# Smoking, health care costs, and imprisoning drug users because they cost us money to imprison

Earlier this week I posted an article on the Globe’s Economy Lab blog on lifestyle and health care costs. Here’s a little more exposition on a couple of key points, phrased a little more formally.

The article is about the extremely common claim that people with healthy lifestyles save the health care system money, basically the argument: `You can kill yourself with cigarettes if you want, but not with my tax dollars.’ ( I’ll use smoking as my example so I don’t have to keep saying “unhealthy lifestyle,” while recognizing that of course different behaviors will have different effects on health care utilization.) There are at least two important objections to that argument.

The first is the argument I gave in the Globe: it’s not so obvious that the a given person will consume more health care during their lifetime if they smoke than if they don’t smoke. This is an argument about arithmetic and I think people should do the arithmetic correctly. The second argument is more philosophical: do we want to set up publicly provided goods, then enact laws to try to change behaviors which tend to increase demand for those goods?

### Costs and smoking again.

Consider arithmetic first. The argument that smoking costs non-smokers money through the health care system can be more formally expressed: the average causal effect of smoking on the present value of health care consumption is positive. In terms of counterfactuals, let $$y_i^1$$ denote person $$i$$’s net present health care costs if they smoke and $$y_i^0$$ costs if they do not smoke. The cost of treating smokers is (where all sums are taken over the set of smokers):

total cost of treating smokers = $$\sum y_i^1$$.

A high fraction of treating smokers is the cost of treating smoking-related illnesses, and in many studies and in the popular mind it is those costs which are the social burden of smoking. But those costs are not the causal effect of smoking on costs. That effect is instead

total causal effect of smoking = $$\sum y_i^1 – \sum y_i^0$$.

Since the second term on the right hand side is empirically roughly the same size as the first, the causal effect of smoking on costs is much, much lower than the cost of treating smokers, or perhaps even negative. Again, this is arithmetic, and it’s hard to argue with arithmetic. In this literature, the former expression or something close to it is referred to as the “gross” health costs of smoking and the second term is referred to as the “net” health care costs of smoking. Statistically, the “net” health care costs are by definition equal to the average causal effect of smoking on smokers. The gross costs do not measure a causal effect and they tell us nothing in and of themselves about external effects of smoking operating through public health care.

### Costs are only part of the story.

I tried, and judging by the comments apparently failed miserably, to point out clearly in the Globe article that the fact that smoking does not have a large impact on lifecycle costs does not mean that there is no rationale for smoking control policies: there are other external effects of smoking, such as second hand smoke and risk of fires. We should be particularly interested in controlling access to children, and tax policy can be a powerful instrument in that context as children are usually estimated to behave more elastically with respect to price than adults. The health care argument also ignores lots of other financial transfers, such as the effect of smoking on the tax revenues collected from smokers (which is related to, but not the same, as productivity arguments, which mostly concern strictly private costs), or the cost of old-age pensions, which tend to benefit non-smokers.

Generally, we should be interested in policies which improve our standard of living, and preventive medicine can be good policy, sometimes producing more health for a given investment than primary care. Put another way, we should want to implement policies which benefit society more than they cost society, which is clearly not to say that we should not enact any policy with positive costs.

But none of those considerations changes the fact that, again, the gross costs of treating smoking-related illnesses are not the causal effect of smoking on health care costs. In much of the public’s minds, and even sometimes in the literature, the arithmetic gets messed up. Since the arithmetic involves the repugnant calculation that smokers dying early save the health care system costs they otherwise would not have incurred had they not smoked and thus lived longer, people argue that we should not make that calculation and instead treat the gross costs of treating smokers the net costs: external, social, costs. But we cannot just ignore arithmetic when arithmetic displeases us: we cannot argue that smokers cost non-smokers lots of health care dollars simply because we disapprove of the arithmetic that proves otherwise.

### Should costs even be part of the story?

But now consider the second argument: should we be attempting to control behaviors which influence demand on the public health, or other, systems? Notice that if health care were privately funded, this externality would go away: if I choose to increase my health care costs by smoking (or perhaps by not smoking), I have to pay those extra costs. My behavior does not affect your wallet and there is no financial externality to worry about, although, again, there are other good reasons to enact smoking control policies. The financial external effect, of whatever sign, is created by risk pooling induced by public health insurance: now when I choose behaviors which affect my life cycle health costs, it affects your wallet. But do we want to enact policies which attempt to reduce these costs?

If we do want to control these externalities, we should enact policies which encourage behaviors which reduce demand on the health care system and discourage behaviors which increase demand, all else equal. So suppose we’ve already decided that we want to subsidize healthy behaviors because we value health. If healthy behaviors wind up increasing lifecycle health care costs, we should either subsidize less than we otherwise would, or perhaps even tax, healthy behaviors. Healthy behaviors in this scenario benefit the person exhibiting the behavior but impose costs on everyone else, and this logic demands that we discourage healthy behavior relative to whatever policies we would otherwise have enacted.

This argument does not sit well with me. I dislike the argument that we should penalize smokers because of the health care costs of treating smoking-related illnesses, and I dislike the argument that we should penalize non-smokers because of the health care costs of treating smoking-related illnesses. These external effects smack of standard pecuniary externalities—externalities that operate through market mechanisms and do not require policy to fix, although they are not conventional pecuniary externalities per se. The perverse aspects of arguing that we need to control externalities which are artifacts of government programs is illustrated more forcefully by studies which treat the cost of investigating, arresting, and imprisoning illicit drug users as external costs of drug use itself! (“We are arresting you for this doobie.” “Why?” “Because the costs of arresting you are a negative externality!”)

I am unaware of a literature on the issue of control of externalities which exist only in the presence of government programs. Anyone know of relevant stuff?