"Fining parents for taking children out of school in term time in Wales has had no effect on overall absence rates, a review has found.It shows the number of unauthorised family holidays actually increased after fixed penalty notices were introduced in 2013."
If there was an increase, then there was an effect on absence rates, though perhaps not the one expected. (It might perhaps be that the increase was attributable to something else, and the fine judged to have no effect either way, but there's no indication in the article that anything else was responsible for this increase.)
This isn't so surprising if you're familiar with the literature in the area. One of the most referred to studies is this one, concerning the introduction of fines for late collection of children from day care centres. Again, the study found that more parents were late to collect their children after the introduction of fines.
The usual interpretation is that the extrinsic motivation provided by the fine 'crowds out' intrinsic motivation provided by a sense of duty. Without the fine, people feel a moral obligation to collect their children on time. When there is a fine, they feel that they are paying for being late, so the feeling of moral obligation not to be late recedes. It seems there may be a similar effect in the case of term-time holidays.