It's this: so far we've heard a lot of suspiciously confident predictions about the way robots and digitisation are about to destroy millions of jobs, a lot of anecdotes about law-breaking employers, a lot of scary stories about "the gig economy" and "portfolio jobs", a lot of adults assuring impressionable school children they'll have 10, or is it 17, different jobs in their working lives, a lot of propagandising by the unions about the rise of "precarious employment" and a lot of speculation about how all this somehow explains why wages growth is the slowest it's been since the early 1990s.Know what we haven't got a lot of? Hard evidence that any of all that has actually started happening to any significant extent.This is not to sayversion of all that won't happen at some time in the future. I can't say it won't sincedon't know that the future holds, unlike all the self-proclaimed experts with their precise predictions.(Next time you hear someone telling you exactly how many jobs robots will have destroyed by 2020, or how many jobs or occupations you'll have in the next 40 years, ask yourself this question: How – would – they – know?)But if there's no evidence this frightening future has got going yet, there's no way it can explain why wage growth has been so weak for the past three or four years.For once, let's take a close look at what we actually know has been happening.It is true that, as we saw in this column two weeks ago, the structure of occupations in the workforce is changing. Research by Dr Alexandra Heath, of the Reserve Bank, shows the share of routine jobs has fallen by 14 percentage points, while the share of non-routine jobs has risen by 14 points.Similarly, the share of manual jobs has fallen by 5 percentage points, while the share of cognitive jobs has risen to the same extent.But this is atrend. These figures are for the change over the 30 years to 2016, and there's no sign of the trend accelerating over recent years.A lot of detailed – and reassuring – research on the official statistics has been done by one of our leading labour-market economists, Professor Jeff Borland, of the University of Melbourne, and reported on his website, Labour Market Snapshots For one thing, Borland's been searching for evidence that our jobs are being taken by robots – and failing to find it. He breaks the issue into two parts.First, has computerisation reduced the total amount of work needing to be done by humans, as many people assume?No. The total amount of work available per head of population has bounced around with the ups and downs of the business cycle but, overall, has shown no downward trend. The latest figures show, if anything, a bit more hours of work per person than there were in the mid-1960s.Second, consistent with Heath's research, Borland finds evidence that the progressive introduction of computers, which began in the early 1990s, is probably changing theof jobs being done by workers.But he, too, finds that the pace of change in the composition of employment "is no quicker today than in the period before computers"."So while computers may be having some impact on the Australian workplace, most claims about their impact are vastly overstated," Borland concludes.Next, Borland shines his statistical spotlight on all the claims about work becoming more insecure or "precarious".You don't have a proper, full-time permanent job. You get a bit of work here and a bit there. If you do have a job, it never lasts long.The Australian Bureau of Statistics has long published figures for job "tenure" – how long people have been with their current employer.If all the talk of growing instability was a genuine trend – as opposed to the experience of a relatively small number of individuals – you ought to be able to see it in the job tenure figures.But you can't. The reverse, in fact. Borland finds that, from the early 1980s to the present, the proportion of workers who've been in their job for 10 years or more has been steadily increasing. This is greatest for women, for whom it's gone from 12 per cent to 25 per cent.At the same time, the proportion of all workers in their job for less than a year has been decreasing.Next, how insecure do workers feel? When the bureau asks employees whether they expect to be with their present employer for the next 12 months, the proportion of men whohas been steady at about 9 per cent between May 2001 and May this year.Over the same period, the proportion for women has fallen steadily from 11 per cent to 9.5 per cent.From all the talk, you'd expect the proportion of employees working for labour hire companies and temporary agencies to be rising strongly.It ain't. Actually, between 2001 and 2015 it's fallen from a tiny 3.1 per cent to a tinier 2.2 per cent.And though it's true the proportion of jobs that are part-time is continuing to rise, over the 10 years to 2016 it rose at the slowest rate for any decade since the mid-1960s.Of course, none of this is to deny that wages growth in Australia has been surprisingly weak for several years, as it has been in other developed economies.But in our guessing game about what might be causing that weakness, let's not get too fanciful.