Friday, December 31, 2010

Rational Expectations

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.

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
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.