Theory of the Second Best

There have been some interesting economics blog postings in recent weeks about the theory of the second best. Dani Rodrik of Harvard argues (“Why do economists disagree“) that economists can generally be viewed as first-best economists and second best economists. For instance, first-best economists would claim that all healthcare should be privately financed, with a private insurance system. Second-best economists will argue that the medical insurance market is far from perfect (e.g.: adverse selection and moral hazard issues, informational uncertainties). The second best economists may argue for government intervention. In the second best world, however, a narrowly guided policy may make things worse and not better.

Healthcare example

For instance, to correct the problem of adverse selection, economists may wish to create a single payer, government-run healthcare system. This government-run healthcare system will eliminate the problem of adverse selection and increase equality (good) but may create deadweight loss due to increased progressive taxation or inefficient procurement of medical services due to the influence of lobbyists (bad). Does the good outweigh the bad? The answer is-of course-it depends.

What about an employer mandate?  Again, this issue likely will eliminate problems of adverse selection and increase equality.  The mandate, however, will likely increase costs significantly for small business–small business have much higher load factors than large businesses–which could stymie economic growth and reduce GDP for the entire society.  Again, whether or not the good outweighs the bad in this situation is unclear.

Second-best Examples from the Economics Literature

The Economist‘s Free Exchange blog (“Making the second best of it“) cites a paper by Lipsey and Lancaster (Rev Econ Studies 1956).  In the introduction, the Lipsey-Lancaster paper states:

It is well known that the attainment of a Paretian optimum requires the simultaneous fulfillment of all the optimum conditions. The general theorem for the second best optimum states that if there is introduced into a general equilibrium system a constraint which prevents the attainment of one of the Paretian conditions, the other Paretian conditions, although still attainable, are, in general, no longer desirable. In other words, given that one of the Paretian optimum conditions cannot be fulfilled, then an optimum situation can be achieved only by departing from all the other Paretian conditions. The optimum situation finally attained may be termed a second best optimum because it is achieved subject to a constraint which, by definition, prevents the attainment of a Paretian optimum.

The paper also gives an example from the trade literature.  What happens when a country decides to join a customs union (i.e.: free trade zone), such as NAFTA or the European Union?

…under these circumstances, a customs union will tend to raise welfare by encouraging trade between the member countries but that, at the same time, it will tend to lower welfare by discouraging the already hampered trade between the union area and the rest of the world. In the final analysis a customs union will raise welfare, lower it, or leave it unchanged, depending on the relative strength of these two opposing tendencies.

Another example of the problems of the second best is derived from the optimal taxation literature.

Consider a community of two individuals having different taste patterns [for goods X, Y and leisure]. The “government” of the community desires to raise a certain sum which it will give away to a foreign country. The community has made its value judgement about the distribution of income by deciding that each individual must contribute half of the required revenue. It has also been decided that the funds are to be raised by means of indirect taxes. It follows from the Corlett and Hague analysis that the best way to raise the revenue is by a system of unequal indirect taxes in which commodities “most complementary” to leisure are -taxed at the highest rates while commodities “most substitutable” for leisure are taxed at the lowest rates. But the two individuals have different tastes so that commodity X is substitutable for leisure for individual 1 and complementary to leisure for individual 2, while commodity Y and leisure are complements for individual 1 and substitutes for 2. The optimum way to raise the revenue, therefore, is to tax commodity X at a low rate when it is sold to individual 1 and at a high rate when it is sold to individual 2, while Y is taxed at a high rate when sold to I but a low rate when sold to 11. A second best optimum thus requires that the two individuals be faced with different sets of relative prices.”

But this ‘optimal’ solution violates the principal of anonymity.  If one was to invoke anonymity, this would impose another constraint and thus lead us to another ‘optimal’ solution.

As you can see, in a world filled with uncertainty, it is very difficult to make policies which are unequivocally welfare enhancing (especially in the health care setting).