It seems unlikely that the decrease in tobacco-related harm is strongly proportional to the reduction in tobacco consumption. I base this on an article in Circulation about the adverse health effects of light or intermittent smoking. In particular:
Light and intermittent smoking carry nearly the same risk for cardiovascular disease as daily smoking. The dose-response relationship between tobacco exposure and cardiovascular mortality is highly nonlinear. . . . [L]ow levels of tobacco exposure as seen in light smoking (4 to 7 cigarettes per day) has ≈70% of the effect of heavy smoking (≥23 cigarettes per day).
Reduction in consumption can be both an individual and societal measure and measured via both outright quitting and reduction of cigarettes consumed per day (to a non-zero number). My focus here is on quitting at the societal level and I have been basing it on using price elasticity to measure taxation’s effects on population prevalence of smoking, which would be unaffected by your concerns.
However, I dug deeper into the mechanics of these price elasticities numbers, and it appears some can be measures of cigarette sales (i.e. general reduction of consumption) and others measures of smoking prevalence in the population (i.e. quitting or not initiating).
I am still working my way through this information, so I don’t have a full informed view yet, but here (at the bottom of this comment) are some things that caught my eye in the NIH’s Tobacco Control Monograph’s section on “Using Price Elasticity Estimates to Project the Future Impact of Tobacco Tax Increases.”
This has important implications because:
Charity Entrepreneurship’s model (which mine and Moritz’s is based off of) translates price elasticity into a reduction of consumption which is then translated 1:1 for reduction in prevalence.
Open Philanthropy’s model (which also uses hinges on price elasticity) assumes the reduction in consumption has 1:1 effect with reduction in DALYs.
So the CE model is solid so long as the median price elasticity used (for LMICs) reflects the average of price elasticities calculated on prevalence.
Both models are vulnerable regardless to overestimating the DALYs averted from prevalence change if the people that go onto quit/not initiate were disproportionately less of the DALY burden. A reason to believe that was the case is that smokers that smoke less cigarettes are more likely to quit. (This though is also reason to be less concerned with your original point about the nonlinear association between harm and consumption i.e. even if they don’t quit, taxes put them in a closer position to quitting in the future)
However, buffering the above for the CE model is that it’s not capturing DALYs averted for reduced consumption that is short of quitting—a source of underestimating the impact.
The Open Phil model has issues regardless because it applies reduction in consumption to 1:1 reduction in DALYs without mapping out quit/prevalence rates, which as you rightly point out are likely not interchangeable with just reducing the non-zero amount you smoke each day.
And both models might have significant overestimation if their price elasticity numbers are reflections of cigarette sales instead smoking prevalence.
Quotes of interest from the monograph
These and other projections generally start with the overall price elasticity of cigarette demand, typically obtained from econometric estimates based on tax-paid cigarette sales data, and assume that the tax increase being modeled will be fully passed on to consumers in the price paid for cigarettes.
It is also important to use both adult and youth prevalence elasticities in projecting the public health impact of a cigarette tax increase because youth and adults are not equally price sensitive.
Similarly, adult and youth prevalence elasticities are used in projecting the public health impact of a cigarette tax increase. Given the available estimates, many of these projections assume that the impact on adult prevalence is half of the overall elasticity and that youth uptake of tobacco use is two to three times as responsive to price. When projecting the impact on youth, these projection models often assume that young people will take up smoking at the same rate as adults or young adults have. Continuing the example above, if the state has one million adults and adult smoking prevalence is 20% (200,000 adult smokers), the US$ 1.00 tax increase will reduce the prevalence of adult smoking by 4%, or induce 8,000 adult smokers to quit smoking. If there are 500,000 young people in the state, and it is assumed that they will take up smoking at the same rate as adults have and youth smoking is twice as sensitive to price, then the US$ 1.00 tax increase maintained over time in real terms will prevent 8,000 young people from taking up smoking.
Econometric studies of the impact of tax and price on tobacco use employ two primary measures of tobacco use: (1) macro-level aggregate measures of consumption, such as country-level data on tobacco sales (this literature developed earlier, growing rapidly before the 1990s); and (2) household or individual-level data taken from surveys, such as national surveys of drug use or health risk behavior.
Additionally, studies have assessed the impact of tax and price on specific outcomes, such as prevalence of tobacco use, smoking cessation, initiation of smoking by youth, cross-price elasticity, and health outcomes.
It seems unlikely that the decrease in tobacco-related harm is strongly proportional to the reduction in tobacco consumption. I base this on an article in Circulation about the adverse health effects of light or intermittent smoking. In particular:
(footnotes omitted).
Reduction in consumption can be both an individual and societal measure and measured via both outright quitting and reduction of cigarettes consumed per day (to a non-zero number). My focus here is on quitting at the societal level and I have been basing it on using price elasticity to measure taxation’s effects on population prevalence of smoking, which would be unaffected by your concerns.
However, I dug deeper into the mechanics of these price elasticities numbers, and it appears some can be measures of cigarette sales (i.e. general reduction of consumption) and others measures of smoking prevalence in the population (i.e. quitting or not initiating).
I am still working my way through this information, so I don’t have a full informed view yet, but here (at the bottom of this comment) are some things that caught my eye in the NIH’s Tobacco Control Monograph’s section on “Using Price Elasticity Estimates to Project the Future Impact of Tobacco Tax Increases.”
This has important implications because:
Charity Entrepreneurship’s model (which mine and Moritz’s is based off of) translates price elasticity into a reduction of consumption which is then translated 1:1 for reduction in prevalence.
Open Philanthropy’s model (which also uses hinges on price elasticity) assumes the reduction in consumption has 1:1 effect with reduction in DALYs.
So the CE model is solid so long as the median price elasticity used (for LMICs) reflects the average of price elasticities calculated on prevalence.
Both models are vulnerable regardless to overestimating the DALYs averted from prevalence change if the people that go onto quit/not initiate were disproportionately less of the DALY burden. A reason to believe that was the case is that smokers that smoke less cigarettes are more likely to quit. (This though is also reason to be less concerned with your original point about the nonlinear association between harm and consumption i.e. even if they don’t quit, taxes put them in a closer position to quitting in the future)
However, buffering the above for the CE model is that it’s not capturing DALYs averted for reduced consumption that is short of quitting—a source of underestimating the impact.
The Open Phil model has issues regardless because it applies reduction in consumption to 1:1 reduction in DALYs without mapping out quit/prevalence rates, which as you rightly point out are likely not interchangeable with just reducing the non-zero amount you smoke each day.
And both models might have significant overestimation if their price elasticity numbers are reflections of cigarette sales instead smoking prevalence.
Quotes of interest from the monograph
These and other projections generally start with the overall price elasticity of cigarette demand, typically obtained from econometric estimates based on tax-paid cigarette sales data, and assume that the tax increase being modeled will be fully passed on to consumers in the price paid for cigarettes.
It is also important to use both adult and youth prevalence elasticities in projecting the public health impact of a cigarette tax increase because youth and adults are not equally price sensitive.
Similarly, adult and youth prevalence elasticities are used in projecting the public health impact of a cigarette tax increase. Given the available estimates, many of these projections assume that the impact on adult prevalence is half of the overall elasticity and that youth uptake of tobacco use is two to three times as responsive to price. When projecting the impact on youth, these projection models often assume that young people will take up smoking at the same rate as adults or young adults have. Continuing the example above, if the state has one million adults and adult smoking prevalence is 20% (200,000 adult smokers), the US$ 1.00 tax increase will reduce the prevalence of adult smoking by 4%, or induce 8,000 adult smokers to quit smoking. If there are 500,000 young people in the state, and it is assumed that they will take up smoking at the same rate as adults have and youth smoking is twice as sensitive to price, then the US$ 1.00 tax increase maintained over time in real terms will prevent 8,000 young people from taking up smoking.
Econometric studies of the impact of tax and price on tobacco use employ two primary measures of tobacco use: (1) macro-level aggregate measures of consumption, such as country-level data on tobacco sales (this literature developed earlier, growing rapidly before the 1990s); and (2) household or individual-level data taken from surveys, such as national surveys of drug use or health risk behavior.
Additionally, studies have assessed the impact of tax and price on specific outcomes, such as prevalence of tobacco use, smoking cessation, initiation of smoking by youth, cross-price elasticity, and health outcomes.