Can Coase or Pigou stop my friend from smoking?

Knowledge of counterfactuals is a critical component of Coasean bargaining, likely to fail in many simple settings.

I hate that my friend Robby smokes the occasional cigarette. I contend that his smoking causes me genuine disutility because I value his health and longevity.[1] We both agree that his smoking causes me a negative externality and are both committed to finding some mechanism that will lead to the economically efficient level of smoking. I’m an environmental economist so this should be easy, right?

Unfortunately, economics has no good solutions for this simple problem. The core problem is that neither of us can credibly share the information that is necessary for implementing the efficient solution. We both agree on the following premises:

· Robby gets some, diminishing marginal utility from smoking.

· I get locally constant marginal disutility from his smoking.

· Since Robby does not internalize my disutility, his quantity of smoking is too high.[2]

· Nevertheless, the efficient amount of smoking for Robby is likely positive.

But we have two major sources of uncertainty:

· Robby does not know how large my disutility from his smoking really is, and does know that I have incentives to lie about my disutility in many mechanisms.

· I do not know how many cigarettes Robby would smoke in the absence of my disutility or any mechanism we set up, and I cannot predict it since it is a repeated decision made on multifactorial considerations. I do know that under certain mechanisms he has an incentive to lie about this.

The classic solutions that economists propose for externalities are Pigouvian Taxes and Coasean Bargaining. But subject to the uncertainties above, neither approach works for this simple problem.

Alfred Pigou showed that in settings with a negative externality, a corrective tax equal to the size of the externality will deliver the efficient solution. So, perhaps we could implement a tax on Robby smoking equal to the disutility it causes me and *boom* we’ve got efficiency! But what should that Pigouvian tax be? Suppose I could choose a tax to impose on Robby for each cigarette he smokes. If the “tax revenue” goes to me, or something I value (like charity), then when I set the tax rate I would not pick a number equal to my marginal disutility from his smoking. Instead, I would increase the tax rate by a little (based on the inframarginal number of cigarettes and my best guess of Robby’s elasticity of demand) because I value the tax revenue in addition to the smoking reduction the tax would induce. If, alternatively, we set up the tax so that Robby just burns the money, then I would pick an arbitrarily high tax rate since there’s no reason for me not to—if I don’t have to trade off the disutility of his smoking and the utility of the tax revenue, then I might as well set his smoking to zero.

Coasean bargaining is supposed to save the day in situations like these. Ronald Coase showed that under stylized conditions, private bargaining could deliver the efficient solution to externalities as long as property rights were well defined. In this case there are just two of us, we actively want to contract over our well-defined preferences, and we’d be happy to create imaginary property rights. Why can’t we just arbitrarily assign property rights and then negotiate from there? Well, if I have the property rights and Robby starts negotiating a price he can pay me in order to smoke each cigarette, we’ve just replicated the tax situation from above where I would charge Robby above the efficient price. It’s true that we would reach a Pareto efficient allocation, but I would have too much surplus in that world because the property rights allocation has given me a financial interest in Robby’s smoking behavior beyond my original altruistic (or paternalistic) concerns. The root of the problem is inframarginal units: though there is some amount of smoking that “should” happen, I still benefit from taxing it. This leads me to pick a tax rate that won’t deliver the efficient allocation on the margin, since there will be a marginal cigarette that Robby values above my disutility but below the price I set.[3]

But maybe this is moot, since it’s much more natural to think Robby should start with the property right to smoke and I should have pay him to stop! Unfortunately, I think Coasean bargaining is actually just useless for a host of problems that resemble smoking, where there is no credible counterfactual, repeated uncertain emissions, and many inframarginal units. Suppose I want to pay Robby to smoke one fewer cigarette than he would have absent the payment—how could I ever know that my payment is working? Robby can tell me that he would have smoked X cigarettes and instead has decided to smoke X-1, but he is the one deciding X. How much he will want to smoke on a given night will depend on a host of factors that only he can really know, and he has no incentive to credibly report or commit to. This makes it effectively impossible to contract on abatement.

This is the case in many pollution problems, and is a pervasive issue for carbon offsets, payments for ecosystem services, catch and release programs, and many other Coasean approaches to environmental externalities. How can we contract on abatement relative to a counterfactual we do not know? In environmental economics classes we generally skirt this issue by just assuming we know the counterfactual. Sometimes we can look at historic behavior, but often decisions respond in real time to many factors (and of course grandfathering has its own problems when anticipated). If the desired emissions are allowed to be uncertain, then contracting for abatement will be fraught.

Perhaps instead we could contract on emissions? That is, I could pay Robby some agreed upon amount so that he will agree not to smoke more than X cigarettes in a given interval of time. This is probably the most promising approach, but it can only get us to an ex ante efficient solution. Since the externality on me is approximately constant but Robby’s marginal utility of consumption varies over time, setting a constant cap on cigarette’s smoked cannot give us the ex-post efficient quantity. And deciding on the cap repeats many of the problems discussed above: I do not know what cap to propose that achieves an ex-ante efficient amount of abatement, and Robby has no incentive to tell me.

The more typical solution is to binarize the choice, so there are either unconstrained emissions or none. In this case, I could buy the rights to whether Robby smokes at all (perhaps in an interval of time). This works theoretically because it gets rid of the problematic inframarginal units, but it is not suitable for this case because we believe the efficient allocation involves some smoking (not none) and the binary approach cannot deliver that allocation. Alternatively, we could set some baseline maximum number of cigarettes and negotiate from there, but coming up with that maximum has its own problems. If he chooses, it will be too high; if I choose, it will be too low. And, like some choices above, I would not want to base it on historic amounts, lest I encourage Robby to smoke more on the margin now.

So, Robby and I are at an impasse. Despite both believing he should smoke less, we have no good way to design a mechanism that reveals how much smoking he should actually do.[4] Coase and Pigou have failed us here, and I strongly suspect they fail us far more often than environmental economists would generally like to admit.

In the case of Pigouvian taxes, environmental economists often discuss the failure of governments to impose corrective taxes at all, especially in cases where we think we have some good estimate of the externality. I would argue we don’t discuss enough the problem of letting affected communities pick their own externality estimates, at least not in those terms, because these situations are generally framed as regulations rather than taxes. In the case of housing regulation, or liquor license, or public order regulations, etc, local regulations effectively allow the community to impose additional costs on activities that they consider to have some externality. Unfortunately, the community has no incentive to accurately report the size of that externality, and, if given the power to choose a tax whose revenue they do not collect, they will choose to set an infinite tax. This framing does suggest that simply moving to a world where regulations are replaced by taxes rebated to the local community could at least move you closer to efficiency! And in many settings, it is reasonable for a third party to directly estimate the true externality and set the appropriate Pigouvian tax, which solves my concerns here.

For Coasean bargaining I think the problem is more significant. If we cannot expect Coasean bargaining to work with just two people, simply because the counterfactuals are unknown and efficiency probably involves an interior solution, then I am skeptical about its utility in many other situations. The saving grace for Cosean bargaining in practice has been that there are many useful situations where one or both of these issues don’t apply. Often we might know the potential pollution and can contract on abatement just fine (e.g. if we easily observe a factory’s emissions capacity). Other times binarizing our choices is fine, since we expect the efficient level is zero (e.g. if we want to end all deforestation in a place with a PES scheme). But as a general principle, I am convinced that the most prominently discussed “conditions” for the Coase Theorem to hold (no transaction costs, few parties, no credit constraints/income effects) are actually insufficient, and environmental economists should pay greater attention to “knowledge of counterfactuals” as a key component of success.

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[1] Here I refer to all cigarettes Robby smokes, even if I am not around (in fact Robby is polite enough not to smoke around me). I acknowledge it is cheap talk, but I consider my disutility from Robby’s smoking (away from me) to be 20 cents per cigarette.

[2] We have some disagreement about whether he can just mentally internalize the costs he was imposing on me because he cares about my disutility. I contend that this means he gets disutility from my disutility, but that this does not get rid of the externality. In any case, Robby would like to find a mechanism that accurately measures my disutility.

[3] I should note that it is not feasible for us to negotiate over every cigarette: we cannot communicate frequently or quickly enough for this to work, and if I held the rights I would have an incentive not to reveal my true disutility (separate from my financial incentive).

[4] Some more complicated options we’ve considered include running VCG, creating a prediction market for counterfactuals, creating a dynamically evolving tax, or trying to use published estimates of the elasticity of demand for cigarettes. I consider these infeasible, and believe some still have information revelation problems similar to those discussed here.