On externalities and Pigouvian taxation

The issue

Most people don't know how to deal with an externality, and don't understand the purpose of Pigouvian (not Pigovian - see footnote) taxes. 'Most people' is more likely than not to include you too.

Shock value

The extent to which people change their actions as a result of pigouvian taxation is irrelevant. So, a pigouvian tax on carbon emmissions is the best response to global warming, even if it does not lead to any reductions in carbon emissions.

The snappy part

An externality is generated when I do not take into account the full social costs of my actions when making decisions. In other words, I do something I like which you don't, but because I don't care about your feelings I end up doing it too much.

For an externality to create problems, two things must be going on:

a. no clearly established property rights (am I entitled to polluting or are you entitled to a clean environment?)

b. trade between the holder of the property rights and the non-holder is not possible (i.e. I can't compensate you to allow me to pollute if you are entitled to a clean environment, or you can't pay me to not pollute if I am entitled to pollute).

Let's stick with carbon emmissions. Property rights are well established: they are held by governments, and they can choose to represent the rights of all people of the world, the fauna and the flora of the world and generations yet unborn as they see fit. So no problems there.

The means to trade are also present: enter pigouvian taxation.

Now, most people think that a pigouvian tax ought to be imposed to reduce pollution, full stop. If the pigouvian tax has only a small effect on carbon emmisions, the thinking goes, then the pigouvian tax has 'failed' and other measures ought to be taken, namely non-price restrictions (e.g. banning carbon emmissions above a certain level, restricting the supply of oil, etc).

This is wrong. The degree to which the production of carbon emmissions changes is irrelevant. As long as your pigouvian tax equates the private to the social costs, you are in the best possible world. If you don't agree, then your problem lies with the initial allocation of property rights or with the distribution of the pigouvian tax revenue or with democracy itself, not with correcting for the externality in the world in which we live in.

The only 'problem' stemming from an 'uncorrected' externality is inefficiency, and the best way to deal with that inefficiency is to apply an appropriate pigouvian tax. Any perceived problems beyond inefficiency should not be addressed in the context of 'correcting' the externality.

Illustrative example - post starts getting boring from here onwards

I like driving my car around your garden. You like your garden to be car-free. I produce an externality in that my private actions affect your welfare.

Possibility A: You own the garden. If driving my car is worth more to me than having a car-free garden is worth to you, I can pay you so that you let me drive in your garden. If not, I don't pay you and you have a car-free garden. That's Pareto efficiency; you can't make anyone better off without making someone worse off.

Possibility B: I own the garden. If driving my car is worth less to me than having a car-free garden is worth to you, you can pay me so that I don't drive around. If not, you don't pay me and I keep driving around. That's Pareto efficiency again.

Now, substitute 'you tax me' for 'I pay you' and you can relate this to the rest of the post.

And if you believe that the outcome is not socially optimal, then you really have a problem with the initial allocation of property rights, not with the means by which the externality is handled. Voicing your concerns now doesn't make sense; your grievances have nothing to do with the externality we discuss here.

What you believe is that the initial allocation of wealth is wrong on grounds of fairness. The way to combat this is by moving some wealth from the garden guy to the car guy or vice versa. The tax/subsidy on car-driving is not really central to your argument.

Now you may want to skip to the footnote; for the remainder of the post I simply repeat everything I said earlier in an irritating manner

Tyler Cowen, who easily ranks amongst the top thinkers we have on social and economics issues, shocked me with this post. (One of the most powerful economists in the world also shocked me for similar reasons in a talk I attended recently, but I expected more from Tyler).

Tyler's post discusses whether it makes sense to drill in Alaska (the ANWR), and here's an excerpt:

2. There is a general global warming case against developing the resource. Note that supply restrictions can be far more effective than a Pigou tax. A Pigou tax doesn't guarantee the stuff won't be pumped anyway, albeit at lower profit.

There can be no 'general global warming case'. Fighting global warming is a means to an end, not an end in itself. I don't want a guarantee the stuff won't be pumped away, I just want those who suffer from the externality (be it non-users of fuel, Africans, wild animals or children yet to be born) to be adequately compensated by those who benefit from burning fuel. Remember the Coase theorem! The Pigouvian tax can be seen as the result of the bargaining between the different social groups with their different preferences. A crude instrument, I know, but the problems associated with establishing the optimal Pigouvian tax rate do not go away when considering non-price restrictions (and what is banning something if not an extremely large Pigouvian tax, implying an extremely large externality?).

If you are arguing against developing ANWR 'because supply restrictions can be far more effective than a Pigou tax' then why don't you also make a 'general global warming case' against developing Africa (you could use the resources to install solar panels), against reading books (you could use the resources spent reading them to pay people not to use fuel) and against living and breathing (you produce carbon emmissions)?

3. The Pigouvian case against developing ANWR makes sense only if we are taking other systematic actions to raise the price of fossil fuels and restrict fossil fuel use.

Again, the point is not to restrict fossil fuel use for its own sake, or even to raise the price because we want less consumed for the fun of it. All a Pigouvian tax has to do is equate the private with the social costs of polluting; if that is the case, whatever carbon emmissions there are at equilibrium represent the optimal amount.

Why does this misunderstanding about externalities and pigouvian taxation persists? I can only speculate. Firstly, standard textbook treatments do not bother with where the funds go (beyond stressing that, to get a neat solution, they are not to be redistributed back to the externality generators - polluters). Secondly, the sloppy ('common sense') thinking often applied requires that we should be looking to eliminate anything 'bad' such as carbon emissions, not merely restricting it to socially optimal levels.

The footnote

Pigovian is the most funny Americanism there is. You can spell labour 'labor' and behaviour 'behavior', but the guy wasn't called Pigo.


  1. MrArt Says:

    Well, you could argue that the rich-world carbon taxes *aren't* going to be redistributed to poor African nations to compensate them for the effects of global warming. Instead they'll probably substitute for other taxes (e.g. on rich-world labour). I suppose that's the same point you make about moving wealth from the garden guy to the car guy.

  2. Luis Enrique Says:

    I think this is the same point as mrart makes. Although I am probably muddled; my useless intuition tends to drag me in the wrong direction in this case.

    So, say we calculate and implement a Pigouvian tax from now, carbon emissions don't change too much, and later generations experience what they consider to be some pretty catestrophic consequences. And everyone is supposed to think "that's all right then, because the taxes raised since 2008 fully compensated us for these terrible things happening."

    I suppose if I find that hard to swallow, I have a problem with the initial distribution of property rights, rather than with Pigouvian taxation per se.

    In which case, if you agree that this (possible, probable?) outcome I have sketched seems unacceptable, because the initial allocation of property rights is so far from that which would produce a more desirable outcome, then isn't it pretty irresponsible for people to be talking blithely about Pigouvian taxation as a solution to global warming, when what would actually happen is a few rich nations shuffle some money around between themselves and the world gets screwed anyway and most of the victims don't see a dime because of it? Seems to me that focussing on changing carbon emitting behaviour is a more sensible approach. Is my reasoning flawed? it wouldn't surprise me.

  3. datacharmer Says:

    Luis Enrique - Don't be so harsh on yourself! There's nothing wrong with your reasoning, and the same goes for nmart.

    The issue here is that, regardless of whether or not poor African nations or future generations are adequately compensated for suffering environmental change, imposing a pigouvian tax leads to the efficient outcome.

    Whether we then choose to pass these resources on to poor African and future generations or we prefer to keep them ourselves is a second-order decision.

    If what we care about is welfare rather than global warming per se, there's no reason to try to maximise it by focusing on the amount of global warming alone.

  4. Anonymous Says:

    I think there are a bunch of problems with your analysis:

    1) You describe an externality as: "I do something I like which you don't, but because I don't care about your feelings I end up doing it too much." In general, this conveys the right idea, but it is not strictly correct (in particular, the "I end up doing it too much" part). A negative externality can be modeled by a marginal social cost function above the marginal private cost function. If a Pigouvian tax "equates the social and private costs" (that is, the amount of the tax is "correct") and "does not lead to any reductions" in the externality-producing activity, then -- according to standard neoclassical economic theory -- there was not "too much" of that activity (there was no allocative inefficiency) to begin with. Look at it this way: If the Pigouvian tax (which shifts up the marginal private tax curve) does not cause any reduction in the activity, demand must be perfectly inelastic. (Assume this is true even in the long run.) Using standard welfare economics, there will be no "deadweight loss" (DWL) triangle. That is, the externality-producing activity simply results in a welfare transfer to those engaging in the activity from those on whom the negative externality is inflicted. It certainly possible, in real life, that a "Pigouvian tax" is implemented and does not bring about a reduction (or much reduction) in a negative-externality-producing activity, but that may be because the tax was not big enough. Why would you assume, in a real-world case, that the tax was the "correct" amount?

    2) You state, "The only 'problem' stemming from an 'uncorrected' externality is inefficiency." No idea what the single quotes mean, but that's only true if you don't care about distribution or individual rights. From a distributional standpoint: As noted above, the "uncorrected" externality in the case you describe does not involve allocative inefficiency. It does involve a welfare transfer from some people to others. If you care about distribution, you may consider this transfer a problem. One way to deal with this is to use the revenue from a Pigouvian tax to compensate those harmed by the externality. When there is a DWL due to a negative externality, the allocative inefficiency can be corrected without compensating those harmed. In the case you describe, there is no DWL (allocative inefficiency) to be corrected in the first place, and it's not clear what purpose the tax would serve except to reverse the welfare transfer. There may be other ways to deal with the distributional issue, as by a redistribution of "initial" property rights, as you describe in your Coasian bargaining example, but a tax on the polluters is certainly one way to do it. In cases where, for example, there are diffuse harms to many people and -- even if those harmed were aware of the harms, their sources, and had clear legal standing to extract compensation -- it would be costly for them to engage in bargaining, a tax on a polluting activity may be used not only to correct allocative inefficiency, but to extract compensation. (You conflate the ideas of Pigouvian taxes and the Coase theorem, which is not helpful. The latter was intended as a critique of Pigou. If there were efficient bargaining, Coase argued, there would be no need for corrective taxes. One of the reasons for such taxes is that bargaining is not efficient.)

    4) On individual rights, a big portion of the ethical case neoclassical economists make for the desirability of "free markets" is that voluntary market transactions (if they take place between rational self-interested agents) are mutually beneficial. People have the right to participate or not participate, and this means (given these assumptions) that they will only participate if doing so would leave them -- at the very least -- no worse off than they would have been had they not participated. If there is a negative externality, some people can be forced to accept some costs without their consent and without compensation. That is, the activity is not Pareto-improving. The Coase theorem tries to get around this by saying: well, if the people inflicting the harm have the property right, then this does not count as a harm to those on whom the harm is inflicted. So you can give a polluter right to the air, and you tell those who get sick from breathing it that they had no right to clean air to begin with!

    5) Your statement of the Coase theorem is not really correct, as it requires efficient (costless) bargaining. Coase states in his Nobel lecture, "What I showed ... was that in a regime of zero transaction costs ... negotiations between the parties would lead to those arrangements being made which would maximize wealth ..." (quoted in Bowles, Microeconomics: Behavior, Institutions, and Evolution (2004), p.222). Zero transaction costs! In addition, the Coase theorem requires that people are not credit constrained. Suppose that we have a group of high-wealth individuals who engage in negative-externality-producing activities, and low-wealth individuals on whom the harms are inflicted. If the relevant property rights are assigned to the rich, here's no guarantee that the poor will be able to pay the them to stop the activity (even if the latter's welfare loss exceeds the former's welfare gains) in the absence of unlimited access to credit.

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