"We found no evidence of intermediate-term effects of passage of state MMLs on the prevalence or frequency of adolescent nonmedical marijuana use in the states evaluated, with 2 minor exceptions. From 2003 through 2009, adolescent lifetime prevalence of marijuana use and frequency of daily marijuana use decreased significantly in Montana, as compared with a more modest decrease in lifetime prevalence and an increase in daily frequency observed in Delaware (Ps = .03). These 2 statistically significant findings do not appear to represent real effects. Our difference-in-differences study design involved 40 planned comparisons (before---after differences in treatment vs comparison states), and naturally 2 significant results (at the P < .05 level) of a possible 40 can be expected according to chance alone.
"Moreover, the pattern is not consistent with an effect of MMLs. A significant effect was found for lifetime marijuana use but not past-month marijuana use. Self-reported lifetime use requires a much longer recall period than past-month use and is characterized by higher measurement error.13 Also, one would expect the 30-day use measure to be more sensitive than lifetime use to the effects of a change in MMLs, because most of the period covered by respondents’ lifetime reports occurred before passage of an MML.
"Finally, the significant increase in daily marijuana use was observed for the comparison state of Delaware, which had not enacted an MML during the years under evaluation, whereas the frequency of daily marijuana use in Montana decreased. This is the opposite of
what would be expected if MMLs had the deleterious effect of increasing the frequency of nonmedical marijuana use.
"Conversely, the significant effects observed were found between the 2 states that differed the most on the timing of MML enactment, maximizing the length of the follow-up period. Hence, it is reasonable to suspect that enacting an MML may influence the prevalence and frequency of adolescent nonmedical marijuana use half a decade later, despite no evidence of more proximal effects."

Source

Sarah D. Lynne-Landsman, Melvin D. Livingston, and Alexander C. Wagenaar. 2013. Effects of State Medical Marijuana Laws on Adolescent Marijuana Use. American Journal of Public Health 103, 1500_1506. doi.org/10.2105/AJPH.2012.301117