Public-private sector wage differentials in Germany: evidence from quantile regression +

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1 Public-private sector wage differentials in Germany: evidence from quantile regression + Blaise Melly University of St. Gallen, Swiss Institute for International Economics and Applied Economic Research (SIAW), Dufourstrasse 48, 9 St. Gallen, Switzerland, blaise.melly@unisg.ch, April 22 Abstract This paper measures the differences in earnings distributions between public sector and private sector employees in Germany in 2. results suggest that wages are lower in the public sector for men but higher for women. The use of quantile regressions indicates that the public sector wage premium is highest at the lower end of the wage distribution and then decreases monotonically as we move up the wage distribution. Separate analyses by work experience and educational groups reveal that the most experienced employees and those with basic schooling do best in the public sector. Keywords: regression, public-private wage differential, Germany. JEL classification: J3, J45. + I am grateful to Michael Lechner, Ruth Miquel and seminar participants at University of Konstanz for helpful comments. I thank Michael Lechner and the Centre for European Economic Research (ZEW), Mannheim, for letting me work with the full sample of the German Socio-Economic Panel (GSOEP). 1

2 1. Introduction Public sector pay has always attracted policy attention. Obviously the size of the public sector wage bill has implications for both monetary and fiscal policy. The government remains by far the largest employer in Germany. In 2, 4.91 million people or 13.4 percent of the labor force received his wage or salary from the public sector (Federal Statistical Office 21). Furthermore, the wage settlements in the public sector could have a substantial impact over those in the private sector. Because of this spillover effect, the existence of a public sector wage premium may induce private sector employers to pay higher wages to their employees. The concern is that such general wage increases can jeopardize competitiveness in the global economy and further fuel inflation. There are a number of reasons that earnings differential between the private and the public sector could exist. The public sector is subject to political constraints and not to profit constraints. Therefore the political system may have different objectives from those of the private sector. Issues of pay equity and fairness can survive in the political market place more than in the economic market place. Governments are also under pressure to be a model employer and not pay low wages to its less skilled workforce. Similarly, voters seem to refuse that high-level officials receive comparable remuneration to the high salaries of the private sector. Nevertheless, the pursuit of theses equity goals could have a serious impact on the efficiency of the labor market. If the government pays too much, employees in the private sector may decide to queue for relatively high-paying jobs in the public sector. Moreover, this policy leads to higher taxes or budget deficits. If the public sector pays wages that are too low, it will not find skilled and loyal employees. The consequences will be public services of poor quality. Given these differences in the wage setting procedures and the possible consequences for the labor market, many researchers have sought to ascertain whether an identical employee working in the same job in the public and in the private sector would earn the same or a different amount. Early research comparing the earnings of public sector employees has been undertaken in the United States by Smith (1976 and 1977). She found that rates of pay were higher for public sector than private sector employees and that the earnings premium was larger for female than for male public sector employees. Subsequent research has taken up the same question as Smith and confirmed her findings. Ehrenberg and Schwarz (1986) and Gregory and Borland (1999) have surveyed this voluminous literature. Such wage comparisons using German data are not as voluminous. Dustmann and Van Soest (1997) used data from the German Socio-Economic Panel for the years to analyze developments and differences in public and private sector wage distributions. They found that conditional wages are higher in the private sector for males but higher in the public sector for females. Dustmann and Van Soest (1998) estimated switching regression models for males and models that endogenise education. Their later results are stronger than the results for men that they reported in Poterba and Rueben (1995) were the first to apply quantile regression to study publicprivate wage differentials. This is a natural arena for quantile regression, since there is a suspicion that the public sector compresses the distribution of earnings of employees who 2

3 work in that sector relative to private sector employees. Therefore, the least squares estimate of the mean public sector wage premium gives an incomplete picture of the conditional distribution. Evidence to this effect is available for Canada (Mueller 1998), UK (Disney and Gosling 1998) and Zambia (Nielsen and Rosholm 21). regression has apparently not yet been applied to study the wage structure in the private and public sectors in Germany. This is the object of this paper. Section 2 provides a brief introduction to quantile regression methods. Section 3 describes the data set along with some descriptive statistics. The two following sections estimate conditional wage differentials. In section 4, the dummy variable approach is applied and, in section 5, the decomposition approach is used. Section 6 gives some concluding remarks. 2. Introduction to quantile regression The quantile regression model introduced by Koenker and Basset (1978) extends the notion of ordinary quantiles in the location model to a more general class of linear models in which conditional quantiles have a linear form. The most common form is median regression (Least Absolute Deviations or LAD), where the object is to estimate the median of the dependent variable, conditional on the value of the independent variables. The remaining conditional quantiles are estimated by minimizing an asymmetrically weighted sum of absolute errors. Thus, these models can be used to characterize the entire conditional distribution of a dependent variable given a set of regressors. The point of departure is an elementary definition of the quantiles. Let < θ < 1. The θ th quantile of the distribution of a random variable Y is a value ξ θ such that θ = Pr ( Y ξθ ) = F ( ξθ ) where F is the cumulative distribution function of Y. Let {,..., } yi y n be a random sample of size n drawn from the distribution of Y. By analogy to (1), the sample quantile is estimated by ˆ ξ = inf y : F y θ (2) θ { n ( ) } where F n is the empirical distribution function of Y. To extend this idea to the estimation of conditional quantile functions we need a new way to estimate the quantiles. By circumventing the usual reliance on an ordered set of sample observations, we can define the quantiles as an optimization problem. It is straightforward to show that ξ ˆθ solves ˆ ξθ = argmin θ y m + θ y m. i:yi m i:yi< m i ( 1 ) i (3) regression extends these ideas to the linear model generating a new class of statistics. Let { xi,... x n} be vectors of explanatory variables that correspond to { yi,..., y n}. It is assumed that: ( ) y = x β + u and Quant y x = x β, (4) i i i i i i θ θ θ θ (1) 3

4 where Quant ( yi xi) θ denotes the θ th quantile of y i conditional on x i. The θ th regression quantile is then defined in the same manner as the sample quantile by the minimization problem ˆ βθ = arg min θ y x ' β + θ y x ' β. i:yi x i β i:yi< x i β i i ( 1 ) i i (5) The problem can be formulated as a linear program and simplex-based methods provide efficient algorithms for most applications (Koenker and d Orey 1987). Increasing θ continuously from to 1, we can trace the entire distribution of y i conditional on x i. Let ( θ1,..., θ p) θ and let β ( β θ1,..., βθ p) ˆ β = ˆ β ˆ β denote the estimated values obtained by solving (5) separately for p alternative s = denote the population s true values. Under mild ˆ,, where d regularity conditions (see for instance Buchinsky 1991), n( β β ) N( Λ ) Λθ = and fu ( x) { Λjk },,...,, jk= 1 p ( { } ) ( ) θ j θ θ θ ( ) ( )( ( ) k ) 1 1 jk = min j, k j k fu x xx xx fu x xx Λ θ θ θ θ Ε Ε Ε denotes the density of the error term u θ θ evaluated at conditional on x. The ˆ β β consistently (Hahn 1995). bootstrap is known to estimate the distribution of n ( θ θ ) There are several alternative schemes for estimating the covariance matrix, for an overview see Buchinsky (1998). In the present application standard errors are obtained by design matrix bootstrap with 1 replications. f x = f and any two quantile parameter vectors In the case of homoscedasticity, ( ) ( ) β θ 1 and θ 2 uθ uθ β should differ only in their intercepts but not in their slope coefficients. As suggested in Koenker and Basset (1982), equality of all or selected subsets of slope parameters across different quantiles may be tested using a Wald test. Different estimates at distinct quantiles may be interpreted as differences in the response of the dependent variable to changes in the regressors at various points in the conditional distribution. Such effects cannot be captured by mean regressions. Models for conditional quantile functions offer a number of advantages over more familiar mean regression (least squares) methods. They have inherited a natural interpretability and an inherent robustness from the behavior of the ordinary quantiles. When the error term is nonnormal, quantile regression estimators may be more efficient than least squares estimators. By replacing a monolithic model of conditional central tendency with a family of models for conditional quantiles, we are able to achieve considerably greater flexibility and a much more complete view of the effect of the covariates on the dependent variable, allowing them to influence location, scale and shape of the response distribution. (6) 4

5 In application, a variety of heterogeneity phenomena are rendered observable. Prime examples of economic applications in the literature include Buchinsky (1994, 1995), Chamberlain (1994) and Fitzenberger et al. (1995). Since then, there is a rapidly expanding empirical quantile regression literature. Buchinsky (1998) and Koenker and Hallock (21) have recently surveyed it. 3. Data description The analysis in this paper draws on data from the German Socio-Economic Panel (GSOEP) for the year 2 1. After reunification, the panel was extended to include the eastern part of Germany, but we focus here on West Germany only because undeniable economic differences subsist between East and West Germany. Since many public sector jobs are not open to foreign nationals, the analysis is based on the subsample of Germans only. Furthermore, the sample is restricted to include those who were between 18 and 65 years old and were in fulltime or part-time employment in 2. Finally, all observations with a missing value for one of the variables have been excluded. The final data set has 2972 observations. As the sample includes only wage earners, the results must be interpreted conditional on the selected sample. Issues of sample selection bias and the potential problem of endogeneity of sector choice and education are considered the scope of the present paper, which concentrates on distributional aspects. This is, of course, a more descriptive approach and some caution must be exercised in interpreting the results. Table A.1 in Appendix describes the variables we use for our descriptive analyses and in the regressions. Table A.2 presents descriptive statistics for male and female public and private sector employees. Means of relevant variables show that average hourly earnings are higher in the public sector than in the private sector. They also show that public sector employees are, on average, better educated than private sector employees. For instance, 19 per cent of the employees in the public sector have achieved a university degree (Ed level 6), while they are only 9 per cent in the private sector. Public sector employees have acquired more labor market experience and tenure, too. These differences in work experience, education and tenure may explain the higher average wages of public sector employees. Another part of disparity between average compensation in the public and the private sectors may be due to the greater concentration of professionals and clerks in the public sector. To get a picture of the unconditional wage dispersion in each sector, the 1 th, 25 th, 5 th, 75 th and 9 th percentiles of the log wage are displayed in Table 1. A measure of the wage dispersion, the.9-.1 spread, is also shown in this table. For both genders, this spread is clearly higher in the private sector than in the public sector, indicating that the unadjusted earnings are more compressed in the public sector. For males, public sector employees at the 1 st decile of the public sector earnings distribution enjoy an earnings advantage over private sector employees at the same point in the private sector distribution of wages; but the reverse holds for employees at the 9 th decile of the public sector and private sector earnings 1 For an English language description of the GSOEP see SOEP Group (21). 5

6 distribution. With higher floors and lower ceilings, the public sector compresses the unconditional wage distribution. Table 1: Percentiles of the log wage Males Females 1% 25% 5% 75% 9%.9-.1 spread Public sector Private sector Public sector Private sector A first visual summary of the public and private sector wage distributions is provided in Figures 1 and 2 for men and women respectively. The density functions were estimated using an Epanechnikov kernel estimator. Silverman s rule of thumb was used to choose the bandwidths. It can be seen from these figures that the distributions are quite distinct between sectors. For both genders, the public sector earnings distribution is characterized by a higher density function around the mode and a lower dispersion. Of course, differences in earnings dispersion between public and private sector employees using raw earnings data may confound the effects of a worker s sector of employment with the effects of differences in the distribution of worker characteristics between sectors. In order to control for these differences and to study conditional wages and wage differentials, we will estimate wage regressions in the next sections. Figure 1: Kernel density estimates of the wage distributions for men Private sector Public sector Log gross hourly wages Note: Epanechnikov kernel density estimates; the bandwidths were chosen using Silverman s rule of thumb. 6

7 Figure 2: Kernel density estimates of the wage distributions for women Private sector Public sector Log gross hourly wages Note: Epanechnikov kernel density estimates; the bandwidths were chosen using Silverman s rule of thumb. 4. Single equation method This and the next section compare earnings of individual workers corrected for differences in productivity-related characteristics and job attributes. In this section, the basic dummy variable approach is applied and, in the next section, the decomposition approach will be used. 4.1 Public sector wage premium Following Smith (1977), the first and basic methodological approach is identical to that used in studies of sex, race, or union wage differentials. It involves estimating an earnings regression using pooled data for public sector and private sector employees and including a dummy variable for a worker s sector of employment. That is: ( ) ln wage = x β + psectδ + u, (7) i i i i where x i includes experience (specified in quartic form), job tenure, marital status, part-time status, education and occupation. The descriptive statistics of these variables are given in Table A.2. The reference educational category is Ed level 1 and the reference occupational category is Professional. Equation (7) has been estimated separately for males and females using standard and quantile regressions. The estimates of the public sector dummy are reported in Table 2. The estimates for the other variables reveal a familiar pattern and displayed in Table A.3. The coefficient on the public sector dummy estimated with equals 7.9% for men, indicating that wages in the public sector are about 8 per cent lower than wages in the private sector. For 7

8 females, on the other hand, the public sector appears to pay a significant premium of 8.8 per cent. Both coefficients are strongly significant. If the distribution of the error terms is symmetric, mean and median regressions estimate the same quantity. The and LAD ( θ=.5 ) estimates are actually similar. At the median, the public sector pay premium is 9.1 per cent for men and 7 per cent for women. Again, both coefficients are significant. These results are similar to that of Dustmann and Van Soest (1997). Table 2: Estimates of the public sector pay premium Males Females Coefficient Standard error Coefficient Standard error θ = θ = θ = θ = θ = Note: Variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. Standard errors are obtained by bootstrapping (1 repetitions) for quantile regression and using the Huber-White estimator for. The regression does not consider the possibility that the distribution of actual wages around their predicted values differ across sectors. In fact, both the unconditional and the conditional wage distribution in the public sector are more compressed than those in the private sector. Therefore, to complete the analysis, Table 3 presents also estimates from quantile regressions with θ =.1,.25,.75 and.9. The estimated public sector wage premium varies strongly with θ. For males this premium decreases from 3.4% at θ =.1 to 15% at θ =.9. For females, this premium varies from 16.6% at θ =.1 to.9% at θ =.9. The quantile regressions reveal dispersion in the public sector that cannot be captured using. This sector compresses the pay dispersion and, therefore, reduces the within-group pay inequality. The quantile regression model can be used to characterize the entire conditional distribution. Figure 3 and 4 present a concise visual summary of the quantile regression results. 99 quantile regressions with θ =.1,...,.99 have been estimated separately for males and females. For comparison, the estimate is also shown. The monotone decrease of the public sector wage premium as we go from the lowest to the highest quantiles appears clearly. The pattern is the same for both sexes. The extreme quantiles are particularly interesting, although they must be interpreted with caution because the standard deviations are very high at these points of the distribution. At the first percentile, the premium is 11% for men and 48% for women. On the other hand, at the last percentile, the wage penalty in the public sector is 16% for men and 24% for women! 8

9 Figure 3: Estimated public sector wage premium for men.2.1 regression with control for occupation with control for occupation s regression without control for occupation without control for occupation Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, marital status, tenure and part-time status. There is disagreement in the literature on discrimination about whether differences in the occupational status of the individual should be controlled for. As can be seen in Table A.2, the public sector work force is predominantly white-collar with large proportions of workers in professional an clerical occupations and relatively few workers in sales and blue-collar occupations. It is appropriate to control for such occupational differences if they are indicative of what is necessary to do the job. However, if occupational titles are inflated in the public sector to justify higher wages, then it is not appropriate to control for such occupational differences since they in fact are a part of the public sector rents. As differences in occupation could be the result of segregation, it is usual to run two regressions, with and without control for job characteristics. Therefore, the premiums estimated without control for job characteristics (occupations and part-time status) are also plotted in Figures 3 and 4. They show that the public sector wage premium is slightly lower without control for job characteristics for the men but approximately 3.5% higher for women. So, as in Poterba and Ruben (1994), the inclusion of occupational dummies reduces the absolute value of the premium but the differences between the two specifications are much less important in Germany than in the USA. How to interpret these results? It is likely to regard differences in the occupational distribution of males and females as indicative of discrimination and not of differential tastes by women for the jobs they want to hold. It has been found that the gender occupational integration proceeds more rapidly in the public sector than in the private sector (Gregory and Borland 1999). For example, 4% of the women in the public sector are employed in the 9

10 professional occupational group when they are only 14% in the private sector. For women in professional occupations, the public sector is capital as employment opportunities: 54% are publicly employed. For men, this proportion is only 31%. Thus, it seems that not only direct labor market discrimination but also occupational discrimination is less in the public sector than in the private sector. The results of section 5.2 will confirm these hypotheses. Figure 4: Estimated public sector wage premium for women regression with control for occupation with control for occupation s regression without control for occupation without control for occupation Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, marital status, tenure and part-time status. 4.2 Public sector wage premium stratified by educational attainment Since the wage differential may vary across education levels, the public wage premium is now estimated for four ranges of schooling. The observations are stratified in four educational groups: Low education (corresponds to Ed level 1 and 2), Medium education (Ed level 3), High education (Ed level 4 and 5) and University (Ed level 6). The public sector dummy is then separated into 4 dummies, one for each level of education. The other regressors are the same as in (7). Figures 5 and 6 combine the results by qualification and quantile to look at the impact of public sector status on pay within and between educational groups. The four panels of Figure 5 provide the information for men. regression estimates show the same pattern for the 4 educational categories: the public sector premium declines as we move up the income distribution. Hence, for the 3 top education categories, the public sector wage penalties become significant only at the highest quantiles: from the 3 rd quartile for the medium education group, from the median for those with high education and from the 1 st quartile for men with a university degree. Thus, the story of Figure 3 is confirmed: the public sector reduces the within-group inequality by compressing the wage distribution. 1

11 The comparison of the four or LAD estimates shows that the public sector wage premium decreases monotonically as the educational qualification increases. At the mean, the public sector wage premium falls from 2% for the lowest education group at 2% for the second group, -1% for the third and 23% for the top education category. The picture is the same at the median. Since the average wage increases with the number of years of schooling, there is an equalizing effect between educational groups attached to public sector status. The political pressure on the government not to pay low wages to its less skilled employees could explain why the return to education is higher in the private then in the public sector. Figure 5: Public sector wage premium stratified by educational attainment for men.2 Low education.2 Medium education th 25th 5th 75th 9th ** -.4 1th ** 25th 5th 75th ** 9th *.2 High education.2 University ** 1th 25th 5th 75th 9th -.4 1th 25th 5th 75th 9th Note: Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. One (two, three) star(s) under the bar indicates that the estimated coefficient is statistically significant at the 1 (5, 1) per cent level. Figure 6 illustrates the results for women. At least for the three lowest education categories, there is again evidence of a negative gradient in public sector premium across the income quantiles, as shown in Figure 4. The premium is significant positive at the low percentiles for the low and medium education groups and significant negative at the high quantiles for the high education group. Thus, the within-group equalizing effect is clear for these three categories. For women with a university degree, no estimate of the public sector dummy is significant different from zero, maybe due to the smaller number of observations. The evidence of within-group equalization of pay within the public sector is not apparent. 11

12 As for men, there is evidence of an equalizing effect between groups attached to public sector status. At the median or the mean, the public sector wage premium is strong significant positive for the two lowest educational categories but negative for the two highest. While the level of the public sector wage premium is about 15% higher for women than for men, the differences between the educational levels are very similar for both sexes. Thus, it seems that the government tends to be a model employer and refuses to pay low wages to its less educated employees. An implicit minimum wage in the public sector arises from this policy. Similarly, the government has the tendency to underpay its most skilled workforce. Very high salaries in the public sector seem to be not accepted by voters. Figure 6: Public sector wage premium stratified by educational attainment for females.3 Low education.3 Medium education th 25th 5th 75th * 9th -.2 1th 25th 5th 75th 9th *.3 High education.3 University * 1th 25th 5th 75th 9th * -.2 1th 25th 5th 75th 9th Note: Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. One (two, three) star(s) under the bar indicates that the estimated coefficient is statistically significant at the 1 (5, 1) per cent level Public sector wage premium stratified by levels of experience The public sector wage premium may also vary across different levels of experience. Instead of the quartic equation in experience, the observations are now stratified in four experience groups: those with less than 11 years of experience, 11-2 years, 21-3 years and more than 3 years. The public sector dummy is then interacted with the set of 4 indicator variables, one for each level of potential experience. Figure 7 for men and Figure 8 for women combine the results by experience and quantile in the same way as Figures 5 and 6 did. 12

13 With a few exceptions, we observe again the equalizing effect of the public sector relative to the private sector, with a negative gradient of premiums as we move up the income distribution. The public sector wage premiums tend to be (significantly) positive at the low quantiles and negative at the high quantiles. The less experienced groups seem to make exceptions. Here, there is no evidence of a change in the coefficient across the conditional wage distribution. Figure 7: Public sector wage premium stratified by levels of experience for males.25 1 or less years of experience From 11 to 2 years of experience th 25th 5th 75th 9th From 21 to 3 years of experience th 25th 5th 75th ** More than 3 years of experience.25 9th th 25th 5th 75th 9th th 25th 5th 75th * * 9th Note: Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. One (two, three) star(s) under the bar indicates that the estimated coefficient is statistically significant at the 1 (5, 1) per cent level. If we compare the level of the public sector wage premium across experience groups for men, it seems that the premium does not vary with the experience of the workers. The coefficient of the public sector dummy is negative for all categories but it is significant only for the employees with 11 to 2 or 21 to 3 years of experience. On the contrary, the level of the public sector wage premium depends significantly on experience for women. The public sector wage premium estimated at the median is negative for the least experienced groups and increases monotonically to a strongly significant 24% for the most experienced groups. This difference between both sectors could be explained by the rigid hierarchical pay structure in the public sector. Salaries increase more or less mechanically with seniority. Wage decreases are difficult if not impossible. Moreover, A part of the discrimination of women takes the form of slower promotion rates. The centralized pay system in the public sector could reduce 13

14 this form of discrimination. On the other hand, it may be easier to retain the same job after a maternity break or to change from full-time employment to part-time employment in the public sector. Therefore, females in the public sector could have more human capital than females in the private sector with the same age and the same education level (Dustmann and Van Soest 1997). It should be noted, however, that the experience pattern reflects a combination of age, experience and cohort effect. Figure 8: Public sector wage premium stratified by levels of experience for females 1.5 or less years of experience From 11 to 2 years of experience th 25th 5th 75th 9th th ** 25th 5th 75th 9th * From 21 to 3 years of experience More than 31 years of experience th ** 25th 5th 75th 9th ** ** th ** 25th 5th 75th ** 9th Note: Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. One (two, three) star(s) under the bar indicates that the estimated coefficient is statistically significant at the 1 (5, 1) per cent level. 4.4 Public and private sector wages in specific occupations Our analysis so far has compared individuals with similar human capital attributes but we have not considered the possibility that the pay differential between both sectors may differ across occupations. To address such differences, we estimate now a wage equation similar to (7) for several occupational categories with substantial employment in both sectors. Figure 9 gives a picture of the estimates with and quantile regressions. The compression of the wage distributions by the public sector is again evident but not always significant, probably because of the reduced number of observations. Concerning the differences between occupations, the results confirm the earlier evidence that the public sector pay premium is higher in low-skill occupations. For both genders, the professionals are less 14

15 paid in the public than in the private sector. The pay differential is strongly significant for the males, with as with quantile regressions alike. Clerks in the public sector are relatively better paid than professionals. Their public sector pay premiums are around as high as the average premium across all occupations. For male blue-collar workers, a slightly negative but not significant public sector pay premium has been found. Finally, the occupational group which profits most from being employed in the public sector are the women in sales and services occupations. Their public sector premium of about 25% is strongly significant. Figure 9: Occupation-specific estimates of public sector wage premium.15 Professionals, men.15 Clerks, men th 25th 5th 75th 9th th * 25th 5th 75th * 9th * Blue-collar, men.3.2 Professionals, women * 1th 25th 5th 75th 9th ** -.1 1th 25th 5th 75th 9th Clerks, women Sales and service workers, women th 25th 5th 75th 9th ** -.1 1th ** 25th 5th 75th 9th ** Note: Premia are based on ordinary least sqares and quantile regressions. Variables controlled for in the regressions are education, experience, marital status, tenure and part-time status. One (two, three) star(s) under the bar indicates that the estimated coefficient is statistically significant at the 1 (5, 1) per cent level. 15

16 5. Decomposition method 5.1 Methodology One problem with the dummy variable approach is that the returns to productivity-related characteristics and job attributes are constrained to be equal across sectors. The effect of a worker s sector of employment (public or private) is limited to be an intercept effect. An alternative approach involves estimating separate earnings functions for individuals in the public and private sectors. Following Blinder (1973) and Oaxaca (1973), the difference in average earnings between workers in each sector can be decomposed into differences in personal characteristics and job attributes and differences in coefficients. The first term is referred to as the justifiable earnings or characteristics differential. The second term is called the surplus or rent payment and is interpreted as providing a measure of whether an identical employee working in the same job in the public and private sector would receive the same wage. Formally, the first step is to estimate j j ln ghearn = x β + u j = public, private (8) i i i where x i is the same as in equation (7). The second step is to calculate where pub priv pub priv ( ) ˆ priv pub pub priv β ( ˆ β ˆ β ) ln ghearn ln ghearn = X X + X, (9) ln ghearn j j and X are average log hourly wages and characteristics of employees in j sector j, ˆβ is the estimated vector of returns to worker characteristics in sector j. The first term on the right-hand side is the component of the log wage differential due to differences in endowments between public and private sector employees. The second term shows the component due to differences in returns to these endowments. A disadvantage of this approach is that it only focuses on differences at the means of the two earnings distributions. However, the decomposition technique may be combined with quantile regressions to determine the rent component at various points in the wage distribution (Mueller 1998 and Garcia et al. 21). The difference in the conditional quantile of the log wage between the public and private sector evaluated at the level of covariates corresponding to the mean for each sector is decomposed as follows pub pub priv priv ( ) θ ( ) Quant lnghearn X Quant lnghearn X = θ pub priv ( ) ˆ priv pub pub priv β ( ˆ ˆ θ βθ βθ ) X X + X. (1) Note that, contrary to (9), where X ˆ j j j β = ln ghearn, j X ˆ β is not equal to the θ th sample j quantile of lnearn. That is, the conditional quantile evaluated at the mean of the covariates is not equal to the unconditional quantile. j θ 16

17 5.2 Empirical analysis Separate earnings equations for the public and the private sector and for both sexes have been estimated 2. It is interesting to note the differential rate of return found between sectors on a number of characteristics. The returns to education are clearly higher in the private than in the public sector for both sexes. This explains why the public sector reduces the between educational group inequality. Concerning the occupational variables, the results confirm the findings of section 4.4. Employees in professional occupations earn more in the private sector while sales and service workers earn more in the public sector. An important difference between both sectors exists concerning the part-time dummy. The wage penalty associated with the part-time status of the employee is higher in the public sector than in the private sector for men: -18% vs. -11% but smaller for women: -4% vs. -15%. Another, maybe more anodectical difference between both sectors is that married men earn 14% more than single in the public sector but only 7% more in the private sector. For women, the coefficient of the marrital status dummy is not significant in both sectors. The results of section 4 suggest that the gender gap in wage could be smaller in public employment than in private employment. To confirm or reject this hypothese, the gender pay differential has been estimated separately for each sector, once using a gender dummy variable and once by decomposing the wage differential (using the male coefficients as nondiscriminatory wage structure). Table 3 shown the estimated gender gaps along with their standard errors obtained by bootstraping. Whatever method we use, the magnitude of pay discrimination by gender is clearly (more than 1 %) smaller in the public than in the private sector. By decomposing the wage differential, the gender gap is even not significant different from zero in the public sector. Table 3: Estimates of the male female earnings differential with and quantile regressions Dummy variable Decomposition Public sector Private sector Public sector Private sector Coef. Std. err. Coef. Std. err. Coef. Std. err. Coef. Std. err θ = θ = θ = θ = θ = Note: Other variables controlled for in the regressions are education, experience, occupation, marital status, tenure and part-time status. Standard errors are obtained by bootstrapping (1 repetitions). Interestingly, these results contradict standard economic theory. Unlike the private sector, the public sector is not subject to profit constraints. Becker (1971), for instance, suggests that profit-maximizing behavior is incompatible with the existence of discrimination. Following this argument, we might expect the adjusted male-female earnings differential to be smaller in 2 The detailed results are available upon request from the author. 17

18 the private sector. Why should nevertheless the male-female earnings differential be smaller for public sector than private sector employees? First, the pay system for all public sector employees is uniform and centralized. It is regulated in the Federal Act on the Remuneration of Civil Servants (Bundesbesoldungsgesetz), which requires equal pay for all individuals with the same seniority and qualifications who are employed in a given job. Equal opportunity and anti-discrimination policies are therefore more effectively implemented in public sector than private sector labor markets. Second, we have found that the distribution of wages is more compressed in the public than in the private sector. Blau and Kahn (1992) have shown that the more compressed the pay distribution, the lower the level of wage inequality. Their evidence rely on cross-national comparisons of the impact of different wage distribution on the gender wage inequality. Here, there are two different pay systems within one land. A consequence of this large wage advantage of females in the public sector is the overrepresentation of women in the public sector. They represent 49% of the public sector employees but only 39% of the private sector employees. Whether this wage policy is efficient or not depends on the interpretation of the gender earnings differentials. If it is believed that wage discrimination against females in private sector labor markets is causing inefficient resource allocation decisions, the presence of the public sector wage premium for women will reduce the degree of wage discrimination and improve the efficiency of the labor market. Using equation (9) and (1), total log wage differentials are broken into rent and characteristics differentials. Tables 5 and 6 show the decomposition of public/private sector earnings differential for males and females respectively. The upper part of the tables decomposes the sectorial differential in the predicted log wage into rent payment (coefficients component) and justifiable differential (characteristics component). The lower part of the tables shows how much of the total difference in characteristics is due to specific sets of variables. Table 4: Decomposition of public/private sector earnings differential for men θ =.1 θ =.25 θ =.5 θ =.75 θ =.9 Differences in estimated ln(wage) Rent payment Characteristics differential Differences due to characteristics: Experience Tenure Education Occupation Married Part-time Note: Totals may not sum exactly due to rounding. 18

19 Dealing with male employees first, the estimates obtained by decomposing the quantile regression results show a similar pattern to those obtained in section 4 by estimating the coefficient of a dummy variable. The public sector wage premium declines from 3% at the 1 st decile to 17% at the 9 th decile. The characteristics component shows that public sector employees should earn more than private sector employees at all points of the wage distribution. Compared with private sector employees, public sector workers are better educated and have more years of job tenure and more experience. We do not observe substantial differences in occupations or part-time employment. The characteristics differential decreases as we move up the wage distribution, in particular because of the declining importance of job tenure. That shows that the more compressed wage distribution in the public sector is partly due to differences in characteristics. Table 6 shows the results for female employees. Again, the rent payment is very similar with that obtained in section 4 with the dummy variable approach. The breakdown of the characteristics component is very different from that of males. Differences in experience and the part-time status are of less importance for women than for men. Occupations, which were insignificant for men, are now the characteristics that explain the most part of the justifiable differential. Thus, the decomposition of the wage differential shows that there are no occupational differences between the private and the public sector for men but there are important differences for women. Interpreting the occpuational differences of men and women as indicative of discrimination, these results suggest that women are not only better paid for the same job in the public sector but they have also better possibility to find a wellpaid occupation in that sector. Interestingly, occupations seem to be the only characteristics differential which varies across the quantiles. Table 5: Decomposition of public/private sector earnings differential for women θ =.1 θ =.25 θ =.5 θ =.75 θ =.9 Differences in estimated ln(wage) Rent payment Characteristics differential Differences due to characteristics Experience Tenure Education Occupation Married Part-time Note: Totals may not sum exactly due to rounding. 19

20 8. Conclusions and policy implications The wage structure in the public and private sectors in West Germany has been examined using the 2 GSOEP. results suggest that wages are about 8 per cent lower in the public sector for males but substantially higher for females (about 9 per cent). The results of quantile regressions indicate that the conditional pay distribution is more compressed in the public sector. The public sector wage premium is highest at the lower end of the wage distribution and then decreases monotonically as we move up the wage distribution. Thus, the public sector reduces within-group inequality. Allowing the premium to be different for four categories of education, we find that the public sector reduces also the between-group inequality. Those with basic schooling obtain the highest public sector wage premium. The stratification of the premium by levels of experience suggests that the premium increases with the years of experience for women. Upon decomposing these wage differences, we find similar results to those obtained by using a public sector dummy variable. The breakdown of the characteristics component shows that, for men, differences in education, tenure and experience explain most of the unconditional wage differences. For women, however, differences in occupation play a major role. Are these differences in wages between the public and private sector true premiums, or are there other factors at work? The differences may reflect unobserved individual characteristics. The results may also be biased as a result of omitted explanatory variables. There may be compensating differentials, such as working conditions and fringe benefits. All these issues as well as the problems of selectivity and endogeneity have not been explored in this study. Therefore, the results do not necessarily have a causal interpretation. Rather they provide a descriptive comparison of earnings distribution for public and private sector employees. regression estimates show that the distribution of earnings is less dispersed for public than for private sector employees. This reduces the inequality of the wage structure but this may also have implications for how workers with different abilities and productivities sort between those sectors. Employees at the bottom of the wage distribution, especially among the less skilled, may decide to queue for relatively high-paying jobs in the public sector rather than take low-paid jobs in the private sector (Blackaby et al. 1996). This can lead to wait unemployment. Katz and Krueger (1991) have found empirical relevance for this prediction. On the other hand, the wage penalty at the upper end of the public sector pay scale is useful in explaining the exodus of senior managers to the private sector. Many observers have voiced concern that the government will be increasingly unable to recruit highly skilled employees such as scientists, engineers and judges. Reforms allowing for more vertical flexibility in the public sector wage structure seem to be especially important in order to link more closely wage rates to individual performance and underlying labor market conditions. 2

21 Appendix Data Table A.1: Explanation of variables Variable Description Wage Gross hourly earnings from employment. Gross hourly wage are derived by dividing gross monthly earnings by monthly actual hours worked. Ln(wage) The natural logarithm of wage. Expr Number of years of potential work experience the individual has accumulated. It is measured by min(age-schooling-6, age 18). Gender Dummy; 1 if women. Tenure Number of years with current employer Part-time Dummy; 1 if the individual is part-time or marginally employed. Married Dummy; 1 if married. Ed level Ordered variable on education:+ Ed level 1 Dummy; 1 if basic or intermediate schooling with no training or no degree. Ed level 2 Dummy; 1 if basic schooling with apprenticeship. Ed level 3 Dummy; 1 if intermediate schooling with apprenticeship. Ed level 4 Dummy; 1 if high school (Abitur or Fachabitur) with no training or with apprenticeship. Ed level 5 Dummy; 1 if high school with technical school or polytechnic. Ed level 6 Dummy; 1 if university. Management Dummy; 1 if occupation in management. Professional Dummy; 1 if professional. Clerk Dummy; 1 if clerk. Salesperson Dummy; 1 if salesperson. Service worker Dummy; 1 if service worker. Agriculture Dummy; 1 if occupation in agriculture. Blue collar Dummy; 1 if blue collar. Others Dummy; 1 if occupation in others categories. Psect Dummy; 1 if employed in the public sector. 21

22 Table A.2: Descriptive statistics, means Variable All observations Men Women All Public Sector Private Sector All Public Sector Private Sector All Public Sector Private Sector Ln(wage) Experience Gender Tenure Married Part-time Education: Ed level Ed level Ed level Ed level Ed level Ed level Occupation: Professional Management Clerk Salesperson Service Worker Agriculture Blue collar Others Number of observations