Wade Hands on the Representative Agent Assumption in Macroeconomics and Revealed Preference Theory

Note : This post has been originally published at the blog “Rationalité Limitée

I am currently doing the ultimate refinements on my working paper “Sen’s Critique of Revealed Preference Theory and Its Neo-Samuelsonian Critique”. In the process, I have just finished to read several papers by Wade Hands on Paul Samuelson’s contribution to revealed preference theory and general equilibrium analysis. Hands’ papers are mainly historical but they also contain many interesting methodological and theoretical insights regarding the significance and the relevance of the representative agent assumption in modern economics.

Hands emphasizes several important points regarding how the representative agent assumption (RAA) came to be standard in macroeconomics but also – less obviously – in microeconomics. I start first with the macro side. In his paper “The Individual and the Market: Paul Samuelson on (Homothetic) Santa Claus Economics”, Hands convincingly argues that the RAA was not part of the standard Walrassian model of perfectly competitive markets of the mid-twentieth century. Indeed, this assumption was regarded as contrary to the fact that the Walrassian model is about decentralized economies with interacting and heterogeneous agents. As Arrow and Hahn put it on the very first page of their classical General Competitive Analysis:

“Whatever the source of the concept [equilibrium], the notion that a social system moved by independent actions in pursuit of different values is consistent with a final coherent state of balance, and one in which the outcomes may be quite different from those intended by the agents, is surely the most important intellectual contribution that economic thought has made to the general understanding of social process”.

In this book and in their subsequent writings, Arrow and Hahn (and others) do note that it is possible to assume the existence of some representative agent. They also note that this assumption would considerably simplify the theoretical work but at the cost of removing all the interesting content and findings from the analysis. This is in sharp contrast with the standard practice in contemporary macroeconomics through the so-called dynamic stochastic general equilibrium (DSGE) models where the economy is routinely modeled through the interaction between a representative household and a representative firm. Most of the time, regarding the demand side, the RAA is based on the key postulate of homogenous homothetic preferences (or utility functions). Homothetic preferences display an interesting feature: they do not exhibit income effects (i.e. the households’ preferences are invariant to income changes). When combined with the assumption that these homothetic preferences are identical across the population, this entails that the population of households behaves as a single rational agent maximizing utility under budget constraints. In other words, the market demand function exhibits the very same properties as individual demand functions and this function is “well-behaved”. The Walrassian model with the assumption of homogenous homothetic utility functions is an instance of what Samuelson used to call “Santa Claus economics”, i.e. economics based on models with very strong and unrealistic assumptions. As Hands show, though Samuelson himself has built and used such models several times, he was in general very skeptical regarding their relevance for general equilibrium analysis. The reason was not only empirical (preferences heterogeneity as well as income effects are clearly empirically significant features of modern economies) but also theoretical and methodological. For instance, Hands points out that assuming homogeneous homothetic preferences is the same than to apply directly the axioms of revealed preference theory to market (and not individual) demand functions. It also makes unnecessary all Samuelson’s contribution in the Foundations of Economic Analysis on the stability of competitive equilibrium since obviously if the representative agent’s preferences are well-behaved, we have a standard maximization problem with a unique and stable equilibrium.

This connects with the micro side of Hands’ papers. Hands shows that the RAA has also gained much popularity in microeconomics, though practitioners demonstrate less reflexivity about this than their macroeconomist colleagues. The rise of the RAA in microeconomics is particularly related to the development of a specific approach in demand analysis that Hands calls “contemporary revealed preference theory”. In a nutshell, contemporary revealed preference theory starts from a “restrictive domain” (i.e. a finite set of data regarding prices and quantities) and use some set of tools and axioms to infer a utility function “rationalizing” these data. This allows making prediction regarding demand in case of some parameters shift (e.g. changes in prices). Interestingly, the individuals almost completely disappear from the analysis: the axioms of revealed preference theory are directly applied to market demand functions without assuming that individual agents are “rational”. As Hands suggests, this is nothing but an instance of the RAA: it is simply assumed that market demand behaved as an individual agent and the axioms of revealed preference theory allow determining a utility function for this representative agent.

Samuelson is of course the pioneer of revealed preference theory. However, Samuelson’s aim was quite different. Essentially, it was to show the mathematical equivalence of ordinal utility theory and revealed preference theory and thus to demonstrate the possibility of conducting demand analysis without the use of psychologically-charged concepts such as utility. But, as for general equilibrium analysis, he was also reluctant to apply directly the revealed preference axioms to market demand function as it would be the same as to assume that there is some representative agent.

An interesting issue is of course how the RAA has gained such popularity in contemporary economics. Hands discusses several possibilities in his paper “The Contemporary Conundrum: Behavioral Economics, Rational Choice Theory, and the Representative Agents”. He suggests that social and technological features like the relative economic stability from the 1950s onwards on the one hand and the rise of computational power on the other have contributed to make issues of coordination and disequilibrium less salient and to facilitate empirical analysis of demand respectively. Another important factor (at least regarding the micro side) is the fast development of experimental economics and particularly the rise of the notion of “ecological rationality”. The latter has contributed to recognition that market rationality does not necessarily depend on individual rationality.

Interestingly, among the possible explanations, Hands rejects the possibility that the RAA is just the emanation of a deep trend in economics regarding the “profusion” (or the “proliferation”) of agency, i.e. the fact that the tools of choice theory are applied in a more and more abstract way to wider range of different types of economics agents: persons, firms, states, selves, … Hands argues that this explanation does not work in the case of the RAA because contrary to firms or states, the representative household does not actually exist in the world and does not make decisions. This is a fair point but it depends on an ontological commitment regarding what an economic agent actually is. A counterargument could be that an economic agent is simply but anything that can be represented as making consistent choice. This is indeed a nice way to rationalize (rather than to explain) at least part of the use of the RAA, as Don Ross demonstrates in several writings. A serious problem with this rationalization is that it almost inevitably leads to a divorce between positive and normative economics: if welfare is broadly defined as preference-satisfaction, then to assume that the representative agent is a “real” agent is of course very problematic. Incidentally, this was also one of the reasons why Samuelson rejected the RAA for general competitive analysis.

As a more personal conclusion, Hands’ history of the RAA highlights the fact post-WWII standard economics has struggled from its beginning with the difficult problem of reconciling issues of agency with issues of aggregation. The RAA is an obvious way of sidestepping problems related to aggregation as exemplified by the SMD theorem. But this led economics to a very abstract and formal view of agency (and rationality) which is made possible by the fact that the tools of choice theory (choice functions à la Sen or Arrow, decision theory) are themselves very abstract. This is not a problem per se; it depends on the problems economists are interested in. But the worry is precisely that in some cases this approach may not be adapted to the problem at stakes (the RAA in macroeconomics) while in others it may lead to a problematic redefinition of the scope of economics (such as to exclude whole part of normative economics from the field).


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