0.0 0.1 0.2 0.3 0.4 0.5
$10,000 $100,000 $1,000,000 $10,000,000 $100,000,000 Networth
(Log scale)
Density
A: Senate
0.0 0.2 0.4 0.6
$100 $100,000 $100,000,000
Networth (Log scale) B: House
Figure F.11: Distributions of Net worth in the Two Chambers of Congress.
-0.2 -0.1 0.0 0.1
10.0 12.5 15.0 17.5 20.0
Net Worth (108th-110th Senate) Marginal Effect of Contract Size (Career Specification)
A: Net Worth in the Senate
-0.1 0.0 0.1
16.00 16.25 16.50 16.75 17.00
Net Worth (108th-110th Congress) B: Net Worth in the House
Figure F.12: Moderating Effect of Net Worth in Committee Specifications.
Note: Effects estimated within tertiles using the Hainmueller et al. (2019) binning esti-mator. Robust confidence intervals are 95 percent.
G Diagnostics of cluster analyses
In this appendix, I consider some diagnostics of the different specifications of the Ward’s hierarchical cluster analyses, I use in my main results. While the exact specification of the number of clusters to extract can be debated, the diagnoses clearly illustrates that senators are clustered in the pre-Senate career trajectories, and distinct types of career paths, thus, can be measured by applying cluster analysis in this way. Thus, the overall approach is validated. Given that the results are highly robust to the exact specification, the number of clusters that is used is of less concern.
Figure G.13 shows two dendograms with the baseline numbers of clusters (five and six) emphasized. For both denodograms, it seems clear that the first two clusters are well-fitted and cohesive. While it is clear that the three final groups should be broken up in some way, it is less clear, whether the best fit is provided by five clusters, or – alternatively – the fourth group should be integrated in one of the other two groups.
Next, I show the model fit of a number of different cluster specifications. For the clus-ter analysis of pre-Senate careers, the marginal improvement in total within-clusclus-ter sum of squares decreases markedly between the specifications with three and seven clusters. A specification somewhere between them (e.g. the baseline of five clusters), thus, seems ap-propriate. For the cluster analysis on committee assignments, the marginal improvement is large over the range of different clusters, but there is not single cluster specification, which alone yields a very large improvement over the former. The speed of improvement does seem to level off after including eight clusters, which is why I limit the number of clusters based on committee assignment used in my various specifications to be between four and eight.
Finally, I plot the within cluster cohesion for all the different specifications. Figures G.15 and G.16 show the silhouette for, respectively, the career and committee based cluster analyses. For the cluster analyses of pre-Senate careers, we can see that cohesion is far from perfect in any single specification, but reasonable levels of cohesion are reached for most groups in different specifications. It seems clear that the specification extracting three clusters has too large within-group differences. This is improved upon in the
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05101520253035
Dendogram of Careers
hclust (*, ”ward.D”) Senators in Career Clusters
Height
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Dendogram of Committees
hclust (*, ”ward.D”) Senators in Committee Clusters
Height
Figure G.13: Dendogram of different career clusters.
Note: The five baseline career clusters are highlighted by red rectangles.
cluster specification, but at the cost of decreasing cohesion in the first group. Using five clusters improves cohesion in the final group. Including more (six and seven) clusters improves somewhat on the poor cohesion in the first couple of groups, but decreases cohesion in the best fitted groups.
Alternative number of clusters (robustness models)
0 25 50 75 100
1 2 3 4 5 6 7 8 9 10
Number of clusters k
Total Within Sum of Square
Fit of career clusters
Alternative number of clusters
20 30 40 50
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of clusters k
Total Within Sum of Square
Fit of Committee Clusters
Figure G.14: Fit of different number of clusters.
Note: The vertical dashed line is for the baseline specification of clusters (five and six, respectively). The gray-shaded areas show the alternative specifications that are used to test the robustness of the main results (3-7, and 4-8, respectively).
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
n = 238 3 clusters Cj
j : nj — avei∈Cj si
1 : 113 — 0.35
2 : 46 — 0.64
3 : 79 — 0.07
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
n = 238 4 clusters Cj
j : nj — avei∈Cj si 1 : 86 — −0.04
2 : 53 — 0.51
3 : 44 — 0.66
4 : 55 — 0.10
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
n = 238 6 clusters Cj
j : nj — avei∈Cj si 1 : 37 — 0.03 2 : 52 — 0.20 3 : 37 — 0.64
4 : 52 — 0.40 5 : 28 — 0.39 6 : 32 — 0.21
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
n = 238 7 clusters Cj
j : nj — avei∈Cj si 1 : 31 — 0.14 2 : 50 — 0.19 3 : 11 — 0.51 4 : 37 — 0.63
5 : 48 — 0.43 6 : 28 — 0.39 7 : 33 — 0.15
−0.2 0.0 0.2 0.4 0.6 0.8 1.0
n = 238 5 clusters Cj
j : nj — avei∈Cj si 1 : 81 — −0.05
2 : 53 — 0.52
3 : 44 — 0.65 4 : 26 — 0.44 5 : 34 — 0.20
Figure G.15: Cohesion of career clusters.
Note: This figure shows the cohesion – as measured through the silhouette score – of the different number of career groups that can be extracted from the cluster analysis. While we can see that cohesion is far from perfect in any single specification, reasonable levels of
A-57
Again, for most senators in my sample, the specification with five clusters seems like a reasonable one. Again it should be noted that, I am further reassured by the fact that the same substantive results are obtained using any of these alternative number of clusters – thus, the results are not an artefact that comes by because of poorly fitted cluster analyses.
Turning to the cohesion in the committee based clusters, the picture is more messy.
No solution obtains high levels of cohesion, which suggests that there is considerable amounts of noise in the assignments of senators to committees. Since the results are the same across specifications and when using the clusters based on pre-Senate careers, the lack of cohesion should not be of too much concern. Similarly, adjusting for measurement error in various ways in Appendix E does not change the results.
0.0 0.2 0.4 0.6 0.8 1.0
n = 235 4 clusters Cj
j : nj — avei∈Cj si 1 : 56 — 0.07
2 : 73 — 0.02
3 : 62 — 0.05
4 : 44 — 0.11
0.0 0.2 0.4 0.6 0.8 1.0
n = 235 5 clusters Cj
j : nj — avei∈Cj si 1 : 51 — 0.07
2 : 63 — 0.006
3 : 38 — 0.06 4 : 40 — 0.09 5 : 43 — 0.10
0.0 0.2 0.4 0.6 0.8 1.0
n = 235 7 clusters Cj
j : nj — avei∈Cj si 1 : 39 — 0.05 2 : 41 — 0.05 3 : 32 — 0.06 4 : 28 — 0.16 5 : 27 — 0.04 6 : 33 — 0.09 7 : 35 — 0.04
0.0 0.2 0.4 0.6 0.8 1.0
n = 235 8 clusters Cj
j : nj — avei∈Cj si 1 : 29 — 0.04 2 : 31 — −0.04 3 : 27 — 0.06 4 : 27 — 0.17 5 : 30 — 0.06 6 : 37 — 0.04 7 : 35 — 0.09 8 : 19 — 0.12
0.0 0.2 0.4 0.6 0.8 1.0
n = 235 6 clusters Cj
j : nj — avei∈Cj si 1 : 53 — 0.04
2 : 46 — 0.05 3 : 33 — 0.07 4 : 28 — 0.17 5 : 37 — 0.09 6 : 38 — 0.05
Figure G.16: Cohesion of committee clusters.
Note: This figure shows the cohesion – as measured through the silhouette score – of the different number of reference groups based on committee assignment that can be extracted from the cluster analysis. While cohesion is generally low, the results are highly robust,
A-59
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