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 unrelated 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 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 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 has to say:

What is a multiplier? It’s:


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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About Scott Sumner 492 Articles

Affiliation: Bentley University

Scott Sumner has taught economics at Bentley University for the past 27 years.

He earned a BA in economics at Wisconsin and a PhD at University of Chicago.

Professor Sumner's current research topics include monetary policy targets and the Great Depression. His areas of interest are macroeconomics, monetary theory and policy, and history of economic thought.

Professor Sumner has published articles in the Journal of Political Economy, the Journal of Money, Credit and Banking, and the Bulletin of Economic Research.

Visit: TheMoneyIllusion

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