Sunday, May 18, 2014

Models matter


This morning I caught Scott Sumner quoting Mark Sadowski:
Now, one can argue that things would have been much worse in the absence of this massive infrastructural spending, but as Kaminska goes on to note, Japan didn’t lose monetary policy traction until much later. In fact the BOJ’s call rate didn’t really hit the zero lower bound until March 1999.
That's the crux of it, isn't it? The monetarist argument is as coherent as the Keynesian argument, so assuming the each side isn't comprised of morons one could argue that things would have been the same or worse (or better!) minus the massive spending by the Japanese government. It's all angels on the head of a pin without a model, though. You need to know that counterfactual. And in order to know the counterfactual, you have to be able to decompose the impact of monetary policy and the impact of fiscal policy.


Let me call up a previous post (and the relevant graph, updated with a red dashed line at a constant interest rate ~ 5%):


The graph shows the impact of an equal percentage increase in NGDP (blue arrows) and MB (red arrows) . For concreteness, let's say a spending package of 3% NGDP [1], or a 3% increase in the currency component of the monetary base. We'll also simplify the discussion by assuming the central bank has an inflation target (this is not an important assumption; the argument still applies if the central bank targets something else like the Fed's dual mandate of stable prices and low unemployment).

This graph is great because it also shows the effect of fiscal and monetary policy on interest rates. Before the 1980s, monetary expansion tended to increase interest rates. After the 1980s, monetary expansion tended to decrease interest rates. This is due to the changing relationship between the income/inflation effect and liquidity effect. Fiscal expansion always increase interest rates (i.e. crowding out).

We can see in the 1960s and 70s, the vectors are not orthogonal. In this world, monetary offset exists. If the government tries to spend more money to cause inflation (blue arrow), the central bank will just make its red arrow slightly smaller (do slightly less expansion) to achieve the inflation target it wants. After the 1990s, the vectors are closer to orthogonal. The central bank has no power to offset fiscal expansion without ludicrous contraction in the base e.g. a ~ 10% decrease in the base might have offset a 3% expansion in 1991 (figure is approximate):


The key takeaway in this post is not the particulars of the model, but rather the capability to show counterfactuals. The information transfer model can decompose the fiscal/monetary vector. The monetarist vs Keynesian/zero lower bound debate is precisely an argument about orthogonality. Monetarists assume the fiscal vector is parallel to the monetary vector; Keynesians assume they are orthogonal at the zero lower bound [2] (Never forget! Modern Keynesians like Paul Krugman assume the vectors are parallel away from the ZLB, just like monetarists). The information transfer model makes no assumptions about being parallel or orthogonal; the relationship comes from the underlying model. The interesting contribution from the information transfer model is to say that both these views are correct ... at different ratios of MB/NGDP.

A side note on the latter part of the quote. Paul Krugman (a proponent of the theory of the zero lower bound) frequently refers to the US and EU being at the "zero lower bound" even though they technically aren't at "zero" (the Fed has an upper bound of 0.25% and the EU was at 1.75% or higher from 2008 until as recently as 2012 and is now at 0.75%). By this usage, Japan was below 1.75% starting in 1995, so the piece at the end about not really being at zero obviously misunderstands the liquidity trap argument. The basic idea behind Keynes was that there is a lower bound to interest rates below which monetary policy will fail to spur people to forego liquidity. Later, this lower bound was considered to be (always) near zero. How do we make sense of Krugman's insistence that the EU at 1.75% was at the ZLB? Because the Taylor rule (or Mankiw's rule) calls for a negative interest rate. It doesn't matter what the actual interest rate is -- actually going to zero would be dandy, but it's because the interest rate favored by a Taylor rule is negative you have a zero lower bound problem. The target interest rate is relevant, but it alone doesn't define a liquidity trap (i.e. the Fed can't set the interest rate at 1% and make the liquidity trap vanish magically).

In the information transfer model, the liquidity trap interest rate depends on the size of the economy and the monetary base. The zero lower bound is only approximately equal to the liquidity trap rate (ZLB ≈ LT).

[1] Note that NGDP = C + I + G + (X − M), so a boost in G to first order increases NGDP. The crowding out effect of government spending is included in the model.

[2] It really is an assumption in the case of monetarists. Don't believe me? Check out Scott Sumner's paper on monetary offset [pdf]. In the first figure it just assumes that it is always possible for AD increase = AD decrease. It assumes the central bank can always hit their targets. For Keynesians, the monetarist position is the assumption. The liquidity trap (orthogonal monetary and fiscal vectors) is derived from something like the IS-LM model at zero interest rate.

38 comments:

  1. Jason, another interesting post! The first chart is the US, right? I drilled down about four posts trying to find out... into uncharted territory for me (more reading to do on my list!).

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    1. If I'm correct about it being the US, do you have a similar one for Japan?

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    2. OT: I hope you don't mind me posting links to your site everywhere, but if folks disagree with you for good reason, I'd like to see their arguments. (I also posted one at David Andolfatto's site last week... he responded but basically said he'd have to do more reading to understand your argument).

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    3. Thanks!

      And it is for the US. I haven't updated the version for Japan since the switch to M0 from the full MB.

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    4. And no I don't mind you posting links across the internet. It helps bring in differing viewpoints and can help strengthen arguments :)

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  2. Krugman's right that you can be in a liquidity trap with interest rates above zero. But he's wrong in assuming that if interest rates are above zero and rising, fiscal policy can still be effective for zero bound reasons. And in 2011 eurozone interest rates were above zero and rising.

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    1. Hi Scott,

      Before the crisis the EONIA rate (Euro OverNight Index Average) effectively matched the ECB main refinancing rate (the center of the ECB corridor). After the crisis, EONIA fell to almost the lower end of the corridor. That is abnormal for the Euro area.

      During 2011, if you squint through the noise, EONIA only rose back at best to the main refi rate -- is this a genuine rise in rates based on fundamentals, or a market that thought EONIA might go back to the refi rate? After the rise in 2011, EONIA fell back to the lower rate.

      My guess is that as long as EONIA is below the main refi rate, Krugman would say we're in a liquidity trap, regardless of the direction of the fluctuations in the EONIA rate. (I could be wrong about that.) The effective Fed Funds rate has risen and fallen a couple of times (by a much smaller relative amount, but still there is movement in the market).

      Difficult to use EuroStats (it's not on FRED) is preventing me from making a nice graph at this late hour, but I'll put one up tomorrow ... for now here is a graph of the ECB data:

      http://pfmag.com/what-is-the-ecb-refi-rate/

      And here is the analogous FRED data:

      http://research.stlouisfed.org/fred2/graph/?g=B2Y

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    2. True, many Euro Area banks are getting unsecured overnight funds at the EONIA rate, but banks on the periphery, which is about a third of the Euro Area by NGDP, are partially or totally cut out of the unsecured interbank market and can only finance themselves through the ECB’s operations at the MRO rate. Thus the MRO may not the most important rate in Germany or France, but it almost certainly is the most important rate in Italy and Spain.

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    3. Mark -- that may apply, but in that case Spain an Italy are basically acting like independent nations without their own currencies (not as e.g. states in the US); they would be unable to use monetary policy. That strengthens the argument for fiscal policy. In some sense, monetary policy becomes part of the ceteris paribus. The central bank can't act to offset fiscal stimulus in just part of the Euro area -- it would literally have to be disinflationary for the whole union to cancel out Spain's fiscal expansion.

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    4. I think you're missing the whole point.

      The ECB raised the MRO rate in April and July 2011. The Euro Area entered a 6-quarter double-dip recession the following quarter. Whereas RGDP declined by 1.4% in the Euro Area as a whole between 2011Q3 and 2013Q1, it declined by 2.7% in Spain and 4.1% in Italy, and similarly hit the entire periphery much harder than the core.

      What's the point of Spain and Italy doing a fiscal stimulus (assuming it wouldn't have caused their respective bond markets to do somersaults, which given what was happening at the time is not even debatable) if the ECB is simply going to offset it?

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    5. Mark -- I agree that the monetarist viewpoint is a coherent one that is consistent with empirical observations. The problem I have is that it's not the only one and it is difficult to unambiguously associate the raising of interest rates with monetary contraction that directly impacts AD.

      For example, did the ECB raising interest rates impact Spain through fiscal policy? 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 loss. It is interesting that Italy had a larger impact -- Italy's debt to GDP is higher.

      So we have two coherent stories:

      [Monetary] Did the ECB raise rates signalling contractionary monetary policy, lowering the growth in the price level and causing Spain's NGDP to take a 3% hit, with zero fiscal impact of higher interest rates?

      [Fiscal] Did the ECB raise rates in an an environment of ineffective monetary policy (no impact on the price level), leading to a 3% of NGDP increase in debt service, leading to a 3% impact on NGDP?

      The point of my blog post was that the information transfer model has the potential to unambiguously say it was one case or the other ... without pre-judging which one (the explanation depends on the fits to the data and both explanations are a priori possible).

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  3. "Fiscal expansion always increase interest rates (i.e. crowding out)."

    I can see circumstances under which fiscal expansion could decrease rates. For example if gov spending is used productively which would increase productivity and inflation and hence rates.

    In Australia until about 2008 fiscal policy was balanced and rates were around 7% under monetary expansion. That would be because the income inflation effect was stronger than the liquidity effect right?

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    1. Above comment is meant to read:

      "would increase productivity and reduce inflation and hence reduce rates"

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    2. Yes it would be possible for government spending to be used in a way that is more (or less) productive that might not be seen at the leading order analysis in this model. I guess I should say "fiscal expansion always increases interest rates to leading order".

      And regarding Australia, that seems to be on the right track. If rates stayed constant under monetary expansion, that would mean the income/inflation effect balanced out the liquidity effect, leaving rates constant.

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    3. Rates increased while government ran persistent surpluses for an extended period of time. That could just mean the income/inflation effect exceeded the liquidity effect.

      Interesting ideas on this blog. Just need to get my head around it all if possible. I don't even know what leading order analysis means. Gonna look it up.

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  4. Jason, I'm not sure you understood the implication of my comment. Even if you are in a liquidity trap it is possible to tighten monetary policy. And the ECB did that in 2011---it drove the eurozone into a double-dip recession. In that environment fiscal policy is useless for monetary offset reasons. BTW, market interest rates are not a reliable indicator of the stance of monetary policy.

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    1. How did the ECB tighten policy?

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    2. Scott, I originally understood your comment as "you can't be in a liquidity trap if interest rates are rising" but I see now that you were claiming that if the ECB can raise rates (i.e. giving forward guidance of contractionary policy), it can offset fiscal expansion.

      The Keynesian view is that expansionary monetary policy in a liquidity trap results in money hoarding (so the extra money has no effect on the price level); the ECB's contractionary move in that case should only de-hoard that money. I would imagine that even Keynesians believe that eventually the central bank could take away everyone's hoards and start producing some real deflation -- but we are assuming an inflation target (that is currently not being met due to slack in AD). Another way, the central bank can't reach 2% (stuck at 0% because of the liquidity trap), so fiscal policy comes into raise inflation to 2%. The central bank would have to then offset by ignoring its inflation target (but that contradicts the assumption of an inflation target).

      I think that is the Keynesian view (or at least how I understand it) -- the information transfer model says that monetary expansion (in reserves or currency) has only a small effect on the price level when the base is large relative to NGDP ... quite literally ∂P/∂MB ≈ 0. So even contraction doesn't do much to the price level.

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    3. "the information transfer model says that monetary expansion (in reserves or currency) has only a small effect on the price level when the base is large relative to NGDP"

      Would it be even more accurate to measure private debt to ngdp (instead of MB to ngdp) to ascertain the effectiveness of monetary expansion (effect on price level)? Because affecting the interest rate is changing the price of credit wouldn't the overhang of credit to ngdp indicate the effectiveness of credit expansions on the economy?

      The higher MB to NGDP was a consequence of ineffective monetary policy because affecting credit prices becomes less effective once credit is too high. It seems the cause of ineffectiveness is the actual credit market.

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    4. @dannyb2b Using the monetary base has some deeper theoretical meaning -- see e.g. here

      http://informationtransfereconomics.blogspot.com/2014/03/how-money-transfers-information.html

      But ostensibly you could set up a market P:NGDP→PD where PD is private debt and see where that leads you empirically.

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    5. I find the ideas on here really insightful in comparison to other blogs out there.

      I completely agree that MB to ngdp correlatives with diminishing effectiveness of policy. But I'm trying to understand what causes an increase in MB to NGDP. The efficiency of the transmission of MB into the system will determine its effect on NGDP. If money didn't transmit into the system (information medium) then its the same as if the MB didn't increase at all.

      I believe you would call it an inefficient transfer of information. Or even information not traveling at all.

      If the credit market is blocked due to demand/supply for credit low then MB effect on NGDP is diminished becuase most NDGP activity involves credit exchanges for goods and services in current system. Therefore MB increases and then NGDP doesnt or not much.

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    6. It is possible also for NGDP to increase if the MB is stable. Just imagine the fed maintained MB stable and transferred all the excess reserves evenly into the hands of the public. People would spend and NGDP would increase.

      The people could get these reserves if the fed converted them into currency and mailed them out to everyone of if the fed allowed all people to hold reserve accounts and transact in them like commercial bank deposits.

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    7. Scott, Jason,

      It's interesting that you are talking about the Eurozone. In some parts of the Eurozone we do indeed have a liquidity trap with real rates well above zero, because risk premia are higher than elsewhere in the currency union. In such an environment fiscal expansion itself causes real rates to rise. The central bank can offset to some extent by explicitly committing to specific asset purchases in those areas - but Scott, I don't think full offset is possible or desirable. After all, if the central bank offsets completely there is no reason for fiscal reforms or deleveraging, is there?

      It's fair to say this is all about expectations, not reality: OMT is currently subject to legal challenge and may never be used, but as long as markets believe in it, rates will stay low. But in the end, permanent falls in risk premia can only be reduced by fiscal reforms, deleveraging and return to growth.

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    8. duh, "achieved" not "reduced"....

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  5. My two favorite monetary guys chatting. I am in heaven. Keep it up.

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  6. Jason, also, it's phenomenal that MB>NGDP rises nonlinearly as rates approache absolute zero. This is the incentive mechanism whereby stagnant reserves are exchanged for NGDP-positive currency. It's a feature of the system, not a bug.

    They will never reach absolute ZLB, because MB goes infinite. I'd like to see them try.

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  7. Jason, Marcus raises some good questions here, but I'm wondering if you might have an alternative set of answers:

    http://thefaintofheart.wordpress.com/2014/05/19/inflationary-tinder/

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    1. Wrong, link, I meant this one:

      http://thefaintofheart.wordpress.com/2014/05/19/to-geithner-the-fed-was-the-hero/

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    2. The "forward guidance" points on the graphs don't appear in the same place (nor where forward guidance was actually issued in mid-Q3 of 2003 -- i.e. August).

      For unemployment and inflation, the dots appear just after 2003Q3 (this are the only ones in the right place).

      For employment, the dot appears between Q2 and Q3 of 2003.

      For NGDP it appears at just before 2003Q2. This one is the killer. If it was to fall when forward guidance was issued (August 2003, or mid Q3), then the FG dot would appear in the middle of the rise it was supposed to have caused.

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  8. Jason, "I stand by my dots". The right place is 2003.II. Because after that things changed significantly. Also, Forward Guidance was widely discussed in the June FOMC meeting (so there was someting in the air before the formal implementation).
    Also, the NGDP "killer" dot is right on Q2 2003! My point was that FG was effective in changing 'trends'. And you must agree it was.

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    1. You are suggesting a strong EMH interpretation, then?

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  9. Jason, O/T: does ITM have anything to say about possible inflation targets for "Chindia?":

    http://thefaintofheart.wordpress.com/2014/05/20/will-chindia-join-the-europa-america-stagnation-westernized-central-bankers-battle-prosperity-globally/

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    1. I haven't run the models -- India is currently at a monetary base (currency component) of ~12% of NGDP vs the US at ~7%, so it is possible India could run into stagnation. But I'd really have to get some good time series data, not just the current values.

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  10. So I'm (slowly) attempting to re-create your models. So far quite interesting and very educational and here is my first-ish attempt:

    http://imgur.com/vqGMUC3

    Couple of questions/points:

    1) I'm a little stuck on how you're getting the blue & red vectors. I grok the general concept but are those vectors representing changes in P or NGDP? My first attempt was just taking the gradient of the P surface but that doesn't seem to line up...

    2) I don't know if this is just the vagaries of the Matlab solver(s), but I'm not getting the exact fits that you are for the parameters. A lot of the time I don't seem to get proper fits at all and it's extremely dependent on starting values.. is this your experience as well?

    3) Do you have a data source for countries other than the US? I'm struggling to find good data series for places like Japan etc. and have had it with navigating the often byzantine central bank websites of these countries

    4) When you put multiple countries on one chart, how are you normalizing P? I assume with a P0, but is that fitted value.. or do you say normalize all your CPIs before feeding them in..?

    5) I've been trying to read up on information theory and the original paper - curious as to if there's any way of combining multiple sources, detectors etc. into one model - my math/intuition is not developed enough to work out how that might be done but it seems like an interesting avenue to explore...

    Thanks anyway, and sorry for the long list!

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    1. That's awesome!

      I started a comment and realized that it would work better as a new post dedicated to these questions. I should have it up sometime today and I'll post a link here when it's ready.

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  11. The title of this one reminded me of your post here Jason (it was a link from Noah's blog: the response to his book review):

    http://arambachan.blogspot.com/2014/05/caveat-importance-of-models-in-macro.html

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    1. Thanks for the link; that's an interesting take on Big Ideas: macroeconomics as assumption organization.

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