On the perils of Taylor rules

In the Seven Faces of "The Peril" (2010), St. Louis Fed president Jim Bullard speculated on the prospect of the U.S. falling into a Japanese-style deflationary outcome. His analysis was built on an insight of Benhabib, Schmitt-Grohe, and Uribe (2001) in The Perils of Taylor Rules.

These authors (BSU) showed that if monetary policy is conducted according to a Taylor rule, and if there is a zero lower bound (ZLB) on the nominal interest rate, then there are generally two steady-state equilibria. In one equilibrium--the "intended" outcome--the nominal interest rate and inflation rate are on target. In the other equilibrium--the "unintended" outcome--the nominal interest rate and inflation rate are below target--the economy is in a "liquidity trap."

As BSU stress, the multiplicity of outcomes occurs even in economies where prices are perfectly flexible. All that is required are three (non-controversial) ingredients: [1] a Fisher equation; [2] a Taylor rule; and [3] a ZLB.

Back in 2010, I didn't take this argument very seriously. In part it was because the so-called "unintended" outcome was more efficient than than the "intended" outcome (at least, in the version of the model with flexible prices). To put things another way, the Friedman rule turns out to be good policy in a wide class of models. But mostly, I figured that other factors were probably more important for explaining the events unfolding at that time.

Well, maybe I was a bit too hasty. Let me share with you my tinkering with a simple OLG model (similar to the one I developed here.) Unfortunately, what follows is a bit on the wonkish side. If you catch any errors, or otherwise have any comments to make, please let me know.

Basics 

People live for two periods; they are "young" and then "old." Everyone only values consumption when old. Their objective is simply to maximize (expected) future consumption.

The young are endowed with some output y. The are also each endowed with an investment technology such that k units of output invested today yields f(k) units of output tomorrow. Assume that f(k) is increasing and strictly concave; i.e., f'' < 0 < f'.

The autarkic (also competitive) outcome is one where the young save their entire endowment and consume f(y) when old. The competitive equilibrium (gross) real rate of interest is equal to the marginal product of capital, r = f'(k). [Note that time-preference plays no role in determining the real rate of interest here.]

An economy with real debt

Assume that there is a government that issues one-period real debt b. Let r denote the gross real rate of interest paid on this debt. I assume that the government finances the carrying cost of its debt via a lump sum t tax applied to old agents. In a steady state,

[1] t = (r-1)b.

By construction, the savings decision is trivial: the young save all their income y. The interesting decision entails a portfolio allocation choice problem between capital and bonds, y = k + b. Conditional on a choice of b (hence, k), future consumption is given by:

[2] c = f(y-b) + rb - t 

Assuming an interior solution, (expected) rate of return equality implies:

[3] r = f'(y-b)

Technically, [3] determines bond demand. In equilibrium, the supply of bonds (determined by policy) must equal the demand for bonds. Hence, by choosing b in this model, the government can choose the prevailing real rate of interest. Lump-sum taxes are simply adjusted by way of [1] to finance the carrying cost of the debt. Equilibrium consumption is then given by [2]; i.e., c = f(y-b) + b.

The real GDP in this economy is given by Y = y + f(y-b). Notice that this model delivers a standard IS curve. That is, by increasing b, the government increases r, capital is crowded out, and output falls. Likewise, lowering the real interest rate stimulates (investment) demand, leading to an increase in output.

In what follows, I assume that a socially desirable outcome is associated with some 0 < b* < y. The "natural" rate of interest is defined as r* = f'(y-b*), and potential GDP is defined by Y* = y + f(y-b*). [Note that r* may be either greater or less than one. Some of you may argue that r* should equal 1 here. That's fine. The qualitative results below do not hinge on this issue.]

An economy with nominal debt

Let P denote the price of output denominated in some abstract unit of account. Let B = Pb the nominal debt. Let P+ denote "next period's" price level. Then a young person faces the following sequence of budget constraints:

Py = Pk + B 
P+C+ = P+f(k) + RB - T+

where R denotes the gross nominal interest rate, and T is the nominal lump-sum tax. Define Π+ = P+/P, the expected gross rate of inflation. Then using b =B/P and t = T/P, rewrite the budget constraints above as

y = k + b
c+ = f(k) + (R/ Π+)b - t+ 

Desired real bond holdings must now satisfy the condition

[4]  f'(y - b) = R/ Π+

with the demand for nominal bond holdings given by B = Pb. If I define r = R/ Π+ as the expected real rate of interest, then we see that [4] is equivalent to [3].

The government budget constraint is given by T+ = RB - B+. In real terms,

[5] t+ = (R/ Π+)b - b+ 

so in a steady state with b = b+, we have t = (r-1)b, which is equivalent to [1]. Consumption is given by [2].

The model to this point is riddled with indeterminacy, even restricting attention to steady states. What determines the nominal interest rate, the inflation rate, the price level, etc.? Note that this indeterminacy is not present in the model with real debt. In that world, I assumed that b was a policy instrument. This (along with the lump-sum tax instrument) pins down an equilibrium. In the world I am describing now, the government does not pick b. It need not even pick B if, in particular, it is willing to let demand determine quantity at a given rate of interest. How to proceed? As usual, in small steps.

A Monetarist regime

We can think of B as interest-bearing money. The nominal interest rate on money is commonly assumed to be zero, so R = 1. But there is nothing that requires this to be the case; we are free to pick any interest rate supportable by taxes here. The key assumption is that R is determined and that it is constant over time.

The monetarist views B (and the time path for B) as determined by policy. With the demand for real money balances determined by [4], market clearing requires B = Pb for all time. Since B is determined by policy, and b is determined by agents, the price level is determined by P = B/b. The inflation rate must therefore be determined by

[6]  Π+ = (B+/B)(b/b+)

Let B+ = μB. Now combine [6] with [4] to derive:

[7]  b+ = (μ/R) f'(y - b)b

which is a first-order difference equation in real money balances. The model has two steady states. In one, b = 0; in the other, b > 0 satisfies f'(y - b) = (R/μ). It seems darn easy to construct the optimal policy here. Just set  (R/μ) = r* and we're done.

Well, not so fast. As it turns out, even for the case of a fixed stock of money B, there generally exists a continuum of nonstationary equilibria indexed by an initial condition 0 < b0 < y, with the time path for b asymptotically approaching zero; see Figure 1 in Woodford (1984). Of course, since P = B/b with B fixed, this implies that the price level approaches infinity (in fact, these are hyperinflation dynamics). Isn't it interesting to note that Friedman's k percent rule is dynamically unstable here?

The undesirable hyperinflation dynamic here appears to an artifact of (among other things) the assumed passivity of policy (the nominal interest rate and money growth rate are held fixed forever). But evidently, there exists a simple "activist" policy rule that uniquely implements the desired outcome:

[8]  ln(R) = ln(R*) + α[ ln(Π+) - ln(Π*) ]

where Π* = μ (arbitrary), R* = r*Π*, and α = 1.  The policy rule [8] is a Taylor rule. The rule dictates that the policy rate be increased one-for-one with expected inflation. Such a policy keeps the expected real rate of interest pinned to its natural rate. As such, the economy is always at potential (this would not necessarily be the case if I was to introduce other shocks, of course). Note that the price level is now determined, P = B/b* with P+ = Π*P.

Would the ZLB restriction R ≥ 1 limit the ability of policy here? I do not think so. First, the problem in this model is a the possibility of a self-fulfilling hyperinflation -- deflationary equilibria do not exist. As such, policy only needs to threaten to raise, not lower, the nominal interest rate. Second, I believe that the optimal monetary policy may alternatively be expressed as a money growth rate that varies in proportion to the expected growth rate in real money demand. That is, targeting the inflation rate is feasible here (and contrary to Eagle (2006), an inflation target policy seems consistent with price level determinacy here).

A Wicksellian regime

Following the approach taken in the New Keynesian literature, we might instead assume that the quantity of nominal debt B (money) is entirely demand-determined. The only policy instrument is R (and, of course, the lump-sum tax). I assume that policy follows the Taylor rule [8] with α = 1.

As far as I can tell, all of the math developed in the previous section continues to hold. But giving up the quantity variable B as a policy instrument must have some implication. Indeed, it does. What we seem to lose is any fundamental economic force determining the price level and inflation rate. That is, the level of debt and its growth rate simply accommodate themselves to the prevailing price level and inflation rate, respectively. According to [8], exogenous movements in the expected rate of inflation (inflation shocks) are met one-for-one with movements in the nominal interest rate, leaving the real rate of interest pegged to its natural rate.

Note something interesting here: the inflation target Π* is completely irrelevant. Inflation in this model can be whatever it "wants" to be. If the community expects an inflation rate Π+ < Π*, the inflation rate Π+ becomes a self-fulfilling expectation (and is hence a "rational expectation"). In this case, the monetary authority simply sets its policy rate R < R*. A situation like this can last indefinitely in this model.

Of course, everything works just fine here as long as the ZLB is not a constraint. Suppose, instead, that the policy rate is constrained by the ZLB, so that [8] becomes:

[9]  ln(R) = max{ 0, ln(R*) + α[ ln(Π+) - ln(Π*) ] }

Imagine that the economy is initially operating at potential with Π+ = Π* (without loss). Then, out of the blue, individuals suddenly believe that the inflation rate is going to be permanently lower Π+ = Π' < Π*. Moreover, suppose that this inflation shock is sufficiently large to make the ZLB bind. What happens?

What happens is that output drops permanently below potential (the economy continues to grow, however, at the rate implied by technological progress and population growth, both of which are normalized to zero here). Why does this happen?

It happens (here) because the real rate of interest rises above its natural rate, r' = 1/Π' > r*. The real interest rate is too high. The effect is to depress (investment) demand, r' = f'(k') implies k' < k*. The real GDP falls below potential, Y' = y + f(k') < Y*.

Because there is no nominal anchor for inflation in this economy, all sorts of bad things can happen at the lower bound. Contrary to the Friedman rule prescription, deflation is bad (generally, any inflation rate sufficiently low to make the ZLB bind). Not that the monetary authority could actually implement the Friedman rule if it wanted to. In this economy, the monetary authority has absolutely no control over the inflation rate!

A nominal anchor

An obvious way to provide a nominal anchor (in the model) is to adopt the monetarist approach and control the supply of the monetary aggregate. But perhaps this is something that is difficult to do in reality. What then?

Everything seems to hinge here on how individuals form inflation expectations. The theory here provides no guidance as to how these expectations should be formed. One can assert that individuals are likely to use the inflation target Π* as a nominal anchor. But this is just a bald-faced assertion. That is, if individuals do use Π* as a nominal anchor, then it will become a nominal anchor. The monetary authority, however, has no way enforcing the target Π* (unless it adopts a monetarist approach). 

Well then, let me assume a particular inflation expectation formation rule:

[10]  ln(Π+)  = (1 - ρ)ln(Π*) + ρln(Π) + δ[ ln(Y+) - ln(Y*) ] + ε

where 0 ≤ ρ ≤ 1, δ≥ 0, and where ε represents an inflation shock (say, i.i.d. and zero mean). Students may recognize [10] as a type of Phillips curve. 

Actually, now that I stare at [10], I see that the δ > 0 opens up another source of indeterminacy. It may be possible, for example, that if people suddenly expect a recession Y+ < Y*, that the downward revision in inflation forecasts implied by [10] could make the ZLB bind, generating a self-fulfilling prophecy.

Anyway, let's just set δ = 0 here. In the Wicksellian approach above, I adopted a special case of [10]; i.e., ρ = 1 and δ = 0;. But now, for 0 ≤ ρ < 1, any given inflation shock is mean-reverting (to the inflation target). The "lift off" date -- the date at which the monetary authority begins to raise its policy rate according to [9] depends on how quickly inflation expectations rise. The speed of adjustment here is governed by the parameter ρ--a lower ρ implies faster adjustment.

Is there anything the monetary authority can do here to "talk up inflation" (i.e., lower ρ)? We really can't say without a theory of expectation formation. But it seems to me that "promising to keep R = 1 for an extended period of time" may have the effect of increasing ρ, extending the period of adjustment. That is, by postponing the "lift off" date, agents may rationally expect inflation to remain below target for a longer period of time.

Concluding thoughts

Let me be clear that I do not think the 2008 drop in output below its previous trend was caused by a negative inflation shock. A negative inflation shock possibly played a role, but there had to be more to the story than this. In the analysis above, a negative inflation shock represents a movement along a stable IS curve; the real interest rate goes up, and output goes down. To make sense of recent events, we also have to consider shocks that shift the IS curve "leftward." (I describe just such a shock here.)

Nevertheless, I think it is interesting to explore what potential effects future downward revisions to inflation expectations may have on the economy at the ZLB. In the Wicksellian regime I study above, there appears to be no nominal anchor apart from what agents believe it to be. And if agents come to believe in a persistent deflation, it may come to pass, and the economy may be stuck below potential for a very long time. Convincing agents that the nominal interest rate is likely to remain at zero for a long time may be counterproductive, depending on how individuals interpret such policy announcements.

I want to stress, however, that while getting inflation and inflation expectations back to target (and firmly anchored to target) may be a solution to one problem, it is unlikely to be a solution to every problem currently facing the U.S. economy. To put it another way, suppose that the current real interest rate of -1% is too high relative to the current "natural" rate of -x%. Somehow driving the real return on bonds to -x% may then help things a bit, but it does nothing to address the more pressing question of why the "natural" rate is so low to begin with.

The hawkish nature of the Evans Rule

From Bloomberg Businessweek:
The Fed Turns Aggressively Dovish with 'Evans Rule'

The headline above seems to capture the general sentiment surrounding the FOMC's recent  policy announcement. The recent move is characterized by many as "dovish" in nature because

...the Fed will keep short-term interest rates near zero as long as unemployment remains above 6.5 percent and the inflation it expects in one to two years is no higher than 2.5 percent. That replaces the previous plan to keep rates near zero until mid-2015. Given the slow pace of job growth, the current plan could mean that rates stay super-low past mid-2015.

Sure. Of course, the FOMC could alternatively have just extended the "lift off" date into the more distant future (as they have done in the past). But that's neither here nor there. What I want to talk about is the move to a state-contingent policy that makes explicit reference to the unemployment rate. St. Louis Fed President James Bullard has long advocated a move to state-contingent policy (see here). The actual form of the policy turned out to be one subsequently advocated by Chicago Fed President Charles Evans (hence, the "Evans Rule"). Maybe it's not perfect, but perhaps it's a move in the right direction.

In any case, here is the relevant part of the FOMC statement:

In particular, the Committee decided to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee’s 2 percent longer-run goal, and longer-term inflation expectations continue to be well anchored.

According to the Bloomberg article above,

This is essentially what Charles Evans, President of the Federal Reserve Bank of Chicago, has been arguing for over the last year. Dubbed the Evans Rule, the argument holds that monetary policy shouldn’t be tightened until the economy heals pasts a certain predetermined threshold.

This makes it sound like that by making explicit reference to the unemployment rate in a policy rule, one necessarily makes the rule more "dovish" in nature. A comment left by "K" in my previous post got me to thinking, however, that the opposite might be true in this case. 

To see what I mean by this, consider the following visual depiction of the Evans Rule:

 
Since near term inflation is currently projected to be less than 2.5% and since the unemployment rate is currently above 6.5%, the U.S. economy is currently located in Region 4 of the diagram above. The Evans Rule in this case says: keep the policy rate at zero (actually, 0.25%). The rule also suggests that if the economy happens to drift into any one of the remaining four quadrants, the Fed would consider increasing the policy rate.
  
What role is the 6.5% threshold playing in the Evans Rule? One could make a case that its role is to dictate a tighter monetary policy over a greater range of circumstances. 

To see this, simply ask what the diagram above would look like absent the 6.5% threshold on unemployment. Region 3 would now look like Region 4. That is, the rule would now specify that the policy rate should remain low over a greater range of unemployment rates. 

As Chairman Bernanke stressed in his press conference, the new policy does not imply that the Fed will necessarily raise its policy rate should the unemployment rate fall below the 6.5% threshold (Region 3). But surely, if the unemployment rate crosses this threshold, the perceived probability of an imminent rate hike is likely to spike up. Absent the unemployment rate threshold, the market would likely expect the policy rate to instead remain low for a longer period of time. This is the hawkish nature of the Evans rule. 

Shadow Banking

The Arrow-Debreu model provides the foundation for modern macroeconomic theory and the theory of finance. This is probably as it should be. But like most foundations, it is just a place to start. As John Geanakoplos explains here, the AD model is "relentlessly neoclassical." And what this means, among other things, is that the basic AD model offers no explanation for phenomena related to money, liquidity, banking, and corporate finance (just to offer a partial list). 

 

To make sense of phenomena like money, liquidity, and collateral, we need to model the "frictions" that make intertemporal trade difficult. Frictions like private information, limited commitment, and limited communication. Absent such frictions, debtors could spend their promises easily. Creditors would not not have to worry about promises being broken. Such a world is not likely be free of the business cycle. But business cycles would likely be muted (small shocks would not be magnified as much, or propagated throughout the economy to the same extent). 

 

Of course, economists throughout the ages have thought about these sort of frictions. And there is a substantial body of modern macroeconomic theory that attempts to formalize these notions. A heretofore neglected area of research, however, is what economists have come to call the "shadow banking" sector (see here, here and here). Some recent theoretical work can be found here: 

A Model of Shadow Banking, Gennaioli, Shleifer, Vishny
Shadow Banks and Macroeconomic Instability, Meeks, Nelson, Allesandri

The shadow banking sector is still very large--take a look at this recent news story: Shadow Banking Still Thrives. According to Gary Gorton (Shadow Banking Must not be Left in the Shadows) the shadow banking sector needs to be regulated...somehow. It seems like we're still not exactly sure how this should be done or, indeed, if it is even feasible. 

 

What I mean about "feasibility" is the observation that private agents, particularly those in the financial industry, seem to be extremely good at innovating their way around existing bank legislation. Shedding light on one dark place in the room just causes the little critters to find other shadows. Who knows, maybe that's even a good thing. But I haven't really seen any theoretical papers on the subject (please send if you have). 

Here is Ken Rogoff on the subject: Ending the Financial Arms Race. Here is an excerpt:

Legislative complexity is growing exponentially in parallel. In the United States, the Glass-Steagall Act of 1933 was just 37 pages and helped to produce financial stability for the greater part of seven decades. The recent Dodd-Frank Wall Street Reform and Consumer Protection Act is 848 pages, and requires regulatory agencies to produce several hundred additional documents giving even more detailed rules. Combined, the legislation appears on track to run 30,000 pages. 

As Haldane notes, even the celebrated “Volcker rule,” intended to build a better wall between more mundane commercial banking and riskier proprietary bank trading, has been hugely watered down as it grinds through the legislative process. The former Federal Reserve chairman’s simple idea has been co-opted and diluted through hundreds of pages of legalese. 

The problem, at least, is simple: As finance has become more complicated, regulators have tried to keep up by adopting ever more complicated rules. It is an arms race that underfunded government agencies have no chance to win.

No more bubble talk (please!)

I am currently at the Institute of Advanced Studies in Vienna, which hosts one of the best little macro conference in Europe: The Vienna Macro Cafe. Excellent papers, lively discussions, wonderful camaraderie, and an unbeatable location. (Let me know if you'd like to be placed on our mailing list.) 
  
After this uplifting experience, I made the mistake of checking the econ blogosphere. Blah. 

I guess it all started with Paul Krugman (who else?), who goes off here in his usual assertive style: Bubble, Bubble, Conceptual Trouble. Steve Williamson takes issue with some of the claims that Krugman makes here: The State of the World. And then Noah Smith steps in to attack one part of Williamson's post here: Money Is Just Little Green Bits of Paper! Noah gets it all wrong, but that doesn't stop both Krugman and DeLong in congratulating him for an argument that even they apparently do not understand. And so it goes. 

Let me now explain why I think Noah gets the "bubble" issue wrong. Here is how Noah starts off. 

Have you ever heard people say that "money is just little green pieces of paper"? Well, that is exactly what Steve Williamson claims in this post.

Um, no...Steve never said that "money is just little green pieces of paper." So right away, we're off to a bad start.
To understand what Steve meant, we have to start with Krugman's own "definition" of a bubble:

Over and over again one hears that we can’t expect to return to 2007 levels of employment, because there was a bubble back then. But what is a bubble? It’s a situation in which some people are spending too much.

It's a situation in which some people are spending too much? Thanks for that, Paul. To which Steve replies:

What is a bubble? You certainly can't know it's a bubble by just looking at it. You need a model. (i) Write down a model that determines asset prices. (ii) Determine what the actual underlying payoffs are on each asset. (iii) Calculate each asset's "fundamental," which is the expected present value of these underlying payoffs, using the appropriate discount factors. (iv) The difference between the asset's actual price and the fundamental is the bubble. Money, for example, is a pure bubble, as its fundamental is zero. There is a bubble component to government debt, due to the fact that it is used in financial transactions (just as money is used in retail transactions) and as collateral. Thus bubbles can be a good thing. We would not compare an economy with money to one without money and argue that the people in the monetary economy are "spending too much," would we?

The only quibble I have with this reply is Steve's use of the word "bubble." Bubbles mean different things to different people. As Steve emphasizes, the definition should be made relative to a specific model. "Bubbles" are not something you can actually "see" in the data -- "bubble dynamics" are an interpretation of the data. 

In any case, what word might Steve have used instead of "bubble?" While less colorful, I think that the label "liquidity premium" is more accurate. It is the market price of an asset above it's "fundamental" value. The distinction here seems similar to the one that Marx made between "use value" and "exchange value;" see here.

Here is how I like to think about it. Imagine an economy with just one person, as in Robinson Crusoe. Crusoe likes to eat coconuts. So he values coconuts. And he values the trees that produce coconut dividends. One way to measure value here is to ask "how many coconuts would Crusoe be willing to give up to have one more coconut tree?" The answer to this question will provide a measure of the tree's "fundamental" value. Because there are no other people on the island (prior to Friday), there is no exchange value associated with tree ownership. There is no "bubble" in a Robinson Crusoe economy.

The situation can be quite different, however, in an economy consisting of more than one person wanting to trade intertemporally in credit markets. One friction that hampers intertemporal trade is what economists call a lack of commitment. Essentially, people cannot be relied upon to keep their promises. Monetary theorists have shown that in this type of world, various objects may be employed to enhance the volume of intertemporal trade. These objects are called exchange media.

Exchange media may take the form objects that are commonly viewed as "money"--objects that circulate widely from hand to hand, or from account to account. They may also take the form of collateral objects, like the senior tranches of MBS that (until recently) circulated widely in the repo market. Because U.S. treasuries are used widely to facilitate financial transactions, they too constitute an important medium of exchange.

Abstracting from risk, the market price of an exchange medium can be broken down into two components: fundamental value and market value. We can estimate the fundamental value of an asset by assessing its value under the assumption that it is illiquid (i.e., does not circulate as an exchange medium). The difference between market price and fundamental value is a measure of liquidity value. Because an asset may be priced above its fundamental value, there is a sense in which the asset price embeds a "bubble" component according to many popular definitions. But the word is more trouble that it's worth--our discussions might be clearer and more productive if we avoided the term entirely.

Aside: Steve's point is that in a world of financial frictions, exchange media and their associated "bubble" prices may be useful for increasing the level of spending closer to socially optimal levels. If so, then how does Krugman's definition of a bubble--a situation where people are spending too much--make any sense? There may be bubbles that have this property. But then there may be bubbles that do not. Williamson is telling Krugman that he needs to be more careful. The message, unfortunately, seems hopelessly lost. 

  

Alright then, back to Noah, whose whole column is based on Steve's throwaway comment: 

Money, for example, is a pure bubble, as its fundamental is zero.

To which Noah replies:

Can this be true? Is money fundamentally worth nothing more than the paper it's printed on (or the bytes that keep track of it in a hard drive)? It's an interesting and deep question. But my answer is: No. 

First, consider the following: If money is a pure bubble, than nearly every financial asset is a pure bubble. Why? Simple: because most financial assets entitle you only to a stream of money. A bond entitles you to coupons and/or a redemption value, both of which are paid in money. Equity entitles you to dividends (money), and a share of the (money) proceeds from a sale of the company's assets. If money has a fundamental value of zero, and a bond or a share of stock does nothing but spit out money, the fundamental value of every bond or stock in existence is precisely zero.

While it may not have been clear to the average reader, I happen to know that Steve was referring to a special kind of monetary object: a pure "fiat" currency. "Fiat" in the modern sense of the word means "intrinsically useless" or "zero use value."The USD issued by the Fed may not fit this description exactly because, as others have pointed out, government money does have the power to discharge a real tax obligation. On the other hand, pure fiat money does seem exist; see my post: Fiat Money in Theory and in Somalia. The point is that even fiat money can have exchange value, and if it does, then its value is entirely a liquidity premium or "bubble" and that, moreover, it is probably a "good" bubble to the extent that fiat money facilitates trade. 

What of Noah's claim that if money is a bubble, then nearly every financial asset is a bubble? This just seems plain wrong to me. Financial assets are typically backed by physical assets. For example, the banknotes issued by private banks in the U.S. free-banking era (1836-63) were not only redeemable in specie, but they constituted senior claims against the bank's physical assets in the event of bankruptcy. Mortgages are backed by real estate, etc.

Of course, there is the problem of dividing up the physical assets, but at some level, someone ends up with property rights in the physical asset--and it is this property right that gives most assets a "fundamental" value.

Note: I see that Steve Williamson has his own reply here: Money and Bubbles. 

How Canada Saved Its Bacon

Interesting to see that Canada's former finance minister (and prime minister) Paul Martin issuing a "stern warning" to U.S. policymakers; see here.

The similarity between the current U.S. slump and what happened to Canada in the 1990s is quite interesting, and I've written about it here: The Great Canadian Slump: Can it Happen in the U.S.?
 
I know that economists like Tiff Macklem and Pierre Fortin debated the issue some time in the mid 1990s, but I haven't really seen any work on the subject since then. If I recall correctly, I believe that Fortin was ascribing blame to the Bank of Canada, and possibly Paul Martin's "austerity" measures. Macklem (and coauthors) did not share the same view.

If you know of any more recent work that investigates the great Canadian slump, please pass it along.

Is the Fed missing on both sides of its dual mandate?

With the unemployment rate still above 8% and some inflation measures below 2%, many people argue that the Fed is "missing on both sides of its dual mandate;" see, for example, Fed Harms Itself By Missing Goals.

Jim Bullard, president of the St. Louis Fed, has a different view, which he just published here: Patience Needed for Fed's Dual Mandate.

My interpretation of  his critique is as follows.

People who make this critique invariably organize their macroeconomic thinking along "Keynesian" (or New Keynesian) lines. An important pillar of this way of thinking is some version of the Phillips Curve (see here for Mike Bryan's humorous critique of the concept). Here is what a Phillips curve is supposed to look like:

Now, imagine that the economy is hit by a large negative "aggregate demand shock." Unemployment rises, and inflation falls--there is a movement along the PC, downward, from left to right (see diagram above).

Next, suppose that the Fed has the power to exploit the PC relationship (this is a questionable supposition, in my view, but it's what people like to believe, so let's run with it). What would the unemployment-inflation dynamic look like in response to such a shock under an optimal (or near optimal) monetary policy? (Bullard references the Smets and Wouters NK model: Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach.)

Bullard's suggests that a non-monotonic transition path for inflation is unlikely to be part of any optimal policy in a NK type model. The optimal transition dynamics are typically monotonic--think of the optimal transition path as a movement back up the PC in the diagram above. If this is true, then the optimal transition path  necessarily has the Fed missing on both sides of its dual mandate.

Of course, conventional NK models frequently abstract from a lot of considerations that many people feel are important for understanding the recent recession and sluggish recovery. The optimal monetary policy may indeed dictate "inflation overshooting" in a different class of models. Please feel free to put forth your favorite candidate. Tell me why you think Bullard is wrong. 

QE3 and Inflation Expectations

Some interesting data here on the TIPS measure of expected inflation following the Fed's QE3 announcement (courtesy of my colleague, Kevin Kliesen).

The first chart shows that the announcement had a significant impact on inflation expectations at short and long horizons.

Here's the same data, together with the 10-year inflation forecast, and for a longer sample period.

The impact on real yields, especially at the short end, seems significant (but let's see how long this lasts). 

 
Here's the same data over an even longer sample period.

 
And here's a truly remarkable graph...

Notes: Inflation-Indexed Treasury Yield Spreads are a measure of inflation compensation at those horizons, and it is simply the nominal constant maturity yield less the real constant maturity yield. Daily data and descriptions are available at research.stlouisfed.org/fred2/. See also Statistical Supplement to the Federal Reserve Bulletin, table 1.35. The URL for MT is: http://research.stlouisfed.org/publications/mt/