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

Saturday, December 28, 2013

The most obvious source of cyclical asymmetry is not a nominal rigidity

I've long been interested in the apparent cyclical asymmetry in business fluctuations. So it's nice to see Paul Krugman publicize the issue here: On the Asymmetry of Booms and Slumps. His post, in turn, was motivated this one, by Antonio Fatas: Four Missing Ingredients in Macroeconomic Models. Fatas writes:
1. The business cycle is not symmetric. Most macroeconomic models start with the idea that fluctuations are caused by a succession of events that are both positive and negative (on average they are equal to zero). Not only this is a wrong representation of economic shocks but it also leads to the perception that stabilization policy cannot do much. Interestingly, it was Milton Friedman who put forward the "plucking" model of business cycles as an alternative to the notion that fluctuations are symmetric. In Friedman's model output can only be below potential or maximum. If we were to rely on asymmetric models of the business cycle, our views on potential output and the natural rate of unemployment would be radically different. We would not be rewriting history to claim that in 2007 GDP was above potential in most OECD economies and we would not be arguing that the natural unemployment rate in Souther Europe is very close to its actual.
Let me dissect the passage above.

1. "The business cycle is not symmetric." Agreed.
2. "Most macro models assume a symmetric impulse mechanism." Agreed.
3. "Not only is this a wrong representations of economic shocks..."

Not sure what to make of this claim. I think it's alright to assume that the shocks are symmetric (unless there is compelling evidence to suggest otherwise). The asymmetry in question is more likely to be the byproduct of human interaction -- the economy's propagation mechanism.

4. "...but it also leads to the perception that stabilization policy cannot do much."

I'm also not sure what to make of this statement. We probably can't infer much about the desirability of policy interventions solely on the basis of the statistical properties of time-series data. And in any case, there are plenty of symmetric models suggesting beneficial policy interventions.

5. "If we were to rely on asymmetric models of the business cycle, our views on potential output and the NRU would be radically different."

Presumably, he means that our views would be more in line with Milton Friedman's plucking model. 

6. "We would not be rewriting history to claim that in 2007 GDP was above potential..."

I often hear people make this claim. Sometimes, they are the same people who claim that the last recession was caused by a bursting asset-price bubble -- of an overheated real estate sector -- of a booming construction (and related) sectors--and over-accumulated debt. According to Larry Summers, this was all needed to get the economy to potential (in this era of secular stagnation). 

In any case, on to Krugman's pet idea that asymmetry is explained by DNWR (downward nominal wage rigidity). Maybe there's something to this idea, but my own view is that any such effect is not likely to be very important. Why is this?

I've explained why before here, but let me summarize the argument here. I claim that economists who rely on sticky wage theories are unwitting slaves of Marshall's scissors--static supply and demand curves. If unemployment exists, it must be because reality does not correspond with scissor-intersection: markets do not clear.

But Marshall's scissors are meant to describe what happens in an anonymous spot market for goods like wheat or oil. The labor market is a market for relationships. Relationships are durable. Relationships are a form of capital. We have to move away from Marshall's scissors to understand these relationships (search theory is one way to do this). The economic surplus generated by a productive relationship is divided through a bilateral or multilateral bargaining process that specifies (among other things) how wages are to evolve through time over the life of the relationship. The spot wage (the wage that an econometrician might observe in a data set) plays no allocative role in the relationship. Stickiness in the spot wage does not matter.

That's the theory, anyway. But then, there is also some evidence: Evaluating the Economic Significance of Downward Nominal Wage Rigidity (Michael Elsby) and here: The Effect of Implicit Contracts on the Movement of Wages over the Business Cycle (Beaudry and DiNardo).

Well then, if not a nominal rigidity, what might account for the asymmetry in the unemployment rate?

As it turns out, the sharp rise in unemployment followed by a slow decline follows as a natural property of labor market search models, something that I showed here (the example I alluded to above).

The basic idea is very simple. As I explained above, the labor market is a market for productive relationships. It takes time to build up relationship capital. It takes no time at all to destroy relationship capital. (It takes time to build a nice sandcastle, but an instant for some jerk to kick it down.)

We see the same sort of phenomenon in population dynamics--the so-called "heat wave effect." That is, mortality rates spike up during a spell of bad weather, causing a sudden decline in the population. There is no corresponding spike up in the population during a spell of good weather for obvious reasons (unless you believe in zombies returning suddenly to life).


PS. Some related papers where a shock destroys (reshuffles) match capital and takes time to recover: Adaptive Capital, Information Depreciation, and Schumpeterian Growth (Jones and Newman) and Distributional Dynamics Following a Technological Revolution (Andolfatto and Smith). 

Tuesday, December 24, 2013

In gold we trust?

I've written before that a desirable property of a monetary instrument is for it to hold its value over short periods of time (See: Why Gold and Bitcoin Make Lousy Money).

In other words, a good monetary instrument should have a stable short-run rate of return. If I earn some money today, I don't want to see its value decline by 50% tomorrow. If I spend a dollar today, I don't want to see its value rise by 50% tomorrow. Even if these fluctuations cancelled out in the long run, it would be terribly inconvenient and annoying. I'd rather live in a world where my money lost value at a slow but steady rate. Of course, I would not want to store my wealth in the form of such an instrument. But that's not how we store wealth anyway. To store wealth, we can always sell the money we do not need for transaction purposes and purchase other securities.

Now let's take a look at some data -- the type of data Ron Paul likes to use. Let p(t) denote the price-level at date t (I will use the consumer price index). Then 1/p(t) measures the purchasing power of money. If p(t) rises over time (inflation), the purchasing power of money falls over time. And so we have this familiar picture:

I've written about this before here: Ron Paul's Money Illusion.

Now, we can perform the same sort of exercise for gold. Let q(t) denote the USD price of gold at date t. Then the purchasing power of gold is measured by q(t)/p(t). So, if the price of gold rises as fast as the price level, the purchasing power of gold remains constant. If the former rises faster than the latter, then the purchasing power of gold is rising; and vice-versa.

We know that over very long horizons, the rate of return on gold exceeds that of money. But all this says is that gold is a better store of value than cash over long periods of time. (I discuss here whether gold is a good store of value relative to other assets.). How has the purchasing power of gold held up over the last little while?

Here is the purchasing power of gold vs the USD since the beginning of the year:

OK, so this past year was not a good one for gold. If you had earned your wages in gold at the beginning of the year, that gold would now buy you 25% less bread. That's like a tax. And it was not the Fed doing it to you. In fact, if you had instead held on to your USD over same period of time, you would have experienced a much smaller decline in purchasing power.

What if we look at the past 2 years? Here is the picture:

What we see from the picture above is that the purchasing power of gold held up with that of the USD in 2012, but that its short-run rate of return was more volatile. It's rate of return then fell down a  steep hill in 2013.

Let's go back 3 years now:

Gold can't even beat the rate of return on cash over a three-year horizon? That's pretty sad for a store of value.

The main lesson I take away from this is not that people shouldn't invest in gold. By all means, go ahead and invest in all sorts of stuff, including gold. The main lesson is that commodity prices tend to be highly volatile over short periods of time and that this short-run volatility makes them undesirable as payment instruments. There is a better alternative available, and the United States has it in the form of the Federal Reserve.

Happy 100th birthday, Fed!

And a Merry Christmas to all.

PS. My colleague Christian Zimmermann points me to this potentially interesting paper: The Gold Dilemma by Claude Erb and Campbell Harvey.

Saturday, December 14, 2013

Labor Force Participation Gaps (U.S. vs. Canada)

This post is meant as a complement to my earlier posts: [1] Employment Gaps, [2] Employment Slumps in Canada and the U.S., and [3] U.S. Labor Force on Trend?

In what follows, I report the labor force participation rates (LPRs) for Canada and the U.S., for males and females, and across various age groups (1976-2013). Let's take a look first at  prime-age males and females.

To the extent that one can consider the Canadian LPR a measure of a common trend (the Canadian recession being less severe than in the U.S.), one might be able to support the idea of a 1-2ppt LPR "gap" for the U.S. 

The behavior of prime-age females across the two countries appears quite similar up until the mid-to-late 1990s. The divergence since then has been quite remarkable. (Has anyone heard of any explanation for why this might be the case?)

Here we have teen-aged males and females. In both cases, we see big gaps emerging some time around 2000.

Next we have young males and females. 

And finally, older males and females:

Any comments or suggested references that speak to these patterns would be appreciated. 

Thursday, December 12, 2013

U.S. Labor Force Participation Rate on Trend?

The labor force participation rate (LPR) is defined as the share of the civilian noninstitutionalized that is employed (working) or unemployed (looking for work). In 1970, the U.S. LPR was about 60%. It rose steadily for 30 years, reaching peak of 67.1% in 2000. It has been declining since that time, dropping sharply in the recent recession, and currently sits at around 63%.
Question: How much of the recent decline in LPR is due to a bad economy (cyclical factors)? And how much of it might be due to long-term trends associated with changing demographics (structural factors)?

The answer to this question is important for policy because a cyclical interpretation suggests the presence of an undesirable "output gap," whereas a structural interpretation does not.

Christopher Erceg and Andrew Levin have a new paper out which suggests that cyclical factors are responsible (Labor Force Participation and Monetary Policy in the Wake of the Great Recession). Much of their estimate of LPR trend, however, seems to be based on a particular BLS projection. On pages 9-10, they state:
In our view, the labor force projections published by the BLS in November 2007 serve as an invaluable resource in assessing the influence of demographic factors on the subsequent decline in the LFPR. In making such projections, BLS sta¤ consider detailed demographic groups using state-of-the-art statistical procedures in conjunction with micro data from the Current Population Survey (CPS) and various other sources, including interim updates from the U.S. Census Bureau.
But as the following figure demonstrates, BLS projections of trend LPR seem to vary quite a bit over time:

The figure above is drawn from
A Closer Look at the Decline in the Labor Force Participation Rate (Maria Canon, Peter Debbaut, and Marianna Kudlyak). The authors state:
It is tempting to interpret the prerecession projections as reflecting the long-term trend in the LFP rate. However, we observed that the BLS's projections did not necessarily capture the long-term trend; rather, to a substantial degree, they were influenced by the most recent data points. Consequently, this cautions against treating the difference between the actual LFP in 2012 and its BLS projection released in 2007 as entirely due to cyclical factors.
[Note: Erceg and Levin do not rely solely on BLS measures of trend LPR. Much of their empirical work is based on state-level differences in labor market variables.]

It is of some interest to note that this is not the first time policymakers have been interested in the cyclical vs. structural decomposition of LPR. The same questions were being asked nearly a decade ago following a much milder recession (and jobless recovery).

In 2006, economists Stephanie Aaraonson, Bruce Fallick, Andrew Figura, Jonathan Pingle, and William Waacher published this interesting study: The Recent Decline in the Labor Force Participation Rate and Its Implications for Potential Supply.

The authors use a cohort-based model to estimate LPR trend. They state their conclusions as follows:
On balance, the results suggest that most of the decline in the participation rate during and immediately following the 2001 recession was a response to business cycle developments. However, the continued decline in participation in subsequent years and the absence of a significant rebound in 2005 appear to derive from other, more structural factors. Indeed, the participation rate at the end of 2005 was close to our model-based estimate of its longer-run trend level, suggesting that the current state of the labor market is roughly neutral for the participation rate. Finally, projections from the model suggest that many of these structural factors will continue to put downward pressure on the participation rate for some time, so that any future cyclical fluctuations in participation will take place around a declining trend.
The most remarkable picture they produce is, in my view, their Figure 12 (pg. 111):

Their 2006 forecast of the U.S. LPR for 2013 was 63%. Not bad.

Sunday, December 1, 2013

Is QE lowering the rate of inflation?

The answer may be "yes," according to a new paper by Steve Williamson. In examining the effects of a QE experiment in his model economy, he reports the following (p. 16):
Some of the effects here are unconventional. While the decline in nominal bond yields looks like the "monetary easing" associated with an open market purchase, the reduction in real bond yields that comes with this is permanent, and the inflation rate declines permanently. Conventionally-studied channels for monetary easing typically work through temporary declines in real interest rates and increases in the inflation rate. What is going on here? The change in monetary policy that occurs here is a permanent increase in the size of the central bank's holdings of short-maturity government debt - in real terms - which must be balanced by an increase in the real quantity of currency held by the public. To induce people to hold more currency, its return must rise, so the inflation rate must fall. In turn, this produces a negative Fisher effect on nominal bond yields, and real rates fall because of a decline in the quantity of eligible collateral outstanding, i.e. short maturity debt has been transferred from the private sector to the central bank.

Williamson describes these findings on his blog here: Liquidity Premia and the Monetary Policy Trap

Well, it must have been a slow news day on the economics front. The normally mild-mannered Nick Rowe set off a tempest in a teapot when he wondered out loud what "went the hell went wrong with the best and brightest in the profession?"  Nick's little tirade was then picked up by the charming duo of Brad DeLong and Paul Krugman

So what happened? It all started out by Williamson discussing two "fearsome equations" that emerge as theoretical restrictions in a wide class of macroeconomic models. Some people call these restrictions "Fisher equations." I like to think of them as no-arbitrage-conditions.

Let's make some assumptions. There is no uncertainty. We are (the model economy is) in a state-state, so that output grows at the gross rate G. The level of output may be above or below its "natural" level (the level that would prevail if all frictions were absent). Let B denote the discount factor. Absent all frictions, the "natural" rate of interest is given by (G/B).

Let P denote the gross rate of inflation. There are two nominal assets, a bond that yields a gross nominal return R >= 1, and money, which yields a gross nominal return equal to 1. Money is assumed to be more liquid than bonds (bonds cannot be used in a subset of transactions).

The "Fisher equations" that emerge from the model can be written as follows:

[1] R*K = (G/B)*P and [2] 1*L = (G/B)*P

where K and L denote "liquidity premia." In most models, K=1. In this case, the two equations above imply R = L. That is, the liquidity premium on money is equal to the nominal interest rate.

In the "newmonetarist" models that Steve studies, assets apart from money may serve in some manner as exchange media. If financial markets do not work perfectly well (say, because of limited commitment and asymmetric information frictions), then the supply of exchange media may be "scarce." In the present context, this implies K>1, and equations [1] and [2] imply: R*K = L.

The traditional Friedman rule policy implies R = 1, K = L =1, so that P = (B/G). But Steve is assuming the government does not have enough instruments to implement the Friedman rule. In fact, he makes a distinction between the monetary and fiscal authorities. And, as he stresses in his paper (not his blog post), a lot hinges on exactly how one models this relationship.

One scenario that emerges in Steve's model is R =1 and K = L > 1. In this case, the economy is at the ZLB, but government liabilities (cash and bonds -- they are perfect substitutes in this case) exhibit a liquidity premium. On open market operation of cash for bonds in this case has absolutely no effect -- this is the classic liquidity trap -- something that Krugman stressed long ago. From [1] and [2], the equilibrium inflation rate is given by P = (B/G). The equilibrium real rate of interest on government liabilities is 1/P = G/(B*L), which is less than the "natural" real rate of interest (G/B). This is the sense in which the real rate of interest is "too low." (Of course, if you have a different theory of the way the world works, you may be thinking that the real rate of interest is "too high"--but I'm not here to talk about that theory.)

Suppose that the bond we are talking about above is a short-maturity instrument. Imagine that the fiscal authority also issues a long-maturity instrument. Moreover, assume that this long-bond is less liquid than the short-bond (the short-bond is, in present circumstances, viewed as a perfect substitute for cash). Steve then asks what the model implies when the open market operation consists of a swap of cash for the long-bond. In this case, not surprisingly, QE matters. But how does it matter?

The effect of this policy in Williamson's model is to lower the nominal interest rate at the long end of the term structure. Because the Fed is sucking out relatively less liquid assets and replacing them with relatively liquid assets, liquidity premia decline (as one would expect). So, if we take a look at equation [2], we see that the model implies that inflation must decline: P = (B*L)/G. What is the economic intuitions for this? Evidently, one of the effects of QE (in the model) is to increase the real stock of currency held by the private sector, and agents require an increase in currency's rate of return (a fall in the inflation rate) to induce them to hold more currency. (Remember that the results are all contingent on the way monetary and fiscal policy are modeled.)

So this is kind of interesting for a couple of reasons. First, the model offers an explanation for why we do not observe deflation, given that we are at the ZLB (a bit of a puzzle, for conventional theory.) Second, it offers an explanation for how QE may be putting downward pressure on inflation. How quantitatively important these effects are relative to others remains an open question.
Krugman and DeLong seem to want to argue that Williamson's results are "incorrect" because the model equilibrium he is focusing on is "unstable." I'm pretty sure I know where they're coming from, but I'm not sure that the criticism applies here.

First, to demonstrate the "stability properties" on an equilibrium, one actually has to go and work out the math. I think it's fair to say that nobody has done that.

Second, what Krugman writes in his "Little Arrows" post is correct, but it is correct only in the context of a particular theory. As I've mentioned before, Peter Howitt demonstrates here how pegging the nominal interest rate is unstable under a wide class of algorithms that govern the manner in which inflation expectations are formed (essentially, adaptive expectations). This led Howitt to argue that stability required a policy to raise interest rates more than one-for-one with inflation expectations. Hence, Howitt came up with the "Taylor principle" before Taylor did.

It is interesting to note, however, that the "stability properties" induced by the Taylor principle in standard New Keynesian models (which embed rational expectations) is something very different. At the opposite extreme, one might take the view that inflation expectations are formed in a manner described here, by Stephanie Schmitt-Grohe and Martin Uribe. Let me reproduce the diagram I used in that blog post here:

As you can see, it is identical to Krugman's "Little Arrows" diagram. The one big difference here is that--under this particular theory of expectations formation--rational expectations--A is unstable and B is stable. So the "little arrows" run in the opposite direction here.

The little circle in the picture above demonstrates how the New Keynesians use the "Taylor principle." Essentially, they restrict attention to trajectories around the steady state point A that never leave that circle. If the Fed follows the Taylor principle, then there is only one point that satisfies this property, and it is point A. Viola-we say that point A is "locally stable" (Yes, I know it sounds weird, but I'm just reporting the facts.) In their Perils of Taylor Rules, Benhabib, Schmitt-Grohe, and Uribe argue that only point B (the liquidity trap) is globally stable. (The fact that Japan has spent decades around a point like B suggests that it may in fact be stable.)

The other thing I'd like to add is that Williamson's results continue to hold even away from the ZLB. So, Krugman's post in particular, which focuses on the properties of Taylor rules (absent in Williamson's model) seems a little off target.

So my interpretation of the criticisms I am hearing of Williamson's paper is that his critics are claiming that he is wrong because his results are inconsistent with the type of models these people are used to working with. It seems to me that the critics should have instead attacked his results and interpretations with empirical facts (or am I too old-fashioned in this regard?). After all, Williamson at least motivated his post with some data (the diagram at the top of this post). And he makes what is potentially a testable prediction (notice the if-then structure of the statement):
In general, if we think that inflation is being driven by the liquidity premium on government debt at the zero lower bound, then if the Fed keeps the interest rate on reserves where it is for an extended period of time, we should expect less inflation rather than more.
I have a little more difficulty in understanding Nick Rowe's objection. Certainly, a part of it seems to be what I just described above. Partly, I think that Nick is disagreeing not with Williamson's model, but with the way Williamson seems to run off at the end of his post with his "the Fed is in a trap" ideas.

And so, this now leads me to my own criticism of Williamson's post.

I wish he had spent a little more time elaborating on this statement he makes:
But the power of monetary policy to mitigate the inefficiency is limited. Basically, it's a fiscal problem. The U.S. government could issue more debt, by temporarily running a higher deficit. But that's not happening, so what can the central bank do about it?
It's a fiscal problem (well, the fundamental problem is limited commitment and asymmetric information in these models). The Treasury could alleviate the "asset shortage" by expanding the supply of Treasury debt! I discussed this idea here some time ago: Not Enough Debt? So isn't this nice? Different models, but similar policy conclusions. Implicitly, Williamson is taking the view that political constraints are preventing this from happening, so let's move on to study Fed policy.

The tone of his post near the end strikes me as odd. He seems rather critical of the way Fed economists generally think about the way monetary policy works. Fair enough. On the other hand, if we read his paper we find the following statement:
QE is a good thing, as purchases of long-maturity government debt by the central bank will always increase the value of the stock of collateralizable wealth.
That is, QE is a good thing in his model economy. In fact, I think his model suggests that the Fed should buy up all outstanding treasury debt (but that even that would not be enough because the problem is the limited supply of the stuff).

So what's his problem? Well, it seems that conventional Fed thinking is that QE is inflationary and, well, as Williamson's paper shows, it may have the opposite effect. O.K., well, so what?

Then Williamson remarks that if the Fed really wants inflation, it should raise its policy rate (IOER). This, of course, is the statement that drew all sorts of criticism when Narayana Kocherlakota suggested something similar a few years back (thanks to Nick Rowe for once again starting that one). Williamson believes that raising the policy rate would be disruptive in the short-run, but that this is the way to achieve higher inflation in the long-run. I am not sure, however, whether his model suggests that higher inflation is a good thing (I don't think so.) These are all positive (not normative) statements.

So, the Fed is "stuck." That is, the Fed seems compelled to continue QE and keep the IOER at 0.25%. Williamson's model seems to suggest this is a good thing. But his model also suggests that the policy is ultimately deflationary (perceived to be a bad thing). The only way to prevent this trajectory is to raise the IOER (another way would be to expand the supply of treasury debt). But doing so will cause a recession because of monetary non-neutralities.

Not sure what any of this has to do with eating more crow though. What would the Fed be doing differently if they took this view? Not much, as far as I can see.