By Steve Keen
This article is the 2nd of a series of posts. To see the first, click here.
Now the bad times are back, Paul Krugman is trying resuscitate IS-LM, a model published by John Hicks in 1937 that seeks to explain the relationship between interest rates, and real output in goods and services and money markets. I argue that Krugman should leave it dead – not for the reasons that the new classicals killed it off (being inconsistent with neoclassical microeconomics is a plus in my books) but because it’s a lousy model for what we’re experiencing right now. There’s no better way to show this than to outline how Krugman is trying to use it, and show that he gets it wrong.
Krugman’s Derivation
Krugman describes his derivation of IS-LM in two posts that feature as “essential reads” on his blog: ‘IS-LMentary‘ and ‘Liquidity preference, loanable funds, and Niall Ferguson (wonkish)‘. He portrays IS-LM as “a way to reconcile two seemingly incompatible views about what determines interest rates”.
“One view says that the interest rate is determined by the supply of and demand for savings – the ‘loanable funds’ approach,” Krugman says. “The other says that the interest rate is determined by the trade-off between bonds, which pay interest, and money, which doesn’t, but which you can use for transactions and therefore has special value due to its liquidity – the ‘liquidity preference’ approach.
In his attack on Niall Ferguson, Krugman guesses that Ferguson has a simplistic view of the Loanable Funds model in isolation as the basis of his opposition to fiscal stimulus. That model shows the supply of saved money as increasing as the rate of interest rises, while the demand for borrowed money falls as the rate of interest rises. Where the two lines intersect, the demand for savings from firms equals the supply of savings from households (see figure 3, from Krugman’s takedown of Niall Ferguson).
Figure 3: Step 1 in Krugman’s derivation of an IS curve
Krugman speculated that this vision, and this alone, explained why Ferguson thought “that fiscal expansion will actually be contractionary, because it will drive up interest rates”. But Krugman points out that this picture alone ignores the fact that both the investment demand for money (I) and the household supply of money (S) depend on the level of GDP: a higher level of GDP will enable a higher level of savings, and it will also be associated with a higher level of investment. So you need to know GDP as well to work out the interest rate in the market for Loanable Funds.
Both the S and the I lines will shift out as GDP rises – which one will shift more. Here is the first bit of ‘shifty’ logic: to ensure that the IS curve slopes downwards, Krugman assumes that savings will rise more than investment does for a given increase in GDP:
“Suppose GDP rises; some of this increase in income will be saved, pushing the savings schedule to the right,” he says. “There may also be a rise in investment demand, but ordinarily we’d expect the savings rise to be larger, so that the interest rate falls.”
Krugman concludes his derivation of the IS curve with a dynamic observation: that a fall in the interest rate (for some other reason – say an attempt by the Fed to stimulate the economy) can cause both savings supply and investment demand to expand.
“Suppose that desired savings and desired investment spending are currently equal, and that something causes the interest rate to fall. Must it rise back to its original level? Not necessarily. An excess of desired investment over desired savings can lead to economic expansion, which drives up income. And since some of the rise in income will be saved – and assuming that investment demand doesn’t rise by as much – a sufficiently large rise in GDP can restore equality between desired savings and desired investment at the new interest rate.”
Given that assumption, the intersection of I2 and S2 – which represent investment demand and savings supply at a higher level of GDP than I1 and S1 – is lower than the intersection for I1 and S1. If you join these equilibrium points up, you get Krugman’s downward-sloping IS curve (which I’ve added in to figure 4 as a red dotted line).
Figure 4: Step 2 in Krugman’s derivation of an IS curve
Then there’s the LM curve. Krugman explains this as follows:
“Meanwhile, people deciding how to allocate their wealth are making trade-offs between money and bonds. There’s a downward-sloping demand for money – the higher the interest rate, the more people will skimp on liquidity in favour of higher returns. Suppose temporarily that the Fed holds the money supply fixed; in that case the interest rate must be such as to match that demand to the quantity of money. And the Fed can move the interest rate by changing the money supply: increase the supply of money and the interest rate must fall to induce people to hold a larger quantity.”
Krugman doesn’t provide a diagrammatic derivation of the LM curve, so I’ll provide mine from Debunking Economics (you can download the supplement with all the figures from that book here; and the figure 5 below is figure 61 on page 25 of the supplement). A key part step is the proposition that the Federal Reserve controls the supply of money, and that it can move it at will – so the money supply is an ‘exogenous’ factor in the model since it is not controlled by the market. Therefore the money supply is shown as a fixed vertical line in the model: it’s impervious to both the rate of interest, and the level of income.
The demand for money however depends on both those things: a lower interest rate will increase the demand for money, since there’s less benefit in foregoing ready access to your money and buying bonds instead; a higher income will increase the demand for money, since there are more transactions taking place and you need more money on hand for them. The first factor is shown by having a downward-sloping demand for money curve for any given level of income; the second is shown by moving the demand curve out to the right as income rises.
Figure 5: Deriving the LM curve – Figure 61 in Debunking Economics
Equilibrium in the LM market thus depends on both the rate of interest and the level of GDP. When you plot these equilibrium points on a diagram with GDP on the horizontal axis and the rate of interest on the vertical, you get an upward-sloping LM curve – the second half of the overall IS-LM model.
Put the two curves together and the equilibrium of both – the point where the two curves cross – gives you the equilibrium interest rate and GDP for the economy. As Krugman puts it, “the point where the curves cross determines both GDP and the interest rate, and at that point both loanable funds and liquidity preference are valid.”
Figure 6: The IS-LM model (from Krugman’s IS-LMentary)
Well Yada Yada. After all that, we’re staring at the economist’s favourite abstraction, a pair of intersecting lines. How does Krugman use them to explain the current crisis – and why is he wrong?
I’ll cover those topics in the next post.
Editor’s note: Steve has invented an innovative way to build models of the economy that actually include banks and debt. He has started a campaign to support that model called “Kickstarter”. The goal is to pay programmers to develop software for the model called Minsky, after famed economist Hyman Minsky. There are only nine days left to help kickstart Minsky and help Steve reach his stretch goals:
$100,000: About 1400 hours of total programming time will enable Russell to complete the “Mun” release, which will focus on improving the graphics and presentation aspects of the program.
Nathan will also be able to develop a version of Minsky for iPad and Android Tablets.
$250,000: With twice as much as the original INET Grant, we should be able to complete stage 2 of Minsky—the “Quesnay” release named in honor of the person I regard as the world’s first dynamic economist, Francois Quesnay—in which the platform could support the construction of multi-bank model of the financial sector, and a multi-commodity model of production.