# Arithmetic of gender equality in Germany’s federal parliament

In an interview last week, Minister of Justice and Consumer Protection Katarina Barley expressed concern about the declining share of wmomen in the Germany's current federal parliament (see e.g. here). That share decreased from 36 percent to 30 percent after the most recent election. Barley suggests that this could imply “a step backwards in gender equality.”

I am skeptical, though. The figure below shows that no party in the current parliament reduced the share of women by 6 percentage points or more (which would be required to reduce the average share over all parties by 6 percentage points).

Instead, part of the decline seems to be explained by a compositional effect: Parties with a women's share below 36 percent won seats relative to parties with women's share above 36 percent. This is especially true for the FDP and the AfD that weren't in the previous parliament but also for the SPD that had a women's share of about 44 percent in the previous parliament but that also suffered losses in the most recent election. The vote share decline for the CDU-CSU (which, holding everything else equal, helps the women's share in parliament) is not enough to compensate for the other dynamics.

At a somewhat more technical level, we can decompose the change in women's share from parliaments 18 (the parliament from 2013-2017) to 19 (the current parliament) into two effects: First, holding current women's shares by party in parliament fixed, how did election results change the overall share (election effect)? Second, holding election results fixed, what's the effect of changes in women's shares by parties (gender composition effect)?

In other words, if $w_p^j$ denotes the women's share in each party in parliament $j$ and $v_p^j$ denotes the vote share of party $p$ in parliament $j$, then the difference in women's share in parliaments 18 and 19,
$\sum_p w_p^{19}v_p^{19} – \sum_p w_p^{18}v_p^{18}$
can be decomposed into
$\sum_p w_p^{19}(v_p^{19}-v_p^{18}) – \sum_p v_p^{18} (w_p^{18}-w_p^{19})$

The first sum denotes the election effect, while the second denotes the gender composition effect. Recall that the difference in overall women share is 6 percentage points. Using data from this election and last election, one can calculate the two sums above and find that the election effect and the gender composition effect each contribute about 3 percentage points to the total decline. Hence, about half of the total decline can be explained by election results in the most recent election.

To increase the share of women in parliament, it could suffice for the SPD to win voter shares back in the next election, or more generally, for parties with a high representation of women to win more seats. Recent results of the Green party in regional elections suggest that they might also improve their vote share in the next federal election. The share of women in parliament will most likely increase then, without any need to change electoral law (as was suggested by Barley).