Monday, February 1, 2016

liquidity, solvency, and Ponzi schemes

I think I've noted here that fractional-reserve banking will fit most natural definitions of "Ponzi scheme" — "We have 125 $100 deposits, of which 26 or more will certainly be withdrawn in the next 10 years, but we're going to make a 10-year loan for $10,000, and it's okay because we'll get money from new depositors with which to pay the old depositors." Sure. — and it occurs to me that there's some smaller degree of this in a lot of other contexts. The working cash a business keeps on hand is typically not a huge multiple of the rate at which it acquires new supplies, and often a business will count on being able to collect on some of its receivables in order to pay some of its payables; simply sitting on enough cash to pay all "current" liabilities is bad practice, at least when it earns a much lower interest rate than the company's cost of capital, and yet there is something of a Ponzi feel even to that.

I might note right now that many classic Ponzi schemes are "actual" fraud, in that the person promoting it knows that there is no value being generated within the scheme and that the "investors" have no legitimate likelihood, at least on average, of making money; for more sophisticated designs (or dumber promoters), the promoter may actually believe that there is a social benefit to it, and where there is some actual economic activity, such as in "multi-level marketing" schemes in which the participants do actually do some sales but make most of their money (if any) from recruiting new marketers who pay a "franchise fee" to join the scheme, it can be quite hard to tell what legitimate expectations the class of marketers might have.  With much fraud, stupidity is a defense — by which I mean that as long as you sincerely believe the claims you're making, you aren't guilty of fraud.[1]  Ponzi schemes, however, are constructively fraudulent; if you're found to have been promoting an illegal Ponzi scheme, it doesn't matter whether you believed in it.  The multi-level marketing schemes in particular are fairly controversial, with some courts deciding some schemes are illegal pyramid schemes and other courts deciding other schemes are not.  None of the courts particularly investigates, in any case, whether the promoters are particularly competent at basic arithmetic.

A lot of the Ponzi-like set-ups that are clearly on the good side of the law, though, have in common that the Ponzi character is one of liquidity-mismatch rather than a solvency issue; there is some public consensus that these sorts of practices are being used by entities that almost always have assets on hand that, in some intermediate or long-term sense, are worth more than the liabilities.  If the stream of new cash were to come to a sudden stop and the firm unable to pay cash on a timely basis to claimants to whom it was due, it would not be because the firm was "insolvent", but because it was unable to quickly or efficiently sell assets.  Distinguishing between "illiquidity" and "insolvency" is a famously fraught problem, especially for financial or other firms with a lot of short-term liabilities;[2] saying that my Ponzi problem is perhaps answerable in terms of solvency versus liquidity is not, in practice, a solution to the problem, but a hopefully enlightening observation that it's related to another not-entirely-solved problem.

[1]New Jersey consumer fraud laws actually do not have this provision; even perfectly good faith inaccuracies leave you liable not only for compensation but for tripled damages. It's also worth noting that, even if the law to which you're subject does have such a provision, if what you said was ignorant enough, a jury may not believe you.

[2]GE, somewhat famously, spent many years leading up to The Crisis borrowing a lot of short-term debt, rolling it over when it came due, while building large capital equipment that took a long time to build and sell.  As the markets began to unravel GE Capital was actually providing about 40% of the company's profits, but even the industrial portion of GE was operating a lot like a bank in some ways, and was subject to the same difficulties when it became hard to borrow money.

Monday, January 11, 2016

thoughts on capital

While I can't quickly locate it, I'm sure I've written about GDP and related measures in the past; in particular, while the calculation of GDP subtracts out the costs of most inputs into final goods (so, for example, when cloth is produced, and a suit is produced from that cloth, the value of the cloth produced is not double-counted), it does not subtract out the capital that is used.  This isn't such a big deal when the capital being used is a sewing machine, which can produce suits worth many times the cost of the machine before it wears out, but is a bigger deal when much of the capital being used is computers and software that become obsolete within five years — and, for purposes of measuring growth, is an even bigger deal when the economy is switching to a large degree from the former to the latter.  From the beginning of 1980 to the beginning of 2010, the growth in GDP exceeded the growth in Net Domestic Product — i.e. GDP minus capital depreciation — by an average of .25 percentage points on an annualized basis for three decades, as the amount of depreciation as a fraction of GDP doubled.

There's an introductory microeconomics model in which the amount that a firm produces is a function of the quantity of labor used and the quantity of capital used, and a profit-maximizing firm will hire more workers as long as the "marginal product" — how much more can be produced with an additional worker — exceeds the cost of employing that extra worker.  Similarly, capital is employed at a rate such that the marginal product of capital is equal to its cost.  The cost of capital is typically denoted by the letter r, which in other contexts is used for the real interest rate, and sometimes sources will go so far as to call it the interest rate — but this is wrong.  It will include financing costs, indeed, but will also include depreciation; if I start the year with a $10,000 piece of equipment, and end the year with an $8,000 piece of equipment, using the capital has cost me both the financing cost (say $500) of the $10,000 [1] and the extra $2,000; in particular, if one imagined that there was a perfect market for buying and selling partially depreciated equipment, I could literally just buy it at the beginning of the year, sell it at the end, and it would be quite clear that I need to make an extra $2,500 for having used that equipment in order to justify its temporary ownership.[2]

Again, in these models, the production function takes capital and labor as its arguments; one occasionally sees land or natural resources added as an argument, but one rarely sees "intermediate goods" or the like — cloth, for example, for the tailor.  Obviously there is some sense in which that's a major oversight; a tailor couldn't double the production of suits with the same initial allocation of cloth.  "Production", here, is taken to mean something like "the value of production minus the cost of the materials" — a sort of value added by the labor and the capital to the other inputs to get the outputs.  Adding this up for all economic units, whether they are producing capital goods, final consumption goods, or intermediate goods, gets us to GDP; if you were either to exclude production of capital goods, or were to subtract out depreciation, you would get, at least in a long-run average, the Net Domestic Product.  As it stands, though, GDP is the better publicized figure, even though it essentially double-counts the capital used in production of goods.[3]

In these models one often sees the expression rK called the "capital share of income" or some such; similarly, wL is the "labor share of income", where w is for "wage" and L is for "labor".  It was noted in the early middle twentieth century that the income share of labor was uncannily stable[4] over time, and Cobb and Douglass wrote down an economy-wide aggregate production function now called the Cobb-Douglass production function that more or less explains that.  What that function would predict, as we move toward capital that depreciates more quickly, is that r would increase, the amount of capital per unit labor being used would decrease, and wL would continue to constitute the same fraction of GDP as before.  Insofar as can be discerned from the data, this is actually not what has happened; while it's still hard to definitively declare a break in the trend, wL seems to have started to decrease somewhat as a fraction of GDP — but maintained a fairly stable portion for NDP.  In the standard simplistic sense, workers are getting the same fraction of net production as they were in the twentieth century, but a smaller fraction of the "production" that the usual "production functions" are measuring.

I will also note here, though it's something of an undeveloped tangent, that rK is often viewed as though K should have units of dollars and r should have the units of an interest rate; I've adopted that above, mostly because it's standard.  Much of the model goes through unchanged, though, if we interpret K as the real units of capital (assumed, at least initially, to be implausibly homogeneous) and r as either units of output per unit time per unit capital, or even as dollars per unit time per unit capital if we incorporate the price of the output (but not the capital) into it.  This approach seems more useful to me as we attempt to improve the ability of our models to link financial developments with the real economy; in particular, the price of capital — not r, but the actual dollar cost of capital equipment — may change relative to the price of the firm's output, and it's going to be hard to treat the effect of that on the firm's behavior if you've bound it up implicitly with the quantity of capital.

[1]That is to say, the interest paid on a $10,000 loan to buy it, the return that would otherwise have been earned on $10,000 that was used to buy it, or some combination of these, perhaps with an adjustment for risk.

[2]I should perhaps let the complications go to a greater extent than I am, but will note that (1) accounting depreciation is an estimate of true economic depreciation, which, in the absence of perfect markets, may not be easy to make precise, especially over short periods of time, and (2) in the real world, where there aren't such markets, it will still work out; if and only if the use of the machine is worth its cost over the period of its ownership and use, there will be some way to attribute its depreciation over time such that its implied value started at its purchase price, ended at its disposal price (if any), and provided capital services equal to the capital costs along the way.  Depreciation will end up being a real cost, and often an important one, for any asset that decreases in value over time as it gets used.

[3]Surely part of the reason is that it is simpler.  Consider another wrinkle: your personal car.  It may, in fact, be a piece of equipment that is worth $10,000 at the beginning of one year and $8,000 at the beginning of the next; perhaps, in addition to gas, maintenance, etc., owning the car for that year in some sense costs $2,500.  We typically consider the car to be a "final good", but on some level the final good is your use of the car — a distinction that could in some sense be made of apples as well, but is less useful for goods that get purchased and used up quickly.  A careful accounting would perhaps include the $2,500 in "imputed rent" that you paid to use the car — and here I'll note briefly that some countries charge homeowners taxes on the "imputed rent" associated with the use of their own houses — but would then also subtract out the depreciation of your car.  It's easier and basically equivalent to count cars as being "consumed" when they are purchased rather than as they depreciate.  What we want to subtract out are the capital costs associated with the production of something else that is purchased later — the capital cost is part of its cost of production.  If you use your car for business, for example, it becomes capital used for the production of something else.  How much do you use it for personal purposes and how much for business?  If you have a car that costs $12,500 per year, and could be just as productive with one that costs $2,500, isn't $10,000 of that basically just your consumption?  Economics is simpler in theory than in practice sometimes; you can start to get a feel for why the corporate tax code is so complicated.

[4]It bounces up and down a bit, which becomes important later in the paragraph, but generally returns to its long-run average within several years.

Friday, December 11, 2015

non-recourse unsecured debt

This is one of those ideas that is not at all well thought-out and is probably a bad idea, but is here because it struck me as interesting when it popped into my head and maybe it can inspire a better idea.

The Obama administration (I believe) has implemented an income-based repayment program for federal student loans; even if you have a lot of debt and low income, you don't have to pay more than 10% of your income toward the loans.  Student loans are special in some ways; most notoriously, to some extent on the premise that they're secured by your education which can't be repossessed, they can't generally be discharged in bankruptcy.[1]  In practice (and I assume from a formal legal standpoint) it's unsecured debt, but the ability of the lender to come after your assets if you aren't paying on the original official schedule has been curtailed.

Now, one of the nasty things about the design of our welfare systems, though it's much improved from a generation ago, is the speed at which benefits sometimes "phase out" as income goes up. Under AFDC, from 1935–1996, if you made an extra $3000 in a year, your benefits were cut by at least $2000, and for most of those 61 years your benefits were actually cut by the full $3000; there was no particular point in gaining work experience or making similar investments that might help you ultimately get out of poverty.  The successor program to AFDC is much more variable from state to state, but phase-out rates are (I believe) universally lower than 67%, usually no higher than 50%.  SNAP, however, phases out at a 30% rate, which might not seem too bad, but this means that if you earn an extra $100 and are on both programs, you may lose $50 in TANF benefits and $30 in SNAP benefits.  Some programs, like Medicaid, are even worse, where if you're $1 below the eligibility threshold, making an extra $2 can cost you your health care; Obamacare subsidies, depending on the circumstances, have a similar structure, where they will decrease gradually until you get to a certain point, but drop discontinuously to zero at a particular threshold.  These health insurance cliffs both seem like bad program design, but often even reasonably designed phase-out rules become problematic when they're phasing out together.  I've suggested that one be able to elect to split 50/50 with the IRS any portion of one's income in exchange for having it officially removed from income for all tax and welfare benefit calculations; this would provide something of a safety valve where, if one found oneself in an income range with 80% in aggregate phaseouts or just above the Medicaid cutoff, one could get 30% of the extra earned dollars back or pay a small amount to get your health insurance back.  More importantly, one would be able to take on extra work without worrying that one is risking eligibility for these programs.

My thought, then, is that perhaps there are other debts we would want to treat similarly to student loan debt, but we might want to lump together with it.  Debtors with those kinds of debt could pay 60% off the top to be at a lower income level for purposes of taxes, benefits, and also income-based debt payment plans, with $10 of each $60 earmarked for creditors, but perhaps more than that if the debtor/taxpayer is not in an extensive phaseout income range.  The debts could include student loans, fines, and judgments from courts, including back child support; in all cases, debts that one wants to see paid, but with the understanding that someone with little reason to work isn't going to be paying them off.

[1]I feel better about this rule in Chapter 7 than Chapter 13, where I would at least be inclined to allow them to be reduced, but that's a bit off topic.

Thursday, December 10, 2015

tax incidence

I've been thinking a bit about "value added" taxes, which are a substantial source of revenue in many European countries, but not in the United States.  The "value added" of a company is essentially the revenue it takes in minus the expenses it pays to other companies; equivalently, it is the profits of the company plus the money it spends paying its employees. [1]  The total production of the economy is then the sum of the "value added" by different economic units.  If markets are competitive, the price of a good is the cost of producing it, and a 20% value added tax translates ultimately to a 25% increase in the final price[2] above the other costs of production; for example, if XYZ corp sells widgets for $3 a piece, with $1 in capital costs (including depreciation), $1 in labor costs, and $1 for inputs purchased from ABC corp, and ABC has no suppliers,[3] then (if supply is inelastic) a 20% VAT tax raises the final price to $3.75, of which $2.50 is value added and $1.25 is paid to ABC; XYZ thus pays 50 cents per widget in taxes, and ABC pays 25 cents per widget in taxes.  It is hoped that the reader will see (or trust) that the result is similar when supply is elastic.

Because of the argument given, the VAT is typically viewed as equivalent to a consumption tax; it gets collected along the supply chain, but is equivalent to, in this case, a 25% tax applied at the end.  At the risk of being wrong — and, note, that is well in the spirit of this blog — it seems to me that a 20% tax on corporate profits combined with a 20% flat income tax on the workers is also equivalent.[4]  If corporations are paying a 36% tax and workers are paying a 20% tax, replacing that with a 20% corporate tax and a 20% value added tax with no income tax seems likely to be equivalent.[5]

There is always, with tax policy, the question of true economic incidence of taxes, which especially in the long-run is likely to be independent of legal incidence; one of the reasons a lot of people like corporate taxes, and a lot of wonks don't, is that it is officially paid by companies, and it's not entirely clear who the actual payers are. (Some quick searching pops up this 2005 working paper on the subject; my recollection is that recent research is unable to exclude, insofar as the question is well-defined, the proposition that about one third of it is borne each by the shareholders or owners of the company, the employees of the company, and the customers of the company, though I don't have a source for that; it probably would depend on the industry, and of course over the entire economy consumers and employees and shareholders are not remotely mutually exclusive groups.)  Possibly because of my American bias, or the fact that I'm just not in that sort of literature generally, I haven't to my recollection seen much analysis of how much of a value-added tax actually falls on consumers, ultimately, and how much is absorbed by someone else.

[1]As with many economic concepts, it gets rough around the edges, so that the first definition I gave is not entirely "equivalent" to the second.  The money a company pays to a company providing its employees health insurance wouldn't be subtracted from "value added"; that's part of paying your employees, only in-kind.  Is the money spent on air conditioning for your office an expenditure on externally-produced inputs or an implicit labor cost?  A reasonable argument could be made for the latter, but I'm sure it's never treated that way.  Whatever the definition of "value added", the tax base for the value added tax is typically closer to the former definition than the latter, so that a company pays "value added tax" on exactly that portion of its revenue on which no other company is paying "value added tax".

[2]The age old confusion about percentages rears its head here; the upshot is that the tax is 20% of the cost with taxes and is 25% of the cost without taxes, so e.g. an item that ends up costing $5 includes $1 in taxes and $4 of "other".

[3]To keep things simple.

[4]Here's where perhaps it's worth emphasizing again that in practice the two definitions given previously for "value added" are effectively very similar.

[5]On the corporate side, $1 before taxes becomes .8×.8=.64 cents after taxes, just as without the VAT.

Sunday, December 6, 2015

endowments, public commitment, and coordination

I somewhat avoid the news here, but the news hook here is pretty tangential; Mark Zuckerberg recently announced that he's giving away most of his fortune to an LLC, not a tax-deductible organization.  One of the reasons for that is the 5% rule; most tax-deductible organizations, as part of the terms of their tax classification, have to spend at least 5% of their endowments every year on expenses that are fairly directly relevant to their official charitable purpose.  I don't know whether non-profit universities are typically incorporated differently or are given an explicit exemption, but they are generally exempt; there has been some talk, at the periphery of American political discussion, of removing the exemption.  In all cases, the idea is that an organization that gets some kind of special exemption from tax laws shouldn't be allowed to simply stockpile and invest an ever increasing endowment without substantial ongoing evidence that it is serving a socially beneficial purpose.

Why do universities (and other organizations) build up endowments in the first place?  Imagine two universities, Typical University which establishes an endowment early in its existence and uses some of it over time, in addition to ongoing donations, tuition, etc., to pay for programming, and Paygo University, which happens to receive in donations each year an amount equal to what TU receives in donations plus what TU withdraws from its endowment; each then funds the same programming.  Presumably they do the same social good; the endowment that TU has at any given time is the present value of the amount of donations TU received in excess of those PU received in the past, where the discount rate is the rate-of-return on the endowment.  If TU is simply letting its endowment pile up, then it has received more in donations, while doing less good, but presumably, one hopes, has enhanced its ability to do good in the future; if TU is pulling substantial funds out of its endowment to fund programs, then there is some sense in which it has not so much taken in more donations than PU, but took them in sooner, perhaps largely taking them in at its foundation while taking in less than PU ever since.

The obvious (at least to me) reason to build up a foundation is to smooth variations in both fund-raising and expenditure; often new buildings are accompanied by special fund-raising campaigns, but there will be times (e.g. capital expenditures) when cash-flow expenses are lumpy and times (recessions, or simply random fluctuation) when contributions are lower than usual, and it makes some sense to have an endowment to smooth that out.  Even ignoring the special capital-spending campaigns (and naming rights that are often a part of that), though, this isn't nearly enough to explain the endowments at most large universities.  If they are smoothing over time and saving for precautionary reasons, they are smoothing over generations and protecting themselves from cataclysms.

It may well be that (especially large) endowments are better at investing money than the donors are, in which case it might make sense to accumulate a large endowment for that reason — the donors can be encouraged to give sooner than they would naturally, perhaps discounting at a lower private discount rate than the university's discount rate — and I neglect that possibility, except for this sentence, not because I think it's unlikely to be important but because I don't think it's as interesting as my other idea.  The other idea, though, is that smoothing over generations and cataclysms avoids coordination failures in which the various participants in a university community — donors, students, professors, and quite possibly others — worry that the university could run into trouble in several years, and thereby avoid it, initially to a small degree, but then, as the prophesy begins to fulfill itself, to an ever greater degree.  A large endowment forestalls that possibility in some ways and serves as a coordination device in others; the number itself makes the university look not just sturdy but reputable.  I wonder, in fact, whether university endowments might be an example of the "overhoarding of liquidity" that Tirole has mentioned as a theoretical possibility that is probably of little practical importance in the settings in which we think of it in those terms.

Friday, December 4, 2015

market safety

It is moderately well-known — Arrow's impossibility theorem is better known, but the Gibbard-Satterthwaite theorem is probably more apposite — that there's no ideal way to aggregate preferences into a jointly optimal outcome, so we're left making tradeoffs of different features when we design systems for coordinating group decisions, such as voting systems and market systems.  One real-world criterion that isn't even part of the impossibility results is "simplicity", partly because that can be hard to formally define; still, it is certainly the case that people process information in certain ways that work better if they find a system to be simple and intuitive than if they don't.  One of the practical consequences of this is that the revelation principle, even if useful for theoretical understanding of constraints, is in some practical sense not something that can be put into practice; the revelation principle says that the best possible aggregation system is in practice equivalent to some "strategy-proof" system, wherein each agent reports all of its private information and the mechanism is such that it is incentive-compatible for them to do so, but in practice even developing the information to report is too complex for realistic agents, and the resulting direct mechanism is often unintuitive to laymen in certain ways in order to understand the constraint.

A good example, perhaps, is the Myerson-Satterthwaite (same Satterthwaite) result for two agents trying to trade an object.  One of them owns it, and has a value of it between $10 and $20, and the other places on it a value between $10 and $20 as well.  As far as I and the buyer know, the seller's value is uniformly distributed in that range, and as far as the seller and I know, the buyer's value is uniformly distributed in that range, but the buyer and seller each know their own valuations.  How do I design an "efficient" mechanism — determining, as a function of the private values, whether and at what price the buyer buys the object?  "Efficiency" here is just measured as the private value of the agent who ends up owning the object, and I'd like to simply give it to whoever has a higher value, but because the price at which it trades would have to be a generally increasing function of the reported values, the buyer will tend to understate the value (and the seller would tend to overstate it) unless doing so substantially reduces the probability of a profitable trade.  They find a fairly generally applicable rule, even when distributions aren't uniform, and it's a bit complicated, though also elucidating; what's relevant for my purposes now, though, is that with uniform distributions it turns out to be equivalent to the nonfatuous Bayes-Nash equilibrium of the mechanism "each side states a price and, if the buyer's price is higher, trade at the midpoint."  It is not the case, in this latter mechanism, that each agent's stated price will be equal to the private value — the buyer will certainly shade low and the seller will shade high — but strategically sophisticated traders will buy in exactly the same circumstances as in the direct mechanism, and for the same prices.

Realistic agents may not be strategically sophisticated, but it's hard to tell which direction that cuts; there are human subject experiments (Kagel, Harstad, and Levin (1987): "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, 55(6): 1275–1304) in which subjects seem to find it harder to simply report their own value, even when they are given it, than to do the shading they're used to doing in small bilateral trade situations, and that's when they have been given their value — in the real world, agents asking themselves "how much is this worth to me?" are surely less likely to find it easy to give the right number. They aren't used to this task; they're used to (at a supermarket) deciding whether they are willing to trade at a given price or (at a bazaar, e.g. at an arts or crafts fair) to making a conservative bid.  In a lot of these situations one side or the other may gain an advantage from being better informed or more strategically sophisticated, but the gains tend to be small and not to too badly impair the interests of people who are toward the low end in information or sophistication.

Some simple mechanisms, though, do not have this property.  I've noted that my biggest problem with the Borda count is not that the best strategy isn't to list candidates in order of preference — just as I don't think you're "lying" if you offer to pay $10 for an item for which you would willingly pay $20 — but that even if all of the agents in a Borda count vote are unrealistically well-informed about strategic information, near equilibrium, if one candidate's voters are somewhat more informed than others, that candidate will generally win — essentially without regard to the candidate's popularity.  Systems like approval voting might require some strategic awareness, but once most agents are somewhat aware of what other agents' preferences are, being a lot more knowledgeable than the others only helps under exceptional circumstances.  Often it is, in fact, reasonable to expect the agents generally to be somewhat more aware of each others' preferences than the mechanism designer is, or can reasonably take into account; for example, if there are three candidates, one of whom is the last choice of 90% of voters, the Condorcet winner is likely to win a first-past-the-post vote, while an informed mechanism designer might find it awkward to publicly and formally declare the irrelevant candidate to be irrelevant.  This is a situation in which the mechanism works, and does so in part by letting voters use strategic information that the designer cannot use in a more direct fashion.

What triggered this post, though, was the concept of "spoofing" in the financial markets, and whether or not spoofing is bad. My first visceral response is that, if some agents are making inferences from the public bids and offers of other agents, it's on them if the information content of those bids and offers is other than what they think it is — even if it's other than what they think it is by the design of the people placing those bids and offers.  Let the market seek its strategic equilibrium.  With markets, perhaps the best analysis is to figure out whether this impedes the functions of the market — moving risky assets to their highest-value owners, with information discovery as part of the process of doing that — and that end may well be better served by a rule against spoofing that is nebulous around the edges but, in practice, is often not that hard to discern.  One other criterion to consider, though, is whether the strategic equilibrium that the market would find in the absence of such a rule is one in which agents would find it profitable to devote a lot of resources to gaining strategic information (as opposed to fundamental information), which, in the voting context, I consider to be one of the very most important considerations in evaluating a system.

Tuesday, November 10, 2015

policy of money as a unit of account

A lot of my conclusions here aren't much different from those of a previous discussion, but I'm going to frame/derive them slightly differently.

Suppose two agents are exogenously matched and given an exogenous date in the future for which they can construct a bilateral derivative; maybe we even require zero NPV, or maybe we allow for some cash transfer now, but either way if they're infinitely clever (and assuming e.g. that they don't anticipate future opportunities to insure before that date, etc.) then I believe the negotiations should leave the ratio of marginal costs of utility for the two agents at that date pre-visible. If we add constraints we modify that, but probably in relatively intuitive ways; if we can only condition on certain algebras of events (coarser than what would in principle be measurable at the final date), for example, then there's an expected value on each of those events that should give the same ratio, and if in some states an agent is unlikely to be able to make a payment, that agent is allowed to be better off than the other agent in that state relative to the usual ratio. Further, if there are a bunch of pairs of agents doing this, and the agents can be put into large classes, but need then to have very similar contracts, I'm probably doing more averaging over agents in each class.

I don't know whether this gets me any closer to an answer, but perhaps this is a useful framework for thinking about monetary policy as the medium of exchange consists increasingly of electronic (even interest-bearing) accounts and centrally-managed money is mostly about the unit of account. Buyers and sellers and debtors and lenders still referencing a given unit of account will tend to have certain risk similarities intraclass and differences interclass that one can try to optimize; if a surprise causes borrowers more pain than lenders, I try to weaken the unit of account, and if a surprise causes sellers more pain than buyers[1], then I try to strengthen the unit of account, and everyone ex ante looks at this and says "doing my contract (legal and explicit or customary and implicit) in this unit of account affords me a certain amount of insurance".

[1] A further note on the inclusion of "buyers" and "sellers" here: on some level this only matters for forward contracts, i.e. if we're entering an agreement to an immediate transaction there's none of this sort of uncertainty that resolves itself between the creation of the contract and its conclusion. Parties to a forward contract take on a lot of the properties of borrowers and lenders, insofar as there is a (say) dollar-denominated transfer in the future to which they've committed. Further, in principle borrowers, lenders, and parties to forward contracts can, as above, create their own risk-sharing contract. As a practical matter, of course, this is likely to be impossible to do perfectly, and it's likely that the extent to which it can be done practically leaves a lot of room for a central bank to come in and improve things. This is a usual theory-meets-practice kind of dynamic, especially in monetary theory; somewhat famously, perfect Walrasian economies don't need money, so a useful theory of money will have to figure out what parts of reality outside of Walrasian economics matters, and incomplete contracts would seem to be a biggie.

I believe, though, that more important than difficulties in contracting formally are informal contract-like substances that result from various incompletenesses in information. Buyers and sellers form long-term relationships that may be "at will" for each party, but are formed typically because one or both parties would incur some expense in looking anew for a counterparty each time a similar transaction was to take place. It seems likely to me that this would result in similar long-term dynamics to a contract, and is likely to involve prices that are sticky in some agreed-upon unit of account, whereupon a benevolent manager of that unit of account would again be trying to optimize as discussed above.