Monday, August 31, 2015

Whither inflation?

(Note: This post uses mathjax to display equations and has several graphs. I've noticed that the blog gets picked up here and there and mangled along the way. If you can't read it or see the graphs, come back to the original .)

The news reports from Jackson Hole are very interesting. Fed officials are grappling with a tough question: what will happen to inflation? Why is there so little inflation now? How will a rate rise affect inflation? How can we trust models of the latter that are so wrong on the former?

Well, why don't we turn to the most utterly standard model for the answers to this question -- the sticky-price intertemporal substitution model. (It's often called "new-Keynesian" but I'm trying to avoid that word since its operation and predictions turn out to be diametrically opposed to anything "Keyneisan," as we'll see.)

Here is the model's answer:

Response of inflation (red) and output (black) to a permanent rise in interest rates (blue). 

The blue line supposes a step function rise in nominal interest rates. The red line plots the response of inflation and the black line plots output.  The solid lines plot the answer to the standard question, what if the Fed suddenly and unexpectedly raises rates? But the Fed is not suddenly and unexpectedly doing anything, so the dashed lines plot answers to the much more relevant question: what if the Fed tells us long in advance that the rate rise is coming?

According to this standard model, the answer is clear: Inflation rises throughout the episode, smoothly joining the higher nominal interest rate. Output declines.

The model: \begin{equation} x_{t} =E_{t}x_{t+1}-\sigma(i_{t}-E_{t}\pi_{t+1}) \label{one} \end{equation} \begin{equation} \pi_{t} =\beta E_{t}\pi_{t+1}+\kappa x_{t} \label{two} \end{equation} where \(x\) denotes the output gap, \(i\) is the nominal interest rate, and \(\pi\) is inflation. The solution  is \begin{equation} \pi_{t+1}=\frac{\kappa\sigma}{\lambda_{1}-\lambda_{2}}E_{t+1}\left[ i_{t}+\sum _{j=1}^{\infty}\lambda_{1}^{-j}i_{t-j}+\sum_{j=1}^{\infty}\lambda_{2} ^{j}E_{t+1}i_{t+j}\right] \label{three} \end{equation} \begin{equation*} x_{t+1}=\frac{\sigma}{\lambda_{1}-\lambda_{2}}E_{t+1}\left[ (1-\beta\lambda_1^{-1}) \sum _{j=0}^{\infty}\lambda_{1}^{-j}i_{t-j}+(1-\beta \lambda_2^{-1}) \sum_{j=1}^{\infty}\lambda_{2}^{j}E_{t+1}i_{t+j}\right] \end{equation*} where \[ \lambda_{1} =\frac{1}{2} \left( 1+\beta+\kappa\sigma +\sqrt{\left( 1+\beta+\kappa\sigma\right)^{2}-4\beta}\right) > 1 \] \[ \lambda_{2} =\frac{1}{2}\left( 1+\beta+\kappa\sigma -\sqrt{\left( 1+\beta+\kappa\sigma\right)^{2}-4\beta}\right) < 1. \] I use \(\beta = 0.97, \ \kappa = 0.2, \ \sigma = 0.3 \) to make the plot. As you see from \((\ref{three}\)), inflation is a two-sided geometrically-weighted moving average of the nominal interest rate, with positive weights. So the basic picture is not sensitive to parameter values.

The expected and unexpected lines are the same once the announcement is made. This standard model embodies exactly zero of the rational expectations idea that unexpected policy moves matter more than expected policy moves. (That's not an endorsement, it's a fact about the model.)

The Neo-Fisherian hypothesis and sticky prices

A bit of context. In some earlier blog posts (start here) I explored the "neo-Fisherian" idea that perhaps raising interest rates raises inflation. The idea is simple. The nominal interest rate is the real rate plus expected inflation, \[ i_t = r_t + E_t \pi_{t+1} \] In the long run, real rates are independent of monetary policy. This "Fisher relation" is a steady state of any model -- higher interest rates correspond to higher inflation.

However, is it a stable steady state, or unstable? If the nominal interest rate is stuck, say, at zero, do tiny bits of inflation spiral away from the Fisher equation? Or do blips in inflation melt away and converge steadily towards the interest rate? I'll call the latter the "long-run" Fisherian view. Even if that is true, perhaps an interest rate rise temporarily lowers inflation, and then inflation catches up in the long run. That's the "short-run" Fisherian question.

One might suspect that the new-Fisherian idea is true for flexible prices, but that sticky prices lead to a failure of either the short-run or long-run neo-Fisherian hypothesis. The graph shows that this supposition is absolutely false. The most utterly standard modern model of sticky prices generates a short-run and long-run neo-Fisherian response. And reduces output along the way.

Multiple equilibria and other issues 

Obviously, it's not that easy. There are about a hundred objections. The most obvious: this model with a fixed interest rate target has multiple equilibria. On the date of the announcement of the policy change, inflation and output can jump.

Inflation response to an interest rate rise: multiple equilibria

The picture shows some of the possibilities when people learn rates will rise three periods ahead of the actual rise. The solid red line is the response I showed above. The dashed red lines show what happens if there is an additional "sunspot" jump in inflation, which can happen in these models.

Math: You can add an arbitrary \(\lambda_{1}^{-t}\delta_\tau \) to the impulse-response function given by (\(\ref{three}\)), where \(\tau\) is the time of the announcement (\(\tau=-3\) in the graph), and it still obeys equations \( ( \ref{one})-(\ref{two})\). These are impulse response functions and sunspots must be unexepected. So the only issue is the jump on announcement. Response functions are thereafter unique.

A huge amount of academic effort is expended on pruning these equilibria (me too), which I won't talk about here. The bottom two lines show that it is possible to get a temporarily lower inflation response out of the model, if you can get a negative "sunspot" to coincide with the policy announcement.

But I think the plot says we're mostly wasting our time on this issue. The alternative equilibria have the biggest effect on inflation when the policy is announced, not when the policy actually happens. But we do not see big changes in inflation when the Fed makes announcements.  The Fed is not at all worried about inflation past that is slowly cooling as the day of the rise approaches, as these equilibria show. It's worried about inflation or deflation future in response to the actual rate rise.

The graph suggests to me that most of the "sensible" equilibria are pretty near the solid line.

The graph also shows that all the multiple equilibria are stable, and thus neo-Fisherian. At best we can have a short-run discussion. In the long run, a rate rise raises inflation in any equilibrium of this model.

Yeah, there's lots more here -- what about Taylor rules, stochastic exits from the zero bound, off-equilibrium threats, QE, better Phillips curves with lagged inflation terms, habits in the IS curve, credit constraints, investment and capital, learning dynamics, fiscal policy, and so on and so on. This is a blog post, so we'll stop here. The paper to follow will deal with some of this.

And the point is made. The basic simplest model makes a sharp and surprising prediction. Maybe that prediction is wrong because one or another epicycle matters. But I don't think much current discussion recognizes that this is the starting point, and you need patches to recover the opposite sign, not the other way around.

Data and models

I started with the observation that it would be nice if the model we use to analyze the rate rise gave a vaguely plausible description of recent reality.

The graph shows the Federal Funds rate (green), the 10 year bond rate (red) and core CPI inflation (blue).

The conventional way of reading this graph is that inflation is unstable, and so needs the Fed to actively adjust rates. Inflation is like a broom held upside down, with inflation on the top and the funds rate on the bottom. When inflation declines a bit, the Fed drives the funds rate down to push inflation back up, just as you would follow a falling broom. When inflation rises a bit, the Fed similarly quickly raises the funds rate.

That view represents the conventional doctrine, that an interest rate peg is unstable, and will lead quickly to either hyperinflation (Milton Friedman's famous 1968 analysis) or to a deflationary "spiral" or "vortex."

And this instability view predicts what will happen should the Fed deliberately raise rates. Raising rates is like deliberately moving the bottom of the broom. The top moves the other way, lowering inflation. When inflation is low enough, the Fed then quickly lowers rates to stop the broom from tipping off.

But in 2008, interest rates hit zero. The broom handle could not move. The conventional view predicted that the broom will topple. Traditional Keynesians warned that a deflationary "spiral" or "vortex" would break out. Traditional monetarists looked at QE, and warned hyperinflation would break out.

(I added the 10 year rate as an indicator of expected inflation, and to emphasize how little effect QE had. $3 trillion dollars of bond purchases later, good luck seeing anything but a steady downward trend in 10 year rates.)

The amazing thing about the last 7 years in the US and Europe -- and 20 in Japan -- is that nothing happened! After the recession ended, inflation continued its gently downward trend.

This is monetary economics Michelson–Morley moment. We set off what were supposed to be atomic bombs -- reserves rose from $50 billion to $3,000 billion, the crucial stabilizer of interest rate movements was stuck, and nothing happened.  

Oh sure, you can try to patch it up. Maybe we discover after the fact that wages are eternally sticky, even for 7 to 20 years while half the population changes jobs, so, sorry, that deflation vortex we predicted can't happen after all. Maybe the Fed is so wise it neatly steered the economy between the Great Deflationary Vortex on one side with just enough of the Hyperinflationary Quantitative Easing on the other to produce quiet. Maybe the great Fiscal Stimulus really did have a multipler of 6 or so (needed to be self-financing, as some claimed) and just offset the Deflationary Vortex.

But when the seas are so quiet, and the tiller has been locked at 0 for seven years, it's awfully hard to take seriously the Captain's stories of great typhoons, vortices, and hyperwhales narrowly avoided by great skill and daring.

Occam's razor says, let us take the facts seriously: An interest peg is stable after all.  The classic theories that predict instability of an interest rate peg -- and consequently that higher rates will lead to lower inflation -- are just wrong, at least in our circumstances (important qualifier follows).

But if those classic theories failed dramatically, what can take their place? Fortunately, I started this post with just one such theory. The utterly standard sticky-price model, sitting in Mike Woodford's and Jordi Gali's textbooks, predicts exactly what happened: inflation is stable under a peg, and thus raising interest rates to a new peg will raise inflation.

The difference between traditional Keynesian or Monetarist models and this modern sticky-price model is deep and essential. In this model, people are forward-looking. In the standard unstable traditional-Keynesian or Monetarist model, people look backward. When written in equations, the traditional "IS" curve (\(\ref{one}\)) does not have \(E_t x_{t+1} \) or \(E_t\pi_{t+1}\) in it, and the "Phillips curve" (\(\ref{two}\)) has past inflation in it,
not expected future inflation.

Forward looking people generates stability, and backward looking people generates instability. If you drove a car by looking in the rear-view mirror, the car may indeed regularly veer off the road, unless the Fed sitting next to you yells about things to come and stabilizes the car. But when people drive looking through the front windshield, cars are quite stable, reverting to the middle of the road when the wind buffets them to one side or the other.

The response function is also consistent with the experience of a few countries such as Sweden which did raise rates and swiftly abandoned the effort. Those rises didn't do much either way to inflation, but they did lower output. Just as the graph says.

What to do? A robust approach

I will not follow the standard economists' approach -- here's my bright new idea, the government should follow my advice tomorrow. Is this right? Maybe. Maybe not. I'm working on it, and hoping by that and this blog post to encourage others to do so as well.

But if you're running the Fed, you don't have the luxury of waiting for research. You have to face an uncomfortable fact, which the news out of Jackson hole says they're facing: They don't really know what will happen or how the economy works. Nor does anyone else. They know that their own forecasts and models have been wrong 7 years in a row -- as has everyone elses', except a few bloggers with remarkably spotty memories -- so pinpoint structural forecasts of what will happen by raising rates made by those same models and logic are darn suspect.

A robust policy decision should integrate over possibilities. So as far as I'll go is that this is a decent possibility, and should add to the caution over raising rates. Raising rates if there is a fire -- actual inflation -- might be sensible. Raising rates because of inflation forecasts from models that have been wrong seven years in a row seems a bit diceyer.

Of course, there is a bit of divergence in goals as well. The Fed wants more inflation, so might take this model as more reason to tighten. And if this model is right, the Fed will produce the inflation which it desires and can then congratulate itself for foreseeing!

I like zero.  Zero rates are pretty darn good. Zero inflation is pretty darn good too. We get the Friedman-optimal quantity of money. And more. Financial stability: With no interest cost, people and businesses hold a lot of money, and don’t conjure complex but fragile cash-management schemes. Three trillion dollars of reserves are three trillion dollars of narrow banking. Taxes: You don’t pay taxes on inflationary gains and taxes erode less of the return on investments.  We don't suffer sticky-price distortions from the economy.  Yeah, growth is too slow, but monetary policy has nothing to do with long-run growth.

So, face it, the outcomes we desire from monetary policy are just about perfect. We don't really know how this happened, but we should savor it while it lasts.

This last point might be the main one. The model I showed above is utterly standard, as is the main result. "New-Keynesian" papers about the "zero bound" have been analyzing this state for nearly 20 years. The result that inflation is stable around the steady state is at least 20 years old.  All the effort, however, has been about how to escape the zero bound. But why? If a very low interest peg is stable, and achieves the optimum quantity of money, why not leave it alone? OK, there's this multiple equilibrium technicality, but that hardly seems reason to go back to "normal."

The only real concern is that some hidden force might be building up to upend this delightful state of affairs. That's behind most calls for raising rates. But clearly, nobody knows with any certainty what that force might be or how to adjust policy levers to head it off.

One warning. In the above model, the interest rate peg is stable only so long as fiscal policy is solvent. Technically, I assume that fiscal surpluses are enough to pay off government debt at whatever inflation or deflation occurs.  Historically, pegs have fallen apart many times, and always when the government did not have the fiscal resources or fiscal desire to support them. The statement "an interest rate peg is stable" needs this huge asterisk.


  1. So Prof Cochrane concludes that an increase in real interest rates will cause and increase in inflation??

  2. Couple of questions:

    1) why the assumption that real rates are independent of nominal? The point of raising nominal rates is to affect the economy and output, which will affect real rates

    2) if the fed raises rates in response to rise in inflation, then we know in advance that inflation causes nominal rate hikes, not the other way around

    seems like this is a case of confusion of causes and effects vs accounting identities

    1. I do not assume real rates are independent of nominal. That's the whole point of the sticky price model. Real rates are the difference between the nominal rate (blue line) and the inflation rate.

  3. "The picture shows some of the possibilities when people learn rates will rase three periods ahead of the actual rise."

    I think this should be:

    "The picture shows some of the possibilities when people learn rates will rise three periods ahead of the actual rise."

  4. I'd be curious how you read this graph:

    It should show the Fed Funds rate, the 5-year breakeven rate, and the CPI (I don't use core, because straight CPI is what the TIPS is based on).

    One reading might be that the breakeven rate was steady even as the Fed dramatically cut the Fed funds, because the market thought the Fed would move the rate around to hit it's target over 5-years. Then the Fed flinched and lost control. They didn't cut in August 2008, when the Fed Funds was still at 2%, and the sky started falling down and the breakeven rate reflects that. The Fed spent the next year doing everything it could to signal that it would hit it's 2% target in the future. It worked and the breakeven rises to 2%.

    That's just a story, but I'm curious about the one you'd tell. Is the dramatic Fed Funds rate decline actually causing the breakeven rate decline to come?

    Regardless, I think the forward looking view of inflation is an interesting complementary graph to look at, but I am in no way qualified to figure out how it fits into these models.

    1. That's a good graph. It shows today's actual CPI much below the 5 year breakeven. It also shows past CPI bouncing around. It suggests to me the breakeven is doing a good forecasting job: When CPI diverges from breakeven, CPI comes back to where breakeven was. So I see a very slow declining trend in breakeven, consistent with a Fisher view but with an amazingly long time constant. Too long, really.

    2. I agree, and I think the announcement effects on the breakeven rates can teach us some important things. If your interested, I was blogging the big Japan QE announcements in real time. I took some snap shots of the Japan Breakeven rate. There are concerns about the data (the market is reportedly small and illiquid), but the data seems to capture an important shift.

      There's also a possibly confounding VAT / sales tax increase.

  5. I belive than more than 7 years of almos zero lower bound rates is an enough time period to consider we might be living in the long-run (prices have adjust enough), for the i = r + E(pi) to hold

  6. other countries also have almost zero rated and inflation an GDP, production and employment down big (south eurozone), so maybe is not that relevant, expecially becasuse last time a near "perfect condition" like this happened was in 2006-2007 and turned was a setup for lots of trouble.

    Ray Dalio says the FED over-emphasized the importance of the "cyclical" (i.e., the short-term debt/business cycle) and underweighted the importance of the "secular" (i.e., the long-term debt/supercycle). But of course is very hard to model that interaction, I do not recall anybody tryng it with math. It might be that "models" in this juncture can't do much. Let us say tha Dalio general idea is sensibile of a long term debt cycle kicking in now, can you stick it into a "..general equilibrium structure, in which individuals maximize the expected present value of utility, firms maximize their value, and markets clear.etc...? I guess not

  7. Thank you, great article. So the Fed bought up ~3 trillion of Treasuries/MBS with no bad effects? That means congress can deficit spend with no bad effects? Or is that the seniorage for being the worlds' reserve currency? So MV=PQ is dead? I always thought of it as almost a tautology. I guess if V is very elastic it can still be a tautology.

  8. 1) Yes. remember, the Fed simultaneously sold $3 trillion of reserves. They made change -- took 20s and gave back 2 fives and a ten. 2) No. 3) No. There is no seignorage at zero rates 4) Yes, at least at the zero bound. As you point out, V = PY/M when M and B are perfect substitutes

  9. Professor Cochare,
    regarding Milton Friedman analysis that interest rates peg are unstable, I remember that Friedman also advocated for monetary policy based on "Monetary peg" (the famous k% rule), in which money growth should be held constant no matter what happens in the economy.
    In my opinion, a monetary peg is just the other-side-of-the-coin of an interest rate peg. If this is the case, it is not clear to me that Friedman though that interest rate pegs could be unstable (unless he changed his views later on).

    What is your opinion about it?

  10. Interesting. What are some concrete examples of conceivable sequences of future events which would convince and satisfy you that the model you've presented here is false and should be abandoned? I'm not suggesting it IS false and should be abandoned (for all I know it's pretty good), I'd just like to hear from you what specifically would convince you to abandon it.

  11. Your last point about fiscal policy suggests that it determines inflation in this context. Is that correct?

  12. "We don't really know how this happened, but we should savor it while it lasts."

    What if you were aware of competing model, with fewer parameters that explains why this happened, and does a better job of predicting key future macro measures as well, across multiple countries? Would you be inclined to give such a model a chance even if it were non standard? Would you accept an empirical challenge in that regard (given the above model, or any other that you like)? The challenge could be heavily weighted towards future events (say over the next decade in whatever countries you like).

    I don't personally have such a model, but I'm just curious what your attitude would be to such a challenge.

  13. Why didn't they invite you to Jackson Hole?

  14. John,

    "I like zero. Zero rates are pretty darn good. Zero inflation is pretty darn good too."

    Zero rates are good for borrowers and bad for lenders. And so to say that zero rates are "pretty darn good" misses that any lending arrangement should benefit both parties involved.

    As a consumer, I like gasoline and cars and houses and televisions with a price of zero ($0.00). Not sure the person selling me a new car would like zero so much.

    1. Firstly Restly, the zero rates being talked about do NOT mean 0% interest on all lending within the economy. If the Fed set a permanent 0% rate, that would not stop merchants and banks from charging whatever % interest they wished on their financing.
      Secondly, free consumer goods is not even remotely the same as low intrabank lending rates on reserves.

    2. Greg,

      First, the exact line from Cochrane's post is:

      "But in 2008, interest rates hit zero."

      The fed funds rate (singular) was reduced to zero. The fed discount rate remains at 0.75%. What are the other interest rates (plural) that John is referring to?

      Yes, banks and merchants can come to terms on a lending arrangement irrespective of what the Fed does, but it does not appear that Cochrane was referring to the singular Fed Funds rate.

      Finally, the point I was making remains - any transaction (lending or otherwise) should be mutually beneficial.

    3. If the Fed set a permanent 0% rate, do you need a Fed after that point?

      Is it in the best interest of the Fed to set a permanent 0% rate recognizing that a permanent 0% rate may threaten it's own existence?

  15. Are you saying:
    In the perfect world, inflation is zero, rates are near zero, and growth is positive...
    Right now, monetary policy is as close to perfect as it has ever been?

    I hadn't thought of it that way, and will have to grok until fullness.

  16. I think the "QE was just a swap of bonds for reserves" argument is flawed. When the Fed buys bonds, it does so from the 22 primary dealers. And then places reserves into the commercial bank accounts of those 22 primary dealers. The Fed prints up the money to give to the primary dealers.

    But the 22 primary dealers do in fact buy bonds from the public and pay cash for those bonds.

    Ergo the ultimate bond-sellers have $3 trillion or was it $4 trillion in cash that before they did not have, and the primary dealers also have $3 year--$4 trillion.
    That is the power of a central bank. You can print or digitize money.

    It is true the Fed has engineered a near elimination of inflation. However since real GDP is about 10% to 15% below capacity. I would call this a failure.

    The period 1982 - 2007 was marked by real GDP growth a little north of 3% and inflation a little south of 3%. That is a 25- year long real world experience, not a theoretical outcome.

    And it was a real world experience good enough for me!

    1. "Ergo the ultimate bond-sellers have $3 trillion or was it $4 trillion in cash that before they did not have"

      But they are no wealthier than they were before.

      The banks have new additional reserves (assets), but they also have an equal amount of new deposits (liabilities), so it's a wash.

    2. Ben, how does this bit grab you?:

      "So, face it, the outcomes we desire from monetary policy are just about perfect. We don't really know how this happened, but we should savor it while it lasts."

  17. "The only real concern is that some hidden force might be building up to upend this delightful state of affairs... but nobody knows with any certainty what that force might be or how to adjust policy levers to head it off.

    Much of this essay is, as C3PO would say, "quite beyond my capacity" (having had no formal economics education), but it certainly seems to me that a government (such as ours) can print tons of money ("quantative easing" and so forth) without causing massive inflation if much of that currency is stored under overseas mattresses (so to speak)... until the day of recocking comes when that "hidden force" that has been "building up" bursts like a dam as all that currency is redeemed (spent), flooding America and causing extreme inflation.

    1. "until the day of recocking comes when that "hidden force" that has been "building up" bursts like a dam as all that currency is redeemed (spent), flooding America and causing extreme inflation."

      What concrete evidence would it take to satisfy you that this is incorrect? I know an amateur hyperinflation enthusiast. He has a blog and a model. He put his ideas to the test with a concrete prediction (1.5 years ago): hyperinflation in Japan starting in the beginning of 2016 and running more than one consecutive month in a row. His threshold for declaring hyperinflation is low: 26% annual.

      I know another guy with a model that purports to explain why Japan, and the US (amongst other countries) have not had inflation, and why other counties have. His model is non-standard, but he's also willing to make predictions about numerous countries. He predicted more than 1 year ago that Canada would start undershooting it's inflation target by the end of this year. We'll see how he does. He and the hyperinflation guy have a bet about Japan. The loser has to let the other guy do a post on his blog explaining why they think the other guy ended up being wrong.

    2. One-data-point prognostication combining a model and its intuitive use by a prognosticator is not a good way to do science. It's barely soothsaying.

    3. I agree about the single data point thing, and that "intuitive use" is to be avoided. But you've got to start somewhere in building a good track record, right? There's no opportunity to build any confidence in a framework / model at all until the model starts demonstrating an unbroken chain of relevant accurate predictions.

  18. I will guess this post will generate lots of blogging pushback, which should prove both educational and entertaining!

    So additional comment on how to solve the "growth is too low" problem along with a comfortable zero is eagerly anticipated.

  19. Your conclusions regarding the zero-interest rate as optimal might help explain the rationale of biblical restrictions on charging interest.

    Essentially, we might explain that interest-free debt maximizes utility when there is no risk, and no inflation.

    (note that in the biblical era, bankruptcy laws didn't protect debtors, so debt was less risky)

  20. There has been an inflationary effect, except not in the goods markets, but in asset markets.

    The QE money has gone to people mainly in the money elites. How many extra shoes or TV's or yachts do they need?


  21. Replies
    1. I detest it. I also think that the kinds of monetary policy we're talking about -- the timing of a few percentage point differences in the rate that the Fed pays banks on reserves -- has next to nothing to do with long run growth. Prayer is more effective.

    2. Just to clarify a couple of points.

      1. When you say you detest zero growth, I assume that would extend to the loss of actual output. Is the economy back at long term trend in terms of actual output. Or just back on trend in terms of the current growth rate.

      2. Even if actual output were back at trend, do we not care about the lost output while the economy was below trend.

      3. Regarding "timing... in the rate that the Fed pays banks on reserves." Had the Fed not decided to start paying IOR in October of 2008 while still increasing the monetary base at the rate which they actually did, would this have had no effect on output? Or would it just have impacted prices? Or would a fourfold expansion in the base with no significant increase in reserves have had no effect on either output or prices? Or... does the rate paid not have any effect on the level of reserves?

  22. If I am reading your simulation graph correctly, the model predicts that inflation will rise in response to an increase in interest rates but that output would also decline. I have a basic question: Why would someone undertake this kind of policy which causes output to fall and inflation to rise? Maybe governments that want to inflate their debts away would undertake such a policy but the negative growth in output (and for quite a while at that based on the simulation) would almost certainly result in the government getting thrown out of office.

    The Neo-Fisherian approach you are advocating suggests that money supply falls less than output when interest rates increase - only then can you have inflation in the sense of "too much money chasing too few goods". Exactly why should this happen? Stated differently, why is output so much more sensitive to rates than money supply? What evidence do we have to support this differential in the relative sensitivities?


  23. John,

    These equations are linearized around a zero inflation steady state. In a FTPL world with a positive nominal interest rate, inflation is positive. Is that a problem? The solution will not be as accurate, right?

  24. John,

    The last time we had an effective sustained peg was during the Great Depression and more explicitly during the era that culminated in the Treasury/FED accord. The attached link shows nominal short rates, CPI inflation, and the unemployment rate (spliced from different series). I understand that during this period we were still tied to some version of a gold standard but what explains the inflation response during this period (assuming these variables were appropriately measured). The response is much more pronounced than the current period. It seems we had bursts of high inflation and disinflation during this period. I suspect it may have something to do with the stance of fiscal policy at the time (2 wars).

    I'd be interested in your thoughts on this and particularly on the FED/Treasury accord episode because it is, at least i think so, an example of explicit coordination between fiscal and monetary policy. This state of affairs resembles some aspects of your model described in "monetary policy with interest on reserves" (though i'm only halfway through it).

    Here is a link to the graph with just inflation and short rates.

    1. Good graph, good question, and good hunch (fiscal policy). The third issue is the "natural rate." It's very hard to measure, and it varies. The non-inflationary real rate varies over time, so the non-inflationary nominal rate should vary over time as well. That makes a fixed peg a dubious monetary policy over long periods of time. After WWII, with a huge need to rebuild capital, arguably the natural rate was higher. Of course it's darn hard to define let alone measure. All this episodes need serious investigation, not just punditry.

    2. John,

      I have always had a problem with the notion of a single "natural rate" of interest.

      Picture a barter economy with debt contracts negotiated in terms of real goods - for instance iron ore, steel, and locomotives.

      I lend iron ore now to receive steel at some future point in time. There will be a iron ore / steel interest rate.

      You lend steel now to receive a locomotive at some future point in time. There will be a steel / locomotive interest rate.

      These two interest rates will not be the same. You see the same type of thing today with different interest rates for corporate debt reflecting credit risk (AAA thru junk).

      If we try to create a "single good" by creating a price index (NGDP Deflator for instance) and then back calculate real GDP from nominal GDP, we can look at the "real growth rate" and interpret that as some measure of the natural rate of interest.

      But the composition of the price index is always backward looking (what price was paid for goods that were previously purchased), while a central bank trying to hit a "natural rate" of interest should be forward looking.

      Potential GDP (real and nominal) measures are forward looking, but they will miss technological leaps and destructive events.

    3. Thank you for the insightful response.

  25. John,

    I have been studying your paper “Monetary Policy with Interest on Reserves”. I am wondering if you could clarify some issues for me.
    The first equation you present says essentially (dispensing with the summation operator for clarity):
    Nominal value of bonds/price deflator = expectational operator X real discount rate X future surpluses
    To me this is a tautology, an accounting relationship almost and not a functional relationship at all.
    You then switch price deflators around and end up with:
    Nom. Value of bonds/price deflator X expect op. X inflation index = expect op. X real dis. rate X future surpluses
    To me this is still a tautology with some manipulations added.
    You then immediately conclude that:
    -unexpected inflation is determined entirely by expectations of future surpluses

    -govt. can determine expected inflation by nominal bonds sales.
    To me, this is like saying the following:
    Weight of box of apples = no. of apples X unit weight (i.e. a tautology)
    Weight of box apples X price index = no. of apples X unit weight X price index
    And then conclude:
    Price index is a function of the no. of apples (just because these variables are on opposite sides of an equality sign) which of course is absurd.
    I’m afraid this does not make sense to me.
    Can you clarify?

    1. Is price = expected present value of dividends a tautology? It's the same equation. Of course, if you discount at the ex-post rate of return it is a tautology, so in some sense both equations require you to be specific about discount rates to be useful. But price = expected present value of dividends seems to be very useful, and, again, it's the same equation.

    2. I can begin to see that adding expectational operators appears to turn the equation into a functional relationship, although I'm not quite convinced or can't quite see it. If you took your price = exp'd pv of divs equation and multiplied both sides, to preserve the equality, by the price of fish and then you could say the price of fish is a function of the exp'd pv of divs. That's what it seems you are doing with your first few equations in your paper.

      Going back to apples, if you said:

      Weight of box = no. of apples X unit weight


      unit weight = funct(rainfall, sunlight, fertilizer)


      weight of box = no. of apples X funct(rainfall, sunlight, fertilizer)

      This is clearly a functional relationship. It bears a hypothesis which can be tested.

      It seems to me the price = e'd pv of divs isn't quite the same sort of relationship and heading for the realm of tautology in which case nothing new is being said.



  26. So if you average Keynesian and neo-Keynesian don't you get the right answer?

    I've assumed since the 90's that we would have deflation as the boomers retired and it sounds like that is what's going on.

    I haven't been paying close attention but, given the apparent current stability, can it not unwind the QE open market operations and let inflation land where it will?

  27. Equations (1) and (2) of the model describe expectations at time t of inflation (π) and output gap (x) in the period labelled t+1. Eq. (1) and (2) can be resolved to obtain uncoupled equations describing the inflation and output gap expectations at time t. If the model specification is, using output gap as an example, x(t+1) = f(x(t), π(t) ; β, κ, σ) + ε(t) where f(...) is the function describing the expected path of x(t), and ε(t) is a disturbance term having zero mean and variance ν(t), then the equations (3) and (4) are mis-specified. In other words, eqn. (3) and (4) omit the possibility of innovations (disturbances) affecting the path of x(t) and π(t), i.e., actual output gap and actual inflation. Beyond that narrow observation, the model also omits the possibility of shocks as might be generated in one or more time-varying Poisson processes. Issues around 'controllability' and 'observability' would also have to be explored if the model is intended as a specification of a control system (i.e., FRB policy moves).

    1. For a blog post, equation (3) is the perfect-foresight solution. The stochastic solution has an E_{t+1} on the right hand side. I wrote down the solution at time t+1 just because it made the sums on the right hand side prettier. When you're looking at an impulse-response function, which this is, expected future shocks are zero.

  28. Raising Rates could actually Stimulate the US Economy

    Given that private sector borrowing demand for investment may well be inelastic to the current ultra-low level of interest rates, raising rates could actually stimulate the economy.

    Since interest on excess reserves would likely be funded by additional government borrowing, the sectoral balances identity means higher rates would be stimulative as long as aggregate private sector borrowing was inelastic to a rate rise.

    If rate policy was well communicated, raising rates from zero to 1% could plausibly have no negative effect on aggregate borrowing demand. But the Fed should clearly resolve its "dot-plot disconnect" (ie. the Fed's expectation of its terminal rate is far above current market consensus) as soon as possible, to placate fears that rates would become restrictive too quickly. Indeed such a disconnect may be the true cause of volatility rather than a rate rise, per se.

    Vice versa, QE is actually a form of austerity when borrowing demand is inelastic. Unless QE stimulates private sector borrowing demand enough to offset the Fed's own profits (money taken out of the economy), then the sectoral balances identity means QE must have a net restrictive effect.

    Everything hinges on the response of private sector borrowing to changes in current ultra-low interest rates, which itself depends on the quality of Fed communication as they withdraw from unprecedented market manipulation. It is plausible that a return to unmanipulated bond markets could spur greater borrowing for investment.

    Thus Larry Summers may himself be making a dangerous mistake (FT article: “The Fed Looks Set to Make a Dangerous Mistake, FT August 24th):

    Similarly Bridgewaters' expectations of QE4 could prove erroneous:

    In summary, given that 1) current economic conditions have no precedent, 2) the response of private sector borrowing for investment depends critically on Fed communication as well as other factors, 3) future Fed communication cannot be predicted with any certainty, then dire forecasts from high profile commentators could be more damaging to the US economy than a small rate rise.

  29. John, would incorporating a "net base money" figure help? Bank reserves are effectively equity capital. A seriously overleveraged banking system might absorb immense volumes of excess reserves - perhaps with the shadow banking liabilities as the non-book offsetting liabilities - without moving the needle of NGDP much. Preexisting debt has already immunized the effects of additional reserves. Base money netting out liabilities might be the better NGDP/inflation metric.

  30. Prof. John, what about non-linearity of your described process?
    I mean look and plot rising nominal rates and inflation: when they both starts from even more low levels, it seems less and less manageable the rising in CPI!
    Remember we are at zero bound at a pixel time. FED could be wiped out of all its capital. Ugly times ugly, maybe Nomura's Chief Economist was right (he had a similar conclusion like you) ==>
    ...from min. 45.00 till end
    Fasten our seatbelts

    1. John, I would also add that along marrying your Theory, we should convene that extreme volatility can also occur during hyperinflation periods (honestly I don't know how this could happen, but maybe an asteroid!

      I suggest you the reading of Cole's original idea about that:

    2. I here have many questions that only time and an open mind will solve, as you mentioned many ideas had been proven wrong in the last seven years. What once was considered fact now is mere rumor, this idea of slower growth and how inflation will steadily keep rising in the long term. The idea of raising rates subject to a healthy state of the economy (unemployment, inflation) everything must be aligned, nothing can be left to error. FED authorities as you rightly mention have this impeding question to solve, the faster the better. And again the idea of this new bomb, and how this rates will shake the foundations. Thank you very much for posting this professor Cochrane.

  31. Inflation likely has to do much more with fiscal policy than monetary policy. Let us use an extreme scenario consider likely outcomes. Suppose tomorrow that the the US government decided to cut all tax rates to 1% and committed to this for the foreseeable future. This would add a large amount of money to circulation and likely inspire inflation. The opposite would be true if the US government decided to raise all tax rates to 90%. This would drain large amounts of money from the economy and likely cause deflation.

    The central bank has much less ability to control inflation and deflation. Consider if it raised interest rates to 20% tomorrow. The immediate reaction may likely be to inspire deflation. However, once bondholders started receiving 20% interest on their money the amount of money in circulation would be much greater than if bond holders were receiving 2% on their money. So the outcome could actually be a quick deflation, followed by a slow inflation. Ultimately the effect is ambiguous. Regardless, as compared to tax/fiscal policy, monetary policy is much less potent a device for affecting inflation. So in the interest rate data we mostly see the effect of fiscal policy overwhelming the monetary policy.

    Note the curious case of Japan. Even with all the deficit spending, and low interest rates, inflation is subdued. That's because they haven't committed to lower tax rates.

    The market is indicating low expected inflation because it does not foresee any drastic commitments by governments to cut taxes or drastically increase deficit spending. In fact, most economies have been signaling the opposite and adopting austerity policies (or at least overtures). Thus governments are signaling a commitment to low deficits and status quo tax policies. Or in other words, tight money.

    -Greg V

  32. Those upper limits on the sums should be "t"? Or relative to whatever time the future policy change was announced?

    Also in this model, if there's a positive "inflation shock" - inflation tries to jump away and above from the equilibrium path given by (3), if that makes sense - then that is expansionary, no? In order to get back on the stable path the output gap has to also increase.


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