Mechanical metaphors for monetary policy

This is a post for people who find mechanical metaphors useful. And remember, any theory that can be translated into math and put on a computer (even if it doesn't need to be) has a mechanical counterpart, because a computer is a machine.

I am going to use mechanical metaphors to think about different monetary policy control instruments. "Quantitative easing", if you like.

The machine metaphor itself is useful. Think of the economy as a box with different control levers sticking out. Inside the box all the levers are connected up with some sort of mechanism. When the central bank moves one control lever, all the other levers move too. The equilibrium conditions of a structural economic model is just a description of the internal mechanism that lets us figure out how the levers will move in relation to each other.

At first sight, it would seem that it wouldn't matter which lever the Bank grabbed hold of and used as a control instrument. If levers A and B are connected up inside the box, the Bank could do the same thing whether it controlled lever A or controlled lever B. If one moves, the other moves. And if one lever is over as far as it will go, there is no point in trying to move the other lever. "In normal times, QE is just interest rate control by other means, and in abnormal times, if the interest rate has hit the zero bound, QE won't work either".

But it's easy to think of slightly more complicated mechanisms where that's not true.

There might be strings, so that pushing one lever does nothing, but pulling another lever moves both.

There might be worm gears, so you can't move the pinion wheel at all, but can move both worm and pinion by turning the worm. (I might have the terminology wrong, and I don't understand the engineering, but this was definitely true for my toy trains, because you could not get the electric motor to turn by turning the wheels).

There might be cranks. If a crank is at the very top or bottom of its travel, you can neither push or pull the lever, but can still turn the crankshaft and move the lever. (I had a pedal-powered fire engine like this once: if you pushed with the wrong foot it ran backwards; and if the pedals were in the wrong place neither foot would do anything, and I had to turn the rear wheels by hand. Central banks currently remind me of myself in my fire engine at 3 years old, before I figured out the rear wheel trick, crying in frustration, and waiting for a push from fiscal policy Mum to get me started.)

Or the position of one lever might affect the rate of change of all the other levers, and that relationship might be unstable.

Let me build on that last observation.

Controlling monetary policy via an interest rate instrument is like balancing a pole upright in the palm of your hand. The bottom of the pole is the nominal rate of interest. The top of the pole is the rate of inflation (or the growth rate of nominal GDP). Theory tells us that if you keep the actual rate below the natural rate, inflation will accelerate without limit; and if you keep the actual rate above the natural rate, deflation will accelerate without limit. And the actual real rate is the actual nominal rate minus expected inflation. So the metaphor is consistent with theory.

If you stay still, while the pole is being buffeted by winds, the pole will fall over. You have to keep moving to keep the pole upright. And if you want to move the top of the pole north, you must first move the bottom of the pole south, so the pole starts to lean northward, then begin to move the bottom north again, and eventually you end up to the north of where you started.

Now add the zero bound on nominal interest rates to the metaphor. There is a low wall to the south, and you can't move the bottom of the pole past that wall. Suppose you are up against that wall now, and still the pole is leaning southwards (or there's a strong northerly wind blowing). You can do nothing, except pray for a southerly wind.

But you can do something. Attached to the top end of the pole are lots of short strings. Each of those strings represents some nominal variable, like the price of gold, plywood, stock prices, etc. In fact, since CPI or nominal GDP inflation is just an average of those nominal variables, the top of the pole is really just a bunch of short strings, like a mop. Monetary policy needs to let go of the bottom of the pole, grab hold of one of those strings, and move it north.

Notice that once you move the top of the pole north the bottom of the pole will move north too, away from the wall. The old nominal interest rate control instrument will increase when you successfully loosen monetary policy by using a different control instrument. Theory tells us this will happen, for three reasons:

1. An increase in actual and hence expected inflation will increase the nominal rate for any given real rate.

2. An increase in expected future real AD and expected future real output and employment will increase current investment demand and reduce current savings supply and so increase the current real natural rate of interest.

3. An increase in expected future inflation and real output and employment will reduce risk, reduce liquidity preference, increase the capital values of financial institutions, and all of these will reduce the spreads between short safe liquid assets and long risky illiquid assets, increasing the former, and reducing the latter.

And Scott Sumner tells me this is pretty much what actually happened in the 1930's when gold prices were increased.

Or think back to the "crank" metaphor. If one of the pistons in a car engine (or one of the pedals in my old fire engine) is at the bottom of its travel, a rise in the piston can mean the engine moves forward, or it can mean the engine moves backwards. If I said "the Bank of Canada should raise the overnight rate" everybody would assume I meant that it should tighten monetary policy. But the overnight rate increasing would be equally compatible with the Bank loosening monetary policy.

It all depends on which is the control instrument, and which is the direction of causation. And mechanical metaphors can be helpful in thinking about this too.

An equilibrium model of the economy (and I am using the word "equilibrium" in a very broad sense here, to describe a system of simultaneous equations, so am saying nothing about market-clearing, things not changing over time, etc.) describes the relationship between all the different variables, both exogenous and endogenous. Often, we can switch which variables are exogenous and endogenous, and those equilibrium conditions stay the same. We just invert the original reduced form solution, so that left hand side variables get switched with right hand side variables. The same model which shows imports as a function of a tariff can sometimes be inverted to show the price of a quota as a function of the quantity of import quotas.

It's sometimes the same when we switch from one control lever to another. The clockwork inside the box stays the same, and the levers may still move in exactly the same relationship with each other. But our story of the causal mechanism whereby moving one lever causes the other lever to move will change. Instead of "Pulling A pushes B which turns C which pulls D", we say "Pushing D turns C which pulls B which pushes A".

The clockwork is a simultaneous equilibrium system, and everything moves at the same time. But when we tell the story of how it works, it's a causal chain, with first one thing changing, then the next, and so on.

Similarly, the story we tell of the transmission mechanism of monetary policy will change drastically when we change the monetary policy control lever, even if our equilibrium model stays exactly the same. A different story, even in exactly the same model, may be unrecognisable. It will sound very weird to someone who has always been moving the other policy lever.

Comments

[JKH]

Nick,

The pole is a very good metaphor; the pole is the yield curve.

I think it would be very interesting to extend this story to the idea of a world without central banks. That’s the alternative world I sometimes think of when the short rate is determined by the market. I think this is more or less consistent with the Austrian view.

In other words, a world where the short rate is determined by the market could either be a world where the central bank is operating a non short rate lever, or one in which it operates no levers.

[Chris S]

There are worm and pinions where the 'pinion' can move the worm - one version appears in a 'spiral adjustable wrench', while another is sometimes known as a Yankee Spiral.

... which is NOT a term for the current American financial crisis!!!

[Nick Rowe]

Chris S:
I can find a Yankee spiral screwdriver (I had never heard the term before)
https://www.josephmarc.com/page-62047.html
I see now you are right, I think.

But the monkey wrench (or adjustable spanner) makes my point
http://en.wikipedia.org/wiki/Monkey_wrench
http://en.wikipedia.org/wiki/Adjustable_spanner
You can't open the jaws directly. You have to use the other control instrument.

My reply to JKH seems to have disappeared. Let me try again:
Yes, the pole works well for the yield curve. The only difference is that prices are perfectly flexible over 30 years, so changes in the short rate can have very big effects (in the opposite direction) on the 30 year rate, if people interpret a cut in the short rate as evidence of higher target inflation in the long run, or very little effect if they see no change in the long run target.

If we didn't have central banks, would we have money? And who would control it, and how? But yes, the relation between short rates and aggregate demand could look very different.

[Scott Sumner]

Nick, I like what you are doing here. Do you see those strings as perhaps being more like elastic bands--so that the farther you stretch them the more it pulls on the economy? Let's consider an exchange rate string. Because of long run PPP, the $/euro probably tends to stay in the .80 to $1.60 range. If the dollar is moved from 1.20 to 1.60, the public might see that is a normal real exchange rate adjustment, but if it was moved another 40 cents to 2.00, then the public would realize that American inflation was soon going to greatly exceed Eurozone inflation. And of course expectations affect how a nominal string will affect future expected NGDP, and hence current NGDP growth. Recall that due to the IPC, at a given nominal interest rate, each change in the exchange rate is expected to be fairly permanent. So a 2.00 euro might really shock U.S. inflation expectations.

Here's two differences between targeting a single nominal price, and targeting a futures contract linked to the goal variable:

1. In both cases you are going to try to anticipate changes in the wind, and move your target to the position expected to hit the goal, assuming wind comes in as predicted. But with a single nominal price, you must be the sole weatherman. With an NGDP futures contract regime, your wind forecast is the average of all weather forecasters.

2. With a single nominal price target, you will pull on the pole with your string, or elastic band, and hope that the distance between your hand and the pole stays about the same, or at least moves only to the extent you forecast it to move. With the NGDP futures target, you put your fist on top of the pole, and move it to the exact spot you want to. Whether it stays there depends on only one factor---whether your average weatherman is a good forecaster.

In case this was hard to follow, here is the real world analogy. The BOC might decide to set the CAN$ at 72 cents, in the hope that that will make the Canadian GDP rise 5%. After they set the target, the relationship may seem to change, so that even the BOC no longer expects to hit the target. But even if they do succeed in making it so that their internal forecast unit produces a 5% growth forecast, that forecast may be inferior to the market forecast. If the BOC is allowed to move the exchange rate around until the internal NGDP forecast equals the goal, then the futures targeting approach only would have one advantage--more forecasters. But of course this is not the way actual central banks behave. They do not set their monetary instrument at a level that equates the policy forecast with the policy goal--at least the Fed, ECB, and BOJ do not. And even if they did try to do that there is a sort of "circularity problem" identified by Bernanke and Woodford in 1997, that does not affect NGDP futures targeting. So in the last few months I have discovered that the argument for futures targeting (CPI or NGDP) is much stronger than I had ever envisioned.

Feel free to ignore my futures comments, which is my pet theory, I think the pole analogy is very fruitful, and I hope you pursue this further. The part I find trickiest is expectations---I don't know if there is a mechanical analogue for expectations/credibility, etc.

The string solution to the liquidity trap has two difficulties as a real world policy:

All flexible nominal prices are either things the Fed doesn't want to buy lots of (gold) or assets where there is political friction from price manipulation (exchange rates.) It is possible to manipulate the price of something without buying up a lot of it (as FDR did with gold prices in 1933) but it raises some tricky issues regarding expectations. Indeed it is very analogous to the expectations problems associated with getting out of a liquidity trap. Even so, I much prefer pulling on strings to pushing on strings. (Pardon the pun.)

[Patrick]

"mechanical analogue for expectations/credibility"

I'll bite... Maybe a motor, a fly wheel, a clutch, and a brake? Here goes nothing:

The external motor keeps the fly wheel spinning at a constant and very high rate, and we can ignore it otherwise. The clutch is engaged automatically by an device that measures the change in angular velocity of the drive train. The fly wheel and clutch make the machine run faster than it would run on it's own. If the clutch is engaged all the way, the machine will run so fast that it explodes. The operator has a partial override, but it works with time delay, and then not very reliably.

If the machines drive speeds-up, the clutch is engaged, which tends to speed up the machine even more, similarly if the machines slows down. Without an operator constantly intervening, the machine will enter a self-reinforcing loop that either causes it to blow-up by running way too fast, or it will stop completely. Unfortunately for the operator, her control over the clutch is lousy and it takes an awful lot of attention to keep the machine from blowing-up.

In the owner's manual, they say it's best if the clutch isn't engaged at all. But the machine isn't perfectly constructed so there's internal friction that tends to slow the machine to a halt over time. To compensate, the operator tries to keep the clutch engaged just a little bit, but it's tricky due to the lousy controls and the accelerometer constantly trying to either run the machine so fast it explodes or grind it to a halt.

In a Kafka-eske fit of evil genius, the machine's designer also attached the accelerometer to a brake on the main drive shaft via an evil control unit. The operators both loath and fear the control unit. You see, the control unit is programmed to do nothing so long as the accelerometer is reading mildly negative, zero or positive. But if the accelerometer reads a very negative value, the brake is engaged and the machine can come to a halt very quickly. To make matter worse, the control unit will not release the brake until the machine's operating speed returns to the level at which the brake was engaged. The operators are usually able to prevent the control unit from kicking in, but when it does engage the brake the operators first tend to soil themselves, then they engage the clutch on the flywheel as much as they can (while still balancing the pole). Usually, they do manage to keep the machine from grinding to a halt, but once the break releases they also have to work furiously to release the clutch to keep the machine from running out of control and exploding.

Hope that isn't totally stupid.

[Nick Rowe]

Not stupid Patrick, but overly complex I think. A lot of engines (steam-powered traction engines, lawnmowers) have a governor that opens the throttle more when the rpm drops, and closes the throttle when the rpm rises. The point is to keep the rpm roughly constant when the load on the engine varies. Old ones work with centrifugal force. Just hook the governor up the wrong way round. But I think the pole already does the same thing. The more it leans, the more quickly it leans, because the centre of gravity is further away (horizontally) from the pivot point.

But those mechanical devices don't have expectations in the sense of forming opinions about which way you will move your hand.

Trying to drive a herd of cattle in a straight line across a field (another thing I did in my youth) is a better metaphor (but less familiar to most people). It's a lot easier when they know where you want them to go, along a familiar route (or at least if the boss cow does, because the rest just follow her). Father once gave up trying to drive a flock of geese, so grabbed the gander, then ran towards the pen with the rest of the geese chasing after him and the furious gander.

Scott:

Yes, the strings would be elastic, because first there would be a change in the relative price of the control instrument when you moved it away from equilibrium, and the transmission mechanism would work via the deviation of that relative price from its equilibrium or natural rate.

I fully agree with you on the advantages of using a basket of goods, rather than a single good, as a *control instrument* (I like to keep instrument and target conceptually distinct, even if we consider examples where we might make them the same good, as under the classic gold standard with 100% reserves).

But buying the CPI basket, or GDP basket, itself, as a control instrument, is of course impractical (where would the Bank of Canada store all those restaurant meals?) Which is where your futures contract comes in.

I am still getting my head around the futures contract idea, as a control instrument. It is ideal in the sense that there's a very close relationship between the instrument and the target; I get that point. I get the point that you elicit the wisdom of crowds/markets to help get the right setting.

But I don't have a clear answer in my head on whether it is like trying to control the temperature by moving the dial on the thermometer (another mechanical metaphor).

And I also don't have a strong intuitive understanding yet of whether and when the Bernanke and Woodford "circularity" argument is correct. (Is it like the stock market: if everyone else is a fundamentalist it is better just to buy the index; and if everyone else just buys the index it is better to do the costly research and be a fundamentalist?)

Sometimes I just have to let ideas percolate in my head until I can see them "my way".

Until I can get these issues straight in my head, my personal preference would probably be for a TSX300 (read S&P500) index as a control instrument. The Bank can buy, sell, and store it in reserves costlessly (and earn a return). And the transmission mechanism would be via Tobin's Q, and should be at least as robust and broad a channel to AD as any nominal interest rate instrument.

By the way, I might be misunderstanding exactly what you are saying about the Fed, ECB, and BoJ. When I spoke to senior people at the BoC and said "What you do is set the overnight rate, conditional on the indicators, so that your expectation (which should be rational) of future inflation at an 18-24 month horizon equals 2%", they basically agreed.

In other words, E(P/{R,I})=2% fits all their public pronouncements better than Minimise[(y-y*)^2 + (p-p*)^2].

(This does not make them "inflation nutters", because 18-24 months is not zero.)

[Adam P]

"But I don't have a clear answer in my head on whether it is like trying to control the temperature by moving the dial on the thermometer (another mechanical metaphor)."

It depends on what you want monetary policy to do. We haven't been clear in our agruments which of two distinct issues we are talking about:

1) controlling the price level
2) manipulating AD

These are distinct, in a fully flexible price world monetary policy is neutral but still determines the price level. However, in the flexible price world monetary policy can't fight a recession (the only recessions would be of the RBC adverse productivity shock variety). In the fully flexible price world all monetary policy can ever do choose the units in which prices are measured.

On the other hand, if it can maipulate AD then monetary policy can change the actual temnperature.

[Nick Rowe]

I see 1 and 2 as the same (unless prices are permanently fixed, which they aren't).

I see monetary policy as shifting the AD curve (in {P,y} space). In the short run a shift in AD has most of its impact on y, and in the long run all of its impact on P. (The division of the effects between y and P over time is determined by the AS or PC).

How we think about the AD curve (its slope) depends on the control instrument (what we hold constant when we draw it).

If we hold the interest rate constant, the AD curve is vertical (and P eventually explodes up or down, because the LRAS is vertical too).

If we hold the stock of money constant, it's downward-sloping.

If we hold the price of gold (or the nominal exchange rate) constant, it also slopes down, but not with the same slope.

If (like Scott) we hold NGDP futures constant, AD is a rectangular hyperbola.

My worry is that if manipulating NGDP futures is like messing with the dial on a thermometer, we can't even shift the AD curve.

[bob]

"My worry is that if manipulating NGDP futures is like messing with the dial on a thermometer, we can't even shift the AD curve."

I'm pretty certain that is the case. I've been reading this blog and Scott's, and I haven't found a response from him on this point yet.

My guess is that Sumner may put such a heavy emphasis on rational expectations etc., that he views actual intervention as besides the point. My view is that even if you never intend to "fire the bazooka" it is important to have it there. If the government had the capability of buying and selling mass amounts of "spot GDP", they would rarely have to do so and could just focus on guiding expectations, but without the ability to influence "spot GDP" I don't see why anyone would care about what the government-controlled NGDP futures indicate.

[Scott Sumner]

Bob, The government would peg the price of NGDP futures, but it would also be the free market price. The base would adjust to make it the free market price. In that sense it is exactly like a gold standard. The only difference is that you are pegging NGDP futures, not gold prices. It's not an economy with stable NGDP, its an economy with stable expected NGDP growth (and you can do "level targeting" if you are worried about a string of errors in the same direction.)

Nick. I'm a bit confused about your worry that you couldn't shift AD under a NGDP target. In a sense that's true (although I would actually prefer to increase it at a steady 5% rate.) But stable AD is assumed to be the goal. If you prefer some other goal (like 2%inflation), then futures targeting would allow you to shift the AD curve (which is a hyperbola as you suggest.)

Like you, I also had trouble wrapping my head around the idea about what it really meant until about 20 years after I first thought up the policy. Then I realized it just amounted to expanding the FOMC from 12 to 300,000,000 members, and rewarding people on how skillfully they voted. I also have trouble figuring out how important Bernanke and Woodford's circularity problem is. My sense is that in practice it would not be much of a problem. And in any case it would not apply to a proposal like mine, where the market forecasts not NGDP, but rather the instrument setting expected to hit the NGDP target.

I'm almost certain the Fed, ECB, and BOJ currently forecast inflation and nominal growth to come in below target for several years. Indeed I know this for a fact regarding the Fed. If the ECB and BOJ don't realize they are likely to come in below target, they are pretty dense. I recently read that NGDP in Japan will soon return to 1993 levels. Is this really what the BOJ wants? Who knows, but they certainly claim to not want this sort of deflation. If I am wrong, and they expect to hit their target over the time frame when policy has an impact, then the world currently faces no macro "problem" that even needs to be solved (and we are all wasting our time on these blogs.)

I don't view a stock index target as optimal, but it might be better than an interest rate target. At least you'd avoid the worst extremes. One problem, however, stocks did poorly (at least in the U.S.) during the high inflation of the late 1960s-early 80s. So what if inflation actually depressed the stock market? Do we then need even more monetary expansion?

[Adam P]

Scott, I don't think you've addressed Bob's point. Scott says "The government would peg the price of NGDP futures, but it would also be the free market price. The base would adjust to make it the free market price. In that sense it is exactly like a gold standard. The only difference is that you are pegging NGDP futures, not gold prices."

But that is not how a gold standard works. Under a gold standard, when the government says that a dollar is redeemable for x ounces of gold that is not a price target, it's the definition of a dollar. Furthermore, it's a fiscal regime. The government supports that value for a dollar by actually having the gold or the resources to get more, thus the redemption promise is credible.

Similarily, when a government pegs its exchange rate, say to the US dollar, that is maintained by actually having the dollars or sufficient resources to get them and thus maintaining the ability to redeem the domestic currency for the specified number of dollars.

So the question to Scott is, (and I think this is basically Bob's point), can the government redeem dollars for a specified number of units of GDP?

[Patrick]

"can the government redeem dollars for a specified number of units of GDP"

Isn't that taxation? The gov't can obtain 'units' of GDP via taxation, and they only accept dollars as payment, so units of GDP are redeemable as dollars. So dollars are convertible to units of GDP ... in dollars. So if you want to redeem a dollar for units of GDP you get a dollar in return. Which would be useless, so nobody cares. Ugh. This must be wrong.

[Adam P]

Patrick, in a sense you've just described the fiscal theory of the price level which I'm a big fan of. However, the key word in my sentance was "specified" by which I meant prespecified. Can the gov't define a dollar to be x units of GDP? It would seem they would need a storable stock of GDP to back that up with or they would have to completely prespecify both the composition of GDP and each price like the Soviets were trying to do.

[Adam P]

I haven't been reading Scott's blog so I don't know his fundamental arguments (if he wants to post a link to some posts where he makes the basic case I'll be sure to take a look).

However, I think the key comes down to his statement: " just amounted to expanding the FOMC from 12 to 300,000,000 members, and rewarding people on how skillfully they voted." It sounds like what Scott has in mind is basically having the Fed use a Taylor rule with modified functional form (growth and inflation enter multiplicitively instead of linearly) and establish this futures market to serve as the key leading indicator. Well then, there's nothing particularly new or controversial here.

But then, if this is the case then, while we may agree with Scott as to a good target for policy he hasn't helped us with the instrument. What we've been debating here with Nick though are what instruments monetary policy can use to increase AD in recessions, both in general and especially in the current mess. And what I was saying just above, and what I understood Bob to be saying, was why I (we?) don't think that NGDP futures are useful as the instrument of policy.

[Nick Rowe]

We might have some terminological differences here.

Under the old-fashioned "instrument, indicator, target" terminology, the Bank of Canada for example uses overnight rate as a control instrument, looks at almost everything as an indicator (giving it information on where it needs to set the instrument), and has CPI inflation as the target. (It also speaks of the level of the overnight rate it wants to hit for the next 6 weeks as a "target", just to confuse the issue, but this is a short-term target, not the real target, which is 2% CPI inflation.)

I do not want TSX300 as a target (I did once, 15 years ago, when I was a younger guy!). But I see it as playing a role as an instrument under current circumstances. The Bank of Canada could buy and sell the TSX300 and adjust its price over time to better hit the CPI target.

Under the classic gold standard, where the Bank did nothing other than buy and sell gold at a fixed price, the price of gold was all 3 at once: instrument, indicator, and target.

Under the "indirect convertibility" of Irving Fisher's "compensated dollar" plan, (if I remember it correctly), the price of gold was the instrument, but the Bank varied the price of gold to hit a CPI level target. So money was directly convertible into gold, at a varying price, but indirectly converted into the CPI bundle of goods, at a fixed and pre-specified price.

Under Scott's plan, if I understand it right, the target variable is NGDP, with a prespecified growth of 5%. (leave aside the question of whether it's a growth rate target or a growing level path target). The indicator would be the price of NGDP futures. Would the instrument also be the price of NGDP futures? In other words, would the Bank buy and sell NGDP futures, or would it buy and sell something else, while watching NGDP futures to see how much of that something else to buy and sell? Is the NGDP futures price the instrument, as well as the indicator?

Scott: I think it's just a terminological confusion again here:

"Nick. I'm a bit confused about your worry that you couldn't shift AD under a NGDP target. In a sense that's true (although I would actually prefer to increase it at a steady 5% rate.) But stable AD is assumed to be the goal. If you prefer some other goal (like 2%inflation), then futures targeting would allow you to shift the AD curve (which is a hyperbola as you suggest.)"

Scott wants the AD curve (seen in price level - real GDP space) to be shifting steadily rightwards at 5% per year. My worry is whether using the NGDP futures price as an instrument would enable the Bank to do this. Is there a causal link between buying and selling the NGDP futures contract, and thus its price, to the position of the AD curve? We know there's a causal link in the other direction. like from temperature to the thermometer dial, but is that causal link reversible? Another way of putting it is in terms of Goodhart's Law: "Any index the government tries to control becomes meaningless" (or words to similar effect). Of course, if the NGDP futures price is indicator rather than instrument, this worry disappears (to maybe or maybe not be replaced by a "circularity" worry). But then what is the instrument?

[JKH]

Scott is definitely referring to NGDP futures as the instrument of intervention. I also don’t understand the reasoning behind it, as I noted earlier here and on Scott’s blog. He has referred to academic work that has developed the theory. (i.e. “There is a circularity problem if you simply try to target an external futures market. If the policy is credible the price will be on target, and then you don’t have any information about where to set the monetary instrument. Bernanke and Woodford (JMCB, 1997) discuss this issue.”) It would be nice to see an intuitive summary. Not only do I not understand why it would be useful, but also why it would not distort prices in the futures market. The problem I see boils down to the non-existence of a cash market and therefore the absence of any concept of cash/futures convergence. Is there an existing example of a central bank using a futures market instrument as intervention, when there is no cash market in the same instrument? In this case, not only is there no cash market, but there is no concept of a cash market. This is a pure bet that will be settled by cash differential at contract expiry. What does it accomplish as an intervention instrument if it has no direct effect on the pricing of a corresponding cash market?

[Nick Rowe]

JKH:

Here is VV Chair's intuitive summary of the Bernanke and Woodford 1997 circularity argument: http://www.allbusiness.com/finance-insurance/credit-intermediation-related-activities/643700-1.html See page 2. Here is the money quote:

" Bernanke and Woodford show that naive rules that use private sector forecasts can lead to undesirable outcomes. The logic is simple and beautiful. Suppose, for instance, that the central bank wants to stabilize inflation rates and private forecasters have information that is not available to the central bank about future inflation. The central bank could use private forecasts of inflation to choose its policy instrument. The problem is that if the central bank is completely effective in using its policy instrument to stabilize inflation, private forecasts of inflation should rationally be the central bank's inflation target in which case, private forecasts provide no information about inflation! This paradox arises because market forecasts of a goal variable depend upon the central bank's policy rule and if the central bank uses the information well, market forecasts will not be informative."

V V Chari's intuition matches my intuition. It is analogous to the paradox of efficient pricing of stocks (originally due to Stiglitz, if I remember correctly). If you think that everyone else in the stock market is doing a careful Graham and Dodds analysis, and prices reflect that, then you would be better off saving the costs of doing a fundamental analysis, and just buying the index. But if you think everyone else is just blindly buying the index, it pays to do a Graham and Dodds fundamental analysis.

Only in the Bernanke and Woodford case, it's Bank vs Market. If the market gets it right, the Bank can get it right by simply looking at the market. But if the market knows the bank can get it right, the market will just rely on the Bank getting it right.

Here is V V Chari's interpretation of the solution:

"This problem can be ameliorated if the central bank could obtain private forecasts that are conditional on the setting of the monetary policy experiment. Bernanke and Woodford show, in a simple example, that policy rules that depend both upon private forecasts of the target variable, say inflation, and the instrument, say short-term interest rates, can resolve the informativeness paradox."

I don't think this circularity problem is a central one for Scott.

I'm more interested in the exact role of the NGDP futures price.

Suppose it's just a betting market, like Intrade, and there is no way to arbitrage directly between NGDP futures and NGDP iself (unlike, say copper). But this wouldn't matter for Scott if he used the NGDP futures price as just an indicator, and used something else as an instrument. For example, Scott could say: "Use OMO to control base money, and watch the NGDP futures price as an indicator to tell you whether to buy or sell bonds."

As long as there's a link from OMO to actual future NGDP, and the NGDP futures market is a good predictor, it should work.

[JKH]

Nick,

Thanks. The circularity thing is interesting. Seem fairly relevant to EMH versus fundamental strategies. And maybe it’s a variation on this:

http://en.wikipedia.org/wiki/Keynesian_beauty_contest

Like you, I can certainly see an OMO instrument based on NGDP futures as an efficient predictor of actual future NGDP.

But that’s not what Scott is proposing. He’s proposing central bank targeting of and intervention in NGDP futures. So maybe his reference wasn’t so relevant to this idea.

[Adam P]

Nick, it was Stiglitz with Sandy Grossman, 1981 AER, great paper.

[JKH]

Here is Scott’s other response on the subject of NGDP futures intervention, on this blog:

“The Fed would buy and sell unlimited 12 month NGDP futures at a 5% premium. Each sale by the Fed would represent a purchase by the public--a bet that next year's NGDP would rise more than 5%. This would trigger offsetting open market sales in securities by the Fed. (and vice versa) The process would continue until the public expected exactly 5% NGDP growth. This has been run by lots of famous economists in the past 23 years. No flaws found yet.”

From:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/04/an-alternative-universe-with-gold-price-control.html

April 21, 2009 at 08:57 PM

[Nick Rowe]

Adam P.: Yes, that's the one. And the resolution to the Stiglitz/Grossman paradox (to the extent that we have a satisfactory resolution) is to add "noise traders" (who buy and sell stocks for personal reasons unrelated to fundamental values), so that those with a comparative advantage in doing research become fundamentalists, and make enough to cover their costs, and those that just buy and hold the index. Wasn't that resolution originally proposed by Bernanke, and someone?

JKH: Good find and analogy. The Bernanke/Woodford paper was that if the central bank relied on the futures market, the outcome would degenerate into a Keynesian beauty contest.

I think Bernanke and Woodford are wrong. The Keynesian beauty contest is a coordination game where anything on the 45 degree line (where they all choose the same) is an equilibrium. I think it's more like "Chicken". http://en.wikipedia.org/wiki/Chicken_(game)

If the market players think the bank does not do fundamental/structural analysis (if it drives down the white line in the middle of the road), the market players will do fundamental/structural anlysis (they will swerve). If the bank does do fundamental/structural analysis (swerves), the market players will not.

[Nick Rowe]

It ate my follow-up comment.

It's like Chicken, except that if neither swerves (if neither does the fundamental research), they end up playing the Keynesian beauty contest game. A 2-stage game, if you like. Beauty contest inside Chicken.

[Scott Sumner]

I'm sorry I hijacked this with the NGDP stuff. The way it works is as follows. If investors think NGDP growth will be less than 5% (like right now) they would buy NGDP futures contracts. Each time they bought one, the Fed would do a parallel OMP (probably involving T-bills) to actually change the base. As long as investors thought actual future NGDP would fall short of 5% growth, they would keep buying NGDP futures. If at some point growth was expected to exceed 5%, investors would sell NGDP contracts. And this would trigger Fed OMSs. Because the Fed offers to buy and sell unlimited NGDP contracts at the target price, it becomes the market price, and the monetary base adjusts until expected NGDP growth is 5%. For this to work there must be some monetary base capable of producing 5% expected NGDP growth.
The issue of what to buy is less important than it seems at first glance. I know that this issue seems important when we are in a liquidity trap, but remember that NGDP futures targeting would immediately eliminate the liquidity trap. Instead of 0% expected NGDP growth, you'd have 5% expected NGDP growth. At that rate the demand for cash and bank reserves is much lower, and thus the Fed wouldn't have to buy as many bonds as you'd think. Indeed they'd probably have to sell hundreds of billions worth, as the base is currently bloated by the liquidity trap. (By analogy, the most expansionary monetary policy in U.S. history was between March and July 1933---and the base actually fell around 7%.)
During normal times, the Fed would incur almost no risk, as they'd set the base at the estimated equilibrium level before trading began (to minimize their net long or short position. But during a transition period like right now, there would be some risk because right now it's hard to know the equilibrium monetary base for 5% NGDP growth. The market would discover that equilibrium.

[Adam P]

So it works by controlling the money supply. That puts it right in the middle of the conversation.

But this: "remember that NGDP futures targeting would immediately eliminate the liquidity trap" requires a detailed explanation.

[Adam P]

I should add, I'm not saying it won't work in a liquidity trap. I think it will. However, IT WORKS BY PROMISING FUTURE INFLATION AND THUS LOWERING THE REAL RATE.

[Nick Rowe]

Scott: Not a hijack. On topic. The whole idea of the mechanical metaphors post was to help us understand plans like yours better. With your last comment, it has now succeeded.

Under your proposal, the NGDP futures price is both the target and the indicator, but it is not the instrument. The instrument is base money via OMOs. The central bank promises a time path for the NGDP futures contact: 100, 105, 110, etc. (excuse the simple not compound growth rate), and looks at the same NGDP futures price as an indicator of whether it is meeting its promise. (True, you could say there is an underlying more ultimate target, of NGDP itself, but the Bank promises are about the futures price, not NGDP itself.)

Mechanical metaphor: the car driver buys a really clever speedometer, that can accurately anticipate future speed, and looks only at that speedometer, but uses the speedometer to decide whether to press more or less on the gas pedal (OMO). He does not try to move the dial on the speedo by grabbing hold of it.

I would modify Adam P's statement. I would say: It works (if it does work), to get us out of the liquidity trap, by "promising" a mix of EITHER inflation, which would lower the actual real rate, OR real NGDP growth, which would raise the short-run real natural rate (because higher expected future real income would increase current investment demand and also reduce current savings supply).

But suppose people accept that the Bank is really and genuinely trying to do this, but believe it won't work. (I am running through the stability experiment). Would there be a transmission mechanism that forced them to revise their beliefs? Might the transmission of the car be stuck in neutral, so that pressing on the OMO gas pedal does not affect the speed? I can imagine a car with a clever anticipatory speedometer, but where the gearshift only goes into Drive if the speedometer gets up to 5mph.

With a TSX 300 instrument/gas pedal, I can see just such a mechanism, that works whether people believe it or not. Tobin's Q.

[JKH]

Scott,

Eureka! I think I got it. (Maybe)

Here’s how I would describe it.

The Fed initially uses OMO to steer the market price of NGDP futures toward target. Once the market price reaches target, the Fed establishes a rule for both NGDP futures and OMO intervention.

E.g. the rule for intervention is that if NGDP futures touch the boundaries of a 4.85 per cent to 5.15 per cent range, the Fed intervenes by being an unlimited seller or buyer respectively, and at the same time intervenes with OMO until the market moves itself off the lower or upper bound for NDGP futures.

Assuming the Fed is always successful in defending the boundaries, which it should be, it will actually make money since it will always have a short position at 4.85 per cent and a long position at 5.15 per cent, and these positions will never be out of the money.

The fed funds rate floats based on the natural market and OMO activity. All other interest rates float as they do now.

It would also be possible to establish the intervention level for futures at the fixed point of 5 per cent as you describe, but I prefer the range approach for some reason I can’t figure out just now. It has something to do with liquidity, volatility, transaction costs and maybe other things.

The suggested NGDP futures range is quite analogous to the current fed funds trading range when interest rates are normally positive, such as 2.75 per cent to 3.25 per cent.

I would modify Nick’s interpretation above slightly by saying that there are dual instruments here – NGDP futures and OMO. That’s the tricky part that I couldn’t see before.

BTW, I think it would also be possible to target NGDP futures without futures market intervention, as was my previous interpretation. The Fed would simply use OMO. The downside of this approach is that the NGDP futures might be more volatile than the suggested range, as it could take time in certain circumstances for the futures to react constructively to the OMO signal. I prefer the futures intervention idea, where the Fed basically stands in at its chosen line in the sand, until the OMO effect moves futures off the bound.

I like it!

Sound right?

[Adam P]

Well, yes Nick. I was assuming that in a liquidity trap we don't just get the real GDP growth.

The important point though is here when Scott says "For this to work there must be some monetary base capable of producing 5% expected NGDP growth".

I would modify that statement to say there must be some PATH for the base that produces the NGDP growth. This breaks the liquidity trap by promising to keep on printing the money and not take it back until we've hit the target, this is exactly Krugman's presciption. It's now just down to credibility.

[JKH]

Nick,

“But suppose people accept that the Bank is really and genuinely trying to do this, but believe it won't work. (I am running through the stability experiment). Would there be a transmission mechanism that forced them to revise their beliefs? Might the transmission of the car be stuck in neutral, so that pressing on the OMO gas pedal does not affect the speed?”

Suppose the car is stuck after the Fed has sold mass quantities of NGDP futures at 4.85 per cent (in my example), while doing parallel OMO’s. This has failed to move futures back above the lower bound. Then you continue to sell NGDP futures, but you call for a cab and invoke credit easing and/or fiscal stimulus.

[JKH]

Given the dual OMO instrument in this proposal, and the free floating fed funds rate, it strikes me that the boundary between normal easing and quantitative easing is seamless. Quantitative easing is merely a question of degree, and in fact is invoked regularly at the lower bound of the OMO target range.

[bob]

If I'm understanding Scott correctly, the actual price of the futures contract would never move? ie. a contract for one year out would be priced at $105 on the dot, and the Fed would simply respond to the volume of buying and selling at this price point with OMOs until buying and selling it brought into equilibrium? The indicator is not the price, but rather the supply vs. demand at a fixed price?

[Nick Rowe]

bob: I think it's: 2009 100, 2010 105, 2011 110, etc. For a given year the price stays constant, but as we go out along the futures curve, it rises at 5% p.a.

[Scott Sumner]

A brief point on credibility. If the BOJ tries to get out of a liquidity trap by creating inflation, they might promise to sell unlimited quantities of yen at 200 to the dollar. What if they are not able to make the price stick? What if their promise is not credible? Well, as long as they are actually selling yen at 200 to the dollar, credibility doesn't matter. I will not buy yen at my local bank where I only get 120 to the dollar, I will go to the BOJ where I can get 200 to the dollar. So it automatically becomes the market price, there is no credibility issue. Similarly, if the Fed promises to buy and sell unlimited numbers of NGDP futures at 105, that becomes the price. The next questions are:

1. Is the price equal to the expected future NGDP?

Answer--pretty close.

2. Are market forecasts of NGDP optimal?

Close enough. None of the current policy disputes revolve around whether the market forecast is slightly different from the Fed's internal forecast, they revolve around why the Fed isn't even coming close to equating their internal forecast and their policy goal. NGDP targeting automatically equates the forecast and the goal.

Nick's response to Adam on the liquidity trap issue is exactly my view. I was sloppy by not spelling out the details, because Adam is right that NGDP is not exactly inflation

JKH, Your interpretation is a version I published in the JMCB in 1995. Bernanke and Woodford criticized that version on "circularity grounds." Thus I now use the version where the market price is always exactly 5%, as the Fed makes the market. There is no steering of the price toward 5%, all trades occur at precisely 5%. Instead, markets steer the MB toward the level expected to produce 5% NGDP growth.
Nick, You may be right about the instrument question. I had always thought that people called the fed funds rate an "instrument." (Even though the MB is actually used to target the ffr.) So perhaps I was confused about terminology.

[bob]

yes, sorry I should be more clear.

what I'm saying is that the curve would stay exactly at "2009 100, 2010 105, 2011 110, etc" (w/ compounding). My point is that for any contract, there is no trading range of the type that JKH described. The prices are fixed to reflect 5% NGDP growth, and the Fed simply looks at supply vs. demand at these price points in order to determine what OMO are necessary.

Basically, the speedometer is fixed but still attached to its motor, and the driver has a device that measures the pressure on it in either direction (supply vs. demand) indicating which way the market is pushing. I'm pretty sure that this is what Sumner has in mind.

[bob]

oops, I see that Scott has just made the point

[Adam P]

Ok, I really think Scott needs to do some explaining here.

Scott says:
"1. Is the price equal to the expected future NGDP?

Answer--pretty close."

No, this is not correct as stated (or not determinate). The correct statement is as follows:
1. Is the price equal to the RISK-NEUTRAL expected future NGDP? Answer--yes.

Which brings us to Scott's second question, correctly formulated it is:
2. Are market forecasts of NGDP, IN THE RISK-NEUTRAL MEASURE, optimal for monetary policy?
Answer -- not so clear.

[Adam P]

quick follow up on my last comment.

Scott apparently is assuming the validity of the EMH and my last comment also presumed rational markets. However, the validity of the EMH is disputed by a lot of really smart guys (Shleifer and Barberis come to mind) and since it is also entirely untestable I think we might pause a bit before hanging the most important questions of macro policy on that hook.

[Adam P]

Also, while I agree that the BOJ can always devalue the yen by paying 200yen for each dollar where's the guarantee that it can always raise the value of the currency (fight inflation). This requires fiscal resources, in the yen/dollar case you need dollars.

A related question, what does the central bank do in a closed economy. It can't buy dollars for 200 yen each so I guess it buys real goods? Now we have a central bank engaging in large scale fiscal stimulus.

And finally, credibility still matters. Inflation, without growth, is usually considered bad. Markets could reasonably worry that if the growth is not forthcoming then the fed will change course, this worry then prevents the growth from materializing.

[Scott Sumner]

Adam, Any monetary regime faces the problem that it's anti-inflation policies must be consistent with the overall fiscal budget constraint. Mine is no different, but that's not really much of a problem for developed economies.

I don't understand your credibility argument. Does it refer to the log run credibility, out beyond the maturity of the futures contract?

Regarding your previous comment, it is very simple to explain. You want the optimal forecast. There are two parts to the difference between the NGDP futures price and the optimal forecast:

1. The difference between the NGDP futures price and the market expectation of next year's NGDP.

2. The difference between the market forecast of next year's NGDP and the optimal forecast of next year's NGDP.

If you look closely you will see than my assertion is logically indisputable. The difference between A and C is the sum of the difference between A and B and the difference between B and C. So I didn't ask the wrong question.

Question 1 is about risk premia, which I think are likely to be very small, and not very time--varying. The second question is about the EMH, which I think is roughly true for this type of market.

I don't think relying on market forecasts is nearly as risky and unproven as relying on an FOMC that we know for certain has let NGDP fall at better than a 6% rate. I highly doubt the market could do much worse over a 12 month span.

[Adam P]

The credibility problem refers to whether the market believes the fed will stick to the regime even in really bad outcomes. Suppose we find ourselves in a situation where real GDP growth is -6% like it is now. For the 5% NGDP growth target to be maintained we'd need roughly 11% inflation, this is a really bad situation and the market might reasonably suppose that once this point is reached the fed might adjust the target. I agree that a promise of future inflation is what we need right now but the promise needs to be credible. Furthermore, since 11% inflation is certainly higher than we need perhaps the fed coming and saying 6% will be more credible exactly because it's less painful.

Now, I imagine you have in mind a story where the promise of inflation prevents us from ever reaching this equilibrium but that only works if the market believes the fed will carry through if we got to this point. It would be perfectly reasonable for agents to believe the fed will not carry through its inflation promise in such a bad case and that belief directly makes the bad case possible.

Finally, where in your story is the guarantee that we won't reach an equilibrium with say zero real growth, 5% inflation and unemployment stuck on 12%? The canonical NK Phillips curve allows for this and it is roughly what happened in the seventies.

[Adam P]

About the difference between market prices and optimal forecasts I'm not sure I see what you're point. I suppose you mean:

A = Futures price;
B = Market expectation (in the physical measure)
C = Optimal forecast.

Well, it is true that A-C = A-B + B-C. However, that equation is still true if B were to equal my mother's forecast. What you need to establish is that A-C is sufficiently small.

[Adam P]

Sorry, just to finish my last comment. You claim that you believe that risk premia would be small and that the EMH is roughly true.

Well the claim that risk premia would be small and not very time varying has absolutely no empirical support and it's quite a claim you make when virtually every asset that is traded has a reasonably large and time varying risk premium.

As for your belief in the EMH, since it's untestable there can't really be empirical support. Furthermore it's not like the EMH is accepted as true by a vast majority of economists. Some believe in it religiously, some believe religiously believe it's false and a lot are somewhere in between.

These are incredibly weak answers from someone who seems so sure the idea is a good one.

[Scott Sumner]

Adam, I cannot put an entire journal article into a blog comment. You can read one of my futures articles if interested. I believe that I cited at least one paper in defense of my low risk premia assumption, but I don't have it at my fingertips. Are you sure no studies have shown this? Surely you wouldn't argue that the risk premia is large on assets likely to show relatively small price variations? I admit that I am not an expert on finance, but some people who know an awful lot about finance have looked at the proposal, and haven't seen any big problems. So we'll just have to agree to disagree on the risk premium issue.

I don't understand your credibility argument. Are you assuming the price would deviate from 105, or that even at that price the policy would not be credible? In the former case my answer is the price cannot deviate from 105, because the Fed makes the market, in the latter case we are back to arguing over risk premia.

Regarding the EMH, it actually is not central to my proposal. Even if it was shown not to hold, I would still favor NGDP futures targeting, unless risk premia were large, as we know the Fed doesn't even come close to targeting the forecast, indeed they admit as much.