A mismatch made in heaven: a hedonic analysis of overeducation and undereducation.

1. Introduction

Over the past two decades, there has been much concern by researchers and policymakers over the apparent lack of coordination between the labor market and the education system that leads some workers to have educational qualifications in excess of those specified for the job (overeducation) and others to have less (undereducation). Cross-sectional studies using U.S., European, and Asian data sources indicate that between 30% and 40% of workers have educational qualifications that either exceed or fall short of firm requirements at a particular point in time (e.g., Sicherman and Galor 1991; Alba-Ramirez 1993; Ng 2001). Moreover, a meta-analysis by Groot and Maassen van den Brink (2000) shows no significant change in the extent of this mismatch between workers and firms over the past 20 years. Thus, overeducation and undereducation appear to be pervasive and persistent phenomena in industrialized countries.

A large empirical literature treats both overeducation and undereducation as evidence of an imbalance in the supply of and demand for skills (Rumberger 1981, 1987; Manacorda and Petrongolo 2000). For example, short-run coordination failure between worker qualifications and firm requirements could occur if rapid technological advancement draws educated workers into jobs traditionally held by lower-skilled workers who cannot readily acquire more education (Borghans and de Grip 2000). Mismatch in the skills market is supported by a number of empirical wage studies that include years of required education and measures of whether the worker has more or less education than required. These studies find that workers whose qualifications equal firm requirements earn a higher return to education than those who do not (Duncan and Hoffman 1981; Hersch 1991; Vahey 2000).

Recently, two equilibrium rationales have been proposed for the presence of overeducation. First, several papers examine whether worker qualifications might exceed firm requirements due to the substitutability or complementarity between education and on-the-job training (de Oliveira, Santos, and Kiker 2000). Workers might be identified as overeducated if, for example, education and on-the-job training are substitutes in production such that job entrants who possess more than the minimum educational requirements do not require further training. While not explicitly examined in prior work, substitutability between education and on-the-job training can also lead to undereducation if workers can use on-the-job training as a substitute for formal education, whereas complementarity between education and training could imply that human capital differences increase throughout a career because well-educated workers benefit more from training (Sloane, Battu, and Seaman 1996). An empirical paper by van Smoorenburg and van der Velden (2000) finds that substitutability and complementarity between initial education and on-the-job training are both possible and depend on factors such as the match between the job and field of study and the "narrowness" of educational training.

Second, several papers model overeducation as a result of career mobility. For example, Sicherman and Galor (1990) develop a theoretical model in which workers start in jobs for which they are overeducated in exchange for a higher probability of moving up the job hierarchy. They test this hypothesis using data for working-age males from the 1976-1981 waves of the Panel Study of Income Dynamics (PSID) and find that the correlation between the effect of education on wages and the probability of moving to a "better" job is negative and significant. This result suggests that overeducated workers trade off a lower return to education for career mobility reflected in an increased probability of promotion. Nonetheless, an equilibrium rationale has not been put forward for the presence of undereducated workers.

In this paper we develop a discrete hedonic pairing model where worker qualifications do not always match firm requirements in equilibrium. Workers can be overeducated in equilibrium when they start in lower-paying, entry-level jobs in return for the promise of higher-paying future positions that do, in fact, require their educational background. However, undereducated-type pairings can also arise when workers begin in lower-paying jobs for which they are exactly educated but then receive the necessary training for promotion into a higher-skilled and hence higher-paying job. The missing element in most models is time: Workers who now appear overeducated may be waiting for promotion to jobs requiring their level of education, while workers who now appear undereducated may have received training in the past that provided them with the skills they need to perform the higher-paying job. Yet worker qualifications will meet firm requirements at some time in every worker-firm pairing.

An implication of this analysis is that the observed educational match in a cross section or a short panel (used in prior work) will misidentify some pairing types. However, the discrete hedonic pairing process is shown to yield a jointly determined ordered probit model of worker qualifications and firm requirements that can be used to impute the pairing type (i.e., overeducated, undereducated, and exactly educated), which is estimated using uniquely detailed data for British working-age males contained in the Social Change and Economic Life Initiative survey (SCELI). The predicted pairings correctly identify most of the observed overeducated and undereducated worker-firm pairs but also show that many apparent exactly educated worker-firm pairs are properly characterized as overeducated or undereducated types of pairings. Several empirical analyses exploit the forward-looking and backward-looking data contained in SCELI to show that past and future opportunities for on-the-job training and promotion differ across the pairing types consistent with the hedonic pairing model.

We supplement our cross-sectional results with analyses using the British Household Panel Study (BHPS) that permit us to track the career path of respondents over a 12-year period. The BHPS analyses confirm our training and promotion findings from SCELI and permit the estimation of wage growth equations over a career path that show that overeducated and undereducated pairing types have steeper wage profiles than those in exactly educated pairings. Collectively, the results provide some of the first formal evidence that overeducation and undereducation can occur in a labor market equilibrium that is mutually beneficial for workers and firms and that a proper empirical assessment of the pairing process must account for these worker-firm pairings occurring over multiple periods.

2. Empirical Model

Two Illustrations of Career Mobility

By definition, overeducation or undereducation occur when the observed educational qualifications of the worker (Q) do not match the stated educational requirements for the job (R) at a given time. However, a worker-firm pairing often occurs over multiple periods and, thus, may reflect the objectives of the worker and the firm over the course of their pairing and not just for a single period. We develop an empirical model of a hedonic pairing process that shows that an overeducated-type (undereducated-type) pairing yields Q > R (Q < R) over a portion of their employment relationship and results from the fact that, in such pairings, workers move up the job-skill hierarchy with experience. To lay a foundation for the empirical model, it is useful to begin with two simple illustrations where career mobility can yield an overeducated- or an undereducated-type pairing.

There are a number of practical examples of an overeducated-type pairing. For example, most UK police officers enter the force with secondary school qualifications that qualify them to be a patrol officer. However, entrants into the force who have a university degree also begin as patrol officers because this experience improves their subsequent performance when they are promoted into jobs that require their qualifications (e.g., detective). In other words, university-educated patrol officers accept jobs for which they are overeducated in exchange for training and an expected future promotion into a job for which they are exactly educated.

Career mobility can also potentially yield an undereducated-type pairing. For example, whereas many detectives have a university degree, patrol officers with only secondary school qualifications can be promoted to detective if their on-the-job field experience reveals that they have the necessary skills and personal attributes to be a successful detective. These secondary school-educated detectives begin in a patrol officer job for which they are exactly educated but are promoted into jobs for which they may be viewed as undereducated because their qualifications are below those of many detectives who have a university degree. It follows that the experience of these secondary school-educated detectives substitute for the skills and/or a signal of ability provided by a university degree and permit them to move up the job hierarchy (Groot and Oosterbeck 1994; Chatterji, Seaman, and Singell 2003).

These simple illustrations highlight two important points. First, the wage profile of an overeducated-/undereducated-type pairing may well be steeper than for a pairing where worker qualifications always equal firm requirements. Specifically, a university-educated patrol officer accepts a position that requires lower qualifications in order to obtain the requisite training and subsequent promotion to detective. Thus, overeducated workers trade off a low initial return to education by entering into a job that does not require their university degree for a subsequent promotion return (e.g., Sicherman and Galor 1990). Likewise, a secondary school-educated patrol officer who is promoted to detective is likely to experience faster wage growth than one who is not promoted to detective. In both cases, the greater wage growth likely reflects heterogeneity across firms in the opportunity for promotion and heterogeneity across workers in their willingness to acquire on-the-job training and their ability to take advantage of such promotion opportunities throughout their career.

Second, the observation of all pairings where Q > R or Q < R at a particular time does not constitute the full set of overeducated or undereducated pairings. In particular, the pool of exactly educated workers includes, in addition to workers who are exactly educated throughout their career, previously overeducated workers who have been promoted into exactly educated jobs. This pool also includes undereducated-type workers who are (at present) exactly educated because they have yet to move up the job ladder. Prior work has compared observed worker-firm pairings in a cross section or short panel. Thus, these studies have been unable to distinguish between workers who are in an exactly educated-type pairing where worker qualifications always equal firm requirements from workers in an overeducated- or undereducated-type pairing who have educational qualifications that match firm requirements over only a portion of their career.

We develop an empirical model that can indirectly distinguish between the pairing types, overeducated, undereducated, and exactly educated, within a cross section. In particular, the empirical model identifies the pairing types by comparing the discrete, observed educational qualifications of the worker (Q) and discrete, observed educational requirements of the firm (R) with their predicted, continuous values ([Q.sup.*] and [R.sup.*]) that exploit the information contained in the correlation of the unobservables in each worker firm pairing. (2)

The Worker Qualification and Firm Requirement Choice

The analysis first considers workers' utility-maximizing qualification choice and firms' profit-maximizing requirement choice in isolation before considering the joint pairing process. For simplicity, the qualification choice of the worker and the requirement choice of the firm are assumed to be made prior to and independent of the worker-firm pairing and to remain constant over the course of the pairing. Nonetheless, the pairing process yields a correlation between Q and R that is explicitly part of the hedonic pairing model. (3)

For the qualification decision, individuals are assumed to choose their education level in order to maximize utility, which depends on the rate of return to education. To formalize this process, we adopt a random utility approach where an individual i obtains a level of education, [Q.sup.*.sub.i], if the utility from this choice exceeds that of its alternatives. The actual level of education for individual i, [Q.sup.*.sub.i], is unobserved and is modeled as a linear index function:

[Q.sup.*.sub.i] = [alpha]'[X.sub.i] + [[epsilon].sub.i] (1)

where [alpha]' is a vector of parameters associated with personal, family background, and labor market measures, [X.sub.i], that determine the rate of return to education and [[epsilon].sub.i] is a normally distributed error term that measures individual-specific random variation in the education level. In other words, Equation 1 indicates that workers choose [Q.sup.*.sub.i] based on the rate of return to education, which depends on factors such as personal ability and attitudes toward work, access to financial and human capital through family resources, and differences in the job mix and job market information of local labor markets.

The optimal education level in Equation 1 is continuous, but a qualification is obtained when a worker's education level meets or surpasses a discrete, externally verifiable threshold. For example, in England an individual must attend school from age 5 until age 16, at which point they can sit General Certificate of Secondary Education exams. However, a student who continues on to age 18 can take exams that, if passed, yield a superior secondary school qualification (i.e., "A" levels). At the same time, students who have one year of university have not crossed the threshold for a university degree, and thus their secondary school qualifications are their highest qualification (Jaeger and Page 1996).

Our qualification and requirement variables are measured in a five-unit ordinal range from 0 (no qualifications) to 4 (a higher education degree) using the Non-Vocational Qualifications (NVQ) scale. (4) Thus, following our subsequent empirical analysis, Equation 1 can be expressed as

[Q.sub.i] = 0 if [alpha]'[X.sub.i] + [[epsilon].sub.i] [less than or equal to] 0, (2.1)

[Q.sub.i] = 1 if [[mu].sub.1] [greater than or equal to] [alpha]'[X.sub.i] + [[epsilon].sub.i] > 0, (2.2)

[Q.sub.i] = 2 if [[mu].sub.2] [greater than or equal to] [alpha]'[X.sub.i] + [[epsilon].sub.i] > [[mu].sub.1], (2.3)

[Q.sub.i] = 3 if [[mu].sub.3] [greater than or equal to] [alpha]'[X.sub.i] + [[epsilon].sub.i] > [[mu].sub.2], (2.4)

[Q.sub.i] = 4 if [[mu].sub.4] [greater than or equal to] [alpha]'[X.sub.i] + [[epsilon].sub.i] > [[mu].sub.3], (2.5)

where [Q.sub.i] = 0 represents a worker with no qualifications (NVQ0) and so on. Equations 2.1 through 2.5 form the basis of an ordered-probit model of qualification choice for individual i. The term [Q.sub.i] is the qualification level that results from the latent, utility-maximizing education level. (4)

Likewise, we assume that a firm hires workers with a given education level in order to maximize profits, where the profit-maximizing education level for a worker in a given job ([R.sup.*.sub.k]) is unobserved and is expressed as a linear index function:

[R.sup.*.sub.k] = [beta]'[Z.sub.k] + [u.sub.k]. (3)

In Equation 3, [beta]' is a vector of coefficients for a set of firm, job, and labor market characteristics, [Z.sub.k], that affect the return to a given education level and [u.sub.k] is a normally distributed error term that measures firm-specific random variation in the return. In other words, firms' required qualifications, [R.sup.*.sub.k], depend on factors such as how firm and job attributes affect the net return to education and how labor market conditions affect the cost of changing educational requirements.

Although the education level is continuous, a qualification requirement is the smallest discrete qualification that is sufficient to properly perform the job. For example, a firm may require a university degree because a secondary school qualification does not provide the necessary skills to perform the job properly. On the other hand, while a university degree may be sufficient, one year of university may be what is necessary to properly perform the job. Thus, the stated educational qualification may exceed what is necessary to properly perform the job, particularly if on-the-job training can substitute for formal education.

Similar to the individual qualifications data, a five-point NVQ job requirement scale can be represented as an ordered-probit model using Equation 3:

[R.sub.k] = 0 if [beta]'[Z.sub.k] + [u.sub.1] [less than or equal to] 0, (4.1)

[R.sub.k] = 1 if [[mu].sub.1] [greater than or equal to] [beta]'[Z.sub.k] + [u.sub.k] > 0, (4.2)

[R.sub.k] = 2 if [[mu].sub.2] [greater than or equal to] [beta]'[Z.sub.k] + [u.sub.k] > [[mu].sub.1], (4.3)

[R.sub.k] = 3 if [[mu].sub.3] [greater than or equal to] [beta]'[Z.sub.k] + [u.sub.k] > [[mu].sub.2], (4.4)

[R.sub.k] = 4 if [[mu].sub.4] [greater than or equal to] [beta]'[Z.sub.k] + [u.sub.k] > [[mu].sub.3], (4.5)

where [R.sub.k] represents the discrete required qualification level necessary to properly perform the job, which must meet or exceed the latent, profit-maximizing education level, [R.sup.*.sub.k].

The Q-R Pairing Process

The error term in the individual's qualification equation, [[epsilon].sub.i], reflects worker skill heterogeneity for a given qualification level. Similarly, the error term in the firm's requirement equation, [u.sub.k], reflects job skill heterogeneity for a given requirement level. On average, we expect the error terms for Q and R to be positively correlated: A worker with unusually high unobserved qualifications (i.e., a high value for [[epsilon].sub.i]) is likely to pair up with a firm with unusually high unobserved requirements (i.e., a high value for [u.sub.k]). Our empirical model confirms this expectation by estimating Equations 2 and 4 simultaneously and taking explicit account of the correlation between the errors.

Our previous illustrations also suggest that the correlation provides some information regarding the pairing type. Specifically, workers may pair with a firm that has low initial job requirements but that provides training and/or a signal that permits a move up the job-skill hierarchy in a subsequent period. Thus, a worker with a low value for [[epsilon].sub.i] is likely to pair with a firm with a low value for [u.sub.k]. This correlation thus provides some information regarding the pairing type. The observed qualification of the worker is Q and the predicted qualification from the jointly estimated ordered probit model is [Q.sup.*]. The term [Q.sup.*] reflects the correlation of worker qualifications with the pairing firm's requirements. If a firm provides career mobility through training and signaling, then its low value for [u.sub.k] will lead to a predicted worker qualification level that is lower than the actual value: [Q.sup.*] < Q. Similarly, workers with unusually high skill levels have high values for [[epsilon].sub.i], and these high values lead to predicted firm requirement levels that are higher than the actual values: [R.sup.*] > R. The pairing types can be identified by the differences between Q and [Q.sup.*] and R and [R.sup.*] because these differences vary systematically across the pairing types.

Two examples help illustrate how this comparison of predicted and actual values permits us to identify pairing types. First, consider an overeducated pairing such as a university-educated detective who begins his career in a patrol officer job that requires a secondary school qualification while providing training for detective work. If the pairing is considered from the perspective of the worker's optimization problem, the observed qualification of a university degree is likely to be greater than would be predicted for a typical worker in a patrol officer's job. In other words, controlling for the type of job and firm, workers who find it utility maximizing to be in an overeducated-type pairing are more likely to place in a job such that the observed qualification exceeds the predicted qualification, Q > [Q.sup.*]. However, from the perspective of the firm's optimization problem, the observed requirement of a secondary school qualification for a patrol officer's job is likely to be less than would be predicted for a typical worker who has a university degree. Specifically, controlling for the type of worker, firms that find it profitable to be in an overeducated-type pairing are more likely to hire a worker such that the observed requirement is less than the predicted requirement, R < [R.sup.*].

For the second example, consider an undereducated pairing such as a patrol officer with a secondary school education who has been promoted into a detective job that typically requires a university degree. From the perspective of the worker's optimization problem, the observed secondary school qualification is likely to be less than would be predicted for a typical detective. In other words, controlling for the type of job and firm, workers who find it utility maximizing to be in an undereducated-type pairing are more likely to place in a job such that the observed qualifications are less than the predicted qualifications, Q < [Q.sup.*]. From the perspective of the firm's optimization problem, the observed requirement of a university degree is likely to exceed the predicted requirement for a typical detective. Specifically, controlling for the type of worker, firms that find it profitable to be in an undereducated-type pairing are more likely to hire a worker such that the observed requirements exceed the predicted requirements, R > [R.sup.*].

The overeducated- and undereducated-type pairings can be compared to one in which there is relatively little movement up the job hierarchy; that is, worker qualifications match the firm requirements throughout the life of the pairing. Specifically, controlling for the type of job, the observed qualification of a particular worker equals the predicted qualification of other workers in similar jobs such that Q = [Q.sup.*]. Likewise, controlling for the type of worker, the observed requirement for a particular job equals the predicted requirements of other workers who are similarly educated, R = [R.sup.*]. The exactly educated pairing forms the base case where Q = [Q.sup.*] and R = [R.sup.*], which compares to an overeducated-type of pairing where Q > [Q.sup.*] and R < [R.sup.*] and an undereducated-type of pairing where Q < [Q.sup.*] and R > [R.sup.*].

3. Analysis Using Cross-Sectional Data 

The Ordered Probit Specification

Our empirical model indicates that the pairing types can be identified in a cross section by comparing the predicted worker qualifications and firm requirements ([Q.sup.*] and [R.sup.*]) obtained by jointly estimating the ordered probit models in Equations 2 and 4 with their actual values (Q and R). The ordered probit model is estimated using the Social Change and Economic Life Initiative (SCELI) data set, which includes 6110 surveyed people from six different labor markets: Aberdeen, Coventry, Kirkcaldy, Northampton, Rochdale, and Swindon. SCELI is a stratified random sample of British working-age adults conducted in June and July 1986 that includes wage and salary workers, along with people who are self-employed, unemployed, or out of the labor force. The joint-ordered probit model for Q and R is estimated using the SCELI data, and the resulting coefficients (along with the observed attributes of the firm and the worker in these data) are used to predict [Q.sup.*] and [R.sup.*], which are conditional on the observed worker-firm pairing. The predicted and observed values of Q and R are then used to identify the pairing type in several training and promotion specifications to examine how the typical career path differs across the pairing types.

The SCELI data offer several advantages. Our model implies that workers need to be observed from the initial time of hire through subsequent promotions in order to detect the effects of overeducation and undereducation. A long, comprehensive panel would be ideal for testing the model, but existing U.S. panel data sets (e.g., PSID or National Longitudinal Survey of Youth) do not have the necessary length or pairing information to properly test our model. On the other hand, whereas the British education system offers the advantage of a clear classification of overeducation and undereducation, a disadvantage of UK data sources is that they typically include relatively few worker attributes. The SCELI data provide a cross section of workers at different stages in their careers and include uniquely detailed individual, job, and firm attributes that permit us to identify the pairing type. Moreover, these data also include backward-looking and forward-looking questions regarding opportunities for training and promotion that permit us to examine whether the typical career profile differs across the pairing types. Our analysis uses a subset of these data that includes 1556 observations for male wage and salary workers who report all relevant information. (5)

The values of Q and R were determined for employed SCELI respondents who were asked to indicate which qualifications (from a list of 20 qualification types) would now be necessary to obtain the job that they currently held and later on in the survey for their current qualifications (from the same list of 20 qualification types). Values for Q and R were determined by using the NVQ scale to map their responses into an ordinal scale running from 0 (no qualifications) through to 4 (a higher education degree). These categories are sufficiently narrow to ensure differences among the Q and R levels (i.e., 4 > 3 > 2 > 1 > 0) but are sufficiently broad to ensure that each category has a similar Q or R (e.g., nurses and teachers have a similar level of education, namely, NVQ4).

Our five-point, NVQ-based scale yields proportions of overeducated and undereducated workers (i.e., 26% and 21%) within the ranges found in prior work (see Sloane, Battu, and Seaman 1999). Nonetheless, asking employed respondents for the qualification requirements for their current job provides an opportunity to conceal a disappointing career by inflating the job requirement given to the interviewer. The effect of this would be to lower the reported incidence of overeducation in the data. However, in their meta-analysis of the overeducation literature, Groot and Massen van den Brink (2000) find little evidence of systematic self-reporting bias; specifically, the proportion of employees identified as overeducated in studies using a "subjective" measure of overeducation that compares self-reported qualification and requirement data (such as that presented here, as well as Duncan and Hoffman [1981] and Sicherman and Galor [1991]) is "similar" to those studies using an "objective" measure of overeducation based on job classification indices such as the Dictionary of Occupational Titles (e.g., Rumberger 1981, 1987; Sicherman and Galor 1990). Moreover, we find qualitatively equivalent promotion and training results when we use an alternative three-point scale that categorizes workers as low skill (no qualifications), medium skill (qualifications lower than "A" level), and high skill (qualifications at least as high as "A" level).

Following the empirical model, the ordered-probit specification for Q includes family attributes that measure access to financial and human capital. The specification for Q also includes attitudinal/first-job attributes that measure labor market commitment and opportunities. The ordered-probit specification for R includes measures of firm, job, and labor market attributes. For brevity, the means of the explanatory variables used to estimate the ordered-probit models for Q and R are included in Appendices A and B, respectively, with separate sets of mean data for each of the five levels of Q (Appendix A) and R (Appendix B) and for the observed pairing types Q > R, Q = R, and Q < R (both appendices). The maximum-likelihood estimates of the joint ordered-probit models for Q and R are presented in Table 1.

The statistically significant estimated correlation coefficient of 0.497 between the errors for Q and R supports the contention that Q and R are positively correlated and should be estimated simultaneously. However, the correlation coefficient is also significantly less than one, indicating that the pairing process on unobserved attributes is far from exact. The coefficients on the explanatory variables are generally significant and suggest that family background and labor market opportunities affect the choice of actual qualifications, whereas firm and job attributes affect required qualifications. However, we focus on the primary rationale for estimating the joint ordered-probit specification, that is, to predict [Q.sup.*] and [R.sup.*] conditional on the observed worker-firm pairing, which assist in identifying pairing types.

The cross-sectional tests of the model hinge on correctly predicting the pairing types of each worker. Table 2 presents a comparison between the predicted qualifications and requirements from the joint-ordered probit model, [Q.sup.*] and [R.sup.*], along with their observed values, Q and R. Predictions are listed separately for the overeducated (Q > R), exactly educated (Q = R), and undereducated (Q < R). The bold cells in Table 2 indicate that 74% of the 409 workers who are observed to be overeducated are predicted to have an overeducated type of pairing (i.e., Q > [Q.sup.*] or R < [R.sup.*]). Similarly, 81% of the 326 workers who are observed to be undereducated are predicted to have an undereducated type of pairing (i.e., Q < [Q.sup.*] or R > [R.sup.*]). Moreover, whereas nearly half (49%) of exactly educated workers place in the center cell ([Q.sup.*] = [R.sup.*]), 51% of workers are predicted to be in the surrounding cells that are not expected to have Q = R for each and every period they are paired with the firm. Thus, Table 2 broadly supports the hypothesis of pairing types that differ in regard to the relationship between the predicted versus actual qualifications and requirements.

The Estimated Pairing Types

To test the empirical model and its ability to identify pairing types, we utilize the longitudinal aspects of the SCELI data to examine whether workers who are in an overeducated or undereducated type of pairing have greater training and promotion opportunities than those who are exactly educated throughout their career. The pairing types are identified by binary variables that are used to focus on the broad ability of the joint ordered-probit model to identify the pairing type as opposed to continuous probability measures that rely more directly on the identification strategy and the precision of the estimates. The excluded pairing type is defined by those observations where the observed and predicted qualifications and requirements match (i.e., Q = R and [Q.sup.*] = [R.sup.*]); they have been exactly educated throughout their careers, and they are given the name MATCHMATCH.

Our empirical model predicts four additional pairing categories that correspond to binary variables for overeducated- and undereducated-type pairings:

* i. "OEOE" workers who are predicted to be in an overeducated-type pairing (i.e., [Q > [Q.sup.*] and R < [R.sup.*]] or [Q = [Q.sup.*] and R < [R.sup.*]] or [Q > [Q.sup.*] and R = [R.sup.*]]) and are observed to be overeducated presumably because they have yet to rise up the job hierarchy

* ii. "MATCHOE" workers who are predicted to be in an overeducated-type pairing (i.e., [Q > [Q.sup.*] and R < [R.sup.*]] or [Q = [Q.sup.*] and R < [R.sup.*]] or [Q > [Q.sup.*] and R = [R.sup.*]]) but are observed to be exactly educated presumably because they have risen up the job hierarchy and therefore appear matched on the basis of their current pairing

* iii. "MATCHUE" workers who are predicted to be in an undereducated-type pairing (i.e., [Q < [Q.sup.*] and R > [R.sup.*]] or [Q = [Q.sup.*] and R > [R.sup.*]] or [Q < [Q.sup.*] and R = [R.sup.*]]) but are observed to be exactly educated presumably because they have yet to rise up the job hierarchy and therefore appear matched on the basis of their current pairing

* iv. "UEUE" workers who are predicted to be in an undereducated-type pairing (i.e., [Q < [Q.sup.*] and R > [R.sup.*]] or [Q = [Q.sup.*] and R > [R.sup.*]] or [(2 < [Q.sup.*] and R = [R.sup.*]]) and are observed to be undereducated presumably because they have risen up the job hierarchy

Our analysis builds on the previous educational mismatch literature that has "merged" the excluded group MATCHMATCH with the MATCHOE and MATCHUE groups, that is, that combines those who are expected to have Q = R over the course of the pairing with those who, while observed to be matched, are truly in an overeducated or undereducated type of pairing.

The four binary variables mentioned previously plus the excluded group make up 1234 of the 1556 observations. Thus, beyond the categories predicted by our model, there are three additional dummy variables included in the training and promotion specifications that are not predicted by our model but that are observed in the data:

* i. "OEMATCH" workers who are predicted to be in a matched-type pairing (i.e., [[Q.sup.*] = [R.sup.*]]) but are observed to be overeducated (i.e., [Q > R])

* ii. "UEMATCH" workers who are predicted to be in a matched-type pairing (i.e., [[Q.sup.*] = [R.sup.*]]) but are observed to be undereducated (i.e., [Q < R])

* iii. "OEUE" workers for whom our model cannot account for their type of pairing (i.e., [Q< [Q.sup.*] and R < [R.sup.*]] or [Q > [Q.sup.*] and R > [R.sup.*]])

OEMATCH and UEMATCH make up 166 of the 322 remaining observations not directly predicted by our model (11% of our complete sample of 1556 workers). These 166 observations may be thought of as workers who "should" be matched but are currently not matched--a definition of overeducated and undereducated workers used in prior work. (6) The OEUE binary variable (10% of our complete sample) represents a pairing that is inconsistent with both our model and the traditional view of overeducation and undereducation and may be thought of as a general form of mismatch. (7)

The construction of the four binary variables that measure the overeducated- and undereducated-type pairings along with the three binary variables that measure some genuine form of mismatch is summarized in Table 3 and are used as explanatory variables in training, experience, and promotion regressions in comparison to the excluded MATCHMATCH pairing. If our model is correct, the training and promotion opportunities of workers predicted to be in overeducated- and undereducated-type pairings should be superior to those of the excluded group. Although it is not clear, a priori, how the groups that are "mismatched" will differ from the excluded group, the sign of their three binary variables may provide some insights into the overall worker-firm pairing process. (8)

Training

The first two columns of Table 4 include the results from two probit models that test whether the roles of on-the-job experience and training differ by pairing type as expected after controlling for standard employment variables. Specifically, the dependent variable in column 1 is a forward-looking, binary variable that equals one if the worker indicates that already working in the organization is an advantage when trying to secure a better job that becomes available in that organization, whereas the dependent variable in column 2 is a backward-looking, binary variable that equals one if the worker indicates that previously acquired similar experience is important for success in the current job. Although the results indicate that most of the explanatory variables are statistically significant in our models, the discussion focuses on our binary pairing variables for sake of brevity. The means of the dependent and independent variables in the SCELI data are provided in Appendix Table C.

In column 1 of Table 4, the coefficients on the first four binary variables for overeducated and undereducated pairing are positive, suggesting that having a prior relationship (and perhaps the associated two-way knowledge of worker attributes and firm characteristics) is important for subsequent success in these pairing types. But we find that for the overeducated-type workers, only the coefficient on the OEOE dummy is significant, suggesting that this knowledge that the firm has of the worker (and vice versa) early on in the pairing when the worker is initially overeducated affects their belief of subsequent promotion within the job. The insignificance of the coefficient on MATCHOE may indicate that such two-way knowledge may be less important when the overeducated worker has moved up the job hierarchy into an exactly educated pairing. The positive "insider" effect may be mitigated for MATCHOE workers if a promotion occurs for firm switchers who move up the job hierarchy by leaving their initial pairing firm for which they were overeducated; indeed, their new firms may indicate a lack of "insider effect" by promoting from without rather than within. Thus, following our illustration, the university degree holder is more likely to be hired initially as a detective if having first worked as a patrol officer. However, once promoted to detective, future experience does not necessarily facilitate further promotion at the current police station (although it might facilitate promotion at another police station). (9)

For undereducated-type pairings, only the coefficient on UEUE is significant. This result, which would not be present in a new worker-firm pairing, suggests that reputation within an undereducated-type pairing is essential for promotion. In fact, the positive but insignificant coefficient on MATCHUE could reflect the possibility that these workers are yet to personally experience the promotion benefits that insider status confers on those with good reputation within their current firm. Thus, again following our illustration, experience as a secondary school-educated patrol officer is not sufficient to be promoted to detective, but such experience is necessary for promotion. In fact, our findings that only UEMATCH is significant of the remaining three "mismatch" variables is broadly consistent with this contention. Specifically, the fact that UEMATCH workers who are observed to be undereducated but who are predicted to be matched might well be expected to occur in a firm where being an insider matters. In other words, the relative importance of such firm-specific connections explains the worker's above-expected career development.

The results in column 2 in Table 4 for the backward-looking variable measuring the importance of past experience in the current job also support the predictions of the model. In particular, the coefficients on OEOE and MATCHUE (i.e., the two states that are expected to occur early in a career path, prior to the movement up the job hierarchy) are both negative and significant. These results suggest that workers in these pairing types are at the start of a process of career development, such that their prior (prepairing) training and experience does not benefit them in their current position. However, the coefficients on MATCHOE and UEUE (i.e., the two states that are expected to occur later in a career, after the movement up the job hierarchy) are both positive (and significant in the case of MATCHOE). The significantly positive coefficient for MATCHOE supports the contention that overeducated pairings reward on-the-job experience, whereas the insignificance of UEUE in model 2 combined with the significance in model 1 suggest that promotions in undereducated jobs are not as closely tied to experience as they are with having inside knowledge of the firm. Thus, in our illustration, a secondary school-educated patrol officer is promoted to detective based less on experience and more on insider reputation. It follows that experience and training play a different role in the overeducated versus the undereducated pairings types.

The three binary variables measuring general "mismatch" are also significant in model 2. Specifically, the OEMATCH dummy (representing workers doing less well than our model predicts) is, not surprisingly, negative and significant: Any relevant experience they may have is not benefiting them in their current position. This finding, combined with the prior result that they are unlikely to receive benefits from being an insider in their current firm, suggests that their current job is unlikely to be part of any career development path (i.e., a case of genuine and unfortunate mismatch). On the other hand, the MATCHUE dummy (representing workers doing better than our model predicts) is positive and significant (at the 10% level), providing suggestive evidence of unusually high returns to previous on-the-job training. This finding, combined with the earlier result that these workers benefit from an insider effect, suggests that these workers (who would otherwise be in a matched state) have benefited from working in a firm where training and promotion opportunities are superior to those expected of their career development state (a case of genuine and fortunate mismatch). Thus, there are plausible explanations for both OEMATCH and MATCHUE.

Finally, the positive and significant coefficient on OEUE suggests that workers who our model suggests are "generally mismatched" believe that their experience on the job improves their subsequent opportunities for success more than those workers who are observed and predicted to be matched. Although our model cannot explain this expectation, the finding does suggest that prior work that emphasized the inefficiency of apparent labor market mismatch may not have taken full account of nonwage benefits arising in current mismatched pairings that could manifest themselves in better subsequent opportunities.

Promotion

Columns 3 and 4 of Table 4 include the results from forward-looking and backward-looking discrete choice models of promotion, where the explanatory variables are the same as those included in the training models in Table 4. Again, for brevity, the focus of the discussion is on the binary match variables. The dependent variable for the specification in the first promotion model is a forward-looking binary variable that equals one if the worker reports that he has a good chance of promotion in the next two years. The coefficient OEOE is positive and significant, which is consistent with the expectation that overeducation occurs early in a career and prior to a movement up the job hierarchy. However, MATCHOE is also positive and significant, suggesting that workers who start in an overeducated type of pairing have an ongoing expectation of a series of career progressions. Thus, following our illustration, the university-educated police officer expects a promotion to detective and possibly subsequent promotions within the police force with experience.

On the other hand, the coefficients on MATCHUE and UEUE are both insignificant. The lack of a positive, significant coefficient on MATCHUE may reflect the fact that promotion for undereducated-type workers (whose promotion may require the acquisition of on-the-job experience to substitute for their lack of formal education) takes longer than for an overeducated-type worker who already has the formal education. Likewise, the positive but insignificant coefficient on UEUE supports the notion that any ongoing career progression for undereducated-type jobs will be more gradual than for overeducated-type jobs. Thus, unlike for a university-educated patrol officer, a secondary school-educated patrol officer may have to spend many more years on the job to be promoted up the job hierarchy to detective, inspector, and so on.

The three pairing types representing general mismatch are all positive, but only the coefficient on OEUE (that is not accounted for by our model) is significant. Consistent with our findings for experience, it suggests that apparent educational mismatch between workers and firms may yield other unobserved benefits for the worker and firm that are reflected in the lower current wages observed in prior work but are reflected here by expectations of a greater return to experience and subsequent promotion. (10)

Column 4 of Table 4 presents the results of an ordered discrete choice model with a dependent variable that takes on a value of -1, 0, or 1, depending on whether the current job is, respectively, in a lower job segment, similar job segment, or higher job segment than the worker's first job. (11) Thus, the dependent variable is a backward-looking assessment of the discrete movements within the job hierarchy. The coefficient for the OEOE dummy is small and insignificant, whereas the dummy for MATCHUE is negative and significant, suggesting that undereducated types of workers tend to be in lower socioeconomic job segments than comparable exactly educated workers early in their career. However, the coefficients on the MATCHOE and UEUE dummies are both positive and significant, suggesting that overeducated and undereducated types of workers do move up the socioeconomic hierarchy relative to comparable exactly educated workers. Overall, the results support the conclusions of our model that overeducated and undereducated workers have steeper promotion profiles than their exactly educated counterparts.

The coefficients on the second set of variables measuring mismatched pairings for the backward-looking promotion model in column 4 in Table 4 confirm our prior career development findings. Specifically, the negative and significant coefficient for the underperforming OEMATCH workers does indeed indicate underperformance in their careers to date, while the positive and significant coefficient for the overperforming UEMATCH workers suggests that they have indeed experienced a progression our model did not predict for them. Interestingly, the results from column 3 suggest that the OEMATCH workers are not confident that they can reverse their career setback, while the UEMATCH workers are not confident that they can extend their career advantage. In this sense, OEMATCH and UEMATCH may represent true mismatch categories, where workers end up mismatched because of the vagaries of working life rather than by following a regular career development path. On the other hand, the coefficient on the OEUE mismatch category is positive but insignificant. Thus, OEUE workers have not experienced a significantly greater movement up the job hierarchy to date than exactly matched workers, even though these OEUE-pairing-type workers have greater current expectations of promotion in the near future.

Overall, overeducated and undereducated pairing types are not mismatched in the sense that only these pairing types have forward-looking expectations regarding their careers that are realized ex post when they look backward over their career. The general pattern emerging from the promotion results in Table 4 suggest that overeducated-type workers experience a more immediate career advancement than is the case for undereducated-type workers; one explanation for this might be that the type of career advancement seen by undereducated-type workers is more likely to be gradual and within their job segment, while for overeducated-type workers their career advancement is more rapid and likely to involve movement between job segments.

4. Analysis Using Panel Data

The Data

The identification of the pairing types depends crucially on the exclusion restrictions. For example, omitting the current job measures from the requirement model (which might be argued to be endogenous) reduces both the predictive power of the model with regard to the pairing types and the significance level of these pairing types in the subsequent training and promotion models (not presented). Thus, to ensure that our training and promotion findings are robust across samples and not directly attributable to an invalid cross-sectional identification strategy, we conducted an analysis that makes use of panel data from a stratified random sample of the British population. The panel nature of these data permits direct observation of overeducated and undereducated pairing types and the training and promotion opportunities of workers over their career. Specifically, comparable to our analysis using the SCELI data set, we use a sample of male wage and salary workers drawn from 12 waves of the BHPS over the period from September 1991 to September 2002, which includes 1540 respondents who reported all the relevant information necessary to estimate the promotion and training equations. These panel data offer an additional advantage by also permitting us to directly examine the predictions that overeducated and undereducated pairing types have greater wage growth than other workers, which could not be observed in a cross section. The wage analysis is conducted for 1273 of the original 1540 observations that include earnings information. (12)

The BHPS is the longest and most detailed British panel data set available (12 waves were available for our use), but it does not contain a required education measure. However, both the SCELI and the BHPS data sets contain the detailed Hope-Goldthorpe job-level variable (for the current job in the case of the SCELI data set and each job in the case of the BHPS data set), which enables us to impute a separate required education value for each of the jobs held by the BHPS respondents during the panel period. Specifically, each job in the BHPS data was assigned the required education value that was the most common among the SCELI respondents reporting the same Hope-Goldthorpe value. (13) Naturally, as the BHPS respondents changed jobs during the period of the panel, their Hope-Goldthorpe value and associated required education value were subject to change. Thus, the career development status for each worker was calculated for each job held using the imputed values for required education and the observed values of actual education already present in the BHPS.

The BHPS data, while not containing the rich array of variables used in the SCELI-based analysis that permitted us to empirically distinguish among the various pairing types, allow us to directly identify individuals who were overeducated at some point during the first three waves of the panel (ceteris paribus, earlier on in their careers) and individuals who were undereducated at some point during the last three waves of the panel (ceteris paribus, later on in their careers). (14) The joint ordered-probit analysis suggests that, while some workers may genuinely be mismatched, the majority of workers who are observed to be overeducated (74%) and undereducated (81%) fall into the OEOE and UEUE categories. Thus, we define two binary variables that equal one if a worker is observed to be (i) overeducated early in the panel (OVEREDUCATED) or (ii) undereducated later in the panel (UNDEREDUCATED). (15) These pairing types are compared to an excluded group of workers who are not in an overeducated or undereducated pairing type. The pairing-type variables, to the extent they are mismeasured, would be expected to have coefficients attenuated toward zero in the promotion, training, and wage growth models. Moreover, the BHPS does not permit a clear distinction of within- and between-firm job changes, which our model suggests may be driven by different forces and further work against finding significant differences between the pairing types.

In addition to the pairing-type variables, the empirical models include largely the same variables used in the SCELI analysis, which are the standard set of controls used in wage and employment models. The dependent variables include two training measures, one promotion measure, and a wage growth measure calculated over the 12 years of the BHPS. Descriptive statistics for the explanatory variables used in the promotion, training, and wage regressions for all workers and disaggregated by match type are found in Appendix D. Our subsequent analyses of training, promotion, and wages show that these workers exhibit the career development path expected for these pairing types.

Training, Promotion, and Wage Growth Results

Table 5 presents the BHPS results for the two training and one promotion models. Specifically, the dependent variables in columns 1 and 2, respectively, are binary variables that equal one if the worker indicates that, in the first half of the BHPS panel, they had some form of training or training aimed at a future job. The promotion variable in column 3 equals one if the last job in the second half of the panel is in a higher job segment than the first job in the first half of the panel. It is important to emphasize that we exploit the panel nature of the BHPS to track a single observation of workers' career paths (i.e., training early in a career, promotion later in a career, and wage growth and pairing type over a career). In other words, since the career path is the unit of observation for both the dependent variables and the pairing type that occurs over the full length of the 12-year panel, we cannot conduct a panel analysis. Thus, even though the pairing types might well reflect unobserved heterogeneity in worker and firm attributes that could explain the observed pairing, we are restricted to a cross-sectional analysis. In any case, the coefficients on most of the explanatory variables are significant at traditional levels and are qualitatively similar to those found using the SCELI data. Thus, the discussion once again focuses on the pairing-type variables, OVEREDUCATED and UNDEREDUCATED.

The results using the BHPS data in columns 1 and 2 of Table 5 support the findings using the SCELI data. The results indicate that overeducated-type workers are more likely to receive some form of training compared to otherwise similar matched workers (column 1) and that this training is in preparation for future jobs (column 2). This finding supports our claim that identifying the overeducated on the basis of their circumstances in the first three waves of the BHPS panel is indeed picking up those workers who are acquiring skills that are preparing them for future, higher-level jobs. On the other hand, the coefficient on UNDEREDUCATED is positive but insignificant at traditional levels in both training models. Thus, relatively greater training as preparation for future jobs appears to occur solely in overeducated-type pairings.

In addition, the BHPS promotion results in column 3 of Table 5 strongly support the SCELI-based results presented in Table 4; the BHPS results include a binary dependent variable that equals one if the last job in the second half of the panel is in a higher job segment than the first job in the first half of the panel. In line with the predictions of our model, these results show that workers in either an overeducated-type position early in the panel or an undereducated-type position late in the panel have moved to a higher-ranked job over the course of the panel. It follows that through training in the case of overeducated workers and through (insider) on-the-job experience in the case of undereducated workers, the overeducated and undereducated pairing types appear to be more likely to move up the job hierarchy than workers matched in alternative pairing types.

The training and promotion results collectively support the contention that workers in an overeducated- and undereducated-type pairing ascend up the job hierarchy differently than those workers who are exactly educated throughout a career, which may also be expected to yield a different wage profile across these pairing types. Specifically, the first two columns of Table 6 examine this differential wage profile expectation by estimating regressions for the percentage change in wages over the first six years and second six years of the BHPS panel, where the explanatory variables are the same as those in the training and promotion models. (16) Both of the coefficients on the binary variables for overeducated and undereducated pairings are positive in the wage equations, consistent with expectations. However, the binary pairing variable is significant at traditional levels only in the case of the undereducated workers, indicating approximately 7% higher wage growth in both the first and the second six-year interval. Thus, undereducated-type workers, through on-the-job training and experience, appear to reveal a productivity level that is relatively higher than comparable exactly educated workers, which results in higher real wage growth and in their eventual placement in a job for which they are "technically unqualified." Illustratively, then, the secondary school-educated patrol officer who ultimately moves into an undereducated pairing reveals skills on the job that are generally not possessed by other secondary school-educated police officers and permit them to be promoted to the ranks of detective.

On the other hand, workers in an overeducated type of pairing do not experience greater wage growth than exactly educated workers. Following our illustration, this result could suggest that the university educated earn a similar average wage growth over a career whether they accept an overeducated type of pairing such as offered in the police force or an exactly educated type of pairing that requires their university degree (e.g., management training job). In fact, our training and promotion results suggest that, unlike undereducated workers, overeducated workers appear to expect a movement up the job hierarchy to occur over a relatively short time horizon such that a small difference in wage growth may be sufficient to compensate an overeducated worker for his or her short stay in the overeducated state.

Nonetheless, our model predicts a different source for the wage growth reflecting that overeducated workers initially trade off a lower return to education for a later return to promotion. Thus, the third specification in Table 6 examines whether the post- versus prepromotion wage growth (as approximated by the differential wage growth in the second vs. the first six-year interval) can be attributed to the trade-off of a lower initial return for education for overeducated workers (as measured by the coefficient on an interaction between the binary variable for overeducation and years of education) and a positive return for accepting an overeducated pairing (as measured by the coefficient on the binary variable for overeducation). Consistent with expectations, the results in column 3 of Table 6 confirm that overeducated workers experience greater growth in wages later in a career in exchange for a lower up-front rate of return to education. A similar specification estimated for undereducated workers yields insignificant coefficients on both the binary variable for undereducation and its interaction with years of education (not presented). Thus, collectively, the training, promotion, and wage results suggest that overeducation is more clearly a hedonic pairing process on worker and firm attributes, whereas undereducation appears more directly related to unobserved heterogeneity in worker productivity.

5. Concluding Remarks

Prior evidence from North America, Europe, and Asia indicates that the educational qualifications of up to a third of the world's workforce either exceed or fall short of the employer-specified education requirements for the job. Our paper provides the first holistic empirical examination of the matching process that shows how workers and firms can benefit from both an overeducated- or an undereducated-type pairing where worker qualifications do not always equal firm requirements. Importantly, the paper demonstrates that, although workers and firms may not always be appropriately paired, the degree of educational mismatch in the labor market is likely to be smaller than the 30% to 40% of workers who are overeducated or undereducated at any point in time in the labor market.

In addition, our hedonic pairing model shows that any comparisons in prior work between overeducated or undereducated workers and exactly educated workers using a cross section or short panel data set are likely to be misleading. Specifically, the overeducated are predicted to begin in low-paying, entry-level jobs early in their career that train them for higher-paying future positions that require their educational background, whereas the undereducated start in low-paying, exactly educated jobs that, in time, can provide the training and signal that the worker has the necessary skills for promotion into a job that might otherwise require more education. Our results support the hypothesis that most worker-firm pairings are likely to have worker qualifications that match firm requirements during some portion of their career such that the "pairing type" (i.e., overeducated, undereducated, or exactly educated) cannot be directly observed. Nonetheless, our empirical model demonstrates how the educational pairing type can be imputed using joint-ordered probit estimates of the differences between predicted and observed qualifications of the worker and predicted and observed requirements of the firm.

The empirical analysis uses two data sets that collectively provide evidence supporting the empirical model. First, uniquely detailed data for British working-age males contained in the SCELI data set are used to estimate the hedonic pairing model that identifies the overeducated, undereducated, and exactly educated pairing type. The SCELI data set also provides forward-looking and backward-looking data that allow us to show that on-the-job training and promotion opportunities are better for workers who are identified in overeducated/ undereducated versus an exactly educated type of pairing.

Second, the BHPS data set allows us to use an extended panel to demonstrate not only that the overeducated see greater training in general but also that for them (and, to a lesser extent, the undereducated) this difference is evident when the focus is on the all-important training for future jobs. The BHPS analysis also finds that these training opportunities result in clear and measurable promotions for workers in both overeducated- and undereducated-type pairings. The panel data also permit us to show that these superior training and promotion opportunities for overeducated- and undereducated-type workers yield differential wage growth over a career. In particular, relative to workers who are continuously exactly educated, overeducated workers experience greater wage growth later in a career in exchange for a lower return to education, whereas undereducated workers experience higher wage growth throughout a career reflecting the on-the-job revelation of higher-than-expected productivity for a given education level.

Overall, this study provides the first formal evidence that both overeducation and undereducation may occur in labor market equilibrium and that tests of this hypothesis should be conducted over the life of the worker--firm pairing. Moreover, undereducated- and overeducated-type employment relationships are shown to yield benefits over the course of the pairing that are often inconsistent with inefficient labor market mismatch. Thus, policymakers should not be too quick to proscribe labor market fixes that seek to ensure that worker qualifications always match firm requirements.

Appendix A
Variable Means for Qualifications (SCELI) (a)

                            Q = 0    Q = 1    Q = 2    Q = 3
                             (398     (147     (502     (156
Variables                   obs.)    obs.)    obs.)    obs.)

Family background
  Mother out of work
    when while in
    school and
    living at home (=1)     0.445    0.333    0.305    0.263
  Mother white collar
    when while in
    school and
    living at home (=1)     0.003    0.027    0.008    0.032
  Mother self-employed
    when while in
    school and
    living at home (=1)     0.010    0.014    0.006    0.026
  Father out of work
    when while in
    school and
    living at home (=1)     0.136    0.156    0.090    0.103
  Father white collar
    when while in
    school and
    living at home (=1)     0.028    0.082    0.088    0.128
  Father self-employed
    when while in
    school and
    living at home (=1)     0.078    0.068    0.076    0.109
Worker attitudes
  Current age              41.048   36.129   36.084   33.135
  Person was married
    at age 20 or
    earlier (=1)            0.158    0.122    0.137    0.096
  Person had kids
    at age 20 or
    earlier (=1)            0.013    0.014    0.004    0
  Person expects
    to work during
    his working
    life (=1)               0.093    0.095    0.072    0.071
  Person would work
    even if he
    became rich (=1)        0.595    0.633    0.649    0.686
  Person believes
    men should be
    the primary
    income earner (=1)      0.123    0.156    0.225    0.276
  Person believes
    a husband's
    job should come
    first (=1)              0.168    0.238    0.219    0.269
Labor market attributes
  Person works in
    a public
    sector job (=1)         0.118    0.197    0.187    0.301
  Person works
    35-40 hours
    a week (=1)             0.420    0.537    0.468    0.545
  Person works
    more than 40
    hours a week (=1)       0.538    0.429    0.488    0.353
  Person has
    supervisory
    responsibilities
    (= 1)                   0.010    0.014    0.030    0.051
  Person's coworkers
    are primarily
    men (=1)                0.751    0.680    0.769    0.622
  Firm generally
    has good
    promotion
    prospects
    (=1)                    0.377    0.469    0.482    0.571
  Person born in
    central England (=1)    0.317    0.224    0.297    0.263
  Person born in
    northern England (=1)   0.168    0.116    0.219    0.135
  Person born in
    urban Scotland (=1)     0.291    0.456    0.283    0.417
  Person born in
    rural Scotland (= 1)    0.005    0.007    0        0.006
  Person born in
    other countries (=1)    0.030    0.014    0.016    0.019

                            Q = 4    Q > R    Q = R    Q < R
                             (353     (409     (821     (326
Variables                   obs.)    obs.)    obs.)    obs.)

Family background
  Mother out of work
    when while in
    school and
    living at home (=1)     0.269    0.286    0.342    0.359
  Mother white collar
    when while in
    school and
    living at home (=1)     0.014    0.022    0.007    0.012
  Mother self-employed
    when while in
    school and
    living at home (=1)     0.008    0.012    0.011    0.006
  Father out of work
    when while in
    school and
    living at home (=1)     0.068    0.115    0.106    0.086
  Father white collar
    when while in
    school and
    living at home (=1)     0.238    0.105    0.124    0.080
  Father self-employed
    when while in
    school and
    living at home (=1)     0.116    0.088    0.096    0.067
Worker attitudes
  Current age              36.776   33.971   37.503   40.580
  Person was married
    at age 20 or
    earlier (=1)            0.042    0.110    0.112    0.132
  Person had kids
    at age 20 or
    earlier (=1)            0        0        0.006    0.012
  Person expects
    to work during
    his working
    life (=1)               0.031    0.073    0.069    0.067
  Person would work
    even if he
    became rich (=1)        0.734    0.645    0.680    0.613
  Person believes
    men should be
    the primary
    income earner (=1)      0.303    0.245    0.205    0.206
  Person believes
    a husband's
    job should come
    first (=1)              0.314    0.215    0.252    0.215
Labor market attributes
  Person works in
    a public
    sector job (=1)         0.363    0.218    0.233    0.199
  Person works
    35-40 hours
    a week (=1)             0.484    0.528    0.476    0.399
  Person works
    more than 40
    hours a week (=1)       0.385    0.411    0.443    0.555
  Person has
    supervisory
    responsibilities
    (= 1)                   0.119    0.027    0.065    0.021
  Person's coworkers
    are primarily
    men (=1)                0.598    0.707    0.688    0.733
  Firm generally
    has good
    promotion
    prospects
    (=1)                    0.657    0.460    0.516    0.521
  Person born in
    central England (=1)    0.215    0.225    0.278    0.322
  Person born in
    northern England (=1)   0.210    0.174    0.205    0.153
  Person born in
    urban Scotland (=1)     0.252    0.357    0.291    0.288
  Person born in
    rural Scotland (= 1)    0.023    0.015    0.005    0.006
  Person born in
    other countries (=1)    0.037    0.017    0.028    0.025

(a) The family background variables are all binary variables that
equal one if the variable description was true for the individual
when he lived at home. Worker attitudes include a continuous
explanatory variable "age" and several binary variables that equal
one if the variable description regarding attitudes toward work
apply. The labor market attributes are comprised of binary variables
that measure the individual work experience that are correlated
with overall labor market opportunities and regional dummies that
equal one for region of employment that permit labor market
opportunities to differ by region.

Appendix B
Variable Means for Requirements (SCELI) (a)

                           R = 0     R = 1     R = 2     R = 3
                            (503      (169      (378      (126
Variables                  obs.)     obs.)     obs.)     obs.)

Firm attributes
  Current firm has
    more than 500
    employees (=1)         0.239     0.290     0.254     0.349
  Insider is important
    for success
    in current
    firm (=1)              0.755     0.817     0.775     0.770
  Current firm
    is unionized (=1)      0.551     0.538     0.492     0.627

Job attributes

  Current job is
    a professional
    job (=1)               0.083     0.142     0.127     0.310
  Current job is
    nonmanual
    job (=1)               0.127     0.172     0.204     0.437
  Current job is
    a skilled
    manual
    job (=1)               0.338     0.444     0.550     0.206
  Requirements
    necessary to
    perform the
    job (=1)               0         0.704     0.749     0.698
  Months on the
    job before
    worker is
    proficient             0.668     1.243     1.754     1.594
  Years of
    training
    prior to the
    current job            0.199     0.654     0.797     0.988
  Promotion
    prospects
    are good
    for current
    job (=1)               0.469     0.633     0.630     0.730
  Worker supervision
    effects work
    effort (=1)            0.235     0.272     0.323     0.294
  Current job has
    been reorganized
    in last
    five years (=1)        0.364     0.432     0.429     0.524
  Current job is
    part time (=1)         0.022     0.024     0.013     0.016
Log of hours worked
  during typical
  workweek                 3.664     3.694     3.675     3.624
Labor market attributes
  Unemployment
    rate for city
    where worker
    lives and works       13.580    12.399    13.373    13.559

                           R = 4     Q > R     Q = R     Q < R
                            (380      (409      (821      (326
Variables                  obs.)     obs.)     obs.)     obs.)

Firm attributes
  Current firm has
    more than 500
    employees (=1)         0.329     0.222     0.275     0.359
  Insider is important
    for success
    in current
    firm (=1)              0.818     0.770     0.786     0.794
  Current firm
    is unionized (=1)      0.476     0.496     0.536     0.525

Job attributes

  Current job is
    a professional
    job (=1)               0.516     0.154     0.238     0.279
  Current job is
    nonmanual
    job (=1)               0.395     0.225     0.258     0.218
  Current job is
    a skilled
    manual
    job (=1)               0.084     0.289     0.320     0.399
  Requirements
    necessary to
    perform the
    job (=1)               0.776     0.284     0.560     0.641
  Months on the
    job before
    worker is
    proficient             1.740     1.061     1.377     1.555
  Years of
    training
    prior to the
    current job            1.040     0.587     0.670     0.742
  Promotion
    prospects
    are good
    for current
    job (=1)               0.787     0.597     0.622     0.666
  Worker supervision
    effects work
    effort (=1)            0.263     0.271     0.273     0.270
  Current job has
    been reorganized
    in last
    five years (=1)        0.518     0.411     0.419     0.518
  Current job is
    part time (=1)         0.016     0.020     0.016     0.021
Log of hours worked
  during typical
  workweek                 3.638     3.675     3.649     3.671
Labor market attributes
  Unemployment
    rate for city
    where worker
    lives and works       12.761    12.856    13.335    13.291

(a) Firm attributes are all measured by binary variables that
equal one if firm has the described attribute. Job attributes
are measured by several continuous variables including time to
proficiency, years of training, the log of hours worked, and
binary variables that equal one if job has the described attribute.
Labor market attributes are measured by the unemployment rate in
the city where the worker lives and works.

Appendix C
Variable Means for Career Development States (SCELI) (a)

                       All
                      Cases     OEOE    MATCHOE   MATCHUE    UEUE
                      (1556     (304     (127      (133      (265
Variable              obs.)    obs.)     obs.)     obs.)    obs.)

Being an insider
  is useful for
  getting promotion
  in your
  current firm         0.401    0.434     0.417     0.398    0.430
Previous similar
  experience is
  useful for
  success in the
  current job          0.668    0.602     0.795     0.496    0.732
Very or quite
  good chance of
  a better job
  in the next two
  years                0.430    0.510     0.512     0.383    0.374
Job-level changes
  over the
  career to date       0.308    0.300     0.669    -0.031    0.456
Years of education    11.198   11.214    11.480    10.917   10.498
Total experience      14.934   13.868    16.522    10.634   17.404
Employees >500         0.279    0.224     0.339     0.218    0.347
Trade union member     0.523    0.474     0.472     0.519    0.509
Unemployment rate     13.200   12.637    12.870    13.928   13.268
Married                0.702    0.628     0.780     0.526    0.800
No. of dependent
  children             0.790    0.694     0.882     0.707    0.794
First job was
  professional         0.224    0.201     0.449     0.045    0.253

(a) The variable OEOE (MATCHUE) is a binary variable
that equals one if a worker who is predicted to be
in an overeducated-type (OE) match is observed to
have qualifications that exceed (equal) requirements.
The variable UEUE (MATCHUE) is a binary variable that
equals one if a worker who is predicted to be in
an undereducated-type (UE) match is observed to have
qualifications that fall short of (equal) requirements.

Appendix D
Variable Means for Different Match States (BHPS) (a)

                              All       Over      Under
                             Cases    educated   educated
                             (1540     (289       (424
Variable                     obs.)     obs.)      obs.)

Receiving training
  of any form                 0.719      0.796      0.733
Receiving training
  for future jobs             0.518      0.602      0.533
Is the final job in the
  panel a higher level job
  than the first job?         0.186      0.315      0.267
Years of education           17.058     17.934     16.401
Years of experience           5.992      4.899      6.211
Employees >500                0.145      0.208      0.134
Trade union member            0.825      0.778      0.816
Unemployment rate             8.907      9.023      8.918
Married                       0.651      0.550      0.665
No. of dependent children     0.400      0.353      0.394
Current job professional      0.502      0.502      0.488
Current job nonmanual         0.264      0.308      0.304
Current job manual            0.581      0.682      0.608

(a) The variable OEOE is a binary variable that equals one
if a worker is observed to be overeducated at any point during
the first three waves of the panel. The variable UEUE is a
binary variable that equals one if a worker is observed to be
undereducated at any point during the last three waves of the
panel. For each of the three current job type variables (and
the fourth, omitted variable, namely, an unskilled job), a
value of one is given where the worker has a job of that
type during any one or more of the first six waves of the
panel; therefore, given that a worker can be in a professional
job in one of those six waves and in a nonmanual job in another
of those six waves, the proportions of these variables
add to more than one.

The authors wish to thank Nachum Sicherman, the two anonymous referees, and the editor, Julie Hotchkiss, for their comments, which greatly improved this manuscript. The authors take responsibility for all remaining errors.

Received April 2004; accepted May 2006.

References

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(1) It is important to note, however, that jobs that offer a potential promotion return would be more desirable than those that do not, all else being equal. Thus, from a market perspective, overeducated and undereducated jobs may have to pay less early on in a career to ensure that jobs that require "similarly educated" workers have the same life cycle earnings, which would reinforce their steeper wage profile.

(2) Bauer (2002) uses a large German panel data set to show that the difference in the returns to over- and undereducation disappears after controlling for differences in unobserved heterogeneity, which suggests that wages may reflect characteristics of the match that are known to workers and firms but not generally observed by the econometrician. Likewise, Robst (1995) shows that the likelihood of being overeducated declines with a measure of college quality, which again suggests wage heterogeneity in the pairing type.

(3) The assumed independence between Q and R may not be valid. For example, a police department might be more apt to promote a secondary school--educated police officer if they are unable to hire a university-educated officer. Nonetheless, an undereducated pairing resulting from this process does not yield empirical predictions consistent with our findings in regard to training, promotion, and wages.

(4) The NVQ scale is actually a six-point scale: (0) no qualifications; (1) the lowest school qualifications (typically taken at the age of 16) and lower-level postschool training schemes such as the Youth Training Scheme; (2) better passes at the school exams typically taken at the age of 16, modest performance in the school exams typically taken at the ages of 17 or 18, and standard postschool trade apprenticeships; (3) superior performance at the school exams typically taken at the age of 18 (often the basis for university entrance) as well as the lower-level further education qualifications; (4) most university degrees as well as the higher-level further education qualifications; and (5) higher degrees such as MSc and PhD degrees. However, a five-point scale is used because our cross-sectional data do not distinguish between first degrees (NVQ4) and higher degrees (NVQ5).

(5) From a starting sample of 6110 observations in SCELI, 3414 women are excluded to make our analysis comparable to prior work and to abstract from issues of career interruption and labor market intermittency (e.g., Verdugo and Verdugo 1989; Sicherman and Galor 1991; Cohn and Khan 1995). In addition, 1003 males who are not employed and 137 males who have missing data are dropped, yielding a sample of 1556 observations.

(6) Duncan and Hoffman (1981) describe overeducation and undereducation arising from the temporary nonrealization of the plans of firms and workers, where the duration of such "mismatch" depends on the lag in the adjustment process; empirically, however, they aggregate together several of the pairing types that we keep distinct in this paper.

(7) Beyond the pairing types identified by the default category and the seven binary variables, there are two pairings that are not observed in the data but that could conceivably occur, specifically, workers who are predicted to be in an overeducated-type pairing (i.e., [Q > [Q.sup.*] and R < [R.sup.*]] or [Q = [Q.sup.*] and R < [R.sup.*]] or [Q > [Q.sup.*] and R = [R.sup.*]]) but are observed to be undereducated and workers who are predicted to be in an undereducated-type pairing (i.e., [Q < [Q.sup.*] and R > [R.sup.*]] or [Q = [Q.sup.*] and R > [R.sup.*]] or [Q < [Q.sup.*] and R = [R.sup.*]]) but are observed to be overeducated. The fact that these two potential but extreme pairings are not observed adds further support to our empirical model of the hedonic pairing process.

(8) Job attributes that measure labor market conditions (e.g., a public sector job) in the Q equation and job status variables (e.g., professional or skilled manual) that measure job attributes in the R equation improve the predictive power for [Q.sup.*] and [R.sup.*] but may also be endogenous. Specifically, of the 1556 workers in our sample, 1184 (76%) of them remain in the same predicted pairing type when we move from a joint-ordered probit model not containing these labor market and job attribute variables to one containing these variables. While this high correlation suggests that these labor market and job attributes variables are not critical for identifying the pairing types, 127 of the 372 workers who change their pairing type when including these variables move out of the "problematic" OEUE category, that is, the one observed category not predicted by either our hedonic pairing model or the standard mismatch hypothesis. Given the potential sensitivity of the pairing type to issues of identification using cross-sectional data, we subsequently examine the sensitivity of promotion and training results using panel data that permit direct observation of overeducation and undereducation over a career.

(9) It is possible that overeducated workers seek to justify their present "unfortunate" employment circumstances by self justifying their position. Self-justification bias would provide an alternative explanation for the positive coefficient on OEOE workers (who have yet to receive the "insider-aided" promotion) and the insignificant coefficient on MATCHOE (who have presumably received their "insider-aided" promotion). However, the self-justification rationale is mitigated in SCELI because the insider survey question occurs before the worker's overeducation status has been established.

(10) Overeducation may well be considered a temporary phenomenon that is eliminated by subsequent within-firm or between-firm promotions. However, Dolton and Vignoles (1997) find that around one-quarter of sampled graduates are unable to obtain employment in graduate-type jobs within 80 months of graduation; likewise, Battu, Belfield, and Sloane (1999) find that a significant proportion of graduates never permanently escape overeducation. Furthermore, Chevalier (2003) argues that the expansion in universities during the past 20 years has led to a more heterogeneous graduate skill distribution, which has resulted in an increase in the number of insufficiently skilled graduates that are technically overeducated with the associated earnings penalty. In a wider context, Sloane, Battu, and Seaman (1999) find that, compared to the default "matched" respondents, overeducated respondents tend to spend a shorter time in each of their previous jobs (although these promotions are found to reduce rather than eliminate their overeducation status).

(11) There are a total of eight job segment--from highest to lowest they are management (1), professional (2), intermediate nonmanual (3), junior nonmanual (4), foreman/supervisor (5), skilled manual (6), semiskilled manual (7), and unskilled (8); although the bottom of the nonmanual scale may overlap with the top of the manual scale, most job segment changes will involve movement within (rather than between) the nonmanual or manual scales.

(12) From a starting sample of 11,197 observations in the BHPS, 5856 females and 3401 males who were not employed at some point in both the first half and the second half of the panel, were dropped from the sample, yielding 1940 observations; a further 400 observations were lost by missing nonearnings data, leaving 1540 observations for the nonearnings equations. The earnings equations lose an additional 267 observations because of missing earnings data, yielding the 1301 observations used in the wage equations. For political reasons, early years of the BHPS excluded Northern Ireland and later years oversampled both Scotland and Wales. However, because respondents are required to be present in both the early and the later stages of the panel, panel design changes did not affect the representativeness of the sample we actually used.

(13) Our approach using Hope-Goldthorpe is similar to Rumberger (1981, 1987) and Sicherman and Galor (1990), who use the U.S. Dictionary of Occupation Titles to impute required education values using U.S. data.

(14) With only 12 waves in the BHPS, it is possible that MATCHOE workers were promoted prior to the start of the panel and that MATCHUE workers will be promoted after the end of the panel.

(15) There are seven workers observed to be both overeducated at least once and undereducated at least once in the first three waves of the BHPS and a further 50 such cases in the last three waves of the BHPS. Because these workers do not follow the specific pattern of employment predicted by our model, all 57 workers are classified in the excluded category for that respective section of the panel. Nonetheless, excluding these observations or relaxing this narrow definition to include these observations as overeducated early in the panel and undereducated later in the panel yields the same qualitative conclusions.

(16) The two wage growth variables are calculated as the difference between the log of the last and the log of the first wage observation for the relevant six-year period. The number of observations declines from 1540 to 1273 because of missing earnings data and the fact that we need two observations of earnings in each six-year subpanel to calculate all the dependent variables used in Table 6.

Daniel P. McMillen, * Paul T. Seaman, ([dagger]) and Larry D. Singell, Jr.([double dagger])

* Department of Economics, University of Illinois at Chicago, 601 South Morgan 2103UH M/C144, Chicago, IL 60607, USA; E-mail [e-mail].

([dagger]) Department of Economic Studies, University of Dundee, Nethergate, Dundee DD1 4HN, UK; E-mail [e-mail].

([double dagger]) Department of Economics, University of Oregon, Eugene, OR 97403-1285, USA; E-mail [e-mail]; corresponding author.

Table 1. Bivariate Ordinal Probit Results (a)

Qualifications of Worker (Q)

                                                              Asymp.
Variable                                             Coeff.   t-value

Mother out of work when while in school and
  living at home (=1)                                -0.236    -4.21
Mother white collar when while in school and
  living at home (=1)                                 0.169     0.75
Mother self-employed when while in school and
  living at home (=1)                                -0.294    -1.17
Father out of work when while in school and
  living at home (=1)                                -0.118    -1.38
Father white collar when while in school and
  living at home (=1)                                 0.502     5.61
Father self-employed when while in school and
  living at home (=1)                                 0.115     1.24
Current age                                          -0.009    -3.49
Person was married at age 20 or earlier (=1)         -0.221    -2.68
Person had kids at age 20 or earlier (=1)            -1.21     -3.25
Person expects to work during his working life (=1)  -0.263    -2.66
Person would work even if he became rich (=1)         0.116     2.12
Person believes men should be the primary income
  earner (=1)                                         0.392     5.81
Person believes a husband's job should come
  first (=1)                                          0.264     4.11
Person works in a public sector job (=1)              0.322     5.01
Person works 35-40 hours a week (=1)                 -0.200    -1.81
Person works more than 40 hours a week (=1)          -0.628    -2.86
Person has supervisory responsibilities (=1)          0.652     4.66
Person's coworkers are primarily men (=1)            -0.097    -1.68
Firm generally has good promotion prospects (=1)      0.235     4.47
Person born in central England (=1)                  -0.227    -3.01
Person born in northern England (=1)                 -0.059    -0.70
Person born in urban Scotland (=1)                   -0.020    -0.27
Person born in rural Scotland (=1)                    0.742     2.22
Person born in other countries (=1)                  -0.32     -0.17
Constant                                              1.134     6.85
[[mu].sub.1]                                          0.300    12.80
[[mu].sub.2]                                          1.258    30.42
[[mu].sub.3]                                          1.627    34.74
No. of observations = 1556
Log likelihood = -3758.29
Estimated correlation ([rho]) = 0.497,
  standard error = 0.029

Requirements of Firm (R)

Current firm has more than 500 employees (=1)         0.257     4.14
Insider is important for success in current firm     -0.036    -0.55
  (=1)
Current firm is unionized (=1)                       -0.055    -0.95
Current job is a professional job (=1)                1.342    13.06
Current job is in a nonmanual job (=1)                1.139    11.85
Current job is in a skilled manual job (=1)           0.542     6.29
Requirements necessary to perform the job (=1)        1.035    16.58
Months on the job before worker is proficient         0.127     5.60
Years of training prior to the current job            0.060     2.60
Promotion prospects are good for current job (=1)     0.163     2.75
Worker supervision effects work effort (=1)          -0.009    -0.15
Current job has been reorganized in last five
  years (=1)                                          0.211     3.77
Current job is part time (=1)                        -0.433    -1.60
Log of hours worked during typical workweek          -0.371    -2.34
Unemployment rate in city where worker works          0.006     0.79
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
--                                                     --       --
Constant                                             0.328     0.54
[[mu].sub.1]                                         0.497    13.91
[[mu].sub.2]                                         1.479    27.74
[[mu].sub.3]                                         1.845    31.74

(a) In the qualification equations, the explanatory variable "age" is
continuous, while the rest are binary variables that equal one if the
variable description is true. In the requirement equation, the
explanatory variables time to proficiency, years of training, the log
of hours worked, and the unemployment rate are continuous, while the
rest are binary variables that equal one if the variable description
is true. The excluded region is southern England.

Table 2. Predicted versus Observed Qualifications and Requirements
Comparisons (a)

          Overeducated: Q > R (No. of Observations = 409)

                   R <        R =           R >        Total
                [R.sup.*]   [R.sup.*]    [R.sup.*]

Q = [Q.sup.*]      10.02      10.76        0.00        20.78
Q < [Q.sup.*]      16.38      13.20        1.71        31.30
Q > [Q.sup.*]       9.54      30.56        7.82        47.92
Total              35.94      54.52        9.54       100.00

          Exactly-educated: Q = R (No. of Observations = 821)

                   R <        R =           R >        Total
                [R.sup.*]   [R.sup.*]    [R.sup.*]

Q < [Q.sup.*]      8.40       12.06        0.49       20.95
Q = [Q.sup.*]      2.92       49.33        3.65       55.91
Q > [Q.sup.*]      1.58       10.96       10.60       23.14
Total             12.91       72.36       14.74      100.00

          Undereducated: Q < R (No. of Observations = 326)

                   R <        R =           R >        Total
                [R.sup.*]   [R.sup.*]    [R.sup.*]

Q < [Q.sup.*]     17.18       15.03       10.12       42.33
Q = [Q.sup.*]      6.13       8.59        25.77       40.49
Q > [Q.sup.*]      0.00       3.99        13.19       17.18
Total             23.31      27.61        49.08      100.00

(a) Each figure measures the percent in that category.
Q and R are the observed qualifications and requirements that can
take on a value from 0 (NVQO) to 4 (NVQ4/NVQ5). [Q.sup.*] and
[R.sup.*] are the predicted qualification and requirement levels
from the joint-ordered probit model. Overeducated types of matches
are predicted to have R < [R.sup.*] and Q > [Q.sup.*], whereas
undereducated types of matches are predicted to have R > [R.sup.*]
and Q < [Q.sup.*].

Table 3. Construction of the Career Development State Dummies (a)

            Career Development Path Predicted

                            OE
              [Q >  [Q.sup.*] and R <  [R.sup.*]]
                            or
              [Q =  [Q.sup.*] and R <  [R.sup.*]]
Currently                   or                            MATCH
Observed      [Q >  [Q.sup.*] and R =  [R.sup.*]]  [Q =   [Q.sup.*] and
                                                    R =  [R.sup.*]]

   OE                      OEOE                          OEMATCH
 N = 409                  N = 304                        N = 105
             These people have presumably not
              yet risen up the job hierarchy

  MATCH                   MATCHOE                      MATCHMATCH
 N = 821                  N = 127                        N = 405
               These people have presumably
                risen up the job hierarchy

   UE       This combination does not exist in           UEMATCH
 N = 326                 the data                        N = 61

                                UE
             [Q <   [Q.sup.*] and R >  [R.sup.*]]
                               or
             [Q =   [Q.sup.*] and R >  [R.sup.*]]
Currently                       or
Observed     [Q <   [Q.sup.*] and R =  [R.sup.*]]

   OE       This combination does not exist in the data
 N = 409

  MATCH                       MATCHUE
 N = 821                      N = 133
            These people have presumably not yet risen
                       up the job hierarchy

   UE                          UEUE
 N = 326                      N = 265
             These people have presumably risen up the
                           job hierarchy

(a) The seventh category that we defined, workers for whom our
model cannot account for their type of pairing (i.e.,
[Q < [Q.sup.*] and R < [R.sup.*]] or [Q > [Q.sup.*] and R >
[R.sup.*]]), does not fit naturally within this table and
accounts for 156 observations (10% of the sample).

Table 4. Training and Promotion Specifications Using SCELI (a)

                                                     Training

                                                 Being an Insider Is
                                                 Useful for Getting
                                                  Promotion in Your
                                                  Current Firm (1)

                                                                Asymp.
Variable                                    Coeff.              t-value

OEOE--overeducated worker predicted to be
  overeducated (=1)                          0.249                 2.51
MATCHOE--matched worker predicted to be
  overeducated (=1)                          0.164                 1.26
MATCHUE--matched worker predicted to be
  undereducated (=1)                         0.168                 1.28
UEUE--undereducated worker predicted to
  be undereducated (=1)                      0.239                 2.31
OEMATCH--overeducated worker predicted to
  be matched (=1)                            0.046                 0.32
UEMATCH--undereducated worker predicted
  to be matched (=1)                         0.400                 2.27
OEUE--worker predicted to be both
  overeducated and undereducated             0.129                 1.07
Worker's years of education                  0.014                 0.83
Worker's years of experience                -0.001                -0.29
Firm size greater than 500 employees (=1)    0.182                 2.46
Worker is trade union member (=1)            0.085                 1.26
Unemployment rate in city where worker
  lives and works                           -0.002                -0.26
Marital status of worker (=1)               -0.098                 -1.1
Worker has dependent children (=1)           0.065                 1.82
First job after completing school is
  professional (=1)                          0.308                 2.10
First job after completing school is
  skilled nonmanual (=1)                     0.219                 2.33
First job after completing school is
  skilled manual (=1)                        0.121                 1.51
Constant                                    -0.718                -2.66
Threshold 1                                    --                   --
Threshold 2                                    --                   --
No. of observations                                    1556
Log likelihood                                       -1029.89

                                                       Training

                                                   Previous Similar
                                               Experience Is Useful for
                                                Success in the Current
                                                     Job (2)

                                                                Asymp.
Variable                                    Coeff.              t-value

OEOE-overeducated worker predicted to be
  overeducated (=1)                         -0.251                -2.50
MATCHOE-matched worker predicted to be
  overeducated (=1)                          0.285                 1.98
MATCHUE-matched worker predicted to be
  undereducated (=1)                        -0.471                -3.59
UEUE-undereducated worker predicted to be
  undereducated (=1)                         0.146                 1.34
OEMATCH-overeducated worker predicted to
  be matched (=1)                           -0.667                -4.59
UEMATCH-undereducated worker predicted to
  be matched (=1)                            0.349                 1.78
OEUE-worker predicted to be both
  overeducated and undereducated             0.285                 2.16
Worker's years of education                  0.043                 2.34
Worker's years of experience                -0.001                -0.03
Firm size greater than 500 employees (=1)   -0.048                -0.61
Worker is trade union member (=1)           -0.264                -3.73
Unemployment rate in city where worker
  lives and works                           -0.005                -0.52
Marital status of worker (=1)                0.067                 0.72
Worker has dependent children (=1)           0.037                 0.96
First job after completing school is
  professional (=1)                          0.200                 1.25
First job after completing school is
  skilled nonmanual (=1)                     0.150                 1.54
First job after completing school is
  skilled manual (=1)                        0.215                 2.63
Constant                                     0.032                 0.11
Threshold 1                                    --                   --
Threshold 2                                    --                   --
No. of observations                                    1556
Log likelihood                                       -927.65

                                                      Promotion

                                                 Very or Quite Good
                                               Chance of a Better Job
                                                   in the Next Two
                                                      Years (3)

                                                                Asymp.
Variable                                    Coeff.              t-value

OEOE--overeducated worker predicted to be
  overeducated (=1)                          0.332                 3.27
MATCHOE--matched worker predicted to be
  overeducated (=1)                          0.374                 2.82
MATCHUE--matched worker predicted to be
  undereducated (=1)                        -0.022                -0.16
UEUE--undereducated worker predicted to
  be undereducated (=1)                      0.113                 1.06
OEMATCH--overeducated worker predicted to
  be matched (=1)                            0.155                 1.05
UEMATCH--undereducated worker predicted
  to be matched (=1)                         0.212                 1.13
OEUE--worker predicted to be both
  overeducated and undereducated             0.322                 2.61
Worker's years of education                  0.065                 3.66
Worker's years of experience                -0.023                -5.69
Firm size greater than 500 employees (=1)    0.097                 1.26
Worker is trade union member (=1)           -0.397                -5.74
Unemployment rate in city where worker
  lives and works                           -0.015                -1.74
Marital status of worker (=1)               -0.074                 -0.8
Worker has dependent children (=1)           0.048                 1.30
First job after completing school is
  professional (=1)                          0.041                 0.27
First job after completing school is
  skilled nonmanual (=1)                     0.125                 1.31
First job after completing school is
  skilled manual (=1)                       -0.012                -0.15
Constant                                    -0.377                -1.37
Threshold 1                                    --                   --
Threshold 2                                    --                   --
No. of observations                                    1556
Log likelihood                                       -972.18

                                                      Promotion

                                                  Job-Level Changes
                                                 over the Career to
                                                     Date (4)

                                                                Asymp.
Variable                                    Coeff.              t-value

OEOE--overeducated worker predicted to be
  overeducated (=1)                         -0.008                -0.09
MATCHOE--matched worker predicted to be
  overeducated (=1)                          0.930                 6.72
MATCHUE--matched worker predicted to be
  undereducated (=1)                        -0.58                 -4.77
UEUE--undereducated worker predicted to
  be undereducated (=1)                      0.379                 3.82
OEMATCH--overeducated worker predicted to
  be matched (=1)                           -0.907                -6.61
UEMATCH--undereducated worker predicted
  to be matched (=1)                         0.698                 3.89
OEUE--worker predicted to be both
  overeducated and undereducated             0.168                 1.47
Worker's years of education                  0.116                 6.81
Worker's years of experience                 0.013                 3.48
Firm size greater than 500 employees (=1)   -0.091                -1.29
Worker is trade union member (=1)           -0.212                -3.26
Unemployment rate in city where worker
  lives and works                           -0.006                -0.75
Marital status of worker (=1)                0.002                 0.02
Worker has dependent children (=1)           0.122                 3.46
First job after completing school is
  professional (=1)                         -2.19                -14.55
First job after completing school is
  skilled nonmanual (=1)                    -1.148               -12.07
First job after completing school is
  skilled manual (=1)                       -1.055               -13.13
Constant                                       --                   --
Threshold 1                                 -0.540                -2.06
Threshold 2                                  0.694                 2.64
No. of observations                                    1511
Log likelihood                                       -1304.47

(a) OEOE (MATCHOE) is a binary variable that equals one if a worker
who is predicted to be in an overeducated-type (OE) match is observed
to have qualifications (equal) requirements. UEUE (MATCHUE) is a
binary variable that equals one if a worker who is predicted to be in
an  undereducated-type (UE) match is observed to have qualifications
that fall short of (equal) requirements. OEUE is a binary variable
that equals one if a worker is observed to have both overeducated and
undereducated indicators. OEMATCH (UEMATCH) are overeducated
(undereducated) workers who are predicted to be matched.

Table 5. Training and Promotion Specifications Using BHPS (a)

                                                     Training

                                                     Receiving
                                                    Training of
                                                     Any Form
                                                       (1)

                                                                Asymp.
Variable                                    Coeff.              t-value

Worker observed to be overeducated (=1)      0.297                 2.94
Worker observed to be undereducated (=1)     0.105                 1.25
Worker's years of education                  0.032                 1.83
Worker's years of experience                -0.018                -4.97
Firm size greater than 500 employees (=1)    0.406                 3.53
Worker is trade union member (=1)            0.049                 0.51
Unemployment rate in city where worker
  lives and works                            0.019                 0.73
Marital status of worker (=1)                0.113                 1.30
Worker has dependent children (=1)          -0.092                -1.11
Current job is professional (=1)             0.371                 4.12
Current job skilled nonmanual (=1)           0.245                 2.73
Current job skilled manual (=1)             -2.272                -2.73
Constant                                    -0.262                -0.65
No. of observations                                    1540
Log likelihood                                       -827.676

                                                  Training

                                                      Receiving
                                                    Training for
                                                    Future Jobs
                                                       (2)

                                                                Asymp.
Variable                                    Coeff.              t-value

Worker observed to be overeducated (=1)      0.251                 2.81
Worker observed to be undereducated (=1)     0.046                 0.59
Worker's years of education                 -0.012                -0.79
Worker's years of experience                -0.016                -4.52
Firm size greater than 500 employees (=1)    0.369                 3.82
Worker is trade union member (=1)           -0.060                -0.68
Unemployment rate in city where worker
  lives and works                            0.052                 2.26
Marital status of worker (=1)                0.007                 0.09
Worker has dependent children (=1)           0.040                 0.52
Current job is professional (=1)             0.356                 4.32
Current job skilled nonmanual (=1)           0.184                 2.30
Current job skilled manual (=1)             -0.128                -1.43
Constant                                     -0.36                -1.01
No. of observations                                    1540
Log likelihood                                       -1006.59

                                                      Promotion

                                                 Is the Final Job in
                                                  the Panel a Higher
                                                 Level Job Than the
                                                     First Job?
                                                       (3)

                                                                Asymp.
Variable                                    Coeff.              t-value

Worker observed to be overeducated (=1)      0.549                 5.52
Worker observed to be undereducated (=1)     0.509                 5.74
Worker's years of education                  0.024                 1.31
Worker's years of experience                -0.005                -1.14
Firm size greater than 500 employees (=1)   -0.205                -1.73
Worker is trade union member (=1)            0.039                 0.37
Unemployment rate in city where worker
  lives and works                           -0.023                -0.84
Marital status of worker (=1)               -0.073                -0.76
Worker has dependent children (=1)          -0.048                -0.51
Current job is professional (=1)             0.124                 1.35
Current job skilled nonmanual (=1)           0.816                 8.90
Current job skilled manual (=1)              0.625                 5.92
Constant                                    -1.988                -4.53
No. of observations                                    1540
Log likelihood                                       -653.943

(a) See footnote a in Table 3 for more detailed description of match
variables. There are fewer observations for job-level changes because
some workers have not changed jobs. The other human capital and
promotion results are not qualitatively affected if the observations
are restricted to the 1506 for observed job changers.

Table 6. Wage Growth Regression (a)

                                            Wage Growth, First
                                                Six Years

Variable                                Coeff.            t-value

Overeducated (=1)                        0.034               1.02
Undereducated (=1)                       0.064               2.17
Years of education                       0.003               0.54
(Overeducated) * (years of education)      --                 --
Years of experience                     -0.003              -1.99
Firm size > 500 employees (=1)          -0.005              -0.15
Trade union member (=1)                  0.052               1.57
Unemployment rate                        0.004               0.44
Marital status of worker (=1)           -0.111              -3.57
Dependent children (=1)                 -0.040              -1.34
Current job is professional (=1)         0.033               1.05
Current job skilled nonmanual (=1)      -0.028              -0.93
Current job skilled manual (=1)         -0.043              -1.26
Constant                                 0.065               0.048
No. of observations                               1273
[R.sup.2]                                        0.0345

                                            Wage Growth, Last
                                                Six Years

Variable                                Coeff.            t-value

Overeducated (=1)                        0.019             0.68
Undereducated (=1)                       0.061             2.43
Years of education                       0.010             2.16
(Overeducated) * (years of education)      --             --
Years of experience                     -0.002            -1.72
Firm size > 500 employees (=1)           0.021             0.68
Trade union member (=1)                 -0.020            -0.72
Unemployment rate                       -0.013            -1.72
Marital status of worker (=1)           -0.124            -4.66
Dependent children (=1)                 -0.020            -0.78
Current job is professional (=1)         0.005            -0.18
Current job skilled nonmanual (=1)       0.056             2.20
Current job skilled manual (=1)          0.024             0.82
Constant                                 0.120             1.030
No. of observations                               1273
[R.sup.2]                                        0.0494

                                             Wage Growth Last
                                            vs. First Six Years

Variable                                Coeff.            t-value

Overeducated (=1)                        0.495               1.95
Undereducated (=1)                       0.004               0.11
Years of education                       0.016               1.86
(Overeducated) * (years of education)   -0.029              -2.04
Years of experience                      0.001               0.38
Firm size > 500 employees (=1)           0.027               0.59
Trade union member (=1)                 -0.079              -1.81
Unemployment rate                       -0.016              -1.42
Marital status of worker (=1)           -0.014              -0.33
Dependent children (=1)                  0.018               0.47
Current job is professional (=1)        -0.035              -0.85
Current job skilled nonmanual (=1)       0.093               2.34
Current job skilled manual (=1)          0.075               1.65
Constant                                -0.093              -0.48
No. of observations                               1273
[R.sup.2]                                        0.0105

(a) Overeducation is a binary variable that equals one for those
workers observed to be in an overeducated pairing in the first six
waves of the panel, whereas Undereducation is a binary variable
that equals one for those workers observed to be in an undereducated
pairing in the last six waves of the panel. There are fewer
observations in the wage regression than the promotion and human
capital models because some workers do not report earnings.
The qualitative conclusions of the previous promotion and human capital
specifications do not change if the sample is restricted to
those workers for whom there are wage data.