Are Poles stuck in overeducation? Individual dynamics of educational mismatch in Poland

ABSTRACT

The paper investigates the short-run job mobility of educationally mismatched workers, examining the validity of the Sicherman-Galor hypothesis, which predicts that overeducation is a temporary condition from a worker’s perspective associated with higher upward occupational and wage mobility. The study uses data from the Polish Labour Force Survey, investigating yearly changes in employment status, occupation, and wages. The results show that overeducated workers are more likely to remain employed compared to their properly matched colleagues. Both overeducated and undereducated workers tend to move towards jobs for which they are better matched. However, the rate of this adjustment is very low, contradicting the Sicherman-Galor hypothesis. On the other hand, overeducated workers, but mostly prime-aged ones, are found to experience faster wage growth compared to properly matched individuals, aligning with the Sicherman-Galor hypothesis. The higher wage growth of overeducated workers can be partially attributed to workers improving their match status over time.

JEL CODES:

• I21
• J24

KEYWORDS:

• overeducation
• educational mismatch
• occupational mobility
• wage mobility

1. Introduction

Overeducation is a situation that a worker’s level of education exceeds the level required for his or her job. Such situation raises concerns about the underutilization of human capital and has been of interest to researchers for a long time. Determining whether the educational mismatch is temporary or persistent phenomenon is crucial from a policy perspective. Numerous studies have found that overeducation is a negative situation for individuals. Overeducation suppresses wages of overeducated workers (Duncan & Hoffman, 1981; Hartog, 2000), leads to lower job satisfaction, and may cause human capital depreciation (for comprehensive literature reviews, see: Leuven & Oosterbeek, 2011; Quintini, 2011). If overeducation is a persistent phenomenon, it calls into question the rationale behind policies aimed at the universal expansion of tertiary education. It also raises the need for further discussion on what policies can lead to an improvement in the quality of job matches. However, if overeducation is found to be short-lasting from a worker’s perspective, i.e. overeducated workers quickly move to jobs that better utilize their education, there is less cause for concern.

There are several possible theoretical explanations for the existence of overeducation, which have different implications for the persistence of educational mismatch. Sicherman and Galor (1990) proposed the career mobility theory which suggests that young individuals may voluntarily accept being overeducated at the beginning of their career paths in order to gain job experience to enhance their chances for faster promotion. In light of the Sicherman-Galor hypothesis, overeducation mainly affects young, inexperienced individuals, but it is also associated with increased rates of upward occupational mobility and wage growth in subsequent periods. In this view, overeducation is a stepping stone to better career prospects. If Sicherman and Galor are correct, overeducation should vanish over time and initially overeducated workers should be eventually better-off.

Another possible explanation is that overeducated workers might differ from their equally educated peers in terms of human capital components other than formal education, such as skills or innate ability. Thus, overeducation might be merely an apparent phenomenon reflecting differences in unobserved human capital endowments between overeducated and properly matched workers (the so-called compensation hypothesis, Sicherman, 1991). In this view, the disappearance of overeducation would only be observed if there is an improvement in unobserved human capital components.

An alternative perspective is offered by Thurow’s job competition model (Thurow, 1975), in which a worker’s productivity is defined by their job, while jobs differ in terms of training costs, and workers differ in terms of their trainability. In light of Thurow’s model, formal education is used by employers to assess a worker’s trainability. As a result, the best-educated workers get the highest-ranked jobs, while workers with lower education levels are crowded down in the job ranking. Similarly, under Spence’s signalling theory (Spence, 1973), formal education is a means of demonstrating a worker’s innate ability. Hence, both Thurow’s and Spence’s models suggest that workers have an incentive to overinvest in formal education to maximize their chances of getting the highest-ranked jobs. This explains individuals’ rationale behind excessive schooling.

Overeducation can be also seen as a result of frictions of the matching process in the labour market. Since job searching is resource-consuming and associated with an opportunity cost, individuals looking for a job might eventually accept positions which do not properly match their education level because they simply cannot afford to continue searching. Overeducation disappears over time as mismatched workers obtain information on job offers that better match their education. The speed of transition to properly matched jobs likely depends on the effectiveness of labour market institutions. However, under conditions of information asymmetry, current overeducation might send a negative signal to the labour market about a worker’s actual productivity and reduce his or her chances of transitioning to better matched jobs (Grunau & Pecoraro, 2017). Finally, overeducation might result from an aggregate mismatch between the high supply of well-educated workers and the low demand for high qualifications in the economy. From this perspective, overeducation would be persistent as long as the mismatch between supply and demand sides remains.

The aim of this study is to contribute to the empirical literature testing the dynamic implications of the Sicherman-Galor model predicting that overeducation is a temporary condition from a worker’s perspective, leading eventually to a better employment situation, i.e. higher-ranked and better-paid jobs. In the paper, several aspects of job mobility are investigated: the probability of remaining employed, upward occupational mobility, and wage dynamics. Such a broad scope of analysis is needed to have a comprehensive view of the validity of the Sicherman-Galor hypothesis. The empirical strategy builds on previous studies in this area, especially Rubb (2006) and Korpi and Tåhlin (2009). The analysis uses data from the Polish Labour Force Survey and covers the period from 2011 to 2018.

The rest of the paper is organized as follows. Part 2 discusses the empirical literature investigating the job and wage mobility of overeducated workers. Part 3 presents the data, discusses the empirical strategy employed in the study, and reports descriptive statistics. Part 4 presents the results of the econometric analysis. Part 5 includes a discussion of findings and concludes.

2. Literature review

Sicherman (1991) was the first researcher to empirically test the implications of the Sicherman-Galor hypothesis by investigating the firm and occupational mobility of overeducated workers using US data for the late 1970s. To identify upward mobility, he constructed a ranking of occupations using an eclectic measure of the human capital needed for an occupation, which combined information on formal schooling, previous experience, and required training. Overeducated individuals were found to experience more firm and occupational mobility, including upward occupational mobility, compared to properly matched workers of the same education level. However, the size of the identified effect was moderate: additional 3 p.p. of probability to move to a higher-ranked occupation for overeducated individuals. Furthermore, undereducated workers¹ were found to have increased chances of moving to higher-ranked occupations compared to properly matched workers.

Robst (1995a) pointed out a methodological flaw in Sicherman’s study that was controlling for actual schooling rather than required schooling.² Robst argued that, due to this flaw, the findings of increased mobility of overeducated workers might simply reflect the greater average mobility of workers in jobs that require less schooling. After addressing this issue using the same data source as Sicherman, Robst found results that partially diverged from Sicherman’s findings. Overeducated workers were again found to be more likely to move to jobs requiring more schooling in subsequent years compared to properly matched workers (of the same required education). However, they did not experience more job and occupational mobility in total. Undereducated workers were found to be more likely to experience job and occupational mobility in total, but less likely to move to jobs requiring more schooling compared to properly matched workers.

In line with the Sicherman-Galor model, Alba-Ramírez (1993), who analysed the situation of Spanish workers, found that overeducated workers experience shorter job durations, higher job turnover, and tend to improve their match status over time. Further evidence in favour of transitory overeducation was provided by Frei and Sousa-Poza (2012) in a study for Switzerland. The overeducation spells identified by Frei and Sousa-Poza were relatively short-lasting. About 60% of overqualified workers left overeducation within the next year, and about 90% within a four-year time horizon.³

Contrary to the hypothesis of short-lasting overeducation, Sloane et al. (1999) showed that overeducated workers tend to experience more frequent job changes that do not necessarily lead to an improvement in their education match. Furthermore, a group of studies for different economies reported large shares of overeducated workers remaining in the mismatch. Battu et al. (1999), who analysed the situation of British tertiary education graduates 1, 6, and 11 years after graduation, demonstrated that around 30% of graduates failed to find a well-matched job at any point in time. Similarly, Dolton and Vignoles (2000) reported that among the British graduates of 1980 38% were overeducated in the first job, and even six years later the share of overeducated workers was still 30%. Further evidence for the United Kingdom was provided by Lindley and McIntosh (2009) who reported that out of individuals identified as overeducated in 1991, 46% were still overeducated in 1996, and 18% in 2006. Rubb (2003) presented descriptive statistics for the US for the 1990s showing that 74% of the overeducated workers remained in overeducation after one year, less than one-fifth became properly matched, while the rest left full-time employment.⁴ Similarly, Clark et al. (2017) reported that 66% of overeducated workers in the US remained in overeducation after one year. Frenette (2004) provided an evidence of the persistent overeducation among graduates in Canada showing that only one-fourth of those who were overeducated two years after graduation improved their match three years later. Furthermore, some of the abovementioned studies also found that there is a non-negligible share of properly matched workers who become overeducated, a feature that cannot be explained by the Sicherman-Galor model. For instance, in Frenette’s (2004) study, one-eighth of those who were not overeducated became overeducated.

Two recent studies using panel data from Germany also provide evidence of persistent overeducation. Boll et al. (2016) ran a dynamic mixed multinomial logit model to overcome the problem of individual heterogeneity. They found that overeducation, especially self-reported one, is highly state-dependent. According to their results, the probability of being in self-assessed overeducation increases by 28%-43% if an individual was in overeducation in the previous year. Similarly, Erdsiek (2021) reported strong persistence of overeducation among young university graduates. Being overeducated 5 years earlier increases the chances of current overeducation by 45 p.p. However, results from a dynamic random-effects probit model run by Erdsiek indicate that most of this effect can be explained by observable and unobservable heterogeneity of individuals.

There is growing empirical evidence suggesting that transitions to properly matched jobs might be hindered by the scarring effect associated with overeducation. Studies by Baert et al. (2013) and Meroni and Vera-Toscano (2017) showed that for young graduates at the beginning of their careers, taking up a job for which they are overeducated decreases their chances of finding a well-matched job in subsequent periods compared to staying longer in unemployment. Further evidence of the scarring effect of overeducation was provided by Clark et al. (2017), who showed that past episodes of overeducation exert a negative impact on current wages, even if an individual moves to a matched job.

Another dynamic implication of the Sicherman-Galor model is the greater upward wage mobility of overeducated workers. This implication started to be tested later than the implication of increased job mobility. The first paper to address this issue was Büchel and Mertens (2004). They pointed out that studies such as Sicherman (1991), although demonstrating that overeducated workers experienced more job mobility, missed the aspect of the quality of subsequent jobs. Based on data for Germany, Büchel and Mertens found that overeducated workers experienced lower wage growth than properly matched workers. In the context of job mobility, they also found that overeducated workers experienced less mobility to higher-ranked jobs, while greater mobility was found for undereducated workers.

In turn, Korpi and Tåhlin (2009) argued that the results by Büchel and Mertens were dependent on the inclusion of workers’ actual schooling, rather than required schooling, in the regression model. This meant that that the overeducation indicator reflects low occupational rank rather than mismatch, which is similar to Robst’s critique (1995a) of Sicherman’s study (1991). In their study for Sweden, which applied the ORU specification⁵ for the percentage change of wages, Korpi and Tåhlin found that each year of excess schooling (overeducation) adds positively to wage dynamics. This effect is of a similar size as for required schooling when the initial wage level is not controlled, while it is half the size of the effect for required schooling when the initial wage level is controlled. This means that overeducated individuals experience faster wage growth on average compared to their properly matched colleagues (of the same required education). However, they are penalized compared to equally educated workers who are properly matched. Lacking schooling (undereducation) was found to add negatively to wage dynamics.

Rubb (2006) verified both dynamic implications of the Sicherman-Galor model using US data. Similarly to Korpi and Tåhlin, Rubb estimated the ORU wage model, controlling for the initial wage level, and also investigated the probability of upward occupational mobility. He found that excess schooling increases the chances of upward occupational mobility, while lacking schooling decreases them. Years of excess schooling positively contribute to wage dynamics, but this effect is about half the size of the effect of required schooling (which is in line with Korpi and Tåhlin). Lacking schooling contributes negatively to wage dynamics. Following Rubb (2006) and Korpi and Tåhlin (2009), this paper incorporates the ORU specification-based approach to investigate the mobility of overeducated workers.

Frenette (2004) also investigated the impact of mismatch status on wage change. Rather than using initial mismatch status, the identification was based on individuals changing their mismatch status between two periods (over a three-year period). He found that moving from overeducation to non-overeducation increases wages (by about 3–11% depending on the type of tertiary education degree). It is worth mentioning that the overeducation wage penalty identified based on those who switch from overeducation to non-overeducation is greater than the penalty identified based on individuals who switch from non-overeducation to overeducation (for them it is closer to zero).

Grunau and Pecoraro (2017) analysed upward career mobility, defined as a promotion to managerial positions, in Germany. They found that overeducated workers have greater chances of being promoted to managerial positions compared to equally educated peers, which supports the Sicherman-Galor hypothesis. When differentiating between promotions within firms and between firms, they found that overeducated workers are less likely to be promoted when changing firms, which suggests that overeducation is a negative signal to other employers. They also found that overeducated workers experience a relative wage improvement when being promoted, while non-promoted overeducated workers staying with the same employer experience a wage decrease compared to equally educated workers.

Recently, Wen and Maani (2019) employed a dynamic random effects probit model, using data for Australia. They found that overeducated workers have a lower likelihood of upward occupational mobility and slower wage growth, which opposes the Sicherman-Galor model. The study also suggests that previous upward occupational mobility and previous wage growth increase current upward occupational and wage mobility, respectively. In turn, in a recent study for Germany, Roller et al. (2019) found that overeducated workers experience faster wage growth than their properly matched colleagues.

The evidence on the persistence of overeducation in Poland is limited. Notable exceptions are two papers by Kiersztyn (2011, 2013), using data from the longitudinal survey POLPAN. In the first paper, Kiersztyn reported that about 50%–68% of overeducated workers remained overeducated after 5 years. In the second paper, she demonstrated that overeducated workers faced about four times higher probability of being in overeducation after 5 years compared to not-overeducated workers. She interpreted these results as opposing the Sicherman-Galor hypothesis. Because Kiersztyn’s studies cover only the period 1988–2008 and do not address wage mobility, there is an apparent gap in the literature.

To sum up the literature review, the implication of the temporary nature of overeducation has been tested by many researchers, yielding mixed results. There is a substantial body of literature supporting the Sicherman-Galor hypothesis of overeducation as a stepping stone in one’s career (Alba-Ramírez, 1993; Frei & Sousa-Poza, 2012; Grunau & Pecoraro, 2017; Korpi & Tåhlin, 2009; Robst, 1995a; Roller et al., 2019; Rubb, 2006; Sicherman, 1991), alongside a considerable number of papers presenting contrary evidence (Battu et al., 1999; Boll et al., 2016; Clark et al., 2017; Dolton & Vignoles, 2000; Erdsiek, 2021; Frenette, 2004; Lindley & McIntosh, 2009; Rubb, 2003; Sloane et al., 1999). Nevertheless, the literature seems to have reached a consensus that both occupational and wage mobility should be investigated to provide a comprehensive picture of the validity of the Sicherman-Galor model.

3. Data and methodology

In the study, I use microdata from the Polish Labour Force Survey (Badanie Aktywności Ekonomicznej Ludności). The timespan of the analysis is 2011–2018. Changes in overeducation status can be analysed as the LFS data allow for the construction of short panels up to six quarters. For the purpose of this study, I construct a sample in which each individual is observed twice. The second observation is made exactly one year after the first one. The sample consists of individuals aged 19–65 who worked in the first period. The sample size is at best 242,560 observations. When analysing the mismatch change, the sample size is reduced to 225,736 observations as individuals who do not work in the second period are excluded. The sample size for the wage change estimations is much smaller. The reason behind this is the large number of respondents declining to answer the question about their wages. Furthermore, I also purposely delete observations for 1% of the lowest and 1% of the highest values of the percentage change of wages to prevent the results from being driven by outliers. As a result, the sample for the wage change regression is reduced to 51,497 observations (which makes up 23% of individuals working in both periods).

To identify education mismatch, I follow the so-called realized matches approach. This approach is one of three main approaches frequently used to identify overeducation, along with the job analysis approach and the subjective approach. The realized matches approach is apparently the most popular one due to the simplicity of its application. A researcher who wants to apply this method needs no information other than the education distribution within occupations. The other two approaches, although often said to be more preferable than the realized matches approach, require additional data on an analyst’s assessments of required education for different types of occupations (for the job analysis approach) or workers’ self-assessment of their match quality (for the subjective approach). However, these additional data are seldom available. According to the realized matches approach, the required level of education for a given occupation is defined as a measure of central tendency of years of schooling in that occupation. Verdugo and Verdugo (1989) proposed using the mean value of years of schooling.⁶ Alternatively, Kiker et al. (1997) proposed using the modal value of schooling of workers in a given occupation. Besides the mean and modal values, one might also consider using the median number of years of schooling of workers in a given occupation. In this paper, I use all three measures of central tendency, which allows me to check whether the results are sensitive to using a different measure of required education (they are not).⁷

To determine education mismatch, I first assign the number of years of schooling typically corresponding to the reported education level to all individuals in the sample. This means that all individuals with the same highest level of education are assigned the same number of years of schooling. For instance, individuals with only primary education (ISCED 0–1) are assigned the lowest schooling of 6 years, while people with a doctorate degree (ISCED 8) are assigned the highest schooling level of 21 years. However, this does not necessarily reflect the actual years of schooling for individuals who followed non-regular education paths.

Occupations are reported by their two-digit codes according to the Polish classification of occupations, which is consistent with the International Standard Classification of Occupations (ISCO). At this level of representation, there are 51 different occupations in the sample. To obtain required schooling for each occupation, I calculate the mean, mode and median values of schooling for all workers in that occupation. Observations from different years are pooled together so that required schooling remains the same for each year. If education requirements were calculated separately for each year, it would be difficult to interpret changes in overeducation. This is because changes could arise either from workers changing jobs or from changes in required schooling. I want to avoid this ambiguity.⁸ I also assume that a worker’s education level remains the same in the second period as it was in the first period. Therefore, any changes in mismatched schooling must be due to workers changing their occupation.

The degree of education mismatch (mismatched schooling) is calculated as the difference between the number of years of schooling corresponding to a worker’s actual level of education and the number of years of schooling required for a worker’s occupation. See Figure 1 for the distribution of mismatched schooling in the first period. Following the approach of Duncan and Hoffman (1981), I express workers’ education using the so-called ORU decomposition. This method is well-established in the overeducation literature and is commonly used in studies on the impact of overeducation on workers’ wages. According to the ORU decomposition, a worker’s schooling ($\mathrm{edu}$) is the sum of schooling required for their occupation ($\mathrm{redu}$) and one of two components representing the number of years of mismatched schooling: excess schooling ($\mathrm{oedu}$) or lacking schooling ($\mathrm{uedu}$). Depending on whether a worker’s actual education exceeds required education, there are three possible cases:

• if $\mathrm{edu}>\mathrm{redu}$, actual education is represented as a sum of required education and excess education, $\mathrm{edu}=\mathrm{redu}+\mathrm{oedu}$, and workers are labelled as overeducated;

• if $\mathrm{edu}<\mathrm{redu}$, actual education is represented as required education minus lacking education, $\mathrm{edu}=\mathrm{redu}-\mathrm{uedu}$, and workers are labelled as undereducated;

• if $\mathrm{edu}=\mathrm{redu}$, there is no mismatched schooling and workers are labelled as properly matched.

Figure 1. The distribution of mismatched schooling in the sample, first period.

Since I address the different aspects of the job mobility of educationally mismatched workers, I adopt different dependent variables and econometric strategies. They are needed to comprehensively test whether overeducation is a temporary condition leading to improvement in a worker’s employment situation. In the first model (model 1), I analyse how the education mismatch is associated with the chances of staying in employment in the second period of observation. In this model, the dependent variable is a dummy variable taking the value 1 if a worker continues working in the second period, and 0 otherwise. The second model (model 2) investigates whether workers who stay in employment experience the upward occupational mobility. To analyse this issue, I use a dependent variable that is a dummy variable taking the value 1 if a worker reports an occupation in the second period that requires more schooling than the occupation reported in the first period, and 0 otherwise. In the third model (model 3), I examine the change in the number of years of required schooling between the two periods. In this model, the dependent variable is continuous. Positive values of the dependent variable indicate that workers who were initially overeducated reduced their years of excess schooling and moved towards properly matched jobs. On the other hand, workers who were initially undereducated increased their lacking schooling and moved away from properly matched jobs. In the next model (model 4), I rerun model 3 addressing the selection issue. Finally, I investigate the wage mobility (models 5 and 6). The dependent variable in models 5 and 6 is the percentage change in full-time equivalents of monthly real wage.

For the dummy dependent variables the logistic regression is used (models 1 and 2). For the continuous dependent variables models (models 3, 5 and 6) are estimated with the OLS method. For model 4, the Heckman correction method is used.

The explanatory variables used in the econometric analysis are:⁹

• $\mathrm{redu}$ – the number of years of required education for a given occupation.

• $\mathrm{oedu}$ – the number of years of excess schooling, i.e. positive values of the difference between the years of schooling assigned to a worker’s education level and the number of years of schooling required for their occupation.

• $\mathrm{uedu}$ – the number of years of lacking schooling.

• $\mathrm{female}$ – a dummy variable taking the value 1 for females and 0 for males.

• $\mathrm{age}$ – a worker’s age (continuous variable).

• $\mathrm{tenure}$ – a variable describing how long a worker has worked for their current employer.

• $\mathrm{disability}$ – a dummy variable taking the value 1 for people with disabilities and 0 otherwise.

• $\mathrm{unemployment}$ – a regional unemployment rate.

• $\mathrm{region}$ – a categorical variable for voivodeships.

• $\mathrm{urbanisation}$ – a categorical variable for the size of place of a worker’s residence (degree of urbanization). The reference level is cities with more than 100 thousand inhabitants. The other categories are towns with 20–100 thousand inhabitants, towns with less than 20 thousand inhabitants, and rural areas.

• $\mathrm{sector}$ – a categorical variable for the sector of economic activity according to the NACE classification.

• $\mathrm{year}$ – a set of yearly period dummies. The dummies aim to capture the effect of changing labour market conditions.

• $\ln (\mathrm{initialwage})$ – the natural logarithm of a worker’s (real) wage in the first period. Full-time equivalents are used. (The variable is used in models 5 and 6).

• $\mathrm{positive}.\mathrm{redu}.\mathrm{change}$ and $\mathrm{negative}.\mathrm{redu}.\mathrm{change}$ – changes in the number of years of required schooling between periods, respectively positive and negatively values (used in model 6).

• $\mathrm{child}$ – a dummy variable taking value 1 if there is a child aged 3 or younger in a worker’s household (used in the selection equation in model 4).

• $\mathrm{other}\mathrm{worker}$ – a dummy variable taking value 1 if there is another working individual in a worker’s household (used in the selection equation in model 4).

Since the study focuses on the occupational and wage mobility of overeducated workers, the estimates of coefficients for the number of years of excess schooling, $\mathrm{oedu}$, are of my main interest.

The general form of models 1, 2, and 3 is as follows: $\mathrm{dep}.\mathrm{va}{r}_i=\alpha +{\beta }_1\mathrm{red}{u}_i+{\beta }_2\mathrm{oed}{u}_i+{\beta }_3\mathrm{ued}{u}_i+\mathit{\beta }{\mathit{X}}_{\mathit{i}}+{ϵ}_i$where $X_i$ is a vector of control variables, $\alpha$ is a constant, and ${ϵ}_i$ is an error term.

Due to the fact that not all workers stay in employment in the second period, there is a potential problem of sample selection that might bias the results. It is plausible to think that selection is not random and depends on variables in the model. In fact, the results for model 1 (Table 4) suggest that workers who were overeducated in the first period are more likely to remain in employment in the second period. Thus, as a robustness check, I also use the model with the Heckman correction (model 4).¹⁰ The selection model is a probit regression with additional variables: a dummy for individuals with children aged 3 or younger, a dummy for individuals living in households with other working individuals, and interaction terms of each of these two variables with a female dummy. The model is estimated using the two-step procedure.

Model 5 describing the percentage change of the full-time equivalent monthly wages has the following specification: $\mathrm{wagechang}{e}_i=\alpha +{\beta }_1\ln (\mathrm{initialwag}{e}_i)+{\beta }_2\mathrm{red}{u}_i+{\beta }_3\mathrm{oed}{u}_i+{\beta }_4\mathrm{ued}{u}_i+\mathit{\beta }{\mathit{X}}_i+{ϵ}_i$Compared to previous models, the specification for the percentage change in wages is augmented with an additional variable, which is the logarithm of the initial wage level, added following Rubb (2006) and Korpi and Tåhlin (2009). The variable is included to control for the fact that for individuals with a lower starting wage level it is easier to experience faster percentage wage growth. On the other hand, those who have already high wages tend to experience slower wage growth in percentage terms.

Model 6, which also examines the percentage change of the full-time equivalent monthly wages, includes other two additional variables, $\mathrm{positive}.\mathrm{redu}.\mathrm{change}$ and $\mathrm{negative}.\mathrm{redu}.\mathrm{change}$. These continuous variables reflect the difference in required schooling between two periods (the same as the dependent variable in models 3 and 4). The variables aim to control whether the wage change is associated with a change in mismatch status.¹¹ However, values for positive and negative changes are included as separate variables following Frenette (2004), who demonstrated that switching from overeducation to non-overeducation is associated with a different size of the wage effect than switching from non-overeducation to overeducation. Hence, the model 6 has the following specification: $\begin{array}{r}\mathrm{wagechang}{e}_i=\alpha +{\beta }_1\ln (\mathrm{initialwag}{e}_i)+{\beta }_2\mathrm{red}{u}_i+{\beta }_3\mathrm{oed}{u}_i+{\beta }_4\mathrm{ued}{u}_i\\ +{\beta }_4\mathrm{pos}.\mathrm{redu}.\mathrm{chang}{e}_i+{\beta }_4\mathrm{neg}.\mathrm{redu}.\mathrm{chang}{e}_i+\mathit{\beta }{\mathit{X}}_i+{ϵ}_i\end{array}$The robustness of the results is addressed in three ways. Firstly, different approaches to identify education mismatch are used. With mean, modal and median schooling used as measures of required schooling, I examine whether the findings are dependent on how educational mismatch is identified, at least within the family of the realized matches approach. Secondly, the estimations are presented starting from the most parsimonious model, containing only the ORU variables, to the fully specified model, which enables to check the stability of coefficients depending on the model specification. Thirdly, I rerun estimations on subsamples for different age groups. While the Sicherman-Galor hypothesis offers a theoretical framework for understanding overeducation among young workers, it does not address the issue of overeducation among prime-aged and older workers. Hence, it might be the case that workers belonging to different age groups face different mismatch and job mobility patterns. Including age as a control variable might not be enough to capture this variation. Hence, I split the whole sample according to three age groups corresponding to different stages of work career: young workers (under 30), prime-aged workers (30–49), and older workers (50 or older).

3.1. Descriptive statistics

Let us summarize the prevalence of education mismatch in the data. Table 1 describes the average number of years of schooling in the sample, broken down according to the ORU decomposition. For required education calculated as the mean number of years of schooling of workers in a given occupation, the average number of years of required schooling in the sample is 13.06 in the first period and slightly increases to 13.10 in the second period. The average number of years of excess schooling is 0.70 in the first period and decreases to 0.65 in the second period. For lacking schooling, it is 0.77 years in the first period and 0.71 years in the second period. Similar results are obtained when required schooling is calculated as a mode or median. For each approach, required schooling slightly increases in the second period, while excess and lacking schooling decrease. Thus, the results suggest that there is a reduction in mismatched schooling in the second period.

Table 1. Average number of required, excess and lacking years of schooling in the sample.

	t = 1			t = 2
Required schooling calculated as	redu	oedu	uedu	redu	oedu	uedu
mean	13.06	0.70	0.77	13.10	0.65	0.71
mode	13.30	0.56	0.86	13.34	0.52	0.79
median	13.05	0.65	0.71	13.09	0.60	0.65
obs. (workers)	242,560			225,736
share of working	100%			93.1%

However, the decreased mismatched schooling in the second period might be potentially driven by mismatched individuals flowing out of employment. In fact, the share of non-working individuals in the second period is 6.9% (cf. Table 1). Table 2 examines those who stayed in employment in both periods and changed their required schooling. Changes in required schooling are rather uncommon. Results based on the mean approach for calculating required schooling indicate that 5.3% of individuals who worked in both periods changed their degree of required schooling in the second period. For the two other approaches, the share of workers changing required schooling is much smaller: 2.3% for the mode approach, and 3.1% for the median approach. For those who change required schooling, the average change is 0.07 for the mean approach, and 0.22 for the mode approach, and 0.12 for the median approach. This means that, on average, workers tend to move upward on an occupational ladder to jobs that require more schooling. Also the median change in required schooling suggests the upward occupational mobility.

Table 2. Change in required schooling in the sample.

Required schooling calculated as	Average change	Median change	% of workers changing required years schooling
whole sample
mean	0.07	0.04	5.3%
mode	0.22	2.00	2.3%
median	0.12	1.00	3.1%
edu > redu in the first period (overeducated workers)
mean	1.33	1.45	8.3%
mode	3.22	4.00	3.4%
median	1.88	2.00	4.3%
edu < redu in the first period (undereducated workers)
mean	−0.96	−0.90	5.9%
mode	−2.34	−4.00	3.1%
median	−1.39	−2.00	3.8%

Notes: Individuals who did not change years of required schooling were excluded.

Table 2 also includes information on changes in required schooling for two subsamples of overeducated and undereducated workers, respectively. For overeducated workers, i.e. workers for whom actual schooling exceeded required schooling in the first period, a clear upward shift in required schooling is observed. For overeducated workers who change their required schooling, the average change ranges from 1.33 for the mean approach to 3.22 for the mode approach. The reverse tendency is observed in the case of undereducated workers. Undereducated workers who change their required schooling tend to move to occupations requiring less schooling. To sum up, the descriptive statistics suggest that although a small fraction of mismatched workers change their occupation, those who change move to jobs that better match their education.

Table 3 provides an additional insight into the distribution of the educational mismatch in the sample. It features ORU decompositions reported for two genders, three age groups and the years of the analysis. The breakdown by gender reveals that women work in occupations requiring substantially more schooling compared to men. The difference in average required schooling between women and men is 0.9–1.4 year. However, there is no clear picture of differences in mismatched schooling between two genders: women have on average more excess schooling than men according to the mean approach, the opposite holds for the mode approach, whilst the median approach shows almost equal levels of excess schooling for women and men. According to the breakdown by age, the highest level of required schooling is found among the prime-aged workers, whilst young and older workers work in occupations requiring somewhat less schooling. The level of excess of schooling is the highest among the young workers and the lowest among the older ones, which is in line with the Sicherman-Galor hypothesis. The exact opposite holds for lacking schooling. The breakdown by year reflects the changes occurring in occupational composition. It shows that workers were increasingly finding employment in occupations that require higher levels of education.¹² However, it appears that the actual composition of education was improving at a faster rate. This is reflected in a steady increase in the average number of years of excess schooling and a steady decrease in the average number of lacking schooling.

Table 3. Average number of required, excess and lacking years of schooling in the sample (detailed breakdown, t = 1).

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	redu	oedu	uedu	redu	oedu	uedu	redu	oedu	uedu
all	13.06	0.70	0.77	13.30	0.56	0.86	13.05	0.65	0.71
males	12.62	0.67	0.77	12.65	0.62	0.76	12.53	0.66	0.67
females	13.57	0.73	0.76	14.04	0.49	0.98	13.65	0.64	0.75
aged 29 or less	13.00	0.93	0.54	13.19	0.84	0.64	12.94	0.94	0.49
aged 30–49	13.21	0.73	0.70	13.46	0.55	0.77	13.21	0.67	0.64
aged 50 or more	12.85	0.50	1.04	13.08	0.40	1.15	12.85	0.44	0.97
2011	12.94	0.63	0.84	13.16	0.50	0.93	12.92	0.58	0.77
2012	13.00	0.67	0.80	13.23	0.53	0.90	12.99	0.61	0.74
2013	13.02	0.69	0.77	13.25	0.55	0.87	13.00	0.64	0.71
2014	13.03	0.70	0.76	13.26	0.57	0.86	13.02	0.66	0.70
2015	13.05	0.72	0.75	13.27	0.58	0.83	13.03	0.68	0.69
2016	13.26	0.76	0.69	13.52	0.60	0.79	13.26	0.71	0.64
2017	13.29	0.79	0.68	13.55	0.62	0.78	13.28	0.74	0.63

4. Empirical analysis

In this part, I present and discuss the results of the econometric analysis. To enhance comparability, the general outline of the tables is very similar. Each table has nine columns, with three columns for each approach to calculate required schooling, starting from the most parsimonious specifications to the fully specified models. This way of presentation shows whether the coefficients for explanatory variables are robust to changes in model specification and approach used to identify required schooling.

4.1. Probability of staying in employment

Firstly, let us discuss the results for the logistic regression model of the probability of staying in employment in the second period (model 1). The estimation results are presented in Table 4. First of all, we see that people working in occupations requiring more schooling had a higher probability of staying in employment in the second period. In all estimations presented, excess schooling increases the chances of staying in employment in the second period. However, the size of this effect is smaller compared to required schooling. The average marginal effect of a one-year increase in required schooling is about 0.007–0.009 based on the results from the fully specified models. The average marginal effect for excess schooling is about 0.002–0.003, also based on the fully specified models. In contrast, lacking schooling decreases the chances of staying in employment in the second period, by 0.004–0.005. Introducing controls for age and tenure – undereducated workers are usually older and have longer tenures, while overeducated workers are typically found among the young with short tenures – increases the coefficients for excess schooling. The coefficients for the controls are in line with intuition: being a woman decreases the chances of staying in employment, a larger tenure increases them, and having a disability decreases them. A higher regional unemployment rate is associated with lower chances of staying in employment. Generally, the results for the mean, mode and median methods are very similar. Concluding, mismatched schooling differentiates the chances of staying in employment in the second period. Overeducated workers are slightly more likely to stay in employment compared to their properly matched colleagues working in the same occupations. However, if they are compared to individuals of the same education level but working in occupations of higher schooling required, they have lower chances of staying in employment. The reverse conclusion applies to undereducated workers.

Table 4. Results of logistic regression of probability of staying in employment in the second period (model 1).

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
redu	0.130***	0.139***	0.153***	0.098***	0.112***	0.114***	0.117***	0.131***	0.139***
oedu	0.015**	0.046***	0.033***	0.018**	0.057***	0.047***	0.021***	0.052***	0.043***
uedu	−0.063***	−0.068***	−0.070***	−0.082***	−0.080***	−0.080***	−0.068***	−0.069***	−0.070***
female		−0.377***	−0.433***		−0.375***	−0.439***		−0.384***	−0.438***
age		0.281***	0.286***		0.281***	0.286***		0.281***	0.286***
age sq.		−0.003***	−0.003***		−0.003***	−0.003***		−0.003***	−0.003***
tenure		0.042***	0.035***		0.042***	0.037***		0.042***	0.036***
disability		−0.351***	−0.397***		−0.360***	−0.404***		−0.362***	−0.403***
unemployment			−0.061***			−0.061***			−0.061***
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	0.969***	−4.564***	−4.132***	1.379***	−4.225***	−3.638***	1.134***	−4.455***	−3.934***
LR chi2	1157	7934	9702	1038	7840	9587	1119	7925	9675
prob. > chi2	0	0	0	0	0	0	0	0	0
pseudo R2	0.009	0.066	0.081	0.008	0.066	0.080	0.009	0.066	0.081
obs.	242,560	240,072	239,813	242,560	240,072	239,813	242,560	240,072	239,813
average marginal effects
redu	0.0084	0.0085	0.0092	0.0063	0.0068	0.0069	0.0075	0.0080	0.0084
oedu	0.0010	0.0028	0.0020	0.0011	0.0035	0.0029	0.0014	0.0032	0.0026
uedu	−0.0040	−0.0041	−0.0042	−0.0053	−0.0049	−0.0048	−0.0044	−0.0042	−0.0042

*** p < 0.01, ** p < 0.05, *p < 0.1.

4.2. Upward occupational mobility

Now, let us move to the results of the logistic regression describing the probability of a worker moving to a higher-ranked occupation requiring more schooling (model 2, Table 5). This situation means that individuals either reduce their excess schooling or increase their lacking education. First, we see that the coefficients associated with required schooling are negative, which means that workers in occupations that already require higher levels of schooling are less likely to move to occupations requiring even more schooling. The coefficients for excess schooling are positive and statistically significant in all estimations. It means that overeducated individuals are more likely to move to occupations requiring more schooling in the second period compared to properly matched individuals. In contrast, the coefficients for lacking schooling are negative, which means that undereducated individuals are less likely to move to jobs that require more schooling. The similar results are obtained regardless of the approach used to identify required schooling. Hence, the results confirm that there is some degree of shift to better matched jobs in the second period, as was already suggested by the descriptive statistics reported in Table 2.

Table 5. Results of logistic regression of probability of moving to occupation requiring more schooling (model 2).

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
redu	−0.192***	−0.204***	−0.316***	−0.180***	−0.212***	−0.409***	−0.126***	−0.147***	−0.317***
oedu	0.292***	0.258***	0.247***	0.410***	0.372***	0.354***	0.379***	0.345***	0.327***
uedu	−0.057***	−0.035***	−0.030**	−0.166***	−0.162***	−0.136***	−0.132***	−0.123***	−0.103***
female		0.125***	0.101***		0.490***	0.436***		0.344***	0.249***
age		−0.110***	−0.109***		−0.155***	−0.152***		−0.137***	−0.133***
age sq.		0.001***	0.001***		0.002***	0.002***		0.001***	0.001***
tenure		−0.033***	−0.027***		−0.033***	−0.018***		−0.033***	−0.020***
disability		−0.005	−0.059		0.099	−0.001		0.067	0.004
unemployment			−0.074***			−0.076**			−0.091***
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	−1.360***	1.423***	3.766***	−2.527***	1.240***	4.457***	−2.871***	0.398*	3.680***
LR chi2	2044	3259	4280	2409	3200	4171	2097	2890	3982
prob. > chi2	0	0	0	0	0	0	0	0	0
pseudo R2	0.036	0.059	0.077	0.083	0.114	0.148	0.056	0.080	0.111
obs.	225,736	223,707	223,473	225,736	223,707	223,464	225,736	223,707	223,464
average marginal effects
redu	−0.0051	−0.0053	−0.0081	−0.0021	−0.0024	−0.0045	−0.0020	−0.0022	−0.0047
oedu	0.0077	0.0066	0.0063	0.0047	0.0041	0.0039	0.0059	0.0052	0.0049
uedu	−0.0015	−0.0009	−0.0008	−0.0019	−0.0018	−0.0015	−0.0021	−0.0019	−0.0015

*** p < 0.01, ** p < 0.05, * p < 0.1.

Table 6 presents the results of estimations where the dependent variable is a continuous variable for the change in years of required schooling between two periods (model 3). A positive change in required schooling means that either years of excess schooling decrease or years of lacking schooling increase. The level of required schooling in the initial period is negatively associated with the change in required schooling in the second period. The higher the initial level of required schooling, the smaller the increase in required schooling in the second period. This may be explained by the fact that if a worker is initially in a job which requires a high level of schooling, there are few jobs with even higher levels of required schooling and many jobs with lower levels of required schooling. Therefore, it is more probable for the worker to move to a job that would decrease their level of required schooling than to move to a job that would further increase it.

Table 6. Results of regression of change in years of required schooling (model 3).

	required education calculated as mean schooling			required education calculated as mode schooling			required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
redu	−0.018***	−0.018***	−0.029***	−0.014***	−0.015***	−0.025***	−0.016***	−0.017***	−0.026***
oedu	0.033***	0.032***	0.031***	0.041***	0.039***	0.038***	0.036***	0.035***	0.033***
uedu	−0.010***	−0.009***	−0.008***	−0.018***	−0.017***	−0.015***	−0.012***	−0.012***	−0.010***
female		0.018***	0.013***		0.033***	0.027***		0.024***	0.018***
age		−0.003***	−0.003***		−0.003***	−0.002***		−0.003***	−0.003***
age sq.		0.000***	0.000***		0.000***	0.000**		0.000***	0.000***
tenure		0.000***	0.001***		0.000**	0.001***		0.000**	0.001***
disability		−0.004	−0.005		0.004	0.002		0.003	0.003
unemployment			−0.000			−0.001			−0.001
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	0.221***	0.284***	0.425***	0.184***	0.239***	0.387***	0.197***	0.258***	0.404***
F	1589	601	108	1629	620	109	1623	615	109
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.021	0.021	0.025	0.021	0.022	0.025	0.021	0.022	0.025
obs.	225,736	223,707	223,473	225,736	223,707	223,473	225,736	223,707	223,473

*** p < 0.01, ** p < 0.05, * p < 0.1.

Overeducated individuals tend to move to better matched jobs, as the coefficients for the number of years of excess schooling are positive and highly statistically significant. For models where required schooling is obtained as the mean of years of schooling within a given occupation, one year of excess schooling increases the number of years of required schooling in the second period by about 0.03. The results for models for required schooling calculated with other approaches give estimates that are only slightly higher. The estimated coefficients for lacking education are about −0.01 for models with required schooling calculated as the mean or median schooling and slightly lower (larger in absolute terms) for models with required schooling calculated with mode schooling. It means that in the second period, undereducated individuals tend to move to occupations for which they become better matched, but it means a decrease in required education.

Positive coefficients for excess schooling and negative coefficients for lacking schooling indicate a tendency to reduce mismatch from both sides of the mismatch distribution. Overeducated workers move upward and undereducated workers move downward in terms of required education. Nevertheless, the coefficients for mismatch schooling are very small. The quickest speed of convergence of overeducated workers to a proper match is implied by the model for required schooling calculated using the mode approach (0.04). Simple and naive extrapolation of this coefficient means that it would take about 25 years for overeducated individuals to become properly matched workers. For undereducated individuals, the speed of transition towards properly matched jobs is even much smaller. Theoretically, it would take over 50 years to become properly matched, which is more than the length of a worker’s total career span. Thus, the transition to better matched jobs is a very sluggish process.

Let us now look at the coefficients associated with the controls. Tenure and age are statistically significant variables but have very small coefficients. The dummy variable for females has a positive coefficient which means that women move to higher-ranked occupations faster than men. However, the total explanatory power of the model is very small. At best, only 2.5% of the variance of the dependent variable is explained by the explanatory variables. However, this is largely due to the large number of zeros in the dependent variable since changing occupations is relatively infrequent.

Table 7 presents the results of the same regressions as in Table 6 but with individuals who do not change required schooling excluded from the sample. The sample size is substantially reduced, but explanatory power of the models improves significantly (up to 72%). The signs of coefficients of the ORU variables are the same as in the full-sample estimations, but the size of them is increased. Given individuals change their jobs, or more precisely move to jobs requiring a different level of schooling, one year of required schooling in previous job decreases required schooling in a new job by between 0.5 and 1.2 year (for fully specified models). Overeducated workers who change their jobs move to better matched jobs such that one year of excess schooling adds 0.4–0.5 year of required schooling in a new job. The opposite holds for undereducated workers. One year of lacking schooling decreases required schooling in a new job by 0.1–0.2 year.

Table 7. Results of regression of change in years of required schooling (model 3) with zero changes excluded from the sample.

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
redu	−0.364***	−0.378***	−0.494***	−1.037***	−1.052***	−1.174***	−0.665***	−0.681***	−0.777***
oedu	0.426***	0.416***	0.387***	0.555***	0.540***	0.497***	0.574***	0.562***	0.521***
uedu	−0.139***	−0.139***	−0.127***	−0.207***	−0.199***	−0.160***	−0.211***	−0.210***	−0.186***
female		0.258***	0.225***		0.447***	0.441***		0.287***	0.301***
age		−0.017**	−0.015**		−0.006	−0.011		−0.014	−0.017
age sq.		0.000	0.000		−0.000	−0.000		0.000	0.000
tenure		0.007***	0.012***		0.022***	0.022***		0.022***	0.022***
disability		−0.163**	−0.189***		−0.222	−0.274		−0.119	−0.096
unemployment			−0.020			−0.020			−0.045
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	4.548***	5.000***	6.856***	13.913***	14.047***	16.117***	8.660***	9.000***	11.101***
F	2019	758	135	3647	1348	234	2745	1019	175
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.335	0.342	0.381	0.682	0.686	0.715	0.540	0.545	0.574
obs.	12,045	11,678	11,655	5,096	4,935	4,927	7,033	6,815	6,800

*** p < 0.01, ** p < 0.05, * p < 0.1.

Because not all workers stay in employment in the second period, there is a potential problem of sample selection that might bias the results. In fact, the results of the model for probability of staying in employment (model 1), which are presented in Table 4, show that selection is not random and depends on variables in the model, including initial mismatch status. To address this problem, a Heckman correction model is applied (model 4). The results of this model are reported in Table 8. For the sake of brevity, only results for the fully specified model are presented. The high statistical significance of coefficients for the inverse Mills ratio implies that sample selection is present. However, accounting for sample selection does not alter the main results from Table 6. One year of required schooling decreases required schooling in the next year by between 0.02 and 0.03 year, one year of excess schooling adds 0.03–0.04 year of required schooling, whilst one year of lacking schooling decreases required schooling by 0.01–0.02 year (note that that individuals who do not change their jobs are included in the estimations). Hence, the estimated coefficients for the years of required, excess and lacking schooling using the Heckman correction model are very close to those presented in Table 6, which does not address the problem of sample selection. Thus, we see that selectivity of observations in the second period does not largely bias the results and the OLS method gives estimates fairly close to true values.¹³

Table 8. Results of regression of change in years of required schooling (Heckit results, model 4).

	Required education calculated as mean schooling		Required education calculated as mode schooling		Required education calculated as median schooling
	redu change	selection	redu change	selection	redu change	selection
redu	−0.026***	0.077***	−0.023***	0.058***	−0.023***	0.070***
oedu	0.032***	0.022***	0.039***	0.027***	0.034***	0.026***
uedu	−0.010***	−0.034***	−0.017***	−0.040***	−0.012***	−0.035***
female	0.005**	−0.158***	0.019***	−0.163***	0.008***	−0.161***
age	0.004***	0.148***	0.005***	0.148***	0.006***	0.148***
age sq.	−0.000***	−0.002***	−0.000***	−0.002***	−0.000***	−0.002***
tenure	0.001***	0.016***	0.002***	0.017***	0.001***	0.017***
disability	−0.015***	−0.209***	−0.009	−0.212***	−0.010	−0.211***
unemployment	−0.001	−0.030***	−0.002	−0.030***	−0.002	−0.030***
region dummies	yes	yes	yes	yes	yes	yes
urbanization dummies	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes
child under 3		0.101***		0.101***		0.100***
child under 3 x female		−0.412***		−0.410***		−0.411***
other worker		0.052***		0.052***		0.053***
other worker x female		0.017		0.019		0.018
constant	0.238***	−2.058***	0.201***	−1.815***	0.176***	−1.952***
inv. Mills ratio (lambda)	0.190***		0.197***		0.237***
rho	0.478		0.356		0.505
sigma	0.398		0.553		0.470
Wald chi2(52)	5308		5584		5392
prob. > chi2	0		0		0
obs.	239,822		239,822		239,822
uncensored obs.	223,473		223,473		223,473
censored obs	16,349		16,349		16,349

*** p < 0.01, ** p < 0.05, * p < 0.1.

4.3. Wage mobility

Now, let us discuss the results for the wage change regressions. The results are presented in Table 9 (model 5) and 10 (model 6). First, we see that the initial level of wages negatively affects wage growth in the second period. This is what we expected – workers who already have high wages experience lower wage changes expressed in percentage terms. An increase in the initial wage level by 10% lowers wage growth in the second period by about 0.5 percentage points (for fully specified models). Second, workers working in occupations requiring more schooling experience faster wage growth. Each year of required schooling adds about 0.3 percentage points to wage dynamics in the second period.

Table 9. Results of regression of percentage wage change (model 5).

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
ln wage fte	−3.831***	−4.125***	−4.975***	−3.768***	−4.029***	−4.870***	−3.806***	−4.093***	−4.960***
redu	0.203***	0.302***	0.347***	0.165***	0.236***	0.260***	0.187***	0.272***	0.312***
oedu	0.200***	0.189***	0.158***	0.183***	0.155***	0.119***	0.185***	0.171***	0.140***
uedu	−0.070**	−0.047	−0.037	−0.134***	−0.121***	−0.108***	−0.096***	−0.079***	−0.064**
female		−0.912***	−0.950***		−0.878***	−0.953***		−0.910***	−0.960***
age		−0.051*	−0.014		−0.053*	−0.016		−0.051*	−0.015
age sq.		0.000	−0.000		0.000	−0.000		0.000	−0.000
tenure		−0.015***	−0.009*		−0.013***	−0.008		−0.014***	−0.008*
disability		−0.502**	−0.461**		−0.507**	−0.461**		−0.522***	−0.472**
unemployment			0.108			0.106			0.107
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	27.611***	30.524***	32.207***	27.694***	30.746***	32.667***	27.675***	30.737***	32.638***
F	338	174	60.6	335	171	61.1	337	173	60.6
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.0256	0.0296	0.0601	0.0254	0.0291	0.0596	0.0255	0.0295	0.0600
obs.	51,497	51,305	51,257	51,497	51,305	51,257	51,497	51,305	51,257

*** p < 0.01, ** p < 0.05, * p < 0.1

With regard to mismatched schooling, the results presented in Table 9 suggest that excess schooling increases wage growth in the second period, while lacking schooling has a negative or zero impact on wage dynamics. In fully specified models, the estimated coefficients for excess schooling are between 0.12 and 0.16. Hence, one year of excess schooling adds about half as much to wage dynamics as one year of required schooling.¹⁴ A coefficient for lacking schooling is found to be statistically insignificant in the fully specified model with required schooling calculated using the mean approach, but statistically significant for mode and median approaches. The strongest effect of lacking education on wage dynamics is identified in the model using the mode approach (−0.11). This means that undereducated workers are penalized in terms of wage growth prospects compared to their properly matched colleagues.

Table 10 (model 6) further clarifies the relationship between excess schooling and wage growth. Compared to Table 9, the estimations in Table 10 are augmented with the change in years of required schooling, similar to the dependent variable in one of the previous estimations (as in Table 6), but here it is broken down into two separate variables, as positive and negative changes are treated separately. The results reveal that positive and negative changes have an asymmetrical effect on wage growth. A positive change in required schooling is found to have a positive effect on a worker’s wage. This effect is strongly statistically significant and present in all estimations reported in Table 10. For instance, moving to a job that requires one more year of schooling increases the wage growth rate by additional 1.2–2.0 percentage points in the fully specified models. The coefficients for a negative change in required schooling are usually statistically insignificant, meaning that moving to a job which requires less schooling does not change wage dynamics. Only in two parsimonious models the coefficients for a negative change in required schooling are negative and statistically significant at the 10% level, which means an improvement in wage dynamics.¹⁵ At the first glance, it might seem counterintuitive that there is no negative wage effect associated with moving to jobs that require less schooling. However, when workers decide to change jobs, they are motivated, inter alia, by wage prospects in a new workplace. Workers who are offered a new job in an occupation requiring lower schooling with a lower wage would simply decide to stay in a current job. Thus, the occupational change is dependent on wage growth prospects and the near-zero wage effect for a decrease in required schooling is not as surprising.

Table 10. Results of regression of percentage wage change (model 6).

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
ln wage fte	−3.839***	−4.152***	−5.002***	−3.772***	−4.046***	−4.893***	−3.819***	−4.127***	−4.994***
pos. redu change	1.977***	2.003***	2.028***	1.140***	1.179***	1.189***	1.619***	1.649***	1.688***
neg. redu change	−0.318*	−0.226	−0.272	−0.176	−0.116	−0.118	−0.253*	−0.171	−0.202
redu	0.211***	0.313***	0.365***	0.166***	0.239***	0.269***	0.187***	0.276***	0.322***
oedu	0.147***	0.139***	0.111***	0.142***	0.115***	0.080**	0.139***	0.127***	0.097***
uedu	−0.074**	−0.053*	−0.043	−0.134***	−0.122***	−0.109***	−0.097***	−0.081***	−0.067**
female		−0.930***	−0.962***		−0.892***	−0.964***		−0.931***	−0.977***
age		−0.043	−0.007		−0.047*	−0.011		−0.044	−0.008
age sq.		0.000	−0.000		0.000	−0.000		0.000	−0.000
tenure		−0.014***	−0.008*		−0.013***	−0.008		−0.013***	−0.008
disability		−0.499**	−0.457**		−0.506**	−0.457**		−0.522***	−0.469**
unemployment			0.122*			0.115*			0.121*
region dummies			yes			yes			yes
urb. dummies			yes			yes			yes
year dummies			yes			yes			yes
sector dummies			yes			yes			yes
constant	27.543***	30.379***	31.818***	27.696***	30.691***	32.508***	27.741***	30.734***	32.413***
F	252	157	61.7	242	150	60.2	251	156	61.6
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.029	0.033	0.063	0.027	0.031	0.062	0.028	0.032	0.063
obs.	51,497	51,305	51,257	51,497	51,305	51,257	51,497	51,305	51,257

*** p < 0.01, ** p < 0.05, * p < 0.1.

Another important finding is that in the specifications augmented with the additional variables for the change in required schooling, the coefficients for excess schooling are reduced by roughly 1/3 compared to the results in Table 9. It means that when we control for whether overeducated workers change their mismatched status over time, the initial mismatch status becomes less relevant for explaining wage growth. Hence, the positive association between excess schooling and wage dynamics identified in the results presented in Table 9 can be partially attributed to those overeducated individuals who change their position for an occupation requiring more education.

4.4. Robustness check: estimations on age-specific subsamples

In this part, I briefly discuss the results of estimations on age-specific subsamples. Three age groups are considered: young workers (under 30), prime-aged workers (aged 30–49) and older workers (50 or older). Estimations on subsamples address the possibility that job mobility patterns of educationally mismatched workers might differ between age groups. The results are reported in Tables A1–A6 in the Appendix. The subsample estimations correspond to the fully specified models presented in Tables 4–6 and Tables 8–10. Age is excluded from explanatory variables. The subsample regressions give results largely similar to the full-sample regressions and most findings presented in the previous paragraphs are upheld, although some interesting differences between age groups are revealed.

Table A1 presents the results for probability of staying in employment in the second period for each age group separately (model 1). As in the full-sample regressions (Table 4), required schooling and excess schooling increase chances to stay in employment, whilst lacking schooling decreases them. Moreover, schooling differentiates probability of staying in employment more strongly for young workers than prime-aged and older workers. For each age group, the effect of required schooling is stronger than the effect of excess schooling. In other words, regardless of a worker’s age, overeducated workers face higher chances to stay in employment compared to properly matched workers in occupations requiring the same schooling, but lower chances when compared to properly matched workers of the same level of schooling.

The estimation results for probability of moving to occupation requiring more schooling (model 2) are reported in Table A2. As in Table 5, the results from age-specific regressions indicate that each year of required schooling decreases chances of moving to occupations requiring more schooling in the next period, whilst excess schooling increases them. Lacking schooling is associated with lower chances, however, the effect is very small, close to zero. Similar findings hold for estimations with continuous dependent variable, i.e. change in years of required schooling (model 3, Table A3), and accounting for selectivity does not change results (model 4, Table A4). Regardless of the age group, more required schooling and more lacking schooling are associated with less required schooling in the next period, whilst excess schooling is associated with more required schooling in the next period. The size of the effects is the largest for young workers and decreases with age. It is probably due to the fact that occupation changes become less frequent with age.

Finally, let us discuss the results for wage regressions (models 5–6) on the age-specific subsamples (Tables A5 and A6). Each year of required schooling adds between 0.2 and 0.4 p.p. to wage growth. This effect seems to be slightly larger for younger workers compared to prime-aged workers. An interesting observation is made regarding excess schooling. Excess schooling increases wage growth for prime-aged workers, while there is no such effect in any regression for young workers and in two out of three regressions for older workers. In other words, the positive relationship between overeducation and wage growth, reported in the full-sample results in Table 9, must be driven by prime-aged workers. Young overeducated workers do not experience such an increase in wage growth. Lacking schooling has either a negative or zero effect on wage growth, but there is no consistent pattern across methods used to identify education mismatch and age groups. Similarly to the full-sample results in Table 10, changes in required schooling between periods have an asymmetric effect on wage growth in all age groups (cf. Table A6). Moving to occupations requiring more schooling improves wage growth for all age groups. However, this effect is of much smaller magnitude for older workers. On the other hand, moving to occupations requiring less schooling is associated with no wage change in most estimations presented in Table A6, except for two, which show a slight improvement in wage growth for prime-aged workers. The finding of a positive effect of excess schooling on wage growth of prime-aged workers and no such effect for young workers is upheld when a change in mismatch status is controlled for.

5. Conclusions

The paper investigates the short-run job mobility in the context of educational mismatch. The issue of job mobility of overeducated workers has been introduced to the literature by Sicherman and Galor (1990), who presented a theoretical model of the career mobility theory. It implies that overeducation is a transitory condition affecting young workers. Overeducation fades out over time as workers gain experience and on-the-job training, helping them in the upward occupational mobility. Hence, the Sicherman-Galor hypothesis predicts that overeducated workers should experience more upward job mobility and faster wage growth compared to their properly matched colleagues. However, the empirical studies addressing these predictions have provided mixed evidence of the validity of the Sicherman-Galor model.

The aim of this study is to contribute to the empirical literature testing the dynamic implications of the Sicherman-Galor model. The paper examines three aspects of the job mobility of overeducated workers: the probability of staying in employment, upward occupational mobility, and wage growth. Such a broad scope of analysis is needed to comprehensively test the predictions of the Sicherman-Galor hypothesis referring to the temporary nature of mismatch, higher probabilities of upward job mobility and faster wage growth for overeducated workers. The paper’s empirical strategy builds on previous studies, especially Rubb (2006) and Korpi and Tåhlin (2009). Yearly changes in employment status, occupation and wages are analysed.

The study finds that overeducated workers are more likely to stay in employment compared to their properly matched colleagues in the same occupations. The reverse holds for undereducated workers. Higher labour market attachment suggests that overeducated workers might be more productive to their properly matched colleagues in the same occupations. It corresponds to the well-documented fact that overeducated workers experience a wage premium compared to properly-matched workers in their occupations (Leuven & Oosterbeek, 2011; Quintini, 2011).¹⁶

The study finds weak evidence for educational mismatch to fade over time, at least from the short-run perspective. Although the results for upward occupational mobility analysis show that overeducated individuals tend to move to jobs requiring more schooling for which they become more properly matched, it is a sluggish process. Based on simple extrapolation of the estimated coefficients for yearly changes, the average time of overeducated workers to fully move to properly matched occupations would be decades rather than years, starkly contradicting the predictions of the Sicherman-Galor hypothesis. Hence, one can say that in Poland overeducation is not a temporary phenomenon from a worker’s perspective. Undereducated workers are found to move to jobs requiring less education, but the rate of this change is negligible. Because chances to stay in employment differ between educational mismatch statuses, it might potentially make the results for upward occupational mobility biased. The Heckman correction model is used to address this issue, but main results do not alter.

Finally, the percentage growth of full-time equivalent real wages is analysed. The results show that overeducated workers experience increased wage growth compared to their properly matched colleagues in the same occupations, which is in line with the predictions of the Sicherman-Galor hypothesis. In turn, undereducated workers experience lower wage growth compared to properly matched workers. The estimations controlling for the change in required schooling show that faster wage growth for the overeducated can be partially attributed to those overeducated workers who improve their match status. In other words, initially overeducated workers can expect faster wage growth than their properly matched colleagues, especially when they move to jobs requiring more schooling. However, the estimations run on age-specific subsamples reveal that the increased rate of wage growth associated with overeducation is driven by prime-aged workers, while there is no such effect for young workers.

In order to test the robustness of the results, this study utilizes three alternative methods to identify overeducation, all of which fall under the realized matches approach. The level of required schooling for a worker’s job is calculated as either a mean, modal or median value of schooling among all workers in the same occupation. While the use of mean or modal values is standard in the literature, the application of a median value is somewhat a novelty. Despite this, the study’s findings remain virtually the same regardless of the method used to approximate required schooling. This suggests that operationalization of the realized matches approach does not influence the results. For additional robustness checks, regressions are re-estimated on three age-specific subsamples, each corresponding to a different stage in a worker’s career. The primary findings, besides a positive relationship between excess schooling and wage growth, remain largely consistent across different age groups, supporting the robustness of the results. However, this consistency also suggests that the Sicherman-Galor hypothesis cannot be the sole theoretical explanation of educational mismatch. The Sicherman-Galor hypothesis explains overeducation among young workers, but says little about overeducation in other age groups. This opens the door for complimentary overeducation theories.

From the public policy point of view, the finding of infrequent transitions of educationally mismatched workers to properly matched jobs should spark a discussion on how well the education system meets the needs of the labour market. This calls for an examination of the composition of educational programmes and the quality of teaching provided by the educational institutions. However, any changes to the education system would reduce educational mismatch for future workforce entrants. To counteract the mismatch among workers who are already in the labour market, other measures supporting the life-long learning and addressing skill deficits could be considered. Also demand-side measures that stimulate demand for the high-ranked occupations could be explored.

Despite the insights provided, there are some limitations of the analysis that open avenues for further research. The study’s findings stem from the investigation of yearly changes in a worker’s employment status, occupation, and wages, leaving unanswered questions about the frequency of such transitions over a longer timeframe. For instance, the study provides evidence that transitions of educationally mismatched workers to properly matched jobs are infrequent over one year’s time, but this may not necessarily be true over 3, 5, or 10 years. While Kiersztyn (2013) found evidence of persistent overeducation in Poland spanning several years, this was based on older data, making it uncertain if such findings hold true in more recent contexts.

Furthermore, while this study provides consistent results across various versions of the realized matches approach, alternative approaches to identify educational mismatch could be applied. Both the subjective approach and the job analysis approach, often considered superior to the realized matches approach, could be potentially examined. It would necessitate to use an alternative dataset, as the Polish Labour Force Survey does not enable to use them. Assessing the findings’ validity using alternative methods is especially relevant given studies that report poor correlation in mismatch identification across different approaches (Battu et al., 2000; Groot & van den Brink, 2000).

To sum up, the results presented in the paper give mixed support for the Sicherman-Galor career mobility theory. The prediction of faster upward occupational mobility of overeducated workers is hardly confirmed as the rate of additional upward mobility is extremely low. On the other hand, the overeducated workers are found to experience increased wage growth, which is in line with the Sicherman-Galor model. However, it is driven by prime-aged workers, while there is no positive relationship between overeducation and wage growth for young workers. These results add to the already mixed picture emerging from other studies, which might suggest that there are country-specific factors, such as characteristics of a country’s education system, influencing the validity of the Sicherman-Galor model. In this context, Poland stands out with the rapid expansion of tertiary education which was characterized by a large share of non-regular study programmes and deteriorating quality (Herbst & Rok, 2014). However, exploring the factors that differentiate the persistence of overeducation across countries is an area for future research.

Disclosure statement

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

Additional information

Funding

Research was funded by the Polish National Science Centre grant under the contract number DEC-2016/23/N/HS4/03626.

Notes on contributors

Jan Aleksander Baran

Jan Aleksander Baran is a Ph.D. candidate in economics at the University of Warsaw.

Notes

1 Contrary to overeducated workers, undereducated workers have a level of schooling that is below what is required for their occupations.

2 By controlling for workers’ actual schooling, as Sicherman (1991) originally did, overeducated workers are compared to properly matched workers with the same level of schooling. Since Robst’s critique, most studies control for the level of schooling required for a given occupation, so that overeducated workers are compared to their properly matched colleagues in occupations requiring the same level of schooling.

3 However, because Frei and Sousa-Poza used workers’ subjective declarations to identify overeducation, changes in the mismatch status were weakly associated with actual job changes. 87% of individuals who moved out of subjectively reported overeducation did not change their job or employer. This suggests that subjectively perceived mismatch might be less persistent than mismatch identified with other methods.

4 However, Rubb’s study has some apparent issues that limit the clear interpretation of the results. Firstly, the methodology based on realized matches, calculated separately for each of the two periods, allows education requirements to vary. As a result, the flows in and out of overeducation might be, to some extent, a purely statistical effect. Secondly, there is also a small share of individuals who reported a decrease in their education level between periods.

5 ORU is an acronym standing for overeducation, required education, and undereducation. It refers to the way of representing a worker’s years of education as a sum of years which are required in their job, and either excess (for overeducated workers) or lacking ones (for undereducated workers).

6 Precisely, in the Verdugo & Verdugo method the required level of education is a mean value of schooling plus/minus one standard deviation.

7 Although, to my knowledge, there is no other study on overeducation which uses median values to calculate required schooling, I purposely use this method, along with other two, to demonstrate that the different operationalization of the realized matches approach does not change the findings and the median method can substitute for the other two.

8 On the other hand, one can argue that the technological change leads to an increase in skill and education requirements within occupations over time. However, given the limited timeframe of analysis spanning from 2011 to 2018, this appears to be a relatively minor issue.

9 Unfortunately, the Polish Labour Force Survey does not cover a worker’s other characteristics that some studies identify being associated with educational mismatch such as the quality of received education (Robst, 1995b) or socio-economic family background (Capsada-Munsech, 2015; Erdsiek, 2016). This could potentially lead to a problem of omitted variables bias.

10 Nevertheless, studies on overeducation usually do not address selection issue (Vera-Toscano & Meroni, 2021).

11 For the sake of simplicity, I assume that a worker’s actual schooling does not improve in the second period, so changes in required schooling perfectly translate into changes in educational mismatch.

12 Note that the calculation of education requirements is based on a pooled sample. Consequently, each occupation is assigned the same required level of schooling for each year.

13 Similarly, Dolton and Vignoles (2000) find that sample selection has a negligible effect on the overeducation coefficients.

14 Similarly, Korpi and Tåhlin (2009) found that excess schooling adds to wage dynamics a half as required schooling when the initial wage level is included as a control (see results of model 4 in Table 5 in their paper).

15 With a negative change in required schooling and the negative coefficients, the impact is positive.

16 Moreover, there is evidence of overeducation improving firm-level productivity (Kampelmann & Rycx, 2012; Mahy et al., 2015).

Appendix

Table A1. Results of logistic regression of probability of staying in employment in the second period (model 1), age-specific subsamples

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
redu	0.162***	0.180***	0.136***	0.116***	0.131***	0.114***	0.149***	0.157***	0.127***
oedu	0.054***	0.028**	0.078***	0.062***	0.044***	0.074***	0.068***	0.039***	0.078***
uedu	−0.102***	−0.070***	−0.071***	−0.117***	−0.081***	−0.082***	−0.093***	−0.075***	−0.075***
female	−0.457***	−0.300***	−0.332***	−0.451***	−0.312***	−0.338***	−0.458***	−0.308***	−0.335***
tenure	0.180***	0.075***	0.018***	0.181***	0.076***	0.019***	0.180***	0.076***	0.019***
disability	−0.199*	−0.497***	−0.545***	−0.211*	−0.510***	−0.549***	−0.205*	−0.507***	−0.549***
unemployment	−0.032	−0.046*	−0.101***	−0.032	−0.046*	−0.102***	−0.032	−0.047*	−0.102***
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb. dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	0.308	0.684**	1.820***	0.887***	1.298***	2.114***	0.452	0.989***	1.955***
LR chi2	2044	3247	1391	2012	3184	1379	2037	3221	1387
prob. > chi2	0	0	0	0	0	0	0	0	0
pseudo R2	0.061	0.069	0.039	0.060	0.068	0.038	0.061	0.069	0.038
obs.	44,494	124,731	70,588	44,494	12,4731	70,588	44,494	124,731	70,588
average marginal effects
redu	0.0169	0.0077	0.0087	0.0121	0.0056	0.0073	0.0156	0.0067	0.0081
oedu	0.0056	0.0012	0.0050	0.0065	0.0019	0.0047	0.0071	0.0017	0.0050
uedu	−0.0106	−0.0030	−0.0046	−0.0123	−0.0035	−0.0053	−0.0097	−0.0032	−0.0048

*** p < 0.01, ** p < 0.05, *p < 0.1

Table A2. Results of logistic regression of probability of moving to occupation requiring more schooling (model 2), age-specific subsamples.

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
redu	−0.476***	−0.285***	−0.242***	−0.521***	−0.401***	−0.312***	−0.460***	−0.291***	−0.252***
oedu	0.174***	0.271***	0.271***	0.264***	0.396***	0.390***	0.241***	0.355***	0.381***
uedu	−0.054*	−0.046**	−0.002	−0.101**	−0.130***	−0.185***	−0.084**	−0.133***	−0.073**
female	0.194***	0.069*	−0.011	0.492***	0.382***	0.418***	0.340***	0.219***	0.169*
tenure	−0.159***	−0.039***	−0.017***	−0.177***	−0.024***	−0.007	−0.163***	−0.027***	−0.012***
disability	0.072	−0.049	−0.022	0.143	−0.031	0.035	−0.060	−0.021	0.168
unemployment	−0.077*	−0.056*	−0.130**	−0.123**	−0.040	−0.069	−0.115**	−0.040	−0.186**
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb. dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	4.066***	0.744*	0.564	3.855***	0.414	−0.698	3.691***	−0.173	0.339
LR chi2	1249	1861	594.4	1239	1880	555	1113	1818	630
prob. > chi2	0	0	0	0	0	0	0	0	0
pseudo R2	0.081	0.068	0.051	0.134	0.143	0.111	0.104	0.103	0.090
obs.	38,919	118,956	65,595	38,731	118,950	65,595	38,919	118,950	65,595
average marginal effects
redu	−0.0217	−0.0067	−0.0041	−0.0123	−0.0038	−0.0019	−0.0132	−0.0039	−0.0023
oedu	0.0080	0.0063	0.0046	0.0063	0.0037	0.0024	0.0069	0.0048	0.0035
uedu	−0.0025	−0.0011	0.0000	−0.0024	−0.0012	−0.0011	−0.0024	−0.0018	−0.0007

*** p < 0.01, ** p < 0.05, * p < 0.1

Table A3. Results of regression of change in years of required schooling (model 3), age-specific subsamples.

	required education calculated as mean schooling			required education calculated as mode schooling			required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
redu	−0.060***	−0.027***	−0.018***	−0.050***	−0.023***	−0.017***	−0.052***	−0.025***	−0.018***
oedu	0.042***	0.029***	0.016***	0.050***	0.036***	0.019***	0.040***	0.032***	0.019***
uedu	−0.020***	−0.009***	−0.006***	−0.037***	−0.015***	−0.010***	−0.025***	−0.011***	−0.007***
female	0.048***	0.007***	0.004*	0.074***	0.017***	0.019***	0.053***	0.011***	0.010***
tenure	−0.002*	0.000***	0.001***	−0.002	0.001***	0.001***	−0.003***	0.001***	0.000***
disability	−0.003	−0.010	−0.002	0.023	0.002	−0.001	0.010	0.001	0.004
unemployment	−0.004	0.000	0.001	−0.008	−0.000	0.002	−0.005	0.001	−0.001
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb. dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	0.832***	0.329***	0.198***	0.762***	0.295***	0.184***	0.748***	0.301***	0.221***
F	35.0	58.1	20.0	34.6	58.5	20.9	32.1	59.0	21.7
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.044	0.024	0.015	0.043	0.025	0.016	0.040	0.025	0.017
obs.	38,921	118,956	65,596	38,921	118,956	65,596	38,921	118,956	65,596

*** p < 0.01, ** p < 0.05, * p < 0.1.

Table A4. Results of regression of change in years of required schooling (Heckit results, model 4), main equation, age-specific subsamples.

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
redu	−0.058***	−0.025***	−0.017***	−0.051***	−0.022***	−0.016***	−0.048***	−0.023***	−0.017***
oedu	0.043***	0.030***	0.016***	0.050***	0.037***	0.019***	0.042***	0.032***	0.020***
uedu	−0.021***	−0.010***	−0.006***	−0.036***	−0.016***	−0.011***	−0.027***	−0.012***	−0.008***
female	0.044***	0.004	0.003	0.075***	0.014***	0.015***	0.042***	0.008***	0.007*
tenure	−0.001	0.001***	0.001***	−0.002	0.001***	0.001***	0.000	0.001***	0.001***
disability	−0.005	−0.017**	−0.005	0.023	−0.005	−0.008	0.004	−0.007	−0.003
unemployment	−0.005	−0.001	0.000	−0.008	−0.001	0.001	−0.006	0.000	−0.002
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb.dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	0.800***	0.292***	0.187***	0.766***	0.265***	0.165***	0.677***	0.265***	0.204***
inv. Mills ratio (lambda)	0.062	0.133***	0.048	−0.010	0.127**	0.096	0.147*	0.142***	0.082
rho	0.114	0.355	0.163	−0.010	0.244	0.226	0.234	0.315	0.233
sigma	0.543	0.375	0.296	0.762	0.522	0.424	0.629	0.449	0.351
Wald chi2(52)	1734	2848	986	1757	2940	1056	1575	2921	1089
prob. > chi2	0	0	0	0	0	0	0	0	0
obs.	44,496	124,737	70,589	44,496	124,737	70,589	44,496	124,737	70,589
uncensored obs.	38,921	118,956	65,596	38,921	118,956	65,596	38,921	118,956	65,596

*** p < 0.01, ** p < 0.05, * p < 0.1.

Table A5. Results of regression of percentage wage change (model 5), age-specific subsamples.

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
ln wage fte	−7.161***	−4.586***	−4.712***	−7.055***	−4.500***	−4.533***	−7.123***	−4.589***	−4.651***
redu	0.409***	0.304***	0.399***	0.300***	0.234***	0.288***	0.336***	0.284***	0.350***
oedu	0.066	0.202***	0.194**	0.098	0.158***	0.088	0.096	0.179***	0.127
uedu	−0.023	−0.043	−0.057	−0.029	−0.121***	−0.146***	−0.026	−0.066	−0.102**
female	−1.453***	−0.949***	−0.663***	−1.464***	−0.942***	−0.660***	−1.441***	−0.963***	−0.670***
tenure	−0.167***	−0.034***	−0.001	−0.166***	−0.034***	0.001	−0.166***	−0.034***	−0.000
disability	−1.649*	−0.616*	−0.105	−1.667*	−0.622*	−0.093	−1.642*	−0.628*	−0.112
unemployment	−0.048	0.141	0.152	−0.052	0.138	0.150	−0.051	0.140	0.150
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb.dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	50.308***	28.768***	27.713***	50.966***	29.117***	27.891***	50.992***	29.109***	27.999***
F	13.6	31.7	19.4	13.5	31.5	19.0	13.5	31.7	19.3
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.070	0.057	0.064	0.070	0.057	0.063	0.070	0.057	0.067
obs.	9,408	27,102	14,747	9,408	27,102	14,747	9,408	27,102	14,747

*** p < 0.01, ** p < 0.05, * p < 0.1.

Table A6. Results of regression of percentage wage change (model 6), age-specific subsamples.

	Required education calculated as mean schooling			Required education calculated as mode schooling			Required education calculated as median schooling
	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+	age < 30	age 30–49	age 50+
ln wage fte	−7.168***	−4.621***	−4.726***	−7.070***	−4.526***	−4.545***	−7.135***	−4.629***	−4.669***
pos. redu change	2.015***	2.291***	0.844**	1.185***	1.267***	0.765***	1.711***	1.886***	0.679**
neg. redu change	−0.303	−0.456*	0.457	−0.066	−0.265	0.332	−0.112	−0.407**	0.393
redu	0.449***	0.323***	0.406***	0.319***	0.241***	0.294***	0.358***	0.292***	0.357***
oedu	0.012	0.150***	0.178**	0.057	0.114**	0.072	0.055	0.128***	0.113
uedu	−0.028	−0.050	−0.056	−0.031	−0.124***	−0.143***	−0.028	−0.069*	−0.100**
female	−1.481***	−0.958***	−0.668***	−1.477***	−0.950***	−0.673***	−1.471***	−0.976***	−0.679***
tenure	−0.153***	−0.033***	−0.001	−0.157***	−0.034***	0.000	−0.154***	−0.033***	−0.000
disability	−1.705*	−0.596*	−0.106	−1.677*	−0.608*	−0.092	−1.659*	−0.611*	−0.113
unemployment	−0.036	0.164*	0.151	−0.047	0.155*	0.146	−0.033	0.160*	0.149
region dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
urb.dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
year dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
sector dummies	yes	yes	yes	yes	yes	yes	yes	yes	yes
constant	49.646***	28.490***	27.731***	50.738***	29.038***	27.951***	50.520***	29.053***	28.055***
F	13.9	32.8	18.8	13.6	31.7	18.5	13.8	32.9	18.7
prob. > F	0	0	0	0	0	0	0	0	0
R2	0.074	0.061	0.065	0.073	0.059	0.064	0.074	0.062	0.064
obs.	9,408	27,102	14,747	9,408	27,102	14,747	9,408	27,102	14,747

*** p < 0.01, ** p < 0.05, * p < 0.1.