Saturday, November 5, 2011

Does Nominal GDP Targeting Imply Instability?

Adam P, writing at Canucks Anonymous, claims that Greg Ip's citation of Lawrence Ball's 1999 paper shows that "targeting NGDP is simply a horrible idea." Why is it a horrible idea? According to Adam P.:
Well, I sat down this morning and worked out the implied policy rule for the interest rate that stabilizes expected NGDP two periods ahead (this took just a few minutes) and it generates exactly the large oscillations in real income and inflation that Ball obtained with the rule that actually would be correct in his model
He then quotes Ball:
The overshooting result appears robust; it arises, for example, in Dennis’s
model, as long as the lagged-inflation term in the Phillips curve has a positive
weight. In that model, the oscillations die out over time, implying finite variances.
But the variances are still large relative to efficient policies.
He criticizes Ryan Avent for thinking that the fluctuations were supposed to be in nominal GDP. Quite the contrary, he insists:
Ryan, you have to understand the paper to critique it intelligently! What happens in the model is not that NGDP swings above and below the target, NGDP stays basically on target, it's just that this isn't necessarily good! The reason it's bad is because while NGDP stays on target inflation and real output are oscillating above and below target and real output is the thing we actually care about most!
Adam P. was even so kind as to consider my position on the matter, I had said:
"I don’t believe this is realistic. That is, Ball did develop a model that has this consequence. His model of the macroeconomy was pretty standard. However, I don’t believe that it is realistic to expect inflation and real output to wander arbitrarily far from their long run levels when nominal GDP grows on a target growth path. Something is wrong with these models"
He responds:
That is an incredibly weak response, "I don't believe..." is hardly an argument. Where is the reasoning to believe something is wrong with "these models" instead of something being wrong with NGDP targeting?
Scott Sumner has responded to Adam P, and I share his irritation. Why would any economist take seriously the claim that a constant nominal GDP could possibly cause prices to veer off to infinity and output to zero, and then have output veer off to infinity and prices fall to zero?

Firms are going to produce nothing and charge infinite prices? Doesn't that seem a bit foolish? Worse., firms are going to produce infinite amounts of output and give it away? How is that consistent with maximizing profit?

Why would anyone worry that there is no solution to a system of equations that holds nominal GDP constant? What would that mean in the real world? Total spending on final output is $17 trillion dollars, and... what? Firms set no prices or quantities? Everyone just stands around not knowing what to do?

That is absurd.

If a model fails to have a solution for prices and output, then it is a problem with the model. Firms will do something and they must be setting prices and producing output in order for nominal GDP to be $17 trillion. The model evidently fails to tell us anything about what they are doing if there is no solution.

The infinite absurdities--the deflationary booms that are completely inconsistent with the scarcity of resources should create doubts about the value of the model. Do we just change the coefficients a bit so that our deflationary booms are not utterly absurd?

If nominal GDP targeting is successful, that is, nominal GDP stays on target, then it is like having a unit elastic demand curve in microeconomics. The profit maximum for a monopolist would be where marginal revenue equals marginal cost. The price is what the market will bear at that quantity. Quantity and price are determined. How likely would it be that a monopolist would oscillate between a price higher and quantity lower than the profit maximum and a price below and quantity higher than that maximum? And what about even more extreme oscillations between giving the product away for free and producing whatever buyers will take or else producing and selling nothing and setting a price of infinity? And then, suppose there is "no solution" to the equations. Does the monopolist just do nothing?

Now, suppose instead there is a competitive market with unit elastic demand. The usual micro approach is that quantity supplied equals quantity demanded. Is it possible that firms will set prices above equilibrium, and limit production to the quantity demanded? Then, they will respond to the surplus in the market by producing an amount beyond the equilibrium quantity and setting a price below equilibrium?

In microeconomics, this is called cobwebbing. And while having firms give away infinite amounts is a stretch, myopia can lead to cobwebbing.

Consider a microeconomics where firms set their prices, not at the level expected to clear the market, but rather based upon the past rate of price change. Overshooting would be inevitable, right? There is a shortage. Firms raise prices. Once the price reaches equilibrium and the market clears, they raise their prices because prices have been rising in the past. So, the price is above equilibrium.

Now, prices are cut. This clears up the surplus. When the price is at equilibrium, the firms continue to cut prices, even though markets are clearing, because prices have been falling. This creates a shortage.

With nominal GDP targeting, the equilibrium price level is the target for nominal GDP (if it actually will be reached,) divided by potential output. If the system is expected to work, the expected equilibrium price level is the target for nominal GDP divided by expected potential output. And, as usual, the equilibrium level of output is potential output. If the price level is set at the expected equilibrium price level, and nominal GDP is on target and potential income is at the expected level, then real expenditure will equal potential output. The price level will clear markets and real expenditures will purchase potential output.

That has to be the where any model begins. If you start with a model inconsistent with that result, especially one that requires cobwebbing, then nominal GDP targeting will not be "optimal."


  1. Nice work, great blogging

    The feeble nature of the anti-NGDP arguments is interesting. Really, that nominal targeting would lead to increasing oscillations or exacerbated cycles flies in the face of common sense. You know, like a bridge where people are marching in unison.

    My only question is why didn't we adopt NGDP targeting decades and decades ago?

    I think today we would, save the liberals want to spend, and the conservatives want Obama to lose.

    The two parties have become so ossified, both intellectually and by interest-group pressures, that NGDP targeting still has a steep road.

    Thanks to bloggers like Woolsey, the blog debate has been won by Market Monetarists, and the print debate is being won too.

    But can we win where it counts: In the Fed?

    Forward Market Monetarists!

  2. I can come with a way in which inflation and output can be arbitrarily far away from trend under an NGDP level target that does make sense.

    It involves arbitrarily large supply shocks.

    So for instance, consider a near-extinction event that kills 90% of the population. You've just reduced potential output by (roughly) 90%. If the 10% of central bankers who are left maintain an NGDP level target based on before the calamity, and there are not huge waves of immigration from outside, then the price level will go up by 10x.

    Similarly, if we get to the other side of a friendly AI singularity and suddenly potential output becomes essentially unlimited, maintaining an NGDP target is going to result in incredible deflation. Comapnies will in fact produce nearly infinite amounts of output and sell it for nearly nothing (by our current standards), because productivity will be so high (by our current standards) that it is profitable to do so.

    What's interesting is that even in these etremely corner case scenarios, NGDP targeting is probably better than inflation targeting.

    In the positive singularity scenario, I'm not sure it matters what your monetary policy is, but NGDP targeting and massive deflation will make sure that anyone with a significant positive net worth when the singularity happens will be effectively rich on the other side. It's potentially brutal for those who are in debt, but so is almost every post singularity scenario where the prime holders of capital are not willing to share. The smaller your deflation rate (or higher your inflation rate), the more people will be reduced to a malthusian competition with robots/ems/whatever under a "post-singularity capital holders behave like 2011 capital holders" scenario.

    For the calamity negative supply shock, it seems like massive NGDP catch up growth is the best way to pursuade holders of capital that it is crucially important to get your capital matched up as efficiently as possible with remaining labor. What other money supply rule would be better?

  3. I feel like you and Sumner make the same mistake when you blog. You essentially say, "First, assume we are right. Now, prove us wrong."

    How is anyone supposed to raise concerns with your models if you obtusely demand that everyone first accept all of your assumptions.

    That's not a defense of any particular problem with Adam P, just a question of rhetorical methodology. You're not building a strong case for NGDP targeting, you're instead obfuscating every objection raised against it by demanding that your own assumptions always hold true.

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