Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Saturday, January 4, 2014

What is the OLG model of money good for?

I want to say a few things in response to Brad DeLong's post concerning the usefulness of overlapping generations (OLG) models of money (and on the value of "microfoundations" in general). Let's start with this:
As I say over and over again, forcing your model to have microfoundations when they are the wrong microfoundations is not a progressive but rather a degenerative research program.
Why is he saying this "over and over again" and to whom is he saying it? What if I had said "As I say over and over again, forcing your model to have hand-waving foundations when they are the wrong hand-waving foundations is not a progressive but rather degenerative research program."? That would be silly. And the quoted passage above is just as silly.

A theory usually take the following form: given X, let me explain to you why Y is likely to happen. The "explanation" is something that links X (exogenous variables) to Y (endogenous variables). This link can be represented abstractly as a mapping Y = f(X).

There are many different ways to construct the mapping f. One way is empirical: maybe you have data on X and Y, and you want to estimate f. Another way is to just "wave your hands" and talk informally about the origins and properties of f. Alternatively, you might want to derive f based on a set of assumed behavioral relations. Or, you may want to deduce the properties of f based on a particular algorithm (individual optimization and some equilibrium concept -- the current notion of "microfoundations"). Some brave souls, like my colleague Arthur Robson, try to go even deeper--seeking the biological foundations for preferences, for example.

I don't think we (as a profession) should be religiously wedded to any one methodological approach. Which way to go often depends on the question being asked. Or perhaps a particular method is "forced" because we want to see how far it can be pushed (the outcome is uncertain -- this is the nature of research, after all). And I'm not sure what it means to have the "wrong" microfoundations. (Is it OK to have the wrong "macrofoundations?") Any explanation, whether expressed verbally or mathematically, is based on assumption and abstraction. Something "wrong" can always be found in any approach -- but this is hardly worth saying--let alone saying "over and over again."

Now on to the OLG model of money. Here is DeLong again:
Yes, it seemed to me that handwaving was not good. But saying something precise and false–that we held money because it was the only store of value in a life-cycle context, and intergenerational trade was really important–seemed to me to be vastly inferior to saying something handwavey but true–that holding money allows us to transact not just with those we trust to make good on their vowels but with those whom we do not so trust, and that as a result we can have a very fine-grained and hence very productive division of labor.
Not many people know this, but the OLG model (invented first by Allais, not Samuelson) is just an infinite-horizon version of Wicksell's triangle. The following diagram depicts a dynamic version of the triangle. Adam wants to eat in the morning, but can only produce food at night. Betty wants to eat in the afternoon, but can only produce food in the morning. Charlie wants to eat at night, but can only produce food in the afternoon (assume food is nonstorable).

In the model economy above, there are no bilateral gains to trade (if we were to pair any two individuals, they would not trade). Sometimes this is called a "complete lack of coincidence of wants." There are, however, multilateral gains to trade: everyone would be made better off by producing when they can, and eating when they want to (from each according to their ability, to each according to their need).

Consider an N-period version of the triangle above. Adam still wants bread in period 1, but can only produce bread in period N. Now send N to infinity and interpret Adam as the "initial old" generation (they can only produce bread off into the infinite future). Interpret Betty as the initial young generation (they produce output in period 1, but want to consume in period 2), and so on. Voila: we have the OLG model.

I've always considered Wicksell's triangle a useful starting point for thinking about what might motivate monetary trade (sequential spot market trade involving a swap of goods for an object that circulates widely as an exchange medium). In particular, while there is an absence of coincidence of wants, we can plainly see how this does not matter if people trust each other (a point that DeLong alludes to in the quoted passage above). If trust is lacking--assume, for example, that only Adam is trustworthy--then Adam's IOU (a claim against period N output) can serve as a monetary instrument, permitting intertemporal trade even when trust is in short supply.

An exchange medium is valued in an OLG model for precisely the same reason it is in the Wicksell model or, for that matter, any other model that features a limited commitment friction. So if anyone tries to tell you that the OLG model of money relies on money being the only store of value to facilitate intergenerational trade, you now know they are wrong. The overlapping generation language is metaphorical.

In any case, as it turns out, the foundation of monetary exchange relies on something more than just a lack of trust. A lack of trust is necessary, but not sufficient. As Narayana Kocherlakota has shown (building on the work of Joe Ostroy and Robert Townsend) a lack of record-keeping is also necessary to motivate monetary exchange (since otherwise, credit histories with the threat of punishment for default can support credit exchange even when people do not trust each other).

Also, as I explain here, a lack of coincidence of wants seems neither necessary or sufficient to explain monetary exchange. (Yes, I construct a model where money is necessary even when there are bilateral gains to trade.)

Are any of these results interesting or useful? Well, I find them interesting. And I think the foundations upon which these results are based may prove useful in a variety of contexts. We very often find that policy prescriptions depend on the details. On the other hand, I have nothing against models that simply assume a demand for money. These are models that are designed to address a different set of questions. Sometimes the answers to these questions are sensitive to the assumed microstructure and sometimes they are not. We can't really know beforehand. That's why it's called research.

Finally, is a "rigorous microfoundation" like an OLG (Wicksell) model really necessary to deduce and understand the points made above? I suppose that the answer is no. But then, it's also true that motor vehicles are not necessary for transport. It's just that using them let's you get there a lot faster and more reliably.


  1. I would put it like this:

    Understood metaphorically, where "generation" does not literally mean generation, and so the velocity of circulation of money is not once per three score and ten years, the OLG model of money is rather interesting.

    Understood literally, where "generation" really does mean generation, an OLG model is a bad model of money (but a good model of pension plans).

    It took me some time to realise that it could be understood metaphorically.

    I think we are saying the same thing.

  2. Interesting comment from Neil Wallace:

    "For a while there, I thought the overlapping-generations model was going to be the model of money. My attitude was to try to put that model to work in a number of applications. A classic problem in monetary economics, identi…ed by Hicks back in 1935, is why money exists when there are higher return assets around. I had this idea that if we legally inhibit intermediation, then rate of return dominance would emerge. I wrote a couple of papers about that using an overlapping-generations model. In retrospect, I think the profession was right to reject that view of money...I don’t think it dealt with Hicks'’s question very well. But the overlapping-generations
    model really failed miserably in explaining why economies have money in the following sense. People have had in mind for, I think, a couple of thousand years that something like money is a useful thing. It helps an economy achieve outcomes that it couldn't achieve in its absence. So it’s natural to have as a goal of monetary theory to invent settings where that is the case."

    1. Yes JP, it is interesting. I am very familiar with Neil's view on this matter. But I don't think it comes across in the passage you provided above.

      First of all, to Neil, *money* means a pure fiat currency. I reject this view. To me, money is an object that circulates widely as a payment instrument. So Neil would reject the Wicksell model above as a model of money. But this is why he initially turned to the OLG model: it can accommodate the existence of a pure fiat currency under some circumstances.

      Second, what led Neil to discard the OLG model as a theory of money? In the passage above, he suggests he did so because money is not "essential" in the OLG model.

      What does "essential" mean? It means that money is the *unique* way to implement a constrained-efficient allocation. In the OLG model, if we have enough record-keeping, we don't need money (credit is sufficient).

      The thing you should note here, however, is that virtually every model I know of is subject to this "criticism." There are conditions that make money essential -- anonymity, for example. Maybe Neil doesn't like that assumption, I don't know. But if that's the hurdle he's set for himself, I don't know of any model that passes this test. And I know for a fact that Neil also rejects the Lagos-Wright models of money (presumably for the same reason but also because the distributional aspects of monetary policy are killed off in quasilinear models -- ironically, the OLG model *does* possess distributional consequences of monetary policy).

  3. What is the difference between money and credit?

    1. Bob, I think of money an object (physical or virtual) that circulates (from hand-to-hand, or account-to-account) widely as payment instrument. The payments made are quid-pro-quo and the exchange is settled immediately.

      Credit is an intertemporal exchange that entails delayed settlement. You acquire something today and you pay for it by issuing a promise to return something of value in the future. There is no sense of "circulating media" in credit exchanges (although, of course, promises can and often do entail the future delivery of exchange media).

      You may also wish to consult:

  4. Thanks, David

    I just read your post from 2010 on asset-shortages-and price-bubbles. Very interesting! I’ve been thinking about transactions as a fundamental concept. A transaction is like factoring an exchange; money for goods, and then goods for money. Trust on the part of the seller must be established when an IOU or a contract is substituted for money. Your explanation of credit gives me the idea of thinking of extended transactions; initiated at one time and completed sometime later.

    Incidentally, I have been looking for macroeconomic models where money and credit play essential roles, along with heterogeneous agents, and propensities to buy, sell, lend, and save. Do you have any suggestions?

    1. Bob, there are many papers out there that model the coexistence of money and credit (generally, the coexistence of multiple assets with rate of return differentials driven by liquidity premia).

      Here is one such paper:

      See also the Corbae and Ritter (1999?) paper. Nosal and Rocheteau have an advanced textbook on modern monetary theory. For elementary theory, check out the textbook by Champ, Freeman and Haslag. I also point you here, in case you find it useful:

      Let me know if you have any questions.

    2. Bob, there are many papers out there that model the coexistence of money and credit (generally, the coexistence of multiple assets with rate of return differentials driven by liquidity premia). A common assumption is that some trades can be monitored (so that a public record exists) and some exchanges cannot be monitored (so unsecured credit is impossible).

      Here is one such paper:

      See also the Corbae and Ritter (1999?) paper. Nosal and Rocheteau have an advanced textbook on modern monetary theory. For elementary theory, check out the textbook by Champ, Freeman and Haslag. I also point you here, in case you find it useful:

      Let me know if you have any questions.

  5. Thanks again David. I really appreciate your taking the time to send me some references! I'll track them down and start reading.

  6. David- Is it appropriate to refer to microfoundations that, in a (more or less) well-specified model, produce implausible results as 'wrong?' For example, if my model assumes all arguments in the representative consumer's utility function to be perfect substitutes, could the central flaw of my model be this assumption?

    1. Hi Jonas.

      If I was to write down a model of the countryside and call it a "road map," how many details would have to be missing before it could be labeled "wrong?"

      The answer is that it depend on the question that is being addressed. If the road map helps you navigate through unknown terrain, then we are happy that it omits most other details. If it leads us over a cliff, we will label the road map wrong. But we say it is wrong not because it abstracts--we call it wrong because it abstracted the wrong way for the question being addressed.

      Does this help?

    2. I'm with you on the map analogy; abstraction is the art of our discipline, after all. I think of 'wrong' microfoundations as analogous to the cliff example. The problem is not the abstraction per se; it's the mis-writing of a detail. If the location of the (real-life) cliff was instead marked on the map 'here be dragons,' a careful traveler would avoid it just the same. The mis-marking would significantly impact our big-picture view of the territory, however.

      I found this Friedman quote on Instrumentalism in some lecture slides of a subtle and insightful professor: "Competing theories should be evaluated on the accuracy of their predictions, not on the descriptive realism of their assumptions." []

      This is what I meant when I referred to 'implausible results.' It's all well and good to abstract artfully and appropriately to the situation being modeled. Since the goal of Lucas-robust models is to build up a model (abstract) economy from rational intertemporal choice, writing down a nonsense price-adjustment rule, for example, could doom the results of the model, no?

      [As a meta-aside, I really appreciate your engagement on these questions. I really am trying to figure this stuff out, and I haven't got many that are will to help.]

    3. Ha ha, yes, I'm sympathetic to Friedman's view.

      "Since the goal of Lucas-robust models is to build up a model (abstract) economy from rational intertemporal choice, writing down a nonsense price-adjustment rule, for example, could doom the results of the model, no?"

      Well, I guess it might depend on what you mean by a "nonsense" assumption. Note that there is no price-adjustment mechanism in neoclassical theory -- the price-mechanism is just assumed. Whether this is good/bad, where it makes sense/nonsense, depends, ultimately on what the model is being used for and how well it performs relatively to competing models. (And this, by the way, holds true for any type of "model" -- including the models that live in everyones' heads.)

      And happy to oblige! I'm still trying to figure this stuff out as well.

  7. Very clear explanation of money and its usage.

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