birth year, to further control for state-specific time trends. Some “long” models included other control variables, including family history of alcohol problems, state beer taxes when the respondent was 18, and state per capita alcohol consumption when the respondent was 18. The ‘longest’ models tested whether a few potential mediating variables – such as age of onset of regular drinking, educational attainment, current marital status or presence of young children in the home – seemed to explain the association between legal purchase age and later substance use problems. We also compared interaction terms in both probit and logit models to test for additive or multiplicative interactions between MLDA exposure and gender, race, survey, age at assessment, parental alcohol problems, early versus later cohort, and onset of own drinking before or after age 16. Age-restricted models were limited to respondents living in the 39 states with changing MLDA laws, and included separate indicators for early and later cohorts for each state. In each of these models, the coefficient of interest is bMLDA, which captures the average effect of legal purchase age on the outcome of interest.
