Macro Musing Podcast

I did a podcast with David Beckworth, in his "macro musings" series, on the Fiscal Theory of the Price Level, blogging, and a few other things.



(you should see the link above, if not click here to return to the original).

You can also get the podcast at Sound Cloud, along with all the other ones he has done so far, or on itunes here.  For more information, see David's post on the podcast.

Lessons Learned I

I spent last week traveling and giving talks. I always learn a lot from this. One insight I got:  Real interest rates are really important in making sense of fiscal policy and inflation.

Harald Uhlig got me thinking again about fiscal policy and inflation, in his skeptical comments on the fiscal theory discussion, available here. At left, two of his graphs, asking pointedly one of the standard questions about the fiscal theory: Ok, then, what about Japan? (And Europe and the US, too, in similar situations. If you don't see the graphs or equations, come to the original.) This question came up several times and I had the benefit of several creative seminar participants views.

The fiscal theory says
 \[ \frac{B_{t-1}}{P_t} = E_t \sum_{j=0}^{\infty} \frac{1}{R_{t,t+j}} s_{t+j} \]
 where \(B\) is nominal debt, \(P\) is the price level, \(R_{t,t+j}\) is the discount rate or real return on government bonds between \( t\) and \(t+j\) and \(s\) are real primary (excluding interest payments) government surpluses. Nominal debt \(B_{t-1}\) is exploding. Surpluses \(s_{t+j}\) are nonexistent -- all our governments are running eternal deficits, and forecasts for long-term fiscal policy are equally dire, with aging populations, slow growth, and exploding social welfare promises. So, asks Harald, where is the huge inflation?

I've sputtered on this one before. Of course the equation holds in any model; it's an identity with \(R\) equal to the real return on government debt; fiscal theory is about the mechanism rather than the equation itself. Sure, markets seem to have faith that rather than a grand global sovereign default via inflation, bondholders seem to have faith that eventually governments will wake up and do the right thing about primary surpluses \(s\). And so forth. But that's not very convincing.

This all leaves out the remaining letter: \(R\). We live in a time of extraordinarily low real interest rates. Lower real rates raise the real value surpluses s. So in the fiscal theory, other things the same, lower real rates are a deflationary force.

The effect is quite powerful. For a simple back of the envelope approach, we can apply the Gordon growth formula to steady states. Surpluses \(s\) grow at the rate \(g\) of the overall economy. So, in steady state terms,
 \[ \frac{B_{t-1}}{P_t s_t} = E_t \sum_{j=0}^{\infty} \frac{(1+g)^j}{(1+r)^j} \approx \frac{1}{ r - g} \]
\[ \frac{P_t s_t}{B_{t-1}}  \approx  r - g \; \; (1) \]
(and exact in continuous time). The left hand side is the steady state ratio of surpluses to debt. The right hand side is the difference between the real interest rate and the long-run growth rate.

So, with (say) a 2% growth rate g, and a 4% long-run interest rate r, surpluses need to be 2% of the real value of debt. But suppose interest rates decline to 3%. This change cuts in half the needed long-run surpluses! Or, holding surpluses constant, if long-run interest rates fall to 3%, the price level falls by half.

You can see the punchline coming. Long term real interest rates are really low right now. If anything, we're flirting with \(r \lt g\), the magic point at which governments can borrow all they want and never repay the debt.

With this insight, Harald should have been asking of the fiscal theory, where is the huge deflation? And the answer is, well, we're sort of there. The puzzle of the moment is declining inflation and even slight deflation despite all our central bankers' best efforts.

Pursuing this idea, there is a larger novel story here about growth, interest rates, and inflation.

Obviously, there is an opposite prediction for what happens when real interest rates rise. Higher real rates, unless accompanied by higher surpluses, will drive inflation upwards.

In conventional terms, looking at flows rather than present values, suppose a government that is $20 Trillion in debt faces interest rates that rise from 2% to 5%. Well, then it has to increase surpluses by $600 billion per year; and if it cannot do so inflation will result.

A similar story makes sense for the cyclical falls in inflation. What happened to our equation in 2008?  Surpluses fell -- deficits exploded -- and future surpluses fell even more. Debt rose sharply. Why did we see deflation? Well, real interest rates on government debt fell to unprecedentedly low levels. This really isn't even economics, it's just accounting. The equation holds, ex-post, as an identity!

To think a bit more about real rates, growth, and inflation, remember the standard relation that the real interest rate equals the subjective discount rate (how much people prefer current to future consumption) plus a constant times the per capita growth rate
\[ r = \delta + \gamma (g-n) \]
The constant \(\gamma\) is usually thought to be a bit above one.

With \(\gamma=1\) (log utility), then we have \(r-g = \delta-n\). The magic land of unbounded government debt can occur because government surpluses can grow at the population growth rate, while interest rates are determined by the individual growth rate. But population growth is tapering off, and must eventually cease, and bondholders prefer their money now. With \(\gamma \gt 1 \) ,
\[ r-g = \delta - n + (\gamma-1)(g-n) \; \; (2)\]
The new term is the per capita growth rate, which is positive, further distancing us from the land of magic.

More to the point, though, we now have before us the central determinant of long run real interest rates. Real interest rates are higher when economic growth is higher. And \(r-g\) rises when economic growth \(g\) rises.

So, going back to my equation (1), we actually had a puzzle before us. Higher real interest rates would mean lower values of the debt, and would thus be inflationary if not accompanied by austerity to pay more to bondholders. But higher real interest rates must come with higher economic growth, and higher economic growth would raise surpluses, helping the situation out. Which force wins? Well, equation (2) answers that question: With \(\gamma \gt 1\), the usual case (a 1% rise in consumption growth comes with a more than 1% rise in real interest rates), higher growth g comes with higher still interest rates r, and thus remains an inflationary force, again holding surpluses constant.

All in all then, we have the hint of a fiscal theory Phillips curve: Inflation should be procyclical. In good times, interest rates rise and the real value of government debt falls, producing more inflation. In bad times, interest rates fall and the real value of government debt rises, producing less inflation.

Central banks have been absent in all this. The natural next question is, does this provide another reinforcing channel by which central banks might raise inflation if they raise interest rates? I don't think so, but one needs more equations to really answer the question.

What matters here are very long-term real interest rates, the kind that discount expectations of surpluses -- yes, we need some surpluses! -- 20 to 30 years from now to establish bondholder's willingness to hold debt today.

In no model I have played with can central banks affect real interest rates for that long. I think a quick look out the window convinces us that central banks cannot substantially raise interest rates in a slump, with supply of global savings so strong compared to demand for global investment. Long-term interest rates really must come from supply and demand, not monetary machination. Higher real interest rates require higher marginal products of capital, and thus higher economic growth, not louder promises, more speeches, or more energetic attempts to avoid the logic of a liquidity trap.

Deflation Puzzle

Larry Summers writes an eloquent FT column "A world stumped by stubbornly low inflation"

Market measures of inflation expectations have been collapsing and on the Fed’s preferred inflation measure are now in the range of 1-1.25 per cent over the next decade.

Inflation expectations are even lower in Europe and Japan. Survey measures have shown sharp declines in recent months. Commodity prices are at multi-decade lows and the dollar has only risen as rapidly as in the past 18 months twice during the past 40 years when it has fluctuated widely

And the Fed is forecasting a return to its 2 per cent inflation target on the basis of models that are not convincing to most outside observers. 

Central bankers [at the G20 meeting] communicated a sense that there was relatively little left that they can do to strengthen growth or even to raise inflation. This message was reinforced by the highly negative market reaction to Japan’s move to negative interest rates.

So why is inflation slowly declining despite our central banks' best efforts? Here is a stab at an answer. I emphasize the central logical points with bullets.

• Interest rates have two effects on inflation: a short-run "liquidity" effect, and a long-run "expected inflation" or "Fisher" effect.  

In normal times, to raise interest rates, the central bank sells bonds, which soaks up money. Less money drives up interest rates as people bid to borrow a smaller supply, and less money also reduces "demand," which reduces inflation.  In the long run, higher inflation and higher interest rates go together, as they did in the 1980s.

However, we are now in a classic "liquidity trap." Interest rates have been zero since 2008. Money and bonds are perfect substitutes. The proof of that is in the pudding: the Fed massively increased excess reserves from less than $50 billion to almost $3,000 billion, and inflation keeps trundling down.

• In a liquidity trap, the liquidity effect is absent. 

The liquidity effect will remain absent as the Fed starts raising interest rates, and would remain absent if the Fed were to cut rates or reduce them below zero as other central banks are doing. You can't have more than perfect liquidity.

The Fed isn't even planning to try. It plans to keep the $3,000 billion of excess reserves outstanding and raise interest rates by raising the interest rate on reserves. There will be no open market operations, no "tightening" associated with this interest rate raise.  But even if it did, we're $2,950 billion of excess reserves away from any liquidity effect, so it wouldn't matter.

• When the liquidity effect is absent, the expected inflation effect is all that remains. Inflation must follow interest rates. 

Central banks thought they were raising inflation by lowering interest rates, following experience from the normal-times liquidity-effect correlation between lower interest rates and higher inflation. But that experience does not apply when its liquidity effect is turned off.

With no liquidity effect, lowering interest rates further below zero can only, slowly, lower inflation further. Central banks desiring inflation may have followed a classic pedal mis-application.

Do I "believe" this story? Belief has no place in science. It is the simplest coherent story that explains the last few years, not needing lots of frictions, irrationalities, and other assumptions. I have some equations to back it up. But we don't "believe" anything at least until it's published and has survived critical examination, replication and dissection. Still, I think it merits consideration.

Shh. I like zero inflation. If central banks have the wrong pedal but are driving the right speed anyway, why wake them up? Even Larry seems to have given up on the Phillips curve:

...suppose that officials were comfortable with current policy settings based on the argument that Phillips curve models predicted that inflation would revert over time to target due to the supposed relationship between unemployment and price increases.

There is no sign of the dreaded "deflation vortex," any more than there is any sign of dreaded monetary hyperinflation. We're drifting down to the Friedman rule. As Larry emphasizes, don't get excited over forecasts from models that rather spectacularly did not forecast where we are today. 
Central banks' desire for 2% inflation, and the Fed's rather puzzling interpretation of its "price stability" mandate to mean perpetual 2% inflation may also be relics of the bygone liquidity-effect regime. 

Appreciate the first half of the column which turns the signs around. It's a great bit of rhetoric.

I have to register mild disagreement with Larry's "solution" to the supposed "problem," 

In all likelihood the important elements will be a combination of fiscal expansion drawing on the opportunity created by super low rates and, in extremis, further experimentation with unconventional monetary policies.

He doesn't say which monetary policies would work, given they have not done so yet. But these are topics for another day.

(Note: If quote and bullet formatting doesn't show up, come back to the original.)

MacDonell on QE

Gerard MacDonell has a lovely noahpinion guest post "So Much for the QE Stimulus" (HT Marginal Revolution). Some good bits here, with my bold on noteworthy zingers.

The post is unusual, because practitioners tend to regard the Fed and QE as very powerful. But here he expresses nicely the skeptical view of many academics such as myself.

the Fed leadership has now abandoned its original story about how QE affects the economy and has conceded that the tool is weak

It has long been obvious that QE operated mainly through signaling and confidence channels, which wore off on their own without any adjustment in the size or composition of the Fed’s balance sheet....

Obvious to us skeptics, not to the Fed or to the many academic papers written trying to explain the supposed powers of QE

The story initially told by the Fed leadership starts with the claim that large scale asset purchases (LSAPs) [lower interest rates]... by removing default-free interest rate duration from the capital markets. ...

Translation: buying bonds to drive up bond prices

That story does not hold much water.

 

The theoretical foundations supporting QE were invented – or really revived from the 1950s [Preferred habitat theory]– in an effort to justify a program that had been resolved upon for other reasons. 

LSAPs did not actually succeed in reducing the stock of government rates duration because they were fully offset by the fiscal deficit and the Treasury’s program of extending the maturity of the federal debt. 

Translation: The Treasury sold as much as the Fed bought.

 And while the estimated term premium and bond yields did go down during the QE era of late 2008 through late 2014, they had a disconcerting tendency to rise while LSAPs were ongoing.

 Translation: When the Fed actually bought securities, yields went up.

Peak QE gullibility seems to have been reached in the late summer of 2012, with Ben Bernanke’s presentation to the Kansas City Fed’s monetary policy conference at Jackson Hole. ...

Evidence that the Fed doesn't believe it any more

...the Fed has abandoned the flock it once led. If the leadership still believed the official story, it could not promise both to maintain the size of the balance sheet and raise rates at an historically slow pace. That would deliver far too much stimulus, particularly with the economy now near full employment. The obvious way to square this circle to recognize that the Fed does not believe the story, which is an advance.

... according to the original story, little of this presumed stimulus would unwind without asset sales or a passive shortening of maturities, both of which have largely been excluded for now.

...Readers of this comment may recall those charts circulated by Wall Street showing the fed funds equivalent going deeply and shockingly negative after 2009. In retrospect, those charts are cringe-inducing and best forgotten. It is a mercy that the Fed has participated in the forgetting. 

This is consistent with my view. The large balance sheet is a great thing. Narrow banking has arrived. We live the optimal quantity of money. Interest-paying reserves generate zero stimulus, but great liquidity. Alas, the Fed, having touted the world-saving stimulus of QE, without qualifying that effects might be temporary, now is in a tough spot to turn around and say "never mind." All it can do is be silent and wait.

...This raises the question of why the Fed initially promoted a story that so obviously would not stand the test of time. We can imagine three possibilities...

The first possibility relates to the first round of event studies, which measured the immediate effects on the term premium and bond yields of QE-related news....

Announcement effects are a poor measure of fundamental effects that will endure long enough to affect the economy... markets typically act more segmented in the short run than over time,.... But smart and credentialed people argued otherwise and the FOMC may have been comforted by that.

I have puzzled at this as well. Many studies find price impacts of large unannounced trades. But price impact melts away. Why would we treat announcement effects as permanent -- as many Fed speeches did?

The second possibility is that the Fed wanted to raise confidence in the markets and real economy and thus chose to communicate that it was wielding a new and fundamentally powerful tool, even if Fed officials had their own doubts. ...

This is the "signaling" channel.

It is best to lift confidence with tools that have a mechanical force and do not rely purely on confidence effects. But if such tools are not readily available, then it probably does not hurt to try magic tricks and pyrotechnics.

Nice phrases. But..

The problem looking forward is that people may not be so responsive to the symbolism of QE next time around. ... Moreover, the Bank of Japan has got hold of QE, which raises the odds it will be properly discredited, if history guides.

OK, not very nice, but a good snark prize, as much to the B of J as to its many critics. But far more interesting..

The third possibility ..[is] that Bernanke and his colleagues in Fed circles were durably confused by Bernanke’s early and mistaken relation of the Quantity Theory to the efficacy of LSAPs...:

"The general argument that the monetary authorities can increase aggregate demand and prices, even if the nominal interest rate is zero, is as follows:..The monetary authorities can issue as much money as they like. Hence, if the price level were truly independent of money issuance, then the monetary authorities could use the money they create to acquire indefinite quantities of goods and assets. This is manifestly impossible in equilibrium. Therefore, money issuance must ultimately raise the price level, even if nominal interest rates are bounded at zero. .."

This is indeed the crucial point. In simple quantity theory thought, MV=PY, so you can raise M even at zero rates, and eventually PY must rise. But that's wrong, alas. V becomes undefined when the interest rate is zero, or money pays interest.  As Gerard explains,

... one must wonder if this misapplication of the Quantity Theory to LSAPs created in Bernanke and associates an excessive confidence in the efficacy of the program...

...Bernanke would later argue this point himself, and demonstrate it by paying interest on excess reserves, thereby by converting them from money to debt. Bernanke’s money injection actually had ZERO maturity. Or more to the point, it did not even happen.

Stop and savor just a moment. When the government pays interest on reserves, reserves become the same thing as overnight government debt. They are held as a saving vehicle, and have no "stimulus."

To be fair, I think Bernanke's point might hold if there were a huge QE, a clear promise to leave reserves outstanding when interest rates rise above zero, and then possibly future inflation might work its way back to current inflation. But exit principles that clearly state the large reserves will pay interest so as not to give future inflation undo the possibility.

Gerard leaves out, I think, the most telling mistake in the Bernanke quote,  "monetary authorities could use the money they create to acquire indefinite quantities of goods..." Monetary policy does not buy goods; it does not drop money from helicopters. Monetary policy only gives one kind of debt in return for another kind; roughly speaking making change, giving you two 5s and a 10 for each 20. Buying goods is fiscal policy, and fiscal policy can cause inflation.

Bottom line

...The Fed leadership has come a long way from believing that QE had something to do with the power of the printing press to a recognition that the program is a combination of an indirect and transitory rates signal, a confidence game, and a duration take out that probably achieved much less than was advertised. But at least the journey has been made....

I share this view.

To be clear, both my post and Gerard's are not really critical of the Fed. If "pyrotechnics'' helped, good. If QE is not "mechanically" that powerful, great, we all learn from experience. A large interest-paying balance sheet and silence is probably the best thing for the Fed to do right now.  This question is most important to academic and historical analysis, to learn  what causal mechanisms really did play out, and what will work in the future.