Strategy space and monetary policy

Or, "Why central banks should stop talking about interest rates".

Game theorists know that a change in the "strategy space" can change the equilibrium of a game. The classic example, now over a century old, is the difference between the Cournot-Nash equilibrium and the Bertrand-Nash equilibrium in oligopoly theory.

For a monopolist, it makes no difference whether the firm chooses output to maximise profit or chooses price to maximise profit; we get exactly the same equilibrium either way. In oligopoly it does make a difference. In Cournot-Nash, each firm chooses output taking other firms' outputs as given. In Bertrand-Nash, each firm chooses price taking other firms' prices as given. The Cournot-Nash equilibrium has a higher price and lower output than the Bertrand-Nash equilibrium, even when everything else is the same.

Oligopolists that play Cournot-Nash will earn higher equilibrium profits than oligopolists that play Bertrand-Nash. If you were an oligopolist, you would want to shut up about your price, and the other firms prices. You would want to talk about your output, and the other firms' outputs, instead. You would want to change the game you are playing from a Bertrand-Nash game into a Cournot-Nash game. And maybe you can change the strategy space by shutting up about one strategy space and talking a lot about the other strategy space.

I think that central banks should shut up about interest rates too, and talk about something else instead. That way they might change the strategy space into a different strategy space that leads to a better equilibrium.

It makes no sense to argue about whether an oligopolist, taking the other firms' decisions as given, is really choosing price or output. By picking a point on his demand curve, by choosing price he is ipso facto choosing output, and vice versa. What matters is not whether he is in fact choosing price or output (a distinction that makes no sense anyway), but whether other firms think of him as choosing price or output (and whether he thinks of them as choosing price or output). And the oligopolist wants the other firms to think of him as choosing output, not price. Which is why he should shut up about price, and talk about output instead.

It also makes no sense to argue about whether central banks choose an interest rate or something else. Since interest rates are linked to a lot of other things, by choosing an interest rate the central bank is ipso facto choosing a lot of other things, and vice versa. What matters is not whether a central bank in fact chooses an interest rate or something else, but whether other people think of the central bank as choosing an interest rate or something else. Which is why central banks should shut up about interest rates, and talk about something else instead.

To think of central banks as choosing a rate of interest is a social construction of reality. What is so very unfortunate is that this is a social construction of reality that is not merely maintained but created by central banks themselves in how they talk about what they are doing. It is like oligopolists spending all their time talking about prices, and discouraging any talk about quantities.

Why is it so bad if people think of central banks as choosing an interest rate? What's wrong with that strategy space? Right now the most important reason is this: if people think of central banks as setting an interest rate, then they think the central bank must be powerless to increase demand for goods if the interest rate is at the lower bound. And most of the power of a central bank comes from its ability to influence people's expectations of the future. Like governments, police, armies, and referees, most of central banks' power comes from belief in their power.

The strategy space matters when others' expectations of your choices matter. Those expectations are defined over the strategy space. Expectations of monetary policy matter. That means the strategy space matters.

So, central banks: stop talking about choosing an interest rate; stop talking about the time-path of future interest rates; just shut up about interest rates altogether. Start talking about something else instead.

Like what? Something that moves in the right direction, for starters. Nominal interest rates move in the wrong direction. If you think about monetary policy in terms of interest rates, then if the bank chooses to loosen monetary policy you think of that as the bank choosing a lower interest rate. But if the bank is successful, and monetary policy is in fact loosened, so expected inflation rises, and expected future income rises, then nominal interest rates will rise. So you have no idea what success means. Does it mean falling or rising nominal interest rates? So success cannot be self-promoting. Central banks' power, and belief in their power, move nominal interest rates in opposite directions.

Instead, talk about something that moves in the same direction when you choose to loosen monetary policy and when you succeed in loosening monetary policy. Share prices maybe, commodity prices, or whatever. Anything but interest rates.

Comments

[Just visiting from macleans]

If the market is efficient, your advice will be widely disseminated, and people will know why the central banks no longer talk about interest rates, so they'll pester them until they do. Pavlov's dog, I believe, predates.

[Jon]

So what about the (base) money multiplier?

[Kosta]

Very interesting ideas, thank you.

[Bill Woolsey]

I have been reading Woodford's Interest and Prices. Why does he focus on short term interest rates? Is there any other reason but that Central Banks focus on them?

I favor talking about the growth path for nominal expenditure, but there needs to be some connection to what the central bank actually does--base money?

[Just visiting from macleans]

I have to admit, I have a disconnect with much of economic theory, and practical real world stuff. So, say I had an economist on staff, and I operated a company in an oligopoly of some sort. They advise me to maximize profit by either choosing price or output.

So, what does this mean, how does one find that point, and how does one know when one is there? If someone could pick an industry and give me a practical example of how this would work, I'd appreciate it. Thx.

[anon]

In other words, you want central banks to pretend that they don't do what they do - which is set short term interest rates.

[Nick Rowe]

When we teach monopoly, we always teach it as if the monopolist were choosing output, not price. "Take the derivative of profits wrt q, so you get MR-MC, then adjust q until MR=MC". My guess is that most real-world monopolists think of themselves as setting p, rather than q. And we could teach it this way if we wanted, though it would be a little bit more complex. Just substitute the demand function in for q, so profits are a function of p, then take the derivative of profits wrt p.

So anon: what is it that a monopolist *really* sets? What does "sets" mean? Do you always believe everything a monopolist tells you? Do you always view what someone is doing by using the same language that he himself uses to describe what he's doing? Even, I don't know, crazed religious fanatics?

Bill: the short, only semi-flip, answer to your question, is that Michael Woodford, like anon, is "inside the Matrix". He is so committed to one way of constructing the social reality that he cannot but see it as concrete. He can't see it as a duck, only as a rabbit. "Look! See there's its ears! They're real!"

Another answer would be to say that it is sometimes easier to model monetary policy as setting an interest rate, since you only need an IS curve. Just like modeling the monopolist as setting q. And after you have modeled something in a particular way for some time, you start to think of your model as concrete. And if the bank itself uses the same model to describe what it is doing, then that just adds to the sense of concreteness, since the bank, after all, must be an expert when it comes to "knowing" what it is that it is doing.

"I favor talking about the growth path for nominal expenditure, but there needs to be some connection to what the central bank actually does--base money?"

Yes. That's important. The bank (of Canada, anyway) also talks about choosing inflation. And that's a construction of reality I want it to maintain. But unless people can see an actual transmission mechanism in place, and believe it can work, the inflation-targeting reality can break down. People lose confidence in that reality. It could better maintain the inflation targeting reality if it moved away from talking about interest rates. (And it's harder for the Fed, since it doesn't talk about choosing inflation.) I'm not sure, but I think that talking about choosing the price of real-return bonds would be better. (Or the TSX index, or Trills). I've ducked that question, a bit.

Jon: the trouble is, people have become so used to thinking about the interest-rate channel that the base money channel would just be re-interpreted as an indirect route to interest rates. Just like in ISLM.

Just visiting: I think in this case there will be positive feedback from what the bank says it is choosing to what people focus on, in forming their expectations, and therefore what actually matters. I'm going to skip your question on Bertrand vs Cournot, since it takes me too far off-topic.

Kosta: Thanks!

[Just visiting from macleans]

OK. I wasn't looking for a comparison. Just an example of picking a point and getting there. Goes counter to my understanding of how companies actually operate. Maybe a later blog.

[David Pearson]

Nick, you suggest that the Fed may want to talk about "share prices". Imagine a situation in which the stock market believes that the Fed is targeting a smooth trajectory for the S&P, one that matches the desired target growth rate of NGDP. What would be the implications?

First, the market would perceive a lower volatility of nominal equity returns. This would create a step-function rise in share prices. The share prices of firms with nominal pricing power (commodities, oligopolies, consumer staples, real estate-related) would perform better. Firms, in turn, would interpret these price signals as an impetus to increasing investment in those sectors. The result would be significant mal-investment.

Second, the more credible the Fed's promise to smooth nominal returns, the more leverage both investors in financial securities AND firms will build up. What is the ultimate cap on leverage? Financial firms use Value At Risk models that incorporate price volatility, so extremely low price volatility leads to extremely high leverage ratios. Some of this can be controlled through regulation, but as we have seen in the 2000's, the issues of regulatory capture and financial innovation trump attempts to limit leverage during times of smooth and high nominal returns.

So, I am arguing that targeting NGDP, or its proxy, the S&P 500, leads to mal-investment and leverage. There are many who believe that asymmetric monetary policy from 1998-2008 produced exactly that result, and that it landed us in our current predicament. How do you respond to that argument?

[Nick Rowe]

David: my post is a lot stronger on why I don't like interest rates than on suggesting a good alternative. That's a definite weak point in my argument.

But let me try to tackle your arguments anyway.

First, there's a distinction between central banks talking about a share price index as a short-term "instrument" (or indicator), and targeting a long-term time path of that index. I'm talking about the former. And it's not obvious to me that this would result in a smoother time path of the share price index. Though it might.

But suppose it does. Why is that a bad thing? Sure share prices would be higher (and different shares might be affected by different amounts). P/E multiples would increase. Shares would be more liquid. And that would change the pattern of investment, and generally increase investment. But why would you say that those changes constitute *mal*investment? To me it would seem to be the correct response to a change in circumstances.

If you describe that as *mal*investment, you must have at the back of your mind some concept of a "neutral" monetary policy framework under which there would be no malinvestment, and actual investment would be equal to the hypothetical optimal Walrasian level. What is that "neutral" monetary policy? And how do you know that my proposal isn't it (or at least closer to neutral than any other known policy)?

To my mind, if share prices became smoother, people would be more willing to own shares than corp[orate bonds, so firms' debt/equity ratios would fall, and that would mean a decrease in total leverage across the economy. Even if I'm wrong on this point, and people did use more leverage to buy shares now that share prices are smoother, so what? If shares are indeed safer than before, then you could increase leverage without increasing overall risk.

Take the limit, where the central bank really did target the total return index to grow at some constant rate. Then that share index would become the ideal investment vehicle for widows and orphans. Bonds would disappear. Debt would disappear. Firms with 0% debt-equity ratios cannot go bankrupt. That sounds like a very stable financial system. (The dot.com crash had few repercussions, because the dot.coms were mostly share-financed.)

The current monetary system "privileges" debt against shares (equity). So we get malinvestment in debt-financed investments (like government borrowing).

[Patrick]

Is there some instrument/index/spread/whatever that serves as a market based indicator of the natural rate (i.e. the real interest rate consistent with output equaling potential)?

[Scott Sumner]

Nick, I like this post and I like the reply you gave David Pearson. Anything that mixes monetary theory with the "social construction of reality" is right up my alley.

I notice you didn't mention the targeting of the base. I had always assumed that it was a better indicator that interest rates, but given recent events in the US and Japan, I'm not so sure.

In the US the price of shares is probably negatively related to the rate of inflation, and almost certainly positively related to the price level. So that might make targeting the S&P a bit tricky. I still think NGDP expectations are best.

You and I (and Woolsey) seem to have similar intuition about the drawbacks of interest rate targeting. What I like about your posts is that you know mainstream econ better than I do, so you are able to develop the points using models like game theory that would be appealing to other economists.

You really need to do a journal article to get these ideas more visibility.

[Nick Rowe]

Patrick: you mean is there a Philosopher's Stone? Yes, sort of, I think. It's the ratio between the current price and the strike(?) price of a futures contract on whatever nominal variable it is the central bank is targeting (or something like that). Getting into Scott Sumner's territory here. But you still need a transmission mechanism between the Philosopher's Stone and the nominal variable you are targeting.

[David Pearson]

Nick,

I think we come to different conclusions on the debt/equity issue. The risk-adjusted rate of return on debt and equity depends on leverage. If investors want to earn a positive return on debt, then firms will create debt instruments that deliver those returns -- despite the infinitely small volatility -- by having infinitely small equity. It is equity that would disappear in that scenario. Think of equity as merely the "cushion" that debt holders require to protect against bankruptcy risk. That risk, if near zero, will result in a near-zero cushion. This was essentially the rationale that securities and rating firms used when peddling AAA-rated "super senior" tranches of high-LTV subprime deals.

So, I think that, rather than eliminating debt, near-constant NGDP growth would virtually eliminate equity, and that is what we saw in the more-affected sectors of the economy that were impacted by the Fed's asymmetric monetary policy (which effectively "guaranteed" a nominal floor under asset prices). You argue that under a "constant NGDP" environment, leverage would not be bad thing. Sure, in a theoretical sense, you are on solid ground. We know, however, that the vulnerability of an economy to shocks increases with leverage. In the real world, there is no near-constant equilibrium of NGDP expectations, even under a highly credible Federal Reserve. The danger of nominal targets is that they create the ILLUSION of constancy, into which the real world intrudes. The stronger the illusion, the more adverse the effect of that intrusion, and this was the real lesson to be learned from the "Great Moderation" and asymmetric policy.

BTW, as an aside, and to open up a huge can of worms, there is no possibility of knowing, a priori, whether targeting would work. It would be an experiment. My thesis is that strong a strong consensus surrounding economic theory generates more risky experimentation, and it is debate, combined with policy pragmatism, that reduces that risk. "Asymmetric policy" was a failed experiment, the results of which are still yet to be fully determined.

[Min]

Sorry, you lost me. In your analogy a central banker is an oligopolist, along with other central bankers. As an oligopolist, I would generally want to collude with other oligopolists. There is nothing illegal about central bankers getting together, and they do it a lot, don't they? What is the problem?

Also, your analogy for prices are interest rates, but you offer no analogy for output. You also offer no analogy for profit, either. What are central bankers trying to maximize or optimize?

"Why is it so bad if people think of central banks as choosing an interest rate? What's wrong with that strategy space? Right now the most important reason is this: if people think of central banks as setting an interest rate, then they think the central bank must be powerless to increase demand for goods if the interest rate is at the lower bound."

Lower bound? Not for Sweden, right? (BTW, how is that working out for them?)

I also have a question about the idea of central bankers increasing demand for goods. They are not advertisers, marketers, or salesmen, right? Why should we expect them to increase demand for goods? Now, we might want them to decrease demand for money, which presumably they could do by increasing the supply enormously. But we don't want them to do that, do we?

"Expectations of monetary policy matter."

Now, you want regulators not to be transparent to those that they are regulating. A big sign on the highway saying, "Speed trap in 2 miles," if honest, is to some degree counterproductive, as it will reduce the number of speeders caught. OTOH, you do want regulators to conform to the expectations of the general public, and to do so in a way that is apparent to them. So in that way you want them to be predictable. You want the highway patrol to say that they set up speed traps, but not to say where they are.

[JP Koning]

How would the Fed target a growth path for stock prices? The Fed can control the Fed funds market because it's relatively tiny. But would the Fed be able to use its tiny $1T balance sheet to finely tune prices in a market with a total value of over $15T?

If the Fed focuses on a narrow selection of 10 securities with a more reasonable combined market cap of, say, $500m, then the prices of those 10 companies will benefit, funds flowing to them and not their competitors.

[Min]

JP Koning: "But would the Fed be able to use its tiny $1T balance sheet to finely tune prices in a market with a total value of over $15T?"

Believe it or not, I have heard that last year's run-up in the U. S. stock market was abetted by the Fed, which secretly bought index futures. ;) Not a bad conspiracy theory, eh?

[JP Koning]

I've heard that one too. And that the ESF is keeping the gold price down, that's a popular one too.

On second thoughts, I can understand how the Fed can keep a growth path for stock prices when it wants to loosen policy, after all it can create dollars at will. But I don't think it can maintain a declining path when it wants to tighten policy. It would have to have immense amounts of stock available for sale to enforce that path - equity markets are huge - and its balance sheet doesn't have that kind of capacity.

[Nick Rowe]

Scott: Thanks! (we were posting our last comments at the same time).

"I notice you didn't mention the targeting of the base. I had always assumed that it was a better indicator that interest rates, but given recent events in the US and Japan, I'm not so sure."

Same here.

"In the US the price of shares is probably negatively related to the rate of inflation, and almost certainly positively related to the price level. So that might make targeting the S&P a bit tricky."

The fact that share prices (being a nominal variable) are positively correlated to the price level (both theoretically and empirically) is a feature, not a bug. That means that targeting the share price can serve as a nominal anchor. The negative correlation to inflation worries me. Theoretically there should be a positive relation between share price inflation and CPI inflation, if the shocks were permanent changes to the money growth rate. The negative correlation id probably an artefact of previous monetary regimes, is my guess. If loose money let inflation get high, people anticipate a future tightening of monetary policy to bring inflation down, which would also have short-term real effects.

"You really need to do a journal article to get these ideas more visibility."

Thanks, yes, I ought to. But nowadays I feel just like a kid with ADD (or a crack-addict who needs the instant hit off a blog post). And nobody ever read my journal articles anyway. More and better economists read my blog posts (I bet you never read any of my articles, not that there are that many to read!). Plus a lot of people who have never read an economics journal in their lives, but who can sometimes give beneficial feedback from a totally unexpected direction. Those who read and write in a particular journal are often all of the same religion. (Now that's an idea I ought to expand on....in another post!)

David: I find it hard to understand why debt exists in equilibrium anyway. Add bankruptcy costs to Modigliani-Miller and debt disappears. It must be that some people just want something simple, and giving a safe nominal return. If an equity index delivers that, debt should disappear.

Min: Yep, I must have totally lost you!

I'm not saying that central banks are an oligopoly. I just use oligopoly as an example to illustrate what I mean by "strategy space", because that oligopoly example is the one that's most widely known where strategy space affects the equilibrium.

Over the last year, we have very definitely wanted central banks to increase the demand for goods. Because it was an insufficient demand for goods, in terms of money, that caused the recession.

JP: how can central banks, with their tiny balance sheets, control markets, including financial markets, 1,000 times their size?

1. because all those other markets use a media of exchange (money). So the value of money traded in any week is equal to the value of all other goods combined traded in that week (except for a few barter exchanges). And all other media of exchange (commercial bank monies) are redeemable on demand into the medium of exchange controlled by the central bank, but not vice versa.

2. Because it wants to.

3. Because people know 1 and 2.

[JP Koning]

I agree with your points 1-3 for setting an upwards path. But they don't work with tightening; a downwards path. That would involve sales of stock off the Fed's balance sheet to drain money. But with a equity markets being so much larger than the Fed funds market, the Fed could run out of stock to sell before reaching its target.

Just like how in 1968 the Fed ran out of gold to sell to keep the price at $35 and had to let the market fly. Running out of treasuries to sell when tightening in the tiny ff market was never really an issue. Anyways, this is far from the main point in your post, but your last 2 sentences make one wonder.

[Adam P]

Nick,

consider the two oligopolists, in parallel universes, the first is choosing output and the second is choosing price (and suppose they can't change strategies, that is the price guy is legally required to produce as much output as is demanded at the price he chooses, the quantitiy one is legally requried to sell at the market price his quantity decision implies).

They both face identical competitors and identical demand curves.

Now suppose that both face a legal requirement that the real price of their good be above a certain minimum, say PL (so now the quantity guy must set price equal to the larger of the market price and PL).

Clearly the price guy is stuck if he wants to sell more output than what he sells at PL, the legal price constraint binds.

What about the quantity guy?

The quantity guy is just as stuck, THEY FACE THE SAME DEMAND CURVES. The quantity guy can produce more than is demanded at PL all he wants, he CAN'T SELL more than is demanded at PL and so the rest stays as excess reserves (which are sometimes called excess inventory if the good is not money).

Other than the level of excess inventory the lower bound on price does exactly the same thing in both economies, and if the good is a non-produced one like money, then the level of employment is the same in both universes.

[Nick Rowe]

Adam P: Good to see you back!

In the oligopoly case, I agree with what you say.

But the oligopoly case is only an analogy, to show that strategy space can matter. The (or one) difference between the oligopoly game and the monetary policy game is that the former is a one-shot game, while in the latter expectations of future policy matter. And expectations of a rise in future nominal interest rates above zero can be consistent with a tightening of future monetary policy and also with a loosening of future monetary policy. Expectations can be self-fulfilling in the monetary policy game. Changing the strategy space could change the focal point around which those expectations form.

My oligopoly analogy does not constitute a proof that changing the strategy space could change the equilibrium in monetary policy. It's meant to be suggestive, to open the door to the possibility that it could work. My real argument comes near the bottom of my post, when I talk about how success, and the belief in success, move the instrument in the same direction.

JP: If the Fed has assets (that don't have to be gold) of value equal to the monetary base, then it can reduce the base to zero, by selling all those assets.

[Scott Sumner]

Nick, Of course I don't follow the advice I gave you. I am also addicted to the blog.

It's easy to explain why inflation hurts stock prices. Inflation dramatically increases real tax rates on capital, as earning on capital aren't indexed in our tax system (don't know about Canada, but given how tricky indexation of capital is, I doubt you do it either.)

Under the gold standard, where long run prices are anchored, expected inflation is generally near zero. In that case higher prices often help stocks, as they don't lead to higher expected inflation. By the 1970s, higher than expected CPI figures were often hurting the stock market.

[JP Koning]

The Fed either will either be successful in guiding a huge market down, or in its attempt to reduce the base to zero, private actors will see fit to ignore laws and step in to supply the demand for a medium of exchange. The bigger the market you try to push down, the greater the threat of de-dollarization (or dollarization if the country is Canada); the spontaneous loss of your monopoly on money issuance, and your ability to control monetary policy. That's why I think targeting the massive equity market would be pretty dangerous, from the Fed's perspective. But you've convinced me it could be possible.

Re: your articles. I read the one on Cuba, and the one on Simmel too, come to think of it. Enjoyed both. Would be nice to see an update on Cuba, my understanding is they're trying to dedollarize with some sort of convertible peso.

[dlr]

Peanut gallery comment: I am glad to see Adam P posting on this thread, and I hope the conversation doesn't get stuck amidst the oligopoly analogy. In Nick's initial "Social Construction" blog post on this topic, Adam P challenged the underlying idea (which really has nothing to do with the currently analogy) that there is a relationship between money and the price level that is simple enough to make just any potential transmission mechanism work in accordance with simple expectations about its effects:

However, now I see the problem. You think that "The basic relationship is between money stock and the price level". ACTUALLY NO, although I'm beginning to realize that this is the most mis-understood point in economics (already the most mis-understood disipline in history).

I'll say it again, in caps again, JOINTLY DETERMINED. We're talking general equilibrium here. With fiat money the relationship between the money stock and price level is determined in a system of equations that jointly determine rates of substitution across goods, time and states of nature. And that's when we have frictionless markets (costless and perfect intermediation) to facilitate the solution. Right now we far from perfect intermediation

This seems like the interesting dispute. I know Scott Sumner at least and presumably Nick will disagree with Adam here, but I would love to hear the conversation play out.

[himaginary]

Adam P via dlr:"The basic relationship is between money stock and the price level"

Chris Sims, who thinks "The basic relationship is between budget and the price level" (so-called FTPL), wrote a paper which Scott quoted. He seems to think that "quantity guy" (as Adam P called it) should be the government. He says "Markov perfect" equilibria between price guy (=central bank) and quantity guy (=government) determines the price level. Maybe he is in the vein of this post's suggestion in that he's trying to see beyond interest rate policy.

[Adam P]

himaginary, i've read Sims' paper and Scott's quote and the truly comical thing is that Scott completely misunderstands the paper. Scott claims that Sims appears to agree with him when nothing of the sort is true. What Sims actually says in the paper has absolutely nothing in common with what Scott thinks he's saying:)

[Patrick]

via CalculatedRisk, Bernanke says:

"the Federal Reserve is considering the utility, during the transition to a more normal policy configuration, of communicating the stance of policy in terms of another operating target, such as an alternative short-term interest rate."