From the Wikipedia entry for “Pigovian Tax”:
A Pigovian tax is considered one of the “traditional” means of bringing a modicum of market forces, and thus better market efficiency, to economic situations where externality problems exist. More recently, particularly in the United States since the late 1970s, and in other developed nations since the 1980s, an alternative to Pigovian taxation has arisen: the creation of a market for “pollution rights.” Pollution rights markets are not generally more efficient than Pigovian taxes but are often more appealing to policy makers because giving out the rights for free (or at less than market price) allows polluters to lose less profits or even gain profits (by selling their rights) relative to the unaltered market case. Markets for emissions trading have been set up to bring better allocative efficiency and improved information sharing to the pollution externality problem. Pollution rights markets are a part of the field of Environmental Economics generally, and Free-market environmentalism specifically.
One difficulty with Pigovian tax is calculating what level of tax will counterbalance the negative externality. Political factors such as lobbying of government by polluters may also tend to reduce the level of the tax levied, which will tend to reduce the mitigating effect of the tax; lobbying of government by special interests who calculate the negative utility of the externality higher than others may also tend to increase the level of the tax levied, which will tend to result in a sub-optimal level of production ..
A key problem with the Pigovian tax is the “knowledge problem” suggested in Pigou’s essay “Some Aspects of the Welfare State” (1954) where he writes, “It must be confessed, however, that we seldom know enough to decide in what fields and to what extent the State, on account of [the gaps between private and public costs] could interfere with individual choice.” In other words, the economist’s blackboard “model” assumes knowledge we don’t possess — it’s a model with assumed “givens” which are in fact not given to anyone. Friedrich Hayek would argue that this is knowledge which could not be provided as a “given” by any “method” yet discovered, due to insuperable cognitive limits; chaos theory argues for other cognitive limitations.
A counter-argument is that perfect knowledge of the gaps between private and public costs is not necessary: So long as a tax level reflects a negative externality better than no tax, it should increase efficiency. Sometimes these differences are obvious – for example the effect of petroleum use on pollution, global warming and traffic congestion. In such a case, the levying of a Pigovian tax approximating such costs would be better than no tax at all.
Aside from efficiency, Pigovian taxes may increase the equity or fairness of how costs of negative externalities are borne. For example, even if a tax on air pollution is not at the perfect level to achieve optimal efficiency, it transfers cost associated with pollution from the public (e.g., via reduction of other taxes or benefit from public spending of the pollution tax proceeds) to the polluter.