Why $500bn and not $500 quadrillion? I bothered to do the Math.

Scott Sumner responded to my first post about NGDP futures. He seems to think I pulled the $500bn number out of thin air. He is wrong.

Before I get started, I’d once again like to express my support for NGDP level targets. NGDP level targets are superior to our current dual mandate.

Also, I’d also point out the critique I am making has absolutely nothing to do the quality or usefulness of information which might be given to Central Bankers if NGDP futures existed and traded. Bernanke and Woodford do not address the problems I am raising here.  I say there is no possible futures market. I am not saying that if a futures market for NGDP levels existed, the information the CB would get from that futures market would be useless.There is no can opener.

Here’s Scott:

“The traders might be so smart that they steal $500 billion from the Fed.  I wonder why he didn’t pick $500 quadrillion? Seriously, I’d argue the market need be no larger that $100 million, maybe $10 million.  And I’ve published proposals where the Fed would not take a net long or short position. “

Here is commenter dwb with a version of the same concern:

“err, 500 BN or 3% of nominal GDP? some faulty analysis there. there are a whole lot of flawed assumptions in your analysis, i don’t have time to go through them all, but 3% of gdp does not even pass the smell test. “

There are a few different ideas in Scott’s response worthy of further discussion, but in this post I am only going to address the $500bn number.

And dwb, you should find the time to let me know those flawed assumptions, because otherwise NGDP level futures will be a smoldering heap of ash in 2 weeks.

But back to the $500bn question, “How did I get $500bn?”

I did the math.

First, I’ll give an explanation of the thinking behind the math. Then I’ll show the math. You’ll see $500bn is a decent estimate for how large of a payment the fed would have made to Goldman Sachs and hedge funds on January 30th, 2009.

First, here is some background information about NGDP levels. David Beckworth’s chart shows the Bank of England (BoE) was extremely successful in targeting 5.3% NGDP for decades – until The Event. The BoE missed by about 10% during The Event. It’s pretty clear a central bank can be extremely successful in targeting NGDP.


The U.S. federal reserve isn’t targeting NGDP, but here is a similar chart for the U.S. Not too shabby for a CB not even trying to hit a nominal NGDP target.

But something to notice about both of these charts is the difference between success and failure. There are very few “slight misses”. The series is binary – either extremely close to the NGDP target, or huge misses of 10%.

The success of the Central Bank in hitting the NGDP target during normal times is the source of the $500bn.

We want to create an NGDP level futures contract with specifications economically useful to end users during non-recessionary periods. If the Central Bank is to get useful information from this the NGDP level futures, somebody must trade the contract.

To do this, we need to create a contract hedgers can use in a capital efficient manner to hedge fluctuations in NGDP levels during normal times. We need a contract hedgers can use during the times when NGDP is close to the target line.

Economically Useful Futures Contracts

Economically useful contracts apply to every possible futures contract design. If the contracts aren’t economically useful, nobody trades them. This means the Central Bank does not get private sector forecasts from NGDP level futures.

Scott Sumner says in his response:

“I would add that the “futures” market being proposed is unlike any real world futures market.”

I think he’s implying I wouldn’t understand a futures market with an unusual design. Hmmm. He’s also implying he’s discovered some special new futures market which the real world futures markets didn’t feel worthy of launching over the last 175 years. Hmmm.

But every futures market, of any structure, must be economically useful to the participants. There are no special designs, no magic tricks, and no special “designed by an economist, not that dumbass Mike Sankowski” exemptions to being economically useful to the participants. The contract must make economic sense for the participants, or they don’t use it, and the fed doesn’t get information.

This means the leverage on the contract is above 50 to 1, most likely above 80:1, and perhaps as high as 100:1.

Why must leverage be this high?

  1. NGDP doesn’t move around that much during good economic times.
  2. Firms do not and cannot tie up large amounts of capital on hedging operations

David Beckworth’s famous chart shows us how this works for the UK. NGDP has minor fluctuations around the NGDP target level. NGDP growth doesn’t vary enough to justify high margins/low leverage.

Any possible futures contract needs to be capital efficient for end users. Futures contracts don’t have high leverage by accident. Futures have high amounts of leverage in order to be capital efficient for the target audience of the futures markets, hedgers and speculators.

Consider what degree of leverage Walmart would require to even consider using NGDP futures to hedge either top line sales or corporate profits. If Walmart is hedging top line sales, they need to hedge $440 billion of sales. If the hedge ratio is 1:1, they will need to sell $440bn of NGDP futures.

How much money is Walmart willing to use to hedge their sales? Are they willing to put up the entire $440bn in margin? Of course not. They may be willing to tie up $4bn in cash every year to hedge their exposure to NGDP. But anything more than $4bn starts to be not worth the cost. That’s a ton of money to be sitting on a hedge, doing nothing for a company)

If Walmart is hedging profits, the issue facing Walmart is still the same. Margins in the futures markets are extremely low – and leverage extremely high – because participants have cash efficiency concerns.

I’d argue with the minor fluctuations around the NGDP target level, the Walmarts of the world will push for even higher levels of leverage than 100:1

(Now, there are HUGE PROBLEMS with the uncertainty of the NGDP index. The uncertainty of measuring NGDP will cause constant tension between the margin/leverage of the contract and the economic requirements of hedgers. This is a problem with the underlying index – another issue not addressed by economists, but extremely important to end users. I am ignoring these problems for right now, but these problems are yet another problem for NGDP futures which will be difficult to overcome.)

So, we are puttering along with economic good times, and people are using this contract with 100 to 1 leverage.
Then, something like 2008 happens. If the fed is the market maker at the target NGDP level (so the fed can judge hpw much OMO the need to do to push NGDP to target), when the fed makes its 2008 mistake, somebody makes $500bn.

The most common formulation for NGDP level futures was “fed as market maker at a static price” – at least up until a few days ago. Scott used the “fed as market maker at a static price” design to push back against Noah Smith’s critique of volatility.

Here is Scott Sumner responding in an email to Noah Smith on NGDP level futures contract design:

“In an email exchange, Scott Sumner has clarified the nature of his NGDP futures market proposal. In a nutshell, he proposes that the Fed act as a market maker, buying and selling infinite quantities of NGDP futures at the target price. Demand for NGDP futures would then be used to determine Fed policy; if NGDP futures demand increased, the Fed would commence open-market operations to bring down expected NGDP. The price of NGDP futures would not move, but demand would swing from positive to negative, moving Fed policy as it swung.” [Bold Mine]

Well, if the fed is the target price market maker for infinite quantities at target NGDP, and leverage is 100:1, somebody makes $500bn on January 30th, 2009.

How do we know this?

NGDP fell 4.1% in Q4 of 2009:

“Current-dollar GDP — the market value of the nation’s output of goods and services — decreased 4.1 percent, or $148.2 billion, in the fourth quarter to a level of $14,264.6 billion. In the third quarter, current-dollar GDP increased 3.4 percent, or $118.3 billion.”

5% growth per year means each quarter needs to grow at 1.22% per quarter.

I think 5% is a low NGDP level target. A reasonable NGDP target really needs to be a “NGDP per capita target” and should include population growth. The U.S. population is growing at .98% per year.

This means NGDP levels should grow at 6.0% annually to hit 2% inflation and 3% per capita real GDP growth. 6% annual NGDP growth translates to 1.47% growth per quarter.

So how much notional contract value would it take for the Fed to give away $500bn? If the NGDP level growth target is 5% – which I believe is low – then we missed the growth rate target by 5.012% for Q4 2008.

How much notional value of contracts are necessary to generate $500bn in profits? Math tells us

$500,000,000,000/.0532 = $9,398 bn of notional contract value. At 100:1 leverage, we only require 1% of this amount to be put up in margin. This is $93.9bn of margin required to fund this position.

If the target level is 6% – which makes more sense – then the margin required is only $89bn.

That sounds like a lot of money. It is not. The hedge fund industry has $2.3 Trillion under management.

As of 2009, hedge funds represented 1.1% of the total funds and assets held by financial institutions.[3]As of April 2012, the estimated size of the global hedge fund industry is US$2.13 trillion.[4]

$96bn is roughly 5% of the assets of the hedge fund industry. This number does not include what firms like Goldman Sachs and UBS commit to their active trading.

We need to recognize the utter certainty of the NGDP number coming in below target on January 30th, 2009. The concern wasn’t if GDP would be close to positive 1%, but rather if we should start stocking up on guns and potable water. It was 100% clear NGDP was coming in below target – it was the most certain outcome I’d ever seen. The U.S. was in a massive recession, and there was no doubt NGDP would come in below target.

People like George Soros and Paul Tudor Jones would have bet the farm on this trade. People like John Paulson would have sold billions, while every family office and hedge fund would have sold NGDP level futures as well.

Of course, they would have done their trading on the last day possible, which is a month after the end of Q4 2008.

Recall, the only way a short position loses money selling NGDP futures at positive 1.012% is if the NGDP number comes in at a number larger than 1.012%. This simply didn’t and probably couldn’t of happened.

It’s easy to see how the $500bn number is probably too low. It is entirely possible we would have seen the Fed hand over several trillion U.S. dollars to financial institutions on January 30th, 2009. It’s easy to imagine the problems for countries smaller than the United States adopting NGDP level futures.

Recall the chart from David Beckworth and how it’s obvious the BoE was targeting NGDP levels at 5.3%. This chart is utterly damning for this contract design. The BoE- a Central Bank actively targeting NGDP levels – missed the NGDP level target by a massive amount!

So to recap, any futures contract needs to be economically efficient for participants to trade. This is entirely independent of the final specifications and market structure for the contract. If the “the Fed act(s) as a market maker, buying and selling infinite quantities of NGDP futures at the target price”, then we will eventually see a situation where the Central Bank hands over a significant percentage of GDP to speculators.

I think this fully disposes with the possible contract design where “the Fed act(s) as a market maker, buying and selling infinite quantities of NGDP futures at the target price.”

In his response to Noah Smith, Scott proposes the market for NGDP level futures does not need to be very large. He also proposes alternative contracts where the Fed is not the market maker at a set NGDP target level. Instead this alternative contract design has a floating price level set by market participants.

Before we go on, I think Scott entirely misses how damaging the correlation issue is for NGDP level futures.

In another post, I’ll show allowing the level of NGDP level futures to vary means the market size of the NGDP level futures will be tiny. Then, I’ll demonstrate why an tiny NGDP level futures market is the equivalent of an online survey and prone to massive manipulation. Having an online survey dictate U.S. Federal  policy is a bad idea in another post.



Expert in business development, product development, and direct marketing. Developed strategic sales plans, product innovations, and business plans for multiple companies. Conceived the patent pending Spot Equivalent Futures (SEF) mechanism, which allows true replication of spot and swap like products in the futures space.

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124 Comments on "Why $500bn and not $500 quadrillion? I bothered to do the Math."

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4 years 11 months ago

Speaking of nonresponsive, why is no one else from “Your team” here Morgan? Usually dwb is all over the comments section.

I’m surprised there aren’t more Market Monetarists here. Scott must be preparing a response.

Morgan Warstler
4 years 11 months ago

Sax, there is no team, there is MY PLAN. Which is stated clearly, and BEATS Michael’s now two long winded post response.

That’s it, MY PLAN works for NGDP futures… it stands supreme. Saxie, I’m very tricky at making these things precisely so that MMT folks are stuck.

It is actually a derived argument from Cochrane from a couple years ago, and Scott was so focused on getting the “information” bit right he didn’t see the bigger cooler piece, which is how the money gets removed from the system, and printed and put into the system WITHOUT the government having any control over it.

Scott gets his little precious NGDLT and the Ron Paul guys get a Fed that fucks Goldman Sachs out of their pole position (which is a pretty good consolation prize for the Gold Bugs).

THAT SAXIE is why Michael is stymied by my plan, because the REAL motivation of MMT is govt. control – and my plan accomplishes it WITHOUT the govt. getting any control, they in fact lose control.

And that’s the unstated, now stated reason that everyone on the MMT side is so silent when I come calling.

I expose them as dirty hippies, my boy… DIRTY HIPPIES.

You should learn to think for yourself Sax, note where Michael is afraid to tread.

Tom Hickey
4 years 11 months ago

Morgan: “THAT SAXIE is why Michael is stymied by my plan, because the REAL motivation of MMT is govt. control – and my plan accomplishes it WITHOUT the govt. getting any control, they in fact lose control.”

And you really think that politicians aren’t going to figure this out? As I have said, the Fed doing fiscal is already illegal, and the politicians would have to be convinced to change the present law.

4 years 11 months ago

Actually the Fed could do this without going back to Congress though they’d need approval from the President. The Gold Reserve Act gives him authority to allow Tsy or an agency it designates (let’s say… the Federal Reserve) to trade gold, foreign exchange and other instruments of credit and securities. The term “securities” is broad as a barn and certainly includes option contracts.

Remember too, the Fed is off-budget (independent of congressional appropriations committees) and has a “negative capital account” to shift any losses to, the accounting equivalent of putting them on a rocket and shooting them into the Sun.

The Fed would just be writing options–I guess they’re put options since the investor wants GDP “closing price” to be lower than option “strike price”. Losers would be out their option premiums, winners would be paid from the Fed’s bottomless checking account.

Morgan Warstler
4 years 11 months ago

I though they might do it and call it Research. Issue is that overall at the start they will routinely be taking money off table destroying it to slow down economy, and printing to increase it – but IF they could say this is research to start like a pilot program, then when they have proof it stabilizes NGDPLT growth at 4.5%, then getting it done truly legally is easy.

4 years 11 months ago

“Consistent with the obligations of the Government in the International Monetary Fund on orderly exchange arrangements and a stable system of exchange rates, the Secretary or an agency designated by the Secretary, with the approval of the President, may deal in gold, foreign exchange, and other instruments of credit and securities the Secretary considers necessary.”

“The term “security” means any note, stock, treasury stock, security future, security-based swap, bond, debenture, certificate of interest or participation in any profit-sharing agreement or in any oil, gas, or other mineral royalty or lease, any collateral-trust certificate, pre-organization certificate or subscription, transferable share, investment contract, voting-trust certificate, certificate of deposit for a security, any put, call, straddle, option, or privilege on any security, certificate of deposit, or group or index of securities (including any interest therein or based on the value thereof), or any put, call, straddle, option, or privilege entered into on a national securities exchange relating to foreign currency, or in general, any instrument commonly known as a “security…”

Tom Hickey
4 years 11 months ago

My political sense it is that it would far easier to get a dole through Congress than to get politicians to go along with any NGDP sceme that allow the Fed to act fiscally, especially to the tune of $500 billion.

The problem with any NGDP scheme that could actually work is that the transmission has to involve fiscal. The Fed is not permitted to undertake fiscal other than in limited ways such as buying gold and paying IOR in non-ordinary situations.

Carlos (beowulf) has pointed out before that for the Fed to do anything fiscal beyond the ordinary, it takes an order by the Tsy Sec, which effectively involves the president in taking responsibility. The executive would be asking for trouble by endrunning Congress, probably even in his own party, and I doubt a president would approve such a plan unless it was deemed absolutely necessary before Congress could act. NGDP targeting scheme are not on that order. They are substituting fiscal for monetary to the degree they could be effective.

The difference between fiscal and monetary has been pointed out repeatedly at sites discussing NGDP and it seems to be ignored. The MM’s are substituting fiscal for monetary to the degree their schemes could be effective. Forget expectations. Dead in the water.

I won’t go into the many other political considerations but suffice it to say that anything like this would provoke a firestorm. There is just no way to sneak $500 billion in spendable funds into the economy .

Morgan Warstler
4 years 11 months ago

Tom, I’ved already beat the $500B argument, and your team as no response.

READ CAREFULLY, it makes you look non-responsive…. assuming you just missed it.

$500B is off the table for your side.


Tom Hickey
4 years 11 months ago

Morgan, see my reply to Mike Sax above.

4 years 11 months ago

“My political sense it is that it would far easier to get a dole through Congress than to get politicians to go along with any NGDP sceme that allow the Fed to act fiscally, especially to the tune of $500 billion”

Tom, I’m not, as the Market Monetarists are, opposed to fiscal stimulus at all-indeed, I’d like to see it done. However, I don’t think it’s easy at all to get a dole through Congress based on recent history. I’m not saying the NGDP targeting would be easier. In theory though, it could be.

The beauty of the Fed-in this sense-is that it can circumvent the whole political process. Maybe many don’t like that idea. But look at Volcker-he went Monetarist for a time and there was absolutely no debate about it in Congress.

If we go by what’s happened since 2008, neither are easy to get done. Both monetary and fiscal stimulus are difficult to achieve and are deemed controversial.

Tom Hickey
4 years 11 months ago

Two huge problems in my view. First, Congress would be giving up power, and constitutional power at that. Secondly, inflationary concerns. They think that it is borrowing before spending that prevents inflation. The Fed pouring money into the economy in addition to what they see as the Fed pouring money into the banks would run into strong opposition. Thirdly, a whole lot of people would object to this money going to “gamblers.”

Some have objected to a job guarantee on political grounds. In my view, it would be easier to get social programs through Congress than permit the Fed to run what is essentially a lottery. If there were to be a federal lottery, voters would only go for it if they thought it was sure to lower their taxes.

Morgan Warstler
4 years 11 months ago

HOLY SHIT, Tom Hickey!

A MMT idiot just argued POLITICAL REALITY – OMG, let’s mark this day down on our calendar!

Thomas, simmer down.

It is a “Futures Market” with the top 1/3 of America – the A Power – the true Hegemony – the Tea Party – the SMB Big fish in small ponds – all gaining power while Goldman Sachs loses power.

When the god fearing Christians are for it dear boy, that is REALITY.



MMT pretending the A POWER the top 1/3 will ever let the govt. increase and decreases taxes wherever they want to COOL OFF the economy, after it has been handing out public sector jobs paid for with printed money.

You friggin TARD.

A Job Guarantee ONLY gets done my way, and it WILL HAPPEN because it directly benefits the top 1/3, who get to buy up all the cheap labor for pennies ont he dollar.

MY WAY weakens the government – and that is how you get things done.

Tom, get over it, I BEAT YOU.

Tom Hickey
4 years 11 months ago

Not until it is implemented, Morgan. Never happen because the politics. But this is no reason not to propose ideas. I am just bringing up a practical consideration.

BTW, I support MMT not because I think it is the best solution. I have made clear here and elsewhere that I am far more radical. However, I also recognize practicality and will support policy that I think will make the social, political and economic system better nationally and internationally.

As Mike said the big issue is transmission, and the transmission needs to be fiscal. There is huge legal problems standing the way of the Fed doing fiscal, which would necessitate a change in the law through the political process. Not going to happen anytime soon.

Don’t count your chickens before they are hatched. Anyone can come up with a plan. The design problem is to come up with one that works practically. This is not just economics since it involves changing not only policy but also law.

4 years 11 months ago

OT, but I think this conversation is very damaging for MMT. I hope one of the MR founders might chime in.


4 years 11 months ago


Keep this nonsense on other sites. The last thing I want is you dragging your battles over here. I’ve had quite enough of the MMT vs MR wars. We’ve made a concerted effort not to stoke that fire so don’t bring the battle here. If you want to wage internet wars on other sites then be my guest. Just don’t do it here or at Pragcap.


I’d appreciate it if you did the same. We’ve hashed out our differences and we disagree. That’s that. “Irreconcilable” as you said. We’re not pushing your buttons and FDO doesn’t represent our work so just do everyone a favor and put him on ignore. No one “wins” in these arguments. We just all end up looking bad. There are no winners and there never will be.



Tom Hickey
4 years 11 months ago

You lost.

4 years 11 months ago

“First, here is some background information about NGDP levels. David Beckworth’s chart shows the Bank of England (BoE) was extremely successful in targeting 5.3% NGDP for decades – until The Event. The BoE missed by about 10% during The Event. It’s pretty clear a central bank can be extremely successful in targeting NGDP.”

He he.

Next Sumner will claim the Bank of England controls the global temperature as well!

The graph of Beckworth is drawn so as to create an illusion that its perfect. The data shows it fluctuates around 4-6%.


Mike Sax
4 years 11 months ago

Ross, what NGDP targeting comes down to for the Market Monetarists is that expectations are everything.

If you ask them about a transmission mechanics you get accused of being overly “hdydrualic” of being “The People of the Concrete Steps.”

Ross Thomas
4 years 11 months ago

I just did a search for “concrete steppes” and I see the post to which you refer, I think:

“You want me to tell you a story in which the central bank pulls a lever, and that lever causes another lever to move next, followed by another lever, then another, spelling out a causal chain from beginning to end, where the end is a higher level of NGDP.

“But economics isn’t like that. Because people aren’t like that.”

So it’s mostly the confidence fairy, then?

Ross Thomas
4 years 11 months ago

Reading on:

“The US economy is currently in equilibrium. It’s not a market-clearing equilibrium. It’s not a very good equilibrium. But it is an equilibrium. If it wasn’t an equilibrium, it would be somewhere else. But it isn’t somewhere else, so it must be.”

If that were true then a photo of a collapsing pile of sand would show a pile of sand in equilibrium, because in that instant it was where it was and nowhere else…

Apart from his fundamentally misunderstanding complex dynamic systems, and his claim not to require any identifiable means by which his idea could actually work, I see nothing wrong here.

Mike Sax
4 years 11 months ago

That’s the exact post, and, yes.

4 years 11 months ago

It’s “steppes.”

4 years 11 months ago

But that’s not true. They do propose asset purchases.

Mike Sax
4 years 11 months ago

Oops! Right you are, it’s Steppes. They do propose QE, true. Though the resaon they think this works seems to be mostly through expectations. As I read Sumner, he has conceded QE may not do all that much but it’s effective in trasmitting to the market the Fed’s intentions.

QE is really the be all and end all of proposals-beyond simply having the Fed announce a NGDP target.