LABOUR force participation has been in the news recently. Falling participation is masking the weakness of the labour market, we're told. Unemployment rose through 2013, but only from 5.4 per cent to 5.8 per cent of the available labour force. It was a small rise, even though employment growth was the weakest for years. And if the participation rate - the labour force as a proportion of the working-age population - had stayed steady rather than falling, there would have been 110,000 more people left over to be classed as unemployed. And the jobless rate would have risen to 6.7 per cent. But there are different explanations for the fall in the participation rate from 65.2 per cent of the working age population to 64.6 per cent. One influential view is based on last year's budget papers. The ageing population accounted for "around 80 per cent of the decline in the participation rate since 2010," Treasury said. On the other hand, Bank of America Merrill Lynch (BAML) economists Saul Eslake and Alex Joiner interrogated the data earlier this year and came to a different conclusion. The ageing population will eventually drag the participation rate down, but that's doesn't explain what's happened recently, they said. They put it down to "lack of participation of younger people, cyclical weakness and likely increasingly the transition of workers from the resources sector to other industries." But treasury, the BAML economists - and anyone else with an opinion - can be right. It's all about timing. The strength of the jobs market is by far the main influence on participation from year to year. More jobs equals higher participation, fewer jobs - or,what the BAML economists would call "cyclical weakness" - mean lower participation. And the jobs market fluctuates a lot from year to year. As a result, so too does participation. It's possible to play around with the Australian Bureau of Statistics data to see what would have happened if the proportions of the population in each age group - five-year brackets from 15-19 to 65-69, then 70-plus - had not changed. Or to hold participation rates steady in each group as the age structure changed. It's a headache inducing exercise in number crunching. But it's doable. And it confirms the importance of the time frame chosen to study. It shows that, over the past five years, the changing age structure reduced the measured unemployment rate by about a fifth of a percentage point a year. And that effect changed very little from year to year. But the impact of other factors, mostly a response to the ease of finding a job, varied wildly. At times these other factors have muted the impact of strong jobs growth, slowing the fall in the unemployment rate by as much as 0.8 percentage points over a single year (to November 2010). But through 2013, labour market weakness enhanced the effect of ageing, lowering participation further and resulting in the smaller rise in unemployment we saw.