Monday, July 2, 2012

Some Doubts About NGDP Targeting

Nominal GDP (NGDP) targeting as a monetary policy rule was first proposed in the 1980s, the most prominent proponent being Bennett McCallum. The NGDP target was a direct descendant of the money growth target - Milton Friedman's proposal from 1968. Of course, money growth targeting was adopted by many central banks in the world in the 1970s and 1980s. It's rare to hear central bankers mention monetary aggregates in public these days. Why? Constant money growth rules failed miserably, as one central building block of the quantity theory approach - the stable money demand function - does not exist.

McCallum's reasoning (and here I may be taking some liberties - I'm working from memory) was basically the following. We all know that MV=PY. That's the equation of exchange - an identity. M is the nominal money stock, however measured, P is the price level, and Y is real GDP. Thus, PY is nominal income. V is the velocity of money, which is defined to be the ratio of nominal income to the money stock. That's what makes that equation an identity. A typical quantity theory approach to money demand (for example read some of Lucas's money demand work) is to assume that the income elasticity of money demand is one, so from the equation of exchange, the theory of money demand reduces to a theory that explains V. Friedman would have liked V to be predictable. The problem is that it's not. Technology changes. Regulations change. Large unanticipated events happen in financial markets and payments systems. As a result, there is considerable unpredictable variation in V, at both low and high frequencies.

So, McCallum looked at the equation of exchange and thought: The central bank controls M, but if M is growing at a constant rate and V is highly variable, then PY is bouncing all over the place. Why not make PY grow at a constant rate, and have the central bank move M to absorb the fluctuations in V? As economists we can disagree about how growth in nominal income will be split between growth in P and growth in Y, depending in part on our views about the sources and extent of non-neutralities of money. But, McCallum reasoned, NGDP targeting seems agnostic. According to him, we don't really have to fuss with the complications of what the non-neutralities are, or whether non-monetary factors are to some extent driving business cycles.

Central bankers and macroeconomists did not pay much attention to NGDP targeting. To the extent that central banks adopted explicit policy rules, those were inflation targets, for example in New Zealand, Australia, Canada, the UK, and elsewhere. The reasoning behind this seemed to be that, central banks get in trouble when they become overly focused on "real" goals, e.g. the level of real GDP, the unemployment rate, etc. In an overconfident attempt to "stimulate" the economy, the central bank may just stimulate inflation, and then have to backtrack. Producing a sustained low inflation rate when that rate has been high for a long time produces a recession, as in the U.S. in 1981-82. But if the central bank commits to a low inflation rate forever, we can get the benefits of low inflation and less real instability to boot.

An early 1990s development was the Taylor rule, which became a component of New Keynesian models, and crept into the language of central bankers. American central bankers find the Taylor rule particularly appealing. Their past behavior appears to fit the rule, so it does not dictate they do anything different. Great! As well, the Taylor rule seems to conform to the intent of Congress's dual mandate.

The Taylor rule takes as given the operating procedure of the Fed, under which the FOMC determines a target for the overnight federal funds rate, and the job of the New York Fed people who manage the System Open Market Account (SOMA) is to hit that target. The Taylor rule, if the FOMC follows it, simply dictates how the fed funds rate target should be set every six weeks, given new information.

So, from the mid-1980s until 2008, everything seemed to be going swimmingly. Just as the inflation targeters envisioned, inflation was not only low, but we had a Great Moderation in the United States. Ben Bernanke, who had long been a supporter of inflation targeting, became Fed Chair in 2006, and I think it was widely anticipated that he would push for inflation targeting with the US Congress.

In 2008, of course, the ball game changed. If you thought economists and policymakers were in agreement about how the world works, or about what appropriate policy is, maybe you were surprised. One idea that has been pushed recently is a revived proposal for NGDP targeting. The economists pushing this are bloggers - Scott Sumner and David Beckworth, among others. Some influential people like the idea, including Paul Krugman, Brad DeLong, and Charles Evans.

In its current incarnation, here's how NGDP targeting would work, according to Scott Sumner. The Fed would set a target path for future NGDP. For example, the Fed could announce that NGDP will grow along a 5% growth path forever (say 2% for inflation and 3% for long run real GDP growth). Of course, the Fed cannot just wish for a 5% growth path in NGDP and have it happen. All the Fed can actually do is issue Fed liabilities in exchange for assets, set the interest rate on reserves, and lend at the discount window. One might imagine that Sumner would have the Fed conform to its existing operating procedure and move the fed funds rate target - Taylor rule fashion - in response to current information on where NGDP is relative to its target. Not so. Sumner's recommendation is that we create a market in claims contingent on future NGDP - a NGDP futures market - and that the Fed then conduct open market operations to achieve a target for the price of one of these claims.

So, what do we make of this? If achieving a NGDP target is a good thing, then variability about trend in NGDP must be bad. So how have we been doing?
The first chart shows HP-filtered nominal and real GDP for the US. You're looking at percentage deviations from trend in the two time series. The variability of NGDP about trend has been substantial in the post-1947 period - basically on the order of variability about trend in real GDP. You'll note that the two HP-filtered time series in the chart follow each other closely. If we were to judge past monetary policy performance by variability in NGDP, that performance would appear to be poor. What's that tell you? It will be a cold day in hell when the Fed adopts NGDP targeting. Just as the Fed likes the Taylor rule, as it confirms the Fed's belief in the wisdom of its own actions, the Fed will not buy into a policy rule that makes its previous actions look stupid.

There's another interesting feature of the first chart. Note that, during the 1970s, variability in NGDP about trend was considerably smaller than for real GDP. But after the 1981-82 recession and before the 2008-09 recession, detrended NGDP hugs detrended real GDP closely. But the first period is typically judged to be a period of bad monetary policy and the latter a period of good monetary policy.

Here's another problem. There is a substantial source of variability in real and nominal GDP that we rarely think about, as we are always staring at seasonally adjusted data. Indeed, the Bureau of Economic Analysis makes it really hard to stare at unadjusted National Income Accounts data. I couldn't unearth it, and had to resort to Statistics Canada which, in their well-ordered Canadian fashion, puts all of these numbers where you expect to find them. The next chart shows the natural logs of Canadian nominal GDP, seasonally adjusted and unadjusted.
The seasonal variation in unadjusted NGDP is pretty clear in that picture, but to get an idea of the magnitude, the next two charts show HP-filtered seasonally adjusted and unadjusted Canadian NGDP, respectively.

The first chart looks roughly like what you would see for the same period in the US. Typical deviations from trend at business cycle frequencies range from 2% to 5%. In the unadjusted series, though, the deviations from trend are substantially larger - typically from 5% to 10%.

The second chart is interesting, as you can see both the seasonal variation and the cyclical variation in NGDP. If we want just the percentage deviations of unadjusted NGDP from seasonally adjusted NGDP, we get the next chart.
There's a substantial amount of variation there - on the order of what we see at business cycle frequencies.

So, if variability about trend in NGDP is a bad thing, why should we not worry about the seasonal variability? I can't see how any answer that the NGDP targeters would give us to that question could make any sense. But they should have a shot at it.

The monetary models we have to work with tell us principally that monetary policy is about managing price distortions. For example, a ubiquitous implication of monetary models is that a Friedman rule is optimal. The Friedman rule (that's not the constant money growth rule - this comes from Friedman's "Optimum Quantity of Money") dictates that monetary policy be conducted so that the nominal interest rate is always zero. Of course we know that no central bank does that, and we have good reasons to think that there are other frictions in the economy which imply that we should depart from the Friedman rule. However, the lesson from the Friedman rule argument is that the nominal interest rate reflects a distortion and that, once we take account of other frictions, we should arrive at an optimal policy rule that will imply that the nominal interest rate should be smooth. One of the frictions some macroeconomists like to think about is price stickiness. In New Keynesian models, price stickiness leads to relative price distortions that monetary policy can correct.

If monetary policy is about managing price distortions, what does that have to do with targeting some nominal quantity? Any model I know about, if subjected to a NGDP targeting rule, would yield a suboptimal allocation of resources.

The idea that it is important to have the central bank target a NGDP futures price as part of the implementation of NGDP targeting seems both unnecessary and risky. Current central banking practice works well in the United States in part because the Fed (pre-financial crisis at least) is absorbing day-to-day, week-to-week, and month-to-month variation in financial market activity. Some of this variation is predictable - having to do with the day of the week, reserve requirement rules, or the month of the year. Some of it is unpredictable, resulting for example from shocks in the payments system. I think there are benefits to financial market participants in having a predictable overnight interest rate, though I don't think anyone has written down a rigorous rationale for that view. Who knows what would happen in overnight markets if the Fed attempted to peg the price of NGDP futures rather than the overnight fed funds rate? I don't have any idea, and neither does Scott Sumner. Sumner seems to think that such a procedure would add extra commitment to the policy regime. But the policy rule already implies commitment - the central bank is judged by how close it comes to the target path. What else should we want?

Finally, there is no guarantee that the central bank could always hit a given NGDP target, even if it wanted to. The reason some prominent Old Keynesians like the NGDP rule is that they think they can't lose with it. Suppose we are Old Keynesians, and our view is that NGDP is now 10% below where it should be. So, being Old Keyensians, we think monetary policy should be more accommodative. Even if all we accomplish is a 10% increase in prices, that will deflate some private debts, and at worst redistribute wealth toward those who were hurt by the recession. Good deal! The problem is that we are in a more severe liquidity trap than even Paul Krugman wants to think about. The only policy instrument that currently matters is the interest rate on reserves (IROR). If the Fed moves the IROR, or signals how it will move the IROR in the future, that matters. Otherwise, there is no effect on any quantities or prices. Making promises about future NGDP cannot help the Fed do a better job of making promises about the future path for the IROR, so NGDP targeting appears to be of no use in our current predicament.


  1. Interesting post Steve. One thought, just off the top of my head.

    The seasonality question is interesting. We could push it further. Should we want the same level of NGDP on weekends as during the week? What about nighttime?

    But then I think the same question could be asked for inflation targeting, or price level path targeting, because there is a seasonal pattern to CPI too. And (my guess is) the CPI is higher on weekends. Not sure if the CPI is lower or higher at night.

    Monetary aggregates are seasonal too, IIRC.

    There used to be a seasonal pattern in nominal interest rates, in the olden days, IIRC, until central banks removed it.

    The question is not should monetary policy remove seasonality, but *which* seasonality should it remove, if any?

    Perhaps seasonality, and day of the week effects, are different from other real "shocks", simply because they are so forecastable, regular, and repeatable. It's easier for a decentralised system to coordinate in response to this sort of "shock". "Yep, it's Monday again."

    1. Yes, I could have gone on about this, but it's already on the long side. You can run any time series through X11 (or X-whatever) and it will do something. In the US they seasonally adjust everything, including the CPI, but it's not clear there is a seasonal in there. Indeed, my memory is that Statistics Canada does not seasonally adjust the CPI (I may be wrong, or things may have changed). Bruce Smith, Bruce Champ, and I wrote a paper that included some stuff on seasonality in money and interest rates, and Jeff Miron wrote about it, I think. In the US, prior to 1913 the seasonal is in the nominal interest rate and not in the money stock. After 1913, the Fed puts the seasonal in the money stock and takes it out of the nominal interest rate. Interestingly, Canada in the pre-1913 period looks like the latter (without a central bank).

      A lot of what we are seeing is coordination - Christmas, weekends, regular hours of work. The question is, how is that different from business cycle fluctuations, or is it?

    2. StatsCan reports both seasonally adjusted and unadjusted CPI every month. Core gets seasonally adjusted too.

      The Bank of Canada cleverly ducks the question, by saying it targets the 12-month inflation rate. If it were price level targeting, that dodge wouldn't work.

      "Interestingly, Canada in the pre-1913 period looks like the latter (without a central bank)."

      Hmmm. That is interesting. Something for students of Canadian monetary history to explain. It must tell us something. Dunno what.

      "The question is, how is that different from business cycle fluctuations, or is it?"

      My guess: weekends are a bit like "drive on the left or right side of the road". The business cycle is like StagHunt (JJ Rousseau). 2 person game, each person alone can catch a hare, but it takes both to catch a deer. One deer is bigger than 2 hares.

  2. Actually, thinking about seasonality is a regular repeated shock reminds me of something Lucas once said about rational expectations equilibria. I don't remember his precise words, but it was something to the effect that we should be very wary of assuming the economy will hit the RE equilibrium after a shock that is genuinely new, but if the shock is regular and repeated agents will have figured out the RE equilibrium. Seasonality, and day of the week effects, will be presumably like that.

    A second thought: You say: "If the Fed moves the IROR, or signals how it will move the IROR in the future, that matters. Otherwise, there is no effect on any quantities or prices."

    Lets suppose that's true.

    "Making promises about future NGDP cannot help the Fed do a better job of making promises about the future path for the IROR,..."

    Yes it can. Just as the Bank of Canada's promise of a 2% inflation target helps us understand the implied conditional promise about how it will adjust the overnight rate in response to various events.

    Suppose I want to know where you are driving. You drive by turning the steering wheel. But which tells me more? Your promise to drive to Toronto, or your promise to turn the steering wheel right, then left, then hold it straight for a bit....?

    The same nominal interest rate would be both very high if expected future NGDP is low and very low if expected future NGDP is high.

    It's that indeterminancy of nominal variables under interest rate control thing again.

    1. Are you telling me you can get the same nominal GDP path with different paths for the nominal interest rate?

    2. I meant it the other way round. You can get different paths for NGDP for the same path of the nominal interest rate. (Nearly all of those paths would be either explosive or implosive eventually, but hey, maybe the economy *will* be expected to explode or implode eventually, unless the Fed does something different.)

    3. Path one: the Fed sets the IROR and target FFR at zero till the end of time, come hell or high water. Result: hyper-NGDP growth.

      Path two: the Fed promises to raise the IROR and target FFR whenever inflation ticks up, but to keep them at zero as long as inflation is too low. Consequently, both stay at zero till the end of time. Result: NGDP contraction.

      Where am I going wrong?

    4. You're going to have to be more specific. I don't know what model you're thinking about.

    5. Basic Woodford setup. Point is what you need for determinacy besides a policy rate path is a policy goal. The policy rate may remain at zero forever because the Fed is trying to maximize inflation, or it may remain at zero forever because the Fed is trying accommodate negative real rates due to expectations of perpetually tight money. Aren't both possible in Woodford?

    6. Take a (say) consumption-Euler equation:

      real interest rate = alpha(E(Y(t+1))-Y(t))
      where Y is log real GDP.

      Add expected inflation to both sides, assume alpha=1, fudge just a little on the math, and you get:

      Nominal interest rate = E(NGDP(t+1))-NGDP(t)

      Sloppy and crude, but good enough for the basic idea.

      (I think I'm saying basically the same thing as Ram, but I'm not 100% sure.)

    7. Right. What Nick said.

    8. Keep it simple. Suppose Y(t)=Y forever. It's a representative agent endowment economy, and C=Y forever. To make it a little more interesting, put money in the model, say cash-in-advance. Now consider equilibria where the nominal interest rate is zero forever. First, there are many money supply paths that support the zero nominal interest rate. See Ricardo Lagos's paper:

      Journal of Economic Theory, 145(4) (July 2010): 1508-1524

      That's Lagos-Wright, but there is an early cash-in-advance paper by Charles Wilson that Lagos cites which gives you something similar.

      In any equilibrium with a zero nominal interest rate, the price level has to be decreasing at the rate of time preference. That comes from your Euler equation that prices the nominal bond. So Nominal income has to be falling at the rate of time preference. Of course, the level of nominal income is indeterminate.

    9. Steve: Yep. We are on the same page. It's the same basic idea. The only difference is that those of us who are of the sticky-price persuasion think that the falling NGDP path might be some mix of falling price level and falling Y(t), due to falling Aggregate Demand.

  3. ...and the job of the New York Fed people who manage the System Open Market Account (SOMA) is to hit that target.

    Actually, it is not their job to hit any particular target. Their job is to get the best deal possible in purchases and sales of bonds.

    Just as the Fed likes the Taylor rule, as it confirms the Fed's belief in the wisdom of its own actions, the Fed will not buy into a policy rule that makes its previous actions look stupid.

    Steve...just who is "the Fed?" FOMC members? Why would the current generation of Fed leaders care about not make previous generations look bad if they were wrong?

    1. 1. Someone at the New York Fed is responsible for hitting the fed funds target (not now of course, they really don't do anything as the interest rate on reserves determines the overnight rate). Who is it if it's not the SOMA manager?

      2. The Fed is you and your buddies. Every institution does this. There's an implicit agreement that you always defend the institution. The institution does not like people who don't do that.

  4. Friedrich Hayek proposed a version of NGDP targeting in a widely circulated 1975 publication, and in a series of published interviews and conversations over the next decade.

  5. Regarding NGDP deviations from trend, here is an old post of Beckworth on that topic: here

    Also, see Josh Hendrickson's new paper on the Fed effectively targeting NGDP during the Great Moderation: here

  6. Agree with Ram. A sane central bank never makes promises about the path of IROR. All that would do is redistribute wealth to interest rate arbitragers. Rather, a sane CB sets IROR to hit its target as best it can. If IROR is stuck at 0%, then it makes a big difference whether the target is a rate target or a level target (with a level target inflation expectations will eventually rise).

    1. I'm not saying that making announcements about the future path of IROR is a sensible thing to do. This is what I think matters in the current context.

  7. Scott Sumner responds here.

  8. SW if I read you right you think what matters is IOR.

    Do you think that if the Fed stops paying interest-or even charging interest this would jumpstart growth and would you see that as desirable?

    I seem to read you as saying you don't think the Fed would ever consider doing this. Why not-it chose to start paying them in 2008 couldn't it just decide to stop?

    1. Yes, the interest rate on reserves is currently 0.25%, and the Fed could set it to zero. That wouldn't do much, but why don't they do it? Bernanke is on record as saying that there are "technical reasons." I think this has to do with money market funds, which I will write about another time. In principle the Fed could charge negative interest on reserves. That's not an option, as it's not allowed here. Here's a post about it:

  9. Incidentally just in case you aren't aware of it. Lars Christensen has an answer to your answer to Sumner's answer...

    Think I said that right

    To sum up he's "perplexed" why you're a Monetarist.

    "Williamson claims that he does not agree with everything Friedman said, but I wonder what Friedman said he agrees with. If you don’t believe that NGDP is determined by the central bank then it makes absolutely no sense to call yourself a monetarist."