## 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.

## 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.

## 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.

### Real Business Cycle

The basic setup of a real business cycle (RBC) model is surprisingly simple. There is one firm that produces one good for consumption by one consumer. Production depends on two inputs, labor and capital, as well as the level of technology. The consumer chooses how much to work, how much to consume, and how much to save based on its preferences, the current wage, and interest rates. Their savings are added to the capital stock, which, combined with their choice of labor, determines how much the firm is able to produce.

There is no money, no government, no entrepreneurs. There is no unemployment (only optimal reductions in hours worked), no inflation (because there is no money), and no stock market (the one consumer owns the one firm). There are essentially none of the features that most economists before 1980 as well as non-economists today would consider critically important for the study of macroeconomics. So how are business cycles generated in an RBC model? Exclusively through shocks to the level of technology (if that seems strange it’s probably even worse than you expect – stay tuned for part 4). When consumers and firms see changes in the level of technology, their optimal choices change which then causes total output, the number of hours worked, and the level of consumption and investment to fluctuate as well. Somewhat shockingly, when the parameters are calibrated to match the data, this simple model does a good job capturing many of the features of measured business cycles. The following graphs (from Uhlig 2003) demonstrate a big reason for the influence of the RBC model.

Looking at those graphs, you might wonder why there is anything left for macroeconomists to do. Business cycles have been solved! However, as I will argue in part 4, the perceived closeness of model and data is largely an illusion. There are, in my opinion, fundamental issues with the RBC framework that render it essentially meaningless in terms of furthering our understanding of real business cycles.

### The Birth of Dynamic Stochastic General Equilibrium Models

Although many economists would point to the contribution of the RBC model in explaining business cycles on its own, most would agree that its greater significance came from the research agenda it inspired. Kydland and Prescott’s article was one of the first of what would come to be called Dynamic Stochastic General Equilibrium (DSGE) models. They are dynamic because they study how a system changes over time and stochastic because they introduce random shocks. General equilibrium refers to the fact that the agents in the model are constantly maximizing (consumers maximizing utility and firms maximizing profits) and markets always clear (prices are set such that supply and demand are equal in each market in all time periods).

Due in part to the criticisms I will outline in part 4, DSGE models have evolved from the simple RBC framework to include many of the features that were lost in the transition from Keynes to Lucas and Prescott. Much of the research agenda in the last 30 years has aimed to resurrect Keynes’s main insights in microfounded models using modern mathematical language. As a result, they have come to be known as “New Keynesian” models. Thanks to the flexibility of the DSGE setup, adding additional frictions like sticky prices and wages, government spending, and monetary policy was relatively simple and has enabled DSGE models to become sufficiently close to reality to be used as guides for policymakers. I will argue in future posts that despite this progress, even the most advanced NK models fall short both empirically and theoretically.

## What’s Wrong With Modern Macro? Part 2 The Death of Keynesian Economics: The Lucas Critique, Microfoundations, and Rational Expectations

Part 2 in a series of posts on modern macroeconomics. Part 1 covered Keynesian economics, which dominated macroeconomic thinking for around thirty years following World War II. This post will deal with the reasons for the demise of the Keynesian consensus and introduce some of the key components of modern macro.

### The Death of Keynesian Economics

Although Keynes had contemporary critics (most notably Hayek, if you haven’t seen the Keynes vs Hayek rap videos, stop reading now and go watch them here and here), these criticisms generally remained outside of the mainstream. However, a more powerful challenger to Keynesian economics arose in the 1950s and 60s: Milton Friedman. Keynesian theory offered policymakers a set of tools that they could use to reduce unemployment. A key empirical and theoretical result was the existence of a “Phillips Curve,” which posited a tradeoff between unemployment and inflation. Keeping unemployment under control simply meant dealing with slightly higher levels of inflation.

Friedman (along with Edmund Phelps), argued that this tradeoff was an illusion. Instead, he developed the Natural Rate Hypothesis. In his own words, the natural rate of unemployment is

the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is embedded in them the actual structural characteristics of the labour and commodity markets, including market imperfections, stochastic variability in demands and supplies, the costs of gathering information about job vacancies, and labor availabilities, the costs of mobility, and so on.
Milton Friedman, “The Role of Monetary Policy,” 1968

If you don’t speak economics, the above essentially means that the rate of unemployment is determined by fundamental economic factors. Governments and central banks cannot do anything to influence this natural rate. Trying to exploit the Phillips curve relationship by increasing inflation would fail because eventually workers would simply factor the inflation into their decisions and restore the previous rate of employment at a higher level of prices. In the long run, printing money could do nothing to improve unemployment.

Friedman’s theories couldn’t have come at a better time. In the 1970s, the United States experienced stagflation, high levels of both inflation and unemployment, an impossibility in the Keynesian models, but easily explained by Friedman’s theory. The first blow to Keynesian economics had been dealt. It would not survive the fight that was still to come.

### The Lucas Critique

While Friedman may have provided the first blow, Robert Lucas landed the knockout punch on Keynesian economics. In a 1976 article, Lucas noted that standard economic models of the time assumed people were excessively naive. The rules that were supposed to describe their behavior were invariant to policy changes. Even when they knew about a policy in advance, they were unable to use the information to improve their forecasts, ensuring that those forecasts would be wrong. In Lucas’s words, they made “correctibly incorrect” forecasts.

The Lucas Critique was devastating for the Keynesian modeling paradigm of the time. By estimating the relationships between aggregate variables based on past data, these models could not hope to capture the changes in individual actions that occur when the economy changes. In reality, people form their own theories about the economy (however simple they may be) and use those theories to form expectations about the future. Keynesian models could not allow for this possibility.

### Microfoundations

At the heart of the problem with Keynesian models prior to the Lucas critique was their failure to incorporate individual decisions. In microeconomics, economic models almost always begin with a utility maximization problem for an individual or a profit maximization problem for a firm. Keynesian economics attempted to skip these features and jump straight to explaining output, inflation, and other aggregate features of the economy. The Lucas critique demonstrated that this strategy produced some dubious results.

The obvious answer to the Lucas critique was to try to explicitly build up a macroeconomic model from microeconomic fundamentals. Individual consumers and firms returned once again to macroeconomics. Part 3 will explore some specific microfounded models in a bit more detail. But first, I need to explain one other idea that is essential to Lucas’s analysis and to almost all of modern macroeconomics: rational expectations

### Rational Expectations

Think about a very simple economic story where a firm has to decide how much of a good to produce before they learn the price (such a model is called a “cobweb model”). Clearly, in order to make this decision a firm needs to form expectations about what the price will be (if they expect a higher price they will want to produce more). In most models before the 1960s, firms were assumed to form these expectations by looking at the past (called adaptive expectations). The problem with this assumption is that it creates predictable forecast errors.

For example, assume that all firms simply believe that today’s price will be the same as yesterday. Then when the price yesterday was high, firms produce a lot, pushing down the price today. Then tomorrow, firms expect a low price so don’t produce very much, which pushes the price back up. A smart businessman would quickly realize that their expectations are always wrong and try to find a new way to predict future prices.

A similar analysis led John Muth to introduce the idea of rational expectations in a 1961 paper. Essentially, Muth argued that if economic theory predicted a difference between expectation and result, the people in the model should be able to do the same. As he describes, “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.” Since only the best firms would survive, in the end expectations will be “essentially the same as the predictions of the relevant economic theory.”

Lucas took Muth’s idea and applied it to microfounded macroeconomic models. Agents in these new models were aware of the structure of the economy and therefore could not be fooled by policy changes. When a new policy is announced, these agents could anticipate the economic changes that would occur and adjust their own behavior. Microfoundations and rational expectations formed the foundation of a new kind of macroeconomics. Part 3 will discuss the development of Dynamic Stochastic General Equilibrium (DSGE) models, which have dominated macroeconomics for the last 30 years (and then in part 4 I promise I will actually get to what’s wrong with modern macro).