What’s Wrong With Modern Macro? Part 8 Rational Expectations Aren't so Rational

Part 8 in a series of posts on modern macroeconomics. This post continues the criticism of the underlying assumptions of most macroeconomic models. It focuses on the assumption of rational expectations, which was described briefly in Part 2. This post will summarize many of the points I made in a longer survey paper I wrote about expectations in macroeconomics that can be found here.


What economists imagine to be rational forecasting would be considered obviously irrational by anyone in the real world who is minimally rational
Roman Frydman (2013) – Rethinking Economics p. 148

Why Rational Expectations?

Although expectations play a large role in many explanations of business cycles, inflation, and other macroeconomic data, modeling expectations has always been a challenge. Early models of expectations relied on backward looking adaptive expectations. In other words, people form their expectations by looking at past trends and extrapolating them forward. Such a process might seem plausible, but there is a substantial problem with using a purely adaptive formulation of expectations in an economic model.

For example, consider a firm that needs to choose how much of a good to produce before it learns the price. If it expects the price to be high, it will want to produce a lot, and vice versa. If we assume firms expect today’s price to be the same as tomorrow’s, they will consistently be wrong. When the price is low, they expect a low price and produce a small amount. But the low supply leads to a high price in equilibrium. A smart firm would see their errors and revise their expectations in order to profit. As Muth argued in his original defense of rational expectations, “if the prediction of the theory were substantially better than the expectations of the firms, then there would be opportunities for ‘the insider’ to profit from the knowledge.” In equilibrium, these kinds of profit opportunities would be eliminated by intelligent entrepreneurs.

The solution proposed by Muth and popularized in macro by Lucas, was to simply assume that agents had the same model of the economy as the economist. Under rational expectations, an agent does not need to look at past data to make a forecast. Instead, their expectations are model based and forward looking. If an economist can detect consistent errors in an agent’s forecasting, rational expectations assumes that the agents themselves can also detect these errors and correct them.

What Does the Data Tell Us?

The intuitive defense of rational expectations is appealing and certainly rational expectations marked an improvement over previous methods. But if previous models of expectations gave agents too little cognitive ability, rational expectations models give them far too much. Rational expectations leaves little room for disagreement between agents. Each one needs to instantly jump to the “correct” model of the economy (which happens to correspond to the one created by the economist) and assume every other agent has made the exact same jump. As Thomas Sargent put it, rational expectations leads to a “communism of models. All agents inside the model, the econometrician, and God share the same model.”

The problem, as Mankiw et al note, is that “the data easily reject this assumption. Anyone who has looked at survey data on expectations, either those of the general public or those of professional forecasters, can attest to the fact that disagreement is substantial.” Branch (2004) and Carroll (2003) offer further evidence that heterogeneous expectations play an important role in forecasting. Another possible explanation for disagreement in forecasts is that agents have access to different information. Even if each agent knew the correct model of the economy, having access to private information could lead to a different predictions. Mordecai Kurz has argued forcefully that disagreement does not stem from private information, but rather different interpretations of the same information.

Experimental evidence also points to heterogeneous expectations. In a series of “learning to forecast” experiments, Cars Hommes and coauthors have shown that when agents are asked to forecast the price of an asset generated by an unknown model, they appear to resort to simple heuristics that often differ substantially from the rational expectations forecast. Surveying the empirical evidence surrounding the assumptions of macroeconomics as a whole, John Duffy concludes “the evidence to date suggests that human subject behavior is often at odds with the standard micro-assumptions of macroeconomic models.”

“As if” Isn’t Enough to Save Rational Expectations

In response to concerns about the assumptions of economics, Milton Friedman offered a powerful defense. He agreed that it was ridiculous to assume that agents make complex calculations when making economic decisions, but claimed that that is not at all an argument against assuming that they made decisions as if they knew this information. Famously, he gave the analogy of an expert billiard player. Nobody would ever believe that the player planned all of his shots using mathematical equations to determine the exact placement, and yet a physicist who assumed he did make those calculations could provide an excellent model of his behavior.

The same logic applies in economics. Agents who make forecasts using incorrect models will be driven out as they are outperformed by those with better models until only the rational expectations forecast remains. Except this argument only works if rational expectations is actually the best forecast. As soon as we admit that people use various models to forecast, there is no guarantee it will be. Even if some agents know the correct model, they cannot predict the path of economic variables unless they are sure that others are also using that model. Using rational expectations might be the best strategy when others are also using it, but if others are using incorrect models, it may be optimal for me to use an incorrect model as well. In game theory terms, rational expectations is a Nash Equilibrium, but not a dominant strategy (Guesnerie 2010).

Still, Friedman’s argument implies that we shouldn’t worry too much about the assumptions underlying our model as long as it provides predictions that help us understand the world. Rational expectations models also fail in this regard. Even after including many ad hoc fixes to standard models like wage and price stickiness, investment adjustment costs, inflation indexing, and additional shocks, DSGE models with rational expectations still provide weak forecasting ability, losing out to simpler reduced form vector autoregressions (more on this in future posts).

Despite these criticisms, we still need an answer to the Lucas Critique. We don’t want agents to ignore information that could help them to improve their forecasts. Rational expectations ensures they do not, but it is far too strong. Weaker assumptions on how agents use the information to learn and improve their forecasting model over time retain many of the desirable properties of rational expectations while dropping some of its less realistic ones. I will return to these formulations in a future post (but read the paper linked in the intro – and here again – if you’re interested).

 

What Does it Mean to Be Rational?

One of the most basic assumptions that underlies economic analysis is that people are rational. Given a set of possible choices, an individual in an economic model always chooses the one they think will give them the largest net benefit. This assumption has come under attack by many within the profession as well as by outsiders.

Some of these criticisms are easy to reject. For example, it is common for non-economists to make the jump from rationality to selfishness and denounce economics for assuming all humans only care about themselves. Similar criticisms point to economics for being too materialistic when real people actually value intangible goods as well. Neither of these arguments hits the mark. When an economist talks of rationality, they mean it in the broadest possible way. If donating to charity or giving gifts or going to poor countries to build houses are important for you, economics does not say you are wrong to choose those things. Morality or duty can have just as powerful an impact on your choices as material desires. Economics makes no distinction between these categories. You choose what you prefer. The reason you prefer it is irrelevant for an economist.

More thoughtful criticisms argue that even after defining preferences correctly, people sometimes make decisions that actively work against their own interests. The study of these kinds of issues with decision-making  has come to be called “behavioral economics.” One of the most prominent behavioral economists, Richard Thaler, likes to use the example of the Herzfeld Caribbean Basin Fund. Despite its NASDAQ ticker CUBA, the fund has little to do with the country Cuba. Nevertheless, when Obama announced an easing of Cuban trade restrictions in 2014, the stock price increased 70%. A more recent example occurred when investors swarmed to Nintendo stock after the release of Pokemon Go before realizing that Nintendo doesn’t even make the game.

But do these examples show that people are irrational? I don’t think so. There needs to be a distinction between being rational and being right. Making mistakes doesn’t mean that your original goal wasn’t to maximize your own utility, it just means that the path you chose was not the best way to accomplish that goal. To quote Ludwig von Mises, “human action is necessarily always rational” because “the ultimate end of action is always the satisfaction of some desires” (Human Action, p. 18). He gives the example of doctors 100 years ago trying to treat cancer. Although the methods used at that time may appear irrational by modern standards, those methods were what the doctors considered to be the best given the knowledge available at the time. Mises even applies the same logic to emotional actions. Rather than call emotionally charged actions irrational, Mises instead chooses to argue that “emotions disarrange valuations”  (p. 16). Again, an economist cannot differentiate between the reasons an individual chooses to act. Anger is as justifiable as deliberate calculation.

That is not to say that the behavioralists don’t have a point. They just chose the wrong word. People are not irrational. They just happen to be wrong quite often. The confusion is understandable, however, because rationality itself is not well defined. Under my definition, rationality only requires that agents make the best decision possible given their current knowledge. Often economic models go a step further and make specific (and sometimes very strong) assumptions about what that knowledge should include. Even in models with uncertainty, people are usually expected to know the probabilities of events occurring. In reality, people often face not only unknown events, but unknowable events that could never be predicted beforehand. In such a world, there is no reason to expect that even the most intelligent rational agent could make a decision that appears rational in a framework with complete knowledge.

Roman Frydman describes this point nicely

After uncovering massive evidence that contemporary economics’ standard of rationality fails to capture adequately how individuals actually make decisions, the only sensible conclusion to draw was that this standard was utterly wrong. Instead, behavioral economists concluded that individuals are less than fully rational or are irrational
Rethinking Expectations: The Way Forward For Macroeconomics, p. 148-149

Don’t throw out rationality. Throw out the strong knowledge assumptions. Perhaps the worst of these is the assumption of “rational expectations” in macroeconomics. I will have a post soon arguing that they are not really rational at all.

What’s Wrong With Modern Macro? Part 7 The Illusion of Microfoundations II: The Representative Agent

Part 7 in a series of posts on modern macroeconomics. Part 6 began a criticism of the form of “microfoundations” used in DSGE models. This post continues that critique by emphasizing the flaws in using a “representative agent.” This issue has been heavily scrutinized in the past and so this post primarily offers a synthesis of material found in articles from Alan Kirman and Kevin Hoover (1 and 2). 


One of the key selling points of DSGE models is that they are supposedly derived from microfoundations. Since only individuals can act, all aggregates must necessarily be the result of the interactions of these individuals. Understanding the mechanisms that lie behind the aggregates therefore seems essential to understanding the movements in the aggregates themselves. Lucas’s attack on Keynesian economics was motivated by similar logic. We can observe relationships between aggregate variables, but if we don’t understand the individual behavior that drives these relationships, how do we know if they will hold up when the environment changes?

I agree that ignoring individual behavior is an enormous problem for macroeconomics. But DSGE models do little to solve this problem.

Ideally, microfoundations would mean modeling behavior at an individual level. Each individual would then make choices based on the current economic conditions and these choices would aggregate to macroeconomic variables. Unfortunately, putting enough agents to make this exercise interesting is challenging to do in a mathematical model. As a result, “microfoundations” in a DSGE model usually means assuming that the decisions of all individuals can be summarized by the decisions of a single “representative agent.” Coordination between agents, differences in preferences or beliefs, and even the act of trading that is the hallmark of a market economy are eliminated from the discussion entirely. Although we have some vague notion that these activities are going on in the background, the workings of the model are assumed to be represented by the actions of this single agent.

So our microfoundations actually end up looking a lot closer to an analysis of aggregates than an analysis of true individual behavior. As Kevin Hoover writes, they represent “only a simulacrum of microeconomics, since no agent in the economy really faces the decision problem they represent. Seen that way, representative-agent models are macroeconomic, not microfoundational, models, although macroeconomic models that are formulated subject to an arbitrary set of criteria.” Hoover pushes back against the defense that representative agent models are merely a step towards truly microfounded models, arguing that not only would full microfoundations be infeasible but also that many economists do take the representative agent seriously on its own terms, using it both for quantitative predictions and policy advice.

But is the use of the representative agent really a problem? Even if it fails on its promise to deliver true “microfoundations,” isn’t it still an improvement over neglecting optimizing behavior entirely? Possibly, but using a representative agent offers only a superficial manifestation of individual decision-making, opening the door for misinterpretation. Using a representative agent assumes that the decisions of one agent at a macro level would be made in the same way as the decisions of millions of agents at a micro level. The theoretical basis for this assumption is weak at best.

In a survey of the representative agent approach, Alan Kirman describes many of the problems that arise when many agents are aggregated into a single representative. First, he presents the theoretical results from Sonnenschein (1972), Debreu (1974), and Mantel (1976), which show that even with strong assumptions on the behavior of individual preferences, the equilibrium that results by adding up individual behavior is not necessarily stable or unique.

The problem runs even deeper. Even if we assume aggregation results in a nice stable equilibrium, worrying results begin to arise as soon as we start to do anything with that equilibrium. One of the primary reasons for developing a model in the first place is to see how it reacts to policy changes or other shocks. Using a representative agent to conduct such an analysis implicitly assumes that the new aggregate equilibrium will still correspond to decisions of individuals. Nothing guarantees that it will. Kirman gives a simple example of a two-person economy where the representative agent’s choice makes each individual worse off. The Lucas Critique then applies here just as strongly as it does for old Keynesian models. Despite the veneer of optimization and rational choice, a representative agent model still abstracts from individual behavior in potentially harmful ways.

Of course, macroeconomists have not entirely ignored these criticisms and models with heterogeneous agents have become increasing popular in recent work. However, keeping track of more than one agents makes it nearly impossible to achieve useful mathematical results. The general process for using heterogeneous agents in a DSGE model then is to first prove that these agents can be aggregated and summarized by a set of aggregate equations. Although beginning from heterogeneity and deriving aggregation explicitly helps to ensure that the problems outlined above do not arise, it still imposes severe restrictions on the types of heterogeneity allowed. It would be an extraordinary coincidence if the restrictions that enable mathematical tractability also happen to be the ones relevant for understanding reality.

We are left with two choices. Drop microfoundations or drop DSGE. The current DSGE framework only offers an illusion of microfoundations. It introduces optimizing behavior at an aggregate level, but has difficulty capturing many of the actions essential to the workings of the market economy at a micro level. It is not a first step to discovering a way to model true microfoundations because it is not a tool well-suited to analyzing the behavior of more than one person at a time. Future posts will explore some models that are.

 

 

 

Competition and Market Power Why a "Well-Regulated" Market is an Impossible Ideal

Standard accounts of basic economics usually begin by outlining the features of “perfect competition.” For example, Mankiw’s popular Principles of Economics defines a perfectly competitive market as one that satisfies the following properties

  1. The goods offered for sale are all exactly the same
  2. the buyers and sellers are so numerous that no single buyer or seller has any influence over the market price.

    The implication of these two properties is that all firms in a perfectly competitive market are “price takers.” If any firm tried to set a price higher than the current market price, their sales would immediately drop to nothing as consumers shift to other firms offering the exact same good for a cheaper price. As long as firms can enter and exit a market freely, perfect competition also implies zero profits. Any market experiencing positive profits would quickly see entry as firms try to take advantage of the new opportunity. The entry of new firms increases the supply of the good, which reduces the price and therefore pushes profits down.

After defining the perfectly competitive market, the standard account begins to extol its virtues. In particular, a formal result called the First Welfare Theorem shows that in a perfectly competitive equilibrium, the allocation of goods is Pareto efficient (which just means that no other allocation could make somebody better off without making somebody else worse off). So markets are great. Without any planner or government oversight of any kind, they arrive at an efficient outcome on their own.

But soon after developing the idea, we begin to poke holes in perfect competition. How many markets can really be said to have a completely homogeneous good? How many markets have completely free entry and no room for firms to set their own price? It’s pretty hard to answer anything other than zero. Other issues also arise when we begin to think about the way markets work in reality. The presence of externalities (costs to society that are not entirely paid by the individuals making a decision – pollution is the classic example), causes the first welfare theorem to break down. And so we open the door for government intervention. If the perfectly competitive market is so good, and reality differs from this ideal, doesn’t it make sense for governments to correct these market failures, to break up monopolies, to deal with externalities?

Maybe, but it’s not that simple. The perfect competition model, despite being a cool mathematical tool that is sometimes useful in deriving economic results, is also an unrealistic benchmark. As Hayek points out in his essay, “The Meaning of Competition,” the concept of “perfect competition” necessarily requires that “not only will each producer by his experience learn the same facts as every other but also he will thus come to know what his fellows know and in consequence the elasticity of the demand for his own product.” When held to this standard, nobody can deny that markets constantly fail.

The power of the free market, however, has little to do with its ability to achieve the conditions of perfect competition. In fact, that model leaves out many of the factors that would be considered essential to a competitive market. Harold Demsetz points out this problem in an analysis of antitrust legislation.

[The perfect competition model] is not very useful in a debate about the efficacy of antitrust precedent. It ignores technological competition by taking technology as given. It neglects competition by size of firm by assuming that the atomistically sized firm is the efficiently sized firm. It offers no productive role for reputational competition because it assumes full knowledge of prices and goods, and it ignores competition to change demands by taking tastes as given and fully known. Its informational and homogeneity assumptions leave no room for firms to compete by being different from other firms. Within its narrow confines, the model examines the consequences of only one type of competition, price competition between known, identical goods produced with full awareness of all technologies. This is an important conceptual form of competition, and when focusing on it alone we may speak sensibly about maximizing the intensity of competition. Yet, this narrowness makes the model a poor source of standards for antitrust policy.
Demsetz (1992) – How Many Cheers For Antitrust’s 100 Years?

Although the types of competition outlined by Demsetz are a sign of market power by firms, they are not necessarily a sign that the market has failed or that governments can improve the situation. Let me tell a simple story to illustrate this point. Assume a firm develops a new technology that they are able to prevent other firms from immediately replicating (either because of a patent, secrecy, a high fixed cost of entry, etc.). This firm is now a monopoly producer of that product and can therefore set a price much higher than its cost and make a large profit. The government sees this development and orders the firm to release its plans so that others can replicate the technology and produce their own version. Prices fall as new firms enter and profits go to zero. Consumers are better off since prices are lower and they have a larger choice of products. (A similar story could also be told if the government simply mandated a lower price by monopoly firms).

But the story isn’t over. If I’m another entrepreneur (or even an existing firm) watching this sequence of events, I’m a bit worried. That new idea I was thinking about is going to cost a lot. If I had the possibility to make a large profit, maybe I would be willing to take the risk and go for it anyway. If, on the other hand, I knew for sure that even when I achieve success the government immediately reduces my profits to zero, am I still going to undertake that project? Not a chance. The potential for future profits is an incredibly important incentive for innovation.

Here’s another example from the real world that illustrates the opposite case. In the late 1990s, Microsoft tried to bundle Internet Explorer with their Windows operating system (essentially giving away Explorer for free). This move made it difficult for independent internet browsers to compete (Netscape was the market leader at the time). An antitrust lawsuit was brought against Microsoft and they were initially ordered to break up (which never actually occurred in the end as far as I know, but that doesn’t matter for the story). In the EU, they were required to provide a browser choice page when installing Windows.

In each of the two examples above, there is a clear tradeoff. In the first, consumers are better off in the short run (lower prices), but potentially worse off in the long run (less innovation). The second case is exactly the opposite. Consumers are worse off in the short run (they don’t get a browser for free) but potentially better off in the long run (more browser competition). Can we say for sure whether regulation helps or hurts in either case? Can we even say whether the regulation would push the market to be more competitive or less? I don’t see how (but which browser you are using right now despite the relatively lenient restrictions on Microsoft might give some indication).

I’m not saying regulation is never a good idea in theory. But in practice, it turns out to be really hard. Even in the cases above where it is obvious that a firm is trying to take advantage of monopoly power, it remains unclear whether a move closer to “perfect competition” will result in an increase in actual competition. You can of course pick apart the stories above and come up with some regulatory scheme that balances present and future costs and benefits. But doing so in general would require governments to have even more information than the already ridiculous knowledge assumptions implicit in the perfect competition model. It’s easy to point out imperfections in markets. It’s much harder to figure out what to do about them.

Notice that I haven’t necessarily made an argument against regulation. The takeaway from this post should not be that markets always work or that regulation always fails (I’ll leave that for future posts!). My point is simply that pointing out a flaw in the free market does not automatically imply an opportunity for a regulatory solution. The question is much more complicated than that.

But having said that let me leave you with one final thought. Markets are incredibly dynamic. Whenever the market “fails,” all it takes is one clever entrepreneur to come up with a better method and correct the failure. When government fails? Well, maybe we can come back to that in ten years when they get around to discussing it.

Kevin Malone Economics

Don't Be Like Kevin (Image Source: Wikimedia Commons)
Don’t Be Like Kevin (Image Source: Wikimedia Commons)

In one my favorite episodes of the TV show The Office (A Benihana Christmas), dim-witted accountant Kevin Malone faces a choice between two competing office Christmas parties: the traditional Christmas party thrown by Angela, or Pam and Karen’s exciting new party. After weighing various factors (double fudge brownies…Angela), Kevin decides “I think I’ll go to Angela’s party, because that’s the party I know.” I can’t help but see parallels between Kevin’s reasoning and some of the recent discussions about the role of DSGE models in macroeconomics. It’s understandable. Many economists have poured years of their lives into this research agenda. Change is hard. But sticking with something simply because that’s the way it has always been done is not, in my opinion, a good way to approach research.

I was driven to write this post after reading a recent post by Roger Farmer, which responds to this article by Steve Keen, which is itself responding to Olivier Blanchard’s recent comments on the state of macroeconomics. Lost yet? Luckily you don’t really need to understand the  entire flow of the argument to get my point. Basically, Keen argues that the assumption of economic models that the system is always in equilibrium is poorly supported. He points to physics for comparison, where Edward Lorenz showed that the dynamics underlying weather systems were not random, but chaotic – fully deterministic, but still impossible to predict. Although his model had equilibria, they were inherently unstable, so the system continuously fluctuated between them in an unpredictable fashion.

Keen’s point is that economics could easily be a chaotic system as well. Is there any doubt that the interactions between millions of people that make up the economic system are at least as complex as the weather? Is it possible that, like the weather, the economy is never actually in equilibrium, but rather groping towards it (or, in the case of multiple equilibria, towards one of them)? Isn’t there at least some value in looking for alternatives to the DSGE paradigm?

Roger begins his reply to Keen by claiming, “we tried that 35 years ago and rejected it. Here’s why.” I was curious to read about why it was rejected, but he goes on to say that the results of these attempts to examine whether there is complexity and chaos in economics were that “we have no way of knowing given current data limitations.” Echoing this point, a survey of some of these tests by Barnett and Serletis concludes

We do not have the slightest idea of whether or not asset prices exhibit chaotic nonlinear dynamics produced from the nonlinear structure of the economy…While there have been many published tests for chaotic nonlinear dynamics, little agreement exists among economists about the correct conclusions.
Barnett and Serletis (2000) – Martingales, nonlinearity, and chaos

That doesn’t sound like rejection to me. We have two competing theories without a good way of determining which is more correct. So why should we rigidly stick to one? Best I can tell, the only answer is Kevin Malone Economics™. DSGE models are the way it has always been done, so unless there is some spectacular new evidence that an alternative does better, let’s just stay with what we know. I don’t buy it. The more sensible way forward in my opinion is to cultivate both approaches, to build up models using DSGE as well as alternatives until we have some way of choosing which is better. Some economists have taken this path and begun to explore alternatives, but they remain on the fringe and are largely ignored (I will have a post on some of these soon, but here is a preview). I think this is a huge mistake.

Since Roger is one of my favorite economists in large part because he is not afraid to challenge the orthodoxy, I was a bit surprised to read this argument from him. His entire career has been devoted to models with multiple equilibria and sunspot shocks. As far as I know (and I don’t know much so I could very well be wrong), these features are just as difficult to confirm empirically as is the existence of chaos. By spending an entire career developing his model, he has gotten it to a place where it can shed light on real issues (see his excellent new book, Prosperity for All), but its acceptance within the profession is still low. In his analysis of alternatives to standard DSGE models, Michael De Vroey writes:

Multiple equilibria is a great idea that many would like to adopt were it not for the daunting character of its implementation. Farmer’s work attests to this. Nonetheless, it is hard to resist the judgement that, for all its panache, it is based on a few, hard to swallow, coups de force…I regard Farmer’s work as the fruit of a solo exercise attesting to both the inventiveness of its performer and the plasticity of the neoclassical toolbox. Yet in the Preface of his book [How the Economy Works], he expressed a bigger ambition, “to overturn a way of thinking that has been established among macroeconomists for twenty years.” To this end, he will need to gather a following of economists working on enriching his model
De Vroey (2016) – A History of Macroeconomics from Keynes to Lucas and Beyond

In other words, De Vroey’s assessment of Roger’s work is quite similar to Roger’s own assessment of non-DSGE models: it’s not a bad idea and there’s possibly some potential there, but it’s not quite there yet. Just as I doubt Roger is ready to tear up his work and jump back in with traditional models (and he shouldn’t), neither should those looking for alternatives to DSGE give up simply because the attempts to this point haven’t found anything revolutionary.

I’m not saying all economists should abandon DSGE models. Maybe they are a simple and yet still adequate way of looking at the world. But maybe they’re not. Maybe there are alternatives that provide more insight into the way a complex economy works. Attempts to find these alternatives should not be met with skepticism. They shouldn’t have to drastically outperform current models in order to even be considered (especially considering current models aren’t doing so hot anyway). Of course there is no way any alternative model will be able to stand up to a research program that has gone through 40 years of revision and improvement (although it’s not clear how much improvement there has really been). The only way to find out if there are alternatives worth pursuing is to welcome and encourage researchers looking to expand the techniques of macroeconomics beyond equilibrium and beyond DSGE. If even a fraction of the brainpower currently being applied to DSGE models were shifted to looking for different methods, I am confident that a new framework would flourish and possibly come to stand beside or even replace DSGE models as the primary tool of macroeconomics.

At the end of the episode mentioned above, Kevin (along with everybody else in the office) ends up going to Pam and Karen’s party, which turns out to be way better than Angela’s. I can only hope macroeconomics continues to mirror that plot.

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.