## 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

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.

## What’s Wrong With Modern Macro? Part 5 Filtering Away All Our Problems

Part 5 in a series of posts on modern macroeconomics. In this post, I will describe some of the issues with the Hodrick-Prescott (HP) filter, a tool used by many macro models to isolate fluctuations at business cycle frequencies.

A plot of real GDP in the United States since 1947 looks like this

Although some recessions are easily visible (like 2009), the business cycle is not especially easy to see. The growing trend of economic growth over time dominates more frequent business cycle fluctuations. While the trend is important, if we want to isolate more frequent business cycle fluctuations, we need some way to remove the trend. The HP Filter is one method of doing that. Unlike the trends in my last post, which simply fit a line to the data, the HP filter allows the trend to change over time. The exact equation is a bit complex, but here’s the link to the Wikipedia page if you’d like to see it. Plotting the HP trend against actual GDP looks like this

By removing this trend, we can isolate deviations from trend. Usually we also want to take a log of the data in order to be able to interpret deviations in percentages. Doing that, we end up with

The last picture is what the RBC model (and most other DSGE models) try to explain. By eliminating the trend, the HP filter focuses exclusively on short term fluctuations. This shift in focus may be an interesting exercise, but it eliminates much of what make business cycles important and interesting. Look at the HP trend in recent years. Although we do see a sharp drop marking the 08-09 recession, the trend quickly adjusts so that we don’t see the slow recovery at all in the HP filtered data. The Great Recession is actually one of the smaller movements by this measure. But what causes the change in the trend? The model has no answer to this question. The RBC model and other DSGE models that explain HP filtered data cannot hope to explain long periods of slow growth because they begin by filtering them away.

Let’s go back one more time to these graphs

Notice that these graphs show the fit of the model to HP filtered data. Here’s what they look like when the filter is removed

Not so good. And it gets worse. Remember we have already seen in the last post that TFP itself was highly correlated with each of these variables. If we remove the TFP trend, the picture changes to

Yeah. So much for that great fit. Roger Farmer describes the deceit of the RBC model brilliantly in a blog post called Real Business Cycle and the High School Olympics. He argues that when early RBC modelers noticed a conflict between their model and the data, they didn’t change the model. They changed the data. They couldn’t clear the olympic bar of explaining business cycles, so they lowered the bar, instead explaining only the “wiggles.” But, as Farmer contends, the important question is in explaining those trends that the HP filter assumes away.

Maybe the most convincing reason that something is wrong with this method of measuring business cycles is that measurements of the cost of business cycles using this metric are tiny. Based on a calculation by Lucas, Ayse Imrohoroglu explains that under the assumptions of the model, an individual would need to be given $28.96 per year to be sufficiently compensated for the risk of business cycles. In other words, completely eliminating recessions is worth about as much as a couple decent meals. Obviously to anyone who has lived in a real economy this number is completely ridiculous, but when business cycles are relegated to the small deviations from a moving trend, there isn’t much to be gained from eliminating the wiggles. There are more technical reasons to be wary of the HP filter that I don’t want to get into here. A recent paper called “Why You Should Never Use the Hodrick-Prescott Filter” by James Hamilton, a prominent econometrician, goes into many of the problems with the HP filter in detail. He opens by saying “The HP filter produces series with spurious dynamic relations that have no basis in the underlying data-generating process.” If you don’t trust me, at least trust him. TFP doesn’t measure productivity. HP filtered data doesn’t capture business cycles. So the RBC model is 0/2. It doesn’t get much better from here. ## Was the Great Recession a Return to Trend? As I was putting together some graphs for my post on HP filtering (coming soon), I started playing around with some real GDP data. First, as many have done before, I fit a simple linear trend to the log of real GDP data since 1947 Plotting the data in this way, the Great Recession is clearly visible and seems to have caused a permanent reduction in real GDP as the economy does not seem to be returning to its previous trend. Taking the log of GDP is nice because it allows us to interpret changes as percentage increases. Therefore, the linear trend implies a constant percentage growth rate for the economy. But is there any reason we should expect the economy to grow at a constant rate over time? What if growth is not exponential at all, and instead grows at a slowly decreasing rate over time? Here’s what happens when we take a square root of real GDP instead of a natural log I have no theoretical justification for taking the square root of RGDP data, but it fits a linear trend remarkably well (slightly better than log data). And here the Great Recession is gone. Instead, we see a ten year period above trend from 1997-2007 followed by a sharp correction. If economic growth is following a quadratic growth pattern rather than an exponential one, it implies that the growth rate is decreasing over time rather than remaining constant. Here’s an illustration of what growth rates would look like in each scenario Fitting one trend line doesn’t necessarily mean anything, so to better test which growth pattern seemed more plausible, I decided to try to fit each trend through 1986 and then use those trends to predict current RGDP. Actual annualized RGDP in 2016 Q2 was$16.525 trillion. Assuming exponential growth and fitting the data through 1986 predicts a much higher value of $23.353 trillion. A quadratic trend understates actual growth, but comes much closer, with a prediction of$14.670 trillion. I then did the same experiment using data through 1996 and through 2006 and plotted the results

From these graphs, it appears that assuming quadratic growth, which implies a decreasing growth rate over time, would have done much better in predicting future GDP. Notice especially how close a GDP prediction would have been by simply extrapolating the quadratic trend forward by 10 years in 2006. Had the economy stayed on its 2006 trend through the present, RGDP in the last quarter would have been $16.583 trillion. It was actually$16.525 trillion for a difference of about $58 billion (off by 3 tenths of a percent). That is an astonishingly good prediction for a ten year ahead forecast (Just for fun, extending the present trend to 2026 Q2 predicts$20.200 trillion. Place your bets now).

Of course, this analysis doesn’t prove anything. It could just be a coincidence that the quadratic growth theory happens to fit better than the exponential. But I think it does show that we need to be careful in interpreting the Great Recession.

Using the above pictures, I can come up with two plausible stories. In the first, the Great Recession represents a significant deviation from trend. There was no fundamental reason why we needed to leave the path we were on in 2006 and we should do everything we can to try to get back to that path. Whether that comes through demand side monetary or fiscal stimulus or supply side reforms like cutting regulation and government intervention I will leave aside. But we should do something.

The other story is a bit more pessimistic. In this version, economic growth had been trending downwards for decades. We made a valiant effort to prop up growth on the strength of the internet in the late 1990s and housing in the early 2000s. But these gains were illusory, generated by unsustainable bubbles waiting to be popped rather than true economic progress. The recession, far from an unnecessary catastrophe, was an essential correction required for the economy to reorganize resources and adapt to the low growth reality. Enacting policies that attempt to restore previous growth rates will only fuel new bubbles to replace the old ones, paving the way for future recessions. Doing something will only make things worse.

Which story is more plausible? I wish I knew.

## What’s Wrong With Modern Macro? Part 4 How Did a "Measure of our Ignorance" Become the Cause of Business Cycles?

Part 4 in a series of posts on modern macroeconomics. Parts 1, 2, and 3 documented the revolution that transformed Keynesian economics into DSGE economics. This post begins my critique of that revolution, beginning with a discussion of its reliance on total factor productivity (TFP) shocks.

In my last post I mentioned that the real business cycle model implies technology shocks are the primary driver of business cycles. I didn’t, however, describe what these technology shocks actually are. To do that, I need to bring in the work of another Nobel Prize winning economist: Robert Solow.

### The Solow Residual and Total Factor Productivity

Previous posts in this series have focused on business cycles, which encompass one half of macroeconomic theory. The other half looks at economic growth over a longer period. In a pair of papers written in 1956 and 1957, Solow revolutionized growth theory. His work attempted to quantitatively decompose the sources of growth. Challenging the beliefs of many economists at the time, he concluded that changes in capital and labor were relatively unimportant. The remainder, which has since been called the “Solow Residual” was attributed to “total factor productivity” (TFP) and interpreted as changes in technology. Concurrent research by Moses Abramovitz confirmed Solow’s findings, giving TFP 90% of the credit for economic growth in the US from 1870 to 1950. In the RBC model, the size of technology shocks is found by subtracting the contributions of labor and capital from total output. What remains is TFP.

### “A Measure of Our Ignorance”

Because TFP is nothing more than a residual, it’s a bit of a stretch to call it technical change. As Abramovitz put it, it really is just “a measure of our ignorance,” capturing the leftover effects in reality that have not been captured by the simple production function assumed. He sums up the problem in a later paper summarizing his research

Standard growth accounting is based on the notion that the several proximate sources of growth that it identifies operate independently of one another. The implication of this assumption is that the contributions attributable to each can be added up. And if the contribution of every substantial source other than technological progress has been estimated, whatever of growth is left over – that is, not accounted for by the sum of the measured sources – is the presumptive contribution of technological progress
Moses Abramovitz (1993) – The Search for the Sources of Growth: Areas of Ignorance, Old and New p. 220

In other words, only if we have correctly specified the production function to include all of the factors that determine total output can we define what is left as technological progress. So what is this comprehensive production function that is supposed to encompass all of these factors? Often, it is simply
$Y=AK^\alpha L^{1-\alpha}$

Y represents total output in the economy. All labor hours, regardless of the skill of the worker or the type of work done, are stuffed into L. Similarly, K covers all types of capital, treating diverse capital goods as a single homogeneous blob. Everything that doesn’t fit into either of these becomes part of A. This simple function, known as the Cobb-Douglas function, is used in various economic applications. Empirically, the Cobb-Douglas function matches some important features in the data, notably the constant shares of income accrued to both capital and labor. Unfortunately, it also appears to fit any data that has this feature, as Anwar Shaikh humorously points out by fitting it to fake economic data that is made to spell out the word HUMBUG. Shaikh concludes that the fit of the Cobb-Douglas function is a mathematical trick rather than a proper description of the fundamentals of production. Is it close enough to consider its residual an accurate measure of technical change? I have some doubts.

There are also more fundamental problems with aggregate production functions that will need to wait for a later post.

### Does TFP Measure Technological Progress or Something Else?

The technical change interpretation of the Solow residual runs into serious trouble if there are other variables correlated with it that are not directly related to productivity, but that also affect output. Robert Hall tests three variables that possibly fit this criteria (military spending, oil prices, and the political party of the president), and finds that all three affect the residual, casting doubt on the technology interpretation.

Hall cites five possible reasons for the discrepancy between Solow’s interpretation and reality, but they are somewhat technical. If you are interested, take a look at the paper linked above. The main takeaway should be that the simple idealized production function is a bit (or a lot) too simple. It cuts out too many of the features of reality that are essential to the workings of a real economy.

### TFP is Nothing More Than a Noisy Measure of GDP

The criticisms of the production function above are concerning, but subject to debate. We cannot say for sure whether the Cobb-Douglas, constant returns to scale formulation is close enough to reality to be useful. But there is a more powerful reason to doubt the TFP series. In my last post, I put up these graphs that appear to show a close relationship between the RBC model and the data.

Here’s another graph from the same paper

This one is not coming from a model at all. It simply plots TFP as measured as the residual described above against output. And yet the fit is still pretty good. In fact, looking at correlations with all of the variables shows that TFP alone “explains” the data about as well as the full model

What’s going on here? Basically, the table above shows that the fit of the RBC model only works so well because TFP is already so close to the data. For all its talk of microfoundations and the importance of including the optimizing behavior of agents in a model, the simple RBC framework does little more than attempt to explain changes in GDP using a noisy measure of GDP itself.

Kevin Hoover and Kevin Salyer make this point in a revealing paper where they claim that TFP is nothing more than “colored noise.” To defend this claim, they construct a fake “Solow residual” by creating a false data series that shares similar statistical properties to the true data, but whose coefficients come from a random number generator rather than a production function. Constructed in this way, the new residual certainly does not have anything to do technology shocks, but feeding this false residual into the RBC model still provides an excellent fit to the data. Hoover and Salyer conclude

The relationship of actual output and model output cannot indicate that the model has captured a deep economic relationship; for there is no such relationship to capture. Rather, it shows that we are seeing a complicated version of a regression fallacy: output is regressed on a noisy version of itself, so it is no wonder that a significant relationship is found. That the model can establish such a relationship on simulated data demonstrates that it can do so with any data that are similar in the relevant dimensions. That it has done so for actual data hardly seems subject to further doubt.
Hoover and Salyer (1998) – Technology Shocks or Coloured Noise? Why real-business-cycle models cannot explain actual business cycles, p.316

Already the RBC framework appears to be on shaky ground, but I’m just getting started (my plan for this series seems to be constantly expanding – there’s even more wrong with macro than I originally thought). My next post will be a brief discussion of the filtering method used in many DSGE applications. I will follow that with an argument that the theoretical justification for using an aggregate production function (Cobb-Douglas or otherwise) is extremely weak. At some point I will also address rational expectations, the representative agent assumption, and why the newer DSGE models that attempt to fix some of the problems of the RBC model also fail.

## What’s Wrong with Modern Macro? Part 3 Real Business Cycle and the Birth of DSGE Models

Part 3 in a series of posts on modern macroeconomics. Part 1 looked at Keynesian economics and part 2 described the reasons for its death. In this post I will explain dynamic stochastic general equilibrium (DSGE) models, which began with the real business cycle (RBC) model introduced by Kydland and Prescott and have since become the dominant framework of modern macroeconomics.

“What I am going to describe for you is a revolution in macroeconomics, a transformation in methodology that has reshaped how we conduct our science.” That’s how Ed Prescott began his Nobel Prize lecture after being awarded the prize in 2004. While he could probably benefit from some of Hayek’s humility, it’s hard to deny the truth in the statement. Lucas and Friedman may have demonstrated the failures of Keynesian models, but it wasn’t until Kydland and Prescott that a viable alternative emerged. Their 1982 paper, “Time to Build and Aggregate Fluctuations,” took the ideas of microfoundations and rational expectations and applied them to a flexible model that allowed for quantitative assessment. In the years that followed, their work formed the foundation for almost all macroeconomic research.