In fact, the unemployment rate stayed the same not because employment isn't growing - it is, and strongly - but because large numbers of people have moved into the labour force, encouraged by the improved likelihood of getting a job in this improved economy, even if they haven't landed one quite yet.
This rise in the "participation rate" isn't always and everywhere necessarily a good sign. You could imagine, for example, that in tough times, when one partner in a relationship loses their job, the other partner rallies to the cause and stops (say) child-minding or home-running and moves into the labour force as well, to try and help find some replacement source of income. The kids could be drafted, too, to start looking for part-time or full-time work. The participation rates goes up, with both partners and maybe the older kids, all now looking for work in the labour market where only one was before - but out of necessity in hard times, not because the economy has improved. Tough times might, in principle, drive the participation rate up.
In reality, though, it doesn't work that way at an aggregate national level (though there may well be individual families in the 'driven to it' position). A rising participation rate is reliably correlated with improving economic conditions, as the graph below shows for New Zealand since 1986 (which is as far back as the online data on Statistics' Infoshare site go).
You'll note the strong rises in the good times of the mid 1990s and the first half of the 2000s, and conversely the sharp fall in the troubled late 1980s and the more modest fall post GFC. More recently, since a low point in March '13, the participation rate has been rising very strongly to record levels. People may not be the economic calculating machines that economists sometimes depict them as, but they're certainly capable of knowing a better job market when they see one.
It's the same picture overseas, by the way: the participation rate tends to fall in worse times, and rise in better. Here's the US experience over the past half century or so.
The vertical shaded bars are periods when the US was in recession, and you can see that recessions tend to, at the least, stop the participation rising, and more usually lead to a lower participation rate. And generally good times - like the Reagan and Clinton eras - see the participation rate go up. You'll also note why some people reckon the US economy is still fragile - this far past the GFC, you'd expect the participation rate to have turned for the better, but at most it's stabilised, and certainly isn't clearly on the up yet. Evidently there are a lot of people in the US who are still pessimistic about their chances of finding a job.
'FRED' in the graph, by the way, is the Federal Reserve Economic Database hosted by the Fed of St Louis, which is free to access and holds a treasure trove of US data.
It's not just the US that we stack up well against, either. In the Stats data on the household labour force survey, there's this comparison of unemployment rates across the OECD.
Not bad, is it? As developed economies go, we're doing pretty well in a world economy that's still a bit sub-par in terms of its economic growth rate. Incidentally, you can also see why President Hollande's party got slaughtered in the recent municipal elections: there's only Slovakia and the 'PIIGS' to the right of France in this graph.
If there's anything slightly troubling in the latest data, it's the NEET rate - the 'Not in Education, Employment or Training' rate for 15-24 year olds. This is an important social indicator, as - for their and our sakes - we don't want a large group of alienated, unskilled, unemployed young people, and thus far, as I've noted before, we're a bit worse than the average OECD country on this score. Here's the latest data: hopefully the uptick in the NEET rate in the March quarter is an aberration (there's a fair bit of random volatility in the data) and the generally improving trend will reassert itself from June onwards.
I'm pretty sure both our relative and absolute performance is indeed going to improve further over the next few quarters: the participation rate can't go on climbing indefinitely, and any slowdown is going to see the strong demand from employers translate straight into a lower unemployment rate - possibly much lower. The most recent (March) set of consensus forecasts collated by the NZIER had the unemployment rate dropping to 5.4% over the next year and to 5.1% in the year to March '16, and there are even some especially optimistic souls in the forecasting community who see it going below 5% within the next twelve months.