# Does Macroeconomics Need Microfoundations?

The representative-agent in macroeconomics analyzes the gas as if there is one big molecule subject to the law that governs real molecules.

Kevin D. Hoover (2007).
Are only acceptable macroeconomic models those with adequate microfoundations?

This question is one of the fundamental problems that led me to study macroeconomics. This post will try to sum up the fundamental ideas encapsulated in the chapter seventeen of the following book:

The Philosophy of Economics: An Anthology by Daniel Murray Hausman.

In this chapter, Kevin Douglas Hoover begins by recalling that the idea of microfoundations does not originate from the new classical macroeconomics, but the domination of this school of thought from the early 1970s to the crisis of 2008 has cemented it in the mind of virtually all economists.

The profession has sworn allegiance to the ideal of microfoundations. Are they right to do so?

## A Brief History

An early definition of macroeconomics is based on an analogy between the management of the household and the management of the state. Thus, the earliest empirical economics is macroeconomics. The transition to individualism has not been achieved until the marginalist revolution in the middle of the nineteen century with the works of Augustin Cournot and Léon Walras. It is worthwhile to recall that Smith, Ricardo, and other classical economists were mainly concerned by market phenomena and, thus, the individual was not at the center of their analysis.

Marshall discussed the role of the particular firm and the particular worker or consumer, but it was, as for its English and Scottish forefathers, to illuminate markets. The aim was to illustrate how the market functions in reality. Even proto-macroeconomics of earlier time has not completely vanished, economics appears to be mainly microeconomics by the 1930s.

The term macroeconomics has been used for the first time in 1931 by Ragnar Frisch. But, it was John Maynard Keynes that clarified the distinction between macroeconomics and microeconomics in the General Theory (1936). As Marshall, Keynes looks at the individual decision problem to illuminate market mechanisms. Although, he stresses the heterogeneity of individual responses as a central feature of aggregate behavior, he never explores the relationship between the individual and the aggregate in a really systematic way.

Microeconomics was so dominant in this epoch in economic thinking that microeconomic critiques of the General Theory have been published by Jacob Viner and Wassily Leontieff in 1936. After World War II, the main research program in macroeconomics was to give a “micro-economic flesh” to the Hicks’s aggregate general equilibrium, IS-LM model seen, at that time, as the formalization of the Keynes’s General Theory.

In the mid-1970s, Robert Emerson Lucas and Leonard Rapping began to model unemployment as an optimization problem. I was the first step that announced the domination of the representative agent model in new classical macroeconomics.

## Reductionism and Supervenience

After this brief history of microfoundations, we come to the central question of this blog: What are the intellectual roots of this urge to ground macroeconomics into the individual?

One possible explanation could be that a theory is explanatory when it achieves parsimony: if a complex phenomenon can be reduced to a smaller number of governing principles, then we consider this complex phenomenon as explained.

An analogy can be drawn with the law of ideal gas formulated in the eighteen century. The Boyle-Charles law states that:

pV=nRT

where p is pressure, V is volume, n the number of moles of the gas, R is the universal gas constant, and T, is the temperature. This law is an idealization of the results of empirical observations that holds at low-temperature and moderate pressure.

Physicists were not satisfied by the sui generis quality of the law and explored the molecules properties in the kinetic theory of gases. The kinetic theory of gases is also based on an idealization. With the hypothesis that every molecule is equally likely to move in every direction, it is possible to derive the gas law. Interestingly, there is a problem a denomination here, the temperature (gas level) corresponds to the mean energy of the molecules and the pressure (gas level) corresponds to the mean momentum transferred by contact with the containing vessel. The kinetic theory constitutes a reduction of the macrophysical gas laws to the microphysical Newtonian mechanics.

In this reduction, we can notice that the categories that apply to the gas law and the Newton’s law are very different. A single molecule has momentum and energy, but it does not have pressure or temperature. The phenomena of temperature and pressure can be thought as emergent properties of the molecules.

More recently, the philosophical body / mind problem has led to a debate about reductionism. The question is whether it is possible to completely determine the mental state by granular knowledge of the brain state or not. The difference between the two levels is larger than in the example on the gas law.

There is no one-to-one mapping between the macro phenomena of mind and the micro phenomena of brain states. This observation has led to the notion of supervenience. Mental states are said to supervene on brain states in the sense that any time one could exactly reproduce a certain brain state (any pattern of neuron firings), the mental state (seeing a face and find it beautiful, aesthetic appreciation appears to be an emergent property) could occur, even though that mental state may occur in other configurations of brain states.

Supervenience guarantees the autonomy of the macro level in the sense that it ensures that one can rationally use independent language and categories to describe the macro level and that it cannot be a simple deduction from the micro level. Yet, this concept underlines the connection between the micro and the macro level: no macro state exists unless an appropriate (but not a unique) micro state exists.

## Ontological Individualism Versus Empirical Individualism

What about reductionism in economics? It depends on the definition of economics. The classic definition can be summarized by one word: plutology, the science of wealth. This classical definition can be found inter alia in the writings of John Stuart Mill and Alfred Marshall. However, the modern definition, due to Lionel Robbins, describes economics as the science of choice. Economics is, in modern terminology, microeconomics. Once microeconomics is seen as the very nature of economics, any macroeconomic phenomenon needs a reductive explanation. But, it is one thing to want a reductive explanation and to have one. Of course, it is impractical to dispense with a measure of temperature and pressure and to keep track of the velocities of each molecule even in a small volume of gas. Similarly, it is impractical to track the individual decisions and constraints facing each individual in the economy, a problem that can be called the Cournot problem.

The quest for reduction has different motivations in economics relatively to biological sciences. The reduction of mental life to the neurological is appealing for scientists since it induces a reduction of teleology. After all, human life may have a goal (it could be directed to ends), but neurons, molecules and such do not have ends or intentional states. The reduction banishes teleology in biological sciences. In economics, it is the reverse. Macroeconomics relationships have no intentions, the Okun’s law, for example, relates the unemployment rate and the GDP growth rate has no intentional content. But, if macroeconomics is regarded as the product of human actions, this could be seen as a defect. The goal of reducing macroeconomics to microeconomics is to recapture human intentions. In economics, reduction reclaims teleology.

The success of microfoundations is not based on methodological individualism, but on ontological individualism. Methodological individualism consists in a strategy of basing all empirical explanations on the behavior of all individuals. Obviously, this strategy faces the Cournot problem. Ontological individualism is the conviction that the only real entities in the economy are individuals. The ontological individualist is reluctant to say that GDP or the general price level are real because they think that saying this implies that these entities are independent of the micro level. These entities are obviously not independent of the micro level. Of course, the first claim (the GDP or the price level are real) does not imply that the second claim (the GDP or the price level are independent of individuals).

The relationship between microeconomics and macroeconomics could be one of supervenience. Any identical reconfiguration of the agents and their situation results in the same configuration of the macroeconomic entities, but the mapping is not one-to-one. Furthermore, the supervenience of macroeconomics on microeconomics is not just a weak form of reductionism. This is because of intentionality at the microeconomic level. When I try to make plans about my future expenses, I use simple macroeconomic models (indeed crude time series models) because individuals, just like economists, face the Cournot problem. But this means that I cannot completely reduce macroeconomics to microeconomics. Microeconomics of the real world necessarily uses macroeconomic models and concepts as input. The macroeconomy supervenes on the microeconomy, but is not reducible to it. In the example of gas, the gas molecule does not rely on properties of the macro level to exist and to have its own properties.

## Aggregation

The physicist who had successfully reduced the ideal gas law to the kinetic theory of gases does not then abandon the language of pressure, temperature, and volume when working with gases or try to use momentum, mass, and velocity as the principal phenomenological categories for discussing the macroscopic behavior of gases. In economics, the same techniques, the same mathematics, the same language is used for the macro level and for the micro level. This is puzzling.

### Two simple examples

In the first example, we will see that the conditions for perfect aggregation are never met in real life. Consider an economy with two consumers and two goods. Let each individual (i) choose the goods (c1 and c2) by maximizing a Cobb-Douglas utility function:

u^{i}=log.c_{1}^{i}+\alpha^{i}.log.c_{2}^{i}

subject to a budget constraint

y^{i}-c_{1}^{i}-p.c_{2}^{i}=0.

where y is exogenously given income, and p is the price of good c2 in terms of the numeraire, good c1. With the first order conditions and the budget constraint with find the demand for good c1:

c_{1}^{i}=\frac{y^{i}}{1+\alpha^{i}}.

Let the superscripted, lower-case variables that apply to individual and upper-case letters variables apply to aggregates, the idea of the representative agent is simple. We have the aggregate demand for good 1:

C_{1}=\frac{Y}{1+\alpha}.

But, in our simple economy of only to agents, we can easily find the exact aggregate form:

\begin{aligned}
C_{1}=&\ c_{1}^{1}+c_{2}^{1}\\
C_{1}=&\ \frac{y^{1}}{1+\alpha^{1}}+\frac{y^{2}}{1+\alpha^{2}}\\
C_{1}=&\ \frac{Y+\alpha^{1}y^{1}+\alpha^{2}y^{2}}{(1+\alpha^{1})+(1+\alpha^{2})}.
\end{aligned}

since Y = y1 + y2. The previous equation has the same form of the aggregate demand for good 1 only if the tastes, α1 and α2, are the same. The conditions of perfect aggregation are almost certainly never fulfilled in real life.

Why should one accept the representative agent model and the facile analogy from the micro to the macro?

Rolf Ricardo Mantel, Hugo Freund Sonnenschein and Gérard Debreu have shown that, for example, if every underlying production function is Cobb-Douglas, there is no theoretical reason to conclude that the aggregate production function will be also Cobb-Douglas. Conversely, if the aggregate function for an economy is Cobb-Douglas, there is no reason to believe that this tells us anything at about the underlying production functions.

In the second example, we will see that aggregation alters the fundamental categories of economics. Whereas in physics, molecules have one sort of description and gases, even though they are an aggregation of molecules, quite another, in economics real GDP is much like any real good.

This illusion comes from the view that perfect aggregation represents a possible limiting case of actual aggregation. The possibility of prefect aggregation suggests the analogy of real GDP to an individual good. If for example, relative prices are constant (that is, Pj/Pk is constant for all j and k), then Σ Pj,t.Qj,t (where the t subscript indicates the base time, period t) can be normalized by choosing the units for the Qj,t so that each Pj,t = 1. Then, nominal GDP at time n can be written

\sum_{j=1}^{n}P_{j, t+n}Q_{j, t+n} = P_{t+n}\sum_{j=1}^{n}Q_{j, t+n}.

Under the assumed assumptions P is unique. Some conclude therefore that in this limited case, one can treat the summation on the right-hand side of the previous equation as a natural aggregate quantity analogous to an individual quantity. The condition of constant relative prices are never fulfilled; but even if they were, the summation is not analogous to an individual quantity. The general price level P still has the dimension period-n dollars/period-t dollars (i.e., base period). To sum heterogeneous goods, they must be converted to a common denominator, and in this case, the summation still has the dimensions of period-t dollars. This would be more perspicuous if the previous equation were written as

\sum_{j=1}^{n}P_{j, t+n}Q_{j, t+n} = P_{t+n}\sum_{j=1}^{n}1_{j, t+n}Q_{j, t+n}.

where the subscripted numeral 1 is a placeholder for the dimensional conversion.

The point here is that the aggregate remains analogous to the macro gas of ideal gas law and is not obviously some natural extension of a single molecule. The ideal gas laws fit well only within a limited range of temperatures and pressures. Outside that range, the individual molecules vary in manner that can be accounted for by using the kinetic theory. The equivalent is found in the efforts of Alan Kirman, Kathryn Dominguez and Ray Fair to account for distributional effects in macroeconomic relationships.

## Final thoughts

The representative-agent models are just as aggregative as the old-fashioned Keynesian aggregative models. They do not solve the problem of aggregation; rather they assume that it can be ignored. There is no agent who maximize a utility function that represent the whole economy subject to constraint that takes GDP as a limiting quantity. This is the simulacrum of microeconomics not the genuine article.

The question is : do representative-agent models provide a useful idealization? The question depends on its empirical successes (cf. the failure to predict the crisis of 2008). The advocate of the representative-agent model has no right to attack other macroeconomists for failing to provide microfoundations, for he fails to provide genuine microfoundations himself.

For Marshall, the representative firm was a typified firm at a point of its life cycle at which the extreme behaviors associated with very small and very young firms, on the one hand, or very large and very old, on the other hand could be set aside. In the terms of the physicist’s ideal gas example, Marshall wanted to describe the usual behavior of a molecule of gas under certain ideal conditions. The use of the representative-agent in macroeconomics is quite different. It attempts to describe how the gas behaves (its pressure and volume), not by considering seriously how the molecules behave in aggregate, but by analyzing the gas as if there is one big molecule subject to the law that governs real molecules.

What happens to the microeconomy matters to the macroeconomy but macroeconomics has its own descriptive categories and may have its own mode of analysis. It shall remain necessary to the serious economist to switch back and forth between microeconomics and a relatively autonomous macroeconomics depending upon the problem at hand.

Nota bene: This note is accessible on the ERMEES website in French.

## Reference

• Kevin Douglas Hoover. Does Macroeconomics Need Microfoundations? In The Philosophy of Economics: An Anthology, Cambridge: Cambridge University Press, pp. 315-333, 2007, 10.1017/CBO9780511819025

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