Wednesday, August 6, 2014

QE and interest rates

Source: Wall Street Journal
In an August 3 article, the Wall Street Journal made the graph at left.

The US and UK have done a lot of "Quantitative easing," buying up long-term government bonds and mortgage-backed securities, to the end of driving down long-term interest rates. Europe, not so much, and the WSJ article quotes lots of people imploring the ECB to get on the bandwagon.

It's a curious experiment, as standard theory makes a pretty clear prediction about its effects: zero.  OK, then we dream up "frictions," and "segmentation," and "price pressure" or other stories. Empirical work seems to show that the announcement of QE lowers rates a bit.  But those theories only give transitory effects, and there is no correlation between actual purchases and interest rates. (p.2 here for example.)

So back to the graph.

Here is the current US Treasury yield curve, from the really snazzy website provided by the Treasury. (It's nice to get something useful for our tax dollars!)  Yields rise from zero out to 3% at the 30 year horizon.

Here is the same graph from the European Central Bank. I'm too lazy to download the data and put them on the same graph, so you'll have to squint a bit. The US graph compresses the x axis. Overall though, you see Euro rates rising from the same zero to about 2.2%.

Hmm. If massive QE is supposed to lower long rates, why are Europe's long rates a full percentage point below ours?

OK, I admit this isn't serious.  It's got a "thesis topics" label on it for a reason. As always one can bring up other things that are not held constant. The WSJ article mentions the ECB's commitment to "do what it takes," meaning a threat to buy a lot of southern sovereign debt in the future. Though, if all it took was more promises from central bankers -- say to "do what it takes" to keep state pensions afloat -- to lower rates another percentage point, it would be strange that Fed officials haven't provided the needed hot air.

So I'll leave it as a suggestion, or maybe a request to let me know if the paper is already written and I just don't know about it. The large difference in QE across US/UK and EU seems like a fruitful way to measure its effects, and especially to get past announcements and measure its permanent effects. If any.

(Thanks to an anonymous correspondent for pointing out the WSJ graph and making the interest rate point.)


A correspondent put a US and Euro yield cure on the same graph for me. (I only use people's names if they say it's ok. You don't need my hate mail. Thanks though!)


  1. What is the "standard theory" that says QE has no effect on interest rates??

    1. Modigliani-Miller theorem. Price = expected discounted value of payoffs.

    2. John,

      Except when the non-discounted value of all payoffs is infinite. In this case, the payoffs on government bonds come from tax revenue. The non-discounted value of all future tax revenue is infinite. Therefore, the price can be whatever the central bank decides the price should be.

      Modigliani-Miller rests on the assumption that a firm when borrowing is limited in the duration that it can borrow for. If a firm could borrow for an unlimited amount of time (perpetual monopoly), then the price of its debt can float independently of the payoffs.

    3. I dont understand. QE has no effect on interest rates under MM theorem? QE affects prices and therefore the discount rate.

      "If massive QE is supposed to lower long rates, why are Europe's long rates a full percentage point below ours?"

      Economists should isolate the effects of QE. QE increases demand for longer bond if the CB is buying them so this decreases rate. At the same time more expansionary monetary policy generates growth which sends rates up. So QE could do anything to rates depending on the relative strengths of the effects it generates.

    4. @Frank Restly, just because future tax revenues are infinite (in aggregate) it does not follow that the discounted value of them is infinite. Surely there would be some sort of curve that would trend towards an asymptote at a point. And the value of that asymptote would impact the current valuation at least to some extent.

    5. Noah, Frank, CMA:

      QE neutrality is shown in Wallace (1981) "A Modigliani-Miller theorem for open-market operations" or Eggertson-Woodford (2003) "The Zero Bound on Interest Rates and Optimal Monetary Policy". Woodford's Jackson Hole paper includes a great discussion as well.

    6. Paul,

      Can government pull tax revenue from any point in time out to an infinite future to satisfy current expenditures? If it can, then discounting tax revenue is meaningless.

    7. I don't think MM is a good answer, because everyone accepts that MM far from holds in the real world. It's always taught as the starting point, and then you go into the major things that make it not hold to a large extent. It looks to me like Wallace's MM for open market operations is the same.

      I basically commented this at Noah's site:

      With "Wallace neutrality":

      1) You assume the central bank will at some time in the future 100% undo the QE.

      2) You assume that you, and all 100% of your fellow investors, are perfectly skilled, rational, and informed.

      3) You assume that markets are 100% complete (you can synthetically construct any asset), and frictionless (no transactions costs, no time and money costs to gather, input into your brain, and analyze information,…)

      Because of these, there really is a perfect arbitrage if Wallace neutrality doesn't hold, that investors will immediately jump on until it disappears. But in the RW there isn't a perfect arbitrage that all investors will immediately jump on until it disappears. What you'll get, all other things equal, is that some assets will now become better deals, better risk-adjusted returns; that may make some savvy investors hold more of them, but it won't be nearly enough to push prices to Wallace neutrality. A good deal is far from a perfect arbitrage. It can have a great deal of risk, and on top, it's only a good deal to a given investor in a quantity that doesn't too unbalance his portfolio.

      I had a couple of posts on this that were well received (for me), by Miles Kimball, for example, and at Bruegal. See:

    8. Maybe this is a better explanation (from my new blog post):

      In Wallace's model, the government is like a big MM firm. And the citizens are shareholders of the government. When the government does the Wallace version of a QE, it basically is like it borrows more money (really lends, but let's go with this example for now). That makes its citizens overall debt level higher than they like, so they borrow less by an equal amount to get back to their optimal overall debt level. The total demand for debt in the market remains unchanged. Government demand goes up by X, and private demand goes down by X, so the interest rate remains the same.

      In Wallace, all people are perfectly expert, with perfect public information, can do all analysis and information gathering and digesting instantly, at zero cost, and are perfect rational optimizers. They start the model in equilibrium with their optimal level of debt, and if the government, that they're "shareholders" in, borrows more, then they just instantly borrow less by an equal amount. So, interest rates don't change.

      More specifically in Wallace, as I remember it, there is a single consumption good. I called it C's. People save some of their C's for period two of their two period lives. The government's "QE" is to print dollars and exchange them for C's, which it will store for one period. Then it will sell all of those C's back again out into the market for dollars – with 100% certainty. That's their plan, everyone knows it, and they're going to stick to it.

      The people own the government. They're its shareholders; they get dividends in the form of government transfer payments, so when this government "firm" saves more C's, by selling newly printed dollars to get C's, and puts them into storage, then the people's overall savings goes up – up above their optimum that they had settled on in equilibrium.

      So they sell C's out of their private stores in an equal quantity to compensate. The total demand overall for the market to save C's for the future does not change, and so the interest rate doesn't either. And that's the thinking; that's why it works in Wallace's model. That's why you can prove no change when you do the math in this model.

      But why wouldn't this work in the real world?

      Well, first off, people are far from perfectly expert (especially in the super complex modern world), with perfect public information that they can gather, digest, and analyze at zero time, effort, or money cost.

      So, when the government "firm" starts to borrow a lot more, almost no one thinks, MM style, or Wallace style, I'm going to start selling some of my bonds to compensate in equal measure as I see them doing that. And so total borrowing in the market does, in fact, go up, and so do market interest rates. And vice-versa, when the government starts to lend more. People just don't react that way. And it won't be nearly enough if a savvy minority do. They won't control enough money to drive us to Wallace neutrality.

      It's like in Miller and Modigliani's model, if the firms start borrowing a lot more, but the shareholders are mostly not really paying attention, and/or don't know well the implications, so for the most part they don't borrow any less to compensate. In that case, aggregate demand for borrowing would not remain unchanged. The aggregate demand curve for borrowing would, in fact, shift out, and the interest rate would rise.

  2. Badger of Bothwell StreetAugust 6, 2014 at 11:46 AM

    Surely looking at real rates here is more appropriate than nominal rates. Collapsing inflation expectations in Europe dragging down nominal rates (see Japan) out does the QE effect. But it is falling real rates that matter to the economy. I am certain had the US failed to do any QE in long dated assets long dated nominal rates would be much lower but we would certainly not be better off.

    1. But inflation comes from...monetary policy. Oh I get it, the US QE so successfully lowered long rates that this created more inflation expectations, so that's why US long rates are higher. Boy this monetary stuff is tough.
      Seriously, if you have data that european inflaiton expectations are a percentage point and more lower than the US -- within one standard error, send them on.

    2. According to Bloomberg (ILBE function), 10-yr US inflation breakeven is 2.23 vs. 1.35, 1.25, and 1.07 in France, Germany, and Italy, respectively. Five-year US inflation breakeven is 1.97 vs. 0.52 and 0.50 in Germany and Italy, respectively. (I can't vouch for Bloomberg calculations/methodology, though.)

    3. I found the zero-coupon inflation swap rates (Bloomberg: ILBM), which are probably better than the breakeven rates. For Euro, the 5 and 10 yr inflation swap rates are 1.10 and 1.57, respectively. For US, 5 and 10-yr inflation swap rates are 2.28 and 2.57, respectively.

    4. So the question for Prof. Cochrane is: in a world of open capital accounts, what, other than QE, explains the fact that real rates in the US are uniformly less than or equal to those in Europe?

  3. Doesn't QE potentially weaken the currency, since the fed's balance sheet is more risky?

  4. To add insult to injury:

    1. The evidence is that there is little relationship between interest rates an investment spending. 2. The is NO RELATIONSHIP between base rates and credit card rates. 3. Interest rate adjustments are DISTORTIONARY in that, if they work at all, they boost just one type of spending: investment spending. We might as well implement stimulus by boosting just car sales and restaurant meals. 4. To maximise GDP, the price of everything, including the price of borrowed money should be MARKET PRICE, not a price determined by incompetents in central banks. 5. Adjusting interest rates causes gyrations in the value of the currency relative to other currencies, which is a nuisance for exporters and importers.

    In short, rather than adjust demand via interest rate changes, it would make more sense to have an African witch doctor ask the gods to implement more/less aggregate demand.

    1. " would make more sense to have an African witch doctor ask the gods to implement more/less aggregate demand."

      Yeah! Once again, Ralph, you made my day! (Glad I decided to get caught up today.)

  5. The Badger is right, US inflation expectations at least 80bps higher for as far as the eye can see, makes real rates in US lower especially at the short end.

  6. I thought European interest rates were so low because lending money to France for 10 years at 1.5% makes such darn good sense.

  7. - you can get data on market inflation expectations up to 30y from inflation swaps and breakevens, the ecb also looks at these instruments when it mentions inflation exp
    - should the rate comparison also mention expected differences in forward libor rates, which not necessarily mirror central bank base rates? Or maybe they also reflect cross currency differences?

  8. The Badger of Bothwell StreetAugust 7, 2014 at 4:05 AM

    I believe you are looking at the wrong indicator here by looking at nominal and not real rates. I have attached a chart of the price of European and US forward inflation from the inflation swap market. I have used the 3y3y point (2017-2020). The spread at this point is currently 0.98% and has been achieved by a fall in European expectations as US inflation expectations have remained broadly stable, furthermore 20y spot inflation in the US is 77bps higher than in Europe an 30y spot (a less liquid point) is 70bps higher in the US. I conclude that near to medium term real rates are substantially lower in the US than Europe and long term real rates are basically the same.

    Additionally, I have looked into the price of insuring against above target inflation (using caps on US CPI and European HICPx as the liquid traded products) in both the US and European and found it would cost more than double the amount to insure a portfolio of above 2% inflation for any period starting in 5y time.

    Simply put to ignore the difference in inflation expectations in US vs Europe is similar to ignoring them in Japan over the past 20 years.

  9. Jose Romeu RobazziAugust 7, 2014 at 7:06 AM

    QE may not have effect on interest rates, but it certainly shifts asset holdings around. This paper from the FED shows who is selling to the FED ( In short, Private Investors (hedge funds / wealthy individuals) are selling treasuries to the FED, and to some extent, Pension Funds are selling MBSs to the FED. Considering this, and the size of the FEDs balance sheet, this is how I see the effect of QE: Private Investors are shifting interest rate risk to the FED, and Pension Funds are shifting credit risk to the FED. Given the long duration, let's say 10 years, of these bonds and MBSs, should inflation surprise on the upside in the next couple of years (and should nominal rates follow through and rise by the same amout), the mark to market of the FED's balance sheet (a big loss!) will have created a wealth transfer from the public sector to the private sector of , let's say, 10% of 4 trillion, or 400 billion. This if nominal rates rise by only 1%. In addition, the liquidity in the system could spill over to other asset classes, and potentially, not necessarily, creating asset bubbles elsewhere. And we know, as has been said time and again, we only know of asset bubbles after they happen, so, why take the risk? why increase the possibility that they might happen in the future ?

  10. These graphs are not highly informative without graphs of the yield curves before QE. Doesn't the real growth rate affect the real interest rate? The unemployment/inflation rate in the US is closer to the Fed's target than the rate in the Eurozone is to the ECB's target. Were US interest rates not expected to rise faster and to a higher level than Eurozone rates before QE was announced?

    Interest rates are not the most informative measure here. If QE has a signal effect, then, if QE is effective, the liquidity effect and signal effect push interest rates in opposite directions and the net effect is ambiguous -- its direction may switch as the magnitudes of the two effects change. On the other hand, if QE is effective, both effects push NGDP and RGDP expectations in the same direction (up). Those are better measures for a test of whether QE is effective.

  11. Ultimately, it depends on how much selling of foreign reserves offset the purchases' effects.

    OK, I know this depends on expectations on future purchases, but if no foreign reserves are sold, and bond purchases are expected to continue, rates could actually go up to offset the expected future decline in USD:FX values.

    I suppose what's happening here is that people think the Fed is not going to sell all that much FX, so there's going to be inflation. But, the ECB is going to neutralize by selling USD, so not all that much inflation is expected.

    Another thing to think about is that when the US offsets QE by selling bonds to cover budget deficits, the effects of QE are neutralized even without selling FX.

    This is all just simple textbook stuff. But note that sales of FC reserves are hardly ever talked about, but have just as large an effect as bond sales and purchases.

  12. Quantitative easing occurs when the Fed buys longer-term government bonds or other securities in order to drive up bond prices, lower the interest rates, and allow for greater investment. When the Fed buys government bonds, the monetary base expands. QE is a type of monetary policy used to stimulate the economy. It does not involve the printing of money.

    Quantitative easing also depends on people's expectations and the distinguishing between nominal interest rates and real interest rates, which are not taken into account in the graphs provided above.

    Monetary policy is typically implemented by a central bank and has to do with the money supply and inflation, whereas fiscal policy decisions are set by the government and have to do with changes in aggregate supply and aggregate demand. The combination of both monetary policy and fiscal policy are necessary in order to renew prosperity.

  13. I agree with the statement that QE has no impact on long term interest rates -- coming at it from a different point of view:

  14. I still don't get it. If QE has no effect on inflation or interest rates, why not use QE to pay off the entire national debt and have the interest from those Fed-owned bonds funneled into the US Treasury?

    1. FWIW, given the odds anyone will read this, in the "standard theory", which is Neil Wallace's 1981 AER paper/model, QE doesn't matter for a lot of reasons that might not/will not hold in the real world. A big one is the QE in Wallace is not a permanent print dollars and sell them. Next period those newly printed dollars are exchanged back for all the stuff that was accumulated on the balance sheet during the QE.

      Also, Wallace has complete and frictionless markets and 100% perfectly expert and informed investors, so everyone just funges away perfectly what the government did with the QE to keep their consumption at the same optimal level -- it's also assumed that any proceeds from the QE go to them, and some other things.

      So, lots of ways Wallace Irrelevance, or neutrality, can not hold in the real world. I finally really understand this model inside out and really intuitively, and what goes wrong in the real world. Should have it really well explained in an upcoming post(s). And, one can hope, an offshoot model or two, maybe even with my 5 minutes of free time per week.

    2. I should reword: In Wallace '81, the government prints more dollars, buys the composite consumption good, stores/invests it, and then next period buys back every one of those newly printed dollars, and any profit or loss from this is reflected in taxes net of transfers (for generation t to be more precise). How do I know? It's the only way requirement (b) of Wallace's Irrelevance Proposition can be met (along with other things he requires), not hard to prove.


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