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There's no getting away from the fact that you can't find an optimal rule without the 'true' model; and you can never have the true model, because it's Joan Robinson's map on a scale of 1:1 which is no use to anybody. I'm pleased to see the Friedman zero-nominal-interest-rate rule enter the discussion, courtesy of Stephen Williamson. That points to what strikes me as the most sensible answer: use powerful automatic fiscal stabilisers so that interest rates are kept consistently low.


Friedman's rule leads to zero rates only because he was writing about a world with no interest on reserves. In a world with interest on reserves, it reduces to ffr = ior. Friedman wanted marginal cost (hence zero) pricing of liquidity, but form the perspective of modern central banking, had a slightly warped view of what constitutes liquidity itself. In modern frameworks, interest rate policy can be viewed under the Wicksellian framework ( + Tobin's q) and liquidity policy can then be viewed under the Friedman rule hypothesis, where central bankers like Goodhart would argue that the strategic benefits of finite elasticity i.e. non zero liquidity costs outweigh the deadweight losses of the pricing at a markup to marginal cost.

Automatic fiscal stabilizers (which would stabilize the real rate presumably) only help in maintaining the nominal rates constant and low only if trend inflation has simultaneously been perfectly targeted by the central bank. So you don't need a nominal rates policy separate from an inflation rate policy. And then they have the problem of the lack of a nominal anchor.

Kevin: "That points to what strikes me as the most sensible answer: use powerful automatic fiscal stabilisers so that interest rates are kept consistently low."

If you are talking about keeping *real* interest rates *consistently* (i.e. permanently) low, you aren't talking about automatic stabilisers, which is about getting changes in T and G when Y and P change. You are talking about permanently high T and/or low G. Depending on the model, you might end up with a negative debt/GDP ratio, and the government owning everything! (It's the old "fiscal conservatism, carried to extremes, ends up in communism!" argument.

If you are talking about keeping *nominal* interest rates permanently low, you end up with the central bank owning everything.

Nick, Great post. I completely agree. George Selgin did some work on this and claimed NGDP targeting was the fairest to debtors and creditors.

If I understand this correctly, monetary policy in the "insurance view" is supposed to make all nominally fixed debt more like equity - sharing gains and losses with stakeholders. Isn't there some Modigliani-Miller and EMH reason why that can't be optimal?

If risk aversion led both creditors and debtors to prefer to smooth the real value of the contract they have between them, why wouldn't they just include some equity features in the first place: "If the creditor does badly, this repayment will increase in value by 0.5x(percentage change in creditor's wealth)".

Of course, there are transaction cost, asymmetric information and money illusion reasons why it might be optimal to do the debt-to-equity conversion of contracts at the currency union level. But then, shocks do not hit everyone equallly, so stakeholder-specific equity-like agreements might be preferable - if neither one of the parties to an agreement has been affected by a shock, leaving their nominal repayment unchanged seems preferable.

In short, in this simplified model, why wouldn't contracts be optimally "equity-like" without monetary policy adjusting the price level?


In this matter I have (as Stephen Williamson would say) taken Jean-Pascal Bénassy as my personal saviour: in particular this paper (PDF). Mind you I'm under no illusions about him wanting the likes of me as a disciple. Also, obviously, discussions of this kind are far removed from practical politics. But then Scott Sumner's notion of a NGDP futures market under the sway of a central bank isn't practical policy either.

The CB doesn't end up owning everything in that Bénassy model because it starts writing cheques as soon as inflation drops below its target level (which typically is negative to ensure i=0).


In an earlier post you mentioned the issue of several interest rates on different goods.

But I think a more relevant and pervasive problem is different interest rates to specific sectors, such as chinese financial repression (say a government owned bank lends at below market rates).

Assume this paralel banking system comprises half the total lending. What are the implications for the level of the policy rate?


Hmmm. I'm a little surprised i didn't get more pushback on this post. Not that I'm complaining. I took quite a flyer when I said "This is what is really going on in David's model".

Nobody challenged me to say "No, you misunderstood David's model".

And nobody challenged my guess, saying "OK, you've got David's model right, but your guess about which benchmark is closest to the real world is way off; there are good reasons to believe that aggregate real shocks affect the gross wealth of creditors more than debtors, so NGDP targeting is a bad policy from that POV".

Thanks Scott!

Delfim: Off-topic (comments on the own-rate post are still open) but never mind. I think it would be like a mixture of a tax and a subsidy on saving and investment. There will almost certainly be an effect on the policy rate needed to hit a particular target, but I don't think we could say whether it causes that rate to go up or down without knowing a lot more. It depends.

Very good post. After reading the first David's post I was perplexed and had an urge to immediatelly write something about this part

"The intuition is this. When the news is bad concerning the future return to investment, it is optimal for investment to contract (and for savings to flow into more stable return vehicles, like government securities)."

My intuition was completely different. And then I saw that Bill basically said everything I wanted to say - that is this OLG model is at best irrelevant to the whole issue, as real interest rate on government bonds would have to equalize the lower expected capital gains for younger generation. Or alternatively, if young generation can really consume only when they are old and only consumer goods that are produced while using capital goods that they are going to accumulate for the still unborn generation, it has to be better for current young to actually invest into something real instead of buying worthless pieces of paper that do not contribute in any way to the long term aggregate supply. If investing into capital goods that are going to produce consumer goods next generation has negative yields, maybe they can invest into capital goods that are going to be used to produce future capital goods that in turn are going to have positive return? I really have to admit that I do not understand what David meant.

Then the second blogpost David seems to have a quite complicated way of saying that what we really have is an economy capital and money. Then he says a weird thing in teh context of the whole article:

"Now, let me describe how this economy behaves over time, assuming a "passive" government policy of keep the nominal supply of debt fixed."

So we not only fix the interest rate of so called "debt" but we also its fix its "supply" that I understand as quantity supplied. To be honest I find it very confusing that David uses debt and money interchangably as it needlessly muddles things especially when he calls for price level targeting that would surely be quite hard if there are only two goods (money and capital) and if the quantity of one of those goods (money) is to be kept stable.

Anyway, this whole debate reminded me this very good article by David Eagle about NGDPLT being better then PLT from welfare point of view (after I found the link I realized that commenter 123 already linked it in the discussion under David's article without any response): http://marketmonetarist.com/2012/01/20/guest-blog-the-two-fundamental-welfare-principles-of-monetary-economics-by-david-eagle/

JV: Thanks!

I confess I found it very hard to get the intuition behind David's model, and, more importantly, the intuition behind why his model was giving him the result that PLP was best. It's one thing to be able to solve a model (though that's hard enough, and that's what we spend most of our time teaching); it's another thing to understand it.

And it is a fascinating model, just because of those two shocks, and how the first shock is simply news about the second shock, where the news is imperfectly accurate. But those two inter-related shocks makes it hard to get your head around.

My interpreting his result as an optimal insurance policy is a conjecture. There has to be that aspect to it. But there's just a chance I'm missing a second aspect. Because it's an OLG model with a dynamic inefficiency (without govt bonds the real interest rate would be below the growth rate) so a Ponzi scheme is sustainable and welfare-improving. And those shocks affect the real interest rate and growth rate, at least temporarily, so might require the optimal amount of Ponzi-finance to expand and contract in response.

Yes, I find it easier to interpret the asset as "bonds" rather than "money". And think of what the government is doing in his model as fiscal policy rather than monetary policy. But I let that bit go, because I wanted to focus on the wider question. But some people do use OLG models as models motivating monetary exchange. I can only accept that if we interpret "generation" very metaphorically. What matters is that young and old can meet once but never meet again, because the old will be dead. But if people meet randomly or anonymously in the forest you get the same result, and the same motivation for money.

Nick: Yes, what you says makes sense for me. Maybe it would be better to look at things in a way David Eagle did in his article I linked. He differentiates between "bad" aggregate demand induced inflation(deflation) and "good" aggregate supply induced inflation(deflation). What Andolfatto seems to be implying is that he operates with unexpected aggregate supply inflation/deflation (productivity shock). If we have NGDPLT then risk of unexpected shocks to aggregate supply will be spread between creditors and debtors. This is a Pareto improving measure in real terms and it has to be a better policy that agents would agree if they did not know about these schocks. As we know from reading MM blogs NGDPLT maintains the "bad" aggregate demand inflation/deflation at minimum so we may even forget this.

I appreciate Scott's reference to my work on this topic, but would say that my position isn't so much that NGDP is the most "fair" policy--I'm not sure in any event that there's any such thing--but rather that the common claim that any fluctuation in P involves "unfair" redistribution of wealth between debtors and creditors falls apart when the movement is based on AS rather than AD shocks. (That this is so is most painfully obvious in the case of adverse AS shocks, where foolishly consistent proponents of price level stabilization or zero inflation would have it that we should protect the interest of creditors by engineering a decline in nominal incomes! But it is equally true for positive AS shocks.)

More to the point, everything that's being hashed out again here and in the works cited is very old hat: a wheel is being wastefully reinvented. I urge everyone who hasn't to have a look at my 1995 HOPE paper (which goes into the history of thought much more than my Less Than Zero does), "The “Productivity Norm” versus Zero Inflation in the History of Economic Thought." Here I quote from a long list of economists who, prior to the Keynesian avalanche, recognized the points Nick makes here--and very explicitly, I should add. Certainly it is time to stop imagining that the distinction between "good" (AS based) and "bad" (AD based) changes in the price level is a MMT discovery!

George: what's the saying: "Those of us who never learn history are condemned to repeat it"?

Yep. A whole lot of interesting ideas (especially interwar stuff) got lost in the Keynesian avalanche. Just like a lot of interesting ideas got lost in the later Lucasian revolution. Sometimes I wonder if the whole point of scientific revolutions, a la Kuhn, is so students can say "Thank God, it means we can ignore reading all that old stuff because it assumes full employment/sticky prices/irrational expectations (take your pick for the excuse depending on the revolution in question)".

But sometimes, just sometimes, it is quicker and easier to just re-invent the wheel than to hunt through the library to find the old blueprints and try to figure out what they say.

Indeed, Nick, once a good set of arguments has been neglected long enough, rediscovering them can be as much or more work than coming up with them from scratch. But as I've done the necessary slogging already, I think many people can benefit, with little cost to themselves, by discovering second-hand the care with which past authorities, from Samuel Bailey to Dennis Robertson, addressed the issues being considered here.

For my part, I found it most helpful to treat the matter as boiling down to this question: In a world in which P (or the inflation rate) is assumed to be unchanging, is it necessarily correct to suppose that, if P does change over the course of a loan, parties to the loan, had they possessed perfect foresight, would have settled upon a different (fixed) nominal interest rate than the one that their imperfect foresight led them to? The answer is that it isn't, the exception being cases in which unanticipated innovations to P are linked to opposite unanticipated innovations to y. In that case we have not one but two incorrect forecasts, one of which, considered alone, causes i to be set too low, while the other causes it, ceteris paribus, to be set too high. The mistakes therefore cancel. A corollary is that, where the monetary authority to attempt to "protect" the parties by preventing the P innovation, while still allowing them to be surprised by the innovation to y (which it is of course powerless to prevent), it would in fact cause them to regret fixed debt agreements that they might not have regretted otherwise.

Fisher himself understood this, by the way.

By the way, Nick, it occurs to me that your argument with D.A. very much resembles my exchange with Kevin Dowd in the J. Macro some years ago. Kevin, like David, invoked a very special (and utterly unrealistic) case to argue for zero inflation as against my productivity norm, and I took him to task for doing so.

[edited to fix link NR]

George, you seem to suggest that I believe in PLT and that the reason I do so is because it turns out to have some desirable properties in my simple model. Moreover, you seem to suggest that Nick has rightly taken me to task for this. If this is what you are suggesting, you understand very little.

Sorry, I forgot to sign in. That last post by "David" was by me.

Nick, I am still mulling over your assessment of my model. One thing that struck me was your claim that the model result was a complete fluke. That may be true, but notice that one can only make such a claim against a model that has been formalized the way I have done. I will never be able to make the same claim against you because, well, I am never really sure about the full set of assumptions you are employing to make the case for NGDP targeting.

David, I apologize for the implication, which was quite unintentional. I ought to have made it clear that "your model" supplied a case for PLT, rather than suggesting that you yourself "argued" for PLT, and that it was Nick's "observations regarding the advantages of PLT implied by your particular model" that resemble those I made regarding Kevin Dowd's arguments for PLT."

Nick:"David's case is somewhere between my 1 and my 3."

I think David's case is your case 3 with one debtor (government) and two creditors (young and old). He says "the bad news event causes a surprise drop in the price-level ... The decline in the price level makes the real value of nominal government debt more expensive" in the first post, so there is positive indexation of the price level to the real shock, and the debtor does share in the gains and losses. However, the object function in his model is not to equalize the gains and losses of creditor and debtor. It is to equalize the gains and losses of two creditors. I think that's where his model deviates from your classification.

Nick and everyone else: thank you for your feedback (George, I apologize for being so sensitive.)

Some of you are interpreting the OLG structure too literally. Woodford has shown that OLG dynamics are present in even "standard" models with debt constraints; see Stationary Sunspot Equilibria in a Finance Constrained Economy (Woodford, Journal of Economic Theory, 1986).

The basic intuition of the model is (or should be) very simple: When the news over future capital returns is bad, people rationally substitute into government money (I do not make a distinction here between interest-bearing and non-interest-bearing money.) The increase in the demand for money leads to a surprise drop in the price-level. If debt is nominal, the real burden of the debt increases. This leads to a decline in the purchasing power of a large class of individuals (investors, in my model). This "debt overhang" problem is something that Krugman and others make a big deal about. I'm not sure why Nick is somehow suggesting it is "small potatoes" (not his words, but that's the impression I get.)

In the event of a bad news shock, the economy "wants" lower capital expenditure. It "wants" a lower future real GDP (at least, in expectation). Stabilizing (in the sense of holding constant) the NGDP in this context makes no sense.

Now maybe you want to argue that this is not the type of shock that hit the US economy. Fine. Then tell me what sort of shock did, and I'll model it for you. (I am working on a version of the model with "liquidity shocks"--the shocks that David Beckworth seems to like.)

Maybe you want to argue that a price rigidity is important. Well, I did model that. I assumed a "sticky" nominal debt. Guess what? It didn't work.

OK, so now you want to argue that a nominal wage rigidity is important. OK, I can do that too. Give me some time. But really, I think you are confused in your interpretation of nominal rigidities. I explain why here: http://andolfatto.blogspot.ca/2010/07/sticky-price-hypothesis-critique.html

Nick, you say that you do not want to formally model things and that there is a time for "intuition." My reply to that is: screw it. I've had enough "intuition." It's time to get serious and write down some theory. I do not mean this exercise to be a substitute for intuition -- I mean for it to be a complement. But there is clearly not enough of it, in my view.

Thanks again for taking the time to comment--I really do appreciate it.

"When the news over future capital returns is bad, people rationally substitute into government money (I do not make a distinction here between interest-bearing and non-interest-bearing money.)"

Maybe there are two types of bad news. One is that actually brings down future capital returns no matter what you do. The other is a kind of self-fulfilling prophecy that doesn't materialize if you supply people with enough money and make them confident by targeting NGDP, but does bring down future capital returns if you do nothing. In this context, the question you want to ask would be: If the former type of bad news arrives with probability 1-p and the latter with p, what p value justifies targeting NGDP all the time ?

David: I'm going to respond to this bit in particular, both because it's important, and because we might get somewhere:

"Maybe you want to argue that a price rigidity is important. Well, I did model that. I assumed a "sticky" nominal debt. Guess what? It didn't work.

OK, so now you want to argue that a nominal wage rigidity is important. OK, I can do that too. Give me some time. But really, I think you are confused in your interpretation of nominal rigidities. I explain why here: http://andolfatto.blogspot.ca/2010/07/sticky-price-hypothesis-critique.html"

Suppose you and I haggle over a wage, and I agree to supply you with 10 hours of my labour next year and you agree to pay me $100 next year. When next year rolls around, conditions have changed unexpectedly, but my wage of $10 hour is fixed.

I would not call that a sticky wage model.

Even if there is a law (or something) saying we can only make that agreement in $ terms, and can't index it to anything, I still do not call that a sticky wage model.

I do not call your model a model with nominal rigidities. (I also got into an argument with Steve Randy Waldman when he called fixed nominal interest rates on long-term debt "the stickiest price"). And it's for exactly the same reasons that Barro talks about in that 77 paper you reference in your post last year you link to here.

Once a contract has been signed to deliver a *specified quantity of goods* at a specified price, that price is no longer a "price" in the economic sense of the word. Because it has no effect at the margin on quantities demanded or supplied. Economically, it is just a transfer payment, not a price which measures the marginal cost or benefit of any current decision I make. If the economy started from scratch today, the only way those old contracts affect the current and future equilibrium is in the same way that changes in the endowment affect the current and future equilibrium. They *are* changes is the endowment. My endowment is $100 bigger and 10 hours labour smaller than it otherwise would be.

If instead we sign a contract this year that says my wage working for you next year will be $10 per hour, but you and I can choose next year however much we want to buy and sell at that wage, but cannot buy and sell at any other wage, now *that's* a sticky wage economy.

Funny how that 1970's literature is still so important. You and I both read that same Barro 77 paper. And we went off in different directions after reading it. You said (I think) "OK, so that's how we can think about nominal rigidities". And I threw away all my notes and copies of Azariades, Bailey, and Gordon, (which I was always suspicious of because I suspected something like Barro 77 was what was going on underneath) and started thinking about nominal rigidities from scratch again. (And failing, of course).

For a model that "proves" NGDP targeting is best:

1. AD: Y=M.V/P

2. Production function: Y=S.L^alpha

3. Labour supply L=(W/P)^beta

4. Nominal wage rigidity: W(t)= A.E(t-1)[W*(t)] where W*(t) is market-clearing wage, and A is some constant greater than one.

5. L=Ld (demand-determined employment)

Where V and S are iid shocks.

I think that will work, if you set alpha and beta to the right values, and if I've rigged the functional forms right.

The intuition is that a positive shock to productivity S means that the economy "wants" a higher level of Y and W/P, but the only way to get W/P to rise is if P falls as Y rises, since W is fixed.

Thanks for this Nick.
Let me work on it; will get back to you soon(er or later).

Nick, after quickly glancing through your model above, I do have a few clarifying questions.

[1] Your "aggregate demand" function Y = VM/P.

The assertion built into this behavioral equation is that the aggregate demand for goods and services depends primarily on the household's sector real cash balances (at least, for fixed V).

I just want to make sure that you want me to take this seriously. Cash is such a tiny fraction of household wealth, and the contemporaneous demand for output surely depends on forecasts of future income, etc. Maybe I'm just asking you for your favorite defense of this behavioral assumption (e.g., is it a good approximation for some questions and if so, why?)

[2] The market-clearing wage W*(t). I think you mean this to be the *real* wage, not the nominal wage, right? And if so, then your nominal wage adjustment formula seems not quite right.

[3] The nominal wage adjustment formula says something like "the contemporaneous nominal wage is determined by last period's expected nominal wage." But if your shocks are i.i.d., as you assume, I guess that this expected nominal wage must never vary over time, correct?

David - Nick's away for a few days - Frances

What?! Nick takes vacations?! Thanks, Frances. Hope we get a chance for coffee on your western tour.

Hi David: Yep, I took a few days away. Lovely to be swimming in Lake Huron in this weather.

1. No, I don't take that AD function seriously. I just wanted something very simple, because the exact AD function doesn't matter for this question, just as long as the central bank has some effect on AD. (The main thing it misses is the effect of expected future M, but if you read "M" as some sort of index of current and expected future central bank actions it works OK).

Oh, I should have written it as Y(t)=M(t).V(t)/P(t), but you probably figured that.

2. W*(t) is the market-clearing *nominal* wage. You can re-write W*(t) as R*(t).P(t) if you like, where R*t) is the market-clearing real wage.

Nominal wages are set one period in advance, based on the expected future market-clearing real wage and the expected future price level.

(You can ignore that constant term A if you like. I only stuck it in there so that wages would almost always be set above the market clearing level, so we were always on the demand-side of the labour market, so I didn't have to justify L=Ld.)

3. Yep, if the shocks to V(t) and S(t) are iid, then W(t) will be constant over time, unless M(t) growing over time.

BTW, this model is roughly JoAnna Grey's old model. I don't take the sticky wage/perfectly flexible P assumption literally, but I think it gives a slightly better approximation of the stickiness that matters in the face of real shocks than the alternative sticky P/flexible W model of the standard NK model.

Nick, I believe I have worked things out (sufficiently to understand your point). Let me see if I understand you correctly.

First, consider a basic model in which the classical dichotomy holds. For fixed vM, the supply shocks cause RGDP to vary over time (with the price level moving opposite to output). As NGDP (vM) is fixed by assumption, it follows that a fixed NGDP is consistent with "full employment" in the face of "supply shocks."

Now let's suppress the supply shocks and instead hit the economy with your "demand" shocks -- the shocks to "velocity." The RGDP remains constant and, for fixed M, the NGDP varies over time. However, one may, without loss, offset the velocity shocks with changes in M to keep NGDP constant. This outcome too is consistent with "full employment," in this case, in the face of "demand shocks."

Conclusion: One may, without loss, target the NGDP. If the economy works well, the NGDP target is innocuous. If it doesn't, then the policy improves the allocation.

Alright, I can see the logic in this. But really, I do not see how one can attach so much confidence to the prescription, the way you and Scott appear to, on the basis of this model.

The main problem I have with your model is in how you model your "demand shocks." What are these things? If they are simply representing the effects of irrational psychology, then I can see the desirability of mitigating their adverse affects. I mentioned this in my original post.

However, what if there are "fundamental" reasons for (say) the shift in velocity? In my model, this fundamental reason took the form of information about *future* productivity. IF that is what is causing velocity to shift (and who is to say it isn't?), then the prescription of stabilizing NGDP in the face of a "velocity shock" may not be desirable. If information arrives that leads the business sector to rationally revise downward its forecast of investment return, then perhaps real and nominal spending should decline.

In the model I studied (the one with nominal debt), some NGDP stabilization was desirable (keeping the price level fixed was desirable). But full NGDP stabilization, as in your model above, leads to "excessive" wealth redistribution in my model. I find these differences interesting and worth exploring.

So my question now boils down to this: What is causing AD to fluctuate? I want a deeper explanation for your v shocks. I do not believe that the optimal policy is invariant to the nature of this shock. This is perhaps where you (and Scott) differ most from my view. Thanks!

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