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Tobacco Use, Taxation and Self Control in Adolescence Jason Fletcher, Yale University Partha Deb, Hunter College and the Graduate Center, CUNY Jody Sindelar, Yale University and NBER Discussed by: Donna Gilleskie, Univ of North Carolina at Chapel Hill and NBER October 2-3, st Annual Health Econometrics Workshop

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We’ve just sent for a taxi to take us to the airport for our $2500 ‘Round-the-World’ trip. Ooh! I’ve just sent $2500 up in smoke this year.

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Authors’ Motivation Empirical Literature: – Is youth smoking behavior responsive to price? – Do different kids respond differently? by observable exogenous characteristics: lower responses for the poor, girls, white teens, younger teens by observable endogenous* characteristics: lower responses for previous smokers * Note this is important because the researcher has to model the unobservables that influence both lagged behavior and current behavior.

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Authors’ Motivation Theoretical Literature: – What model of behavior accurately characterizes youth smoking behavior? Rational kids influenced by addiction/habit Time-inconsistent kids (lack of self-control) Cue-triggered kids (some irrational behavior) Peer-influenced kids (other motivations) – Why does it matter? Different welfare effects.

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Authors’ empirical approach y isg = number of cigarettes smoked per day* by individual i in school s in state g The authors find a statistically significant tax effect: a 100% tax increase implies a 0.19 (OLS), 0.09 (poisson), or 0.11 (negbin) reduction in the number of cigarettes smoked per day. * Wave 1 Add Health data (on adolescents ages 12 to 21 in 1995)

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Exploring differential responses with a finite mixture model Suppose f(y i | x i, θ) does not adequately capture the tax effect. Rather, f 1 (y i | x i, θ 1 ) explains behavior better for some people and f 2 (y i | x i, θ 2 ) fits better for others. In general, we might suspect that f j (y i | x i, θ j ) best explains the behavior of j = 1, …, C distinct classes or subpopulations. Thus, the density of y i can be defined as a weighted mixture of many densities: weight j component model j

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How do the component models differ and what does the final mixture look like?

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How should we think about these C distinct classes and where do their weights (π j ) come from? C may have a direct interpretation – e.g., C = {male, female} C may have a broader interpretation – e.g., clusters of students C may depict a latent variable – e.g., degree of forward-looking behavior or impulsivity

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Use the data and the model to determine the posterior weight Bayes Rule: p(A|B) = p(A and B)/p(B) = [p(B|A) p(A)]/p(B) Prior probability of class membership Posterior probability of class membership

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They estimate a 2-class mixture model of negative binomial components. The weights for the 2 classes are: 0.87 and 0.13 One group reflects a statistically significant and negative response to tax increases: a 100% increase in taxes results in a decrease of cigarettes per day The other group’s response is not stat. significant. They characterize these groups of individuals as -a tax-responsive group (87%) -an unresponsive group (13%) Authors’ Findings

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The consumption of the two groups differ: 0.29 vs. 5.8 cigarettes per day How do these groups differ? Tax responsive group Unresponsive group * Predicted mean for each negative binomial component

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To investigate the differences in the groups, the authors estimate an OLS regression explaining the probability of being in the unresponsive group. – Include same set of x’s that explain consumption – Also include a measure of self control degree of making decisions by “going with your gut” – And a measure of time preference respondent’s prediction of surviving to age 35 – Also estimate using siblings only and include a family fixed effect In what other ways do the groups differ?

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Authors’ Contribution They identify differences in the responsiveness of youth to cigarette taxes, which has implications for the efficiency of taxation as a policy tool. Their data allow them to examine the role of psychological measures on smoking behavior. Their method of analysis allows them to evaluate the role of these measures in distinguishing the latent groups… and perhaps providing evidence against particular models of behavior.

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Suggestions for further study Unobserved attitudes toward smoking Different measures of smoking behavior Interactions of observable variables with tax Other modeling approaches – Allow for different effects of observables at different points of support of the distribution of the dependent variable – Model the unobserved heterogeneity

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Cigarette Prices, Taxes, and Smoking Rates Real State Tax Rate, 1984 cents/pack Real Prices, cents/pack Smoking Rate, % 18 yrs or older

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Cigarette Prices, Taxes, and Smoking Rates by State Real State Tax Rate, 1984 cents/pack Real Prices, cents/pack Smoking Rate, % 18 yrs or older

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Price Elasticities from a dynamic model of youth smoking behavior using NELS data ( ) Without state fixed effects With state fixed effects Source: Gilleskie, Donna and Koleman Strumpf. “The Behavioral Dynamics of Youth Smoking.” Journal of Human Resources 40(4), 2005, p In the authors’ cross sectional work examining state-level taxes, they can’t add state fixed effects. As a test, I added other state characteristics to the model. In another test, I included school fixed effects (s = 146). The significant tax effects disappeared in both cases for all models.

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Appropriate dependent variable?

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Distribution of cigarettes per day and days smoked in 30 days Marginal Marginal (0, 5](5, 20](20, 95] Cigarettes per day light moderate heavy light moderate heavy N = 5,050 out of 20,446 Compared to the authors N = 5,055 out of 20,497 Days smoked In last 30 (0, 5] (5, 20] (20, 30]

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Characteristics of the discrete data 25% are smokers Of the 20,479 observations 15% smoke greater than 2/day 5% smoke greater than 10/day 1% smoke greater than 20/day #/day if 30 days/month

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Might there be a more flexible way of modeling the density that allows for different effects of covariates at different points of support of y? ?

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But how do we estimate this conditional density? Determine cut points such that 1/K th of individuals are in each cell. Define a cell indicator Replicate each observation K times and create an indicator of which cell an individual’s observed expenditures fall into. Interact X’s with α’s fully. Estimate one logit equation (or hazard), Then, the probability of being in the k th cell, conditional on not being in a previous cell, is

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Conditional Density Estimation Gilleskie, Donna and Thomas A. Mroz. “A Flexible Approach for Estimating the Effects of Covariates on Health Expenditures.” Journal of Health Economics 23(2), 2004 Allows marginal effects of explanatory variables to differ at different points of support of the distribution of the dependent variable. Is very flexible with regard to shape of the distribution: does not require assumptions about the “underlying” distribution. Can include point masses such as zero expenditures or zero cigarettes, or even at non-zero points such as 1 pack or 2 packs, etc.

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Interact observable characteristics with the tax variable to capture different responses to tax changes Age Gender Race Parental income Family background Psychological measures Lagged behavior Peer behavior Authors’ variables:Additional variables: Other ways to measure differential responses? Estimate a random coefficients model y isg = δ 0 + α i log(tax g ) + β’X is + ε isg where α i =α + σ i

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But the authors’ point is… individuals might make different decisions based on unmeasured characteristics The mixture modeling approach allows the researcher to capture different responses without knowing the source of the heterogeneity. The discrete factor random effects approach does also! And the latter does not require distributional assumptions about the unobservables. And can be applied in a number of estimation models.

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Unobserved Heterogeneity Specification Permanent: rate of time preference, impulsivity Time-varying: unmodeled stressors ε e t = ρ e μ + ω e ν t + u e t where ε e t is the unobserved component for equation e decomposed into permanent heterogeneity factor μ with factor loading ρ e time-varying heterogeneity factor ν t with factor loading ω e iid component u e t distributed N(0,σ 2 u ) for continuous equations or Extreme Value for dichotomous/polychotomous outcomes, etc.

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Discrete Factor Random Effects a la Heckman & Singer (1983), Mroz (1999) Rather than estimate f(y i | x i, θ), estimate the density conditional on permanent unobserved heterogeneity μ

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Extensions to discrete factor random effects y isg = δ 0 + (α + ρ 1 μ )log(tax g ) + β’X is + ρ 2 μ + u t The researcher can specify a linear relationship across equations or allow for a non-linear relationship The unobserved heterogeneity can be interacted with the X’s

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Final remarks… It has been quite informative for me to read and study this paper. Thank you for the opportunity. It forced me to, literally, “get my hands dirty with the data” and actually estimate a finite mixture model. I look forward to seeing it in a journal so that others can learn from the authors’ work.

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