Guess who discussed negative interest rates on money in 1998?

Part one will have some fun with a golden oldie from 1998.  Part two will be more serious, and might be the first journal article to come out of this blog.  Nothing earthshaking, but a different way of thinking about the zero rate bound.  I’ll let you guys be the referees.

Part 1.    The following quotation was taken from a longer discussion of a 1978 paper (JMCB, by Joan and Richard Sweeney) that used the example of a babysitting co-op to illustrate the monetary model of recessions.  The price of babysitting services was arbitrary fixed by the co-op.  Who said this about their paper in 1998?

Now what happened in the Sweeneys’ co-op was that, for complicated reasons involving the collection and use of dues (paid in scrip), the number of coupons in circulation became quite low. As a result, most couples were anxious to add to their reserves by baby-sitting, reluctant to run them down by going out. But one couple’s decision to go out was another’s chance to baby-sit; so it became difficult to earn coupons. Knowing this, couples became even more reluctant to use their reserves except on special occasions, reducing baby-sitting opportunities still further.

In short, the co-op had fallen into a recession.

Since most of the co-op’s members were lawyers, it was difficult to convince them the problem was monetary. They tried to legislate recovery–passing a rule requiring each couple to go out at least twice a month. But eventually the economists prevailed. More coupons were issued, couples became more willing to go out, opportunities to baby-sit multiplied, and everyone was happy. Eventually, of course, the co-op issued too much scrip, leading to different problems …

If you think this is a silly story, a waste of your time, shame on you. What the Capitol Hill Baby-Sitting Co-op experienced was a real recession. Its story tells you more about what economic slumps are and why they happen than you will get from reading 500 pages of William Greider and a year’s worth of Wall Street Journal editorials. And if you are willing to really wrap your mind around the co-op’s story, to play with it and draw out its implications, it will change the way you think about the world.

For example, suppose that the U.S. stock market was to crash, threatening to undermine consumer confidence. Would this inevitably mean a disastrous recession? Think of it this way: When consumer confidence declines, it is as if, for some reason, the typical member of the co-op had become less willing to go out, more anxious to accumulate coupons for a rainy day. This could indeed lead to a slump–but need not if the management were alert and responded by simply issuing more coupons. That is exactly what our head coupon issuer Alan Greenspan did in 1987–and what I believe he would do again. So as I said at the beginning, the story of the baby-sitting co-op helps me to remain calm in the face of crisis.

Or suppose Greenspan did not respond quickly enough and that the economy did indeed fall into a slump. Don’t panic. Even if the head coupon issuer has fallen temporarily behind the curve, he can still ordinarily turn the situation around by issuing more coupons–that is, with a vigorous monetary expansion like the ones that ended the recessions of 1981-82 and 1990-91. So as I said, the story of the baby-sitting co-op helps me remain hopeful in times of depression.

That’s right; it’s Paul Krugman, back in the days he wrote for Slate.com.  Back in the days when right-wing economists looked forward to reading his delightful posts.  Back before he became a political analyst.  You know; the sort of guy who now thinks Obama’s biggest problem is that he hasn’t moved far enough to the left.  How does such a first rate international economist forget about the concept of comparative advantage?

[I know.  Who am I to talk?]

My favorite parts are his counter-intuitive assertions that even if a recession seems to be caused by some sort of real factor, it is actually caused by too little money:

Above all, the story of the co-op tells you that economic slumps are not punishments for our sins, pains that we are fated to suffer. The Capitol Hill co-op did not get into trouble because its members were bad, inefficient baby sitters; its troubles did not reveal the fundamental flaws of “Capitol Hill values” or “crony baby-sittingism.” It had a technical problem–too many people chasing too little scrip–which could be, and was, solved with a little clear thinking. And so, as I said, the co-op’s story helps me to resist the pull of fatalism and pessimism.

Yes, there was a time when Krugman found it easy to avoid fatalism and pessimism.  But here I can’t blame him for changing his stripes, in those halcyon days I shared his optimism that the Fed could and would, do what’s necessary to avoid a shortfall in AD.

So banking crises may appear to cause recessions (the crony remark was a reference to recent banking problems in East Asia) but the real problem is monetary.  Where have we heard that idea before?  Not only have I been arguing that monetary policy is the real problem, I’ve also been arguing that with each new recession most economists initially get fooled into thinking real shocks are the problem.

Krugman fans will say; “Scott, he still believes this, but only if we aren’t in a liquidity trap.”  Sorry to tell you this, but he’s got that base covered too:

But what about Japan–where the economy slumps despite interest rates having fallen almost to zero? Has the baby-sitting metaphor finally found a situation it cannot handle?

.   .   .

The basic problem with the winter co-op is that people want to save the credit they earn from baby-sitting in the winter to use in the summer, even at a zero interest rate. But in the aggregate, the co-op’s members can’t save up winter baby-sitting for summer use. So individual efforts to do so end up producing nothing but a winter slump.

The answer is to make it clear that points earned in the winter will be devalued if held until the summer–say, to make five hours of baby-sitting credit earned in the winter melt into only four hours by summer. This will encourage people to use their baby-sitting hours sooner and hence create more baby-sitting opportunities. You might be tempted to think there is something unfair about this–that it means expropriating people’s savings. But the reality is that the co-op as a whole cannot bank winter baby-sitting for summer use, so it is actually distorting members’ incentives to allow them to trade winter hours for summer hours on a one-for-one basis.

But what in the nonbaby-sitting economy corresponds to our coupons that melt in the summer? The answer is that an economy that is in a liquidity trap needs expected inflation–that is, it needs to convince people that the yen they are tempted to hoard will buy less a month or a year from now than they do today.

But it is a bit misleading to call this proposal “expected inflation.”  The price level is fixed in the co-op, one unit of script pays for one hour of baby-sitting.  Rather his proposal is analogous to expected inflation.  What is it actually?  A negative nominal interest rate on money.  Silvio Gesell’s idea, rediscovered last year by a grad student at one of those Ivy League econ PhD programs that don’t think it is worthwhile to study monetary history.  And of course there are technical barriers to actually paying negative interest on currency, but not on bank reserves.  Negative interest on reserves; hmmm . . . where have we heard that idea before?

Part 2.  Reflections on the end of the zero rate bound.

A few days ago I did what I thought was one of my more important posts, pointing out that the Fed’s likely new operating target will eliminate the problem of the zero rate bound.  There are always some misunderstandings in the comment section when I bring up negative rates on reserves.  What about vault cash?  What about the impact on bank profits?  What if firms don’t want to borrow even at very low rates?  The simple answers are vault cash can be dealt with in many ways–it isn’t a problem.  And the system can be set up in a way that bank profits aren’t hurt.  And the purpose of the plan is not to get firms to borrow more, but to reduce bank demand for the medium of account.  This is all discussed in earlier posts like this one.

But I also anticipate some push-back from serious economists on another point.  Negative interest rates on reserves would not drive free market short term rates significantly below zero.  So have we actually solved the problem of the zero rate bound?  The answer is an emphatic yes.  But it doesn’t seem that way, and it is worth considering why.

I am pretty sure that many economists are confused about the nature of the liquidity trap.  In particular, they confuse two very distinct issues:

1.  The inability of the Fed to move the fed funds target lower once it has reached zero.

2.  The inability of monetary policy to boost AD once rates hit zero.

Krugman and I both agree that monetary policy can still be highly effective once rates hit zero.  And we both agree that conventional monetary policy is ineffective once rates hit zero, if ‘conventional monetary policy’ is defined as adjusting the fed funds target, and/or a temporary injection of reserves into the banking system.  But if the Fed doesn’t use either fed funds targeting or temporary base injections as the policy lever, then monetary policy doesn’t become ineffective once short term rates hit zero.  To explain this, it will be helpful to consider some potential operating targets for the Fed:

1.  The fed funds rate

2.  The interest rate on reserves (IOR)

3.  The monetary base

4.  The exchange rate (or price of gold)

5.  CPI or NGDP futures targeting

Although there appear to be zero bounds on the exchange rate and the monetary base, in practice there are no limits to either policy lever.  No matter how low the base or exchange rate fall, they can always be cut another 10%.  Of course if you think of absolute changes there is a lower bound of zero.  But if that were the exchange rate it would mean the Fed handed out free money to anyone that wanted it.  I think we can assume that policy would boost NGDP (to infinity.)  And as you approach a zero monetary base, you would approach hyperdeflation.  So I think we can rule that one out as well, as few governments are frustrated by an inability to create hyperdeflation.  Indeed few want any sort of deflation.  So for all practical purposes there are no zero bounds, except for the fed funds target.

But then you might wonder; “What happens if the Fed increases the monetary base and short term rates stay stuck at zero?”  Doesn’t this mean you are still stuck in a liquidity trap, even if the policy lever can still be moved around?”  If you think this way, you are probably confusing the two issues I discussed above.  You are probably thinking (in the back or your mind) that the fed funds rate is part of the transmission of monetary policy, and that without a lower fed funds rate you cannot get a boost in AD, in NGDP.  But in fact the fed funds rate does not play an important role in the monetary transmission mechanism.  When you are deciding whether to buy a new car, a new house, or construct a new office building, the last thing you care about is the nominal fed funds rate.  Rather, you care about expected RGDP growth, or asset prices, or real wages, or perhaps longer term real interest rates.

So the real question isn’t whether the fed funds rate might stay at zero in response to changes in some alternative policy lever, but rather whether these alternative policy levers can boost AD.  Almost everyone agrees currency depreciation is a foolproof way of boosting NGDP; the only question is whether it is politically feasible.  And even Krugman concedes that increases in the monetary base that are expected to be permanent will be expansionary, even at the zero bound.

[BTW, I’ve never heard anyone else note that money supply increases that are expected to be temporary will have little or no impact on the price level, even if you aren’t at the zero rate bound.  So the question of temporary currency injections is essentially unrelated to the zero bound problem.]

But the interest on reserve lever is different from all the other policy levers discussed above.  It is a policy lever that works by changing the demand for base money, not the supply.  In addition, it only applies to the portion of the base that is held by banks.  Thus once the IOR goes a couple points below zero, further decreases have essentially no impact on excess reserves.  This is because at even a negative 2% IOR, banks will cut excess reserve holdings to the bare minimum, and further rate cuts will not have any additional impact on ER demand, or market interest rates.  So isn’t that a sort of zero bound?

One answer is that changes in the IOR can have a huge impact between 0% and negative 2%, whereas the fed funds rate is already spinning its wheels at 0%.  Between 0% and negative 2% almost all of the monetary base (except required reserves) moves out into circulation.  But I don’t find that a satisfactory answer.

The best way to think of the IOR policy lever is that it is analogous to reserve requirements.  In most money and banking textbooks reserve requirements are the only Fed tool that impacts the demand for base money, not the supply.  I have a feeling that textbooks are about to change.  IOR also affects the demand for base money.  And just as reserve requirements cannot lower the demand for required reserves below zero, no change in the IOR can lower the level of excess reserves below zero.  So again, why isn’t that a sort of zero bound to expansionary monetary policy?

The answer is that like reserve requirements, the IOR allows another degree of freedom.  The Fed can still control the supply of base money.  If the Fed wants to boost AD, it can lower the IOR enough to drive ERs to the bare minimum, and then any further open market purchases will go straight to currency held by the public, or to required reserves and hence the broader aggregates.  And of course there is no zero rate bound problem for changes in the monetary base, which can be increased as much as the central bank wishes.

Indeed the Fed has already begun this two-track policy.  They prefer to have a large monetary base for the time being, and plan to tighten by raising the IOR in the future.  But the same macro objectives could be achieved through open market sales, if they so desired.  They now have one extra degree of freedom.  Personally, I don’t think the IOR tool is very valuable, but if it ends the silly superstitions about zero rate bounds, it will all have been worthwhile.

Perhaps the best way to summarize all this is to go back to Nick Rowe’s observation that the fed funds rate (and hence the zero bound) matter if people believe they matter.  Ironically just one day before I noticed the article hinting at the Fed’s imminent policy change, Nick made this cryptic statement:

There are probably two (stable) equilibria: one in which monetary policy *is* interest rates, and we can get stuck in liquidity traps; and a second in which it isn’t, and we don’t get stuck. Social construction of reality, again, which is just an extreme form of a convention, which not only affects how we behave, but how we see the world. It defines the “social facts” of what central banks “do”.

Question: if this (above) view is correct, what exactly is it that Scott Sumner is *doing* (on this blog)? What *is* he? Not a policy advocate, in the standard sense.

And, if this view is correct, forget about trivia like cutting the overnight rate by 0.25%. Banning all public mention of the overnight rate would be a more effective policy!

It didn’t take long for the Fed to see the wisdom of Nick’s suggestion.  So thank you very much Nick Rowe.  Now perhaps Rasputin, I mean Nick, could do the following post:

Mr. Bernanke, look into this glass ball

Repeat after me

There is no such thing as inflation

There is no such thing as inflation

There is only NGDP

HT:  Marcus Nunes


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30 Responses to “Guess who discussed negative interest rates on money in 1998?”

  1. Gravatar of StatsGuy StatsGuy
    28. January 2010 at 13:03

    ssumner

    – Very interesting, and insightful. If I could identify only one weakness in your perspective, it would not be ABCT. It would (again) be the need to account for international finance.

    If domestic banks are compelled to lend by below-zero deposit rates, there’s simply no reason to think they’d need to lend in the US. They simply lend money to carry traders (or their own internal hedge funds) to buy foreign assets or hard assets that are internationally tradeable. In equillibrium, this will bid up prices globally (because the US is 20-25% of the world GDP, still), BUT the US will pay a significant inflation price. Meanwhile, only a portion of this forced-lending is put into actual investment DOMESTICALLY.

    Crudely speaking, we might get only 25% of the investment kick that we might get in a closed economy for any given amount of inflation. Observe the response of commodity prices over the last year, vs. the response of actual business investment.

    Id we get 5% nominal growth, MUCH of that will be in the form of inflation due to higher commodity prices (which act like a tax) and higher interest rates (which will threaten viability of nominal debt). In a closed economy model, these downsides are overwhelmed. This is not so clear in an open economy. Expectation of _future_ devaluation could create capital flight, and capacity non-utilization could go UP even as inflation goes UP.

    In a simple Fisher Curve story, expectations of future inflation are based on prior inflation (it’s entirely backwards facing). In reality, expectations of future inflation are also based on the debt repayment capacity of the US economy. Think of a bank’s willingness to lend – it’s based on income + debt + collateral + repayment history (credit rating).

    Now, I’m not arguing against NGDP targeting – it’s much better than what we have now (e.g. running as fast as we can toward a brick wall). But in an international context, it’s limited in effect until the dollar is devalued enough that people look at the US and decide it’s a good investment (or other countries devalue due to the threat of a lower dollar, which Germany is already whining about). I’d suspect we’d be better off devaluing the dollar once, repairing our fiscal deficit, and moving forward. This is – in effect – what the IMF does with countries having a currency crisis. The US is different because of the world AD effect, but we can’t just ignore international finance markets.

    This is why some argue the Fed’s cheap rates in the US have blown a bubble in developing markets, and that Japanese cheap rates blew a US asset bubble.

    Anyway, if you don’t believe me about the constraints created by carry trades, maybe you will believe this nobel prize winner. (No, not that one, the OTHER one.)

    http://www.youtube.com/watch?v=H6ilTUHyO5Y

    And he makes the same points I’ve been arguing about lack of investment.

    You really really need to think this through – the closed monetary loop is not closed.

  2. Gravatar of Marcus Nunes Marcus Nunes
    28. January 2010 at 13:05

    Scott
    I see you had fun writing the first part. Krugman must really be suffering. Nobody goes through such a metamorphosis unscathed! Or maybe being an NYT colummnist+Nobel is bad for your intelectual health.
    (BTW: So it´s OK if a keep sending “gems” for you to elaborate upon?)

  3. Gravatar of malavel malavel
    28. January 2010 at 13:21

    Controlling interest rates or base money is so passé. For the 21’st century, central banks should control penalties on counterfeiting. If the economy needs more money, simply change the penalty to a low fine.

    Now, some economists might argue that this scheme will also be powerless in a liquidity trap since they can’t lower the penalty below zero. But this is not true since the FED could mandate a negative fine on counterfeiting.

  4. Gravatar of ssumner ssumner
    28. January 2010 at 13:53

    Statsguy, I listened to the Stiglitz, but I should tell you that I like Krugman’s macro much more than Stiglitz’s.

    You said;

    “Crudely speaking, we might get only 25% of the investment kick that we might get in a closed economy for any given amount of inflation.”

    So you are saying the current SRAS curve is much steeper than it would be if the economy were closed? I don’t agree. I think 75% of any increase in NGDP would show up in higher RGDP. But even if you are right, what is the policy implication? Surely you aren’t saying the SRAS curve would be flatter in response to some sort of non-monetary stimulus like government spending?

    And don’t forget about exports; if the dollar falls, commodity prices may rise, but so will exports.

    It seems to me that you are confusing money and credit. When banks lend “money” to LDCs it is not money leaving the country, it is credit.

    Money has been very tight recently, that’s one reason why investment in the US is less robust than in China. It’s not like we’ve had an easy money policy, and the effects have been diluted by funds leaving the country. The tight money reduces NGDP, this reduces investment. We’d have the same problems in a closed economy.

    BTW, I have no interest in “compelling” banks to lend, rather I want to compel them to hold less ERs. I’d rather the free market determine the amount of bank lending, perhaps with regulations to insure adequate collateral.

    Also keep in mind that NGDP targeting is likely to result in more stable exchange rates than when NGDP fluctuates unexpectedly. So if it’s exchange rate instability you are worried about, NGDP targeting may not be so bad.

    But my main problem is your assumption about the slope of the SRAS. It isn’t nearly as steep as you assume in an open economy.

    Marcus, Thanks for reminding me, I just added your name. And yes, feel free to send me more articles, they are often very helful. Many of my posts are triggered by articles you send.

    MALAVEL, Why did you have to rain on my parade? Just when I thought I had a clever idea, you come along with something even more clever. 🙂

  5. Gravatar of William William
    28. January 2010 at 14:58

    Scott,

    Sorry to ask such a basic question, but if too many people are offering babysitting services, and not enough people want babysitters, why doesn’t the price of babysitting adjust downward and solve the problem? I know in Keynesian thinking that isn’t supposed to help, but I really don’t understand why. Can you point me to something I might read on this subject (not the General Theory), please?

  6. Gravatar of Doc Merlin Doc Merlin
    28. January 2010 at 14:58

    “Controlling interest rates or base money is so passé. For the 21’st century, central banks should control penalties on counterfeiting. If the economy needs more money, simply change the penalty to a low fine.”
    Rofl, awesome. Actually if the fed didn’t make its own money, just taxed money creation, the same thing would happen.

    “Now, some economists might argue that this scheme will also be powerless in a liquidity trap since they can’t lower the penalty below zero. But this is not true since the FED could mandate a negative fine on counterfeiting.”

    Not sure if it would need to, because counter fitting doesn’t create debts. It might lower the savings rate, which would raise the net debt, and that is a problem, however.

  7. Gravatar of StatsGuy StatsGuy
    28. January 2010 at 15:23

    ssumner:

    “It’s not like we’ve had an easy money policy, and the effects have been diluted by funds leaving the country.”

    Not necessarily money per se, but credit. The credit is used to buy physical assets and securities that earn higher than 0.25% to 4%, on the expectation that when the money is repaid, dollars will be cheaper because of future monetization (and the interest rates were higher too). So if you allow for the time dimension (as our Austrian friends remind us), “money” is leaving the country. The flows are quite large…

    http://www.bis.org/publ/qtrpdf/r_qt0709e.pdf

    This does not necessarily have to mean the SRAS is steep. Your presumption is that looser money (I won’t call it loose) carries through perfectly to AD – when, in fact, people will first shift into other forms of storable wealth first, which could raise prices if some of those forms are used in production.

    The extent to which prices get raised before investment (or even AD) is forced (and I am interested in forcing investment) is dependent on many things. Eventually equillibrium will be achieved, but the real component of NGDP growth could be lower than in a closed economy.

    Moreoover, those with preferential access to credit will benefit greatly from the price increases long before the money makes it into real investment. (note the trading profits at banks as asset prices were forced higher, long before that money reached people; and note this pattern held for 20 years as financial profits rose as % of net corporate profits in the US – this a tax we pay on any attempt to force money into the system using rate policy.)

    In practice, price signals will encourage investment in commodities and outside the US (yep). This will pick up AD somewhat. But our Austrian friends will again note that some of this investment could encourage excessive production of hedging assets (which some might call a bubble). And they might be right.

    While it is true that devaluation eventually contributes to higher exports, this involves a serious lag. If the increase in domestic economic activity (or outputs) is low relative to inflation, the debt overhang + higher interest rates could be terminal.

    I think the Fed is desperately trying to let Treasury lengthen its maturity dates as much as possible before everything hits the fan – in order to give the economy breathing room (e.g. allow exports to pick up after devaluation) when they are forced to devalue. And, I believe the bond market continues to predict this in the yield curve.

    OH, policy implications:

    1) Sharp, sudden devaluation/monetization, accompanied by cuts in spending and/or increasses in taxation to create credible commitment to future money stability
    2) Very large universal investment tax credits
    3) Much higher capital/asset ratios and more effective bank regulation

    But it can’t happen. The US polity is designed to prevent it.

  8. Gravatar of azmyth azmyth
    28. January 2010 at 16:09

    “I’ve never heard anyone else note that money supply increases that are expected to be temporary will have little or no impact on the price level, even if you aren’t at the zero rate bound.”

    I don’t quite understand what you’re saying here. I know that you are very careful in distinguishing temporary from permanent and consider temporary injections to stimulate AD far less (not at all?). Do other economists not agree with you? (Is not, why?)

    People are not all that good at reverse induction, and I think that money injections that were long lasting but not permanent would have some impact. If the Fed increased the money, and said they were taking it back out in 20 years, I think it would have at least half the stimulus of a permanent injection. This is why I argued that increasing government debt would increase AD (I had long term debt in mind), since bonds are a partial substitute for cash balences and reserves.

    William: Excellent question. In Krugman’s orginal story, the tickets were for a fixed time of babysitting. By using an example where prices are completely fixed, he highlights what happens in the short run when prices are sticky. Classical economists would have said that prices adjust quickly enough for that not to be a problem. Google “Say’s Law” for more information.

  9. Gravatar of Phil Koop Phil Koop
    28. January 2010 at 18:13

    I have a lot of sympathy for you, because I too find that when people disagree with me it is because they misunderstand me. And when I can’t understand them, it always seems to be because they aren’t serious enough.

    So, duly chastened, I returned to reread some of the earlier posts you indicated. And what have I found?

    1. The real problem is monetary.

    Certainly it is. And since the supply of credit money dwarfs the supply of base money, most of the real problem is credit money.

    2. Charging interest for excess reserves (a “negative IOR”) while paying for required reserves would affect behavior at the margin.

    Indeed it would, and that behavior would be to maximize profit (minimize loss) at the margin. Given a choice of lending at negative returns or holding reserves at negative returns, the rational course would be to do neither, but to shrink the asset side of the book, presumably by imposing negative rates on deposits.

    3. That’s OK, because there’s no need to create credit money; once base money is pushed out of deposits, it will quickly be spent, thus raising AD.

    That is what the lawyers call special pleading. People do not distinguish between deposits and paper cash when measuring wealth, so they won’t feel any richer. And the reason they were holding deposits in the first place was that they had no immediate desire to spend. The logical assumption is that they will continue to hold their base money, but as paper.

    4. Yes, that’s what Mankiw thought too. But since we have never had negative rates, he is just speculating.

    Quite unlike Scott Sumner.

    5. Anyway, forget that other stuff. The Fed can just peg CPI futures at 103. Or 105. Or 107. That will raise inflation expectations!

    I don’t know what to make of this. There is not, so far as I know, a CPI futures contract currently trading. The old CME contract was priced at 100 – inflation, so that 103 would correspond to a deflation rate of roughly 3%. How that would help raise inflation expectations I don’t know. And this pegging – as near as one can make out, it would be accomplished by making an unlimited market at the peg price. Assuming that the market takes the right side of the trade, and that the trade is paid for with new base money, that would succeed in putting new money in the pockets of futures traders. No doubt the demand for Ferraris and Petrus would rise, but it seems a peculiarly inefficient method of raising aggregate demand. Plain old helicopters would be better.

    6. But surely you agree that currency depreciation is a foolproof way of boosting NGDP. Almost everyone does!

    Yes, here is something we can all agree on. But since currency depreciation is accomplished by creating money, I don’t see that it gets us very far.

    The new money must come from new credit money or new base money. Neither can be accomplished by negative reserve rates.

  10. Gravatar of Leigh Caldwell Leigh Caldwell
    28. January 2010 at 18:34

    William – Scott may have his own reply (Nick Rowe is also great on this kind of stuff) but here’s my version:

    Technically, a downward price adjustment could work. In fact, it’s theoretically equivalent to an increase in the amount of scrip. But there are a couple of practical (actually, psychological) reasons why it might not.

    First, the price of babysitting in terms of what? In this economy, babysitting can only be exchanged for vouchers for more babysitting. If a babysitting voucher entitles you to one hour of babysitting, then what does it mean if you offer an hour of babysitting for less than one voucher? Although it stacks up theoretically, it is highly confusing (to non-economists at least!), and that in itself is a barrier to trade. This is just a sticky prices argument – everyone assumes one voucher = one hour, so it’s tough to get people to trade at a different price.

    Second, even if you get over that, what does the prospective spender of the voucher think about their own future babysitting duties? “So I’m now going to be expected to do 1.5 hours of babysitting for each voucher…so everyone else is going to be collecting more vouchers…I better try and save more myself so I have more options”. Just as inflation begets expected inflation, a single deflationary step can kick off a deflationary cycle.

    The problem is a combination of two things: sticky prices (it’s no accident this blog is called TheMoneyIllusion) and uncertainty about other people’s future behaviour.

  11. Gravatar of Doc Merlin Doc Merlin
    28. January 2010 at 20:44

    “Sorry to ask such a basic question, but if too many people are offering babysitting services, and not enough people want babysitters, why doesn’t the price of babysitting adjust downward and solve the problem? ”

    The coupons were for babysitting, so technically it was a babysitting based currency. The only way to adjust the price downward would be by fiat or black market in babysitting.

  12. Gravatar of cucaracha cucaracha
    29. January 2010 at 01:21

    I understand you intend to increase the stock of bank credit with the NIO.

    But I have a question about the banks:

    What about their leverage ?

    What about that oooooolld problem with their equity ?

    Yes, the quality of their assets improved, but their equity didn’t increase that much, apparently ?

  13. Gravatar of Kevin Donoghue Kevin Donoghue
    29. January 2010 at 02:14

    William,

    There’s a 1992 paper by Tobin which is well worth reading. On the 10th page he gets to the “Pigou effect” so skip directly to that if you want. If you really can’t stomach Keynes’s own writing (and for some reason many people can’t), Tobin is the next best thing.

  14. Gravatar of dan dan
    29. January 2010 at 09:50

    scott, slightly off topic here, but NGDP came in at 6.4%, Final Sales at 2.2% for the fourth quarter. at least 6.4% is above trend 5%. does this confirm that the Fed is targeting NGDP “with a memory”? these numbers at least look to be moving in the right direction…

  15. Gravatar of Zdeno Zdeno
    29. January 2010 at 11:48

    Ugh. The baby-sitting coop story.

    The problem in the Sweeney example is not that there are too many or too few scrips, but that the price of real goods is fixed by fiat. If scrips were divisible, and the price of a night of babysitting were permitted to fluctuate, the coop would function smoothly – the price ratio of babysitting/scrips would fluctuate cyclically based on their supply and demand (i.e, couples’ willingness to babysit and desire to go out). In the Sweeney/Krugman world though, price adjustments cannot, or do not happen. Does this match up with reality? Judging by my Grandpa’s whinging about the price of a chocolate bar in his day, no.

    Somehow this little meme has survived for decades, justifying Keynesian poppycock all the way, when it actually breaks down as soon as you un-assume perfectly sticky prices.

  16. Gravatar of ssumner ssumner
    29. January 2010 at 14:08

    William, This co-op didn’t allow price cuts. In the real world price cuts would occur, but prices and especially wages are too sticky for prices to absorb all the effects of a monetary shock—in the short run output is also affected.

    Statsguy, I don’t understand your argument. You say higher NGDP might show up in the form of higher prices, not higher real output. Then you claim you aren’t assuming the SRAS is steep. That doesn’t make sense to me.

    Regarding credit leaving the country, that’s the least of our problems. As you know we are the world’s biggest net borrower from the rest of the world.

    My general impression is that you are too focused on minutia. You suggest that higher NGDP might lead to a bubble here or there. My response is “so what?” I suppose if someone’s house in on fire the firehose might cause water damage to the drapes. But is that what we should be most concerned about? You could have a bubble at any time, regardless of what monetary policy is doing. We need much higher NGDP, other concerns should be dealt with through regulation, if there is some sort of market failure.

    azmyth; You said;

    “I don’t quite understand what you’re saying here. I know that you are very careful in distinguishing temporary from permanent and consider temporary injections to stimulate AD far less (not at all?). Do other economists not agree with you? (Is not, why?)”

    I think some would agree with me. That’s why I found Krugman’s model of the expectations trap to be so weird. He tried to argue that a monetary injection at the zero bound wouldn’t boost AD, because it wouldn’t be expected to be permanent. But why is this a theory of the liquidity trap? It seems to me that the logic implies monetary injections would never have much effect.

    Here’s what else I think is weird. I have heard many economists talk about how meaningless it is to swap cash for zero coupon T-bills. But why? If the injections are permanent, they’ll still boost prices. And if they aren’t expected to be permanent, then they won’t boost prices even if T-bill yields are 5%.

    Phil Koop; You said;

    “Certainly it is. And since the supply of credit money dwarfs the supply of base money, most of the real problem is credit money.”

    Credit and money are two different things. I define money as the monetary base. So when I say money is the problem, I mean the supply and demand for base money. I am not concerned with credit.

    You said;

    “Indeed it would, and that behavior would be to maximize profit (minimize loss) at the margin. Given a choice of lending at negative returns or holding reserves at negative returns, the rational course would be to do neither, but to shrink the asset side of the book, presumably by imposing negative rates on deposits.”

    But banks may not be able to do this. People might simply hold cash instead. At best, you could have a slightly negative rate, just enough to compensate for the convenience of deposits compared to cash in safety deposit boxes.

    You said;

    “That is what the lawyers call special pleading. People do not distinguish between deposits and paper cash when measuring wealth, so they won’t feel any richer. And the reason they were holding deposits in the first place was that they had no immediate desire to spend. The logical assumption is that they will continue to hold their base money, but as paper.”

    I never said people would feel richer. I am not talking about dumping cash out of helicopters, but rahter exchanging cash for T-securities (OMOs.) So there is no wealth effect. Monetary theory is not primarilty based on looking at cash as a part of wealth, but rather as a specific asset with a specific real demand. If you inject more cash, and the real demand doesn’t change, then prices will rise. Of course the real demand may change, but it isn’t infinite.

    Regarding points 5 and 6, you might first spend the time trying to understand the ideas I am putting forth before ridiculing them. Funny that none of the referees of the 6 papers I published on CPI futures targeting noticed the elementary errors you discovered. I did not advocate targeting the CPI contract in the CME. And it would be easy to set the system up in a way where the Fed took little or no risk. There are lots of threads where all the objections you raise have been thoroughly discussed.

    Here is a particularly silly comment you made:

    “Yes, here is something we can all agree on. But since currency depreciation is accomplished by creating money, I don’t see that it gets us very far.”

    For someone so cocky, you are remarkably ignorant of the arguments for currency depreciation. Have you read Svensson’s explanation of why it is a foolproof escape from liquidity traps?

    And then there is this gem:

    “The new money must come from new credit money or new base money. Neither can be accomplished by negative reserve rates.”

    For your information, monetary economics is about policies that affect both the supply and demand for money, not just the supply. Do your homework next time before being so insulting.

    cucaracha, You said;

    “I understand you intend to increase the stock of bank credit with the NIO.”

    No, I am not trying to target bank credit. And what is the “NIO.”

    dan, I discuss that at the end of my newest post.

    Zdeno, Actually is is a useful way of understanding the importance of sticky prices, even in a world where they are not completely rigid. I agree that Keynesians sometimes overplay the importance of sticky prices. But if prices were perfectly flexible then nominal shocks wouldn’t have real effects.

  17. Gravatar of Don the libertarian Democrat Don the libertarian Democrat
    29. January 2010 at 15:57

    Wow. This topic reminds me of this post:

    http://blogsandwikis.bentley.edu/themoneyillusion/?p=684

    It seems like a lifetime ago.

  18. Gravatar of dlr dlr
    29. January 2010 at 16:24

    Here’s what else I think is weird. I have heard many economists talk about how meaningless it is to swap cash for zero coupon T-bills. But why? If the injections are permanent, they’ll still boost prices. And if they aren’t expected to be permanent, then they won’t boost prices even if T-bill yields are 5%.

    I may be responding to a rhetorical question here.

    Let’s say the first-degree argument is just that the excess cash balance mechansim doesn’t work when swapping zero rate T-bills for money, on the assumption that people’s demand for money will increase in line with a decrease in the supply of T-bills when T-bills and money are considered roughly equivalent at the margin. Without this mechanism, you need a more direct expectations mechanism, where people not only believe the excess supply of money is permanent, but also that the increased demand for money (or maybe decreased supply of zero rate T-bills) is temporary. Who knows if this will happen? There is no excess cash mechanism in this special case to make it inevitable. And since people are already all these zero rate T-bills voluntarily, you obviously can’t do so much swapping that the money would eventually buy up all the assets on earth. Swapping money for 0% T-bills might work or it might not, but it seems easy to see how it would not. Money for Trills, on the other hand, would work.

  19. Gravatar of StatsGuy StatsGuy
    30. January 2010 at 06:30

    ssumner:

    “You say higher NGDP might show up in the form of higher prices, not higher real output. Then you claim you aren’t assuming the SRAS is steep. That doesn’t make sense to me.”

    I knew you’d disagree, but before you discount the argument – remember, stiglitz is basically arguing the same thing.

    Let’s imagine a two part economy – commodities and production goods. SRAS is flat in the latter, steep in the former. Commodities are used as inputs in production goods and are mostly imported.

    My argument hinges on differentiating between two types of demand inside the AD function: consumption/investment demand, and speculative demand. This distinction is similar to the distinction inside the liquidity demand function in the IS/LM framework (between transaction demand for money, and speculative demand).

    In the context of the IS/LM framework, money supply goes up and investors shift into assets (and the rate drops at the same time). LM shifts out, rate goes down, and the equillibrium IS increases (taking AD with it).

    The breakdown is that there are two kinds of assets – assets that can get stored (substitutes for money), and assets that improve productivity (that will earn money if AD picks up in the future). In the presence of high future uncertainty, investors will favor storable goods (which may double as production inputs, like oil or platinum). The short run supply of these goods is somewhat inelastic. This bids up the price of these goods, which are often imported; this increase costs of production for other goods (notably, the ones with highly elastic production), but the output prices of these other goods does not go up quickly (lots of slack capacity, high fixed cost sectors). While the markets will invest in new production of hedging goods, this doesn’t immediately stimulate the sectors of the economy with slack capacity (which generate most employment, unless you live in Australia).

    The carry trades raise asset prices of storable commodity imports first; at some point money supply will stimulate domestic demand, but by then the commodity/input prices will have increased significantly. But this price increase doesn’t stimulate domestic activity because these are largely produced outside the US.

    Short version:

    dual economy (commodities with high imports, other goods)
    dual SRAS curves
    dual demand functions (hedging demand which is correlated with liquidity demand, production/consumption demand)

    If liquidity demand is high, increases in money supply first force commodities much higher BEFORE they increase investment/consumption. Indeed, if there is an EXPECTATION of this, a carry trade will form which will create a price increase BEFORE money supply even loosens, and the if the dumb Fed doesn’t follow through with its intent (because they see commodity inflation in the rear view mirror – August 08), the result is a total demand collapse.

    You might consider this ‘minutae’, but the sheer dominance of the carry trades are partly what killed Japan and helped cause US ‘bubbles’. The low dollar rates – rather than immediately helping the US – are FIRST causing bubbles elsewhere…

    http://www.businessinsider.com/imf-issues-giant-anti-dollar-carry-trade-report-2009-11

    The power of unilateral monetary action – while not eliminated – is weakened by international financial arbitrage. (But it could force competitive devaluation, which if not coordinated would create instability – which is still better than the ‘stability’ of no devaluation.)

    NGDP targeting would help a lot – but we’re still going to see lower than historical demand/utilization even with 5% NGDP in the short term because most of that will be inflation. Really, we need a lot of inflation, because the dollar is just way too high (still), and we consume way too much internationally. Even so, 2% inflation targeting is terrible because we’ll end up with 1.5%-2% growth. I’d rather have 2.8% inflation and 2.2% growth until the dollar finishes a 20 year devaluation.

    As an aside, here’s an interesting China blog you might like:

    http://mpettis.com/

  20. Gravatar of cucaracha cucaracha
    30. January 2010 at 11:08

    No, I am not trying to target bank credit”

    But it is the only way I see a negative interest rate exclusively set on narrow money bank reserves being effective. By forcing banks to lend more.

    “And what is the “NIO.””

    Ooops…
    I meant NIR – negative interest on reserves…

    By the way, forget what I said about bank equity, because with more liquid assets the banks’ capital requirements are reduced.

    Narrow money holdings have a 0% weight on Tier I capital and their share in the us banks’ assets increased a lot.

    So the banks leveraging capacity did increase not by raising their capital but by making their assets more liquid thus reducing capital requirements

  21. Gravatar of Doc Merlin Doc Merlin
    30. January 2010 at 14:13

    @StatsGuy
    “If domestic banks are compelled to lend by below-zero deposit rates, there’s simply no reason to think they’d need to lend in the US. They simply lend money to carry traders (or their own internal hedge funds) to buy foreign assets or hard assets that are internationally tradeable. In equillibrium, this will bid up prices globally (because the US is 20-25% of the world GDP, still), BUT the US will pay a significant inflation price. Meanwhile, only a portion of this forced-lending is put into actual investment DOMESTICALLY”

    I agree completely, StatsGuy. This is one reason why artificially low interest rates cause problems. They raise PPI much too fast. Australia and other raw material exporters will do very well as a result in the short run, but dollar dependent business will suffer in the longer run.

  22. Gravatar of ssumner ssumner
    30. January 2010 at 15:25

    Don, Yes, it’s been a long year.

    dlr, Everything you say is true, but you overlook the fact that it is almost equally true if T-bill yields are 5%. If the Fed injects lots of money, but the injection is expected to be temporary (as with the Y2K injections) prices will not rise even if T-bill yields are 5%. It is always true (according to Woodford), that what matters is changes in the expected future path in the money supply, not the current money supply.

    Statsguy, You said;

    “I knew you’d disagree, but before you discount the argument – remember, stiglitz is basically arguing the same thing.”

    You do realize that mentioning Stiglitz makes me less likely to agree, don’t you. 🙂

    You said:

    “In the context of the IS/LM framework, money supply goes up and investors shift into assets (and the rate drops at the same time). LM shifts out, rate goes down, and the equillibrium IS increases (taking AD with it).”

    I don’t agree with the IS/LM framework. I don’t think expanasionary monetary policy reduces interest rates.

    You said:

    “If liquidity demand is high, increases in money supply first force commodities much higher BEFORE they increase investment/consumption. Indeed, if there is an EXPECTATION of this, a carry trade will form which will create a price increase BEFORE money supply even loosens, and the if the dumb Fed doesn’t follow through with its intent (because they see commodity inflation in the rear view mirror – August 08), the result is a total demand collapse.”

    I discussed this before with someone. This seems to imply commodities investors are irrational. If commdity prices rise it is because investors expect more demand for commdities, i.e. more real output. Remember, future prices tend to rise with spot prices, so it isn’t just a temporary storage thing. And that implies investors expect higher real GDP. I.e demand is shifting to the right. You can’t then argue the higher prices will reduce the demand for commodities, as that confuses a shift in demand with a movement along the demand curve.

    I am still confused about your multiple AS and AD curves (an oxymoron.) I don’t think the traditional laws of macro apply to “aggregate” curves that merely reflect a sector of the economy.

    You said;

    “You might consider this ‘minutae’, but the sheer dominance of the carry trades are partly what killed Japan”

    Well, you are certainly a better speller than me. But I just don’t see where these sweeping statments come from. Why would the carry trade hurt Japan? Does it cause less employment? If so, why? If it doesn’t affect employment does it affect output per worker?
    As you know, I think unemployment is caused by sticky wages, adn NGDP grwoth is determined by the BOJ.

    You said;

    “The low dollar rates – rather than immediately helping the US – are FIRST causing bubbles elsewhere…”

    The low dollar rates reflect an excessively tight money policy, which weakens the US economy. I’m not surprised that investment flows to areas where NGDP is rising faster. Let’s increase NGDP growth here.

    You said;

    “NGDP targeting would help a lot – but we’re still going to see lower than historical demand/utilization even with 5% NGDP in the short term because most of that will be inflation.”

    We just had 6.36% NGDP growth in the fourth quarter, and 0.6% inflation.

    If we had 2% inflation we’d have 6-8% real growth. The SRAS is really flat right now. I know you don’t agree, but the 4th quarter numbers give me no reason to change my mind.

    Yes, Pettis is very knowledgeable about China.

    cucaracha, The goal isn’t to increase bank lending, but to reduce bank demand for base money. A decrease in money demand is the same as an increase in money supply, regardless of what banks do.

    Doc Merlin, Interest rates are positively correlated with prices. There is no evidence at all that low interest rates raise prices. Instead, it is easy money that raises prices.

  23. Gravatar of StatsGuy StatsGuy
    30. January 2010 at 15:38

    Actually, it’s ‘minutiae’, so I neither quoted you correctly (my intent) nor corrected you correctly… A double failure. I will let my argument stand as is – I can’t make it any better, and your replies are clear enough.

  24. Gravatar of ssumner ssumner
    30. January 2010 at 16:56

    Thanks Statsguy, If it makes you feel any better, your post is not one of those arguments that I immediately understand and reject with confidence. It is a very complicated argument, and I am someone who likes to boil macro down to the simplist models possible. I am good at getting to the core of an argument, not weighing complicated situations. And of course the world is very complicated. So don’t be discouraged by my response. You might be reading poetry to a cow.

  25. Gravatar of Doc Merlin Doc Merlin
    30. January 2010 at 19:15

    @Scott:
    I didn’t say “low interest rates.” I said “artificially low interest rates.” Its a subtle distinction, but an important one. “Artificially low interest rates” are just another way of saying “easy money.” When money is too easy, interest rates are pushed lower than they should be. That is all I was saying, I wasn’t disagreeing about easy money. This is why I italicized “artificially low” so it would stand out.

    6 on one hand, half a dozen on the other.

  26. Gravatar of dlr dlr
    31. January 2010 at 07:13

    Everything you say is true, but you overlook the fact that it is almost equally true if T-bill yields are 5%. If the Fed injects lots of money, but the injection is expected to be temporary (as with the Y2K injections) prices will not rise even if T-bill yields are 5%. It is always true (according to Woodford), that what matters is changes in the expected future path in the money supply, not the current money supply.

    I feel like you sometimes write as if expectations were wholly exogenous, or at least exogenous to the current state of the world. I agree that permanent expectations about supply and demand are all that ultimately matter, but because these expectations aren’t set like a clock (and certainly not under any recent monetary regime), proximate factors influencing those expectations matter.

    If the Fed drop a single $100 bill into Times Square with a note saying “more to come” it would be just as inflationary in a liquidity trap as in a case where inflation was already alarmingly high if people expected it would drop another $100 bill every millisecond for the next ten years. But the likelihood of how those beliefs develop are not created equal, and not fully determined by the Fed’s traditional attempts to communicate intent. As I see it, when the Fed buys 5% T-bills, this may or may not trigger an increase in demand for money, and thus may or may not trigger the beginnings of an excess cash balance mechanism as a result. That’s part of the tautological process of the bubbling up of “expectations.” But when the Fed buys 0% T-bills, we know there is a higher likelihood that this immediately increases the temporary demand for money (all else equal!), because of the momentary indifference between money and T-bills. Almost irrespective what the Fed says, it is in part only sending a message saying it will currently print money such that it also increases the demand for money. Not very powerful. And people don’t just have to believe that the new money is permanent, they have to also believe that the increased money demand that likely results is temporary. The message and the possible bubbling up of expectations feels a lot different with 5% T-bills or anything else that is less equivalent to money. Although this isn’t the only thing that matters for expectations, it sure seems like it might matter.

    You could use Woodford to argue that a Fed program swapping two $5 bills for every $10 bill will be perfectly inflationary if people believed that the injections of the $5 bills were permanent but the removal of the $10 bill was temporary. Agreed. But what you are really saying is that the swapping is mostly irrelevant and expectations can be set verbally (without any swapping). Same with T-bill swapping. To the extent the actions matter, their possible influence on expectations matters, especially in a world where Fed words travel a bumpy road before turning into people’s expectations.

  27. Gravatar of scott sumner scott sumner
    1. February 2010 at 06:24

    Doc merlin, OK, but the only way to identify whether rates are too low is to look at inflation expecxtations. So I don’t bother looking at interest rates at all. But technically you are correct.

    dlr, I understand your point, and I partly agree. But I think people often draw the wrong implications from what you are saying. The most common view of a liquidity trap is that it is a situation where the central bank wants to inflate but cannot. One explanation, (offered by Krugman) is that it is an “expectations trap,” that the central bank wants to inflate but their actions have no credibility. The public doesn’t believe them.

    When I studied real world liquidity traps I found this was NEVER THE CASE. Liquidity traps occur because central banks adopt tight money policies, or at best are afraid of adopting easy money policies. Sometimes they are confused by real and nominal rates. But it is never a situation where the central bank is saying “we’re shooting for 3% inflation, but that darn public just doesn’t believe us. The public ALWAYS correctly interperted what the central bank was up to. (US 1930s, Japan 1990s, US 2008.)

    Here’s my claim. If the central bank adopts the Svenssonian policy of setting the monetary base at a level expected to produce 2% inflation, or 5% NGDP growth, then they will be equally able to do so at 5% T-bill rates and 0% T-bill rates. In fact, if the policy is adopted it is quite likely that T-bill rates will rise above zero.

    But if the Fed is targeting T-bill rates, and using them as a signal of future policy intentions, then their policy is much less effective at 0% rates than 5% rates. That is one case where you are correct.

    But if the Fed is targeting the MB growth rate at a permanent rate (like Friedman’s 4% rule.), than an increase in the MB growth rate that is announced as being permanent, will be just as effective at 5% than 0%. An increase in the base that is announced as being temporary, won’t be very effective in either case. If they are being cagey, not really clearly comunicating whether the increase is temporary or permanent, then I don’t really know. But my intuition tells me you might be right in that case, as if rates are 0% the public might discount the MB increase as mere accommodation of cash hoarding. But if rates are 5% perhaps they think it more likely to be permanent. And a point in your favor is that that ambiguous middle case might describe the real world.

    But this hypothetical feeds into my earlier claim that the economics of liquidity traps is really the economics of flawed monetary policymakers. You cannot construct a plausible model of liquidity traps in a world where central banks have a sensible monetary regime, with clearly laid out goals. And not necessarily my prefered regime, ANY sensible regime. Once you do that the zero bound becomes a non-issue for policymakers. They continue to target their goals, whatever they may be, and the MB endogenously adjusts to be whatever the public wants to hold when expectations of the goal variable are equal to the policy target. If the public wants so much cash that that exhausts the supply of zero yield T-bills, so be it. I could imagine a world with no T-bills at all, and yet no one would say monetary policy is impossible in such a world.

    The reason people think a liquidity trap is a trap, is because it exposes the fact that an ambiguous monetary procedure that was always (potentially) highly flawed, doesn’t work at all under certain conditions. And those conditions are zero short term rates. Does this make sense?

  28. Gravatar of dlr dlr
    1. February 2010 at 16:26

    Does this make sense?

    I agree with pretty much every word. Of course, we actually live under a less sensible monetary policy regime, where the CB aims at a secret target (some combination of inflation % and activity indicators as seen by the FOMC) by sending out a largely arbitrary bat-signal (the FFR), via a tool (T-bill OMO) that is not likely to produce any other signals if the bat-signal stops working. But given that actual regime, where the Fed may never be genuinely easy in the “clear eyes, full hearts” sense that is required for instant credulity, and instead sits on a mountain with vague and mysterious intent, specific actions matter a lot. So things like the expectational impact of T-bill swapping at 0% versus 5% can probably make a big difference.

  29. Gravatar of Doc Merlin Doc Merlin
    1. February 2010 at 23:10

    “Doc merlin, OK, but the only way to identify whether rates are too low is to look at inflation expecxtations. So I don’t bother looking at interest rates at all. But technically you are correct.”

    Mostly agreed there, although exogenous supply side shocks would still throw things off. (Although not as much as they do now.)

  30. Gravatar of ssumner ssumner
    3. February 2010 at 14:12

    dlr, It could, but not at all for the reasons many assume, which is that cash abnd T-bills have become perfect substitutes. But I don’t disagree with your broader point. The basic problem is the Fed’s flawed policy regime, everything else flows from that, and almost any hypothesis is possible once we enter this Alice in Wonderland world.

    Nick Rowe has a post today that you might like on this same topic, he applies game theory in an interesting way to the signaling problem.

    Doc, Supply shocks affect a price level target more than a NGDP target.

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