Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Friday, December 28, 2012

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.


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 rR/ 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). It seems darn easy to construct the optimal policy here. Just set  (R) = 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 Πis 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.

Thursday, December 20, 2012

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. 

Wednesday, November 21, 2012

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.

Tuesday, October 23, 2012

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

Monday, September 24, 2012

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.

Thursday, September 20, 2012

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. 

Tuesday, September 18, 2012

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 See also Statistical Supplement to the Federal Reserve Bulletin, table 1.35. The URL for MT is:

Friday, September 14, 2012

Paul Krugman's Baltic Problem

Well, since I'm writing about the K-man today, I thought I'd link up to this interesting piece by Swedish economist Anders Aslund: Paul Krugman's Baltic Problem.
Seems like Krugman's little IS-LM model made a few wrong predictions too. I guess the science isn't quite a settled as he would like us all to believe.

In any case, I haven't studied the Baltic region in any great detail. If there are any experts out there that would like to weigh in here, please do. My prior is that both Krugman and Aslund have some legitimate explanations for what is driving the Baltic recovery and expansion. But maybe one side is more persuasive than the other? What is the evidence? Would be interested to hear what people have to say, especially from those who know the area well. 

Thursday, September 6, 2012

Not enough workers to meet demand for new homes

Wow, how's that for a headline?!

But it appears to be true, as Diana Olick reports here.
The shortage is across the spectrum, but especially in need are framers, concrete workers, plumbers, roofers and painters. The shortage is also felt most in areas where housing is coming back strongest, and permitting is easiest, like Texas and much of the West. 
Ms. Olick also links up to a column she wrote earlier US Homebuilders Begin to See Credit Thaw
Much of the demand is coming from potential buyers who have been shut out of the lower-priced, distressed market by avid, all-cash investors. The big public builders, almost across the board, reported huge jumps in new orders in the first half of this year. Smaller builders are still hampered by lack of credit to build and therefore meet the demand. Construction loans nearly ground to a halt after the latest housing crash.
I wonder whether these smaller credit-constrained  homebuilders are quantitatively important in holding back aggregate construction expenditure? 
In any case, it certainly looks like things are looking brighter for the homebuilders. Toll Brothers, for example, is up around 100% over the past year. Have we turned the corner here? 

Update: 07 Sept 2012: Help Wanted: Auto Makers Revving up Engineering Jobs
As the auto industry rebounds in the U.S. it is creating a strong demand for engineers. In fact, one recruiter said the auto industry is seeking more than a thousand engineers.

The demand is so great, applicants often have multiple job offers and not just for jobs in the auto industry. 
“The demand is as strong as I have ever seen it,” said Andrew Watt, CEO of the recruiting firm iTalent. “There is a huge shortage and anyone you can find with auto engineer experience of any kind will get an interview and probably get a job right now.”

Sunday, September 2, 2012

Evil is the root of all money

For the love of money is the root of all evil.
1 Timothy 6:10

A basic question in the theory of money is "why does money exist?"  Or, put another way: where does the demand for money come from? 
The phenomenon of monetary exchange is so familiar to us that many may view the question ridiculous and/or the answer obvious. But if we stop and think about it, we'll discover that a surprising number of our everyday transactions are made without any reference to money at all. In particular, we regularly trade favors with family members, friends, and associates via implicit credit arrangements known as gift-giving economies. Indeed, the phenomenon seems quite prevalent in smaller (and more "primitive") communities throughout history. 

So if money is not necessary in transactions--even credit transactions--then why is it used? Monetary theorists have been asking this question for a long time. The standard answer to be found in virtually every undergraduate macro textbook is that "money solves the double coincidence problem."  That is, without money, trade is restricted to barter transactions. And because it is difficult to find a trading partner who happens to want precisely what you have to sell and vice versa (a double coincidence), barter exchange is inefficient. 

I want to argue here that this familiar story is all wrong. (John Quiggin offers a related critique here.) Up until recently, I used to think that a lack of double coincidence was necessary--but not sufficient--to rationalize the use of money. I now question whether a lack of double coincidence is necessary at all. 

What does seem fundamental to the question is a lack of commitment. Kiyotaki and Moore label this friction an evil (hence, their play on Timothy, which I borrow as the title of this post). But the basic insight, as far as I can tell, seems attributable to Doug Gale (The core of a monetary economy without trust). 

Before I proceed, I should take a moment to define what I mean by monetary exchange.  I define money to be an object that circulates as payment instrument across a sequence of spot exchanges. In the models I describe below, money takes the form of a perfectly divisible and portable income-generating asset. Equivalently, it takes the form of perfectly divisible, non-counterfeitable, and enforceable claims to an income-generating asset. It is not even important what form these claims take--they can be paper or book-entry objects, for example. The only requirement is that the claims constitute well-defined property rights (the same assumption is made by the fact of possession of a physical asset). 

Wicksell's triangle

Consider an economy consisting of 3 people, Adam, Betty, and Charlie. There are 3 time periods: morning, afternoon, and evening. There are 3 (time-dated and nonstorable) goods: morning-bread, afternoon-bread, and evening-bread. 

Each person is endowed with an asset--a bread-making machine. Adam's machine produces bread in the evening, Betty's machine produces bread in the morning, and Charlie's machine produces bread in the afternoon. 

While each person values their own production "a little bit," they value someone else's production "a lot more." In particular, Adam wants morning-bread (from Betty), Betty wants afternoon-bread (from Charlie), and Charlie wants evening-bread (from Adam).

This economy features a complete lack of double-coincidence. That is, for any pairing of individuals, there are no bilateral gains to trade. On the other hand, this economy features a triple-coincidence of wants: there are multilateral gains to trade. The efficient allocation has everyone getting the good the value highly, and disposing of the good they value less.

Notice that each person is in a position to issue an IOU promising a bread delivery at some specified date (morning, afternoon, or evening). 

Just to start things off, imagine that our group meet at the beginning of time (just before morning) to arrange their affairs. If everyone is perfectly trustworthy, then everyone can just promise to "do the right thing" and that's the end of the story. That is, if people can commit to their promises, then monetary trade is not necessary, despite the lack of double coincidence. 

Suppose instead that our group is not so trustworthy. Suppose Adam takes his morning delivery of bread and consumes it, but then refuses to make his promised night-delivery (consuming it for himself)? Well, in this case, our traders could agree to swap bread-machines at the beginning of time or--equivalently--swap securities (IOUs) representing clear titles to machines and their produce. (This latter type of exchange is what happens in an Arrow-Debreu securities market). In this case too, there is no role for an asset to circulate as a payment instrument.

O.K., let me now give the double-coincidence problem more bite by assuming that people meet sequentially and bilaterally over time. In particular, assume that Adam meets Betty in the morning, Betty meets Charlie in the afternoon, and then Charlie meets Adam in the evening. In each pairwise meeting, there are no gains to trade. But as long as people are committed to "doing the right thing," then this should pose no problem. In the absence of evil, money is not necessary.  

But what if the members of this society are not so trustworthy? Then Adam asks for Betty's morning bread, Betty will demand a quid-pro-quo exchange of property. The only thing Adam has to offer is his night-bread machine--something that Betty has absolutely no taste for. Nevertheless, she will take it as payment because she expects to be able to use it as money at a later date. Indeed, Charlie should be willing to make his afternoon delivery to Betty in exchange for the night-bread machine because Charlie wants to consume at night. Evil--the lack of commitment--is a problem that can be solved here by the institution of monetary exchange. (Technical note: money is the unique solution if allocations cannot be conditioned on individual trading histories.)

Conclusion: A lack of double coincidence problem is not sufficient to explain monetary exchange. A lack of commitment is necessary to explain monetary exchange. 

Monetary exchange with no double coincidence problem

My ideas about monetary exchange and the role of exchange media in general began to evolve after reading Gary Gorton's informative paper Slapped in the Face by the Invisible Hand (I recall telling Gary that getting slapped in the face by the visible hand was no less painful, but he only laughed). 

I was intrigued by Gorton's description of how the shadow banking sector worked hard to create high-grade assets (e.g., senior tranches of diversified pools of mortgage debt) that ended up playing an important role in the payments system. The activity looks a lot like standard banking, i.e., issuing a set of senior liabilities backed by a diversified portfolio of assets. In standard banking, these senior liabilities (whether in the form of banknotes or book-entry items) circulate as money. The shadow banking sector's liabilities seem to have "circulated" as collateral in repo markets. The stuff sort of looked like money. And yet, it did not seem to be solving any double coincidence problem. 

So here is my little model. There are only two people this time, Adam and Betty, but still 3 periods. Each person is in possession of two assets: a human capital asset, and some other asset (K) that produces some specialized product that only the original owner values. 

Assume that Adam is good at working in the afternoon and that Betty is good at working in the morning. Moreover, Adam wants a morning service, while Betty wants an afternoon service (so Adam is impatient, Betty is patient). Assume that the special asset K delivers output only in the evening for both parties.

The efficient trading pattern should be clear enough: Betty makes a morning delivery to Adam, Adam makes an afternoon delivery to Betty, and then both parties retire in the evening to consume the fruit of their special asset K. 

As before, if people could commit to their promises, then a credit market implements the efficient allocation: Adam borrows bread from Betty and pays her back in the afternoon. 

But what if people cannot be trusted to keep their promises? If I replaced "human capital" with the earlier bread machines, then a simple swap of bread machines would do the trick. But suppose it is impossible to transfer human capital in this way (indentured servitude is legally prohibited). What can be done?

Well, it would seem that one solution would be for Adam to use his special asset K to pay for his morning service. But why would Betty agree to such a transfer? After all, she does not attach an intrinsic value to Adam's special asset. 

The answer seems clear. Betty could use Adam's K asset as money in the afternoon. In particular, she could offer to return the asset to Adam in exchange for the afternoon service she desires. Adam should be amenable to such an exchange as he attaches an intrinsic value to this special asset. 

Conclusion: A lack of double coincidence of wants is not necessary to explain monetary exchange. A lack of commitment is necessary to explain monetary exchange. 

(Technical notes: the monetary object here cannot be playing any record-keeping role. Also, I realize that bilateral credit relationships can be sustained via the threat to suspend all future trade in the event of default. Understanding this does not diminish the role played by the special asset above--it can still be used to increase the threatened pain of default, thereby expanding the supply of credit.)

Relation to the repo market

Another way to implement the efficient allocation above is via a sale and repurchase agreement (repo) or, what amounts to be the same thing--a collateralized loan. 

Note that the fundamental role played by Adam's special asset is that of a hostage. Betty is saying "you better pay me back, or you'll never see your beautiful asset again!" 

And so, Adam and Betty might agree beforehand to a repo transaction: Betty agrees to buy the asset in the morning and resell back to Adam in the afternoon. Equivalently, Adam borrows a morning service using his special asset as collateral. In all of these transactions what is important is that property rights are transferred to Betty (the creditor). 

How these rights are most efficiently transferred would seem to dictate the method of payment--i.e., whether by quid pro quo exchange, a repo agreement, or as a collateralized credit arrangement. In all of these cases, the asset is playing the same economic role--it is being used to support an intertemporal credit arrangement in the absence of commitment. In this sense, we could legitimately label the asset an exchange medium, even if it is not literally circulating from hand-to-hand (it is circulating from account-to-account, however). 


A lack of double coincidence is neither necessary or sufficient to explain the demand for money. Evil appears to be the root of all money. The sermon is now concluded!

Friday, August 31, 2012

Is wage rigidity the problem?

Many economists claim that wage rigidity plays an important role in the (mis)allocation of resources in the labor market. Both "Keynesian" (Krugman) and "Monetarist" (Sumner) thinking emphasizes sticky nominal wages. "Labor Search" theories (Hall and Shimer) emphasize real wage stickiness; see here.

I've always been somewhat skeptical of these stories (note: Keynes himself did not emphasize stick wages in the GT--in fact, he argued that wage flexibility makes matters worse!).

My skepticism is fueled by stories like the one I read today: Majority of New Jobs Pay Lower Wages, Study Finds. An excerpt:
The report looked at 366 occupations tracked by the Labor Department and clumped them into three equal groups by wage, with each representing a third of American employment in 2008. The middle third — occupations in fields like construction, manufacturing and information, with median hourly wages of $13.84 to $21.13 — accounted for 60 percent of job losses from the beginning of 2008 to early 2010.  
The job market has turned around since then, but those fields have represented only 22 percent of total job growth. Higher-wage occupations — those with a median wage of $21.14 to $54.55 — represented 19 percent of job losses when employment was falling, and 20 percent of job gains when employment began growing again.  
Lower-wage occupations, with median hourly wages of $7.69 to $13.83, accounted for 21 percent of job losses during the retraction. Since employment started expanding, they have accounted for 58 percent of all job growth.
Seems to me that even if nominal wages appear to be sticky within occupational groups, there is a high degree of de facto flexibility via occupational choices (on both the supply and demand sides).
My gut feeling is that theories that rely on some "wage stickiness hypothesis" are barking up the wrong tree. The assumption of wage stickiness is often supported by appealing to the empirical evidence. But as I explain here, wages that appear to be sticky to an econometrician may not be sticky in any economically meaningful sense. And as the evidence above suggests, there seems to be much more wage flexibility out there than is commonly assumed. But I'm willing to listen to the other side of the story...

Wednesday, August 29, 2012

Kotlikoff Speaks Out

Laurence Kotlikoff
I haven't had much time to blog lately, but I thought I'd link up to this piece by Laurence Kotlikoff, which caught my eye: Economists Risk Labeling as Political Hacks. An excerpt:
Professional Rot 
The decision of the 500 U.S. economists, many from the leading ranks of the profession, to trade in their credentials as economists for that of campaign workers is just the latest sign that something’s rotten in economics. The documentary “Inside Job,” demonstrated how prominent economists failed to disclose, as standard ethics require, when they are being paid for their professional opinions. 
Then there is the increasingly nasty op-ed war pursued by political economists, such as Paul Krugman and Glenn Hubbard, who have so closely aligned themselves with one of the two parties that it’s impossible to know where their politics stop and their economic analyses begin. 
The worst part of all this is that the new political economics routinely diverges so far from economic theory and fact.
Agree? Disagree? (Please -- no mindless drivel -- I will delete) 

Sunday, July 29, 2012

The Microfoundations Windmill

Well done, Don Paul!
I can't help it. I just have to say something about  Paul Krugman's latest complaint (in a series of seemingly never-ending laments) concerning yet another "problem with the economics profession." See here: Making Ourselves Useless.

A well-aimed critique constitutes an important step in helping us understand things better. In this case, however, I think he is largely making things up--methinks our fair knight is chasing windmills.

Krugman begins by quoting Simon Wren-Lewis (who I happen to find quite sensible most of the time, just not in this case) in reference to the profession's alleged obsession with "microfoundations:"
If you think that only ‘modelling what you can microfound’ is so obviously wrong that it cannot possibly be defended, you obviously have never had a referee’s report which rejected your paper because one of your modelling choices had ‘no clear microfoundations’. One of the most depressing conversations I have is with bright young macroeconomists who say they would love to explore some interesting real world phenomenon, but will not do so because its microfoundations are unclear.
Oh, please. Papers are rejected all the time and for all sorts of reasons. That goes even for papers with microfoundations. And as for those "bright" young economists, they sound truly misguided. Not sure who's to blame for that, however. 

It is true that "microfoundations" are valued in the profession (and Wren-Lewis has several excellent pieces explaining why). But just what are these pesky "microfoundations," anyway?
A narrow view of  "microfoundations" is reflected in the idea that the methodology of microeconomic theory (specifying individual preferences, information sets, endowments, constraints, together with an equilibrium concept) can and should be brought to bear on macroeconomic questions. This is in contrast to an earlier methodology that specified and estimated behavioral relations at the aggregate level. (One can legitimately weigh the pros and cons of these (and other) methodologies.)

Not many macro models are "microfounded" in a pure sense. Almost all models make at least some assumptions that may be viewed as ad hoc and provisional (subject to further investigation). I think of an ad hoc assumption as a restriction on behavior that is inconsistent with other aspects of the model, like maximizing behavior.

To give an example, in most "microfounded" models of money there are ad hoc restrictions placed on the set of assets that might serve as exchange media. Consider a model with money and bonds. The modeler typically assumes that money is used to buy things and that bonds are not. While a "cash-in-advance constraint" of this sort may be descriptively accurate, it does not explain why bonds cannot be used to buy things. In short, liquidity is assumed and not derived. It is generally understood that shortcuts of this sort may matter for some questions and not for others. Understanding where and how these assumptions matter for the particular question at hand is part of the skill set that defines a good economist.

Sticky nominal wages is another popular example. Actually, in this case, I think it's rather worse. As I explain here, sticky nominal wages are likely only relevant if one adopts the questionable assumption that the labor market operates as a sequence of  anonymous spot markets.

Anonymity is a very bold assumption. In particular, it rules out the formation of relationships--something that most of us would recognize as being an important element of most labor market transactions. If the labor market works more like a marriage market, then spot wages (whether real or nominal) are inconsequential for resource allocation. What matters is the manner in which surplus is divided. And generally, there are many wages paths (real and nominal) that are equivalent to dividing the surplus in a particular manner. (This is something Barro (1977) pointed out long ago.)

So why do I mention this? Well, let's see what Krugman has to say:
And this [Lucas Critique] is fair enough. But what if you have an observed fact about the world — say, downward wage rigidity — that you can’t easily derive from first principles, but seems to be robust in practice? You might think that the right response is to operate on the provisional assumption that this relationship will continue to hold, rather than simply assume it away because it isn’t properly microfounded — and you’d be right, in my view. But the profession, at least in its academic wing, has largely chosen to take the opposite tack, insisting that if it isn’t microfounded — and with all i’s dotted and t’s crossed, no less — then it’s not publishable or, in the end, thinkable.
Can you spot what's wrong in that passage? No, it's not the first sentence--it's everything that follows.

First, I see a lot of other facts in the labor market that I might like to model, like the coexistence of large gross flows of workers into and out of employment--something, sticky nominal wage models frequently ignore. So maybe I want to ignore sticky nominal wages because I'd rather model worker flows--not because I can't "microfound" the phenomenon.

Second, and more important, it is clear that he is just making things up here. Why do I say this? Well, just take a look at one of the dominant paradigms in macroeconomic theory--the New Keynesian framework. As anyone who is familiar with the paradigm knows, it is built around models that embed ad hoc assumptions reflecting the alleged costs associated with nominal wage and price adjustments in auction-like settings. It seems to me, on the basis of this (and plenty other) evidence, that the profession cannot be obsessed with microfoundations in the way that Krugman suggests. On the whole, the profession is much more pragmatic than he makes it out to be.

By the way, I like to take a broader view of "microfoundations;" or, rather, the search for microfoundations. Microfoundations does not, in my mind, mean stopping at preferences and technology, or anywhere else, for that matter. It simply means seeking a deeper understanding. (My colleague, Arthur Robson, for example, is exploring the "microfoundations" of preference formation.) I certainly hope that this search for deeper understanding is not the "obsession" that Paul Krugman is concerned with.

What I find puzzling is that I'm pretty sure that the K-man knows all this. But if so, then what motivates his insatiable desire to tar-and-feather the profession as a whole in this manner? I find the following passage illuminating:
Now we’re having a crisis that makes perfect sense if you’re willing to accept some real-world behavior that doesn’t arise from intertemporal maximization, but none at all if you aren’t — and to a large extent the academic macroeconomics profession has absented itself from useful discussion.
Well, maybe not that illuminating. I mean, he can't literally believe this given that he has a paper with Gauti Eggertsson that makes use of use of intertemporal maximization that purports to explain recent events.

At root, I think the source of the man's bitterness toward the profession is that in his view, we are doing this stuff called "research" into questions for which we already know the answers (the answer is to increase G, something I partially agree with here). We are fiddling like Nero while the economy burns.

I would like to ask Krugman whether he believes there is anything left to learn about how an economy functions in the aftermath of a financial crisis. Is the profession wrong in devoting a good part of its time searching for a deeper understanding ("microfoundations") of how monetary and fiscal policies work using its best available tools? How would he rather we spend our professional time?

Or is the science now settled?

Sunday, June 24, 2012

NGDP Targeting in an OLG Model (Another Try)

I would like to follow up on my earlier post: NGDP Targeting in an OLG Model. The purpose of that post was to evaluate the desirability of an NGDP target policy within the context of an explicit (mathematical) macroeconomic model. Josh Hendrickson does a good job of explaining the motivation behind my approach here (and btw, thank you for the kind words, Josh.) Josh goes on to provide a list of reasons for why an NGDP target is a good policy prescription, but he does not really address the point I was trying to make with my simple model. And so, let me try again, this time in less technical terms.

First, let me describe the model economy I employed in my earlier post. The economy is populated by different types of people. At any point in time, there are people with relatively large wealth positions and high consumption propensities--and there are people with relatively small wealth positions who have high saving propensities. This is not a "representative agent" model economy: people are different--and these differences matter.

There are two types of assets in the economy, that I label "capital" and "money" (or government debt). I model capital as physical capital, but it should be clear that one may substitute any form of private investment in its place, including human capital investment, or recruiting investment (as would be the case for a labor-market search model). Capital investment is just a metaphor for any activity involving a sacrifice today for an uncertain return reward in the future. In the model, peoples' perceptions of this future reward (whether such perceptions are rational or not) are a key driver of investment demand (and hence, aggregate demand). Does this sound crazy? (I don't think so.)

The government money/debt plays an important role in this model economy. In particular, the competitive equilibrium turns out to be inefficient without it (there is a dynamic inefficiency). Of course, this does not mean that the government can print paper haphazardly. From a social welfare perspective, it will want to manage the supply of its paper in a particular way (that I will describe below).

There is a "sticky" nominal price in the economy: the nominal interest rate on government paper cannot be made contingent on any contemporaneous information (in particular, the expectations shocks that afflict investment demand). I imagine that one could also include nominal private debt (like mortgage debt), but it would not affect the qualitative results I report below. All other prices are flexible.

Now, let me describe how this economy behaves over time, assuming a "passive" government policy of keep the nominal supply of debt fixed.

There are two types of shocks: (1) a news-shock that affects investment demand (and so looks like an AD shock), and (2) a productivity shock that affects the ex post return on capital (and so looks like an AS shock).

Good news creates a rational optimism: investors revise upward their forecast over future returns to capital investment. Agents "dump" money/bonds and substitute in private securities. The money dump results in a surprise jump in the price-level. The real value of outstanding government debt declines. There is a redistribution of wealth from bondholders to investors.

The opposite happens when the news is bad (a productivity slowdown?). A sequence of bad news shocks results in a deflation. Capital spending contracts, and with it, future GDP. There is a redistribution of purchasing power away from investors toward bondholders that further depresses investment spending.

I claim that qualitatively, this model generates dynamics that most people would have a hard time distinguishing from the data. 

The optimal policy here turns out to be a price-level target (PLT). The role of the PLT here is to prevent variation in the real value of nominal debt that is not indexed to the price-level. Ex ante, agents want to avoid transfers of wealth stemming from uninsurable price-level shocks interacting with nominal debt.

So, if the news is bad, the government should increase the supply of money to accommodate the increase in demand for money (via the asset substitution induced by bad news over the expected return to investment). But if the news truly is fundamentally bad, the future real GDP should decline, and along with it, the NGDP should decline as well (it's decline is stemmed in part by maintaining the price level target). Stabilizing the NGDP in this context would mean increasing the price-level so high as to create a transfer of wealth from creditors to debtors (instead of debtors to creditors) --something these agents would have wanted to prevent ex ante if nominal debt could have been indexed to the price-level.

This was the gist of my argument. I was just curious to see what NGDP targeting advocates thought of it. What is missing in my model? Are frictions other than nominal debt required? I have a hard time seeing how the presence of sticky nominal wages or prices are going to alter my conclusion here. But who knows, maybe someone can tell me?

Note: If the expectation shocks I describe above are not rational (e.g., possibly psychological "animal spirits"), then obviously there is a role for NGDP (and RGDP) targeting. However, I don't really hear Scott Sumner and others making this claim (or do they?). 

Friday, June 15, 2012

European Bond Yields

It is a fascinating picture (h/t Frances Wooley at WCI):

Frances asks "what were they thinking?" It seems clear enough that with the introduction of the Euro, bond traders came to view the debt of several European sovereigns as very close substitutes--a perception that seems to have vanished since the beginning of the financial crisis.

The better question, as Frances points out, is why were they thinking that? Actually, the "they" in this question should probably be replaced with a more uncomfortable "we." Yes, what were we thinking--if we were thinking anything at all. (If you were thinking otherwise, I presume you were holding significant short positions throughout the episode?)

I remember what I was thinking when I was teaching my section on International Monetary Systems years ago. After discussing the benefits of a common currency (or multilateral fixed exchange rate agreement), I'd turn to the evidence and discuss why the experiment seems to have worked in some cases and not others. A recurring theme for success appeared to be (among other things) some notion of "fiscal coordination" among potentially disparate regions of the union. I came to view this conclusion as a "duh, kinda obvious" sort of lesson that any future monetary union would surely respect and deal with accordingly.

Oops. So maybe I was being unduly naive in this respect. But is it reasonable to suppose that agents managing large bond portfolios were equally naive?

Anyway, if you have an interesting take on the picture above, please comment below.

In the meantime, you may be interested in this piece by my colleagues Fernando Martin and Chris Waller: Sovereign Debt: A Modern Greek Tragedy, and by my colleague Silvio Contessi: An Application of Conventional Sovereign Debt Sustainability Analysis to the Current Debt Crisis.

And here's a piece by Ferguson and Roubini in Der Spiegel: This Time, Europe Really is on the Brink.

Interesting times...

Monday, June 4, 2012

NGDP targeting in an OLG model

I'm still trying to work through this NGDP targeting idea. A lot of people graciously replied to my earlier query here, including David Beckworth here (David links up to others who have also contributed their thoughts.)

So much material. So little time. I find myself reading, and then re-reading these replies, trying to absorb the arguments. As I continue to do so, I thought that I'd reciprocate with a gift of my own; something that people strongly in favor of NGDP targeting can mull over and reflect upon. I am going to approach things a little differently here, however. I want to present my argument within the context of a formal economic model, where the assumptions are laid bare. Along the way, I'll try to present the economic intuition as best I can.

Let me consider a simple OLG model. Before I begin I should like to say that if you have something against the OLG model relative to standard macro models, you should read Michael Woodford (1986). Woodford shows that the dynamics of debt-constrained economies can look a lot like OLG dynamics. So I could use the Woodford model in what I am about to say, but I stick to the OLG model because it is simpler and the economic intuition is the same.

An OLG Model

There is a constant population of 2-period-lived overlapping generations (and an initial old generation). All agents care only for consumption when old; in particular, the preferences for a date t agent are Etct+1 (expected future consumption).

The young are endowed with y units of output and they possess an investment technology such that kt units of output invested at date t yields zt+1f(kt) units of output at date t+1. Capital depreciates fully after it is used in production. The future productivity of capital is a random variable. There is another random variable nt that is useful for forecasting future productivity zt+1. Let z(nt) = E[zt+1 | nt] and assume that z(nt) is increasing in nt. I call nt "news", higher realizations of nt "good news," and lower realizations of nt "bad news." Assume that nt is an i.i.d. process.

Note that because there is no growth in this economy, the "natural" real rate of interest is zero.

There is a second asset in this economy in the form of interest-bearing government money/debt (I make no distinction here between money and bonds). Let Rt denote the gross nominal interest rate paid on the outstanding stock of government money/debt Mt-1.

Nominal debt is an important consideration for the arguments in favor of an NGDP target and so, I make the assumption here. In particular, I assume that the nominal burden of the debt RtMt-1 is not indexed to the price-level pt; see also, Champ and Freeman (1990). Because agents differ at a point in time with respect to their wealth portfolios, a surprise change in the price-level will induce unexpected wealth transfers.

The budget constraints for a representative young agent are given by:

when young: ptkt + mt = pty - ptTt
when old: pt+1ct+1 = pt+1zt+1f(kt) + Rt+1mt

So the young "work" to produce output y, pay taxes ptTt,  investment in capital kt, and money mt (from the old). When the young become old, they consume out of the returns from capital and money/bond investments (that is, they consume the returns to their capital and sell their money to the new generation of young for goods and services).

It turns out to be convenient to express things in "real" terms. To this end, define qt = mt/pt (real money balances) and Πt+1 = pt+1/pt (the gross inflation rate). The two equations above may now be combined and expressed as follows:

ct+1 = zt+1f(y - qt  - T) + (Rt+1 / Πt+1)qt

So, conditional on news n, a young person chooses his demand for real money balances q (and implicitly capital investment k) to maximize expected consumption (after-tax wealth, in this case). Since f(.) is increasing and strictly concave, the first-order condition describing money demand is:

z(nt)f ' ( y - q - T) = Rt+1 E[1 /Πt+1 | nt]

The equation above implicitly defines the aggregate demand for investment kt = y - qt. The RHS is the expected real interest rate. An increase in the expected real interest rate reduces investment demand. A good news shock increases investment demand (for any given expected real interest rate). Notice how a news shock looks like an aggregate demand shock (the aggregate demand for output rises with no contemporaneous increase in output). If you want, you can think of  the equation above as defining an IS curve, with y pinned down by exogenous factors (labor market clearing, in a neoclassical model). In short, I think this is all pretty conventional.

I consolidate the monetary and fiscal authority, so that the government budget constraint (GBC) is given by:

ptGt + (Rt - 1)Mt-1 = (Mt - Mt-1) + ptTt

The LHS is the sum of government purchases plus (net) interest on the debt; the RHS is new debt plus net tax revenue. In what follows, I assume G = 0 for all t.

Let Mt = μtMt-1 and rearrange the GBC as follows:

 (Rt -  μt )Mt-1 /pt  = Tt

Notice  here that a surprise increase in the price-level reduces the real burden of the debt.

Finally, impose the market-clearing conditions:

ptM t= qt for all t

which implies:

Πt+1  = μt+1qt/qt+1

Combine this with the FOC above to form:

(*) z(nt)f ' (y - q-Tt ) qt = Rt+1 E[ qt+1  /  μt+1  | nt]

Finally, we have: NGDPt = pt[ y + ztf(kt-1) ]

A Benchmark Policy

Set Rt = μt = 1 for all t, so that Tt = 0 for all t.

Notice that since n is i.i.d., we have E[ qt+1 | nt] = Q (some constant). Consequently, condition (*) may be written as:

z(nt)f ' (y - qt)qt = Q

Proposition 1: q is a decreasing function of nt.

The proof follows from the strict concavity of f(.), the fact that z(.) is increasing in  nt , and that Q is a constant. The intuition is as follows: Good news raises the expected return to capital formation--the demand for capital rises, and the demand for government money/debt falls. This is a strait forward portfolio reallocation effect. If the news is "bad" (a decline in  nt), then the demand for government securities rises -- this looks like a "flight to safety" event.

Consider a bad news event. There is a collapse in investment demand kt, and an increase in the demand for government securities qt. From the market-clearing condition, pt = M / qt. That is, the bad news event causes a surprise drop in the price-level (a sequence of such events would lead to a surprise deflation).

The surprise drop in the price-level leads to a surprise increase in the purchasing power of government securities. In this simple set up, the stock of government securities is held entirely by the old (the high propensity to consume agents) prior to the realization of the news shock. The young (the high propensity to invest agents) wish to acquire these securities as part of their wealth portfolios. The decline in the price level makes the real value of nominal government debt more expensive. In this way, bond holders are able to secure more labor power (y) from the young, so that fewer resources are now available for investment. The decline in capital spending leads to an expected decline in future NGDP (and RGDP). Note: I say expected because the future capital stock is lower; but future GDP may turn out to be higher or lower than expected depending on the realization of the productivity shock z.

Stabilizing the (expected) NGDP

It is possible here for the government to stabilize the expected NGDP path by conditioning the nominal interest rate on news (or, if the lower bound is a constraint, the same effect could be achieved by altering the expected inflation rate via money creation). The key is to stabilize capital spending; and the way to do this is to lower the nominal (hence real) interest rate on government securities. In this way, the decline in the price-level can be avoided. And NGDP remains elevated, despite the bad news, because capital spending is "subsidized" and the price-level remains stabilized.

But is stabilizing the NGDP path a desirable policy?

Well, it depends on what one means by "desirable." If you objective is to stabilize NGDP, then the answer is "yes." In terms of maximizing the expected utility of the representative young agent, however, the answer appears to be "no;" at least, not in this case. (Welfare calculations in heterogeneous agents economies, like this one, can be complicated--as is the case in reality.)

The intuition is this. When the news is bad concerning the future return to investment, it is optimal for investment to contract (and for savings to flow into more stable return vehicles, like government securities). To put it in more colloquial terms: the real rate of return on capital spending sucks (at least, in expectation). In fact, the real return would be less than the population growth rate -- the natural rate of interest in this economy.

Animal Spirits?

Implicit in a lot of discussions about the desirability of stabilization policy is the idea that the business cycle is inefficient. One way in which they may be inefficient is if expectations are prone to fluctuate purely for "psychological" (exogenous) reasons. In the context of the model developed above, we might instead assume that "news events" are instead just "animal spirits" that move expectations around for no particular reason. Assuming that policymakers are somehow immune to such effects, it would indeed be desirable to stabilize NGDP in this model.

Is this what proponents of NGDP targeting have in mind?  I have no idea as they rarely, if ever, are explicit about what they assume are the driving forces of the business cycle. All I mostly ever hear is a "negative AD shock," whatever that is supposed to be. (The two examples above, rational pessimism and irrational pessimism, both lead to a reduction in AD in some sense, for example.)

An Alternative Policy

Let me modify policy in a minor way; i.e., Rt = R > μt = μ = 1.

From the GBC above,  (Rt -  μt )Mt-1 /pt  = Tt, so that under this policy, the young are required to finance the carrying cost of the public debt.

It is easy to see that if the young must allocate more resources to service the debt, less resources will be available for capital spending. And a surprise decrease in the price-level now has two effects. First, there is the effect described above. Second, the real tax burden on the young must rise, if the government's nominal obligations are to be met.

Although I haven't fully worked it out, it seems to me that this second force constitutes a drag on capital spending that should be avoided, if possible. In particular, a better policy would apply the tax Tto the old, instead of the young.

So in this case, it seems that some policy designed to support the price-level (hence NGDP) might be desirable. Although, once again, if the information that leads agents to reduce capital expenditure is the best information available, then one would not want to stabilize NGDP perfectly.


The model presented above is highly abstract. Nevertheless, I think that it captures some forces that may presently be at work in real world economies. Pessimistic expectations over the future return to investment (whether via a productivity slowdown, as documented here, or through the rational--or irrational--expectation of a higher tax rate on investments) will act as a drag on the economy, and make competing savings vehicles, like US treasuries, relatively more attractive. The effect is deflationary and, to the extent that nominal debt is not indexed, there will be redistributive consequences.

Even though the model delivers a plausible interpretation of some recent macroeconomic developments, a NGDP target is not an obvious solution. But of course, as I said, the model is highly abstract. It is likely missing some features of the real world that NGDP target proponents think are important. If this is the case, then I'd like to hear what they are, and how these elements might be embedded in the model above. If nothing else, it would be a contribution to the debate if we could just get straight what assumptions we are making when stating strong propositions concerning the desirability of this or that policy.


There are still a lot of theoretical issues to resolve concerning the relative merits of different monetary policy rules, especially in the context of an open economy. One such paper that explores this question is: "What to Stabilize in the Open Economy" by Bencivenga, Huybens, and Smith (IER 2002). Among other things, the authors find a price-level target gives rise to an indeterminancy, and endogenous volatility driven by expectations.

Postscript June 15, 2012: Josh Hendrickson offers an extended comment here. Thanks to Josh for this; I will reply soon.