2.5 Estimation results
2.5.1 First estimation step: Wage regression
To calculate the within-firm GWG under the assumption that male employees have the same characteristics as female employees within each establishment (Gap2), we first have to determine wage estimates for all establishments in our sample. For establishments with at least 100 male employees, we estimate 1,704 wage equations with a Tobit model in order to account for censoring. The estimated firm-specific wage coefficients are used to determine Gap2 according to equation (2.3). This estimation strategy is not applicable for establishments with fewer employees because the within- firm estimation would yield no statistically meaningful results. For this reason, we estimate a pooled wage equation across all male employees in establishments with less than 100 male employees. The summary statistics of the dependent and explanatory variables are presented in Table A3 and A4 in the appendix.
Table 2. 2: Coefficients of the wage estimations in a Tobit model (establishments ≥ 100 male employees)
No. of
Obs. Mean of the coeff. Mean of the t- value Share of significant coeff. Share of same sign Std. deviation of coeff. Quotient Variable (1) (2) (3) (4) (5) (6) (2)/(6) Potential experience 1,704 0.024 7.624 0.887 0.978 0.015 0.625 (Potential experience)2/100 1,704 -0.040 -6.011 0.799 0.952 0.029 -0.725
Job tenure (in days)/1000 1,704 0.412 7.072 0.808 0.892 0.787 1.910 Low education without
vocational training 1,192 -0.424 -11.077 0.898 0.972 0.219 -0.517 Vocational training 1,669 -0.130 -4.433 0.796 0.693 0.265 -2.038 Secondary school 904 0.054 0.823 0.746 0.516 0.323 5.981 College of higher education
or university 1,118 0.336 9.066 0.814 0.953 0.239 0.711
Note: Coefficients result from wage regressions in establishments with at least 100 male and 20 female employees. Further explanations are given in the text.
As the coefficients from the 1,704 large establishments cannot be displayed in detail, we present a summary of the firm-specific estimation results in larger establishments in Table 2.2.
Column 1 in Table 2.2 describes the number of estimated coefficients for each characteristic. Note that some characteristics are missing in some establishments, such that specific coefficients cannot be determined in every establishment. The second column presents the mean of the coefficients of the firm-specific wage estimations and column 3 shows the corresponding mean of the t-values. Table 2.2 contains coefficients for all possible education levels because the left-out category differs from establishment to establishment. The means of the estimated coefficients show that the variables have the expected effect on the wage rate. That is, the wage rate increases with the education level and potential experience on average. As predicted by Mincer (1974), the squared term of potential experience is negative, hinting at diminishing returns to experience. Longer spells within the same establishment also cause small but positive effects on the wage rate. In order to obtain a more exact impression of the significance of the estimated coefficient, column 4 shows the shares of the estimated coefficients which are significant at the 5 percent level. We can see that about 75 to 90 percent of the estimated coefficients are statistically different from zero. Note, however, that not all coefficients show in the same direction. Column 5 describes the share of coefficients with the same sign as the mean of the coefficient in column 2. The firm-specific coefficients of vocational training and secondary schooling exhibit the smallest share of consistent signs. Furthermore, Table 2.2 includes the standard deviation of the estimated coefficients to illustrate the heterogeneity of the wage regressions across establishments (see column 6). The last column presents a sort of variation coefficient, which is a quotient of the standard deviation of the coefficient and the absolute value of the corresponding mean. Hence, this figure illustrates the standardized variation of coefficients across establishments. High values of this quotient indicate that the variation of firm-specific coefficients is high, supporting our supposition that the wage setting process differs tremendously across establishments. Small values signal moderate heterogeneity of wage returns to the corresponding characteristics. The results in Table 2.2 point out, for example, that the remuneration of job tenure varies much more across establishments than the coefficients for experience. In consideration of the varying coefficients, the wage estimation in each establishment
seems to be advantageous in determining the correct remuneration of the characteristics.
In addition to these summary statistics, we also present the 25th, 50th and 75th percentiles of the estimated coefficients in Table A6 in the appendix. The results show that the rather “extreme” values of the estimated coefficients also indicate the well known fact that education, establishment tenure and experience have a positive effect on individual wage levels.
Table 2. 3: Coefficients of the pooled wage estimations in a Tobit model (establishments with 20 to 99 male employees)
Standard deviation
Variables Coefficients of coefficients t-value
Potential experience 0.036 0.000 98.19
(Potential experience)2/100 -0.063 0.001 -80.62
Job tenure (in days)/1000 0.263 0.003 75.87
Low education without vocational training -0.299 0.002 -124.87
Vocational training (reference group) - - -
Secondary school 0.204 0.003 62.79
College of higher education or university 0.432 0.003 135.89
No. of observations 120,091
Log likelihood -26,970
Note: The regression includes male employees from establishments with 20 to 99 male and at least 20 female employees. Instead of a constant variable we include all year dummies.
Source: own calculation; LIAB cross-sectional model 1997-2001.
Table 2.3 presents the estimation results of the pooled Tobit regression for smaller establishments. Note that the education level vocational training serves as the only reference group in this setting. The estimated coefficients are highly significant and also exhibit the expected sizes and signs.