Don't have the figures to hand but I'm fairly certain that the incidence of child abductions etc is DOWN from 20/30 years ago.
What has increased is the publicity etc.

Perception rules over facts

The data on child abductions is very sketchy, and made complicated by the fact that many abductions (approximately two thirds) are made by persons known to the child and/or parents in dispute. About 60-100 "stranger abductions" are said to take place in Britain annually, if anything the statistical trend seems fairly even.

Although there are misperceptions on the general crime level, I don't think that can necessarily be extrapolated onto abductions. In any case it is not the statistics that matter but the risk. Children have dramatically less freedom than they did a few decades ago (90% less by one account) and yet abductions persist. Who knows where the incidence of abduction would be if the kids were permitted to roam freely again. The high profile cases we hear of in the news each year are enough to discourage most parents from tempting fate.

By that line of reasoning you could argue that the degree of freedom a child has , has no impact on their likelihood of being abducted.
The hysteria of seeing pedophiles everywhere we choose to look has a detrimental impact on a child's development

How do you deduce that ???

You state that children have considerably less freedom yet the abduction rate remains the same
You could draw the conclusion then that there is no link between the two factors

Surely if less children are out and about yet the number of abductions remain the same, then more children are being abducted than before.

You could jump to that "false negative" conclusion, agreed, but it would be wrong.

Unless of course you don't accept that there is a relationship between "opportunity to abduct" and "incidence of abduction"?

That's another way of looking at it, yes. Greater incidence of abduction.

Are we talking abduction by strangers or Uncle Fred?

Strangers only.

But if they aren't found how do we know?

? They're reported missing. We're talking about abductions, not deaths.

It hardly matters. If there are, as suggested above, 60 abductions per year in a population of 60 million people then the risk is about the same as that of being struck by lightning (http://www.torro.org.uk/site/lightning_info.php), that is, not sufficient to warrant taking any particular precaution against.

60 children reported missing isn't the same as 60 abducted. How many were just lost in the woods?

Kid population (untethered). Perhaps lightning whilst sitting on the church roof?