The Fable of the Ants, or Why the Representative Agent is No Such Thing

Image reproduced from here

Earlier in the summer, I had a discussion on Twitter with Tony Yates, Israel Arroyo and others on the use of the representative agent in macro modelling.

The starting point for representative agent macro is an insistence that all economic models must be ‘microfounded’. This means that model behaviour must be derived from the optimising behaviour of individuals – even when the object of study is aggregates such as employment, national output or the price level. But given the difficulty – more likely the impossibility – of building an individual-by-individual model of the entire economic system, a convenient short-cut is taken. The decision-making process of one type of agents as a whole (for example consumers or firms) is reduced to that of a single ‘representative’ individual – and  is taken to be identical to that assumed to characterise the behaviour of actual individuals.

For example, in the simple textbook DSGE models taught to macro students, the entire economic system is assumed to behave like a single consumer with fixed and externally imposed preferences over how much they wish to consume in the present relative to the future.

I triggered the Twitter debate by noting that this is equivalent to attempting to model the behaviour of a colony of ants by constructing a model of one large ‘average’ ant. The obvious issue illustrated by the analogy is that ants are relatively simple organisms with a limited range of behaviours – but the aggregate behaviour of an ant colony is both more complex and qualitatively different to that of an individual ant.

This is a well-known topic in computer science: a class of optimisation algorithms were developed by writing code which mimics the way that an ant colony collectively locates food. These algorithms are a sub-group of broader class of ‘swarm intelligence’ algorithms. The common feature is that interaction between ‘agents’ in a population, where the behaviour of each individual is specified as a simple set of rules, produces some emergent ‘intelligent’ behaviour at the population level.

In ants, one such behaviour is the collective food search: ants initially explore at random. If they find food, they lay down pheromone trails on their way back to base. This alters the behaviour of ants that subsequently set out to search for food: the trails attract ants to areas where food was previously located. It turns out this simple rules-based system produces a highly efficient colony-level algorithm for locating the shortest paths to food supplies.

The key point about these algorithms is that the emergent behaviour is qualitatively different from that of individual agents – and is typically robust to changes at the micro level: a reasonably wide degree of variation in ant behaviour at the individual level is possible without disruption to the behaviour of the colony. Further, these emergent properties cannot usually be identified by analysing a single agent in isolation – they will only occur as a result of the interaction between agents (and between agents and their environment).

But this is not how representative agent macro works. Instead, it is assumed that the aggregate behaviour is simply identical to that of individual agents. To take another analogy, it is like a physicist modelling the behaviour of a gas in a room by starting with the assumption of one room-sized molecule.

Presumably economists have good reason to believe that, in the case of economics, this simplifying assumption is valid?

On the contrary, microeconomists have known for a long time that the opposite is the case. Formal proofs demonstrate that a population of agents, each represented using a standard neoclassical inter-temporal utility function will not produce behaviour at the aggregate level which is consistent with a ‘representative’ utility function. In other words, such a system has emergent properties. As Kirman puts it:

“… there is no plausible formal justification for the assumption that the aggregate of individuals, even maximisers, acts itself like an individual maximiser. Individual maximisation does not engender collective rationality, nor does the fact that the collectivity exhibits a certain rationality necessarily imply that individuals act rationaly. There is simply no direct relation between individual and collective behaviour.”

Although the idea of the representative agent isn’t new – it appears in Edgeworth’s 1881 tract on ‘Mathematical Psychics’ – it attained its current dominance as a result of Robert Lucas’ critique of Keynesian structural macroeconomic models. Lucas argued that the behavioural relationships underpinning these models are not be invariant to changes in government policy and therefore should not be used to inform such policy. The conclusion drawn – involving a significant logical leap of faith – was that all macroeconomic models should be based on explicit microeconomic optimization.

This turned out to be rather difficult in practice. In order to produce models which are ‘well-behaved’ at the macro level, one has to impose highly implausible restrictions on individual agents.

A key restriction needed to ensure that microeconomic optimisation behaviour is preserved at the macro level is that of linear ‘Engel curves’. In cross-sectional analysis, this means individuals consume normal and inferior goods in fixed proportions, regardless of their income – a supermarket checkout worker will continue to consume baked beans and Swiss watches in unchanged proportions after she wins the lottery.

In an inter-temporal setting – i.e. in macroeconomic models – this translates to an assumption of constant relative risk aversion. This imposes the constraint that any individual’s aversion to losing a fixed proportion of her income remains constant even as her income changes.

Further, and unfortunately for Lucas, income distribution turns out to matter: if all individuals do not behave identically, then as income distribution changes, aggregate behaviour will also shift. As a result, aggregate utility functions will only be ‘well-behaved’ if, for example, individuals have identical and linear Engel curves, or if individuals have different linear Engel curves but income distribution is not allowed to change.

As well as assuming away any role for, say income distribution or financial interactions, these assumptions contradict well-established empirical facts. The composition of consumption shifts as income increases. It is hard to believe these restrictive special cases provide a sufficient basis on which to construct macro models which can inform policy decisions – but this is exactly what is done.

Kirman notes that ‘a lot of microeconomists said that this was not very good, but macroeconomists did not take that message on board at all. They simply said that we will just have to simplify things until we get to a situation where we do have uniqueness and stability. And then of course we arrive at the famous representative individual.’

The key point here is that a model in which the population as whole collectively solves an inter-temporal optimisation problem – identical to that assumed to be solved by individuals – cannot be held to be ‘micro-founded’ in any serious way. Instead, representative agent models are aggregative macroeconomic models – like Keynesian structural econometric models – but models which impose arbitrary and implausible restrictions on the behaviour of individuals. Instead of being ‘micro-founded’, these models are ‘micro-roofed’ (the term originates with Matheus Grasselli).

It can be argued that old-fashioned Keynesian structural macro behavioural assumptions can in fact stake a stronger claim to compatibility with plausible microeconomic behaviour – precisely because arbitrary restrictions on individual behaviour are not imposed. Like the ant-colony, it can be shown that under sensible assumptions, robust aggregate Keynesian consumption and saving functions can be derived from a range of microeconomic behaviours – both optimising and non-optimising.

So what of the Lucas Critique?

Given that representative agent models are not micro-founded but are aggregate macroeconomic representations, Peter Skott argues that ‘the appropriate definition of the agent will itself typically depend on the policy regime. Thus, the representative-agent models are themselves subject to the Lucas critique. In short, the Lucas inspired research program has been a failure.’

This does not mean that microeconomic behaviour doesn’t matter. Nor is it an argument for a return to the simplistic Keynesian macro modelling of the 1970s. As Hoover puts it:

‘This is not to deny the Lucas critique. Rather it is to suggest that its reach may be sufficiently moderated in aggregate data that there are useful macroeconomic relationships to model that are relatively invariant’

Instead, it should be accepted that some aggregate macroeconomic behavioural relationships are likely to be robust, at least in some contexts and over some periods of time. At the same time, we now have much greater scope to investigate the relationships between micro and macro behaviours. In particular, computing power allows for the use of agent-based simulations to analyse the emergent properties of complex social systems.

This seems a more promising line of enquiry than the dead end of representative agent DSGE modelling.


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