What is the difference between "aggregation" and a "representative agent?"

Question

What is the difference between "aggregation" and a "representative agent?" I'm sorry if I'm not entirely clear on this question, but that's why I ask. It seems to me as if a representative agent is defined as a situation in which a competitive equilibrium can be reached by maximizing the utility of an object that can be interpreted as a "representative agent" whereas "aggregation" refers to a related situation where in competitive equilibrium prices don't depend on the distribution of an initial endowment. (Something to this effect.)

Could somebody clarify what these two concepts are and how they are related and/or different?

Answer 1

(I cannot say if my answer will respond to your questions, which indeed, are a bit unclear).

If one browses through many-many economic papers, one will get the impression that "representative" just means identical. Indeed in large chunks of literature this is the case, for historical reasons.

The drive behind the adoption of the "representative consumer" modelling framework came from the Lucas critique on the previous-generation macro-models, and the requirement that macroeconomic models are "micro-founded". But true theoretical aggregation (with heterogeneity present) requires some skill and knowledge and the bulk of the discipline appeared to have quickly settled for the "representative means identical" framework.

The problem is that in such a case, you don't really have a macro-model, just a blown-up version of a micro-model (note: here the words micro/macro are not to be mapped to the partial/general equilibrium concepts). There is nothing to "aggregate" here: the whole point of aggregation is to see whether the behavior of the collective differs from the behavior of the individual. And in the "representative means identical" approach, no such thing can happen, by construction: Instead of micro-founded macro-models, we ended up having blown-up micro-models posing as macro-ones (this is not opinion, I am just describing).

There are some models where the term "representative" obtains some intuition -especially in models with more than one classes of agents (say, labor owners and capital owners). Here we model two agents, and each is "representative" of its class. In-class are all identical, but here it sounds more appropriate to call the two individuals "representative".

The funny thing is, the concept "representative consumer" (RC) does have a special meaning: the representative consumer represents all consumers as regards basic structure, not measurement or quantities. E.g. "all individual maximize utility from consumption ("same structure"), but their utility parameters may differ("different measure"). All consumers have wealth, but the level of wealth may differ. Etc. RC is still a modelling abstraction, but it does leave room for heterogeneity.

A good source on the matter is

Caselli, F., & Ventura, J. (2000). A representative consumer theory of distribution. American Economic Review, 909-926.

Apart from their focus on developing a theory of distribution in the context of an RC model, they make a good job in presenting what can be done in an RC framework and what not. An excerpt:

The RC is a fictional consumer whose utility maximization problem when facing aggregate resource constraints generates the economy's aggregate demand functions. The RC assumption does not rule out consumer heterogeneity, but only requires that potential sources of consumer heterogeneity have sufficient structure to ensure that the sum of all consumers behaves as if it were a single consumer.

Answer 2

Maybe someone else has more to say about this, but here is what I understand to be the difference.

A model in which there is either a unit measure of homogeneous agents or a single agent is typically called a "representative agent economy." This seemed (and seems) to be how many papers model consumers. The obvious shortcoming of this is that consumers are not identical. In particular, if you want to measure distributional effects of different policies then a representative agent economy is a really bad idea. For example, distributional effects are important in this paper and I think she briefly discusses it in her introduction.

A model which admits aggregation is exactly what you said. It is a model in which aggregate variables do not depend on the distribution of wealth, instead they can be expressed in terms of aggregates. The problem is that this basically takes you right back to a representative agent economy. If you go through the details of writing an economy with heterogeneous consumers then you need to make sure aggregation doesn't hold or else to some degree you will be missing the heterogeneity that you tried to capture. There are some standard aggregation results that I can think of off the top of my head: Gormann Aggregation, Negishi Aggregation. I know there is a good literature survey out there, but for the life of me I can't find it. I'll check some of my notes when I have them tomorrow and hopefully edit.

Edit: Found one of the papers that I was thinking of:

Guven 2012 deals with heterogeneous agent models. Both aggregation and "near aggregation"(Think Krussel Smith) are discussed.