Friday, October 9, 2015

mechanism design and voting

"Voting systems" are mechanisms, but we also design mechanisms for situations that aren't usefully construed as voting; in terms of practically used mechanisms, I'm thinking especially of auctions and other allocation and matching mechanisms.  Typically these allocation mechanisms try to optimize the outcome in some sense; where centralized matching mechanisms have replaced decentralized systems, they often serve to overcome coordination problems and result in Pareto-efficient outcomes, for example, but Pareto-efficiency is famously weak, and it has been shown, for example, that different school-choice algorithms are optimal under different circumstances, even using a single ex ante expected social welfare criterion.

In the literature, there is typically a natural or convenient social welfare criterion, but in many real-life contexts, different people have different ideas about the "right" social welfare criterion — which brings us back to voting mechanisms.  Insofar as people vote on the basis of ideas at all, people vote primarily on the basis of their conception of the "social good", and only to a much smaller extent, if at all, on "self-interest".[1]  One might therefore imagine a two-step procedure in which some mechanism elicits from people their conception of "justice" or "social welfare" in the first step and then asks them for their personal preferences as to their own allocation in the second step, using a mechanism tuned to maximize the criterion selected in the first step.

It is generally the case in theory that a single combined mechanism for doing two things will perform better than multiple separate mechanisms; roughly, if you assume agents are strategic, you sometimes have to "buy off" agents to get them to reveal as much information as possible, and if you combine the mechanisms you can "buy off" the agents in one stage with compensation in the other stage, sometimes at a lower overall cost.  There's some level on which it may be useful to think of proportional representation voting schemes themselves in this way; putting aside practical reasons for them related to information-gathering and gaining buy-in from electoral minorities (avoiding e.g. criminal behavior in response to laws perceived to be invalid), one might have a higher-order desire that a committee reflect other people's preferences as well as one's own, even if bills supported by the majority and opposed by the minority are going to be passed under either system, whether by a close vote of proportionally elected representatives or a landslide vote in a chamber dominated by the electoral majority.  I suspect there might be other interesting mechanisms that join what are more clearly separate "What is our consensus social goal in terms of heterogeneous and unknown preferences?" and "What are our different preferences, and what outcome therefore maximizes the socially preferred criterion?" questions even in a purely instrumental kind of set-up.  One caveat to add before posting this, though, is that I expect the strictly "best" theoretical mechanism in this kind of situation to be weird and complex in some important ways, and thus impractical; it might elucidate more practical conjoined mechanisms, but it might turn out that the best approach in practice is to go back and use a two-stage approach in which agents can readily understand each stage.

[1] Interestingly, a lot of people know that they vote primarily on the basis of what is "right" rather than their own self-interest, but believe that most other people, especially their opponents, do not!

Wednesday, September 30, 2015

market manipulation

My most recent post invited, in a couple of places, tangents on "market manipulation".  I decided to make that a separate post.

There has been some recent suggestion (mostly by uninformed parties) that corporate stock repurchases constitute "market manipulation", i.e. an attempt to artificially drive up the price of their stock.  There is, in fact, apparently a safe harbor provision in relevant regulations dating back to 1980 that indicate that a company is presumed not to be manipulating the market in its stock provided that its purchases constitute no more than a particular fraction of the trade volume over a particular period of time, which suggests that the idea is not entirely novel.  Relatedly, over the last ten years there have been complaints that countries, especially China, are "manipulating" the market for their currencies, and there are provisions in various trade agreements that apparently forbid that, apparently also without particularly well defining it.

My visceral response to the China accusation in particular, the first time I heard it, was "of course they're manipulating the market; that's their prerogative", with a bit of surprise that it was considered untoward; under certain circumstances intervention in the foreign exchange market seems like the easiest way to implement monetary policy, and I kind of think the US should have tried buying up assets in Iceland, India, Australia, and New Zealand at various times in the last seven years when the currencies of those countries have had moderately high interest rates.  The purpose here is not to create prices that are incorrect; it's to change the underlying value of the currency. The same is true of stock repurchases, at least classically; repurchase of undervalued shares increases the value per share of the remaining shares, increasing their value, with the price rising as a consequence.

This is basically the distinction I make in these contexts; I have some sympathy for rules against trying to drive the price away from the value, whereas influencing the value of assets is often on some level the essential job of the issuer of those assets.  While "value" is even more poorly defined than "price", this motivation is frequently somewhat better defined, if perhaps hard to witness; if a company releases false information, that will affect the price and not the value, whereas a repurchase, especially one that is announced in advance and performed in a reasonably non-disruptive way, is more likely an attempt to influence the value of the asset, which is well within the range of things the company ought to be doing.

prices and market liquidity

Assets don't have prices; trades have prices, and offers to trade have prices.  When a market has a lot of offers to buy and a lot of offers to sell at very nearly the same price, the asset can be said informally to have that price (with that level of precision), and if trades take place frequently (compared to how often the price changes by an amount on the order of the relevant precision) you can (for most purposes) reasonably cite the most recent trade price as the asset price, but in corner cases it's worth remembering that that is emergent and only partial.

Most "open-ended" mutual funds these days allow you to buy or sell an arbitrary number of shares of the mutual fund from the mutual fund itself, which (respectively) creates or destroys those shares and sells them shortly after the market closing that follows the placing of the order; that is, if you place an order on a weekend before a Monday holiday, your transaction takes place late Tuesday afternoon, at the same time as if you place it early Tuesday afternoon.  The price at which the transaction takes place is the "Net Asset Value" (NAV); the fund calculates the price of all of the assets it owns, divides it by the number of shares outstanding, and buys or sells the shares pro rata.  For large cap stock mutual funds, this works quite smoothly almost always, and it's extraordinary for it to work poorly; the assets have closing auctions on various stock exchanges that tend to be fairly competitive and result in official "closing" prices that are fairly unbiased and accurate predictors of the price at which the asset may next be bought and/or sold (or, indeed, the prices at which they may have been bought or sold earlier that afternoon).  These assets have prices to a sufficient extent to make this rule work.

There has been increasing concern lately about other kinds of funds, which own assets that do not have very well-defined prices, and here's an example of a fund whose client doesn't like how it made up the prices, but I tend to think the procedure was reasonable. The client sold a very large amount of shares back to the fund — the fund would have to sell assets (at the very least to get back to its usual level of cash holdings), and to value some of the assets that were particularly hard to sell, asked a few dealers how much it could sell them for. They got, naturally, a lower price than they would have had to pay to buy them, or the price at which they last traded; this resulted in a lower NAV than one of those higher prices would have.

It seems to be conventional to use "last-traded price" in many contexts where that isn't a particularly unbiased predictor of where the asset can be sold in the future; if bonds have dropped in price over the last couple days, and a mutual fund has a fair number of bonds that haven't traded in that time, the "last-traded price" is an overestimate of any meaningful "price" that the bond has now, and fund holders redeeming at the (inflated) NAV will be overpaid, to the disadvantage of continuing fund-holders. A bank — I think it was Barclays; I should have made a note — has indicated that, for the high-yield bond mutual funds it was looking at, this problem could be solved by letting sellers (i.e. people redeeming their mutual fund holdings) choose between a 2% discount in the price or a 30 day delay in settlement, either compensating the fund (i.e. the other, continuing investors in the fund) for the adverse selection problem or waiting until bond prices have updated.
While this is mostly intended as a solution to the adverse selection problem, it also somewhat mitigates the problem I'm noting here; a fund with 30 days' advanced notice can sell assets more carefully than one trying to raise a lot of cash before 4:30 this afternoon.

I kind of think that funds (especially with illiquid assets) should quote bid-offer spreads that reflect the bid-offer spreads of the underlying assets; if all of the assets have bids that are 95% of their offers, the fund-wide spreads might be somewhat tighter than that, reflecting the fund's discretion in choosing which assets to sell and a level of liquidity support (cash holdings or perhaps a short-term line of credit, if that's allowed); they should probably, as with most active exchanges, depend to some degree on traded volume, so that large orders to sell would face larger discounts, and they should probably allow orders to buy to net off against orders to sell before hitting either the bid or the offer.  What I'm mostly looking at is essentially a closing auction with the fund filling imbalances; as I may have noted before, open-ended funds with fees for orders that create imbalances and closed-ended funds that make markets in their own stocks kind of converge on each other, and that's what seems like the right approach to me.

Thursday, September 24, 2015

shortcomings of mathematical modeling

Over the course of the twentieth century, accelerating in the second half, the discipline of economics became increasingly mathematical, to the chagrin of some people.  I myself think it has gone too far in that direction in many ways, but I feel like some of the critiques aren't exactly on point.

One of the benefits — perhaps most of the benefit — of mathematical modeling is that it forces a precision that is often easier to avoid in purely verbal arguments. This precision in certain contexts allows one to make deductions about the behavior of the model that goes beyond what is intuitive, for better or worse — most of the time it will ultimately drag intuition along with it.  Certainly if you want a computer to simulate your model, it needs to be precise enough for the computer to simulate it.  Further, any model in which forces are counteracting each other in interesting ways is going to have to be quantitative to some degree to be useful; if you want to know what effect some shock will have on the price of a good, and the shock increases both supply and demand for the good, if you don't have enough detail in your model to know which effect is bigger, you can't even tell whether the price will go up or down.

I think there are basically four problems one encounters with the mathematization, or perhaps four facets of a single problem; all of them are to varying degrees potential problems with verbal arguments as well, but they seem to affect mathematical arguments differently.
It is tempting to use a model that is easy to understand rather than one that is correct.
All models are wrong, but some models are useful; if you're studying something interesting, it is probably too complex to understand in full detail, and an economic model that requires predicting who is going to buy a donut on a given day is doomed to failure on both fronts. The goal in producing a model (mathematical or otherwise) is to capture the important effects without making the model more complicated than necessary to do so.  There are sometimes cases in which models that are too complex are put forth, but the cost there tends to be obvious; a model that is too complex won't shed much light on the phenomena being studied.  The other error — leaving out details that are important but hard to include in your model — is more problematic, in that it can leave you with a model that can be understood and invites you to believe it tells you more about the real world than it really does.
It can be ambiguous how models line up with reality.
I've discussed here before the shortcomings of GDP as a welfare measure, and have elsewhere a fuller discussion of related measures of production, welfare, and economic activity; most macroeconomic models will have only a single variable that represents something like "aggregate output", and when people try to compare their models to data they almost always identify that as "GDP", which is almost always, I think, wrong; one of the proximate triggers for this post was a discussion of an inflation model that made this identification where Net Domestic Product was probably the better measure, and if you're comparing data from the seventies to data today — before and after much "fixed investment" became computers and software instead of longer duration assets — one isn't necessarily a particularly good proxy for the other. Similarly, models will tend to have "an interest rate", "an inflation rate", etc., and it's not clear whether you should use T-bills, LIBOR, or even seasoned corporate bonds for the former or whether you should use the PCE price index, the GDP deflator, or something else for the latter.
One can write models that leave out important considerations.
One of the principles of good argumentation — designed to seek the truth rather than score points — is that one should address one's opponents' main counterarguments. This is as true for mathematical arguments as for verbal ones. I occasionally see a paper on some topic that is the subject of active public policy debate in which the author says, "to answer the question, we built a model and evaluated the impact of different policies," and the model simply excludes the factor at the heart of the arguments of one of the two camps. Any useful model is a simplification of reality, but a useful model will necessarily include any factors that are important, and an argument (mathematical or verbal) that ignores a major counterargument (mathematical or verbal) should not be taken to be convincing.
Initiates and noninitiates, for different reasons, may give models excessive credence.
People who don't deeply understand models sometimes accept models that make their presenters look smart. I like to think that most of the people who produce mathematical models understand their limitations, but there is certainly a tendency in certain cases for people who have a way of understanding the world to lean too heavily on it, and there is a real tendency in academia in particular for people who have extensively studied some narrow set of phenomena to think of themselves as experts on far broader matters.
As I noted, these problems can be present to some degree even in non-mathematical arguments; certainly Keynes talked about "interest rates" without always specifying which ones, he made tacit assumptions that were crucial to his predictions and weren't well spelled out, and he seems to have been very confident about predictions that haven't always panned out, all without mathematics.  (To the extent that we learn mathematical "Keynesian" economics in introductory macroeconomics, the math was largely introduced by Hicks a few years later attempting to make Keynes's arguments clearer and more precise.)

Ultimately, it may be that the best argument against excessive math in economics is that is has sometimes crowded out other ways of thinking; having some mathematical papers that are related to economics is a good thing, but if papers that do mathematics that is far removed from economics are displacing economic arguments that are hard to put in mathematical terms, then the discipline has moved well past the optimum, which almost certainly has a diversity of approaches.

Sunday, September 13, 2015

truncated proportional representation

It's been a while since I've had a voting systems post.  I'm going to propose a voting system for a small panel of people that will attempt to give voice to a somewhat broad range of opinions, but also allows blocks of voters to exclude candidates whom they really dislike.  The original hope was that this would lead to something of a consensus panel, though that probably really depends a bit on what sort of electorate you have; in some of my generic frameworks it leads to representation that is somewhat uniform but with extremes cut off; the relative distribution is probably typically smoother than that, with centrists disproportionately elected but even somewhat extreme characters occasionally elected, but this seems like a useful concise name for the time being.  This will be a dynamic voting system, which is to say it is to be used in an environment in which it is practical to allow voters to vote, for results to be tabulated, and for voters to change their votes.  Unlike my previous such system, this one may actually invalidate some previously valid votes along the way, such that voters are to a greater degree "forced" to change their votes.

To begin, allow each voter to vote for, against, or neutral on each candidate; each candidate accrues +5 for each vote in favor and -4 for each vote against.  This is generically strategically identical to approval voting, where voters (with probability 1 for certain assumptions) will never be neutral on a candidate.  However, after some period of time, a maximum number of votes for/against is imposed; at each point in time the maximum number of votes in favor of candidates is equal to the maximum number of votes against candidates, and that maximum is gradually reduced from infinite to 1.  Votes for more than one candidate or against more than one candidate will be dropped at some point before the final vote, but may help voters to coordinate on preferred candidates in the meantime.  At the end the panel consists of the top net vote recipients.

Note that one could well jump to the final vote; if an environment makes dynamic systems impractical but has other means of disseminating information, especially strategic information, the earlier phases may be less useful than impractical.  The dynamic mechanism is intended to increase the likelihood of convergence to a good equilibrium.

For the models I tend to use, if there are a lot more candidates than positions, many of those candidates will converge toward zero in both votes for and votes against.  Some smaller number of candidates, still typically bigger than the size of the ultimate panel by at least one candidate, will remain "relevant".  These candidates will tend to include a number of centrists receiving relatively few votes in favor but even fewer votes against, with a disproportionately smaller number of candidates who are more polarizing, with more votes in favor and more votes opposed.

Thursday, June 11, 2015

bond fund liquidity

There has been a lot of metaphorical ink spilled over the last year or so about liquidity in the bond market; my understanding is that for most bond issues buying and selling a small quantity incurs roughly the same transaction costs as it did ten years ago, or possibly less, but buying and selling a large quantity is a lot harder and more expensive; no single dealer will take your entire trade without a significant price penalty, and even breaking up your trade and going to multiple dealers is probably not going to get you in and out of your position at the sort of spread that was expected several years ago.  The big concern, though, seems to be with tail risk, namely
  1. at some point in some/many/all important issues, the ability of holders to sell will suddenly disappear altogether, perhaps at a point at which many holders would like to be able to sell
  2. bond funds in particular, which are substantially short a kind of "liquidity risk", will find themselves trying to liquidate a lot of bonds in a hurry in response to a spate of redemptions.
These are obviously tied to each other, and the first (more general) concern should distinguish between the closely related phenomena of "everyone trying to sell at the same time" and "suddenly nobody willing to buy". Microstructure models typically distinguish between "informed" sellers and what are often called "liquidity" sellers, and in an idealized world one might hope that a wave of people selling because they all happen to need cash would be met by a lot of people who don't need cash buying without a large price movement, while one might have substantially less expectation that new investors would buy in response to a wave of selling caused by the expectation of a price drop. In reality, insofar as one of the attractions of a "liquid" investment over an "illiquid" one is that it can become cash if cash is suddenly needed, if the expected value of the effective bid conditional on one's needing cash is low, one doesn't so much care whether that's because the market is thin and transaction costs are high or because one's own need for cash is strongly correlated with fundamental risks underlying the asset — that is to say this distinction is probably important to people trying to understand market dynamics, but may not matter to any individual investor.

Let's talk about bond funds, though.  Like banks, they seem to be intermediating uncomfortably between liquid liabilities and (increasingly) illiquid assets, and this works well (and even creates value) as long as the imbalances between inflows and outflows are small and gradual, but seems susceptible to a run; if I think a lot of other people are going to ask for withdrawals, leading to a heavily discounted sale of assets, I may be inclined to get out first.  It's a little bit softer here, and a little bit more like the fire sale than the bank run in that I probably don't get all of the non-run value if I sell near the beginning of a run and won't lose all of my value if I don't, but it's more like the run than the fire sale in that the fund is probably selling assets on the basis of their liquidity rather than their long-term value, and thus real value is being destroyed instead of being largely reallocated to brave long-term buyers.

One of the arcana I remember learning when I was doing Series 7 back in like 2006 or 2007 is that open-ended mutual fund shares can be transferred, though they usually aren't. "Open-ended" mutual funds are the usual kind — you expect to go to them (perhaps through a broker), given them some new money for them to invest, and get some new shares from them — shares that didn't exist before. Later you take your shares back to them, and they figure out how much they're worth, and they give you cash, and the shares disappear. In principle, unless my memory is wrong or this has changed, you could buy or sell the shares from your cousin Fred at whatever price you and he agreed on (though I'm not sure who the relevant transfer agent would be or how the transfer would otherwise be effected).  I don't know whether there is a prohibition on their being listed on an exchange; certainly it's not usually done, but I don't believe it couldn't be done if a mutual fund company thought served some purpose.

A "closed-end" fund is an idea that has become a lot less popular in the last generation or two, and was a bit more like a traditional stock-issuing company in that it would issue stock in an IPO, invest the proceeds, and return some of the earnings to investors as dividends, while investors bought and sold its stock on an exchange; what distinguished it was only that it would "invest the proceeds" in other publicly traded securities rather than a "real business".  I don't know whether it is allowed to buy or sell its own stock in the secondary market, or under what conditions; presumably it could do a shelf offering, or announce a repurchase, and I think I saw something a month or two ago suggesting that a closed ended fund dedicated to gold had some stated policy of buying back its stock if the price fell too far below the underlying value of the gold.  In practice a lot of closed-ended funds trade at substantial discounts to the assets they own, and sometimes they trade above the value of their assets, and a case could be made for their responding to these deviations by liquidating in a strategic manner and buying back stock when it is below their NAV and selling new shares and investing the proceeds when their stock is above NAV.  In both cases one would expect a soft collar, rather than an absolute peg of the price to the underlying assets, that would take account of transaction costs; in particular, a large drop in the price of the fund shares should lead to sales of liquid assets, but not to a fire sale of illiquid assets; the level of desperation with which assets are sold could be tailored to the extent and persistence of the discount of the fund price to its assets value.

An open-ended mutual fund with listed shares could do something similar from sort of the opposite direction; in particular, it could announce that, if it is faced with a lot of redemption requests, it will start throttling them, liquidating in a responsible fashion over days or weeks but not necessarily by 4PM.  Investors who really need to cash out now can sell at some discount in the market, where more patient investors who trust that the fund will eventually liquidate assets at a decent price will buy the funds shares. (I offered similar idea for bank runs a few years ago.)  Similarly, when a sudden flow of investment leads to the fund's being closed to new investment (as sometimes happens), the more bullish bulls can buy at a premium on the market, and the fund can sell new shares as opportunities to deploy the cash become available.

Either or both of these seem likely to mitigate the liquidity mismatch that bond funds face; if you want to look in the details, I suspect that taxes and management fees (and the associated incentives for increasing assets under management) would be fertile sources of devils.  In principle, when one is looking to sell an illiquid asset, one faces a trade-off between the speed at which the asset can be sold and the price at which it can be sold, and that ideally would match the discount rate of the ultimate investor; how to set up the rules to make that most likely to work out in practice is a question to which the answer is likely to require more care than is the bailiwick of this blog.

It does occur to me, since starting this post, that this is related to my attempted dissertation chapter on shortages and market structure, and should probably even be incorporated into it.

Monday, May 18, 2015

strategy and theories of mind

Economists are sometimes criticized for using expected-utility maximizers in their models more because that gives precise (in some sense) predictions than because it matches the way in which individual people typically make decisions.  Economists who use expected-utility maximizers in their models sometimes respond, at least in part, "Well, yeah;" particularly where "framing effects" seem to be important, "behavioral economics" can often give contradictory predictions, depending on how you read the situation, and other times gives no prediction at all; there are many more ways to be irrational than to be rational, and particularly if your criticism ends at "people are sometimes irrational", it is completely useless.

While there is, in fact, at least some consistency to the way in which people deviate from traditional economic models, I think exactly this potential variety in ways to deviate — even ways to deviate just slightly — may well be important to understanding aggregate behavior.  Since at least Kreps et al, (1982)[1], it has been reasonably well-known that a population of rational agents with a very small number of irrational[2] agents embedded in it may behave very differently from a population of which all members are commonly known to be rational. In that paper the rational agents knew exactly how many people were irrational and in what way — they had, in fact, complete behavioral models of everyone, with the small caveat that they didn't know which handful of their compatriots followed the "irrational" model and which followed the "rational" model. In the real world, we have a certain sense that people generally like some things and behave in certain ways and dislike other things and don't behave in other ways, but there is far less information than even in the Kreps paper.

It is interesting, then, that in a lot of lab experiments, the deviations from the predictions of game theory take place "off-path" — that is, a lot of the deviations involve subjects responding rationally to threats that don't make sense. Perhaps the simplest example is the "ultimatum game"; two subjects are offered (say) $20, with the first subject to propose a division ("I get $15, you get $5"), and the second subject to accept or refuse the split — with both subjects walking away empty-handed if the split is refused. This is done in an anonymous way, as essentially a single, isolated interaction; gaining a reputation, in particular, is not a potential reason to refuse the offer. Different experiments in different contexts find somewhat different results, but typically the first subject proposes to keep 3/5 to 2/3 of the pot, and the responder accepts the offer at least 80% of the time. It is certainly the case that respondents will refuse offers of positive amounts of money, especially if the offer is much less than one third of the pot, but the deviation from the game-theoretic equilibrium that is most often observed is that the offeror offers "too much", in response to the (irrational) threat that the respondent will walk away from the money that is offered. This does not require that they be generous or have strong feelings about doing the "right" thing, or that they hold a universally-applicable theory of spite, only (if they are themselves "rational") that they believe that some appreciable fraction of the population is much likelier to reject a smaller (but positive) offer than a larger offer.

Game theoretic agents typically have fairly concrete beliefs about the other agents' goals, and from that typically formulate fairly concrete beliefs about other agents' actions. There may be very stylized situations in which people do that, but I think people typically use heuristics to make decisions, in somewhat more reflective moments make decisions after using heuristics to guess what other agents are likely to do, and only very occasionally circumscribe those heuristics based on somewhat well-formulated ideas of what the other agents actually know or think. The reason people don't generally formulate hierarchies of beliefs is that they aren't useful; a detailed model of what somebody else thinks yet another person believes another person wants is going to be wrong, and is not terribly robust. The heuristics are less fragile, even if they don't always give the right answer either, and provide a generally simpler and more successful set of tools with which to live your life.

[1] Kreps et al, (1982): "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Journal of Economic Theory, 27: 245--252

[2] I feel the need to add here that even with their "irrational" agents, it is possible (easy, in fact) to write down a utility function that these agents are maximizing — that is, they are "rational" in the broadest sense in which economists use the term. Economists often do, sometimes in spite of protestations to the contrary, suppose not only that agents are expected utility maximizers but that they dislike "work", they don't intrinsically value their self-identity or their identity to others (though they will value the latter for instrumental reasons), etc. Often, without these further stipulations, mainstream economic models don't give "precise" predictions in the sense I asserted at the beginning of this post; in the broad sense of the term "rational", there may be a smaller set of ways to be rational than to be irrational, but there are a lot of ways to be rational as well, and restricting this set can be important if you want your model to be useful. For this post I mostly mean "rational" in the more narrow sense, but it should be noted that challenges to this sense of "rational" are much less of a threat to large swaths of economic epistemology than the systematic violations of expected utility maximization are.