Chapter 5. Goods and Financial
Markets: The IS-LM model
I. MOTIVATING QUESTION
How are output and the interest rate determined simultaneously in the short run?
Output and the interest rate are determined by simultaneous equilibrium in the goods and money markets.
In the short run, we assume that production responds to demand without changes in price (i.e., price is
fixed), so output is determined by demand.
II. WHY THE ANSWER MATTERS
The determination of output is the fundamental issue in macroeconomics. The interest rate affects output
(through investment) and output affects the interest rate (through money demand), so it is necessary to
consider the simultaneous determination of output and the interest rate.
III. KEY TOOLS, CONCEPTS, AND ASSUMPTIONS
1. Tools and Concepts
i. The chapter introduces the IS-LM framework.
ii. The chapter introduces the concept of policy mixes to achieve macroeconomic goals.
iii. The chapter introduces the use of “+” and “-” below the argument of a function to indicate the
effect of an increase in the value of the argument on the value of the function.
2. Assumptions
i. This chapter maintains the fixed price assumption of previous chapters, but relaxes the assumptions
that investment is independent of the interest rate (assumed in Chapter 3) and that nominal income is
fixed (assumed in Chapter 4). Investment is also allowed to depend on output. The point of this chapter
is to show how goods and financial markets are related and thus how output and the interest rate are
simultaneously determined.
ii. The chapter continues to assume that inventory investment is zero and that the economy is closed.
IV. SUMMARY OF THE MATERIAL
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1. The Goods Market and the IS Relation
First, relax the assumption that investment is endogenous. In terms of the framework developed thus far,
investment should depend on two factors: sales and the interest rate. A firm facing an increase in sales
will need to purchase new plant, equipment, or both to increase production. Thus, investment increases
when sales increase. An increase in the interest rate will increase the cost of borrowing needed to
purchase new plant and equipment. Thus, investment decreases when the interest rate increases. This
discussion describes an investment function of the following form:
I=I(Y, i). (5.1)
+ –
Although the discussion suggests that investment should depend on sales, rather than income, the chapter
continues to assume that inventory investment is zero, so income equals sales.
With the revised investment function, the closed economy, goods market equilibrium condition becomes
Y=C(Y-T)+I(Y,i)+G. (5.2)
For a fixed interest rate, the Keynesian cross analysis of Chapter 3 holds with two caveats. First, demand
for goods and services (the RHS of equation (5.2)) is no longer assumed to be linear. Second, an
additional assumption is required to ensure that an equilibrium exists (i.e., that the ZZ curve intersects the
45-line). A sufficient assumption for this purpose is that the sum of the (marginal) propensity to
consume out of income and the (marginal) propensity to invest out of income is less than one.
Equation (5.2) is called the IS relation, because (as shown in Chapter 3) goods market equilibrium is
equivalent to the condition that investment equals saving. To trace out an IS curve, start with a Keynesian
cross with a given interest rate, then vary the interest rate. A decrease in the interest rate increases the
level of investment for any level of output, so the ZZ curve shifts up and output increases. Therefore, the
IS curve has a negative slope in Yi space (Figure 5-2).
2. Financial Markets and the LM Relation
Start with the money-market equilibrium condition from Chapter 4, rewrite nominal income as PY (where
P is the price level), and divide by P to derive the real money market equilibrium condition:
M/P=YL(i). (5.3)
Real money market equilibrium is characterized by the same graph developed in Chapter 4, but the real
money supply (M/P) is substituted for the nominal money supply (M). The chapter maintains the
short-run assumption of a fixed price and, abstracting from details of monetary policy, assumes that M is
under the control of the central bank.
Equation (5.3) is called the LM (Liquidity-Money) relation. Since the central bank chooses the money
supply, and therefore the interest rate, the LM curve is graphed as a horizontal line as shown in Figure 5-4.
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3. Putting the IS and the LM Relations Together
The equilibrium values of i and Y are those that satisfy simultaneously the goods market equilibrium
condition (equation (5.2)) and the money market equilibrium condition (equation (5.3)). Graphically,
these values are determined by the point of intersection of the IS and LM curves, as illustrated in Figure
5-5.
Changes in the equilibrium values of output and the interest rate (Y* and i*) can be brought about only as
the result of shifts in the IS curve, the LM curve, or both. An increase in the money supply, which shifts
the LM curve down, increases equilibrium output and reduces the equilibrium interest rate. An increase in
taxes (or a reduction in government spending), which shifts the IS curve to the left, reduces equilibrium
output and reduces the equilibrium interest rate. An increase in taxes has an ambiguous effect on
investment, since the output effect tends to reduce investment, but the interest rate effect tends to increase
it. More generally, although deficit reduction increases public (government) saving, it does not
necessarily increase investment, because private saving is endogenous.
Fiscal expansions (i.e. lower taxes or higher government spending) shift the IS curve to the right and
result in higher output. In contrast, fiscal contractions (i.e. higher taxes or lower government spending)
shift the IS curve to the left and result in lower output. See Figure 5-6.
Changes in monetary policy shift the horizontal LM curve up or down as the central bank increases or
decreases interest rates through changes in the money supply. A monetary expansion lowers the interest
rate and shifts the horizontal LM curve down resulting in higher output. See Figure 5-7. In contrast, a
monetary contraction increases interest rates and shifts the LM curve upward resulting in lower output
(Y).
4. Using a Policy Mix
The text considers the consequences of combinations of fiscal and monetary policy through two
examples: the recession of 2001 and the deficit reduction during President Clinton’s first term. A box in
the text argues that the proximate cause of the recession of 2001 was a drop in (nonresidential) investment
spending and that the policy response—a sharp cut in interest rates by the Fed and large tax cuts
spearheaded by the Bush administration—lessened the severity of the recession. Although the tax cuts
provided useful stimulus, they also played the major role in creating large budget deficits in the United
States. Many economists worry about these deficits, and argue that the tax cuts should not have been
made permanent. Long after the recession of 2001, the loss of tax revenue associated with the Bush tax
cuts continues to affect government finances.
During the recession of 2001, monetary and fiscal policy both became more expansionary. In the
President Clintons first term, by contrast, fiscal policy became more contractionary while monetary
policy became more expansionary. The Federal Reserve supported the Clinton deficit reduction policy (a
fiscal contraction) with a monetary expansion, and interest rates fell. As a result, there was a deficit
reduction without a slowdown in growth. In fact, there was a large economic expansion—an outcome
supported by the policy mix but also aided by other factors.
5. How Does the IS-LM Model Fit the Facts?
So far, the discussion has ignored dynamics. In fact, it takes some time for consumption, investment, and
output to adjust to an economic disturbance. How long is an empirical question. To discuss this question
and to provide evidence of the empirical relevance of the IS-LM model, the text describes the results
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presented in Christiano, Eichenbaum, and Evans, “The Effects of Monetary Policy Shocks: Evidence
From the Flow of Funds,” Review of Economics and Statistics, February 1996. The paper describes the
dynamic responses of several important macroeconomic variables to an increase in the federal funds rate,
i.e., a monetary contraction. An interest rate increase does lead to a decline in output, as the IS-LM model
would predict, but adjustment happens relatively slowly. It takes almost two years for monetary policy to
have its full effect on output. The price level remains more or less unchanged for about six quarters and
then declines. The behavior of the price level supports the assumption that the price level is fixed in the
short run.
V. PEDAGOGY
1. Points of Clarification
i. The Meaning of the IS and LM Curves. The derivation of the IS and LM curves will take time
for students to understand. It is important to emphasize that each point on the IS curve represents an
equilibrium in the goods market and each point on the LM curve represents an equilibrium in the money
market. Keep in mind that in some texts you will see the LM curve as downward sloping instead of
horizontal. If this is the case the value of i on the LM curve associated with any given level of output is
given by the intersection of (real) money supply and (real) money demand (given the level of output) in
the money market equilibrium diagram. Money demand refers to a portfolio decision, the amount of fixed
wealth that the nonbank public desires to hold in money as opposed to bonds. Money demand does not
refer to the demand for income or wealth.
ii. The Interest Rate and Shifts of the IS and LM Curves. Students may wonder why an increase
in the interest rate does not shift the IS curve, since the interest rate affects investment, or the LM curve,
since the interest rate affects money demand. It is worthwhile to emphasize that the effects of the interest
rate on the goods market and the money market are reflected in the slope of the IS curve and the level of
the LM curve. Output and the interest rate are endogenous variables. Only changes to variables
exogenous to the IS-LM model can shift the curves.
VI. EXTENSIONS
1. Behavioral Parameters, the Slopes of the IS and LM Curves, and Policy
Effectiveness
The text assumes a horizontal LM curve but many other presentations show a downward sloping LM
curve. It is worth noting that the slopes of the IS curve and the LM curve do have policy implications.
With respect to the slopes, the more sensitive money demand is to income relative to the interest rate, the
steeper the LM curve. Likewise, the more sensitive goods demand (C+I+G) is to income relative to the
interest rate (through investment), the steeper the IS curve.
On the effectiveness of policy, there are two options to bring out the basic points. The first option is to
choose a simple linear specification and work out the relationship between the output effect of policy and
behavioral parameters. The second option is to discuss the issue more heuristically. For example,
consider an increase in government spending, and proceed in three steps.
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i. For any given interest rate, the effect of fiscal policy on output will depend on the multiplier,
modified to include endogenous investment. The larger the multiplier, i.e., the greater the
sensitivity of consumption and investment to output, the larger the initial response of output.
ii. Since an increase in G will increase Y, it will also increase the quantity of money demanded
for any interest rate, and thus increase the interest rate, in order to maintain money market
equilibrium. The increase in the interest rate will be small to the extent that money demand is not
very sensitive to income, but is very sensitive to the interest rate.
If money demand is not very sensitive to income, then the excess demand for money created by
the increase in G will be small. If money demand is very sensitive to the interest rate, the
increase in the interest rate needed to restore equilibrium in the money market will be small.
iii. Finally, the increase in the interest rate will tend to reduce investment and thus offset some of
the initial increase in output. This effect will be small to the extent that investment is not very
sensitive to the interest rate.
In sum, fiscal policy will have a greater effect on output to the extent that the multiplier is large, money
demand is not very sensitive to income, money demand is very sensitive to the interest rate, and
investment is not very sensitive to the interest rate.
One could carry out the same exercise with respect to monetary policy. An increase in the money supply
affects output by reducing the interest rate and increasing investment. Thus, an increase in the money
supply will tend to have a large effect on output when it has a large effect on the interest rate, which will
be true when money demand is not very sensitive to the interest rate. The interest rate will have a large
effect on output when investment is very sensitive to the interest rate, which calls forth the initial response
of output, and, again, when the multiplier is large. The increase in output increases the quantity of money
demanded for any interest rate and tends to increase the interest rate, offsetting some of the initial effect
of the increase in the money supply. This effect will be small when the demand for money is not very
sensitive to income.
In sum, monetary policy will have a greater effect on output to the extent that money demand is not very
sensitive to the interest rate, investment is very sensitive to the interest rate, the multiplier is large, and
money demand is not very sensitive to income.
These exercises are relatively sophisticated, but they make clear the linkages between the goods market
and the money market through the interest rate.
2. Tax Cuts and the Recession of 2001
The debate over the tax cuts during the recession of 2001 was broader than whether the tax cuts should be
permanent. Many economists argued that a stimulus package would be most effective when aimed at
those with high propensities to consume. It seems reasonable to assume that low income taxpayers would
have higher propensities to consume than high income taxpayers. This implies that tax cuts would be
more effective when targeted toward low income taxpayers. The Bush tax cuts were not targeted toward
low income taxpayers. An exercise at the end of Chapter 3 examines this issue from the point of view of
the Keynesian cross model.
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