I got a leash, for number 2 (of 4).
He had no sense of staying near mommy, and I was disabled by a back injury and literally *couldn't* catch him if he ran ... I had to hope he got interested in something and stopped. Obviously, not acceptable, safety-wise.
Interestingly, with both #2 and #3 (who had rebellion escape issues, due to her parents separating), only two(?)ish, maybe three, times of using the kid-leash and they didn't really try to escape anymore--because I was very clear that if they *did* try to escape, they would have to wear the leash again. And I did do what I said I would.
And I didn't use it to "drag them around," I walked with them holding their hand like I preferred, but if they dashed, then the leash--around their torso and my wrist--would stop the escape. Which was key from the safety point of view.
Now I am mostly recovered from my back injury and I just make sure I have a very firm grip on hands. Or use the not-as-looked-down-upon-but-it's-still-actually-a-leash method of keeping the runaway risk strapped into a stroller or a shopping cart. Same idea, really. (Really, it's a bit ridiculous to look down on a leash if you have ever used a cart or stroller as a containment device, isn't it? Kids hate them just as much, if they want to be running.)
If my older kids are being a problem (on a walk or in a store), I require them to keep one or both hands on the cart/stroller handle/mommy's beltloops--depending on the type of their inappropriate behavior (wandering off = one hand, grabbing stuff off of shelves = both hands).
If you do decide to try the leash thing, the current social taboo about them (and yes, you will get oh, so nasty glares--remember, if you choose the leash, that you are choosing it because you think it is the best way to keep your child from running into the street or getting lost in a department store, or whatever is the reason big enough to face the social scorn) ... anyhow, the current taboo about them means they are hard to find at stores that cater to people with strong aristocratic social assumptions (or who would like to think they have such assumptions ;) ). I found mine at Kmart, and it is a solidly constructed, carefully designed to fit safely on the toddler/small child leash.
OK, that's my countercultural Mamasource for today (sigh).
Good luck with solving the running away!