Wednesday, October 20, 2010

How Large Will QE2 Be?

In most of the public statements by Fed officials I have seen recently, there is little talk that is not leaning towards some type of second-round quantitative easing program (i.e. "QE2"). However, no one in power is saying much about how large these upcoming purchases of (presumably) long-term Treasury securities by the Fed will be.

Of course, you can find plenty of speculation outside the Federal Reserve System about he size of QE2. The New York Times editorial page writers think that the purchase should be at least $1.7 trillion. These people survey some economists, who think the intervention will be in the range of $500 billion to $1.25 trillion. This guy, who's including the asset purchases required to replace the mortgage-backed securities which he is assuming run off at a faster rate, says $3 trillion.

Maybe these people are just blowing hot air, but maybe they know something I don't, in which case this seems quite disturbing. Suppose I do the following mindless calculation. Assume the Fed wants 2% inflation per year, which requires an increase of maybe one percentage point in the inflation rate. The monetary base in the US is currently $1.96 trillion, so suppose therefore that I want this to increase by 1%, or 19.6 billion over the next year, which if this translates directly into inflation, gives me the extra 1% I want. This implies that QE2 could involve something like a purchase of $19.6 billion in long Treasuries over a year, or about $1.6 billion per month. What are these people thinking?


  1. Are the billions and trillions mixed up here? 1% of $1.96 trillion is $19.6 billion. So $19.6 billion over the next year, $1.63 billion per month?

  2. Stephen, excess inflationary pressures could be eliminated with IOR. IOR + massive QE is a foolproof combination that removes the limitation caused by the zero rate bound without creating excess inflation.

    By the way, I've just read your "Liquidity, Financial Intermediation, and Monetary Policy in a New Monetarist Model" paper. It has lots of nice features such as IOR and costs of financial intermediation. My main disagreement is with the desirability of variable inflation rate. Before the crisis, expectations of stable 2% inflation rate were embedded in a huge mass of sticky financial contracts (debt/GDP ratio is very high, in addition there are lots of derrivative transactions), and there are costs associated with the violation of stable inflation expectations. Your model is applicable to the situation where economic agents are expecting variable inflation rates (such as in 1980), and a very long transition period is needed at this time before the Fed could start targeting variable inflation rates. Here is a good post about stability of inflation expectations in terms of actual price level:

  3. I'm not sure I understand this New Monetarism.

    Old Monetarism tells me that MV = PY, with V fixed. Thus, taking logarithms and differenting with respect to time, I get that the inflation rate is equal to the money growth rate minus the growth rate of real output. Thus, unless you're expecting real output growth to be negative, with a current inflation rate of less that 0.5%, I can't see how a 1% increase in the money supply would lead to a new inflation rate of 2%.

    Does this come out of some Williamson-Wright model?

  4. David,

    Exactly. That's what I get for running of to the seminar without proofing this. Corrections are in there now.

    Money Demand Blog,

    Yes, if you have nominal debt contracts of different maturities, then inflation uncertainty could matter a lot, and you therefore should want your inflation target to be predictable. Modeling that is obviously a tough thing, but I think you are right that it is important.

    Old Monetarist,

    Yes, I was thinking Old Monetarism, or New Monetarism under the assumption that the new outside money is split between reserves and currency in the same proportions as the old outside money. I'm looking at year-over-year CPI headline inflation, which exceeds 1%, or year-over-year implicit-GDP-deflator inflation (about 0.8%) the last I checked. Then, take the current inflation rate to be 1%, assume that will persist in the absence of QE2, and that QE2 will not affect the GDP path.

  5. "Stephen, excess inflationary pressures could be eliminated with IOR. IOR + massive QE is a foolproof combination that removes the limitation caused by the zero rate bound without creating excess inflation."

    I forgot to reply to this part of your comment. IOR is always available. The problem is that, the larger the Fed's stock of long-maturity assets, the more it has to lose from increasing short-term interest rates. Increase IOR and everything has to go up - fed funds rate, T-bill rate, etc. Prices of long-maturity assets go down, and if the Fed wants to sell the assets it takes a loss.

  6. Stephen,

    This brings up something I have noticed about economists' discussions of QE: they tend to ignore the money multiplier.

    Effective reserve ratios are low enough so that $100b in ER's, to be 100% converted to RR's, would produce about $3tr in credit. Of course, no one is predicting that. Why not? It must be some SWAG about how much cash, exactly, the banking system wants to hold. In other words, QE proponents are saying, "inject $1tr, and maybe the banks will use $30b to support $1tr in loans/deposit creation. What about the other $970b? It sits in ER's. But why would banks want to hold $970b in ER's and not $1tr or $500b? How can we know, precisely, what the desired ER holding might be? Of course, it is unknowable.

    Inflation expectations targeting proponents make the above problem go away by saying, "the Fed doesn't need to know banks' preferences in advance, it just needs to tighten when inflation expectations overshoot the target." What do you think of this argument? The obvious problem is that expectations themselves can be jacked around by every small Fed move rather than settling at a stable equilibrium.

  7. There is more than one reason why thinking in terms of money multipliers does not help, among them the fact that reserve requirements essentially do not bind in normal times, let alone now when virtually all of the reserves are in excess of reserve requirements. The key question is: if the Fed swaps reserves for long-term Treasuries, do the banks just sit on the reserves? If not, what happens to them? For me, the critical part of the transmission mechanism, if it happens (rather than some deposit creation story) is that reserves can turn into currency (in that currency can be withdrawn by banks from their reserve accounts with the Fed), currency can be used in transactions, and more currency means higher prices. I don't know about the "inflation expectations" argument, but if the Fed begins to see too much actual inflation, they can always increase the interest rate on reserves, which in current circumstances will increase all short-term market interest rates. This puts them in a bind though, if the Fed is holding a huge quantity of long-maturity assets. If the Fed wants to undo the quantitative easing by selling the assets, it suffers a capital loss.

  8. Stephen,
    I share your concerns with possible losses on Fed's long duration portfolio, but I think that net benefits of removing zero rate bound limitation with aggressive QE are positive.

    Of course there are several alternatives that remove zero rate limit with lower costs:

    1. The fed could buy a diversified portfolio of short duration private sector bonds

    2. Some time ago you wrote about Ricardian fiscal stimulus: "When there are credit-constrained economic agents, a temporary tax cut for everyone, with a promise to pay off the resulting debt with higher future taxes, is effectively a large government credit program. It does not require any new government bureaucracy, and just works through the existing income tax mechanism. "

    3. The Fed could publish an expected path of future fed funds rates in each policy announcement. This approach was successfully used by Swedish central bank.

  9. 1. I think this is dangerous. I think the Fed did a bad thing when it acquired that large stock of mortgage-backed securities. This opens the door to all manner of credit market interventions that favor particular sectors, or indeed individual firms. It's best to stick to a Fed portfolio of Treasuries only.

    2. I think we are well past the phase where this type of intervention would have been useful. In any event, the key here is the commitment to future tax increases so that there is zero effect in terms of the present value of tax liabilities. Our federal government never seems fond of commitments to future tax increases.

    3. Perhaps better than this would be a commitment to an inflation target. Fed officials have been more explicit recently about the implicit 2% inflation target, but I think Plosser's idea of a new Accord with the Treasury is a good one.

  10. Nice post, Stephen.

    1. M in the equation of exchange should be M1, right? So, your calculations assume that M1 moves proportionally with M0.

    2. Velocity is beginning to increase and monetary policy should have a short-term impact on real economic growth. Assuming that velocity is growing faster than the extra economic growth coming from monetary policy, M1 would have to grow by less than what you suggested.

    3. Given that the money multiplier is variable and not constant, the calculation is much harder than running the numbers through the equation of exchange. M1 is likely to respond much less than M0, and that would suggest that M0 should grow at a (substantially) higher rate to get the desired impact on M1 (in the short-term).

    4. Currently the Fed is running huge surplusses, but what would happen if capital losses caused the Fed to experience losses? Could the Fed just print the money or would they have to take a loan from the Treasury?


  11. KP,

    I was just thinking about base money. I was thinking that at least the demand for currency is relatively predictable, and then the only problem I have with respect to the effects of quantitative easing is how an increase in base money affects the quantity of currency held. The effect could be zero, if the banks hold the additional reserves, or it could be larger than what I am saying if all the additional reserves end up in currency. I am taking some middle road where one extra unit of base money gets split between reserves and currency according to existing proportions. On (4), any losses get passed on to the Treasury, and they have to make it up, either by issuing more debt or raising taxes. If they issue more debt, and the Fed buys it, we are making up the losses by printing money.

  12. Stephen,

    I agree that interventions that favour specific sectors are very dangerous. However financial innovation has created new tools, such as indexes that represent the broad sectors of bond market universe. These new tools let us design credit market interventions in a non-discriminatory manner. Purchases of long term Treasuries have two problems - they have a potential in driving duration risk premium below zero, and they discriminate in favour of public vs. private sector. Non-discriminatory intervention in short term private sector securities has none of these disadvantages, as it is clear that credit risk premium is positive at this point.

    I share your concerns about credibility of Ricardian fiscal stimulus. Germany is an excellent example - when they have passed their fiscal stimulus package, they amended their constitution to limit structural budget deficits to 0.35% starting with 2016. Such stimulus coupled with similar constitutional amendment would be very advisable to the US in the current circumstances, as inflation expectations are very volatile while zero rate bound on interest rates is binding.

    I think that commitment to a price level target path is a very good idea.

  13. 1. I'm not sure why confining central bank purchases of assets to government debt amounts to favoring the public sector. The central bank is basically just manipulating the maturity and liquidity structure of the outstanding consolidated government debt (i.e. consolidating central bank and fiscal authority).

    2. Yes, I didn't go into this, but targeting a price level path would seem to be superior to an inflation rate targeting regime where you don't have to make up for the errors in hitting the target.

  14. Dear professor,
    I am confused about your argument as it seems to me that the relation between monetary base and inflation (the way you used it), does not seem to work in the context of the last 2-3 year's expansion of monetary base.

    If you look at monetary base figure here
    you see that the base has expanded from $800 billion to $2 trillion in 2 years, yet the inflation has not become 200 percent.

    Most of it seems to sit at excess reserves of banking institutions, and the pattern of accumulating excess reserves is totally different now compared to before 2008:

    As such, I would not be surprised if I see the size of QE2 to be much much larger than $20 billion and yet no materialization of one-to-one effect on inflation or credit.

    The fed does not seem to be targeting inflation when determining the size of QE2 but rather supporting some markets and credit channel.

  15. Stephen,

    don't you worry that inflation expectations could become unanchored should a price level target be implemented?

    A cycle of massive disinflation followed by massive reflation could spook households and investors into believing that the Fed has lost control of inflation (i.e. the public doesn't believe that the Fed is credibly committed to fighting inflation).


  16. "I am confused about your argument as it seems to me that the relation between monetary base and inflation (the way you used it), does not seem to work in the context of the last 2-3 year's expansion of monetary base."

    Yes, exactly. The recent data hardly conforms to the quantity theory of money. That doesn't mean that new money injections, at the margin, are all held as reserves. If you have some other way of thinking about this that can help to predict what the effects would be, I would be glad to hear about it.

    "The fed does not seem to be targeting inflation when determining the size of QE2 but rather supporting some markets and credit channel."

    This is not correct. In their public statements, Fed officials are explicitly concerned about inflation. They also have some ideas about how this might affect real activity.

    "don't you worry that inflation expectations could become unanchored should a price level target be implemented?"

    No. When a central bank targets a price level path, they can do it in such a way that people always know what inflation rate to expect, over various horizons.

  17. Stephen,

    I assume that you have a "standard" DSGE model in mind when you draw the conclusion that the Fed without problem could implement a price level target.

    What if people don't have rational expectations and are non-optimizers? In that case I would assume that an inflation target would work better given its simplicity.


  18. "I'm not sure why confining central bank purchases of assets to government debt amounts to favoring the public sector. The central bank is basically just manipulating the maturity and liquidity structure of the outstanding consolidated government debt (i.e. consolidating central bank and fiscal authority)."

    If bond markets were perfectly efficient, there would be no problem. But in fact central bank operations have a potential to distort prices of long term government debt. The price of long term government debt should reflect sovereign default risk premium and duration risk premium, central banks in some cases are able to drive these premiums below values that are socially optimal. This has real consequences, as public sector investments appear more attractive to policymakers than they really are.

    One famous example of bond market inefficiency is Greece - in 2006 Greek and German sovereign default risk premia were virtually equal. Another good example is Iceland.

  19. KP,

    What I had in mind was pretty vague. I was thinking about a world where the costs of unanticipated inflation have to do with nominal debt contracts of various maturities. Suppose that, in that world, if the central bank sets an inflation target, year-by-year for example, at 2%. Then, suppose that actual inflation is 2.1% per year for 30 years. The central bank would have done quite well according to its target, but the cumulative unanticipated inflation over a 30-year horizon, for someone issuing 30-year debt, would be substantial. If 2.1% actual inflation this year implies that the target should be 1.9% (roughly) next year, then I know what to expect, both over a 1-year horizon, and over a 30-year horizon. If you think of "standard DSGE" as a model where people are rational, then yes, that is what I'm thinking about. I don't think about models where people are irrational, as I don't think those are useful.

  20. Stephen,

    I believe that economics as a science will be dead (stop being taken seriously) within the next 20 years if we continue with our rational agent models.

    Keep general equilibrium, but: replace rational expectations with learning and replace complete rationality with bounded rationality.

    Primarily because we can't "prove" models like in physics, macro theory is evolving super slowly and we cling on to obsolete models.

    I agree with you: IS-LM, Keynesian Cross, Phillips Curve, Money Multiplier, etc. are all terminology we need to get rid off. But, so are rational expectations and complete rationality.

    In a world where people are learning and bounded rational, I believe that the KISS principle applies to economic policy. In short, an inflation target range, say 1-3% core pce inflation, would work better to anchor inflation expectations than a price level target.

    Should the Fed follow a price level target, I worry that the puplic would misunderstand the Fed's eagerness to keep inflation (much) hihger following the financial crisis, and begin to increase their expectations of inflation. Once they look at (or hear about it in the news) the size of the Fed's balance sheet, we are heading for double digit inflation.


  21. In a world where people are stupid, I guess the policymakers have to be just as stupid, as well as the economists trying to model all this stupidity. Maybe we should just quit and go hiking then. Once we start admitting stupidity into our models, it goes nowhere. There is plenty you can do with other frictions. Private information is quite rich in what it allows. We have hardly begun to explore that fully.