Do you think crime would not increase if punishment were reduced?

Fundamentally I think law enforcement is just one piece of the puzzle. Intrinsic factors (culture, biology, economics, psychology) also play a major role - all else held equal, the US is likely to be more violent than India (important exception being sexual violence). But law enforcement does matter - how else to explain how clean little India is in Singapore and Kuala Lumpur?

I'll certainly look at your studies.