Winner of the New Statesman SPERI Prize in Political Economy 2016

Friday 10 May 2013

Sheedy on NGDP targeting and debt contracts

An argument that is sometimes made for a monetary policy that targets a path for nominal GDP (NGDP) is that it reduces risk for most borrowers who take out debt contracts with repayments fixed in nominal terms (see, for example, Nick Rowe here). However, as far as I am aware, this argument has not been quantified in a way that allows it to be compared with the more familiar benefits of inflation targeting. A recent paper by Kevin Sheedy does just that.

Before getting to the punchline, it is worth setting out the argument more precisely. A good deal of the borrowing that goes on in the economy is to smooth consumption over the life cycle. We borrow when young and incomes are low, and pay back that borrowing in middle age when incomes are high. To do this, we almost certainly have to borrow using a contract that specifies a fixed nominal repayment. The problem with this is that our future nominal incomes are uncertain - partly for individual reasons, but also because we have little idea how the economy as a whole is going to perform in the future. If the real economy grows strongly, and our real incomes grow with it, repaying the debt will be much easier than if the economy grows slowly.

As most individuals are risk averse, this is a problem. In an ‘ideal’ world this could be overcome by issuing what economists call state contingent contracts, which would be a bit like a personal version of equities issued by firms. If economic growth is weak, I have a contract that allows me to reduce the payments on my debt. However most people cannot take out debt contracts of that kind, or insure against the aggregate risk involved in nominal debt contracts. We have what economists call an incomplete market, which imposes costs.

Monetary policy can reduce these costs by trying to stabilise the path of nominal GDP, because it reduces the risks faced by borrowers. Of course monetary policy cannot remove the uncertainty about real GDP growth, but if periods of weak growth are accompanied by periods of moderately higher inflation, then this is not a problem from the borrower’s point of view. (Koenig discusses this in detail in a paper here.)

How do we quantify this benefit of NGDP targeting, and compare it to the benefits of inflation targets? Sheedy defines a ‘natural’ debt to GDP ratio, which is the private debt to GDP ratio that would prevail if financial markets were complete. Under certain conditions the natural debt to GDP ratio is likely to be constant, and Sheedy suggests that departures from this benchmark are unlikely to be great. So a goal for monetary policy could be to close as far as possible the gap between the actual and natural debt to GDP ratio, in an analogous way to policy trying to close the output gap. To do this it would target the path of NGDP.

The current standard way of modelling the welfare costs of inflation, due to Woodford, is to measure the cost of the distortion in relative prices caused by prices changing at different times to keep up with aggregate inflation. This suggests monetary policy should have an inflation target rather than a NGDP target. (I note here that typically in the literature these costs are far greater than costs associated with output gaps.) What Sheedy does is set up a model which has these costs of inflation present, but also has the costs of nominal debt contracts discussed earlier. With these two different goals, an optimal monetary policy will go for some combination of inflation targeting and NGDP targeting. The key question is which kind of costs are more important. [1]

Sheedy’s answer is that the costs of nominal debt contracts are more important. The optimal monetary policy gives a 95% weight to the NGDP target, and just 5% to the inflation target. Now of course this is just one result from a highly stylised model, and Sheedy shows that it is sensitive to assumptions about the duration of debt contracts and the degree of risk aversion. Nevertheless it is very interesting result.

A very simplistic way of describing why this may be very important is as follows. If the focus of monetary policy is always on the cost of inflation, NGDP targets will appear to non-economists at least (e.g. politicians) to be second best. They are a nominal anchor, so we will not get runaway inflation or deflation by adopting them, but why not just target inflation directly? Who cares about nominal GDP anyway? This paper suggests a simple answer - borrowers care. If we see monetary policy has being important to the proper functioning of financial markets, as we now do, then reducing the risk faced by borrowers is a legitimate goal for policy. It may make sense for inflation to be high when real growth is low, and vice versa, because this reduces the risks faced by borrowers. I think a politician that was not beholden to creditors could sell that.

[1] For those interested in government debt, there is an interesting parallel in the literature. Some authors (e.g. Chari, V. V. and Kehoe, P. J. (1999), “Optimal fiscal and monetary policy", in J. B. Taylor and M. Woodford (eds.), Handbook of Monetary Economics, vol. 1C, Elsevier, chap. 26, pp.1671-1745.) developed the idea that nominal government debt contracts could be a useful way of avoiding costly changes in distortionary taxes following fiscal shocks, because inflation could change real debt. However Schmitt-Grohe and Uribe (Schmitt-Grohe, S. and Uribe, M.  (2004), “Optimal fiscal and monetary policy under sticky prices", Journal of Economic Theory, 114(2):198-230) showed that once you added in nominal rigidity to the model so that inflation was costly, inflation costs dwarfed any gains. This example makes the fact that we get the opposite result with private debt contracts particularly interesting, although as Sheedy and others have noted, this may be partly because this earlier literature assumed short maturity government debt.


  1. "Sheedy’s answer is that the costs of nominal debt contracts are more important. The optimal monetary policy gives a 95% weight to the NGDP target, and just 5% to the inflation target."

    That answer really surprised me. I didn't think it would be that big, especially in a model which (in my opinion) puts too much weight on the costs of variable inflation via the relative price channel. My priors were fairly flat, but centered on 50-50, till I read that bit.

    Plus, it would presumably be even bigger than 95%, if he added in real costs of default?

  2. But surely in a NGDP targeting world, lenders would require indexing? Inflation linked bonds are well established and they are even used by some corporates. Once it's clear that a recession will cause bond real values to go down, lenders will demand indexing. At that point NGDP would have no effect through this channel.

  3. This is an interesting point that I had not fully grasped until now.

    From both the borrowers and the lenders perspective I think that knowing the real future value of loans (and repayments on loans) should enable optimizations in the loan market that could easily outweigh the costs of variable inflation

    However at the level of an individual loan what is more important than either the rate of NGDP growth or inflation is the risk associated with the borrowers income (they may lose their job). If it can be shown that NGDP targeting on average stabilizes individual incomes over time as well as in aggregate compared with IT (less cyclical unemployment) then this would be a huge selling point compared with the relatively minor difference between comparing the value of loan repayments in PPP terms rather than current dollar value terms.

    1. In addition the fact that NGDPT tends to stabilize the debt/GDP ratio no matter what direction RGDP moves in also tends to minimize the chances of a dip in RGDP turning into a financial panic.

  4. Most people are not nett borrowers they are nett lenders.
    Therefor not having sufficient real yield (for mainly pensions) is a much bigger problem than what we see now on loans. Most pensionschemes in the UK (including extra private savings for that purpose) are simply under water at today's market conform yields and proper calculationinterest.

    From the other side. Look at the UK mortgages, under water isnot really that huge. High other debt is probably but mainly caused by borderseeking behaviour (compared to most other countries). Businesssector as well doesnot seem to be such a huge problem.

  5. Simon:

    "The current standard way of modelling the welfare costs of inflation, due to Woodford, is to measure the cost of the distortion in relative prices caused by prices changing at different times to keep up with aggregate inflation. This suggests monetary policy should have an inflation target rather than a NGDP target."

    This does not seem right if there are productivity shocks that alter relative prices. A strict inflation target would have to respond to such shockes by forcing distortionary changes on the new relative prices to maintain its target. A NGDP target would ignore theses relative changes (i.e. not worry about the resulting change in the price level)and focus just on NGDP. So in addition to the debt benefit, I would add the supply shock benefit.

    Here is an earlier discussion along these lines:

  6. I just sold a building to a not for profit org. I am holding the mortgage and charging zero interest, but adjusting payments annually based upon CPI-U. It's an adjustable principal motgage

  7. "If the real economy grows strongly, and our real incomes grow with it"....that is the key issue, isn't it? Something that NGDP advocates are not really focussing on. How realistic is that assumption? When stagnation is due depressed aggregate demand due to highly indebted households busy deleveraging, rasing expected inflation rates (as required by NGDP targeting) might paradoxically lead to further belt-thightening, since households would be fearful that their salaries won't keep up with raising inflation (due to a slack labour market). This will tend to offset the certainty benefits you talk about.
    Again, I have been making this point time and time again, but none of you guys has so far addressed it.....

  8. This is further confirmation of what quality your blog is.

    Keep writing and i will keep on publicising it downunder

  9. Methodology
    I probably would have started in making a pro-forma (virtual) BS (and P&L) of John Average and family. Virtual as say pensionrights will constitute the main part of the asset side (but wil not be there in a real BS most at least).
    Amounts insurance cies can give prices probably which makes calculating the present value not that difficult. Otherwise you end up with a calculationinterest discussion.
    Assets like pensionrights should be split how they are invested. Cannot take them all as parts will be in something else.
    Other assets probably a correlation with inflation can give some results.
    Pension problems will hit in rather late as it can be disguished for a time by the way bookkeeping is done. However they are already structurally underfunded in most countries making that worse will create an even bigger future problem. With basically two solutions: the printingpress (plus inflation) or default on pension obligations (hardly a blueprint for social success story).

    BSs are very useful for matching allthough you have to be careful basically you will only match amounts (and there is also a timefactor that might be relevant). Obo the ECB study Joe Average seems however to be a nett lender iso nett borrower.

    Probably wages (and similar) and tax effects are substantial as well.
    Wages as more inflation in bad times means basically lower real wages.
    Tax because of the progression (and usual late adjustment of that by governments especially in bad times). Both work negative as well for Jim Average if inflation risis.

    What has happened is that interestrates have been stabilised and reduced the last 2 decades or so. So has inflation.
    Stabilising interest makes things more predictable so investors see less risk and will accept lower yields. CB policies have done basically the same interestrates were structurally lower than a 'sort of free market' would likely give.
    Same with inflation as this is may be the biggest determinant of rates. The lower inflation the lower rates. More stable inflation the lower the risk the lower the risk premium the lower the rates.
    You donot see that in most systems as most simply assume risk of say UST to be zero anyway and that zero to be stable over time. It simply isnot, but that makes calculating very difficult so only few bother.

    Anyway low rates (based for a substantial part on low and stable inflation) have been priced in in assets. And simply constitute a big part of people's assets/wealth (and of the BS of banks but also of the market value of companies (as low COC and that sort of things). So you come into the Catch22 either you make clear that high inflation is temporary (and it will not work properly) or you donot and people assume it will be longer time and the mechanism starts (higher inflation to assumed higher nominal interest to lower asset prices to extra saving for pensions etc).

    Imho this makes this process very difficult to reverse. You would likely simply cut of large slices of people's wealth, but also of the BS of the bankingsector.
    Have a look at what happened in Holland there with the RRE market. Good example for the effect of hitting people's assets. To solve another problem they indirectly cut off a large slice of people's other main asset (housevalue) and the whole economy tanked.
    An effect we are likely to see when you increase inflation.
    Mind there is a huge difference between CB interest rates and marketrates. Have a look at Japan at the moment rates almost doubled because of the new inflation policies. They there kept asset prices high by massive cash injections.
    It is a complicated thing to design a system that doesnot have more risks than potential benefits and to oversee them. But clearly a good thing to be studied further.

  10. Another current issue. CBs blowing new bubbles.
    Your colleague Krugman has some ideas on that. And to be frank these ideas look undiluted rubbish.
    Just give you my thoughts.

    3 sort of assets (US bonds, PIIGS/French bonds, Shares).
    -Start with the first.
    There is a bubble. It is clearly not all bubble, imho most is likley not, but there some some components of the assterprice that are bubbly.
    Basically the 4 parts are:
    -bad economy;
    -safehaven effect;
    -QE (liq injection)
    -QE (directed at US paper).
    The first 2 I donot consider bubbly. The might create higher bondprices but not from a structural fundamental valuation pov. Insurance premium, or simply the normal way markets behave (economy bad ==> rates of safe stuff go down).
    The other 2 however are and the FED is even confirming that for point 4 at least. And it is hard to see if everybody is doing it with eg FED money how it would not increase bondprices.

    French/PIIGS paper.
    There is a lot of bubble in that. The extra risk carried with that is in no way reflected in the spread with say Germany or the US.
    Mainly to be explained by the liq injections all over the world and look for yield. Look for yield is btw also mainly caused by keeping the yield for safe paper very low.

    Shares. Looks also clearly bubbly. Estimated/prognosed yields are lower than anytime I can remember. Peak in sharemarket in economic at best so-so times is very unusual.
    What is most dangerous it looks to be mainly caused by short term buyers. Longer term investors (>1 Year have even decreased) while shorter term have considerably increased.
    You never know beforehand, but it has a very high bubbly factor in it. But especially a peak in an economic crisis should have alarmbells ringing.

  11. Isn't this classic Fischer? I am not sure what is added to the idea of debt deflation?


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