My previous post (here) looked at the UN's gender equality measure (GEM) and its components. Across countries, there was not a strong relationship between parliamentary representation of women and their representation in professional and technical jobs. I decided to look at the relation in more detail.

The first graphics show the ratio of women's share in parliamentary seats to their percentage representation in professional and technical jobs. For ease of representation, I have split the data into two graphs, showing high and low ratios. At the top of the list comes highly gender equal countries in Northern Europe, as measured by the GEM, highly unequal countries in South Asia, and a scattering of other countries including the two East African countries of Tanzania and Ethiopia. At the base of the list is low gender equality former socialist countries and Middle Eastern countries.

The third graph shows the ratio plotted against the GEM measure. As the ratio of parliamentary representation to professional representation increases, gender equality increases but more slowly than the ratio.

The relationship between the ratio and GEM appears to be non-linear, so I took logs before regressing GEM on the ratio. Including the three South Asian countries of Pakistan, Nepal, and Bangladesh weakened the relation considerably and were dropped. The outcome was a good-fitting relation

ln(GEM) = -0.12 [0.06] + 0.40 [0.06] * ln(parl/prof) + robust error

(R^2=0.61; n=78; s.e.s in brackets)

or GEM = 0.89*(parl/prof)^0.4, with some error.

The regression and graphs raises some questions:

1. if there is a causal link for parliamentary representation increasing gender equality more than professional representation does, or

2. if it is the other way round, so gender equality brings increased parliamentary representation above increased professional representation,

3. why East Africa (and into the Great Lakes regions too) have high levels of female parliamentary representation,

4. why in South Asia parliamentary representation is associated with less gender equality than elsewehere, and

5. why former communist countries have far more professional equality than political equality.

[A technical clarification on spurious regressions:

I thought a little about the estimation ln(GEM) = -0.12 [0.06] + 0.40 [0.06] * ln(parl/prof) + robust error. There is a technical issue that many readers may wish to ignore, but I should really clarify to avoid misleading impressions.

GEM has a form (approximately) like parl+prof+another term. ln(GEM) may be roughly approximated as parl+prof+other term. ln(parl/prof) may be roughly approximated as parl-prof. Thus we have a regression that looks a bit like parl+prof = a + b*(parl-prof). Now if parl and prof are independent, we would have a regression estimate for b (assuming parl and prof are zero mean to simplify the algebra) of sum((parl-prof)*(parl+prof))/sum((parl+prof)^2). Taking expectations and using limiting theorems we have b=sum(E(parl^2)-E(prof^2))/(positive number). If E(parl^2) does not equal E(prof^2) then we obtain a positive coefficient for b. It has arisen solely by virtue of the algebraic manipulations used; any two variables parl and prof would serve equally well.

If there is a further relationship between parl+prof and parl-prof not produced solely by manipulations, then by the reverse argument we would have parl and prof not independent (perhaps this statement could be made more precise). Now the observation made in the earlier post was that there is not a strong relationship between the two; in fact correlation is very low. But looking at their graph, there seems to be a relationship over much of the variables' domains. So the variables do not seem to be independent, although having a low correlation. Thus, the relationship between ln(GEM) and ln(parl/prof) does not seem to be spurious.]

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