## Thursday, December 19, 2013

### What if we got the sign wrong on monetary policy?

I've been following with interest the rumblings of economists playing with an amazing idea -- what if we have the sign wrong on monetary policy? Could it be that raising the interest rate raises inflation, and not the other way around?

Most recently, Steve Williamson plays with this idea towards the end of a recent provocative blog post.   Most of Steve's post is about the Phillips curve, but he concludes
If the Fed actually wants to increase the inflation rate over the medium term, the short-term nominal interest rate has to go up.

So, here's the policy advice for our friends on the FOMC...If there's any tendency for inflation to change over time, it's in a negative direction, as long as the Fed keeps the interest rate on reserves at 0.25%. Forget about forward guidance...So, as long as the interest rate on reserves stays at 0.25%...you're losing by falling short of the 2% inflation target, which apparently you think is important. And you'll keep losing. So, what you should do is Volcker in reverse.. For good measure, do one short, large QE intervention. Then, either simultaneously or shortly after, increase the policy rate. Under current conditions, the overnight nominal rate does not have to go up much to get 2% inflation over the medium term.
Conventional wisdom says no, of course: raising interest rates lowers inflation in the short run and and only raises inflation in a very long run if at all.

The data don't scream such a negative relation. Both the secular trend and the business cycle pattern show a decent positive association of interest rates with inflation, culminating in our current period of inflation slowly drifting down despite the Fed's $3 trillion dollars worth of QE. To be sure, I left the grand Volcker stabilization out of the picture here, where a sharp spike in interest rates preceded the sudden end of inflation. And to be sure, there is a standard story to explain negative causation with positive correlation. But there are other stories too -- the US embarked on a joint fiscal-monetary stabilization in 1982, then under the shadow of an implicit inflation target gradually lowered inflation and interest rates. Other countries that adopted explicit inflation targets have similar-looking data. And every time George Washington got sicker, his doctors drained more blood. So much for data, how about theory? Why do we think that higher interest rates produce lower inflation? We are now, in fact, in a new environment, and old theories may not apply any more. The first standard story was money. In the past, when the Fed wanted to raise rates, it sold bonds, cutting down on the$50 billion of non-interest-paying reserves. The standard story was, with less "money" in the economy and somewhat sticky prices, nominal interest rates would rise temporarily.  The less money would eventually mean less inflation, and then and only then would nominal rates decline. In this  view, running the Fed was a tricky job, like driving 68 Volkswagen bus in a crosswind, since the steering was connected to the wheels in the wrong direction in the short run.

However, we are likely to stay with huge excess reserves and interest on reserves. When the Fed wants to raise interest rates now, it will simply pay more on reserves and bingo, interest rates rise. We will remain as awash in interest-paying reserves as before. So this 1960s monetary mechanism just won't apply. Is it possible that in the interest-on-reserves world, raising interest rates translates right away into larger inflation?

More recent economic thinking has (rightly, I think) left the money vs. bonds distinction in the dust. The "Paleo-Keyneisian" (credit to Paul Krugman for inventing this nice word) models in policy circles state that the Fed raises rates, this lowers "demand," and through the Phillips curve, lower demand means less inflation. No money in sight here, but yes a negative effect. The first half of Steve's blog post tearing apart the Phillips curve at least should question one's utter confidence in that mechanism.

Paleo-Keynesian models aren't really economics though. What do new-Keynesian (DSGE)  models say? Interestingly, new-Keynesian models can quite easily produce a positive effect of interest rates on inflation. Here are two examples (The models I use here are discussed in more depth in "Determinacy and Identification with Taylor Rules" and "The New-Keynesian Liquidity Trap")

Lets' start with the absolutely simplest New-Keynesian model, a Fisher equation and a Taylor rule,
$i_t = E_t \pi_{t+1}$ $i_t = \phi_{\pi} \pi_t + v_t$
The standard solution ( $$\phi_{\pi} \gt 1$$ and choosing the nonexplosive equilibrium) is
$\pi_t = -E_t \sum_{j=0}^{\infty} \phi^{-(j+1)} v_{t+j}.$
So, suppose $$v_t$$=0 for $$t \lt T$$ and imagine an unexpected permanent tightening to $$v_t=v$$ for $$t \ge T$$. Interest rates and inflation are zero (deviations from trend) until T, and then

$\pi_t =i_t = -\frac{1}{\phi_{\pi}-1} v$
Both inflation and the interest rate jump down together. Wait, you say, I thought this was a tightening, why are interest rates going down? It is a tightening -- v is positive. The Fed deviates from its Taylor rule, so interest rates are higher than they would be for this inflation rate. But an observer sees interest rates and inflation move together, both going down. Conversely, if the Fed were to "loosen" by deviating from its Taylor rule in a lower direction, then we would see inflation and interest rates move immediately and positively together. I'm not sure news papers would call this "tighter interest rates!"

A better way to think of this experiment is, what if the Fed adopted a higher inflation target? Rewrite the Taylor rule as
$i_t = \phi_{\pi} \left(\pi_t -\pi^*_t \right)$
You see this is the same, with $$v_t = -\phi_{\pi}\pi^*_t$$. So, if the Fed suddenly (and credibly!) raises its inflation target from $$\pi^*_t=0$$ to $$\pi^*_t=\pi^* \gt 0$$ at $$t=T$$, inflation and interest rates jump from zero to
$\pi_t =i_t = \frac{\phi_{\pi}}{\phi_{\pi}-1}\pi^*.$
The higher inflation target gives instantly higher inflation -- and must come with a sudden rise in the Fed's interest rate target!

Blog readers will know I'm not much of a fan of the standard New-Keynesian equilibrium selection devices. But since this "model" is only an Fisher equation, obviously it's going to be even easier to see a positive connection between interest rates and inflation in other equilibria of this model. For example, take $$\phi_{\pi}=0$$ (as we must at the zero bound anyway) and choose the equilibrium that has zero fiscal effects, i.e. no unexpected inflation at time T.
$i_t = E_t \pi_{t+1}$ $i_t = v_t$ Now, a sudden unexpected rise from $$i_t=0$$ to $$i_t=v$$ for $$t \ge T$$ gives us $$\pi_T$$=0 (no unexpected inflation) but then $$\pi_t=v$$ for $$t=T+1,T+2,....$$. In words, the Fed raises rates at $$T$$, there is a one-period pause and then inflation rises to match the higher interest rate after this one-period pause.

"But what about price-stickiness?" I hear you protesting, and rightly. The whole story about a temporary effect in the wrong direction hinges on price stickiness and Phillips curves. I happen to have a paper and program handy with explicit solutions so let's look. The model is the standard continuous time New-Keynesian model,
$\frac{dx_{t}}{dt} =i_{t}-\pi _{t}$ $\frac{d\pi _{t}}{dt} =\rho \pi _{t}-\kappa x_{t}.$
Now, suppose the Fed raises the interest rate from zero to a constant i starting at time T. This is a simple matrix differential equation with solution
\begin{equation*} \left[ \begin{array}{c} \kappa x_{t} \\ \pi _{t} \end{array} \right] =\left[ \begin{array}{c} \rho \\ 1 \end{array} \right] i+\left[ \begin{array}{c} \lambda ^{p} \\ 1 \end{array} \right] e^{\lambda ^{m}\left( t-T\right) }z_{T} \end{equation*}
where
\begin{eqnarray*} \lambda ^{p} &=&\frac{1}{2}\left( \rho +\sqrt{\rho ^{2}+4\kappa }\right) \geq 0 \\ \lambda ^{m} &=&\frac{1}{2}\left( \rho -\sqrt{\rho ^{2}+4\kappa }\right) \leq 0. \end{eqnarray*}
There are multiple solutions, as usual, indexed by $$z_T$$, equivalently by what inflation does at time T. The inflation target or Taylor rule selects these, but rather than get in to that, let's just look at the possibilities:

Here I graphed an interest rate rise from 0 to 5% (blue dash)  and the possible equilibrium values for inflation (red). (I used $$\kappa=1\, \ \rho=1$$ ).

As you can see, it's perfectly possible, despite the price-stickiness of the new-Keynesian Phillips curve, to see the super-neutral result, inflation rises instantly. The equilibrium I liked in "New-Keynesian Liquidity Trap" with no instantaneous response produces a gradual rise in inflation. The only way to get a big decline in inflation is to imagine that by a second "equilibrium selection policy" the Fed insists on a quick jump down in inflation.

Obviously this is not the last word. But, it's interesting how easy it is to get positive inflation out of an interest rate rise in this simple new-Keynesian model with price stickiness.

So, to sum up, the world is different. Lessons learned in the past do not necessarily apply to the interest on ample excess reserves world to which we are (I hope!) headed. The mechanisms that prescribe a negative response of inflation to interest rate increases are a lot more tenuous than you might have thought. Given the downward drift in inflation, it's an idea that's worth playing with.

I don't "believe" it yet (I hate that word -- there are models and evidence, not "beliefs" -- but this is the web, and it's easy for the fire-breathing bloggers of the left to jump on this sort of playfulness and write "my God, that moron Cochrane 'believes' monetary policy signs are wrong" -- so one has to clarify this sort of thing.) We need to explore the question in a much wider variety of models. But it is certainly a fascinating question. What is the connection between interest rates and inflation in the interest-on reserves world? If one wants to raise inflation, is Steve right that raising rates does the trick?

By the way, none of this is an endorsement of the idea that more inflation is a good thing. If interest rates stay low, and we trend to zero inflation or even slight deflation, why wouldn't we just welcome the Friedman rule -- inflation  policy has attained perfection, on to other things? Technically, welfare calculations come after understanding policy in these models, and "believing" that all our seemingly endless doldrums can all be fixed with a little monetary magic like taxing reserves is another proposition that needs a lot more support.  More likely, if you don't like the long-term economy, go fix "supply" and growth where the problems are.  Nobody's Phillips curve gives a big output gap with steady inflation.

History: I last thought about this question here, in response to a John Taylor Op-Ed also suggesting that raising rates might be stimulative. This sign is an old question. The last time it came up was around the stabilization of 1980-1982. A school suggested money was "superneutral." They were wrong, I think, in the short run, at the time. I wrote my thesis showing there is a short run effect of money on interest rates, in the expected direction, which tells you a bit about how long monetary controversies go on. But both interest rates and unemployment did come down much faster than the Paleo-Keynesians of the time thought possible.  It's definitely time to rethink it.

There is lots more good stuff in Steve's post. Like causality and Japan:
.. There used to be a worry (maybe still is) of "turning into Japan." I think what people meant when they said that, is that low inflation, or deflation, was a causal factor in Japan's poor average economic performance over the last 20 years. In fact, I think that "turning into Japan" means getting into a state where the central bank sees poor real economic performance as something it can cure with low nominal interest rates. Low nominal interest rates ultimately produce low inflation, and as long as economic stagnation persists (for reasons that have nothing to do with monetary policy), the central bank persists in keeping nominal interest rates low, and inflation continues to be low. Thus, we associate stagnation with low inflation, or deflation.
and the value of forward guidance without commitment
You've [Fed] pretty much blown that, by moving from "extended period" language, to calendar dates, to thresholds, and then effectively back to extended periods. That's cheap talk, and everyone sees it that way
And the whole Phillips curve thing is good stuff too.  But we're here to talk about the possible negative sign.

(Thanks to Frank Diebold for showing me how to get MathJax to work in blogger. )

1. John,

"Could it be that raising the interest rate raises inflation, and not the other way around?"

If the federal reserve raises nominal short term interest rates:

AND

1. Credit demand in the macro economy remains unchanged
2. Liquidity preference in the macro economy remains unchanged
3. Productivity in the macro economy remains unchanged
4. The credit default percentage in the macro economy remains unchanged
5. Long term interest rates rise in tandem (no destruction of credit intermediation by the banking system)
6. The federal government does not change its definition of inflation (such as the 1983 conversion to owners equivalent rent or the 1995 Boskin commission)

THEN

1. The inflation rate is likely to rise

2. The possibility that the cause and effect of monetary policy could reverse under certain "Japan" conditions has been in my mind for some time. Unfortunately, this is something that the Fed is ill prepared to consider. Can you tell us if the money supply in Japan in the last 20 years shrank (or stopped growing) as drastically as it has in the US in the last 5 years?

3. “We are now, in fact, in a new environment, and old theories may not apply any more.”

Beginning at the beginning, QE and Keynesian deficit spending were theories developed in a low public and private debt environment as well as theories developed before the advent of the welfare state.

Deploying QE and Keynesian deficit spending in a public and private hyper-debt environment in an advanced welfare state, within an advanced economy, was tried, in the main, first in Japan [2002-2004]. That is, old theories were deployed in a new environment and the result was abysmal.

Another environment that has changed greatly in the US economy since 1960 and can‘t be discounted as a factor to reckon with is: legislation leading to regulation [Epstein, Simple Rules for a Complex Word]. The technocratic wonderland as it were.

Further, the old government privilege economies of pre-1700 have returned, beginning circa 1935, advancing to the point today which looks a lot like 1600 when it comes to government privilege economy as the organization of an economy.

Hence the extended order which is an infinite series doesn’t so much exist upon particular time and particular circumstance of freely made decision by free individuals as it does by political solutions to economic problems. -Or- if you prefer, dupery and nitwitery.

So yes, “old theories may not apply any more.”

4. Thanks for the excellent post. But as someone who has done such a good job highlighting the potentially capricious nature of equilibrium selection implicit in the NK model, is it really helpful to leave the "equilibrium selection policy" so far in the background like Williamson does in his model? If we just have a passive fiscal authority in place of a CB reaction function and then essentially "find out" the equilibrium selection policy via the interest rate target as if it did not come with an intended message that was itself an attempt to select an equilibria, are we getting anything interesting at all? Inflation is always and everywhere an equilibrium selection policy!

5. I think the source of the problem is that the Fed can control only the supply of money but not what people do with that money (aka the demand for money). Since the financial collapse, there has been a dramatic increase in the demand for money. The Fed has obliged by pumping cash through the QE program. However, QE money has gone straight into excess reserves which is the equivalent of stuffing money in mattresses or holes in the ground. Raising short-term interest rates will only encourage such behavior. Instead, the Fed is trying to get people to spend and invest by stoking inflation and making it costly to be invested in cash. The only tool it has right now is more QE, which means the money hoarding will continue.

Taxing excess reserves could have unintended consequences - specifically, banks passing costs to depositors, which may prompt conversions into cash and even more hoarding. An alternative could be giving the Fed full control over fiscal deficits and surpluses, which will enable it to expand and shrink the supply of money through monetary flows in the real economy. This is a more efficient tool than printing money that people can turn around and stuff in their mattresses. Politically, though, this is a very radical idea and may require a grand compromise such as a constitutional amendment requiring Treasury to run a balanced budget, while giving the Fed the power to run deficits and surpluses in order to achieve its inflation and employment target.

6. I have to say this whole exercise is a bit incredible, especially when performed by a guy, whose personal hero is Fama. So, lots of models can produce the opposite reaction to the conventional one? Now, why not look at the correct model? Like the market expectations at the announcement of Fed policy? Like yesterday for example? What conclusion do you come to about inflation and interest rates/QE when you actually look at evidence? The cleanest one possible?

I guess curve fitting to historical spot data is more fun.

7. Two observations:

1. "The only way to get a big decline in inflation is to imagine that by its "equilibrium selection policy" (essentially an inflation target) the Fed insists on a quick jump down in inflation."

Here, you sound an awful lot like market monetarists, who would claim that the mistakes of the Fed and BOJ are in not wanting to choose the equilibrium paths with "too much" inflation.

2. Identifying the effect of interest rate changes on demand is tricky because central banks are not passive; the Fed is likely to raise interest rates if it thinks inflation will be too high in the future. As long as the Fed does not fully offset any expected changes in inflation, then we'll see interest rates move in the same direction as inflation.

8. I think you mixed up nu and phi in "you see..." If not please disregard....

Also what is zt in the continuous time model?

1. Fixed, thanks! z_T indexes the multiple equilibria, fixed that too.

9. Ugggh i meant nu and pi

10. Could the FED be responding to changes in the inflation rate? Inflation up - FED raises rates? Inflation down - FED cuts rates?

11. Is it possible the FED is simply responding to changes in the inflation rate? When inflation rates rise the FED raises interest rates and when the inflation rate falls the FED lowers interest rates. Is this possible?

12. "the US embarked on a joint fiscal-monetary stabilization in 1982"

What do you mean by "joint fiscal-monetary stabilization in 1982"? Those were the Reagan years, a period of large fiscal deficits. I'd rather call it plain monetary stabilization cum inconsistent fiscal policy.

1. I got a bit ahead of myself here... Next paper, in process of writing it. But it's true. When rates rose in the early 1980s, interest costs on the debt grew to over 2% of GDP. Actual deficits were not that big, most of the "Reagan deficits" were interest payments on the debt. A tax reform followed and huge growth. We paid off that debt. Had we not convinced investors that the US could borrow against future taxes, and then had the means to pay back that debt, the stabilization effort would have failed, as so many stabilization efforts without fiscal and economic reform failed. More to come...

2. John,

Federal interest expenditures grew to 5% of nominal GDP (and an even higher percentage of Real GDP):

"We paid off that debt."

We rolled over that debt. Not the same thing.

"Had we not convinced investors that the US could borrow against future taxes…"

Investors in government bonds needed convincing that the interest payments would be made from future taxes? Was there some effort in Congress to repeal the 14th Amendment to the Constitution?

"...and then had the means to pay back that debt, the stabilization effort would have failed."

Like I said, we never paid back that debt, we rolled it over.

3. This comment has been removed by the author.

13. "Is it possible the FED is simply responding to changes in the inflation rate? When inflation rates rise the FED raises interest rates and when the inflation rate falls the FED lowers interest rates. Is this possible?"

That is the conventional wisdom, shared by the vast majority of the profession, in academia, policy-making circles and financial markets.

1. Thanks. You'd think after all these years I could get this much algebra right on the first pass...

15. "Conventional wisdom says no, of course: raising interest rates lowers inflation in the short run and and only raises inflation in a very long run if at all."

My understanding is that raising interest rates may have ambiguous effects on inflation in the short run but that the long-run effect is always to reduce inflation. What model or evidence says differently?

1. In the long run we are all dead….I think you point to death as a determining cause of lower inflation rather than interest rates.

16. I think it really matters HOW the Fed affects "the nominal interest rate". Imagine two scenarios: The fed promises to deposit money in everyone's checking account at a rate of \$1000 a day until the TIPS spread reaches 4%. This would surely raise the federal funds rate via the Fisher effect. On the other hand, the fed could just increase IOER. This would also raise the federal funds rate. I don't think we should take seriously models that don't distinguish between these two scenarios.

17. Scott Sumner has been pounding the table on the association of low interest rates with tight money (and high rates with loose money) for some time now. Really, since he started blogging. He views rates as being closer to an epiphenomena than a cause. What's important is expectations of nominal flows of money (NGDP), and the real "policy lever" central banks have is the monetary base (and indicators of what they will do with it). Interest on reserves complicates things a lot though, positive interest is strikingly deflationary (particularly in an environment where banks are already expecting to earn low returns), while if they implemented "negative interest" on reserves (as I believe occurred in Sweden) it would be inflationary.

1. Not sure about Sweden (anyone feel free to chime in on that one), but that definitely occurred in Denmark. And Denmark's central bank has been quite happy with the results it got.

1. Good post. Is your model written down somewhere with equations? It seems too good for just a blog post. I suppose I could look, or you could put in a link.

2. Thanks John!

Ummm. I can't do math! I was hoping some bright young grad student could do the math, and tighten up my argument. All I've got is that blog post. I can't write anything else nowadays. All I can do is blog.

3. And what Wonks Anonymous says above about Scott Sumner is right. I get a bit mad at poor Steve Williamson and N. Kocherlakota every so often about their assuming that raising nominal interest rates automatically means higher inflation. But I'm not a lot happier with the Keynesians who say that high nominal interest rates means "tight money".

Your post here (plus your previous stuff on indeterminacy in NK models) is starting to get us to the root of this question.

Thinking of monetary policy as the central bank setting nominal interest rates is a really bad social construction of reality. And central banks are to blame for making us think of monetary policy like that.

4. Nick, I sympathise. I can't do math either. You need a tame quant.

5. John, from a financial perspective - I've argued that negative interest rates on reserves are actually contractionary, because banks are bound to pass the tax on to customers in some way - whether through deposit charges or higher interest rates to borrowers, or if they choose to absorb the tax, in lower dividends and lower wages. I suppose this rather supports your thesis (though I had a big argument with Nick about it!)

I think that low positive interest rates reduce the velocity of money, particularly if there is an expectation that interest rates might rise soon. Very low rates are a disincentive to financial intermediaries to lend.

19. I am beginning to wonder is central bank policy has now entered into the area of a pin prick on an elephant? What I mean is that increasingly it seems that larger and larger movements are needed to get very unsatisfying results. The classic prediction would have been that all this QE would be inflationary but maybe the global economy is simply too big now to be much effected by the movements of any single central bank.

20. When's the last instance where a central bank raised interest rates and inflation went up?

1. MaysonicWrites,

Just from looking at the graph you can't establish causality. Though in the 1968-1970 and 1973-1975 periods you can see that changes in the fed funds rate tending to be a leading indicator of inflation rather than a lagging response to higher
inflation.

2. It could be that the Fed had an information advantage and raised FF rate in anticipation of higher inflation. There is some empirical evidence that inflation initially spikes in response to a monetary contraction before it eventually falls consistent with LRN.

3. It could be that the Fed cannot determine how borrowed money is used and raised interest rates to spur nominal economic growth without concern as to how that growth manifested itself - any combination of real growth / inflation was perfectly acceptable.

21. Given your comments on Reagan, look forward to your highest praise for Clinton's tax reforms http://en.wikipedia.org/wiki/Jobs_created_during_U.S._presidential_terms

22. Not only left-wingers disagree with John Cochrane----I do!
Hey, cut federal spending in half, and I think it could be done and we would all be better off...but raising interest rates will not stimulate the economy.
Central banks have been able to keep interest rates above inflation (for a couple decades after the 1980s), and thus drive inflation down...until they hit the zero bound. Now, their traditional tool works like fighting a flood with a water hose.

The experience of Japan suggests that wallowing in misery is not the right course. Oddly enough, John Taylor wrote a paper in 2006 gushing--gushing!---about Japan's then-QE efforts. Indeed, from 2002-6, coincident to steady QE, Japan had its longest post-1980s expansion. Now they are doing QE again and maybe it is working.

In the USA, since the Fd went to open-ended results-dependent QE (QE3), really has the economy done so poorly? Since September 2012 we are talking almost 3 million jobs created in the private sector (or about 200k jobs per month. 4 percent plus GDP growth for one quarter.

Maybe this would have happened without QE. Hard to know, but I doubt it.

Actually I do not see how the Fed could raise rates anyway. They could raise rates, slow the economy, and we get chronic gluts of capital, ala Japan.

A more interesting question is, "Has the Fed effectively monetized several trillion dollars in US debt, and we have no inflation?"

Should not that be stimulative? We are taking trillions in debt-monkey debt off the backs of US taxpayers for generations to come....this is a taboo subject, but if Cochrane is so concerned about long-term federal debt, I would think he would find this an mesmerizing topic...

23. There is a very simple way to look at this. Hussman has shown that higher interest rates make for a higher velocity of money. A higher velocity of money will make for higher prices.

http://howfiatdies.blogspot.com/2014/01/how-we-know-inflation-is-coming.html

1. In the short term the interest rate and velocity of money are dominant. In the long run lower interest rates will result in a higher quantity of money and more inflation. So on the question of the sign it depends on if you are asking about the short run or long run.

2. Vincent,

A higher velocity of money corresponds with higher nominal economic growth. That higher nominal economic growth can be comprised of any combination of real growth and / or inflation.

3. Frank, what is your point? My point is that interest rates and inflation rates seem to have a big impact on the velocity of money. When interest rates are going down the velocity will go down and when they are going up the velocity will go up. In the short term changes in the velocity can dominate the change in the quantity of money. But over a long enough time period more money means higher prices.

4. Vincent,

My point is this:

"But over a long enough time period more money means higher prices."

Not entirely correct. You are missing productivity improvement and newly invented goods.

With increasing productivity (more real goods per unit of money) and higher nominal interest rates, you get a higher velocity of money and a falling inflation rate.

Hence my point, higher interest rates are positively correlated with higher nominal economic growth. Whether that growth is real or inflationary depends on productivity, not whether we are talking short run / medium run / or long run.

Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.