### Microfoundations of Macro: One Direction

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If you read nothing but Rajiv Sethi's and Interfluidity's blogs, and developed all the consequences of what they said, you'd get a spectacular career in economic research out of it.

Fortunately, Mark Thoma reads them - as well as hundreds of others - and has a good commentary on a recent post of Rajiv's. I won't quote the whole thing, but here is the key message. Without the assumption of a representative agent - the idea that everyone in the economy behaves identically - current macroeconomic models can't work. But this assumption misses some of the key dynamics in the economy - the fact that some people borrow and others save; the fact that different people have different beliefs and preferences - which are fundamental to both why and how economic activity occurs. We need a way to introduce heterogeneous agents into macroeconomics.

On top of this, we can see that in the real world, people have mutually inconsistent expectations - and therefore at least one of them must be wrong. Thus, we have to abandon the idea of rational expectations with its assumption that people's expectations always adjust to match the most probable future outcome of the world.

Duncan Foley's essay, on which Rajiv's article is based, identifies the problem very clearly.

Instead my preference is for the other solution, which Foley describes as "to fiddle with general equilibrium theory in the hope of introducing money into it in a convincing and unified way". In fact, I think even that fiddling is at too high a level. We need to go to a deeper micro model, and here is my sense of what the model - and the mathematics - might look like.

The standard micro model is built from two basic concepts: preferences and expectations. As Foley says, the expectations question is assumed away either by inventing rational expectations, which are guaranteed consistent with reality, or by allowing complete markets in futures and options on all goods. Then we are left with preferences, and are forced to make lots of strange assumptions about preferences in order to explain the inefficiency we observe in the real economy. Some of those assumptions may be correct; others (strongly sticky prices) hint at the truth but are hard to justify in the way the models use them.

Instead, imagine the basic micromodel is recast in terms of two new concepts. The first is a more fundamental, slow-to-change kind of preference which we will call a

Agents and goods remain in the model as before. An agent ends up possessing a bundle of values and beliefs and an endowment of goods. So how does this help?

First, we have an explicit model of beliefs. This means that expectations can be addressed directly within the model, instead of making assumptions about their consistency or accuracy. A successful model is likely to examine the transmission of beliefs between agents. The belief concept is also general enough to capture a number of other phenomena - for instance attitudes to laws, saving or taxes - which in conventional models have to be tacked on as assumptions. We can discuss analytically the consistency of beliefs, because our model actually defines the referent of a belief and the statement that an agent makes about it.

As a side-effect of this, money is analysable in terms of the beliefs of agents about the future exchange value of certain goods (for example, dollar bills).

Second, we have the potential for a realistic model of behaviour. Behavioural experiments show that values and beliefs both influence behaviour, in some predictable (though not conventionally "rational") ways. Of course there are many different ways to model individual decision-making. But a simple model of choice arising from

Third, the model has the potential to be simple enough to be tractable. Agent-based models, even those which are relatively realistic with respect to actual human behaviour, are too full of ad hoc assumptions and tweaks to permit analytic solution. A model which is simpler at its base (containing only three key entities) is more likely to allow for solutions in mathematics rather than simulations. These kind of solutions provide much greater generality and predictive power than computational ones.

What the actual mathematics of this theory will look like is not yet obvious. But it seems likely that there will be a greater role for discrete mathematics and fewer of the assumptions of differentiability, convexity and the like which typically constrain preference functions in economic models. Discrete mathematics has its own challenges, and in some cases new mathematical techniques may have to be developed to handle these models.

Of course there is a lot of work to do before we will even know whether a model like this makes sense, let alone whether it can explain all the observations that the standard models don't. But my strong sense is that this is a useful direction in which to travel.

*Apologies to X-Factor fans: this article is about "one direction" towards a new model of macroeconomics, not about the band. But do feel free to stick around and join in the discussion.*]If you read nothing but Rajiv Sethi's and Interfluidity's blogs, and developed all the consequences of what they said, you'd get a spectacular career in economic research out of it.

Fortunately, Mark Thoma reads them - as well as hundreds of others - and has a good commentary on a recent post of Rajiv's. I won't quote the whole thing, but here is the key message. Without the assumption of a representative agent - the idea that everyone in the economy behaves identically - current macroeconomic models can't work. But this assumption misses some of the key dynamics in the economy - the fact that some people borrow and others save; the fact that different people have different beliefs and preferences - which are fundamental to both why and how economic activity occurs. We need a way to introduce heterogeneous agents into macroeconomics.

On top of this, we can see that in the real world, people have mutually inconsistent expectations - and therefore at least one of them must be wrong. Thus, we have to abandon the idea of rational expectations with its assumption that people's expectations always adjust to match the most probable future outcome of the world.

Duncan Foley's essay, on which Rajiv's article is based, identifies the problem very clearly.

Rajiv's summary is also excellent:In my view, the rational expectations assumption which Lucas and Sargent put forward to "close" the Keynesian model, was only a disguised form of the assumption of the existence of complete futures and contingencies markets.

Foley talks about two approaches to resolve this problem. The first of these, rewriting Keynesian macro to be compatible with general equilibrium, is an interesting engineering problem. And the model he describes sounds like an effective one - distinguishing between stocks and flows, and using the Hicksian concept of temporary equilibrium to explain the evolving dynamics of the system over time. But my intuition is that it will result not in a real solution - merely a better patchwork than the one we have now.To my mind the most appealing feature of the Foley-Sidrauski approach to microfoundations is that it allows for the possibility that individuals make mutually inconsistent plans based on heterogeneous beliefs about the future. This is what the rational expectations hypothesis rules out. Auxillary assumptions such as sticky prices must then be imposed in order to make the models more consonant with empirical observation.

Instead my preference is for the other solution, which Foley describes as "to fiddle with general equilibrium theory in the hope of introducing money into it in a convincing and unified way". In fact, I think even that fiddling is at too high a level. We need to go to a deeper micro model, and here is my sense of what the model - and the mathematics - might look like.

The standard micro model is built from two basic concepts: preferences and expectations. As Foley says, the expectations question is assumed away either by inventing rational expectations, which are guaranteed consistent with reality, or by allowing complete markets in futures and options on all goods. Then we are left with preferences, and are forced to make lots of strange assumptions about preferences in order to explain the inefficiency we observe in the real economy. Some of those assumptions may be correct; others (strongly sticky prices) hint at the truth but are hard to justify in the way the models use them.

Instead, imagine the basic micromodel is recast in terms of two new concepts. The first is a more fundamental, slow-to-change kind of preference which we will call a

*value*. The second is a*belief*about the world: either a belief that a good will satisfy one of your values, or a belief about the present or future exchange value of a good. Beliefs are tightly defined and do not include just any old assertion about the world: these beliefs are clear relations between agents, goods and values.Agents and goods remain in the model as before. An agent ends up possessing a bundle of values and beliefs and an endowment of goods. So how does this help?

First, we have an explicit model of beliefs. This means that expectations can be addressed directly within the model, instead of making assumptions about their consistency or accuracy. A successful model is likely to examine the transmission of beliefs between agents. The belief concept is also general enough to capture a number of other phenomena - for instance attitudes to laws, saving or taxes - which in conventional models have to be tacked on as assumptions. We can discuss analytically the consistency of beliefs, because our model actually defines the referent of a belief and the statement that an agent makes about it.

As a side-effect of this, money is analysable in terms of the beliefs of agents about the future exchange value of certain goods (for example, dollar bills).

Second, we have the potential for a realistic model of behaviour. Behavioural experiments show that values and beliefs both influence behaviour, in some predictable (though not conventionally "rational") ways. Of course there are many different ways to model individual decision-making. But a simple model of choice arising from

*values, mediated by beliefs, under constraints on attention, accuracy and myopia*provides a parsimonious and expressive description of reality. By implementing a realistic theory of decision-making into the model, we will have a closer match to the real world than current theories.Third, the model has the potential to be simple enough to be tractable. Agent-based models, even those which are relatively realistic with respect to actual human behaviour, are too full of ad hoc assumptions and tweaks to permit analytic solution. A model which is simpler at its base (containing only three key entities) is more likely to allow for solutions in mathematics rather than simulations. These kind of solutions provide much greater generality and predictive power than computational ones.

What the actual mathematics of this theory will look like is not yet obvious. But it seems likely that there will be a greater role for discrete mathematics and fewer of the assumptions of differentiability, convexity and the like which typically constrain preference functions in economic models. Discrete mathematics has its own challenges, and in some cases new mathematical techniques may have to be developed to handle these models.

Of course there is a lot of work to do before we will even know whether a model like this makes sense, let alone whether it can explain all the observations that the standard models don't. But my strong sense is that this is a useful direction in which to travel.

**Update**: having re-read some of the comments on Rajiv's post I feel it would be useful to add a couple of points:- The "model" I described above is perhaps more accurately a framework for a class of models. It is likely that, if this framework proves to be fruitful, various models would be developed to explore different assumptions about learning, herding of beliefs, the nature of privileged agents with high influence over the beliefs of others, the structure of institutions, and many other extensions.
- Foley's work includes some interesting research on mathematical approaches borrowed from physics - notably the idea of a
*statistical equilibrium*. This is a technique that I have long believed would be valuable in macroeconomics. But one of the main attractions of the approach is that it enables you to ignore microfoundations in favour of purely statistical descriptions of large-scale objects (an economy, or a box of gas). If we have a successfully microfounded theory, much of the rationale for a statistical thermodynamics-inspired method goes away. Still, it is worth exploring.

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