market outcomes are due to the benefits from interdisciplinary learning.Some degrees may benefit little from acquiring knowledge from other disciplines, particularly if they required applied technical knowledge.Differences may also be because of deficiencies in the design of programmes in certain fields at NTHU, or macro-economic conditions impacting starting graduates in specific sectors during the period of our analysis.Understanding the causes of differences in graduate labour market outcomes have the potential to improve the design and labour market value of interdisciplinary learning education.

Notes
1. We appreciate the referee for posing the concern about why transitioning directly into the labour market is (solely) beneficial.We would like to clarify that our intent is not to definitively label direct entry into the labour market as a benefit.Rather, our analysis concerning future career path choices aims to predict the plausible effects of interdisciplinary learning based on relevant theoretical frameworks.2. The hierarchical structure of NTHU Bachelor degree programmes and the graduation requirement of credits for each programme in 2017 are shown in Table A1 in Appendix A. 3. We thank the referee for raising the concern regarding potential selection into the programmes.We have chosen not to account for this issue in our analysis for the reasons of the regulation for applying to university in Taiwan and the data evidence.First, as mentioned in Section 3, the admission methods in Taiwan underscore that students are not able to secure enrolment in specific programmes based solely on their preferences.This mechanism serves to mitigate the potential issue of self-selection into particular programmes, ensuring a more equitable distribution of students across programmes.Second, in Appendix D.1, we have conducted mean-comparison t-tests to investigate potential significant variations in individual attributes between graduates from traditional disciplinary programmes and those from specialised interdisciplinary programmes.The results show that there are no systematic patterns in individual attributes between traditional disciplinary and specialised interdisciplinary graduates across schools.This observed absence of systematic trends underscores the neutrality of the attributes considered when comparing these two distinct academic trajectories.4. We have undertaken a Chow test to examine whether the two programmes had significantly different regression coefficients of each independent variable.Our findings reveal significant disparities in the relationships between outcomes and variables such as cohorts, schools, gender, and family background, discernible across these two programme categories.The test results support our initial conjectures, providing evidence in favour of the sample split approach.Small differences exist between graduates from traditional disciplinary and specialised interdisciplinary degree programmes.Figure D1 reveals that graduates from specialised interdisciplinary degree programmes are less likely to continue to engage in further studies and more likely to transition into the workforce after graduation, compared to graduates from traditional disciplinary programmes.Figure D2 indicates that salary tends to be slightly higher for traditional disciplinary graduates than for those from specialised interdisciplinary degree programmes, but these differences are statistically insignificant.

Figure 1 .
Figure 1.The structure of a student module credits.

Figure 2 .
Figure 2. Cross-classified multilevel structure of the data.

Figure 3 .
Figure 3. Random effects for the log of average monthly real salary.Notes: This figure depicts estimated random slopes capturing variations in the effect of interdisciplinary learning on programme-level salary across programmes and over time.Subfigure (a) presents the effects based on utilising the school-level index to measure the extent of interdisciplinary learning, while subfigure (b) displays the results obtained using the field-level index.The level for confidence intervals is 90%.The corresponding programmes are 7 specialised interdisciplinary programmes: Interdisciplinary Programme of Sciences (IPSCI), Engineering (IPE), Humanities and Social Sciences (IPHSS), Nuclear Science (IPNS), Life Science (IPLS), Electrical Engineering and Computer Science (IPEECS), Management and Technology (IPMT) and 17 traditional disciplinary programmes: Chemistry (CHEM), Mathematics (MATH), Physics (PHYS), Chemical Engineering (CHE), Industrial Engineering and Engineering Management (IEEM), Materials Science and Engineering (MS), Power Mechanical Engineering (PME), Chinese Literature (CL), Foreign Languages and Literature (FL), Life Science (LS), Medical Science (DMS), Engineering and System Science (ESS), Biomedical Engineering and Environmental Science (BMES), Quantitative Finance (QF), Economics (ECON), Computer Science (CS), Electrical Engineering (EE).

Figure 4 .
Figure 4. Random effects for the employment rate.Notes: This figure depicts estimated random slopes capturing variations in the effect of interdisciplinary learning on the employment rate across programmes and over time.Subfigure (a) presents the effects based on utilising the school-level index to measure the extent of interdisciplinary learning, while subfigure (b) displays the results obtained using the field-level index.The level for confidence intervals is 90%.The corresponding programmes are 7 specialised interdisciplinary programmes: Interdisciplinary Programme of Sciences (IPSCI), Engineering (IPE), Humanities and Social Sciences (IPHSS), Nuclear Science (IPNS), Life Science (IPLS), Electrical Engineering and Computer Science (IPEECS), Management and Technology (IPMT) and 17 traditional disciplinary programmes: Chemistry (CHEM), Mathematics (MATH), Physics (PHYS), Chemical Engineering (CHE), Industrial Engineering and Engineering Management (IEEM), Materials Science and Engineering (MS), Power Mechanical Engineering (PME), Chinese Literature (CL), Foreign Languages and Literature (FL), Life Science (LS), Medical Science (DMS), Engineering and System Science (ESS), Biomedical Engineering and Environmental Science (BMES), Quantitative Finance (QF), Economics (ECON), Computer Science (CS), Electrical Engineering (EE).

Figure D1 .
Figure D1.The share of individual post-graduation study plan choices by types of programmes.Small differences exist between graduates from traditional disciplinary and specialised interdisciplinary degree programmes.FigureD1reveals that graduates from specialised interdisciplinary degree programmes are less likely to continue to engage in further studies and more likely to transition into the workforce after graduation, compared to graduates from traditional disciplinary programmes.FigureD2indicates that salary tends to be slightly higher for traditional disciplinary graduates than for those from specialised interdisciplinary degree programmes, but these differences are statistically insignificant.

Figure D2 .
Figure D2.The average programme-level labour market outcomes by types of programmes and years after graduation.

Figure D4 .
Figure D4.Overall effects of interdisciplinary learning on the log of average monthly real salary based on the fieldlevel interdisciplinarity.Notes: The corresponding schools are as below: HSS: Humanities and Social Sciences; CTM: Technology Management; EECS: Electrical Engineering and Computer Science; ENGI: Engineering; LS: Life Science; NS: Nuclear Science; SCI: Science.

Figure D5 .
Figure D5.Overall effects of interdisciplinary learning on the employment rate based on the school-level interdisciplinarity.Notes: The corresponding schools are as below: HSS: Humanities and Social Sciences; CTM: Technology Management; EECS: Electrical Engineering and Computer Science; ENGI: Engineering; LS: Life Science; NS: Nuclear Science; SCI: Science.

Figure D6 .
Figure D6.Overall effects of interdisciplinary learning on the employment rate based on the field-level interdisciplinarity.Notes: The corresponding schools are as below: HSS: Humanities and Social Sciences; CTM: Technology Management; EECS: Electrical Engineering and Computer Science; ENGI: Engineering; LS: Life Science; NS: Nuclear Science; SCI: Science.

Table 1 .
Description of outcome variables.

Table 2 .
Marginal effects of individual post-graduation plan choices.This table reports the marginal effects between our two measures of interdisciplinary learning and four post-graduation plan choices holding all other covariates fixed at their sample means.In Row 'Traditional', we present the effect of interdisciplinary learning for graduates from traditional disciplinary programs, whereas in Row 'Interdisciplinary', we present the results for specialised interdisciplinary graduates.Column (1) and (2) display the effect of interdisciplinary learning, with the schoollevel index and the field-level index being used to measure the extent of interdisciplinary learning, respectively.To account for variations in students' plan choices related to individual and household attributes, we included a set of control variables such as gender, cohorts, schools, university entrance grades, and family income status.Standard errors are in parentheses.*p < .1,**p < .05,***p < .01.

Table 3 .
Multilevel model: fixed effects of interdisciplinary learning on programme-level early career outcomes.This table presents the results of the estimated fixed-effect coefficients related to interdisciplinary learning in our multilevel models.Column (1) and (2) display the effect of interdisciplinary learning, with the school-level index and the field-level index being used to measure the extent of interdisciplinary learning, respectively.Standard errors are in parentheses.*p < .1,**p < .05,***p < .01