I want to say just "Yes", but it is a much more complicated answer that I am not entirely sure how to articulate in depth, so here are the "dot points" of my thought on the matter:
- Overall, yes
- Children should, however have autonomy
- They should not have the autonomy to harm others (be it physically or financially)
- Is the parent to be held liable with what - fines, prison time with their little loin spawn?
- Will it really stop it from happening again, or just drive the kid to keep doing worse things?
- What would you do if your child did something really bad and you were held liable?
Yes, it is more complicated. I wouldn't actively campaign for this as a "yes" answer, but there should be some considerations perhaps.
Depends on what they did I guess. If they were a school shooter, or was committing home invasions, or stealing cars at 2am at 10 years of age - should take some blame?