## 09 March 2016

### Market Monetarism

My list of questions and/or criticisms that I don't think have been properly addressed for/of Market Monetarists has increased to such a degree that I think the best way to deal with everything is just to write one blog post and send it to a Market Monetarist (probably Nick Rowe, who seems to be the most reasonable one, from my experience, and probably the only one who will bother to respond).

Natural Rate Hysteresis:

The Wicksellian natural rate is completely forward looking in sticky price NK models (with either Calvo or Rotemberg pricing). Does switching to something like Taylor Contracts for the price level or nominal wage result in a backward looking natural rate? If not, why do you think that there is natural rate hysteresis (theoretical explanation, please. I don't care if you think you see it in the data, because the natural rate is unobservable).

Falsification:

What, if anything, would you have to observe in the data to determine that liquidity traps genuinely exist? Apparently low inflation despite high monetary base growth (i.e., money demand at unprecedented levels) since 2009 doesn't convince you, so what would?

Concrete Steppes:

Since central banks don't commit to monetary policy in the very long run (or, if they do, the commitment doesn't suggest anything quantitative), is it not reasonable to conclude that deliberately communicated actions by a central bank (forward guidance can be included here) are necessary for actual changes in monetary policy?

NGDP Targeting:

In sticky price models, NGDPLT does not prevent the zero lower bound from binding when there are large persistent negative shocks to the real natural rate. Does wage stickiness remove this problem? If so, what evidence is there for wage stickiness (I mean, there has to be a reason why the profession switched to sticky prices and I'm fairly certain that reason is usually stated as 'there's no evidence for a high degree of wage stickiness').

Liquidity Traps:

Imagine we're in a multi-period version of Krugman (1998) in which the CIA constraint is not binding and will not bind for the next five periods. Do you agree that any current OMO will be completely useless? Of course, the central bank can simply increase the money supply five periods in the future (when it once again has control over the price level) and recursively set the nominal interest rate to be greater than zero, so there is a way out when the liquidity trap is finite. But, in the real world, the length of the liquidity trap is not set in stone. What if this is the case, so the central bank has no idea how far in the future it must induce expectations of the money supply to be higher in order to escape the liquidity trap. In this case, would you agree that the only reliable way to escape the liquidity trap is to decrease the current money supply until the CIA constraint binds?

Fiscal Policy:

I'm assuming you would agree that, ceterus paribus, fiscal stimulus raises the real natural rate. Given this, what reason do you have to oppose fiscal stimulus at the zero lower bound -- I know you don't think monetary policy is impotent in this case, but, given the possibility that us Keynesian's are right, what's wrong with a higher natural rate (and, correspondingly, a higher nominal interest rate), especially since we all agree that monetary policy is effective off of the zero lower bound. Similarly, why support austerity if it lowers the natural real rate; what's wrong with making the job of a central bank easier?

Money Demand:

Does your preferred money demand function more closely resemble MIUF (in which the nominal interest rate can never actually hit zero, lest money demand be infinite) or CIA (in which a zero nominal interest rate implies indeterminate money demand, which means that OMO's are completely useless as long at the nominal interest rate equals zero)?

1. 1. Natural rate hysterisis. Examples. The natural rate depends on stocks of capital, and technology, and distribution of wealth, and a recession will have long-lasting effects on all those things. But there's nothing specifically MM about that.

2. Falsification: Hmmm. Ideally some sort of controlled experiment, with large n. Some central banks are ordered, with penalties for failing, to target a higher NGDP or Price level path. And this is made public. If they do no better than the control group, that would be evidence against MM.

3. Concrete steppes. I think there's a typo in your question. I don't understand it.

4. If the real natural rate is negative enough, and the targeted growth rate in NGDP low enough, there is no equilibrium where currency pays 0% nominal. You either raise the NGDP target growth rate, tax currency, or have a Miles Kimball crawling peg depreciation on currency.

In Krugman 1998 just announce a permanent OMO.

Fiscal policy may or may not raise the natural rate. Fiscal policy has other objectives, and it cannot do two things at once, if those other objectives conflict with getting AD right.

There are many different nominal rates, not just one. Because there are many different assets, not just one type of "bond". OMOs are never tapped out, until the CB runs out of assets to buy. And other things equal, people always prefer more liquidity to less. The CIA constraint being binary only makes sense in a simple discrete time model. People are never satiated in liquidity. You never know if you might want to spend everything the next minute.

I think I have addressed all the above questions in various blog posts over the years.

1. Regarding Concrete Steppes:

I'm basically challenging your (paraphrasing) "monetary policy is 99% expectations" claim.

I think that 1) expectations about monetary policy in the distant future are too uncertain to matter, 2) the 'forward guidance puzzle' exists (i.e. forward guidance is not as awesome as basic NK models predict), so expectations about the nominal interest rate are not very useful, 3) because of 1) and 2), the importance of expectations in monetary policy is limited.

Regarding Krugman 1998:

A permanent OMO won't work unless CB commits to raising the nominal interest rate, which can only be reliably done by reducing the current money supply until CIA constraint binds.

By 'reliably,' I mean that this is the only option that the CB can actually do without relying on HH expectations of the nominal interest rate, which, once the ZLB binds, are indeterminate.

Other Assets:

I agree that government bonds and other assets are not necessarily perfect substitutes, so OMO's with non-government bonds could be effective, but I'm not sure about how effective they could be.

2. Any financial asset (including money) is just a worthless bit of paper with a promise written on it. It's worth as much as the promise is believed. I should not have said "99% expectations". I should have said "100% expectations". (For Canadian dollars, the promise is currently: "I will try to make this bit of paper (actually plastic) depreciate at around 2% per year against the CPI basket of goods".

"A permanent OMO won't work unless CB commits to raising the nominal interest rate, which can only be reliably done by reducing the current money supply until CIA constraint binds."

?? I'm pretty sure PK would agree with me that you are wrong there. Or I'm misunderstanding you.

1. Think about it this way.

In period 0, the central bank makes a credible promise to shrink the money supply by more than the rate of time preference over the next period. This causes the ZLB to bind and the CIA constraint to not bind. Now the CB can do literally anything to M(0) and nothing will happen to the price level, unless it reduces M(0) to a level lower than it was originally.

Now we enter period 1. Is the CIA constraint binding? This is only the case if 1) the CIA constraint will bind in the next period or 2) the money supply is low enough for the CIA constraint to currently bind (i.e., the money supply is below what what would be consistent with deflation at the rate of time preference).

Continue this forward: whether or not the current CIA constraint binds depends ultimately on whether or not the CIA constraint at t=infinity binds, which is no longer determined the minute the CIA constraint ceases to bind.

So, in theory, you could do a permanent OMO that doesn't have any effect.

2. Also, let's look more deeply at hysteresis in the natural rate. You mentioned the capital stock, which, given production technology $Y_t = F(K_{t-1},L_t) = K_{t-1}^\alpha L_t^{1-\alpha}$ would imply the natural rate $r^n_t = F_K(K_t,L_{t+1}) = \alpha K_t^{\alpha-1}L_{t+1}^{1-\alpha}$. Given that $0 < \alpha < 1$, the natural rate is a decreasing function of the current (non-fixed) capital stock, which means that natural rate hysteresis of the kind MM's talk about requires recessions to result in higher equilibrium $K_{t-1}/L_t$ -- something that makes literally zero sense to me.

Demand shocks having an effect on TFP seem to be anything but standard, unless you're referencing some consensus endogenous growth business cycle model that I don't know of.

I'm at a loss as to how the distribution of wealth is supposed to affect the natural rate.

3. In PK's model, if the natural rate is permanently negative, than a permanent OMO will not work. Is that what you are saying? If the natural rate is temporarily negative, a permanent OMO will work.

4. "In PK's model, if the natural rate is permanently negative, than a permanent OMO will not work."

Not quite. In my thought experiment, the real interest rate is constant at the rate of time preference. The only difference between my thought experiment and PK 1998 is that I don't just assume the liquidity trap ends in the next period.

I'm pretty sure (from what I think amounts to hours antagonizing over it in my head) that, once the liquidity trap starts, the reliable only way out is to tighten monetary policy (reduce the current money supply).

A permanent OMO won't work unless agents (irrationally) expect the liquidity trap to end; they never need to economize on their cash balances so long as the nominal interest rate is zero and if the nominal interest rate is zero forever, then even a permanent OMO will do nothing.

So, then the job of the CB is to raise the nominal interest rate without cutting the current money supply. It can only do this is the nominal interest rate is positive in the next period, or the next period, and so on.

My reasoning is really hard to explain and I'm annoyed at my inability to actually simulate a model that can handle indeterminacy properly, so there's a large chance I'm wrong, but I don't think I am.

5. OK. I think I sorta see where you are going. But it's too early in the morning for an old guy like me.

"I'm pretty sure (from what I think amounts to hours antagonizing over it in my head) that, once the liquidity trap starts, the reliable only way out is to tighten monetary policy (reduce the current money supply)."

But that part sounds wrong. Unless you mean reduce M in period 2, so it will be increasing again in period 3??

I did a post where I took PK's model, and merely by changing the notation, got a very different result!!! Define m(t) = M(t)-M(t-1). CB controls m(t). Then monetary policy works! ;-)

6. Basically, the important thing in the model is $\frac{M_{t+1}}{M_t}$. If this ratio ever goes below $\beta$, then there is a liquidity trap. At this point, the only way out is to reduce $M_t$, since all the future price levels are no longer determined by any $M_t$ (i.e., increasing $M_{t+1}$ will have no effect on $P_{t+1}$, so the only way to escape the liquidity trap is to lower $P_t$). At least I think that's how it works.

Of course, in the real world liquidity traps aren't expected to last forever, so, specifically in the case of Japan, what really matters is how credible the monetary expansion is.

The only issue is that, somehow, the BOJ thinks it can control the nominal interest rate and the monetary base independently. This should only be the case if there is a liquidity trap (i.e., money demand is indeterminate), which tells me that they still are in a liquidity trap and will be in one until they 1) stop setting the nominal interest rate and announce that they will continue to grow MB absurdly quickly until the nominal interest rate goes up or 2) wait until the economy improves to the extent that they can end the liquidity trap by tightening monetary policy normally.