## Sunday, April 17, 2011

### Desirability of Market Completeness...

Have been re-reading Lord Turner's (of the FSA) recent speech on the role of banking in the economy.  Based on his speech, I would like to put forward the following proposition for discussion.
If financial markets are self-equilibrating systems, then market completeness is desirable (almost axiomatically).  However, if financial markets are not self-equilibrating systems, then the desirability of market completeness is at best ambiguous (and more likely destabilizing).
I feel like a thorough understanding of the desirability of market completeness is important from both a theoretical and practical perspective.  I think I will bring this up at the summer school in Jerusalem and see if I can get anyone interested...

1. A paper which may be relevant, though I haven't read it, is Bowman and Faust, "Options, Sunspots, and the Creation of Uncertainty", JPE 1997. The authors show that with incomplete markets, increasing an options market can increase uncertainty (it introduces the possibility of sunspot equilibria), rather than completing markets as is often assumed.

I learned about this paper from the following quite delightful website:
http://www.rieti.go.jp/users/kobayashi-keiichiro/serial/en/08.html

Of course to answer your question we need a theory of non-self-equilibrating markets, which we don't have (but then I would say that...). Another place to look may be Blume and Easley's papers on the market selection hypothesis'; they consider a population of agents with heterogeneous beliefs and prove that under complete markets (and other conditions), markets select for agents with rational expectations. (Although this would seem to go against your proposition.)

2. I find it hard to think about 'market completeness' in financial markets. I think the simplest real example (I think this is probably related to the B+F paper Keshav mentions) is in reinsurance - its quite possible in the insurance markets to write reinsurance-on-reinsurance contracts (retrocession). Obviously there is now a market for reinsurance-on-retro, and this chain continues ad infinitum. Obviously there are a million-and-one examples, eg CDOs => CDO^2 => CDO^x.

Given this, how would you define market completeness to answer the proposition?

3. @David/Keshav,

Is there any proof in general equilibrium theory that, given incomplete markets (say S states of the world, N = S-2 AD securities) a 'non-completing' increase in markets (say to N = S-1 AD securities) invariably results in a Pareto improvement?

4. Rob,

No, in fact an increase in markets (even a completing' increase) need not be Pareto improving. Here is a counterexample:

There is one commodity (corn), 2 periods and 2 states which are realized between period 0 and 1. There are 3 agents: savers' who have only a period 0 endowment and value consumption in period 1, state 2 more highly than period 0 consumption; safe borrowers' who have an endowment in period 1 in either state, and only value period 0 consumption; and risky borrowers' who only have a period 1, state 2 endowment and only value period 0 consumption. Suppose first that the only asset traded is a riskless bond which pays out one unit of corn in period 1, in either state. The only agent who can issue such a bond is the safe borrower', since only he can meet his obligation to pay out corn if state 1 occurs.

Now suppose we replace the riskless bond with the two Arrow securities. The security paying off in state 1 will have no value since no-one values state 1 consumption. Now, both types of borrower can issue securities paying out in state 2. Since the supply of these securities is greater than under incomplete markets, their price will be lower. This fall in price reduces the safe borrower's income, so he consumes less in period 0. So completing markets is not Pareto improving.

5. Ah amazing thank you.

So irt David's proposition, even though market completeness may be desirable, market 'completing' is not necessarily desirable.

In terms of "(and more likely destabilizing)", say in the B&F paper you point out, it doesn't strike me as intuitively obvious that sunspot equilibria should always be less stable than normal equilibria, given S-M-D (although I don't know how to even begin to think about this). Maybe this is on the wrong track.

In any case, most financial markets that were supposedly destabilizing were derivative markets of one form or another, which are often interpreted as being 'redundant' anyway (in the sense that an investor can construct any given payoff in any state of the world with more than one portfolio). In the B&F paper there is in fact a model where 'over-completeness' leads to sunspot equilibria!

6. Glad to see that my proposition is generating some discussion. I will add the B&F paper to my reading pile...

7. Rob,

Well, many economists might consider market completion desirable even if it is not Pareto improving, just as many economists support free trade even though removing tariffs is generally not Pareto improving. A more interesting question may be whether completing markets is necessarily a Kaldor-Hicks improvement (i.e. the winners could compensate the losers). My intuition is that fully completing markets must be a K-H improvement, but increasing the number of Arrow-Debreu securities need not be (and may even make things worse in the Kaldor-Hicks sense), but I don't have a proof.

Having said all that, I am not personally a fan of Kaldor-Hicks welfare economics... an even more interesting question is what effect moving towards market completeness has on the distribution of wealth and welfare in society, e.g. the different effects on borrowers, savers, owners of capital, workers, etc.

8. Keshav and Rob,

Along these lines, it seems plausible that (in practice at least) financial innovations that "complete markets" could be seen as a form of rent-seeking. I think that the BoE and the FSA (in particular see the recent Adair Turner speeches/presentations) are beginning to view certain types of financial innovations from this perspective.

Research in this area might be of interest to them as they seek to design new financial regulations...