Friday, August 08, 2014

Can the Fed set interest rates?

Most people think that in normal times - i.e. when the Federal Funds Rate is well above zero - that the Fed is able to set that interest rate through open market operations. You don't hear a lot of people saying that OMOs have no effect on interest rates.

But that's exactly what's implied by the famous "Wallace Neutrality" paper, also known as Wallace (1979). Neil Wallace was a leading light of the "New Classical" or "freshwater" generation of macroeconomists who revolutionized the discipline in the 70s and 80s. He is one of the main intellectual predecessors of Steve Williamson, Randy Wright, and the rest of the current "New Monetarist" or "money search" movement.

Wallace shows that if the government works in a very specific way, then Open Market Operations can't change interest rates. Specifically, the government has to set fiscal policy to exactly cancel out monetary policy, by making sure that OMOs leave A) government consumption, B) taxes and transfers, and C) income distribution completely unchanged. 

In other words, Wallace Neutrality is very much like the so-called "Sumner critique" of fiscal policy. It says that fiscal policy can cancel out monetary policy if it wants to. That makes sense, at least in an idealized world, and it implies that monetary policy is inextricably bound up with fiscal policy, which is interesting.

But I don't think Wallace Neutrality should be our jumping-off point or "base case" for thinking about how monetary policy works!

In a recent post about QE, John Cochrane wrote:
[S]tandard theory makes a pretty clear prediction about [QE's] effects [on interest rates]: zero.  OK, then we dream up "frictions," and "segmentation," and "price pressure" or other stories.
The "standard theory" he's talking about is the Modigliani-Miller result. But Modigliani-Miller is about the value of firms, not of government bonds. So what he's really talking about is Wallace Neutrality, which bills itself explicitly as "A Modigliani-Miller Theorem for Open-Market Operations."

But Wallace neutrality is not Modigliani-Miller, for two reasons.

First, a sufficient condition for Modigliani-Miller to hold is the existence of frictionless complete markets. But that is not sufficient for Wallace Neutrality to hold - for that, you need a certain government policy rule. We can think about frictionless complete markets as a sort of "natural base case", and that sort of makes sense. But it doesn't really make sense to use a certain government policy rule as a "base case", especially when that policy rule seems nonsensical in the first place (Why the heck would the fiscal authority try to exactly cancel out the monetary authority's actions??). Modigliani-Miller seems deep and fundamental, while Wallace Neutrality seems more arbitrary and specific. 

Second, the government is a policy-maker, not a price-taker. Its decisions create the overall economic environment in which agents act. So even a small departure from Wallace Neutrality-enforcing behavior, or from the other conditions required for Wallace Neutrality, will allow the Fed to target interest rates, simply by doing enough OMOs. See Miles Kimball on this point.

In other words, when someone says that Modigliani-Miller doesn't hold, it makes sense to ask "Why not?" But when someone says Wallace Neutrality does hold, it makes sense to ask "Why?" 


  1. The Badger of Bothwell Street10:47 AM

    Nice post Noah

  2. If Wallace Neutrality does not hold, then neither does monetary offset. The Sumner Critique is contradicted by Wallace (& Sargent). And it does not appear to operate in practice either.

    1. Anonymous11:49 AM

      I suppose that if fiscal policy is considered exogenous then monetary policy could be used to cancel it out and the Sumner effect would hold. If monetary policy is considered exogenous then fiscal policy could be used to cancel it out and the Wallace Neutrality would hold.

      If both try to cancel each other out (because they are targeting different things) you would get an interesting arms race

    2. Anonymous2:42 PM

      Doesn't the Fed "move last," so to speak?

    3. Yes. This is why it's occasionally possible to use monetary policy to shift employment, inflation, etc.

      Of course, that assumes functional financial institutions too. Oops.

    4. The game of chicken (& egg) between central bank and Treasury to my mind means that neither fiscal nor monetary policy can properly be considered exogenous. It's fun trolling market monetarists by pointing out that monetary offset implies fiscal dominance, though.

  3. It doesn't sound like Kimball agrees with you:
    [Theoretically modelling Wallace Neutrality departures] is worth many dissertations because it is not good enough to have a departure from Wallace neutrality in your model, it needs to be plausible as a description of why the real world departs from Wallace neutrality.

    It seems to be taking Wallace neutrality as the natural state.

  4. Why the heck would the fiscal authority try to exactly cancel out the monetary authority's actions

    Let us take a weak form of Wallace neutrality: that fiscal policy can under looser conditions partially offset the effects of monetary policy. Conversely monetary policy can partially offset fiscal policy under loose conditions.

    To answer your question: If, for example, democratically elected Congressmen thought it would be a good idea to enact spending cuts, caps and sequesters, shut down repair projects on the nations highways and threaten to default on the national debt and some pointed headed academic know nothing thought those policies were bat shit crazy then said pointy headed academic might be tempted to use monetary policy to partially offset and frustrate the policies of the democratically elected government. One can imagine a circumstance where monetary and fiscal authorities are so at odds they each seek to cancel the effects of the other's policies. Theoretically speaking of course.

    1. I do think QE3 was done sort of as insurance against the debt ceiling clown show.

      Also look at Japan. They've been doing massive QE with some success but the recent sales tax negated it somewhat.

    2. Anonymous8:15 PM

      Yes, this

  5. If money is neutral then MM and Wallace neutrality always hold in long run it seems. In short run I doubt MM holds and Wallace may if fiscal is offsetting exactly what monetary policy does.

    Money neutrality (real variables stay the same in long run regardless of MP) should imply that real interest rates stay the same I think. I think the same is true for nominal rates.

    Asset purchasses by fed bring down rates in short term which increases ngdp and inflation. Higher ngdp and inflation increase rate back to where it was without asset purchase in long term. So rates in long run appear to not be affected by monetary policy anyway.

  6. Well, I once spent about 50 hours studying this paper, and did a couple of blog posts on it, that for me were well received (by Miles, for instance, and Cohen-Setton). A far harder paper to nail than MM, but I think I sucked out some good intuitions.

    "Specifically, the government has to set fiscal policy to exactly cancel out monetary policy, by making sure that OMOs leave A) government consumption, B) taxes and transfers, and C) income distribution completely unchanged."

    I mean, he does assume real fiscal policy is held constant, but that seems perfectly fine, as no one argues that real fiscal policy can't have a huge effect.

    I think the problem with interpreting this model literally to the real world is at least that it treats all investors (people) as too skilled and knowledgeable, in fact perfectly skilled and knowledgeable, so that as soon as any asset's fundamentals, its risk-adjusted return, goes above normal, they immediately pounce on it and push it back down. So, in other words, it treats any "good deal" like a perfect, and perfectly obvious, arbitrage. But a good deal, an above average risk-adjusted return, is not at all a perfect arbitrage. It can still have great risk, and it is only an above average risk-adjusted return to you personally so long as it's not in a quantity that too unbalances your portfolio.

    Another issue is that the model does assume that any QE the central bank does will 100% be reversed at some time in the future, with perfect certainty. In the RW investors can't be so certain of that.

    For details on my thoughts, see:

    1. Ok, I'll add to this. Wallace neutrality (WN) assumes that private investors will just completely undo whatever the Fed does, just like in MM private investors just completely undo whatever the firm does.

      But this assumption is based on a few things which will far from perfectly hold in the real world – just like MM is (well acknowledged everywhere in academia, practice, and by its authors) to be based on some things which will far from hold in the real world.

      With regard to WN:

      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.

      Because of these, there really is a perfect arbitrage if WN 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.

  7. "First, a sufficient condition for Modigliani-Miller to hold is the existence of frictionless complete markets. But that is not sufficient for Wallace Neutrality to hold - for that, you need a certain government policy rule."

    Actually, the model Wallace uses to illustrate the neutrality of open market operations is one with frictions - it's an OG model. So apparently lack of frictions isn't necessary for neutrality.

    1. By no frictions I meant no trading costs, no information gathering and analysis costs of time and money, no delayed action due to time to realize and analyze,...

      I wasn't aware that OG (overlapping generations?) was a friction?

    2. The demographic OLG structure prevents agents from different generations to trade, this is a friction or markets incompleteness. Money (or any other transferable store of value) helps to overcome this problem and is a bubble in the model (Samuelson, 1958).

  8. I actually agree with Cochrane, coming at it from a different point of view:

    QE affects short interest rates, not long. "Printing money" affects long term rates, however the direction of impact depends on the relative strengths of the income/inflation effect (low today, so don't rise with expansionary) and the liquidity effect (high today, so rates would fall with expansionary policy). In the 1970s, the income/inflation effect would have dominated.

  9. 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.

  10. I am disappointed - I thought you were going to discuss an even more fundamental question than that, which has troubled me for years!

    In normal times, the central bank balance sheet is a tiny fraction of the overall banking system balance sheet. I have never understood how any interest rate change that the central bank tries to make away from the market equilibrium is not simply overwhelmed by the effects of a significant change in the underlying interest rate on the huge stock of loans and deposits on the banking system balance sheet. In the early days of economic blogging, I had a long and inconclusive discussion of this with jkh (here: ), and I felt a little vindicated by the fact that central banks expanded their balance sheets massively as they held interest rates at zero.

    Perhaps the explanation is that central banks have limited power to "set" interest rates by market operations in normal times.

  11. Noah,

    Do economic models and rules apply for every national economy in the same manner?

    Do models and rules that work for the U.S. economy apply only to the U.S. economy because it is the printer of the world's reserve currency?