Session 4: ISLM Derivation; the stylised Keynes v Classics argument; Crowding Out/In
The simplified “Keynesian cross” model we looked at in the previous session contains only a goods market. It is a “real” model (the price level is assumed constant), and it is “demand driven” (changes of the model are brought about entirely through changes in components of aggregate demand). Crucially for this session, the Keynesian cross model contains no “money market” (or more generally, no “assets market”). Keynes thought money important; indeed his General Theory starts with the topic. Modern macroeconomic textbooks develop bring the “assets market” into the analysis by introducing the ISLM model. This model was first formalized by John Hicks at Oxford University in 1937, and subsequently was popularized in the United States by Alvin Hansen at Harvard and, after the war, by Paul Samuelson in his famous textbook.
In reality the assets market contains many different monetary instruments, but for the sake of simplification, we can think of a “stylised” market as comprising only money and bonds. Money supply and demand determines the interest rate, and thus bond prices---bond prices move inversely to interest rates. The ISLM model thus contains a “real” and a “monetary” side, thus enabling the economist to analyse the impact of fiscal and monetary policy respectively. However, the model cannot be used to analyse inflation; in the ISLM model, the general price level is assumed fixed. Below we develop both sides of the model. However, the reader should note at the outset that the IS side of the model contains a crucial new relationship. Unlike the Keynesian cross model where I is assumed exogenous (I*), in the ISLM the money market feeds back into the real sector by making I-demand depend partly on i-rt; ie,
4.1 I = I* - bi
II. LM derivation
Let us start with the expression for money supply (Ms) and money demand (Md).
4.2 Ms = M*/P*
4.3 Md = kY - hi
Expression 4.2 says that the money supply (Ms) is exogenous and though shown in nominal terms, the general price level is assumed to be fixed (P*). Expression 4.3 says that money demand is positive function of Y (transactions) and negative function of the interest rate.
What does Md = kY mean? It means that the higher our level of income, the more money we want in our pocket (or equivalently our debit card) to finance our everyday purchases of goods and services; is our “transactions demand”. Equally what does Md = - hi mean? It means that the higher the rate of interest, the higher is the opportunity cost of “being liquid”; ie, holding cash as opposed to yield-bearing securities.
The accompanying figure shows the derivation of the LM curve. In simple terms, an LM curve described by drawing different Md curves (each for a different Y level) through a vertical Ms curve; ie, assuming the money supply to be fixed and invariant to the interest-rate.
Figure 4-1: LM Curve Derivation
The accompanying figure shows how the LM curve is derived. The right hand quadrant shows a fixed (vertical) money supply curve (Ms*) and two money demand curve, the lower one corresponding to the initial level of national income (Yo) and the higher curve corresponding to the higher income-level, Y1. These intersect the Ms curve at points 0 and 1 respectively, corresponding to interest-rates io and i1 respectively. We can now map the co-ordinates (Y0, i0) and (Y1, i1) to the left-hand quadrant to produce two points. The line passing through these two points is the LM curve. (We could repeat this exercise for many different levels of Y and equilibrium i, thus yielding many different points defining the LM curve.)
III. Derivation of the IS Curve
4.4 I = I* - bi
In the simple Keynesian cross system, investment (I) was autonomous. In the ISLM system, I is in part autonomous and in part inversely dependent on the rate of interest (i) as shown in expression 4.4.
Figure 4-2: IS Derivation
The derivation of the IS curve is more easily understood than that of the LM curve. All one needs to remember is that a fall in the interest rate stimulates I, thus driving up Y to some new level of equilibrium.
The top quadrant of Figure 4-2 depicts a Keynesian-cross system while the lower quadrant depicts an IS system; note that in the latter the interest-rate is on the Y-axis. To understand the top quadrant, assume the initial level of aggregate demand is AD, the interest rate is i and the corresponding level of national income is Y. If i now rises to i', this rise causes investment (I) to fall reducing aggregate demand to level AD’ and national income to level Y’. The interest rates i and i' together with the corresponding levels of national income, Y and Y’, can be plotted on the bottom quadrant and the line passing through these points is the IS curve. Further changes in i could be used to define further combinations of (i, Y) to improve the definition of the IS curve.
Figure 4-3: ISLM
Figure 4-3 shows an ISLM system. In such a system we can show overall equilibrium of the goods market (IS) and the bond (or assets) market (LM). Algebraically, the IS side can be written:
4.5 Y = C + I + G + NX
The only difference is that when substituting the full expressions for C, I, G and NX, I must be written I = I* - bi. The LM side is of course:
4.6 Ms = Md
Md = kY – hi
Since for IS = LM, i and Y must be the same, a simultaneous solution for the two unknows (i, Y) is required.
The point about the ISLM system is is not merely that it includes an asset side. The key point is that the interest rate feedback from the assets to the goods market tends to stabilise the system. In a slump, a cut in the interest rate can stimulate investment and get economy moving! In other words, feedback from assets to goods market is entirely via the interest rate’s impact on investment. Any increase in the money supply (Ms) shifts LM to the right; ie, it leads to excess demand for bonds driving down the interest rate and stimulating investment. Note indirectness of mechanism; excess money is assumed not to be spent directly on consumption goods, but on investment goods.
The above figure conveniently depicts both curves as lying at 45 degrees from the horizontal. Shifts in the curves brought about by fiscal (IS) or monetary (LM) policy can thus be analysed. For example, if we wish to raise national income but leave the interest rate unchanged, we must use both fiscal and monetary policy; expansionary fiscal policy alone would tend to raise interest rates (leading to possible “crowding out”) while expansionary monetary policy alone would tend to lower the interest rate (leading to possible capital outflow). In reality, economists disagree fundamentally about the slope of the above curves. Keynesians generally think the IS curve to be relatively interest-inelastic and the LM curve to be relatively interest-elastic. Monetarists generally believe the LM curve to be interest-inelastic (nearly vertical), either in the medium to long term. For members of the “new classicist” or “rational expectations” school of thought, the LM curve is always vertical at a level of national income coincident with the “natural rate of unemployment”.
Figure 4-4: The Keynesian and Classical Cases
These contrasting positions are sometimes stylised (ie, simplified to their essentials) by introducing extreme assumptions about the elasticity of the LM curve. The accompanying diagram contrasts an ISLM system where LM is perfectly interest elastic (the so-called Keynesian case) with one in which the LM curve is perfectly interest inelastic (the so-called Classical case). Because the model can be used to represent both the Keynesian and Classical positions, the ISLM model is sometimes called the “synthesis” model.
The top half of Figure 4-4 shows the “Keynesian” LM, which is perfectly elastic (horizontal). Note that the use of monetary policy (as represented by a shift in LM) has not effect on the equilibrium level of national income. In short, monetary expansion cannot cure a depression.
This depiction of LM as perfectly elastic is sometimes called the “liquidity trap”. In reality, the “trap” can only exist as less that full employment when demand is depressed and the real interest rate cannot fall any further. Keynes believed that at some low (but positive) interest rate---or equivalently at some high level of bond prices---investors would begin to feel that interest rates could fall no lower (or bond prices could rise no higher). Such a “floor” on interest rates would prevent real investment from being stimulated and national income from rising. In consequence, even if the Central Bank expanded the money supply, the non-bank public would absorb the extra liquidity.
In reality, Keynes also believed that long-term investment depended far more on entrepreneurs’ expectations about aggregate demand and long-term profits than on interest rate movements; is, he believed the IS curve was relatively interest inelastic, something which is not shown in the diagram. In short, the IS-LM depiction of the Keynes-Classical debate, because it focuses exclusively on the LM curve, simplifies matters greatly---some would say far too greatly. Nevertheless, the analysis is not irrelevant. In the USA, the Federal Reserve Bank (the US Central Bank) has relied strongly on monetary policy. In 2001 alone, Alan Greenspan has cut the interest rate repeatedly in an attempt to prevent the economy from going into a serious slump (or making a “hard landing”). The Japanese economy has for some year operated at a rate of interest close to zero in order to stimulate investment, while in the EU the European Central Bank has criticised repeatedly for refusing to “loosen” monetary policy. So monetary policy is important, particularly in the way it affects “sentiment” in world financial markets. At the same time, on should not lose sight of the fact that fiscal policy is important in the real world. Japan has repeatedly introduced fiscal stimuli to economic growth in the recent past. In the EU, the Delors plan for an EU-wide high-speed railway network is an example of a large fiscal boost---unfortunately rejected by the EU Counsel of Ministers. In the US, The Bush administration’s tax cut and repackaged “star wars” initiatives constitute a very large pump-priming package for the economy, however dubious their merits on other grounds.
In the Monetarist or “Classical” situation depicted in the lower half of Figure 4-4, LM is perfectly inelastic (vertical). Here, fiscal policy is totally ineffective while only monetary policy works. Fiscal expansion cannot cure a depression because any shift in IS brought about by fiscal stimuli will fully crowd out private investment. The key assumption here is that money demand is perfectly interest-inelastic---a change in the interest rate has no effect on the rate of interest. This case was first argued by Chicago economist, Milton Friedman, in the late 1960s. Friedman’s argument is that household assets are typically too diverse to respond to an interest rate change in the simplified manner characterised by stylised bonds. In Friedman’s view, a rise in the rate of interest is unlikely to change households demand for cash; rather, households will switch between different types of non-liquid assets. While we cannot cover the matter here, there much empirical work has been on estimating the demand curve for money. Needless to say, this work has generated contradictory results and the only agreement amongst economists on the nature of the money-demand curve is that no overall conclusion can be drawn.
V. Financial and Non-Financial Crowding Out:
Figure 4-5: Financial Crowding Out
Above it was said that when the LM curve is less than perfectly elastic (flat), expansionary fiscal policy will lead to some degree of financial “crowding out”. In essence, the steeper the LM curve, the more crowding out will take place. Figure 4-5 depicts what happens when a rightward shift in the IS curve (expansionary fiscal policy) takes place under different assumptions about the elasticity of the LM curve (the nature of the money-demand function).
“Financial” crowing out occurs where a rise in the interest rate leads to a reduction in private investment. How much crowding out occurs depends on the slope of the LM curve (and slope of IS too)
To analyse this situation, imagine that Government increases fiscal spending, as shown by a rightward shift from IS to IS’. In the figure, three possible LM curves are shown. If the LM curve (LM) is horizontal (or "Keynesian" at less than full-N) then no crowding out takes place and national income rises from Yn to Y1. In the “classical case however where LM is vertical (shown by LM”), there is full crowding out; ie, fiscal policy is totally ineffective and national income does not rise. In the intermediate case (shown by LM’), national income will rise from Yu to Y2 and there is “partial” financial crowding out .
What is happening in the diagram is that increased fiscal spending, unless accompanied by a loosening of monetary policy, leads to a rise in interest rates. This rise causes private investment to contract. Thus, fiscal expansion by the public sector is offset by a contraction of investment in the private sector, an effect which results in national income growing less than it would have had the rate of interest not risen. In general the steeper the LM curve, the more crowding out takes place. "Crowding out" will be strongest close to full-employment where the LM segment is steepest. “Full” crowding out (or a vertical LM curve means that an increase in aggregate demand brought about by increased Government spending causes such a rise in the interest rate that private investment falls by an amount that exactly offsets the expansionary effect of the initial change in G.
The reader should bear three further points in mind. First, “financial” crowding out via the interest-rate mechanism is only one potential form of crowding out. If foreign exchange is scarce or rationed and if private and public investment, more public spending might use up foreign exchange thus limiting its availability to the private sector; ie, “foreign exchange crowding out”. Again, if an investment licensing system exists, more public investment might mean a reduction is the licences available to the private sector; ie, “administrative crowding out”. In general, “crowding out” can take place in different ways.
Secondly, the “full financial crowding out” scenario depicted in the classical case above seems unlikely to occur in practice. Whether increased fiscal expenditure leads to an interest-rate rise depends on how it is financed (a matter to which we return). Even if DG is financed by borrowing from the non-bank public, rising domestic interest rates may serve to attract overseas capital. More generally, full crowding out is unlikely because the private sector investment decision does not depend on the interest rate alone but on a variety of factors including; crucially, it depends on entrepreneurial expectations about the buoyancy of future demand. Increased public spending, as Keynes argued, may serve to stimulate aggregate demand, raise incomes and improve the economic outlook in a manner leading entrepreneurs to invest more, not less. This is called the “crowding in” argument. The argument for “crowding in” gains greater force where public spending is directed at improving the economic and social infrastructure in a manner which complements private investment, an argument put forward in the early economic development literature by such writers as Nurkse and Gershenkron.
If the “crowding out” argument has been examined in some detail, it is because is has become all too common to hear economic journalists and policy makers (including these from multilateral institutions) use the argument as a strong reason for limiting public spending. While there may be good reasons for limiting public spending---particularly where it is likely to contribute to inflation---in the author’s view, the argument for strong “crowding out” is not terribly convincing. Worse still, policy makers often use the concept in contradictory ways. One example is that of the European Central Bank (ECB). The ECB currently argues (a) that public spending must not be increased because it might lead to “crowding out”; and (b) that interest rates must remain high because of the danger of inflation. The contradiction should be apparent to any student studying economics.
1. What assumption is made about prices in the ISLM model?
2. How does the interest rate enter the LM side of the model?
3. How does the interest rate enter the IS side of the model?
4. In the LM model, explain the meaning of the money-demand function?
5. Suppose the Central Bank reduces the money supply, how is this shown in the ISLM model; ie, which curve changes and how?
6. Suppose Government increases fiscal spending, how is this shown in the ISLM model; is, which curve changes and how?
7. What determines the slope of the IS curve?; of the LM curve?
8. Write out the full algebraic expression for joint equilibrium in the goods and assets markets.
9. Explain what is meant by “financial crowding out”?
10. Explain what other forms of crowding out might exist besides that caused by an upward movement in the interest rate?
11. What is the meaning of “crowding in”?
12. Why do monetarists generally believe that fiscal expansion is “fully crowded out”?
13. Review the arguments for and against crowding out?