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Saturday, December 20, 2014

Monetary Impotence And The Triumph Of The Fiscal Theory Of The Price Level

There has been an ongoing debate about how monetary policy interacts with the zero bound on interest rates. Paul Krugman has recently posted an article, "The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something about monetary policy when at the zero bound. When I look at the model, it appears that there are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined by the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads lead to the FTPL.


Simon Wren-Lewis outlines what this debate is about:
There are a significant group of people who think that monetary policy must be the right answer even in a liquidity trap because of the centrality of money in macroeconomics, and because of ‘basic’ ideas like money neutrality. Call them market monetarists if you like. They dislike fiscal stimulus because - in their view - it just has to be second best, or a fudge, compared to monetary policy. Their view is not ideological, but essentially based on macro theory. Now it may not be very relevant to the real world, but for many holding the theoretical high ground is important [emphasis added - BR], because it colours their view of the real world.
In my view, both Krugman and his opponents are on the low ground; and the Fiscal Theory of The Price Level is on the high ground (see my discussion here explaining the FTPL), at least within the context of neoclassical economics. (The true high ground is found somewhere within Post-Keynesian economics, but that is another topic of discussion.)

Since I believe that both neoclassical sides of the debate ("New Keynesians" versus "Market Monetarists") are theoretically wrong, I make no attempt to judge which side offers useful policy views.

Krugman's Simplified Model

In his article, Paul Krugman greatly stripped down the standard New Keynesian model so that the infinite horizon has been replaced with essentially two time periods: the first period, in which the economy is in a liquidity trap, and the second in which the economy has entered a steady state.

Since his article is a blog post, he has eliminated almost all of the formal mathematical overhead. Since he has won the The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, I will assume that he did the mathematical manipulations correctly. (If the math is wrong, please send nasty feedback to the Riksbank and not to me, thanks.)

He assumes a simple (logarithmic) utility function, and he arrives at the key Euler equation:

C = C*(P*/P)/(1+r).

The future (steady state) values are denoted with the *, and C is consumption, P is the price level, and r is the nominal interest rate. (This means that P*/P is expected inflation from the first period to the second.) 

  • Since we are in a "New Keynesian" model, we have temporarily sticky prices, and P is fixed.
  • Since we are in a liquidity trap, r=0
  • By the "steady state" assumption, C* is fixed at some "full employment" level. (If there is a mathematical weakness in his derivation, it would be here.)
This means the expression collapses to:

C = (Full Employment Consumption)(Expected inflation for first time step).

This means that we can ramp up current consumption by raising expected inflation.

Marginal Analysis Is Not Enough

His results appear consistent with other treatments of DSGE models. The problem I see is that just looking at what is happening at the margin is not enough, he needs to look at the entire set of constraints for the system.

Total consumption is set by total production (there are no inventories). Since the representative household has model-consistent expectations, it knows that this constraint cannot be violated. It will increase consumption in the first period only until the point of the "disutility" of increased labour matches the added utility of increasing utility of consumption. Krugman's simplified framework gives us no information about that tradeoff, but without it, we cannot conclude what will happen to consumption.

Changing the expected inflation should have no effect on the solution. The representative household is essentially a sole proprietor that purchases its own production, and all money used to purchase goods will return to itself either via wages or profits. The level of consumption in the first period has no impact on the financial assets (money or government bonds) at the beginning of the second period. The only thing that can effect the amount of financial assets held by the household is the fiscal deficit, which is the primary balance plus interest payments (assumed to be zero for the first period). This holds from the 1-period governmental accounting identity, which must hold (as otherwise the accountants would get very angry). Since household consumption decisions cannot affect the (expected) value of its future financial asset holdings, those financial assets do not act as a constraint upon those decisions.

Since Krugman assumes that intertemporal governmental governmental budget constraint holds ("Ricardian Equivalence"), I believe that you can demonstrate that the real value of government debt will equal the present value of future surpluses. Since the amount of government debt initially outstanding is an inherited fixed condition, this relationship acts to pin down the price level. (You will have to ask someone like John Cochrane how this derivation works when we have the extreme sticky price assumption that Paul Krugman uses here.) This brings us back to the Fiscal Theory of the Price Level.

The relationship between the FTPL and the financial asset constraint is that since there consumption decisions within these models do not affect household's true financial constraints, financial assets only matter relative to tax obligations. That is, money has value because it is needed to extinguish future tax payments. (In an overlapping generations DSGE model, money acts as a 'Ponzi scheme' and has a value independent of fiscal policy.)

It's All About Expectations - Expected Fiscal Policy

Nick Rowe is on the other side of the debate from Paul Krugman, and he argues that "Monetary policy is always and everywhere about expectations". Within the context of a DSGE model framework, that is undoubtedly correct. By assumption, the expected value of a Treasury bill (which gives us the 1-period interest rate) is directly related to the expected 1-period inflation. (I would note that Post-Keynesian analysis disagrees with that assumption, but I am not going there in this article.)

That said, within that framework, this only tells us about the rate of change of the price level. The determination of the price level is driven by the expected stance of fiscal policy. Since that is directionally consistent with Chartalism, I agree qualitatively with that assessment. (However, it appears that the FTPL generates empirical predictions about the price level that do not hold up; that is a sign that there is no empirical basis for the entire DSGE mathematical framework.)

(c) Brian Romanchuk 2014


  1. Nice post.

    I believe this discussion about PK's 1998 proposal and its relevance for Japan yesteryear and the US today is really important. As I wrote in my last post, there are serious problems in the NK assumption relating to inflation and expected inflation. That said, I thought PK's follow-up is interesting. He says he wrote-up the model as a way to be consistent, not as a preferred course of action (this completely blew my mind when I read this in his last post "More Macro Modelling). He seems to be saying IS-LM provides the most realistic option (ie, combined fiscal and monetary stimulus).

    Now, he's putting others to the task (market monetarists, Nick Rowe, Sumner) to put their cards on the table, show their model and demonstrate how they see how monetary policy can be used to boost spending.

    Looking forward to reading more on your take from a post-keynesian position.

    1. My problem is that I do not see how Krugman's model works; when I look at the optimisation problem, what I see as the optimum is not what he says it is. Since the solution I am looking at maximises the utility function, I cannot see how people are arriving at other solutions.

      Using a "big tent" definition of Post-Keynesian thought, MMT is Post-Keynesian. (I believe that some of the self-identified Post-Keynesians prefer to use a narrower definition.) Most (all?) of the MMT writers view "helicopter drops" etc. to be fiscal policy, and although they "work", they are not really monetary policy. I would guess that the other strands of Post-Keynesians have a similar view, but I am less familiar with them.

      Under a Gold Standard, I believe the Central Bank could monetise a lot of gold. This would also act like a "helicopter drop". Although I would prefer to classify that as fiscal policy as well, but I would be fighting convention on that one.

      In a modern setting, you might be able to classify the monetisation of foreign currency as monetary policy. Once again, this is an increase of aggregate government liabilities, which I would prefer to view as fiscal. It also could be ineffective, if two central banks started buying each other's currency.

    2. For all intents and purposes, the MMT/PK prescription is the same as the IS-LM solution, essentially, "helicopter drops" or monetizing the debt.

      As for the difference between fiscal and monetary, I consider that any transaction that the CB can do within its legislative mandate can be defined as monetary. If the CB doesn't have the statutory authority, then it should be considered fiscal (as it would be done by the fiscal authority). I guess outright purchases could be considered fiscal operations but then almost everything the BC does would fall under this category, no?

    3. "Under a Gold Standard, I believe the Central Bank could monetise a lot of gold. This would also act like a "helicopter drop". Although I would prefer to classify that as fiscal policy as well, but I would be fighting convention on that one"

      In Cochrane's paper on interest on reserves, he refers to the gold standard as a fiscal commitment.

    4. I cannot remember what he wrote, but it makes sense. The fiscal authority is hamstrung within a gold standard, as the central bank cannot ensure that Treasury Bills can always be rolled over.

      There is a monetary commitment (convertability), but convertability is not an issue if fiscal policy is sufficiently tight.

  2. You might be interested in this chart at the Federal Reserve web site.

    It shows private GDP divided by the accumulated Federal Borrowing which I would call the velocity of Federal Borrowing..

    I think of private GDP (PGDP) as the equation GDP less government expense. If we use accumulated federal borrowing as the money supply (the MMT money supply?), we could use the Federal Reserve series "Federal Debt Held by the Public" (FYGFDPUN) .

    The reference chart shows PGDP / FYGFDPUN. It shows a declining number of turnovers over the 40+ years of display. If monetary policy were strongly affecting prices, I would expect to see a line closer to level (with the horizontal axis).with bumps up for periods of increased bank borrowing. I see the bank borrowing but not the horizontal relationship.

    Just thought you might be interested. Merry Christmas.

    1. Thanks, I will take a look. Merry Christmas to you too.


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