Simpsons' paradoxes and GDP per hour worked

Bernard Hickey's been on a bit of a tear about GDP per hour worked and employment rates.

So NZ created 179k jobs in the last 2 yrs, but unemployment actually rose 1k to 128k. Jobs soaked up by net migration & more >65 yrs working

— Bernard Hickey (@bernardchickey) November 2, 2016

NZ actually worse since 2012. Flat real gdp per hour worked. We're just pumping more low wage workers in the economy and working more hours. pic.twitter.com/9uKE0UV1vR

— Bernard Hickey (@bernardchickey) November 2, 2016

There's another potentially relevant chart.

And, one more:

I wonder what GDP per hour worked would look like if we could isolate out demographic changes. 

At the same time as the recent flatlining in GDP per hour worked, we've had substantial numbers of beneficiaries moving out of benefit and into work. The first of my charts has number of people on benefit over the period. The proportion of working-age people on benefits was 12.1% in 2011. It is now 9.8%. Average productivity among those moving off of benefits will likely be rather lower than average productivity among other workers. But while that would worsen average productivity or GDP per hour worked, it won't worsen anyone else's productivity unless they're making other workers less productive just by being there. 

The second of my charts has employment rates sorted by age cohort. Recall that the employment rate is the number of employed people divided by the population in that cohort - it isn't the inverse of the unemployment rate. You can have rising employment rates and rising unemployment rates if people are being drawn into the labour force who were previously not seeking work. 

I've dropped out prime age workers, which have been much flatter, so you can see the compositional changes in the tails. The youngest workers are least productive. They hugely dropped out of the labour market with the changes to the youth minimum wage, but that decline's since reversed a bit. There's been a long trend growth in hours worked among older workers, but typical wage patterns over the lifecycle have wages flattening out from the early 50s or thereabouts. Big increases in employment rates among cohorts with lower than average productivity, or at points in the life cycle where wage profiles (and presumably productivity) flatten out, will both flatten or worsen GDP per hour worked. 

And, obviously, net migration's increased over the last few years. New workers getting settled in New Zealand might take a bit to find their feet as well, while still being better off than they were before.

The classic Simpson's Paradox shows how you can have a declining average measure for a group despite improving average measures for each cohort within the group if changes in the proportions of the overall group coming from the different cohorts change. 

So suppose that you have a classroom with 5 Canadians and 10 Kiwis. The Canadians all get 70% on their tests this year and the Kiwis all get 90%. Average is 83%. Next year, there are 10 Canadians and 5 Kiwis. The Canadians all get 75% and the Kiwis all get 95%. The group average drops to 82%. Every cohort has improved by five points, but the average performance looks bad. 

And so I wonder what the GDP per hour worked figures would look like isolating for these compositional changes.

Note too the strength of the employment rate. Only four years in the series back to '86 had higher employment rates: 2005-2008.