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!


Related post:

The thinking of a Great Moderation economist

Leave a comment


  1. merijnknibbe

     /  January 4, 2013


    I read your ‘Market monetarism’ paper. Some comments:

    1. Y = C+I+O+Ex-Im. That’s (one of the many) the basic relations of the national accounts, not of Keynesian economics. The sectors are spelled out in the System of National Accounts, the protocol we use to actually estimate the economy (and money as well). You should however not use this formula to estimate the velocity of money. The formula calculates ‘income’, based upon FINAL demand, not total demand, only the ‘net’ demand leading to income. Money is however used in all transactions, not just in final demand transactions. This at the least means that you should not subtract imports from Y, you should add them to Y (which leaves you with the well known ‘means and expenditure’ formula. But all the second hand trade, like the selling and buying of (existing) houses and stocks, has to be added, too. By the way: the modern national accounts of course contain the banking sector as well as the financial stock and the (net) financial flows of the economy, the flow-of-funds is basically a subset of the national accounts.

    2. This of course leads to money creation. Buying houses and financing these with mortgages leads to money creation (and overvalued houses), as we enable banks to finance this lending with freshly created money. That’s the way it happens. This led, in 2005-2007, for instance Ireland, to money growth higher than anything seen in for instance Greece, during the last thirty years. Long story short: house prices plummeted and seem to have bottomed out at 50% of 2007, debts, however, well, you know the drill. The point: monetarists have a ‘single accounting view’ of money while we should use the quadruple accounting view inherent in the monetary statistics which we use to estimate money (economics can be a science, after all). And these show that money and debt are, though ‘joined at the hip’, not symmetrical. You will have to take account of this (and poor overvalued Denmark is of course suffering the consequences of ‘single accounting thinking’, at this very moment and in fact since some years already: I agree with you that, given a functioning market system, macro trumps micro during slumps. It’s also highly relevant to compare Poland with the neighbouring Baltics).

    3. Which leads to another consideration: the central bank is not in charge of money creation. We outsourced money creation to the MFI’s (for a definition: look at the SNA). The money multiplier doesn’t exist as banks can (at a price) always get reserves. Read this: http://rwer.wordpress.com/2012/01/26/central-bankers-were-all-post-keynesians-now/ Of course, the ECB could start to buy Spanish mortgages (or in fact should monetary finance Spanish/irish/Dutch/Danish debt owers to pay their mortgages off, which by the way would not lead to an increase in the amount of money, just in less debt and interest income for the MFI’s). But something tells me this is not in the books at the moment. Which means that money creation is still outsourced, which in the Eurozone leads to bizar situations: see this graph: compare Germany with Greece: http://www.luxetveritas.nl/blog/?attachment_id=2823

    We will have to learn to see the economy as a genuine macro-event, in which quadruple accounting bonds between the atomist actors so beloved by anglosaxons (well, in fact sometimes even eightfold accounting) rule our behaviour and possibilities. We’re in fact more like nerve cells, defined by our connections to other nerve cells, than like atoms… Modern Monetarism still has to rise to this challenge.

  2. merijnknibbe

     /  January 4, 2013

    Oops. I can understand that you disable comments in a post about Hjalmar Schacht. But Schacht completely agreed with Keynes about the gold standard, ‘a barbaric relic’. And Schacht resigned as president of the Central Bank when Buring was president (to be reinstated when the Nazi’s took charge). He was not responsible for deflation. But he did print 8 billions worth of ‘Mefo-bills’, a kind of parallel money, when put in charge again by the Nazi’s, which did the trick. These were of course used to finance the military equipment, alas. But money printing did work (though we do have to think, alas, about the complementary role of dedicated government policies).

  3. I agree with you 100%. Leave the macroeconomics until after microeconomics, and even after reading-the-tea-leaves economics and casting-the-bones economics.

  4. tesc

     /  September 25, 2013

    Hello, I am graduate student and I was interested in the monetarist view of IS-LM. I remember I saw the IS-LM model with the vertical LM but the author just made a small comment and moved on to the LM being horizontal. I would like to update the IS-LM model with a more monetarist insight.

    What do you think about using the rate of money supply increase as independent variable instead of nominal interest rates? The IS curve would be positive because more money induces more spending. The LM would be horizontal because the central bank chooses the rate of money growth. There would be no ZLB.

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