Brad DeLong on the Sumner Critique and why the fiscal multiplier is zero

This is Brad DeLong:

An optimizing central bank that cares only about inflation and unemployment because it does not find itself at the zero nominal lower bound and does not fear engaging in nonstandard monetary policy will engage in full fiscal offset: it will take care to make sure that if fiscal policy becomes more stimulative then it will make monetary policy less stimulative by the same amount.

What Brad of course here is expressing is the so-called Sumner Critique – that is the fiscal multiplier will always be zero if the central bank directly or indirectly targets aggregate demand either as a result of an inflation target, an NGDP level target or for that matter a Bernanke-Evans style monetary rule.

Brad has a nice little model to illustrate his point. In some ways Brad’s model is similar to Nick Rowe’s game theoretical discussion of what Brad calls “full fiscal offset” (see my earlier post on the topic here). My simpler IS/LM+ model illustrates the same point (have a look at the model here).

Brad, however, thinks that the fiscal multiplier is positive at the Zero Lower Bound (ZLB):

… this argument breaks down at the zero nominal lower bound. At the zero lower bound the central bank does care only about inflation and unemployment. It cares as well about the magnitude of the non-standard monetary policy measures it must take in order to achieve its net monetary policy impetus value m.

This argument is somewhat harder for me to get. The Zero Lower Bound only exists as a mental construction in the heads of central bankers. Central banks can always ease monetary policy – even if interest rates are close to zero. That is exactly what the Fed and the Bank of Japan are doing at the moment.

Furthermore, it might of course be right that “real world” central banks prefer not to use other instruments rather than interest rates and therefore prefer the government to “push” aggregate demand (hence that is why Brad argues that the “instrument” should enter into the utility function of the central  bank). However, that would still be monetary policy (rather than fiscal policy) as government spending would only impact aggregate demand/NGDP because the central bank chose not to offset the increase in government spending. If the central bank on the other hand used for example a money base rule or McCallum’s MC rule where the policy instrument is a combination of the exchange rate and interest rates then the central bank would not pay any attention to the ZLB.

PS I find it “interesting” to read the comment section on Brad’s blog. It is clear that some of the more ideologically inclined Keynesians have a very hard time accepting the fact that the fiscal multiplier might be zero. (yes, I similarly have a very hard time accepting arguments that it might be positive so I am no saint…)

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This one is pretty funny (HT Daniel Brackins)

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Daniel Lin is teaching macro! Lets introduce his students to the IS/LM+ model

This semester professor Daniel Lin is teaching a class in Macro at the American University and I have a tradition to interfere with how Daniel should teach his students – so I will not let down the opportunity to do it once again.

I have already written a post on how I think Econ 101 should be taught. So I don’t want to go through that once again and I have also written about why Daniel should be happy about his earlier class on Micro.

I have for sometime been thinking about the impact on how macroeconomics is taught to economics students as I fundamentally think most “practicing economists” for example civil servants or financial sector economists think about macroeconomic issues based on what they learned by reading the first 150 pages of their first (and only?) macroeconomic textbook. Few practicing economists ever think about intertemporal optimization, rational expectations, monetary policy reactions functions etc. Yes, everybody know about New Keynesian models and most central banks will proudly show off their DSGE models, but the fact is that most central bankers, civil servants and commercial bankers alike really are just using a rudimentary paleo Keynesian model to think about macroeconomic issues.

My first macroeconomic textbook was Dornbusch and Fischer’s textbook “Macroeconomics”. It is a typical American textbook – far too many pages and far too many boxes and graphs. Nonetheless I still from time to time have a look in it – even though I read it first time in 1990. The book consists of three parts, but since we will only focus on the first 150 pages (remember that is what the practicing economists remember) so we will only get half through the first part of the book (yes, US textbooks are far too long).

On the first 150 pages we are introduced first to the simple (paleo) Keynesian model and we learn that Y=C+I+G+X-M. There are really no prices, no financial markets and no money in the model. A shocking number of practicing economists in reality think about macroeconomics based on these simple (and highly problematic) models. The more clever steudent gets to the next 50 pages, where money and a very rudimentary financial sector (the bond market) is introduced. This is the IS/LM model.

Daniel – lets try to introduce a monetary policy reaction function early on

I am really not happy about this way of introducing future economists to macroeconomics – I would much prefer starting from a more clear micro foundation as I have described in an earlier post. Anyway, lets assume that we are stuck with one of the standard macroeconomic textbooks so we will have to go along with the paleo Keynesian model and the IS/LM stuff.

But lets also assume that we can do that in 140 pages – so we now have 10 pages to add something interesting. I would use the last 10 pages to introduce a monetary policy reaction function into the IS/LM model – let call this model the IS/LM+ model.

The IS/LM+ model

Most economic students are taught that central banks have an inflation target, but that is not really a proper target in the IS/LM model as there is no inflation in the IS/LM model as prices are pegged (actually most students and there professors don’t even notice that there are prices in the model). So lets instead imagine that the Market Monetarists’ propaganda has been successful and that nominal GDP targeting has become commonly accepted at the target that central banks should have.

Lets return to the monetary policy target below, but lets first start out with the IS and LM curves.

We start out with the two standard equations in the IS/LM model. This is from my earlier post on the IS/LM model:

The money demand function:

(1) m=p+y-α×r

Where m is the money supply/demand, p is prices and y is real GDP. r is the interest rate and α is a coefficient.

Aggregate demand is defined as follows:

(2) y=g-β×r

Aggregate demand y equals public spending and private sector demand (β×r), which is a function of the interest rate r. β is a coefficient. It is assumed that private demand drops when the interest rate increases.

This is basically all you need in the textbook IS/LM model. However, we also need to define a monetary policy rule to be able to say something about the real world.

So lets introduce the NGDP target. The central bank targets a specific growth rate for NGDP: p*+y* and the central bank will change the money supply to hit it’s target. That gives us the following monetary policy reaction function:

(3) m=-λ((p+y)-(p*+y*))

Lets for simplicity assume that p*+y* is normalized at zero:

(3)’ m=-λ(p+y)

Put (1) and (3)’ together and we have a LM curve:

LM: r=((1+λ)/α)×(p+y)

And we get the IS curve by rearranging (2):

IS: r =(1/β)×g-(1/β)×y

Under normal assumptions about the coefficients in the model the LM curve is upward sloping and the IS curve is downward sloping. This is as in the textbook version.

Note, however, that the slope of the LM does not only depend on the money demand’s interest rate elasticity (α), but also on how aggressive  (λ) the central bank will react to deviations in NGDP (p+y) from the target (set at zero). This is the key difference between the IS/LM+ model and the traditional IS/LM model.

The Sumner Critique: λ=∞

The fact that the slope of the LM curve depends on λ is critical. Hence, if the central bank is fully committed to hitting the NGDP target and will do everything to fulfill it then λ will equal infinity (∞) .

Obviously, if λ=∞ then the LM curve is vertical – as in the “monetarist” case in the textbook version of the IS/LM model. However, contrary to the “normal” LM curve we don’t need α to be zero to ensure a vertical LM curve.

With  λ=∞ the budget multiplier will be zero – said in another way any increase in public spending (g) will just lead to an increase in the interest rate (r) as the central bank “automatically” will counteract the “stimulative” effects of the increase in public spending by decreasing the money supply to keep p+y at the target level (p*+y*). This of course is the Sumner Critiquemonetary policy dominates fiscal policy if the central bank targets NGDP even in a model with sticky prices and interest rates sensitive money demand.

Daniel lets change the thinking of future practicing economists

I think this is all we need to fundamentally change the thinking of future practicing economists – one more equation (the monetary policy reaction function) in the IS/LM model. That would make practicing economists realize that we cannot ignore the actions of the central bank. The central bank – and not government spending – determines aggregate demand (NGDP) even in a fundamentally very keynesian model.

Take if away Daniel!

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Related post:

The thinking of a Great Moderation economist

The fiscal cliff and the Bernanke-Evans rule in a simple static IS/LM model

Sometimes simple macroeconomic models can help us understand the world better and even though I am not uncritical about the IS/LM model it nonetheless has some interesting features which from time to time makes it useful for policy analysis (if you are careful).

However, a key problem with the IS/LM model is that the model does not take into account – in its basic textbook form – the central bank’s policy rule. However, it is easy to expand the model to include a monetary policy rule.

I will do exactly that in this post and I will use the Federal Reserve’s new policy rulethe Bernanke-Evans rule – to analysis the impact of the so-called fiscal cliff on a (very!) stylised version of the US economy.

We start out with the two standard equations in the IS/LM model.

The money demand function:

(1) m=p+y-α×r

Where m is the money supply/demand, p is prices and y is real GDP. r is the interest rate and α is a coefficient.

Aggregate demand is defined as follows:

(2) y=g-β×r

Aggregate demand y equals public spending and private sector demand (β×r), which is a function of the interest rate r. β is a coefficient. It is assumed that private demand drops when the interest rate increases.

This is basically all you need in the textbook IS/LM model. However, we also need to define a monetary policy rule to be able to say something about the real world.

I will use a stylised version of the Bernanke-Evans rule based on the latest policy announcement from the Fed’s FOMC. The FOMC at it latest meeting argued that it basically would continue to expand the money base (in the IS/LM the money base and the money supply is the same thing) to hit a certain target for the unemployment rate. That means that we can define a simple Bernanke-Evans rule as follows:

(3) m=λ×U

One can think of U as either the unemployment rate or the deviation of the unemployment rate from the Fed’s unemployment target. λ is a coefficient that tells you how aggressive the fed will increase the money supply (m) if U increases.

We now need to model how the labour market works. We simply assume Okun’s law holds (we could also have used a simple production function):

(4) U=-δ×y

This obviously is very simplified as we totally disregard supply side issues on the labour market. However, we are not interested in using this model for analysis of such factors.

It is easy to solve the model. We get the LM curve from (1), (3) and (4):

LM: r= y×(1+δ×λ)⁄α+(1/α)×p

And we get the IS curve by rearranging (2):

IS: r =(1/β)×g-(1/β)×y

Under normal assumptions about the coefficients in the model the LM curve is upward sloping and the IS curve is downward sloping. This is as in the textbook version.

Note, however, that the slope of the LM does not only depend on the money demand’s interest rate elasticity (α), but also on how aggressive  (λ) the fed will react to an increase in unemployment.

The Sumner Critique applies if λ=∞

The fact that the slope of the LM curve depends on λ is critical. Hence, if the fed is fully committed to its unemployment target and will do everything to fulfill (as the FOMC signaled when it said it would step up QE until it hit its target) then λ equals infinity (∞) .

Obviously, if λ=∞ then the LM curve is vertical – as in the “monetarist” case in the textbook version of the IS/LM model. However, contrary to the “normal” the LM curve we don’t need α to be zero to ensure a vertical LM curve.

Hence, under a strict Bernanke-Evans rule where the fed will not accept any diviation from its unemployment target (λ=∞) the (government) budget multiplier is zero and the so-called Sumner Critique therefore applies: Fiscal policy cannot increase or decrease output (y) or the unemployment (U) as any fiscal “shock” (higher or lower g) will be fully offset by the fed’s actions.

The Bernanke-Evans rule reduces risks from the fiscal cliff

It follows that if the fed actually follows through on it commitment to hit its (still fuzzy) unemployment target then in the simple model outlined above the risk from a negative shock to demand from the so-called fiscal cliff is reduced greatly.

This is good news, but it is also a natural experiment of the Sumner Critique. Imagine that we indeed get a 4% of GDP tightening of fiscal policy next year, but at the same time the fed is 100% committed to hitting it unemployment target (that unemployment should drop) then if unemployment then increases anyway then Scott Sumner (and myself) is wrong – or the fed didn’t do it job well enough. Both are obviously very likely…

I am arguing that I believe the model presented above is the correct model of the US economy. The purpose has rather been to demonstrate the critical importance of a the monetary policy rule even in a standard textbook keynesian model and to demonstrate that fiscal policy is much less important than normally assumed by keynesians if we take the monetary policy rule into account.

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