RIF decomposition

Given the local nature of the RIF methodology, our strategy is to apply RIF decompositions separately to our three subperiods 1995-2001, 2001-2006, 2006-2010, and to aggregate (i.e.

add up) the contributions of the different factors over the subperiods.¹⁰ We start with a graphical analysis of the effects changes of our covariates have on unconditional quantiles.

Figure 2.3 shows that the change of the distribution of log hourly wages between 1995 and 2010 was such that unconditional quantiles below the 35th percentile fell, while those above the 35th increased. This pattern is distinctively different from the changes in the US wage distribution over similar periods which featured a U-shaped pattern, i.e. especially middle quantiles lost in comparative terms, while lower and upper quantiles gained (Autor et al., 2008, Firpo et al., 2014).

Decomposing the overall change into composition and wage structure effects, we find that the pattern of composition effects shows the same monotonic behavior as the overall change, but that additional wage structure effects played some role in the upper middle range of the distribution. In the detailed plot of individual composition effects (figure 2.4), the most striking effect is that of de-unionization. The shrinking share of workers paid according to union pay schedules both substantially depressed quantiles at the lower end of the

distri-10The RIF-regression approximates the effects of marginal changes in the distribution of covariates on inequality measures. The approximation error will be the larger the bigger changes in the distribution of covariates are. In order to keep approximation errors small, it is therefore best to consider changes in covariates over the smallest subperiods available. In a previous version of this paper, Biewen and Seckler (2017), we report more details on individual subperiods. For our estimates, we provide bootstrapped standard errors based on 100 resamples. The resamples are a simultaneous draw from all four years and take account of the clustering at the firm level.

Chapter 2. Unions, Internationalization, . . . 2.5. Empirical results

Figure 2.3– Aggregate decomposition 1995-2010

Figure 2.4– Composition effects 1995-2010

Figure 2.5– Wage structure effects 1995-2010

Source: Structure of Earnings Surveys 1995, 2001, 2006, 2010 and own calculations.

Chapter 2. Unions, Internationalization, . . . 2.5. Empirical results

bution and lifted quantiles at the upper end. These effects were so strong that they have the potential to account for much of the overall inequality change. Second to effects of de-unionization, compositional effects of changes in personal characteristics also played an important role. This was particularly true for quantiles in the upper half of the distribution of hourly wages, which significantly gained. This result is consistent with the population aging and educational upgrading described in the previous section. The composition effects of all other groups of covariates were relatively modest, although we observe some increases in unconditional quantiles in the upper quarter of the distribution associated with interna-tionalization, and very modest changes in the upper half of the distribution related to task compositions.

Figure 2.5 provides the break-down of wage structure effects that are related to the different groups of covariates considered by us. These effects are less smooth than the composition effects, and some of them counteract each other. In particular, wage structure effects related to firm characteristics and internationalization tended to favor higher quantiles, while those related to region, unionization and personal characteristics were detrimental for higher quantiles. For tasks, we observe small effects whose patterns are consistent with the polarization hypothesis, i.e. the middle of the distribution lost compared to the bottom and the top of the distribution. Importantly, all of these effects were dominated by general wage structure effects represented by the constant of the RIF regression. As discussed above, the regression constant represents changes in the wage structure that cannot be attributed to particular groups of covariates or that may be related to factors not included as covariates in the analysis. According to figure 2.5, these general wage structure effects were such that the upper middle part of the distribution gained, while the very top part suffered losses.

Chapter 2. Unions, Internationalization, . . . 2.5. Empirical results

Table 2.3– Aggregated RIF-decompositions 1995-2010

Inequality measure 85-15 85-50 50-15 Gini Logvar 99-90 99-95 95-90

Total change 19.21^∗∗∗ 8.93^∗∗∗ 10.28^∗∗∗ 4.61^∗∗∗ 6.21^∗∗∗ 7.26^∗∗∗ 6.23^∗∗∗ 1.03^∗∗

(0.93) (0.73) (0.64) (0.20) (0.27) (1.00) (0.89) (0.45)

Total Composition 19.83^∗∗∗ 13.68^∗∗∗ 6.14^∗∗∗ 6.09^∗∗∗ 7.06^∗∗∗ 5.50^∗∗∗ 0.06 5.44^∗∗∗

(0.67) (0.55) (0.48) (0.17) (0.21) (0.82) (0.68) (0.39)

Personal 4.63^∗∗∗ 3.32^∗∗∗ 1.32^∗∗∗ 1.38^∗∗∗ 1.61^∗∗∗ 0.70^∗∗ 0.41^∗ 0.29^∗∗

(0.26) (0.18) (0.13) (0.06) (0.08) (0.27) (0.24) (0.15)

International 1.72^∗∗∗ 1.49^∗∗∗ 0.24 0.47^∗∗∗ 0.51^∗∗∗ -0.46 -0.94^∗∗ 0.49^∗∗∗

(0.38) (0.33) (0.26) (0.09) (0.11) (0.49) (0.44) (0.18)

Sector -0.13 -0.45^∗∗ 0.31 0.06 0.09 1.29^∗∗∗ 1.00^∗∗∗ 0.29^∗

(0.27) (0.23) (0.29) (0.07) (0.09) (0.41) (0.33) (0.15)

Firm -0.13 -0.02 -0.11 -0.01 -0.03 0.27 0.29 -0.02

(0.15) (0.09) (0.16) (0.03) (0.04) (0.24) (0.21) (0.07)

Region 0.48^∗∗ 0.08 0.40^∗∗ 0.08^∗ 0.14^∗∗ -0.05 -0.12 0.06

(0.22) (0.10) (0.17) (0.05) (0.07) (0.15) (0.12) (0.06)

Task 1.18^∗∗∗ 0.86^∗∗∗ 0.31^∗∗∗ 0.30^∗∗∗ 0.31^∗∗∗ -0.03 0.03 -0.06

(0.20) (0.14) (0.08) (0.05) (0.06) (0.13) (0.11) (0.06)

Unionization 12.08^∗∗∗ 8.41^∗∗∗ 3.67^∗∗∗ 3.82^∗∗∗ 4.44^∗∗∗ 3.77^∗∗∗ -0.61 4.38^∗∗∗

(0.42) (0.31) (0.18) (0.11) (0.13) (0.53) (0.44) (0.25)

Total Wage Structure 0.15 -3.21^∗∗∗ 3.36^∗∗∗ 0.04 0.55^∗∗ 6.85^∗∗∗ 5.52^∗∗∗ 1.33^∗∗

(0.82) (0.67) (0.63) (0.18) (0.23) (1.52) (1.41) (0.59)

Personal 0.30 4.11^∗∗∗ -3.80^∗∗∗ -0.68^∗∗ -1.11^∗∗∗ -8.82^∗∗∗ -3.48 -5.34^∗∗∗

(1.03) (0.91) (0.66) (0.28) (0.36) (2.39) (2.29) (1.02)

International 3.10^∗∗∗ 2.11^∗∗∗ 0.99 0.65^∗∗∗ 0.81^∗∗∗ 0.14 -0.42 0.56

(0.85) (0.66) (0.61) (0.22) (0.29) (1.59) (1.33) (0.63)

Sector 0.41 1.17 -0.76 -0.04 -0.11 -4.04^∗∗ -2.77^∗∗ -1.28

(0.89) (0.82) (0.55) (0.25) (0.31) (1.64) (1.27) (0.86)

Firm 4.90^∗∗ 2.85 2.05 1.26^∗∗ 1.59^∗∗ 5.72^∗∗ 3.74 1.97

(2.47) (1.86) (1.48) (0.57) (0.78) (2.73) (2.57) (1.20)

Region -1.60^∗ -3.41^∗∗∗ 1.81^∗∗∗ 0.01 0.02 4.62^∗∗∗ 2.55^∗∗ 2.07^∗∗∗

(0.88) (0.70) (0.65) (0.19) (0.26) (1.35) (1.13) (0.52)

Tasks 4.56^∗∗∗ 3.74^∗∗∗ 0.82 0.73^∗∗∗ 0.77^∗∗∗ -2.83^∗ -2.90^∗ 0.07

(1.03) (0.90) (0.69) (0.23) (0.29) (1.69) (1.49) (0.80)

Unionization -2.98^∗∗ -3.34^∗∗ 0.37 -0.36 -0.26 5.25^∗∗∗ 1.99 3.27^∗∗∗

(1.42) (1.51) (1.11) (0.29) (0.39) (1.45) (1.22) (0.86)

Constant -8.54^∗∗ -10.42^∗∗∗ 1.88 -1.53^∗ -1.15 6.82 6.81 0.00

(3.52) (3.05) (2.19) (0.81) (1.11) (6.15) (4.97) (2.43)

Specification Error -0.85 -0.18 -0.66^∗ -1.29^∗∗∗ -1.27^∗∗∗ -3.35^∗∗∗ 1.50 -4.85^∗∗∗

(0.61) (0.50) (0.36) (0.12) (0.15) (1.02) (1.07) (0.55)

Reweighting Error 0.08 -1.36^∗∗∗ 1.44^∗∗∗ -0.23^∗∗∗ -0.13 -1.73^∗∗∗ -0.84^∗∗∗ -0.89^∗∗∗

(0.39) (0.29) (0.21) (0.09) (0.11) (0.30) (0.23) (0.12)

Source: Structure of Earnings Surveys 1995, 2001, 2006, 2010 and own calculations.

Log wage differentials×100.^∗∗∗/^∗∗/^∗statistically significant at 1%/5%/10%-level.

Bootstrapped standard errors clustered at establishment level in parentheses (100 replications).

Chapter 2. Unions, Internationalization, . . . 2.5. Empirical results

In table 2.3, we provide a detailed break-down of the importance of the different factors for the overall change in inequality. Consistent with the graphical analysis, the numbers show that composition effects fully accounted for the overall inequality change, while wage struc-ture effects compensated each other, resulting in a combined effect of zero. For our main inequality measure, the 85-15 log wage differential, the strongest composition effects came from de-unionization (12.08 out of 19.83 points) and from personal characteristics (4.63 out of 19.83 points). Some smaller compositional effects were contributed by internation-alization (1.72 out of 19.83 points) and by shifts in occupational tasks (1.18 out of 19.83 points). Turning to wage structure effects, there were inequality increasing wage structure effects coming from internationalization (3.10 points), firm differences (4.90 points) and tasks (4.56 points). However, these were fully compensated by inequality reducing wage structure effects related to union pay schemes (-2.98 points), regional convergence (-1.60 points), and the RIF constant (-8.54 points). As explained above, the latter represent gen-eral wage structure effects that cannot be attributed to any particular group of covariates.

The results for the Gini coefficient and the variance of logs generally reproduce the results for the 85-15 log wage gap (columns five and six of table 2.3).

Distinguishing between effects on the upper half (85-50 log wage differential) and on the lower half of the distribution (50-15 log wage differential), we find that the same groups of covariates generally turn out significant, but that the effects in the upper half of the distribution generally dominate. This is also true of the strong compositional effects of de-unionization, contrary to the results in Dustmann et al. (2009, 2014), who found that de-unionization affected mainly the bottom of the distribution. Below, we investigate dif-ferences between Dustmann et al. (2009, 2014) and our results in more detail, and provide an explanation why de-unionization affected the whole of the distribution rather than just the bottom.

The last three columns of table 2.3 display the results for top 10 percent of the distribution.

As shown earlier, most of the inequality increase occurred at the very top, i.e. within the

Chapter 2. Unions, Internationalization, . . . 2.5. Empirical results

top 5 percent. Compared to the rest of the distribution, we find weaker composition effects and much stronger unexplained wage structure effects. Overall, the patterns found for the top 10 percent of the distribution look more erratic and less precisely estimated. Also, specification errors are larger than in the main part of the distribution. The main conclusion is that the factors responsible for changes in the main part of the distribution do not explain changes at the top.