Thursday, November 13, 2014

Neo-Fisherians: Unite and Throw off MV=PY and Your Phillips Curves!

I've noticed a flurry of blog activity on "Neo-Fisherianism," and thought I would contribute my two cents' worth. Noah Smith drew my attention to the fact that Paul Krugman had something to say on the matter, so I looked at his post to see what that's about. The usual misrepresentations and unsubstantiated claims, apparently. Here is the last bit:
And at the highest level we have the neo-Fisherite claim that everything we thought we knew about monetary policy is backwards, that low interest rates actually lead to lower inflation, not higher. At least this stuff is being presented in an even-tempered way.

But it’s still very strange. Nick Rowe has been working very hard to untangle the logic of these arguments, basically trying to figure out how the rabbit got stuffed into the hat; the meta-point here is that all of the papers making such claims involve some odd assumptions that are snuck by readers in a non-transparent way.

And the question is, why? What motivation would you have for inventing complicated models to reject conventional wisdom about monetary policy? The right answer would be, if there is a major empirical puzzle. But you know, there isn’t. The neo-Fisherites are flailing about, trying to find some reason why the inflation they predicted hasn’t come to pass — but the only reason they find this predictive failure so puzzling is because they refuse to accept the simple answer that the Keynesians had it right all along.
Well, at least Krugman gives Neo-Fisherites credit for being even-tempered.

Let's start with the theory. Krugman's claim is that "all of the papers making such claims involve odd assumptions that are snuck by readers in a non-transparent way." Those sneaky guys, throwing up a smoke screen with their odd assumptions and such. Actually, I think Cochrane's blog post on this was pretty clear and helpful, for the uninitiated. I've written about this as well, for example in this piece from last year, and other posts you can find in my archive. More importantly, I have a sequence of published and unpublished papers on this issue, in particular this published paper, this working paper, and this other working paper. That's not all directed at the specific issue at hand - "everything we thought we knew about monetary policy is backwards" - but covers a broader range of issues relating to the financial crisis, conventional monetary policy, and unconventional monetary policy. If this is "flailing about," I'm not sure what we are supposed to be doing. I've taken the trouble to formalize some ideas with mathematics, and have laid out models with explicit assumptions that people can work through at their leisure. These papers have been presented on repeated occasions in seminars and conferences, and are being subjected to the refereeing and editorial process at academic journals, just as is the case for any type of research that we hope will be taken seriously. The work is certainly not out of the blue - it's part of an established research program in monetary and financial economics, which many people have contributed to over the last 40 years or so. Nothing particular odd or sneaky going on, as far as I know. Indeed, some people who work in that program would be happy to be called Keynesians, who are the only Good Guys, in Krugman's book.

So, let me tell you about a new paper, with David Andolfatto, which I'm supposed to present at a Carnegie-Rocheser-NYU conference later this week (for the short version, see the slides) . This paper had two goals. First, we wanted to make some ideas more accessible to people, in a language they might better understand. Some of my work is exposited in terms Lagos-Wright type models. From my point of view, these are very convenient vehicles. The goal is to be explicit about monetary and financial arrangements, so we can make precise statements about how the economy works, and what monetary policy might be able to do to enhance economic performance. It turns out that Lagos-Wright is a nice laboratory for doing that - it retains some desirable features of the older money/search models, while permitting banking and credit arrangements in convenient ways, and allowing us to say a lot more about policy.

Lagos-Wright models are simple, and once you're accustomed to them, as straightforward to understand as any basic macro model. Remember what it was like when you first saw a neoclassical growth model, or Woodford's cashless model. Pretty strange, right? But people certainly became quickly accustomed to those structures. Same here. You may think it's weird, but for a core group of monetary theorists, it's like brushing your teeth. But important ideas are not model-bound. We should be able to do our thinking in alternative structures. So, one goal of this paper is to explore the ideas in a cash-in-advancey world. This buys us some things, and we lose some other things, but the basic ideas are robust.

The model is structured so that it can produce a safe asset shortage, which I think is important for explaining some features of our recent zero-lower-bound experience in the United States. To do that, we have to take a broad view of how assets are used in the financial system. Part of what makes new monetarism different from old monetarism is its attention to the whole spectrum of assets, rather than some subset of "monetary" assets vs. non-monetary assets. We're interested in the role of assets in financial exchange, and as collateral in credit arrangements, for example. For safe assets to be in short supply, we have to specify some role for those safe assets in the financial system, other than as pure stores of wealth. In the model, that's done in a very simple way. There are some transactions that require currency, and some other transactions that can be executed with government bonds and credit. We abstract from banking arrangements, but the basic idea is to think of the bonds/credit transactions as being intermediated by banks.

We think of this model economy as operating in two possible regimes - constrained or unconstrained. The constrained regime features a shortage of safe assets, as the entire stock of government bonds is used in exchange, and households are borrowing up to their credit limits. To be in such a regime requires that the fiscal authority behave suboptimally - basically it's not issuing enough debt. If that is the case, then the regime will be constrained for sufficiently low nominal interest rates. This is because sufficient open market sales of government debt by the central bank will relax financial constraints. In a constrained regime, there is a liquidity premium on government debt, so the real interest rate is low. In an unconstrained regime the model behaves like a Lucas-Stokey cash-in-advance economy.

What's interesting is how the model behaves in a constrained regime. Lowering the nominal interest rate will result in lower consumption, lower output, and lower welfare, at least close to the zero lower bound. Why? Because an open market purchase of government bonds involves a tradeoff. There are two kinds of liquidity in this economy - currency and interest-bearing government debt. An open market purchase increases currency, but lowers the quantity of government debt in circulation. Close to the zero lower bound, this will lower welfare, on net. This implies that a financial shock which tightens financial constraints and lowers the real interest rate does not imply that the central bank should go to the zero lower bound. That's very different from what happens in New Keynesian (NK) models, where a similar shock implies that a zero lower bound policy is optimal.

As we learned from developments in macroeconomics in the 1970s, to evaluate policy properly, we need to understand the operating characteristics of the economy under particular fiscal and monetary policy rules. We shouldn't think in terms of actions - e.g. what happens if the nominal interest rate were to go up today - as today's economic behavior depends on the whole path of future policy under all contingencies. Our analysis is focused on monetary policy, but that doesn't mean that fiscal policy is not important for the analysis. Indeed, what we assume about the fiscal policy rule will be critical to the results. People who understand this issue well, I think, are those who worked on the fiscal theory of the price level, including Chris Sims, Eric Leeper, John Cochrane, and Mike Woodford. What we assume - in part because this fits conveniently into our analysis, and the issues we want to address - is that the fiscal authority acts to target the real value of the consolidated government debt (i.e. the value of the liabilities of the central bank and fiscal authority). Otherwise, it reacts passively to actions by the monetary authority. Thus, the fiscal authority determines the real value of the consolidated government debt, and the central bank determines the composition of that debt.

Like Woodford, we want to think about monetary policy with the nominal interest rate as the instrument. We can think about exogenous nominal interest rates, random nominal interest rates, or nominal interest rates defined by feedback rules from the state of the economy. In the model, though, how a particular path for the nominal interest rate is achieved depends on the tools available to the central bank, and on how the fiscal authority responds to monetary policy. In our model, the tool is open market operations - swaps of money for short-term government debt. To see how this works in conjunction with fiscal policy, consider what happens in a constrained equilibrium at the zero lower bound. In such an equilibrium, c = V+K, where c is consumption, V is the real value of the consolidated government debt, and K is a credit limit. The equilibrium allocation is inefficient, and there would be a welfare gain if the fiscal authority increased V, but we assume it doesn't. Further, the inflation rate is i = B[u'(V+K)/A] - 1, where B is the discount factor, u'(V+K) is the marginal utility of consumption, and A is the constant marginal disutility of supplying labor. Then, u'(V+K)/A is an inefficiency wedge, which is equal to 1 when the equilibrium is unconstrained at the zero lower bound. The real interest rate is A/[Bu'(V+K)] - 1. Thus, note that there need not be deflation at the zero lower bound - the lower is the quantity of safe assets (effectively, the quantity V+K), the higher is the inflation rate, and the lower is the real interest rate. This feature of the model can explain why, in the Japanese experience and in recent U.S. history, an economy can be at the zero lower bound for a long time without necessarily experiencing outright deflation.

Further, in this zero lower bound liquidity trap, inflation is supported by fiscal policy actions. The zero nominal interest rate, targeted by the central bank, is achieved in equilibrium by the fiscal authority increasing the total stock of government debt at the rate i, with the central bank performing the appropriate open market operations to get to the zero lower bound. There is nothing odd about this, in terms of reality, or relative to any monetary model we are accustomed to thinking about. No central bank can actually "create money out of thin air" to create inflation. Governments issue debt denominated in nominal terms, and central banks purchase that debt with newly-issued money. In order to generate a sustained inflation, the central bank must have a cooperative government that issues nominal debt at a sufficiently high rate, so that the central bank can issue money at a high rate. In some standard monetary models we like to think about, money growth and inflation are produced through transfers to the private sector. That's plainly fiscal policy, driven by monetary policy.

In this model, we work out what optimal monetary policy is, but we were curious to see how this model economy performs under conventional Taylor rules. We know something about the "Perils of Taylor Rules," from a paper by Benhabib et al., and we wanted to have something to say about this in our context. Think of a central banker that follows a rule

R = ai + (1-a)i* + x,

where R is the nominal interest rate, i is the inflation rate, a > 0 is a parameter, i* is the central banker's inflation target, and x is an adjustment that appears in the rule to account for the real interest rate. In many models, the real interest rate is a constant in the long run, so if we set x equal to that constant, then the long-run Fisher relation, R = i + x, implies there is a long-run equilibrium in which i=i*. The Taylor rule peril that Benhabib et al. point out, is that, if a > 1 (the Taylor principle), then the zero lower bound is another long run equilibrium, and there are many dynamic equilibria that converge to it. Basically, the zero lower bound is a trap. It's not a "deflationary trap," in an Old Keynesian sense, but a policy trap. At the zero lower bound, the central banker wants to aggressively fight inflation by lowering the nominal interest rate, but of course can't do it. He or she is stuck. In our model, there's potentially another peril, which is that the long-run real interest rate is endogenous if there is a safe asset shortage. If x fails to account for this, the central banker will err.

In the unconstrained - i.e conventional - regime in the model, we get the flavor of the results of Benhabib et al. If a < 1 (a non-aggressive Taylor rule), then there can be multiple dynamic equilibria, but they all converge in the limit to the unique steady state with i = i*: the central banker achieves the inflation target in the long run. However, if a > 1, there are two steady states - the intended one, and the zero lower bound. Further, there can be multiple dynamic equilibria that converge to the zero lower bound (in which i < i* and there is deflation) in finite time. In a constrained regime, if the central banker fails to account for endogeneity in the real interest rate, the Taylor rule is particularly ill-behaved - the central banker will essentially never achieve his or her inflation target. But, if the central banker properly accounts for endogeneity in the real interest rate, the properties of the equilibria are similar to the unconstrained case, except that inflation is higher in the zero-lower-bound steady state. How can the central banker avoid getting stuck at the zero lower bound? He or she has to change his or her policy rule. For example, if the nominal interest rate is currently zero, there are no alternatives. If what is desired is a higher inflation rate, the central banker has to raise the nominal interest rate. But how does that raise inflation? Simple. This induces the fiscal authority to raise the rate of growth in total nominal consolidated government liabilities. But what if the fiscal authority refused to do that? Then higher inflation can't happen, and the higher nominal interest rate is not feasible. In the paper, we get a set of results for a model which does not have a short-term liquidity effect. Presumably that's the motivation behind a typical Taylor rule. A liquidity effect associates downward shocks to the nominal interest rate with increases in the inflation rate, so if the Taylor rule is about making short run corrections to achieve an inflation rate target, then maybe increasing the nominal interest rate when the inflation rate is above target will work. So, we modify the model to include a segmented-markets liquidity effect. Typical segmented markets models - for example this one by Alvarez and Atkeson are based on the redistributive effects of cash injections. In our model, we allow a fraction of the population - traders - to participate in financial markets, in that they can use credit and carry out exchange using government bonds (again, think of this exchange being intermediated by financial intermediaries). The rest of the population are non-traders, who live in a cash-only world.

In this model, if a central banker carries out random policy experiments - moving the nominal interest rate around in a random fashion - he or she will discover the liquidity effect. That is, when the nominal interest rate goes up, inflation goes down. But if this central banker wants to increase the inflation rate permanently, the way to accomplish that is by increasing the nominal interest rate permanently. Perhaps surprisingly, the response of inflation to a one time jump (perfectly anticipated) in the nominal interest rate, looks like the figure in John Cochrane's post that he labels "pure neo-Fisherian view." It's surprising because the model is not pure neo-Fisherian - it's got a liquidity effect. Indeed, the liquidity effect is what gives the slow adjustment of the inflation rate.

The segmented markets model we analyze has the same Taylor rule perils as our baseline model, for example the Taylor principle produces a zero-lower-bound steady state which is is the terminal point for a continuum of dynamic equilibria. An interesting feature of this model is that the downward adjustment of inflation along one of these dynamic paths continues after the nominal interest rate reaches zero (because of the liquidity effect). This gives us another force which can potentially give us positive inflation in a liquidity trap.

We think it is important that central bankers understand these forces. The important takeaways are: (i) The zero lower bound is a policy trap for a Taylor rule central banker. If the central banker thinks that fighting low inflation aggressively means staying at the zero lower bound that's incorrect. Staying at the zero lower bound dooms the central banker to permanently undershooting his or her inflation target. (ii) If the nominal interest rate is zero, and inflation is low, the only way to increase inflation permanently is to increase the nominal interest rate permanently.

Finally, let's go back to the quote from Krugman's post that I started with. I'll repeat the last paragraph from the quote so you don't have to scroll back:
And the question is, why? What motivation would you have for inventing complicated models to reject conventional wisdom about monetary policy? The right answer would be, if there is a major empirical puzzle. But you know, there isn’t. The neo-Fisherites are flailing about, trying to find some reason why the inflation they predicted hasn’t come to pass — but the only reason they find this predictive failure so puzzling is because they refuse to accept the simple answer that the Keynesians had it right all along.
Why? Well, why not? What's the puzzle? Well, central banks in the world with their "conventional wisdom" seem to have a hard to making inflation go up. Seems they might be doing something wrong. So, it might be useful to give them some advice about what that is instead of sitting in a corner telling them the conventional wisdom is right.


  1. My own view is that the statement:

    (ii) If the nominal interest rate is zero, and inflation is low, the only way to increase inflation permanently is to increase the nominal interest rate permanently.

    is unecessarily provocative. The equations in the model make it clear that there must be an underlying fiscal accommodation (a passive fiscal policy, to use Leeper's language) to support the higher nominal interest rate and inflation rate.

    1. David: suppose I said: "The only way to increase inflation permanently is to print more M and B permanently, and use that printed M and B to increase the nominal rate of interest paid on B permanently".

    2. Yes, well, to be fair, Steve does say as much in his explanation above. I just wanted to reiterate it because I don't think the statement "increase R to increase P" can be made in isolation of the supporting policy regime.

    3. I could have said it more impolitely though.

  2. There are two media of exchange: one called "M" and one called "B". Both are issued by the government.

    M can be used in both markets, B can only be used in market 2.

    In the "constrained" equilibrium, the government insists on a fixed amount of seigniorage, so the equilibrium is not optimal. Both M and B will have a liquidity premium.

    I am trying to figure out why the Friedman rule (where M and B have the same real rate of return) is not constrained optimal. In other words, why ought the central bank price discriminate and charge a higher liquidity premium on M than on B?

    My guess is that it is because K > 0, where K is the fixed amount of credit in market 2. My guess is that this affects the elasticity of demand for the medium of exchange in market 2 relative to market 1. So the Ramsey principle says it is optimal for the central bank to tax M at a higher rate than B.

    But that's just a guess.

    1. No, it has nothing to do with K. But you ask a good question. Let me see if I can offer some intuition.

      Suppose we are in the constrained case and at the Friedman rule. Consumption in both markets is equated (good insurance) but at depressed levels.

      Now, consider increasing the nominal interest rate a little bit. Underlying this action are "open market operations" that increases the bond-to-money ratio (permanently). That is, the central bank sells bonds for money (looks like tightening). At the same time, the growth rate in the nominal supply of money/bonds is increased, and taxes are cut.

      The effect of having the central bank sell bonds is to relax the debt constraint in market 2. Consumption in that market expands.

      What happens to consumption in market 1? We can show that for log preferences, it does not change. In general though, it may rise or fall. There must be some offsetting substitution and income effects here. The higher interest rate makes market 1 consumption more expensive, so ppl would want to substitute into the market 2 good. On the other hand, relaxing the debt constraint has a kind of positive wealth effect--ppl would want to increase consumption of both goods.

      So, close to the Friedman rule, an increase in the interest rate increases GDP and welfare.

      This is also consistent with the theory of the 2nd best. We know that introducing an additional friction (in this case, the nominal interest rate wedge) does not necessarily reduce welfare in a 2nd best world. Indeed, it may increase welfare, and this is the case here.

    2. Thanks David. So you don't get the Friedman rule even if K=0.

      My gut tells me the Ramsey rule must be at work here. "Have a higher tax rate on the good with the less elastic demand, and a lower tax rate on the good with the more elastic demand." That is consistent with the theory of second best.

      That would work if the demand for B/P were more elastic than the demand for M/P. Which sounds empirically plausible, but I can't see why it would be true in your model, because the only relevant difference is that M can be used in both markets while B can only be used in one market. Though it *might* be true in your model. But I can't figure out why.

      The other thing I can't figure out is why a change in the composition of the tax, lowering the tax on B and increasing the tax on M, holding total tax revenue constant, should increase the total tax base (M+B)/P, and so lower P initially. My guess is that that has something to do with the relative demand elasticities for M and B too, just like the Ramsey result above.

    3. Re-reading your 5:56 comment David, I think you *are* telling me that the demand for B is more elastic than the demand for M. In which case your results are consistent with the Ramsey rule, which pleases me.

      But I still can't figure out why the demand for B is more elastic.

    4. Let me talk to Steve about this--it may very well be the case. Regarding your earlier comment, note that real tax revenue is *not* being held constant in the exercise. The real market value of the government's outstanding debt is being held constant.

    5. Mum and Dad give M to the boys, and B to the girls, and the boys and girls go shopping, while Mum and Dad go off to work. I don't see why the central bank would tax the boys' shopping more than the girls' shopping. The only difference is that the girls use some credit, which can't be taxed at all, but that shouldn't matter for the optimal marginal tax rate on shopping. And the math says it works even with no credit. There's a non-negativity constraint on both M and B, I think.

      It looks symmetric to me. Either I'm missing some asymmetry, or there's a typo somewhere in the equations.

      Other than that, this paper makes sense to me. I don't buy the assumption about the fiscal authority holding (M+B)/P constant when the central bank does something, but it makes more sense as a nominal anchor than those models which don't have M and B and just assume the Fisher relation holds.

    6. OK, I think I've got it.

      The fiscal authority holds (M+B/(1+i))/P constant. So if the central bank increases i above 0%, (M+B)/P increases, so the total amount of shopping increases, which increases welfare. But increase i too much and it reduces boys' shopping relative to girls' shopping too much, and reduces welfare.

      Hmmm. I'm not sure I'm happy with that assumption. It seems a very thin reed on which to base a violation of the Friedman rule. If the bonds were n-period, rather than one-period Tbills, it would gives some very different results. Even more if the bonds were perpetuities.

    7. Yes, I think that's right. And yes, it is interesting/discouraging to see how much hangs on just precisely how the fiscal policy is modeled. But I think it should be made much more explicit when we speak of "monetary policy."

    8. David: sadly (because of the 'discouraging" bit), I agree.

    9. Why are you guys so sad? You can find plenty of instances in which people have tried to get across ideas about the fiscal side of monetary policy. It's in "unpleasant monetarist arithmetic" and the fiscal theory of the price level, for example. Seems pretty interesting, if not exciting. No need to get depressed. Maybe David feels discouraged because his power as a central banker doesn't seem so imposing.

    10. If the truth or falsity of the Friedman rule (in a second-best world) depends on something so trivial as whether the fiscal authority targets (M+B)/P or [M+B/(1+i)]/P, that's a bit sad.

      Me, I would rather say that the truth or falsity of the Friedman rule depends on the Ramsey rule.

    11. You can stop being sad. I don't think that matters much qualitatively.

  3. Assuming for a moment there is no practical constraint (due to the division of monetary and fiscal policy), how would the notion of direct cash transfers in the form of a basic income grant factor into your findings? It would seem to me that this would be the most direct way of creating inflation and this could be entered directly into the household part of your model. Would your findings support these conclusions:

    1. That's correct. But given that, what do you think would happen to the nominal interest rate?

    2. Well I suppose it might depend on the scenario- theoretically speaking if we image the BIG stimulates consumption without having a significant impact on the ability of the central bank to continuously accumulate new debt to keep its stock of government debt constant (ie perpetual QE), then we can assume the same-> "the lower is the quantity of safe assets (effectively, the quantity V+K), the higher is the inflation rate, and the lower is the real interest rate" would apply in this case.

      Of course the most salient question might be what level of BIG are we talking about, as certainly one would need to image a government transfer program large enough to meaningfully affect consumption and inflation (and possibly for the coordination of other deflationary measures like taxes to work in conjunction with interest rates). In other words if we assume $3k/month for every American adult we are talking about $7.5tril in new government debt annually, and assuming the Fed can continue to hold around 25% of total UST stock, then this would mean $156bil in QE per month, not unfathomable, but it would be easier to imagine in a scenario where a country is flirting with negative rates. For example, I do not see a theoretical reason why Switzerland could not enact a BIG as a way of preventing the overvaluation of the CHF.

  4. I'm a little lost on your basic premise. Currency is a safe asset. If I want it, I have only to go to the bank and request it, then lock it away in a vault. This is a little less efficient than holding a repo, but not terribly so, since I could buy and sell paper claims on that vault cash. These claims could be used to collateralize any financial transaction, just as government bonds do today. Currency is just a type of liability of the government, one that never earns interest and can't be redeemed. At any level of the policy rate, there is infinite supply available for "financial exchange". If this is the case, how can there be a shortage of safe assets?