1 Introduction

The use of administrative data sets in economics and especially labour economics has become more and more important for policy evaluation and empirical research (see, e. g., Card et al. 2010 as an example). Apart from their large sample size, such data sets have the advantage of covering long time periods and offering precise longitudinal information on key variables such as earnings and labour market states. A further strength of most administrative data sets is that they mitigate problems of panel attrition that typically arise with survey data. In this study, we focus on the 0.25% scientific-use-file of the BASiD (2007) data set (henceforth referred to as BASiD), which supplements a sample of the German Pension Register (VSKT) with information from the Federal Employment Agency.Footnote 1 The data provide longitudinal information on individuals’ pension-relevant biographies up to the year 2007. Compared to other administrative data such as the Integrated Employment Biographies (IEB) from the German Federal Employment Agency, BASiD encompasses entire individual employment biographies (in general starting with the age of 14).

An important feature of the BASiD data set is that it is particularly attractive for studying the Eastern German labour market. While recent studies based on administrative data have been highly constrained to the period after unification (see e. g. Kohn and Antonczyk 2013), much of the economic literature dealing with the labour market in the German Democratic Republic (GDR) has relied on the German Socioeconomic Panel (GSOEP) (see e. g. Bird et al. 1994).Footnote 2 These survey data provide retrospective GDR information for the years 1988 and 1989. A great advantage of BASiD over the GSOEP is that it contains full employment biographies of former GDR citizens prior to German unification. However, a shortcoming of BASiD is that it fails to provide information on individual covariates before 1992 (exceptions are gender and age), including the entire time period prior to unification. Given that especially information on educational attainment is of major relevance to many labour market applications, this study proposes different procedures to impute the pre-unification education variable in the BASiD data.

While the precision of key variables such as earnings is generally considered to be high, educational information from administrative records is often subject to measurement error.Footnote 3 In proposing an imputation procedure for the BASiD data, our paper is therefore related to the literature dealing with measurement error and missing values (Little and Rubin 2014, Schafer 2010, Manzari 2004). While much of the literature on German administrative data has proposed procedures to eliminate inconsistencies (Huber and Schmucker 2009) and to impute missing values of earnings (Büttner and Rässler 2008) or education (Fitzenberger et al. 2006, Wichert and Wilke 2012), our approach has to deal with a complete lack of educational information prior to unification. Instead of eliminating inconsistencies of an existing variable, we therefore have to provide a rule that indirectly infers educational information from other variables in the data set. We do so by exploiting information on education-related periods that are creditable for the pension insurance (see Table 13 in the Appendix). Combining these periods with information on the educational system in the former GDR, we propose three different imputation procedures. The first one, IMP1, attempts to match the six education categories provided by the IEB imposing detailed age constraints from the institutional information on the GDR educational system. The second one, IMP2, gives up the age constraints and aims to match somewhat broader education categories, into which the six categories in the IEB have been typically summarised in many empirical applications. Finally, the third one, IMP3, defines the education level based on potential years of education.

We validate our procedures by using external GDR census data provided by the German Statistical Office (see also Steiner 1986 and Maaz 2002). These data allow us to compare the fraction of individuals in specific education-age group cells resulting from our imputations with the corresponding fractions from the census data for comparable cohorts in 1984. The general picture that emerges is that IMP2 and IMP3 tend to overpredict the share of medium-skilled workers and underpredict the share of high-skilled for all age groups, whereas they underpredict (overpredict) the share of low-skilled for the younger (older) age groups. The latter is also true for IMP1. Compared with IMP2 and IMP3, IMP1 gives rise to smaller deviations for the share of medium-skilled, whereas it overpredicts the share of high-skilled especially for the younger age groups. Overall, when balancing out the trade off between goodness of fit and data coverage, the more narrowly defined procedure IMP1 performs best. However, once one re-classifies those with a GDR Fachschule degree as medium skilled workers, IMP2 is to be preferred over IMP1 and IMP3. After discussing potential sources of misclassification, we proceed by comparing our education variable prior to unification with educational information from the IEB right after unification. To do so, we first improve the IEB education information according to the algorithm proposed by Fitzenberger et al. (2006). For comparison purposes, we then follow Wichert and Wilke (2012) by performing a regression analysis in order to identify the importance of observables for a deviation of our imputed educational information from that in the IEB. While misclassification with respect to IEB information is clearly related to observables, we do not find any systematic pattern across skill groups.

The remainder of the paper is structured as follows. Sect. 2 describes the BASiD data and provides descriptive statistics. Sect. 3 describes the educational system of the GDR and discusses the three imputation rules. Sect. 4 validates the imputation results using external census data. Sect. 5 compares the results from our imputations with educational information from the IEB right after unification. The final Sect. 6 concludes.

2 The BASiD data and descriptive statistics

BASiD Data. The BASiD data supplement information from the German Pension Register with various data sources from the German Federal Employment Agency. In this contribution we use the scientific use file (BASiD-SUF) provided by the German Pension Insurance, which is a stratified random 0.25% sample. This data set samples individuals within the age range of 30 and 67, who have an active pension account in 2007. The data therefore comprise the birth cohorts from 1940 to 1977,Footnote 4 leading to an overall sample of about 60,000 individuals. The sample has been drawn in a disproportionate manner and can be made representative using a weighting factor that is part of the data set (for a detailed description see Bönke 2009, Himmelreicher and Stegemann 2008). To identify former GDR citizens, we first select all individuals who prior to monetary union (i. e., the 30th of June 1990) had exhibited at least one monthly spell of pension-relevant activities in the GDR, i. e. those individuals who had gained East German credit points prior to unification. This gives rise to a sample of 11,331 individuals with a total of 2,790,600 monthly spells.

The data provide longitudinal information on individuals’ entire pension-relevant biographies up to the year 2007. Individual work histories cover the period from the year individuals were aged 14 until the age of 67. Panel attrition may arise only due to individuals’ death or migrating abroad. In Germany, statutory pension insurance is mandatory for all employees in the private and public sector, thus only excluding civil servants and self-employed individuals.Footnote 5 In addition, contributions to the pension insurance are paid by the unemployment or health insurance during periods of unemployment and prolonged illness.

As stressed at the outset, the BASiD data provide an ideal basis for analysing labour market related questions of former GDR citizens for several reasons: First, it is the only German administrative data source that encompasses full employment biographies. In particular, the Pension Register contains information on all periods for which contributions were paid (employment, apprenticeship training, long-term illness, unemployment) as well as periods without contributions, but which were still creditable for the pension insurance. The latter refers to activities for which an individual receives pension credits, such as periods of school or university attendance after the age of 16 and periods of child rearing and caring.

Second, the BASiD data is the only individual level data set that contains employment biographies of former GDR citizens before German unification. After unification, former GDR citizens became entitled to transfer their pension-relevant activities to the FRG (Federal Republic of Germany) pension insurance system. For this purpose, the FRG Pension Insurance recorded all periods prior to unification which were creditable for the pension insurance (see above) as well as earnings up to the GDR social security cap. Given that also entitlements from the so called “Freiwillige Zusatzversicherung” could be (partly) transferred to the Western German system, the data cover the full GDR population for whom past pension-relevant periods have been recorded. The pension data therefore allow researchers to track former GDR workers’ entire pre- and post-unification employment histories up to the year 2007. Apart from the individual information on pension-relevant activities and earnings, the Pension Register provides information on age and gender.

Starting from 1975 in Western and from 1992 in Eastern Germany, employment spells subject to social security contributions from the Pension Register can be merged with data from the German Federal Employment Agency, the IEB and the Establishment History Panel (BHP). The Establishment History Panel contains information on the establishment’s workforce composition, establishment size as well as sector affiliation (see Table 14 in the Appendix). Finally, the IEB provide further time varying individual information on blue- or white-collar status, occupational status, educational status (see Table 15 in the Appendix) and an establishment identifier. A shortcoming of the BASiD data is therefore that apart from age and gender most covariates (except for those that can be retrieved from the pension-relevant activities listed in Table 13 in the Appendix) are available after unification only, starting with the year 1992.

3 Education system in the GDR

Before we turn to our imputation procedures, we provide some institutional background information on the educational system in the former GDR. Due to their common roots the educational systems in the former GDR and Western Germany (FRG) exhibit some similarities. However, in the course of the GDR’s history, the systems considerably diverged with a strong effect on educational outcomes. While in Western Germany a first selection generally took (and still takes) place during primary school after four years of schooling, GDR students used to spend their first eight years together. Thus, completion of 8th grade may be considered the first official school degree as compared with 9th grade in Western Germany. The completion of 10th grade [referred to as “Polytechnische Oberschule” (POS)] was the second highest formal degree in the former GDR. As will be discussed below, in the 1950s and 1960s only a minority obtained a POS degree, whereas in later years the majority of students was expected to attend school for ten years (Fuchs–Schündeln and Masella 2016). After completion of POS, attending high school two more years [referred to as “Erweiterte Oberschule” (EOS)] gave rise to a degree equivalent to the Western German “Abitur” after the completion of the 12th grade. However, as a result from an increasing influence of the “state-governed labour force allocation”, access to high school became highly limited since the late 1960s and was not only determined by students’ performance but also by their own as well as their parents’ political orientation (Hegelheimer 1973; Huinink and Solga 1994).

Regarding the quantitative relevance, the POS degree was of minor importance in early GDR years. In the 1960s, the fraction of students leaving school with 8th grade or less was about 50%. This share decreased gradually, until eventually completion of POS became the most common qualification. At the end of the socialist regime about 80% finished 10th grade (Maaz 2002). Restrictive access to high school resulted in a stable low fraction of students completing high school of slightly above 10% (Solga 2002). This development diverged considerably from that in Western Germany, where in 1989 a much higher share had attained lower educational qualification (30%) and a high school degree (25%) (Maaz 2002).

As to vocational training, the length of an apprenticeship period was strongly determined by prior educational attainment from schooling. In general, vocational training after completing 8th grade took about 3 to 3.5 years, whereas an apprenticeship period following POS lasted only two years (Hegelheimer 1973). Moreover, there was also the possibility to combine a three year apprenticeship training with the completion of a high school degree, which enabled individuals to enter a university afterwards. Given the low share of students with a highest degree of 8th grade or less, in 1987 about 78% of apprenticeship periods exhibited a duration of two years, 11% of 2.5 years and 11% of three years (Fuchs–Schündeln and Masella 2016).

As a further possibility of post-secondary education, individuals could enter a so called Fachschule. Admission to a Fachschule was either possible after completion of POS or, alternatively, after completion of an apprenticeship training. The second type gave rise to a kind of technical university degree (equivalent to that in Western Germany), whereas the first type was closer to a vocational degree (Biermann 2013). The average length of Fachschule period took about three years, whereas the length of university periods was about four years, on average (Krueger and Pischke 1995).

4 Imputation based on educational periods

4.1 Distribution of educational periods

The imputation procedures described in the next section will be basically derived from education-related periods that are creditable for the pension insurance. As spelled out earlier, the Pension Register records periods for which contributions were paid (employment, long-term illness, unemployment) as well periods without contributions, but which are still creditable for the pension insurance, e. g. in terms of waiting times. While vocational training periods generally include periods with paid contributions, school and university episodes belong to the second type. By law, the former periods are creditable for the pension insurance of up to 36 months, whereas the latter periods are creditable for the pension insurance for individuals in full time education after the age of 16 for up to 8 years.

To infer information on educational attainment from vocational training and schooling episodes, it is instructive to look at the distributions of these spells. A further relevant issue relates to the question as to what extent individuals experienced educational interruptions and what happened during these interruptions. Fig. 1 displays the distributions of school and apprenticeships spells in our data set.

Fig. 1
figure 1

Distribution of school and apprenticeship spells. (Source: BASiD 2007. Notes: The figure shows the distribution of the length of schooling (a) and apprenticeship spells (b). Schooling spells are coded as ses = 1. Apprenticeship spells are coded as ses = 2. We close interruptions of type 1 and type 3 (see Table 1) if the length of the interruption is less than or equal to six months and if the interruption is not due to a regular employment spell)

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As can be seen from Fig. 1, a considerable number of individuals exhibits schooling spells of less than six months. There appears to be a further peak around three as well as six years of schooling. The first peak most likely reflects technical school students, whereas the latter peak relates to university graduates.Footnote 6 Apprenticeship spells are, as expected, much more concentrated. Most spells last around two years with a further peak at three years. However, there are many spells that lie in between, indicating either measurement error, errors that may have occurred when transferring pension entitlements to the Western German pension system or uncompleted spells. Breaking down the descriptives by decades (1970s, 1980s, 1990s) shows, however, that the distributions appear to be similar across decades with only some minor differences. In the 1970s, for example, most of the apprenticeship spells lasted three years compared to the 1990s (see Fig. 4 for a detailed graphical illustration over time).

Table 1 shows that among the total number of 11,331 individuals, about 21% (2,414 individuals) experienced some kind of educational interruption. About 46% of the interruptions were rather short. However, 54% of all interruptions lasted longer than six months. Breaking down the descriptions by gender shows that females were slightly more likely (58%) to exhibit educational interruptions. On average, the interruptions started at the age of 18.

Table 1 Description of the BASiD sample
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Panel B distinguishes four types of interruptions. The figures show that most interruptions occurred between two apprenticeship spells. However, with about 28%, there are also sizeable shares of interruptions between two schooling spells (type 1) and those after a period of vocational training followed by a schooling spell (type 4). The distribution does not substantially differ over time and across gender. For males as well as during the 1980s and 1990s, the third type was slightly more prevalent.

A further interesting information stems from the socio-economic status during the interruption and after the completion of the educational period. This may give some hint of whether individuals interrupted an educational episode due to (regular) employment or due to some other reasons, such as sickness absence.

Fig. 2
figure 2

Socio-economic status during the educational interruption. (Source: BASiD 2007. Notes: The figure shows the socio-economic status during the educational interruption. Sub-figure a pools all available observations. Sub-figure b conditions on short interruptions defined as those less than six months. Sub-figure c conditions on long interruptions defined as those lasting at least six months or more. See Fig. 3 for a differentiation by type of interruption)

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Fig. 2a shows that most individuals experienced a regular employment spell during the educational interruption (40%) followed by sickness absence with 37.5%. A third important reason is child rearing with about 12%. In 11% of the interruptions, the socio-economic status is missing. The middle part of the figure shows that for short interruptions (defined as those lasting less than six months), sickness absence was the most common reason followed by child rearing (18.8%) and regular employment (17.9%). Individuals experiencing an interruption longer than six months were primarily in regular employment (78%), whereas for about 22% the socio-economic status is not known. Overall, these findings suggest that short-term interruptions are mainly interruptions occurring within one (longer) educational spell.

Panel 1 of Fig. 3 shows the distribution of the socio-economic status in the first month after the educational period. The figure reveals that regular employment is the most frequent status after a school or apprenticeship spell. After schooling periods, the socio-economic status is missing for about 30% of all observations, whereas missing information after an apprenticeship spell is less relevant.

Fig. 3
figure 3

Socio-economic status after the eduction period. (Source: BASiD 2007. Notes: The figure shows the socio-economic status after completion of the eduction period. Sub-figures a and b focus on the first month after the eduction period. Sub-figures c and d plot the 6 month mode of the socio-economic status)

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The lower two figures plot the distribution of the main/dominant socio-economic status within the first six months after the educational period. Also at this stage, the main status is regular employment. Interestingly, missing values after schooling episodes do not matter at all as there is no individual with the dominant status being missing after schooling.

4.2 Imputation rules

In what follows, we propose three different imputation procedures, by combining the length of the educational periods described above with information on the educational system in the former GDR. The first procedure, IMP1, attempts to match the six education categories provided by the IEB imposing detailed age constraints from the institutional information on the GDR educational system. The six categories include (ND) no vocational and no highschool degree (henceforth referred to as “No degree”), (HS) a high school degree, (VT) a completed vocational training, (VTHS) a completed vocational training plus high school degree, (TUD) a technical university degree and finally, (UD) a university degree. The second one, IMP2, gives up the age constraints and aims to match the broader education categories, into which the six categories in the IEB are typically being summarised in many empirical applications: According to these, (1) low-skilled workers are those without any postsecondary degree, (2) medium-skilled workers have a completed apprenticeship training and (3) high-skilled workers obtained a degree from university or a technical university. Our last procedure, IMP3, simply defines these three categories based on potential years of education.Footnote 7

In general, the three different procedures involve a trade-off between precision and data coverage. IMP1 bears the potential of losing information on individuals who exhibit school or vocational training spells, but not at the required age. By giving up or loosening the age constraints, IMP2 and IMP3 may overcome this loss of observations at the expense of less precision. Table 2 summarises IMP1 imposing the age constraints (for a graphical summary of the procedures see also Figure C.1. in the Appendix). For this procedure, we need to know at what ages the different degrees were typically completed in the socialist system. As documented by Krueger and Pischke (1995), 8th grade and 10th grade were passed at age 14 and 16, respectively. High school was generally completed at age 18.

According to IMP1, individuals are assigned “No degree” if they exhibit a first employment spell and are younger than 17. Note that in this case the skill status may change once individuals have experienced school or apprenticeship spells according to the rules spelled out below. We choose an age limit of 17 because students passing an apprenticeship of three years after the 8th grade were on average 17 years old. Thus, even in the case of missing values, the first employment spell should be observed at the age of 17 or older. A student with a high school degree (EOS) should have completed high school at the age of 18 and should exhibit 12 months of schooling in the data. Thus, individuals having experienced a schooling episode between 1 and 1.5 years at the age of 17 or 18 are assigned a high school degree (category (HS) from the IEB). To match categories (VT) and (VTHS) from the IEB, we distinguish between those with a completed vocational training after 8th or 10th grade and those combining high school with apprenticeship training. Individuals are assigned to category (VT) (8th grade or 10th grade with apprenticeship) if they have experienced a vocational training spell at the age of 18 or younger with the length of the training lasting between 1.5 and 3.5 years.Footnote 8

Table 2 Imputation Procedure (1)
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As already mentioned, a further possibility was to combine a three year apprenticeship training with the completion of a high school degree. Thus, individuals having experienced an apprenticeship spell lasting between 2.5 to 3.5 years at the age of 19 or 20 are assigned an apprenticeship plus high school degree (VTHS).

In the IEB data, the high-skilled comprise those with a technical university degree and a university degree. In what follows, we will simply match the IEB technical university degree with a GDR technical school (Fachschule) degree.Footnote 9 Our assignment rule relies on the fact that completion of a Fachschule took three years, whereas the completion of a university degree took four years on average. To capture the completion of a Fachschule degree after POS, individuals having experienced a schooling episode of at least 2 up to 3.5 years at the age of 19 to 20 are assigned (TUD). The same assignment is made for individuals having experienced a schooling episode of at least 1.5 up to 3.5 years at the age of 20 or older.Footnote 10 As we observe a considerable fraction of individuals having experienced an apprenticeship period of at least 2.5 years after the age of 20, those individuals are assigned a Fachschule degree as well. This is to account for the possibility that a Fachschule degree, which was frequently associated with the completion of a vocational training, might have been (mis)reported as a vocational training period in the Pension data.Footnote 11 Finally, individuals are assigned a university degree (UD) if they have experienced a schooling spell of at least 3.5 years at the age of 22 years or older.

Procedure (2) is summarised in Table 3. Low-skilled workers are those assigned “No degree” (see IMP1). Medium-skilled workers need to have at least 1.5 years of formal apprenticeship training, whereas high-skilled workers are those with school spells of at least three years.

Table 3 Imputation Procedure (2)
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The third approach relies on potential years of education (IMP3). Given that formal unemployment was officially barely present in the GDRFootnote 12, the idea of this rule is that the first employment spell should have immediately followed the completion of an educational degree. We define individuals as low-skilled if they are less than 17 years old and are labeled as employed (employment subject to social security contributions excluding apprenticeship periods). Individuals starting employment between 17 and 20 are defined as medium-skilled, whereas high-skilled individuals are those with a first employment spell at the age of 21 to 28. Note that this approach does not account for potential changes in educational attainment over individuals’ life courses.Footnote 13

5 Qualification structure

This section attempts to externally validate our proposed imputation procedures. To do so, we compare the qualification structures by age groups obtained from our procedures with those from GDR census data from 1981 for the whole residential population. Note that due to the coverage of the pension data and basically zero unemployment, the working population should not substantially differ from the residential population.

The first three panels in Table 4 show the imputed qualification structures distinguished by five age groups, whereas the last two panels display the figures from the census data. Note that our imputed figures refer to the same age groups three years later in 1984 as the cohort structure of our data set allows us to provide figures for the oldest age group (40–44) only from 1984 onwards. For comparison, the first Census panel reports the shares of all individuals who were within the relevant age groups in 1981. The bottom Census panel displays the skill shares of those individuals who would have been in the respective age groups in 1984. The purpose of this comparison is to obtain some information on cohort-specific trends.

Table 4 Qualification structure by age groups – 1984, I
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The census figures shown in the upper bottom panel indicate that the share of low-skilled workers is U‑shaped, whereas the share of medium-skilled workers is decreasing with age. For high-skilled individuals, we observe a kind of inverse U‑shaped picture with the largest share of high-skilled individuals in the second oldest age group. For the younger age groups, IMP1 assigns substantially more individuals to the high-skilled group compared to the census figures and less to the medium and low-skilled category. For the older age groups, it assigns substantially more individuals to the low-skilled and less to the high-skilled category. IMP2 generates high and low-skilled (medium-skilled) shares that are substantially lower (higher) for most of the age groups than those from the census data. IMP3 leads to an even more pronounced underprediction of the share of high-skilled in all age groups. This reflects that IMP3 does not account for completed school episodes at the age of 21 or younger that might have led to a Fachschule (technical school degree) after completion of POS. Looking at the low-skilled share obtained from IMP3 suggests that the average age of the first labour market spell increased over time. This is due to the fact that the dominant school degree moved from 8th grade or less (about 30% of school-leavers had less than 8th grade in the 50s and up to 60% had 8th grade) to the 10th grade over that time period (see for a detailed description Solga 2002).

The bottom panel displays the census data of those who would have been in the respective age groups in 1984. This creates substantial deviations for the youngest group, given that some of these individuals were only 17 years old at time of the interview. Because most of the high-skilled individuals were still in the educational system, we observe a higher share of low-skilled and a lower share of high-skilled individuals. This suggests that the comparison is less meaningful for the youngest age group. For the older age groups, however, the pictures does not change substantially. Only those in the age group 40 to 44 in 1984 exhibit lower low-skilled and higher high-skilled shares.

Overall, the discrepancies are non-negligible for each of our proposed procedures. To rank the procedures in terms of the implied deviations from the census data, we calculate the sum of squared differences and the absolute differences between the imputed and the census figures over the different age-skill cells. Table 5 presents the results. IMP1 results in a sum of squared differences equal to 688, whereas IMP2 involves a sum of squared differences equal to 2243. Using IMP3 we obtain a number of 3552.

Table 5 Differences among imputation procedures – 1984, part 1
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Based on these numbers, we would prefer the first procedure over the second and the last one. The ranking remains the same by using absolute differences. However, the different procedures capture different numbers of observations. Dividing Q by the number of individuals (or equivalently by the coverage rate), the ranking stays the same. The same conclusion holds when using absolute differences.

What still remains to be resolved is the question as to why we observe these differences, especially for the share of high-skilled. One possible explanation for the strong deviations produced by IMP2 and IMP3 could be that the census data are biased towards an over-reporting of high-skilled individuals. An alternative explanation could be that there is a reporting error for school and apprenticeship spells in the administrative data set. Regarding the second explanation (reporting error) we do not think that this is a major problem as especially IMP2 and IMP3 should also capture those, whose pension accounts in terms of schooling and apprenticeship episodes might have been incomplete.

Moreover, note that even procedure IMP1, which explicitly attempts to distinguish those with a Fachschule from those with a university degree, substantially underpredicts (overpredicts) the share of high-skilled especially for the older (younger) age groups. To obtain a more precise picture of potential misclassification sources, we break down the results from IMP1 by female and male workers as well as by those with a technical school and university degree (see Table 6). The resulting figures show that the way we assigned the education variable performs relatively well for university graduates (for both male and female workers) and medium-skilled male workers as compared to the technical school degree, where large discrepancies can be observed for all age groups.

Table 6 Qualification structure by age groups and gender – 1984
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To account for a potential misclassification of a technical school as a vocational degree, one approach to handle this difficulty could be to re-classify the medium-skilled by assigning all technical school graduates to the medium-skilled. After this re-classification, the high-skilled group would only include university graduates. In terms of the Western German skill categories, such a re-classification could e. g. be justified by the fact that in the GDR individuals could enter a technical school after completion of POS (Krueger and Pischke 1995), which would be rather equivalent to a Western German vocational training degree. The results from this re-classification are shown in Table 7. The upper part of Table 7 shows that the share of high-skilled workers decreases and becomes closer to the official data particularly for the older age groups. Thus, treating former Technical School graduates as medium-skilled may help to draw a somewhat clearer picture for the high-skilled group. The table also shows again the shares generated by IMP2 and IMP3. After the re-classification, for IMP2 six out of 15 cells are not significantly different from the census data.

Table 7 Qualification structure by age groups – 1984, II
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After the re-classification, the sum of squared and absolute differences become smaller for all three imputation procedures, with IMP2 and IMP3 showing stronger improvements.Footnote 14

Table 8 Differences among Imputation Procedures – 1984, part 2
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The ranking of the procedures changes as well. Based on the Q measure and the number of individuals (coverage rate), IMP2 is now preferred over IMP3 and IMP1.

Given the substantial deviations for the older age groups that result from all three procedures, we next check whether our procedures are at least able to reproduce the documented decline in the fraction of those leaving school at 8th grade or less. We do this by estimating our skill shares at a later point in time (five years later in 1989). Individuals from the oldest age group (those aged 44) in 1989 were born in 1945 and were potentially available for the labour market in 1960/1961. Given that the share of those leaving school at 8th grade or less was twice as high in the 1950s as compared to the 1960s (Solga 2002), we expect a sharp decline in the predicted low-skilled share especially for older age groups. Table 9 presents the results for IMP1.

Table 9 Qualification structure by age groups – 1989
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As can be seen, our expectations are borne out by the figures, which are also in line with the descriptive statistics shown in Solga (2002). (Unreported) results reveal that the share of low-skilled obtained from the other two procedures drop by a similar magnitude. Thus, our procedures at least appear to provide consistent results in terms of the decline of those leaving school at 8th grade or less.

Taken together, our comparison with the census data suggests that all three procedures exhibit non-negligible deviations from our external data source. In order to finalise our decision about which procedure to use, we further compare our imputation results to information provided by the IEB subpart of the data set.

6 Comparison with educational information from the IEB

We next compare the results from our imputation procedures with educational information from the IEB, which can be merged to the BASiD data. Even though the IEB information starts in 1992, we use January 1993 as a reference point as there is evidence that education information is more reliable from 1993 onwards. With this comparison we have to keep in mind that the IEB education information may be subject to measurement error as well. To mitigate this issue, we correct the IEB education information using the imputation algorithm IP1 proposed by Fitzenberger et al. (2006). The authors suggest three different imputation rules without a strict order. The idea behind their rules is based on the assumption that individuals cannot lose their educational degrees. In what follows we use IP1, since according to Wichert and Wilke (2012) imputation procedure 1 (IP1) leads to a stronger reduction in measurement error.

We perform this exercise for all of our imputation procedures. Table 10 first cross tabulates the results from procedure IMP1 using the categories described in Table 2 with education information from the IEB.

Table 10 Cross tabulation of IMP1 vs. IEB, I
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Table 10 shows that the best match is obtained for the vocational training (VT) category with a fraction of 61% receiving this category from both our imputation procedure IMP1 and the IEB. In contrast, among those assigned a vocational training plus high school degree (VTHS) in the Pension data, over 50% exhibit only a vocational training degree (VT) in the IEB. Note that this may either reflect that our imputation procedure wrongly assigns a vocational plus high school degree or, alternatively, that the GDR high school degree has either not been reported or recognised by Western German employers.

Moreover, the IEB comparison also produces large deviations for those assigned no degree in the Pension data (ND), who mostly exhibit a vocational training (VT) in the IEB. A potential explanation would be that our defined rules from procedure IMP1 might have changed over time, such that older workers could have completed an apprenticeship within a shorter duration. If this was the case, the deviation of IMP1 from IEB information should be mitigated using IMP2, as this procedure requires only a cumulative apprenticeship spell of at least 1.5 years. The second panel of Table 11 shows that this does not account for the observed deviation in Table 10. In Table 11 the share of those assigned no degree ND in the Pension data, who exhibit a vocational training (VT and VTHS) in the IEB, remains basically the same for IMP2. Note that the share of low-skilled decreased substantially for all age groups between 1984 and 1989, such that over-reporting a low-skilled status is unlikely to explain the deviation for the low-skilled in Table 10. An alternative explanation would be vocational on-the-job training, which generally cannot be ruled out as a source of any deviation between the (imputed) pension data and IEB information.Footnote 15

Given the problem with correctly assigning the technical school [or technical university degree (TUD)], over 50% of those assigned TUD in the Pension data exhibit only a vocational training degree (VT or VTHS) in the IEB. This highlights again the difficulty in distinguishing between a GDR technical school and a vocational degree. Note that this misclassification might also reflect the fact that educational degrees obtained during GDR times might have not been recognised by Western German employers after unification. The overlap of TUD with a university degree (UD) is only moderate with 4.5%.Footnote 16 From the 929 individuals who were assigned UD in the Pension data, about 40% exhibit also a UD in the IEB. 25% have missing values in the IEB and about 17% intersect with vocational training (VT).

The cross tabulation of the results from IMP2 and IMP3 with education information from the IEB is shown in Table 11. As these procedures target three education categories – low-skilled, medium-skilled and high-skilled, we also provide the shares for the first imputation procedure IMP1 using the three categories in the upper panel.

Table 11 Cross tabulation of IMP1, IMP2 and IMP3 vs. IEB, II
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The picture that emerges from Table 11 is that all three procedures show again very similar patterns. The best match is obtained for the medium-skilled, whereas the worst match results for the low-skilled.Footnote 17 Overall, for the 11,331 individuals in the BASiD data set we obtain the highest number of missing values (4,234) for procedure IMP1. The number of missing values in the IEB (3,643) variable is lower compared to IMP1 but twice as large compared to IMP2, indicating a substantial gain in information resulting from our imputation procedures.Footnote 18 As mentioned earlier, there exists generally a trade-off between precision and coverage in terms of missing values. Given that the main diagonal values are largest for IMP2, which simultaneously reduces the number of missing values by almost 50%, procedure IMP2 seems to provide a quite reasonable compromise between matching IEB information and data coverage.

Table 12 Marginal effects of a logit regression
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To analyse whether any deviation from IEB information is systematically related to observables, we next perform a logit analysis using the results from procedure (IMP2) for the year 1993. The dependent variable is one if the educational degree assigned in the Pension data deviates from the educational information in the IEB and is zero otherwise. Table 12 presents the estimated marginal effects for the probability of misclassification in the pooled sample separately for each skill group. While the results suggest that misclassification is related to some observables, there appears to be no systematic pattern across skill groups. In particular, the marginal effects of the covariates vary considerably across skill groups. Being female increases the probability of being misclassified by about 17 p. p. for the high-skilled. Individuals in the age group 25 to 35 have a higher probability of being misclassified if they are assigned high-skilled in the Pension data [Column (4)], whereas the coefficient is negative for the medium-skilled category. Individuals employed by smaller establishments are more likely to be misclassified in all skill groups than in the reference group of medium-sized establishments (not significant for low-skilled workers). Individuals employed by large establishments exhibit a higher probability of misclassification only if they are assigned medium-skilled [Column (3)], whereas the marginal effects for low and high-skilled in the Pension data [Column (2) and (4)] are not significant. The signs of the marginal effects of different industry affiliations do not reveal any systematic pattern either and also vary greatly across skill groups.

7 Conclusions

The BASiD data set provides the only available data source that contains full employment biographies of former GDR citizens prior to German unification. However, a shortcoming of BASiD is that it fails to provide information on individual covariates prior to unification (exceptions are gender and age). Given that especially information on educational attainment is of major relevance to many labour market applications, this study proposes different procedures to impute the pre-unification education variable in the BASiD data.

Our proposed procedures exploit information on education related periods that are creditable for the pension insurance. Combining these periods with information on the educational system in the former GDR, we investigate three different imputation procedures. The first one, IMP1, attempts to match the six education categories provided by the IEB imposing detailed age constraints from the institutional information on the GDR educational system. The second one, IMP2, gives up the age constraints and aims to match somewhat broader education categories, into which the six categories in the IEB have been typically summarised in many empirical applications. Finally, the third one, IMP3, defines the education level based on potential years of education.

We validate our procedures by using external GDR census data provided by the German Statistical Office. These data allow us to compare the fraction of individuals in specific education-age group cells resulting from our imputations with those from the census data for comparable cohorts in 1984. The general picture that emerges is that IMP2 and IMP3 tend to overpredict the share of medium-skilled workers and underpredict the share of high-skilled for all age groups, whereas they underpredict (overpredict) the share of low-skilled for the younger (older) age groups. The latter is also true for IMP1. Compared with IMP2 and IMP3, IMP1 gives rise to smaller deviations for the share of medium-skilled, whereas it overpredicts the share of high-skilled especially for the younger age groups. Overall, when balancing out the trade off between goodness of fit and data coverage, the more narrowly defined procedure IMP1 performs best.

Finally, a comparison of our (imputed) education information prior to unification with educational information from the IEB right after unification suggests that the best fit is obtained for those assigned a vocational training degree in the Pension data. The largest discrepancy is observed for those assigned a technical university degree in the Pension data of whom a large fraction (over 50%) exhibits only a vocational training degree in the IEB. This highlights again the difficulty in distinguishing between a GDR Fachschule and a vocational training degree. A simple approach to handle this difficulty could be to redefine the medium-skill category by assigning all technical (school) university graduates to the medium-skilled, such that the high-skilled group would only include university graduates. After doing so, IMP2 would be preferred over IMP1 and IMP3. Given that IMP2 simultaneously gives rise to the least number of missing values and provides the best match to the IEB information, our proposed procedure IMP2 seems to provide a quite reasonable compromise between matching external information and data coverage.