Comparing Fully and Partially Synthetic Data Sets for 

Statistical Disclosure Control in the German IAB 

Establishment Panel 

Jörg Drechsler*, Stefan Bender*, and Susanne Rässler* 

* Institute for Employment Research (IAB), Regensburger Straße 104, 

90478 Nürnberg, Germany 

joerg.drechsler@iab.de, stefan.bender@iab.de, susanne.raessler@iab.de 

Abstract. For data sets considered for public release, statistical agencies have to face the dilemma 

of guaranteeing the confidentiality of survey respondents on the one hand and offering sufficiently 

detailed data for scientific use on the other hand. For that reason a variety of methods that address 

this problem can be found in the literature. 

In this paper we discuss the advantages and disadvantages of two approaches that provide 

disclosure control by generating synthetic data sets: The first, proposed by Rubin (1993), 

generates fully synthetic data sets while the second suggested by Little (1993) imputes values only 

for selected variables that bear a high risk of disclosure. 

We apply the two methods to a set of variables from the 1997 wave of the German IAB 

Establishment Panel and evaluate their quality by comparing regression results from the original 

data with results we achieve for the same analyses run on the data set after the imputation 

procedures. 

Introduction 

In recent years the demand for publicly available micro data increased dramatically. On the other 

hand, more sophisticated record linkage techniques and the variety of databases readily available 

to the public may enable an ill-intentioned data user (intruder) to identify single units in public use 

files provided by statistical agencies more easily. Since the data usually is collected under the 

pledge of confidentiality, the agencies have to decide carefully what information they are willing 

to release. Concerning release on the micro level, all agencies apply some statistical disclosure 

techniques that either suppress some information or perturb the data in some way to guarantee 

confidentiality. A certain amount of information loss is common to all these approaches. Thus, the 

common aim of all approaches is, to minimize this information loss while at the same time 
 

 

 

 

 

 

 

 

 

 

 

 

 

minimizing the risk of disclosure. For that reason, a variety of methods for disclosure control has 

been developed to provide as much information to the public as possible, while satisfying 

necessary disclosure restrictions (Willenborg and de Waal, 2001, Abowd and Lane, 2004). 

Especially for German establishment data sets a broad literature on perturbation techniques with 

different approaches can be found (for example Brand 2000, Brand 2002, Brand et al. 1999, 

Gottschalk 2005, Ronning and Rosemann 2006, Ronning et al. 2005, Rosemann 2006). 

A new approach to address this problem was suggested by Rubin in 1993: Generating fully 

synthetic data sets to guarantee confidentiality. His idea was to treat all the observations from the 

sampling frame that are not part of the sample as missing data and to impute them according to the 

multiple imputation framework. Afterwards, several simple random samples from these fully 

imputed data sets are released to the public. Because all imputed values are random draws from 

the posterior predictive distribution of the missing values given the observed values, disclosure of 

sensitive information is nearly impossible, especially if the released data sets don’t contain any 

real data. Another advantage of this approach is the sampling design for the imputed data sets. As 

the released data sets can be simple random samples from the population, the analyst doesn’t have 

to allow for a complex sampling design in his models. However, the quality of this method 

strongly depends on the accuracy of the model used to impute the “missing“ values. If the model 

doesn’t include all the relationships between the variables that are of interest to the analyst or if 

the joint distribution of the variables is miss-specified, results from the synthetic data sets can be 

biased. Furthermore, specifying a model that considers all the skip patterns and constraints 

between the variables can be cumbersome if not impossible 

To overcome these problems, a related approach suggested by Little (1993) replaces observed 

values with imputed values only for variables that bear a high risk of disclosure or for variables 

that contain especially sensitive information leaving the rest of the data unchanged. This approach, 

discussed as generating partially synthetic data sets in the literature, has been adopted for some 

data sets in the US (see for example Abowd and Woodcock, 2001, 2004 or Kennickell, 1997). 

In this paper we apply both methods to a German Establishment Survey (the Establishment Survey 

of the Institute for Employment Research (IAB) and discuss advantages and disadvantages for 

both methods in terms of data utility and disclosure risk. 

The remainder of this paper is organized as follows: Section 2 provides a short overview of the 

multiple imputation framework and its modifications for disclosure control. Section 3 introduces 

the two data sets used. Section 4 describes the application of the two multiple imputation 

approaches for disclosure control to the IAB Establishment Panel. Section 5 evaluates these 

approaches by comparing regression results from the original data with results achieved for the 

same analyses run on the data set after the imputation procedures. The paper concludes with a 

general discussion of the findings from this study and their consequences for agencies willing to 

release synthetic data sets of their data. 
 

 

 

 

 

 

 

 

 

 

 

 

2 Multiple Imputation 

2.1 Multiple Imputation for Missing Data 

Missing data is a common problem in surveys. To avoid information loss by using only 

completely observed records, several imputation techniques have been suggested. Multiple 

imputation, introduced by Rubin (1978) and discussed in detail in Rubin (1987, 2004), is an 

approach that retains the advantages of imputation while allowing the uncertainty due to 

imputation to be directly assessed. With multiple imputation, the missing values in a data set are 

replaced by m > 1 simulated versions, generated according to a probability distribution for the true 

values given the observed data. More precisely, let Yobs be the observed and Ymis the missing part 

of a data set Y, with Y=(Ymis,Yobs), then missing values are drawn from the Bayesian posterior 

predictive distribution of (Ymis|Yobs), or an approximation thereof. Typically, m is small, such as m 

= 5. Each of the imputed (and thus completed) data sets is first analyzed by standard methods 

designed for complete data; the results of the m analyses are then combined in a completely 

generic way to produce estimates, confidence intervals and tests that reflect the missing-data 

uncertainty. In this paper, we discuss analysis with scalar parameters only, for multidimensional 

quantities see Little and Rubin (2002, Section 10.2). 

To understand the procedure of analyzing multiply imputed datasets, think of an analyst interested 

in an unknown scalar parameter θ, where θ could be e.g. the mean of a variable, the correlation 

coefficient between two variables or a regression coefficient in a linear regression. 

Inferences for this parameter for datasets with no missing values usually are based on a point 

estimate θ

ˆ , an estimate for the variance of θˆ 

, Vˆ and a normal or Student’s t reference 

distribution. For analysis of the imputed datasets, let θ

ˆ

i and Vˆ

i

 for i = 1,...,m be the point and 

variance estimates for each of the m completed datasets. To achieve a final estimate over all 

imputations, these estimates have to be combined using the combining rules first described by 

Rubin (1978). 

For the point estimate, the final estimate simply is the average of the m point estimates 

m 1 1

θ

ˆ 

MI = ∑θ

ˆ 

i with i = 1,...,m . Its variance is estimated by T =W +(1+m

−

)B , where 

m i=1 

m m

−1 1 W ˆ = m ∑ Vˆ

l is the “within-imputation” variance B = ∑(θ

ˆ 

i −θ MI )

2 is the “betweenl=1 m −1 i=1 

+

−1

imputation” variance, and the factor (1 m ) reflects the fact that only a finite number of 

ˆ completed-data estimates θ , i = 1,...,m is averaged together to obtain the final point estimate. i 

The quantity γˆ = + m BT −1

(1 / ) estimates the fraction of information about θ that is missing due 

to nonresponse. 
 

 

 

 

 

 

ˆ

Inferences from multiply imputed data are based on θ MI , T, and a Student’s t reference 

ˆ distribution. Thus, for example, interval estimates for θ have the form θ MI ± t(1−α / 2) T , where 

t(1−α / 2) is the (1 −α / 2) quantile of the t distribution. Rubin and Schenker (1986) provided the 

approximate value vRS = (m −1)γˆ −2 for the degrees of freedom of the t distribution, under the 

assumption that with complete data, a normal reference distribution would have been appropriate 

(that is, the complete data would have had large degrees of freedom). Barnard and Rubin (1999) 

relaxed the assumption of Rubin and Schenker (1986) to allow for a t reference distribution with 

−1 1− −1

complete data, and suggested the value ν = (ν +νˆ ) for the degrees of freedom in the BR RS obs 

multiple-imputation analysis, where νˆ = (1 −γ ν ˆ)( )( ν +1) /( ν + 3) and ν denotes the obs com com com com 

complete-data degrees of freedom. 

 2.2 Fully Synthetic Data Sets 

In 1993, Rubin suggested to create fully synthetic data sets based on the multiple imputation 

framework. His idea was to treat all units in the population that have not been selected in the 

sample as missing data, impute them according to the multiple imputation approach and draw 

simple random samples from these imputed populations for release to the public. 

For illustration, think of a data set of size n, sampled from a population of size N. Suppose further, 

the imputer has information about some variables X for the whole population, for example from 

census records, and only the information from the survey respondents for the remaining variables 

Y. Let Yinc be the observed part of the population and Yexc the nonsampled units of Y. For 

simplicity, assume that there are no item-missing data in the observed data set. 

Now the synthetic data sets can be generated in two steps: First, construct m imputed synthetic 

populations by drawing Yexc m times independently from the posterior predictive distribution 

f(Yexc|X,Yinc) for the N-n unobserved values of Y. If the released data should contain no real data for 

Y, all N values can be drawn from this distribution. Second, make simple random draws from these 

populations and release them to the public. The second step is necessary as it might not be feasible 

to release m whole populations for the simple matter of data-size. In practice, it is not mandatory 

to generate complete populations. The imputer can make random draws from X in a first step and 

only impute values of Y for the drawn X. 

The analysis of the m simulated data sets follows the same lines as the analysis after multiple 

imputation (MI) for missing values in regular data sets (see Section 2.1). However, the calculation 

of the total variance slightly differs from the calculation of the total variance in MI settings for 

treating missing data: 

m +1 

vaˆr(θ

ˆ 

MI ) = Tf = B −W 

m 

This difference is due to the additional sampling from the synthetic units for fully synthetic data 

sets. Hence, the variance B between the data sets already reflects the variance within each 
 

 

 

 

 

 

 

 

 

imputation. For a formal justification see Raghunathan et al. (2003). 

If m is large, inferences can be based on normal distributions. For moderate m, a t reference 

distribution is more adequate. The degrees of freedom are given by 

−1 

− 2 (1+ m )B

ν f = (m −1)(1− r 

1

) where r = .

W 

A disadvantage of this variance estimate is that it can become negative. For that reason, Reiter 

(2002) suggests a slightly modified variance estimator that is always positive: 

n * syn T = max(0,T ) +δ ( W ) , where δ=1 if Tf<0, and δ=0 otherwise. f f 

n 

Here, nsyn is the number of observations in the released data sets sampled from the synthetic 

population. 

2.3 Partially Synthetic Data Sets 

In contrast to the creation of fully synthetic data sets, this approach replaces only observed values 

for variables that bear a high risk of disclosure (key variables) or very sensitive variables with 

synthetic values (see for example Reiter 2003). The variables with a high risk of disclosure could 

be variables known to the public from other easily available databases or information from 

statements of accounts for incorporations. Masking these variables by replacing observed with 

imputed values prevents re-identification. The imputed values can be obtained by drawing from 

the posterior predictive distribution f(Y|X), where Y indicates the variables that need to be 

modified to avoid disclosure and X are all variables that remain unchanged or variables that have 

been synthesized in an earlier step. 

Imputations are generated according to the multiple imputation framework as described in Section 

2.1, but comparable to the fully synthetic data context, the variance estimation differs slightly 

from the MI calculations for missing data. Yet, it differs from the estimation in the fully synthetic 

−1

context as well - it is given by Tp = W + m B . 

Similar to the variance estimator for multiple imputation of missing data, m

−1B is the correction 

factor for the additional variance due to using a finite number of imputations. However, the 

additional B, necessary in the missing data context for averaging over the nonresponse mechanism 

(Rubin, 1987), is not necessary here, since the selection mechanism, set by the imputer, is not 

treated as stochastic. For a formal justification, see Reiter (2003). This variance estimate can never 

be negative, so no adjustments are necessary for partially synthetic data sets. Inferences for θ can 

be based on a Student’s t reference distribution with ν = (m −1)(1+

W ))2 degrees of freedom. p

B / m 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 The Data Sets1 

For the imputation of the IAB Establishment Panel, we use additional information from the 

German Social Security Data. In the following Section both data sets will be described in detail. 

3.1 The German Social Security Data 

The German employment register contains information on all employees covered by social 

security. The basis of the German Social Security Data (GSSD) is the integrated notification 

procedure for the health, pension and unemployment insurances, which was introduced in January 

1973.2 This procedure requires employers to notify the social security agencies about all 

employees covered by social security. 

As by definition the German Social Security Data only includes employees covered by social 

security - civil servants and unpaid family workers for example are not included - approx. 80% of 

the German workforce3

 are represented. However, the degree of coverage varies considerably 

across the occupations and the industries. 

The notifications of the GSSD include for every employee, among other things, the workplace and 

the establishment identification number. We use this number to match the selected establishment 

characteristics aggregated from the employment register with the IAB Establishment Panel. As we 

use the 1997 wave of the panel, data are taken from the register for June, 30th 1997 (see Figure 2 

in the Appendix for all characteristics used). 

3.2 The IAB Establishment Panel 

The IAB Establishment Panel4 is based on the employment statistics aggregated via the 

establishment number as of June 30 of each year. Consequently the panel only includes 

establishments with at least one employee covered by social security. The sample is drawn 

following the principle of optimum stratification. The stratification cells are defined by ten classes 

for the size of the establishment, 16 classes for the region, and 16 classes for the industry5

. These 

cells are also used for weighting and extrapolation of the sample. The survey is conducted by 

interviewers from TNS Infratest Sozialforschung. For the first wave, 4,265 establishments were 

interviewed in Western Germany in the third quarter of 1993. Since then the Establishment Panel 

has been conducted annually – since 1996 with over 4,700 establishments in Eastern Germany in 

addition. The response rate of units that have been interviewed repeatedly is over 80%. Each year, 

the panel is accompanied by supplementary samples and follow-up samples to include new or 

1 This chapter follows the description given in Alda, Bender & Gartner (2005). 

2 On the structure of the insurance number and on the data office of the pension insurance providers cf. 

Steeger (2000). 

3 An overview of the data is given in Bender, Hass, and Klose (2000), a detailed description can be found in 

Bender, Hilzendegen, Rohwer, and Rudolph (1996). 

4 The approach and structure of the establishment panel are described for example by Bellmann (2002) and 

Kölling (2000). 

5 From 2000 onwards 20 industry classes are used. 
 

 

 

 

 

 

 

 

 

 

 

 

reviving establishments and to compensate for panel mortality. The list of questions contains 

detailed information about the firms’ personnel structure, development and personnel policy. An 

overview of available information in 1997 is listed in the Appendix, Figure 2. 

4 Application of the Two Synthetic Data Approaches to the IAB Establishment Panel 

4.1 Generating Fully Synthetic Data Sets 

In a first step, we only impute values for a set of variables from the 1997 wave of the IAB 

Establishment Panel. As it is not feasible to impute values for the millions of establishments 

contained in the German Social Security Data for 1997, we sample from this frame, using the 

same sampling design as for the IAB Establishment Panel: Stratification by establishment size, 

region and industry (see Table 4 in the Appendix for an example). Every stratum contains the 

same number of units as the observed data from the 1997 wave of the Establishment Panel. We 

gain further information by adding variables from the German Social Security Data and matching 

these variables to the observations in the Establishment Panel via establishment identification 

number. After matching, every data set is structured as follows: Let N be the total number of units 

in the newly generated data set, that is the number of units in the sample ns

 plus the number of 

units in the panel np, N=ns+np. Let X be the matrix of variables with information for all 

observations in N. Then X consists of the variables establishment size, region and industry and the 

variables added from the German Social Security Data (see Figure 2 in the Appendix). Let Y be 

the selected variables from the Establishment Panel, with Y=(Yinc,Yexc), where Yinc are the observed 

values from the Establishment Panel and Yexc are the hypothetic missing data for the newly drawn 

values in X (see Figure 1). 

missing data 

data from the 

new sample 

data from the IAB 

Establishment Panel 

Yexc

Yinc

X 

Fig. 1. The full MI approach for the IAB Establishment Panel 

Now, values for the missing data can be imputed as outlined in Section 2 by drawing Yexc m times 

independently from the posterior predictive distribution f(Yexc|X,Yinc) for the N-np unobserved 

values of Y. 

After the imputation procedure, all observations from the Establishment Panel are omitted and 

only the imputed values are kept for analysis. Results from this analysis can be compared with the 

results achieved with the real data. 
 

 

 

 

 

 

 

 

 

 

 

4.2 Drawing a New Sample from the German Social Security Data 

Due to panel mortality a supplementary sample has to be drawn for the IAB Establishment Panel 

every year. In the 1997 wave, this supplementary sample primarily consisted of newly founded 

establishments because in that year the questionnaire had a focus on new foundations. Therefore, 

start-ups are overrepresented in the sample. Arguably, answers from these establishments differ 

systematically from the answers provided by establishments existing for several years. Drawing a 

new sample without taking this oversampling into account could lead to a sample after imputation 

that differs substantially from that in the Establishment Panel. For simplicity reasons, we define 

establishments not included in the German Social Security Data before July 1995 as new 

foundations and delete them from the sampling frame and the Establishment Panel. For the 1997 

wave of the Establishment Panel, this means a reduction from 8,850 to 7,610 observations. 

Additionally, we have to make sure that every establishment in the survey is also represented in 

the German Social Security Data for that year. Merging the two data sets using the establishment 

identification number reveals that 278 units from the panel are not included in the employment 

statistics. These units are also omitted leading to a final sample of 7,332 observations. 

Furthermore, we have to verify that the stratum parameters size, industry and region match in both 

data sets. Merging indicates that there are some differences between the two records. If the data 

sets differ, values from the employment statistics are adopted. 

Cross tabulation of the stratum parameters for the 7,332 observations in our sample provides a 

matrix containing the number of observations for each stratum. For example, one cell of the matrix 

contains companies specialized in investment goods that are located in Berlin-West with 20 to 49 

employees (see Table 4 in the Appendix). Now, a new data set can be generated easily by drawing 

establishments from the German Social Security Data according to this matrix. 

4.3 Generating Partially Synthetic Data Sets for the IAB Establishment Panel 

For this study, we replace only two variables (the number of employees and the industry, coded in 

16 categories) with synthetic values, since these are the only two variables that might lead to 

disclosure in the analyses we use to evaluate the data utility of the synthetic data sets. If we 

intended to release the complete data to the public, some other variables would have to be 

synthesized, too. Identifying all the variables that provide a potential disclosure risk is an 

important and labour intensive task. The research project that deals with this problem is still 

running. Nevertheless, the two variables mentioned above definitely impose a high risk of 

disclosure, since they are easily available in public databases and especially large firms can be 

identified without difficulty using only these two variables. 

We define a multinomial logit model for the imputation of the industry code and a linear model 

stratified by four establishment sizes defined by quartiles for the number of employees. 
 

 

 

 

 

 

 

 

 

 

 

 

5 Comparison Between the Original and the Imputed Data Sets 

5.1 Data Utility 

To create the fully synthetic data sets we draw ten new samples from the German Social Security 

Data as described in Section 4.2 and impute every sample ten times using chained equations as 

implemented in the software IVEware by Raghunathan, Solenberger and Hoewyk. For the 

imputation procedure we use 26 variables from the GSSD and reduce the number of panel 

variables to be imputed to 48 to avoid multicollinearity problems. For the partially synthetic data 

sets, we use the same number of variables in the imputation model (26 from the GSSD 48 from the 

establishment panel), but no samples are drawn from the GSSD, since the original sample is used. 

We generate the same number of synthetic data sets, but the modelling is performed using own 

coding in R. 

For an evaluation of the data utility of the synthetic data, we compare analytic results achieved 

with the original data with results from the synthetic data. The first regression is based on an 

analysis by Thomas Zwick: ‘Continuing Vocational Training Forms and Establishment 

Productivity in Germany’ published in the German Economic Review, Vol. 6(2), pp. 155-184 in 

2005. 

Zwick analyses the productivity effects of different continuing vocational training forms in 

Germany. He argues that vocational training is one of the most important measures to gain and 

keep productivity in a firm. For his analysis he uses the waves 1997 to 2001 from the IAB 

Establishment Panel. 

In 1997 and 1999 the Establishment Panel included the following additional question that was 

asked if the establishment did support continuous vocational training in the first part of 1997 or 

1999 respectively: ‘For which of the following internal or external measures were employees 

exempted from work or were costs completely or partly taken over by the establishment?’ Possible 

answers were: formal internal training, formal external training, seminars and talks, training on the 

job, participation at seminars and talks, job rotation, self-induced learning, quality circles, and 

additional continuous vocational training. Zwick examines the productivity effects of these 

training forms and demonstrates that formal external training, formal internal training and quality 

circles do have a positive impact on productivity. Especially for formal external courses the 

productivity effect can be measured even two years after the training. 

To detect why some firms offer vocational training and others not, Zwick runs a probit regression 

using the 1997 wave of the Establishment Panel. The regression (see Table 5 in the Appendix for 

details) shows that establishments increase training if they expect to loose workers. One reason 

could be that the market for skilled labour in Germany is small and establishments have 

difficulties in finding new skilled workers. Furthermore, establishments tend to offer more training 

if high qualification needs are expected. This is also the case if establishments give a higher 

priority to additional apprenticeship training and continuing vocational training efforts instead of 

hiring externally qualified employees when they have vacancies for skilled jobs. Larger 
 

 

 

 

 

 

 

 

 

 

establishments tend to qualify employees more often because they usually have own training 

departments and can therefore train workers more efficiently. For firms with a high share of 

qualified employees, state-of-the-art technical equipment or investments in information and 

communication technology (IT) it is also essential to offer more training. Collective wage 

agreements are often associated with fringe benefits such as training, while works councils usually 

attach high importance to continuing vocational training. Therefore both have a positive effect on 

the amount of training offered. 

In the regression, Zwick uses two variables (investment in IT and the co-determination of the 

employees) that are only included in the 1998 wave of the Establishment Panel. Moreover, he 

excludes some observations based on information from other years. As we impute only the 1997 

wave eliminating newly founded establishments, we have to rerun the regression, using all 

observations except for newly founded establishments and deleting the two variables which are 

not part of the 1997 wave. Results from this regression are given in Table 6 in the Appendix and it 

is evident that the new regression differs only slightly from the original regression. All the 

variables significant in Zwick’s analysis are still significant. Only for the variable “high number of 

maternity leaves expected”, the significance level decreases from 1% to 5%. 

For his analysis, Zwick runs the regression only on units with no missing values for the regression 

variables, loosing all the information on establishments that did not respond to all questions used. 

This might lead to biased estimates if the assumption of a missing pattern that is completely at 

random (see for example Rubin, 1987) does not hold. For that reason, we compare the regression 

results from the synthetic data sets that by definition have no missing values, with the results, 

Zwick would have achieved if he would have run his regression on a data set with all the missing 

values multiply imputed. Comparing results from Zwick`s regression run on the original data and 

on the synthetic data sets are presented in Table 1. 

All estimates are very close to the estimates from the real data and except for the variable “high 

number of maternity leaves expected”, for which the significance level decreases to 5% for the 

fully synthetic data, remain significant on the same level when using the synthetic data. Obviously 

Zwick would have come to the same conclusions in his analysis, no matter if he would have used 

the fully synthetic data or the partially synthetic data instead of the real data. 

However, if we compare the results from the partially synthetic and the fully synthetic data sets 

more closely, we see that the estimates from the partially synthetic data sets are closer to the 

original estimates for most coefficients, although the industry dummies are used as covariates in 

the regression. Note that the univariate distribution of the industry will always be identical to the 

true distribution for the fully synthetic data sets, because the industry code is part of the sampling 

design which is identical for the original and for the fully synthetic data. 
 

 

 

 

 

 

 

 

Table 1. Comparison between the regression coefficients from the real data and the coefficients from the 

synthetic data 

Coeff. from Fully syn- Partially Exogenous variables βfully - βorg βpartially - βorg org. data thetic data synt. data 

Redundancies expected 0.250*** 0.251*** 0.260*** 0.001 0.010 

Many employees are expected to be 

on maternity leave 

High qualification need exp. 

0.266**

0.648***

 0.244*

 0.625***

 0.318** 

0.642*** 

-0.021 

-0.023 

0.052 

-0.006 

Apprenticeship training reaction on 

skill shortages 

Training reaction on skill shortages 

Establishment size 20-199 

0.113*

0.527***

0.686***

 0.147*

 0.523***

 0.645***

 0.118* 

0.547*** 

0.702*** 

0.034 

-0.004 

-0.041 

0.005 

0.019 

0.017 

Establishment size 200-499 1.355*** 1.203*** 1.329*** -0.152 -0.027 

Establishment size 500-999 1.347*** 1.340*** 1.359*** -0.007 0.012 

Establishment size 1000 + 1.964*** 1.778*** 1.815*** -0.187 -0.149 

Share of qualified employees 

State-of-the-art technical equipment 

Collective wage agreement 

Apprenticeship training 

0.778***

0.169***

0.254***

0.484***

 0.820***

 0.168***

 0.313***

 0.406***

 0.785*** 

0.170*** 

0.268*** 

0.503*** 

0.043 

-0.001 

0.059 

-0.078 

0.008 

0.001 

0.014 

0.020 

Number of observations 7,332 7,332 7,332 

15 industry dummies and East Germany dummy 

Notes: *** Significant at the 0.1% level,** Significant at the 1% level, * Significant at the 5% level; the standard errors 

are heteroscedasticity-corrected. 

Source: IAB Establishment Panel 1997 without newly founded establishments and establishments not represented in the 

employment statistics of the German Federal Employment Agency; regression according to Zwick (2005) 

Another way to determine the data utility is to look at the overlap between the confidence intervals 

for the estimates from the original data and the confidence intervals for the estimates from the 

synthetic data as suggested by Karr et al. (2006). For every estimate the average overlap is 

calculated by: 

1 U over,k − Lover,k U over,k − Lover,k 

J =



 +



,

k 2 U − L U − L

 org,k org,k syn,k syn,k 

where Uover,k and Lover,k denote the upper and the lower bound of the overlap of the confidence 

intervals for the estimate k, Uorg,k and Lorg,k denote the upper and the lower bound of the confidence 

interval for the estimate k from the original data, and Usyn,k and Lsyn,k denote the upper and the 

lower bound of the confidence interval for the estimate k from the synthetic data. This utility 

measure is more accurate in the sense that it also considers the significance level of the estimate, 

because estimates with low significance might still have a high confidence interval overlap and by 

this a high data utility even if their point estimates differ considerably from each other, because 

the confidence intervals will increase with lower significance. For more details on this method see 

Karr et al. (2006). Results for our regression example are presented in Table 2. 
 

 

 

Table 2: Comparison of the average confidence interval overlap between the original data set and the 

synthetic data sets 

CI overlap for the CI overlap for the Exogenous variables fully synthetic data partially synth. data 

Redundancies expected 0.950 0.954 

Many employees are expected to be on maternity leave 0.945 0.861 

High qualification need exp. 0.923 0.980 

Apprenticeship training reaction on skill shortages 0.846 0.973 

Training reaction on skill shortages 0.897 0.908 

Establishment size 20-199 0.760 0.901 

Establishment size 200-499 0.421 0.923 

Establishment size 500-999 0.955 0.973 

Establishment size 1000 + 0.735 0.792 

Share of qualified employees 0.846 0.972 

State-of-the-art technical equipment 0.953 0.996 

Collective wage agreement 0.675 0.916 

Apprenticeship training 0.594 0.883 

Average overlap 0.808 0.926 

The confidence interval overlap is high for both approaches, often more than 90%, but again the 

partially synthetic approach yields better results than the fully synthetic approach. The overlap is 

higher for all estimates except for the variable that indicates whether the establishment expects 

many employees to be on maternity leave. Especially, if we look at the average CI overlap over all 

estimates, the improvements for the partially synthetic datasets become clearly evident with an 

increase of the average overlap from 80.8% to 92.6%. 

The advantages of the partially synthetic approach become even more obvious, if we look at a 

regression of the number of employees transformed on a logarithmic scale on the 16 industry 

dummies. This model might not be the most interesting model from an economic perspective (the 

R

2

 is low, 0.134 for the original data) but it provides useful information for our study, since it 

contains exactly the two variables that are synthesized for the partially synthetic approach. Table 3 

shows the estimates for both approaches compared to the real estimates and the average 

confidence interval overlap. 

Again, the partially synthetic approach provides better results, although the estimates for the fully 

synthetic data sets are based on exact marginal distribution for the industry. The deviation from 

the original estimates is lower for eleven of the 16 estimates. The significance level changes 

slightly for six estimates when using the fully synthetic data sets, but only for two estimates when 

using the partially synthetic data sets. The confidence interval overlap is higher for 13 estimates if 

only some variables are synthesized and the average overlap over all estimates further underlines 

the higher data utility for partially synthetic data sets. 
 

 

 

 

 

 

 

 

Table 3: Comparison of the estimates and confidence interval overlaps for a regression of the number of 

employees on industry dummies (the 16th dummy is the reference category) 

CI overlap

part. synt. 

data 

Exogenous 

variables 

Coefficients 

from org. data 

Fully synthetic 

data 

Partially 

synthetic data 

CI overlap 

fully synt. data 

Industry dummy 1 -1.606*** -1.794*** -1.531*** 0.653 0.834 

Industry dummy 2 0.774*** 0.757*** 0.723*** 0.849 0.919 

Industry dummy 3 0.098 -0.006 0.148 0.731 0.878 

Industry dummy 4 -0.029 -0.204* 0.016 0.470 0.864 

Industry dummy 5 -0.96*** -1.162*** -0.923*** 0.477 0.908 

Industry dummy 6 -1.276*** -1.495*** -1.234*** 0.470 0.880 

Industry dummy 7 -1.696*** -1.884*** -1.600*** 0.507 0.718 

Industry dummy 8 -0.505*** -0.286* -0.605*** 0.515 0.786 

Industry dummy 9 0.334* 0.362** 0.320* 0.871 0.975 

Industry dummy 10 -0.547* -0.62** -0.713*** 0.914 0.799 

Industry dummy 11 -1.431*** -1.531*** -1.342*** 0.781 0.781 

Industry dummy 12 -0.318** -0.346*** -0.258* 0.929 0.851 

Industry dummy 13 -0.442*** -0.623*** -0.395*** 0.537 0.883 

Industry dummy 14 -1.641*** -1.844*** -1.529*** 0.589 0.731 

Industry dummy 15 -0.703*** -0.719** -0.820*** 0.966 0.841 

Intercept 4.831*** 4.85*** 4.779*** 0.926 0.774 

0.699 0.839 Average overlap

Notes: *** Significant at the 0.1% level,** Significant at the 1% level, * Significant at the 5% level 

Of course, partially synthetic data sets will always provide results that are at least as good as the 

ones from the fully synthetic data set for analyses that are based solely on variables left unchanged 

in the partially synthetic data. So, in terms of data utility, partially synthetic data sets will 

outperform fully synthetic data sets in most cases. Furthermore, there might be instances where 

defining models for all variables is simply impossible, because there are so many logical 

constraints, bounds, and skip patterns in the data that a useful model cannot be obtained. And if it 

is possible to come up with a model, the imputed values might be biased and this bias is then 

introduced in all the other variables that are imputed on a later stage, based on the imputations for 

this variable. 

However, the data utility benefits of the partially synthetic data sets come at the price of an 

increased disclosure risk that should be discussed in the following Section. 

5.2 Disclosure risk 

In general, the disclosure risk for the fully synthetic data is very low, since all values are synthetic 

values. It is not zero however, because, if the imputation model is too good and basically produces 

the same estimated values in all the synthetic data sets, it doesn’t matter that the data is all 

synthetic. It might look like the data from a potential survey respondent an intruder was looking 
 

 

 

 

 

 

 

 

 

 

 

 

for. And once the intruder thinks, he identified a single respondent and the estimates are 

reasonable close to the true values for that unit, it is no longer important that the data is all made 

up. The potential respondent will feel that his privacy is at risk. Still, this is very unlikely to occur 

since the imputation models would have to be perfect and the intruder faces the problem that he 

never knows if the imputed values are anywhere near the true values. 

The disclosure risk is higher for partially synthetic data sets especially if the intruder knows that 

some unit participated in the survey, since true values remain in the data set and imputed values 

are generated only for the survey participants and not for the whole population. So for partially 

synthetic data sets assessing the risk of disclosure is an equally important evaluation step as 

assessing the data utility. It is essential that the agency identifies and synthesizes all variables that 

bear a risk of disclosure. A conservative approach would be, to also impute all variables that 

contain the most sensitive information. Once the synthetic data is generated, careful checks are 

necessary to evaluate the disclosure risk for these data sets. Only if the data sets proof to be useful 

both in terms of data utility and in terms of disclosure risk, a release might be considered. 

For this study, the disclosure risk evaluation is still in progress. First results show however that the 

disclosure risk is still very low for the partially synthetic data sets considered here. 

6. Discussion and Conclusion 

Releasing microdata to the public that guarantees confidentiality for survey respondents on the one 

hand, but also provides a high level of data utility for a variety of analyses on the other hand is a 

difficult task. In this paper we discussed two closely related approaches based on multiple 

imputation: The generation of fully and partially synthetic data sets. While fully synthetic data sets 

will never contain any originally observed values, original values are replaced only for key 

identifiers and/or sensitive values in partially synthetic data sets. Since imputed values can be 

generated for the whole population with fully synthetic data sets, but only for the survey 

respondents with partially synthetic data sets, knowing that a certain unit participated in a survey 

will be a benefit for the intruder only for the partially synthetic data sets. 

Nevertheless, partially synthetic data sets have the important advantage that in general the data 

utility will be higher, since only for some variables the true values have to be replaced with 

imputed values, so by definition the correlation structure between all the unchanged variables will 

be exactly the same as in the original data set. The quality of the synthetic data sets will highly 

depend on the quality of the underlying model and for some variables it will be very hard to define 

good models. But if these variables don’t contain any sensitive information or information that 

might help identify single respondents, why bother to find these models? Why bother to perturb 

these variables first place? Furthermore, the risk of biased imputations will increase with the 

number of variables that are imputed. For, if one of the variables is imputed based on a ‘bad’ 

model, the biased imputed values for that variable could be the basis for the imputation of another 

variable and this variable again could be used for the imputation of another one and so on. So a 

small bias could increase to a really problematic bias over the imputation process. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

The findings in this paper underline these thoughts. The partially synthetic data sets provide higher 

data quality in terms of lower deviation from the true estimates and higher confidence interval 

overlap between estimates from the original data and estimates from the synthetic data almost for 

all estimates. Still, this increase of data utility comes at the price of an increase in the risk of 

disclosure. Although the disclosure risk for fully synthetic data sets might not be zero, the 

disclosure risk will definitely be higher if true values remain in the data set and the released data is 

based only on survey participants. Thus, it is important to make sure that all variables that might 

lead to disclosure are perturbed in a way that confidentiality is guaranteed. This means that a 

variety of disclosure risk checks are necessary before the data can be released, but this is a 

problem common to all perturbation methods that are based only on the information from the 

survey respondents. 

Agencies willing to release synthetic public use files will have to consider carefully, which 

approach suites best for their data sets. If the data consists only of all small number of variables 

and imputation models are easy to set up, the agencies might consider releasing fully synthetic 

data sets, since these data sets will provide the highest confidentiality protection, but if there are 

many variables in the data considered for release and the data contains a lot of skip patterns, 

logical constraints and questions that are asked only to a small subgroup of survey respondents, 

the agencies might be better off to release partially synthetic data sets and include a detailed 

disclosure risk study in their evaluation of the quality of the data sets considered for release. 

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Appendix 

Information contained in the IAB Information contained in the German 

Establishment Panel (wave 1997) Social Security Data (from 1997) 

Available for establishments in the survey Available for all German establishments with at 

least one employee covered by social security 

- number of employees in June 1996 

- qualification of the employees - number of full-time and part-time employees 

- number of temporary employees - short-time employment 

- number of agency workers - mean of the employees age 

- working week (full-time and overtime) - mean of wages from full-time employees 

- the firm‘s commitment to collective agreements - mean of wages from all employees 

- existence of a works council - occupation 

- turnover, advance performance and export share - schooling and training 

- investment total - number of employees by gender 

- overall wage bill in June 1997 - number of German employees 

- technological status 

- age of the establishment 

- legal form and corporate position 

- overall company-economic situation 

- reorganisation measures 

- company further training activities 

- additional information on new foundations 

Covered in both datasets 

 establishment number, branch and size 

 location of the establishment 

 number of employees in June 1997 

Fig. 2. Data comparison 
 

 

 

 

 

 

 

Table 4. Stratification matrix 

Federal 

state 

Branch of trade (16 categories) 

Establishment 

size6 

1 

Agriculture 

, forestry 

2 

Mining and 

quarrying 

3 

Raw material 

processing 

... 

16 

Non-profit 

organization 

Total 

BerlinWest 

1 0-4 0 0 1 ... 6 42 

2 5-9 2 0 0 ... 0 25 

3 10-19 1 0 2 ... 3 35 

4 20-49 0 1 1 ... 5 29 

5 50-99 0 0 1 ... 1 13 

6 100-199 1 0 2 ... 2 31 

... ... ... ... ... ... ... 

10 5,000+ 0 1 0 ... 1 5 

Total 4 3 9 ... 40 275 

BerlinEast 

1 0-4 0 0 0 ... 1 52 

2 5-9 0 0 1 ... 3 45 

... ... ... ... ... ... ... 

10 5,000+ 0 0 0 ... 1 1 

Total 3 2 4 ... 41 303 

Branden 

-burg 

1 0-4 5 0 2 ... 8 96 

... ... ... ... ... ... ... 

... 

... ... ... ... ... ... ... 

... ... ... ... ... ... ... 

6

 Number of employees covered by social security 
 

 

 

 

 

Table 5. Probit estimation to explain if an establishment trains or not from Zwick (2005) 

Exogenous variables Coefficients z-Value 

Redundancies expected 

Many employees are expected to be on maternity 

0.303***

0.332**

 4.72 

 3.21 

leave 

High qualification need exp. 

Apprenticeship training reaction on skill shortages 

Training reaction on skill shortages 

Establishment size 20-199 

0.565***

0.222***

0.652***

0.616***

 6.94 

 4.32 

 13.08 

 12.67 

Establishment size 200-499 1.119*** 10.47 

Establishment size 500-999 1.239*** 7.32 

Establishment size 1,000 + 

Co-determination 

1.661***

0.258***

 5.38 

 3.81 

Share of qualified employees 

State-of-the-art technical equipment 

Investor in IT 

0.633***

0.199***

0.244***

 9.03 

 4.65 

 5.29 

Collective wage agreement 

Apprenticeship training 

0.213***

0.457***

 4.82 

 10.01 

15 sector dummies and East Germany dummy 

Pseudo-R2

 0.32 

Number of observations 5,629 

Notes: *** Significant at the 0.1% level, **Significant at the 1% level; the standard errors are heteroscedasticity-corrected. 

Source: Zwick (2005), p. 169. 
 

 

 

Table 6. Probit estimation to explain if an establishment trains or not after modifications described 

in Section 5.1 

Exogenous variables Coefficients z-Value 

Redundancies expected 0.261*** 4.58 

Many employees are expected to be on maternity 

leave 0.252*

 2.49 

High qualification need expected 

Apprenticeship training reaction on skill shortages 

Training reaction on skill shortages 

Establishment size 20-199 

0.641***

0.176***

0.597***

0.683***

 8.10 

 3.40 

 11.91 

 15.19 

Establishment size 200-499 1.351*** 15.71 

Establishment size 500-999 1.398*** 11.75 

Establishment size 1,000 + 

Share of qualified employees 

State-of-the-art technical equipment 

Collective wage agreement 

Apprenticeship training 

1.972***

0.766***

0.175***

0.245***

0.420***

 9.15 

 10.28 

 4.16 

 5.46 

 9.31 

15 sector dummies and East Germany dummy 

Pseudo-R2

 0.32 

Number of observations 6,258 

Notes: *** Significant at the 0.1% level, **Significant at the 1% level; * Significant at the 5% level, the standard errors are 

heteroscedasticity- corrected. 

Source: IAB Establishment Panel 1997 without newly founded establishments and establishments not represented in the 

employment statistics of the German Federal Employment Agency; regression according to Zwick (2005).