Currently, 23 states have legalized cannabis for medical use. Looking at the ten states with the largest populations that have legalized medical marijuana, Bernstein found in the year immediately following the legalization, per capita beer consumption went up by about 0.5 percent but then went back into decline.
"It is not a statistically proven thing and shows there isn't a major impact on beer from legalization of medical marijuana and if anything it could be positive," Stirling, one of the authors of the report said.
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Due to the short time that recreational weed has been legalized it is difficult to study a long-term view.
Craft beer to boom?
Bernstein also noted another interesting trend: Colorado - where cannabis is legalized - is the second biggest producer of craft beer, followed by Alaska, Delaware and Oregon which are all considering legalization.
"Industry observers point to the similarities of the craft beer and cannabis cultures and feel that legalizing weed could help craft beer grow sales while eating into the larger brewers' market share," according to Bernstein, adding that it's "far from clear if the potential linkages between weed and craft beer reflect causality or correlation."
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Many craft brewers have already embraced the weed buzz through clever marketing ploys. Oskar Blues has signs printed on cans showing how it can be turned into a bong for smoking the drug. Redhook Ale Brewery has released a beer called "Joint Effort" brewed with hemp seeds, but it does not contain the chemical in weed that causes someone to get high.
Alcoholic weed drinks?
While traditional brewers could certainly be under pressure, some analysts said that the whole drinks industry could feel the pain.
But the most innovative could find a tasty opportunity in the $1.5 trillion global alcoholic drinks industry.
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"There will be a degree of antagonism towards the brewers struggling to keep up with the cool factor," Spiros Malandrakis, alcoholic drinks analyst at Euromonitor, told CNBC by phone.
"But the combination of alcohol with weed in drinks could provide opportunities where the two industries could become symbiotic."
- By CNBC's Arjun Kharpal