Literacy and numeracy abilities of overeducated and undereducated workers: Revisiting the allocation process in the labour market

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1 Literacy and numeracy abilities of overeducated and undereducated workers: Revisiting the allocation process in the labour market Philipp Grunau 1 Institute for Employment Research January 2014 Abstract Both the theory of allocation and the human capital model imply that over- and undereducated individuals systematically differ from correctly-educated workers with respect to marketable human capital components beyond formal education. Using an innovative German dataset 2 entailing test scores on survey attendants literacy and numeracy competencies, I find evidence that overeducated (undereducated) workers possess inferior (superior) reading and math abilities compared to their educational peers. However, when compared to correctly allocated employees in jobs of the same level of required education, in line with the signalling theory, the findings are reverse. Controlling for employment biographies to account for mismatch-induced skill alterations over time strengthens the relevance of the selection into over- and undereducation based on competencies. Moreover, a certain part of the wage effects associated with educational mismatch can be attributed to the more comprehensive account for human capital components. [216 words] JEL classification: I21, J24, J31, M53 Keywords: overeducation, undereducation, ability, literacy, numeracy, wages, allocation, human capital, signalling. 1 Institute for Employment Research, Department Establishments and Employment, Regensburger Str. 104, Nuremberg, Germany. philipp.grunau@iab.de. 2 This paper uses data from the National Educational Panel Study (NEPS): Starting Cohort 6 Adults, doi: /neps:sc6: From 2008 to 2013, NEPS data were collected as part of the Framework Programme for the Promotion of Empirical Educational Research funded by the German Federal Ministry of Education and Research (BMBF). As of 2014, the NEPS survey is carried out by the Leibniz Institute for Educational Trajectories (LIfBi) at the University of Bamberg in cooperation with a nationwide network. 1

2 Introduction Fostered by politics, most countries have recently faced a phase of substantial educational expansion. In Germany, for example, during 1976 and 2012 the proportion of (all) individuals holding a university (of applied science) degree rose from 4.8% to 13.0%, whereas the share holding the lowest secondary qualification (Hauptschulabschluss) meanwhile more than halved itself from 74.0% to 35.6% (Statistisches Bundesamt, 2013). This development is in fact intended by politics. The European Union sets the goal for successful completed tertiary education (for the population aged 30 to 34) at 40% in Meeting this goal seems far from unrealistic, since until 2012 the proportion has already risen up to 35.7% (European Commission, 2013). Moreover, the OECD recently attested to Germany that its rise in the share of tertiary educated adults between 2000 and 2012 is comparably low and hence, the nowadays share is even below the OECD average (OECD, 2014). However, this politically intended development bears the peril of rising overeducation in case the increased supply of higher educated workers is not adequately met by a respectively enhanced demand (McGuinness, 2006). Furthermore, undereducation may arise, too, for example if in certain occupations the demand for university graduates exceeds its supply (e.g., in STEM 3 -related jobs), forcing hiring firms to employ undereducated workers from these fields, perhaps in combination with the provision of intense training measures. Frequently, the phenomena of over- and undereducation are regarded to result from a dysfunctional allocation mechanism. However, in light of the occurrence of over- and undereducation, both the theory of allocation and human capital theory stipulate that these groups should systematically differ in terms of other marketable qualities beyond formal education that are observable to the employer during the application process. To be more precise, overeducated (undereducated) workers should therefore be worse (better) endowed than correctly-matched educational peers, which is what Sloane et al. (1999) refer to as substitutability hypothesis and which is also pointed out by several other authors. 4 Addressing the increasing importance of this, Chevalier and Lindley (2009) argue that the expanded access to higher education through the last decades has led to an increased heterogeneity of graduates as it implies the admission of students from lower parts of the ability distribution. Moreover, due to considerations from the signalling theory (Spence, 1983) as well as concerning skill updating caused by educational attainment, when compared to correctly-educated workers of deviating levels of attained education but in jobs with the same amount of required education, overeducated (undereducated) workers should possess superior (inferior) marketable properties. However, despite these conceivable mechanisms, most analyses restrict explicit consideration of human capital endowments to formal educational attainment, labour market experience, and on-the-job training, presumably because other parts of human capital are usually not observed. 3 STEM refers to the fields of science, technology, engineering, and mathematics. 4 e.g. Green and McIntosh, 2007; Jochmann and Pohlmeier, 2004; Allen and van der Velden, 2001; and Groot,

3 Considering discrepancies in the returns to wages, to date the results relying on the restricted consideration of human capital endowments lead to the rejection of human capital theory (HCT). According to this theory, wage discrepancies can solely be originated in differences in individuals human capital. The detected wage penalty (wage premium) for overeducation (undereducation), controlling for formal education, therefore cannot be explained by HCT. If selection into over- and undereducation is nonrandom and the hypothesis mentioned above proves right, the hitherto restricted consideration of human capital endowments might turn out to be responsible for at least part of the differences between adequately-allocated and educationally mismatched workers. Depending on the size of this effect, the validity of HCT for explaining wage differences may to some part be restored and the problems associated with formal educational mismatch only be due to misspecification. Taking into consideration what is mentioned above, this study is devoted to elucidate the following research questions: (1) Do workers equipped with more (less) formal education than required by their current job possess worse (more) literacy and numeracy skills when compared to their educational peers?, (2) Do overeducated (undereducated) employees have superior (inferior) literacy and numeracy abilities than correctly allocated colleagues of similar jobs?, and (3) Can this more comprehensive account of human capital components contribute to explain the wage penalty (wage premium) compared to educational peers that is usually found accompanying overeducation (undereducation) when only considering formal education and work experience? To address these questions I use data from the German National Educational Panel Study (NEPS) which encompass information on individuals employment, including a measure for required education, and several socio-demographics. Exploiting the subjective assessment on the educational attainment that is usually required by the job currently pursued allows identifying required education and hence, when compared to the highest educational degree currently held, the (vertical) adequacy of attained education for the current job. In the second wave of the adult starting cohort this comprehensive set of information for the first time is further enriched by test scores from comprehensive tests on basic competencies with respect to reading speed, reading comprehension, and maths competency. Therefore, it is possible to account for a substantially more comprehensive part of individuals human capital endowment. Theoretical considerations Considering the theory of allocation and adapted versions of the human capital model, the occurrence of over- and undereducation implies that overeducated (undereducated) workers when compared to their educational peers lack (possess) other marketable and observable properties beyond formal education. However, when comparing to correctly-educated workers in jobs of the same level of required education, signalling theory (Spence, 1983), which stipulates that individuals invest in the attainment of formal education according to their amount of ability or productivity, suggests the oppo- 3

4 site. Both hypotheses combined, overeducated (undereducated) workers, although possessing inferior (superior) cognitive abilities compared to their educational peers, should have better (worse) numeracy and literacy competencies than well-matched colleagues in jobs of the same level of required education. Furthermore, these differences in human capital endowments apart from formal education numeracy and literacy abilities should contribute to explaining the discrepancies in the returns to different parts of education if those additional components are in fact marketable. Therefore, in this paper I consider test scores from comprehensive tests on reading and math competencies which are assumed to depict basic abilities that are observable for the employer during the application process. Corresponding studies suggest that such cognitive abilities are positively associated with earnings (e.g. Anger and Heineck, 2010, for Germany; Bronars and Oettinger, 2006, and Murnane et al., 1995, for the US), while others point out the importance of noncognitive skills (Heckman et al., 2006). More similar to the data used in the present paper, McIntosh and Vignoles (2001) utilise test-based measures of basic literacy and numeracy skills from the UK and find that these skills play an important role for the determination of wages. These results are confirmed by Vignoles et al. (2011), again with data from the UK. If now higher basic reading and math skills coincide with both higher wages and the likelihood of being overor undereducated, this could explain the wage discrepancies accompanying over- and undereducation in models that fail to account for these additional human capital components, hence restoring significance of human capital theory and the efficacy of the allocation mechanism. Literature review The phenomenon of educational mismatch is regarded to result from dysfunctional allocation. However, as pointed out by several authors (e.g. Green and McIntosh, 2007; Allen and van der Velden, 2001; Sloane et al., 1999; Groot, 1996), there may be individual heterogeneity within a level of formal education with respect to differences in further components of human capital like ability and competencies In their meta-analysis of 25 studies, Groot and van den Brink (2000) conclude that the phenomenon of overeducation has become increasingly frequent among individuals from the lower area of the ability distribution. For the UK, Green et al. (2002) find that overeducated workers are less able when compared to individuals of the same educational attainment who are well-matched in their jobs. They explain this result with certain groups of similar formal education in which workers of comparably low ability are forced to accept jobs who match their actual skills. Estimating correlations between overeducation and overskilling, Green and McIntosh (2007) come to a similar conclusion. The low correlation of 0.2 the authors detect implies that once additional components of human capital are accounted for, a true mismatch is rather rare. Moreover, Chevalier and Lindley (2009), comparing the graduate labour market before and after the educational expansion in the early 1990s, reveal the dramatically 4

5 rising importance of non-observable characteristics, whose effect has increased more than 10 times over this period. Against this backdrop, they conclude that overeducated workers tend to have less favourable unobservable characteristics. For the Netherlands, Allen and van der Velden (2001) also find evidence for unobserved differences playing a substantial role for the existence of the mismatch between formal education and the requirements of jobs. De Grip et al. (2007) extend this view by investigating on reverse causality. The authors argue that being overeducated leads to a decline in cognitive ability as response to reduced intellectual challenge. On the other hand, undereducation involves an increased intellectual challenge through skill updating (cf. Pazy, 2004; Fratiglioni et al., 2004; Bosma et al., 2003a/b). However, de Grip et al. do not detect deviating abilities for overeducated or undereducated workers. Using Italian data with information on individuals detailed self-assessment concerning the effectiveness of provided skills as proxies for ability, Cainarca and Sgobbi (2012) conclude that employees ability despite being of importance for the determination of wages does not significantly affect the wage effects of required, surplus, and deficit education. For Germany, Buechel and Pollmann-Schult (2004) find that the risk of being overeducated depends on the type of school diploma, which they take as a proxy for educational quality. Moreover, Jochmann and Pohlmeier (2004) point to the importance of the selection into overqualification. In their analysis which is based on a Bayesian approach to account for selection into overqualification, they find that once controlling for this selectivity, the average treatment effect on the treated converges close to zero. This implies that overqualified workers would not receive higher wages if they were employed adequately, again implying that they do not depict a random pick from all individuals. Addressing the probability to be overeducated at a certain time from a different perspective, Clark et al. (2014) find that the probability to exit overeducation is also rather caused by selection on unobservables than by true state dependence. Addressing potential causes, Chevalier and Lindley (2009) argue that the expanded access to higher education through the last decades has led to an increased heterogeneity of graduates as it implies the admission of students from lower parts of the ability distribution. Hence, when the best workers select into the best jobs, selection into overeducation and undereducation, respectively, is non-random and depends on those further components of human capital. This would imply that overeducated (undereducated) workers tend to have less (more) human capital apart from formal education than their wellmatched peers of the same formal education, which is what Sloane et al. (1999) referred to as the substitutability hypothesis. Despite this conceivable mechanism, most analyses restrict consideration of human capital endowments to formal educational attainment and labour market experience, presumably because other parts of human capital are usually not observed. 5

6 Data and estimation approach The German National Educational Panel Study (NEPS), a project funded by the Federal Ministry of Education and Research, has been established to study different educational processes in Germany across the entire life span. Out of the eight stages ranging from early childhood to adulthood, this study makes use of the data on starting cohort 6 (adults). In its second wave from 2012, for the first time test scores from tests on basic reading and math competencies have been collected and provided. Since both education and employment decisions of women may be driven by other important characteristics or circumstances not observed in the data, regressions are restricted to men. Moreover, only full-time working men are used in order to avoid the estimates to be biased due to structural differences between full-time and part-time (or marginal) employment. Additionally, because of the survey design which assigns the time-consuming competence tests on reading comprehension and mathematical competency only to a subgroup of participants who have answered the questionnaire, a full set of information on educational decisions, other important characteristics, and at least one competency test is available for 2,414 full-time working men. The test scores included in the NEPS data contain test scores for reading (Gehrer et al., 2013) and math competencies (Neumann et al., 2013), where the former is divided into reading speed and reading comprehension 5. All these tests are accomplished using the paper-pencil mode. They can be regarded as comparatively objective and comprehensive since participants are not asked their subjective perception of their skills. The scores on reading comprehension and math competency where each consists of several items and takes about half an hour are introduced to the analyses in this paper as weighted maximum likelihood estimates (WLE), which depict the best point estimates of the individual competence scores. In contrast to the application of plausible values, WLE are manifest scores (not latent) that do not account for measurement error. However, for the purpose of this paper WLE appear to be the superior solution, since plausible values correct for the measurement error by shifting competence scores towards the mean of the group whose (observed) characteristics have been used for their calculation, hence implying that there is a measurement error for all individuals and that its direction is away from the group mean. For a description of the scaling of the competence tests see Pohl and Carstensen (2012, 2013). To account for the measurement precision of the competence estimates of each individual, the standard errors of the WLE for both reading comprehension and math competency are included into the wage regression as well. The incorporation of reading speed is realised by introducing the number of correctly judged simple sentences during a 2 minute test (range: 0 to 51) to the estimation equation. 5 There is a further test on procedural metacognition which depicts the knowledge and control of the own cognitive system, identified by asking participants after they have finished their competence tests to rate their own performance. As this concept, however, is not of use in this study, it is neglected. 6

7 To assess the educational adequacy of the current job this study relies on the subjective perception of individuals. During the interview respondents are asked what kind of educational degree is usually required to do their job. By comparing this information with the one on attained education of the interviewee then provides an evaluation of whether an individual s formal education matches the one required by his or her job, allowing to classify each worker as over-, under-, or adequately educated. To acknowledge the fact that there are many ways of measuring educational mismatch and that these measurements can lead to different results, I additionally use an alternative measure as a robustness check. This measure relies on large-scale administrative data on employees liable to social security contributions, allowing me to identify required education per each of the 332 occupations of the occupational classification KldB 1988 via the mode of actually attained educational degrees. When investigating the differences concerning literacy and numeracy competencies between over-, under-, and adequately educated workers, in order to address comparison to both groups of correctly allocated workers i.e. to answer research questions (1) and (2), I utilise two different approaches, which both are widely used in the corresponding literature. The first one, mostly referred to as the ORU approach, has been proposed by Duncan and Hoffmann (1981) in their seminal paper on overeducation in the US. This approach requires information on years of attained education, which are decomposed into years of education required by the job, years of excess education (if years of attained education exceed the years of required education) and years of deficit education (if years of required education exceed the years of attained education). In the NEPS data, while information on the exact years of education is available, years of required education are not and therefore have to be generated. This is achieved on the individual rather than on the occupation level where the respondent s statement on the education usually required for his or her current job has to be translated into (required) years of education. The latter, again, is realised by calculating mean years of education for each of the categories of required education actually observed in the data (confer Table A1 in the appendix). Therefore, within each group of the same educational degree, years of attained education may vary, whereas years of required education are the same by construction. By including variables for required, excess, and deficit years of education into the estimation equation, the coefficients on the latter two variables implicitly exhibit the impact of over- and undereducation on the respective outcome conditional upon the same years of required education, i.e. in comparison to individuals working in a job which is similarly demanding concerning formal education. On the contrary, the dummy approach provides another interpretation. It introduces variables indicating the highest attained educational degree and one for each being over- and undereducated. Thus, for correctly allocated workers, the latter two dummies turn out zero. By this means, the latter two dummy variables indicate the effect of over- or undereducation, respectively, on the respective outcome conditional upon the same educational degree, i.e. in comparison to individuals who have attained the same formal education but are adequately educated for their current job. 7

8 Utilising both estimation approaches thus provides the advantage of investigating on the effects of over- and undereducation in a twofold manner, comparing them to both adequately matched colleagues of different educational attainment doing the same job (ORU approach) and correctly allocated educational peers (dummy approach). Addressing the hypotheses underlying this paper I will regress both wages and the different competency scores on over- and undereducation. The specification based on the dummy approach looks like this: Wage(ln) Comp read speed read comp mat comp = β 0 + β 1 educ + β 2 OE + β 3 UE + β 4 X + ε with educ denoting a vector of dummies for the level of attained education, OE being the coefficient of a dummy indicating overeducation and UE indicating undereducation. The vector X comprises control variables included in the equation such as age, age squared, a dummy indicating whether a person is born in Germany or not, as well as regional dummies indicating the German Länder and 7 sectoral dummies. Alternatively, the specification following the ORU approach looks like this: Wage(ln) Comp read speed read comp mat comp = β 0 + β 1 Yrs RE + β 2 Yrs OE + β 3 Yrs UE + β 4 X + ε with Yrs RE denoting years of required education, Yrs OE those of excess, and Yrs UE those of deficit education. The control variable vector is the same as in the dummy specification. The wage equations addressed thereafter basically follow the same approach, with the only differences being that the vector of control regressors additionally includes dummies indicating the sector a worker is currently employed in. Both the weighted maximum likelihood estimates (WLE) from the tests on reading comprehension and math competency, which are constrained to mean zero and a value range from -5 to +5, and wages will be considered in the estimation utilising OLS regression. However, because the score for reading speed can take values from 0 to 51, for these estimations I apply negative binomial regressions to account for the count nature of this (dependent) variable. Descriptive Evidence Within the restricted estimation sample of 2,414 full-time working men with information on required and attained educational attainment as well as at least on one competency test approximately 66 per 8

9 0 0 kdensity lnwage kdensity wage cent turn out being adequately educated. In contrast, 21 per cent can be regarded as overeducated and about 13 per cent as undereducated for the current job. First, let us take a look at the unconditional distribution of wages illustrated below using kernel density plots (Figure 1a). Both for wages in logarithmic and absolute values it is clear from first sight that employees who have attained more education than required by their current job tend (solid line) to earn less than both the under- and adequately educated. On the other hand, undereducated workers (dashed line) appear to receive higher wages than those with the exact amount of education as required (dotted line). This pattern becomes even more distinct when misallocated workers are compared with adequately matched individuals of the same educational attainment, as is illustrated in Figure 1b. When, however, comparing individuals to workers in jobs with a similar amount of required education (confer Figure 1c), the differences seem to be less distinct (undereducation) or even to vanish (overeducation). Figure 1a: Kernel density plots of gross monthly earnings (left: in logs, right: absolute values), by match of educational attainment Gross monthly wage (log) Gross monthly wage (abs) Source: NEPS starting cohort 6 (adults), wave 2. 9

10 0 0 0 kdensity comp_read_speed kdensity comp_read kdensity comp_math kdensity lnwage2.5 kdensity wage kdensity lnwage kdensity wage Figure 1b: Kernel density plots of gross monthly earnings (left: in logs, right: absolute values), by match of educational attainment; restricted to workers with a vocational degree Gross monthly wage (log) Gross monthly wage (abs) Source: NEPS starting cohort 6 (adults), wave 2. Figure 1c: Kernel density plots of gross monthly earnings (left: in logs, right: absolute values), by match of educational attainment; restricted to workers of jobs with similar required education Gross monthly wage (log) Gross monthly wage (abs) Source: NEPS starting cohort 6 (adults), wave 2. Turning to the workers literacy and numeracy skills, the comparison of the unconditional distribution by educational match status displayed in Figure 2a shows that overeducated workers tend to be worse equipped than correctly allocated employees, whereas there does not seem to be a clear difference between the latter and undereducated workers. Figure 2a: Kernel density plots of test scores on reading speed (number of correctly judged sentences), reading comprehension, and math competency (both WLE); unrestricted Test score of reading speed (between 0 and 51) WLEs of reading competence (constrained to have mean zero) WLEs of math competence (constrained to have mean zero) 10

11 0 0 0 kdensity comp_read_speed kdensity comp_read kdensity comp_math Source: NEPS starting cohort 6 (adults), wave 2. However, as the pivotal hypotheses of this paper stated above suggest, when compared to their educational peers, overeducated workers should be of inferior and undereducated workers should be of superior literacy and numeracy abilities. Consequently, when re-considering the unconditional distributions by restricting those to workers with a vocational degree as highest educational attainment (Figure 2b), the picture sharpens considerably. While overeducated workers (solid line) still tend to have inferior literacy and numeracy skills compared to adequately educated individuals (dotted line), undereducated employees (dashed line) now tend to be better endowed. Figure 2b: Kernel density plots of test scores on reading speed (number of correctly judged sentences), reading comprehension, and math competency (both WLE); restricted to workers with a vocational degree Test score of reading speed (between 0 and 51) WLEs of reading competence (constrained to have mean zero) WLEs of math competence (constrained to have mean zero) Source: NEPS starting cohort 6 (adults), wave 2. To address the mirrored hypothesis that compares cognitive abilities of mismatched workers with those of correctly allocated employees in jobs with the same level of required education, graphics are presented for the sample restricted to individuals whose jobs require the same amount of formal education (here: set to 12.9 years which is the largest group in the dataset). As the graphics in Figure 2c suggest, both over- and undereducated employees tend to have superior reading and math skills than correctly allocated workers in jobs with a similar required education. In the case of overeducation, this result is in line with the corresponding hypothesis, but for undereducation it implies that those possessing deficit amounts of formal education appear to outdo correctly educated workers of both the same attained and required educational attainment. However, of course, these results do not take into account potentially important influence factors; hence, the concluding assessment requires conditional correlations with control variables which is provided throughout the subsequent section. 11

12 0 0 0 kdensity comp_read_speed kdensity comp_read kdensity comp_math Figure 2c: Kernel density plots of test scores on reading speed (number of correctly judged sentences), reading comprehension, and math competency (both WLE); restricted to workers in jobs of similar required education Test score of reading speed (between 0 and 51) WLEs of reading competence (constrained to have mean zero) WLEs of math competence (constrained to have mean zero) Source: NEPS starting cohort 6 (adults), wave 2. To draw an interim conclusion, we have seen that in the cross section of 2012 and without taking into account individual characteristics, workers appear to differ with respect to literacy and numeracy abilities conditional upon the adequacy of the match between their attained formal education and the one required by their current job. Especially when compared to their educational peers, overeducated (undereducated) workers tend to possess inferior (superior) reading and math competencies. However, when compared to correctly allocated employees in job with a similar amount of required education, both over- and undereducated workers appear better equipped with respect to cognitive abilities. Since owing to the survey design not each participant is assigned to each competency test, the estimations that will be exhibited within this study possess deviant subsamples of full-time working men 6. Thus, corresponding summary statistics of the variables incorporated in each regression are provided in Tables A2a and A2b in the appendix. A comparison of these statistics reveals small but mostly insignificant biases in the subsample of those who took part in all three competency tests (N=1,047, specification (5) of Table A2b) compared with the baseline sample of all 2,414 full-time working men with a full set of required information (specification (1) of Table A2a). However, the only significant deviation is that the former exhibit a slightly higher likelihood of being adequately matched with respect to formal education, which turns out to be only marginally significant on the 5 per cent level 7. Econometric results Selection on basic competencies Before turning to the impact on the returns to education, let us first consider the significance of the further human capital components apart from formal education for the state of being over-, under-, or adequately educated, when this state is solely determined by attained formal education. As has been 6 About 50 per cent of the sample have undertaken both tests and approximately each a forth only one of the two tests. 7 A corresponding t-test for the null of equal means across groups reveals a p-value of

13 proposed, the occurrence of both over- and undereducation is assumed to pose a negative selection with respect to literacy and numeracy skills which are also responsible for individual performance. Following this argumentation, overeducated (undereducated) workers should have inferior (superior) competencies than their correctly allocated educational peers. However, when compared to correctly allocated colleagues of lower (higher) educational attainment, overeducated (undereducated) employees are supposed to possess superior (inferior) competencies. Therefore, in terms of these additional components of human capital workers whose education is incommensurate with the one required by their current job ought to lie between those of the same education who are correctly allocated and those well matched colleagues doing the same job (i.e. of different educational attainment). Turning to reading speed (Table 1a), reading comprehension and math competency (both Table 1b), we can see that controlling for sex, working time, age, place of birth, and region (federal states), the results seem to confirm the hypothesis stated above. Relying on the dummy approach (specifications (1), (3), and (5)), where the account for attained education in terms of dummies for the respective highest degree holds attained education fixed, the dummies for over- and undereducation, respectively, convey these statuses impact in comparison to adequately allocated peers of the same educational group. Hence, the negative coefficient for overeducation in column (1) suggests that employees with more education than is required by their current job have a reading speed inferior to those of their well-matched educational peers. In contrast, undereducation is associated with higher reading skills. The same holds true for both reading comprehension and mathematical ability, as can be seen in specifications (3) and (5). Focussing on the alternative ORU specification displayed in column (2), (4), and (6) of Tables 1a and 1b, the comparison differs in that because of the inclusion of required years of education effects now are in comparison to the test performance of individuals in jobs with the same level of required education, which in turn necessarily implies that comparison is made with workers of different attained education. The coefficient on overeducation compares to correctly allocated colleagues of lower education, and vice versa for undereducation. In line with the hypothesis, the coefficient on years of excess education is positive, implying that overeducation corresponds to superior competencies when compared to adequately-educated individuals of lower education. On the other hand, when interpreting this coefficient with the one for years of required education, where the latter is larger, this confirms the conclusion drawn from the results based on the dummy specification, meaning that the overeducated are of superior competencies compared to adequately educated individuals of the same educational attainment. As the association between undereducation on the one hand and both reading and math skills on the other turns out negative but smaller than the effect on required education, conclusions are vice versa: have superior competencies when compared to adequately matched educational peers but inferior competencies when compared to correctly allocated colleagues doing the same job, i.e. of higher educational endowment. 13

14 Table 1a: Negative binomial regression estimates from regressing test scores from reading speed on individual characteristics Reading speed test score 1 Selected regressors: (1) (2) Age.381***.371*** (.141) (.140) Age squared -.006*** -.006*** (.002) (.002) Place of birth (D; 1=Germany) 9.197*** 9.376*** (1.038) (1.009) Education Secondary school leaving certificate/a levels 8.412*** (1.983) Vocational qualification 7.684*** (1.877) University (of Applied Science) degree *** (1.913) Overeducated (D) *** (.437) Undereducated (D) 2.411*** (.529) Years of required education 1.316*** (.084) Years of excess education 1.002*** (.155) Years of deficit education -.658*** (.176) Number of observations 2,423 2,423 α (dispersion coeff.).025*** (.002).024*** (.002) LR test (H 0 : α=0) x ²= (p=.000) x ²= (p=.000) Source: NEPS Starting Cohort 6 (adults), wave 2. Robust standard errors in parentheses. Significance denoted as: *** p<0.01, ** p<0.05, * p<0.1. The constant, 16 state dummies, and 7 industry dummies are included in the regression, but not displayed. 1 The test score is scaled from 0 to 51 depicting the number of correctly judged sentences during a 2-minute test. 14

15 Table 1b: OLS estimates from regressing test scores (WLE) for reading comprehension and math competency on individual characteristics Dependent variable: Test scores 1 on Reading comprehension Math competency Selected regressors: (3) (4) (5) (6) Age.118***.111***.100***.093*** (.022) (.021) (.023) (.023) Age squared -.002*** -.002*** -.001*** -.001*** (2.46e-04) (2.44e-04) (2.69e-04) (2.59e-04) Place of birth (D; 1=Germany).731***.694***.365***.325*** (.131) (.126) (.129) (.118) Education Secondary school leaving certificate/a levels 1.733*** 1.581*** (.260) (.299) Vocational qualification 1.373*** 1.473*** (.235) (.269) University (of Applied Science) degree 2.467*** 2.680*** (.241) (.275) Overeducated (D) -.162** -.268*** (.072) (.072) Undereducated (D).304***.291*** (.089) (.092) Years of required education.269***.325*** (.015) (.014) Years of excess education.224***.227*** (.027) (.028) Years of deficit education -.143*** -.172*** (.027) (.027) Number of observations 1,793 1,793 1,753 1,753 R-squared Source: NEPS Starting Cohort 6 (adults), wave 2. Robust standard errors in parentheses. Significance denoted as: *** p<0.01, ** p<0.05, * p<0.1. The constant, 16 state dummies, and 7 industry dummies are included in the regression, but not displayed. 1 Weighted maximum likelihood estimators (WLEs) based on scores across all test of the respective discipline, constrained to have mean zero, a minimum at -5 and a maximum at +5. As the estimations within the last chapter have shown, depending on their commensurateness of attained and required education, workers differ in their literacy and numeracy abilities. Thus, both hypotheses (1) and (2) can be confirmed. However, from these results it cannot be distinguished between two conceivable effect directions. On the one hand, overeducated (undereducated) workers, when compared to their educational peers, may be employed in a job under-utilising (over-utilising) their formal education because they possess superior (inferior) skills and competencies, as is hypothesised in this paper. On the other hand, due to the decay of unused skills (skill updating due to intellectual challenge) these workers may have inferior (superior) endowments because of being overeducated (undereducated), as has been argued by de Grip et al. (2007). A strategy to encounter this interpretational issue is to take into account the employment biography of each individual observed in the data, which is available due to the retrospective design of the NEPS survey. For instance, apart from considerations on state dependence, there is a correlation between the 15

16 occurrences of overeducation and unemployment, as is shown by (Buechel, 2001). Once controlling for the employment biography, the coefficients on educational (mis)match should convey the conditional correlation for the current state only, hence avoiding them to be corrupted by impacts from former periods of educational mismatch or unemployment. If the coefficients on over- and undereducation lose their significance when comparing an overeducated (undereducated) with an adequately allocated worker conditioning on a similar employment biography, this points to the relevance of the skill alteration hypothesis as skills and competencies need time to develop. On the contrary, if the results remain significant (and retain their effect sign) this strengthens the relevance of the selection into overand undereducation based on cognitive (numeracy and literacy) abilities. To account for the employment biography in a suitable manner, additional variables are added to the regression equations, one of each representing the time spent in adequately allocated employment, in overeducation, in undereducation, and in unemployment. 8 Beyond exploiting the information on the workers employment biography, an additional test for effect direction is to interact job tenure with the indicator variables on over- and undereducation in the dummy specification to account for the duration of the current experience in educational mismatch. If the coefficients of the interaction terms turn out significant, this again would vote in favour of decaying skills due to over- and improving skills due to undereducation. The corresponding results are displayed in Table 2. Except for dummy specification (3) on reading comprehension, all corresponding coefficients on the educational match retain both their sign and their statistical significance, giving validity to the interpretation that workers are overeducated (undereducated) because of an inferior (superior) skill and competency endowment when compared to educational peers. 8 For the calculation of the years spent in each of this states of (un)employment information on a monthly level is utilized, hence resulting in more accurate measures than with exploiting years only. 16

17 Table 2: OLS estimates from regressing test scores (WLE) for literacy and numeracy skills on individual characteristics, including employment biographies Dependent variable: Test scores 1 on Reading speed Reading comprehension Math competency Selected regressors: (1) (2) (3) (4) (5) (6) Age.408***.382***.125***.117***.105***.095*** (.142) (.141) (.022) (.022) (.024) (.023) Age squared -.007*** -.007*** -.002*** -.002*** -.001*** -.001*** (.002) (.002) (2.46e-04) (2.43e-04) (2.71e-04) (2.60e-04) Job tenure (.034) (.032) (.005) (.005) (.005) (.005) Place of birth (D; 1=Germany) 8.982*** 9.005***.721***.660***.347***.293** (1.026) (.996) (.129) (.125) (.129) (.119) Secondary school leaving certificate/a levels 7.831*** 1.630*** 1.528*** (2.007) (.260) (.288) Vocational qualification 6.873*** 1.276*** 1.379*** (1.912) (.236) (.258) University (of Applied Science) degree *** 2.349*** 2.566*** (1.963) (.244) (.266) Overeducated (D) * * (.677) (.118) (.115) Undereducated (D) 1.751** ** (.788) (.132) (.143) Years of required education 1.280***.265***.320*** (.091) (.015) (.015) Years of excess education.979***.238***.259*** (.245) (.049) (.043) Years of deficit education *** -.200*** -.203*** (.270) (.039) (.040) Years of adequate employment (.019) (.018) (.003) (.003) (.003) (.003) Years of under-utilising employment (.021) (.019) (.004) (.003) (.003) (.003) Years of over-utilising employment *** (.038) (.023) (.006) (.003) (.006) (.004) Years of unemployment -.466*** -.444*** -.031* ** -.037* (.123) (.122) (.017) (.017) (.021) (.022) Interaction OE x job tenure (.063) (.017) (.010) (.003) (.010) (.003) Interaction UE x job tenure (.080) (.021) (.013) (.003) (.012) (.003) Number of observations 2,411 2,411 1,784 1,784 1,744 1,744 Source: NEPS Starting Cohort 6 (adults), wave 2. Robust standard errors in parentheses. Significance denoted as: *** p<0.01, ** p<0.05, * p<0.1. The constant, 16 state dummies, and 7 industry dummies are included in the regression, but not displayed. 1 Weighted maximum likelihood estimators (WLEs) based on scores across all test of the respective discipline, constrained to have mean zero, a minimum at -5 and a maximum at

18 Returns to education Considering the returns to education, to the extent that the additional human capital components of literacy and numeracy abilities that reach beyond formal education itself are associated with wages what is implied by corresponding studies, the introduction of these characteristics to the estimation of the returns to education is assumed to explain some part of the wage penalty associated with overeducation (wage premium of undereducation) when compared to educational peers as well as of the wage premium of overeducation (wage penalty of undereducation) when compared to workers in the same job. If this proves to be true, the rejection of human capital theory should be reconsidered. The residual deviation, if still existent, thus would imply either a prevailing mismatch and hence a dysfunctional allocation in the labour market or the existence of other unobserved marketable (=productivity-related) properties of individuals that overeducated (undereducated) workers lack (abound in), as implied by theory for the case of perfect allocation. To pursue this research question I run standard linear OLS estimations regressing wages (in logarithms) on several individual characteristics. In order to produce a viable benchmark, I estimate the standard regression excluding all human capital components beyond formal education on the same subsample for which information is available when estimating the extended specification including both working experience (age and tenure) and numeracy and literacy abilities. These further characteristics are then included step-by-step in specifications (2) and (3) to identify the impact of their consideration on the main coefficients, i.e. on the wage effects of over- and undereducation. The results are presented in Table 3. 18

19 Table 3: Returns to education and the impact of various competencies; dummy specification Dependent variable: Gross monthly wages (log) Formal education only Including Experience Full specification Selected regressors (1) (2) (3) Place of birth (D; 1=Germany).292***.260***.153*** (.048) (.047) (.046) Formal education Secondary school leaving certificate/a levels (.209) (.190) (.181) Vocational qualification (.169) (.147) (.140) University (of Applied Science) degree.531***.479***.265* (.171) (.149) (.144) Overeducated (D) -.096*** -.104*** -.096*** (.034) (.034) (.034) Undereducated (D).208***.202***.167*** (.062) (.058) (.057) Experience-related measures Age.056***.048*** (.015) (.015) Age squared -.001*** -4.82e-04*** (1.49e-04) (1.66e-04) Job tenure.013***.013*** (.005) (.005) Job tenure squared -3.34e-04** -3.29e-04** (1.31e-04) (1.30e-04) Literacy and numeracy abilities Reading speed test score 1.005*** (.002) Reading comprehension test score (WLE 2 ).052** (.021) Reading comprehension test score (SE) (.077) Math competency test score (WLE 2 ).027* (.016) Math competency test score (SE) (.098) Number of observations 1,024 1,024 1,024 R-squared Source: NEPS Starting Cohort 6 (adults), wave 2. Robust standard errors in parentheses. Significance denoted as: *** p<0.01, ** p<0.05, * p<0.1. The constant, 16 state dummies, and 7 industry dummies included in the regression, but not displayed. 1 Test score is scaled from 0 to 51 depicting the number of correctly judged sentences during a 2-minute test. 2 Weighted maximum likelihood estimators (WLEs) based on scores across all test of the respective discipline, constrained to have mean zero, a minimum at -5 and a maximum at +5. Let s start with the basal specification (1) that apart from the state and industry dummies included in every specification only contains formal educational attainment (in degrees) and a dummy on whether the place of birth is Germany. The coefficients appear as suggested by findings from similar studies. Compared to correctly-allocated educational peers, overeducation is associated with a wage penalty of about 9.6 log points (10.1 per cent), whereas undereducation involves a wage premium of 20.8 log points (23.1 per cent). Turning to specification (2) containing labour market experience proxied by age and job tenure (as well as their squared transformations), the coefficients for both over- and undereducation do not change significantly. This points to the restricted importance of work experience for 19

20 explaining the wage discrepancies between over-, under-, and adequately educated employees. Further extending the account for additional human capital components to literacy and numeracy abilities reveals distinctive and positive ceteris paribus correlations for each of the test scores on reading speed, reading comprehension, and math competency (confer specification (3)). First, an increase in reading speed corresponding to one more sentence judged correctly is associated with higher earnings. Although the coefficient appears small (0.5 log points), an increase in the test score for readings speed by one standard deviation is associated with 4.6 log points (4.7 per cent) higher earnings. In comparison, an increase in reading comprehension by one standard deviation is accompanied by higher earnings of around 5.2 log points (5.3 per cent). A corresponding increase in math competency is associated with higher wages by 2.7 log points (2.7 per cent). As opposed to experience-related measures, the inclusion of the literacy and numeracy competencies only shows the expected effect for undereducation in that it drives the corresponding coefficient statistically significant and substantially closer to zero. The coefficient on overeducation by and large retains its size. Thus, the importance of accounting for this competency-related heterogeneity of workers of similar educational attainment appears to be limited for explaining the wage penalty of overeducation but substantial for explaining the wage premium associated with undereducation. Addressing the ORU specification (Table A3 in the appendix), hence shifting comparison from educational peers to workers of the same job, conclusions are similar. However, in this case the coefficients on both returns to over- and undereducation are significantly reduced towards zero when comparing specification (1) and (3), thus implying that part of the wage premium (wage penalty) associated with overeducation (undereducation) can be explained by the heterogeneity with respect to reading and math competencies. Furthermore, as the coefficients are still both statistically and economically significant in both the dummy and the ORU specification it follows that there is a substantial mismatch in the labour market. Hence, this result is in line with similar analyses (cf. Alba-Ramírez (1993); Green et al., 2002; Chevalier and Lindley, 2009). However, there is still the possibility of other unobserved marketable human capital components that significantly affect the relative returns to wages between required, surplus, and deficit education. Such factors could further diminish the unexplained discrepancies in the returns to different parts of attained education, hence reducing the significance of the mismatch in the labour market. Alternative measurement of educational mismatch To acknowledge the fact that there are many ways of measuring educational mismatch and that these measurements can lead to different results, I additionally use an alternative measure as a robustness check. This measure relies on large-scale administrative data on employees liable to social security contributions, allowing me to identify required education per each of the 332 occupations of the occu- 20