Friday, 20 April 2012

The IS/LM Model


Lectures in Macroeconomics
Chapter 9. The IS/LM Model
Note: The Figures for this Chapter are currently missing. They will be posted soon.
We've spent a few lectures going through the Classical theory (Chapters 56, 7), which I think captures many of the important features of the macroeconomy very well: the effects of productivity changes on output, real wages, and employment; the relations among saving, investment, government spending, and real interest rates; and the connections between money growth, inflation, and exchange rates. These are all things that we observe in macroeconomic life. But there are also a few aspects of the macroeconomy that don't mesh easily with this theoretical setup. To some extent that's unavoidable: theory is simplification, and that means you lose some of the complexity of the real world when you boil it down to a small number of graphs or equations. I think the benefits far exceed the costs, in the sense that the theory gave us a fairly simple and unified way of thinking about a broad range of issues.
The Keynesian theory takes many of the elements used in the Classical theory, but adds to them the premise that prices do not clear markets in the short run. Instead, prices have a life of their own, with the price level or its rate of change subject to considerable inertia (think of a runaway truck, if you like metaphors). This sounds plausible on the face of it, and we've often argued that (say) adjustments in the labor market might take some time. What makes this theory interesting, however, is not that the premise is plausible, but that this one modification changes some of the theory's short-run predictions in dramatic ways.
Perhaps the most important change concerns the effect of higher money growth on interest rates. In the Classical theory, you'll recall, higher money growth leads to higher inflation and thus, other things equal, higher nominal rates of interest. But if you read the newspaper, you get the clear idea that higher money growth lowers interest rates. Over the last six months of 1991, for example, the Fed loosened monetary policy (higher money growth) in order to lower interest rates and combat the recession. I think it's pretty unlikely that Greenspan and his colleagues got this wrong (although we may be facing inflation some time down the road). Think of yourself driving a car with the gas pedal reversed: you'd have to have an IQ below room temperature not to figure this out pretty quick. So if Greenspan is not mistaken, the Classical model must be getting the direction wrong. As I said before, the data seem to indicate that the long-run effect of money growth on interest rates is just as the Classical theory predicts, but the data also suggest that the short-run effect is the opposite. Figure 1 gives you some idea of the typical dynamic response of interest rates to money growth. What we need, then, is some way of thinking about this short-run effect.
For this reason and others, we're going to spend some time looking at a second theory, which we label Keynesian. The Keynesian and Classical theories are often presented as competitors. I'd say that's exactly wrong. They choose different simplifications of a complex reality. Which is better depends on the issues you want to think about. Roughly speaking, the Classical theory is better for long-run properties and the Keynesian theory is better for the short run. (To be honest, this is really too simple: the Classical theory does a better job on the effects of oil price shocks even in the short run, for example.) Of course, what we really need is a combination of the two theories. If we had another term we could do this, but I think you'd find that this is a lot of effort and that we can guess many of the properties of this hybrid model without making such a large investment of our time.
So on to the Keynesian theory. This theory was developed by the British economist and man about town John Maynard Keynes in the middle of the 1930s, when it seemed as if the economies of the Western World were stuck in an endless Depression (a term that means recession, only worse).
We've seen in the postwar period that growth rates of real output go up and down, but that the downs never last very long (check the data from the first chapter). Well the Depression seemed to go on a long time, and Keynes thought a different theory was called for. We'll look at a characterization of his theory due to John Hicks, another British economist and one of the first Nobel prize winners in economics. (Keynes died before the prize was established.) This version is referred to as the IS/LM model, since it is based on the IS and LM curves. We'll see what those are momentarily.
The starting point, as we've noted, is to give prices a life of their own. Quantities are then determined by the "demand" for output (who buys it), rather than "supply" (who makes it), as it is in the Classical theory. The difficulty in getting, say, monetary policy to affect output in the Classical theory is that output is determined by the supply side: the production function, the labor market, and the stock of capital. What Keynes did, essentially, was to erase these parts of the model and proceed without them. You can imagine that this leads to some strange possibilities (can we get more output without more inputs?), but Keynes thought it might not be a bad idea in the short run, despite its long run anomalies. His famous comment to classical critics was that it's the short run that matters: "In the long run we're all dead.".The plan, then, is to develop the "demand" side of our model.
Keynesian versus Classical Theory: Why Money May Affect the Level of Output
As seen in Chapter 6, according to the Classical Theory, monetary policy has no effects on the level of real economic variables (such as output, consumption, savings, investment and the real interest rate). In the Classical Theory it is assumed that all prices and (nominal) wages are perfectly flexible both in the short-run and the long-run. Then:
1. An increase in the level of the money supply M will increase proportionally the price level P (and the level of the exchange rate S in an open economy) with no real effects.
2. An increase in the rate of growth of the money supply will increase proportionally the rate of inflation , the nominal interest rate (and the rate of currency depreciation) and will have no real effect on Y, C, I, r.
The basic idea of the Keynesian Theory (IS/LM model) is that prices (and nominal wages) are not flexible in the short-run: they do not clear markets in the short-run. In other terms, there is inertia in the setting of prices (especially when the economy is operating below full capacity /full employment). The rationale of assuming that prices are sticky is that firms and businesses do not change the prices of the goods they sell on a continuous basis: for example, the New York Times has been selling for 60 cents for a number of years in spite of changes in demand, supply and costs of production. Similarly, producers and sellers of many goods change the price at which the goods are sold only infrequently. This simple modification of the assumption about price flexibility changes dramatically the implications of the effects of monetary policy: monetary policy will have real effects on output in the short-run. We will see in this chapter why.
An important issue related to this non-neutrality of money is the behavior of central banks and monetary policy. During recessions, the Fed expands the level and/or growth rate of the money supply to reduce interest rates and stimulate economic activity. What is the logic of such a policy ? If the world was working according to the Classical Theory in the short-run, such Fed policy would have no real effects and will only increase inflation. Figure 1 shows the effects of an increase in the rate of growth of money in the Classical model. An increase in the rate of growth of money leads to an immediate proportional increase in the inflation rate, in the nominal interest rate with no effects on the real interest rate and the level of output. Money is neutral both in the short-run and the long-run.
However, empirical evidence shows that an increase in the rate of growth of the money supply has very different effects in the short-run from those predicted by the Classical Theory. The response in reality is more similar to that shown in Figure 2: higher money growth reduces the nominal and real interest rate in the short run and leads to an increase in the rate of inflation only slowly over time. The reduction in the real interest rate, in turn, leads to a short-run increase in investment, consumption and the level of output. To understand why monetary policy has effects similar to those shown in Figure 2, we have to look at the Keynesian Theory where prices adjust slowly (with inertia) in the short-run.
So to summarize the differences between Classical Theory and Keynesian Theory:
1. In the Classical Theory, quantities (output) are determined by the "Supply" of output (who makes it) that depends on technology (the production function) and the equilibrium in the labor market. "Aggregate Demand" affects only the price level: so monetary policy affects only prices. The left part of Figure 3 presents a graphical representation of the classical theory. Given the equilibrium in the labor market, the level of output (aggregate supply) is given and is independent of the price level; this is represented by the vertical curve AS in the right side of Figure 3. On the same graph we present the aggregate demand for goods (AD) that is a negative function of the price level; in fact, a reduction of the price level increases real income and leads to an increase in demand. The position of the AD curve depends on the other determinants of aggregate demand: an increase in government spending G or a reduction in taxes T lead to a shift to the right (an increase) of the aggregate demand function. Similarly, an increase in the money supply, increases the real money balances (M/P), reduces the interest rate and leads to an increase in investment and consumption, two major components of aggregate demand. The figure shows that, in the classical theory, any increase in aggregate demand induced by an increase in the money supply does not affect the level of output: it only leads to an increase in the price level from P to P'.
2. In the Keynesian Theory, it is assumed that the economy is not operating at full employment. Since some machines and workers are unemployed, the supply of output can be increased without an increase in the price level. This is represented by an horizontal aggregate supply function AS, as in Figure 4: at the given price level that is fixed (sticky) in the short-run, the supply of output is fully elastic. In this Keynesian model, quantities (output) are determined by the "Demand" for output (who buys it), i.e. by the aggregate demand for goods AD. Since prices are sticky (in the short-run) an increase in aggregate demand (generated by an increase in money M or government spending G) will not affect the price level in the short run. Instead, it will lead to an increase in the level of output from Y to Y'. This is shown in the right hand side of Figure 4.
Where is the increase in output coming from in the Keynesian Theory. The Keynesian theory with fixed prices is mute on this point: as long as there are unemployed resources and production is below capacity, it is assumed that firms are willing to increase output when demand goes up without increasing prices. Figure 5 shows a variant of the Keynesian model that gives some consideration to the supply decisions of firms and explains why they might be willing to increase production when demand goes up. In this Neo-Keynesian variant, nominal wages (W) rather than goods prices are sticky in the short run. If the nominal wage is too high, given the level of goods prices, we get unemployment as the demand for labor is below the supply of labor at the initial real wage (W/P1). The employment level N1 is then determined by the demand for labor and output is equal to Y1. An increase in the price level from P1 to P2 reduces the real wage to (W/P2), increases the demand for labor to N2 and increases the supply of output to Y2. So the aggregate supply AS is a positive function of the price level as opposed to the vertical AS curve of the classical theory and the horizontal AS curve of the fixed-price keynesian theory. In this Neo-Keynesian variant, an increase in the money supply leads to an increase in aggregate demand (shown in the bottom panel of Figure 5). This increase in demand leads to an increase in the price level; this, in turn, reduces the real wage (W/P), increases the demand for labor and leads to an increase in the supply of output. As shown in the bottom part of Figure 5, an increase in aggregate demand leads both to an increase in the level of output and an increase in the price level. So, money is non-neutral in the sense that it affects real output but an increase in M also leads to price inflation.
In general the Keynesian Theory is more valuable for short-run analysis ("In the long-run we're all dead") while the Classical Theory is more valuable for long-run analysis where prices and wages adjust. We will now describe in more detail the Keynesian Theory.
Saving and Investment Once More (The IS Curve)
You'll recall that one of the components of the Classical model is a relation between saving and investment:
S= Sp(r,Y-T) - (G-T) = Sp +Sg = I(r) + CA
where Sp is saving by households (private savings), I is new investment in physical capital, and G-T is the government deficit (negative public savings). As before, let's start by omitting the foreign sector (CA=0), so that the equilibrium condition is
Sp(r,Y-T) - (G-T) = Sp +Sg = I(r).
In the earlier theory Y was given by technological factors and the equilibrium in the labor market; here we want to allow Y to change in response to changes in monetary and fiscal policy, as well as other factors. What we need is not a new relation, but a different graphical representation of the same saving and investment relation, which we'll call the IS curve.
The IS curve summarizes equilibrium in what we'll now call the goods market. It's what we called the financial market earlier, but goods make a better story in the present context, as you'll see. Recall that this equation can be thought of as supply and demand for goods, obvious when we express it as aggregate supply equal to aggregate demand (that is the sum of C, I and G):
Ys = Yd = C + I + G
or as supply and demand for funds in capital markets, as when we write
Sp - (G-T) = I
where Sp is equal to Y-C-T. The two equations represent the same information in different ways. Now what we want, to get an analysis of the effects of monetary and fiscal policy on output and interest rates, is a graph with r and Y on the axes. This is a more complex curve than we've seen before, but it makes what follows easier, since we can put the entire theory in one diagram.
Here's what we do. In our former diagram in Chapter 5 we equated Sp-(G-T) with I for given values of Y, G, T and other variables that affect the positions of the S and I curves. This gives us, as illustrated in Figure 6, a single equilibrium point, labeled A in the diagram where r= r'; this point is for a particular value of Y, say Y = 1000. We can draw this point in the diagram to the right that relates r to Y, also labeled A.
This same experiment can be done for other values of Y, for example Y = 1500. For this value of Y the saving curve shifts to the right as higher income leads to higher private savings, and we have the equilibrium condition at point B at which r is lower and equal to r''. If we plot B on the second diagram we have a point that is southeast of A. If we continue this for all possible values of Y, we trace out a downward sloping line in the second diagram. This line gives us all the combinations of r and Y that are consistent with equilibrium in the goods and financial markets. The curve is downward sloping because, given the initial point A where S=I, an increase in income leads to an increase in savings and causes an excess supply of savings in the financial market. Then, in order to restore the equilibrium in the financial market, we need a fall in the interest rate: this fall reduces savings, increases the investment rate and leads savings to become again equal to investment.
There is an alternative explanation of the downward slope of the IS curve, based on the fact that this curve represents also the equilibrium between aggregate supply of goods and aggregate demand. Aggregate demand is made of three components:
G = exogenous value
C = c0+ b (Y-T) - a r
I = i0- d r
Here we assume that government spending G is exogenously chosen by the government.
Private consumption C depends on three factors. First, there is some exogenous (autonomous) level of private consumption (defined by c0) even at zero levels of disposable income. Second, consumption depends on disposable income (Y-T) according to the parameter "b" that represents the marginal propensity to consume: i.e.if b=0.8, when income goes up by a dollar, consumption goes up by 80 cents. Third, consumption is a negative function of the interest rate r; as interest rates go up, consumers will save a larger fraction of their income and consume a smaller fraction of their income.
Private investment I depends on two factors: first, there is some exogenous (autonomous) level of private investment (defined by i0) that does not depend on the level of interest rates. Second, investment is a negative function of the interest rate: as the interest rate becomes higher, firms (who borrow to buy capital goods) are less likely to invest in new capital goods. The parameter "d" represents the sensitivity of investment to changes in the interest rate.
Now let us see why the IS curve represents the equilibrium in the goods market. Suppose that the initial point A in Figure 7 is one where, given the initial income Y' and interest rate r', aggregate demand is equal to aggregate supply. Then, suppose that we maintain the same initial interest rate r' and increase income/output from Y' to Y''; in terms of the Figure we move from the point A to the point X. This increase in output Y will lead to an excess supply of goods: in fact an increase in output of one dollar by definition increases the supply of goods by one dollar but increases the demand for goods only by "b", the marginal propensity to consume income (say 80 cents if b=0.8). So, point X must be a point of disequilibrium in the goods market: aggregate supply is above aggregate demand (Ys > Yd) at X. Then, we need to do something to restore the equilibrium in the goods market. A fall in the interest rate will do that since a fall in r to the level r'' leads to an increase in investment demand and an increase in consumption demand. So as we move from point X to point B, we restore the equilibrium in the goods market: at B demand for goods will be equal to to the higher supply of goods Y'. So to summarize: starting from an equilibrium, an increase in Y leads to an excess supply of goods; then, a fall in interest rate is required to stimulate aggregate demand (C and I) and restore the equilibrium in the goods market. Note that points above the IS curve represent points where aggregate supply is above aggregate demand (Ys > Yd) and savings are greater than investment (S>I); while points below the IS curve are points where (Ys < Yd) and (S<I). Obviously, points along the IS curve represent combination of values of Y and r such that aggregate demand is equal to aggregate supply (Ys = Yd) and savings are equal to investment (S=I).
Formally, the IS curve is derived as follows. Equate aggregate supply and aggregate demand:
Y = C + I + G = [c0+ b (Y-T) - a r] +[ i0- d r] + G
Then solve for Y as a function of r to get:
Y = [(c0+ i0 + G - bT)/(1-b)] - (a + d)/(1-b) r
Since the slope coefficient -(a+d)/(1-b) is negative, the equation above represents a negative relation between Y and r, i.e. the IS curve.
As with all our curves, there are some changes that are incorporated in movements along the curve and others that involve shifts of the curve. The latter are those that are held fixed during our derivation of the IS curve and include changes in G , T and the autonomous components of consumption and investment (i.e. changes in c 0and i0). We'll consider these in turn.
The effect of an increase in government spending G. Let's see how a change in the exogenous government spending G leads to a shift to the right of the entire IS curve: intuitively, a higher G will spur the economy and shift the IS curve out. Lets us start at point A' in the left side Figure 8 where S=I and aggregate demand is equal to aggregate supply at the initial level of income Y' and r' and the initial G'; the same point A' is represented by the IS' curve in the right side of Figure 8. What happens when we increase G from G' to G''? In the left hand diagram the I(r) curve remains the same while the the national supply of savings is reduced as public savings fall with the increase in G. This reduction in national savings leads, for the initial income Y', to a higher rate of interest r''. That means that the point A' shifts to A'', which is above A'. So, in the right side of Figure 8, the original point A' is not anymore an equilibrium point as G is higher; the new equilibrium in the goods/capital market is at point A'' that is on a different new IS curve. This will be true for all points on the IS curve for exactly the same reason: they all shift up. In fact, for any level of initial income Y, a higher G leads to lower savings and higher interest rates. So the IS' curve shifts up or, what amounts to the same thing, shifts to the right to the new IS'' curve in the right side of Figure 8.
The shift in the IS curve to IS'' following an increase in G can also be seen in Figure 9. Given the initial G', the point E in the old IS' curve represents a point where aggregate supply is equal to aggregate demand. When G increases to G'', given the initial Y' and r', we get an increase in aggregate demand with no change in aggregate supply (as Y is fixed at point E). So point E is now a point of excess demand for goods since G is higher than before. In order to restore the equilibrium in the goods market, we can do two things. We can either move from point E to point E' where the interest rate is higher and equal to r'': the higher interest rate r'' reduces aggregate demand and restores the equilibrium between demand and supply at the initial output level Y'; so point E' is a point on the new IS curve. Alternatively, if r remains constant at the initial level r', the excess demand at point E is eliminated via an increase in output from Y' to Y''; this is represented by a movement from E to E'' where E'' is a point on the new IS'' curve (that corresponds to the higher G'').
The effect of an increase in taxes T. You might guess that this shifts the IS curve to the left or down and you'd be right as shown in Figure 10, but it's a little more complicated than the first example. Suppose we start from an initial equilibrium point A' represented both in the left and right hand sides of Figure 10: at point A', given the initial G' and T', demand for goods is equal to supply for goods and S=I. An increase in taxes T (from T' to T'') has the following effects. First, it leads to an increase in public savings (a reduction in the budget deficit) that causes a shift to the right of the curve S representing total national savings. This is the movement of the curve from A' to B in the left side of Figure 10. However, the increase in taxes reduces disposable income (Y-T) and causes a reduction in private savings; this is the shift of the savings curve from B to A'' in the left side of Figure 10. On net, the increase in taxes leads to a increase in national savings for the same reasons explained in Chapter 5; an increase in taxes by one dollar increases public savings by one dollar but reduces private savings only by the marginal propensity to save out of income. Such marginal propensity to save is (1-b)<1, i.e. one minus the marginal propensity to consume. For example if b=0.8, the marginal propensity to save is (1-b)=0.2; so a fall in disposable income of one dollar (because of higher taxes) reduces private savings by 20 cents. Since private savings fall less than the increase in public savings, total savings go up as shown by the move of the savings function S from the point A' to the point A''. At A'' the higher savings cause a reduction in the interest rate and an increase in national investment. The right hand side of Figure 10 shows this change in taxes as a shift of the IS curve. The initial point A' on the old IS curve is not an equilibrium as higher T means higher savings while investment is still unchanged. Therefore a fall in the interest rate from r' to r'' is required to increase investment and restore the equilibrium in the capital market. At point A'' in the right hand side of Figure 10, we get this new equilibrium on a new IS curve denoted as IS''. This shift will be true for all points on the IS curve for exactly the same reason: they all shift down. In fact, for any level of the initial income Y, a higher T leads to higher savings and lower interest rates. So the IS curve shifts down or, what amounts to the same thing, shifts to the left to the new IS'' curve in the right side of Figure 10.
The shift in the IS' curve to IS'' following an increase in T can also be seen in Figure 11. Given the initial T, the point E in the old IS curve represents a point where aggregate supply is equal to aggregate demand. When T increases to T'', given the initial Y' and r', we get an fall in aggregate demand (as lower disposable income leads to lower private consumption) with no change in aggregate supply (as Y is fixed at point E). So point E is now a point of excess supply for goods since T is higher than before and consumption C is lower. In order to restore the equilibrium in the goods market, we can do two things. We can either move from point E to point E' where the interest rate is lower and equal to r'': the lower interest rate r'' increases aggregate demand (C and I) and restores the equilibrium between demand and supply at the initial output level Y'; so point E' is a point on the new IS curve. Alternatively, if r remains constant at the initial level r', the excess supply of goods at point E is eliminated via an reduction in output from Y' to Y''; this is represented by a movement from E to E'' where E'' is a point on the new IS curve (that corresponds to the higher T). Note that a fall in Y reduces supply more than demand (as the marginal propensity to consume "b" is less than unity); so, it helps to reduce the excess supply of goods.
Money and the Rate of Interest (the LM Curve)
The second element of our theory is the money market. As seen in Chapter 8, the equilibrium in the money market is
M/P = L(i, Y) = L (r, Y)
where M is the amount of currency supplied to the public by the Fed (previously called MS in Chapter 6). Note that, in the Keynesian theory the price level is fixed so that we can assume that there is no difference between the nominal and the real interest rate (i.e. r and i are equal). As we discussed in Chapter 8, the Fed affects the level of interest rates by choosing the amount of currency via open market operations. As in Chapter 8, the equilibrium in the money market is shown in the top panel of Figure 12; r (or i) is determined at the point where the real money supply M/P is equal to the real money demand L.
We can now express this equilibrium in the money market as a new relation between the real interest rate r and real output Y, given values of M and P; we will call this relation the LM curve. We derive this relation in much the same way we did for the IS curve. Start with supply and demand for money for a given initial value of Y. We can graph this, as done in the bottom panel of Figure 12, in a diagram with r on the vertical axis and the quantity of real money supplied or demanded on the horizontal axis. Real money supply is fixed since M and P are given (that is, outside the theory). Real money demand L is a downward sloping line. The equilibrium, labeled A, can be drawn as a point in the right hand diagram (also labeled A) as a combination of the initial Y' and the initial equilibrium r'.
Now try a different, higher value of Y, Y'' greater than the initial Y'. This results in greater demand for money (more transactions) and a shift up of the L curve: at any level of the interest rate the demand for money is higher since income is higher. This increase in money demand leads to a higher rate of interest r'', labeled point B in both sides of the diagram. Thus higher output is associated with a higher interest rate along the equilibrium curve for the money market, labeled the LM curve. So the LM curve represents the combination of values of Y and r such that the real demand for money is equal to the real supply of money (L=M/P).
This upward slope of the LM curve makes sense. As shown in Figure 13, starting from an initial equilibrium point A on the LM curve, a higher Y leads to a higher demand for money; since the supply of money is given, to restore the equilibrium in the money market we need an increase in the interest rates that reduces the money demand back to the fixed real money supply. In other terms, starting from an equilibrium point A, an increase in Y (shown as a movement from point A to point X) leads to an increase in the demand for money and an excess demand for money in the money market (L>M/P). Then, to bring back the demand for money to the lower exogenous level of the real money supply (M/P), we need an increase in the interest rate, i.e. a movement from point X to point B. At B, the equilibrium in the money market equilibrium is restored. Note that points below the LM curve are points of excess demand for money (L>M/P) as higher output and/or lower interest rates raise the demand for money above its supply; while points above the LM curve are points of excess supply of money (M/P>L). Points along the LM curve are points where real money demand is equal to real money supply (L=M/P).
The LM curve summarizes equilibrium in the money market for given values of M and P. Changes in any of these variables leads to a shift of the curve. The most important of these is a change in M. You might guess that an increase in M shifts the LM curve to the right or down (raises output or lowers the interest rate), as shown in Figure 14. That's exactly right, as we now show. Suppose you start from an initial equilibrium in the money market at point A in both sides of Figure 14; the initial output, money supply and price level are Y', M' and P'. The equilibrium A is represented by the interest rate r' and the level of output Y' in the right side of the figure. If M increases from M' to M'', this shifts the supply of money function in the left hand diagram of Figure 14 to the right. The result is a lower equilibrium real interest rate, given the initial value of Y, Y'. In the right hand side diagram, this appears as a shift down from point A' to point A''. The new point is labeled A'' in both diagrams. So, an increase in the money supply leads to an excess supply of money, given the initial values of r and Y. Then ,we need a reduction of r (given the level of Y) to increase the demand for money to the new higher level of the money supply. So, the equilibrium is restored on a new LM curve at a point A'' where output is still the same Y' and r has fallen from r' to r''. This increase in the money supply will reduce the interest rate at any level of output Y. In fact, if we started from a different initial Y, say Y'' (before the shift in M), we would be on a point like B' on the original LM curve. Then, an increase in M would still lead to a reduction in the interest rate. So, an increase in M is represented by a shift downward to the right of the entire LM curve from LM' to LM''. An additional way of seeing the shift in the LM is as follows. An increase in M leads to an excess supply of money (M/P > L) at the initial levels of r and Y. Then, to restore the equilibrium in the money market, you need either a lower r (for given Y) to increase the money demand to the higher supply or a higher Y (for given r) to increase the money demand to the higher level of M. Either way, the LM shifts to the right.
Demand-Side Equilibrium
The equilibrium in the Keynesian model consists of intersecting the IS and LM curves, as in Figure 15. Points of intersection are combinations of r and Y (Y' and r' in the figure) such that we have equilibrium in the markets for both goods (the IS curve) and money (the LM curve). We call this the demand side since it involves how much output is demanded (through consumption, investment, and government spending), rather than how the output is produced (the production function, you'll note, plays no part here).
The interesting aspects of this model concern the policy experiments. Note first the effects on r and Y of an increase in the money supply M, considered in Figure 16 . We saw in above in Figure 14 that this leads to a shift of the LM curve to the right. The initial equilibrium (before the increase in M) is at point A where r=r', Y=Y' and the LM curve is represented by LM'. Now, the central bank increases the money supply from M' to M''. Given the initial level of output Y' and interest rate r', the increase in the money supply lead to an excess supply of money and a shift of the LM curve from LM' to LM''. The equilibrium will move from A to B where r is lower at r'' and Y is higher at Y''. Let us see how the adjustment from A to B occurs. Initially, the level of output is fixed at Y' and the increase in M leads to a reduction in the interest rate. Given the initial money demand (for given Y'), the interest rate has to fall from r' to rx to clear the money market; since asset prices adjust faster than goods markets, it makes sense to think that in the short-run output is unchanged and the entire burden of equating money demand and money supply falls on the interest rate. Now, the increase in M caused the interest rates to fall at the much lower level rx represented by the move from point A to point B in the right panel of Figure 16. Note that this is fall in both the nominal and real interest rate since prices and inflation are held fixed. Since real interest rates are lower, the components of aggregate demand more sensitive to interest rates start to increase: firms increase investment by buying more capital goods while households reduce savings and start to consume more (especially big items such as cars, home appliances and other durable goods whose demand is sensitive to interest rates). In turn, this increase in aggregate demand leads firms to produce more as in a Keynesian model aggregate supply is determined by the aggregate demand for goods; so output starts to increase from Y' to Y''. Note that, while the interest rate falls on impact following the increase in the money supply, over time it starts to increase even if at the new equilibrium B, the interest rate is at a level r'' that is lower than its pre-monetary shock level r'. The reason for the increase in r from rx to r'' in the transition from C to B is simple: as output starts to increase, the demand for money will increase too. Since the money supply is now fixed at its new higher level M'', the increase in money demand pushes up the interest rate. So, r initially falls from r' to rx but then crawls back up to r''. In the new short-run equilibrium B, output is higher and the (nominal and real) interest rate is lower. Thus we have delivered on one of our objectives: to have a theory in which more money leads to lower interest rates and higher output. The mechanism, if you stop to think about it, is liquidity: the Fed changes the composition of its debt, raising the fraction of debt in the form of cash. This makes financial markets more liquid and, for a period of time, drives down interest rates. This, in turn, stimulates aggregate demand and leads to an increase in production, output and income.
Over longer periods of time, of course, we might expect that an increase in M would lead the classical effects to take over: inflation and nominal interest rates would rise. You can see this long-run effect by working through the effects of an increase in P on the LM curve in Figure 17. If the initial output level Y' was equal to the full employment output, the increase in output to Y'' puts the economy in a overheated state where output and demand are above the long-run potential level of output. Therefore, the price level starts to increase as bottlenecks in production and increases in wages lead to positive inflation. As the price level P starts to increase, the real money supply M/P falls; in fact, the nominal money supply is now given at M'' while P is now increasing over time. This reduction in the real money supply leads to a leftward shift in the LM curve. In fact, the position of the LM curve depends on the levels of M and P; and an increase in P is equivalent to a fall in M since the position of the LM curve depends on the ratio M/P. Therefore over time, as prices increase, the LM curve shifts back eventually to where it was before the monetary shock; as this backward shift in the LM occurs, the interest rate starts to increase, the demand for goods starts to fall and output falls back towards its full employment level Y'. In the long-run, the initial increase in the money supply has not effects on output and the interest rate and its only effect is an increase in the price level, as predicted by the Classical theory. But in the short run, say 6 to 18 months, the Keynesian model seems appropriate. Figures 16-17 put these two effects together: initially the Keynesian "liquidity" effect dominates, but later on the Classical theory takes over, as inflation catches up with the increase in the money supply.
Another policy change we consider is a rise in government spending G, shown in Figure 18. Note that, since a reduction of taxes T has the same effect on the IS curve as an increase in government spending G, the policy experiment we consider (an increase in G) has similar effect as a reduction in T. In fact, both fiscal policy changes lead to a higher budget deficit; here we assume that this budget deficit is financed by issuing bonds. In Figure 18, we show the short-run effects of this fiscal expansion. We know from the analysis above (and Figure 9) that an increase in G leads to a shift of the IS curve up to the right, from IS' to IS''. Before the increase in G, the equilibrium was at point A; the new equilibrium is at point B where both output and the interest rate are higher. Let us see why a fiscal expansion leads to these effects. Starting from an equilibrium A, an increase in government spending leads to an increase in aggregate demand; initially this leads to an excess demand for goods but since output is demand determined, the increase in demand soon leads to an increase in supply. Therefore, output starts to increase from Y' towards Y''. Note that, as output goes up, the interest rate starts to increase from r' to r''. The reasons why the interest rate goes up are two: first, as income goes up the demand for money increases; but since the supply of money is constant, the increase in the demand for money must lead to an increase in the interest rate. Second, since the higher budget deficit is bond-financed, the increased supply of bonds by the government must lead to a fall in their price and an increase in interest rates; agents will hold these extra government bonds only if their return is higher. Therefore, as output increases from Y' to Y'', the interest rate goes up from r' to r''. Note that the difference between expansionary monetary and fiscal policy, then, is that one lowers interest rates, the other raises them; both of them lead to an increase in output. Note also that, in the case of a fiscal expansion, the increase in the interest rate leads to a "crowding-out" of private investment. In fact, as interest rates go higher, private investment tends to fall leading to a smaller increase in output than would have occurred if interest rates had not gone up. This can be seen by observing that, if the interest rate had remained constant at r', the shift in the IS curve to IS'' would have led to an increase in output from Y' to Yx ; instead, the actual increase in Y is only from Y' up to Y'' since the increase in interest rates leads to an fall in private investment (the crowding-out effect). This is similar to the Classical theory where higher budget deficits lead to higher interest rates and lower investment (see Chapter 5).
As in the case of a monetary expansion, the effects described above are only short-run. Since in the long-run output is determined by supply factors, a fiscal expansion cannot permanently increase output above its long-run full employment level. This transition from the short run to the long run is described in Figure 19. Suppose that the initial Y' was the full employment output. Then, in the short-run the fiscal expansion leads to an overheating of the economy as output Y'' is above its full employment level. This excess demand for goods, in turn, will cause over time some positive inflation. As the price level goes up, the real money supply M/P will fall (since M is exogenously given and P is increasing); this fall in real money balances leads to a shift to the left of the LM curve that starts to move from LM' to LM''. As the LM shifts back, the interest rate will tend to rise from r'' to r'''. This increase in interest rates, in turn, leads to a reduction in aggregate demand, especially demand for investment and durable goods. This fall in aggregate demand, in turn, leads to a fall in output. So, the output level starts to shrink from Y'' back to its original full employment level Y'. The increase in prices terminates when output is back to its full employment level and the excess demand for goods is eliminated. The new equilibrium is at point C where interest rates are even higher than in the short-run. That makes sense: since output is back to its initial level while G is at a higher level, the goods market clears through a permanent reduction in the components of demand that are interest sensitive, i.e. investment and consumption of durable goods (Y = C + ¯I + ­G). So, you get a long-run crowding-out of investment. Note that this permanent long-run crowding-out of investment can be avoided if, over time, the increased budget deficit (caused by the increased G) is financed by an increase in taxes T. If an increase in taxes occurs, the IS curve shifts from IS'' back to the original IS' and the long run equilibrium is not at point C but back at point A. In this new long-run equilibrium, there is no crowding-out of investment as the interest rate falls back to the original r'. However, since Y is constant to its full employment level Y' while G is at a higher permanent level G'', there must be a full crowding-out of private consumption; in fact, the higher taxes reduce disposable income and lead to a permanent reduction in C (again Y = ¯C + I +  ­G).
In summary, in the short-run since prices of goods are fixed the Keynesian effects are at work and both a monetary and fiscal expansion lead to higher output. However, if output ends up being higher than its full employment level, over time the price level will start to increase and the long-run effects of these monetary and fiscal expansions is identical to the implications of the Classical theory. Money cannot affect the long run level of real variables such as output, C, I and the real interest rate. For concerns fiscal policy, government spending and budget deficits cannot affect the level of long-run output but may affect its composition between consumption, investment and G.
Application: The 1981-2 Recession
If you were older, you might recall the 1981-2 recession, the deepest recession of the postwar period. This recession was unusual in a number of respects. For one thing, it coincided with extremely high rates of interest, whereas in most recessions (think of 1990-92) we see low rates of interest. This recession was also interesting for establishing Henry Kaufman, an NYU graduate and current chairman of Stern's Board of Overseers, as the preeminent interest rate forecaster on Wall Street for most of the 1980s, and for spurring the growth of fixed income derivative assets, like options on treasury bonds.
Let's start with the background. As we entered 1979, the US economy was limping along with slow growth and inflation in the range of 10-12 percent a year; see Figure 20. Carter had just appointed Paul Volcker chairman of the Federal Reserve with orders to eliminate inflation. Over the next three years we experienced the most severe recession of the postwar period and inflation fell to about 4 percent, where it stayed for most of the 1980s.
What happened? I think the simplest sensible interpretation of the data is that the Fed adopted a policy of very tight money. We can think of the short-run effects as being a leftward shift of the LM curve, which raises interest rates and lowers output. In the top panel of Figure 21 we see a sharp drop in money growth in 1980, and the middle panel shows that this resulted in a similar drop in real balances, M/P, that lasted for several years. The final panel illustrates the impact on short-term rates of interest: the 3-month tbill rate and the federal funds rate (the rate at which banks borrow and lend from each other on a daily basis, which we'll discuss in a few weeks). For the only time in the postwar period we saw 3-month treasury bill yields well above ten percent, which is exactly what we'd expect from a sharp leftward shift of the LM curve.
Here's where Kaufman comes in. Rates peaked in the fall of 1979 at around 14 percent, then fell under 10 in early 1980. At this point most forecasters regarded the high rates of late 1979 as a freak occurrence that was unlikely to happen again. Kaufman argued the opposite, and predicted that Volcker's tight money policy would drive rates up again. Kaufman turned out to be right when everyone else was wrong, and thus established himself as one of the most influential men on the Street. Curiously, his own firm (Salomon Brothers) reportedly didn't believe him at the time.
This is an example, I think, of where sound economic reasoning (and probably a fair amount of luck) turned out to be useful. In forecasting, if patterns between variables were the same from one business cycle to the next, all you'd need to forecast is a summary of these patterns. But in 1981-82 we saw something that didn't fit past experience: high interest rates in a recession. Economic theory was useful because we could use the same framework to examine the effects of policies that have never been tried, like the Volcker disinflation. Thus theory helps us to make predictions about events that lie outside our range of experience.
If we follow this period along a couple more years, we see, I think, that elements of the Classical theory come to bear. After a couple years of tight money, we see in Figure 20 that inflation fell from about 12 percent in early 1980 to 4 percent in mid-1982. If we compare Figure 21, we see that nominal interest rates declined along with inflation. So I think this episode illustrates both the short-run Keynesian effects of Volcker's tight money policy and the longer-run Classical effects, too.
There's another aspect of this situation that relates to financial markets. If you glance at interest rates over the 1979-81 period you can see that they had more sudden changes than we'd seen ever before in the postwar period. There was a lot more uncertainty about interest rates and bond prices. Now think what this means for a financial business---say one that borrows short and lends long, like a typical commercial bank. If interest rates rise sharply then the prices of long bonds fall (think about this if it seems mysterious). The company is stuck with assets that have declined in value and face higher interest rates on their borrowing: in short, they've been squeezed by the rise in interest rates.
A friend of mine made a large amount of money (by academic standards) explaining to a money-center bank how to hedge itself against such risks. What you do is buy a put on government bonds, so that if the bonds fall the put rises in value to compensate. This advice turned out to be extremely valuable in the early 1980s. Events like this helped to spur the growth of such markets as options on government bonds, and "fixed income derivatives" are still pretty hot in the financial community.
Animal Spirits and Self-Fullfilling Recessions
In this section, we will explore the idea that changes in the households' and firms' optimism and confidence about the economy (animal spirits) can lead to self-fulfilling recessions or economic booms even if the fundamental determinants of income and interest rates have not changes. Suppose that suddenly households and firms become more pessimistic about the future of the economy. This change is the market mood or confidence may occur even if there has been no change in the current fundamentals. For example, households may start to cut consumption even if the the level of their disposable income is unchanged and the level of interest rate is unchanged. This reduction in consumption (in spite of the constancy of the determinants of consumption, disposable income and interest rates) may occur if there is an event that makes households more pessimistic about their future income. For example, when Iraq invaded Kuwait in the summer of 1990, the U.S. economy started to go into a recession. Why ? Part of the story is that households were nervous about the future effects of the invasion on the economy and started to cut their consumption spending in spite of the fact that their current incomes and interest rates were unchanged. This exogenous reduction in consumption led to a fall in aggregate demand; in turn, this fall in aggregate demand led to a fall in production that resulted in the recession of 1991-1992. In other terms, an exogenous change in consumer confidence about the future of the economy led to a self-fullfilling recession. Households started to consume less because they were worried about their future income; according to the conventional lore, in 1990-91 people were staying at home and following the Kuwait crisis on CNN rather than going out and spending their incomes. In turn, this initial concern about future incomes led to a fall in consumption that caused the recession that was being feared in the first place. Similar changes in optimism, investors's mood (otherwise called by Keynes "animal spirits") and consumer confidence may lead to changes in the firms' investment demand even if fundamental determinants of investment (such as real interest rates) have not changed. Firms may suddenly become concerned about the future of the economy and this change in firms' animal spirits may or may not be related to actual changes in the current state of the economy. If this change in firms' sentiment occurs, they may start to cut their investment (their purchases of plant and equipment). This fall in investment demand, in turn, leads to a fall in aggregate demand and a self-fullfilling fall in output. I.e. a recession may end up occurring just because consumers and firms start to believe that a recession might be occurring in the future.
How can we formalize the idea of self-fullfilling changes in output due to animal spirits in the context of out IS/LM model? You remember that when we derived above the consumption and investment demand functions we said that these functions depend on fundamental variables such as Y-T and r for consumption and r for investment. However, we also argued that there are some components of consumption and investment that are exogenous and we called such autonomous components c0 and i0; these autonomous components of aggregate demand are those that are affected by animal spirits as they lead to changes in C or I even if there are no changes in fundamentals (Y-T or r). Formally, the consumption and investment functions are:
C = c0+ b (Y-T) - a r
I = i0- d r
Lets us then consider the effects on the IS curve of exogenous changes in the autonomous components of consumption and investment. A reduction in either c0 or i0 represents a reduction in some exogenous component of aggregate demand. Therefore, if initially the economy was in equilibrium, such exogenous fall in demand is exactly equivalent to other types of exogenous reductions in aggregate demand, such as an exogenous fall in government spending G. We know from the previous analysis that a fall in government spending leads to a shift of the IS curve down to the left. Therefore, an exogenous change in the autonomous components of consumption or investment (due to animal spirits) will also be represented by an exogenous shift downward to the left of the IS curve. This case of a recession caused by animal spirits is then described in Figure 22. Before the change in the investors' and consumers' mood, the equilibrium is at point A where output is at Y' and the interest rate is at r'. Then, an increase in agents' pessimism about the economy leads to a fall in exogenous demand even if the fundamentals Y and r are still unchanged; in turn, this leads to a shift to the left of the IS curve from IS' to IS''. This fall in aggregate demand then leads to a fall in output/income as firms start to cut production in response to the fall in demand. The ensuing fall in income further reduces aggregate demand and exacerbates the initial fall in output. The economy starts to contract and output falls from Y' to Y''. As output falls, the interest rate falls as well: the lower investment demand reduces the demand for loans and borrowing pushing down the interest rate. Also, the fall in output reduces the demand for money and leads, for given supply of money, to a fall in the interest rate. Over time the economy moves from point A to point B and the economy falls into a recession.
This is in part the story of the 1990-1991 recession. Of course, these changes in animal spirits were not the sole cause of that recession as monetary policy and external shocks played also an important role. However, the discussion above suggests that animal spirits can play a role in the observed business cycles in the economy. An exogenous increase in optimism (higher consumer and firms' confidence) can lead an economy out of a recession; conversely, an exogenous fall in consumer and investors confidence can lead to a self-fullfilling contraction in economic activity. A recession may occur just because many people start to believe that it may be occurring!
Application: Bolivian Stabilization
Bolivia in the mid-1980s suffered from rates of inflation in excess of 1000 percent per year. On the advice of Jeffrey Sachs of Harvard, they adopted one of the cleanest examples of an orthodox stabilization: fiscal budget balance, slower money growth, and market-oriented policies. What we saw was a dramatic fall in the inflation rate, as you might predict from the Classical theory. We also saw a substantial decline in output, as the Keynesian theory predicts for the short run. This suggests that the kinds of price inertia we're talking about are also present at very high rates of inflation (which should tell you why it's so hard to get rid of inflation once you get it). Sachs remarked on the latter: "When I came, Bolivia was a poor country with very high inflation. Now Bolivia is simply a poor country."
Application: Is Saving Good for the Economy?
There's an old joke that if you ask twelve economists a question, you get thirteen answers: one from each, plus two from Keynes. Saving is a good example of this. We saw in the Classical theory that saving was good for the economy: a high saving rate translated into higher investment, growth in the stock of capital, and increases in output and wages. This prediction was backed up by data: countries that save the most also tend to invest the most and grow the fastest.
The Keynesian story is just the opposite. A higher saving rate (the ratio of S to Y) is also a lower consumption rate, since saving and consumption sum to after-tax income. In terms of the IS/LM diagram, we can think of an increase in the saving rate as a leftward shift in the IS curve, which (in the theory) reduces output. The story is that if individuals decide to consume less, this hurts firms, who are trying to sell, and leads them to lay people off. This is a demand side story in the sense that we are talking about who demands, or buys, goods, rather than how they are produced. I think the story has some merit.
So who is right? Like our analysis of monetary policy, I think it's a little of both: the Keynesian theory fits the short term, but over periods longer than a couple years saving clearly raises output (ie, the Classical theory is the best guide). For example, the short-run effect of a reduction in budget deficits (via a cut in spending G or an increase in taxes T) may be recessionary according to the Keynesian model; however, over time, the cut in the budget deficit lead to a fall in real interest rates, less crowding-out and an increase in private investment. Over time, this increase in investment leads to a larger capital stock and an increase in potential and actual output. So, while the short run effects of a fiscal contraction may be recessionary, the long-run effects are likely to be expansionary. This tradeoff between short and long term objectives is one of the tough issues facing policymakers. On the whole, I tend to worry that short term thinking has led to policy with poor long term consequences. Businessmen face some of the same problems: when bonuses are tied to annual performance, there may be little gain to adopting policies with long term benefits. (Keller, in Rude Awakening, makes this point over and over about the corporate culture at GM.)
Application: Who Should Make Monetary Policy?
The Volcker disinflation of 1979-1982, and countless other examples, makes it clear that the short run and long run effects of monetary policy are much different. In the short run, monetary expansion lowers interest rates by increasing the level of liquidity in financial markets. In the long run, faster money growth raises inflation and thus raises nominal interest rates, with no effect on the real rate. Experience suggests that if the central bank is too closely connected to the government, short run considerations will dominate with possible adverse consequences in the longer term (unnecessarily high inflation). As a result, many countries give the central bank some autonomy, much as we do for the judiciary. Eg, US Supreme Court Justices are appointed for life, and members of the Board of Governors of the Federal Reserve System are appointed for 14 year terms (we'll discuss the Federal Reserve System in more detail later on). This gives elected officials control, in the longer term, over monetary policy, but insulates monetary policy from day-to-day politics.
Over the last decade or so, there has been increasing pressure in Congress to make the Fed more "accountable." Articles in the Wall Street Journal and elsewhere note that monetary policy is made by people who have not been elected, suggesting that perhaps they should be.
Should the Fed be more accountable to Congress? The evidence seems to be that in those countries with more independent central banks, inflation has been lower and unemployment hasn't been much different. In this sense, independence may be a good idea. That's generally the recommendation to high inflation countries: deny the fiscal authority access to the printing presses by making the central bank independent. The low inflation rates of Germany are surely the result of an extremely independent Bundesbank, which doesn't seem to have affected them adversely in other respects. German output growth, for example, has been as good as any European country in the postwar period. It's strange, then, that Congress would then argue that Fed independence is bad for the US. It's hard, too, to resist a further cheap shot at Congress: would you rather put monetary policy in the hands of the Greenspan and Co., or the people who brought you the S&L fiasco?
Summary
  1. The central idea of the Keynesian theory is that prices, or inflation rates, have a great deal of inertia: they do not respond immediately to changes in economic conditions or policy. That allows monetary policy to influence the real rate of interest and output in the short run.
  2. The IS curve summarizes equilibrium in the goods market. It's downward sloping in the diagram. Increases in G shift it to the right/up. [Write down the equation and draw the graph.]
  3. The LM curve summarizes equilibrium in the market for money. It's upward sloping in the diagram. Increases in M shift it to the right and down. [Write down the equation and draw the graph.]
  4. Equilibrium in the IS/LM model is represented by the intersection of the IS and LM curves. Increases in G raise Y and r. Increases in M raise Y but lower r.
  5. The 1981-2 recession illustrates the impact of monetary policy in the short run, and how elements of both the Keynesian and Classical theories show up in applications.
  6. Stabilizations of hyperinflations suggest that "price inertia" may be relevant there, too.
  7. Finally, autonomy of the central bank may improve its performance by insulating it from short term political pressures.
IS-LM Tutorial

This page presents a geometrical overview of, and introduction to, the IS-LM model.  For the algebra see any standard textbook, like Branson's Macroeconomics, or The Hicks-Hansen IS-LM Model at the excellent HISTORY OF ECONOMIC THOUGHT site.

I'm not currently teaching a course that uses this tutorial, but I've left it up because a few people out there have found it useful.  Please send any criticisms or suggestions to me at danby@u.washington.edu.  Best, Colin Danby

1. Nature of the Model

Any model makes some things endogenous (determined within the model) and some things exogenous (determined outside the model).  Let's go back to the income expenditure model, which you learned in intro macro. In that model Y was endogenous. G and Ip were exogenous. Solving for equilibrium Y required finding the solution to only one equation: Y = C + Ip + G.

To review the income-expenditure model, go here: Macro Notes Section 1.4 and here: Macro Flows Tutorial Section 1.3. (Just use "back" in your browser to return to this page once you've read enough)

Go here to review the macro accounting framework: Macro Flows Tutorial Section 1.2.

Only Y was endogenous in the income-expenditure model. The IS-LM model makes both Y and r endogenous. The key advantage of this is that we can have r determine Ip. Since the level of planned investment is important in the real world and varies a lot, it's nice to have a model in which that is not just set exogenously.

So what determines r? This model attempts to capture Keynes' insights about the money market, which you also studied in intro macro. We regard r as the outcome of the interaction between money demand and money supply. This is why IS-LM is essentially two models stuck together: a model of the goods market, and a model of the money market.
2. Equilibrium

This can be a difficult model to learn. There is a danger that you'll concentrate so hard on the mechanics of it that you'll lose sight of how the model relates to the real world.

Please review the concept of equilibrium: Macro Notes Section 1.3. And recall what equilibrium means in the income-expenditure model: Macro Notes Section 1.8.

Macro models do not claim that the economy is always at equilibrium. What they do claim is that if the economy is not at equilibrium, it will move toward equilibrium. (Near the end of this tutorial are some animations that try to show this movement.)  Thus in the income-expenditure model, if G rises a series of events will raise Y, until a new equilibrium is reached at which there is enough extra savings. Review: Macro Notes Section 1.9.

The notion of equilibrium, and how the macroeconomy is supposed to move toward it, is the key to understanding the IS-LM model. This model is composed of a goods market and a money market. You can think of it as embodying two ideas:

    a. Depending on the interest rate (which determines Ip), there will be an equilibrium level of Y. If Y is below this equilibrium level, it will tend to rise. If Y is above this equilibrium level, it will tend to fall.

    b. Depending on the level of transactions demand for money (set by Y) there will be one interest rate that equilibrates the money market. If r is above this level, it will tend to fall. If r is below this level, it will tend to rise.

What makes things interesting, but also difficult, is that both r and Y can change. Below we will develop our separate models of the goods and money markets, and then put them together. If the terminology of goods and money markets is not familiar, review it here: Macro Notes Section 4.1.

QUIZ for parts 1 and 2
3. Goods Market (IS)

Take the income-expenditure model, which you reviewed above (go back if you didn't). If Ip rises, equilibrium Y rises, right?  This was because a higher level of demand for capital goods caused more to be made, more workers got hired, they bought more stuff, and so on.  Add to this the idea that Ip rises when r falls -- the cheaper it gets to borrow money, the more new capital investment projects firms undertake.

Review this important link between r and Ip here: Macro Notes Section 4.2.

Therefore:

    * If r falls, Ip rises. When Ip rises, equilibrium Y rises, as shown in the income expenditure model.
    * If r rises, Ip falls and equilibrium Y falls.

The different values of r, and the resultant equilibrium values of Y, give us a set of Y,r points that represent "goods market" equilibrium -- a situation in which AD=AS.

Here are some graphs that show how we get this set of points. Click the graphs to enlarge them.

This is theory you already know from intro macro. All we've done is add a new graph with Y on the horizontal axis and r on the vertical axis. The set of (Y,r) combinations that represent goods market equilibrium fall along a line in our graph.

The best way to think about that IS line is as a border -- a boundary in (Y,r) space between points at which AD < AS and Y will tend to fall, and the points at which AD > AS and Y will tend to rise.

Here is another graphical way to represent the IS curve. This picture is essentially the same as the derivation of the IS curve that you looked at above, except that we glued some of the graphs together at their common axes (turning some upside down), to get a "four quadrant" derivation. The depiction of IS itself emphasizes that the line is a frontier between the Y,r points at which Y is below equilibrium, and the (Y,r) points at which it is above its equilibrium level.

It should be apparent from the graphical derivations that if G changes, then the (Y,r) points that equilibrate the goods market change too. In graphical terms, a rise in G will shift IS right, while a fall in G will shift it left.

Additionally, note that the sensitivity of Ip to r will affect the slope of IS. If planned investment is highly sensitive to r, then a small change in r will mean a large change in Y, and IS will be almost horizontal. If planned investment is hardly affected at all by r, then it will take a large change in r to get much change in Y, and IS will be almost vertical.

To recap before moving on: the above is really just the income-expenditure model plus the idea that r affects Ip.  Note that we are reasoning from r to Y, via Ip.

QUIZ for part 3
4. Money Market (LM)

This is also built out of theory you learned in intro macro, but it's a little harder. Try to keep the reasoning about the money market strictly separate in your mind from what you just learned about the goods market.

The notion of equilibrium here is a situation in which money demand equals money supply.  Money demand comes from two sources: transactions and speculative demand. Money supply we will regard as exogenously set by the central bank, acting on the commercial banking system.

Review Money Demand: Macro Section 3.1
Review Transactions Demand for Money: Macro Notes Section 3.2
Review Speculative Money Demand: Macro Notes Section 3.3

An extensive review of what money is and how its supply is set can be found here: Macro Notes Part 2.

You should remember that if bond prices rise, that's the same thing as saying interest rates fall. If that's not clear, review it here: Macro Notes Section 3.5.

If the money market is out of equilibrium, the interest rate changes. You may remember that this happens because individuals hold wealth in a portfolio consisting of money and bonds:

    * When people finding themselves holding more money than the want, they try to turn some of it into bonds by buying bonds, which pushes up bond prices (which is the same thing as r falling).
    * When people find themselves holding less money than they want, they they try to sell bonds to raise money, which pushes down bond prices (which is the same as r rising).

The amount of money held by everyone actually never changes during this story -- rather, the change in r  makes them willing to hold the money they actually hold.  In the first case above, as r falls the advantage of holding wealth as bonds falls, and people stop wanting them as much, which means they're content to hold the money they actually hold.  In the second case above, as r rises the advantage of holding bonds rises, which means people stop wanting to hold more money.  Take some time to think about this -- the key to the argument is this very stark, very simple money/bonds portfolio choice faced by everyone in the economy.  (This is a good time to remember the stock/flow distinction: In the money market we are talking about stock quantities (money supply, money demand, bonds), and our equilibrium is a stock equilibrium.  In the goods market above we are talking about flow quantities (Ip, Y, S, G, T) and our equilibrium is a flow equilibrium.  So keep the two stories straight and strictly separate.)

Got all that?  Then here's the key: the reasoning in this model goes from Y, to transactions demand for money, to an attempt at portfolio adjustment, to a change in the interest rate.

    * A rise in output (Y) is also a rise income (remember Y means both).  A rise in income raises people's transactions demand for money.  Higher demand for money means people want to hold portfolios consisting of more money and less bonds at any point in time.  People attempt this readjustment by selling bonds.  Selling bonds lowers the bond price, which is the same thing as raising the interest rate.
    * A fall in Y lowers transactions demand for money.  People try to adjust by buying bonds with money -- changing their portfolios so they will hold more bonds, less money.  As they try to do this the bond price rises, which is the same thing as saying r falls.

You can put the pieces together and examine interest rate determination here: Macro Notes Section 3.6.

With those ideas, we can determine the r that will equilibrate the money market for any Y. Here is a series of graphs that derives the LM curve.

The best way to think about that LM line is as a border -- a boundary in Y,r space between points at which Md < Ms and r will tend to fall, and the points at which Md > Ms and r will tend to rise. Here is a four-quadrant derivation that emphasizes this.

It should be apparent from the graphical derivations that a change in the money supply will change the (Y,r) points at which the money market is in equilibrium. In graphical terms an increase in Ms shifts LM down, while a decrease shifts it up.

Additionally, note that the degree to which speculative demand for money responds to changes in r will affect the slope of the LM curve. If only a small change in r brings large changes in speculative demand, then LM will be almost horizontal. If a very large change in r is required to change speculative demand for money, LM will be close to vertical.

Note, before moving on, that in the money side of this model we are reasoning from Y to r.  Depending on Y, r changes because of the effects of a given level of Y on the money market.

QUIZ for part 4

5. Assembling the Model (IS and LM)

So far, we've drawn two different boundaries in Y,r space:

Note again, as you look at these pictures, that:

    * on the goods market, or IS, side of the model we go from r to Y.  Pick any value of r, and draw a horizontal line across the graph at that value of r. The line will cross the IS boundary at some point.  If the interest rate is at that level and output (Y) is to the left of that boundary, it will tend to rise -- output and employment will go up.  If Y is to the right of that boundary, it will tend to fall -- output and employment will go down.
    * on the money market, or LM, side of the model we go from Y to r.  Pick any value of Y, and draw a vertical line up the graph at that value of Y. The line will cross the LM boundary at some point.  If output is at that level and r is above that boundary, it will tend to fall.  If r is below that boundary, it will tend to rise.

Putting the two pictures together gives us this geography:

Try to think of this not just as a couple of lines crossing on a graph, but as a 2-dimensional space in which the national economy sort of skates around, with its total output and its interest rate changing.  Once you have that idea, add the notion that the IS and LM boundaries tell you about the forces acting on the national economy at any particular point in this space.  (For another way to visualize this, look at this picture at Prof. Andreas Thiemer's "IS-LM Model: A Dynamic Approach".)

Now we can take the model out for a spin.  Click here for animations of dynamic adjustment.

In intro macro, we noticed that the goods and money markets interacted with each other (Review: Macro Notes Section 4.5). The IS-LM model simply gives us a more formal way to examine these interactions.

These animations show the ways in which fiscal and monetary policy may have effects on output and the interest rate. They also emphasize the fact that adjustment toward a new equilibrium is not instantaneous.

In general, in the stories we start by assuming equilibrium in both markets -- in other words, our macroeconomy has settled down to the one (Y,r) combination that equilibrates both markets at once.  Then we change conditions in one or the other market.  What that means is that the (Y,r) geography shifts and our old (Y,r) point is no longer an equilibrium.  So we start moving, spiralling gently counterclockwise toward the new equilibrium point.

The stories told in the animations boil down to this:

Fiscal Policy Stories:

    1. G changes, raising or lowering AD (throwing goods market out of equilibrium)
    2. As firms respond, Y changes (and a multiplier process is set off, as AS (Y) adjusts to AD)
    3. BUT: as Y changes, Md(t) changes, throwing the money market out of equilibrium.
    4. The change in Md(t) changes r
    (Note: the degree to which speculative demand for money changes as r changes determines how much r changes as a result of this process.)
    5. the change in r affects Ip, which affects Y through the multiplier, modifying initial changes in Y.
    (Note: the sensitivity of Ip to r determines how great this change is.)

    

Monetary Policy Stories:

1. Ms changes, throwing money market out of equilibrium
2. As people either buy or sell bonds to reflect their portfolio preferences, the bond price rises or falls, with r moving the opposite way.
(Note: the degree to which speculative demand for money changes as r changes determines how much r changes as a result of this process.)
3. BUT: as r changes, Ip changes, throwing the goods market out of equilibrium.
(Note: the sensitivity of Ip to r determines how great this change is.)
4. Working through the multiplier, the changed Ip changes Y.
5. The change in Y will affect Md(t), modfiying initial effects on r.

If you can learn these stories as sequences of events, you have a basic grasp of the IS-LM model. Although the pictures are nice, it's more important to be able to follow a concrete story. The geometry is just a supplement, a learning aid. If you memorize the geometry and don't learn what it means, you're not learning economics.

Graphically, the notes in parentheses would affect the steepness or flatness of the IS and LM curves (noted in earlier sections).

QUIZ for part 5
6. Supplemental Notes for the Curious: History and Critiques

The origin of this model is a paper by John Hicks titled "Mr. Keynes and the Classics," which appeared in the journal Econometrica in 1937.  It was an effort to turn some of the insights in John Maynard Keynes' pathbreaking General Theory of Employment, Interest, and Money (1936) into a mathematical model. Keynes liked Hicks' article, but it’s hardly a full embodiment of Keynes' thinking.  It became popular in textbooks.  (See Kerry A Pearce. and Kevin D. Hoover, “After the Revolution: Paul Samuelson and the Textbook Keynesian Model” pages 183-216 in Allin Cottrell and Michael Lawlor, eds., New Perspectives on Keynes, Duke University Press, 1995.)



The model has some internal problems, particularly because of the way it tries to link a flow model (the IS side, where flows adjust) and a stock model (the LM side, where stocks adjust).  These two models really live in different kinds of time. Equilibration on the LM side is very rapid, while equilibration on the IS side may take months. The "r" on the LM side is a short-term rate; the key "r" for the IS side is going to be a longer-term rate. Hicks addressed these concerns 43 years later in his 1980 article "IS-LM: An explanation" (Journal of Post Keynesian Economics, 3:2, 139-54, reprinted in Hicks, ed., Money, Interest and Wages: Collected Essays on Economic Theory, vol. II, Oxford: Basil Blackwell, pp. 318-331).  He concluded that the problems are important enough that the model is of little use for forward-looking policy analysis.

A more formal presentation of the model, plus incisive discussion of subsequent debates over it, can be found here.    If you’re interested in Keynes’ thought, one of the best introductions is Hyman Minsky’s 1975 book John Maynard Keynes (New York: Columbia University Press), which clarifies the differences between Keynes and the versions of his work that you will encounter in most textbooks.  Robert Skidelsky has written an excellent three-volume biography of Keynes; if you want something shorter try Skidelsky’s 136-page Keynes (Oxford University Press (Past Masters), 1996).  If you’re interested in current heterodox economics, one place to start is the Post-Autistic Economics Network.
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