Tuesday, May 20, 2014

Monetary offset: what are the assumptions?

In the lively comments on this post, there was some discussion of monetary offset. Mostly for my own benefit I thought I'd go through the monetary offset mechanism and discuss where model assumptions enter. Hopefully, I won't be too off base -- or if I am, it will be corrected in further lively comments.

I made a rather bold claim that monetary offset is at its heart an assumption about the power of monetary policy in a footnote, citing Scott Sumner's paper [pdf]. I'll use that paper as the primary reference for the discussion here. The assumptions will be titled in bold below, with details after -- Vox-style.

AD/AS model

The basic framework for monetary offset Sumner puts forward is the AD/AS model. I'll just link to the wikipedia page for what assumptions that entails. Here is the diagram from Sumner's paper that I'll refer to a couple times below:


The idea is that the central bank is targeting an economic equilibrium (price level or inflation) at A so that a boost in AD to AD' through fiscal stimulus, moving the equilibrium from A to B, implies that the central bank will tighten (or will be expected to tighten), bringing AD' back to AD and the equilibrium back to their target at A.

AS is unaffected

One assumption in the AD/AS model I'd like to pull out is that AS is unaffected by shifts in the AD curve. A different way of putting that is that the equilibrium point A still exists to return to if the fiscal expansion leading to the shift to AD' occurs.

I discuss the possibility of the original equlibrium A not existing in a different context in a post here. The assumption of the AD/AS model is that A does exist after the fiscal stimulus and monetary offset.

The central bank will meet/is meeting/has met its inflation target

This is one that I brought up with Sumner in the comments. The "inflation target" part itself doesn't matter so much -- it could be any number of targets or monetary policy regimes. The argument for monetary offset is that the central bank has a 2% inflation target so that when fiscal policy tries to move from A to B, rasing inflation above 2%, the central bank tightens (or is expected to tighten), bringing inflation back to 2%.

The "liquidity trap" shows how this assumption is important. In a liquidity trap, the central bank can't meet its inflation target, say only 1% inflation vs a 2% inflation target. Liquidity is hoarded -- not chasing goods and driving up the price level. If fiscal policy brings inflation up to 2%, then the central bank shouldn't be expected to offset it -- and if it did that would contradict the 2% inflation target assumption.

The monetarist counter to this (AFAICT) is that the central bank was really targeting 1% inflation, not 2% inflation -- i.e. the original assumption that the central bank was meeting its target.

The Concrete Steppes aren't too vast

I think it was Nick Rowe who came up with the phrase "the people of the Concrete Steppes" to refer to economists, bloggers and commenters who doubted that central banks could manage expectations and give forward guidance to move inflation or output without actually conducting open market operations (or showing what those operations could be) -- taking concrete steps. However, like Sumner's gold mining company analogy, sure the announcement can move markets, but they have to start producing some gold in the long run.

The assumption here is that the required concrete actions by the central bank are not outside the realm of possibility. To put it more economic terms, the commitments by the central bank are credible. I hope this roundabout way of getting to central bank credibility illuminates the model-dependence of the meaning of credible.

In Nick Rowe's argument, the concrete steps required are assumed to be effortless (humans just change their minds). I.e. the concrete steps are always feasible. Expectations based on these not-incredible steps are assumed to carry us from one equilibrium to another.

In general, monetarists assume any inflation target can be credible (maybe not specific cases -- Zimbabwe might not be able to credibly promise 2% inflation, but theoretically there could exist a central bank that has a given inflation target).

This credibility assumption is one that at least partially breaks down in the liquidity trap argument. As Paul Krugman likes to say, the central bank must credibly promise to be irresponsible to produce inflation. Monetarists will to point out that the central bank can still credibly produce deflation in the liquidity trap argument, hence monetary offset mechanism in the diagram at the top of this post still applies. Again, this counterargument is based on the idea that the central bank is meeting its inflation target -- a central bank cannot credibly create disinflation/deflation if it is undershooting its inflation target and fiscal stimulus brings inflation up to its target. (Although maybe the ECB really is actually this irrational? Its inflation target is 2% without fiscal stimulus, which it can't meet, and 1% with?)

In the information transfer model (ITM), expectations don't matter so much. Regardless of what is expected, the macro variables will generally follow their trends. However the ITM provides an example of the model dependence of credibility. If the monetary base (currency component 'M0') is small relative to NGDP, the assumption of central bank credibility is reasonable. If the base is large relative to NGDP, then some inflation targets may not be credible -- because some inflation rates are impossible in the model. Additionally, the tightening required to offset fiscal policy may be outside the realm of credibility (e.g. taking 10% of currency out of circulation to offset a 3% of NGDP fiscal package, as shown here). This lack of credibility for given inflation rates applies to deflation as well. The idea is that for some economies, ∂P/∂M0 ≈ 0, so both inflation and deflation can require incredibly large increases (decreases) in the monetary base -- if the target price level is even achievable at all.

Small fiscal impacts from monetary policy

One of the things (instruments? tools? this is where the proper technical term should go) central banks use to conduct monetary policy is interest rates. Imagine a budget constrained country with high debt to NGDP; raising interest rates -- considered to be a tightening move by the central bank -- would impact the debt service of that country, impacting the govenment spending package that brought AD to AD' in the diagram at the top of the post. Now the monetary policy required to bring equilibrium B back to equilibrium A is a function of the monetary policy itself! The problem becomes nonlinear and no longer obviously stable to perturbations around the equilibrium A. Additionally, the fiscal impact of debt service can potentially be the same magnitude as the fiscal spending package. In that case, raising interest rates brings you back to equilibrium A without any monetary impact on the price level. This is a bit like finishing building a piece of IKEA furniture and looking back at the box and finding a piece you didn't use.

Before this seems like a just-so story, I'll quote from my response to a comment by Mark Sadowski:
Debt service in Spain jumped fourfold in 2012 after the ECB rate increase, adding 30 G€ in payments, or about 3% of 1 T€ NGDP. Because of the budget constraints, that meant government spending decreased about 3% of NGDP -- accounting for the entire [observed] loss.
I'm not saying this is the definitive answer. This might not be the mechanism that produced the double-dip recession in the EU -- maybe monetary offset is the real reason.

If there are no concrete steps required and the central bank can always meet its targets, the assumption of small fiscal impacts is less of an issue.

More assumptions?

Potential additions in future updates.

21 comments:

  1. "If the base is large relative to NGDP, then some inflation targets may not be credible"

    In MM terms changes in the base affect expectations so they do have a concrete steppe but only one. But its also important whether these changes are permanent. So this implies to me that it is important how the base enters the system. If the fed mailed everyone notes this seems to be permanent whereas expanding excess reserves may simply be not permanent.

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    1. This temporary vs permanent shows up in interest rates;

      http://informationtransfereconomics.blogspot.com/2014/02/the-link-between-monetary-base-and.html

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  2. Off topic.

    I was hoping to get your opinion on whether you agree that a higher MB to NGDP ratio is a symptom of poor information transfer or monetary policy innefectiveness.

    I can give an example where the MB grows 0% but you get growth in NGDP just by taking all the excess reserves converting them to notes and mailing them out to the public.

    There must be additional factors which affect how strong the effect on NGDP from growing the MB is like the transmission mechanism.

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    1. I get sloppy with my language sometimes ... The price level is connected to the currency component of the base in the model. The currency component is related to long term interest rates as well. The monetary base (BASE at FRED) is connected to short term interest rates.

      The issue at high currency to NGDP ratio is the relationship between the unit of account function of money (the definition of dollar) and the medium of exchange function (the amount of dollars).

      The competition between these two effects leads to less monetary effectiveness at large amounts of currency relative to NGDP.

      (Currency component is MBCURRCIR at FRED)

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    2. In your example short term interest rates would stay constant and long term rates would fall. If the currency component was large compared to NGDP you wouldn't get any change in the price level or NGDP growth. If the currency component was small compared to NGDP growth you'd get inflation and NGDP growth.

      (This is in reference to your example where you convert reserves to cash and mail it out ...)

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    3. "If the currency component was large compared to NGDP you wouldn't get any change in the price level or NGDP growth. If the currency component was small compared to NGDP growth you'd get inflation and NGDP growth."

      If Currency/NGDP is large or small you should get a change in NGDP growth in reality it seems. People get this extra money their liquid wealth goes up and a proportion of it will be spent.

      "If the currency component was small compared to NGDP growth you'd get inflation and NGDP growth."

      So does this mean you agree that NGDP can grow even if MB doesnt grow?

      I will give you a better example. Just imagine the federal reserve lets everyone hold reserves directly at the fed and they can be used for transactions just as efficiently as commercial bank deposits. If then these reserves are transfered to the public evenly instead of only commercial banks you would get an increase in spending without growth in MB right?

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    4. Regarding your first question, in the information transfer model, there is a "saturation" of the market with currency (liquidity) after which more currency doesn't impact NGDP very much. The additional currency means that "a dollar" doesn't carry as much information.

      Regarding whether NGDP can grow without currency (M0) growth -- that is dependent on M0/NGDP. For low values of M0/NGDP, NGDP growth at constant M0 is deflationary. For high values of M0/NGDP, NGDP growth can happen without M0 growth.

      Here is a plot of the price level vs changes in NGDP starting from various years (in the US):

      http://twitter.com/infotranecon/status/469193367306649600

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    5. "Regarding your first question, in the information transfer model, there is a "saturation" of the market with currency (liquidity) after which more currency doesn't impact NGDP very much. The additional currency means that "a dollar" doesn't carry as much information."

      "Regarding whether NGDP can grow without currency (M0) growth -- that is dependent on M0/NGDP. For low values of M0/NGDP, NGDP growth at constant M0 is deflationary. For high values of M0/NGDP, NGDP growth can happen without M0 growth."

      I agree historically under all existing monetary policy approaches increases in currency have low impact on NGDP. But that relation wouldnt hold true in an instance where all the excess reserves were made into currency and mailed out. If people deposited this currency at their bank then bank deposits would go up and the actual bank deposits would increase NGDP as they are transacted. It just depends how it is performed.

      Just trying to show how it isnt necesarily true that increases in currency wont impact NGDP even when currency level is high.

      Its probably better to look at MB than currency though for policy implications IMO. Currency mainly comes about when people demand physical money instead of deposits or electronic reserves. The fed uses MB to manage policy and currency is just what people decide to convert into physical.

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    6. The mathematical reason currency increases don't impact NGDP in this model is that the price level P(NGDP,M0) =a k (M0/m)^(k - 1) with k = log NGDP/log M0. As M0 → NGDP, k → 1 and the exponent k - 1 → 0 so that P ~ constant. I.e. the price level is constant with respect to the currency component of the monetary base.

      This means it has to do with k which is the "information transfer index" and relates the number of bits needed to specify M0 vs the number of bits needed to specify NGDP. It has to do with the information content of money in defining a unit of account -- which is different that most other theories of money, but appears to be empirically accurate.

      More on the information transfer index is here:

      http://informationtransfereconomics.blogspot.com/2013/06/what-role-does-information-transfer.html

      You said "Its probably better to look at MB than currency though for policy implications" ... actually it isn't; MB does a much worse job describing the price level:

      http://informationtransfereconomics.blogspot.com/2014/02/the-role-of-central-bank-reserves-in.html

      The most the monetary base seems to be able to do is affect debt service payments by affecting short term interest rates, which can impact fiscal policy in budget constrained economies.

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    7. "the price level is constant with respect to the currency component of the monetary base"

      This doesnt seem to be true empirically. Do you have a source to confirm this empirically?

      "You said "Its probably better to look at MB than currency though for policy implications" ... actually it isn't; MB does a much worse job describing the price level:"

      What I mean by policy implication is 1. How hard the fed is expanding base (stance of policy) and 2. Its effect on ngdp, prices (effectiveness of policy). I know other people have different definitions on what the stance is like Sumner who think NGDP growth is the best definition.

      "The most the monetary base seems to be able to do is affect debt service payments by affecting short term interest rates, which can impact fiscal policy in budget constrained economies."

      Under the current and historical monetary structure this is correct. But under a different structure you can have different effects and hence certain assumptions will be incorrect or only apply in some circumstances. For example high MB/NGDP ratio doesn't always mean inefficient monetary policy if structure is changed when at high ratio of MB/NGDP.



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    8. "[As M0 → NGDP, k → 1 and the exponent k - 1 → 0 so that P ~ constant. I.e.] the price level is constant with respect to the currency component of the monetary base"

      This doesnt seem to be true empirically. Do you have a source to confirm this empirically?


      You cut off the beginning of the quote which I put back in brackets. As k → 1, the price level becomes constant. Japan comes to mind. But if you look at the countries near the top right of this graph then you can see ∂P/∂M0 ≈ 0 as M0 gets large.

      The diminishing impact of monetary expansion is illustrated here:

      http://informationtransfereconomics.blogspot.com/2014/03/the-diminishing-effect-of-monetary.html

      But the reduction of inflation at large monetary base is a well known empirical result -- it appears in Barro's macro text (with a different explanation) and Sumner references it here:

      http://www.themoneyillusion.com/?p=20216

      You said hence certain assumptions will be incorrect or only apply in some circumstances.

      That is certainly true, but I haven't found a country yet with a high M0/NGDP ratio and high inflation.

      Part of the reason I tried applying information theory to markets is to come up with universal economic relationships, not accidents of history. The monetarist view seems to be an accident of history (it came around in two times when the base of many countries was small relative to NGDP). The pure Keynesian view seems to be an accident of history too (it came around at a time when the base was large relative to NGDP). Both of these theories are accurate in their time. The information transfer model gives us a way to interpolate between them. See here for more on this:

      http://informationtransfereconomics.blogspot.com/2013/09/an-information-transfer-history-of.html

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    9. "You cut off the beginning of the quote which I put back in brackets. As k → 1, the price level becomes constant. Japan comes to mind. But if you look at the countries near the top right of this graph then you can see ∂P/∂M0 ≈ 0 as M0 gets large."

      OK I misunderstood what you said.

      "But the reduction of inflation at large monetary base is a well known empirical result "

      Yes but it is not a universal economic relationship IMO becuase once at a high MB/NGDP I can easily envision circumstances like modifying how monetary policy is conducted which would generate this inflation or supply side factors causing inflation too. Does your model also assume low NGDP growth at high MB/NGDP ratio?

      "That is certainly true, but I haven't found a country yet with a high M0/NGDP ratio and high inflation."

      What about latin america?

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    10. In the information transfer model there are just two ways monetary policy can be conducted: exogenously or endogenously. Everything we've been talking about here is endogenous. Exogenous monetary policy results in hyperinflation, so yes, monetary policy can be conducted differently.

      But (if the model is true) there are only those two options.

      1. Monetarist economics when the base is small relative to NGDP; Keynesian economics when the base is large.
      2. Hyperinflation.

      Regarding Latin America, I looked into Argentina with the hyperinflation model here:

      http://informationtransfereconomics.blogspot.com/2014/01/rich-countries-poor-countries-japan-and.html

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  3. Jason, can you possibly back out MB expectations by taking market interest rates, controlling for some NGDP trend, and then letting the MB vary? It seems to me that interest rates suggested MB provision was lacking before the credit crunch.

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  4. Thanks, I wonder if the Fed caught up to the market demands for MB or vice versa. There certainly was a policy change in the MB between 1998-2008.
    http://research.stlouisfed.org/fred2/graph/?g=Bii

    I'm wondering if you'd expand your methodology pre-1947/-1960? http://www.measuringworth.com/ has good data for the US and UK, alongside FRED back to 1918.

    You may be pleased with the 1920s-1930s MB/NGDP relationship to rates. The handoff from reserves to currency in the 1940s is also a topic ripe for exploration.

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  5. This credibility assumption is one that at least partially breaks down in the liquidity trap argument. As Paul Krugman likes to say, the central bank must credibly promise to be irresponsible to produce inflation.

    The problem is, they haven't, in fact they've promised the opposite. The ECB and the Fed haven't materially altered their long-term inflation targets, indeed the Fed has preferred to miss low and the ECB seems bent on containing inflation to the point of inducing recession. BOJ loosened a bit and saw some good results, but they're still in line with ECB and Fed.

    The Fed has teased markets a bit with QE but no one really believes they're going to inflate more than 2%, because they keep promising they won't.

    But there is absolutely no reason CBs can't credibly promise more inflation. They just haven't.

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    1. Hi Dave, you said:

      "But there is absolutely no reason CBs can't credibly promise more inflation. They just haven't."

      That is the monetarist model assumption. I agree that it isn't ruled out by empirical data. But the assumption that the market expected average value of inflation plus error E[i] = 2% + ε is hard to credibly change is also plausible. Both of these interpretations are empirically valid -- they both predict 2% inflation.

      However both these "explanations" assume the answer: inflation is 2% because either 1) it's what the Fed wants or 2) it's what the market expects the Fed to deliver on average. It's the assuming-the-answer part that makes me suspicious of expectations-based models. Additionally, neither of these is consistent with the quantity theory of money where the growth rate of the price level is equal to the growth rate of the base**:

      http://research.stlouisfed.org/fred2/graph/?g=D43

      M growth has averaged higher than CPI growth for the past 10+ years. The data is consistent with a model where log P = k log M (the growth rate in P is proportional to the growth rate in M) and that equation is consistent with long run neutrality.

      ** Not even including QE.

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  6. In a liquidity trap, the central bank can't meet its inflation target, say only 1% inflation vs a 2% inflation target.

    They could simply change to a 3% or 5% target. Markets would have to accept it. Who's going to bet against the Fed's target when they can purchase every asset in existence to support the policy? They might miss by 1%, but not 3%.

    The idea is that for some economies, ∂P/∂M0 ≈ 0, so both inflation and deflation can require incredibly large increases (decreases) in the monetary base -- if the target price level is even achievable at all.

    Hmmm, this model sounds more like the result of certain decisions generally made in certain situations than a natural law. There's always a danger in applying empirically-derived models to make predictions about situations that involve a lot of decision-making by people who are themselves becoming aware of the model.

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    1. Regarding your first paragraph, this is interesting: it breaks the rational expectations assumption by adding a systematic bias δ so that E[i] = i* + ε + δ where ε is the random error. It leaves a hole in the theory -- you now have a regularity, a bias δ ≈ 1%, that is unexplained by the underlying theory.

      Regarding your second paragraph, the general trend towards ∂P/∂M0 ≈ 0 is apparent only when you look across countries:

      http://informationtransfereconomics.blogspot.com/2014/02/it-really-does-seem-to-be-about-size-of.html

      So it is seems unlikely that the same decisions have been made in each country at exactly the right moment. It is true that this may be the result of advanced countries having correlated monetary policies, but the model does have a lot of explanatory power. It even allows the monetarist view and the liquidity trap view to be correct in certain limits (notably when M0 is small and when M0 is large, respectively) -- it doesn't prejudge which scenario is correct and lets the empirical data decide.

      The other issue you raise is effectively the Lucas critique. The model evades the Lucas critique by assuming ignorance about the microfoundations:

      http://informationtransfereconomics.blogspot.com/2014/02/ii-entropy-and-microfoundations.html

      The things that appear to be microfoundation-independent economic results are:
      1. Supply and demand
      2. Long run neutrality of money
      3. Maximally uninformative prices (i.e. the EMH)

      These are properties of large ensembles of economic agents regardless of how they interact with each other as long as they exchange information through transactions -- at least in this model. It may or may not be correct.

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