Second in macro there aren't enough data points to just compare means for treated and untreated subjects -- there is one case of Abenomics treated Japan. Macro theory is unreliable, but imposing some theory on data is necessary. I think it is safe to assume that monetary policy affects employment through interest rates and the price level. Nominal interest rates were very low pre-Abe (also including the 10 year treasury rate = 0.713% the month before he was elected prime minister). The inflation rate remains extremely low. I don't see a path from changed monetary policy to improved employment. But I will check.
OK unemployment. rom the graph can you guess when Shinzo Abe was elected ? I can't (and with failing memory had to go to the Wikipedia but I'm man enough to admit it)
Answer he became prime minister after the DEcember 2012 elections. This was unsurprising after he was elected LDP party president September 26 2013. I see no hint of a change of economic regime September 2012 or December 2012 or at any date after 2008.
I don't see what checking the working age population growth rate has to do with Abenomics. It is determined by fertility 15 years ago and 65 years ago and, a tiny bit (but matters a lot for those uh involved) by the very low death rates of Japanese under 65. I guess that the idea is either that low working age population growth explains low GDP growth in spite of Abenomics or the tweet includes a typo and Yglesias meant to refer to the ratio of employment to the working age population.
That ratio has indeed increased dramatically. It began increasing before Abe but something new and different has been happening.