Actually, there was less drinking during Prohibition, despite popular myth. A fascinating study on this came out in the mid-80's when I was in grad school and taking a course in Law and Society. Laws do have a deterrent effect, particularly as the subject of those laws increases in, for lack of a better term, moral importance. For example, think back to the days of the 55 MPH speed limit on Interstates. In those days, most of us drove between, what, 60 and 65. After the speed limits were raised to 65, most of us figured it was 'safe' to start driving around 70. If you raised the speed limit to 80, I suspect many if not most people would at least go 80. And this is just with the speed limit where the only cost is a ticket and maybe higher insurance rates. Laws do have an impact on human behavior.
Bad law!