30 November 2007

The theory of the second-best

One of the few provable useful results in economics is the one about markets producing an optimal outcome.

If all goods and services in an economy are traded via perfectly competitive free markets, the resulting outcome is efficient (i.e. Pareto-efficient), i.e. there is no other possible arrangement of available resources in which some would be better off and no one would be worse off.

By contrast, an “inefficient” outcome is one where the position of some can be improved without making anyone else’s position worse, e.g. where the benefits of exchange have not been fully exploited.

This is potentially a very useful result, because if we want to ensure that things are as good as they could be (ignoring redistribution issues) we need not first calculate everyone’s happiness under various different conditions. All we need do is set up perfectly competitive (PC) markets and let people trade amongst themselves. This is just as well, since it is impossible in practice to know what people’s happiness level is under different conditions, or to find out all possible preferences between different outcomes for every individual. We may not even need to do anything as active as “setting up markets” since they tend to develop spontaneously.

If we currently don’t have conditions of PC markets, the way to get to efficiency is simple, in theory: do whatever it takes to get to precisely those conditions.

The problem is that, in practice — for various reasons, e.g. political — we may not be able to get to PC conditions. We may therefore have to choose between other, suboptimal alternatives, and try to decide which of those is preferable from the point of view of efficiency.

What does economics have to tell us about how to optimise efficiency, if we cannot achieve perfect competition)? There are two ways of dealing with the "problem of the second best" for policy purposes. The first favours government intervention, the second does not.

1) If we had information about the preferences of every individual in the economy, we could calculate what the range of possible optimal states are, given the constraints we have to work with. (Call these states “second-best solutions".) In that case, it might turn out that, if the economy departs from PC in one specific area but is PC elsewhere, we will only be able to get to a second-best solution by departing from PC in other areas as well. In fact, it can be shown that for very simple scenarios, that is the case — i.e. it is better to deviate from perfect competition in all areas rather than just in some.

This is sometimes taken to prove that in certain cases government intervention is better than laissez-faire as a way of generating the best possible outcome, given the constraints. But note that this conclusion depends on knowing everybody’s preferences, which in practice is impossible. The great benefit of the strict-PC model — of being certain that the outcome will be efficient, without having to know anything about people’s preferences — does not apply here.

2) The other way of treating the problem of the second best is to advocate agnosticism. If we do not have perfect PC conditions and cannot get to them, and we do not know everyone’s preferences, then we can’t know whether any particular policy change will move things in the direction of greater efficiency. Even if a policy change appears to be moving things in the direction of PC conditions, it might easily result in less overall efficiency.

Now there are two ways to interpret treatment (2), either of which might be appropriate depending on the circumstances.

(2a) One is to be conservative, in the sense of being cautious about doing anything, especially major changes. They might do harm on balance, rather than good. This generates the opposite conclusion to that of (1), in the sense that you should avoid tinkering further with an already imperfect system in case you make it worse.

(2b) The other way to react is to adopt a muddle-through approach, for which there is no strict justification, but which might be the best one can do, on a sort of hopeful common-sense basis. This could be taken to mean, we should try to aim at the nearest thing to PC in all markets, being careful to ensure that no major areas are omitted.

The one thing second-best theory can definitely tell us is the following: one should be wary of policy changes which involve partial marketisation of a given area. E.g. if the intergenerational market for private capital (= inheritance) is heavily distorted by estate duties, it is not necessarily a good idea to marketise (i.e. remove subsidies from) cultural institutions such as universities or opera houses.

Also — though one does not really need second-best theory for this — it may well be misguided to impose artificial marketisation, e.g. by making academics or medical professionals try to prove they are generating “value for money”. There is no hard support from economic theory for the idea that anything other than a genuine market (where the genuine end users are able to vote with their wallets) will generate any benefit whatsoever.

The standard textbook interpretation of the point about second-best (originally made by Richard Lipsey and Kelvin Lancaster *) is (1) above, i.e. the version which appears to favour government intervention. This interpretation is at best biased, and at worst simply false, but is very common. Dani Rodrik, for example, uses it when he says that

the First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions.

This is not exactly false, but does seem to exaggerate the case in favour of intervention. The best that could be said is:

The First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that interventions may not necessarily make things worse.

In March I made this point on the Talk page of the Wikipedia article, where the same misinterpretation was being used.

This entry is incomplete as it stands, and in a way which generates a political bias i.e. in favour of state intervention.

Another way of looking at the Lipsey/Lancaster point is as follows. If you are not at a Pareto-optimal point for the economy, you don't know whether any change that doesn't actually take you onto an optimal point is going to improve efficiency (i.e. make everyone better off). Even when you move in what appears to be the direction of greater efficiency, e.g. by changing all controllable parameters to an average of where you are now and where a Pareto optimum is, you might be making things less efficient i.e. making everyone worse off.

So another moral (apart from the one given) is that, when you have a market that is already regulated or otherwise distorted, it is not necessarily a good idea to move in the direction of less distortion. You can be sure that if you can get to a Pareto optimum, that is a good thing (at least in terms of efficiency); apart from that, you can't be certain of the effects of different policy changes. This is a consequence of the severely restricted conclusions of Pareto theory.

In fact, the moral given in the entry is questionable as stated. It isn't really the case that intervention to move things in a direction different from the pro-market one is sometimes a good idea. It's just that such a move might be a good thing, only neither the government nor anyone else can ever know if it would or not.

In a paper published in June, Professor Lipsey himself came out in favour of the second interpretation.

The upshot is that in practical situations, as opposed to theoretical models, we do not know the necessary and sufficient conditions for achieving an economy-wide, first-best allocation of resources. Achieving an economy-wide second best optimum allocation looks even more difficult than achieving the first best. Without a model of the economy’s general equilibrium that contains most let alone all of the above sources, we cannot specify the existing situation formally and so cannot calculate the second best optimum setting for any one source that is subject to policy change. This is an important point since much of the literature that is critical of second best theory assumes that economists know a distortion when they see one and know that the ideal policy is to remove the distortion directly, something that is necessarily welfare improving only in the imaginary one-distortion world.
* R. Lipsey and K. Lancaster (1956), 'The General Theory of Second Best', Review of Economic Studies 24, 11-32.

(originally published on the mediocracy blog)

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