I've recently read in a macroeconomics textbook a comment that the development of rational expectations models was necessary because other expectations models are ad hoc and not well grounded in theory. This is, as a historical matter, largely true of the models that Lucas critiqued 34 years ago; I'm not sure it's necessarily the case of any model that eschews expectations that are fully statistically accurate in the sense that "rational expectations" means to modern economists.*
By way of illustration, I was playing, a month ago, with a rational expectations model rather like the common modern Dynamic Stochastic General Equilibrium models; it linearized to a set of equations equating linear combinations of variables at a time with linear combinations of the agent-expected values of the same variables at the next time. As is the case in modern DSGE models, the coefficients of these linear equations were somewhat complicated functions of underlying parameters. Using rational expectations, agent-expected values were set to statistically-expected values, given the underlying parameters and the distribution of exogenous shocks. The linearized system, with this rational expectations assumption, could be fairly easily solved by finding stable and unstable modes and associating control variables with convergent expressions in expectations for the future, with state variables as convergent expressions in shocks from the past. This is all standard in modern macroeconomics.
Because state variables are expressed as linear combinations of one-period-before state variables plus shocks, however, it is the case in this model that the vector of state variables follows a VAR(1) process. If the state variables are directly observed, it's not remotely "ad hoc" for agents to form expectations based on a VAR(1) regression, especially if the relationship between the coefficients is such that, for any VAR(1) coefficient, there will be a set of underlying parameters that supports that coefficient. More generally, it would seem reasonable to expect that agents would infer the underlying parameters econometrically from past data. It is my understanding — though I am not perfectly clear on this — that rational expectations rejects this.
It may be that this is rejected because, with data going back far enough, agents in a model of this sort would have arbitrarily close estimates for the parameters. In this case, it's reasonable to note that the model, not being perfect or perfectly comprehensive, is, at best, an approximation that works well over finite periods of time, similar to what high-energy physicists would call an "effective-field theory". The underlying parameters may be robust to the Lucas critique, at least within a reasonable domain, and yet not perfectly stationary. It can be useful, even without bounded rationality, to suppose that expectations would be formed over a finite window, or one that weights more recent observations more heavily; with bounded rationality, of course, such an alteration to the model requires no other justification. In any case, asking agents to form expectations in a situation in which they are uncertain about the deep parameters of the model, and infer it only through the observation of macroeconomic variables, reintroduces nonlinearities that are very different from those that were linearized away in the first place, and it seems likely to me they would give behavior that would be interesting, whether or not it actually proved to fit the data better than the rational expectations models.
* I don't want to get sucked into recounting a full history of macroeconomics and macroeconometrics over the last 50 years; I will say that there are nice attributes of the assumption of rational expectations, and, as is so often the case, I tend to feel that its most ardent proponents understate its shortcomings, but its most ardent opponents underappreciate its benefits, and almost always fail both to appreciate its history and to actually understand the somewhat limited scope of what it is used to mean.
Friday, December 31, 2010
Thursday, December 23, 2010
maturity transformation and the firm
One of the primary roles that has traditionally been ascribed to banks is "maturity transformation"; interest rates for long-term loans are higher than those for short-term loans, presumably because (this sort of thing is often the cause of price differences) borrowers are more interested in borrowing for long periods and savers are more interested in lending for short periods. Banks borrow short and lend long, making money on the spread and matching the long-duration borrowers with short-duration savers.
There's a blog post from two months ago newly making the rounds questioning the benefits of maturity transformation, in part arguing that 1) more and more savings are now in the form of retirement planning, and thus are longer-dated, 2) that a lot of borrowing is by companies for working capital — and, he doesn't make this observation, but more investment these days goes into software and electronics, i.e. 3-5 year duration capital, compared to giant factories, i.e. 40 year duration capital, than was the case a generation and two ago — and 3) some of the borrowers are starting to borrow on the short end for the same reason banks traditionally have.
Well, point 3 I would argue is largely a substitution effect in response to prices; he's not so much arguing that there is no mismatch as that the pricing difference it sustains will be a bit more slack. Points 1 and 2 suggest that there should, quantitatively, be less mismatch. This, too, should tend to show up in yield curves, and, while it's hard to separate the noise from the signal, it's not clear that this is true either. It's hard to see his story in the macro data, and it's hard for me to imagine there's anything worth doing about it whether it is or not. (Not that there's anything wrong with that; a lot of interesting ideas are worthwhile even if they don't have immediate practical impact.) Ultimately he concedes — that this is a concession, too, is not his observation — that
It struck me, on reading this, that one obvious way in which savers, "who generally have a preference to be able to access their funds quickly," can lend long while maintaining this is negotiability of the loans, i.e. that a liquid market for corporate bonds essentially allows the corporate borrower to lock-in a rate while the lender, while not shielded from all risks, is at least able to sell the bonds for cash fairly quickly; as long as the need for cash is idiosyncratic, the lender is reasonably likely to get back about the amount lent (saved) with some accrued interest to boot. For a bank to lend instead of the ultimate saver amounts to the mediation of what might otherwise be a market transaction taken into a firm.
This brings us to Ronald Coase, who will be celebrating his 100th birthday next week. What determines whether activity is undertaken within a organized economic entity or between entities is a function of the relative costs of transactions versus management; if finding buyers for your bonds (or a bond issuer for your spare cash) is more expensive than managing a bank, then people can be expected to save at and borrow from the bank, while if it's relatively cheap to work through the bond market, that's what we should expect to happen. As it happens, much of the relevant "transaction cost" here is likely to be informational, related to credit risks — which is perhaps why that is one of the risks that is apparently, in practice, borne by the banks. It also seems like the bank-management cost is more likely to scale with the size of the borrower than is the case with a bond placement — a big borrower will be well-known, easier for lenders to appraise — and suggests that bank lending should predominate to small businesses and individuals, with more big companies borrowing more from decentralized financial markets — which, again, seems to be what we see.
There's a blog post from two months ago newly making the rounds questioning the benefits of maturity transformation, in part arguing that 1) more and more savings are now in the form of retirement planning, and thus are longer-dated, 2) that a lot of borrowing is by companies for working capital — and, he doesn't make this observation, but more investment these days goes into software and electronics, i.e. 3-5 year duration capital, compared to giant factories, i.e. 40 year duration capital, than was the case a generation and two ago — and 3) some of the borrowers are starting to borrow on the short end for the same reason banks traditionally have.
Well, point 3 I would argue is largely a substitution effect in response to prices; he's not so much arguing that there is no mismatch as that the pricing difference it sustains will be a bit more slack. Points 1 and 2 suggest that there should, quantitatively, be less mismatch. This, too, should tend to show up in yield curves, and, while it's hard to separate the noise from the signal, it's not clear that this is true either. It's hard to see his story in the macro data, and it's hard for me to imagine there's anything worth doing about it whether it is or not. (Not that there's anything wrong with that; a lot of interesting ideas are worthwhile even if they don't have immediate practical impact.) Ultimately he concedes — that this is a concession, too, is not his observation — that
the most significant proportion of the difference between long-end and short-end rates comes from the interest rate differential which most banks hedge out to a large degree (ironically with pension funds and insurers).Which is to say, it is not ultimately so much banks that are doing the maturity transformation but "to a large degree" "with pension funds and insurers"; the long-term savers are finding the long-term borrowers, with banks as intermediaries.
It struck me, on reading this, that one obvious way in which savers, "who generally have a preference to be able to access their funds quickly," can lend long while maintaining this is negotiability of the loans, i.e. that a liquid market for corporate bonds essentially allows the corporate borrower to lock-in a rate while the lender, while not shielded from all risks, is at least able to sell the bonds for cash fairly quickly; as long as the need for cash is idiosyncratic, the lender is reasonably likely to get back about the amount lent (saved) with some accrued interest to boot. For a bank to lend instead of the ultimate saver amounts to the mediation of what might otherwise be a market transaction taken into a firm.
This brings us to Ronald Coase, who will be celebrating his 100th birthday next week. What determines whether activity is undertaken within a organized economic entity or between entities is a function of the relative costs of transactions versus management; if finding buyers for your bonds (or a bond issuer for your spare cash) is more expensive than managing a bank, then people can be expected to save at and borrow from the bank, while if it's relatively cheap to work through the bond market, that's what we should expect to happen. As it happens, much of the relevant "transaction cost" here is likely to be informational, related to credit risks — which is perhaps why that is one of the risks that is apparently, in practice, borne by the banks. It also seems like the bank-management cost is more likely to scale with the size of the borrower than is the case with a bond placement — a big borrower will be well-known, easier for lenders to appraise — and suggests that bank lending should predominate to small businesses and individuals, with more big companies borrowing more from decentralized financial markets — which, again, seems to be what we see.
Tuesday, November 9, 2010
the value of money
I wonder whether there has been an attempt to estimate empirically the NPV of the liquidity value of a dollar in cash.
search theory and adverse supply
I heard a hardware store owner on the radio saying that, the high unemployment rate notwithstanding, he's having trouble finding candidates who have the skills he needs -- knowing their way around tools, paint, etc., to be able to help customers. It seems superficially plausible that an increase in the number of people looking for jobs would adversely impact an employer if it induces applicants to look for jobs for which they are less well suited, imposing higher information costs on an employer.
Friday, September 17, 2010
money and bounded rationality
The three functions of money, in freshman economics, are as a store of value, a unit of account, and, last but most, a medium of exchange. Writers occasionally construct examples of something serving one purpose but not another, but by and large crippling any of these functions will to some extent cripple all of them. This is especially true in the case of storing value. If a prospective currency can't store value, then users have to use it in a hurry, and the buying and selling process that a medium of exchange is supposed to allow to be separate are forced to be more temporally proximate; in the extreme, if you have to spend your money within minutes of getting it, you're largely stuck looking for someone who wants to buy what you want to sell and vice versa, and you're effectively back to a barter economy. Similarly, it becomes less useful as a unit of account if its value can't be counted on.
Money as a store of value is also a great technology for savings. A (closed) economy as a whole can "save" only by investing resources in capital — physical capital, intellectual capital (technology), human capital (education) — but an individual can "save" by lending to others who wish to borrow, and in a large economy with a well-run central bank and so on, this typically works better.* If I have a good year, and expect less year will be worse, I can simply pile up cash; if I get paid a lump sum for a contract job, I can spread my spending over the time until my next job. If I want to make a big purchase, I don't have to make a big sale at the same time; I can save up ahead of time — or afterward, by borrowing at the time of purchase and then paying back the loan. The ability to choose between spending today or tomorrow is as valuable as the ability to choose between apples and grapefruit.
It's often noted, and, especially recently, quite notable, that people who are bad at saving money often lose much of this ability. If you don't have the self-control to let hundreds of dollars go unspent for a few weeks, you can't trade spending now for spending later. (If you buy durable goods, you can stretch some of your consumption into the future, but not quite as effectively.) The money, in this case, doesn't provide an effective store of value. This also, as I noted in the first paragraph, will affect its ability even to function as a medium of exchange.
I recently read an example of this; unfortunately, I don't now remember it. It was something along the lines, though, of a person who had trouble saving, and was engaging in a certain amount of barter (and running into the attendant double-coincidence-of-wants problems) due to an inability to build up even enough "working cash" to engage in what I think of as normal quotidian economic activity. If I remember or otherwise reacquire the example, I'll probably update this post.
* It occurs to me I've taken for granted that holding onto currency is the equivalent of lending to the central bank (or "bank of issue", if we still had non-central banks of issue), and that keeping money in a bank account is making a loan to that bank. If that's not obvious, take my word for it.
Money as a store of value is also a great technology for savings. A (closed) economy as a whole can "save" only by investing resources in capital — physical capital, intellectual capital (technology), human capital (education) — but an individual can "save" by lending to others who wish to borrow, and in a large economy with a well-run central bank and so on, this typically works better.* If I have a good year, and expect less year will be worse, I can simply pile up cash; if I get paid a lump sum for a contract job, I can spread my spending over the time until my next job. If I want to make a big purchase, I don't have to make a big sale at the same time; I can save up ahead of time — or afterward, by borrowing at the time of purchase and then paying back the loan. The ability to choose between spending today or tomorrow is as valuable as the ability to choose between apples and grapefruit.
It's often noted, and, especially recently, quite notable, that people who are bad at saving money often lose much of this ability. If you don't have the self-control to let hundreds of dollars go unspent for a few weeks, you can't trade spending now for spending later. (If you buy durable goods, you can stretch some of your consumption into the future, but not quite as effectively.) The money, in this case, doesn't provide an effective store of value. This also, as I noted in the first paragraph, will affect its ability even to function as a medium of exchange.
I recently read an example of this; unfortunately, I don't now remember it. It was something along the lines, though, of a person who had trouble saving, and was engaging in a certain amount of barter (and running into the attendant double-coincidence-of-wants problems) due to an inability to build up even enough "working cash" to engage in what I think of as normal quotidian economic activity. If I remember or otherwise reacquire the example, I'll probably update this post.
* It occurs to me I've taken for granted that holding onto currency is the equivalent of lending to the central bank (or "bank of issue", if we still had non-central banks of issue), and that keeping money in a bank account is making a loan to that bank. If that's not obvious, take my word for it.
Tuesday, September 14, 2010
search theory and prostitution
There's a subfield of macroeconomics dealing with "search theory", though aside from the mathematics (which resembles macroeconomics) it's an issue that's closer in nature to microeconomics. Most macro models seem largely to ignore it, at least as a direct matter; there may be sticky prices or market power layered onto a model that might come from search issues but is typically simply taken as exogenous. There's a certain amount of demand, a certain productive capacity, and the people who want to buy stuff buy stuff from the people who want to sell stuff.
For a lot of goods, that's not an especially good description (though, to be fair, how good a description it is depends on exactly what you care about, and for a lot of macroeconomic treatments it may be adequate). One of the primary roles of advertising, and one of the benefits of being a large (and long-lived) firm, is in the ability of people who want to buy what you're selling to find you. If you open a new business selling erasers, and somebody needs to buy an eraser in your first month in business, there's a good chance they don't know about you. If they've walked by your store a few times a week for the past several years, seen your ads on the subway, and maybe bought an eraser or two from your shop in the past, when they need an eraser, they know where they can get one. Being the answer to the question, "Hey, do you know where I can get an eraser?" is enormously valuable capital.
For illicit markets, it's that much harder; you want people looking to buy to be able to find you, but you don't want the police to. This can be handled in a few different ways. One is ambiguity; you generate a signal that is understood, but perhaps is not explicit enough to be grounds for arrest, or, ideally, even especially heavy levels of suspicion. Word of mouth, where your position in the market is known disproportionately to people whom you have reason to trust, also helps, as do repeat business relationships.
A new paper by Steven Levitt and Sudhir Venkatesh, which apparently I'm not supposed to cite, but let's hope this is okay, discusses the market for prostitution in Chicago.
In a perfectly competitive market, "price discrimination" is unsustainable; if you try to charge less than the going rate to some customers and more than the going rate to others, you only get the customers whom you're charging less. There are a fair number of pimps and prostitutes in the given neighborhoods, and while it's possible they engage in collusion (tacit or explicit, concious or not), this seems likely to be evidence of the search problem; if you charge a white customer more, it's not that easy for him to go find another seller who will charge him the lower rate, so your only real competition is with his going without.
There have been some arrests of Indian actresses for prostitution, in part, it seems, because being an actress is one of these ambiguous signals:
How information of this nature makes it through an economy is of particular interest to me, and is one of the things I can imagine myself studying over the next five years.
For a lot of goods, that's not an especially good description (though, to be fair, how good a description it is depends on exactly what you care about, and for a lot of macroeconomic treatments it may be adequate). One of the primary roles of advertising, and one of the benefits of being a large (and long-lived) firm, is in the ability of people who want to buy what you're selling to find you. If you open a new business selling erasers, and somebody needs to buy an eraser in your first month in business, there's a good chance they don't know about you. If they've walked by your store a few times a week for the past several years, seen your ads on the subway, and maybe bought an eraser or two from your shop in the past, when they need an eraser, they know where they can get one. Being the answer to the question, "Hey, do you know where I can get an eraser?" is enormously valuable capital.
For illicit markets, it's that much harder; you want people looking to buy to be able to find you, but you don't want the police to. This can be handled in a few different ways. One is ambiguity; you generate a signal that is understood, but perhaps is not explicit enough to be grounds for arrest, or, ideally, even especially heavy levels of suspicion. Word of mouth, where your position in the market is known disproportionately to people whom you have reason to trust, also helps, as do repeat business relationships.
A new paper by Steven Levitt and Sudhir Venkatesh, which apparently I'm not supposed to cite, but let's hope this is okay, discusses the market for prostitution in Chicago.
Even for a given sex act, however, the prices paid by black customers are systematically lower than for other customers. These differences appear to be attributable to price discrimination on the part of the prostitutes.
In a perfectly competitive market, "price discrimination" is unsustainable; if you try to charge less than the going rate to some customers and more than the going rate to others, you only get the customers whom you're charging less. There are a fair number of pimps and prostitutes in the given neighborhoods, and while it's possible they engage in collusion (tacit or explicit, concious or not), this seems likely to be evidence of the search problem; if you charge a white customer more, it's not that easy for him to go find another seller who will charge him the lower rate, so your only real competition is with his going without.
There have been some arrests of Indian actresses for prostitution, in part, it seems, because being an actress is one of these ambiguous signals:
Because of the sexualized roles they play, and the fact that many are in scandalous "live-in relationships"— meaning they move in with boyfriends before marriage—the blanket assumption is that all actresses are available for a price. This is obviously false, but it's an illusion that has been exploited by savvy pimps who have created a market for B-list and C-list "starlets"—often unsuccessful actresses from questionable backgrounds—for men who want to have what's sold as a glamorous sexual experience.Being an actress is not per se actionable by the police, but it might help someone looking for prostitution to find you.
How information of this nature makes it through an economy is of particular interest to me, and is one of the things I can imagine myself studying over the next five years.
Tuesday, August 31, 2010
math -- adjoints and preimages
This post is in large part me trying to remember math from 15 years ago that might be useful to me.
If I have sets V and W, I can define duals V* and W* as function spaces, V*={v|v:V→R}, i.e. the spaces of functions from the space into (in this case) R. Given a function f:V→W, then given w*∈W*, we can define v*∈V*: ∀ v∈V, v*(v)=w*(f(v)). Thus f implies a map f*:W*→V*, the adjoint of f.
In the case in which V and W have extra structure, I usually define my dual to be a restricted set of the duals defined above; in particular, if V and W are vector spaces, I can define V* and W* to include only linear maps. Then any linear map from V to W implies a linear adjoint from W* to V*. There exist isomorphisms between V and V*; choosing such an isomorphism is equivalent to choosing something of an inner product, ⟨v1,v2⟩=v1*(v2), though one would typically want to restrict the choice of isomorphism such that this is symmetric. Defined this way, V** is (canonically isomorphic to) V, at least for finite dimensions.
I also don't need to use R; in particular (and the main point of this post), if I use instead the set {0,1} then V* is (canonically isomorphic to) the set of subsets of V (the relevant subset being the set of elements such that v*(v)=1), and the adjoint f*:W*→V* takes sets in W to their preimages (under f).
If I have sets V and W, I can define duals V* and W* as function spaces, V*={v|v:V→R}, i.e. the spaces of functions from the space into (in this case) R. Given a function f:V→W, then given w*∈W*, we can define v*∈V*: ∀ v∈V, v*(v)=w*(f(v)). Thus f implies a map f*:W*→V*, the adjoint of f.
In the case in which V and W have extra structure, I usually define my dual to be a restricted set of the duals defined above; in particular, if V and W are vector spaces, I can define V* and W* to include only linear maps. Then any linear map from V to W implies a linear adjoint from W* to V*. There exist isomorphisms between V and V*; choosing such an isomorphism is equivalent to choosing something of an inner product, ⟨v1,v2⟩=v1*(v2), though one would typically want to restrict the choice of isomorphism such that this is symmetric. Defined this way, V** is (canonically isomorphic to) V, at least for finite dimensions.
I also don't need to use R; in particular (and the main point of this post), if I use instead the set {0,1} then V* is (canonically isomorphic to) the set of subsets of V (the relevant subset being the set of elements such that v*(v)=1), and the adjoint f*:W*→V* takes sets in W to their preimages (under f).
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