Abstract
Highlights
This study estimates lifetime drinking trajectories from adolescence to old age in the United States.
The model uses national survey datasets to simulate real-world alcohol use patterns over time.
Underage alcohol consumption is common in the United States and can lead to harmful outcomes. 1 The 2023 National Survey on Drug Use and Health found that 14.6% of youth ages 12 to 20 y reported past-month alcohol use. 2 This continues a long-term downward trend in adolescent drinking over the past decade. Parallel findings from the 2023 Monitoring the Future survey show that past-year alcohol use among 12th graders fell from 73% in 2001 to 46% in 2023 and declined from 65% to 31% in 10th graders (and from 43% to 15% in 8th graders) over the same period. 3 However, given the adverse effects of underage drinking, the current rate of adolescents drinking alcohol remains of concern for policymakers. 4 Each year, excessive drinking causes more than 3,500 deaths and 225,000 y of potential life loss among people younger than 21 y of age. 5 In 2019, 29% of high school students drank alcohol, 14% were binge drinkers, 5% drove after drinking alcohol, and 17% rode with a driver who had been drinking alcohol during the past 30 d. 6 Adolescent alcohol use has been linked to death by suicides, motor vehicle crashes, homicides, alcohol overdoses, falls, burns, and drowning7–13 and to unsafe sexual behavior. 14 Given these harmful outcomes, many studies have explored interventions to reduce adolescent drinking. 15
When evaluating adolescent drinking intervention programs, there is a significant research gap in determining long-term outcomes. As the benefits of alcohol treatment accumulate over a long period, evaluating them in the short term will underestimate expected health outcomes and overestimate cost and uncertainty. 16 Previous studies have not examined drinking behavior in the United States from adolescence to old age. One possible reason could be the lack of available longitudinal studies that track people from adolescence to old age since these studies are time-consuming and expensive. 17 Connecting information from multiple data sources (i.e., National Longitudinal Survey of Youth [NLSY] and National Survey on Drug Use and Health [NSDUH]) could be a possible solution to overcome these limitations.
This article addresses the need to develop lifetime drinking trajectories of alcohol use from adolescence to old age using a 3-step approach that incorporates longitudinal and updated cross-sectional data to calculate transition probabilities for different drinking levels from adolescence to old age. To estimate transition probabilities, we used 2 nationally representative surveys, the NLSY and NSDUH. A better understanding of lifelong trajectories of alcohol consumption will support a model that can be used for cost-effectiveness analysis that encompasses the broader impact of adolescent alcohol interventions over a lifetime.
Methods
Overview
The study used a 3-step process to model the development of long-term drinking patterns, focusing on estimating transition probabilities among 6 states: abstinence, alcohol dependence, and the 4 World Health Organization (WHO)–defined alcohol risk states of low, medium, high, and very high risk, as illustrated in Figure 1. The transition probabilities were calculated across different demographic groups categorized by age and sex. For men, the WHO defines very high risk as >100 g/d or >7.1 US standard drinks, high risk as >60 to 100 g/d or >4.3 to 7.1 drinks, moderate risk as >40 to 60 g/d or >2.9 to 4.3 drinks, and low risk as 1 to 40 g/d or 1 to 2.9 drinks. For women, very high risk is defined as >60 g/d or >4.3 standard drinks, high risk as >40 to 60 g/d or >2.9 to 4.3 drinks, moderate risk as >20 to 40 g/d or >1.4 to 2.9 drinks, and low risk as 1 to 20 g/d or 1 to 1.4 drinks. 18

Transitions between different health states related to drinking behavior. Each circle in the diagram represents a distinct and mutually exclusive state of drinking behavior. The arrows connecting these circles indicate the potential movement of individuals between these states over time.
Although the Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM-5) has replaced the discrete states of alcohol abuse and dependence form the DSM-IV with a continuum of symptoms across mild, moderate, and severe alcohol use disorder, we chose to incorporate the health state of dependence in our model for 2 reasons. The first is purely practical: DSM-5 symptoms of alcohol use disorder are not fully incorporated into our data sources for all the years that we need, but symptoms of DSM-IV dependence are. The second reason is to better connect our model to International Classification of Diseases, 11th revision, diagnostic categories, 19 which include codes for hazardous alcohol use (primarily determined by consumption patterns), harmful alcohol use (determined by both consumption patterns and evidence of associated physical or mental harm), and alcohol dependence. Alcohol dependence is incorporated in our model by looking at the prevalence rate of alcohol dependence in all 4 WHO drinking categories in the general population of the United States. Each state is mutually exclusive: the “alcohol dependence” state comprises only those meeting DSM-IV criteria and excludes all other risk-level categories.
Step 1 of our approach uses Bayesian simulation to calculate initial transition probabilities 20 based on longitudinal data on a cohort of youth. In step 2, the probabilities are calibrated using simulated annealing21–23 so that the calculated transition probabilities simulate a distribution across states that match the distribution observed in recent national surveys. In step 3, the calibrated transition probabilities are validated against a dataset not used in steps 1 or 2 using a χ2 test.
Data
We used the National Longitudinal Survey of Youth 1997 Cohort (NLSY97) 24 and National Survey on Drug Use and Health (NSDUH) 25 from 2013 to 2017 for Bayesian simulation and calibration of transition probabilities. NLSY97 is a stratified, nationally representative sample of 8,984 respondents born from 1980 to 1984, interviewed annually from 1997 to 2011. NLSY97 provides consistent age-specific self-reports of 5 drinking states (abstinent, low risk, medium risk, high risk, and very-high risk) across ages 12 to 35 y, enabling direct computation of the transition rates. We used the unweighted sample of NLSY97 since the data were used in our Bayesian simulation, and the likelihood was conditioned on the observed sample. i
In addition to the longitudinal NLSY97, we used the cross-sectional NSDUH. The NSDUH is an annual, cross-sectional survey designed to produce reliable estimates of substance use and mental health indicators for the US civilian, noninstitutionalized population aged 12 y and older. Each year, it samples roughly 67,000 respondents using a multistage area-probability design with stratification and clustering, covering all 50 states and the District of Columbia. We used NSDUH 2013 through 2017 for calibration and NSDUH 2018 for validation. When calculating the initial transition probabilities, we do not use the sampling weights from the NLSY97 data, but we do use the sampling weights from the NSDUH for calibration and validation. The weighted NSDUH data served as our “target” prevalence for calibration purposes, ensuring that the estimated transition probabilities align with national prevalence estimates.
In addition to stratifying all transition-probability estimates by age and sex—given well-documented differences in alcohol use initiation and progression—we explored including other demographic covariates available in NSDUH and NLSY97 (race, ethnicity, socioeconomic status, and geography). However, further stratification by these factors introduced sparse data within certain subgroups and substantially increased the computational complexity of the 6-state transition probabilities. Table 1 presents a summary of the demographic characteristics of adolescents obtained from the data sources.
Summary of Demographic Characteristics of Adolescents
NLSY97 estimates are unweighted; NSDUH estimates are weighted.
Step 1: Calculation of Transition Probabilities
We used the NLSY97 to determine the transition rates between abstinence and the 4 WHO alcohol risk states. We extracted information about the current and previous year’s drinking levels for each individual from 1997 to 2011. Next, we calculated age- and sex-dependent transition rates between drinking states (Appendix 1). Because the NLSY97 does not include information on alcohol dependence, we incorporated information on the prevalence of alcohol dependence among different age and sex groups from the 2013 to 2017 NSDUH (Appendix 2) using the Bayesian simulation technique suggested by Briggs et al. 20 for incorporating unobserved health states into Markov models. To calculate the transition probabilities, we set the alcohol dependence prevalence information from NSDUH samples as prior. All transition probabilities were estimated under a first-order Markov assumption, meaning that an individual’s chance of moving to any drinking state in year t+ 1 depends only on their state in year t, not on their earlier history. 26 We assume that the 1-y transition from abstinence to alcohol dependence is zero. This reflects DSM-IV, which requires 3 or more dependence symptoms within a 12-mo period (e.g., tolerance, withdrawal) and therefore presupposes recent drinking. 27 The Bayesian simulation calculated transition probabilities between all states except transition probabilities from alcohol dependence to other states.
The existing literature lacks specific information on the recovery rate of individuals aged 12 to 17 y from alcohol dependence. 28 Previous studies primarily report outcomes such as abstinence or nonproblematic drinking. 28 However, it is important to note that recovery from alcohol dependence does not require total abstinence: individuals may no longer meet dependence criteria yet still drink at risky levels. 29 Given the absence of data on alcohol dependence recovery in the 12- to 17-y age group, we have chosen to use a “vague” or minimally informative prior distribution. 30
For ages 18 y and older, transition probabilities for the dependence state were taken from Dawson et al. 31 They used NESARC wave 1 and 2 data sets to calculate recovery from alcohol dependence over 3 y in 3 categories: still dependent, abstinent recovery, and nonabstinent recovery. 31 The 3-y transition probabilities were first converted to rates and then to 1-y transition probabilities. 30 Since the model has 4 nonabstinent states, we divided the transition probability to a nonabstinent state by 4.
Step 2: Calibration of Transition Probabilities
We used the transition probabilities from step 1 to generate a distribution of individuals across the 6 health states in our model, considering various age groups from 12 to 65+ y, separately for males and females. Subsequently, we computed the root mean square error to quantify the deviation of the simulated distribution from the average distribution reported in the NSDUH 2013 to 2017 datasets, encompassing all age groups. We then used simulated annealing to calibrate the transition probabilities to minimize the root mean square error. We fitted these probabilities to Dirichlet distributions based on the estimated transitions and sample size to account for uncertainty in transition probability estimates. The choice of sample size is critical because it directly affects the width of the uncertainty intervals. When estimating transitions from larger samples, such as those originating from the abstinent state, the resulting intervals become narrower, indicating higher precision of estimates. We used the Dirichlet distribution, which is a multivariate extension of the beta distribution, following best practices for quantifying uncertainty in scenarios involving multinomial data, in which transitions between more than 2 states are considered.20,30,32 We generated 1,000 iterations of each transition matrix using this distribution and then derived the mean and standard deviation of the transition probabilities from the resulting matrices.
Step 3: Validation
A critical aspect of developing a model involves verifying that the model’s predictions align with information from other data sources that describe the model’s outcomes, such as data on the prevalence of the disease. 23 To validate the calibrated transition probabilities, we used χ2 tests to assess whether the simulated distribution of drinking-state categories, generated by our calibrated transition probabilities, matched the weighted distribution observed in NSDUH 2018. This independent cohort was not used to calibrate transition probabilities. If we determined that the 2 distributions were still significantly different after the calibration process, then we repeated the calibration process by changing the search space (i.e., upper and lower bounds) of the algorithm until we found a good fit (i.e., not significantly different) for most of the age groups.
Cohort Initialization and Simulation
Using these transition probabilities, we simulated a cohort of people across drinking states by age and sex. We applied our age- and sex-specific transition probabilities to a cohort of 12-y-olds with a starting drinking state distribution similar to the average of NSDUH 2013–2017: for females 99.23% in the abstinent state, 0.38% in low-risk drinking state, 0.17% in the medium-risk drinking state, 0.06% in the high-risk drinking state, 0.07% in the very high-risk drinking state, and 0.09% in the alcohol dependence state; for males 99.34% in the abstinent state, 0.53% in low-risk drinking state, 0.06% in the medium-risk drinking state, 0% in the high-risk drinking state, 0.04% in the very high-risk drinking state, and 0.03% in the alcohol dependence state. We then ran the model until the cohort was 65 y old.
Results
Transition Probabilities
On average, remaining in the same state from one year to the next has a higher probability than moving to another state. The likelihood of remaining in abstinent, low-risk, and alcohol-dependent states is higher compared with the probabilities of staying in the medium-, high-, and very-high-risk states. These findings are consistent with previous research on alcohol outcomes. 32 A systematic review of studies on the reasons people choose to be abstinent found that health concerns, fear of academic or legal consequences, and personal convictions are the most commonly cited reasons for not drinking. 33 Likewise, broader societal shifts—such as evolving parenting styles, peer-to-peer social media awareness campaigns, and targeted public health messaging on underage drinking—have been identified as key mechanisms driving recent cohort declines in youth alcohol use and reinforcing moderation norms. 34 Alcohol dependence often persists because symptoms such as tolerance, withdrawal, and craving make a swift change unlikely. 35 Because medium-, high-, and very-high-risk drinking lack the stabilizing social norms that support abstinence or low-risk use and the clinical persistence typical of dependence, these states are more fluid, with movement upward or downward shaped by environment and policy. From Figures 2 and 3, we see that females in general have a higher likelihood of remaining in the abstinent state than their male counterparts do. In the United States, women often face stronger social sanctions for drinking, which reinforce decisions to abstain. 36 Details of transition probabilities by age group and sex can be found in Appendix 4.

Average transition probabilities for the male population. The vertical bars represent the 95% confidence interval.

Average transition probabilities for the female population. The vertical bars represent the 95% confidence interval.
Simulated Distribution
Figures 4 and 5 show the distribution across alcohol use states by age. As the cohort gets older, the percentage in abstinent states decreases slowly until age 21 y for both males and females. When both cohorts reach the US legal drinking age of 21, there is a sharp decrease in the proportion in the abstinent state. After age 21, the proportion of males in the abstinent state remains almost the same until age 30 and then steadily increases. After age 21, the proportion of females in the abstinent state starts to increase but is still smaller than in adolescent years.12–20 The percentage of the population in the medium-risk drinking state increases until age 21 and after age 30 gradually decreases. For high risk, very high risk and alcohol dependence, the percentage of the population increases until age 21 to 23 and then slowly decreases. This trend is similar for both males and females. The percentage of people in the abstinent state at age 65 is higher for females than for males. Both the male and female percentage of the population in the low drinking states steadily increases across all the age groups, but the male population has a higher percentage at age 65.

Simulated distribution of the male population from age 12 to 65 y across all drinking states.

Simulated distribution of the female population from age 12 to 65 y across all drinking states.
The sharp drop in abstinence at age 21 y reflects the removal of the structural barrier of the minimum legal drinking age and the corresponding increase in availability and social opportunity to drink. In contrast, the stabilization and rebound in abstinence after the mid-20s are consistent with “maturing out” effects tied to life-course role transitions such as stable employment, marriage, and family formation, which reduce risky use. 37 The rise and peak in medium, high, very-high risk, and dependence in early adulthood likely capture delayed escalation during identity exploration and increased peer influence, 38 with subsequent declines reflecting “maturing out” via role transitions and normative pressures,37,39 accumulating negative consequences and health concerns prompting reductions 39 and natural recovery dynamics. 40 Women’s higher abstinence at older ages likely reflects stronger social norms and gendered expectations discouraging female drinking, greater biological sensitivity to alcohol’s adverse effects that raises perceived costs, and masculine norms among men that normalize heavier use, combining to make sustained abstinence more common among older women than men.41–43
Model Validation
Based on χ2 tests (Appendix 8), across all age groups, we fail to reject the null hypothesis that there is no difference between the simulated and real distributions. This suggests that the transition probabilities have generated a simulated distribution that replicates real-world outcomes for all age groups.
Example Case
To better understand and illustrate the model results, we ran the model on a simulated cohort of 1,000 males and 1,000 females from age 12 to 65 y. Figures 6 and 7 depict different transitions from one drinking state to another for males and females, respectively. The cohorts started in the abstinent state at age 12. For both male and female cohorts, most stayed in their initial state after 1 period. Apart from remaining in the same state, people mostly moved to adjacent states. For example, the number of people transitioning from a low drinking state to an abstinent or medium drinking state was higher than the number transitioning from a low drinking state to a high, very high, or dependence across all age groups. This means most of the people who moved to the dependent state were from very-high- and high-risk drinking states. This pattern of transition was observed across all states except for dependence. In most cases, dependent people either remain dependent or move to the abstinent state. The fact that most transitions into dependence originate from high- and very-high-risk states—while individuals in the low-risk state more often move to abstinence or adjacent moderate states—supports stage-based and threshold progression models of alcohol use rather than abrupt jumps, consistent with hierarchical development frameworks of problematic drinking.44,45 More details about transitions from one state to another are provided in Appendix 9.

Transition from one state to another across different age groups for the male cohort.

Transition from one state to another across different age groups for the female cohort.
Discussion
Adolescent drinking is a costly public health issue, both in terms of immediate consequences such as accidents and injuries and long-term implications such as addiction and chronic health problems. Despite its significant societal and economic burden, research addressing this issue is often constrained by the absence of comprehensive lifetime models. Such models are crucial for understanding the long-term trajectory of alcohol use initiated during adolescence and for evaluating the effectiveness of early interventions. However, developing lifetime models is inherently challenging because the necessary longitudinal data tracking drinking behaviors and outcomes across an individual’s life are rarely available.
In this article, we overcome missing data issues regarding alcohol dependence and concerns over the age of longitudinal data by using Bayesian simulation to incorporate information on the current prevalence of alcohol use states, including dependence, from recent NSDUH datasets with health state transition rates obtained from the much older NLSY97 dataset. The NLSY97 tracks people’s drinking behavior annually from age 12 y in the United States, but it does not have information regarding alcohol dependence. 24 Another limitation of the NLSY97 is that it tracks a specific cohort from 1997, which may not fully capture the evolving drinking behaviors and influences affecting more recent cohorts of adolescents. More recent cohorts of adolescents have a different drinking pattern from the 1997 cohort due to period and cohort effects. 46 For example, rising public health awareness on social media—through peer-created posts, influencer messages, and targeted campaigns—has helped to delay initiation and reduce alcohol consumption overall. 47 As a result, relying on only NLSY97 may not produce an accurate picture of adolescents’ long-term drinking behavior. Updated drinking patterns, including alcohol dependence information, are available in the NSDUH datasets. 25 However, NSDUH datasets are cross-sectional and thus do not follow the same cohort each year, limiting the ability to track changes in drinking behavior as a cohort gets older.
To overcome these data limitations, we used simulated annealing to calibrate the transition probabilities obtained from the Bayesian simulation, targeting more current NSDUH distributions, to achieve a good fit and validated our simulated distribution by comparing it with an independent cohort of NSDUH that was not used for estimating transition probabilities. Our results align with the existing literature on long-term drinking patterns. We found that adults reduce their drinking level as they grow older, as found in previous studies. 48 In our study, we observed a significant decline in the percentage of individuals in the abstinent state at age 21 y, coinciding with the legal drinking age, also found in previous studies. 49 Transition probabilities estimated in this study are based on pre-COVID datasets. As a result, they do not necessarily reflect during and postpandemic drinking behavior. However, our approach allows the transition probabilities to be updated when new datasets are available. Although these transition probabilities are for only the general US population, our approach can be used to develop transition probabilities for the general population of other countries with appropriate data.
This article makes 2 important contributions. First, we present a method that can be used for other health behaviors to overcome common data limitations when estimating transition probabilities: missing data on key health states and outdated longitudinal data. We leverage established statistical and simulation techniques to demonstrate how to calculate transition probabilities using data from 2 national-level surveys. Following this method, we can calculate transition probabilities for another type of harmful behavior such as tobacco use or other substance use for adolescents by using information from these 2 national-level data sets. Our study offers a pathway for future research to estimate transition probabilities for a wide range of public health concerns, enabling more robust policy evaluations and intervention designs.
Second, the transition probabilities derived in this study enable the extension of drinking trajectories from adolescence into old age, allowing for a more complete understanding of long-term alcohol consumption patterns and their consequences. Traditional studies on adolescent drinking interventions tend to focus on short-term effects, often measuring outcomes only a few years after treatment. However, alcohol consumption is a dynamic behavior that evolves over a lifetime, and the health and economic consequences of adolescent drinking may not fully manifest until later in adulthood. By developing long-term drinking trajectories, our study provides a way to assess how early-life drinking behaviors influence future drinking patterns and the risk of developing alcohol use disorders.
Importantly, the transition probabilities estimated in this study can be incorporated directly into policy-simulation models to quantify the long-term impact of real-world interventions. For example, one could simulate how a $1 increase in alcohol excise taxes alters age-specific transition hazards, leading to reductions in lifetime alcohol use disorder incidence and increases in recovery rates. Likewise, raising the minimum legal drinking age by 1 y could be modeled by shifting the transition matrix for late adolescence, allowing forecasts of delayed dependence onset and extended abstinence. School-based prevention programs or campus alcohol-policy changes could similarly be evaluated by adjusting the relevant adolescent transition probabilities. By linking these micro-level state-to-state transitions with macro-level policy levers, our framework provides a powerful tool for policymakers to project both the health benefits and economic returns of alcohol control strategies.
A long-term perspective is essential for evaluating the cost-effectiveness of adolescent alcohol interventions, as short-term assessments may underestimate their full benefits. While many public health initiatives focus on immediate outcomes, such as reducing underage drinking rates within a few years, our approach allows researchers and policymakers to estimate the broader economic impact of early interventions. By tracking individuals’ transitions through different drinking states over decades, we can quantify potential long-term savings in health care costs, increased productivity, and reduced criminal justice expenditures. Furthermore, integrating drinking behaviors into lifetime health economic models enhances resource allocation decisions and strengthens connections between intervention studies and broader public health planning. This framework also provides a predictive tool for assessing the impact of policy measures, such as raising the minimum legal drinking age, implementing school-based prevention programs, or expanding access to treatment for young adults, ensuring that interventions account for both immediate and long-term societal benefits.
This study has 3 key limitations. First, we lacked prior information on recovery from alcohol dependence to other drinking states among adolescents; as a result, we imposed a vague prior and set the probability of transitioning form abstinent to dependent to zero under a first-order Markov assumption, which treats lifetime abstainers and individuals in recovery identically and cannot capture rapid relapse directly into dependence. Consequently, those transition probabilities may not reflect reality, and although modeling additional health states (e.g., a distinct “recovered” category) could better represent dependence intensity and relapse dynamics, it is precluded by current data constraints.
Another limitation is that although we estimated transition probabilities based on age and sex, we did not consider the roles of race, geography, religion, or other demographic characteristics, thus restricting the model’s overall utility and applicability to only the general population. These factors can influence both baseline drinking patterns and transition dynamics, potentially biasing subgroup forecasts. Future research should leverage larger pooled samples or region-specific surveys to estimate and validate transition probabilities within these demographic strata, thereby improving equity relevance and generalizability.
The final limitation is that extrapolating a cohort from age 12 to 65 y under a first-order Markov structure embeds expected developmental patterns but assumes stable transition dynamics; unforeseen period shocks (e.g., pandemics, economic crises) and individual-level heterogeneity limit the precision of lifetime predictions, and future work should explore methods to accommodate nonstationarity or incorporate time-varying external influences.
Despite these limitations, the transition probabilities estimated in this study can be integrated into long-term simulation models to evaluate the cost-effectiveness of adolescent drinking interventions. By linking drinking trajectories with alcohol-related mortality and morbidity data, these probabilities enable a more comprehensive assessment of the long-term consequences of adolescent alcohol use. Incorporating appropriate cost and QALY estimates, they can be used in a long-term decision-analytic model to inform policymakers on the benefits of early interventions, support efficient health care resource allocation, and guide public health strategies aimed at reducing adolescent drinking-related harm. Future research should not only stratify transition probabilities by demographic strata (e.g., race/ethnicity, socioeconomic status, and geography) but also unpack the mediating pathways—such as neighborhood disadvantage, social norms, stress exposure, access to care, and enforcement intensity—through which these factors operate, using causal inference tools to bridge descriptive patterns with underlying causal mechanisms. Finally, cause-based stratification (e.g., early initiation/early heavy drinking) and history-augmented states should be added to contrast an early-onset, fast-escalation pathway with a gradual, dose-dependent pathway, linking these to age-specific patterns.
Supplemental Material
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Footnotes
Acknowledgements
The authors thank William Dowd (RTI International) for his valuable guidance on the simulated annealing process used in this study.
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors received no financial support for the research, authorship, and/or publication of this article
Authors’ Note
This research was presented at the following meetings: 1) The International Network on Brief Interventions for Alcohol & Other Drugs (INEBRIA) 2023 Conference, (2) The International Society for Pharmacoeconomics and Outcomes Research (ISPOR) 2024 Conference; and (3) The Southern Economic Association (SEA) 2024 Annual Meeting.
Ethical Considerations
This study involved a secondary analysis of publicly available, deidentified data from the National Longitudinal Survey of Youth 1997 (NLSY97) and the National Survey on Drug Use and Health (NSDUH) and did not involve any direct contact with human or animal subjects. As such, it was exempt from Institutional Review Board oversight. No ethics approval was required.
Consent to Participate
Not applicable.
Consent for Publication
Not applicable.
Data Availability
The data used in this study are publicly available and can be accessed through the following sources: NLSY97: US Bureau of Labor Statistics (https://www.bls.gov/nls/nlsy97.htm) and NSDUH: Substance Abuse and Mental Health Services Administration (
). The analytic code used in this study (including Bayesian simulation and calibration routines) will be made available upon reasonable request to the corresponding author.
Notes
References
Supplementary Material
Please find the following supplemental material available below.
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