Brain teasers from monetary theory and Scott Sumner

by on December 14, 2010 at 4:31 pm in Economics | Permalink

All this silly nonsense goes under the fold...

First, here is Scott Sumner's ideal world:

In an ideal world, we’d remove all discretion from central bankers. The Fed would simply define the dollar as a given fraction of 12- or 24-month forward nominal GDP, and make dollars convertible into futures contracts at the target price. If the public expected NGDP to veer off target, purchases and sales of these contracts would automatically adjust the money supply and interest rates in such a way as to move expected NGDP back on target. It would be something like the classical gold standard, but with the dollar defined in terms of a specific NGDP futures contract, instead of a given weight of gold. The public, not policymakers in Washington, would determine the level of the money supply and interest rates most consistent with a stable economy.

To proceed, not everyone will understand this post, which is DeLong on Scott Sumner:

As I understand Scott's proposal, it is this: Nominal GDP in the fourth quarter of 2007 was $14.291 trillion. A 5% growth rate from that base would give us a value of $17.455 trillion for the fourth quarter of 2011. Add on another 3% for the average short-term nominal interest rate we would like to see, and we have $18.153 trillion. Therefore the Federal Reserve would, today, announce that it stands ready to buy and sell dollar deposits to qualified customers at a price of $1 = 1/18,155,000,000,000 of 2011Q4 GDP.

If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be lower than $18.15 trillion, they would take the Fed up on its offer: demand the cash now, pay off the contract in a year by then paying 1/18,155,000,000,000 of 2011Q4 GDP, and (hopefully, if they were right) make money–thus the money stock would increase. If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be greater than $18.155 trillion, they would take the Fed up on its offer: give cash to the Fed now, collect the contract in a year by receiving 1/18,155,000,000,000 of 2011Q4 GDP, and (hopefully, if they were right) make money–thus the money stock would fall.

If nominal GDP were expected to fall, the Federal Reserve would be shoveling money out the door at negative expected nominal interest rates. If his scheme were applied today it would be quantitative easing on a pan-galactic scale, as everybody would run to the Fed with bonds to use as collateral for their promises to pay the expected futures contract in a year in exchange for the cash now.

The Federal Reserve would then become truly the lender of not just last but first resort. Why would anybody borrow on the private market even at 0% per year when they could borrow from the Fed at -3%/year? Savers would simply hold cash rather than try to match the terms that the Fed was offering borrowers. Borrowing firms would borrow from the Fed exclusively. The Fed would thus create a wedge between the minimum nominal interest rate that savers would accept (zero, determined by the alternative of stuffing cash in your mattress) and the nominal interest rate open to borrowers.

I expressed related reservations about a related version of the idea in the 1997 JMCB.  I am all for (rough) nominal GDP targeting, and considering the forecast, and for Scott's work in general, but I don't think the "automaticity" versions of it work.  NGDP targeting does best as a general guideline for the central bank, which the central bank follows to make the world a better place, but without renouncing some ultimate degree of discretion with regard to timing and targeting and how good a deal they offer everyone at this new and somewhat unusual version of the discount window.

It's a general problem with strict pegging schemes that some prices (or pxq variables) adjust more quickly than others, or are better and more quickly forecast than others, and that means arbitrage opportunities against the pegger and/or very dramatic swings in nominal interest rates.

So on this question I agree with Brad and not with Scott.

Still, there is a general rule: when Scott Sumner says you are wrong, you are wrong (this is somewhat distinct from the claim that "Scott Sumner is always right," though if he worded all his pronouncements in a particular way I suppose it would not be).

So perhaps Scott will say that Brad and I are wrong.  Or perhaps he will say that I am wrong about the general rule in the first place.  Or perhaps he will say that we have misunderstood him.

The broader underlying question is how strict a nominal GDP target or NGDP forecast target can be and that question is not very well understood.

1 Indy December 14, 2010 at 1:01 pm

It's amazing how much of Sumner's concept you can cram in a few words, "Level Target The Forecast". We will do everything within our power to make sure that NGDP grows at a smooth and stead rate, and even if we make errors and overshoot or fall short, we will *compensate and make up for them* and so, though there may be short-term volatility, in the long-term we can all but guarantee success at stabilizing this particular nominal aggregate.

2 Sean December 14, 2010 at 1:02 pm

I'm confused — isn't Brad's expectation of "QE on a pan-galactic scale" exactly the goal here? The goal of NGDP targeting would essentially be to produce inflation, since real GDP is going down. Once inflation expectations are built in, the attractiveness of the futures should go away.

3 beezer December 14, 2010 at 1:59 pm

I have no effin' idea what you jabroni are talking about. But I'm sure everyone in Lyndhurst NJ can make money at it.

4 FXKLM December 14, 2010 at 2:25 pm

"If nominal GDP were expected to fall, the Federal Reserve would be shoveling money out the door at negative expected nominal interest rates."

This assumes that that nominal GDP is still expected to fall after the Federal Reserve has shoveled money out the door on a pan-galactic scale. It seems to me that DeLong is assuming that implementing Sumner's proposal would not affect expectations for nominal GDP growth, in which case he's missing the point of the proposal.

5 Will Sawin December 14, 2010 at 2:34 pm

This reminds me of an idea I had.

Basically, if you assume that present consumption is as valuable as future consumption (why wouldn't it be? Magic?) then what you get is that the proper discount rate to use is (per capita nominal gdp growth)*(income elasticity of utility)

And if (interest rate)=(discount rate), people should make correct choices, which I think, though I haven't modeled it, means no bad economic volatility.

So if (income elasticity of utility) is 1, which is a reasonable assumption, then this would lead to the correct interest rate for holding dollars. Which would imply the non-existence of government bonds. The Fed and the government's combined levers should allow the government to finance exactly all its debt this way, no?

It would still run into the liquidity trap problem. Of course, there's no fundamental rule saying you're allowed to horde dollars. Expiration date?

6 Tom December 14, 2010 at 3:31 pm

Hm. Can someone explain why Brad adds 3% to the Fed payoff? It seems like the Fed wouldn't need to add a time premium since nominal rates are zero. And then it seems like once you get rid of the 3%, there is no issue with Scott's proposal.

But, I'm pretty confused about this whole thing.

7 Will Sawin December 14, 2010 at 3:37 pm

Thomas: Are future versions of you less valuable? Do their needs matter less? Is, to paraphrase the Greeks, the consumption of the son always less valuable than that of the father?

Suggesting it does seems to me as irrational as suggesting that the consumption of the brown eyed is more valuable than the green eyed.

Now, the consumption of the rich is less valuable than that of the poor, and the people of the future are likely to be richer than us. But we can exactly measure and account for this effect.

8 OneEyedMan December 14, 2010 at 3:51 pm

Negative interest rates on reserves would go a long way to handling the private savings problem that NGDP targeting could cause when nominal rates hit the zero lower bound. Sure, cash could still be horded. But the FED could increase the supply of high powered money if they saw this happening and they wanted to do something about it.

9 Will Sawin December 14, 2010 at 4:01 pm

Josh: If you had the option of reverse life insurance, whereby a private company would finance your consumption or investment in return for the chance to inherit your assets if you die within a specified period, that issue would be removed.

Unless you also discount your consumption for other reasons?

Do people demand this? Are regulations getting in the way? If it would truly simplify monetary policy, shouldn't the government improve it?

10 Bill Woolsey December 14, 2010 at 6:39 pm

I think I have a good grasp of index futures convertibility, and even Sumner's versions of the idea. DeLong lost me. The target for NGDP goes up by 5% but then a target for the nominal interest rate is added?

Anyway, having the Fed trade index futures at a fixed price has no impact on the quantity of money. No one gets money now for selling an index future to anyone, including the Fed. And while people generally do have to put up margin, people don't pay now when they buy a future.

However, the Fed can be obligated to use open market operations (and it shouldn't buy securities with zero yields,) to keep its net position on the contract zero. If the market expects nominal GDP to be above target, the Fed is left with a short position, and it needs to undertake open market sales (of ordinary securities) until the bears in the market balance the bulls at the target value. If, on the other hand, the market expects nominal GDP to be below target (like now, I guess) the Fed is left with a long position. And the Fed needs to make open market purchases of securities with interest rates above zero, until the bulls match the bears at the target value of NGDP.

Scott has traditionally favored making the open market operations compulsorary. The Fed must trade ordinary bonds in paralell with its trades of the index future.

By the way, bears will expect to make money when NGDP falls below target. And bulls will expect to make money when NGDP rises above target. If the Fed keeps its net position at zero, it is perfectly hedged. If NGDP does deviate from target, then either the bulls pay the bears, or the bears pay the bulls.

11 Curt F. December 14, 2010 at 8:13 pm

I'm not an economist, but I wonder whether one problem with the proposed NGDP targeting would be maintaining econometric integrity. With all sorts of vested interests vying for this or that level of NGDP, mightn't the various statisticians and econometricians who compile GDP statistics suddenly face "incentives" to shade the numbers this way or that?

12 cato December 14, 2010 at 9:06 pm

to clarify; theres a distinction between the futures market for NGDP and the mechanism by which money comes into the system.

the two parts of the proposal:

the futures market exists to give the fed the markets guess as to how NGDP is tracking.

open market operations (swapping bonds for currency) enables the fed to increase or decrease the money supply in order for the fed to move the futures price onto its target.

the whole role of the futures market is to find out how much money the market needs. (rather than a fed committee decide this)

the whole role of the open market operations is to expand contract the money supply (as it does now)

this is what sumners somewhat cryptic post above is about.

lets make an analogy to the human body. the head decides what to do (how much money we need) and the body carries it out (by swapping bonds for currency).

right now the fomc (fed open market commitee) is the head. it looks at a bunch of figures to determine how much money we need. the actual body is the open market operations which expand contract the monetary supply. (in australia we have inflation targetting the rba board looks how inflation is tracking, and makes open market operations. in the US its more complicated as the fed looks at prices and unemployment or at least thats its mandate)

in sumners proposal, the fed is decapitated, but the body remains.

who is the new head? well its the futures market that estimates future nominal gdp.

13 cato December 14, 2010 at 9:26 pm

i think where brad is going wrong is he thinks the futures market is the mechanism for changing the money supply, and also he seems to have added 3% nominal interest rate rather than subtracting it.

that is sumner wants 5% nominal growth because the real long term growth rate seems to be 3% plus 2% inflation which is currently thought to be about optimal. (although of course being a good conservative he thinks we might want to over time bring the nominal target down to the real ie no inflation)

14 dirk December 14, 2010 at 10:23 pm

I'm pretty sure when Scott says "in an ideal world" he means both "ideally the Fed would do this" and "ideally it would also work". Scott has acknowledged a number of times that he may be completely wrong and that it might not actually work. He offers a very clever idea that is worth considering and may be worth trying — but he never loses his economist's wisdom of uncertainty over the idea. DeLong dismisses it out-of-hand without displaying any such wisdom of uncertainty.

15 jg December 15, 2010 at 12:04 am

Why you can have soo much trust in the wisdom of the financial markets (future markets) after the recent developments in the US and World economy is beyond me. I think this man with his sceptical remark is on the right track.
"Speculators may do no harm as bubbles on a steady stream of enterprise. But the position is serious when enterprise becomes the bubble on a whirlpool of speculation. When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done.”(JMK)
The US financial markets got the world economy on the brink to a new Depression an d you really want to give them these new powers to decide over our destinies.Your faith in the invisible hand of speculation is really unshakable. Holy God, save us from this religion.

16 Phlebotomist December 15, 2010 at 4:54 am

I've been waiting for years for Tyler to preface one of his posts with the description "silly nonsense." The day has finally arrived! Hallelujah. We may be entering a new era of transparency.

17 The Money Demand Blo December 15, 2010 at 2:19 pm

"Allow for fat tails, volatility clustering and momentum effects and his proposal would be an disaster…"

Most of the time markets function normally, so even in the presence of fat tails, volatility clustering and momentum effects NGDP futures peg would function very well, much better than the current system. The proof is in the monetary history, which knows countless instances where the central bank successfully operated a peg (it may be a foreign currency peg, a commodity peg, or an interest rate peg as we have now in the US).

However it is interesting to take into account what will happen when markets don't function normally. By analogy to the 2010 May flash crash, when for a few brief moments the value of Accenture other companies has dropped to zero, we will sometimes get amusing headlines such as "Yesterday for a few seconds markets thought that the money supply will have to be reduced to zero to keep the economy on the NGDP path." However such type of volatility will create no lasting damage.

More important cases of market malfunction are related to instances where there is excess volatility on the required return in participating in the NGDP futures market, where there is loss of arbitrage between NGDP futures of different expiry dates, and where there is a loss of credibility in the peg that is related to possible insolvency of the Fed. But our current arrangements are not immune to the same problems, as the fed funds rate peg collapsed after Lehman, and it took more than a month to restore the credibility of the fed funds rate peg.

18 Rajiv Sethi December 15, 2010 at 11:45 pm

Bill, I'm sorry for being late to respond, and the somewhat cryptic and abbreviated original comment. I have been traveling.

I mentioned the empirical regularities because they are usually (though not universally) believed to result from the existence of positive feedback trading strategies. At least most models that can generate these patterns allow for the use of such strategies. If they are sufficiently rare this does not pose a problem for market stability but occasionally they become widespread enough to destabilize markets and then we have a major departure of prices from fundamentals followed by a crash or prolonged correction. Major misallocations of real resources can result as a consequence. This is how I understand the dynamics of speculative asset markets at any rate.

What's the relevance to this discussion? If I understand the proposed mechanism correctly (and I may not) then four things seem possible: (i) the fed accumulates a directional position and becomes exposed to profit/loss, (ii) in order to avoid directional exposure the fed trades actively but makes big losses from time to time (this is what happened to the slower intermediaries on May 6; the high frequency traders will crush the fed if it act like a predictable and sluggish market maker), (iii) the fed manages to meet NGDP targets on average over long periods but with large short run swings in the money supply, output and inflation, or (iv) the fed loses credibility and abandons the peg. All of these would be very bad outcomes in my opinion and I don't see how you rule them all out simultaneously.

I also have another concern, which is the diversion of savings into margin accounts to support speculative positions instead of funding capital formation. This effect is discussed in the context of naked CDS in my recent paper with Yeon-Koo Che, discussed here in case you're interested:

<a href="http://www.voxeu.org/index.php?q=node/5472” target=”_blank”>www.voxeu.org/index.php?q=node/5472

Let me repeat that I admire Scott Sumner, the coherence of his vision, and his general approach to blogging (as laid out in his amazing birthday post). But I think that his faith in market efficiency is misplaced and his glib dismissal of those who take bubbles and crashes seriously (we suffer cognitive illusions) baffling.

19 GMC December 17, 2010 at 12:07 pm

"Here's my challenge. I started with real world monetary policy. I moved one step at a time to my preferred policy. At which step did I make a mistake?"

I think the answer is at steps 3, 8, and 10, although it depends on what parts of the analysis you assign to which steps. That isn't to say there -is- a mistake. But to the extent that the model can break down, that's the issue.

Starting early on, you've stated that the price is set based on the median vote. That is not, strictly speaking, how markets arrive at prices, is it?

As to point eight, paying interest on the margin accounts might be relevant to market outcomes.

And once we've arrived at point ten, aren't synthetic positions a problem? (You did cover my first thought, which was the Black Wednesday/George Soros problem).

Incidentally, doesn't this give big holders of Treasuries a lot of say in short run market fluctuations?

20 Rajiv Sethi December 19, 2010 at 8:34 pm

Scott, thanks for responding… I only just noticed that you had done so. I'm not sure if you're still following this thread but just in case, here are a couple of quick comments.

First of all, I believe that traders are the smartest, most sophisticated agents in the economy and would never characterize their behavior as being driven by irrationality or cognitive illusions. In fact, I have often argued against what I see as the excessive application of behavioral economics to finance. Financial market behavior is psychologically rare (due to strong selection effects on entry and through competition) and therefore cannot be deduced from lab experiments.

But the great sophistication of traders does not imply the EMH, contrary to Friedman's famous 1953 claim that speculation can be destabilizing only if speculators lose money. What this neglects is the fact that fundamental research is costly, and extracting information from price movements may be highly profitable when this practice is sufficiently uncommon. Destabilizing strategies can therefore proliferate when rare, not because they lose money but because they make lots of it.

The problem is not the irrationality or illusions of traders but the incredible complexity and non-stationarity of the task they face, and the spectacular heterogeneity of the strategies they use. Changes in the population composition of these strategies affects market stability, but in a manner that makes market timing extremely risky. The result is approximate information arbitrage (or weak form) efficiency, but major failures from time to time of fundamental valuation (or semi-strong form) efficiency.

What does this have to do with your proposal? If the Fed could credibly commit to expanding the money supply without limit whenever market expectations of NGDP were below target, and if a large enough expansion were always sufficient to raise NGDP to the target growth rate, then perhaps the proposed mechanism would never fail. But neither of these hypothesis seems correct to me. If there's a limit to how much monetary expansion is acceptable even as NGDP growth remains below target, then you and your fellow investors could make a killing at the expense of the Fed. The same is true if there's a limit to the extent to which the Fed is willing to take on directional exposure. And finally, there's also the possibility that monetary policy alone is not sufficient to bring NDGP growth to target over a fixed horizon (such as the maturity date of a futures contract). In this case positive feedback trading strategies could result in an abandonment of the peg at great profit to speculators at the expense of the Fed. Not unlike the bouncing of the British pound from the ERM in 1992, which netted Soros a billion dollars and cost the UK Treasury several times that amount. Is this really impossible, or so unlikely an event that it can be safely ignored?

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