Wednesday, October 27, 2021

Transitory Inflation: A Fisherian Fed?

Should the Fed raise interest rates fast? Or should it leave them alone, figuring inflation will be "transitory?" 

Lots of models, including ones I play with, predict that a constant unchanging interest-rate peg leads to stable inflation. If there is a fiscal shock, it leads to a one-period price-level jump, but no further inflation, so long as the interest rate stays where it is. The models in the first few chapters of The Fiscal Theory of the Price Level have this feature, also "Michelson Morley, Fisher and Occam.'' Martin Uribe has also written about this issue, here for example. 

The simplest example is \[i_t = E_t \pi_{t+1}\] \[(E_{t+1}-E_t) \pi_{t+1} = -(E_{t+1}-E_t) \sum_{j=0}^{\infty} \rho^j \tilde{s}_{t+j} \] where \(\tilde{s}\) denotes real primary surpluses scaled by the value of debt. If the interest rate \(i_t\) does not move, expected inflation does not move. A fiscal shock (negative \(\tilde{s}\) ) gives a one-period unexpected inflation, devaluing outstanding debt; essentially a Lucas-Stokey state-contingent default. Sticky prices smooth all this out over a year or two. 

You can replace the latter with standard new-Keynesian equilibrium-selection rules if you want. This isn't really about fiscal theory; the key is rational forward-looking expectations in the first equation, which also hold in the standard sticky-price extensions. This "Fisherian" property is a common though widely ignored prediction of most new-Keynesian models. 

It certainly seems plausible that we are seeing an inflationary fiscal shock, from trillions of money printed up and sent to consumers, while interest rates stay fixed. These models predict that such inflation will indeed be transitory if the Fed does not raise interest rates, and will rise if it does!  

However, like all lower-rates-to-lower-inflation arguments, there are lots of warnings here. In particular, the "transitory" inflation could last a long time once we put in sticky prices. The trick only works if the Fed is completely committed to not raising rates, to waiting as long as it takes for inflation to settle back down on its own.  If people suspect the Fed will raise rates, inflation rises. There are lots of temporary forces that go in the other direction. And there may be more fiscal shocks -- I sort of see one brewing in Congress -- so we may not be done with the unexpected inflation term. 

FTPL section 5.3 has a long discussion of all the preconditions for lower interest rates to bring down inflation, which still obtain. But we haven't been talking about this issue much since the low-inflation zero-bound era ended, and the discussion that maybe determined, permanent, pre-announced interest rate rises could eventually bring up inflation. The opposite sign works as well. 

In these models, with a few more ingredients than I show above, the Fed can also lower inflation by raising rates. Raising rates gives a temporary inflation decline before going the other way. So, the Fed has to raise rates, push inflation down, then quickly get on the other side. That's the historical pattern, and what it will likely do.  But it's only honest, and fun, to remember the prediction of the opposite possibility and to think about how it might work out. 


Update. A second try, with more English. The government, Fed and Treasury, basically printed up about $5 trillion of new cash and treasury debt -- these are largely perfect substitutes so the composition doesn't really matter -- with no change at all in plans to repay debt. By simple FTPL, a 25% increase in debt with no increase in expected future surpluses generates a 25% rise in the price level, 25% cumulative inflation. It basically defaults on outstanding debt and transfers that value to the recipients of stimulus. 

But then it ends. If there is no more issue of nominal debt, without additional surpluses, then there is no more inflation. 

Additional issues of nominal debt can come from more unbacked fiscal expansion, or it can come from monetary policy. Monetary policy also puts extra government debt (same thing as interest-paying reserves) out there, with (of course) no change in fiscal policy. 

So there is the FTPL case for "transitory."In the long run, no change in interest rate puts no extra government debt in the system, and higher nominal interest rates must mean eventually higher inflation and hence more unbacked government debt in the system. 



  1. We all have been reading a lot lately about the difference between sustained inflation, and a one-time boost in prices, due to this or that structural impediment, or other boo-boo.

    Still, for the average guy, a lengthy sustained series of one-time boosts sure looks and feels like inflation.

    For example, if housing markets become chronically tighter over several decades due to property zoning, that may be measured as inflation and will feel like inflation, but may not meet the orthodox definition of inflation.

    If OPEC controls output, raises prices, and then controls at the higher price, that sure feels like inflation.

    If housing and fuel costs rise enough, then employers along the West Coast will find "worker shortages" and have to raise wages.

    I understand, some people say these one-shot higher prices have to be validated by easy money to sustain a higher rate of inflation, or some other prices must come down, but I think that is not true.

    You can have inflation as measured by the CPI (and as seen by average consumers and renters) and lower velocity. So this stair-step inflation can exist, even with a "tight" monetary policy.

    Personally, I think "labor shortages" are a wonderful thing, and I hope they last for several generations. I can think of nothing better for the social fabric of America, especially if accompanied by a reduction in social welfare.

    If inflation, as measured, runs around 3% but we have tight labor markets for a few decades, that is a great trade-off.

  2. John H Chochrane,
    In the analysis of this post you do not give a mechanism of why increasing interest rates would decrease inflation. Who's spending is effected and why. What do you have in mind.

  3. I am honestly stunned that expected future surpluses have apparently had no effect on the interest rates thus far(it appears). The Democrats are proposing a massive spending bill with a bunch of changes to the tax system. Unless there's a widespread view that the bill will be nixed or somehow neutral(or positive, which seems hard to believe); you would assume there would be an effective. Do people just view expected surpluses in 50 year windows instead of 4 or 8 or 10?

  4. So I am now hearing two veins of argument that raising rates will increase inflation. The first being that our debt levels our high enough to be in "Unpleasant Monetarist Arithmetic" territory; and the second is this fisher effect underlies new Keynesian and FTPL models. Do you see them as distinct and one more important that the other?

  5. There's a reason why, after 100 years, macro-economic thinking doesn't lead to any predictions. It's because the equilibrium isn't in rates, it's in levels.

    First you need to model what the equilibrium is in terms of levels, and then the prediction for rates is simply to gravitate toward that equilibrium.

    For example, price levels are a linear function of the money supply, along with the level of technology. If technology doesn't change, and money supply doesn't change, there will never be any long-run inflation ever.

    Changes in price levels, levels of technology and money supply will all upset this equilibrium, and in the short run, prices will move as a function of the rate of shock-entry to the system and rate of gravitation toward the equilibrium.

    So what do interest rates have to do with it? In the long-run, absolutely nothing. In the short term, the Fed is trying to delay entry of printed money into the economy by raising rates, and accelerate entry of printed money into the economy by lowering rates. But, because of the complex nature of the economy, it's rare that the Fed can actually get it right anyway.

    1. "For example, price levels are a linear function of the money supply, along with the level of technology. If technology doesn't change, and money supply doesn't change, there will never be any long-run inflation ever."

      You are forgetting about the velocity of money, remember:
      MV = PY

      Money Supply * Velocity = Price Level * Quantity of Goods

      Interest rates play a role in regulating the velocity of money.

      M2 Velocity

      M2 Supply

      If money supply rises by 10% but the velocity of money falls by 10% then nominal GDP (P * Y) is unchanged.

      John's point regarding interest rates is the fiscal aspect (hence FTPL - fiscal theory of the price level).

      Meaning interest payments on government debt can be considered a transfer payment that requires no additional real output (Y) to receive those payments.

    2. Fish,

      In a simplistic single bank, single interest rate economic model we can relate bonds and money supply in this way:

      M(t) = B(t) * (1 - INT%) * RET% + B(t) * INT% * (1 - RET%)

      M(t) = Money Supply
      B(t) = Bond Supply
      INT% = Interest Rate
      RET% = Bank retainage percentage of the bonds that it creates

      If a bank retains all the loans that it makes (RET% = 100%), then the equation simplifies to this:

      M(t) = B(t) * (1 - INT%) : Money supply is equal to the quantity of bonds (loans) created by our one bank minus the interest expense that the bank receives

      If instead a bank sells all the loans that it makes (RET% = 0%), then the equation simplifies to this:

      M(t) = B(t) * INT% : Money supply is equal to the interest payments that the public receives on the loans that it holds.

      Now you should understand how money supply and interest rates are interrelated.

      To understand how velocity is affected by both money supply and interest, you need to add a liquidity preference
      ( LP%(t) ) term to this equation which will let you solve for the velocity ( V(t) ) of money in terms of M(t), B(t), P(t), and Y(t).

      Further, to add technology to the equation you stipulate that Productivity PR(t) = Y(t) / B(t).

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    4. Adding liquidity preference and productivity gets you the following:

      M(t) * V(t) = P(t) * Y(t)

      B(t) * V(t) * [ (1 - INT%) * RET% + INT% * (1 - RET%) = B(t) * P(t) * PR(t)

      Where productivity: PR(t) = Y(t) / B(t)

      Divide both sides by B(t):

      P(t) * PR(t) = V(t) * [(1 - INT%) * RET% + INT% * (1 - RET%)]

      Solving for the price level gets you:

      P(t) = V(t) * [(1 - INT%) * RET% + INT% * (1 - RET%) ] / PR(t)

      "So what do interest rates have to do with it? In the long-run, absolutely nothing."

      See equation above relating the price level P(t), interest rate (INT%), productivity / technology PR(t), and retainage (RET%).

    5. Cochran's comment on FTPL supports what I was saying. 25% increase in money supply leads, eventually, to a 25% increase in prices. Interest rates, debt (that's paid off, and doesn't lead to an increase in money supply) and velocity really don't have any long-run effect.

    6. Read what John actually wrote:

      "By simple FTPL, a 25% increase in DEBT with no increase in expected future surpluses generates a 25% rise in the price level..."

    7. John's assumption is that debt will be paid off by printing money. Otherwise, prices wouldn't be affected.

    8. John's assumption is that the debt will be paid off by printing money. That's what has to happen if there are no future surpluses to pay off the debt.

      When people expect this to happen, the prices start adjusting instantly. That complicates the ways things gravitate toward equilibrium in economics. Market frictions that make it impossible to act on information instantaneously are the reason why markets take time to gravitate toward efficiency.

    9. Fish,

      "John's assumption is that debt will be paid off by printing money. Otherwise, prices wouldn't be affected."

      John is wrong in his assumption.
      Even when the Fed "prints up money" to purchase the debt, it is not extinguished.

      John takes too many short cuts in his explanations.

      Instead, if you assume that tax revenue rises with an increase in nominal GDP (Price level x Real GDP), then the debt is "inflated away" through the increase in tax receipts.

      This is problematic when the price level is rising and real GDP is falling (stagflation).

      "When people expect this to happen, the prices start adjusting instantly."

      Nope again. Expectations alone are not enough to drive the price level higher.

    10. M(t) * V(t) = P(t) * Y(t) doesn't reflect reality:
      V(t) = P(T)*T/M(T). So, the equation simplifies to T = Y(t), which is true only with a profit margin of 1. So all the equation says is that the amount transacted goes up with the amount transacted.

      For the entire economy, the profit margin(π) is exactly 0.0, because profits from suppliers are offset by losses from consumers.

      If we want a more meaningful understanding of profit margin, we could define it as retained_earnings/transactions, which is similar to profit/revenues. However, retained earnings for the entire economy is M. That means that π = M/PT = 1/V. So profit margins for the entire economy are literally the inverse of velocity.

      What all this means is that the way to boost transactions is to lower people's profit margins. The way you do that is my making them work harder for every penny of savings. This is generally bad for real GDP.

      In a Nutshell: V = PT/M , Y = π*PT , π = M/PT.
      Y = π*PT = π*V*M, because π and V are inverses, adjusting V will have no effect on Y. Similarly, lowering π will just double V, also having no effect on Y.

    11. FRestly, thank you for engaging in this discourse. I realize I read your equation wrong. Yes, Y = goods transacted, but the equation does not connect with any sort of profit unless we describe a profit margin.

      Low velocity of money corresponds with high profit margins, and high velocity corresponds with low profit margins. This is mechanically true in micro-economics, and macro-is just the aggrigate of the micro.

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  7. "By simple FTPL, a 25% increase in debt with no increase in expected future surpluses generates a 25% rise in the price level, 25% cumulative inflation."

    Which is not entirely correct because of the possibility for stagflation - rising inflation, declining real gross domestic product. If there is a 25% rise in the price level, but also a 30% decline in real GDP, then nominal GDP (and associated tax revenue) falls by 5%.

    Have economists learned nothing from the 1970' and early 1980's?
    Or has the salt water at Stanford turned J.C. turned into a full blown Keynesian?

    1. Stagflation is a euphemism for inflation. Real GDP growth naturally lowers prices, so we should expect to see more inflation when real GDP is not growing fast.

    2. "If there is a 25% rise in the price level, but also a 30% decline in real GDP, then nominal GDP (and associated tax revenue) falls by 5%." -- nominal GDP declines by 12.5%, not 5%, under the conditions stated.
      Cf., (1 + .25)(1 - .30) - 1 = 1.25 x 0.70 - 1 = 0.875 - 1 = -0.125.

      Sir Horatio P. B. Blimp, F.R.S., M.A. (Oxon., Hons.), D.S.C., K.G.B., was "a full blown Keynesian", in his day. From all accounts, J.C. may, from time to time, walk on sea-water, but he doesn't ingest it.

    3. OEE,

      Yes, thank you for the correction.

  8. Dear John, Great post. Assuming some deficit reduction in 2021-2024, how should monetary policy respond? Keep rates low not to raise inflation? If you were at the helm at the CB but didn't control the fiscal, but expected some deficit reduction, Would you bet on the neo fisherian effect and keep rates low?

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  10. The Fed reported it was monitoring inflationary expectations, by the great American economist Irving Fisher in 1911 and became the basis. Even though economic slack from high unemployment and idle factory capacity suggest inflationary pressures may be transitory.

  11. The discussion around "transitory" inflation strikes me as ridiculous. Life is transitory. Indeed, life on planet earth is transitory. Or to go back to slightly more serious economics - are shocks to GD(N)P permanent or transitory? Remember that useless debate from the 90's

    The relevant question is how long - what's the expected duration? Your point that a one time run of the printing presses will result in a finite amount of inflation is surely correct though the question is how long will it take for all the frictions to work their way through so we get to cumulative 25% - or whatever. Is that 1 more year or 5 more years?

    And the politicians and central bankers claiming that its all "transitory" is just a meaningless cop out along the lines of saying "its all supply".

  12. This very interesting post raises two questions for me: What is the cause and what is the effect: nominal interest rate or inflation? Second, what if the rational expectations hypothesis is not correct?

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  15. >stable inflation

    So stable theft from productive people is better than unstable theft? Well, I suppose that's Knight's distinction between insurable risk and uncertainy. But, yet, perhaps, re an Aristotelian view of Hazlitt's concern with unintended, long-range effects, stable theft is the potential that actualizes as unstable theft.


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