My once and future dream is that the blogosphere would replace academic journals as the primary medium of intellectual exchange. We are far, far, far from that but this debate over deflation is getting sufficiently wonky that a boy can dream. If only there was some easy way to incorporate an equation editor into a blog writer, we would be off to the races.

Now to the subject at hand. Stephen Williamson rides in to defend Kocherlakota:

What [Krugman, Rowe, Thoma and Harless] are objecting to in Kocherlakota’s speech is one of the most innocuous things he said. Here’s the simplest example I know. Suppose a cash-in-advance model with a representative consumer, period utility u(c), discount factor b, constant aggregate endowment y. c is consumption. The consumer needs cash to buy c each period. Suppose y is a fixed quantity of output received by a firm, which is sold for cash within the period, and then the cash is paid as a dividend to the consumer at the end of the period. Have the money stock grow at a constant rate m. The real interest rate is constant at 1/b -1. The nominal interest rate is (1+m)/b – 1, and the inflation rate is m. Constant m implies a constant nominal interest rate and a constant inflation rate. If m < 0, there is deflation, and the nominal interest rate is sufficiently low to support the deflation. I can think of the instrument the central bank sets as either the money growth rate or the nominal interest rate – that part is irrelevant. This type of result holds in virtually all monetary models, though of course sometimes the real rate may depend on the inflation rate. That’s not a big deal though. What’s the problem?

Let me say again. There is absolutely nothing inaccurate about what Williamson is saying. It falls simply and elegantly out of our monetary models.

The blogosphere is reacting with shock and despair because the conclusion doesn’t look anything like what they would expect to happen in the real world. In the real world if the Fed set a permanent low interest rate target all of our intuition, training and observations say that the result will be hyperinflation not deflation.

The question is: How can we reconcile the two?

As is often the case the key difference is hidden in a seemingly innocuous turn-of-phrase. Williamson writes

I can think of the instrument the central bank sets as either the money growth rate or the nominal interest rate – that part is irrelevant.

In some sense what Williamson is saying here is a mathematical necessity. For every nominal interest rate there exists some path of money which is consistent with it. I can choose one, or I can choose the other.

Where the confusion sets in is that a semi-plausible sounding nominal interest rate target can mathematically imply an obviously insane path for money. Yes, there is a one-to-one correspondence between the two in fact. Where the correspondence breaks down is in intuition.

For our particular example, we are considering a permanent nominal interest rate of .25% On the surface that seems like an, odd, perhaps dangerous, but doable goal. In reality its bat shit crazy and no one would ever believe that the Fed even had the ability to do it.  Allow me to explain.

If the Fed is truly committed to a .25% nominal interest come-what-may then it is committed to expanding the money supply as rapidly as money demand requires. It doesn’t matter how many trillions upon trillions of reserves are required to meet that target, the Fed has committed to meeting it.

The key element you have to rap your mind around is that the Fed is doing this irrespective of the consequences. You have, for the purposes of this thought experiment, fixed the nominal interest rate for all time.

Now then what happens out in the real world.

Well, a permanent short term nominal rate of .25% means that long term rates must also be .25%. Is there some bend to the yield curve? Aren’t investors worried about inflation, deflation, etc? No, they are worried about nothing because the Fed is absolutely going to keep short term nominal rates at .25%. This is fixed and forever true.

If long term rates were any different then I could simply arbitrage the two and make a guaranteed profit. So all long rates are now .25%.

This means that Fannie / Freddie mortgage rates collapse to around .25%. Remember there is no prepayment risk in this world because interest rates will always and forevermore be .25%. In addition, there is virtually no risk to 30 year interest-only balloon mortgages, because rates will always be .25%. So that means I could borrow 300K for my home and my monthly payment to the bank would be $62.50.  So we have essentially free mortgages.

Car loans collapse to .25% plus risk premium. Credit Card offers come through the mail that say 0% APR on all purchases, all balance transfers, all cash advances (plus 3% processing fee) FOREVER. Credit Cards can do this because the cost of funds is only .25% and they make 3% off the merchant fees. Add in the profits from late fees and there is no need to charge the on-time customer a dime, ever.

Similarly, corporate bond rates collapse. Mergers and Acquisitions fly into high gear as massive leveraged by-outs sweep Wall Street. There is nearly free money FOREVER. If you think you can get a return on equity of at least .25% in all periods then buying the company is a slam dunk.

All of this activity sends stock prices sky high, it sends home prices sky high, it sends commercial real estate sky high. The massive increase in paper wealth accompanied by free credit card purchases sends consumers on the shopping binge of a lifetime. The real economy goes white hot, and items are flying off of store shelves. Prices on everything rise: food, soap, paper towels, you name it, they can’t keep it in the store. There is free money – forever – and we are all rich.

In short, the result is massive inflation. This inflation would tend to push up nominal interest rates via the Fisher Effect. However, it can’t because the Fed is committed to .25% come-what-may.

That means that the Fed accelerates the expansion of the money supply so that even given huge inflation expectations the nominal interest rate stays low. This in turn feeds more inflation expectations which feeds more money creation and so on and so on.

Literally the continuous time models tell us that the inflation rate reaches infinity. That is,we shoot to a new, higher price level in zero time. That price level is one that is consistent with stock and home prices being discounted at .25% forever. The price level would have to be such that people as wealthy as they would be from those asset prices and with as easy access to credit as would come from 0% APR FOREVER, still would not want to purchase more output than the economy was capable of producing.

Needless to say these are extremely high prices since people can borrow so cheaply knowing that on paper they are so wealthy.

Like I said, inside the model this happens in zero time. That’s of course because inside the model everyone knows, that everyone knows, that everyone knows . . . that this is the end equilibrium and everyone faces zero costs to jumping straight to it.

So stores go ahead and figure out what the equilibrium price is and they just charge that. Same with homeowners, stock holders, etc. We see an instantaneous jump to a new equilibrium.

In the real world that is not possible. So, if the Fed tried such a policy it would get hyperinflation. It would get inflation that fed on itself in this same way but never actually reached an infinite rate. Eventually, however, we would hit the constraining price level.

What about the deflation?

Well with the nominal rate lower than the real rate, you want to engage in all possible investment today. By assumption in this model there are no adjustment costs so absent price constraints this would be possible. However, there is not an unlimited amount of investment goods and services to go around.

You want to build a thousand factories but there are not enough construction workers to do it. So construction prices go higher and higher to stop people from wanting to do it all today. However, this opens up an arbitrage opportunity.

As the owner of a construction firm, I can go to you and say, John, I know you want this factory built ASAP, but I’m a just completely booked. How about I do it for you next year for a little bit less? Are you willing to go for this?

Well if you don’t have the factory today you loose out on 1% of real return at a cost of only .25% in funds. So, if the factory is at least .75% cheaper next year its just as good of a deal for you to wait. So my firm offers you a cheaper deal next year and you agree to wait.

Next year, the same thing happens to another guy. He wants a factory now, but my firm is all booked up. Will he accept a .75% reduction in cost to wait? Yes, he will.

And the year-after-that, and the year-after-that, and the year-after-that.

So we have set ourselves up for permanent deflation in investment goods. It turns out the same thing has to be true in consumption as well. That’s because way back in the back of this model is a condition that essentially causes the average social discount rate to be equal to the real rate of interest.

That is, our society wide willingness to forgo consumption has to on average be the same as the return on investment. This means that as a society we are also willing to wait on the new TV or the new Ipad if we know its going to be cheaper later. In practice that would mean some people can’t wait and some people will be more than willing to wait. But, getting the average willingness to wait to match up with the realities of production will require .75% price drops each year. Again, permanent deflation.

So that’s how the model works its way into real life.  A commitment to a permanent .25% nominal interest rate would produce permanent deflation but only after a raging period of hyperinflation.

Such a period would be so insane that no one would believe the Fed had the stones to see it through. That’s part of why the argument: a permanently low rate leads to deflation seems so insane to most economists. The process of getting to deflation would be violent and likely untenable.