Stochastic Dynamic Inefficiency, Secular Stagnation, and the Natural Discounted Growth Rate

(I could have put a "wonkish" warning at the top, but come on, just look at the title!)

Let's start with the concept of the natural real interest rate, which is already ubiquitous. The real interest-rate is the interest rate corrected for expected inflation, and the natural real interest rate is the real interest rate consistent with price stability.  (I leave the definition of price stability ambiguous because it depends on your theory of the price level and inflation, which is a whole 'nother blog post.)

Now market monetarists like Scott Sumner and Nick Rowe point to a deficiency in the natural real interest rate concept: the natural real interest rate depends on the expected real growth rate. And monetary policy affects the expected real growth rate, so if policymakers try to set the actual interest rate equal to the natural rate, they are chasing a moving target. To me, this criticism suggests that the appropriate approach is to adjust the nominal interest rate not for expected inflation but for expected nominal growth. (While we're at it, we can also replace "price stability" with "nominal growth stability" and be done with our futile attempts to measure the aggregate price level.)

Most economists think that the natural real interest rate is normally positive. I have my doubts, but never mind, because I'm ditching the whole concept. Once we start correcting for expected normal growth rather than expected inflation, we are clearly not dealing with a natural rate concept that can be presumed to be normally positive.  If we are talking about a risk-free interest rate, then the need for physical capital returns to compensate for risk would make it very hard to achieve a long-run growth rate [an equilibrium with the interest rate] as high as the [growth] interest rate, let alone higher. To come up with a number that's usually positive, I suggest that we reverse the sign. Instead of talking about a "natural growth-adjusted interest rate," let's talk about a "natural discounted growth rate."

We can also talk about an "actual discounted expected growth rate."  (The discount is "actual," determined by the observable interest rate, but the associated growth rate is only "expected" because it is not known with any confidence when the interest rate is set.) If the actual rate equals the natural rate, you get a normal employment level and nominal income growth stability (or price stability, if you insist). If the actual rate is higher, you get accelerating inflation. If the natural rate is higher, you get depressed economic conditions, with excess unemployment and deflationary pressure, if not actual deflation. (Wicksellians, please recall that I have reversed the signs compared to the usual natural rate theory.)

Now that I've defined the natural discounted growth rate, I can define "secular stagnation" in the context of an NGDP target. Secular stagnation means that the natural discounted growth rate exceeds the growth rate of the NGDP target path.  In other words, the target path would require a negative nominal interest rate.  Under a level targeting regime, an attempt to pursue such a path will result in either monetary instrument instability or a "zigzag" growth pattern in which recessions alternate with inflationary catch-up periods. Under a growth rate targeting regime, you'll just keep missing the target from below, much like most of the developed world's central banks today. 

But if you play with the numbers, you can probably convince yourself that secular stagnation, by my definition, seems unlikely. A reasonable NGDP target path growth rate is maybe 5%.  Do we really think that the potential growth rate exceeds the natural interest rate by more than five percentage points? It's remotely conceivable, but my guess would be that our problem today is not secular stagnation (in this sense) but a flawed monetary policy regime.

Now if the target nominal growth rate (and the associated possibility of secular stagnation) is one of our bookends for the natural discounted growth rate, the other bookend is pretty clear: it's zero. Some readers will immediately recognize zero as the criterion for dynamic efficiency. Ignoring the issue of risk for a moment, an economy with a strictly positive natural discounted growth rate would be dynamically inefficient. Overall welfare could be improved by instituting a stable Ponzi scheme that transfers consumption backward across generations.

Does my assertion that the natural discounted growth rate is almost certainly strictly positive imply that we actually live in a dynamically inefficient economy? In an important sense, I think it does.  The thorny issue here is risk, and some will argue that the relevant interest rate for dynamic inefficiency is not the risk-free rate.  But I disagree.  The US government can produce assets that are considered virtually risk free, and a stable Ponzi scheme operated by the US government could presumably produce such assets yielding any amount up to the growth rate.  At today’s Treasury interest rates, which are clearly less than expected growth rates, marginal investors are (we can presume, since the assets are freely traded) indifferent between these low-yielding Treasury securities and investments that represent newly created capital.  So, given the risk preferences of the marginal investor, the government could, by operating a stable Ponzi scheme, be producing assets that have a higher risk-adjusted return than newly created capital.  Given the risk preferences of the marginal investor, it’s inefficient for the government not to be producing such assets.

It’s important to recognize that, under a typical scenario, the marginal investor will end up worse off, in a material sense, from earning the growth rate, compared to earning the actual return on capital.  In a material sense, the economy is dynamically efficient.  But the concept of risk preferences models a subjective good – call it “security” – and we’re not producing enough of this good.  The history of interest rates and growth rates suggests that we have seldom produced enough security, but the deficiency today is clearly worse than usual.  

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product. 

Taper Paradox

Suppose you get invited to a party.  You don’t expect it to be a very good party, because the mood in town is pretty bleak:  most people likely won’t even show up, and those that do won’t be much fun.  So you decide, “Unless I hear something good about this party, I’m just going to stay home.”  

Then you get a call from a friend who is at the party, and he convinces you that it’s better than expected and you should come.  You assure him you’ll be there.  So you start getting ready, but you’re still in no hurry to get to the party.  

Then you get a call from the host:  “Joe tells me you’re coming.  That’s great.  Can I ask you a huge favor?  If you have some rum, can you bring it?  The party is starting to get lively, but we’re going to run out of rum soon, and the liquor stores are closed.  If someone doesn’t bring some rum, we may have to take away the punch bowl earlier than expected.”  You don’t have any rum, unfortunately, but you know you can get to the party quickly if you hurry.  Assuming you like rum punch, does the knowledge that the punch bowl might be taken away early make you more or less eager to get to the party quickly?

I may have strained the traditional punch bowl metaphor here, so let me try to tell the more complicated story in economic terms.  According to some theories, national economies (and the world economy, perhaps) exhibit multiple equilibria.  If everyone expects everyone else to spend a lot, then it’s rational to spend a lot (e.g. buy a new car in anticipation of keeping or getting a job, build a factory in anticipation of selling a lot of output, etc.).  If everyone expects everyone else not to spend a lot, then it’s not rational to spend a lot.  So depression and recovery become alternative self-fulfilling prophecies.  As FDR famously put it, “The only thing we have to fear is fear itself.”

Normally, though, at least from the period from 1940 to 2007 in the US, fear itself isn’t a real problem.  Why not?  Because these equilibria depend on the interest rate, and the Fed controls the interest rate (at least in the short run), and usually the Fed can make the interest rate so low that the “bad,” low-demand equilibrium is no longer feasible.  A lot of projects that normally wouldn’t be worth doing (or purchases that wouldn’t be worth making) when demand is weak, become worthwhile even with low demand when they can be financed very cheaply.   But if people do these projects and make these purchases, demand won’t be weak.  So if the Fed keeps interest rates low enough, or even just credibly threatens to keep interest rates low enough, the low-demand equilibrium reduces itself to absurdity.

But recently we have faced the problem that interest rates can’t go below zero.  So we are back in FDR’s “fear itself” world, with multiple feasible equilibria.  In the low-demand equilibrium, the Fed struggles by keeping interest rates as low as it can get them, but that isn’t enough.  Barring more aggressively creative policies than the Fed has been willing to implement (retroactive NGDP level path targeting, anyone?), it just has to wait until people get more optimistic.  Or until people expect other people to get more optimistic.  Or until people expect other people to expect other people to get more optimistic.  Or until…well, you get the idea.  There’s reason to expect this optimism to come eventually, because capital depreciates (e.g. cars wear out, a growing population needs new places to live, etc.), so there will eventually be reason to expect higher demand.  But, as the Japanese have learned, the wait can be a very long one.

There’s a trick here, if you’re a prescient investor/entrepreneur.  Someday the demand will be back.   Someday the optimism will be back.  And the Fed will no longer have to struggle by keeping interest rates at levels that seem ridiculously low but still aren’t low enough.  But right now interest rates are still very low.  Suppose you could guess when the economy was about to recover and finance a project at the low “bad equilibrium” interest rates while subsequently benefitting from the demand that will come when the economy recovers.  You’d stand to make a lot of money.

So if, for whatever reason – even if it’s for no real reason at all – there’s a shift toward optimism, it’s like yelling fire in a crowded theater.  (If you don’t like my “punch bowl” cliché, I have plenty of others.)  Everyone wants to be that prescient investor/entrepreneur who finances cheaply in the bad equilibrium and gets windfall demand in the good equilibrium.  Once you make your mind up to go to the party, you want to make damn sure you get there before the punch runs out.  As we say in wonkspeak, systems with multiple equilibria often exhibit highly nonlinear dynamics.  There is a tipping point, a straw that breaks the camel’s back.  (Really, plenty of others.)

What happens, then, when the Fed starts to talk about tapering its bond purchases?  It depends.  If we take the camel’s back to represent economic depression, there are (at least) three possibilities.  If the camel’s back is already clearly broken, the tapering talk should already have been anticipated, and it will have little effect.  If the camel’s back is still strong, then the tapering talk will make it even stronger, fortifying the depression against the already ineffectual straws of optimism.  But suppose the camel’s back is just in the process of breaking: some people have concluded that it’s definitely not going to hold, some are getting very close to that conclusion, and some still need convincing.  What happens then?

I’m pretty sure it’s ambiguous, depends on how you set up and calibrate the model, etc..  I imagine someone has tried to model this formally, but I’m too lazy for that (and being a private sector economist, rather than an academic, I don’t get paid to do theoretical modeling).  In any case, it seems quite plausible to me that, under reasonable conditions that may approximate those we have faced over the past month, tapering talk could accelerate the shift from the bad equilibrium to the good one.  That acceleration would be consistent with the observation that the dramatic moves in the bond market have had only a little apparent impact on the stock market.  (If people are discounting the same cash flows at a much higher discount rate, stock prices should have gone down considerably, but they’ve barely declined at all, which suggests that expected cash flows have risen.)

Note that tapering talk implies that (1) the Fed, which may have better information than we do, is more optimistic than we thought and (2) if you were nearly convinced that the depression is over, you had to make up your mind and act on your belief as quickly as possible, or you would lose the opportunity to profit from it.  Given the existence of multiple equilibria, it’s quite possible that the Fed’s tapering talk has had the paradoxical effect of accelerating the recovery, which would explain why markets now seem to expect the Fed to start raising short-term rates sooner than the Fed itself has implied.

Do I think the Fed did the right thing by strategically engaging in verbal tightening at just the time that it would have a paradoxical effect?  No.  For one thing, the Fed obviously didn’t anticipate this response, and in any case the interpretation I’ve suggested here is highly speculative.  And even if my interpretation is right, and even if the Fed is cleverer than we think and actually intended it this way, I still don’t think they did the right thing.  Accelerating the recovery is a good thing, all other things equal, but it’s not the most important thing.  The most important thing is for the Fed to assure us, in no uncertain terms, that it will continue to support the recovery until there is no ambiguity left.  My guess is that, given what I imagine the Fed’s preferences to be, starting to tighten (verbally) now will turn out to have been the right thing to do.  But my guess, even if it is the best guess based on the information I have, is subject to a lot of uncertainty.  From the point of view of the recovery, mentioning the taper last week was a risky move, and even if the risk pays off, I don’t think it’s a risk the Fed should have taken.

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product. 

Why Doves Are Really Hawks

Machismo is a type of commitment mechanism. 

If you’re a perfectly rational nerd, people will always expect you to do the rational thing.  You won’t be able to make credible threats unless it would be rational to carry out the threat.  And it seldom will be.  After all, how often is it really rational to whoop someone’s ass?

On the other hand, if you’re a tough, macho badass, people will always expect you to do the tough, macho badass thing.  You’ll always be able to make credible threats, because carrying out threats is always the tough, macho badass thing to do.  And since the threats are credible, you mostly won’t have occasion to carry them out.

This principle has a traditional application to monetary policy.  If your central banker is a perfectly rational nerd, he’s going to let the inflation rate get too high, because he won’t be able to make a credible threat to cause a recession.  People won’t expect him to carry out the threat, because in most cases it won’t be rational to carry out the threat.  After all, how often is it really rational to cause a recession?

On the other hand, if your central banker is a tough, macho badass, he’s not going to let the inflation rate get too high, because he will be able to make a credible threat to cause a recession.  People will expect him to carry out the threat, because causing a recession is the tough, macho badass thing to do (for a central banker).  And since the threat is credible, people will keep their prices down, and he won’t have to carry it out.  (OK, the economics is a little more complicated, but that’s the general idea.)

So what kind of central banker do you want if you hope to keep the inflation rate from getting too high?  Obviously you want a tough, macho badass.  You want the kind of central banker that likes to pick up small animals in his talons so that he can crush them to death and serve them for dinner.  You sure as hell don’t want the kind who just likes to fly around looking pretty and making cute cooing noises.

That theory made a lot of sense in the 1980’s, but the world has changed.  The inflation rate hasn’t been too high for 20 years.  We are in the middle of a minor depression, and the way to get out of it is to threaten inflation.  Tell people they had damn well better start doing something useful with their cash or else, as soon as you get a chance, you’re going to make its purchasing power start evaporating.  Of course, when the time comes, it won’t be rational to carry out that threat.  If you’re a perfectly rational nerd, the threat won’t be credible.

So what kind of central banker do you want if you hope to get out of this depression?  Obviously you want a tough, macho badass.  You want the kind of central banker that likes to pick up small animals in his talons so that he can crush them to death and serve them for dinner.  I’m certainly no expert in ornithology, but it just seems to me that “dove” is not the right term for that kind of central banker.

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product. 

Inflation vs. Price Level Targeting

I don’t have time for a real blog post, but here’s a quickie in an attempt to keep this blog alive.

Dave Altig and Mike Bryan of the Atlanta Fed’s Macroblog argue here that it wouldn’t make much difference if the Fed were doing price level targeting (in which the future target path stays fixed even when you miss a target, so you need catch-up inflation or catch-up disinflation) rather than inflation targeting.  Their evidence is mostly from a chart like this (my replication using monthly data, which you can confirm looks fairly similar to theirs which appears to use annual data):

Quoting from their blog post:

Consider the first point on the graph, corresponding to the year 1993….This point on the graph answers the following question:

By what percent would the actual level of the personal consumption expenditure price index differ from a price-level target that grew by 2 percent per year beginning in 1993?

The succeeding points in the chart answer that same question for the years 1994 through 2009.

In my case, as I said, it’s monthly, and it goes all the way to 2012, but the idea is the same.

OK, fine.  So here it looks like a price level target would have produced roughly the same results as the Fed’s (unofficial until January 2012) inflation target, and whether it would have undershot or overshot depends on when you start the target path.  In particular, people who argue that we are undershooting right now don’t seem to have much of an argument unless they start the target path in 2008 or later.

BUT…

The problem with this chart is that it uses the headline PCE price index, whereas during most of this time (until January 2012 when the official inflation targeting policy was introduced), the Fed was perceived to be targeting core PCE inflation (excluding food and energy, that is), not headline inflation.  Price-setters were making their decisions largely under that assumption.  It makes no sense to go back to 1993 and set up a target path using the headline price index when that index was irrelevant to the policy that the Fed seemed to be following at the time.

Moreover, targeting the price level using the headline price index is a bad idea anyhow.   If you're going to use a price level target (and I do think it would be better than an inflation target), then you don't want to use a price index that will be subject to shocks that are volatile but persistent. A one-time increase in the price of oil should not require a subsequent compensating decline in other prices to offset it (nor should a one-time decrease in the price of oil require a subsequent burst of inflation to offset it). Theoretical arguments would suggest using an index of sticky prices, but the core is a reasonable approximation.

Here’s what my chart above looks like when you use the core PCE price index instead of the headline index.

Very different.  By this measure we are undershooting now no matter when you start the target path.  And unless you cherry-pick the starting point in 2003 or 2011, the size of the undershoot is not insignificant.  If you compare to the 1990’s, the Fed was already slightly behind when the Great Recession began, and they have fallen further and further behind since then.  Price level targeting, using the core price index, would require the Fed to promise a significant amount of catch-up inflation in the coming years.

DISCLOSURE: Through my investment and management role in a Treasury directional pooled investment vehicle and through my role as Chief Economist at Atlantic Asset Management, which generally manages fixed income portfolios for its clients, I have direct or indirect interests in various fixed income instruments, which may be impacted by the issues discussed herein. The views expressed herein are entirely my own opinions and may not represent the views of Atlantic Asset Management. This article should not be construed as investment advice, and is not an offer to participate in any investment strategy or product.