In Which I try to Defend Janet Yellen from Brad DeLong

Fed Chair Janet Yellen said, among other things,

For this reason, if the economy continues to improve as I expect, I think it will be appropriate at some point this year to take the initial step to raise the federal funds rate target and begin the process of normalizing monetary policy. To support taking this step, however, I will need to see continued improvement in labor market conditions, and I will need to be reasonably confident that inflation will move back to 2 percent over the medium term.

After we begin raising the federal funds rate, I anticipate that the pace of normalization is likely to be gradual. The various headwinds that are still restraining the economy, as I said, will likely take some time to fully abate, and the pace of that improvement is highly uncertain. If conditions develop as my colleagues and I expect, then the FOMC’s objectives of maximum employment and price stability would best be achieved by proceeding cautiously, which I expect would mean that it will be several years before the federal funds rate would be back to its normal, longer-run level.

The news is that “some point this year” means “not next month” A possible increase in June 2015 used to be discussed a lot.

Brad DeLong argues that raising rates “sometime this year” would be crazy. The justification is that unemployment will be low and inflation will not be far below target. This would imply no normal reason to raise rates. Brad’s main point is that the speech includes no consideration of the risk of hitting the zero lower bound due to a shock after raising rates.

After quoting Brad, I’m going to go to a long boring comment. The main point, if any, is that a speech describing a sub-optimal plan for interest rates (as a function of future information) may be an optimal speech. But I also type about optimal control (both of us are trying to do math in our heads using plain English). I want to stress here that I think Brad is making a very important very valid point.

Finally I hand him the mike

If your control variable has a bound–like the zero lower bound on interest rates–the optimal control policy is different. The fact that you cannot lower your control variable below its bound adds an extra term to the math. This extra term makes it unpleasant to be even near the bound. So you should take steps to stay away from it–which means lowering your control variable closer to the bound as you get near it. And the nearer to it you are, the more you lower it below what it would be if there were no bound constraining it.

this bound principle has the implication that if do you wind up at the bound, you want to get off of it as soon as possible in a way that makes it highly unlikely you will wind back at it. Hence you stay at the bound until your optimal policy in the absence of the bound is well away, and then you move your control variable rapidly until it once again is expected to drift only slowly.

Thus Janet Yellen’s declaration today makes no sense: from an optimal control of you, you want to wait to raise interest rates until the economy is sufficiently strong that the appropriate interest rate raise is a substantial one.

I think the last words should be “is sufficiently strong that the interest rate which would be appropriate if there were no lower bound is substantially greater than zero” Way at the end of the post, I explain why this is different from what Brad wrote.

Most of my comment is after the jump

This is a public speech. I have a story for why she thinks it was optimal. It goes as follows

Remember how the markets freaked out when we said we would taper QE3 ? We promised we weren’t going to raise the target federal funds rate and federal funds futures freaked fiercely. It is clear that lots of investors are just waiting for us to turn back into normal central bankers all of a sudden.

Sooner or later, we will have to raise the federal funds rate. There is a risk that investors will assume that we are going to turn into Trichet. This would be very bad. So we have to start now saying it won’t be a huge deal when we raise the target a bit.

I think she is saying we aren’t going to do anything dramatic and scary. Don’t be scared by anything we do. Don’t panic.

It seems to me to be optimal control to say that. The instrument I am discussing is the speech *not* the federal funds rate.

Second there is the goal of also proving that she is not a raging reincarnation of Rudolf Havenstein. Repeated statements that even discussing raising rates is insane are accurate, but would infuriate powerful people. It is useful for Yellen to Clinton and say “I feel your desire to inflict pain.”

Third I don’t see why a the rate increase is large when, finally, an increase is optimal. At all.

Consider a pretend forecast. In the next few months, unemployment falls to to 5% and stays there. I sat keep rates as low as possible. Core inflation creeps up 0.1%/yr each month (with no wiggles cause I am making this up). everything else grows at a normal rate. Some FOMC meeting should raise the target rate certaainly before inflation hits 100% per year.

Say the month of Austember is the one when it should raise the rate, In constrast during Stimember (the month before austember) the target FF rate should be 0-0.25% . There must be two such months if 100% inflation is not optimal. From Stimember to Austember the only change is an 0.1% increase in the core inflation rate. This can have only a small effect on the marginal cost of inflation (which I consider trivial at 4% inflation) and also only a small effect on the expected present discounted cost of the future ZLB (being the value of the option to set interest rates below zero which we wish we had).

All has changed little so the optimal federal funds rate can’t be high — the costs and benefits of raising it to 0.5% have changed a little (just enough so the benefits are greater than the costs). How can it be sensible to raise it to 1% ?

update: Brad explains what he meant (I was tempted to leave out the words, because the figure is enough for me, but I’m not sure I know what is clear ( see the comment including “gibberish” below))