What’s Wrong With Modern Macro? Part 6 The Illusion of Microfoundations I: The Aggregate Production Function

Part 6 in a series of posts on modern macroeconomics. Part 4 noted the issues with using TFP as a measure of technology shocks. Part 5 criticized the use of the HP filter. Although concerning, neither of these problems is necessarily insoluble. With a better measure of technology and a better filtering method, the core of the RBC model would survive. This post begins to tear down that core, starting with the aggregate production function.

In the light of the negative conclusions derived from the Cambridge debates and from the aggregation literature, one cannot help asking why [neoclassical macroeconomists] continue using aggregate production functions
Felipe and Fisher (2003) – Aggregation in Production Functions: What Applied Economists Should Know

Remember that one of the primary reasons DSGE models were able to emerge as the dominant macroeconomic framework was their supposed derivation from “microfoundations.” They aimed to explain aggregate phenomena, but stressed that these aggregates could only come from optimizing behavior at a micro level. The spirit of this idea seems like a step in the right direction.

In its most common implementations, however, “microfoundations” almost always fails to capture this spirit. The problem with trying to generate aggregate implications from individual decision-making is that keeping track of decisions from a diverse group of agents quickly becomes computationally and mathematically unmanageable. This reality led macroeconomists to make assumptions that allowed for easy aggregation. In particular, the millions of decision-makers throughout the economy were collapsed into a single representative agent that owns a single representative firm. Here I want to focus on the firm side. A future post will deal with the problems of the representative agent.

An Aggregate Production Function

In the real world, producing any good is complicated. It not only requires an entrepreneur to have an idea for the production of a new good, but also the ability to implement that idea. It requires a proper assessment of the resources needed, the organization of a firm, hiring good workers and managers, obtaining investors and capital, properly estimating consumer demand and competition from other firms and countless other factors.

In macro models, production is simple. In many models, a single firm produces a single good, using labor and capital as its only two inputs. Of course we cannot expect the model to match many of the features of reality. It is supposed to simplify. That’s what makes it a model. But we also need to remember Einstein’s famous insight that everything should be made as simple as possible, but no simpler. Unfortunately I think we’ve gone way past that point.

Can We Really Measure Capital?

In the broadest possible categorization, productive inputs are usually placed into three categories: land, labor, and capital. Although both land and labor vary widely in quality making it difficult to aggregate, at least there are clear choices for their units. Adding up all of the useable land area and all of the hours worked at least gives us a crude measure of the quantity of land and labor inputs.

But what can we use for capital? Capital goods are far more diverse than land or labor, varying in size, mobility, durability, and thousands of other factors. There is no obvious measure that can combine buildings, machines, desks, computers, and millions of other specialized pieces of capital equipment. The easiest choice is to use the value of the goods, but what is their value? The price at which they were bought? An estimate of the value of the production they will bring about in the future? And what units will this value be? Dollars? Labor hours needed to produce the good?

None of these seem like good options. As soon as we go to value, we are talking about units that depend on the structure of the economy itself. An hour of labor is an hour of labor no matter what the economy looks like. With capital it gets more complicated. The same computer has a completely different value in 1916 than it does in 2016 no matter which concept of value is employed. That value is probably related to its productive capacity, but the relationship is far from clear. If the value of a firm’s capital stock has increased, can it actually produce more than before?

This question was addressed in the 1950s and 60s by Joan Robinson. Here’s how she summed up the problem:

Moreover, the production function has been a powerful instrument of miseducation. The student of economic theory is taught to write O = f (L, C) where L is a quantity of labour, C a quantity of capital and O a rate of output of commodities.’ He is instructed to assume all workers alike, and to measure L in man-hours of labour; he is told something about the index-number problem involved in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next.
Joan Robinson (1953) – The Production Function and the Theory of Capital

60 years later and we’ve changed the O to a Y and the C to a K, but little else has changed. People have thought hard about how to measure capital and try to deal with the issues (Here is a 250 page document on the OECD’s methods for example), but the issue remains. We still take a diverse set of capital goods and try to fit them all under a common label. The so called “Cambridge Capital Controversy” was never truly resolved and neoclassical economists simply pushed on undeterred. For a good summary of the debate and its (lack of) resolution see this relatively non-technical paper.

What Assumptions Allow for Aggregation?

Even if we assume that there is some unit that would allow capital to be aggregated, we still face problems when trying to use an aggregate production function. One of the leading researchers working to find the set of conditions that allows for aggregation in production has been Franklin Fisher. Giving a more rigorous treatment to the capital aggregation issue, Fisher shows that capital can only be aggregated if all firms share the same constant returns to scale, capital augmenting technical change production function (except for a capital efficiency coefficient). If you’re not an economist, that condition doesn’t make much sense, but know that it is incredibly restrictive.

The problem doesn’t get much better when we move away from capital and try to aggregate labor and output. Fisher shows that aggregation in these concepts is only possible when there is no specialization (everybody can do everything) and all firms have the ability to produce every good (the amount of each good can change). Other authors have derived different conditions for aggregation, but none of these appear to be any less restrictive.

Do any of these restrictions matter? Even if aggregation is not strictly possible, as long as the model was close enough there wouldn’t be a real criticism. Fisher (with co-author Jesus Felipe) surveys the many arguments against aggregate production functions and addresses many of these kinds of counterarguments, ultimately concluding

The aggregation problem and its consequences, and the impossibility of testing empirically the aggregate production function…are substantially more serious than a mere anomaly. Macroeconomists should pause before continuing to do applied work with no sound foundation and dedicate some time to studying other approaches to value, distribution, employment, growth, technical progress etc., in order to understand which questions can legitimately be posed to the empirical aggregate data.
Felipe and Fisher (2003) – Aggregation in Production Functions: What Applied Economists Should Know

As far as I know, these concerns have not been addressed in a serious way. The aggregate production function continues to be a cornerstone of macroeconomic models. If it is seriously flawed, almost all of the work done in the last forty years becomes suspect.

But don’t worry, the worst is still to come.