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][1]

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 more 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.

It is not exactly the situation you describe, but the following study fits better what you are looking for: [link][2]

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.

Good guidelines for dealing with lies are also here: [link][3]

  [1]: http://www.child-psych.org/2011/11/liar-liar-pants-on-fire-how-punishment-can-affect-children%E2%80%99s-honesty.html?utm_source=feedburner&utm_medium=email&utm_campaign=Feed:%20ChildPyschologyAndParentingResearch%20%28Child%20Pyschology%20and%20Parenting%20Research%29
  [2]: http://nymag.com/news/features/43893/index2.html
  [3]: http://childrenscenter.sa.ucsb.edu/CMSMedia/Documents/ParentSupport/LyingAndDishonesty.pdf