Thursday, October 22, 2015

Open-Mouth Operations

(Note: This post uses mathjax and has embedded pictures. When posts are reposted elsewhere these often get mangled. If it's not displaying well, come to the original at

Our central banks have done nothing but talk for several years now. Interest rates are stuck at zero, and even QE has stopped in its tracks. Yet, people still ascribe big powers to these statements. Ms. Yellen sneezes, someone thinks they hear "December" and markets move.

Buried deep in the paper I posted earlier this week is a potential model of "open mouth" operations, that might of interest to blog readers.

Use the standard "new-Keynesian" model \[ x_{t} = E_{t}x_{t+1}-\sigma(i_{t}-E_{t}\pi_{t+1}) \] \[ \pi_{t} = \beta E_{t}\pi_{t+1}+\kappa x_{t} \] Add a Taylor rule, and suppose the Fed follows an inflation-target shock with no interest rate change \[ i_t = i^\ast_t + \phi_\pi ( \pi_t - \pi^\ast_t). \] \[ i^\ast_t = 0 \] \[ \pi^\ast_t = \delta_0 \lambda_1^{-t} \] Equivalently express the Taylor rule with a ``Wicksellian'' shock, \[ i_t = \hat{i}_t + \phi_\pi \pi_t \] \[ \hat{i}_t = - \delta_0 \phi_\pi \lambda_1^{-t}. \] In both cases, \[ \lambda_{1} =\frac{\left( 1+\beta+\kappa\sigma\right) +\sqrt{\left( 1+\beta+\kappa\sigma\right) ^{2}-4\beta}}{2} \gt 1 \] Yes, this is a special case. The persistence of the shocks is just equal to one of the roots of the model. Here \(\delta_0\) is just a parameter describing how big the monetary policy shock is.

Now, solve the model by any standard method for the unique locally bounded solution. The answer is \[ \pi_{t} = \delta_0 \lambda_1^{-t}, \] \[ \kappa x_{t} = \delta_0 (1-\beta \lambda_1^{-1}) \lambda_1^{-t} \] \[ i_t = 0 \]

Here is the equilibrium path of inflation and interest rates (flat red line at zero).

And here is the path of output.  In each case \(\delta_0\) in the graph gives the size of the monetary policy shock. It's also the size of the inflation jump at time zero induced by the monetary policy shock.

Watch this mom, no hands... Interest rates do not budge throughout the episode. The Fed announces a monetary policy shock, and inflation moves just enough so that the systematic part of monetary policy offsets the shock, and Fed doesn't end up actually doing anything! We get the traditional results of monetary policy -- lower inflation and lower output, for example -- based just on talk!

If you're inclined to this sort of model, you might want to pursue this sort of solution as a model of our current "open-mouth" regime.

This is too far for me to go. It gives up on traditional "monetary" policy. "Monetary" policy is here pure "multiple equilibrium selection" policy. The Fed makes a different set of off-equilibrium threats and we jump to a different one of multiple equilibria.  Interest rates are completely irrelevant to the standard effects of monetary policy here.

So I view the calculation as an indication of fundamental problems with the model I wrote down above, a reductio ad absurdum.  But others may want to take it seriously. Hence the "thesis topics" tag.

Granted, the standard view of open mouth operations is that Fed statements change expectations of future interest rate paths -- actual, observed, equilibrium interest rate paths, not these shocks which are offset by inflation. But sooner or later rational expectations have to kick in -- you can't endlessly promise interest rate changes that never happen. So the open mouth operation is an interesting limit, in which statements about interest rates matter, but the Fed never has to actually do anything about interest rates.

Also granted, I don't have a better model of why markets move so much on Fed chatter.

The \(\Delta s\) numbers index how much fiscal policy must cooperate in each case. If there is a jump down in inflation, that means greater value of government debt, and fiscal policy must raise surpluses by the indicated percentage. For the fiscal theory of the price level, these paths are then paths that happen when there is a pure change of fiscal expectations, and the Fed does nothing about monetary policy. I find that a much nicer interpretation.

Reserve Bank of New Zealand Governor Donald Brash coined the word "open mouth operations," observing  that he seemed to be able to move interest rates by simply talking, without conducting open market operations. This is a second level of open mouth -- here the Fed can move inflation itself just by talking.


  1. Valter Buffo, Recce'd, MilanoOctober 22, 2015 at 11:51 AM

    This is great: and "open-mouth regime" summarizes almost everything we saw in the last few years. Central Banks here are not acting on "expectations for the future path of interest rates": they act on actual quantities, on the existing stock of securities. As you (better: less than you) "I don't have a better model of why markets move so much on Fed chatter": but I have the undestanding that traders and portfolio managers act on the fear of losing money; they fear the power of a player that could buy unlimited quantities at no cost. I don't have a better model, and still I am deeply convinced that 1) all this "gives up on traditional "monetary" policy"; and 2) "sooner or later rational expectations have to kick in -- you can't endlessly promise interest rate changes that never happen". But to raise rates, you need something to happen in the "real economy", that is: outside the financial markets. Unemployment at 5% is not sufficient (due to the declining workforce), you should see the "acceleration of growth" that has been promised too many times. So the point is: the "open mouth regime" is simply not delivering; in terms of discounted future payoffs, wealth is simply not growing; and rational expectations will eventually kick in. In my opinion that will have a very high cost in terms of Arrow welfare. As a closing argument, let me reproduce here what the WSJ is writing as a comment to today's Draghi show: "Nobody jawbones like Mario Draghi. Jawboning is a crucial skill for central bankers, with investors and traders hanging on every word and looking out for the most arcane change in language for a clue to what actions the central bank will—or won't—take. Look at the confusion surrounding the Fed’s intentions following its September policy meeting for a reminder of what happens when policy makers offer mixed messages. Hardly anyone expected the European Central Bank president to deliver more stimulus Thursday as policy makers met in Malta. And he didn’t. But he still managed to offer up much more than market participants had expected, dropping the biggest hint possible that more action is likely on the way when policy makers next gather on Dec. 3."

  2. +1 for Draghi. No jawbone list is complete without the man whose "Whatever it takes" speech kicked the can for the EZ for over 3 years and counting.

  3. Interesting.

    But we see in the apartment sector that rents rose about 4% in 2015 and are slated to rise 3.7% next year.

    This rise in rents may be tied to artificial constraints on supply due to ubiquitous local building and zoning codes.

    It seems to me the Fed can hold rates at zero, but eventually rising housing costs do impact the CPI.

    That said, if the NeoFisherians are right, and the Fed can kill inflation by holding interest rates at zero, then the goal should be 0% unemployment, as such a low rate of unemployment will not result in any inflation.

    I guess the NeoFisherians recommend holding rates at 0% and running QE at $100 billion a month.

    That might work.

    1. I am a lowly accountant. Would you please explain why "the Fed can kill inflation by holding interest rates at zero.", when Paul Volcker succeeded in killing the inflation of the late 1970's by raising interest rates to over 10 per cent?

    2. Interest rates are a measure of the supply and demand for credit. Currently there is more supply of credit than there is demand. In the 1970s the demand for credit was greater than the supply. Since the interest rate peak in 1982 interest rates have trended lower as the economy and the financial system have been able to steadily increase the supply of credit faster than the demand for it.

      For the past 30+ years a lowering of interest rates was coincident with a decline in inflation. Or did the decline in inflation lead interest rates lower? A test of this question would be to raise interest rates and see if that leads to higher inflation. But no serious policymaker wants to do this test. And for good reason as conventional theory states that raising interest rates would lower inflation and what is desired is higher inflation.

      But is conventional theory correct? For it seems to be the case that credit now operates mainly as a supply side enhancement and is in fact a deflationary force. Cheap credit has allowed has allowed businesses to invest in technology that has lowered the cost of goods. This has especially been the case with shale oil & gas. So it may very well be that increasing the cost of credit would increase prices. Or, in other words, increasing interest rates would be inflationary.

      Of course one wonders why it is desirable to increase inflation. I understand there is a conventional theory for that. But is it true?

  4. Great post! there is a problem with the link after "come to the original..." (I think there is an "h" missing), I clicked on it and it takes you to this other blog, which definitely doesn't seem related :)

  5. Central bank "talking" reveals information about the bank's target. Theoretically, if the bank had a perfectly rigid target, no bias, no politics, etc., then "talking" would have no effect, QE would have no effect, and small interest rate moves would have only a small effect.


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