Thursday, December 18, 2014

medical testing, economics, and the placebo effect

One of the central lessons of introductory microeconomics is that in evaluating an option, there isn't really a relevant absolute standard of "good" or "bad", or (depending on how you want to think about it) that the only baseline for that standard is the best or most likely alternative.  If you have a chance to spend the afternoon bowling or going to the zoo, these might, in a colloquial sense, both seem like "good" options, and if you're trying to decide whether to spend a lot of money getting a car fixed or having it junked, these might seem like "bad" options, but from the standpoint of rational decision-making you're only concerned with whether bowling is better than going to the zoo or going to the zoo is better than bowling — the term "cost", in its most complete sense as economists understand it, is about what opportunities you give up by making the choice you're making, such that, by construction, only one of a mutually exclusive set of actions can be "worth more than it costs".

The FDA requires, at least for certain kinds of drugs and medical devices and procedures, that it be established that they are better than previous standards of care, at least for some patients in some circumstances, and that seems to be consistent with this principle, but that kind of testing tends to come later in the human subject trials than a better known and even more common kind of medical trial, which is testing for bare "efficacy".  Some subjects are given the treatment, and typically others are given a "placebo" treatment, and the results are compared; if there is no difference, the new treatment is deemed not to be efficacious.  This is wrong for a couple related reasons[1]: it may, indeed, be efficacious because of the placebo effect. On a more practical level, and drawing from the economic principle, the resulting information only provides information about whether the treatment should be given to patients if (and to the extent that) they would otherwise be likely to be given the placebo.

I want to emphasize — this seems to me to be the sort of objection someone might raise to what I'm proposing — that anyone lie to a patient here. "This treatment is the standard of care, has been shown to have some effect, and is at least as effective as anything else we know of [with given side effects, or whatever qualifiers are appropriate]," if it is true, is all true, and is all that is relevant to the patient. Indeed, if the patient is not self-sabotaging, you can say "this seems to work, to the extent we can tell, because of the placebo effect." Indeed, I drink orange juice and consume large amounts of vitamin C when I have a cold for this reason; my understanding of the state of scientific knowledge is that 1) vitamin C, for almost all populations,[2] has no more (or less!) effect on the common cold than placebo, and that 2) the common cold is unusually susceptible to the placebo effect.[3] People with whom I have discussed this seem to, at least initially, think I am somehow "fooling" myself, but consider it from a neutral standpoint:
  • If you believe it will work, it will work.
  • If you believe it will not work, it will not work.
My belief is not "foolish"; it is vindicated. Whether the mechanism involves direct action on the immune system or some convoluted, poorly understood neural pathways is only relevant if I'm likely to sabotage the neural-pathway mechanism should someone tell me that it is heavily involved.[4]

What I am proposing, then, is that testing from the beginning be done against the best standard of care; if there is no treatment, then perhaps include three groups in your testing, with a true control group (which receives no treatment) in addition to the placebo group and the test group. If your placebo group ends up having the best balance of effects, side effects, and costs, though, you should also consider making that placebo the standard of care.[5]

[1] Even leaving aside the statistical power of the test, which is surely relevant to medical decision-making but is not the focus of my interest for this post.

[2] One of the populations for which it seems to have some effect is long-distance runners, a group that used to include me. I don't know whether a mechanism has been determined; some scientifically-informed people I know think it's a bit amazing that the idea that vitamin C boosts your immune system ever got off the ground — it mostly helps maintain connective tissue — and so my not-terribly-well justified hypothesis is that long-distance running puts enough strain on your connective tissue that it diverts resources from your immune system to heal your connective tissue, and that higher doses than are usually of use to people may help free up the immune resources of long-distance runners. As I say, the mechanism I propose here is basically something I made up, but the fact of its having an effect is not.

[3] This latter point has been offered as an explanation for the prevalence of folk remedies for the common cold; they all work for the people who believe they work.

[4] Sort of. Certainly improvements on treatments are likely to be triggered by an understanding of the mechanisms; there is also a suite of issues, in the real world, related to the finite power of statistical testing. The mechanisms may give hints to likely drug interactions or long-term effects for which testing is difficult (because there are so many things to test for or because it would risk withholding an effective drug from a generation of potential beneficiaries, respectively). There is also an issue that computer scientists in machine learning call "regularization"; it is related to things like publication bias, and in this case boils down to the idea that understanding the mechanism might help us shade the experimental results, providing a bit more of a hint as to whether a 2σ effect is more likely or less likely than usual to just be noise. This is also related to the base rate problem; essentially, if the mechanism is such that we strongly expect not to see an effect, then a 2σ effect is probably noise (though a 6σ effect perhaps still means we were wrong). These factors all run parallel to my main point, as understanding the mechanism is also useful for a drug that outperforms a placebo than one that, by all indications, is a placebo.

[5] It seems, further, that even two "drugs" that only give their desired effect through the placebo effect are not necessarily ipso facto interchangeable. I have heard that the color of a pill can have an effect on how effective the patient expects it to be; this may be a problem if you're trying to decide which placebo to test against to decide "efficacy", but if you aren't prejudiced against "placebos", the rule that you go with whatever works regardless of mechanism carries over directly: use the best placebo if that beats everything else on effectiveness/cost/side-effects etc., and use something else if it does. (If the color of the pill affects its effectiveness, that is of course something the drug designers should exploit, but red drug, blue drug, red placebo, blue placebo, and no treatment should start on the same footing.)

Tuesday, December 16, 2014

Repugnance and Money

In late September and early October, my son was with his grandmother, and I had more of a chance to spend evenings reading books that I didn't think were related to my dissertation. In particular, I read books on human evolution, and to various extents related prehistoric anthropology and the like, and gain a new appreciation of the importance of in-group/out-group distinctions.

I have been aware for some time of an idea among monetary theorists that money is in some ways a substitute for what game-theorists call "monitoring" — in particular, a 1998 JET article by Kocherlakota (who is now president of the Minneapolis Fed) shows that a particular class of models has the same sets of equilibrium outcomes if you put money into the models, but agents are essentially ignorant of the history of play, as if there is no money in the models, but agents are perfectly informed at each stage as to what everyone did at every previous stage. More recently Randall Wright at Penn State (though I have no academic publications to cite here) has emphasized this substitutability, and in particular has emphasized that tight groups (a fortiori families) tend not to use money to intermediate favor exchange, but with some informal sense of whether members are shirking or being especially pro-social and various social sanctions to respond to them.  In fact, it seems likely that, in richer environments than Kocherlakota's, perfect monitoring is likely to work better than money, and it seems plausible that monitoring works well-enough in tight groups (but poorly enough outside of them) that money is less useful than monitoring in those groups (but better than (almost) nothing outside of them).

My synthesis and slight extension of these ideas is to suggest that we use money with our outgroup; further just-so stories follow.  For example, there is a social psychology a literature about money triggering an anti-social mindset, which I can tie to the idea that we associate "money" with "out-group".  Perhaps more interesting for purposes closer to my dissertation, though, is "repugnance", the only major threat to market function in the list that Roth (2008) provides that my dissertation proposal did not discuss.  While I would certainly not claim to explain all repugnances — as Roth notes, they vary too much in space and time for one to expect a particularly simple universal deep theory — at least some of them can be explained as situations in which in-group and out-group constructs are being conflated or boundaries are being breached. It has been customary, for example, for gifts of cash to be viewed as at least somewhat uncouth in contexts that call for gifts; perhaps giving cash signifies that you consider the recipient to be out-group. Similarly, this goes to one of Roth's examples, that it is okay to bring wine to a dinner party but not to offer the hosts an equivalent amount of cash. Prostitution may constitute an exchange of something that should be in-group for something that should be out-group, and indeed if one accepts for the moment that there is or was an accepted practice of men paying for a woman's dinner and expecting sex in return in a "dating" situation, one may be able to draw the line between this and prostitution in the same way — that it is okay for me to acquire a bottle of wine or a meal from someone in our out-group, and then give that to a member of my in-group (with the expectation that, at some point in some context, I will be the recipient of a gift, and the recipient will be a giver), but that giving money, whether explicitly or implicitly in "exchange" for something, is inappropriate.

There are some caveats to note.  In a modern large society, the in-groups and out-groups are blurred in a way that they largely are not in bands of 50 people in the savannah.  There are people who are somewhat in-between, but there is also a non-transitivity; my good friend might have a good friend whom I don't particularly know, such that it might be reasonably clear that my friend conceptualizes each of us as clearly "in-group" and we consider him the same, but consider each other clearly "out-group".  Also, to clarify, my mental model of in-group "gift-exchange" involves less obvious direct quid-pro-quo than the buy-a-meal-for-sex transaction noted above; I imagine contributions being less bi-lateral and more multi-lateral, but also that when a contribution is made, even if a single recipient receives most or all of the benefit, that it is not known when or in what form any anticipated reciprocity would be made, even if it did come back directly to me.  It may even be that direct quid-pro-quo transactions themselves have a bit of an out-group feel to them, even if they don't involve abstract money.

Human and Group Reason

There's an article from a few years ago theorizing that humans evolved "reasoning" as a way to argue [pdf link], and — I haven't yet read all of that article, but I haven't seen it note this yet — if you were to adopt the naive, non-cynical position that we reason [only] to figure out the correct answers and not [at all] to justify actions and positions taken for irrational reasons, there are some older split-brain experiments to contend with*.  Mercier and Sperber in particular note that the sorts of cognitive biases we see tend to be those that facilitate justification rather than impede it; we pick a wrong answer that is easier to verbally justify rather than an answer that is right for sophisticated or nebulous reasons.

I note a recent article at the Harvard Business Review (with Cass Sunstein as one of the two authors) about group decision-making, and one of the passages that sticks out to me

The psychologists Roger Buehler, Dale Griffin, and Johanna Peetz have found, for example, that the planning fallacy is aggravated in groups. That is, groups are even more optimistic than individuals when estimating the time and resources necessary to complete a task; they focus on simple, trouble-free scenarios for their future endeavors. Similarly, Hal R. Arkes and Catherine Blumer have shown that groups are even more likely than individuals to escalate their commitment to a course of action that is failing—particularly if members identify strongly with the group. There is a clue here about why companies, states, and even nations often continue with doomed projects and plans. Groups have also been found to increase, rather than to lessen, reliance on the representativeness heuristic; to be more prone to overconfidence than individual members; and to be more influenced by framing effects.
With agents whose cognitive biases were not skewed toward wrong choices that are easy to justify to others, one might expect groups of such agents to have biases that are — for example, if you have a good "representative" to buttress your argument, you can explain your argument to others in a more effective way than if you could not, such that the group is more likely to reach a consensus around a decision supported by over-reliance on a representative than one that isn't.  This is to say that one should naturally expect group decisions to be biased toward decisions that are easier to justify after the fact, and that this appears to involve an intensifying of the cognitive biases of individuals is evidence in favor of Mercier and Sperber's hypothesis.

* Human speech is primarily located in one hemisphere of the brain, though the other hemisphere can read and understand writing; human subjects whose hemispheres had been separated for medical reasons had, for the purposes of the experiment, written instructions shown to the non-speech hemisphere, whereupon they performed an action, whereupon the subject was asked why s/he had performed the action, and a perfectly confident and absolutely false answer was given.

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.

Monday, September 29, 2014

interactions and evolution

I've been thinking for a while that it might be possible for a gene that never has a (narrowly construed) positive effect on evolutionary fitness might be (in the long run) beneficial if it imposed a larger evolutionary load on phenotypes that were, in the long-run, kind of in trouble anyway, by hastening to get them out of the way. I still haven't actually put together a solid model that would make this compelling, but I've just discovered Wynne-Edwards, who at least suggested that individual organisms might sacrifice their own survival to benefit a group, especially a kin group; he was building off of work by a guy named Kalela who wrote about voles or shrews suppressing their own fertility when the group was running against the local ecosystem's carrying capacity. At least as I understand it from a second-hand telling by E.O. Wilson.

Tuesday, September 2, 2014


I've asked here before, "What is liquidity?", if not literally then sort of metaphorically or something. One of the problems is that the term "liquidity" is used to refer to a few different related but quite distinct things. When we refer to a corporate (especially bank) balance sheet, we're usually referring to the exposure of a bank to sudden, unexpected obligations and its ability to handle them. In particular, suppose our bank has, by any reasonable estimation, an ability in the long run to meet all of its liabilities, but has maybe $50 in cash on hand, and you have a few hundred dollars in an account and the contractual right to go up and try to withdraw $100. This bank's liquidity would be characterized as "Not good."  On some level, a company that has a $100 loan maturing today and expects to be able to roll it over (i.e. borrow the $100 from someone else to pay the old loan) is in the same position; perhaps in a well-functioning financial market they should be able to do that, and are thus in the long-run "solvent", but if something goes awry they find themselves in breach of some obligation.

So let's compare Matt Levine's description of Lending Club; it appears that Lending Club, with (by the relevant accounting rules) a very high leverage ratio, has little if any liquidity exposure; its contracts are written in such a way that it only owes a creditor money as long as a debtor pays it that money.  While this may, as he says in footnote 6, leave them with a business risk, it leaves them without a risk that they will suddenly have to meet the sort of legal contractual obligation that a bank intermediating lending would have.

Five to ten years ago — and maybe today, but I'm less well-connected now — a lot of hedge funds were making money on liquidity premiums, deliberately buying things like wind farms that were somewhat likely to be profitable but couldn't be sold as quickly as (say) IBM stock if a sudden need for cash arose.  Wind farms are actually a specific example I remember being presented to me of an illiquid asset that was owned by a financial company; if that company had a contractual obligation (possibly requiring a creditor to trigger it, e.g. by showing up at a teller window) to provide dollars on a moment's notice, the wind-farm may be a good asset for the long-run but it won't provide liquidity protection from that event.  If the company had a contractual obligation to provide, say, good title to a wind farm at a moment's notice, all of a sudden this looks like a great asset from a liquidity standpoint; better (at least from the standpoint of that (weird) risk) than cash.

That isn't meant to be entirely* fatuous; certainly traders of derivatives for physical delivery (e.g. oil futures) occasionally find themselves in analogous positions. If the world foreign exchange market were in turmoil, a dollar balance might be useless to fund an obligation in rubles, even if there were some objective sense in which, at any reasonable exchange rate, it would be high enough to cover the debt. What it does mean is that "funding liquidity", which is more or less what we're discussing, is about matching assets and liabilities in a way that is much more general than maturity matching in general, and that to the extent that it is, in practice, something that can be captured usefully in a low-dimensional way, that fact is phenomenological and not theoretically fundamental.

* Only mostly.

Saturday, August 2, 2014

productivity and labor compensation

This post will be much more practically oriented than most of this blog, and a premium is placed on brevity.

It is occasionally noted (though often obscuring important details) that
  • cash income
  • per household
  • deflated with consumer prices (especially if badly chained)
has, in my lifetime, lagged badly behind
  • economic production
  • per hour worked
  • deflated with the GDP deflator
in the United States.  Especially through 2008, almost all of this is because of
  • an increasing portion of labor compensation becoming "in-kind", in part for tax reasons,
  • decreasing household size, and
  • chaining effects and increasing prices of imports relative to exports.
Our worsening terms of trade are certainly interesting, and a reasonable target for policy attention, but most sources that compare the first series to the second series try to imply that the difference means something very different from what it does.

Now, in the last five years labor compensation has lagged behind production in common units of account; this is frequently true early in the business cycle, and the "beginning" of this business cycle has been frustratingly longer than usual, but it's premature to diagnose a secular shift.

Monday, July 7, 2014

the value of markets

One of my favorite financial writers writes:
The job of equity markets is to provide liquidity and price discovery. An efficient market will provide liquidity at a very low cost, and will adjust prices very quickly to respond to changes in demand.
He goes on to mostly ignore the tension between the two.

Suppose you own a large block of stock and decide to sell it to build a deck on the back of your house.  What should a well-functioning market do?  I think most people in the field would say that a perfect market — in particular, a very liquid one — will allow you to sell it all quickly for very close to its current price.  The purpose of the market, after all, is to allow you to buy and sell stocks when you want to, ideally in a cheap and efficient manner.

Now suppose you own a large block of stock and decide to sell it because you've found out that the CEO is laundering money for a drug cartel and most of the reported "profits" of the company are fraudulent.  What should a well-functioning market do?  I think most people in the field would say that a perfect market — in particular, one that is doing its price-discovery job well — should drop precipitously, incorporating the information that your trade conveys about the value of the stock into its price even before you finish trading — such that the last few shares you sell will be at a substantial discount to the earlier, less informed price.

Finally, suppose you own a large block of stock and decide to sell it.  What should a well-functioning market do?  Well, ideally it would know why you're selling.  In practice the best you might expect is that some of the market participants to eventually get a sense of whether certain kinds of trades (placed at certain times of day, in certain size, perhaps in sequences of orders that seem connected to each other) are more likely to indicate that the price is too high than other kinds of trades, which mostly just mean that somebody lacks a back deck and wants one.  If it gets pretty good at this, you might even hear the guy who got the scoop on the CEO's corruption complain about the "lack of liquidity" in the market; he might even badly abuse the term "front running".  For more on that, go read Levine's column.

There is one more important wrinkle to add here, which is time-horizon.  Suppose we're talking about a small cap stock that trades 50,000 shares a day, and you're trying to sell 100,000 shares (for deck-like reasons).  You decide to break it up into smaller orders to sell over the course of two weeks.  After you sell 10,000 shares the first day and 10,000 shares the next day, traders in the stock (such as there are) figure out that there's probably a bunch more sell orders coming over the next several days.  Is that information about the value of the stock or isn't it?

Well, ideally again, perhaps someone would step in and do a block trade with you at (close to) the initial price.  Insofar as the market isn't likely to be perfectly liquid, though, your trade can be expected to lower the price at least a bit, at least for a while. A trader with a time-horizon of months will regard this as a temporary "liquidation" that doesn't really concern the long-term (even months-long) value of the stock, but to a trader with a time-horizon of a day or two, "something's going to push the price down over the next day or two" is as informative as information comes.

So at this point the approximately ideal market with some first-order approximation of reality layered onto it probably drops a little bit for now, with the common expectation that it will bounce back in the next month or two, with the drop at such a size that some extra buyers are willing to come in and in some aggregate sense spread the sale out over the next few months, making a bit of extra profit on the deal, but small enough (and with a small enough expected attendant rebound) that you're willing to forego that "bit of extra profit" in order to get your hands on the cash now.  On some level, perhaps you might as well call up Goldman Sachs and pay them the fee for doing a block trade with you.

Tuesday, June 17, 2014

instruments of Fed policy

If the fed raised the reserve requirement (not now; under the sort of circumstances that we persist in calling "normal" more than five years since they were last seen), that should steepen the yield curve as long-term credit becomes scarcer relative to the supply of demand deposits and other short-term highly liquid investment. In periods historically where the yield curve becomes inverted I imagine some benefit might have been derived from somewhat tighter constraints, and where it's steepest perhaps somewhat looser; perhaps it would make sense to change reserve requirements in tandem with a target for the steepness of the yield curve.

The tl;dr version of the previous post is that, in the short term — on the order of an eighth of a year — the FOMC is likely to continue to ask the New York Fed to aim at something that is readily monitored in something like real-time, and it seems like the difference between long-term rates and short-term rates is a better target over that kind of period than short-term rates alone; in particular, if long-term rates go up over the weeks after an FOMC meeting, presumably that means the market has come to believe that inflation and/or returns to sunk capital will be higher than was believed at the last meeting and a somewhat high short-term rate is appropriate.

So I'm now suggesting that the FOMC set a target for the steepness of the yield curve, and, just as it customarily used to change the deposit rate in lockstep with the FOMC federal funds target, the board of governors would then customarily change the required deposit ratio in lockstep with the target for the steepness of the yield curve. There are clearer reasons for deviating from this from time to time than was the case with the deposit rate, and I'm not denying the board of governors the ability to do that, but rather than "leave them unchanged" as the default, I would suggest something slightly procyclical as the default instead.

Monday, May 19, 2014

long term impacts and empirics

There has been an accumulation of evidence in the past several years that labor markets respond to prices slowly and, at least at the first incidence, through flows rather than stocks; an exogenous increase in wages causes employers to pull back in hiring and increase layoffs, not by a lot (in terms of rate) but for a long time. A lot of previous studies had missed these effects because they looked at employment levels and included "corrections" for trend — when in fact the relevant "trend" was the very signal for which they were looking.

Labor is perhaps the strongest example, but there are a lot of markets in which we participate in which we establish, in some meaningful sense, relationships; if there are five supermarkets nearby, you may almost always go to one or two of them, such that you wouldn't respond to a sale at one of the others.  In other contexts, too, long-term behavior may obey very different rules than short-term behavior, but a lot of the most popular empirical techniques right now involve the use of changes shortly after other changes to infer causal relationships; long-term interrelationships are a lot harder to tease out causally.  (A change that happens in many places two or three months after legislation is announced, passed, or goes into effect is easy to attribute as an effect of the legislation; changes over the course of ensuing years are harder to distinguish from underlying trends that may, in fact, have motivated the legislation in the first place.)  When long-term and short-term impacts differ, I think there's a consensus that the long-term impacts are, from a policy standpoint, generally more important — the long-term is longer than the short-term, after all — but I worry that a lot our empirical studies now are trumpeting results about short-term relationships because teasing out causal directions can be done more convincingly.  Certainly there is something to be said for doing the possible rather than the impossible, but I think more studies of long-term behavior for which the "identification" [technical word] is less compelling should be encouraged, even if they might be harder to interpret in a crystal clear way.

Monday, May 5, 2014

A simple identity for Bayesian updating

For random variables A and X, consider the relationship
E{XA}=E{X}E{A}+ ρXAσXσA
which, up to a bit of arithmetic, is basically the definition of correlation. If A is a binary variable, though, we can do more with this; among other things, in this case σA2=E{A}(1-E{A}). Conflating the variable A a bit with the "event" A=1, and doing a bit of algebra, we get
The effect of the arrival of new information on the expected value of a variable is proportional to the square root of the odds ratio. Among other things, it can't be more than σX times the square root of the odds ratio, though this bound, which (obviously?) is reached when X is a linear function of A and therefore is a binary variable, can be more directly derived in that context.

Saturday, April 5, 2014

fair prices, non-pecuniary exchange, and bargaining costs

I've mentioned earlier my notion that the popularity both of focal prices in very non-competitive markets and of in-kind exchange (rather than the "usual" semi-monetary exchange) may reduce bargaining costs. The former story especially seems to work best where there isn't that much incomplete information; in particular, there should be a common belief that everyone is probably gaining at the likely focal point.  Attempts to negotiate or insist on a price different from the focal point are then interpreted as antisocial attempts to claim more of the surplus.

The case of non-pecuniary exchange, though, seems to be importantly driven by incomplete information, especially of how the thing being exchanged would compare (either in terms of cost or benefit) with dollars, and the fact that it's easier to find a focal point for in-kind exchange that seems obviously "fair" and mutually beneficial without the need for costly bargaining.

The main thought that I've been dwelling on more recently is that, while we often talk about "price discovery" as a function of the market, in both of these situations the cost of performing "price discovery" is being avoided. The market is not, in its ultimate sense, "failing"; the market ensuring that mutually beneficial trades take place, and in fact take place relatively efficiently. Instead of working out the price on the way to a solution to the ultimate problem, it simply routes around the hard part and jumps straight toward the end.

Thursday, January 30, 2014

overfitting and regularization

I'm trying to think through and recast some of the ideas around regularization from fields that do mostly atheoretic modeling of largish data sets.  The general setup is that we have a set of models ℋ — e.g. {yi=mx+b+σεi|m,b,σ are real numbers with σ positive} where ε follows some distribution, though typically we're imagining a set of models that requires far more than 3 real numbers to naturally parameterize it — and we're looking for the one* that best describes the population from which the data are sampled.  Now this really is kind of key; if you mistake your problem for "find the one that best describes the data", that's when you're going to get overfitting — if you have 1000 data that basically follow y=x2+ε and you try to fit a 100-order polynomial to the data, your model is going to depend on the noise in that particular data set and will do less well at fitting "out of sample" — i.e. at describing data from the population that aren't in your sample — than if you had used a simpler model.

On some level it might seem hopeless to account for the data you can't see, but regularization can work quite well, and even makes a certain amount of intuitive sense.  The way it's usually done, I have a set of subsets of ℋ that is much smaller than ℋ (in some sense — typically the set of subsets is of much smaller dimension than ℋ itself, i.e. I can specify a subset with only a couple of parameters even if specifying a particular point in ℋ requires many parameters).  Now I ask, for each subset H, if I randomly select (say) 80% of my data sample and pick the model h in H that best describes that 80% of the data, how well will it tend to fit the other 20% of the data?  Often some of the subsets turn out to do much, much better than others.  It seems reasonable to think that if H does a poor job at this exercise, then even if you pick a model in H that fits all of the data you have, it's going to be hard to trust that that model is a good description of the data you don't see; there's perhaps something about H that makes it prone to pay too much attention to "noise", i.e. to the things about the sample that are not representative of the population.  So you try instead to restrict yourself to subsets of ℋ that seem to do well out-of-sample in-sample, and hope that this implies that they're likely to do well out-of-sample out-of-sample as well.

I've already perhaps recast it slightly from its usual presentation, but I'm trying to recast it further, and look for a way of doing something like regularization but without resort to this set of subsets.  To get there, though, I want to remain focussed on the effect of a single observation on the choice of model within each H.  To some extent, we can take a point x in the population and break down the extent to which it will tend to be poorly fit "out of sample" into two parts:
  • how poorly does it typically fit when x is included in the sample? I.e., for a sample that includes x, if we look at the model in H that best fits that sample, how badly does it fit x?
  • how much worse does it fit when x is not in the sample than when it is?
I wish to emphasize at this point that, even if this depends to some extent on x — i.e. if some points have a greater tendency to be hard to fit out-of-sample than other points — it will still also tend to depend on H, i.e.—some sets of models will be more prone to producing bad out-of-sample fits than other sets of models. Standard optimization techniques allow us to minimize (and observe) how poorly a model fits in sample; I'm looking, then, for an indication of how poorly a model tends to fit out of sample.

Well, here's one potential little gem: if the log-likelihood function of a sample is additively separable in its data points and we can parameterize H such that the log-likelihood functions are continuously differentiable and at least prone toward concavity, then the optimization procedure is fairly straightforward: take derivatives and set to 0.  Well, I think that if, further, the log-likelihood functions associated with different potential observations all have more or less the same second derivatives — in particular, if it is very uncommon that an observation would have a second derivative that was a large (positive or negative) multiple of its average value at that point in H and points somewhat near that point in H — then there shouldn't be much of an overfitting problem; the amount worse that a point tends to fit when it's not in the sample than when it's in the sample is going to be constrained by those second derivatives.

I don't know whether this goes anywhere, but if I can find a reasonable way of looking at an ℋ and constructing a reasonably rich subset that satisfies the second-derivative constraint on a reasonable "support" in the space of potential observations, then that would appeal to me as somewhat less arbitrary than imposing a system of subsets at the beginning.

Insofar as the matching of the second derivatives is exact, this would mean the likelihood functions would only differ from each other or some common standard by functions that are linear in the parameters.  Particularly where ℋ lacks a natural parameterization, but even where it does not, this tempts me to try to use these deviations themselves as a parameterization.  Along manifolds in ℋ that are not robust in this way to overfitting, this parameterization won't work; it might be that this could be put in terms of this parameterization itself, allowing us essentially to carve out a subset of ℋ on the basis of what we can coherently parameterize in terms of the differences between likelihood functions at different potential data points.

* This is probably the usual setup. On some level I'd prefer to work with sets or posterior probability distributions or some such, but I think the ideas are best worked out with "point estimates" anyway.

I don't know whether this will be useful or confusing, but I record here that an element of ℋ can, for the most part, be viewed as a map from the space of potential observations (say X) to the space of log-likelihood functions; this can get confusing insofar as a log-likelihood function is itself a map from measurable subsets of X to ℋ, which is a bit self-referential.

Sunday, January 26, 2014

coordination and liquidity

Effortless "coordination" requires coincidence — Jevons's "double coincidence of wants", for example. Even Jevons understated the problem in the real world, where typically the details will need to be coordinated between buyer and seller; I may most prefer a red 1.3 cubic foot 1000 watt microwave, and find a black 1.2 cubic foot 1100 watt microwave that is good enough; sellers will accommodate what buyers want to varying degrees, but the costs associated with providing each buyer exactly what that buyer wants (frequently giving up economies of scale in the process) often dwarf the value the buyer would put on that.

I want to record some examples:
  • men's suits can be bought off the rack in various sizes but may also, much more expensively, be custom tailored
  • an employer may find it useful to have an employee who can be called in at a moment's notice to deal with an unexpected issue, while an employee may well prefer to have work hours that are limited to certain hours in the day or certain days in the week
  • a buyer might incur a sudden desire to buy something at a different time from that at which the seller finds most convenient to produce it; one or both will have to change the timing of the transaction to suit the other
In some ways the second example here is a special case of a more general subgroup of details on which to coordinate, namely that one party or the other will take the brunt in various ways of unexpected developments; each side would like to be able to plan ahead, and one or both of them will to some extent give up that ability, but presumably in such a way that the deal as a whole is still worth doing to both parties. The third example is similar, although it's a little bit hard to construe it exactly in that set, as the "unexpected event" is the desire of the other agent to do the deal in the first place. I should probably think a bit more about that, probably in the context of repeated/ongoing relationships between buyers and sellers.

I've been thinking about "market liquidity" as essentially a coordination issue, but in the context of the ideas presented here, it seems that what in finance is referred to as "liquidity providing" generally amounts to "conceding flexibility/choice/the ability to plan", and "liquidity taking" generally amounts to "taking advantage of the flexibility offered by someone else". In the context of financial market microstructure it's pretty clear that liquidity provision is in a lot of ways like writing an option that is, at least most obviously, being given away for free; to some extent what I'm trying to do here is to note that the phenomenon is somewhat more general — though especially outside of finance, where heterogeneity is less pervasive than in most markets — and that the final decision to execute a deal (and perhaps to choose its timing) is only one way in which the specifics of a deal will only be fully coordinated when at least one of the parties is willing to go along with something other than what might have been that party's first choice.

Wednesday, January 22, 2014

high-frequency trading and combinatorial auctions

I tend to support a lot of proposals that would somewhat rein-in certain high-frequency trading behaviors; one proposal with some prominent proponents is a system of frequent batch auctions, though I prefer one of my professors' suggestions that orders not be eligible to be cancelled until one second after they are placed. I would also like to note in this context that the discussion of this as a policy question seems usually to conflate regulators with the private institutions running exchanges; a first step by regulators would be to weaken Reg NMS such that privately-run exchanges are clearly allowed to implement these sorts of rules in a way that is not obviously self-defeating; if that proved "insufficient" (in someone's judgment), I hope it would only be later that the costs and benefits of requiring new rules in every market be imposed.

Some of the defenders of high-frequency trading argue that it provides liquidity, and indeed I think it is likely the case that they provide liquidity to somewhat less-high-frequency traders, who in turn provide liquidity to even-lower-frequency traders, and that perhaps that feeds through to a net advantage to savers looking for borrowers and borrowers looking for savers to convert, finally, real goods and services now into real goods and services in the future in an efficient, pro-social way. I think the final ends, though, are very little impeded by gumming up the works at a one-second time scale, and I do believe that a lot of the real investments of real resources into reducing latency and trying to out-strategize the other high-frequency players probably amounts more to wasteful rent-seeking than to socially beneficial creation of infrastructure to improve capital allocation. Some of the opponents of high-frequency traders like to highlight the existence of flash-crashes — which, at some scale, are fairly common, though usually smaller than the most famous such event. I'm not particularly concerned by that, though, and, if that seemed to me like the biggest problem with high-frequency trading, my prescription would probably start and end with the requirement that "market" orders for retail customers be submitted as IOC limit orders at a price that is some multiple (nearish 1) of the price 15 minutes before the order is entered — caveat venditor beyond that.

The summary of the set-up, then, is that I support moderate efforts to curtail high-frequency trading, though I don't think much of some of the arguments that one hears for and against such efforts. What follows, then, is ... well, it's not exactly Devil's Advocacy, but it's an argument that seems plausibly to be stronger than any of these other arguments, and, if someone could convince me that the details I can't work out would point in that direction, I would change my position, or at least modify what sorts of changes I would support.

What I want to note, first, is that markets are incomplete, and that the values of different traded securities are related to each other in possibly occasionally complicated ways. What this means is that, given some (potential) saver's information and risk preferences, in principle that agent could exhibit a fairly complicated demand curve for securities — the price of one security might affect one's demand for another security in an important way, especially if that price is taken to represent the result of some quasi-equilibrium process involving other agents with other information. If markets were complete, this wouldn't be true in any important way, but markets (obviously) are not, and I suspect that this is somewhat important. In some ideal setting, then, we wouldn't run the exchanges for different securities independently of each other; we would run them all together as one big combinatorial auction.

There are at least two problems with big combinatorial auctions, at least of the sort a naive but brilliant mathematician might construct. One is that they are computationally very intense; the complexity is exponential in the number of items being "auctioned", and with thousands of listed securities, we really don't have the computing power to pull this off. The other is that the agents being called upon to submit "demand curves" would themselves face a problem that is way beyond their own ken; they would be asked to specify some possibly complex rule for converting systems of prices into systems of quantities. Even to the extent that people have an intuitive sense of what they think they would like to buy, they tend to be bad at working with more than the simplest of hypotheticals, and it's hard to imagine a language that would allow them to easily but flexibly express what they want to the central computer.

Modern combinatorial auctions address both of these problems, possibly giving up some of the pure perfection that might in principle be available from the impossible straightforward approach by generating a practical and, based on substantial evidence, very good iterative process instead. One of the most popular modern combinatorial auctions is the combinatorial clock auction, sometimes (as at the link) with a finalizing stage, which presents each agent with a much more tractible problem at each step (a single set of hypothetical prices, basically, rather than all possible sets of hypothetical prices), and leaves the computer with a much more tractible problem at each step as well. Details aside, even though the overall algorithm is designed explicitly to handle the fact that agents' values for combinations of items will not simply be a sum of values for each item separately, the iterative process sort of looks as though it's treating each item separately; it's the dynamic nature of the procedure that ultimately takes account of the "complementarity".

Practical combinatorial auctions usually go fewer than 100 rounds (I think), but I have seen results in the matching literature in which an attempt to decentralize the "matching" procedure can require huge number of rounds — typically on the order of the square of the number of agents. What these models have in common with the situations in which combinatorial auctions have found use is that the preferences, while they (in principle) exist in high-dimensional space, occupy a low-dimensional manifold in that space; they are reasonably tightly constrained, even if the constraint isn't "independent values". It's easy for me to imagine that a system with thousands of items and truly complex relationships between them that one might require billions or trillions of iterations to get good convergence to a value near "equilibrium" — and that, short of that, doubling the number of iterations might improve the result by a substantial amount.

If someone can convince me that the incompleteness of the financial markets is ameliorated by something like the current market structure, viewed as a combinatorial auction with many rounds per second, and that reducing the frequency of the "rounds" would significantly reduce the extent to which prices are "correct", then I would at the very least want to be careful about changing the rules.

Monday, January 6, 2014

ASSA conference

The big annual convention of the Allied Social Sciences Associations (I think) took place this past weekend; I attended sessions on Friday and Sunday (spending Saturday with my family instead), and want to record some somewhat random thoughts I had before I lose them elsewhere.
  • One of the sessions I attended yesterday was on "robustness", in which people attempted to say as much as they could about a particular theoretical model while leaving some important part of the model unspecified; often this took the form of bounds, i.e. "without knowing anything about [X], we can still determine that [Y] will be at least [Y0]". In one paper, the author supposed that two agents in the model have the same "information structure", but that the observer (the "we" in the above quotation) doesn't know what it is. The "worst" possible information structure looks a lot like the "worst" possible correlated equilibrium in a related game, a point he never made, and that I still haven't made precise enough to be worth noting to him. I'm not particularly enamored of his paper, but I do like correlated equilibrium, so I might come back and try to figure out what I mean.
  • The godfather of "robustness" is Stephen Morris, who has spent a lot of the last two decades thinking about higher order beliefs (what do I think you think Alice thinks Bob thinks?) and the past decade thinking about what properties of strategic situations are, to varying degrees, insensitive to them, especially in the context of mechanism design. A lot of the 1980's style mechanism design and auction theory says things like "if buyers have valuations that follow probability distribution F, here's the auction that will, in terms of expected value, generate the most revenue". If you don't know F, though, you're kind of lost. So to some extent much of the project is about making things independent of F (and other assumptions, some of them tacit). On a seemingly unrelated note, my brother and I have frequently discussed the idea that some "behavioral" phenomena — people behaving in ways that have internal inconsistencies, or seem clearly in a certain decision problem/strategic situation to be "mistakes" — may result from people's having developed heuristics for doing well in certain common, realistic situations, and carrying them over naively to other scenarios (especially artificial ones in experiments) where they don't work nearly as well. During the conference it occurred to me that this is similar to using a mechanism that has been designed for a particular F. It is also, to some extent, related to the "machine learning" concept of "overfitting" — people adapt so well to some set of experiences that they are overly specialized, and do poorly in more general situations — where "robustness" is related to "regularization", which amounts to restricting yourself to a set of models that is less sensitive to which subset of your data you use, and is hopefully therefore more applicable to data you haven't seen yet.
  • The last set of ideas, and that most closely related to my current main project, is related to a "backward induction" problem I'm having. Traditional game theory solution concepts involve "common knowledge of rationality" — defining recursively, all players are "rational", and all players know that there is common knowledge of rationality. In particular, if everyone knows that a certain action on your part can't be profitable to you, then everyone can analyze the strategic situation with the assurance that you won't take that action. If some action on my part would only be good for me if you do take that action, then everyone can rule out the possibility that I would do that — I won't do it, because I know that you won't make it a good idea. Where this becomes "backward induction" is usually in a multi-stage game; if Alice has to decide on an action, and then I respond to her action, and then you respond to my action, she figures out what you're going to do — in particular, ruling out something that could never be good for you — and, supposing I will do the same analysis, figures out what I am going to do. This is normally the way people should behave in dynamic strategic situations. It turns out that people are terrible at it.
    In my current project, the behavior I'm hoping/expecting to elicit in the lab is ruled out in more or less this way; it's a multi-period situation in which everyone is provided enough information to be able to rule out the possibility that [A] could happen for all of the next 20 periods, and if everyone knows (for sure) that [A] won't happen in the next period, then it's fairly easy to figure out that they shouldn't act in a way to cause [A] to happen in this period. Perfectly rational agents should be able to work their way back, and [A] should never happen. I think it will. I want to be able to formalize it, though. So I'm trying to think about higher-order beliefs, and how one might describe the situation in which [A] happens.
    • One threat to the idea of backward induction is that it requires "common knowledge of rationality", even where "common knowledge of rationality" has been refuted by observed evidence. Suppose you and I are engaged in a repeated interaction with a single "rational" pattern of behavior — you know I will always choose B instead of A because we are both presumed to be "rational" and B is the only choice consistent with backward induction. Typically this last clause means that, if I were to choose A, I know that you would respond in a particular way because you're rational, and because you know how I would respond to that since I'm rational, and that whole chain of events would be worse for me than if I choose B. Having completed the analysis, we decide that if everyone is rational (and knows that everyone else is, etc.), I should choose A. But then, if I choose A, you should presumably infer that I'm not rational — or that I'm not sure you're rational, or not sure you're sure I'm rational, or something. But this seems to blow a hole in the entire foregoing strategic analysis.Now, if this is really the only problem with backward induction, then if nobody acts more than once, we could still get backward induction; if you do the wrong thing, well, that's weird, but maybe it's still reasonable for me to expect everyone whose actions I still have to worry about to be rational. Or maybe it isn't; in any case, I doubt human subjects in such a situation would reliably perform backward induction. It might be interesting to check some day, though, if it happens to fit conveniently into something else.
    • While I'm thinking in terms of which systems of beliefs I think are "reasonable", I should probably look at self-confirming equilibrium; this is the idea that "beliefs" can only evolve in a certain way along a given "path", which would at least constrain how an initial set of beliefs would affect behavior.
    • That might be more compelling if I try to think about normal form. This is kind of an old idea of mine that I've not pursued much, in part because it's not very interesting with rational agents using Bayesian updating, but there was a remark at one of the sessions yesterday that the difference between a "dynamic game" and a "normal-form game" is that in the former one can learn along the way. If you "normalize" the dynamic game and "learn" by Bayesian updating, it turns out that, well, no, there really isn't a difference; if you start with a given set of beliefs in either the dynamic game or its normal form and work out the normal form proper* equilibria or the sequential equilibria of the dynamic game, they're the same. If learning isn't Bayesian, though, then, depending on what it is, different "dynamic" games with the same normal form might result in different outcomes. How this looks in normal form might be interesting, and might be expressible in terms of restrictions on higher order beliefs.

* I think. To get the backward induction right, you need some refinement of Nash equilibrium that at least eliminates equilibria with (weakly) dominated strategies, and I think Myerson's "proper" equilibrium is at least close to the right concept. Actually, there's a paper by Mertens from 1995 that I should probably think about harder. In any case, I think there's a straightforward normal-form equilibrium concept that will encapsulate any "learning" that goes on, and that's really my point.