Monday, January 23, 2012

The real multiplier vs. the nominal multiplier

I've been having some interesting email discussions with Scott Sumner, and thus it is time for a macro post.

Scott Sumner and David Beckworth have recently been arguing that, once you take the Fed into account, the Keynesian multiplier (the effect of fiscal spending on GDP) is zero. This is true, they say, because the Fed acts to counteract any unusually rapid rise in nominal GDP. The idea is basically this: after a recession ( a fall in nominal GDP), in order to return to its previous trend, NGDP must grow faster than its trend rate of growth. But since NGDP = real GDP + inflation, and since a stimulus increases aggregate demand, this will involve higher inflation as well as faster growth. The Fed, Sumner and Beckworth hypothesize, will not allow higher inflation, and so will raise interest rates, thus canceling out the effect of the stimulus on aggregate demand. The multiplier, when measured in NGDP terms, and when defined to take the Fed's "reaction function" into account, will be zero.

Now, in the past, I've argued that the Fed would have to be crazy to do this. It would have to refuse to allow NGDP to grow fast in a recovery even after NGDP plummets in a recession. But maybe the Fed is crazy! If the Fed actually does have an emotional bias against inflation - which some people argue is a desirable quality in Fed governors, because it helps anchor low inflation expectations - then it just might do something very much like what Sumner and Beckworth imagine.

However, does this mean that fiscal stimulus is ineffective? I say no. Why? Because that would only be true if fiscal and monetary policy had identical and opposite effects on inflation expectations.

Realize that when we talk about the fiscal "multiplier," we're taking about a real multiplier - the effect of spending on real gdp growth. The growth rate of NGDP is equal to the real growth rate plus the rate of inflation. So it's possible for the real growth rate to rise in response to a stimulus while the nominal growth rate stays the same. This will happen if inflation falls. For example, you could go from having a 2% RGDP growth rate with 3% inflation before the recession, to a 4% RGDP growth rate with 1% inflation after the stimulus. NGDP growth is 5% before the recession and 5% during the recovery, but RGDP growth is different.

This is called a disinflationary boom. In the case of a stimulus-induced disinflationary boom, the real multiplier is nonzero even after taking the Fed's inefficiently hawkish reaction function into account.

How can a disinflationary boom happen? Well, inflation is determined in large part by expectations of future inflation. If the combination of fiscal stimulus and higher interest rates caused inflation expectations to be lowered (perhaps by giving the Fed an opportunity to prove its hawkishness), the Phillips Curve would shift downward, meaning you could get more real growth for any given rate of inflation. That would allow a disinflationary boom. The stimulus would push RGDP back to trend after a recession, while a permanent change would remain in the NGDP time series. In fact, if the episode increased the Fed's credibility in the long term, the combination of policies would have benefits beyond the effect of the stimulus.

Some people might argue that this describes the 1980s. Reagan's tax cuts, this story would say, acted as a Keynesian demand-boosting stimulus that raised RGDP growth, but that the accompanying inflation was tamed by the hawkish Volcker Fed. I'm not sure I believe that, but it at least sounds plausible.

Anyway, the upshot is that a nominal multiplier of zero, caused by a pathologically hawkish Fed, does not necessarily mean that the real multiplier - the multiplier we care about - must be zero.


  1. Andreas6:17 AM

    Interesting, even for a non-wonk. Won't the measures the Fed takes to combat inflation have an effect on real growth though?

  2. Well, inflation is determined in large part by expectations of future inflation.

    Is this an assumed axiom, or is there some actual reason for believing it to be true? I see this all the time, but never see any explanation better than this one (2nd para) which is very weak tea, indeed.

    Of course, I don't claim to see all and know all.

    Where can I find a convincing argument that expectations are a real inflation driver?


  3. As always, you've highlighted something that others seem to miss. Excellent.

  4. Anonymous3:19 PM

    This seems to be progress in the sense that people are now arguing why fiscal stimulus will have zero impact. That implies that it could, in theory, be non-zero, but they don't think it is. That's something to argue about and it's sure better than some of the previous false arguments based on mixed up ideas regarding accounting identities.

    In those cases, people weren't saying "It's theoretically possible for it to be non-zero, but I think it's actually zero." Instead, they seemed to be saying, "It must, by identity, be zero," which was total rubbish.

    So hey, that's progress! We've moved the discussion along enough to get people to admit that it's at least theoretically possible for it to be non-zero. Now all that's left is to show that, in reality, it is!

  5. (Preface all this with "I'm not an economist" so could easily be missing something). Noah, I don't think it's a point of dispute that if government spending was to, say, allocate real resources better then this could happen. But insofar as a 'recession' is caused by sticky prices, wages etc. then admitting that the Fed does control nominal variables means the government can't do anything about the loss of output / increase in unemployment caused by a nominal shortfall and subsequent disequilibrium. Another way of making a Sumneresque point would be to say that the central bank has the last say on Aggregate Demand, and therefore any 'multiplier' must be on the supply side. Which isn't impossible, but is completely different to the traditional Keynesian argument.

  6. Can't public spending projects get animal spirits up? Can't Fed exapansion of the money supply raise the rate of inflation? Can't inflation help reduce real wages in certain sectors of the economy that need reducing while maintaining or even allowing real wages to rise in areas where steady or rising wages are appropriate? Won't it increase the revenues generated by the graduated income tax and thereby help shrink the federal deficit? Won't it reduce the total debt of the federal government in relation to GDP? Won't it help restore the balance of trade by devaluing our currency, thereby stimulation exports, manufacturing, and employment? What's not to like? We just need a new name for it. Enhancement maybe.

  7. Looking up 'a priori' in the dictionary I find this:

    "existing in the mind prior to and independent of experience"

    Isn't this the nature of Sumner's argument?

  8. Why are economists constantly speculating about the FED´s goal function?

    Couldn’t someone ask the FED whether they would increase the interest rate if faced with a, say, one percent increase in inflation (coupled with some scenario for other variables)?

    If the FED would not answer such a question, an independent central bank is probably the worst institutional arrangement ever.

    PS; My guess is that the FED would keep the interest at zero even if inflation increased somewhat This would imply that the effect of the stimulus is twofold, rather than canceled out. My guess is that the FED would keep the interest at zero even if inflation increased somewhat This would imply that the effect of the stimulus is twofold, rather than canceled out. (I´m at least pretty certain that this is how Bernanke would want it to play out.)

  9. Noah,

    I am having a hard time seeing how expansionary fiscal policy could lead to a disinflationary boom. I can see how a surge in productivity could lead to a disinflationary boom. But fiscal policy stimulus? Help me here.

  10. Well, suppose that the combination of fiscal expansion and monetary tightening reduced inflation expectations by increasing the Fed's inflation-fighting credibility?

  11. Noah: As I understand it, we're assuming for the sake of argument that NGDP expectations don't change (because of the Fed, right?). So, the flip-side of decreasing inflation expectations is increasing real growth expectations. So what's the mechanism by which 'fiscal stimulus' accomplishes this? If we assume that increased spending did good things for real economic growth (e.g. investments in public infrastructure with above-average returns), then I can see why this would happen. But this would be true whether it was funded through debt or taxes. Insofar as 'fiscal stimulus' is normally understood to mean 'deficit spending', the increase in real growth [expectations] wouldn't have anything to do with the 'government spending' simpliciter, but rather that real resources have been allocated to growth-enhancing investments.

    I don't think anyone is denying that if there was an 'investment opportunity' open to the government and would provide (say) a 100% return on investment that this would be growth-enhancing. But it just emphasizes the point that this is nothing to do with 'stimulus' as traditionally understood (see ditches, digging and filling), and more to do with the provision of public goods (which the government should be doing anyway).

    The only other way my limited brain can see this working is through a kind of 'confidence fairy' type argument.

    What mechanism did you have in mind?

  12. Unemployment typically tends to destroy human capital (at least everyone who talks about the problems of getting the long-term unemployment back to work claims to believe this - they may of course be acting in bad faith). This is empirically observable (we still have an overhang of long-term unemployed from the 80s), intuitively sensible (skills benefit from practice), and logically consistent. It also works in different political/ideological frameworks (on the left - unemployment, imposed by capitalism, is bad for you, on the right - the unemployed lose the habit of work and must be disciplined). So I reckon it's probably a thing!

    Also, unemployment is correlated with poor physical and mental health, and it's not like depression or a bad back increases your productivity.

    In so far as a fiscal expansion reduces unemployment at time t, it implies we'll have a bigger stock of human capital at time t+1 and hence be able to grow faster in the recovery than we would in the baseline, no policy input scenario.

    People behave as if this was some weird insight, but I recently cleared out a bookshelf and found my 1990s intro economics textbook (Sloman). And the first page it fell open at covered just this point.

  13. (and this ought to be a serious effect - imagine if the economy suddenly discovered 10 million additional high-human capital workers! We'd surely expect a sizeable boost to GDP.)

    Anyway, there's a fascinatingly religious feel to the whole "well, the Fed will intervene" argument. We could have a stimulus, but the Fed would counter it, so we can't, and as a result we won't, and the question can never be put. Perfect circular logic.

    Of course, it falls down when you say as someone did upthread "well, why don't you ask them?" Or, come to think of it, "why don't you then amend the Federal Reserve Act, or dismiss the Fed chairman and replace him with someone else?"

  14. Noah,
    "Well, suppose that the combination of fiscal expansion and monetary tightening reduced inflation expectations by increasing the Fed's inflation-fighting credibility?"

    I agree that inflation is determined in part by expectations of future inflation but the fiscal expansion will also affect the expectations of future inflation. And would´t the monetary tightening influence negatively the real growth (short run)? If the FED increases its inflation fighting credibility in a situation where there is increasing fiscal expansion it means that the market believes that the FED will keep the monetary tightening for long as it is needed to keep AD in a health path (inflation expectation near the target) and by doing this wouldn´t the fiscal expansion effect on AD be eliminated by the monetary tightening (AD in a health path)?

  15. @ Alex 5.25

    Sounds like an excellent argument for enacting wage subsidies to me, and if the payroll tax cut had been on the employer side it would have done a lot more good for exactly the reasons you list. I'm probably less optimistic about the scope for large-scale increases in government employment, due to the problem of a) finding enough things to do b) using the exact skills of the unemployed so they don't 'lose practice' in the way you describe and c) the politics of when you terminate those jobs, how much you pay people etc. could get very nasty and counterproductive towards the end of the recession in terms of getting those people back into the private sector where their human capital is most effectively employed. My instinctive response is that these considerations outweigh the benefits from simply having employment even if it is not 'productive', but happy to be persuaded on that front as I haven't given it sufficient thought.

    @Alex 5.30

    Sumner et al are, actually, vociferous in their criticism of the Fed/Bernanke. They have been imploring the Fed to allow/create a higher level of aggregate demand and fulfill its stated mandate. From a demand standpoint, the action is at the Fed.