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.
Worthwhile Canadian Initiative 
And if output is at the natural rate of output, and not below it as presumed (as the consequence of a credit bubble) — there is no ‘cure’
Nick, this is getting silly.
In first case (inflation targeting) you and the CB correctly reason that in order to get the price level back to the target they need to engineer a temporary boom and thus they lower the the nominal rate below the natural rate. That is, they obey the Taylor principle.
In the second case (nominal interest rate targeting) they, somewhat mysteriously, don’t do this. Instead they set i=n and get the deflationary spiral because they have violated the Taylor principle. But why don’t they try to engineer the boom in this case?
Now the third case (real interest rate targeting) where they are back to adhereing to the Taylor principle. The trick is that you said they set R=1/(1+n), THAT IS THEY SET r < n!!!! After all, in period 2 after we’ve had a fall in prices the current value of R such that r=n is P/(1+n) with P<1!! So they are back to setting r<n and engineering the boom to get back to the price level target, they are back to following the Taylor principle.
So what does social framing have to do with anything? You engineered the bank to follow the Taylor principle in all but the second case.
Correction to the last sentance in fourth paragraph (discussing the third case), should read:
So they are back to setting r<n.
And of course there’s the problem of how exactly the CB controls R, if you have in mind the CB buying and selling stocks then say so and I’ll begin explaining why that’s a horrible idea that won’t work like you hope it will.
We need to keep in mind that the CB has pretty tight control of overnight inter-bank lending rates. It can’t control other types of nominal rate that easily nor can it control real rates or inflation.
r<n in the correction.
I’m trying to say “r less than n”, apparently everything after the “less than” symbol is getting lost.
btw Nick, the Taylor principle is really saying that what CB’s need to do is adjust nominal rates (viewed in the NK paradigm as a control variable not a target) to target the real rate. So you could view CB behaviour as already targeting the real rate, the problem of course is that they can’t control it that well. You haven’t said how they control it here.
After all, UK and Eurozone had explicit inflation targets and that didn’t prevent recessions in those places.
Adam: the less than symbol is interpreted as opening an html tag. Use < (ampersand ‘l’ ‘t’ semicolon) and it’ll display as < . Greater than is >
Patrick: how do you learn that stuff?
Adam P: If you can credibly communicate monetary policy in terms of an inflation/price level path target, everything is fine. And everything was fine until people doubted banks would be able to hit their targets (“where’s the mechanism?”).
If you can credibly communicate monetary policy in terms of a nominal interest rate target with Taylor Principle coda i=n+(1+a)E(p) then everything is fine. But if people see there’s a contradiction here between that instrument rule and the zero lower bound, it cannot be credible (unless they ignore that contradiction, which they won’t). The coda {my shorthand for (1+a)E(p)) loses its force when implementing it would violate the lower bound. It’s as if the bank says to the people: “if you continue to expect deflation greater than n, I will set nominal interest rates below zero, which will cause actual inflation to be greater than you expect, so you had better revise upwards your expectation of inflation”. It’s not a credible threat.
The bank needs some way to communicate an easing future stance of monetary policy that will, if believed, cause the equilibrium nominal interest rate to rise above zero, so there’s no contradiction between believing the promise and violating the lower bound. That’s where communicating the stance of policy in terms of the price of real bills comes in.
The bank controls r indirectly by controlling the price of real bills. I can’t see any difference between the bank’s ability to control the price of nominal bills and control the price of real bills.
Gary: you are way off topic. I’ve got a serious argument going here with Adam P., who understands what this argument is about. Please stop cluttering up this thread with your own agenda. Copy and paste it as a comment on the “asymmetric redeemability” post if you want. It belongs there.
The same fool @ 5:24 has been banned right here:
Suggest you do your readers a service and do the same now.
anon: thanks. I notice Gary Marshall has been posting almost identical responses to Billyblog as he has posted here, even though Bill and I have very different views on how monetary policy works. Which shows he totally ignores the content of anyone’s response to him. I’m deleting his comment.
Gary: please stay away.
On the same topic, you and Stephen may want to look at similar comments here. It’s a bit disturbing for the National Post to allow this:
http://network.nationalpost.com/np/blogs/fullcomment/archive/2009/10/21/stephen-gordon-economic-illiteracy-goes-viral.aspx
Ah.. credible communication. That magic mechanism that turns nothing into something.
Can anyone please point me to a mechanism by which monetary policy can take effect that has real balance sheet consequences for people today instead of requiring folks to clap and believe in Tinkerbell, that would be awesome.
Fundamentally, for there to be inflation, too many dollars have to be chasing too few goods. So, monetary policy either needs to actively destroy real (not financial) goods OR it needs to somehow convince people who are being crushed by their current debt loans to do some combination of taking on more debt and spending more on things other than debt service.
NICK: I think you and Summers will get more traction if you could point to something that is real enough to appear on a balance sheet instead of increasingly elaborate models that all boil down to people changing their savings preference because of expectations. If that really is all that monetary policy is boiling down now, then would a modern day Nostradamus claiming that the end of the world was nigh (so better start parting!) be conducting monetary policy? If he was convincing enough he might have more luck getting the private sector to start taking on debt again.
Hi Winterspeak!
By the way, one of your previous comments has been favourably noted here!: http://freethinkecon.wordpress.com/2009/11/15/a-pithy-response-to-the-panglossian-theory-of-monetary-economics/
“Fundamentally, for there to be inflation, too many dollars have to be chasing too few goods.”
Not exactly right. The way I would phrase it is this: “For there to be inflation, there would have to be too many dollars chasing too few goods if there weren’t inflation.” Inflation is what prevents there being too many dollars chasing too few goods (prices rise so the dollars are worth less, and now worth the same in total as the goods they are chasing). The equilibrium response of the endogenous variable (inflation in this case) eliminates the very excess demand for goods that causes it.
Yes, monetary policy works by increasing aggregate demand (shifting the AD curve to the right), so that people want to buy more goods. At the existing level of output and prices, there is an excess demand for goods, and an excess supply of the media of exchange (we live in a monetary exchange economy, where one good, the medium of exchange, appears in all markets). You can think of an increase in expected inflation creating this excess supply of money/excess demand for goods either via its direct effect on the real return on holding money, or via its indirect effect on real interest rates. (In this post, since I’m following a Neo-Wicksellian model, where the medium of exchange is only implicit, only the latter transmission mechanism is apparent.)
On interest rates and debt: I have done a number of posts on this topic in the past, and I’m not sure I want to re-enter this debate again (watch Too much Fed jump in here 😉 ), but here is the short version:
For every dollar borrowed there is a dollar lent. An increase in debt requires BOTH borrowers wanting to borrow more AND lenders wanting to lend more. If real interest rates fall, other things equal, borrowers want to lend more, BUT lenders want to lend LESS. It is this excess demand for loanable funds that creates the excess demand for goods, and the rise in AD, output, and prices. In principle, the level of debt could go either way, increase or decrease. And debtors’ ability to service debt, if income rises, is something else again.
A balance sheet shows you ACTUAL levels of assets and liabilities. It doesn’t show DESIRED levels of assets and liabilities. And it is the difference between actual and desired levels that creates the disequilibrium that changes in real output and prices eliminates. I just don’t find it generally helpful to view this sort of process through balance sheets (and I can never remember which side to put the assets and liabilities anyway!).
Nick, This model seems correct to me. The problem we face is making the “real bills” target operative. You know where I stand, but there are a variety of other options as well. These include foreign exchange baskets and commodity baskets. Neither is my preference, but both seem superior to equities. I’m not saying equities wouldn’t work, but the pricing of equities is very complex, and I think there is the risk of multiple equilibria. High stock prices are consistent with very sound macro policy (a la the 1920s and 1990s), but they are also consistent with high inflation. So, in order of preference:
1. NGDP futures
2. CPI futures
3. Forex (samll countries)
3. Commodity basket (big countries)
4. Equities
5. My house
If Adam is concerned about targeting equities, I share his intuition. But I think the model is correct. I don’t do math any more, so I’m not competent to evaluate how it compares to other models out there.
I hope you keep pursuing this issue. What is so fascinating is that the entire world economy may be screwed up because of a subtle intellectual puzzle that we’ve never quite grasped in the right way. Thought experiments like this get us steadily closer to the right way of addressing the issue. Perhaps someday nominal bills will be viewed as a barbarous relic of 20th century monetary policy. Wouldn’t it me ironic if nominal bills targeting was tripped up by the same problem as the gold standard: Deflation.
Nick said: “For every dollar borrowed there is a dollar lent. An increase in debt requires BOTH borrowers wanting to borrow more AND lenders wanting to lend more. If real interest rates fall, other things equal, borrowers want to lend more, BUT lenders want to lend LESS.”
Not exactly right. goldman sachs employees (extremely positive real earners) do not spend more when interest rates fall. They might buy a riskier financial asset (like a newly created piece of currency denominated debt).
In today’s wealth/income inequality world, borrowers with negative real earnings growth might want to borrow more. People who used to save but now need to borrow because of negative real earnings growth might want to borrow more (notice the more borrowers). And, the fewer and fewer with extremely positive real earnings want to lend more (especially if they think the fed/the gov’t will bail them out).
Notice that credit/debt is becoming more concentrated in fewer and fewer entities.
“BUT lenders want to lend LESS.” In today’s wealth/income inequality and bailout world, false but could be true in different circumstances.
Another idea I am thinking about is debt deflation (bad to defaulted debt) with the idea being the fed needs to create new debt/asset gains to make up for the losses when there are big blowups (S&L & others). If the excess savers sold debt to spend, wouldn’t that make things for some lenders worse?
scott sumner, where is real earnings growth for the lower and middle class on your list?
That way they could spend and pay down currency denominated debt and eventually save.
“I just don’t find it generally helpful to view this sort of process through balance sheets (and I can never remember which side to put the assets and liabilities anyway!).”
How about a real world example?
Xal-Mart decides to open colleges teaching economics. They want to be the low price leader so they get the gov’t to allow visa programs (or other ways to lower wages) and hire people for 50% of what people are being paid now. Eventually, everyone goes there for college. The people who were making more and had mortgages with assumptions of no Xal-Mart lowering their wage income during the 30-year mortgage now have a problem of making the interest payments. Do they borrow more and hope, default, or try something else?
Here is another one. What if the lower and middle class were a stock? What people say they have too much currency denominated debt and not enough (wage) income?
From:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/09/who-is-increasing-their-spending-debtors-or-creditors.html
How about “Who was increasing their spending – debtors or creditors?”
Lessons From The Fall: Household Debt Got Us Into This Mess
http://www.npr.org/blogs/money/2009/09/lessons_from_the_fall_househol.html
“Our research suggests that the historic growth in household debt preceding the financial crisis was the primary driver of the onset and deepening of the current recession.
The central lesson we as economists have learned from the crisis is that an unsustainable increase in household debt is one of the most serious threats to the U.S. economy.”
I SERIOUSLY doubt if anyone at the fed has learned anything from this.
Posted by: Too Much Fed | September 11, 2009 at 01:50 AM
Sorry if this is a repeat.
Nick: professional necessity. I earn my living writing software.
From:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/09/who-is-increasing-their-spending-debtors-or-creditors.html
About debt and inequality:
Here is one quote: “Now remember our original assumptions: Income inequality is large. Consumption inequality is smaller. So savings inequality must be huge.”
Posted by: Too Much Fed | September 08, 2009 at 01:46 AM
How about “currency denominated debt” inequality (as in many and many borrowers and fewer and fewer lenders)?
winterspeak said: “Ah.. credible communication. That magic mechanism that turns nothing into something.”
What if credible communication / expectations are wrong vs. reality?
Scott: I’m still not sure the model is doing all I want it to do. Adam P. may have a point (he’s a hard critic, but knows some stuff). The key is the relative importance of the forward and backward-looking elements in the IS-PC equation. I wanted to have a strong backward-looking element in order to model the deflationary death-spiral as happening slowly over time, rather than an instantaneous collapse to a zero price level. But a strong forward-looking element is needed to break the spiral by raising expected inflation, so that real interest rates fall while nominal interest rates rise. I’m wondering if I should have replaced y* with E(y(t+1) after all, despite the extra math, because that would certainly strengthen the forward-looking elements without violating the neutrality postulate that forward and backward-looking coefficients must sum to 1.
Partly it’s math; partly it’s intuition. Wish my brain were younger and keener. But I am going to keep working on it. The key point that a central bank’s ability to commit to future monetary policy depends on the “language” or framing in which such commitments can be made is a valid one. You can’t promise to lose a card game if the promisee doesn’t know whether “losing” means having the highest or lowest card on the table.
The nice thing about real bills, as a modelling device, is the direct parallel between real and nominal bills. Same ability of the central bank to target their price; same transmission mechanism to AD. That’s why I chose them. I’m unhappy about any good that cannot be stored in the basement of the Bank of Canada. Though in principle the Bank could buy houses, but going into the landlord business and collecting rents is not part of its comparative advantage. Clipping coupons is easier. Though there’s no difference in principle. But I don’t see the problem with targeting a share price index, and the Bank owning index mutual funds (except maybe shares traded in Canada aren’t really the same as shares of companies doing business in Canada).
I will keep pursuing this issue. Nominal bills will go the same way as the gold standard. “(Nominal) interest rate fetters” have a hold on our thinking in the same way that gold once did.
[Edit by NR. This comment by Warren should I think be understood as a (sensible) reply to a (not so sensible) comment by Gary Marshall that I deleted that was posted immediately above this. I just added this because it makes it easier to understand the context.]
the currency is a simple public monopoly
the price level is necessarily a function of prices paid by govt when it spends (and/or collateral demanded when it lends)
see ‘mandatory readings’ at http://www.moslereconomics.com
Nick,
you need to decide whether or not you mean for R to be a traded asset and if you want the CB to actually trade it. If R is a share index and the CB will actually buy and sell shares then that is one discussion. If it is just a price target and the CB adjusts the quantity of money to hit it then you haven’t really solved anything, which is my point. That’s what I keep trying to get you to see about Sumners futures targeting scheme, it solves none of the problems because it still works through the quantity of money.
Keep in mind that Euler equations don’t specify cause and effect, just an equilbrium condition. Thus, even if you think that changes in the money supply can have effects on behaviour through some other channel, changing the path of consumption/investment will cause the real interest rate to change because it changes the other side of the Euler equation.
Regardless what you think is the transmission mechanism, if you manage to change consumption/investment decisions then one or more of the following three things MUST have happened:
1) real interest rates changed
2) expected future output growth and/or risk of that output growth changed
3) people/firms stopped maximizing their objective functions
I assume you don’t want to claim that monetary policy can accomplish 3!!
Against the zero bound you can only accomplish 1 with higher inflation expectations and this reqires controlling expected future monetary policy. Changing expected future monetary policy can also change 2 but I repeat that now we are not just talking about the quantity of money today and so all the problems resurface. After all, the BoE had an inflation target and the UK is still in recession.
None of this has anything to do with the framing of monetary policy, Euler equations don’t care how you frame things. You are not being helpful here.
BTW, sorry I went all Gary Marshall on Sumner over the weekend but it’s getting annoying how he fails to see why his pet idea doesn’t solve anything at all but instead introduce more problems.
That said, what he’s been saying recently about the need for a price level/inflation target and need to commit to expansionary policy that actually accomodates some inflation once we start getting some is much better.
warren: Gary Marshall is a boor who breaks into a conversation, changes the subject, goes on at length with his own topic, then pays no attention to your answer to him. He has ignored requests to stop doing this, so I have deleted now 3 comments of his on this thread. At least one other blogger, BillyBlog, has banned him for doing the same thing.
I know you have made a genuine attempt to respond to him, and it’s to your credit, but so have I and others, several times. It just encourages him.
Adam P.
1. My model doesn’t specify whether the central bank trades nominal bills, real bills, and/or output. It has this feature in common with standard Neo-Wicksellian models. They are silent on this question.
The implicit assumption in a Neo-Wicksellian model is that the central bank does not trade output (so cannot target inflation directly) but does trade nominal bills (or trades something else that is a close substitute for nominal bills). Whatever that implicit assumption is about nominal bills in the standard Neo-Wicksellian model, I would like to make the same implicit assumption about real bills. I see them as parallel in this model.
2. From your list of 3, I want to go for 1 (I would like to go for 2 too, but that would mean adding more math to the model).
The Euler equations don’t care about framing, but they do care about expectations. And expectations care about framing. Commitments (as in Kydland/Prescott rules vs discretion) are promises. The interpretation of a promise (indeed, whether it can even be understood) depends on the framing.
Let me try another analogy, from micro. It is well known that the Bertrand equilibrium is generally different from the Cournot equilibrium. Yet the only difference is that firms’ strategies are framed as setting a price in Bertrand, and setting a quantity in Cournot. The framing affects how each player expects the other to respond to an out-of-equilibrium move. These out of equilibrium moves are never observed in equilibrium. Yet they affect the equilibrium.
I wish I had thought of that analogy before. What I am trying to do is to make that same point in a macro context.
In my Bertrand/Cournot analogy: assume firms have the same demand and cost functions whether it’s Bertrand or Cournot, of course.
But Nick, if you want to go for 1 then the whole point is that the key is getting people to believe that in the future you’ll stick to what your promising now. How you frame the promise is beside the point, any of the framings work if the CB is believed and none work if it’s not.
In your example everythign is driven by the CB failing to follow the Taylor Principle in the second case. So what does framing have to do with anything?
Adam: what do you think of the Cournot/Bertrand analogy? Isn’t that an example where framing matters? I think it definitely is, which means framing can matter in principle. I just(!) need to translate it into macro.
I wish my mind were clearer on this, but I think that the Taylor Principle coda is the bank’s attempt to play (say) Cournot, but the public doesn’t see the coda (because it is never observed in equilibrium), and the public thinks the bank is playing Bertrand. So we get the Bertrand equilibrium.
still thinking about the Cournot/Bertrand analogy, I don’t remember what’s the difference. But wouldn’t either framing require promises about future behaviour to generate increased expected inflation?
And if so, wouldn’t either work if the promis is believed and neither work if it’s not?
Nick: Thank you for your response (and the pointer). Again — I’m going to press you for a real mechanism that shows up on a balance sheet.
Your argument is that if interest rates fall, borrowers want to lend more, but lenders want to lend less. Why do lenders want to lend less? Lenders make money by making loans that get paid back. How do low interest rates reduce a profit maximizing lender’s desire to continue making as many good loans as they can subject to capital constraints, market demand, etc.?
Finally, spending a little more time on balance sheets would do a world of good. The gap between “actual” and “desired” did not slow you down in your extension of what causes inflation; similarly you can think about actual and desired in the balance sheet world. If the private sector has an desired target for net financial assets, and it is below that desired target in actual terms today, it will attempt to reach that target by increasing saving, which at a sector level reduced AD and makes that target even more impossible to achieve. This is the classic Paradox of Thrift. Monetary policy may or may not shift the private sector’s demand to collectively increase or decrease the size of its balance sheet, but it CANNOT impact the NET assets that sector holds. In other words, monetary policy is completely impotent at supplying net financial assets within the private sector. And if that is the disease, then monetary policy cannot be a cure.
Also, think operationally about that “expectations of future inflation” would mean operationally at the household level. It would change savings, or V in the quantity of money model. Now think about the forces driving household savings decisions today. (You can be even more radical and think what impact the massive reduction in interest income has had, but I’m not sure you’re ready for that level of Home Economics ; ) )
This savings element (net financial assets) is completely critical because it demolishes and quantity of money theory, and therefore the transmission mechanism in monetarism, and hence monetarism itself. Adam P is completely correct in this. Banks do not lend out savings. Savings just sit there, doing nothing. More savings do not enable more bank lending. And the best analogy I have for savings desire is as an endogenous factor (like WTP in Micro. It is what it is, and it changes as it wants to change). The FFR rate and ramblings by Greenspan, Bernanke, or whomever may impact savings desire, but so may wandering around with a sign saying “the end is nigh”, a slick TV commercial campaign, or a bout of extremely good (or bad) weather. Of you could, you know, actually increase savings through fiscal spending, but again, that’s too straightforward.
Adam P.: In the Cournot-Nash equilibrium, each firm (in a symmetric duopoly with imperfect substitutes, say) chooses q to maximise profit given the other firm’s q’. In Bertrand-Nash equilibrium, each firm chooses p to maximise profit given the other firm’s p’. The Bertrand equilibrium gives a lower price and higher quantity than the Cournot equilibrium, even if everything else is the same.
The intuition is that a firm’s demand curve, drawn taking the other firm’s p as given, is more elastic than the same demand curve, drawn taking the other firm’s q as given.
What matters is not whether a firm chooses p or q (there isn’t really any difference, since each firm is picking a point on its demand curve and you can define that point either way), but whether it expects the other firm to hold p fixed or q fixed if it were to deviate from the Nash equilibrium. If you assume Nash is the correct equilibrium concept, then it all comes down to how each firm “frames” the other firm’s decision, or how it “frames” the strategy space.
What I need to try to do is translate what I am saying about how people frame the central bank’s strategy space into the same kind of game-theoretic language. If I can show a parallel between the distinction between one or other target and the distinction between Bertrand and Cournot, I’ve got all the game theorists on my side.
If the promise to create more inflation were believed, this would mean nominal interest rates increased. So there’s a sort of paradox in promising to create more inflation by lowering nominal interest rates.
Winterspeak: Households choose a point where the marginal rate of substitution between present and future consumption equals 1+r. Firms chose a point where the marginal rate of transformation between present and future net output equals 1+r, where r is the real rate of interest. 1+r is like a relative price, and a change in r changes demand between present and future goods in exactly the same way that a change in the relative price of apples changes the demand between apples and bananas. When r goes down, households choose to consume more today, and firms choose to invest more today.
Absolutely orthodox economics. I can show it with indifference curves and budget lines. But I have no idea how to show it with balance sheets. It’s a substitution effect, not some sort of income, wealth, or balance sheet effect.
Nick:
Thank you for your clarification. In your model, you have households basing consumption/savings decisions based on tradeoffs between current consumption and discounted future consumption, with the discount rate being r (which I assume will be around the FFR, thus creating your mechanism between monetary policy and reality).
I have derived this in the standard ways in the past, so we’re on the same page.
The problem is it is a bad model when you include certain balance sheet conditions, conditions which are very apparent now. All balance sheets have assets, liabilities, and equity (or “savings”) which is in the liability column but is a good thing, and so does not carry the negative associations with equity. Assets – Liabilities = Equity.
Entities pick a degree of leverage they are comfortable with, or how much liability they balance on top of their equity. This preference can change — income to service debt starts to look less reliable, asset values no longer going up that much, etc. So, to reduce leverage, either assets and liabilities can start to get paid down/written off (debt deflation) and/or the sector tries to increase equity. But the sector cannot increase equity by itself, it is impossible by Accounting.
Consumption decisions between now and the future may be driven in part by discounting, but they are certainly also driven by preferences regarding equity and leverage. If the sector is working to reset its equity/leverage position (as is now) then low interest rates become impotent at best, and counterproductive at worst. If people just want more money in their bank account, you cannot get there through monetary policy.
(I’m pretty sure that the not sure if the discounting r model has applicability at the macro level either, but I’ll need to dredge up the old derivations. I believe that it disconnects price from income, which you cannot do at a sector level of course. Many micro formulations do not scale to the sector level, and I believe this is one of them, but I’ll need to double check)
Let’s stay focused on balance sheet effects by me asking you a simple question:
If the private sector wants more savings, (more net financial assets) would you agree that the only way it can get those is by fiscal policy (Govt deficit spending).
Thanks
saving is net financial assets plus gross real investment assets
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.
If desired savings increases (i.e. desired consumption falls), then the rate of interest falls until desired savings falls back to where it started (or desired investment increases, or some mixture of the two).
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.
Adam, I’ve always favored level targeting, indeed I made the argument in a published paper 10 or 15 years ago. I have emphasized it more recently than in the first few months, as we fall further below trend every day. I also think a lot of the Bernanke/Woodford inderterminacy problem relates to proposals for inflation rate targeting, but does not apply to price level targeting.
Nick, On further reflection stocks might work, if you had level targeting. My earlier comment about multiple equilibria reflected the fact that inflation hurts stock prices but higher price levels raise stock prices. In the real world (in real time) it is often not apparent whether a price level increase should be viewed as a rise in the inflation rate, or a one-time rise in the price level. So stocks prices could go either way. If you have level targeting (P or NGDP) it pins down the inflation rate. Then all price level increases would boost the price of real assets. That was roughly true under the gold standard, where expected inflation was roughly zero. That might make the system more stable than I first thought. I’m sorry that I lack both the time and brain cells to help you with the math.
Scott: if stock prices were the target, you would want to target a price level path, for the total return index (i.e. dividends reinvested) growing at (say) 7% per year. The main transmission mechanism would be via Tobin’s Q (if the price of output fell relative to the target price of stocks, Q would rise, so it would be cheaper to finance investment, so AD would rise).
One of the neat features would be that investing in the stock index would give you a risk-free nominal return over all holding periods. Stocks would become the ideal investment for widows and orphans! I bet that would get rid of the equity premium!
But like gold, I don’t think the real equilibrium stock price would be stable enough for it to work well in practice.
ANON: Yes, I’m focusing on financial assets, not real assets.
NICK: For someone who said they weren’t sure which side of the balance sheet assets and liabilities are, you are very quick to dismiss accounting entities. Accounting matters, particularly in finance.
Accounting identities are, in fact, stronger descriptions of the world than economic models like the ones you opened this post with. I’ve experience on both sides of this, so I’m not one of those guys who dismisses models out of hand. Nevertheless, people lose their homes over accounting, lose their jobs over accounting, make fortunes over accounting, go to jail (or gaol) over accounting and more. If I had to pick between an accounting identity and an economic model, I’d pick the identity. And if I’m talking about finance, accounting IS reality.
Desired savings CANNOT increase in the private sector unless the Government runs higher deficits, ie. fiscal policy. It does not matter what the rate of interest does. The mechanism for this is clear — either the number in your checking account lets you make your mortgage payment and you keep your house, or it doesn’t. Or, if you prefer, the number in your checking account lets you make payroll, or you fire all your workers. This is a real, solid lever that shows “expectations” to be the Nostradamus-on-the-street-corner stretch that it is.
I was not sure if you understood balance sheets or accounting well enough to see that interest rates cannot help a sector increase its net financial savings to a new target. But now it is clear, and it’s no wonder to me that you find balance sheet recessions so “mysterious”!
I really enjoy our exchanges on this blog and find them very fruitful. Thank you.
Winterspeak: “Desired savings CANNOT increase in the private sector unless the Government runs higher deficits,..”
Hold investment constant (or assume that by “savings” you mean “savings minus investment”). Assume closed economy.
Then I would say that DESIRED savings CAN, but ACTUAL savings CANNOT, increase unless the government runs higher deficits.
“I was not sure if you understood balance sheets or accounting well enough to see that interest rates cannot help a sector increase its net financial savings to a new target.”
Given the above assumptions. A rise in interest rates indeed cannot help households increase actual savings (holding govt. deficit constant). The purpose of a fall in interest rates is precisely to stop households wanting to save more. (They want to save more, so interest rates fall until they stop wanting to save more.)
Nick: “If the promise to create more inflation were believed, this would mean nominal interest rates increased. So there’s a sort of paradox in promising to create more inflation by lowering nominal interest rates.”
No, longer term nominal rates increase, short term INTER-BANK nominal rates don’t. There is a term structure to expected inflation, it’s future inflation that is being promised here. Current inflation, the rate of inflation that prevails for the life of an overnight loan or 2 week repo is unchanged.
Furthermore, by supplying enough money the CB can always lower real rates (even the longer term ones) because just as inflation lowers the real return on a nominal interst loan (and thus encourages lenders to ask for higher interest rates) there is the offsetting effect that inflation makes it more costly to keep the cash sitting idle earning nothing (velocity increases). Of course, lowering the longer term real rates does require that the extra money growth be expected to continue through the life of the loan.
Nick, just to finish the last thought. If the Fisher effect held completely and immediately then money would be completely neutral because real rates would never change (as a result of monetary policy that is).
This is true no matter what you think of the transmission mechanism because it would leave only option 3 above (my comment at November 16, 2009 at 06:38 AM) and monetary policy can’t make people stop trying to maximize their objective functions.
This is a point that Scott Sumner appears not to understand as he seems to think money can be non-neutral and the Fisher effect hold completely. He got this badly wrong in a small minded and incorrect critique of Keynes a while back.
“I’m focusing on financial assets, not real assets”
I’m focusing on your arbitrary exclusion of the rest of savings; i.e. I = S.
Desired savings CANNOT increase in the private sector unless the Government runs higher deficits
Not if more I is produced at the same time. You actually believe that CANNOT happen?
Nick, I don’t think your Bertrand/Cournot analogy helps you here. The differnce is not due to framing, it’s due to differences in reaction functions. In your example though the market demand curve for the product is constant (this is what generates the differences in reaction functions). What you would need is an example where the framing actually changes the market demand curve. In neither the Bertand game or the Cournot game can the players induce the market to accept a (p,q) pair that is not on the market demand curve.
In the macro case the market demand curve traces out current demand for goods (AD) against it’s relative price where price is relative to future goods. The CB can’t get the private sector accept a (quantity, relative price) pair off that demand curve. But relative price means real rate here! Framing has nothing to do with anything.
Your monoplist example was better, one supplier and one market demand curve. But then whether you say that the monopolist chooses price or quantity (how you frame the problem) doesn’t change the outcome.
Nick:
“Then I would say that DESIRED savings CAN, but ACTUAL savings CANNOT, increase unless the government runs higher deficits.”
Yup, you are correct. If actual savings fall below desired savings, AD will continue to fall as the private sector tries (and fails) to reach its desired savings level. If there is nominal debt in the economy, you’ll get debt deflation.
If the private sector is overly leveraged, then a fall in interest rates will not reduce their desire to save, as it’s driven by balance sheet considerations, and not interest income. That’s my point. Moreover, if AD is falling, then the desire to save more becomes HIGHER, swamping out any effect lower interest rates may have. Lower interest rates start working in reverse as they rob the sector of interest income which could be saved, thus undermining AD further. By savings, I mean the financial assets listed in the equity column on the liability side of the balance sheet. This is net investment, as investment is someone else’s income and savings is not.
I think you understand the model now, but may not agree that it is applicable to our current situation.
ANON: I did not arbitrarily exclude I. In a closed economy Y = I + C + G. So, G-T = Y – I – C – T. Including an export sector does not change this materially. I, like C, is someone else’s income, so is net of savings which is no one else’s income. I passed on Nick’s characterization because it is not critical to the concept.
I hope this makes it clear why the private sector’s net financial assets CANNOT increase unless there is deficit spending. The private sector balance sheet, of course, can expand to any size if it makes more inter-sector loans, or collapse down to just its net financial position, which precisely equals the National Debt.
ADAM P: Thank you for keeping the focus on the core mechanism. If interest rate does not change savings demand, and there are LOTS of factors that impact private sector savings demand, then monetary policy is impotent if (unfunded) savings demand is decreasing aggregate demand.
“I did not arbitrarily exclude I”
You did – you say the only way private sector can increase saving is by increasing net financial saving – which is not true.
Net financial saving = government deficit is obvious; but not full story for private sector saving
“By savings, I mean the financial assets listed in the equity column on the liability side of the balance sheet. This is net investment, as investment is someone else’s income and savings is not.”
makes no accounting sense
Winterspeak: ” If actual savings fall below desired savings, AD will continue to fall as the private sector tries (and fails) to reach its desired savings level. If there is nominal debt in the economy, you’ll get debt deflation.”
Not necessarily. That’s the simple Keynesian mechanism by which desired savings adjusts to actual savings (income falls until they are equal). The alternate classical mechanism is that the real interest rate falls until they are equal. Or you can have a mixture, where both y and r fall. Usual assumption is that the classical is true in the long run, when prices are flexible, but a mixture is true in the short run, when prices are fixed, depending on monetary policy.
You are using the words “saving” and “investment” in different ways than economists, but that’s OK, as long as we remember which version we’re using (or make simplifying assumptions like ignoring investment so they end up the same).
“I think you understand the model now, but may not agree that it is applicable to our current situation.” Man, I learned that simple Keynesian model in high school nearly 40 years ago, and have taught it God knows how many times!
“Lower interest rates start working in reverse as they rob the sector of interest income which could be saved, thus undermining AD further.”
Two points:
1. The main effect of real interest rates on desired savings (and investment) is a substitution effect, not an income effect. And I’m not sure if you understand that that’s my reason why r affects S and I.
2. In a closed economy, no government, there is NO income effect from a change in interest rates (though there may be a distribution effect if opposing income effects on different people do not wash out in aggregate, because of different marginal propensities to consume across different people). For every borrower who is better off when interest rates fall, there is a lender who is worse off. It washes out, unless they have different mpc’s. Some economists don’t understand that. But I do, and have done so for several decades.