Discovering One’s Talent: Learning from Academic Specialization

DISCOVERING ONE’S TALENT: LEARNING FROM ACADEMIC SPECIALIZATION author OFER MALAMUD*

The author examines an exogenous difference in the timing of academic Abstract specialization within the British system of higher education to test whether education yields information about one’s match quality in different ﬁelds of study. In distinguishing between systems requiring early and late specialization, he predicts the likelihood of an individual switching to an occupation unrelated to one’s ﬁeld of study. If higher education serves mainly to provide speciﬁc skills, the model predicts more switching in a system requiring late specialization since the cost of switching is lower in terms of foregone skills. Using the Universities Statistical Record from 1972 to 1993 and the 1980 National Survey of Graduates and Diplomates, he ﬁnds that individuals who specialize early, as in the case of England, are more likely to switch to an unrelated occupation, implying that the beneﬁts to increased match quality are sufﬁciently large to outweigh the greater loss in skills from specializing early.

With regard to instruction, economists have made substantial progress in specifying and identifying the economic value of higher education, as it increases the value productivity of human agents as workers . . . the much neglected activity is that of discovering talent. It, too, can be approached by treating it as a process which provides students with opportunities to discover whether they have the particular capabilities that are required for the type and level of education at which they are working. — Theodore W. Shultz (1968: 331) good example for factual/ indirect writing style

ore than 40 years have passed since Theodore Shultz argued that higher education provides students with the opportunity to discover their talents, but relatively little research has actually explored this important aspect of higher education. In this
*Ofer Malamud is Assistant Professor in the Harris School of Public Policy Studies at the University of Chicago and a Faculty Research Fellow at the National Bureau of Economic Research (NBER). The author wishes to thank Nittai Bergman, Kerwin Charles, Claudia Goldin, Daniel Hamermesh, Caroline Hoxby, Seema Jayachandran, William Johnson, Larry Katz, Bob Lalonde, Derek Neal, Cristian Pop-Eleches, and Bruce Sacerdote for many helpful suggestions. He also appreciates the comments from seminar participants at Clemson University, Hebrew University, Harvard University, Michigan State University, Tel-Aviv

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paper, I use an exogenous difference in the timing of specialization across British systems of higher education to test whether education can provide valuable information about one’s talents. In one system, students are required to choose a ﬁeld of study before introduction, 1st person?!
University, UC-San Diego, UC-Riverside, University of Chicago, and the NBER Higher Education meeting. He is grateful to the Universities Statistical Record, the UK Data Archive, and several university administrators in Scotland and England for assistance. This work was supported by a grant from the Spencer Foundation. A data appendix with additional results, and copies of the computer programs used to generate the results presented in the paper, are available from the author at malamud@uchicago.edu.The raw data ﬁles are available from the UK Data Archive at http://www.dataarchive.ac.uk. - good use of footnotes

- footnotes are not part of word count - no footnotes for referencing!
Industrial and Labor Relations Review, Vol. 64, No. 2 (January 2011). © by Cornell University. 0019-7939/00/6402 $05.00

this is information you will need for your bibliogrpahy/ references 375

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INDUSTRIAL AND LABOR RELATIONS REVIEW England, students apply to a speciﬁc ﬁeld of study at a particular university while still attending secondary school. Once admitted to study a certain ﬁeld, they usually follow a narrow curriculum that focuses on the chosen subject and allows for few courses in other ﬁelds.2 In contrast, Scottish students are typically admitted to a broad faculty or school rather than to a speciﬁc ﬁeld. Moreover, they are generally required to study several different ﬁelds during their ﬁrst two years before specializing. Using university administrative data and survey data on college graduates, I compare the likelihood that Scottish versus English students will switch to an unrelated occupation later on in their careers. I account for non-random selection by instrumenting for English and Scottish degrees with region of prior residence, and I contrast the ﬁndings at the undergraduate level with those at the graduate level at which the timing of specialization between England and Scotland is similar. I focus on the comparison between England and Scotland because, although their educational systems are separate and arguably exogenously different, their labor markets are relatively well integrated and their macroeconomic policies are determined by a common government. Furthermore, students in neighboring Wales serve as a useful “placebo test” because specialization there occurs at roughly the same time as it does in England. The notion that individuals may discover their talents and learn about their match quality to different ﬁelds is a prominent feature in many models of job turnover.3 Relatively few papers, however, have explicitly considered the role of education. Johnson (1978) postulated that education provides workers with information about their general ability and concluded that education
2 More recently, and outside the time period of the present analysis, some English universities have introduced course structures that offer more breadth and greater ﬂexibility. This might suggest a growing perception that specializing too early may have some drawbacks. 3 McCall (1990), Miller (1984), Neal (1999), Shaw (1987) and Jovanovic and Nyarko (1996) have extended the notion of job match quality presented by Jovanovic (1979) to the occupational level and presented some evidence for learning about occupational match quality.

they apply to college. In the other, students must postpone the decision until later in their college careers. Such differences in the timing of academic specialization highlight the trade-off between accumulating skills in a particular ﬁeld versus gathering additional information about alternative ﬁelds before structure selecting one in which to specialize. In this paper, I exploit these differences to examine intro the importance of higher education in helping students to discover their talents and tastes for different ﬁelds of study.1 I introduce a simple model of academic specialization in which individuals, by taking courses in different ﬁelds of study, accumulate ﬁeld-speciﬁc skills and receive noisy signals of match quality to these ﬁelds. Though later specialization provides students with more time to learn about match quality to different ﬁelds, it affords less time to acquire ﬁeld-speciﬁc skills once they have chosen a ﬁeld of specialization. If higher education serves mainly to provide speciﬁc skills, the model predicts that students in a system with late specialization will be more likely to argue switch to an occupation that is unrelated to with strengths their ﬁeld of study. This is because the cost of switching in a late system is lower in terms factual of foregone skills. Conversely, if higher eduindirect cation serves mainly to provide information about match quality, the incidence of switching to an unrelated occupation will be higher in a system requiring early specialization. This is because the beneﬁt associated with the increase in expected match quality when switching in an early system will outweigh the greater loss of ﬁeld-speciﬁc skills. Since its focus is on individuals’ decision to switch to an unrelated occupation, the model generates comparative static predictions that account for individuals’ pecuniary and non-pecuniary considerations. In order to test whether education procreating structurevides valuable information about one’s for talent, I exploit an exogenous difference in reader the timing of specialization within the British system of undergraduate education. In
1 In a related paper, Malamud (2010), I use a similar framework to explore the consequences of early and late specialization on wages and other labor market outcomes.

DISCOVERING ONE’S TALENT may lower job mobility by reducing its role in acquiring information. Altonji (1993) introduced a formal model in which individuals learn their preference between two ﬁelds of study by attending college. More recently, Stange (2009) built on Arcidiacono’s (2004) structural model of student learning to estimate the option value of college enrollment in the presence of uncertainty and learning about academic ability. Stinebrickner and Stinebrickner (2009) documented the role of learning about ability on the college dropout decision. In still another paper, Wiswell (2008) introduced a model in which teacher licensing requires students to specialize in teaching earlier, reducing the accumulation of general skills that are useful for those who decide not to teach. Finally, Hvide (2003) extended Spence’s (1973) signaling model to allow for learning about overall ability and suggested that certain types of education, such as U.S. college degrees, may primarily provide information about ability, whereas others, such as U.K. college degrees, serve to augment productivity. I aim to contribute to this literature by embedding both skill acquisition and learning within a model of academic specialization. Applying this model to the British system of higher education, I am able to derive and test a simple comparative static prediction for the importance of learning about one’s talents through higher education. A Simple Model of Academic Specialization sub-headings/ summaries Suppose individuals take n courses in each of k ﬁelds of study prior to specialization. Each course in a given ﬁeld provides ﬁeld-speciﬁc skills and a noisy signal of match quality in that ﬁeld. In specializing, individuals choose a ﬁeld and take (N nk) additional courses in this chosen ﬁeld of study.4 After completing a total of N courses, individuals choose whether to work in an ocI assume that students are not constrained in choosing their ﬁeld of study. In practice, there may be restrictions due to limited slots. Therefore, in the empirical analysis, I consider a speciﬁcation that restricts attention to students with top high school grades who are clearly
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cupational ﬁeld that is related to their chosen ﬁeld of study or to switch to an unrelated occupation. Upon entering the labor market, match quality is revealed and individuals receive returns that are increasing in both match quality and ﬁeld-speciﬁc skills. I describe this basic setup in greater detail below. Then, I proceed to compare the probability of switching between an early system in which individuals are required to specialize after nE courses in each ﬁeld and a late system in which individuals are required to specialize after nL courses in each ﬁeld, where nE nL. Analytical proofs are relegated to the Mathematical Appendix, which offers a more formal treatment of the model. Setup
Areas linked to the research question hat you will not research, but which you assume to be true possibly because they have already been researched by others

Assume that individuals are risk-neutral and have identical prior distributions on match quality for each ﬁeld. Prior to undertaking schooling, however, match quality is unknown. Speciﬁcally, assume that match quality, θi, in each ﬁeld i is a random draw from a normal distribution with the same mean and variance, so that θi ∼ N (µσ 20 ). , Match quality is therefore uncorrelated across ﬁelds and can include any ﬁeldspeciﬁc components of education that affect returns, such as innate ability or interest, that contribute to productivity or enjoyment of working in a speciﬁc ﬁeld.5 In the empirical analysis, I attempt to control for indicators of predictable match quality so that the remaining components of match quality are random. In fact, prior distributions may differ across ﬁelds. Allowing for different prior means is straightforward and would not alter any of the results from the model. Differences in prior variances would introduce option value considerations similar to ones considered by Johnson (1978) and Miller (1984), so I abstract from them to keep the model parsimonious. In the “extensions” free to choose their ﬁelds, unconstrained by admissions requirements and the availability of slots. 5 More generally, match quality can include imperfect information about the rewards to certain ﬁelds in the labor market or uncertainty regarding the likelihood of completing a ﬁeld of study in university.

again: good use of footnotse to elaborate on issues without 'wasting' word count. Also, assumptions can be clarified further.

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INDUSTRIAL AND LABOR RELATIONS REVIEW als with identical prior distributions across ﬁelds will choose the ﬁeld of study with the highest expected returns: choose i * arg max E u ( θi , si ) {xij }  i 1,...k arg max {αµβ i′ i 1,...k

section, I discuss extending the model to allow for different prior variances and risk aversion. By taking courses in a given ﬁeld, individuals will accumulate ﬁeld-speciﬁc skills and receive noisy signals of their match quality to that ﬁeld. For simplicity, assume that the quantity of skills accumulated in a ﬁeld, si, is equivalent to the number of courses spent studying in that ﬁeld. Each course of study j in ﬁeld i also provides a signal of match quality in that ﬁeld: xij θi εij where εij ∼ N(0, σ2) and j 1, . . . ,n. Noise in the signal may be due to any number of idiosyncratic factors, such as the quality of instruction or the particular circumstances of the student at the time. I assume that skills are perfectly speciﬁc to a particular ﬁeld, but I will discuss the possibility of spillovers across ﬁelds below. The overall returns to ﬁeld i upon entering the labor market is an increasing function of both match quality and skills: ui u(θi, si) with (∂υ/∂θ) > 0 and (∂u /∂s) > 0. Consequently, match quality is revealed upon entering the labor market. For simplicity, I assume that returns are a linear function of match quality and skills: u(θi, si) αθi, βsi. I take (α/β) as an indication of the return to match quality relative to the return to speciﬁc skills. There may be additional random shocks that cannot be learned about in advance. Furthermore, returns may differ across different ﬁelds. In the empirical analysis, I compare outcomes for individuals controlling for ﬁeld of study so that mean differences across ﬁelds can be ignored. Choice of Field at Specialization The posterior distribution of match quality after studying n courses in ﬁeld i is a normal distribution with mean µ´i and variance σ′.6 Further, the quantity of skills in each ﬁeld at the point of specialization is s′ n. In specializing, therefore, risk neutral individuThe posterior mean is a weighted average of the prior mean and the mean of the signals: µ i′ ( µσ 0 2 σ 2 nx i ) / (σ 02 + n 2) where x i n 1 ∑ j x ij . The posterior variance is 2 σ ′ ( σ 0 2 + nσ 2 ) . See DeGroot (1970) for a detailed explanation.
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{

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s ′}

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Since the quantity of speciﬁc skills in each ﬁeld is identical, individuals simply choose the ﬁeld with the highest posterior mean of match quality, i * arg maxi 1,...k { µ i′ } .7 Thus, the posterior mean of match quality in the chosen ﬁeld at the time of specialization will be µ i′*8 Decision on Whether to Switch Following specialization, individuals take (N nk) additional courses in the chosen ﬁeld. Hence, the quantity of skills in the chosen ﬁeld prior to entering the labor market is s ′′ n (N nk). Individuals will also receive additional signals in the chosen ﬁeld, i *. Deﬁne these signals as yi*l θi* εi*l, where l nk, . . . ,N. Consequently, the posterior distribution of match quality in the chosen ﬁeld after (N nk) additional signals will be a normal distribution with mean µ i′′ * and variance σ′′.9 Now, given the opportunity to switch to another ﬁeld prior to entering the labor market, individuals will compare expected returns in the chosen ﬁeld with expected returns in the next best ﬁeld: field switch ⇔ E u ( θi , si )| {x ij }  j 1... N

j < max E u ( θi , si )| {xij }  i i* ′ ⇔ αµβ + s ′′ max {αµβ * i′* i′′ * i i

{

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1... N

  s ′} .

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Strictly speaking, expected future utility should include expected skills rather than the quantity of skills at the point of specialization. But since expected match quality and skills are separable and individuals are riskneutral, this will lead to the same choice at the point of specialization. 8 Speciﬁcally, µ ′ ( µσ −2 + σ −2n maxi xi ) / ( σ 0 2 nσ 2 ). i* 9 So that µ i′′ ( µσ 0 2 σ 2n maxi x i σ 2 (N nk )yi * ) / * ( σ 0 2 nσ 2 σ 2(N nk )σ 2 ) where xi n 1 ∑ j xij , yi (n NK ) 1 ∑ j yi *l and σ ′′ ( σ 0 2 n σ 2 (N nk )σ 2 ) 1 .
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DISCOVERING ONE’S TALENT Individuals will switch if the posterior mean of match quality in the chosen ﬁeld falls sufﬁciently far below the posterior mean of another ﬁeld to outweigh the loss in speciﬁc skills from switching. Note that, if individuals do decide to switch, they will always choose the ﬁeld with the second-highest posterior mean since all ﬁelds other than the one chosen are associated with the same quantity of speciﬁc skills and posterior variance. The decision about whether to switch can therefore be framed as a comparison between the ﬁrst best ﬁeld, i*, and the ﬁeld that was second best at the time of specialization, i a. The ﬁeld selected after the second stage will be denoted i ** where i ** ∈ {i *, ia}. Probability of Field Switching Now consider the likelihood of an individual switching to an alternative ﬁeld prior to entering the labor market. Recall that individuals in an early system are required to specialize after nE courses in each ﬁeld whereas individuals in a late system are required to specialize after nL courses in each ﬁeld, where nE nL. Posterior distributions at the time of specialization will be more diffuse for individuals in the early system. Moreover, these individuals will receive more signals in the chosen ﬁeld after specializing than their counterparts in the late system. Thus, in the early system, assessments of perceived match quality in the chosen ﬁeld will experience relatively greater updating and make individuals more likely to conclude that they made a mistake when they initially inferred which ﬁeld had the highest match quality.10 However, in switching, individuals will lose the additional skills acquired in the chosen ﬁeld of study through special10 Speciﬁcally, the posterior distribution is more likely to shift in response to the additional information received in the early regime. Hence, the mean of the posterior distribution of the chosen ﬁeld is also more likely to move below the posterior mean of the second best ﬁeld at specialization and indicate a perceived mistake. This is particularly intuitive in the case in which individuals specialize immediately prior to entering the labor market. In this case, the probability of perceiving a mistake will be zero since no additional information is received following specialization.

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ization. Individuals will therefore switch only if the posterior mean of the ﬁrst-best ﬁeld falls sufﬁciently below that of the second best ﬁeld to outweigh the loss in speciﬁc skills. Since the loss in speciﬁc skills is always greater in the early system, whether switching is higher in the early or late system will depend on the relative return of match quality. This intuition is expressed more formally in the following proposition: Proposition 1: A system with early specialization, nE, will have a higher rate of ﬁeld switching than a system with late specialization, nL, if and only if the return to match quality is sufﬁciently higher than the return to speciﬁc skills: P (switch )E P (switch )L ⇔ α β C 0.

Figure 1 plots the probability of switching for an early and a late system over the full range of relative returns to match quality, which are normalized by taking β (1 α) so that (α/β) goes from 0 to ∞ as α goes from 0 to 1.11 Since the model abstracts from other reasons for switching ﬁelds, no switching occurs in either system if the return to match quality is sufﬁciently low. However, by introducing an additional stochastic element to the model, such as u(θi, si) αθi βsi εi where εi ∼ N(0, τ2), switching can take place even if the return to match quality is zero. Allowing for these additional random shocks, I derive the following corollary: Corollary 1: If there is no return to match quality (α 0) or courses do not provide information about match quality (σ2 ∞), then a system with early specialization, nE, will have a lower rate of switching than a system with late specialization, nL. Note the distinction between the return to match quality, α/β, and the quality of information on match quality provided by undergraduate courses, σ2. Observing a higher
All simulations are based on 5,000 repetitions for k 2, N 21, µ1 µ2 0 σ2 100 and σ 2 = 25. Early 0 regimes are characterized by nE 2; late regimes are characterized by nl 6. Expected returns are deterˆ mined according to E(ui ) = E(αθi + βs i ) where ˆ s (s i /(N k )) µ are normalized skills.
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Probability of Occupational Switch

Figure 1. Probability of Occupation-Field Switching by Relative Return to Match Quality ideally, graphs/ tables etc 0.35 are 'named' and/ or numbered. Late Also, it might be a good idea Early 0.3 to add a separate 'table of figures' 0.25 to the 'table of contents' in an assignment, with page 0.2 numbers added.
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rate of ﬁeld switching in an early system rather than in a late system would imply that education provides valuable information on match quality and that match quality has a large impact on the returns to education. Focusing on the probability of switching to an unrelated occupation may appear to be an indirect way of testing whether education provides information about match quality. Indeed, according to this model, the tradeoff between learning about match quality and accumulating speciﬁc skills is central to optimal timing of specialization in higher education. With later specialization, students have more time to learn about match quality in each ﬁeld but less time to acquire speciﬁc skills once a ﬁeld is chosen. Figure 2 simulates expected returns for an early and a late system over the full range of relative returns to match quality. Clearly, observing higher overall returns in the late system would also serve to indicate that the relative return to match quality is high. However, it is very difﬁcult to obtain empirical measures that capture all of the returns to occupational choice. Since the decision to switch to an unrelated occupational ﬁeld encompasses non-pecuniary considerations as well as pecuniary ones, there is a signiﬁcant advantage in focusing on the likelihood of switching.12
12 This is especially important in light of Arcidiacono’s (2004) ﬁnding that most sorting across majors is due to

Extensions Throughout I have assumed that individuals are risk-neutral. Introducing risk aversion does not alter the decision at the point of specialization because the variances of the posterior distributions across ﬁelds are identical; individuals would continue to choose the ﬁeld with the highest posterior mean. In considering a switch, however, the presence of risk aversion would make the relative variances of the posterior distributions relevant. Speciﬁcally, switches would be less common because, even in instances where the chosen ﬁeld has a lower posterior mean than another ﬁeld, its lower variance could be sufﬁciently valuable to risk-averse individuals so as to prevent switching. Moreover, this effect is stronger in the early system since the trade-off between the posterior variances at the time of specialization and the posterior variance of the chosen ﬁeld after the receipt of additional signals is more extreme. Field switching would therefore decline more in the early system than in the late system due to the presence of risk aversion. This would lead to a bias towards the conclusion that the accumulation of speciﬁc skills is more important than learning about match quality.

different preferences rather than differential monetary returns to ability.

DISCOVERING ONE’S TALENT Figure 2. Expected Returns by Relative Return to Match Quality
3.5 Late Early 3 Expected Wages

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Notes: All simulations are based on 5000 repetitions for k 2, N 21, µ 0, σ0 25, and σ 100. Early regimes are characterized by nE 2; late regimes are characterized by nL 6. The relative returns to match quality are normalized by taking β (1 α) so that (α/β) goes from 0 to ∞ as α goes from 0 to 1. Expected returns are determined according to E(uj) E(αθi βsi) where si [si/(N/k)] µ are normalized skills.

The assumption that prior distributions on match quality are identical across ﬁelds implies that individuals do not need to consider the possibility of later switching when making their initial choice of ﬁeld at the point of specialization. Allowing for prior variances on match quality to vary by ﬁeld introduces option value considerations. These would push individuals to specialize in riskier ﬁelds because they could switch in the case of a bad realization. Moreover, ﬁelds with a larger prior variance would have greater option value in the early system than in the late system. With more signals following specialization, greater updating in the early system generates a higher probability that the ultimate posterior mean will surpass that of the chosen ﬁeld. Hence, individuals in the early system would be more likely to choose a ﬁeld with a lower posterior mean at the point of specialization because of the greater option value. Since, on average, such ﬁelds have lower expected match quality than those with the highest posterior mean, we should expect more switching in the early system due to option value considerations. This would lead to a bias towards the conclusion that learning about match qual-

ity is more important than gaining speciﬁc skills.13 As it stands, the model contains no truly general skills. A person has general skills only in the sense of having greater levels of speciﬁc skills in a variety of alternative ﬁelds, and this affects returns only when switching into one of these ﬁelds. Nevertheless, it would be relatively simple to incorporate general skills by including some measure of average skill in the ﬁelds not chosen j ≠ j* 1 s j . Allowing for for specialization: s = J such general skills would serve to provide further beneﬁts to later specialization. More generally, we could consider the possibility of spillovers in skills across ﬁelds. This would serve to reduce the trade-off between skills and match quality because additional learning about match quality would be less costly

∑

However, this effect is likely to be small because all ﬁelds are sampled prior to specialization and the option value needs to be greater than the difference in the posterior means of match quality between the relevant ﬁelds. Furthermore, risk aversion would counteract the beneﬁts of having high variance in the posterior distributions.
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INDUSTRIAL AND LABOR RELATIONS REVIEW subjects in your second year. This will then give you a choice from two, or even three, subjects to pursue to degree level, and you can delay this decision until quite a late stage . . . In choosing courses to be taken in the ﬁrst two years, you can select from a very wide range of courses offered across several faculties.

in terms of forgone skill acquisition. Finally, if there is an additional beneﬁt to match quality accrued while taking courses because people enjoy courses to which they are well matched, this would serve to heighten the trade-off between skills and match quality. Background: Higher Education in Britain The British system of higher education provides a particularly appropriate setting in which to examine the predictions of the model. Undergraduate education in England and Scotland, though similar in aim and overall structure, varies widely in the timing of academic specialization. In England, students apply to a speciﬁc ﬁeld of study at a particular university.14 Once admitted to a speciﬁc ﬁeld, English students usually follow a narrow curriculum that focuses on the main ﬁeld and allows for little exposure to other ﬁelds.15 Indeed, most universities in England require students who change ﬁelds of study to start university anew (though some do allow for limited changes). In contrast, Scottish students are typically admitted to a broad faculty or school rather than a department; in some universities, admission is to the university at large.16 Furthermore, they are required to study several different ﬁelds during their ﬁrst two years. As an undergraduate prospectus for the University of Edinburgh explains:
You would normally take courses in three or more subjects in the ﬁrst year and, commonly, these are followed by second courses in at least two of the
14 There are exceptions. For example, students at Cambridge University are accepted to a broad engineering faculty, and students at Keele University are ﬁrst accepted to a year of “foundation studies.” 15 Again, there are exceptions. Cambridge’s system of Tripos allows some ﬂexibility in making changes to courses of study, and the newer universities of Essex, Kent, and Lancaster allow students to study a broader range of subjects. In recent years, even more English universities have introduced course structures that offer more breadth and greater ﬂexibility. 16 For example, faculties at the University of Glasgow include Arts, Biomedical and Life Sciences, Education, Engineering, Information and Mathematical Sciences, Law, Business and Social Sciences, Medicine, and Physical Sciences.

Similar course structures exist in most Scottish universities. They allow for substantial choice among ﬁelds of study within faculties, and, to some degree, across faculties as well.17 Moreover, students in Scotland are required to take a broader range of courses and choose a ﬁeld of study much later than their English counterparts.18 The Handbook for Students and their Advisors for the years 1980–82 (Briggs 1980: 17–18) explains that “the standard English degree, whether in science, humanities or social sciences, is a single subject honours degree” whereas “universities in Scotland had traditionally offered a wide range of subject options with multi-subject examinations at the end of the ﬁrst year.” This information is also supported by empirical evidence, provided in later sections, indicating that the proportion of individuals who change their ﬁeld of study between admission and graduation in Scottish universities is substantially higher than in English universities. Given these differences, it is quite natural to regard the English system of higher education as an early system and the Scottish system of higher education as a late system. There is variation in the average length of the undergraduate degree between England and Scotland. Although there is some heterogeneity among degrees within each nation, most English degrees are completed within three years whereas most Scottish degrees are completed within four years. How17 Note that changing ﬁelds is not always possible. Certain professional faculties, such as medicine and law, are more insular. Engineering is usually a separate faculty but changes from the physical sciences are often permitted. 18 Numerous scholars of British educational systems have noted that Scottish institutions allow for later specialization than English ones. See Evans (1976), Hunter (1971), Osborne (1967), and Squires (1987). Personal conversations and correspondences with university administrators in England and Scotland conﬁrm these observations.

DISCOVERING ONE’S TALENT ever, many Scottish students enter university after 6 years of secondary schooling rather than the seven years customary in England. According to this calculation, English and Scottish students who attain a BA degree receive roughly the same number of years of schooling (and this is conﬁrmed in the data by examining the age of graduation). The ﬁrst year of university in Scotland may be said to correspond to the ﬁnal year of secondary school in England. But even so, since English students apply to university in the beginning of their ﬁnal year of secondary school whereas Scottish students make their ﬁnal choice of ﬁeld only at the end of their second year of university, there is substantial difference in the timing of specialization. The difference between English and Scottish universities arose from their respective historical traditions. English universities were largely independent and free to set their curriculum and course structures. Long into the nineteenth century, Oxford and Cambridge maintained their focus on the traditional subjects (classics, Aristotelian philosophy, and mathematics) with less emphasis on modern subjects, such as natural science (Evans 1975). The provincial civic universities established later in urban centers did not substantially depart from the traditions of the “ancient” universities. Even with the introduction of broad faculties and additional courses of study, admissions remained at the departmental level.19 Conversely, Scottish universities became regulated under the Universities (Scotland) Act of 1858 that set up an executive commission to draw up uniform conditions for courses of study. The Universities (Scotland) Act of 1889 further increased the choice of subjects available in Scottish universities, reﬂecting the “traditional Scottish preference for a broad general education” (Hunter 1971: 237). In large part, these two Acts of Scottish Parliament determined the distinctive characteristics of universities in Scotland,
19 The main exceptions arise in the (Plate Glass) universities established during the 1960s such as the University of Keele, which implemented an experimental modular curriculum.

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including the emphasis on late academic specialization. In addition to differences in higher education, England and Scotland also differ in their system of secondary school education. In England, students need General Certiﬁcate of Education (GCE) Advanced-level examinations (A-levels) in 2 or three subjects to gain acceptance into university. In 1989, a new exam, the Advanced Supplementary examination (AS-level) was introduced to broaden the curriculum; it was to be the same standard as an A-level, but half the content. Students were encouraged to substitute two AS-levels for one of their A-levels, but most universities did not regard these examinations as commensurate alternatives and it did little to change the character of English secondary school education. Alternatively, in Scotland, students need Scottish Certiﬁcate of Education (SCE) Higher Examinations in ﬁve or six subjects to gain acceptance into university. More recently, Advanced Highers and Higher Still certiﬁcations have been introduced to provide the opportunity for further specialization in secondary school. However, universities continue to use Highers as the primary basis for admission and there is little doubt that the Scottish system of secondary education provides a broader curriculum than the English one. Again, the reasons for these differences in secondary school curriculum can be traced to historical antecedents. In effect, specialization trickled down from the universities to secondary schools. Moreover, the early inﬂuence of English universities on secondary school leaving exams was far stronger than that of Scottish universities since Scottish secondary school leaving certiﬁcates had to be approved by the Scottish Education Department. The difference in the timing of specialization between the English and Scottish systems of undergraduate education does not arise at the graduate level. Graduate degrees in both England and Scotland require admission to a speciﬁc ﬁeld of study. Hence, after accounting for any initial differences due to undergraduate specialization, I compare between England and Scotland at the graduate level as a “placebo test”. The discussion above has focused on England and

384

INDUSTRIAL AND LABOR RELATIONS REVIEW 1980 qualiﬁcation, their subsequent labor market experience (occupation, industry, and wages for ﬁrst and current jobs), and further educational pursuits. There is also information about their high school examination results. Although it is not possible to identify speciﬁc universities in the NSGD, there is information on whether students took English or Scottish secondary school leaving exams. Neither dataset is representative of the overall population. Therefore, we might be concerned that the English and Scottish samples of university graduates may not be comparable because of differing participation rates. Using two nationally representative datasets that include all individuals born in Great Britain during one week in 1958 and 1970 (the National Child Development Study and British Cohort Study respectively), I calculated the percentage of individuals who attained a ﬁrst degree from university by age 26. In both of these datasets, participation rates in university are remarkably similar between England and Scotland: 8% of the 1958 cohort and 12% of the 1970 cohort.22 For the sample of students used in the regression analysis, almost all successfully complete their degree. This is because NSGD data was only collected for degree recipients and USR data on occupation is missing for most students who drop-out. Based on the full USR sample of university leavers in 1980, the fraction of students who drop out of university is 15.6%. There are differences across nations, with 14.6% of students dropping out in England and 19.5% of students dropping out in Scotland. I account for the bias introduced by differential dropout rates in a robustness check described below. Table 1 indicates that the average characteristics of those attending English and Scottish universities are quite similar in both the USR and NSGD. Summary statistics are shown for the sample of students used in the regression analysis. There is a slightly larger
22

Scotland, but Britain also includes Wales, which has a distinct system of higher education. In contrast to Scotland, however, undergraduate students in Wales apply to a speciﬁc course of study in similar fashion as in England. Hence, though I exclude Wales from the main empirical analysis, I examine differences between England and Wales at the undergraduate level as another useful “placebo test.” Data and Empirical Strategy Data Data for the empirical analysis come from two sources: the Universities Statistical Record (USR) and the 1980 National Survey of Graduates and Diplomates (NSGD). The USR consists of administrative data on all students in British universities undertaking courses of one academic year or longer between 1972–1993: almost 1.9 million undergraduates and more than 1 million graduate students.20 For the most part, I focus on students who completed their degree in 1980 to correspond with the data from the NSGD. These administrative data include detailed background information on demographic characteristics and entry qualiﬁcations in addition to information related to the degree attained. This is supplemented by information on the occupation, industry, and location of the job held in the ﬁrst year following graduation. The NSGD contains information obtained from a national postal survey of some 8,000 graduates undertaken in 1986–87 by the British Department of Employment. It includes a random sample of one in six university graduates in 1980.21 The NSGD contains information about their

20 Excluded are students enrolled in the Open University, Cranﬁeld University, the independent University of Buckingham, and the former polytechnics and central institutions, which obtained university status from 1992 onwards. 21 The NSGD also includes one in four graduates from other institutions (polytechnics, colleges of education), but I exclude them from the present analysis. Engineering students in Scottish universities are oversampled in the NSGD. Consequently, it is particularly important to control for ﬁelds of study with the NSGD sample.

The oft-mentioned higher participation rate in Scotland usually includes students enrolled in nonuniversity higher education institutions, such as polytechnics and colleges of education.

DISCOVERING ONE’S TALENT Table 1. Summary Statistics for 1980 College Graduates
England Mean Panel A: USR Individual characteristics Female Married (during degree) Average age (upon completion) High School GPA (out of 30) Number of high school subjects Degree characteristics Duration Changed major Occupation-ﬁeld switching Very broad classiﬁcation Broad classiﬁcation Narrow classiﬁcation Panel A: NSGD Individual characteristics Female Married (6 years after degree) Average age (upon completion) High School GPA (out of 30) Number of high school subjects Occupation-ﬁeld switching Very broad classiﬁcation Broad classiﬁcation Narrow classiﬁcation 0.34 0.53 22.01 19.71 3.18 0.44 0.50 0.63 0.47 0.50 1.51 5.84 0.69 0.50 0.50 0.48 1,242 1,242 1,242 1,242 1,242 1,242 1,242 1,242 0.31 0.59 22.26 18.25 5.15 0.29 0.34 0.51 0.47 0.49 2.40 5.77 1.04 0.45 0.48 0.50 0.38 0.03 22.39 20.92 3.22 3.33 0.07 0.39 0.49 0.68 0.48 0.18 2.40 6.39 0.71 0.73 0.25 0.49 0.50 0.47 10,455 10,455 10,455 10,455 10,455 10,455 10,455 10,455 10,455 10,455 0.43 0.05 22.57 19.91 4.78 3.97 0.18 0.35 0.42 0.63 0.50 0.21 2.78 6.06 1.27 0.75 0.39 0.48 0.49 0.48 SD Obs Mean Scotland SD

385

Obs

3,427 3,427 3,427 3,427 3,427 3,427 3,427 3,427 3,427 3,427

213 213 213 213 213 213 213 213

Notes: The base sample for the Universities Statistical Records (USR) includes all individuals who aimed to attain a BA degree in 1980 and were employed in a job during the 1st year following graduation and not pursuing graduate studies. The base sample for the 1980 National Survey of Graduates and Diplomates (NSGD) includes all individuals who attained a BA degree in 1980 and were employed in a job during the 1st year following graduation and not pursuing graduate studies. Median age at the start of the degree is 19 for both nations. GPA is an average measure of the achievement in secondary school leaving exams out of 30 (but standardized by nation in all regressions). Honors is a measure of success at university standardized across nations taking discrete values from 0 (no honors) to 4 (highest honors). Occupation-ﬁeld switch is deﬁned as 1 if ﬁeld of study at the undergraduate level is different from the occupational ﬁeld of ﬁrst job 6 months following degree and 0 otherwise (see Data Appendix for further discussion of classiﬁcation groups).

percentage of women and married students in Scottish universities. The average age upon completion of the ﬁrst degree is almost equivalent in England and Scotland but the average duration of the degree is somewhat longer in Scotland. Further, although the average age that students begin university is slightly lower in Scotland, the median age of students during their ﬁrst year in university is 19 for both England and

Scotland (not shown). The raw high school grade point average (GPA) scores shown in Table 1 are converted from letter grades in the A-level and Scottish Higher school leaving examinations. In the regression analysis, these scores are normalized within each nation so that coefﬁcients represent the effect of a one standard deviation increase in GPA. As expected, there are striking differences in the likelihood that students change their

386

INDUSTRIAL AND LABOR RELATIONS REVIEW rable. As expected, the majority of students in both England and Scotland enter employment in the United Kingdom. The lower rate of unemployment among Scottish individuals is a consequence of the over sampling of engineering graduates who are less likely to be unemployed than others. Note that some individuals do work concurrently while pursuing further study in the United Kingdom. Finally, results from the IEA Third International Mathematics and Science Study (TIMSS) in 1994–95 indicate no signiﬁcant differences between England and Scotland in the mathematics achievement for students in the fourth and eighth grades.25 Using data from the USR, Figure 3 plots the rates of occupation-ﬁeld switching, unemployment, and the continuation of further studies following graduation from 1973–1993 as well as the proportion of students who change a major ﬁeld of study while in university. The raw differential in switching between England and Scotland is persistent over time. Conversely, the rates of unemployment and further study are similar across England and Scotland for most years. It is worth noting that the recessions in the early 1980s and early 1990s appear to be associated with an increase in the rate of occupation-ﬁeld switching. Empirical Strategy The base sample includes all individuals aiming to attain a BA degree in 1980 and employed full-time in the ﬁrst year following completion of their qualiﬁcation. I exclude individuals pursuing graduate studies while working because this may select for weaker students who need to work while pursuing higher degrees. Using the USR, I verify that the main results hold for other years as well. Using the NSGD, I check whether the main results continue to hold 6 years after entry into the labor market. Furthermore, I explore a variety of alternative sampling
25

major ﬁeld of study in university.23 If I exclude the handful of English universities that allow for changes in major ﬁelds, the fraction of English students who change major drops to less than 4%. The model introduces an important distinction between individuals who enter an occupation that is related to their ﬁeld of study and those who switch to an unrelated occupation. I construct a variable, SWITCH, that captures such ﬁeld switching by grouping ﬁelds of study and occupations into categories; I refer to it as an occupation-ﬁeld switch. As Appendix Table 1 shows, I allow for three levels of classiﬁcation: narrow (42 categories), broad (12 categories), and very broad (6 categories). Individuals are said to switch to an unrelated occupation when the ﬁeld of study of their degree and their occupational ﬁeld are in different categories, subject to the level of classiﬁcation. Therefore, SWITCH is coded as 1 if the occupational ﬁeld is different from the ﬁeld of study at university, and 0 otherwise. Broader classiﬁcations indicate lower rates of switching since only drastic changes from ﬁelds of study to occupational ﬁelds will register. But the rate of occupation-ﬁeld switching is substantially lower in Scotland than in England according to all classiﬁcations. For example, in terms of the broad classiﬁcation, the rate of switching in Scotland is 10 to 20 percentage points lower than the rate of switching in England. Most of the empirical analysis will focus on the broad classiﬁcation of ﬁelds.24 Table 2 indicates that the composition of broad ﬁelds of study across the two nations is not too dissimilar. Nevertheless, relatively more students in Scotland study life sciences, health sciences, and business and relatively fewer study mathematical and social sciences. The composition of occupations across the two nations is also largely compa23 In Scotland, students are coded according to a broad code associated with a faculty or school or on the basis of a provisional ﬁeld of study, which changes when they select a speciﬁc ﬁeld. See the Data Appendix for more details. 24 These include Math/Computer Sciences, Physical Sciences, Architecture, Engineering, Biological Sciences, Health, Social Services, Social Sciences, Business, Law, Education, and Arts.

There are, however, some differences in the science achievement scores. English students in the eighth grade do somewhat better than their Scottish counterparts, but there is no signiﬁcant difference for fourth graders.

DISCOVERING ONE’S TALENT

387

Table 2. Further Summary Statistics on Degrees and Destinations for 1980 College Graduates
USR England Degree Field Composition (%) Math and Computer Sciences Physical Sciences Architecture Engineering Life Sciences Health Sciences Social Services and Welfare Social Sciences Business/Accounting Law Education Art Occupational Field Composition (%) Math and Computer Scientists Physical Scientists Architects/Planners Engineers Life Scientists Medical Professionals Social Services Professionals Social Scientists Accountants/Managers Lawyers/Judges Educators/Teachers Artists/Journalists/Entertainers Post-BA Activity (%)ª Entering employment Further Study Unemployed Region of Work (%) England Scotland Wales Northern Ireland Abroad Region of Prior Residence (%) England Scotland Wales Northern Ireland Abroad 6.44 9.52 1.56 11.41 5.96 16.15 2.94 16.06 3.59 8.13 1.23 17.03 5.23 6.74 1.43 10.13 0.39 16.56 1.71 2.09 27.69 7.55 17.24 3.24 76.74 11.64 11.63 87.17 1.15 1.90 0.37 9.40 91.91 0.61 4.75 1.19 1.54 Scotland 4.20 9.22 1.31 8.70 7.56 19.67 3.68 16.72 5.52 6.45 1.28 15.70 4.64 6.36 1.69 7.76 0.50 20.51 2.63 2.92 29.00 6.07 15.76 2.16 79.28 10.11 10.61 32.59 61.04 1.02 0.50 4.84 15.61 81.27 0.35 1.69 1.08 England 7.57 14.65 1.77 21.18 6.76 4.27 2.98 18.92 4.43 1.29 3.14 13.04 11.19 6.04 2.74 21.42 2.17 5.56 3.22 1.85 34.78 0.24 7.89 2.90 61.86 27.65 10.48 87.36 1.77 3.38 0.32 7.17 NSGD Scotland 3.76 7.51 2.35 30.05 7.98 5.16 1.88 15.49 6.10 9.86 4.23 5.63 6.10 4.23 3.29 30.52 3.76 4.69 2.35 2.82 24.88 7.51 7.98 1.88 64.13 29.00 6.88 25.35 70.89 0.47 0.00 3.29

Notes: Composition of ﬁelds of study and occupational ﬁelds are based on a broad classiﬁcation (other classiﬁcations are discussed in the Data Appendix). Occupational ﬁeld represents the ﬁeld of employment in the 1st year after completing degree. Foreign students returning overseas are excluded from counts of Post-BA activity. ª is out of the unrestricted sample including unemployed and graduate students.

388

INDUSTRIAL AND LABOR RELATIONS REVIEW Figure 3. Outcomes by Year of Graduation (USR sample)
Panel A: Occupational Switching .4
Proportion

Panel B: Change in Field of Study

Proportion

0

1

70

75

80
Year

85

90

95

0 70

75

80
Year

85

90

95

Panel C: Unemployment .2 .4
Proportion

Panel D: Further Study

Proportion

0

70

75

80
Year

85

90

95

0 70

75

80
Year

85

90

95

Notes: Closed and open circles represent England and Scotland averages, respectively. Outcomes based on USR samples of undergraduates from 1973–1993. Occupation-Field switching is calculated with the broad classiﬁcation (see Appendix Table 1). Change of ﬁeld of study is determined by students who receive a degree in a ﬁeld different from the one they applied for. Unemployment and Further study occur during the 1st year following graduation.

restrictions: (a) including graduate students who have occupation data; (b) including unclassiﬁed occupations such as manual and clerical occupations instead of coding them as switches since individuals in one nation may be more likely to end up in nonprofessional occupations; (c) coding individuals who end up unemployed as switches since this may be the result of a differential macroeconomic shock across the two na-

tions; (d) excluding the ﬁelds of education and business or coding individuals who study them as non-switches since they are particularly subject to misclassiﬁcation (and similarly with combined ﬁelds); and (e) coding students who dropped out as switches. Additional robustness checks restrict the sample to students with top high school grades who are clearly free to choose their ﬁelds, unconstrained by admissions requirements and the

DISCOVERING ONE’S TALENT availability of slots. Finally, I also focus on the sample of English students from northern England since they are probably most similar to individuals from Scotland. The effect of a Scottish degree on the probability of switching is captured by λ in the following regression equation: (1) SWITCHij β′Xij λSCOTij φj + εij

389

where SWITCHij is a dummy variable for an occupation-ﬁeld switch for individual i in ﬁeld j, SCOTij is a dummy variable indicating the individual received a Scottish degree and therefore specialized late, φj is a set of ﬁeld of study ﬁxed effects, Xij are demographic characteristics, and εij is a disturbance term. The primary demographic controls include sex, age, marital status, high school GPA, and parents’ socioeconomic status (SES). In further robustness checks, I show results from two “placebo tests” in which WALESij or SCOTGRADij are used in place of SCOTij to explore comparisons between England and Wales or between England and Scotland at the graduate level. The identifying assumption for the main regression equation is that students in England and Scotland are no different on unobservable characteristics, that is, Cov(εij, SCOTij) 0. Note, however, that attainment of a Scottish or English degree is not randomly assigned. Rather, once they complete their secondary education, individuals can choose to attend universities in either England or Scotland. Table 2 shows the national breakdown of individuals studying in England and Scotland. The migration patterns from prior residence to university indicate that 3.3% of individuals with English prior residence choose to study in Scotland whereas 7.4% of individuals with Scottish prior residence choose to study in England. There may be systematic differences between those individuals who decide to attend university in the other system. If these differences are uncorrelated with the probability of switching, this should not pose a problem. However, if individuals who migrate to university have a different likelihood of switching, OLS estimates will be biased. This might arise because

individuals who migrate have unobserved characteristics that are correlated with the likelihood of switching. Or more directly, individuals might choose the university system based on their own expected likelihood of switching. For example, individuals from England that have less precise priors on match quality may decide to attend universities in Scotland where academic specialization is postponed. Hence, I will also consider regressions in which I instrument for the attainment of a Scottish or English degree with the region of prior residence. Since the type of degree and region of prior residence are not available in the NSGD, I use the type of school leaving examinations (whether Scottish or English) to estimate a reduced form equation of the probability of switching.26 Results In Tables 3, 4 and 5, the main predictions on occupation-ﬁeld switching with both the USR and NSGD are tested. Across almost all speciﬁcations, the probability of a switch is signiﬁcantly lower for individuals with Scottish degrees than for their English counterparts. The estimated difference in occupation-ﬁeld switching between England and Scotland from the preferred 2SLS speciﬁcation is approximately 6 percentage points, which is substantial considering that the rate of switching in Scotland is about .42. Indeed, the coefﬁcient on SCOT from equation 1 is negative and signiﬁcant in almost every year between 1973 and 1993 (results not shown, but Panel A of Figure 3 displays the raw differences over time). According to the model, these ﬁndings indicate that the return to match quality is high relative to the return to speciﬁc skills. That we observe more occupation-ﬁeld switches in England, a system with early specialization, implies that the beneﬁts to increased match quality are substantial, and, indeed, large enough to outweigh the greater loss of skills.
26

There is some choice available with the type of secondary school, but the correlation between Scottish residence and attendance in Scottish high school is .96. Furthermore, the correlation between attendance in a Scottish high school and sitting Scottish leaving examinations is .98.

390 Main Findings

INDUSTRIAL AND LABOR RELATIONS REVIEW focused and less likely to switch decide to earn their degrees in England, OLS estimates of switching in England will be biased towards less switching. Since individuals with Scottish degrees are, in fact, less likely to switch than their English counterparts, 2SLS estimates should and do indicate an even greater differential in switching. Panel B uses information from the USR to restrict the sample of English students to those from northern England since they are the most similar comparison group to individuals from Scotland.29 The pattern of occupationﬁeld switches between Scotland and northern England appears to be even stronger than the one found when all students from England are included. These ﬁndings are robust to alternative (broader and narrower) classiﬁcations, as well as to the sampling restrictions described in the previous section. In particular, results are similar when assuming that any student who dropped out would have switched to an occupation that was unrelated to his or her ﬁeld of study (since this would otherwise bias towards ﬁnding a lower rate of switching in Scotland than England). Moreover, the ﬁndings remain unchanged when restricting to the sample of students with top high school GPAs and when excluding students at Oxford and Cambridge. Interestingly, the main results do appear to be slightly stronger for women than for men, but there is not much heterogeneity by age and parental SES. A full set of robustness results is available upon request. Table 4 presents evidence on the determinants of occupation-ﬁeld switching within the ﬁeld of engineering. A degree in engineering is associated with a well deﬁned occupation, and the content of such degrees is extremely similar across the two nations. Using the narrow classiﬁcation, I can identify switches by subﬁeld, such as from study29

Using data from the USR, Table 3 shows the pattern of occupation-ﬁeld switching for students who graduated in 1980. As a baseline, Panel A includes all English students. All regressions include controls for gender, marital status, age, high school GPA, and parental SES. In column (1), I estimate the difference in the probability of switching between England and Scotland without controlling for ﬁelds of study or region of work. Once I control for the composition of ﬁelds across nations in column (2), the estimated differential in occupation-ﬁeld switching declines substantially. In other words, not only do individuals in Scotland switch less, but they also tend to study ﬁelds that are associated with less switching.27 In column (3), I add controls for region of work and the coefﬁcient on SCOT becomes smaller still, suggesting that there may be less switching among Scottish employers who prefer to hire individuals with related qualiﬁcations. This speciﬁcation needs to be interpreted with care, however, since the decision to work in England or Scotland is probably endogenous; individuals who decide to switch may also make systematically different decisions about where they wish to work. In columns (4), (5) and (6), I instrument for the attainment of a Scottish degree with the region of prior residence.28 2SLS estimates of the difference in occupation-ﬁeld switching between England and Scotland increase substantially and lend support to the hypothesis of non-random selection. If individuals who are less focused and hence more likely to switch decide to earn their degrees in Scotland, OLS estimates of switching in Scotland will be biased towards more switching. Similarly, if individuals who are more
27 In fact, English students may be endogenously choosing broader ﬁelds that facilitate switching to avoid specializing in an excessively narrow ﬁeld. Much of the variation in ﬁeld switching is explained by differences across ﬁelds of study (the R2 increases from .03 to .39 once controls for ﬁelds of study are included). 28 Coefﬁcient estimates are almost equivalent when instrumenting for attainment of a Scottish degree with the type of secondary school leaving exams completed or with the location of secondary school.

I have also considered reweighting the Scottish and English samples to resemble one another using the methods developed by DiNardo, Fortin, and Lemieux (1996). The coefﬁcients from regressions using the DFL weights are very similar to those from the unweighted speciﬁcations presented in the paper (available by request).

DISCOVERING ONE’S TALENT

391

Table 3. Effect of Scottish Degree on Occupation-Field Switching for 1980 Graduates (USR)
Dependent variable: switched to occupation unrelated to ﬁeld of study OLS (1) Panel A: Scotland vs. England SCOT Main controls Field of study effects Region of work effects R2 Observations Mean of dep. Variable 0.079** [0.016] X 0.064** [0.017] X X 0.39 13,882 0.47 0.048* [0.023] X X X 0.39 13,882 0.47 0.107** [0.034] X 0.089** [0.019] X X 0.39 13,882 0.47 0.099** [0.029] X X X 0.39 13,882 0.47 (2) (3) (4) 2SLS (5) (6)

0.03 13,882 0.47

0.03 13,882 0.47

Panel B: Scotland vs. Northern England SCOT Main controls Field of study effects Region of work effects R2 Observations Mean of dep. Variable 0.086* [0.029] X 0.079** [0.023] X X 0.37 4,921 0.42 0.079** [0.023] X X X 0.37 4,921 0.42 0.093 [0.047] X 0.101** [0.025] X X 0.37 4,921 0.42 0.128** [0.031] X X X 0.37 4,921 0.42

0.03 4,921 0.42

0.03 4,921 0.42

Notes: Huber-White standard errors, clustered by university in brackets. Sample includes all students who aimed to attain a ﬁrst degree in England and Scotland with occupation data and were not pursing further studies. Dependent variable is deﬁned as 1 if broad ﬁeld of study at the undergraduate level is different from the broad occupational ﬁeld of the ﬁrst job in the 1st year following degree and 0 otherwise. SCOT is deﬁned as 1 for Scottish degree and 0 for English degree. SCOT is instrumented with nation of prior residence in columns 4, 5, and 6. Main controls include sex, marital status, age, high school GPA, and parent SES. Panel B is restricted to students in England whose region of prior residence was northern England (including North East and Tyne, and all of Yorkshire). *Statistically signiﬁcant at the .05 level; **at the .01 level.

ing mechanical engineering to becoming an electrical engineer. In order to increase precision, I pool the USR data on engineers from 1980 to 1992.30 The main results are conﬁrmed in this setting—individuals who study engineering in Scotland are generally less likely to switch to an unrelated occupation than their counterparts who study engineering in England. Pooling USR data from 1980 to 1992, I also examined the likelihood of switching for each ﬁeld of study separately
Note that I exclude 1973–1979 and 1993 because there is no information on parental SES. The results are similar if I include these years and drop the measures of SES.
30

(results available upon request). The coefﬁcient on SCOT for social sciences and the arts is negative and signiﬁcant, indicating that this differential is also associated with ﬁelds outside the hard sciences. There are no signiﬁcant differences in switching across England and Scotland for certain ﬁelds such as health, business, and education.31 More generally, these effects may vary across ﬁelds because of differences in the relative returns
A degree in medicine is an extremely specialized course in both English and Scottish institutions. A degree in business may provide a broad set of skills that dampens the differences that arise from early versus late specialization.
31

392

INDUSTRIAL AND LABOR RELATIONS REVIEW Table 4. Effect of a Scottish Degree on Occupation-Field Switching for Engineers (USR, 1980–1992)
Dependent variable: switched to occupation unrelated to engineering subﬁeld OLS (1) (2) 0.037* [0.014] X X 0.29 22,320 0.28 (3) 0.034* [0.016] X X X 0.29 22,320 0.28 (4) 0.064* [0.032] X 2SLS (5) 0.047** [0.012] X X 0.29 22,320 0.28 (6) 0.049** [0.015] X X X 0.29 22,320 0.28

SCOT Main controls Sub-ﬁeld effects Region of work effects R2 Observations Mean of dep. variable

0.062 [0.032] X

0.02 21,819 0.28

0.02 22,320 0.28

Notes: Huber-White standard errors, clustered by university in brackets (that the standard errors are larger for OLS than 2SLS may occur because of the strong ﬁrst stage and the cross-correlations within the clustered groups). Sample includes all students who aimed to attain a ﬁrst engineering degree in England and Scotland with occupation data and were not pursing further studies. Dependent variable is deﬁned as 1 if the engineering subﬁeld at the undergraduate level is different from the engineering subﬁeld of the ﬁrst job in the 1st year following degree and 0 otherwise. SCOT is deﬁned as 1 for Scottish degree and 0 for English degree. SCOT is instrumented with nation of prior residence in columns (4), (5), and (6). Main controls include sex, marital status, age, high school GPA, parent SES and year ﬁxed effects. *Statistically signiﬁcant at the .05 level; **at the .01 level.

to match quality; learning about match quality may be more important in certain ﬁelds than in others. Table 5 presents data from the NSGD to show occupation-ﬁeld switching between England and Scotland. I estimate a reducedform equation in which SCOT is a dummy variable identifying whether students took English or Scottish secondary school leaving exams, because that is the only indicator available in the NSGD. As a result, I cannot restrict the sample to individuals from northern England. Again, all regressions include controls for gender, marital status, age, high school GPA, and parental SES. Columns (1), (2) and (3) show the reduced-form effect of having completed school leaving exams in Scotland on the likelihood of working in an occupation unrelated to the chosen ﬁeld of study in the ﬁrst year following graduation. Conﬁrming our results from the USR, most speciﬁcations show that students from England are more likely to switch than their counterparts from Scotland. However, the NSGD also contains information on stu-

dent outcomes six years following the completion of their degree. Columns (4), (5), and (6) indicate that the differential in switching between England and Scotland remains after six years. Note that the coefﬁcient on SCOT becomes insigniﬁcant when controlling for region of work.32 Stronger results are obtained if I consider all individuals employed six years following completion of the BA degree by including those who were not employed in the ﬁrst year after completing their degree (results not shown). Placebo Experiments In addition to the various robustness checks discussed above, Table 6 presents two
32

The NSGD data contain somewhat more detailed categories for region of work than the USR data, with locations in England classiﬁed as London, Midlands, East Anglia, and Southern and Northern England. As mentioned above, the decision to work in these more speciﬁc regions (such as London) may well be endogenous to occupational switching.

DISCOVERING ONE’S TALENT Table 5. Effect of Scottish Degree on Occupation-Field Switching for 1980 Graduates (NSGD)
Dependent variable: switched to occupation unrelated to ﬁeld of study 1st year after completing degree (1) SCOT Main controls Field of study effects Region of work effects R2 Observations Mean of dep. variable 0.151** [0.035] X (2) 0.086** [0.028] X X 0.35 1,455 0.48 (3) 0.014 [0.045] X X X 0.36 1,455 0.48 6th year after completing degree (4) 0.174** [0.036] X (5) 0.110** [0.029] X X 0.30 1,455 0.52

393

(6) 0.053 [0.046] X X X 0.31 1,455 0.52

0.03 1,455 0.48

0.03 1,455 0.52

Notes: Huber-White standard errors, clustered by university in brackets. Sample includes all students who aimed to attain a ﬁrst degree in England and Scotland with occupation data and were not pursing further studies. Dependent variable is deﬁned as 1 if ﬁeld of study at the undergraduate level is different from the broad occupational ﬁeld of the ﬁrst job in the 1st year following the degree and 0 otherwise. SCOT is deﬁned as 1 for having completed Scottish school leaving exams and 0 for having completed English school leaving exams. Main controls include sex, marital status, age, high school GPA, and parent SES. *Statistically signiﬁcant at the .05 level; **at the .01 level.

“placebo tests” to verify that the differential in occupation-ﬁeld switching between England and Scotland is not due to differences in unobserved characteristics across the two nations. Panel A examines the difference in switching between England and Wales for 1980 college graduates using data from the USR where I can identify whether individuals attended university in Wales. Since undergraduate students in both England and Wales generally apply to a speciﬁc ﬁeld of study in university, we would expect no difference in switching between England and Wales. The speciﬁcations are analogous to those in Panel A of Table 3. Columns (1), (2), and (3) present the results from OLS regressions in which WALES is a dummy variable indicating whether individuals completed university in Wales. Columns (4), (5), and (6) show the results from the 2SLS regressions in which the attainment of a Welsh degree is instrumented with the region of prior residence. None of the speciﬁcations indicates any signiﬁcant difference in switching between England and Wales. Since the timing of academic specialization in Wales is similar to that in England,

the absence of a difference in switching between England and Wales is reassuring and supports the contention that the difference between England and Scotland is a consequence of the timing of specialization. Panel B examines the difference in occupation-ﬁeld switching between England and Scotland, but at the graduate level. As mentioned, the USR has separate ﬁles containing information on students with graduate degress. Since graduate degrees in both England and Scotland are similar in terms of specialization—both require admission to a very speciﬁc ﬁeld of study—we expect to see no difference in switching at the graduate level. Of course, I control for undergraduate degree since the model itself predicts that students who complete an undergraduate degree in Scotland will have higher match quality and lower levels of speciﬁc skills than those in England. I focus on the sample of students who completed their studies in 1980 and entered the labor market at the same time as the undergraduate students analyzed above. Columns (1), (2), and (3) display results from the OLS regressions in which SCOTGRAD is a dummy variable

394

INDUSTRIAL AND LABOR RELATIONS REVIEW Table 6. Placebo Tests

Panel A: Occupation-Field Switching in Wales vs. England (USR sample) OLS (1) WALES Main controls Field of study effects Region of work effects R2 Observations Mean of dep. variable 0.094 [0.051] X (2) –0.001 [0.019] X X (3) –0.003 [0.020] X X X 0.41 12,082 0.51 (4) –0.08 [0.120] X

2SLS (5) –0.02 [0.036] X X (6) –0.034 [0.048] X X X 0.40 12,082 0.51

0.03 12,082 0.51

0.40 12,082 0.51

0.03 12,082 0.51

0.40 12,082 0.51

Panel B: Graduate-level Occupation-Field Switching in Scotland vs. England USR Sample (OLS) (1) SCOTGRAD Main controls Field of study effects Region of work effects R2 Observations Mean of dep. variable 0.005 [0.036] X (2) 0.029 [0.042] X X (3) 0.019 [0.040] X X X 0.19 4,400 0. 50 (4) 0.040 [0.050] X NSGD sample (reduced form) (5) 0.048 [0.047] X X (6) –0.048 [0.070] X X X 0.13 760 0.32

0.01 4,400 0. 50

0.19 4,400 0.50

0.03 760 0.32

0.11 760 0.32

Panel C: Academic Switching in Scotland vs. England USR Sample (OLS) (1) SCOT Main controls Field of study effects Region of work effects R2 Observations Mean of dep. variable 0.038 [0.030] X (2) 0.050** [0.024] X X 0.23 15,038 0.37 (3) 0.002 [0.017] X X X 0.24 15,038 0.37 (4) 0.020 [0.046] X NSGD sample (reduced form) (5) 0.037 [0.040] X X 0.21 1,100 0.61 (6) 0.005 [0.070] X X X 0.23 1,100 0.61

0.01 15,038 0.37

0.01 1,100 0.61

Notes: Huber-White standard errors, clustered by university in brackets. Dependent variable in Panel A is deﬁned as 1 if the broad ﬁeld of study at the undergraduate level is different from broad occupational ﬁeld. WALES is deﬁned as 1 for Welsh degree and 0 for English degree, and instrumented with nation of prior residence in columns 4, 5, and 6 of Panel A. Main controls include sex, marital status, age, high school GPA, and parent SES. Dependent variable in Panel B is deﬁned as 1 if the broad ﬁeld of study at the graduate level is different from broad occupational ﬁeld. SCOTGRAD is deﬁned as 1 for graduate Scottish degree and 0 for graduate English degree. Columns 4, 5, and 6 of Panel B show the reduced form using Scottish school leaving exams as a proxy for a Scottish graduate degree. Main controls for the USR in Panel B include sex, marital status, and type of undergraduate degree, while the corresponding main controls for the NSGD include sex, marital status, age, high school GPA, and parent SES. Dependent variable in Panel C is deﬁned as 1 if the broad ﬁeld of study at the graduate level is different from broad ﬁeld of study at the undergraduate level. Main controls for the USR in Panel C include sex and marital status, whereas the corresponding main controls for the NSGD include sex, marital status, age, high school GPA, and parent SES. The USR regressions in Panel C use students graduating in 1990 (due to the absence of undergraduate ﬁeld for 1980 graduates); all other regressions are restricted to students graduating in 1980. *Statistically signiﬁcant at the .05 level; **at the .01 level.

DISCOVERING ONE’S TALENT indicating whether individuals completed their graduate degrees in Scotland.33 Controlling for undergraduate degree, there is no signiﬁcant difference in the probability of an occupation-ﬁeld switch between England and Scotland at the graduate level. The NSGD includes students who graduated from college in 1980 and completed their graduate degrees some years later. Columns (4), (5), and (6) report results from the reduced form regression where the completion of graduate degrees in Scotland is proxied by whether students took English or Scottish secondary school leaving exams (I cannot control for undergraduate degree in these regressions). Still, there is no significant difference in switching between England and Scotland at the graduate level. These results further support the argument that the difference in occupation-ﬁeld switching between England and Scotland derives from the timing of specialization in undergraduate education and not from some other characteristic inherent to English and Scottish individuals, or from labor market conditions particular to England and Scotland. Finally, I examine the probability of switching to a graduate degree in a ﬁeld that is unrelated to the undergraduate ﬁeld of study—“academic ﬁeld switching”—in Panel C. The probability of switching to an unrelated graduate degree is not signiﬁcantly different for individuals with a Scottish undergraduate degree than for individuals with an English undergraduate degree for most speciﬁcations. Indeed, the sign is actually positive in all cases. One possible explanation is that the relative return to match quality for success in further study is different than for wages in the labor market. If further study at the graduate level depends more on the speciﬁc skills acquired at the undergraduate level, the beneﬁts from switching may no longer exceed the greater loss of skills in the early system. In other words, the relative return to academic skills

395

in graduate education may be substantially larger than in the job market. Alternative Explanations for Switching Occupation-ﬁeld switching may arise for reasons other than those described by my model of academic specialization.34 If certain individuals are particularly indecisive, they may be more likely to switch. Other individuals may simply be more adept at making changes and are therefore more likely to switch to an occupation unrelated to their ﬁeld of study. Although these characteristics are generally unobservable, I can examine whether such switching is correlated with other decisions, such as a change in major ﬁeld of study in university. Regression analysis conﬁrms that individuals who change ﬁelds of study during university are also signiﬁcantly more likely to experience an occupation-ﬁeld switch (not shown). However, as mentioned previously, 18% of Scottish students change their ﬁeld of study during university compared to just 7% of the English students. That students from Scotland are less likely to switch to an occupational ﬁeld unrelated to their ﬁeld of study despite being more likely to change their declared ﬁeld of study after entry into university provides some suggestive evidence that this differential in switching between England and Scotland is not driven by such unobservables. Occupation-ﬁeld switching may also be driven by the availability of jobs in different occupational ﬁelds. If certain sectors experience negative shocks to labor demand, recent graduates may be forced to switch to a different occupational ﬁeld from the one they studied. Appendix Table 2 shows the percentage of individuals employed in different occupational ﬁelds by ﬁeld of study in 1980. As expected, certain ﬁelds of study have substantial outﬂows into unrelated occupational ﬁelds (social sciences, physical sciences, and arts). Other occupational
For this reason, simply observing that switching takes place is not sufﬁcient evidence that education provides valuable information about match quality, and we need to test the comparative static predictions from the model.
34

The USR does not contain information on birth region, so I cannot instrument for whether an individual attained a Scottish degree with their place of birth or place of residence prior to commencing their studies.
33

396

INDUSTRIAL AND LABOR RELATIONS REVIEW majors are also more likely to switch to unrelated occupations, then any unequal distribution of students across universities will yield this correlation. Figure 4 plots the proportion of individuals who switch to an unrelated occupation by the proportion of students who change ﬁelds of study while in university.35 The pattern of occupational switching between England and Scotland conﬁrms the main ﬁndings of this paper and demonstrates that the propensity to switch ﬁelds in English universities is higher than in Scottish universities with comparable proportions of students who change majors. However, the positive correlation between changes in major and occupational switching within both England and Scotland would mistakenly suggest that students attending universities with less stringent penalties for specializing later are also more likely to switch to an unrelated occupation—a rather different result from the one reached by comparing across nations.36 Thus, the presence of selection bias may present serious problems if we don’t focus on exogenous differences in the timing of specialization. Conclusion Substantial research has examined the effect of education on labor market outcomes. Recent work has conﬁrmed that the relationship between education and outcomes such as wages is indeed causal (Card 1999). However, there has been less progress in understanding why education affects labor market outcomes. Education is often thought to provide certain skills that make workers more productive in performing tasks that are valued in the labor market (Neal and Johnson 1996; Cascio and Lewis 2006). Alternatively, education may enhance workers’ ability to deal with disequilibria, which may
35 A similar pattern arises when plotting the residuals in occupational switching and changes in major after controlling for observable differences in the main control variables. 36 This positive correlation is borne out in regression analysis, which compares occupational switching across English universities with high and low rates of switches across ﬁelds of study.

ﬁelds have substantial inﬂows from unrelated ﬁeld of study (business, engineering, education). However, evidence for ﬂows in both directions—for example, from math/ computer sciences to physical sciences and vice versa—suggests that ﬁeld switching is not driven solely by the availability of jobs in different occupational ﬁelds. Variation in Switching across Universities A comparison of labor market outcomes across England and Scotland has the disadvantage of including only two nations. An alternative empirical approach would have been to compare student outcomes across universities. The theoretical model assumes that the cost of changing majors in university following specialization is inﬁnite and identical across all universities within each system. But in fact, there is some variation across institutions. In England, although most universities require students to apply to a speciﬁc ﬁeld prior to entry, there are differences in the penalty to changing ﬁelds of study once students are enrolled in a speciﬁc course. In Scotland, students are either required to write down their expected ﬁeld of study or they are coded with a broad faculty to begin with, which is then changed appropriately when they select a speciﬁc ﬁeld. Since these penalties are difﬁcult to quantify, we might consider using the actual proportion of students changing ﬁelds as a proxy for the penalty. Any comparison across universities, however, will suffer from selection bias since students choose from among the many universities available to them. We expect that individuals who are unsure about what to study would be more likely to choose a university with less stringent penalties and be more likely to switch to an unrelated occupation upon entering the labor force. Moreover, using the actual proportion of students who change ﬁelds as a proxy may well confound the actual penalty with student characteristics that are correlated with these changes and other labor market outcomes. Indeed, if students who change

DISCOVERING ONE’S TALENT Figure 4. Changes in Major and Occupation-Field Switching by University (USR)
1

397

Proportion Switching Occupation

0 0

.1

.2
Proportion Changing Major

.3

Notes: Closed and open circles represent English and Scottish university averages, respectively. Outcomes are based on USR samples of undergraduates from 1980. Occupation-ﬁeld switching is calculated on the basis of the broad classiﬁcation (see Appendix Table 1). Change of ﬁeld of study is determined by students who receive a degree in a ﬁeld different from the ﬁrst ﬁeld of study.

result from technological change (Nelson and Phelps, 1966; Bowles 1970). In this paper, I have examined another important mechanism for why education might improve labor market outcomes. By providing valuable information about tastes and talents for different ﬁelds of study, I have shown how education can help individuals match more successfully to different ﬁelds in university and in the labor market. In order to examine this mechanism, I developed a model of academic specialization in which individuals, by taking courses in different ﬁelds of study, accumulate ﬁeldspeciﬁc skills and receive noisy signals of match quality in these ﬁelds. Distinguishing between educational systems with early and late specialization, I derived a comparative static prediction regarding the probability of

switching to an occupation unrelated to one’s ﬁeld of study. If higher education serves mainly to provide speciﬁc skills, the model predicts more switching in a system with late specialization because the cost of switching is lower in terms of foregone skills. Alternatively, if higher education serves mainly to provide valuable information about match quality, switching may be higher in a system with early specialization because the beneﬁts from higher expected match quality due to switching will outweigh the greater loss of speciﬁc skills. University administrative data and survey data on college graduates show that individuals from Scotland, who specialize relatively late, are less likely to switch to an unrelated occupation than their counterparts from England. The pattern is even more striking

398

INDUSTRIAL AND LABOR RELATIONS REVIEW The ﬁnding that education provides valuable information about tastes and talents also has implications for the timing of academic specialization. Later specialization, which allows students more time to learn about their match quality in different ﬁelds of study, may be preferable when there are large returns to being well matched to a particular ﬁeld. Although I have focused on the differences in the timing of specialization between England and Scotland, there is also substantial variation in the difﬁculty of changing majors across college in the United States. Moreover, there are some countries that require students to specialize while still in elementary or secondary school. In this paper, I have suggested that these structural differences in the timing of specialization may have important consequences for efﬁciency and welfare.

when instrumenting for English and Scottish degrees with region of prior residence. In contrast, there is no difference in the probability of switching between England and Wales where the timing of academic specialization is similar, or between England and Scotland at the graduate level, where the timing of specialization is also similar. These ﬁndings indicate that the return to match quality is high relative to the return to speciﬁc skills. In other words, the fact that England—a system with early specialization—exhibits a higher incidence of switching implies that the beneﬁts to increased match quality are substantial, and, indeed, large enough to outweigh the greater loss of skills. The data thus conﬁrm that undergraduate education has an important role in helping students discover their tastes and talents about different ﬁelds of study.

A. Data Appendix Complete documentation for the Universities’ Statistical Record, 1972–73—1993–94: Undergraduate Records, Postgraduate Records and the National Survey of 1980 Graduates and Diplomates, 1986–1987 are available from the UK Data Archive: http://www.dataarchive.ac.uk (Department of Employment 1988). Details of the variables constructed for this study are described as follows: Occupation-Field Switch: An occupation-ﬁeld switch is deﬁned as a binary variable that takes on a value of 1 if individuals are employed in an occupation unrelated to their major ﬁeld of study at the undergraduate level, and 0 otherwise. In order to determine whether individuals are employed in an occupation that is related or unrelated to their ﬁeld of study, I group ﬁelds of study and occupations into categories. As shown in Appendix Table 1, I allow for three gradations of classiﬁcation: narrow (42 categories), broad (12 categories), and very broad (6 categories). Occupations and ﬁelds of study are coded according to each of the alternative classiﬁcations. Where the occupation and ﬁeld of study are classiﬁed in different categories, the ﬁeld switch variable takes on a value of 1. For example, individuals studying physics at university will have their ﬁeld of study coded as “physics” according the narrow classiﬁcation, “physical sciences” according to the broad classiﬁcation, and “mathematical, computer, and physical sciences” according to the very broad classiﬁcation. If they are employed as computer programmers, the ﬁeld switch variable will take on a value of 1 according to the narrow and broad classiﬁcations and a value of 0 according to the very broad classiﬁcation. Combined ﬁelds are considered switches if the individuals are not employed in any of the ﬁelds mentioned. Change in Major Field of Study: Using the USR, I record changes to the major ﬁeld of study by observing when the ﬁeld of study upon entering university is different from the ﬁeld of study in the degree awarded based on the appropriate classiﬁcation. In Scotland, students are coded according to a broader code representing the combination of ﬁelds in a faculty or school or on the basis of a provisional ﬁeld of study, and subsequently change when they select a speciﬁc ﬁeld. High school GPA: Scores on secondary school leaving exams are ofﬁcially coded as letter grades (A, B, C, and so on). These are converted into numerical scores where A 10, B 8, C 6, D 4, and E 2. Average scores are then standardized by nation and combined so that the overall distribution of high school GPA has mean 0 and standard deviation 1. SES: SES is coded based on parental occupations. It is represented by a series of dummy variables corresponding to the following categories: 0–unstated, retired, or unknown, 1–professionals workers, 2–intermediate workers, 3–skilled non-manual, 4–skilled manual, 5–partially skilled, 6–unskilled, and 7–unemployed. Region of Work: Region of work is classiﬁed as England, Scotland, Wales, Northern Ireland or abroad in the USR. Region of work is classiﬁed as London, Southern England, Midlands, East Anglia, Northern England, Wales, Scotland, Northern Ireland or abroad in the NSGD.

DISCOVERING ONE’S TALENT
B. Mathematical Appendix The mathematical appendix provides a formal treatment of the model of academic specialization presented in the main text. For ease of exposition, the structure of the appendix and most of the notation parallels the main text. Formal Setup Suppose N courses are taken in k 2 ﬁelds of study. Let F1, ... ,Fk be normal populations associated with ﬁelds of study i 1, ... ,k, each with unknown mean θ1, ... ,θk and a common known variance σ2 0. The unknown means θ1, ... ,θk represent unobserved match quality in each ﬁeld. Sequence of observations In Stage 1, n observations from each population Fi are observed. These correspond to observations on match quality from courses taken in each ﬁeld of study prior to specialization. The sample means of these observations, Xi, are independent and distributed N(θi,p 1) with p nσ 2. In Stage 2, one population, i *, is selected for further sampling and (N nk) additional observations are observed from this population. These correspond to observations on match quality in the chosen ﬁeld from courses taken following specialization. The sample mean of the second set of observations, Y, is distributed N(θi*,q 1) with q = (N nk)σ 2 and where θi* is the (unknown) mean of the population chosen after Stage 1.37 Beliefs on match quality Beliefs about match quality θ1, ... ,θk are represented ˆ ˆ by the parameters θ,...,θ k. These parameters are random and follow independent and identical prior distribu− ˆ tions assumed to have θi ∼ N ( µ, ν 1 ) with ν = σ 02 . The ˆ conditional distribution of θ at each stage can be expressed as follows: ˆ θi X  px νµ 1 ,( p ν)  , x∼N i  p ν  i 1,..., k independent x, Y  πµ (x) q i y −1  ,( π qi )  , y∼N i π q   qi * q and 0 otherwise

399

Payoffs The returns associated with ﬁeld Fi are denoted by ui αθi βsi where si is the cumulative number of observations from ﬁeld Fi. This return represents the wage received in ﬁeld i upon entering the labor market. In terms of the model of academic specialization, α is the return to match quality and β is the return to speciﬁc skills. Note that we can express the loss function associated with population Fi as Li(θ,s) αθi βsi.39 Decision Rules After X x has been observed at Stage 1, the Bayes * selection rule i * = d1 (x) can be found by minimizing the posterior expected loss (or in our framework, maximizing posterior expected returns): ˆ E X L ( θ, d1* ( X )) X i 1,...,k

(

x

ˆ max E X ( αθi i 1,...,k

)

βs i X x

x

)

ˆ α max E X ( θi X α max µ i ( X ) βs i 1, ...,k

)

βs

 p ( maxi =1,...,k + νµ  α  + βs p+ν  

)

ˆ θi X

where s corresponds to the speciﬁc skills in each ﬁeld which are equivalent across ﬁelds. The optimal selection, i *, at Stage 1 will therefore be the population with the largest observed sample mean after Stage 1 since * d1 (x) arg maxi 1,...,k x i . This is intuitive since, with identical prior distributions on match quality, the only distinguishing feature of each population is the information received in Stage 1. Let x[1] x[2] ... x[k] denote the order sample means from Stage 1 and µ[1](x) µ[2] (x) ... µ[k] (x) denote the ordered posterior means from Stage 1. Note that, in terms of the notation in the main text, µ i′* µ[k ](x) and µ i′* µ[k 1](x). Similarly, after Y y has been observed at Stage 2, * the Bayes selection rule i ** d 2 (x, y ) will satisfy ˆ * E L θ, d 2 ( X, Y ) X i 1,...,k

( (

where π p ν represents the relative combined (prior plus sampling) information gained from ﬁeld Fi, and where µi(x) = (pxi νµ)/(p ν) represents the estimated mean of ﬁeld Fi after Stage 1. In terms of the notation in the main text, µ i′ µ i (x) and µ i′ µ i (x, y ).38

ˆ max E ( αθi

)

x,Y

y

) y βs i X

x,Y

)

These Bayes selection rules yield the maximum posterior expected returns, or Bayes risk, of their respective problems in Stages 1 and 2. Let µ i′′ µ[k ](x, y ) denote * the posterior mean of ﬁeld, i*, after Stage 2. An important feature of this decision problem is that the selection

Since Xi and Yi* already correspond to the mean of the samples, we will use xi and Yi* instead of x i and yi * . 38 Note also that the conditional distribution of Y given X x is distributed N(µi(x), w) with w (π + q)πq.
37

39 This corresponds to a linear loss function, L (θ, s) = i θ[k], max {θ1, . . . , θk} where is normalized to zero and with an additional negative cost associated with the amount of sampling from the population i.

400

Appendix Table 1 Classiﬁcation of Fields and Occupations Occupational Codes (NSGD) Occupational Codes (USR-1980)

Fields

Subject codes (NSGD/USR-1980)

111 Math/Comp. Science 1111 Math Sciences Mathematician (444); Statistician (242). . . Operational research (441); Statistician (452) Computer Programmer (244); Analyst/ Systems analysis (442); Computer programmer (246). . . programming (443). . . Chemical scientist (442) Geological scientist (445) Physical scientist (443)

Mathematics (81)

1112 Computer Sciences Computer Science (82); Math/Comp. Science (31)

112 Physical Sciences 1121 Chemistry

1122 Geology

Chemistry (34); Environmental Science (36) Geology (35)

1123 Physics

Physics (33); Mathematics/Physics (32)

Scientist (510) + Chemical and allied industries (240–247) Scientist (510) + Oil, mining industries (230–235) Scientist (510) + Atomic energy (284); Other manufacturing Architect (551); Town planning (553); Surveying (554). . . Engineer (520) + Automotive industry (253)

121 Architecture 1210 Architecture Architect (511); Town planning (514); Draughtsman (490). . .

Architecture (51); Town plan (52); Surveying (17)

122 Engineering 1221 Mechanical Mechanical or aeronautical engineer (461) Chemical engineer (481)

Mechanical engineering (12)

1222 Chemical

Chemical Engineering (9)

1223 Civil

Civil Engineering (10)

INDUSTRIAL AND LABOR RELATIONS REVIEW

1224 Electrical

Electrical Engineering (11)

1225 Industrial

Production engineering (13)

1226 Materials

Mining (14); Metallurgy (15)

1227 Aeronautical

Aeronautical engineer. (8)

Engineer (520) + Chemical and allied industries (240–247) Civil, municipal or structural Engineer (520) + Civil engineering contracengineer (451). . . tors (220–225). . . Electrical engineer (471); Electronic engi- Engineer (520) + Electronic (256); Computneer (472,473) ers (257). . . Production engineer (482); Planning engi- Engineer (520) + Food (261); Drink (262); neer (483). . . Textiles (271). . . Mining engineer (452); Metallurgist (485) Engineer (520) + Oil, mining industries (230–235) Mechanical or aeronautical Engineer (520) + Aircraft, aerospace engineer (461) industry (254)

continued

Appendix Table 1 Classiﬁcation of Fields and Occupations Continued Occupational Codes (NSGD) Occupational Codes (USR-1980)

Fields

Subject codes (NSGD/USR-1980)

131 Life Sciences 1311 Agriculture

Agriculture (20); Forestry (23). . .

1312 Biology Medical practitioner (351)

Farmer, farm manager, horticulturist (600) Scientist (510) + Agriculture, horticulture, forestry(210–214) Biology (25); Botany (26); Zoology (27). . . Biological scientist, biochemist (441) Scientist (510) + Health authorities (154)

132 Health Sciences 1321 Physicians

Medicine (3)

1322 Dentists/Vets/ Pharm 1323 Nursing/Related

Dentistry (4); Veterinary (24); Pharmacology (5,6) Studies allied to medicine/health (7)

Medicine (631); Medical & para-medical services (630) Dentist (352); Veterinarian (382); Pharma- Dentistry (632); Veterinary (640); Pharmacy cist (371). . . (634). . . Nurse (360); Physiotherapist (374). . . Nursing (633); Physio-occupational, speech & therapy (636) Psychologist (324) Sociologist (323); Welfare worker (333)...

211 Social Service 2111 Psychology

Psychology (46)

2112 Sociology/Social Work Economist (241) Librarian, information ofﬁcer (294) Inspector (263); General administration (local govít) (280). . . Social or behavioural scientist (325)

Sociology (47)

Psychology (623); Occupational guidance (624) Social, welfare, religious (620); Social/ welfare (621). . . Economic (450); Economist (451) Librarian (721) Archivist (722) Consumer protection, environmental health, safety (653). . . Non-scientiﬁc research (730); Information research (700). . .

DISCOVERING ONE’S TALENT

212 Social Sciences 2121 Economics Economics (41) 2122 History/Geography History (69); Archeology (70); Geography (42) 2123 Govt., Public Government and public administraAdmin. tion (44) 2124 Other Social Social anthropology (48)

221 Business 2211 Accounting, Finance 2212 Management

Accountancy (43)

Business, management studies (40, 53)

2213 Sales

Business, management studies (40, 53)

2214 Related Business

Secretarial studies (84)

Accountant (221); Investment analyst (228). . . Management consultant (296); Manager (561). . . Advertising executive (252); Buying and selling (255). . . Ofﬁce manager (572); Personal assistant (297). . .

Financial (460); Accountancy (461); Banking (462). . . Management & supporting occupations (400). . . Purchasing (431); Selling (432); Marketing (434). . . Clerical, secretarial & related (930). . .

401 continued

402

Appendix Table 1 Classiﬁcation of Fields and Occupations Continued Occupational Codes (NSGD) Judge (211); Advocate, barrister (212); Solicitor (213). . . Teacher (secondary) (311); Teacher (primary) (312). . . Author, writer, journalist, editor (391) Occupational Codes (USR-1980) Barrister (471); Solicitor (472); Trusts (473). . . Primary (611); Middle school (612); Secondary (613). . .

Fields

Subject codes (NSGD/USR-1980)

222 Law 2220 Law

Law (45)

231 Education 2310 Education

Education (1)

232 Arts 2321 English/Languages English (55); French (57); German (59). . . 2322 Art Art (73) Artist, commercial artist (401); Designer (402–406) Actor, entertainer, musician, singer, stage manager (411). . . Clergy, minister of religion (340)

2323 Performing arts

Drama (74); Music (75)

INDUSTRIAL AND LABOR RELATIONS REVIEW

2324 Religion/Philosophy Religion (72); Philosophy (71)

Journalist (811); Technical writer (711); Translator (712). . . Art, sculpture, design (820); Fashion & textiles (823). . . Acting, music, sport (830); Broadcasting/ stage/ﬁlm (840). . . Pastoral (622)

Notes: Subject codes for USR are correct for 1972-1984 (different codes for 1985-1993) and occupational codes for the USR are correct from 1980-1993 (different codes for 1973-1979). Occupational codes omit some categories for brevity and indicated with ì. . .î when excluded. Engineers and scientist in the USR are matched with industry codes in order to identify particular specializations within each category. Further details are available from the author. Broad ﬁelds are in bold. Very broad ﬁelds are expressed by the 2-digit codes.

Appendix Table 2 Percentage Employment in Different Occupational Fields by Field of Study in 1980 BA Degree (USR) Occupational Field Architect 0.1 0.8 57.1 1.1 0.4 0.0 0.2 1.6 0.4 0.0 0.0 0.1 0.0 0.3 74.3 0.3 0.9 0.0 0.5 3.7 0.0 0.0 0.0 0.0 0.3 0.2 0.0 0.3 0.0 0.0 0.0 0.0 0.9 0.2 19.7 0.9 0.0 0.4 0.8 2.2 0.0 1.3 0.0 4.5 2.3 14.8 0.9 74.1 0.9 0.0 0.0 0.2 0.0 0.9 0.0 0.0 3.5 0.1 0.0 0.2 0.0 0.3 0.0 0.2 4.7 97.4 4.5 0.7 0.0 0.0 1.8 0.2 1.2 0.0 26.7 4.5 0.4 0.6 1.8 0.3 3.1 0.9 2.7 8.4 24.1 15.1 10.1 9.9 25.2 0.8 28.5 44.6 94.7 8.7 4.9 24.5 0.0 0.0 0.0 0.0 0.2 0.0 0.9 1.3 0.6 88.1 0.0 0.9 15.6 21.5 0.0 2.9 17.9 0.2 14.5 19.6 0.3 0.0 68.0 38.8 5.7 9.8 0.0 71.3 0.8 0.1 0.2 0.2 0.8 0.1 0.3 0.1 0.0 0.3 0.2 0.1 3.4 0.2 0.4 0.0 0.0 0.0 0.0 0.0 0.1 0.9 0.0 0.2 5.0 94.4 7.6 0.9 0.2 0.1 5.6 1.5 0.8 1.1 0.2 0.5 1.4 0.1 24.2 2.5 0.3 0.5 2.2 2.2 0.4 2.5 0.4 0.3 2.3 1.0 4.1 6.0 0.9 1.8 0.0 4.0 27.9 18.6 28.6 8.9 25.8 1.0 23.6 47.5 87.6 11.8 7.0 26.5 0.1 0.6 0.2 0.1 0.4 0.0 1.0 2.5 0.4 81.8 0.3 1.5 15.8 14.6 0.9 1.5 17.4 0.6 21.4 18.8 1.9 0.9 76.9 34.7 0.8 1.3 0.7 0.6 1.5 0.1 2.0 3.4 0.3 0.7 0.8 11.3 0.0 0.9 0.0 0.0 1.2 0.1 1.4 3.9 0.3 0.0 0.0 14.3 Engineer Bio Health Social Serv. Social Sci. Business Law Educ Arts

Field of Study unclassiﬁed Math/Comp

Physical

ENGLAND Math/Comp Physical Sci. Architecture Engineering Biology Health Social Serv Social Sci. Business Law Education Arts

2.7 6.8 10.0 5.8 12.0 0.3 11.0 13.2 3.9 2.0 5.9 16.6

38.3 11.2 0.2 2.6 3.9 0.1 2.9 3.0 3.3 0.2 0.8 1.6

7.2 31.3 1.5 7.1 25.8 2.2 1.3 0.6 0.2 0.1 0.2 0.1

DISCOVERING ONE’S TALENT

SCOTLAND Math/Comp Physical Sci. Architecture Engineering Biology Health Social Serv. Social Sci.

1.6 6.5 10.1 4.3 14.6 0.0 13.1 9.6

49.8 7.4 0.9 2.1 1.7 0.0 5.0 2.7

6.2 31.7 0.0 5.7 24.9 0.5 2.3 0.7

Business Law Education Arts

2.7 1.1 6.6 12.8

0.3 0.0 0.0 0.8

0.0 0.0 0.0 0.0

Notes: Occupation and ﬁeld of study are categorized according to the broad ﬁeld classiﬁcation. Fraction employed is calculated using all individuals who aimed to attain a BA degree in 1980 and were employed in a job during the 1st year following graduation and not pursuing graduate studies.

403

404

INDUSTRIAL AND LABOR RELATIONS REVIEW
Stage 2; the ﬁrst term on the right-hand side represents the loss in match quality from switching based on beliefs from Stage 1. The second term on the right-hand side represents the loss in skills from switching to the second-best ﬁeld. Individuals will switch ﬁelds when the new information about match quality is sufﬁciently negative so as to outweigh the loss in match quality and skills from switching. Later specialization corresponds to more observations in Stage 1 that decreases the relative importance of new information in Stage 2, increases the relative importance of information in Stage 1, and raises the loss in skills associated with switching. When β is large relative to α, the loss in skills associated with switching will dominate and (d/dn)Pr(switch) 0.41 When α is large relative to β, the loss in match quality associated with switching will dominate and (d/dn)Pr(switch) 0.42 Using numerical methods, we can always ﬁnd a unique constant C 0, so that a system with early specialization, nE, will have a higher probability of switching than a system with late specialization, nL, if α/β C and a system with late specialization, nL, will have a higher probability of switching than a system with late specialization, nL, if α/β C. Proof of Corollary 1: Suppose now that u(θi, si) = αθi + βsi + εi where εi ∼ N(0,τ2). Then, if the return to match quality is equal to zero, α 0, we can express the probability of switching as follows:
 αµ [k 1] ( x ) βn ε[k 1] > αµ[k ] ( x , y ) Pr(switch ) Pr     β (n ( N nk )) ε[k ]    βn ε[k 1] Pr   > β (n ( N   nk )) ε[k ]  nk )

* i ** d 2 (x, y ) after Stage 2 may differ from the selection * i * d1 (x) after Stage 1 since further observations in Stage 2 may reveal that the initial choice was not as good as initially thought. This corresponds precisely to the possibility of switching ﬁelds expressed in the main theoretical framework. Proof of Proposition 1: The probability of switching can be expressed as follows:

Pr (switch ) Pr (u ( µ i′a , s ) Pr u ( µ[k 1](x), s )

(

u ( µ[k ](x, y ), s )

u ( µ i′′ , s ) or *

)

)

where u ( µ i′′ , s ) u ( µ[k ](x , y ), s ) is the wage expected in * the chosen ﬁeld based on the beliefs after Stage 2 and u ( µ i′′′ , s ) u ( µ[k 1](x), s ) is the wage expected in the second-best ﬁeld based on the beliefs after Stage 1. Using the latter notation and since individuals are assumed to be risk-neutral, we can write the probability of switching in terms of skills and beliefs about the mean of match quality: Pr(αµ[k 1](x) βn αµ[k](x,y) β(n (N nk))). We can further decompose µ[k](x,y), into the mean of match quality in the chosen ﬁeld after Stage 1, µ[k](x), and the mean of the observations taken from the chosen ﬁeld in Stage 2, Y[k]:40  α  µ[k 1](x) µ[k ](x, y )  Pr (switch ) Pr     > β ( N nk )   µ[k 1](x) µ[k ](x)    12 q       Pr   π ( π q )     β   ( N nk )  Y [k ]   α
12  q  [k ]   Y   π ( π q )  p Pr  (x[k ] x[k p ν   β  ( N nk )  α

    1] )    

Pr ε[k 1]

 β (nk N )  Φ   2τ 2 

(

ε [k ] < β ( N

)

since ε[k 1]

ε[k −1] ~ N ( 0,2τ2 ) . 2

Where d  p  dn  p ν   

d  dn  π 

(π

qi

 qi )    nk ) 

0, 0.

0 and

d β  (N dn  α

Assume that σ2 ∞ yields the same expression since p = nσ 2 = 0 and q = (N nk)σ 2 = 0. Hence, in either case, a larger n causes the probability of switching to increase. Therefore, if α 0 or σ2 ∞, a system with early specialization will have a lower probability of switching than a system with late specialization.

The left-hand side term represents new information about match quality in the chosen ﬁeld revealed in

40 So Y [k] is a random variable representing observations from an extreme value distribution. See Gupta and Miescke (1994, 1996) and Miescke (1999) for similar decompositions.

41 This holds so long as switching continues to take place (that is, β is not too large relative to α). 42 This is clear if β 0 and there is no loss in skills from switching. In this case, a larger n will make ((q/π(π q)))1/2Y[k] less negative and (p)/(p ν) (x[k] x[k 1]) more negative, reducing the probability of a switch.

DISCOVERING ONE’S TALENT
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____, and Yaw Nyarko. 1997. “Stepping Stone Mobility.” In Carnegie-Rochester Conference Series on Public Policy 46, pp. 289–326. Malamud, Ofer (2010). “Breadth versus Depth: The Timing of Specialization in Higher Education.” Labour, Vol. 24, No. 4, pp. 359–90. McCall, Brian. 1990. “Occupational Matching: A Test of Sorts,” Journal of Political Economy, Vol. 98, No. 1, pp. 45–69. Miescke, Klaus J. 1999. “Bayes Sampling Designs for Selection Procedures.” In S. Ghosh, ed., Multivariate, Design, and Sampling, pp. 93–117. M. Dekker: New York. Miller, Robert. 1984. “Job Matching and Occupational Choice.” Journal of Political Economy, Vol. 92, No. 6, pp. 1086–1120. Neal, Derek. 1999. “Complexity of Job Mobility among Young Men.” Journal of Labor Economics, Vol. 17, No. 2, pp. 237–261. Neal, Derek and William R. Johnson. 1996. “The Role of Premarket Factors in Black-White Wage Differences.” Journal of Political Economy, Vol. 104, No. 5, pp. 869–895. Nelson, Richard R. and Edmund S. Phelps. 1966. “Investment in Humans, Technological Diffusion, and Economic Growth.” American Economic Review, Vol. 56, No. 1/2, pp. 69–75. Osborne, G.S. 1967. Scottish and English Schools: A Comparative Survey of the Past Fifty Years. University of Pittsburgh Press. Schultz, Theodore W. 1968. “Resources for Higher Education: An Economist’s View.” Journal of Political Economy, Vol. 67, No. 3, pp. 327–47. Shaw, Kathryn L. 1987. “Occupational Change, Employer Change, and the Transferability of Skills.” Southern Economic Journal, Vol. 53, No. 3, pp. 702–19. Spence, Michael. 1973. “Job Market Signaling.” Quarterly Journal of Economics, Vol. 87, No. 3, pp. 355–74. Squires, Geoffrey. 1987. “The Curriculum.” In Tony Becher, ed., British Higher Education, pp. 155–77. London: Allen & Unwin. Stange, Kevin. 2009. “An Empirical Examination of the Option Value of College Enrollment.” Unpublished paper, University of Michigan. Stinebrickner, Ralph, and Todd R. Stinebrickner. 2009. “Learning about Academic Ability and the College Drop-out Decision.” NBER Working Paper 14810, March. Trow, Martin. 2000. “From Mass Higher Education to Universal Access: The American Advantage.” Minerva, Vol. 37, No. 4, pp. 1–26. University of Edinburgh. 2003. Undergraduate Prospectus. Communications and Public Affairs for The University of Edinburgh. Edinburgh, UK.

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Discovering One’s Talent: Learning from Academic Specialization

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