The silly multiplier “debate”

I put the term ‘debate’ in quotation marks, as it is not clear what, if anything, is actually being debated.  Much of the debate proceeds as if “the multiplier” is some sort of objective parameter of the universe, sort of like the cosmological constant.  In fact, there is no such thing as “the multiplier,” and indeed much of the debate is total nonsense.Let’s start with the fact that it isn’t even clear what people mean by the term.  Some people seem to be trying to estimate the impact of fiscal stimulus on aggregate demand, or nominal spending.  Others seem to be estimating the impact of fiscal stimulus on real GDP.  Of course these are two totally distinct concepts, but often the debaters don’t even seem aware of the fact that they aren’t debating the same topic.

To simplify things I’m going to start with the mainstream (Keynesian) definition of the multiplier, which measures the response of nominal GDP to an autonomous increase in government spending.  Later I promise to revisit the classical multiplier, which is the response of real GDP to an autonomous increase in government spending.

Even from a Keynesian perspective, the multiplier is a completely meaningless concept, for two separate reasons.  Both problems relate to the “ceteris paribus” assumption.  One is definitional, and the other is behavioral.  Let’s start with definitions.  Generally in economics we use the ceteris paribus assumption, which holds other factors constant.  But of course any change in government spending will change other factors; indeed that is the whole point of fiscal stimulus.  For analytical clarity many economists will assume that the stance of monetary policy is held constant.  But this raises the question of what do we mean by a “constant stance of monetary policy?”  And indeed there are almost as many definitions as there are economists:

1.  A constant fed funds rate (traditional Keynesians)

2.  A constant M2 (Milton Friedman)

3.  A constant monetary base (many right-wing economists)

4.  A constant future expected path of the fed funds rate (new Keynesians like Woodford)

5.  A forward-looking Taylor Rule  (Svensson?)

6.  A stable expected NGDP growth rate  (me)

And every single one of these definitions will give a completely different answer to the questions we are looking at.  Indeed using my definition the multiplier will be precisely zero, and that is likely to be the case with a Taylor Rule as well.  Most economists seem to think there is some sort of well-established meaning for the term ‘monetary policy.’  Unfortunately, they don’t realize that their definition is often not very widely shared.  Nevertheless, this complacency about definitions seems to have led economists to assume that when they debate other economists about “the multiplier” they are actually discussing the same thing.

I do acknowledge that if you get away from blog and op-ed debates, and look at academic articles, the terms are sometimes defined more precisely.  But what I don’t acknowledge is that these articles are any more useful that the babel of voices debating fiscal policy in the media.  And that is because even if we could agree on a definition of monetary policy, and even if all economists agreed to use that definition in discussions of the multiplier, it would not help resolve the question that we really want answered:

What will happen if the government attempts to use fiscal policy to boost NGDP?

Notice that this question is not “What would happen if the government boosted spending and monetary policy remained unchanged.”  Rather, it is an unconditional question.  And this unconditional question is the only question of interest.  For instance, suppose we all agree to define changes in the monetary base as “monetary policy,” and also that an increase in the base is expansionary while a decrease in the base is contractionary.  Also assume that the Fed is targeting interest rates.  If we make the reasonable assumption that fiscal stimulus boosts nominal interest rates, then the Fed will respond by increasing the monetary base to hold interest rates at their target value.  So in that case monetary policy will not be unaffected by fiscal stimulus.

Isn’t it much more useful to estimate what will happen to actual NGDP if we engage in fiscal stimulus, rather that the purely hypothetical issue of what would happen to NGDP if we engaged in fiscal stimulus and if the Fed reacted with some hypothesized policy that it has no intention of using?  In other words, shouldn’t we treat the Fed as any other non-fiscal actor in the economy?  An entity whose response to fiscal policy must be modeled, not assumed?

It seems to me that there are two ways of thinking about how monetary policy would react to fiscal stimulus.  One approach would be to ask:  “What is the optimal Fed response to fiscal stimulus?”  And the answer to that question is rather obvious; the Fed should act in such a way as to completely neutralize the impact of fiscal stimulus, i.e. make sure the multiplier is precisely zero.   This is because the Fed has some optimal level of expected AD growth in mind, and that level should not change just because fiscal policy changed.  So if the Fed is doing its job, which means if it is always targeting expected AD growth at what it sees as the optimal rate, then it will try to completely offset fiscal stimulus and the expected fiscal multiplier will be precisely zero.  That’s why fiscal stimulus almost disappeared from graduate textbooks in recent years.

Now I am sure some of you are saying “Ah, but everything changes if the Fed is not targeting expected NGDP growth, and since they are stuck at the zero rate bound, we can safely ignore any offsetting tightening by the Fed.”  Not at all.  The Fed has made it abundantly clear in recent weeks that they are already reacting to signs of recovery by trying to reduce inflation expectations.  And as Woodford showed (and as the financial markets confirmed last week) a change in the expected future path of policy has identical effects to a change in the current setting of the monetary instrument.  Just a few days ago a top Fed official indicated that the Fed looked at the stance of fiscal policy before making a decision.

Far from being some sort of deep parameter that reflects the structure of the universe, the multiplier will depend on things as trivial as whether Bernanke had a good night sleep, or whether he has read TheMoneyIllusion.com recently.  More importantly, it depends on how the Fed sees the economy, and how it interprets its options.  One thing is clear, the Fed does not agree with those who think it has run out of ammunition, just conventional ammunition.  That was clear from its decision to pay interest on reserves; a decision that was aimed at preventing a breakout of inflation after it nearly doubled the monetary base in just three months.

In an earlier post I argued that this time around the multiplier was probably negative.  My reasoning was as follows:

1.  Bernanke had no intention of allowing another Great Depression.

2.  The Fed overestimated the expansionary impact of the actions it took.

3.  The Fed underestimated the impact of alternative policies aimed at boosting inflation expectations.

4.  The Fed would have adopted those alternative policies if fiscal stimulus had failed in Congress.

You may not agree with my analysis, and may have your own.  Each person’s reading of the likely monetary policy counterfactual produces a different “multiplier.”

As if the preceding isn’t bad enough, it gets even worse.  My impression is that many economists on the right aren’t even looking at the same question as the Keynesians.  They are looking at the impact of fiscal stimulus on real output, not nominal output.  I have to admit that I haven’t had time to research this thoroughly, and am hoping that my excellent commenters can help fill in the gaps.  But when Barro argues that consumption didn’t rise in WWII, he was talking about real consumption.  So his estimates have no bearing on the argument by Keynesians that the multiplier is roughly 1.6.  I’m not a mind reader, but here’s how I think the average freshwater economist would react if a Keynesian actually explained his argument in their language:

“You say fiscal stimulus might boost NGDP by boosting velocity?  Sure, I guess that’s possible, but then wouldn’t that just be giving monetary policy traction?  And why would you ever want to do such a thing?  Why not just print more money (or more government debt) if that’s what you are trying to do?  I thought you were claiming more government spending could boost RGDP.”

Here is a quotation from the paper where (according to Krugman and DeLong) Cochrane showed that he didn’t understand the fiscal multiplier.  As you can see, he does.  In the Keynesian model fiscal stimulus works by reducing the demand for money, if you assume the supply is fixed.  Notice that as soon as Cochrane begins to discuss this possibility, he sees it in terms of monetary policy, not fiscal policy.

A monetary argument for fiscal stimulus, logically consistent but unpersuasive

My first fallacy was “where does the money come from?” Well, suppose the Government could borrow money from people or banks who are pathologically sitting on cash, but are willing to take Treasury debt instead.  Suppose the government could direct that money to people who are willing to keep spending it on consumption or lend it to companies who will spend it on investment goods. Then overall demand for goods and services could increase, as overall demand for money decreases.  This is the argument for fiscal stimulus because “the banks are sitting on reserves and won’t lend them out” or “liquidity trap.”

In this analysis, fiscal stimulus is a roundabout way of avoiding monetary policy. If money demand increases dramatically but money supply does not, we get a recession and deflation. If we want to hold two months of purchases as money rather than one months’s worth, and if the government does not increase the money supply, then the price of goods and services must fall until the money we do have covers two months of expenditure. People try to get more money by spending less on goods and services, so until prices fall, we get a recession. This is a common and sensible analysis of the early stages of the great depression. Demand for money skyrocketed, but the Fed was unwilling or, under the Gold standard, unable, to increase supply.

This is not a convincing analysis of the present situation however. We may have the high money demand, but we do not face any constraints on supply. Yes, money holdings have jumped spectacularly. Bank excess reserves in particular (essentially checking accounts that banks hold at the Federal Reserve) have increased from $2 billion in August to $847 billion in January. However, our Federal Reserve can create as much more money as anyone might desire and more. There is about $10 trillion of Treasury debt still outstanding. The Fed can buy it. There are trillions more of high quality agency, private debt, and foreign debt outstanding. The Fed can buy that too. We do not need to send a blank check to, say, Illinois’ beloved Governor Blagojevich to spend on “shovel-ready” projects, in an attempt to reduce overall money demand. If money demand-induced deflation is the problem, money supply is the answer.

Some people say “you can’t run monetary policy with interest rates near zero.” This is false. The fact of low interest rates does not stop the Fed from simply buying trillions of debt and thereby introducing trillions of cash dollars into the economy. Our Federal Reserve understands this fact with crystal clarity. It calls this step “quantitative easing.” If Fed ignorance of this possibility was the problem in 1932, that problem does not face us now.

Yes, Cochrane does seem to be addressing nominal GDP in that passage, but here is how Barro views the multiplier:

The existing empirical evidence on the response of real gross domestic product to added government spending and tax changes is thin.   (Italics added.)

He estimates the multiplier for military spending to have been only about 0.6 or 0.7 during WWII; but is that really very surprising, given that unemployment was only about 1% during WWII?  I’m not saying Barro underestimates the multiplier, indeed I think it’s about zero.  But he doesn’t offer any evidence that fiscal stimulus is unable to boost nominal spending.  BTW, I’m not criticizing Barro; arguably real GDP is the much more interesting question.  My point is that it is completely unrelated to the concept that Keynesians like Krugman and DeLong are discussing.  Or at least I think it is.  When Krugman criticizes Barro’s WWII study here:

Oh, and the economy was at full employment — and then some. Rosie the Riveter, anyone?

He seems to imply that real GDP is the relevant variable.  So I checked Wikipedia, and they also said the multiplier was defined in terms of real output.  And yet the formula they show for the multiplier applies to nominal output, not real output.  And here is what Menzie Chinn at econbrowser.com has to say:

What is a multiplier? It’s:

ΔY/ΔZ

where Y and Z are measured in real dollars. Note that in principle, one can re-write the multiplier in terms of percentage point change of income relative to baseline income for a given percentage point change of the Z-to-Y baseline ratio.

What is apparent is that some tax cuts, or really rebates, can have a substantial effect. But in most cases, tax policies will have a relatively minor impact on aggregate demand, relative to increases in spending on goods and services.

So it’s real, except it relates to aggregate demand, which is a nominal concept.  So who knows?

Now of course in the current environment it is very likely that an increase in NGDP will also boost RGDP, as the SRAS is currently fairly flat.   But the slope of the SRAS is a separate issue from the impact of government spending on aggregate demand.  That’s why Keynesians often talk about “the multiplier” as if it was a single number.  Obviously if they were talking about real GDP then the estimates would be highly sensitive to the rate of unemployment.  Keynesians have always acknowledged that if we were at full employment then an increase in AD would simply lead to higher prices.

[BTW, perhaps it's not so obvious that the SRAS is now pretty flat.  The Fed's panic about inflation in recent weeks suggests it doesn't buy this argument.  (On the other hand it did recommend fiscal stimulus, so who knows?)  And there are some other arguments that much of the problem is real.  I think these arguments are overstated, but I wouldn't describe them as "nuts."]

So you tell me, does all this mean anything, or is just a big muddle?


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28 Responses to “The silly multiplier “debate””

  1. Gravatar of Bob Murphy Bob Murphy
    4. October 2009 at 16:58

    Wow great post Scott. I had never thought about this distinction before, and I think most of the other economists haven’t either.

    I think they jump back and forth mid-argument. You use nominal spending when you go through the (undergrad) logic of, “So I spend $100, then you spend $80, then the next guy spends $64…”

    But the whole point is to employ more people and close the (real) output gap. So I think the Keynesian believes an increase in nominal spending will drive an increase in real output.

    So yes, that means the Keynesian must admit “the multiplier” is different, depending on the amount of excess capacity. But Krugman does exactly that, when he tries to blow up Barro’s argument about WW2. (BTW was anyone else shocked that Krugman said WW2 wasn’t supposed to be an example of successful deficit pump priming? I thought that was the ONLY example in US history.)

  2. Gravatar of Tom Dougherty Tom Dougherty
    4. October 2009 at 18:04

    “So you tell me, does all this mean anything, or is just a big muddle?”

    A big muddle? – not at all. You are one of the most crystal clear economists I have read. I want to thank you for this excellent blog!

    You have many months worth of posts and I have not looked at them all (yet) and you may have something regarding a reading list, but do you have a list of books that should be required reading for economists?

  3. Gravatar of marcus nunes marcus nunes
    4. October 2009 at 18:05

    Scott
    Yes, it is silly. So are many of the other “debates” going on. It seems different groups are pushing different agendas. For example Krugman and his followers (they sound like a religious sect) are pulling in one direction – more government. Others, like Taylor, defend his namesake rule to the end saying that THE CAUSE of the crisis was the abandonment of the rule back in 2002 – 04. Others (Ron Paul) say the Fed should be abolished. There are even some publicly announced “conversions”, such as Plosner´s, and “resurrections”, such as Minsky (and his moment). And on and on it goes…
    In my view, once upon a time the US went through a quarter century of something called “the great moderation”. It took about 15 years for its existence to be recognized, and when it was, many ascribed it to LUCK! (or bland shocks, nothing like the ones in the 70s). That´s quite false since there were even more shocks and of all kinds shapes and forms since the early 80s. What was different was that policy, especially monetary policy, didn´t allow those shocks to PROPAGATE. As soon as the Fed made a mistake the “flood gates” opened up. Since this mistake is not recognized, more mistakes are likely to be made of which hacking on the value of a so called multiplier and how more stimulus can save us all is just one of them.

  4. Gravatar of Greg Ransom Greg Ransom
    4. October 2009 at 19:16

    “what do we mean by a “constant stance of monetary policy?”

    The original definition of “neutral money” was Hayek’s, which goes something like:

    “a market coordinating money rate of interest which did not create a boom and bust cycle by falsely misdirecting investment through the time structure of production goods”

  5. Gravatar of Greg Ransom Greg Ransom
    4. October 2009 at 19:23

    This was a really helpful post, Scott.

    Thanks.

  6. Gravatar of D. Watson D. Watson
    4. October 2009 at 20:59

    Magnificent. I’m going to save this one with your discussion of confusing price change = demand change.

    Stylistically, I relish your first paragraph. Let’s make it clear where we stand on this.

  7. Gravatar of Current Current
    5. October 2009 at 02:01

    Interesting, I’ve heard of this problem before. (I’m surprised Bob Murphy hasn’t.)

    In the 40s the employment “multiplier” was sometimes called “the acceleration principle of derived demand”. Hayek writes in Appendix III of “The Pure Theory of Capital”…

    Hayek: “It remains to decide in terms of what we are going to measure the two kinds of demand. And it will presently be seen that this decision is indeed crucial for the solution of our problem. If we decide to measure demand in terms of money, the problem will clearly be indeterminate unless we make further assumptions with regard to the effect of a change in final demand on expectations of future prices and on the supply of money. Circumstances are clearly conceivable in which an increase in final demand will bring about an increase in the demand for labour (in terms of money) many times its size. This indeed is the case which is treated as the normal one by the ‘acceleration principle of derived demand’.
    If, on the other hand, we decide to measure demand in real
    terms, as we clearly ought to do so long as we treat the
    proposition as one of pure theory, it will quickly be seen that the opposite proposition becomes almost a pure tautology. An increase in the demand for consumers’ goods in real terms can only mean an increase in terms of things other than consumers’ goods; either more capital goods or more pure input or both must be offered in exchange for consumers’ goods, and their price must consequently rise in terms of these other things; and similarly a change in the demand for labour (i.e. pure input) in real terms must mean a change of demand either in terms of consumers’ goods or in terms of capital goods or both, and the price of labour expressed in these terms will rise.”

    Of course there are thing to object to about Hayek’s treatment above of the multiplier in terms of real variables.

    However, he clarifies later.

    Hayek: “The situation will, of course, be different if at the preexisting level of wages and prices supply exceeded demand, and an increase in final demand makes it possible immediately and proportionately to increase output by employing formerly unemployed resources of all the kinds required. In this case, and in this case only, an increase in final demand will lead to a proportionate increase of employment; and this effect will of
    course be limited to the period during which such unemployed
    reserves are available. There will of course be intermediate
    cases where, although there may not be unemployed resources
    of all kinds available, there will be sufficient reserves in existence of a number of the more important kinds of input to
    make it possible to increase output, although not in proportion to the increase in final demand, yet to some extent. In this case a very slight reduction of real wages may be accompanied by a very considerable increase in employment. In both these cases the “principle of derived demand” will approximately apply if money wages can be assumed to be given and constant, because the effect of an increase in final demand will here not dissipate itself in an increase in the prices of output and – to a lesser extent – input, but can bring about an increase in employment at more or less unchanged prices. That under conditions of under-employment the general principle does not directly apply was of course well known to ‘orthodox’ economists, and to J. S. Mill in particular. In his exposition the statement that ‘industry is limited by capital’, on which, as we have seen, the proposition under discussion is based, is immediately followed by the further statement that it ‘does not always come up to that limit’.1 And few competent economists can ever have doubted that, in positions of disequilibrium where unused reserves of resources of all kinds existed, the operation of this principle is temporarily suspended, although they may not always have
    said so.”

    However, this sort of real/nominal problem has been a problem with discussions of the multiplier in the past.

  8. Gravatar of Current Current
    5. October 2009 at 02:06

    BTW the last sentence is mine, I forgot to close the quote tag.

  9. Gravatar of jean jean
    5. October 2009 at 02:41

    You’re perfectly right: the multiplier is a partial derivative. And partial derivatives only make sense if you precise which variables are hold constant.

    I just don’t understand why Krugman (or Barro) doesn’t mention war bonds which existence means that liquidity trap (i.e. zero interest rates) was over and that financial crowd was quite likely.
    In fact, if people hadn’t wanted to maintain their standard of living and hence work more (cannons for government but some butter for them too), the multiplier could even have been zero or negative.

  10. Gravatar of Bill Woolsey Bill Woolsey
    5. October 2009 at 02:49

    Scott:

    You should think about, and write about) the notion that monetary policy has longer and more variable lags than fiscal policy. That is the weakest point of your argument (and mine.)

    I think it is plausible that increased government spending will immediately raise nominal expenditure faster than the sudden appearance of excess money balances. Of course, by the time the secondary effects roll around (the multiplier,) we are really looking at two sides of the same coin.

    Doesn’t this all come down to the future expected nominal growth channel for impacting current nominal expenditure? This bypasses the messy process by which monetary disequilibrium, one way or another, impacts nominal expenditure without being helped along by rational expectations about the process.

    For what it is worth, I go with the assumption that the Fed is using interest rate targetting. At the zero nominal bound, impacts of fiscal policy and the quantity of T-bills used to finance it plausibly impact money demand strongly, and if money demand isn’t impacted enough, the quantity of money will change. And so, fiscal policy expands nominal expenditure strongly.

    When we add interest rates on reserves, the “zero” nominal bound is pushed up to .25% or whatever they are paying, and still, the argumnet applies.

    Why would the Fed support fiscal policy? Think of it in terms of sharing the blame. Accepting responsibility for nominal expenditure would suggest holding the Fed accountable.

    Also, consider the following–leaving aside the happy expectations expansion channel, market forces are pushing the interest rates on highly liquid, zero risk bonds to something slightly less than zero–the cost of holding currency. But don’t we have to keep those investors happy? So we need to create and issue more zero risk, highly liquid assets.

    The new classical models, where higher government spending causes people to sacrifice present leisure, work harder, and raises the productive capacity of the economy, are not worth considering. It may happen, but this isn’t much of an argument for raising government spending. WW2 (Rosie) seems like a good time to check this out, but who cares? OK, science for science’s sake.

    Cochrane’s “but of course” explanation of monetary disequlibrium theory, marred only by his conventional analysis in terms of “k,” (and that is only a minimal problem,) makes one wonder if he (and the rest of them,) need a better explanation of why nominal expenditure targeting is a good idea, or perhaps it is just the long and variable lags.

    But doesn’t Cochrane say that monetary policy isn’t the issue because there is an excess demand for both government bonds and money? Perhaps I should read it all again, but it seemed to me that he was arguming that the problem isn’t an increase in k (or money demand) but an increae in the demand for all government debt, both base money and bonds.

  11. Gravatar of Nick Rowe Nick Rowe
    5. October 2009 at 04:27

    Good post Scott.

    I have always interpreted the Keynesian multiplier in real terms.

    “Aggregate Demand” can also be interpreted in real or nominal terms. I interpret “AD increases” to mean the AD curve shifts right. This is exactly consistent with pernickety teachers of Econ101 who insist that “an increase in demand” means the demand curve shifts right.

    Only if you assume the AD curve is a rectangular hyperbola(sp?), and that the economy is always ON the AD curve (it ain’t — just look at Cuba) can you interpret “the AD curve shifts right” as “NGDP increases”.

    Bill’s got a good point on lags.

  12. Gravatar of ssumner ssumner
    5. October 2009 at 05:04

    Bob, Yes it seems confused. I don’t doubt that in highly technical articles things are spelled out more clearly, but in their public debates, famous economists seem to be all over the map.

    Tom, It really depends on how much time you have, and your level of expertise. I can certainly recommend looking at the interwar economists like Fisher, Hawtrey, Cassel, and even Keynes. (For Keynes, “The Tract on Monetary Reform” is best.) For monetarism Milton Friedman is best. Both his Monetary History with Anna Schwartz, and his other theoretical books and articles. More recent stuff gets much more technical. If you are not an economist you might just look at a textbook like Mishkin’s, to get the mainstream model. Papers by people like Bennett McCallum and Lars Svensson are more technical, but very interesting. Robert Hetzel wrote a good overview of monetary policy during the 20th century for the Richmond Fed. In general, Fed publications from Richmond and St, Louis tend to be the best. Alternative perspectives by people like Robert Hall and Earl Thompson are also interesting. Then there is the whole Austrian/Free banking school. I am less familiar with this stuff, but people tell me that Mises, Hayek, Selgin, White, Garrison and Horwitz are the best.

    I suppose if you are a masochist and started at the beginning of my blog and went all the way through you’d get an education in my views, which have evolved somewhat even since I started the blog.

    Marcus, Very well put, you should be a blogger.

    Thanks Greg, That’s a good definition, and pretty close to my stable expected NGDP growth policy(albeit at a lower rate.) In my view if the Fed was doing things that way it would mostly offset the impact of fiscal policy, i.e. offset any impact fiscal policy had on velocity.

    I forgot to mention that fiscal policy can theoretically impact RGDP without impacting NGDP, which I think is the issue Barro is trying to address.

    Thanks D Watson.

    Current, Thanks. Yes, there is no doubt that this issue is well understood. I’m still not sure to what extent economists are talking past each other, but based on Krugman’s response to Barro I think we can assume there is at least some miscommunication.

    Jean, Yes, I agree.

    Bill, You said;

    “You should think about, and write about) the notion that monetary policy has longer and more variable lags than fiscal policy. That is the weakest point of your argument (and mine.)
    I think it is plausible that increased government spending will immediately raise nominal expenditure faster than the sudden appearance of excess money balances. Of course, by the time the secondary effects roll around (the multiplier,) we are really looking at two sides of the same coin.”

    Good question. I agree that this view is held by many, but I think it is completely wrong. First of all most of the stimulus has not yet been spent, but the Fed is already discussing when to raise rates. So fiscal policy has a very long implementation lag.

    Second, I strong disagree on the widespread view that monetary policy has long and variable lags. That view comes from misidentification of monetary shocks. Putting more money into circulation right now is not an expansionary policy, the only effective expansionary policy is changing the future expected path of monetary policy. So sometimes the Fed injects more money, and at first it is assumed to be temporary. Only later, when it is understood to be permanent, does it have an expansionary effect. And that effect occurs immediately after expectations change.

    Throughout history we see evidence that a change in the expected path of policy over time has an immediate impact on prices and output, these examples include late 1920, 1929, 1937, 1981, 2008. I actually think the impact lags are about the same, and the implementation lag is far shorter for monetary policy.

    You said;

    “Doesn’t this all come down to the future expected nominal growth channel for impacting current nominal expenditure? This bypasses the messy process by which monetary disequilibrium, one way or another, impacts nominal expenditure without being helped along by rational expectations about the process.”

    Yes it does, and this is why I think the policy lags issue has been misunderstood.

    You said;

    “For what it is worth, I go with the assumption that the Fed is using interest rate targeting. At the zero nominal bound, impacts of fiscal policy and the quantity of T-bills used to finance it plausibly impact money demand strongly, and if money demand isn’t impacted enough, the quantity of money will change. And so, fiscal policy expands nominal expenditure strongly.”

    Just because the Fed uses interest rate targeting, does not imply the Keynesian view of the multiplier is correct. You’d also have to assume that the expected path of interest rates over time was unaffected, an extremely dubious assumption. Indeed the Fed itself denies this, saying they look at fiscal policy and real growth when deciding when to raise rates. If so, the multiplier concept is complete bogus. So the Keynesians must assume that the Fed is lying.

    You said;

    “Why would the Fed support fiscal policy? Think of it in terms of sharing the blame. Accepting responsibility for nominal expenditure would suggest holding the Fed accountable.”

    I think this is the wrong way to look at things. Yes, they are providing “support” in the conventional Keynesian sense of keeping rates low. But we both know that policy could be even far more expansionary through unconventional techniques. And I am arguing that if fiscal stimulus had failed in Congress the Fed would have been almost forced to do more. If so, then the multiplier is bogus.

    You said;

    “But doesn’t Cochrane say that monetary policy isn’t the issue because there is an excess demand for both government bonds and money? Perhaps I should read it all again, but it seemed to me that he was arguing that the problem isn’t an increase in k (or money demand) but an increase in the demand for all government debt, both base money and bonds.”

    Very observant. I seem to recall that if you look at his paper (I linked) in the next few sections he does as you suggest. He argues that if money and T-bills are perfect substitutes we need more of both. But then he says that to get more bonds you don’t need to increase government spending, just swap T-bills for something like agency debt. I thought his fiscal view was a distraction, so I didn’t quote it, but I think I put “or government debt” in parentheses so no one could claim I distorted his views (like certain other people do.)

    So to summarize, I agree with most of your technical arguments, but see two issues slightly differently:

    1. I think money has a short lag.
    2. I see the relevant policy counterfactuals differently. i think the Fed is always reacting to fiscal policy in one way or another.

  13. Gravatar of ssumner ssumner
    5. October 2009 at 05:35

    Nick, Thanks, but I’m not sure I follow your argument on AD. Let’s say we are at full employment, and the AS curve is vertical. Now you increase AD. In that case NGDP rises but real GDP doesn’t. And this is true whether you define AD as the monetarist’s hyperbola, or the Keynesian AD curve. What am I missing? My claim applies to a vertical AS curve, a horizontal AS curve, or anything in between. And AD can have any shape, it doesn’t have to be a hyperbola. As long as AD shifts right, NGDP rises.

    I also have to strongly disagree about lags. If monetary policy lags really were long, how could we possible explain the fact that all of the most clearly identified monetary shocks (which mostly occurred prior to WW2) seem to have had an immediate impact on prices and output. Aren’t those precisely the shocks that give us the best estimates of the policy lags? There is a massive identification problem with postwar data. I think the profession paid far too much attention to Milton Friedman’s views on lags, which we now know were completely inconsistent with efficient markets. If Friedman was right, the markets should have reacted immediately to Fed actions that he identified as policy shocks.

    And with the long implementation lag for fiscal policy, it seems clear to me that if anything, fiscal lags are far longer than monetary lags. The recent fiscal stimulus in the US does not appear to have had any significant impact so far, and yet we are technically already in the recovery phase of the business cycle.

  14. Gravatar of Bill Woolsey Bill Woolsey
    5. October 2009 at 07:15

    Scott:

    I think we disagree on these matters less than you think.

    When I say “weak” point of the argument, I don’t mean to suggest it is wrong.

    “Just because the Fed uses interest rate targeting, does not imply the Keynesian view of the multiplier is correct. You’d also have to assume that the expected path of interest rates over time was unaffected, an extremely dubious assumption. Indeed the Fed itself denies this, saying they look at fiscal policy and real growth when deciding when to raise rates. If so, the multiplier concept is complete bogus. So the Keynesians must assume that the Fed is lying.”

    I don’t understand this.

    Completely bogus?

    I believe that under current conditions, tax cuts or government spending funded by government debt will impact both the demand for money and the quantity of money. That will raise nominal expenditure.

    Your counter argument is that the Fed says that it pays attention to fiscal policy and real growth in determining interest rate targets?

    You know, if the Fed changes it mind and thinks that -5% is too low and that -3% would be better, it hardly prevents changes in the natural interest rate from impacting monetary equilibrium at the zero nominal bound, or the .25% bound that the Fed prefers and has created through interest payments on reserves.

    I presume that none of this caculations of the multiplier is 1/(1-mpc) That expecations of future interest rates might impact investment are taken into account, right?

  15. Gravatar of Philo Philo
    5. October 2009 at 08:07

    “Isn’t it much more useful to estimate what will happen to actual NGDP if we engage in fiscal stimulus, rather tha[n] the purely hypothetical issue of what would happen to NGDP if we engaged in fiscal stimulus and if the Fed reacted with some hypothesized policy that it has no intention of using? In other words, shouldn’t we treat the Fed as any other non-fiscal actor in the economy? An entity whose response to fiscal policy must be modeled, not assumed?”

    Well, who are “we”? If you mean *me and Scott Sumner*, or *some small group of politically insignificant people including me and Scott Sumner*, then *none of this* is “useful”; it’s all idle speculation (though kind of *fun*, to a perverted sensibility). This small-group “we” controls neither fiscal nor monetary policy, and therefore is not going to *do* anything of much practical importance, whatever the outcome of its speculative musings.

    If “we” are *the American government*, or *the American people*, then the Fed is *not* an independent agent–it’s part of “us.” The debate should be about what combination of monetary and fiscal policy would work best (and if there’s some other kind of policy besides monetary and fiscal, that should be thrown into the hopper, too). But that’s pretty unrealistic; if the American people–or even just those in the government–would always act optimally, their behavior would be unrecognizably different from what we observe in the real world.

    Apparently, Scott wants “we” to constitute a group of people (I don’t really think he and I are included, so ‘we’ is not the appropriate term!) who control federal fiscal policy but nothing else–thus, not the Fed. Well, we can do this, just for fun; but why call it “useful”?

    Still, for those of us given to idle speculation–a great post!

  16. Gravatar of Mike Sandifer Mike Sandifer
    5. October 2009 at 08:22

    Dr. Sumner,

    I’m curious as to what implications, if any, perspectives on GDP as a very flawed metric for economic growth have on the NGDP targeting idea. Stiglitz and others have pointed out vsrious problems with GDP.

  17. Gravatar of Bill Woolsey Bill Woolsey
    5. October 2009 at 08:43

    Sandifer:

    Mostly, it is irrelevant.

    The purpose of nominal GDP targeting is not to restrict human welfare.

    It is rather to provide the least bad macroeconomic environment for microeconomic coordination.

    The split between real income and the price level is where issues regarding GDP has a poor measure of welfare are impacted.

    The concern is really between the actual volume of nominal expenditures on current output and the measured volume. There isn’t a problem with there being a persistent gap, but rather with variation in any measurement errors. This means that the targetting regime will “create” or maybe allow for undesirable fluctuations in nominal expenditures.

  18. Gravatar of Dilip Dilip
    5. October 2009 at 12:22

    This might be relevant to the discussion:
    http://www.voxeu.org/index.php?q=node/4036

  19. Gravatar of Current Current
    5. October 2009 at 13:06

    Mike,

    As Bill says the use of NGDP here has little to do with measuring welfare. It is a poor measure of welfare, as many have pointed out.

    Mises wrote (in 1949): “If a business calculation values a supply of potatoes at $100, the idea is that it will be possible to sell it or to replace it against this sum. If a whole entrepreneurial unit is estimated $1,000,000, it means that one expects to sell it for this amount. But what is the meaning of the items in a statement of a nation’s total wealth? What is the meaning of the computation’s final result? What must be entered into it and what is to be left outside? Is it correct or not to enclose the ‘value’ of the country’s climate and the people’s innate abilities and acquired skill? The businessman can convert his property into money, but a nation cannot.”

    Some of the 19th century marginalists were critical of the idea of measuring output too. Oscar Morganstern criticised it. JFK criticised it!

    Unfortunately over the years the criticism hasn’t had much effect. I think the reason is that other indexes constructed by governments are inevitably more political, but people these days still crave figures.

  20. Gravatar of Current Current
    6. October 2009 at 02:02

    On Bill’s comment…. For the employment multiplier to work the following must happen. When the money is first spent by the state the companies who receive it realize that it is only a short-term thing. They will likely not change the liquidity they hold much compared to the offsetting change performed by those lending to the state. Then the money is spent by those companies and passed to others. When this happens things may be different, the next company may believe it is seeing a normal upturn in business. It is like the situation with monetary policy I was explaining in the thread on Brad DeLong.

    Only when a few agents think that the profits they are seeing are permanent will they become more secure and reduce their demand for money. This is the only way an overall reduction can take place and an increase in velocity. So, fiscal stimulus has long and variable lags if monetary stimulus does.

  21. Gravatar of ssumner ssumner
    6. October 2009 at 16:21

    Bill, I certainly agree that if the Fed targets interest rates it makes it a bit easier to argue for the multiplier than if they target the money supply. But I still think there are too many question marks to make any sort of meaningful statement about multipliers. So much is driven by expectations, and the Fed can change expectations quickly. Here is an admittedly extreme example. Congress adopts a tighter fiscal policy. The multiplier theory says NGDP will fall. The same day the Fed responds by saying, “we will keep the interest rate fixed for a year, and then we will lower it enough to create hyperinflation.” The combined impact of both actions would result in higher current NGDP, not lower. I’d be rushing out to buy any real asset I could get my hands on. Now of course it would never happen quite that way, but my point is that Fed signals about future policy intentions can have a huge impact on current AD, even for a given current interest rate. And thus if the Fed responds to fiscal shocks with some offsetting monetary actions, or even hints of future actions, that dramatically complicates any multiplier estimates.

    Their recent hints of future tightening have probably slightly lowered AD, although rates weren’t raised at all.

    And here is something that isn’t far-fetched at all. If the Fed engaged in “level targeting” (either price level or NGDP) the potency of fiscal policy would fall close to zero.

    And of course the (1/1-MPC) formula is just totally useless, under any set of assumptions.

    Philo, If we are all in it together we should just use monetary policy, and then the multiplier is zero. If we aren’t in it together (and we aren’t) then Congress knows full well that it is engaged in a game theory situation with the Fed. And I would think that Congress would want to take the response of the Fed into account. If I was voting on whether to waste $800,000,000,000 of taxpayer money, and I’m a Congressman from Podunk, I’m not going to vote for fiscal stimulus if I don’t think it will actually affect NGDP. But that’s just me.

    Mike, Not really any impact at all, as most of the arguments that RGDP is flawed don’t apply to NGDP, which is far easier to measure.

    Bill, I should have read your answer first, it is better.

    Thanks Dilip, It is relevant, but I don’t think it resolves any of the complex counterfactuals.

    Current. I agree. If our NGDP was 1 trillion times bigger, we wouldn’t be any better of. But if it was 8% bigger, we’d be far better off. That’s one of the endlessly paradoxical things about macro.

    Current#2; I’d put it this way, for people and businesses to want to spend more now, they need to believe that their income in 2 years will also be higher. And the main factor impacting expected income 2 years forward is monetary policy. If they don’t feel things will be better in two years, they’ll hoard most of the tax cut.

  22. Gravatar of Current Current
    7. October 2009 at 00:01

    Scott: “I agree. If our NGDP was 1 trillion times bigger, we wouldn’t be any better of. But if it was 8% bigger, we’d be far better off. That’s one of the endlessly paradoxical things about macro.”

    I wasn’t really criticizing NGDP above, I was criticizing the use of RGDP to measure welfare.

    I think that paradox you mention is fairly easy to understand from the micro-economic perspective.

    Mises: “Inflation works as long as the housewife thinks: ‘I need a new frying pan badly. But prices are too high to-day; I shall wait until they drop again.’ It comes to an abrupt end when people discover that the inflation will continue, that it causes the rise in prices, and that therefore prices will skyrocket infinitely. The critical stage begins when the housewife thinks: ‘I don’t need a new frying pan to-day; I may need one in a year or two. But I’ll buy it to-day because it will be much more expensive later.’

    Scott: “I’d put it this way, for people and businesses to want to spend more now, they need to believe that their income in 2 years will also be higher. And the main factor impacting expected income 2 years forward is monetary policy. If they don’t feel things will be better in two years, they’ll hoard most of the tax cut.”

    I agree. However, there will be people who base their decisions on future plans on whether they are receiving profit now. There will be those who do that to some extent while also looking to the future. That is true of monetary stimulus and fiscal stimulus.

  23. Gravatar of Richard A. Richard A.
    7. October 2009 at 04:56

    From Mankiw’s blog –
    http://gregmankiw.blogspot.com/2009/10/victory-for-mundell-fleming.html

    “[The multiplier estimates] imply that the effects of fiscal policy depend crucially on whether the exchange rate is fixed or floating (flex), precisely as predicted by the Mundell-Fleming model”.

  24. Gravatar of ssumner ssumner
    8. October 2009 at 06:04

    Current, I agree. BTW, one way of explaining the paradox is that prices are sticky in the face of 8% shocks, but totally flexible in the face of trillion percent shocks.

    Richard, Thanks I have a post on that.

  25. Gravatar of Current Current
    8. October 2009 at 07:02

    Scott: “I agree. BTW, one way of explaining the paradox is that prices are sticky in the face of 8% shocks, but totally flexible in the face of trillion percent shocks.”

    Yes, this is what Lachmann wrote about that:

    “Let us suppose that on a market a ‘set of self-consistent expectations’ has had time to crystallize and to create a conception of a ‘normal price range’. Suppose that any price between £95 and £110 would be regarded as more or less ‘normal’, while a wider range of prices, say from £80 to £125, would be regarded as possible. We thus have two ranges, an ‘inner range’ from 95 to 110 reflecting the prevailing conception of ‘normality’, and an ‘outer range’ associated with what is regarded as possible price change.”

    Herbert Simon’s argument was that something similar is true at the level of psychology and marginalism too. I think that’s true. If all the tea the cafe serves is slightly worse than yesterday nobody will notice, they will pay and come back. If everything is much worse than everyone will leave their tea, complain and never come back.

  26. Gravatar of David Stinson David Stinson
    15. October 2009 at 14:13

    Hi Scott.

    Another excellent post. I too have been very confused by what appears to be a lack of precision in describing (if not also specifying) multipliers. It’s just one of many things that I thought I understood when I was young and gullible.

    Even though I am very late to the party, I had a couple of thoughts to add.

    One, I have spent large portions of my professional life working in the area of cash flow or causal economic costing studies in the telecom business. The most rigorous way to conduct these is to compare the two (or more) alternative decisions or scenarios that are being considered – a reference (or base) case and an alternative case. The two scenarios are fully specified over a multi-year period in terms of demand, expenses, capital, etc., and cash flows are determined. The cash flows for each scenario are present valued and the difference between the two present values determined. The difference is “caused by” the alternative. In other words, causality can only be determined with respect to an alternative and the magnitude of any causal impact critically depends not only on the specification of the alternative case but also of the base case. The analogous approach for determining multipliers would presumably require specifying two scenarios – one without the additional government spending and one with, each involving estimates of the relevant economic variables and quantities (including any consequent impacts of the increased government spending in the form of crowding-out, etc.), assumptions regarding the financing of the stimulus and the effects of various assumed monetary policy rules. I don’t sense that sort of rigour is present in many discussions regarding the magnitude of multipliers or their policy implications. Further, it seems unlikely that this sort of exercise could be accommodated by econometric modelling or models based on it.

    Two, am I the only one confused even by the numerical presentation of multipliers? Barro (in his two articles in the WSJ), and I believe others, tend to emphasize a value of 1.0 as some sort of meaningful threshold. Others (including you in the article above) refer to a multiplier of zero as the key threshold. Perhaps this relates to (often less than explicit?) differences in the specification of the multiplier – i.e., whether it’s a “partial derivative” as someone referred to it above or whether it includes the net effect of both direct impacts of the increase in G on output and indirect effects (potentially both negative and positive) via effects on other variables and components of GDP. If the latter, presumably the key threshold is zero – i.e., as long as the impact on GDP is positive, the stimulus can be said to have “worked” in the Keynesian sense. If the former, presumably no policy implications can be inferred in the absence of considering all the other impacts or partial derivatives.

    Third, I note Barro has relied on WWII data. I believe Robert Higgs (the regime uncertainty guy) has argued that WWII economic data are not meaningful. IIRC, his argument was that prices and quantities were so heavily government-prescribed that they ceased to be the reliable indicators of value that (relatively) free market prices and quantities are. If correct, this would presumably have consequences for any analysis that used WWII data to estimate multipliers.

  27. Gravatar of ssumner ssumner
    17. October 2009 at 06:57

    I agree Current.

    David, I agree with you that “plausible counterfactuals” is the most useful way to think about causality. One reason this is so hard to pin down is that we have no way of precisely modelling how the Fed will respond to different fiscal stimuli. There is a “game theory” element to the problem.

    Regarding the muliplier; 1.0 is the minimum if you want to argue that government spending can have a “multplieer effect” on private spending, i.e. can cause private spending to increase as well. Zero is the number if you are interested in the question of whether more G can boost RGDP. I suppose if one is skeptical of the usefulness of government projects, a multiplier of 0.7 might not seem that good. Remember that Keynes said it doesn’t even matter whether the government projects were useful, because of the multiplier impact on private spending. That’s a pretty strong claim.

    Barro focused on WWII becasue the shock was so clearly identified. But he did look at the other wars and found similar coefficients, it’s just that the statistical significance was lower.

  28. Gravatar of Sinnlose Schätzungen des Multiplikators? | Kantoos Economics Sinnlose Schätzungen des Multiplikators? | Kantoos Economics
    20. June 2011 at 08:42

    [...] Euch ersteres merkwürdig vorkommt, seid Ihr in guter Gesellschaft. Wie viele andere war auch ich von einem Eintrag von Scott Sumner zu diesem Thema einigermaßen überrascht. Und doch hat er Recht. Bei den anderen beiden Punkten wundert mich, dass [...]

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