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.

Thursday, April 23, 2015

heterogeneity and aggregation

This post will have less content than usual, so I'll try to keep it short.  This post is mostly here to jog my memory if I look at it in the future.

One of my interests is in how heterogeneity has important effects on aggregate economic variables that get lost with the "representative agent" framework.  One somewhat-well known example is borrowing constraints; if they bind different agents differently those agents may behave, in aggregate, in a way that is very different from how any single agent might be expected to behave.  There's a lot of literature on the idea that many of the homebuyers driving the recent housing price bubble were, in fact, acting at the time they did in part because they had recently had borrowing constraints eased.  Other agents may, in this sort of model, still play a role in magnifying what might be a small bubble if it were left only to the agents whose borrowing constraint was loosened; agents bid up prices in anticipation of each other.  Depending on the response functions, you may only need a small initial impetus to cause a dramatic change.  (The multiplier may even be locally infinite in some sense where you have a no-longer stable equilibrium.)

Thursday, April 16, 2015

Interpretations of Probability

I've been doing some reading (at Stanford's philosophy portal, among other places) and thinking about the meaning of probability — well, to some large degree on-and-off for at least 15 years, but a bit more "on" in the last month again.  The page I linked to groups concepts into three groups, which they describe as "a quasi-logical concept", "an agent's ... graded belief", and "an objective concept" that I will conflate with one of their examples, the "frequentist" idea.  My own interpretation of these ideas is that they form a nexus around "subjective" and "frequentist" ideas, with the formal mathematical calculus of probability connecting ideas to each other in important ways.  What follows are mostly my own thoughts, though clearly building on the ideas of others; that said, I'm sure there is a lot of relevant philosophical literature that I have never seen, and even much that I have seen that I have not understood the way it was meant.

I'll start by referencing a theorem related to rational agent behavior.  The upshot is that under reasonable assumptions, rational agents behave in such a way as to maximize "expected utility", where by "reasonable" I mean not that anybody behaves that way, but that if you could demonstrate to a reasonably intelligent person that they had not behaved that way, they would tend to agree that they had made a mistake somewhere. "Utility" is some numerical assignment of values to outcomes, and "expected utility" is its "expected value" under some mathematically consistent system of probabilities. The theorem, then, is that if a person's decisions are all in some normatively-appealing sense consistent with each other, there is some way of assigning probabilities and some way of assigning "utility" values such that those decisions maximized expected utility as calculated with those probabilities and utilities.

A related result that gets a lot of use in finance is that if "the market" isn't making any gross mistakes — again, in a normatively-appealing way, but also in a way that seems likely to at least approximately hold in practice — then there is some system of probabilities and payouts such that the price of an asset is the expected value of the discounted future cash flows associated with that asset.  In finance texts it is often emphasized that this system of probabilities — often called the "risk-neutral measure" — need not be the "physical measure", and indeed most practitioners expect that it will put a higher probability on "bad outcomes" than the "physical measure" would.  The "physical measure" here is often spoken of as an objective probability system in a way that perhaps sits closer to the "frequentist" idea, but if the market functions well and is made up mostly of rational agents whose behaviors are governed by similar probability measures, the "physical measure" used in models will tend to be similar to those.  The point I like to make is that the "physical measure", in a lot of applications, turns out not to matter for finance; the risk-neutral measure is all you need.  Further, the risk-neutral measure seems philosophically clearer; it's a way of describing the prices of assets in the market, and, implicitly, even prices of assets that aren't in the market.[1] It should be noted, though, that the "physical measure" is what people prefer for econometrics, so when one is doing financial econometrics one often needs both.

These contexts, in which a set of numbers on possible events has all of the mathematical properties of a probability system but need not correspond tightly to what we think of as "probability", play a role in my thinking.[2]

I think the most common definitions you would get for "probability" from the educated layman would fit into the frequentist school; the "probability" of an event is how often it would occur if you ran the same experiment many times.  Now, the law of large numbers is an inevitable mathematical consequence of just the mathematical axioms of probability; if a "draw" from a distribution has a particular value with an assigned probability, then enough independent draws will, with a probability as close to 1 as you like, give that particular value with a frequency as close to the assigned probability as you like.  If you and I assign different probabilities to the event but use the laws of probability correctly, then if we do the experiment enough times, I will think it "almost impossible" that the observed frequency will be close to your prediction, and you will think it "almost impossible" that it will be close to my prediction.  Unless one of us assigns a probability of 0 or 1, though, any result based on a finite number of repetitions cannot be completely ruled out; inferring that one of us was wrong requires at some point deciding that (say) 1×10-25 is "practically 0" or 1-1×10-25 is "practically 1". For any level of precision you want (but not perfect precision), and for as small a probability (but not actually 0) as you insist before declaring a probability "practically zero", there is some finite sample size that will allow you to "practically" determine the probability with that precision. So this is how I view the "frequentist" interpretation of probability: the laws of probability are augmented by a willingness to act as though events with sufficiently low probability are actually impossible.[3]

More often, my own way of thinking about probabilities is closer to the "subjective" probability; "a probability" is a measure of my uncertain belief, and the tools of probability are a set of tools for managing my ignorance.  It is necessarily a function of the information I do have; if you and I have different information, the "correct" probability to assign to an event will be different for me than for you.[4]  If one of us regularly has more (or more useful) information than the other, then one of us will almost certainly, over the course of many probability assessments, put a higher probability on the series of outcomes that actually occurs than the other will; that is to be expected, insofar as my ignorance as to whether it will rain is in part an ignorance of information that would allow me to make a better forecast.  There is a tie-in here to the frequentist interpretation as I cast it in the previous paragraph, related to Mark Twain's assertion that "history doesn't repeat itself, but it rhymes": not only is it impossible to take an infinite number of independent draws from a distribution, it is impossible to take more than one with any reliability. At least sometimes, however, we may do multiple experiments that are the same as far as we know — that is, we can't tell the difference between them, aside from the result. If we count as a "repetition" those events that looked that same in terms of the information we have[5], then we might have enough "repetitions" to declare that it is "practically impossible" that the probability of an observation, conditional on the known information, lies outside of a particular range.

One last interpretation of probability, though, is on some level not to interpret probability.  (One might call this the "nihilist interpretation".)  A fair amount of the "interpretations of probability" program seems oriented around the idea that whether an event "happens" or not, or whether something is "true" or not, is readily and cleanly understood, and there is some push to get probabilities close to 0 or 1, since we feel like we understand those special cases.  We know, though, that our senses and minds are unreliable; everything we know about the world outside ourselves is with a probability that is, in honesty, strictly between 0 and 1.  As we get close to 0, or close to 1, as a practical matter, the remaining distance will make no practical difference — it can't.  But those parts of the world that are practically described by probabilities are in reality on a continuum with those we can practically treat differently, and consistently follow the laws of mathematics and nature, with 0 and 1 as, at the very best, special cases.

[1] If there are a lot of relevant possible assets that "aren't in the market", the risk-neutral measure may not be unique, i.e. there may be several different systems of probability that are consistent with the mathematical rules of probability and market prices; the conditions for existence are more practically plausible than the conditions required for uniqueness. Sometimes you might wish to a price a hypothetical asset whose price depends on which of the available risk-neutral measures you use, in which case existing prices will not fully guide you.

[2] As is noted at the Stanford link, there is some sense in which mass and volume can be made to behave according to the laws of probability; it is probably important to my philosophical development that the systems of "probability" I give in the text are closer in ineffable spirit to the common idea of "probability" than that.

[3] To some extent I'm restricting my discussion to "discrete" probability distributions to avoid having to talk much about "measurability", and to some extent I have failed here; if you flip a fair coin 100 times, any series of outcomes has a probability of less than 1×10-25. There are 161700 different series that contain 3 heads and 97 tails; if I don't distinguish between any of those 161700 different outcomes, then the probability of that single aggregate "3 heads" event is bigger than 10-25, even though any single way of doing it is not. If I insist on rounding the probability of each possible outcome to 0, then it is certain that an "impossible" outcome will result, but if I say "there are 101 measurable events, one for each possible number of heads," then the probability of an "impossible" outcome is extremely low (in this case, there are 6 such "impossible" outcomes, and they are, taken together, "impossible"). Ultimately you would probably want to take account of how many different events you want to distinguish when you're deciding what threshold you're rounding to 0; if you want to distinguish 1025 different events, then a probability threshold substantially smaller than 10-25 should be used.

[4] In some sense, this is what the Stanford site calls "objective probability", insofar as I'm asserting a "right" and "wrong" notion. What might be a conditional probability from the standpoint of the "objective" probability idea — that is, the probability conditional on the information we know — is what I'm thinking of here as my "prior" probability, along with an assertion that what from the "objective probability" standpoint would be a "prior" probability isn't actually meaningful.

[5] This, too, is basically "measurability", which is perhaps unavoidable in any non-trivial treatment of probability, even with finite "sample spaces".

monetary policy and the theory of money

I have several dollars on top of my dresser, but most of my money (in pretty much any sense in which economists regularly use the word) exists as electronically-recorded liabilities of financial institutions.  For most of my bills, it is more convenient to pay them out of such intangible money than the tangible money. Supposing we can still count the zero-interest-rate environment that has persisted for more than six years "abnormal", we have mostly shifted to a medium of exchange that pays interest, and the trajectory of technology (both information technology and financial technology) is toward more of that.

Traditional explanations of how monetary policy work often run more or less like this: the fed controls short-term interest rates, which affect the trade-off people make between holding their money in more liquid versus less liquid forms, and if they increase the amount they have in more liquid forms they spend more.[1] As the most liquid form of money starts to pay interest at a rate that moves more or less one-to-one with other interest rates, we face something of a paradox; the interest rate is effectively zero in terms of the actual medium of exchange, and the "interest rate" that the fed targets simply measures the rate at which the value of the dollar declines relative to that.

If people at that point are largely using interest-bearing deposits and funds as the actual store of value and medium of exchange in the economy, to what extent does this "dollar" whose value declines relative to it even matter?  At least at first, it can continue to serve as a unit of account.  Indeed, at this point it seems to have retained that function in the United States, even as it has largely lost the others; even where you see contracts with "indexing" of some sort, it's far more often to a price index than to something connected to interest rates per se.  Perhaps over time contracts could start to have future cash flows stipulated in terms of the amount of money that would be in a bank account at that point in time if a specified amount had been deposited at the beginning of the contract, but there's no logical reason why the new medium of exchange would need to take over this last function of money.

Thus the dollar, increasingly, serves only as a unit of account, and will maintain its relevance only if it continues to serve for many purposes as a better unit of account than some alternative.[2] What makes a good unit account is not necessarily entirely the same thing that makes a good store of value or medium of exchange.  To the extent that it does not, this new separation is in fact liberating for the Fed; it can focus on making the dollar a good unit of account, possibly allowing more volatility in its value than would be optimal if it were also a widespread store of value.

A business, for example, will typically have inputs that it purchases as it goes along, but will also require long-term inputs into the production process — a lease on a retail store, for example. (Employees who may, in principle, be freely dischargeable at-will employees, are probably in practice at least somewhat long-term inputs due to firm-specific knowledge and training and the costs of hiring and firing.) It also will produce products that may include short-term sales, longer-term contracts to supply clients, or both. It is likely that there will be some "duration mismatch" between inputs and outputs. In each case where the company is locked in to a decision years ahead of time, it risks a change in circumstances; if it is mostly selling as it goes along, it might wish to respond to an unexpected drop in demand by finding a way to cut production costs, but if it is selling mostly by long-term contract but has to buy its inputs day-to-day, it is subject to an increase in costs that it can't pass along. To the extent that it can specify prices in long-term contracts in terms of a unit of account that will drop in value if demand for its product goes down, or increase in value as competition for its supplies goes up, it will be easier for the company to responsibly engage in this business.  A central bank that is trying to optimize its currency for use as a unit of account, therefore, will tend to devalue its currency when the economy in general is slowing down and increase its value (at least relative to expectations) when the economy is especially robust.  These kinds of fluctuations in the value of actual holdings of the currency — long-term, as a store of value, or even short-term, as a medium of exchange, between the sale of one good or service and the purchase of another — will tend to make it less useful for those purposes.  In a world where the central bank doesn't have to trade off these costs against the benefits of a countercyclical unit of account, it can focus on a better unit of account, while the other functions of money are provided elsewhere.

[1] There are (perhaps more compelling) arguments related to intertemporal substitution as well, but note that those explanations implicate the real interest rate rather than the nominal interest rate. You therefore need a story about how inflation and interest rates are simultaneously determined, and in particular why a decision by the fed to raise interest rates would reduce inflation expectations. These stories and explanations typically themselves come back to a "liquidity effect", so we're left with the same conundrum as the role of non-interest-bearing money atrophies.

[2]To some extent, as long as the government is using it as a unit of account — specifying tax liabilities, contract payments, and social security benefits in dollars, and even taxing the deviation between our new electronic currency and the dollar as "interest income" — it can be kept relevant by fiat.

Monday, February 23, 2015


Felix Salmon writes about negative interest rates:
Here’s an example of how the psychology plays out in practice. If you pay a monthly fee on your checking account, you are probably getting negative rates on your money right now. You’re lending your money to the bank, which ends up giving you back less money than you started with. But because the negative interest rates are presented as a fee, rather than an actual negative rate, the banks are able to get away with it.
This strikes me as essentially backward; insofar as you were getting 3% interest on a "free" checking account when the federal funds rate was at 6.5%, you were paying a 350 bp fee; people hate bank fees, but of course the bank has costs, some of which increase with an increase in the number of depositors, so it hides the fees by calling it a negative interest rate (but in an environment in which, aggregated with its cost of funds, it can report a positive overall interest rate.)  That said, the psychology of "0 percent interest" is similar to the psychology of "free" (or "no-fee"); we're seeing the same psychology in different contexts.

Similarly, payday loans are typically accompanied by fees; reporting often divides these by the length of the loan and reports astronomical interest rates.  While it is not necessarily the case that the distinction between fees and interest as stated by the payday loan shops really corresponds to a distinction between transaction costs (or overhead) and a risk-adjusted cost of funds, it is certainly the case that some of the payment really is "fees" in any reasonable disinterested sense; I might just as reasonably accuse McDonald's of charging a huge rate of interest by dividing the gross profits on my sandwich by the time between my paying for it and receiving it.

While I'm on this, I might as well also push back at another common abuse of language,
Does this mean that Nestlé was being paid to borrow money? No. A company has to pay to borrow money if it ends up paying back more money than it borrowed.
He goes on to add up the franc values of the cash flows associated with the Nestlé bond, and notes that the outflows add up to more than the inflows. Even if it had come out the other way, I object to framing this as "being paid to borrow money".

The problem is perhaps clearer in the case of Apple, which does its accounting in dollars.  If Apple had borrowed money at a negative yield in francs, but the franc had appreciated sufficiently over the course of the loan, then Apple would have paid out more dollars than it received.  In the same situation, if Apple did its accounting in francs, it would record the negative interest charges.  One accounting system uses the fiction that dollars in 2020 are equivalent to dollars in 2015; the other uses the fiction that francs are francs.  Of course, we don't currently know whether the franc will appreciate or depreciate against the dollar; the point is that these are not the same thing.

Now, to a good approximation I can convert a dollar now into a dollar in 2020 by holding a physical piece of currency.  There is some nuisance and security cost to doing so; it may be lost or stolen.  These facts notwithstanding, this ability to sit on physical currency is the reason importance is attached to "zero interest rates" and "negative interest rates"; there is, in the lingo, an apparent arbitrage, in which (for example) Apple borrows Swiss francs, holds them in a vault, pays out some smaller number of Swiss francs, and, if it likes, converts the balance to dollars (or cadmium, etc.) at some point in time along the way.  As long as the surplus from this trade is worth the expenses associated with issuing the bond, securing the currency, and making the payments, then it would be worth doing; as a matter of fact, though, those costs are probably at least 10 or 20 basis points; the costs of securing and transacting in physical currency are probably among the reasons bondholders are willing to buy bonds at negative yields in the first place.

The most egregious consequent error that I see smart people make a lot in public policy debate — even smart economists, but ones who think of interest as "the money paid to borrow other money" — is to suggest that, as long as interest rates are 0 or very close to it, we can borrow and spend with impunity.  The simplest retort is that if we borrow the money, we will have to pay back that money. An argument can be made that it is more useful to spend the money now than it will be later, but that argument should be made, not assumed, and the 0 interest rate is not particularly relevant to it.  The tradeoff in value between spending now and spending five years from now may be that $1.10 in spending now is worth $1 of spending in the future, or that it is $1 and $1.10, respectively; there is no reason in economics that precludes the former possibility, in which case any interest rate that is higher than (using rough figures) -2% is higher than should be incurred.

Accounting rules separate interest payments from principal payments, and taxes and regulations sometimes create economic effects, but in and of themselves they are not economically distinct, and the correct way to think about interest rates is that they measure a rate of exchange between (say) dollars at different points in time.  A balance that grows because of "accruing interest" is typically growing, at least in part, because it is being measured in dollars that are worth less and less.

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.)