Design
We used a quasi-experimental controlled interrupted time series (CITS) design (Lopez Bernal et al. 2017, 2019). Quasi-experiments are designs similar to randomized controlled trials, but without random allocation to treatment of control groups. Despite this, quasi-experimental designs (particularly the interrupted time series, or ITS) tend to have higher internal validity than observational studies given the exposures or treatments are exogenous (Biglan et al. 2000; Shadish et al. 2002). Including a control group further strengthens internal validity by accounting for history effects, while having longitudinal data helps addresses maturation bias (Bonell et al. 2011). CITS is an extension of both ITS and DiD, combining the benefits of both by making use of multiple timepoints before and after an intervention (ITS) and incorporating a comparison group that mimics the treated group’s counterfactual (DiD) (Lopez Bernal et al. 2017, 2019). One significant advantage of the CITS design is that non-time varying household factors (both measured and unmeasured) are accounted for (Lopez Bernal et al. 2017). In our study, time series for control units are included to model the counterfactual outcome of the treated unit in the absence of recreational cannabis legalization. Figure 1, adapted from Cook and Campbell (1979), illustrates this design.
Colorado, Oregon, and Washington were designated as policy states. A single control state was selected and paired with each policy state to improve internal validity. Control states were selected through graphical examination of purchasing trends and the strength of the Pearson correlation coefficient for purchasing between the policy state and control state pre-legalization. In the unrestricted sample, New Jersey served as a control for Colorado, Texas for Washington, and Virginia for Oregon. Because the trend in alcohol purchasing changed in the restricted sample, different control states were selected for the restricted sample; North Carolina was a control for Colorado, Illinois for Washington, and West Virginia for Oregon. In addition, we fit models in which all non-policy states (i.e., states that within the timeframe of this study had not legalized recreational cannabis) were treated as controls.
Data sources
Data were obtained from the Nielsen Consumer Panel, a dataset of U.S. households across all 50 states that provide information on their household demographics and the products they purchase. Participating households use in-home scanners to track all of their purchases, where and when they make purchases, and how much they pay for each product. Participants are randomly sampled proportionately based on county population, and are balanced across several household characteristics (e.g., income, education level). In addition, Nielsen provides sampling weights to project its sample to national, regional, and market area levels. Approximately 80% of participating households remains in the panel from 1 year to the next. Each year, the consumer panel consists of between 40,000 and 60,000 households. Using data from 2004 to 2017, two samples were created: a unrestricted sample of households (hereafter referred to as the “unrestricted sample”), including those that may have left the panel prior to legalization or joined following legalization; and a sub-sample, hereafter referred to as the “restricted sample,” that was restricted to households with data both prior to and following legalization. This restricted sample was analyzed because some households may drop out or enters the Nielsen Consumer Panel immediately following legalization (and thus would not contribute data pre-policy or post-policy, respectively). Prior studies on this topic have employed a range of designs (including cross-sectional), however, having data on the same households over a period of time may be better for measuring substitution/complementarity (Subbaraman 2016). Our unrestricted sample consisted of 178,232 individual households across the USA with varying amount of years spent as part of the panel. The restricted sample consisted of 69,761 individual households.
Measures
Alcohol purchasing
Data from the Nielsen Consumer Panel dataset includes information on individual alcohol products purchased and the volume of each individual beverage. A previous validation study of the quantity purchased measurements in the Nielsen Consumer Panel found them to match with sales record data 94% of the time (Einav et al. 2010). We used these data to construct measures of monthly alcohol purchased by each household. To calculate our outcomes, we multiplied the number of beverages purchased by the volume of the product, separately for beer, wine, and spirits (spirits are also referred to as liquor, or alcoholic beverages with higher alcohol content than wine or beer). We then multiplied this by a static proportion that represented the average amount of ethanol in a product for each type of alcoholic beverage. These values (0.05 for beer, 0.40 for liquor, and 0.13 for wine) are based on the American Epidemiologic Data System, where the average proportion of ethanol is 0.045 for beer, 0.411 for liquor, and 0.129 for wine (Doernberg and Stinson 1985). We then aggregated across month and state to create a measure of monthly pure ethanol purchased for each state in milliliters. We also constructed three additional outcome variables for specific types of alcoholic beverages. These outcomes were the pure ethanol purchased of beer, of wine, and of spirits. Because distributions of ethanol purchased across all three beverage types were skewed, we applied a natural logarithmic transformation to each. Estimates were then exponentiated to back-transform them for ease of interpretation.
Legalization of recreational cannabis
We included binary variables that indicated legalization of recreational cannabis for the three policy states: Colorado, Washington, and Oregon. These variables were coded as a 0 before the date of legalization, and a 1 on and after the date of legalization. For example, legalized recreational cannabis in Colorado went into effect on December 10, 2012. The indicator for legalization in Colorado was coded as a “0” for January 2004 through November 2012, and a “1” for December 2012 through December 2017. In a difference-in-difference model, this represents the “time” variable. We also created an indicator variable for “policy” states versus “control” states, which serve as the “treated” variable. Colorado, Washington, and Oregon were coded as a “1” while all other states, which served as potential comparators for the controls, were coded as a “0.”
Household characteristics
Four of the household measures recorded in the Nielsen Consumer Panel were included to adjust for any imbalances between policy and control states: household income, household size, marital status, and race. These characteristics were selected based on their expected impact on alcohol purchasing both prior to and following legalization of recreational cannabis, while also being likely unaffected by the policy change itself. Substance use and purchasing can vary across levels of income and social inequality (e.g., structural racism) (Bailey et al. 2017; D. R. Williams and Mohammed 2013). Thus, we included household income levels and race (a proxy for racism) in our models. Marital status serves as a proxy for social support. Marital status has shown to be an important predictor of alcohol use (Leonard and Rothbard 1999). The size of the household was included to account for households with multiple adult residents who purchase alcohol, and differences between households with multiple purchasers versus households with a single resident. Household income was measured by 11 categories (ranging from < $5,000 per year to over $200,000). Household size measured the number of individuals living in the household in 9 categories (from 1 to 9 or more). Marital status was measured as whether the heads of household were married, widowed, divorced/separated, or single. Race was measured as whether the household was primarily White, Black, Asian, or a different racial identity.
Analysis
First, we calculated descriptive statistics of the households in our analytic sample from January 2004 to December 2017. Each of the measures is presented as weighted averages by incorporating the frequency weights that were included in the Nielsen Consumer Panel. These weights are updated each year and correct for selection bias in sampling of households. The sum of these weights is equal to the total number of U.S. households.
To estimate the relationship between recreational cannabis legalization and alcohol purchasing over time, we used fixed effects linear regression models with an interaction term for legalization of recreational cannabis (binary) and policy/control state (binary) as the test of our primary hypothesis, commonly referred to as difference-in-difference models. This modeling approach was chosen over random effects (or “mixed models”); random effects models offer no important benefits over fixed effects in this context but are vulnerable to violation of the random effects assumption (and consequently produce biased effect estimates). The basic structure of our DiD models is illustrated below:
$${Y}_{ijt}={\beta }_{0}+{\beta }_{1}{Treated}_{j}+{\beta }_{2}{Policy}_{t}+{\beta }_{3}{Treated}_{j}\mathrm{*}{Policy}_{t}+{\beta }_{4}{V}_{ijt}+{\varepsilon }_{ijt}$$
Yijt represents the outcome for household i in state j at time t; Treatedj is an indicator for whether or not a state ever legalized recreational cannabis; Policyt is an indicator for the time t when recreational cannabis has been legalized (this value matches between for households in policy and control states in each model); Vijt is a vector of household-level time-varying covariates. The coefficient β3 for the interaction term between Treated and Policy is the effect estimate of interest and represents the change in alcohol purchasing before versus after recreational cannabis legalization in a given policy state compared to the control state (or states).
We fit separate models for each policy state compared to a matched no-policy state, and models for each policy state compared to all no-policy states. We did this for both the unrestricted sample of households as well as the restricted sample (restricted to households with observations prior to and following legalization). We fit separate models for each policy state because policy implementation dates were staggered (i.e., occurred on different dates); including the three policy states together in one model would induce bias in regression estimates (Goodman-Bacon 2018). Fixed effects for time were included to account for seasonality and time trends. Standard errors were adjusted for clustering at the household level using an extension of the Huber-White sandwich estimator to generate robust cluster standard errors. This can be accomplished using the vce(cluster) option in Stata (Williams 2000). All analyses were done using Stata version 16.
