Deflationary death-spirals and the social construction of monetary policy

I present a simple macro model and use it as a vehicle to explore the idea that it matters how monetary policy is framed. One framing leads to a deflationary spiral, which an alternate framing can avoid or escape. The model is an otherwise bog-standard New Keynesian/Neo-Wicksellian model, but with a minor modification in the financial sector.

Phillips Curve: p = 0.25(y-y*) + 0.5p(t-1) + 0.5E(p)

Lower case p is inflation between this period and the next (sorry, but I can't do Greek), y is real output, y* the natural rate of output, and E(p) expected inflation. There's a 50-50 mix of forward- and backward-looking elements. There's a whole literature on the backward-looking elements, which are needed empirically to give inflation inertia. I need the backward-looking element to slow things down so we can see deflationary spirals evolving slowly when monetary policy makes a mistake under the wrong framing. Otherwise they would happen instantly.

IS curve: y-y* = n-r

Where r is the real rate of interest, and n the (time-varying) natural rate of interest. I am tempted to replace y* with expected future y. This would be better theoretically (the IS curve then has the standard Euler equation interpretation). It would also give more interesting results, because a deflationary spiral would then have an additional channel of positive feedback, since a fall in expected future output would mean the real interest rate would have to fall even further to break the cycle. But it's not needed to illustrate my point, and makes the maths a little harder.

Substituting the IS into the Phillips Curve gives us the IS-PC equation:

p = 0.25(n-r) + 0.5p(t-1) + 0.5E(p)

It is important that the coefficient on the real interest rate be small relative to the coefficient on lagged inflation, if we want to see the deflationary spiral evolve slowly. Otherwise it would happen instantly.

Financial sector. There are two financial assets: nominal bills and "real bills". Firms/households issue both to fund their spending. (As in all Neo-Wicksellian models, there's really a third financial asset, the medium of exchange, that is implicit in the model, because the violation of Say's Law makes no logical sense otherwise.)

A nominal bill is a promise to pay $1 in the next period. If B is the nominal price of a nominal bill, we can define the nominal interest rate i as

B=1/(1+i)

A "real bill" is a promise to pay 1 unit of real output in the next period (or its monetary equivalent). If R is the nominal price of a real bill, and P the current price level, we can define the (ex ante) real interest rate r as

R=P(1+E(p))/(1+r)

(I hate using the term "real bill" in this context, when it already has two different and contradictory meanings in the history of monetary thought. I would rather replace my "real bills" with shares in a stock price index mutual fund, but doing so would complicate the model. I still think of them as representing shares nevertheless.)

People are risk neutral, so in equilibrium the two financial assets give the same inflation-adjusted expected rates of return

(1+i)=(1+r)(1+E(p))

I approximate this as i=r+E(p) when I need to.

Monetary Policy.The central bank wants zero inflation and a constant price level (where P = $1). (I know there's an important distinction between inflation targeting and price level path targeting, but I will largely ignore it, because it doesn't matter for my purposes). The only time-varying parameter in the model is the natural rate of interest, n. Assume the central bank observes n contemporaneously.

If the central bank gets what it wants, we can describe the equilibrium as:

1. P=1 (or p=0 and E(p)=0).

2. B=1/(1+n) (or i=n)

3. R=1/(1+n) (or r=n)

[Update: typos fixed in 2 and 3, thanks to himaginary]

An outside observer, who saw the evolution of data for this economy, would be unable to distinguish between three different ways of "framing", or social constructions of monetary policy: 1. "The central bank is targeting inflation"; 2. "the central bank is targeting the price of nominal bills"; 3. "the central bank is targeting the price of real bills". All three are observationally equivalent, even if the observer knows the structural equations, and observes the natural rate of interest n. And there are many more ways he could describe monetary policy, including complex ways of describing it, like: 4. "targeting the nominal interest rate in order to target inflation".

Suppose the outside observer is a sociologist, who wishes to discover how people in this economy themselves construct reality. He induces a breach in the equilibrium. Suppose there is a temporary drop in the natural rate, n, by one percentage point, but the sociologist hides this fact from the central bank, by falsifying the bank's data. What happens?

What happens next depends on how the population and central bank frame monetary policy. And it is precisely because what happens depends on the framing that the sociologist's experiment succeeds in revealing that framing.

Suppose that people believe the central bank targets inflation, so E(p) stays at zero. And they maintain this belief in inflation targeting, despite temporary evidence that the central bank has failed to hit its target. But the central bank does not target inflation directly, and instead frames monetary policy as targeting the price of nominal bills (equivalent to the nominal interest rate), in order to hit its ultimate target, zero inflation.

In period 1, the natural rate drops, but the bank doesn't see it, so the price of nominal bills stays the same. The real and nominal rates of interest stay the same, and are now above the natural rate. So output drops below the natural rate y*, which means that actual inflation drops below zero.

In period 2, the bank learns that the sociologist has falsified the data, and takes the necessary steps to bring inflation immediately back to target. Because lagged inflation appears in the Phillips Curve, this requires the bank to engineer a boom, with output above y*. This in turn requires setting the nominal interest rate on nominal bills below the natural rate.

In period 3, everything returns to normal, except that the price level is lower than before the sociologist's experiment.

Now suppose people believe the central bank targets the price of nominal bills (the nominal interest rate). (Or they originally believed the bank targets inflation, but lose faith in this framing when they see the bank fail to hit its target.)

In period 1 the results are exactly the same as above, because people don't see what the sociologist is doing, and so continue to expect zero inflation.

In period 2, suppose people expect the bank to set the nominal rate equal to the natural rate. What would they expect to happen? (What would happen if the bank did what people expect it to do?). Substituting the IS into the Phillips Curve, setting i=n, and imposing rational expectations we get

p = 0.25(n-i+E(p)) + 0.5p(t-1) + 0.5E(p) = 0.5p(t-1) + 0.75E(p) = 2p(t-1)

So if the population stops framing monetary policy as targeting inflation, and instead frames it as setting the nominal rate of interest, then they expect a deflationary death-spiral with deflation doubling every period, the real interest rate rising continuously relative to the natural rate, and output falling continuously with the output gap doubling every period.

Central banks are aware of this danger, of course, which is why they don't frame nominal interest rate targeting as setting

i=n+p*, where p* is target inflation.

The above interest rate rule fails to obey the "Taylor Principle". If the population ever loses the frame of monetary policy as targeting inflation, so that expected inflation differs from target, the central bank needs to frame monetary policy as setting:

i = n + E(p) + a(E(p)-p*), where a is some strictly positive number.

But if our central bank (with a target of zero inflation) cannot observe expected inflation, and can only observe lagged actual inflation, it would need to frame monetary policy as:

i = n + (2+2a)p(t-1)

[minor math mistake fixed, thanks to himaginary]

If the inflation target is credible, so that expected inflation never deviates from target, an outside observer would be unaware of the existence of the (2+a)p(t-1) term. It's rather like police reserves. As long as the crowd knows they are there, even if hidden, the crowd obeys the social rules, and we never see the reserves deployed. But if the crowd ever did start to riot, would the reserves be big enough to restore the original social reality -- the mutual expectations of following the rules?

If the central bank ever lost control of expected inflation on the upside, there is no limit on how high it could raise the nominal rate of interest to restore order. But if it ever lost control on the downside, the zero lower bound on nominal interest rates does impose a limit on the bank's ability to restore order. The police have limited reserves, and if too many in the crowd run riot, there won't be enough reserves to restore order; and the crowd knows this. With deflation and expected deflation doubling every period, a central bank that waited too long to call in the reserves would lose control of the inflation target.

Now suppose we change the way monetary policy is framed. Suppose people believe that the central bank targets the price of real bills, rather than nominal bills, in order to maintain its inflation target. Let's re-run the sociologist's experiment.

In period 1 exactly the same thing happens as before. The central bank doesn't learn that the natural rate of interest has decreased, and so sets the price of real bills too low, and the real rate of interest is therefore above the natural rate. Output falls below y*, and inflation is negative.

In period 2 and thereafter the central bank once again learns the correct value of the natural rate of interest, and is expected to set the nominal price of real bills at R=1/(1+n) thereafter. This framing of monetary policy rules out the possibility of a deflationary spiral as a rational expectation. To see why this is so, substitute R=1/(1+n) into the definition of the (ex ante) real rate of interest to get

(1+r) = (1+n)P(1+E(p))

In a deflationary spiral, the price level P would fall without limit, and expected inflation E(p) would fall without limit. If the real interest rate were constant, this would mean the nominal price of real bills would fall without limit too. But if monetary policy were framed as holding the nominal price of real bills constant, a falling price level and falling inflation would mean the real interest rate would fall without limit too, so output would rise without limit, and that rising level of output would put ever-increasing upward pressure on inflation.

My math isn't good enough to solve for the time-path explicitly (though any competent graduate student could probably solve it), but it is easier to show that deflation cannot accelerate into a spiral. Suppose E(p)=p(t-1), and the IS-PC equation yields:

p = 0.25(n-r) + p(t-1)

Since P<1, and E(p)<0, we know that r<n, so there will be less deflation in period 2 than in period 1. With rational expectations, people will know this, which reinforces the brake on deflation. Inflation must eventually turn positive, and the price level must eventually return to its original level. Setting the nominal price of real bills anchors the long run equilibrium price level in a way that setting the nominal price of nominal bills can never do.

[Update: himaginary in comments provides the solution:

"I'm not good either, but here is some try:
p = 0.25(n-r) + 0.5p(t-1) + 0.5E(p)
= 0.25(1+n){1-P(1+E(p))} + 0.5p(t-1) + 0.5E(p)
= 0.25(1+n)(1-P) + {0.5-0.25P(1+n)}E(p) + 0.5p(t-1)
Assuming E(p)=p by rational expectation, it becomes
p={0.25(1+n)(1-P)+0.5p(t-1)} / {0.5+0.25P(1+n)}
The coefficient of p(t-1) is 1/{1+0.5P(1+n)}, which is less than 1. So deflation-spiral surely doesn't happen in this case."]

This result shows that framing monetary policy as targeting the price of real rather than nominal bills can prevent a deflationary spiral from ever getting started. Even if the central bank were permanently ignorant of the natural rate, and set R too low permanently, the cumulative fall in the price level, and rising expected deflation, would eventually mean the real rate would fall below the natural rate, ending the deflationary spiral.

Suppose nevertheless that a deflationary spiral did begin, perhaps because monetary policy had initially been framed in terms of targeting the nominal interest rate. Could a re-framing of monetary policy in terms of targeting the price of real bills break the spiral? Could it do this even if the zero lower bound on nominal interest rates were binding? If the re-framing were successful, and if the central bank can credibly commit to a future price of real bills, the answer is yes.

To see why this is so, remember that the price of real bills anchors the long-run equilibrium price level. By promising a high enough future price of real bills, the central bank can promise a future price level that is high enough to make current expected inflation positive. If monetary policy were framed as targeting the nominal interest rate, there is no way the bank can make this promise. People just wouldn't understand the language in which the promise were made, so it could not be credible.

To repeat what I said in a previous post: it's the framing of what central banks do that caused the mess, not anything central banks are actually doing. (The bank does exactly the same thing in period 1, whether monetary policy is framed as targeting the price of nominal bills or of real bills.) The social construction of reality is what dunnit!

Addendum: if you make two small changes in the model (replace y* with E(y(t+1)) in the IS curve), and change my "real bills" (which I think of as shares) into "nominal GDP futures contracts", my model would come close to what Scott Sumner is talking about. The small change in the IS curve would mean that the level of current output would depend on i-n plus the expected growth rate of nominal GDP (as opposed to the expected rate of inflation). But I can never remember the difference between a forward and a futures contract; the ones I want are where you pay $R this period, in return for a fixed percentage of nominal GDP next period, so a change in R for given expectations affects the real interest rate.

Comments

[winterspeak]

ANON: Really appreciate you tackling this question. I'd love to get a better term for this quantity, and yes, it is only meaningful on a consolidated scale. We are talking macroeconomics here.

Obligations between the Govt sector and the non-Govt (or private) sector should NOT be collapsed, hope that was clear in my phrasing of the question. Also, I am ignoring foreign entities for simplicity sake for now.

So, your answer is "corporate retained earnings" plus "household net worth". Is that right?

If so, we can get even wilder.

[anon]

If you're asking about the balance sheet offset to net financial assets, after eliminating almost all intra-private sector financial assets, it's EQUITY, consisting of SOME PORTION OF corporate retained earnings and household net worth.

[anon]

i.e. SOME PORTION OF TOTAL EQUITY, that portion being "NET FINANCIAL EQUITY" as I defined it, the rest being "REAL EQUITY" as I defined it

[anon]

i.e. TOTAL EQUITY = NET FINANCIAL EQUITY + REAL EQUITY = retained earnings + household net worth

[winterspeak]

ANON:

OK. So, it sounds like, in your best considered opinion, if one was to collapse down all inter-sector assets and liabilities (uncreate all financial assets) in the private sector, then the only financial assets left would be:

retained earnings + household net worth.

Here's where things get really wild:

retained earnings + household net worth = the National Debt.

Can you see why?

[dlr.myopenid.com]

W -- anon is not going to agree with you because he is not stripping real assets out of household net worth and retained earnings and you are.

I find the distinction between consumption and non-consumption to be something you only know in hindsight. Your $200K house -- was it consumption, or investment? Suppose there is a housing collapse (I know, impossible to imagine) and the house is now worth just $100K. How do you classify the $100K you've lost? Or suppose you bought a lottery ticket and got lucky -- did that act of consumption suddenly become a shrewd investment?
I don't like housing as an investment example because it's a mixed-use good, and thus often causes confusion.

To make it simpler, let's say I am building a house purely to rent out that I can never live in because of odd zoning laws. So the house itself is no more consumption to me than it would be for Toll Brothers.

On day one, I have made a meaningful choice to postpone present consumption (the party) for future consumption (rent from the house or income from the house if I sell it down the line). Normally I would call this choice both savings and investment, but here I am calling it non-consumption. You point out that this attempted non-consumption might fail. The house might fall into a sinkhole or just generate lower than expected rents. What would I call that? I would call it a loss of wealth or a supply shock. There’s nothing stopping me from calling it “ex post consumption,” but I would find this very unhelpful because it misses key behavioral distinctions. We know for sure that someone who builds a house versus having a party or going on vacation is choosing the future over the present, and that is an important economic choice.

Say your neighbor was worried that might lose his job in the next couple of years and wouldn’t be able to meet his rapidly rising medical bills. He had just received an inheritance , and has only two choices. He could throw a big party or he could build a rental house . Surely you wouldn’t say that the choices were indistinguishable because both might turn out to look like consumption if the house lost value. One choice clearly equals a very high probability of trading current consumption for future consumption at some ratio, while the other choice equals no probability of such a trade. The riskiness of his future consumption choice is also an interesting issue, which certainly isn’t ignored by economists, but doesn’t render his present versus future decision uninteresting.

Similarly, if I bought a lottery ticket (let’s say it paid out in one year to satisfy my only criteria for non-consumption: the expectation of future rather than present consumption), I am making a similar choice. Let’s say I bought *every* lottery ticket and had every number covered with no duplicate numbers permitted. It costs me $10 million to buy every number and the lump sum options pays me $10.5m million (ignore taxes) in one year for the winning number (yes, a lottery with fair odds, just for simplicity). So I have essentially bought a one year bond from the issuing government. Now let’s say I change my mind and buy every number except one. Suddenly there’s a chance that my “non-consumption” turns into your “ex post consumption” if I hit the wrong number. This possibility doesn’t take away the very interesting information that I am still choosing to postpone present consumption in return for an probability of future consumption, and thus shouldn’t be used to ignore the economic importance of that choice by removing it from the dictionary. I am simply taking slightly more risk of loss in addition to my time trade off.

Time preference is one element in savings, but not the only one. Balance sheet considerations matter too. They may even matter more. At a sector level that is almost certainly true.

I assume we are using your “savings” here. Then I agree. Time preference is not the only element in the demand to hold money, nor is it the only element in what you care most about – the demand to hold money or government debt. But those demands are not the only important economic behaviors worth caring about.

[anon]

You’re not following this at all ... I just finished explaining at length, several times, that retained earnings and household net worth are NOT financial assets.... (P.S. one very, very, technical aside, which I explained, but repeat – the equations I wrote only work if the stock collapse is done at paid in book value...that’s why retained earnings remains split out and why household net worth reflects an equity value corresponding to paid in book value of the collapsed stock instead of market value (the more usual presentation)...the alternative is even more complex.)

Apart from that, the national debt is not at all what you say above...it equals the net financial asset piece of total equity as I defined it...a very small subset of total equity (retained earnings plus household net worth as I defined)...you only have to eyeball the Z1 for 3 seconds to understand this in more practical terms, just from the order of magnitudes involved....

I must leave soon.

[winterspeak]

ANON: OK, I am not following you. I asked you a simple question. i did my best to interpret your answer, and I asked you to clarify. Did not understand your clarification either.

Clearly you understand that, all inter-sector created financial assets net to zero.

Clearly you understand that, after uncreating those assets, you have some financial assets left -- in particular, assets whose liabilities exist out of sector. A simple example: the cash I hold in my wallet will continue to exist even if all inter-sector financial assets are uncreated. So will the money in my bank account.

It seems like you cannot communicate what you would call those assets in a way I can understand. Best to move on. Pity though.

[winterspeak]

dlr.myopenid.com: You're better at understanding anon than I am! Also wish he'd give himself a name.

I understand wanting to shift consumption to the future, and I understand the value of investment and the behavioral differences you are talking about. They are all real, but they aren't helpful to the particular problem under discussion today which is, if the private sector wants to increase its "financial savings", this mysterious entity that no one seems to be able to label even though it is easy to define, and is common sensibly thought of as "savings" it cannot. No matter what one does or does not do with interest rates. And this inability leads to the widespread fall in aggregate demand and unemployment we see today, along with the observed impotence (and arguably, active harm) of monetary policy.

[anon]

“anon is not going to agree with you because he is not stripping real assets out of household net worth and retained earnings and you are.”

Thank you. It seems that one soul has understood the basic idea, one which I “cannot communicate” in a way that can be understood otherwise... perhaps somebody of fairly high intelligence, not trapped on the island of net financial assets, who understands the oceanic context of net financial assets...and probably realizes that although I didn’t strip real assets out, I did identify them as a separable component.

[Ramanan]

Nick @ November 18, 2009 at 04:59 AM,

I will have to make a distinction between saving and savingS. Its also a question of flow vs stock. Of course in a more precise way or doing it, Scott and Winterspeak's terminology is better suited here. I had pointed out an accountingish kind of statement comparing two countries and was talking of a stock but your reply was on the flow.

Also talking about interest rate sensitivies of profits, I do not infer that from the Flow of Funds data. I mean of course there is but there are other parameters - target profits can be sacrificed a bit, employment numbers change due to interest rate changes. Plus as I had mentioned, firms hold a lot of financial assets in their balance sheets.

[Too Much Fed]

Scott Sumner said: "too much Fed, I favor 5% NGDP growth in normal times--enough for 3% real income growth for the average American. In this recession I favor faster NGDP growth for a catchup period, so I don't see my policy as ignoring the middle and lower classes. Like a Democratic politician, I believe jobs are our number one problem. I oppose bailouts for the rich."

Let's assume positive productivity and cheap labor (outsourcing, illegal immigration, and legal immigration) produce price deflation. Should price inflation occur because of an increase in currency or an increase in currecny denominated debt?

Are there not enough jobs or too many workers?

"3% real [wage] income growth for the average American." I'm going to assume from higher wages. Tell that to the fed and see if they don't wince like when fingernails are scratched over a chalkboard.

I'd like to know how many Americans have experienced 3% real income growth since about 1980 using a middle class person's budget and NOT gov't CPI?

[Too Much Fed]

Nick said: "Yep. In a closed economy:

S-I = G-T

That's just an accounting identity. It's a way of using words in a consistent way; it doesn't tell us how the world works."

How about (S-I of the rich) plus (S-I of the lower and middle class) equals G-T [my signs could be wrong]?

That is, if the rich can't get the lower and middle class to go further into currency denominated debt to them, the rich will get the gov't to do it for them so they can maintain/increase their excess savings.

[himaginary]

Very interesting model. I suppose nominal interest rate targeting framework is what BOJ has fallen into.

BTW, on some minor points...

2. B=1/(1-n) (or i=n)
3. R=1/(1-n) (or r=n)
I think divisor should be (1+n) in both equations.

i = n + (2+a)p(t-1)
Substituting E(p) for 2p(t-1) and setting p*=0 in "i = n + E(p) + a(E(p)-p*)", it becomes
i = n + (2+2a)p(t-1)

My math isn't good enough to solve for the time-path explicitly
I'm not good either, but here is some try:
p = 0.25(n-r) + 0.5p(t-1) + 0.5E(p)
= 0.25(1+n){1-P(1+E(p))} + 0.5p(t-1) + 0.5E(p)
= 0.25(1+n)(1-P) + {0.5-0.25P(1+n)}E(p) + 0.5p(t-1)
Assuming E(p)=p by rational expectation, it becomes
p={0.25(1+n)(1-P)+0.5p(t-1)} / {0.5+0.25P(1+n)}
The coefficient of p(t-1) is 1/{1+0.5P(1+n)}, which is less than 1. So deflation-spiral surely doesn't happen in this case.

[Nick Rowe]

Thanks himaginary!

You are right about the two typos. And I think your solution looks right too.

I have updated the post to fix the typos and include your solution.

[Nick Rowe]

himaginary: Looking at your solution, I think I see something very important. But I'm not sure if I'm seeing it right.

Suppose we were already in a deflationary spiral, because the central bank had been targeting nominal interest rates, so p(t-1) is very negative.

Then all of a sudden the bank announces that it will switch to targeting R instead. Suppose it announces a high target for R (call it R*). If it sets R* high enough, and if the target for R* is credible, will p immediately turn positive? Even if p(t-1) is already very large and negative?

If I'm right on this, a credible announcement of targeting R, rather than B, could always make the nominal interest rate suddenly become positive, and so the central bank could always escape a liquidity trap, even if deflation were already very high.

We can't see this result directly from your solution, since I assumed the bank set R to make P=1. But if the bank set R to make P=P* then I think the term (1-P) in your solution would become (P*-P), where P*=(1+n)R*. So if we replace your (1-P) term with ((1+n)R*-P), by setting R* high enough, the bank can make p positive, even if p(t-1) is very negative.

Am I right?

[Adam P]

Nick, suppose the real bill R is a traded asset. Can the bank set its price to be greater than 1?

If you're going to say yes, they could just offer to buy them at price greater than 1 then why can't they do the same with nominal bills to get a negative interest rate?

If you say no and the liquidity trap results from a negative natural rate then can they still break the trap by switching to targeting the price of the real bills?

[Nick Rowe]

Adam P. :

First, I need to re-phrase your question. Because if the equilibrium price level were $0.5, for example, and expected inflation were zero, the equilibrium price of real bills would be $0.5/(1+n) which is less than one. But that's not what you meant.

Let me try to re-phrase it. Suppose n=0 for simplicity. Suppose the bank would need to set the price of real bills so high, in order to create positive expected inflation, despite high deflation last period, that holding currency would dominate holding real bills?

Dunno. I'm not sure I've re-phrased your question correctly. And I need time to think. Right now, my brain is seeing two contradictory visions: yours and mine.

[Nick Rowe]

Should read: "Because if the equilibrium price level were $5, for example, and expected inflation were zero, the equilibrium price of real bills would be $5/(1+n) which is (probably) greater than one. But that's not what you meant."

[Nick Rowe]

Suppose currency pays zero nominal interest.

If himaginary's solution is right, and if I understand his solution correctly, and if my guess about what his solution would look like in the more general case (where the bank targets a time-path for R*) is correct, then:

Even if the natural rate were negative, even if there were lagged deflation last period:

1. There exists a time path for R* (it would start higher than current R, and be upward-sloping) that if announced, and if credible, would mean that real bills would rate-of-return dominate currency at all points along that time-path, starting from the date of the announcement.

2. There exists no such time path for B*, even a conditional one.

My brain can barely think this stuff, let alone be sure I'm right, let alone^2 explain it clearly. But it's all comes from noticing that p(t) is an increasing function of R*, without limit, in himaginary's solution.

[Nick Rowe]

Or maybe I'm wrong, and the forward-looking coefficient (0.25) in the Phiilips curve isn't strong enough for this economy to bootstrap its way out of the liquidity trap. Dunno. I could make it stronger (or add E(y(t+1)) to the IS curve), but then the deflationary spiral would mean instant death, rather than evolving slowly.

[himaginary]

Nick, thank you for incorporating my comment in your post.

On your question, I used equation (1+r)=(1+n)P(1+E(p)) to introduce P into IS-PC equation.
If R=P*/(1+n), this equation becomes (1+r)=(1+n)(P/P*)(1+E(p)).
So we have to replace P/P* for P hereafter, and (1-P) term becomes (1-P/P*), which cannot exceed 1 no matter how large P* becomes. That is, if p(t-1) is less than -0.5, we can never escape deflation immediately (assuming n=0).
However, if p(t-1)=-0.1, P* larger than 1.25P makes p positive. If p(t-1)=-0.2, P* larger than 1.67P makes p positive. So I think your suggestion is right as long as price didn't become less than half in the last period.

And as for nominal bill targeting, incorporating your Tarlor rule
i = n + E(p) + a(E(p)-p*)
into IS-PC equation
p = 0.25(n-i+E(p)) + 0.5p(t-1) + 0.5E(p)
produces similar result. That is,
p = 0.25(-aE(p)+ap*) + 0.5p(t-1) + 0.5E(p)
=0.25ap* + (0.5-0.25a)E(p) + 0.5p(t-1)
Assuming E(p)=p by rational expectation,
p={0.25ap*+0.5p(t-1)} / {0.5+0.25a}
So if p* is high enough, we can escape deflation immediately. But, of course, there is zero boundary for i.

[Adam P]

Nick, so basically you've rediscovered the idea that reducing the real rate through a price level target breaks the liquidity trap. As himaginary says, the key is setting P* high enough.

You've added nothing to the existing discussion and most importantly none of this has anything to do with the framing, price level targets to reduce the real rate can in fact be done with nominal rates as the policy intrument in this model.

[himaginary]

The problem is, CB cannot follow Taylor Rule in the liquidity trap, as shown here. If people believe in inflation targeting framework, they would expect that CB would somehow compensate this gap brought about by the zero boundary of nominal interest rate. But what happens if people start to think that CB doesn't care about deflation anymore once it hits zero boundary? I think that's where Nick's model has something to say. Maybe deflation doubling every period is a bit too extreme, but setting parameter as a=0 in Nick's Taylor Rule makes deflation persistent. And if you set a<0 (i.e. CB responds to deflation less than one-to-one because of zero-boundary constraint), you get deflation spiral.

But is there CB on earth which doesn't care about deflation anymore for the reason that the nominal interest rate has hit zero? Yes, there is.

[Adam P]

himaginary: "But what happens if people start to think that CB doesn't care about deflation anymore once it hits zero boundary? I think that's where Nick's model has something to say."

But that is not what Nick is arguing. The Taylor Principle (not the same thing as the Taylor rule) says nothing more than if the bank wants to have real effects it must change the real rate. We already knew that.

Nick wants to say that using the nominal rate as the policy instrument is a problem due to some framing effect but you can't get that in this model because people have rational expectations, there are no framing problems in this model. Everything works through the real rate here.

The Euler equation cares what the real rate is but does not care how it was set (via trading nominal vs real bonds).

If the CB stops caring about deflation that's an entirely differnt thing but what does that have to do with "the social construction of monetary policy"? The only thing Nick is accomplishing here is to make himself look silly.

[Nick Rowe]

Adam: whenever we try to say something new, we run the risk of saying something that turns out to be silly. That's a risk I'm willing to take.

We agree that if the bank could credibly announce a target path P*, it could escape the liquidity trap. Nothing new there, of course. But since there's no mechanism where the bank can directly influence P (it doesn't intervene in the market for haircuts), there's a credibility problem.

But the mechanism whereby the bank can directly influence R is, in principle, exactly equivalent to the mechanism by which the bank can directly influence B. Real bill market operations and nominal bill market operations are equally plausible/credible as mechanisms. So R targeting can be credible in a way that P targeting may not be.

R* and P* move in the same direction, both in the short and long runs. B* and P* move in the same direction in the short run, but there is zero relation between them in the long run. (Double the time-path of the equilibrium price level, and R doubles too, but B stays the same.)

Putting those last two paragraphs together, announcing a time-path R* may be a way for the bank to *credibly* do what it would otherwise do by announcing a time-path for P*, if only a P* time-path were credible.

And we know that what I call "framing" can matter, because the difference between Bertrand and Cournot equilibrium shows this. It makes no difference whether the economist thinks of a monopolist as setting p or q - the economist gets the same answer either way. But it does make a difference whether dupololists think of their rival as setting p or q - the Nash equilibrium is different. It's not how the economist frames the problem that matters. What does matter is how the economist frames how people/firms frame the problem.

[himaginary]

If the CB stops caring about deflation that's an entirely differnt thing but what does that have to do with "the social construction of monetary policy"?

I think it has everything to do with.

What we have here in Japan now is the CB which deems nominal interest rate as the only tool of monetary policy. Once it hits zero, they think they have done everything what they can do, and take no further action. The next time they take action would be when inflation rises and they need to hike interest rate. (OK, I may be exaggerating a bit, but not so far from the truth.)

On the other hand, there is CB which switches to other tools such as quantitative easing, qualitative easing, or whatever, once nominal interest rate hits zero.

The former can be likened to the army which surrenders or runs away once they are out of ammo. The latter is like the army which resorts to swords, fistfighting, or whatever, once they are out of ammo. I think this difference can be called as the difference in "the social construction of army", because this difference reflects the difference in what each society expects from army. And of course the difference in expectation affects people's behaviour, result of the war, etc.

BTW, I think Krugman here is exactly talking about "the social construction of monetary policy". Is he making himself look silly, too?

[edeast]

Carney uses the word prism, to describe how the BOC view their job.

To put it simply, the Bank looks at everything, including the exchange rate, through the prism of achieving our inflation target.

[Nick Rowe]

edeast: "prism" is a good word to convey how the bank frames what it is doing. But I think "communications strategy" is a better word for how the bank tries to influence others' framing of what it is doing. Of course, the bank generally wants its prism and communications strategy to be mutually consistent (it's hard to think of what you are doing in one "language", but use a different "language" to explain to others what you are doing.

himaginary: I like your army metaphor. I would change it slightly though. At one level, an army is just a bunch of guys with guns and ammo. But an army that thinks of itself as an army can beat an army 10 times the size that thinks of itself as just a bunch of guys with guns and ammo. And the whole point of basic training, military parades, uniforms, etc., is to get a bunch of guys with guns and ammo to think of themselves as an army (or division, platoon, whatever). Generals know that an army is a social construction, and spend a lot of effort trying to build that social construction. And it matters because of expectations, as you say. If the soldiers think of themselves as just a bunch of guys, they expect the others will run away, and it becomes a self-fulfilling prophecy. If they think of themselves as an army, they expect the others to stand and fight, and they do stand and fight.

Another game theory analogy is that of a focal point in a game with multiple equilibria. A change in framing changes the focal point, and changes the equilibrium we actually observe.

If the bank is successful in changing people's expectations, so expected inflation and expected future output both rise, we know that nominal bond prices will fall, and the nominal price of shares/real bills will rise.

Now imagine how the bank can try to inspire confidence in each of those strategies:

1. "We are going to try to raise the price of bonds to stimulate the economy, and if our policy works, and people see that it works, bond prices will fall" People's reaction: "WTF?"

2. "We are going to try to raise the price of shares to stimulate the economy, and if our policy works, and people see that it works, share prices will rise." People's reaction: "OK, if I see it starting to work, I will jump on the bandwagon, so will others, and we will see it working even more".

[Too Much Fed]

himaginary said: "On the other hand, there is CB which switches to other tools such as quantitative easing, qualitative easing, or whatever, once nominal interest rate hits zero.

The former can be likened to the army which surrenders or runs away once they are out of ammo. The latter is like the army which resorts to swords, fistfighting, or whatever, once they are out of ammo."

And in both cases, the CB's should lose because they are fighting a war they should not be. Let them be defeated then abolished!!! Goodbye and good riddance hopefully forever!!!

[Too Much Fed]

Nick's post said: "2. "We are going to try to raise the price of shares to stimulate the economy, and if our policy works, and people see that it works, share prices will rise." People's reaction: "OK, if I see it starting to work, I will jump on the bandwagon, so will others, and we will see it working even more"."

By jump on the bandwagon, do you mean suckering the lower and middle class into taking on more currency denominated debt whether they can afford to or not?

[Adam P]

Nick, you said: "But the mechanism whereby the bank can directly influence R is, in principle, exactly equivalent to the mechanism by which the bank can directly influence B. Real bill market operations and nominal bill market operations are equally plausible/credible as mechanisms. So R targeting can be credible in a way that P targeting may not be."

But we agreed above that for given expectations about future P* there is an upper limit on the price of R just as there is an upper limit on the price of B so you haven't solved the fundamental problem of the liquidity trap.

himaginary worked the arithmetic for you and found that in both cases the only way to break the trap was set high enough P* and that this could be done EQUALLY WELL with R or B by promising future behaviour. IN BOTH CASES (TRADING R OR B) THE KEY IS THAT THE PROMISE OF FUTURE BEHAVIOUR IS BELIEVED, if the promise is believed then trading either works equally well. If the promise is not believed than trading R instead if B helps nothing.

[Adam P]

Nick: "Adam: whenever we try to say something new, we run the risk of saying something that turns out to be silly. That's a risk I'm willing to take."

Let's be clear, I'm not criticizing you for putting out the idea. I respect the fact that you do it in a public forum and put your name to it, unlike us commenters who are basically anonymous. I'm trying to make the point that you're keeping on this even though you simply aren't helping.

The issue is not the framing, you haven't shown that it is. The issue is that, whether R or B is the policy instrument, the CB needs to commit to doing something in the future and the big catch is that when that future comes and it's time for the CB to carry through it's promise, at that time it won't want to. This is a problem of course because people know this today.

Think about it, imagine that the Fed promises that once the economy recovers it will allow 6% inflation for several years. Imagine that this works as hoped and we immediately get a growth spurt.

After employment recovers and inflation is rising won't there be plenty of guys (for example Plosser) saying that we need to get this inflation under control, that we can't be held hostage to a promise made under duress? Won't they be saying that it wasn't the promise that generated the recovery anyway so no need to honour it? Will nobody (RBC theorists etc) say that?

But doesn't everyone today think that it might happen that way. Maybe people today are afraid that ex-post the Fed will even convince itself that it was the quantity of money and not the promise that did it, that it was just the long and variable lags that caused the delay. It was just a conicidence that the recovery began just after the promise was made. You yourself, 6 months ago, would have said it's the quantity and not the promise right?

If you want to help then figure out how a CB can irreversibly commit, don't waste everyone's time claiming the liquidity trap never would have happened if nominal rates weren't the policy instrument.

Like Woolsey likes to say, imagine a world without credit. Better yet imagine no money or credit. THE LIQUIDITY TRAP COULD STILL HAPPEN. Monetary policy can help here but you are not offering a solution here, you're just wasting your own very valuable time. If you do come up with a solution that works people will listen, but this. Woodford would see through this in a nano-second.

[Too Much Fed]

Adam P said: "IN BOTH CASES (TRADING R OR B) THE KEY IS THAT THE PROMISE OF FUTURE BEHAVIOUR IS BELIEVED, if the promise is believed then trading either works equally well. If the promise is not believed than trading R instead if B helps nothing."

IMO, belief has nothing to do with a reality of cheap labor and positive productivity growth along with the ability to make interest payments on the currency denominated debt.

Didn't a lot of people "believe" that housing prices in the USA would rise by at least 5% per year (and never fall) for at least 15 years? That did not make it reality.

[Adam P]

Nick, here's Woodford from http://www.columbia.edu/~mw2230/CRcomment-LongTermInstrument.pdf :

the mere existence of a positive long rate need not imply
the possibility of further stimulus through open market operations, including
open-market purchases of long-maturity bonds. Once short rates have fallen
to zero, Eggertsson and Woodford (2003) show that open-market operations
have no e®ect on long or short rates (or on in°ation or real activity, either),

if the open-market operations do not imply any change in the rule according
to which policy is expected to be conducted in the future. Committing to an
alternative future approach to monetary policy can stimulate the economy,
even when short-term interest rates are zero; but that is possible even in the
case that the instrument of policy is an overnight rate.

It should be clear that what Woodford is saying applies to using shares as well, I'll repeat the last sentance, Woodford's words:

Committing to an alternative future approach to monetary policy can stimulate the economy, even when short-term interest rates are zero; BUT THAT IS POSSIBLE EVEN IN THE CASE THAT THE INSTRUMENT OF POLICY IS AN OVERNIGHT RATE.

[Adam P]

You might also be interested in this http://www.columbia.edu/~mw2230/TwoPillars.pdf

Abstract:

Arguments for a prominent role for attention to the growth rate of mone-
tary aggregates in the conduct of monetary policy are often based on references
to low-frequency reduced-form relationships between money growth and in°a-
tion. The \two-pillar Phillips curve" proposed by Gerlach (2004) has recently
attracted a great deal of interest in the euro area, where it is sometimes sup-
posed to provide empirical support for the wisdom of a \two-pillar strategy"
that uses distinct analytical frameworks to assess shorter-run and longer-run
risks to price stability. I show, however, that regression coe±cients of the kind
reported by Assenmacher-Wesche and Gerlach (2006a) among others are quite
consistent with a \new Keynesian" model of in°ation determination, in which
the quantity of money plays no role in in°ation determination, at either high
or low frequencies. I also show that empirical results of this kind do not in
themselves establish that money growth must be useful in forecasting in°ation,
either in the short run or over a longer run. Hence they provide little support
for the ECB's monetary \pillar."