Two (probably) unstable macroeconomic equilibria

Some people argue about whether the macroeconomy is inherently stable or unstable. I don't think that's a very useful question. Because.....it depends. And one of the things it depends on is monetary policy. And that is a useful discussion to have, because we can actually do something about monetary policy.

Don't adopt a monetary policy that would make an equilibrium unstable. Because if you miss that equilibrium by even the tiniest amount (which you almost certainly will) the economy will move further and further away from equilibrium.

I thank Steve Keen for (inadvertently) reminding me to do something that George Selgin had wanted economists like me to do. It's not often any of us get the chance to write a post that will make both Steve and George happy at the same time. (Well, Steve should be happy, because I'm talking about unstable equilibria, but you never can tell.)

There's nothing new here. Just the old stuff, but perhaps told in a slightly different way.

1. Don't use monetary policy to target unemployment.

Targeting a real variable like unemployment sounds like a really good idea. Because it's real variables like the unemployment rate, and real income, that really matter to people. Much more than nominal variables like the price level, or inflation rate. So why not tell the central bank to target unemployment?

Like most economists, I think that if you loosen monetary policy then inflation goes up and unemployment goes down. At least, temporarily. There's some sort of short run trade-off. But I'm less sure about the long run. If you permanently loosen monetary policy, so that inflation is permanently higher, will unemployment go down, go up, or stay the same?

It is easy to build a theoretical model in which there is no long run trade-off. The Long Run Phillips Curve is vertical. Now any macroeconomist with any ingenuity could tweak that model to make the Long Run Phillips Curve slope in either direction. But I wouldn't trust those tweaks in either direction. The data don't help much either. When I look at the data, I think I see that countries with high average inflation tend to have high average unemployment rates. Which means the Long Run Phillips Curve slopes the "wrong" way. But I don't totally trust my lying eyes. Because it might just be that screwed up countries tend to get everything wrong, and it's not that their loose monetary policy is causing high inflation and high unemployment. It might just be something else that is screwed up in those countries, that is causing both the high unemployment and the loose monetary policy.

But if you want monetary policy to target unemployment, you had better be very confident that the Long Run Phillips Curve slopes the "right" way. Because if it slopes the wrong way, you have got an unstable equilibrium. If you miss the equilibrium by just the tiniest bit, and set a slightly too low target for the unemployment rate, you loosen monetary policy to bring unemployment down, inflation will rise, the unemployment rate will eventually rise too, so you loosen monetary policy further, and so on, getting further and further way from the equilibrium (assuming it even exists).

Even if the Long Run Phillips Curve does slope the right way, and a stable equilibrium exists, it might be very different from what regular folk might think of as stable. A Russian doll is stable, but it sways back and forth a lot in a gusty wind. If the Long Run Phillips Curve slopes the "right" way, but is very steep, small shifts in the Phillips Curve will cause very big fluctuations in inflation if you target unemployment.

Most economists say the Long Run Phillips Curve is vertical, and so monetary policy can't target unemployment in the long run. They don't really mean that. They mean they don't really know which way it slopes, and vertical is probably a good approximation. And they don't want monetary policy to target unemployment, because the risk of the equilibrium being unstable, even if it exists, is far too high for comfort. And even if it is technically stable, it will move around a lot, so it won't look "stable" in the ordinary sense of the word.

As older readers will remember, targeting unemployment has been tried before. And it took a couple of decades to recover from the experiment and get both inflation and unemployment back down again.

Lets not go there again. It's a really bad idea.

2. Don't use monetary policy to target a nominal interest rate.

But that's what the Bank of Canada does, isn't it? Well, yes and no. Mostly no. What the Bank of Canada does is target 2% inflation. It only targets a nominal interest rate for a very short time period, of about 6 weeks. Every 6 weeks it adjusts the interest rate target, as needed, to try to keep inflation at the 2% target.

There (probably) exists a time-path for the nominal rate of interest that is compatible with an equilibrium in which inflation stays at (roughly) 2%. But:

We don't know what it is. It won't be a constant. And, most importantly, it will (almost certainly) be an unstable equilibrium. If we miss that equilibrium, by even the smallest amount, the economy will move further and further away from the equilibrium.

Suppose the central bank sets the rate of interest too low. Demand will be too high, and inflation will start to rise, and keep on rising.

It gets worse. As inflation rises, expected inflation rises too, the real interest rate falls for any given nominal rate, and so demand increases still further.

None of this is news to New Keynesian macroeconomists. They know you will get an unstable equilibrium if the central bank holds the nominal interest rate constant. So they insist that the central bank must adjust the nominal interest rate quickly enough and by a large enough amount to try to turn an unstable equilibrium into a stable equilibrium. And if people are confident that they can and will do this, expected inflation will stay anchored at the 2% target, which helps prevent one of the destabilising forces.

Whether that feedback rule for the nominal interest rate will always operate quickly enough and strongly enough and be credible enough to convert an unstable equilibrium into a stable equilibrium.....is another question. The answer looks a lot different at the Zero Lower Bound than it did before. Maybe it's time to stop using even very short term interest rate targets?

Comments

[rsj]

Nick,

We are taking about the zero bound here. No one questions the ability of interest rate adjustments to affect the economy. But holding the rate fixed, yes the private sector can offset any quantity changes. Irredeemabiity of the CB's liabilities is irrelevant because money in the non financial sector is deposits, which can be redeemed.

[Nick Rowe]

rsj: "Nick,

The issue is that your picture omits how the curves change in response to interest rate changes."

In the picture where the central bank is targeting x% unemployment, then the MP curve, by definition, is vertical in {inflation,unemployment rate} space. It is vertical at x% unemployment by definition (except for a slight lag in the central bank responding to unemployment data). The central bank adjusts the rate of interest (or whatever) to make it vertical and stop it shifting. Until the economy explodes into hyperinflation (in the unstable case) and the MP curve disappears altogether because people stop using the central bank's money. Or it implodes into deflation and the MP curve disappears because people resort to barter.

[rsj]

Actually, Irredeemabiity is a nice way of looking at it. Say that households hold 7 trillion in deposits and one trillion in currency. They can redeem the currency for deposits, by depositing their currency. And they can redeem deposits for bank bonds or bank equity.

As far as the household sector is concerned, money is fully redeemable. It is the banking sector that is stuck with the excess reserves. So once again there is no hot potato effect.

[Nick Rowe]

rsj: "But holding the rate fixed, yes the private sector can offset any quantity changes. Irredeemabiity of the CB's liabilities is irrelevant because money in the non financial sector is deposits, which can be redeemed."

But if the private sector fully offsets any changes made by the central bank, how can the central bank hold the rate fixed where it wants to?

Similarly, if Ricardian Equivalence were true, then the fiscal authority would not be able to use tax policy to hold the rate of interest fixed where it wants to.

Exasperation.

[rsj]

By paying interest on reserved at the policy rate, the cb could control both the quantity of reserves and the rate separately

[Nick Rowe]

Take a very simple economy where central bank currency is the only money. The central bank could tighten monetary policy by: reducing the supply of currency; or, increasing the demand for currency by paying interest on currency.

[rsj]

Look, in Canada, required reserves are zero, and actual reserves are 50 million. Yet the CB can set any policy rate it wants. A corridor system allows that.

Alternately, suppose the government taxed banks r% for every asset they held that was not a liability of the government. At the same time, it gives banks a tax credit for every interest payment made that was not made to bank capital (where capital is determined by the regulators for purposes of capital adequacy). Then, r% is the interest rate paid by the non-financial sector, yet the quantity of reserves can be anything.

If you think creatively, you can come up with other examples. The reason why all of these examples work is because deposits are free money given to banks. They are seignorage income earned by banks. So it is possible to reduce the quantity of that seignorage income to zero. And as deposits are generally much larger than required reserves, there is a lot of economic room to have banks hold more reserves while still creating freedom for the central bank to set policy rates. The banks would get fewer rents, but any positive economic rent is still worth having.

But the above is, in some sense, a distraction. In our current system, there is some amount of reserves that banks need, and the CB must given them exactly that amount if it wants to maintain positive rates. But with the same quantity of reserves you can have a rate of 3% or 10%. Just look at Canada. Reserves are 0 and yet the CB can set rates to whatever it wants.

[K]

Whoa, rsj. You skipped straight to the conclusion, real economy and all. I was hoping to discover the financial equilibrium which should happen within hours, and leave the real effects, which might take months for later.

If you assume Wallace irrelevance you don't get any effect on tbill yields at all.

Even if consumers are willing to hold deposits at zero interest the competitive equilibrium rate ought to be at marginal cost, ie fed funds minus costs. I agree, however, that there is evidence of a market failure in deposit rates, at least in some banking systems.

[rsj]

The main point being, that reserves are plumbing in a two tiered system: central bank --> other banks --> non-financial sector.

Reserves clear transactions in the first system, and their issuance generates seignorage income to the government. Deposits clear transactions in the outer layer -- the economically meaningful layer -- and their issuance generates seignorage income to banks.

Only the inner layer has irredeemable money (reserves). The hot potato effect of that irredeemable money (reserves) is to drive the overnight rate very high or very low. It is not because banks rush out and purchase consumption.

The outer layer does not have irredeemable money (deposits). Deposits are redeemable, and therefore there is no hot potato effect. Banks cannot force households to hold more deposits than they want, even though the central bank can force banks to hold more reserves than what they want.

I don't think the above is very complicated. There are certain ways of simplifying it. E.g. get rid of money entirely, and assume the CB controls interest rates by magic. Or, keep only reserves, but have them be redeemable. Or have the whole shebang -- both levels. One thing you cannot do, is pretend that there are no banks, but that money for the non-financial sector is irredeemable.

[rsj]

Even if consumers are willing to hold deposits at zero interest the competitive equilibrium rate ought to be at marginal cost, ie fed funds minus costs.

There is no free entry and exit -- banks are heavily regulated. They are part of a club, entrance to which allows you to pay your liabilities ex-post, netted against other members of the club. It allows you access to unsecured lending. It allows you access to automatic intra-day loans, as well as overnight loans. Such a club only operates based on trust between members. There is also retribution. If one member of the club goes out of line, other members could refuse to lend to them, imposing large costs on that member.

I think you have all the ingredients for the existence of a cooperating equilibrium between oligopolies.

[K]

rsj,

I agree that how you describe it is exactly how it works, *effectively*. Unfortunately our actual monetary Rube Goldberg has a few confounding elements that can make it tough for people to see how it works in effect:

1) Deposits are redeemable into *something* at the option of the representative household. That something is currency. (This bit is at the core of the illusion held by 99.99% of the population that "the bank stores my money.")

2) The CB doesn't control the quantity of reserves. They control the quantity of base money = reserves + currency. Currency is redeemable into reserves at the option of clearing banks. They perform that conversion with 100% certainty. Clearing banks *never* hold currency unless you put IOR significantly negative.

The effect of all that ends up exactly as you describe. The reason I wanted to play out an actual monetary game with real representative agents was that I think that's the only way to

1) convince someone with a deeply monetarist intuition, that there are monetary systems that do not conform to their perspective (and in which the ZLB is a real problem); and

2) develop one's intuition for the conditions under which monetary systems transition between different regimes of behaviour.

I think at least the first goal might be achievable but obviously it would have been a lot more productive if Nick would play the central bank and tell us what the rules are. (Come on, Nick!) The second goal is the greater benefit, but it may be too hard in a forum such as this.

"I think you have all the ingredients for the existence of a cooperating equilibrium between oligopolies."

I think so too. The history of deposit rates in Canada, for example, points in that direction. I've looked for data for the US, but deposit rates don't seem to be monitored (at least not published) by the regulatory authorities.

[Ritwik]

Regarding deposit rates, things change. UK has among the most oligopolistic banking systems in the world. High street banks hae, however, been competing like mad to get deposits up. 2 yr term deposits pay 5% p.a at most banks. Lloyds recently announced a new current account scheme that pays out 4% p.a. under certain conditions.

Plus, in general, I'm not quite on-board with the description of the banking club as one that evolves naturally. the fact that the government makes it near impossible to set up a bank contributes too.

Goodhart had this proposal where the central bank would be the lender of 'first' resort, not just last resort. I can't quite remember but the aims were to let it exert greater control over the price of the liquidity put option, and to remove the stigma of borrowing from the CB, thus weakening the kind of banking club being described here.

I'm a bit surprised neither K nor rsj have taken up the idea of analytically separating the 'policy rate' and the liquidity scarcity rate. Only the latter is the natural monopoly of the market maker of reserves. The other could even be market determined - leaving no such thing as 'the policy rate' - and Nick could create a model of a central bank as well as monetary policy in which the short rate is truly endogenous and a by-product of monetary policy rather than an instrument.

[rsj]

I think at least the first goal might be achievable but obviously it would have been a lot more productive if Nick would play the central bank and tell us what the rules are. (Come on, Nick!)

Hear, hear!

[K]

Ritwik,

Term deposits are competitive with bonds in Canada too. Yield is a bit lower but no transaction costs and they're puttable. The problem seems to be in overnight savings deposits which have yielded nothing for the past 20 years or so.

I didn't understand your point about there being two distinct rates.

[Min]

Nick Rowe: "You aren't getting what I'm saying. Please draw the picture. See where the MP and LRPC cross? That's an equilibrium. Draw the LRPC as downward-sloping, and it's a stable equilibrium. Draw the LRPC as upward sloping, and it's an unstable equilibrium.

"Words suck; pictures rule."

I know what an unstable equilibrium is, Nick. Do not be deceived. :) (In fact, I am ashamed of myself that, after all this time, you would think that I would not know that. :( )

It seems that you are making some assumptions that do not appear in either the text or the picture, that I do not see. Perhaps when you say that the CB is targeting unemployment or a nominal interest rate, that its target is, in fact, an equilibrium. In that case, if the equilibrium is unstable, then, as you say, "if you miss that equilibrium by even the tiniest amount (which you almost certainly will) the economy will move further and further away from equilibrium".

I challenged that assumption by pointing out that the target does not have to be an equilibrium. How could it be? The CB is not omniscient.

Ah, but you may be making another assumption, that the curves in the picture are straight lines. Near the equilibrium, that is a reasonable approximation, but that assumption is almost certainly false. The curves curve. If they were straight lines, then any target would lead to instability. But surely they are not.

Now I make an assumption. I assume that targeting the current value does not lead to instability. If it did, I think that we would be able to tell. If that is the case, then there is at least one target that does not lead to instability. QED.

¿Es claro? :)

[Min]

In line with the idea that we are currently in a stable regime, but we could move to an unstable regime, a Fed official made a remark that I paraphrase: "We decide on a change that we think is right, and then we do less." (My memory is not specific enough for me to find the actual quote. I think it was on Mark Thoma's site this year.) Such caution is appropriate when you are worried about instability, but the current target seem to be in a stable regime. You do not just throw up your hands and say, well I guess we should not do any targeting, in case the equilibrium is unstable.

[Sergei]

"Some people argue about whether the macroeconomy is inherently stable or unstable. I don't think that's a very useful question. Because.....it depends. And one of the things it depends on is monetary policy. "

Well, English is not my first language as is logic. But the direct conclusion from the above, without any need to read the rest, is:
1. Macroeconomy is always unstable and therefore does not have any stable equilibria. This conclusion does not depend on anything. Macroeconomy is intrinsically unstable.
2. All types of policies are run to try to stabilize macroeconomy within some bearable range of chosen outcomes. What we chose as chosen outcomes are also policy variables.

So my question is - are those chosen outcomes a stable equilibria or not?

[Sergei]

... to be more explicit ...

So my question is - are those chosen outcomes, *as policy variables,* a stable equilibria or not?

[W. Peden]

Ritwik,

If Kirzner is right, then there is no contradiciton between a competitive market and a low number of market participants (even only one seller could be in a competitive market) so the fact that UK banking now takes place in an international context where banks like Santander can (and do) enter makes a big difference. It wasn't always this way: until the reforms of the early 1970s that interest rates stopped being set by a formal cartel; interest rates on sight deposits only became common in the late 70s/early 80s; and banks didn't start really competing with building societies in the mortgage market until the 1980s.

I think that what Kirzner says about competition applies to financial markets as much as anywhere else: what matters are barriers to entry and exit, not the number of buyers/sellers. The error in perfect competition theory is to misidentify what is important in competition- winners, losers and rules that apply to all- and to focus on what is easily quantifiable but doesn't relate to actually equilibriating market processes. A village shop in a remote Scottish Highland village can be operating under conditions of competition and a market like a professional sports league can be very non-competitive in spite of a large number of teams.