A snippet on representative agents

by John Quiggin on October 23, 2009

In response to some comments, I’ve written a little bit about the representative agent assumption in Dynamic Stochastic General Equilibrium Models. I argue that, given the underlying DSGE assumptions, you won’t get very much extra by including heterogeneous agents.

But, I intend to say in the “Where next” section, it seems likely that heterogeneous and boundedly rational individuals, interacting in imperfect and incomplete markets will generate ’emergent’ macro outcomes that are not obvious from the micro foundations. Of course, this is going to be a prospectus for a theory, not the theory itself.

In the meantime, comments on my snippet would be much appreciated.

Update Looking at the responses, I think just about everyone has missed the point, which suggests that maybe I didn’t make it very well.

I’m not saying that heterogeneity doesn’t matter, but that introducing (tractable) heterogeneity into a DSGE model isn’t likely to yield radically different predictions about macroeconomic outcomes. If that’s correct, then if you think DSGE models work well (for some evaluative procedure), you can be relaxed about using representative agents. And if you don’t think DSGE models work well, the representative agent assumption isn’t the problem, or at least it isn’t the only problem.

Since my statement of the situation didn’t help much, I’ll present it as a question instead. Can anyone point me to a DSGE-style model that derives strongly non-classical results from the introduction of heterogeneity? Or, failing that, does anyone have a convincing argument that such results should emerge?

I’m aware of course that, in general, anything can happen with aggregation across heterogeneous agents, so I’m not much interested in arguments for agnosticism starting from that point. End update

Commonly, though not invariably [in DSGE models], it was assumed that everyone in the economy had the same preferences, and the same relative endowments of capital, labour skills and so on, with the implication that it was sufficient to model the decisons of a single ‘representative agent’. This assumption has attracted a lot of criticism, and quite a few critics have suggested that models that take account of individual differences in tastes and endowments would yield more realistic results.

Such criticisms are somewhat off the point in relation to micro-based macro models. As long as the agents in such a model are rational optimizers in the standard sense of neoclassical microeconomics, any initial differences in tastes or endowments will be evened out by trade in competitive markets. In a standard market equilibrium, everyone will have the same preferences ‘at the margin’, namely the preferences given by market prices. If, for example, the market price of oranges is twice the market price of apples, then market equilibrium requires that everyone who trades in that market should be willing, at the margin, to trade two apples for an orange, regardless of whether they prefer to consume a lot of apples and a few oranges, or vice versa. In standard micro-based macro models, this means that not much is lost by aggregating all the participants in a market, and then working with an average or ‘representative’ agent.

{ 22 comments }

1

Bunbury 10.23.09 at 10:12 am

If, for example, the market price of oranges is twice the market price of apples, then market equilibrium requires that everyone who trades in that market should be willing, at the margin, to trade two apples for an orange, regardless of whether they prefer to consume a lot of apples and a few oranges, or vice versa.

In what sense is this true? If agents of type O gain no utility from apples, agents of type A gain none from oranges while agents of type B get something from each we can have an equilibrium where an agent of type B would exchange two infinitesimal apples for one infinitesimal orange but agents of type O and A would not. If the model is shocked by an increase in the supply of oranges, the impact of the shock will depend upon which agents received the oranges giving results different than would be obtained by just considering the equilibrium among agents of type B.

There are also quite different results delivered by overlapping generations models which are common heterogenous agent models so some clarification of what is being claimed here would be helpful. Are the different results not significantly different? Or are they not standard and the claim only applies to standard models?

2

Cosma Shalizi 10.23.09 at 12:37 pm

I am really not happy with that last paragraph, and not just for the reason Bunbury gives. May I recommend Forni and Lippi’s Aggregation and the Microfoundations of Dynamic Macroeconomics (Oxford U.P., 1997)?

3

Glen Tomkins 10.23.09 at 1:28 pm

Rational actor theories vs actual market conditions

It seems to me that financial markets these days are dominated by rent-seekers. This is true to such an extent that we no longer even bother to distinguish between rent-seekers and investors, we just assume that, of course, folks who want to let their money make money for them neither want, nor care, nor are able, to actually oversee how their money is put to use.

Certainly a market has a level of free ridership it can tolerate. As long as the rent-seekers follow the lead of the people who actually can size up assets on a market, and then continue to oversee them, their choices will simply amplify the signals put out by actors who actually are using reason. But once the rent-seekers become so numerous as to dominate a market, then even the folks who are paying attention and acting accordingly, have to start basing their rational decisions, not on underlying values, but on new realities, and new valuations, created by the observed behavior of the herd of unthinking rent-seekers. Stocks actually do provide a reasonable ROI in the current environment because so many people who have no clue about how the NYSE works, or how stock valuations are derived, believe that stocks are a good buy, act on that belief, and bid the prices up. Well, stocks will continue to provide good ROI until they don’t, at which point smart money, first, will start to leave the market, followed rapidly by the even stupider money, and the bubble will burst.

And the NYSE is one of our more staid and sober markets. The tell on the NYSE, for me, was when even smart people started to capitualte on stock-picking and just advised people to buy index funds. We’re not talking about the mistakes that rational actors will make in sizing up investments, index funds are a wilful abdication of the use of reason in the NYSE, an admission that the rational actor is a fustian thing of the past. Things are much worse in more exotic markets like that for securitized mortgages, despite their domination by high rollers, whom you might think would, unlike the herd of 401Kers, be smart investors. But we’ve recently found that everyone, even folks investing in the tens of millions in these markets, so failed to do basic due diligence about these things, that the rather huge and fundamental problem of deeds recordation was not noticed. The folks who bought these turkeys don’t even have clear title to the properties, never did, and none of them bothered to research that before committing millions. Charles Ponzi had a more believable and workable business model to shop around, with his notion of money order/exchange rate arbitrage, than the mortgage securitizers. This is clearly not just a matter of bad or imperfect judgment, it’s a clear case of not even trying to begin to start the process of exercising judgment and rational oversight. Yet that’s the new standard, not imperfect rational oversight, but not even the attempt at rational oversight.

Call me an anti-intellectual and Luddite, but I can’t for the life of me see the point of working within or against a theory that is based on premises that reality has refuted. No one had to bother arguing with Bishop Bossuet about monarchic absolutism being a good or a bad thing after the events starting in 1788 refuted the very idea that there was such a thing as an actual monarchic absolutism to be for or against. It seems to me that the Bishop Bossuets of the free market and its rational actors, are about as relevant.

At least I’m a cheerful Luddite, and would be happy to receive the faith in the rational actor, if anyone would care to defend its premises. It’s these roots that seem to me more fraught, more questionable and more valuable to question, than its outer ramifications.

4

Thomas 10.23.09 at 2:47 pm

everyone who trades in that market should be willing, at the margin, to trade two apples for an orange

Well, if it’s really an equilibrium, that will be the ratio they trade at, if they are willing to trade. I don’t think that’s a very strong conclusion.

If there are more than two goods in the market they only have to be willing to make one of the choose(n,2) possible trades, not all of them (together with some constraints that preventing them all making a living by taking in each other’s washing) and if there’s money they might trade apples for money without buying oranges and get into a recession.

5

puzzled 10.23.09 at 3:56 pm

I guess I have a different view of the state of modern micro-based macro. The view presented in this post is as if there have been no developments since the 1982 Time to Build paper by Kydland and Prescott. It seems to me that most quantitative papers I read and see presented feature:
1) Life-cycle models where agents have finite lives
2) Some degree of altruism towards children, but children are not perceived as extensions of the agent (thus the dynastic interpretation fails).
3) Incomplete markets – people cannot insure against income risks.

So in these circumstance heterogeneity matters!

It’s quite possible there is a selection of what I am reading and paying attention to, but still…

6

JoB 10.23.09 at 4:27 pm

So, I guess you’re not going to convince people using idealized examples.

I thought your prospectus was already in: you had a very good long snippet on risk and how the balance in risk-taking shifted running up to this particular crisis. Risk (I shan’t mention the g*mbling word, so let’s say insurance) and bounded rationality: there just has to be an angle there for you to hook onto without the apples/oranges stuff which is by the way, so-ho (two palms with stretched fingers held just in front of the chest), not now anymore.

PS: on the emerging macro-thing, I worry, taking economics in a broad sense (political theory sense) you’re right of course (that’s the point of Davidson et al.) but narrowly, I mean: abstracting from non-economical goals like world peace and what have you, it is quite probably the case that there is no good model linking micro and macro, but that’s not a reason for discrediting the search for one (Lakoff, emerging properties, hmm, I’d hope it’s not a pseudo-scientific pattern that’s coming about here)

7

Kenny Easwaran 10.24.09 at 2:33 am

The existence of market equilibrium prices suggests that we can abstract away from the preferences of individual agents over possessing different collections of tradeable goods. But it seems that there are other things we prefer where the market equilibrium doesn’t just take care of things. For instance, one person might prefer that some information become public while the other prefers not (as in blackmail). Or different people may have preferences that different laws exist. For goods, and to some extent services, the fact that they can be traded and re-allocated makes the marginal price make sense, but for situations of the world, where there is no margin, it doesn’t seem like this sort of analysis can work.

(Of course, maybe I just say this because I’m a philosopher, and I’ve always worked with decision theory where preferences are over states of the world, rather than objects. Valuing an object almost seems like a category mistake to me!)

8

Kenny Easwaran 10.24.09 at 2:34 am

(To clarify, what does make sense is valuing the state of affairs in which I have an object. States of affairs are the only things that are directly valued, and the ordinary notion of valuing an object is derivative on this notion, at least in the way I standardly tend to think of things.)

9

Alex K. 10.24.09 at 2:57 am

“[…] any initial differences in tastes or endowments will be evened out by trade in competitive markets”
[..]
“not much is lost by aggregating all the participants in a market, and then working with an average or ‘representative’ agent.”

I don’t want to be too harsh, but someone writing a fragment like that in a class paper would deserve to fail the class.

Due to the Sonnenschein-Mantel-Debreu result, we know that with heterogeneous agents *any* path of prices (subject only to very weak constraints) can be possible prices.

This means that you can give examples of just about any “pathological” behavior of prices that you want, and that unless you have access to the heterogeneous utility functions you can have virtually no testable implications for your theory.

Furthermore, if you start thinking about the dynamics of attaining equilibrium –which virtually no economist does, showing the intellectual turpitude of the field — then it matters a great deal whether you have heterogeneous agents or not. It is harder to have nice equilibrium convergence results with heterogeneous agents.

That John Quggin is a professional economists and can still ignore heterogeneity summarily shows how far economics has drifted from serious intellectual inquiry.

10

DCBob 10.24.09 at 4:40 am

One nice thing with forward-looking heterogeneous agents, if they are modeled as facing realistic degrees of uncertainty about life outcomes (in the form of uncertainty about period-by-period productivity shocks and/or lifespan), is that a substantial portion of their saving is precautionary rather than life-cycle, so their response to changes in marginal tax rates are (realistically) muted compared with the response of perfectly-foresighted agents not facing such uncertainty. That seems like a big improvement in at least that piece of economic research.

11

Robert 10.24.09 at 8:33 am

I find Quiggin’s writing disspiriting.

Alan Kirman’s “Whom or What Does the Representative Individual Represent?” (Journal of Economic Perspectives, V. 6, N. 2, 1992: 117-136) is a classic take on the implications of the Sonnenschein-Mantel-Debreu theorem for representative agents.

One implication I take from Kirman is that no reason exists to pay any attention to Robert Lucas’ estimates of the benefits of successful stabilization policy.

While I’m handing out writing assignments, consider Graham White’s “Capital, Distribution, and Macroeconomics: ‘Core’ Beliefs and Theoretical Foundations” (Cambridge Journal of Economics, V. 28, 2004: 527-547). Macroeconomists had a consensus model only in the sense that they ignored some economists.

The problem with “microfoundations” isn’t merely that consumers don’t maximize utility and firms don’t maximize profits. Even if the microeconomic assumptions about individual behavior were valid descriptions of individual behavior, the mainstream macroeconomic models would still be invalid. The conclusions don’t follow from the assumptions in a world with more than one consumer and more than one commodity. But, for decades, mainstream macroeconomists have not cared enough to get their math correct.

12

bunbury 10.24.09 at 8:38 am

Whether heterogenous rational agent models are a fruitful direction for research is a matter of opinion. The claim that they are not would be better supported by, for example, suggesting that they’ve been around for ages and not made much impact than with a suggestion that they aren’t ultimately very different to single agent models.

That such models may not appear to have brought about a revolution may have more to do with the sociology of economics than the content of the models.

To start with some economists put quite a lot of work into showing that there are circumstances where extra model features don’t make any difference — Barro 74 gets interpreted like that for example, even if the paper is less sweeping.

Other investigators take an incremental approach and the reasons for doing so are quite compelling — it helps to pin down the effect under investigation and helps maintain connection with the establishment.

However I think there is a more fundamental issue. The issue with multi agent models is not simply tractability but the expansion of the range of potentially debatable assumptions that are available simply because the models are bigger. That changes the nature of the results you can expect to get and makes research more about what assumptions you make than about what you can conclude from them.

To answer the two questions, I think there are plenty of cases where multi agent models do not yield the same results as single agent models and the equity premium puzzle is a fine area. For a reason to think that they should be relevant I would point to their potential, and the complete inability of single agent models, to address distributional issues.

13

John Quiggin 10.24.09 at 11:20 am

Bunbury, the equity premium point is a good one, and one I will certainly be taking into account. I’ve always liked Mankiw’s explanation which does depend critically on heterogeneity. Having written a lot on this very subject, I’ve been struck by the absence of any significant interest in macro implications of the equity premium such as the invalidity of Lucas’ estimates of the welfare cost of recessions, which I noted in this paper with Simon Grant (paywalled, but this point is in the abstract)

http://www.bepress.com/ev/vol2/iss4/art2/

14

Kevin Donoghue 10.24.09 at 12:38 pm

O/T: Should I feel bad about the fact that I found a freebie version of that Grant and Quiggin paper with ease? Or do the authors prefer it that way? It’s amazing how much supposedly copyright material is freely available online.

15

bianca steele 10.24.09 at 3:33 pm

@3: index funds are a wilful abdication of the use of reason

This is nuts. Delegating decision making wrt technical matters is in no way an “abdication of the use of reason.” No modern person would be able to live a modern life without delegating thousands and thousands of decisions every day.

And what does this question have to do with Ludditism anyway?

16

P O'Neill 10.24.09 at 5:07 pm

I think the earlier mention of overlapping generations is important. Once that is allowed, then you’re into the prospect of dynamic inefficiency, social security schemes, and bubbles. That’s a full plate within a fairly simple and otherwise quite “classical” structure.

17

John Quiggin 10.24.09 at 8:35 pm

@14 do the authors prefer it that way?

Yes

18

JoB 10.25.09 at 1:33 pm

Probably this is out-of-time and, anyway, I’ll just repeat myself:

The core of bounded rationality has to do with risk and certainty – humans love small gambles and hate big risks. There’s no way that this behaviour will average out – quite the contrary. Given the option we’ll all buy some shares hoping to be the first – & we’ll all buy some insurance against loosing out on all of the shares we buy.

What I don’t understand, being a non-economist, is why economists haven’t provided theories that are as simple as the apple/oranges one including this.

What I don’t understand, not being John, is why John had a good general treatment of risk and still chooses apples/oranges to work in bounded rationality.

At the very least one should expect the impact to come at the level of derivatives of an apple/orange stuff, should one not? What’s going to be the price one’s willing to pay in order to be sure one can have an apple in a year from now? At what price do I get some remote chance of winning so many oranges now that I won’t have to worry about them, at all, never again?

Which would explain why economists have had it wrong for such long times; they were sufficiently right during all these times not to really need a correct dynamic equation.

I have no clue whether this makes any sense at all to an economist. Then again most of the economists don’t make a lot of sense to each other, or so it appears ;-)

PS: I always wondered: price theory cannot ever have meant that each individual has a willingness to pay in such and such a proportion? It would be odd that any 2 people are at any time agreeing in the relative preferences they have for anything. No?

19

John Quiggin 10.26.09 at 1:47 am

What I don’t understand, not being John, is why John had a good general treatment of risk and still chooses apples/oranges to work in bounded rationality.

What I meant to say, in this notably unsuccessful snippet was that (contrary to some suggestions) incorporating agents who are heterogeneous in the sense that they have different tastes regarding things like apples and oranges is unlikely to make much difference to the results of a DSGE model.

What’s more likely to be relevant is the kind of ex post heterogeneity that emerges from incomplete markets, overlapping generations and the kind of risk preferences mentioned by JoB. My incautious reference to “emergent properties” was only meant to say that we may not be able to derive analytical solutions to the associated general equilibrium problems, and may instead have to rely on aggregate relationships consistent with observation and with an intuitive understanding of the likely effects of bounded rationality etc.

20

JoB 10.26.09 at 10:28 am

Yeah, we may not but you can sure try. Is there an economic treatment aggregating an unidirectional non-rational preference as to risk and certainty?

21

JoB 10.26.09 at 3:24 pm

Oh boy, did I write thát (20), shame on me!

What I tried to say:

1. John, we ‘may not be able to’ but you should for sure at least try.

and,

2. Is there some mathematical model in modern economics treating this aggregation of what are divergences from rationality in the same direction, for all agents? In point: the general preference to pay more for insurance than is “rational”, based on the extent and the probability of the disaster.

22

Chris 10.28.09 at 3:48 pm

the general preference to pay more for insurance than is “rational”

ISTM that this arises largely from insureds believing that they are getting more insurance than they are, in fact, in the fine print, getting. Many insureds with claims are unpleasantly surprised by the extent of their coverage. The ones without claims never discover their mistake.

This mistake is not an accident, it is deliberately induced by the insurance salesman. It’s not technically fraud because the fine print is there.

(Of course, I’m referring to actual insurance; IIRC there are behavioral economics experiments in which they don’t try to deceive the subject and still find irrational preferences, but I think those are overshadowed by insurance sales tactics in practice.)

Comments on this entry are closed.