The authors argue that local prohibitions lower the price of drugs such as meth relative to alcohol. This is hard to prove, because dry counties share many traits with counties that have meth problems. The authors claim that after controlling for factors including income, poverty, population density and race, legalising the sale of alcohol would result in a 37% drop in meth production in dry counties in Kentucky, or by 25% in the state overall.
Since no one knows exactly how many meth labs there are in America, the paper uses those discovered by the police as a proxy for meth production (see map). They provide further evidence for their argument by noting that lifting the ban on selling alcohol would also reduce the number of emergency-room visits for burns from hot substances and chemicals (amateur meth-producers have a habit of setting themselves alight).