Competitive Innovation

In my previous post I took a crack at understanding Paul Romer's mathiness critique. As far as the post related to Romer (most of it was devoted to Brad DeLong's careless embellishment of the idea), my assessment was that Romer is basically just frustrated that his ideas have not swept away the competition in the field of growth theory. I do not believe that the academics Romer called out are defending indefensible positions for the sake of academic politics. To me, the present situation looks more like a healthy competition between theories of growth emphasizing different mechanisms. This is just what one would expect in a field where the forces at work are complicated and the answers to important questions are hard to come by.
 
Judging by his reply to my post here, it seems that Romer has a rather low opinion of me. Evidently, I am an "Euler-theorem denier." Admittedly, this is not the worst thing I've ever been called. But in addition to this, I am apparently motivated to deny the truth of this mathematical proposition because doing so signals my commitment to an academic club of serpents that includes the likes of Nobel prize-winning economists Bob Lucas and Ed Prescott. Paul, you flatter me.

I want to take some time here to address the specific charge leveled against me by Romer:

Andolfatto’s brazen mathiness involves a verbal statement about a mathematical model that flies in the face of an impossibility theorem. No model can do what he claims his does. No model can have a competitive equilibrium with price-taking behavior and partially excludable nonrival goods.

Romer's proposition is stated clearly enough. Now all we have to do is check whether it's valid or not. If I can produce a counterexample, then I will have shown Romer's proposition to be invalid. Let me now produce the counterexample.

Consider an economy where people combine raw labor (n) with skill (x) to produce labor services (e) according to the formula e = xn. Interpret n as hours worked over given period of time and assume, for simplicity, that everyone has the same n. On the other hand, people generally differ in their skill level, x. People with greater skills (or skill sets) are represented by larger values of x.

What makes people operating in the same environment more or less skilled than one other? Well, it could be several things. Consider two laborers, one of which is endowed with a physical tool that doubles labor productivity. Then we can write x = 1 for the one laborer and x = 2 for the other. Now consider two entrepreneurs, one of which is possessed with a "mental tool" (an idea, or some general know-how) that doubles labor productivity. Then we could similarly write x = 1 for the one entrepreneur and x = 2 for the other.

Physical and mental tools can differ along an important dimension called "rivalry." Economists call physical objects "rival"(or "subtractable") goods because a physical tool can be in the possession of only one laborer at any given time. The same need not be true for a mental good like an idea. Suppose that "knowing how to perform a task at level x" requires knowledge of a certain recipe. Unlike a physical good, an idea is not subtracted from your mind if you share it with someone else. If I teach you my calculus tool, this in no way diminishes my capacity to use the same calculus tool (or what amounts to the same thing, a perfect replica of my calculus tool). Economists call goods with this property "non-rival" or "non-subtractable" goods.

Alright then, let's proceed to the next step. Assume that the aggregate production function takes the form Y = aE, where a > 0 is a scalar and E represents the aggregate labor input measured in "efficiency units." That is, E equals the sum of e = xn over a population of size N. Let me normalize n = 1 and define X as the sum of x over population N. In this case, E = XN.

Notice that the aggregate production function exhibits constant returns to scale in E. The function is also linear in N. Of course, the function displays increasing returns in X and N together. That is, if we double both X and N, output Y is more than doubled.

The question Romer might ask at this point is "where are the books in this economy?" What he means by this is why can't the smartest person in this economy (the one with the largest x) not publish his knowledge in a recipe book and sell it to the others for a huge gain? This is an excellent question. The answer to it is that knowledge is not always very easily communicated and absorbed by all members of society in this manner. To the extent that knowledge transfer is difficult, the smartest guy in the room has a temporary monopoly over the idea that generates the highest x. Personally, I am surprised that Romer is so offended by this assumption of a missing market. Any university professor knows that distributing the course text book does not, by itself (re: Lucas quote 2009), lead to a growth of his/her students' knowledge base. Some types of knowledge can be sold, but other types of knowledge must be absorbed through effort, not through simple purchase. It is an empirical question as to which type of knowledge transfer mechanism is more or less important.

Next, I want to impose perfect competition. I do this not because I am wedded to the idea that this is how one must model the economy. I do it because Romer claims that it cannot be done.

But wait a minute...how can I assume perfect competition when the smartest person has a monopoly over his/her x? The answer is simple. The people in this economy are competing over the supply of efficiency units of labor e. There is no monopoly over the supply of labor services, e. Under perfect competition, the equilibrium price of an efficiency unit of labor is given by w* = a.  Of course, the measured wage per unit of raw labor (w*x) differs across people according to their skill x. The person with the highest x commands the highest price per unit of raw labor.

I should like Paul to note that Euler's theorem does indeed hold in my economy. The entire output is exhausted as payments for labor services (measured in efficiency units). Would people ever devote costly effort to learn something that would give them a higher x in this competitive economy? Sure, why not? Suppose that some raw labor time can be moved away from work and into a learning activity (l). The opportunity cost of this time is the person's foregone wage w*xl. The benefit is the expected value of learning something new (a higher x).

Anyone with an elementary training in economics can plainly see that the model described above has a competitive equilibrium with price-taking behavior and partially excludable non-rival goods. Ergo, Romer is wrong.

I am led to speculate how Romer might object to my counterexample. I suspect he might claim that the x in my model is not really a non-rival good. I get the feeling he might be defining a non-rival good as an idea that can be costlessly disseminated and instantaneously absorbed throughout the population (unless the use of the idea is protected by patent, etc.). If this is the case, then the argument would seem to be one of semantics.

In any case, I have made my point. Romer's proposition above is invalid. One can model a competitive equilibrium with price-taking and partially excludable non-rival goods. This should not be taken as a criticism against Romer's preferred modeling strategy. I'm actually a fan of his research program. My complaint with Romer's mathiness critique is that it ascribes unseen and unknown ulterior motives to a class of economists that find it fruitful to view growth through the lens of competitive equilibrium.

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PS. I see that Nick Rowe has offered a thoughtful response to Romer's "whack-a-mole" comment.

In the after-mathiness of discontent

If you're like me, you're probably still trying to wrap your mind around the debate on "mathiness" in the economics profession. I haven't put an inordinate amount of time into the project, but I have made an honest effort trying to understand the nature of Paul Romer's lamentations.

Just what is mathiness, anyway? I'm not sure that a precise and commonly-accepted definition exists. It's not surprising that such a catchy word was soon interpreted in myriad of conflicting ways. This is what happens with words.

To his credit, Romer soon recognized that the word he invented was being interpreted in ways he did not mean. He offers a sort of mea culpa here: Mathiness and Academic Identity. It is definitely a clarification (and I think, a softening) of his initial position. Here are what I take to be its two main points:

So my objection to mathiness is not a critique of the assumptions or structure of the models that others propose. It is a critique of a style that lets economists draw invalid inferences from the assumptions and structure of a model; a style that authors can use to persuade the reader (and themselves) to adopt conclusions that do not follow by the rules of logic; a style that tolerates wishful thinking instead of precise, clearly articulated reasoning. The mathiness that I point to in the Lucas (2009) paper...involves hand-waving and verbal evasion that is the exact opposite of the precision in reasoning and communication exemplified by Debreu/Bourbaki, and I’m for precision and clarity.

I wrote that the economists I criticize for using mathiness are engaged in a campaign of ACADEMIC politics, not one of national politics. Whatever was true in the past, the now fight is over ACADEMIC group identity. For example, one of the things that the people I criticize are campaigning for is a methodological restriction to models with price-taking. For them, price-taking is dogma. To make the case for this restriction, they are not presenting scientific arguments grounded in logic and evidence.

Hmm. He's critical of a style that lets economists draw incorrect inferences from the assumptions of a model. This is in contrast, I suppose, to all the other styles that permit people to draw incorrect inferences from the assumptions of their pet theories. He gives the example of Lucas (2009), to which I will return in a moment. The other charge is that some economists (them, not us of course) are "dogmatic." They campaign for and adopt methodological restrictions, like price-taking behavior, even when the logic and evidence does not permit it.

The two points above are linked to the same phenomenon: the apparent unwillingness of Romer's competitors in the field of growth theory to see the error of their ways and the superiority of his preferred approach. Mathiness is impeding scientific progress in the field of growth theory (and possibly throughout the economics profession as well).

What is the basis for these charges? As an outsider in the field of growth theory, it's hard for me to say (though I do have a paper in the area, which I'll talk about below). I think that Deitz Vollrath has a reasonable take on the issue here: More on Mathiness. Thankfully, we have Brad DeLong (Putting Economic Models in Their Place) doing his best to embellish the critique and apply it more broadly to macroeconomic theory--a subject more familiar to me.

Let's start with DeLong, who states:

He (Romer) seems, to me at least, to be very worried principally about two aspects of modern economic discourse. The first is to take what is true about one restricted class of theories and generalize it, claiming it is true of all theories and of the world as well.

Is there really any economist who behaves in this manner? Do we all not already know that our assumptions are provisional? That we may make one set of assumptions to address some questions and another set of assumptions to address other questions--that we have no grand unifying theory? So who, pray tell do these folks have in mind? Well, Paul Romer's thesis adviser, for one. Here, they quote Lucas (2009) who writes:

Some knowledge can be ‘embodied’ in books, blueprints, machines, and other kinds of physical capital, and we know how to introduce capital into a growth model, but we also know that doing so does not by itself [my italics] provide an engine of sustained growth. 

Now which parts of the quote above constitute a violation of scientific inquiry in your mind? Probably none. But I think it was the last part that got Romer's goat because he might have interpreted it to mean that "we know that Romer's models do not embody a mechanism that can provide an engine of sustained growth." I don't know--that's not the way I interpret the passage. Let's suppose Lucas had instead written "...but we also know that doing so does not necessarily provide an engine of sustained growth." Would that have been better? Can we all just be friends now?

I think it may be instructive to read the section from which the quote was lifted:

Is this really something to get so riled up over? Romer pg. 91 charges Lucas with making "untethered verbal claims"--an opinion he is of course free to hold. But I contend that it is just an opinion. Moreover, it's an opinion over the use of English, not math. It would have been far more useful and compelling, I think, if Romer had instead critiqued the model's internal logic and its ability to interpret the data. Isn't this the way science is supposed to progress? (Romer might reply that he's tried, but that his supervisor just won't listen because he's so dogmatic. I'll return to this possibility below.)

In any case, nowhere do I see evidence of DeLong's outlandish claim that Lucas is peddling an hypothesis he asserts to be true of all theories and of the world as well. But DeLong continues as follows:

Thus what Lucas claims must be true about the world as a matter of correct theory--that the big secret to successful economic growth cannot lie in creating and acquiring the kind of knowledge that gets "'embodied' in books, blueprints, machines..."--rests on the barely-examined decision to restrict attention to only a few kinds of models.

My goodness...this Lucas character...who does he think he is? You know, I have an idea. Why don't we actually go read the offending article and see what he's really up to? To whet your appetite, here's the introductory paragraph:

You know, call me crazy, but that opening passage does not sound like a call to arms to me. Lucas starts off with an interesting question. He bows respectfully to existing growth theory (including Romer's brand). He notes that they are based on important features of reality and that they are interesting theories. It's just that to him...[now, I want you to brace yourself and to please forgive the man...he is, after all, just an academic trying to explore alternative interpretations of the way the world works]...you see, to him, the existing theories of growth are not central (i.e., they are missing something that Lucas thinks is more important).

Lucas then proceeds in this highly provocative way: "In this paper I introduce and partially develop a new model of technical change..." From the way DeLong is writing, you'd think that Lucas had instead written "In this paper, I introduce and develop the grand unifying theory of economic growth and development. I await my second Nobel prize."

You can see how much fun I am having with this. Let me continue, along with DeLong, who writes:

The problem comes with the second principal aspect of "mathiness": to claim that one and only one mode of interaction and one and only one mode of individual decision-making is admissible at the foundation level of economic models. Here Romer attacks the assumption that the only allowable interaction is one of price-taking behavior: selling (or buying) as much as one wants at whatever the single fixed price currently offered by the market is. And here I would attack the assumption that individual decision-making is always characterized by rational expectations.

While there are certainly economists who make liberal use of the price-taking assumption in their research, there are equally many who do not. And I am not aware of any economist who would make the claim that the only allowable interaction is one of price-taking behavior. Many economists do feel more strongly about the desirability of imposing "rational expectations." But there is, of course, a vibrant community of those who feel otherwise. And it's not as if people who employ non-rational expectations models are ostracized from the community--unless you call being appointed a central bank president a form ostracism (see, for example, this piece by Jim Bullard).

Why do people have such a bee in their bonnet when it comes to the assumption of price-taking behavior? It's just a pricing protocol (a mechanism that determines prices). Many macro models, especially in the search and matching literature, use bilateral bargaining protocols to determine prices. Monopolistic competition is an assumed market structure together with an assumed pricing protocol. The pricing protocol there is usually quite restrictive: a monopolistic competitor is only permitted to charge a single price for his product. That is, nonlinear pricing schedules (which would increase both profit and social welfare) are assumed away--despite the overwhelming evidence of their use (e.g., retail and wholesale establishments often apply price discounts on large quantities purchased.)

[Aside: Many people are under the impression that monopoly is necessarily inefficient. This is not a valid conclusion. The conclusion follows from an auxiliary assumption that rules out an optimal nonlinear pricing protocol. Walter Oi makes this point in what is surely one of the best titles ever for an economics article: A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly.]

For Romer, the issue has to do with (I think) of how to reconcile the costly acquisition of nonrivalous (nonexcludable) ideas with perfect competition. DeLong hints at this when he writes:

Thus Paul Romer sees, in growth theory, the current generation of neoclassical economists grind out paper after paper imposing on the world "the restriction of 0 percent excludability of ideas required for [the] Marshallian external increasing returns" necessary for there to even be a price-taking equilibrium.

But DeLong (and Romer) are (I think) wrong on this dimension, at least, on a technical level. It is in fact possible to write down a growth a model where nonrivalous ideas are partially excludable (subject to costly acquisition) in a competitive equilibrium with price-taking behavior. My paper here (with Glenn MacDonald) constitutes one such example.

[Aside: In an extension of my model with Glenn, entrepreneurs are motivated to discover a technological advancement that, conditional on discovery, is assumed to diffuse rapidly among a small but measurable set of firms. This "small" group of firms on the technological frontier is "large" enough to assume price-taking behavior. The technology leaders earn profits (return on their knowledge capital) while laggards attempt to imitate the leaders--an effort that collectively generates the classic S-shaped diffusion dynamic--a phenomenon ignored by most growth models--including Romer's. An alternative and possibly more appealing set up would have been to permit one firm to have a short-lived monopoly right over a technological discovery. I think it's doubtful that any of our main results would have changed under this alternative specification. It's definitely an interesting question to explore and the alternative specification may have implications for questions that we were not interested in pursuing. The point I want to stress is that we did not assume price-taking behavior out of respect for a dogma. It just turned out to be a convenient way to approach things. And I think the approach is still fine, depending on the set of questions the researcher wants to focus on. Telling me that I must behave otherwise in the interest of science seems rather...what's the word I'm looking for here...I think it starts with a D...].

To many people, the assumption of price-taking behavior and rational expectations is thought to imply no useful role for government policy. In fact, nothing could be further from the truth. It is well-known that the equilibria of noncooperative games are generically suboptimal (so that well-designed interventions can be welfare-improving). For that matter, the equilibrium of a monopolistically competitive model can be efficient (and therefore warrant no government intervention). Adopting any one of these assumptions a priori is not, by itself, going to lead to a predetermined policy recommendation. And yet, DeLong seems to suggest that this is indeed the case when he writes:

And I see, in macroeconomics, paper after paper and banker after banker and industrialist after industrialist and technocrat after technocrat and politician after politician claiming that everything that governments might to to speed recovery must be counterproductive, or at least too risky--because that is what is in the case in a very restricted class of rational-expectations models.  

DeLong claims to see (without providing examples), in macroeconomics, "paper after paper" claiming that everything governments do is worse than useless. As evidence for this this, he cites two economists writing in the 1930s. Why not take a look at what people are publishing in high-level journals today? Here is just one example, drawn from the "freshwater" based Journal of Monetary Economics for March 2015. Among the papers published in this issue, I see:

1. Optimal Taxation with Home Production
2. Macroeconomic Regimes
3. Managing Markets with Toxic Assets
4. Financial Stress and Economic Dynamics: The Transmission of Crises
5. Liquidity, Assets and Business Cycles

I'll let this evidence speak for itself. What of his suggestion that the "austerity" forces are motivated by what is true in a restricted class of rational-expectations models? I'm afraid it's just another preposterous statement on his part. As he notes, recommendations of "austerity" were being made even in the 1930s. But that was well before rational-expectations models even existed. I might add that economists today frequently recommend government interventions that rely on rational expectations (e.g., Michael Woodford's "forward guidance" policy proposal).

Let me conclude now by returning to Romer. I'm still not absolutely sure what the mathiness critique is really all about. I think that Romer might just be frustrated (possibly with some justification) that his ideas haven't swept away his competition. Because his ideas are so firmly rooted in logic and evidence, the only thing that can evidently explain the continued resistance is academic politics shrouded in a cloak of mathiness.

Well, that's one interpretation and, who knows, maybe there's an element of truth to it. But my preferred interpretation is that what we seem to have here is simply a healthy clash of ideas competing in the marketplace for ideas. Let's not get too frustrated when our preferred (and obviously superior) theory does not sweep away the competition.

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Steve Williamson has his own interesting take on the issue here. 

Understanding Lowflation

Lowflation refers to an inflation rate persistently below an official target rate. Here's what the picture looks like for several countries as of January 2014 (source: Contessi): 

Here's what the time-series looks like for the United States (source: Duy):

The apparent inability of a central bank to raise inflation seems truly remarkable for those of who lived through the great "peace-time" inflation (see Romer and DeLong). What's going on here? Isn't high inflation supposed to be easy to get?  Didn't Zimbabwe give us a modern day lesson in creating inflation? Didn't former Fed Chair Paul Volker demonstrate how a sufficiently determined central bank can lower inflation? If so, then why does it appear so difficult to accomplish the reverse?

In this post I want to think out loud about how one might interpret this strange state of affairs. There are two broad themes running through my head these days. The first, and more important theme, is the old Sargent and Wallace idea of potential conflicts arising between independent monetary and fiscal authorities that are linked through a consolidated government budget constraint.

The second, and less important theme, revolves around the concept of a liquidity trap. Think of a liquidity trap as a situation where investors view central bank money and treasury debt as perfect substitutes. Such a condition likely never holds exactly in reality, but that's neither here nor there. Empirical relevance is possible even if liquidity trap conditions hold approximately. In any case, if money and bonds are close to perfect substitutes, then the composition of total government debt (between money and bonds) has little economic significance (in the same way that the composition of the money supply between $5 and $10 bills does not matter).

Let's start with the monetary-fiscal policy game. For those who are interested in a formal description of the model I have in mind, LOOK HERE. The fiscal authority is assumed to choose the time-path for government debt. The monetary authority takes the time-path of debt as given and simply chooses the composition of the debt between low-interest-money and high-interest-bonds. That is, the monetary authority can choose the money-to-debt ratio, but not the total amount of debt (money plus bonds).

If the central bank holds the money-to-debt ratio fixed, then inflation is determined by the growth rate of nominal government debt (minus the growth rate in the real demand for such debt). The two forces determining inflation in this case are (1) the fiscal authority, which chooses the growth rate of nominal debt and (2) the economic forces, domestic and foreign, influencing the rate of growth in the demand for government debt.

Now, suppose that the central bank thinks that the inflation is too high. The central bank could ask the fiscal authority to reign in its nominal deficits. Suppose the fiscal authority does not acquiesce. Suppose that the central bank is determined to lower inflation nevertheless. A permanent reduction in the inflation rate requires a monotonically decreasing money-to-debt ratio. That is, the central must threaten to monetize a progressively smaller fraction of the government's debt. The tighter and tighter monetary policy leads to a higher and higher real rate of interest. Because the inflation rate is pegged, the nominal interest rises as well. Investment collapses and the debt-service cost of the government's debt rises relentlessly. The fiscal authority capitulates, and lowers the growth rate of its nominal debt to accommodate the central bank's lower inflation target.

That is, by the way, one interpretation of the 1981-82 recession. If it is correct, it's rather unfortunate because the theory suggests that it could have been avoided had the conflict been resolved sooner rather than later. [Sargent (1986) has a nice discussion here of Wallace's "game of chicken" between decentralized branches of a government, with application toward interpreting the Reagan deficits.]

In any case, let's move forward to today where we see the opposite situation unfolding: inflation rates persistently below the central bank's target rate. What is the proximate cause of this? The notion of a diminished growth rate in the supply of debt is not tenable. I'm inclined to view countries like the U.S. as having an relatively stable fiscal anchor. Treasury-issuance in the U.S. did rise sharply during the financial crisis, but the growth rate has subsided to more sustainable levels. Here is the growth rate of nominal U.S. debt held by the public:

And here is the debt-GDP ratio for the U.S. 

Well then, if the supply of debt is not responsible for lowering inflation, what is? The demand side, of course. While one can't provide direct evidence pertaining to the demand for debt, we can make reasonable inferences based on its price behavior. Judging by the collapse of U.S. treasury yields since the crisis (see next diagram), I'd say that one can safely infer a robust demand for the product. (I would be curious to know what other conclusion one could come to, especially in light of how much the supply of U.S. treasury debt has increased.)

Alright, so let's imagine, not unreasonably I think, that there's been an uptick in the worldwide demand for high-grade debt. On the first instance, the effect of this growing appetite is to pull yields down. On the second instance, with yields bounded below by zero, the effect is deflationary (a lower price-level is the market's mechanism for increasing the real supply of nominal debt when it is in short supply).

Most central bankers are likely hoping that this demand-driven disinflationary pressure is transitory. But suppose it is not and suppose the central bank wants to act to raise inflation back to target. Again, one way to do this is to ask the fiscal authority to consider raising its nominal deficits (insert laughter here). Alright, we weren't seriously thinking that was going to work, did we?

So our steadfast central bank embarks on the reverse-Volker path, steadily increasing the money-to-debt ratio over time. With larger and larger fractions of the public debt being monetized, real and nominal interest rates decline (I'm assuming that the inflation peg is being held). Will the fiscal authority "blink" this time around in face of the central bank's resolve?

But why should the fiscal authority "chicken out" here? In this case, the government's debt-service costs are declining instead of rising. Moreover, the lower real interest rate is stimulating investment. Why should the fiscal authority capitulate to this sort of "pain?"

Alright then, well suppose the central bank nevertheless carries on with its program of monetary stimulus. What is the end game (assuming that the elevated growth rate in the demand for government debt continues unabated)?

The answer to this question depends on what limits govern the growth and size of a central bank's balance sheet. Let impose a relatively weak condition.

[A1] The central bank cannot forever monetize debt at a rate faster than it is being issued. 

Assumption [A1] is relatively weak because it does permit a central bank to grow the money-to-debt ratio temporarily. It just can't do so forever.

If [A1] holds, then the endgame is clear. Eventually the growth in the money-to-debt ratio must cease. At this point, inflation must decline back to the rate implied by the fiscal anchor. The cards are stacked against the central bank in this game. Sumimasen, Nippon Ginko.

So where does the liquidity trap relate to this discussion? I don't think it's necessary for understanding the logic above, but it does add a bit of contemporary color. In a liquidity trap, even very rapid increases in the money-to-debt ratio will be inconsequential, apart from leading to a correspondingly rapid increase in the level of excess reserves in the banking system. The BOJ is presently trying very hard to prove this prediction incorrect, but so far, with mixed success. And already, cracks are beginning to appear in the resolve of some top Japanese policy advisers.

The seminal modern treatment of the liquidity trap was presented in Krugman (1998).  In that piece, he states (pg. 139):

The traditional view that monetary policy is ineffective in a liquidity trap, and that fiscal expansion is the only way out, must therefore be qualified: monetary policy will in fact be effective if the central bank can credibly promise to be irresponsible, to seek a higher future price level.

I think that this statement is true but that the conditioning factor "if the central bank can credibly promise" does not presently apply to central banks of countries with high-grade sovereign debt. The rapidly growing appetite for high-grade debt depresses yields and inflation. To overcome these deflationary pressures, central banks must threaten to expand their balance sheets far beyond what anyone can sensibly believe is possible. In such circumstances, it really can be more difficult to raise the inflation rate than lower it. Such is the "price" of responsibility.


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PS. Lest there be any misunderstanding, this post is not about why raising inflation back to a central bank's target is inherently a good thing for the economy. I appeal to no theory here of what constitutes an optimal inflation target. The purpose is simply to explain why in some circumstances it might be harder to raise inflation rather than to lower it. 

In defense of modern macro theory

The first economist

The 2008 financial crisis was a traumatic event. Like all social trauma, it invoked a variety of emotional responses, including the natural (if unbecoming) human desire to find someone or something to blame. Some of the blame has been directed at segments of the economic profession. It is the nature of some of these criticisms that I'd like to talk about today.

One of the first questions macroeconomists get asked is: How could you possibly not have predicted the crisis? We all remember when the Queen of England asked this (supposedly embarrassing) question. Put on the spot, I might have replied that the same question could have been asked of her ancestor(*) predecessor King Charles I, whose death in 1649 also came about under rather unexpected circumstances. Or, I might have replied that many economists did in fact predict this crisis...along with the many other crises that failed to materialize (recall the old joke about the economist who successfully predicted 10 out of the past 2 recessions).

But seriously, the delivery of precise time-dated forecasts of events is a mug's game. If this is your goal, then you probably can't beat theory-free statistical forecasting techniques. But this is not what economics is about. The goal, instead, is to develop theories that can be used to organize our thinking about various aspects of the way an economy functions. Most of these theories are "partial" in nature, designed to address a specific set of phenomena (there is no "grand unifying theory" so many theories coexist). These theories can also be used to make conditional forecasts: IF a set of circumstances hold, THEN a number of events are likely to follow. The models based on these theories can be used as laboratories to test and measure the effect, and desirability, of alternative hypothetical policy interventions (something not possible with purely statistical forecasting models).

There is a sense in which making predictions is very easy. Here's one for you: Mt. Vesuvius will experience another major eruption on the scale of AD 79, when it buried the city of Pompeii, tragically killing thousands of people (among them, the famous naturalist Pliny the Elder). While volcanologists are getting progressively better at predicting eruptions, it remains very difficult to forecast their size. So when an event like this arrives, it always comes as a bit of a shock. In any case, like I said, making predictions (unconditional forecasts) that will eventually come true is easy. There are thousands of people predicting that the world will end in 2015, 2016, 2016, etc. Some of these prognosticators will one day be proven correct. Those making predictions that fail to come true hide in the shadows for a while, but then re-emerge bolder than ever. I don't blame these soothsayers: there seems to be an insatiable demand for the likes of Nostradamus, and this is clearly a case of demand creating its own supply. In this spirit then, permit me to deliver my own forecast (remember, you heard it here first): there will be another major financial crisis on the scale experienced in 2008.

While we can't predict when the next major crisis will occur (I hope the Queen can forgive us), it is reasonable to expect experts to make good conditional forecasts. IF Vesuvius blows, THEN a lot of people are going to die. This type of conditional forecast should lead policymakers to think of ways in which the potential death toll can be avoided or reduced. Perhaps citizens should be prohibited from inhabiting dangerous areas. At the very least, an emergency evacuation procedure should be put in place. The same is true for financial crises. Perhaps restrictions should be placed on the exchange of some types of financial products. At the very least, an emergency response strategy should be put in place. Actually, there is an emergency response strategy--the Fed's emergency lending facility--which essentially worked according to plan in 2008-09. Now, maybe you don't like various aspects of the Fed's liquidity facility and that's fine (even if it did make a healthy profit for the U.S. taxpayer). But you can't say that economists hadn't predicted the possible need for such a facility. Indeed, the Fed was set up on the premise that financial crises would continue to afflict modern economies (by the way, financial crises were a common part of the economic landscape well before the founding of the Fed in 1913, so think carefully before you accuse the Fed as the source of market instability).

Alright, so much for blaming economists and their less-than-crystal balls (hmm, a part of me says I should have edited that last sentence.) What else? Well, I notice a lot of blame also being heaped on modern macroeconomic theory and the professors of such theory. "What's Wrong With Macro?" the headlines wail (roll eyes here). Things have become so bad that we now see students telling professors how macro should be taught. Next we'll have teenagers telling their parents how to raise children. Well, we already have that of course. But the point is that while parents patiently hear out these protestations (having been young for much longer than the youth in question), they do not generally capitulate to them. I'm sorry, but you're only 16, I love you, and no, you can't have the keys to the car!

And yet, amazingly, we have to read things like this (source):

Wendy Carlin, professor of economics at University College London, who is directing a project at the Institute for New Economics Thinking, a think-tank set up by billionaire financier George Soros, said at a conference last year that students had become “disenchanted” and lecturers “embarrassed” by the way economics is taught.

Lecturers at UCL are "embarrassed" by the way economics is taught? What does this mean? Are they embarrassed about the way they personally teach their economics classes? Then they should be fired for incompetence. Are they embarrassed by the current state of macroeconomic theory? Then they should be fired and sent back to grad school (or the Russian front, if you're a Hogan's Heroes fan).

The dynamic general equilibrium (DGE) approach is the dominant methodology in macro today. I think this is so because of its power to organize thinking in a logically consistent manner, its ability to generate reasonable conditional forecasts, as well as its great flexibility--a property that permits economists of all political persuasions to make use of the apparatus.

For the uninitiated, let me describe in words what the DGE approach entails. First, it provides an explicit description of what motivates and constrains individual actors. This property of the model reflects a belief that individuals are incentivized--in particular, they are likely to respond in more or less predictable ways to changes in the economic environment to protect or further their interests. Second, it provides an explicit description of government policy. While this latter property sounds straightforward, it is in fact a rather delicate and important exercise. To begin, in a dynamic model, a "policy" does not correspond to a given action at a point in time. Rather, it corresponds to a full specification of (possibly state-contingent) actions over time. Moreover, there is no logical way in which to separate (say) "monetary" policy from "fiscal" policy. The policies of different government agencies are inextricably linked through a consolidated government budget constraint (see A Dirty Little Secret).  Thus, any statement concerning (say) the conduct of monetary policy must explicitly (or implicitly) contain a statement stipulating a consistent fiscal policy. The exercise is delicate in the sense that model predictions can depend sensitively on the exact details of how policies are designed and how they interact with each other. The exercise is important because the aforementioned sensitivity is quite likely present in real-world policy environments. Finally, the DGE approach insists that the policies adopted by private and public sector actors are in some sense "consistent" with each other. Notions of consistency are imposed through the use of solution concepts, like competitive equilibrium, Nash equilibrium, search and bargaining equilibrium, etc. Among other things, consistency requires that economic outcomes respect resource feasibility and budget constraints.

Now, what part of the above manifesto do you not like? The idea that people respond to incentives? Fine, go ahead and toss that assumption away. What do you replace it with? People behave like robots? Fine, go ahead and build your theory. What else? Are you going to argue against having to describe the exact nature of government policy? Do you want to do away with consistency requirements, like the respect for resource feasibility. Sure, go ahead. Maybe your theory explains some things a lot better than mine when you dispense with resource constraints. But do you really want to hang your hat on that interpretation of the world? An internally inconsistent theory that happens to be consistent with some properties of the data is not what I would call deep understanding. (Nor is an internally consistent theory inconsistent with the data something to be happy about, but that's the purpose of continued research.)

The point I want to make here is not that the DGE approach is the only way to go. I am not saying this at all. In fact, I personally believe in the coexistence of many different methodologies. The science of economics is not settled, after all. The point I am trying to make is that the DGE approach is not insensible (despite the claims of many critics who, I think, are sometimes driven by non-scientific concerns).

I should make clear too that by "the DGE approach," I do not limit the phrase to New Keynesian DGSE models or RBC models. The approach is much more general. While one might legitimately observe that these latter sets of models largely downplay the role of financial frictions and that practioners should therefore not have relied so heavily on them, it would not be correct to say that DGE theory cannot account for financial crises. If you don't believe me, go read this (free) book by Franklin Allen and Douglas Gale: Understanding Financial Crises. While this book was published in 2007, it reflects a lifetime of work on the part of the authors. And if you take a look at the references, you'll discover a large and lively literature on financial crises well before 2007. In my view, this constitutes evidence that "mainstream" economists were thinking about episodes like 2008-09. If central bank economists were not paying too much attention to that branch of the literature, it is at most an indictment on them and not on the body of tools that were available to address the questions that needed to be answered. (In any case, as I mentioned above, I think the Fed did act according to the way theory generally suggests during the crisis).

Once again (lest I be misunderstood, which I'm afraid seems unavoidable these days) I am not claiming that DGE is the be-all and end-all of macroeconomic theory. There is still a lot we do not know and I think it would be a good thing to draw on the insights offered by alternative approaches. I do not, however, buy into the accusation that there "too much math" in modern theory. Math is just a language. Most people do not understand this language and so they have a natural distrust of arguments written in it. Different languages can be used and abused. But this goes as much, if not more, for the vernacular as it does for specialized languages. Complaining that there is "too much math" in a particular theoretical exposition is like complaining that there is too much Hiragana in a haiku poem. Before criticizing, either learn the language or appeal to reliable translations (in the case of haiku poetry, you would not want to rely solely on translations hostile to Japanese culture...would you?).

As for the teaching of macroeconomics, if the crisis has led more professors to pay more attention to financial market frictions, then this is a welcome development. I also fall in the camp that stresses the desirability of teaching more economic history and placing greater emphasis on matching theory with data. However, it's often very hard, if not impossible, to fit everything into a one-semester course. Invariably, a professor must pick and choose. But while a particular course is necessarily limited in what can be presented, the constraint binds less tightly for a program as a whole. Thus, one could reasonably expect a curriculum to be modified to include more history, history of thought, heterodox approaches, etc. But this is a far cry from calling for the abandonment of DGE theory. Do not blame the tools for how they were (or were not) used.


(*) My colleague Doug Allen points out that Elizabeth II did not descend from Charles I. The Stuart line dies out with Queen Anne, at which point George I is brought over from Germany. EII is a member of the house of Hanover/Windsor, and not a Stuart. Many also think that EII is a descendant of Elizabeth I, but of course she had no children, and ended the Tudor line. 

The "Audit" the Fed Crowd

Alex Pollock says that It's High Time to "Audit" the Federal Reserve. I'm glad to see that this headline puts the word "audit" in quotes. It suggests what Mr. Pollock means by "audit" differs from how most people understand the word: a complete and careful examination of the financial records of a business or person (Merriam Webster).

You see, just the other day, Senator Rand Paul, a leader in "Audit-the-Fed" movement (a significant step down from his father's "End-the-Fed" movement) was making statements like this one:

“[An] audit of the Fed will finally allow the American people to know exactly how their money is being spent by Washington.”

Of course, the Fed does not control how money is being spent by Washington. The Fed prints money to buy government securities. It sometimes extends loans against high-grade collateral. Everything you want to know about these purchases and loans is publicly available. So Paul's initial line of attack has fizzled out, something that is implicitly acknowledged by Pollock when he writes:

The calls in Washington to “audit” the Federal Reserve are not for a narrow, bean-counting review of the institution’s financial statements.

Good. Progress has been made: the Fed's books are in order. Nothing scandalous to report (sigh). How else then to "audit" the Fed?

Let's be honest here. There is nothing new to discover in further auditing. This movement is motivated by what they perceive to be bad monetary policy. It doesn't even make sense to say we want to "audit" the Fed's policy because the policy is already transparent (which is, after all, what permits critics to label it "bad" in the first place!).

There is, of course, nothing wrong with critiquing Fed policy. Indeed, there are many economists working inside the Fed that critique various aspects of Fed policy all the time. And, as we all know, members of the FOMC can hold very different opinions ("hawks" and "doves"). Thoughtful critiques of policy should be welcomed. Policymakers and researchers at the Fed do welcome them.

Moreover, I'm all for full accountability. The Fed should be accountable to the American people--it is, after all, a creation of the American people through their representatives in Congress. But as I have said, the issue here is not about accountability. It is about a group of individuals who want to see their preferred monetary policy adopted. That's fair enough. I just ask that they be honest about their motives. It has nothing to do with audits or accountability.

Involuntary Labor Market Choices?

My pal Roger Farmer has a lot of good ideas, but he doesn't always use the best language to express them. In a recent post, for example, Roger asserts the following.

Participation is a voluntary choice.  Unemployment is not. 

The idea that unemployment is voluntary is classical nonsense.

I do not like this language. But before I explain why I feel this way, let me first describe what I think Roger is trying to say. I think he means to say that recessions are socially inefficient outcomes, manifesting themselves primarily in the form elevated levels of unemployment and not in low participation rates. The unemployed are people without good-paying jobs, but looking for good-paying jobs. Good-paying jobs are relatively scarce in a recession (especially for individuals with lower skill sets--the young, those without advanced education, etc.) If you were to interview the unemployed during a deep recession and ask them how they're feeling, most of them would are likely to reply that they are not doing well relative to when they were employed. Economists (classical or otherwise) would say that recessions are welfare-reducing events for most people. The "classical" idea that there is little a government can or should do to help society in a deep recession is nonsense.

I think this probably captures Roger's view fairly well. Notice, however, that nowhere did I employ the adjectives "voluntary" or "involuntary" to describe labor market outcomes. I did not because these labels are not useful (which I why we do not see these terms used in the labor literature). Indeed, want to go a step further and argue that the use of these labels might be worse than useless. Now let me explain why I feel this way.

Let's start with some things I think we can all agree on. First, people are endowed with some time, T. Second, there are competing uses for this time. Let me assume, for simplicity, that there are three uses of time: work (e), search (u), and leisure (n). Think of "work" as time devoted toward producing marketable goods and services, "unemployment" as searching for work, and "leisure" as producing non-marketable goods and services. Third, we can all agree that we face a time constraint: e + u + n = T.

Now, suppose for simplicity that T is indivisible: it must be allocated to one and only one of the three available time-use categories (the allocation can, however, change over calendar time). In this case, a standard labor force survey (LFS) will record e = T as employment, u = T as unemployment, and n = T as nonparticipation (or not-in-the-labor-force, NILF). [Note: the LFS never asks people whether they are unemployed or not. It asks whether they have done any paid work in the previous 4 weeks and if they have not, it then asks a series a questions relating to job search activities. If they report no job search activity, they are then classified as NILF.]

Now, Roger seems to be saying that people have a choice to make when it comes to allocating their time to either work (e = T) or leisure (n = T), but that they have no choice in determining time spent unemployed (u = T). Moreover, the idea that people may choose u = T constitutes "classical nonsense." But is this really what he means to say?

Let's start with a basic neoclassical model. In this abstraction, individuals and firms meet in a centralized market place and individuals are assumed to know where to find the best price for their labor. Put another way, there is absolutely no reason to devote precious time to searching for work. To put it yet another way, the neoclassical model was never designed to explain unemployment--it was designed to explain employment (and non-employment). And so, in the neoclassical model, where search is not necessary, individuals rationally choose u = 0.

Now, you may think this is a silly abstraction and that you want to impose (involuntarily) the state u = T on some individuals. But why? Unemployment is not idleness. Unemployment (at least the way the LFS defines it) constitutes the activity of searching for work--it is a form of investment (that hopefully pays off in a better job opportunity in a world where finding jobs is costly). Individuals not working and not searching are counted as out of the labor force (and even these people may not be "idle" because they might be doing housework or schoolwork, etc.).

So back to our neoclassical model. Since there is no unemployment, the time-allocation problem boils down to choosing between work and leisure. Depending on idiosyncratic considerations (the price of one's specific labor, wealth position, the opportunities for home production, schooling, etc.), some individuals choose work and others choose leisure. In the neoclassical model, these idiosyncratic "shocks" are largely beyond an individual's control. If the demand for your labor declines, it will cause the market price of your labor to fall. You will not like that. The shock is involuntary. BUT, you still get to choose whether to work at that (or some other) lower wage, or exit the labor force. To take another example, suppose that a source of non-labor income suddenly vanishes (involuntary). You may now be compelled to take that lousy paying job. Should we label this outcome "involuntary employment?" If so, then what next? Involuntary saving? (oops). Are all choices to be considered "involuntary?"

This is not the way we (as economists) want to go, in my opinion. In my view, it makes more sense to view choices as voluntary and responsive to the incentives imposed on individuals by the economic environment. If we want to view anything as "involuntary," it would be exogenous changes to the environment that reduce material living standards.  If circumstances change for the better, welfare increases. If they change for the worse, welfare declines. In either case, people can be expected to allocate their scarce time toward the activities that promise the highest expected payoff. What room is there left for the "voluntary/involuntary" distinction? None, in my view.

Let's stick with the neoclassical model for a bit longer, but tweak it the way I did here to permit multiple equilibria. Now, this is right up Roger's alley. All individual choices here are rational and "voluntary."  But this doesn't mean that the economy operates perfectly all the time. Indeed, the economy might get stuck in a bad equilibrium, where employment is low, non-employment is high (and unemployment is still zero). What would Roger suggest here in the way of labels? Is this a model of involuntary leisure?  How does this label help us understand anything? I argue that it does not.

Alright, so I don't find the "involuntary leisure" label useful. So what? Well, I don't want to make too much of this, but I think such labels can lead to muddled thinking. The label "involuntary" suggests that individuals may not respond to incentives (after all, they evidently have no choice in the matter). I think it's better, from the perspective of designing a proper intervention, to view the individual's circumstances as beyond their control, but to respect the fact that they are likely to respond to altered incentives. We are economists, after all -- why would we not interpret the world this way? People demonstrably do respond to incentives! 

I could go on and talk at length about abandoning the neoclassical assumption of centralized labor markets and replacing this construct with a decentralized search market. There is a big literature on labor market search and I'm not about to review it here. If you're interested, read my Palgrave Dictionary entry on the subject here. Suffice it to say that I find no value in interpreting an individual's state of unemployment as "involuntary" either. There are all sorts of jobs out there and I think people rationally turn "ill-suited" job opportunities down to search for better matches (the way I did, when I lost my construction job in the 1981 recession). Sometimes, people get "discouraged" and exit the labor force. These are all choices that people make relative to the circumstances they find themselves in. If we want to design programs to help the unfortunate (some of whom are employed or out of the labor force), then we want to design a system that respects incentives. 

What's that you say? You don't believe that incentives matter? Not for the unemployed? This is what I call nonsense. Consider, for example, the well-known "spike" in unemployment exit rates at the point of unemployment benefit exhaustion (see David Card here: "In Austria, the exit rate from registered unemployment rises by over 200% at the expiration of benefits..."). We see clear evidence that the unemployed do respond to incentives--they do have choices, especially in an economy with so many competing uses for time. Interpreting unemployment as "voluntary" does not mean that we are to have no compassion for the the unemployed. We feel bad for anyone (employed or out of the labor force too) who face terrible circumstances beyond their control. What it means is that we should measure economic welfare based on consumption (material living standards), not time allocation choices. It means is that we understand and respect the fact that people make choices based on the incentives they face. It means that a well-designed policy should respect these incentives.

Let me sum up here. Commentators attach the label "involuntary" to unemployment to emphasize the fact that the unemployed are not typically happy with their circumstances. Fine. But then can the same not be said of many people who find themselves "involuntarily" employed (the working poor, for example) or "involuntarily" out of the labor force (looking after a sick relative, for example)? If so, then how can one unequivocally proclaim that "participation is a voluntary choice, unemployment is not?" It makes no sense to me. I want to ask Roger to stop using bad language. 

Lifting Off...Sooner or Later

From Barron's yesterday we have this lovely headline: Two Fed Presidents Contradict Each Other on Same Day.

From the dovish corner, Charles Evans, president of the Chicago Fed, suggested that the Fed should be patient about raising rates and not act until 2016. He said: 

Given uncomfortably low inflation and an uncertain global environment, there are few benefits and significant risks to increasing interest rates prematurely. Let's be confident that we will achieve both dual mandate goals within a reasonable period of time before taking actions that could undermine the very progress we seek.

Weighing in for the Fed hawks, Kansas City Fed president Esther George said she thought the Fed should raise rates mid-year. Her take: 

This balanced approach framework supports taking steps to remove the extraordinary amount of monetary accommodation currently in place. The next phase in this process is to move the federal funds rate off its near-zero setting. While the FOMC has made no decisions about the timing of this action, I continue to support liftoff towards the middle of this year due to improvement in the labor market, expectations of firmer inflation, and the balance of risks over the medium and longer run.

I want to evaluate these two views in the context of a Taylor rule. The Taylor rule is simply a mathematical representation of how the Fed should (or will) set its policy rate in relation to the current state of the economy as measured by inflation gaps (inflation minus target inflation) and output gaps (output minus potential output). Every FOMC member presumably has a Taylor rule in mind if for no other reason than the existence of the Fed's dual mandate (the Congressional mandate that the Fed strive to stabilize inflation and employment around some long-run targets). 

A simple version of the Taylor can be written in this way:

i(t) = r* + p* + A[p(t) - p*] + B[y(t) - y*]

where i(t) is the nominal interest rate (IOER) at date t, p(t) is the inflation rate at date t, and y(t) is the (logged) real GDP at date t. The starred variables are long-run values associated with the real interest rate (r*), the inflation target (p*) and the level of "potential" GDP (y*). The parameters A and B govern how strongly the Fed reacts to deviations in the inflation target [p(t) - p*] and the output gap [y(t) - y*]. 

Let me start with the hawkish view (see also this presentation by Jim Bullard). According to this view, y(t) is below, but very close to y*. So, let's just say that the output gap is zero. PCE inflation is presently around p(t) = 1%. We all know that p* = 2%, so the inflation gap is -1%. Now, we have some leeway here with respect to the parameter A, but let's assume that the Fed responds aggressively to the inflation gap (consist with the Taylor principle) so that A=2. 

Now, if we think of the long-run real rate of interest as r* = 2%, then our Taylor rule delivers i(t) = 2%. Presently, the Fed's policy rate is i(t) = 0.25%. So, if you're OK with these calculations, the Fed should be "lifting off" (raising its policy rate) right now. Oh, and don't call it a "tightening." Instead, call it a "normalization." After all, even with i(t) = 2%, the Fed is still maintaining an accommodative stance on monetary policy because 2% is lower than the long-run target policy rate of r* + p* = 4%. 

What about the doves? Because doves like to emphasize the unemployment rate, the argument of a large negative output gap is now harder for them to make (see also here). But one could reasonably make the case that the output gap--as measured, say, by the employment rate of prime-age males--is still negative, let's say [y(t) - y*] = -1%. Let's be generous and also assume B=1. 

Now, if we continue to assume r*+p* = 4%, our dovish Taylor rule tells us that the policy rate should presently be set at  i(t) = 4% - 2% - 1% = 1%. So the recommended policy rate is lower than the hawkish case, but still significantly above 25 basis points. 

Thus, if we take the historical Taylor rule as a decent policy rule (in the sense that historically, it was associated with good outcomes), then one might say that the hawks have a stronger case than the doves. Both camps should be arguing for lift-off--the only question is how much and how fast. 

On the other hand, something does not seem quite right with the hawk view that things are presently close to normal and that the Fed should therefore normalize its policy rate. All we have to do is look around and observe all sorts of strange things happening. The real interest on U.S. treasuries is significantly negative, for example. Indeed, the nominal interest rate on some sovereigns is significantly negative. This does not look "normal" to a lot of people (including me). And so, maybe this is one way to rescue the dovish position. For example, one might claim that the real interest rate is now lower than it normally was, e.g., r* = 1%. (see this post by James Hamilton). If so, then this might be used to justify delaying liftoff.

Regardless of positions, everyone seems to assume that liftoff will occur sooner or later. But as Jim Bullard observed here in 2010, the promise of low rates off into the indefinite future may mean low rates (and deflation) forever. Few people seem to take this argument seriously except for, gosh, the predictions seems to be playing out (see Noah Smith's post here). For those who hold this position, the question of liftoff becomes more like now or never, rather than sooner or later. 

To conclude, we see that the contradictory views expressed by Evans and George might spring from something as basic as a disagreement on what constitutes the "natural" rate of interest r*. Further disagreement might be based on the appropriate measure of "potential" y* and on the appropriate size of the parameters A and B. There are also other concerns (like "financial stability") that are not captured in the Taylor rule above that might lead Fed presidents to adopt different views on policy. 

In the immortal words of Buffalo Springfield: "There's something happening here, What it is ain't exactly clear." What this something is, its root cause, and what might be done about it seems rather elusive at the moment. And I mean elusive not in the sense that nobody knows. I mean in the sense that everyone seems to have an opinion, most of which are mutually inconsistent. It makes for interesting times, at least.