Sunday, February 19, 2012

Kidney Transplant Chains and Financial Economics

This post is written in part for Richard Moses - an old friend from the place I discussed in this post. Richard is a biologist at the University of Alberta who spent the earlier part of his career as a researcher - a field biologist. Richard taught me about animal behavior - the ones I remember are bats and beavers (didn't advance to the later parts of the alphabet). Later in life, Richard decided he wanted to dedicate himself to teaching. Richard's teaching is hard slogging - he teaches mainly large sections of introductory biology. He's clearly really good at it. Look at the comments on rate my professor. This comment sums up Richard:
I do not understand why Moses doesn't have an overall rating of 5.0. He is an AMAZING prof, utterly hilarious and interesting. Yes, his tests are hard, but its university...just study a lot and read the questions carefully and you will be fine. I always looked forward to his class, and I still find I talk about him probably once or twice a week!
This even shows you something about the weakness of student evaluations as an input to compensation and promotion and tenure for professors. Clearly, if Richard scores low on evaluations it is because he is challenging the students. The ones who are complaining are those for whom getting off their butts is painful. I also know how good Richard is because he told me about how he teaches. He has some particular techniques for dealing with large lectures. One I remember is that he does not post lecture slides, if he uses them, and forces students to write down what he is teaching them in class. Prepared slides that are posted on a web site represent an open door to skipping class, and for good reason. In that context, the Professor might as well be a TV.

Richard, like many commenters on this blog, is not sure what economists have to contribute. He's even suspicious that we might be a serious tax on society. Economists get this a lot from other parts of the university. We're relatively high paid, so if we're really not doing much for anyone, why not get rid of us and use the resources more efficiently?

In the New York Times this morning, I read about the recent record set in a chain of kidney transplants, involving 30 kidneys and 60 people. Here's the problem. Each of us really only needs one kidney, but we are born with two. However, giving up one involves a risk. There is the pain of the surgery, the risk of infection, and the lingering doubt one might have that there may be a good reason why we actually have 2 kidneys. But, when renal failure happens, it's typically both kidneys, and ultimately the only way to save the person may be a kidney transplant. If we can just share our kidneys around, though, that would be great. In the human race, we have more than enough to go around.

How would an economist solve this problem? Plenty of allocation problems we have can be solved by using the idea that markets solve the problem. Pricing parking spaces appropriately can allocate scarce parking lot space in a university. We can solve pollution problems efficiently in some cases through the trading of the rights to pollute (cap and trade, for example). The application of auction theory to the problem of allocating broadcasting bandwidth and resource extraction rights has been one of the big successes of economic science.

But we're not going to use conventional markets to solve the kidney exchange problem. Just think about it a bit, and you'll understand why we can't go there. One bright man figured out a solution. That guy is Garet Hil, and I've linked to the only information I can find on him, which is an account of a photo shoot. Garet Hil has an MBA from the Wharton School, at the University of Pennsylvania. He doesn't call himself an economist, but that's essentially what he is. His key training is in computer science and finance, but as any economist knows, the economics group at Wharton is quite high-powered.

To solve the kidney exchange problem, one has to start with a list. That list consists of two sub-lists: a list of donors and a list of recipients. What motivates a donor is typically an interest in a particular recipient on the list, though some donors are just generally altruistic. Now we have an allocation problem. Every donor does not match with every recipient, for various reasons. Indeed, the recipient who motivates the donor may not match. Thus, the trick is to construct a chain of matches from the two lists. For example, A and B are donors. C and D are recipients. A cares about C and B cares about D, but A and C do not match, B and D do not match, but A matches with D and B matches with C. We do two transplants, and everyone is happy. This extends to much more complicated chains, involving many people, and Hil wrote a general algorithm to solve the problem.

As luck would have it, I actually saw a presentation on kidney exchange by the expert in the field, Al Roth, Harvard University, at Wash U a couple of months ago. Al Roth has many interests, including the application of high end game theory and the theory of matching, to market design. My colleague, David Levine, is interested in high end game theory, but is interested in many other things as well, including what Al Roth does (side note: explore David's web site, particularly his take on modern behavioral economics).

Another example of market design is the allocation of medical residents to medical schools, which has been studied extensively in the economics literature. In this year's new-PhD job marktet, we have had campus visits with economists involved in market design, including SangMok Lee (Caltech), who is a theorist, and Clayton Featherstone, (Stanford), who is doing a post-doc at Harvard with Al Roth.

The key idea we want to extract from kidney exchange is that there are ways to improve on Hil's algorithm, and economists can contribute in important ways in thinking about other kinds of organ exchange, which have their own unique problems. For example, donating some organs would kill the donor. You can see where the research is going on Al Roth's web page.

I hit on an idea when I was talking to SangMok on Thursday, just before I had to run off to class, and then get on a plane to Atlanta. SangMok was working on an allocation problem that is in some sense easier than the kidney exchange problem, but nevertheless quite difficult. SangMok is studying a problem like the allocation of medical residents to schools, where residents have preferences over schools, schools have preferences over students, and we are interested in efficiently matching schools with residents, two by two. That problem shares something with the approach taken in modern monetary economics, what Randy Wright and I call "New Monetarist Economics." Some of the economic models New Monetarists think about are matching models of resource allocation. SangMok's problem involves designing an allocation mechanism to solve a matching problem. In the New Monetarist matching problem, the individual economic agents in the model world are actually working together to solve the resource allocation problem, but in an Adam Smithian fashion - working solely through self interest.

For a New Monetarist, a key problem is understanding the nature of information problems and limited commitment problems (essentially people running away from their debts), that give rise to the the use of money, credit arrangements, and other financial innovations, which the economic agents in our model world discover and use to solve the resource allocation problem. That resource allocation problem is the ultimate one - what goods and services are produced, and how they are allocated across members of our society. The policy problems New Monetarists are interested in concern how governments can intervene - through regulation and monetary policy actions by central banks - to help the individual economic agents in our model do a better job on the resource allocation problem they are solving. Then we translate those results into policy advice that we give directly to policymakers like Jim Bullard, Narayana Kocherlakota, and Ben Bernanke.

Now, here's an idea for the New Monetarists, or anyone else who cares to attempt a solution. We typically work on the two-sided matching problem - two-by-two matches of buyers with sellers. But suppose we think like the kidney exchange people. There is already a little bit of work on this, but it hardly scratches the surface, and may have been going in the wrong direction. I'm think of Kiyotaki-Moore credit chains, work by Lagunoff and Schreft, and some stuff I have seen by Julio Rotemberg. There's an idea out there that the financial crisis had a lot to do with the chain of credit relationships among large and small financial institutions, and the fragility of that chain.

Clearly, in practice there are credit problems just like the kidney exchange problem, that you can solve through a chain of credit transactions. You can see that the kidney chains are somewhat fragile. If one donor backs out, the whole thing can fail. But it's promising that you can actually get a chain involving 60 people and 30 kidneys. That's impressive, and the analogous financial idea is that financial market chains could actually be resilient.

The problem that New Monetarists have that is different, and which gives you the key to why economics can be so hard, has to do with the fact that the individuals who are solving the allocation problem in the New Monetarist world are self-motivated. They will game the system, cheat, steal, and run away, if you let them. We have to design the framework of regulation and monetary policy so that they don't do that, or don't do it much, and so that we get a nice, efficient, allocation of resources as a result.

That's economics. Isn't it interesting?


  1. "That's economics. Isn't it interesting?"
    Yes, very interesting, but I see it as mostly computer science. Seems like the work people like Jon Kleinberg etc. are doing on network theory can be borrowed from if that has not already been attempted (unsuccessfully).

    1. If you're saying economics is mostly computer science, that's not correct. If you're saying that kidney exchange is just computer science, that's wrong too. The problem is rich in economics. Read Al Roth's research on the topic.

    2. I should add, however, that computer science is certainly a tool we use intensively in economics - along with statistics that we adapt for our own purposes (econometrics), and various mathematical tools.

    3. So, I know that economics uses concepts like equilibrium, maximization etc. How often do you guys end up using other powerful concepts in other fields e.g., fixed point theorems, asymptotic analysis (big O notations), NP completeness, information theory (shannon limits) etc. Have these tools been successfully employed? I'm sure someone has tried these things out for economic problems because there are obvious connections. But, I rarely see them discussed in the context of mathematical problems.

      And no, I didn't mean to imply that the kidney problem is just computer science. Meant it as Hil's attack at the problem seems to be a classic comp science solution, rather than much of what he might have learned at Wharton econ. But, I could be completely wrong about that (probably am). Roth's papers are very interesting indeed.

    4. The fixed point theorems are a big deal in economics. That's part of the problem of finding an equilibrium in some contexts, actually. The asymptotic analysis you see in econometrics and elsewhere. Some people I know, like Tom Sargent (last Nobel winner in economics) made a lot of progress in bringing in tools from engineering. One of the most important tools in modern macroeconomics is dynamic programming, which comes in part from Bertsekas, an engineer:

      This is the economics version:

    5. I should add that I misunderstood you on Hil. That was exactly my impression. He solved it like a computer science problem, but there is a richer approach you can take that uses more economics, and potentially allows you to do a lot better, and handle other problems.

  2. "But we're not going to use conventional markets to solve the kidney exchange problem. Just think about it a bit, and you'll understand why we can't go there."

    I'm pretty dull, Steve. 'Splain, please. Why can't we go there?

    Because someone might make a decision that he regrets, ex post? Is donating a kidney more hazardous than being a lumberjack?

    1. If we get paid for giving up kidneys, and kidneys keep us alive, I think we get into some pretty scary stuff.

    2. Bottom line: The elephant in the room that libertarians don't think about is crime.

    3. A friend from Brasil told me it actually happens to some drunken guys that the wake up in a ditch with a scar on their back. Going to Brasil is not that far away... going anywhere in the world is easy today.

      The elephant in the room is if it gets better or worse if you legalise it. I just can't imagine how much worse it could get....I mean, 'stealing' a kidney is illegal now, it would be illegal if you could trade kidneys. No change. Why should it get worse?

  3. @ Anon 11:10,

    I can't claim that economics is always at the cutting edge of every advance in math or stats that comes along. It probably isn't.

    But there are lots of economists who come from those fields or cross pollinate in other ways. I know that there is lots of cross-learning between econometricians and biometricians. Useful concepts are not likely to stay unknown for long.

    Things like fixed point theorems and asymptotics are old hat in economics. There is even a musical band of economists called the "Contractions."

    I don't know what shannon limits are, but I'll bet there are economists who do.

  4. Got any links to the existing work on credit chains?


    2. Here's another thought. A monetary equilibrium (or money bubble) is a kind of credit chain. Society gives the first person a loan, then the next person pays it back, then that person gets a loan, then the next pays it back, ...

  5. Steve,

    Still not following you.

    I think that your new job as Dept Chair is cutting into your time to explain things to me.


    If we allow people to be compensated for donating kidneys, we somehow encourage kidney violent theft/murder?

    How does that work?

    Yes, donating a kidney is harzardous. How harzardous?

    We permit people to do it for free but we don't allow donors to be compensated for it? How does that make any sense?

  6. So, just to make the analogy clear in your credit chain example. Is the idea that relationships that sustain credit arrangements between two parties correspond to "who you care about" in the kidney exchange problem whereas the characteristics of the debt (long vs. short term, risky, liquid etc.) correspond to the characteristics of the kidney?

    1. Something like that. It's a loose analogy. There's exchange involved, but the exchange is going to involve multiple parties in a chain of relationships, and it is possible for that chain to fail - or maybe not; maybe the chain is resilient.

  7. Just a funny note - the mechanism described here was used in Czech republic many years ago in flat exchange schemes - there is even a movie about this absurd situation:

  8. The pain often radiates along the path of the urinary tract.
    kidney stone treatment

  9. We should all help prevent damages to our kidney.
    Skelton Sherborne

  10. Hello Steve,

    I thought this post was extremely interesting so I started reading a bit more to figure out what was in the literature. My impression is that there not much about it, and that everything seems to go back to Kiyotaki and Moore (1997).

    In this respect, I don't see how the kidney problem can be that different from what K&M have in their paper. Could you explain a bit more what is that you have in mind? In what particular direction do you think the research should move? Thanks.

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