Appropriate punishments for children depend on their age, the severity of their misbehavior, and the parent or guardian's personal preferences. It is important to remember that punishments should focus on teaching children the right way to behave, rather than on punishing them for wrong behavior. For younger children, timeouts and verbal corrections can be effective. As children get older, taking away privileges and assigning extra chores can be a good way to ensure that the lesson is learned. Ultimately, the most effective punishments are those that help a child learn from their mistakes and foster positive behavior in the future.
According to Familyeducation.com
"Punishments make children feel bad, or worse yet, suffer. “While punishments may ‘work,’ to interrupt a behavior short term, they have potentially negative long-term effects including causing children to feel bad about who they are (which also makes them more likely to act out again), as well as creating an adversarial relationship between parents and child.”
There are natural consequences and logical consequences.
Natural consequences are those that happen as a direct result of the child's behavior. For example, if the child hits something their hand may hurt.
The logical consequence for this behavior might be that the child loses the ability to play outside for the day.
Harsh punishments can have long term negative effects. It is important to remain calm and firm when giving a punishment to avoid overreaction and potentially a big argument.
It's also important to talk it out with your school age children so they fully understand the consequences of their behavior.
Resource: An Age-by-Age Guide to Setting Discipline Consequences for Kids - FamilyEducation