Tuesday, October 28, 2014

substitution, liquidity, and elasticity of demand

One of my formative (insofar as one can use that term for something that happens when one is 35) experiences was trying to explain to an introductory microeconomics student that the elasticity of demand for eggs is somewhat low, but the elasticity of demand for Farmer Jones's eggs is very high; his eggs are (presumably) very good substitutes for the eggs of a lot of other farmers.  If a single person could set the price of all eggs, the price they choose would have a small effect on the quantity that would sell at that price, but if Farmer Jones tried to unilaterally change only the price of his eggs, the quantity of his eggs that would sell would change a lot.

Yesterday Matt Levine wrote that it doesn't matter whether an individual owns most of the copper in London-Metals-Exchange-approved warehouses because that's a very small fraction of global copper, and Professor Pirrong said that, to a reasonable extent for a moderate period of time, it does, and while the clear theoretical economic categories aren't always clear in practice, in this case it seems more clear and correct to say that global copper can't substitute for LME warehouse copper, but with some time and expense can be converted into it. So if you're looking at a 5-year time horizon, it's probably not worth trying to distinguish the two, but the shorter the relevant time period, the larger the gap that could reasonably open up between the prices of the two.

A lot of what I think of as "demand for liquidity", which isn't quite what other people (e.g. Shin, Tirole, etc.) would mean by that phrase, is time-sensitivity; in a certain language, what I'm thinking about is more of a demand for market liquidity and what they mean is funding liquidity, but to some extent these are both closely tied to "how quickly can I convert one asset into another asset?" or "at what terms of trade can I quickly convert one asset into another asset?", especially as distinct from "at what terms of trade could I convert one asset into another asset if I had a lot of time to try to get a good price?" "Liquidity" then is related to convenience yields, but also to elasticity of intertemporal substitution — whether cash tomorrow (or even this afternoon) is equivalent to cash at some point in the next five years. If you're interested in the price of copper in deciding whether to build a new factory, you can probably use the LME price for delivery over the next couple years as a proxy for global copper prices, but if you need to deliver into an LME futures contract next week, you have a demand for LME copper that doesn't admit the same kind of substitution, and you're going to find that the market is a lot less elastic.

Friday, October 10, 2014

a game theory example

Recording here as much as anything for my further reference an example by Viossat (2008), who credits it to Eilon Solan, who adapted it from Flesch et al (1997):


I have not verified this for myself, but allegedly (for x≥0)
  • If x=0, TLW is the only Nash equilibrium; it is not quasi-strict.
  • Any strategy profile in which players 2 and 3 play L and W and and player 1 plays T with probability of at least 1/(1+x) is a Nash equilibrium.
For x=0, aside from action profile TLW, player 1 gets payoff 0 for matching player 3 and 1 otherwise; similarly 2 wants not to match 1 and 3 wants not to match 2.

Wednesday, October 8, 2014

dispersed information, intermediation, and communication

Intermediation is crucial to a modern economy, but it also creates a lot of principal-agent problems. Some of these are well modeled and studied, but some that, to my knowledge, are not are related to the ease with which some kinds of information can be conveyed relative to other kinds of information; where relevant information is predominantly quantifiable, at least some of the problems that are created and/or solved by intermediation are comparatively minor, whereas when relevant information is effectively tacit, it will often become a large friction in making things work.

To be more concrete, there is a recent story about Ben Bernanke's being unable to refinance his mortgage, and the LA Times says he probably could if went to a lender who meant to keep the loan, as opposed to a lender who wanted to pass it along to other investors in a security.  If you're trying to make a lot of loans on a small capital base, you have to keep selling off old loans in order to get the money to lend to new borrowers, but the people buying the loans may not fully trust your underwriting; on the other hand, the purpose of the intermediation is that the people with the money don't have to go to all of the expense associated with doing a full underwriting themselves.  What's left is to look at a set of easily communicated information about the loan, preferably something that can be turned into a small set of meaningful statistics about a pool of loans.  This means that, even more than in a market where all underwriters were holding their loans until maturity, your ability to get a loan will depend on the information that can be easily gathered and communicated, and less on qualitative and less concrete information.

In an economy in which some agents are good at doing underwriting and other agents have capital to invest, it seems like a good equilibrium would be one in which the underwriters can develop and maintain a reputation such that "This security was underwritten by Jens Corp, which gives it a rating of BB+" or some such; the rating provided by the underwriter incorporates the unquantifiable information and makes it (in some sense) quantitative.*  Note here that I'm asking the issuing agent itself to provide a rating; if an outside credit agency is to provide a rating accounting for all of the information that was put into underwriting the loans, that agency would have to either do all of the underwriting work over again, rely on the issuer's reputation in the same way I'm proposing investors could, or rely again on quantitative metrics.  Ten years ago credit agencies had chosen the last of these three options, and issuers gradually figured out to sell off loans with bad qualitative characteristics and good metrics that fit the credit agencies' bills.  This ultimately is the bias I'm trying to avoid.

There might be some value to having a rating agency that knows the reputation of a number of small shops and can, in some manner, pass that along to investors, but that, too, will depend on an equilibrium in which the issuing financial company is issuing a credible indicator of the quality of the loans.  Even if a financial company could get to that equilibrium, somehow developing this reputation through a history of responsible issuing and pronouncements, maintaining the reputation may depend on outside observers' believing that the company's management and culture and future interests promote its maintaining that reputation, i.e. that the company and its agents will at every stage find it less valuable to sell a set of bad loans for a high price than to maintain its ability in the future to sell a set of good but hard-to-verify loans for a high price; this requires that a disciplined underwriter would expect to maintain a certain amount of business by being able to find a sufficient stream of people who are hard-to-identify good credit risks.  I like to think this could happen, but I'm not sure it's the case.

* It may well be that the most plausible world in which this could come about would be one in which the information conveyed would be effectively multi-dimensional; rather than just "these loans have approximately this likelihood of default", you might convey "the loans have approximately this likelihood of default under each of the following macroeconomic scenarios:", etc. In an age of computers, it might even be acceptable to have something that seems, to humans, fairly complex, as long as it can be readily processed by computers in the right ways; it is worth noting, though, that higher complexity may make it harder to verify, even after the fact, which might hurt reputation building. If I sell off 100 loans and say that each has a 5% chance of default, and maybe 3–7 of them default, that seems about right, and I manage to do it several more times, and it can be noted that my assertions seem to be borne out by experience, but if I say 10 of them are in this bucket, and another 10 are in a different bucket, and so on, then, while overall levels of default can still be verified, it becomes harder to verify that each separate bucket is right, and I think that the opportunity to lie about one tenth of my portfolio, while still (perhaps?) keeping my reputation fairly intact on certain kinds of loans, give me more incentives to attempt to liquidate parts of my reputation and make it more likely for an equilibrium to collapse. The extent to which this is a concern is going to come down to how credible "I guess I'm just not good at underwriting X kind of loan anymore, but we're still doing great at everything else!" is, and how many times I can do it before nobody takes me seriously anymore.