A study conducted by Talwar and Lee shows that harsher punishment only teaches children to lie "better" to avoid punishment. But it doesn't reduce lying link
In this study 46 children of two different schools had to do a “temptation resistance paradigm” tests. It was an object guessing game, where the instructor left the room and the children had the chance to peek. Almost every child did so.
One of these schools was labeled punitive, the other non-punitive. Only half of the children from the non-punitive school lied about their actions (56%), while almost everyone from the punitive school lied (94%).
The children from the punitive school where also five times more likely to cover up their first lie with another.
The researchers concluded that harsher punishment not only increases lying, but also makes children learn more advanced ways to cover up their lies and avoid punishment.
The following study fits even better what you are looking for: link
They also used the temptation resistance game, but this time the researcher read the child a story. Either The Boy Who Cried Wolf (punishment for lying), or George Washington and the Cherry Tree (reward for telling the truth).
The question was which of the books would reduce lying more.
The Boy Who Cried Wolf didn't reduce the lying at all.
George Washington and the Cherry Tree on the other hand reduced it by 43%.
These studies show that it might have a much better long-term-effect to reward telling the truth. E.g. instead of doubling the punishment for lying it might be a better idea to half the punishment for telling the truth. However, I personally prefer to make children experience the natural consequences for their behaviour instead of setting up punishments that don't have to do anything with what they had done wrong. If a child lies to me, they loose my trust and have to earn it back.
Good guidelines for dealing with lies are also here: link