Writer’s introduction

This publish grew out of a rambling, sporadically multi-month play with a bunch of information that turned far too large for a single publish for any believable viewers. So I’ve damaged that work into three artefacts that may be of curiosity in numerous methods to totally different audiences:

• Males’s home chores and fertility charges—(this doc)—dialogue of the substantive problems with the subject material, with charts and outcomes of statistical fashions however no code. Essential viewers is anybody all in favour of what statistics has to say in regards to the precise (non) relationship of the time males spend on home chores and whole fertility fee.
• Males’s home chores and fertility charges – Half II, technical notes—dialogue of technical points reminiscent of how to attract directed graphs with totally different colored edges, methods to entry the UN SDG indicators database, and the equivalence or not of various methods of becoming combined results fashions. Accommodates key extracts of code. The primary viewers is future-me wanting to recollect these items, but additionally anybody else with comparable technical curiosity.
• The code that produces all of the evaluation and outcomes within the two weblog posts.

Additionally, all em-dashes on this publish had been defiantly typed, by me, in HTML, by hand.

OK, onto the weblog publish.

Time-use and variety of kids

An obvious relationship in excessive GDP per capita nations

Some months in the past a publish floated throughout my Bluesky feed making an argument to the impact of “if societies need extra kids, then males ought to do extra of the house responsibilities”, accompanied by a chart from a few-years-old paper. The chart was a scatter plot with one thing like male share of unpaid home chores on the horizontal axis, and whole fertility fee on the vertical axis—every level was considered one of chosen OECD nations at a cut-off date for which knowledge on each variables was obtainable—and there was a particular optimistic correlation.

I can’t discover the chart now, but it surely appeared one thing similar to this one I’ve made for myself:

The case was being made that if you happen to assume the world isn’t having sufficient kids (not one thing I personally subscribe to however let’s settle for it as an issue for some folks), the reply may be extra feminism and gender equality, not much less. And the apparent context being the varied pro-traditionalism, trad-wife, and so on arguments to the other impact, going round within the altogether relatively contemptible (once more, clearly that is simply my very own view) pro-natalism discourse.

Would possibly as effectively get on the file, whereas it’s not related statistically, that I’m totally for extra feminism and gender equality, and I additionally assume “as a result of then girls may have extra kids” is a really dangerous argument for these items.

Sadly each the Bluesky publish I noticed and the unique article have now escaped me, however I do do not forget that the info was a bit previous (2010s), and a few folks commenting ‘ah, woke Scandinavian nation X the place males do numerous house responsibilities, however because the time on this chart they have stopped having as many kids too’. Extra importantly, I used to be intrigued by means of “chosen nations” within the title. Chosen how and why, I puzzled on the time.

Clearly, limiting the evaluation to wealthy nations provides a slim view on a much bigger relationship. As a result of one of many strongest empirical relationships in demography, on a historic scale, is the commentary that as girls and women get extra academic and financial alternatives, they have a tendency to have much less kids, by way of a society-wide common of a rustic going by means of financial improvement.

I’m sufficiently old to recollect when everybody I engaged with appeared to agree this was factor, each by way of the additional alternatives and selections for girls as in itself, and avoiding cramming too many individuals into an already crowded and under-resourced planet. Apparently that is now not a consensus, which simply leaves me, I don’t know, stroking my gray beard and feeling the world’s handed me by.

What causes what?

I might anticipate, world-wide, that girls do the next share of the house responsibilities in nations the place they’ve much less financial alternatives (would you name these extra patriarchal and ‘conventional’ societies? considerably tough to get a non-offensive terminology right here). And that in those self same nations, in addition they have extra kids (see extensively identified historic empirical reality referred to above). In truth, what I’d anticipate is a diagram of causes and results that appears one thing like this:

On this mannequin, financial and schooling alternatives for girls and women results in selections to have much less kids and a lower in whole fertility fee, proven with a pink arrow due to the downwards affect. Males doing extra house responsibilities on account of a rising tradition of gender equality and altering social norms has an affect (most likely smaller) within the optimistic path, with a blue arrow. That tradition of gender equality itself comes about partly from altering financial circumstances (girls transferring in to seen roles) and partly from profitable advocacy.

Naturally, this can be a gross over-simplification of the fact of those processes.

The diagram above isn’t a directed acyclic graph (DAG) as a result of it’s not acyclic – that’s, a number of the arrows are two-way, reminiscent of financial development resulting in extra financial and academic alternatives for girls and women, and financial and academic alternatives for girls and women resulting in financial development. However you can scale back it to a DAG if you happen to restricted it to the three key variables of whole fertility fee, males doing house responsibilities, and alternatives for girls and women.

This simplified model doesn’t make it clear the place elevated alternatives for girls and women come from or why they result in males doing extra of the house responsibilities. The unique, extra advanced, diagram reveals that this was anticipated to occur by way of the (tough to look at and complicated to evolve) mediating issue of a basic tradition of gender equality.

The simplified diagram does assist us assume by means of what to anticipate if we ignore the confounder of “financial and academic alternatives for girls and women” and simply plot male share of unpaid home chores in opposition to whole fertility fee.

• On a easy two-variable scatter plot, we’d anticipate a unfavourable correlation, as a result of the time use variable is definitely standing in as a proxy for the extra vital gender equality of alternatives.
• However if you happen to might get a greater indicator of that confounding alternatives variable and management for it, and if there actually is an affect from male share of house responsibilities on larger fertility choices, you may get a optimistic impact of male share of home work on fertility.

“… all others should deliver knowledge”

Who measures these things?

OK then, let’s have a look at some knowledge.

Sustainable Improvement Targets (SDG) Indicator 5.4.1 is “the Proportion of time spent on unpaid home chores and care work, by intercourse, age and placement (%)”, which is unbelievable as a result of it means we’ve an internationally agreed commonplace on how that is measured. It additionally signifies that what knowledge is accessible will probably be within the United Nations Statistical Division’s definitive database of the SDG indicators.

Knowledge gained’t be obtainable for all nations, and positively not for all years in all nations, as a result of it will depend on a tough and costly time use survey. Only a few nations can afford to prioritise considered one of these often and steadily, and plenty of have by no means had one in any respect.

For the vertical axis of our first plot, we are able to get whole fertility fee from varied sources, however one handy one that provides an estimate for every nation for every year on a standardised, comparable foundation is the UN’s World Inhabitants Prospects.

We now have a number of challenges in utilizing all that knowledge:

• The official SDG indicators don’t truly embrace an apparent single dimensional abstract of gender share of house responsibilities, so we might want to assemble it with one thing like male_share = male / (male + feminine). The place male is the proportion of males’s time spent on dometic chres and carework, feminine the equal for girls. We are able to make a composite indicator like this as a result of the denominator (whole time within the day) for each male and feminine is similar.
• Some nations have a number of observations (multiple yr with a time use survey) and we’d like to include them one way or the other. After we get to statistical modelling, this suggests the necessity for some type of multilevel mannequin with a country-level random impact in addition to residual randomness on the country-year degree. On a chart, we are able to present these a number of observations by connecting factors with segments, and visually differentiating the newest commentary from these in earlier surveys. That is a lot better than simply choosing one survey per nation.
• The years of time use surveys fluctuate considerably over a 20+ yr time interval, so we should always anticipate a doable time impact to complicate any inference we do. We have to take this under consideration each in our statistical modelling and our visualisations.
• Not all of the age teams are equal throughout nations, so we must grit our tooth for some inconsistent definitions of ladies and men (i.e. when does maturity begin). Not least of the implications of that is it provides an annoying knowledge processing step.

A relationship reversed

As soon as I had the info in place, I began with a scatter plot, of all nations, of our two variables.

In stark distinction to the plot of simply high-income nations that began me off, there’s a strongish unfavourable relationship right here. The path of the connection has reversed! That is what I anticipated and is according to my desirous about financial and academic alternatives for girls and women being an vital confounding variable as quickly as we have a look at a broader vary of nations.

What about if we introduce another variables, proxies for the financial alternatives for girls and women? Apparent candidates are revenue or, failing that, GDP per capita, appropriately managed for buying energy parity in every nation and level of time; and a few basic feminine empowerment index like relative literacy (say feminine literacy divided by male literacy, at age 15).

What I’m after right here is drawing some charts like this which is able to get us began in seeing if the obvious relationship between male share of home chores and fertility fee is basically an artefact of confounding variables like general financial improvement.

Right here we do see, for instance, a really fascinating outcome that inside the three decrease GDP per capita classes of nations there’s a unfavourable relationship between male share of home chores and fertility. However within the highest GDP per capita class, that relationship is reversed. In truth, the scatter plot that began me on this complete journey was mainly the underside proper side of this diagram.

Measuring gender inequality

We have to do extra although—we are able to get a measure of feminine financial empowerment (and therefore selections between motherhood and employment). One of the best knowledge I might discover for my goal on this was the Gender Inequality Index produced by the UNDP as a part of their annual Human Improvement Report course of. Right here’s what that quantity appears to be like like for the nations that we’ve sufficient knowledge for this general weblog:

Lastly on this exploratory stage, here’s a plot of all of the pairwise relationships between the variables we’ve been discussing:

There’s lots packed in to plots like these, however what we see right here is that:

• GDP per capita is strongly negatively correlated with fertility fee (wealthy nations have much less kids).
• Gender inequality is strongly positively correlated with fertility fee (unequal nations have extra kids).
• Male house responsibilities is reasonably positively correlated with GDP per capita (wealthy nations have extra male house responsibilities).
• Male house responsibilities is weakly to reasonably negatively correlated with fertility (extra male house responsibilities nations have much less kids).
• Every variable has a weak development over time—downwards for fertility fee and gender inequality, upwards for GDP per capita and male house responsibilities. You possibly can truly see within the left column of the plots the chains of dots representing nations just like the USA which have the posh of a number of time-use surveys and a stunning steady sequence of comparable observations.

Statistical modelling

The kind of mannequin I wish to match is one which has all these options:

• permits us to incorporate a number of measures for nations which have them, however with out making the false assumption that these are unbiased observations (every additional commentary on a rustic is beneficial, however not as a lot additional data as if we had a complete new nation)
• permits for an interplay between GDP per capita and male house responsibilities
• permits relationships basically to be non-linear if that’s what the info suggests
• permits for a nuisance non-linear development over time in fertility
• lets the variance of whole fertility fee be proportional to its imply, however not similar (so a quasi-poisson household distribution)

To do that I opted to make use of the gam operate from Simon Wooden’s mgcv package deal, match with this snippet of code:

model6b <- gam(tfr ~ s(time_period) + 
                     s(gii, ok = 3) + 
                     s(log(gdprppppc), prop_male) + 
                     s(country_fac, bs = 're'), 
                knowledge = model_ready, household = quasipoisson, methodology = "REML")

The forthcoming “behind the scenes” follow-up publish may have extra dialogue of a number of the modelling selections, diagnoses, and statistical assessments.

The top result’s that this mannequin is not an enchancment on a mannequin that drops prop_male—ie the proportion of home work that’s achieved by males—altogether. As seen on this Evaluation of Deviance desk, with just about no additional deviance in fertility defined by the extra advanced mannequin:

Evaluation of Deviance Desk

Mannequin 1: tfr ~ s(time_period) + s(gii, ok = 3) + s(log(gdprppppc)) + s(country_fac, 
    bs = "re")
Mannequin 2: tfr ~ s(time_period) + s(gii, ok = 3) + s(log(gdprppppc), prop_male) + 
    s(country_fac, bs = "re")
  Resid. Df Resid. Dev     Df Deviance      F Pr(>F)
1    82.463     1.0585                              
2    77.330     1.0154 5.1326 0.043118 0.7491 0.5925

This isn’t shocking once we mirror on the pairs plot earlier. GDP per capita and the gender inequality index each have sturdy, apparent relationships with whole fertility fee. It is sensible that between them they take in all of the variance that may be defined on the nation degree.

To see the modelling outcomes visually, here’s a plot exhibiting predictions of the typical degree of fertility fee at various ranges of that male house responsibilities variable, created with the extremely helpful marginaleffects package deal by Vincent Arel-Bundock, Noah Greifer and Andrew Heiss. What we see right here is not any materials relationship:

Distinction that to comparable presentation of the outcomes for gender inequality, and for PPP GDP per capita:

The time relationship is an fascinating one. It appears to be like from the plot under that there is no such thing as a materials relationship, however the statistical proof is fairly sturdy that it’s price holding this variable within the mannequin.

My intuitive clarification for that is that point is extra vital in explaining developments in fertility fee within the nations which have a number of observations on this pattern; and this isn’t simple to choose up visually in a chart of this kind. Anyway, it doesn’t matter, as I’m not within the time development in its personal proper, simply in controlling for it as a doable spoiler of our extra vital statistical conclusions.

Conclusions

• In the event you have a look at simply excessive buying energy parity GDP per capita nations, there’s an obvious optimistic relationship between the quantity of unpaid home chores achieved by males and whole fertility fee, on the nation degree.
• Nevertheless, this affect is reversed if you happen to have a look at the complete vary of nations for which knowledge is accessible.
• Most significantly, the connection vanishes altogether once we embrace it in a statistical mannequin that controls for buying energy parity GDP per capita and for gender inequality extra broadly.
• We are able to conclude that the obvious country-level impact of male house responsibilities on whole fertility is only a statistical artefact standing in for these two, broader—and clearly vital—elements.

Does this imply that males doing house responsibilities doesn’t affect on fertility choices? No! In truth it’s very doable it does. Nevertheless it does imply which you can’t see this within the nation degree knowledge. To actually examine this, you will want family degree knowledge; one thing just like the Australian HILDA survey (Family Revenue and Labour Dynamics in Australia).