The IS–LM Model for a Closed Economy
The orthodox Keynesian model which has had such an important bearing on
the development of macroeconomics, right through to the present day, initially
stemmed from Hicks’s (1937) famous article entitled ‘Mr. Keynes and
the “Classics”: A Suggested Interpretation’. This Hicksian model was subsequently
elaborated upon by Modigliani (1944) and was popularized in the
USA by Hansen (1949, 1953). Indeed, over the next half-century the Hicksian
IS–LM model became the established model for macroeconomic theorizing
and it had a tremendous influence on the direction of macroeconomic policy
right up to the mid-1960s.
It is assumed that most readers will at least be familiar with the derivation
of the IS–LM model, so that in what follows initially we merely review the
main features of the model for a closed economy, in particular the way the
model integrates real and monetary factors in determining aggregate demand
The orthodox Keynesian school 103
and therefore the level of output and employment. Those readers who are
unfamiliar with the derivation of the model (or the extension of the model to
an open economy) should refer to any standard macroeconomics text, such as
Dornbusch et al. (2004). We begin our review with the goods market and the
IS curve.
The goods market and the IS curve
Equilibrium in the goods market occurs where the aggregate demand for and
aggregate supply of goods are equal. In the orthodox Keynesian model the
level of output and employment is assumed to be determined entirely by
aggregate demand; that is, supply constraints are ignored. In a closed economy
aggregate demand comprises the sum of consumption, government expenditure
and investment. In order to simplify the analysis, consumption expenditure
is held to depend positively on disposable income, government expenditure is
taken as being exogenously determined, while investment is treated as being
inversely related to the rate of interest, a variable determined within the
model by the interaction of the goods and money markets.
The IS curve traces out a locus of combinations of interest rates and
income associated with equilibrium in the goods market. The IS curve
derives its name from the equilibrium condition in the goods market where,
in a closed economy with no government sector, investment (I) equals
savings (S). Given the assumption that investment is inversely related to the
rate of interest, the IS curve is downward-sloping (see Figure 3.2). Ceteris
paribus, as the rate of interest falls, investment increases, resulting in a
higher level of income. The slope of the IS curve depends on the interest
elasticity of investment expenditure and the value of the multiplier (see
Chapter 2, section 2.8). The IS curve will be steeper (flatter) the less (more)
investment responds to a change in the rate of interest and the smaller
(greater) is the value of the multiplier. For example, ceteris paribus, the
less investment increases for a given fall in the rate of interest, the less
income will increase, generating a steeper IS curve. Similarly, the smaller
the value of the multiplier, the less income will increase following a given
increase in investment, and hence the steeper the IS curve will be. In the
limiting (extreme Keynesian) case where investment is perfectly interestinelastic,
the IS curve will be vertical.
Finally, it is important to remember that the IS curve is drawn for a given
level of government expenditure, taxation and expectations, so that expansionary
fiscal policy (that is, an increase in government expenditure and/or a
reduction in taxation, or a more optimistic business outlook) shifts the IS
curve outwards to the right, and vice versa. For example, an increase in
government expenditure will be associated with a higher level of income at
any given level of the rate of interest, the outward shift of the IS curve being
equal to the increase in government expenditure times the value of the multiplier.
We now turn to the money market and the LM curve.
The money market and the LM curve
Equilibrium in the money market occurs where the demand for and supply of
money are equal. The money supply is assumed to be exogenously determined
by the authorities. Within the model three main motives for holding
money are identified: the transactions, the precautionary and the speculative
motives. The demand for transactions and precautionary balances is assumed
to vary positively with income. The demand for speculative or idle balances
depends on the current level of the rate of interest relative to the normal rate
of interest. By assuming that different people have different expectations
about the future course of the rate of interest, it is possible to postulate that
the demand for speculative balances will vary inversely with the rate of
interest (see Figure 3.1). The higher the current level of the rate of interest
(relative to the level regarded as normal), the greater the number of individuals
who expect future reductions in the rate of interest (and therefore rising
bond prices) and the less speculative balances demanded, and vice versa. Of
particular importance is the theoretical possibility that, at low interest rates,
which would be expected to prevail in conditions of underemployment equilibrium,
the demand for money could become perfectly elastic with respect to
the rate of interest. This is illustrated by the horizontal section of the curve at
r* in Figure 3.1. At r* expectations converge as everyone expects that the only
future course of the rate of interest is upwards, so that the demand for money
becomes perfectly interest-elastic: the so-called ‘liquidity trap’. With regard
to the liquidity trap, it is interesting to note that Keynes put it forward only as
a theoretical possibility and even commented that he was not aware of it ever
having been operative in practice (see Keynes, 1936, p. 207). Nevertheless,
as we will discuss in section 3.4.2, it became especially important to the
analysis of underemployment equilibrium in the orthodox Keynesian model.
The LM curve traces out a locus of combinations of interest rates and income
associated with equilibrium in the money market. The LM curve derives its
name from the equilibrium condition in the money market where the demand
for money, or what Keynes called liquidity preference (L), equals the supply of
money (M). Given the assumption that the demand for money is positively/
negatively related to income/interest rate, the LM curve is upward-sloping (see
Figure 3.2). Ceteris paribus, as income rises the transactions and precautionary
demand for money increase, which, given the supply of money, necessitates a
higher rate of interest to reduce the speculative demand for money and maintain
equilibrium in the money market. The slope of the LM curve depends on
the income elasticity and the interest elasticity of the demand for money. The
LM curve will be steeper (flatter) the higher (smaller) the income elasticity and
the smaller (greater) the interest elasticity of the demand for money. For example,
ceteris paribus, the more the demand for money increases following a
given increase in income, the larger will be the rise in the rate of interest
required to maintain equilibrium in the money market, generating a steeper LM
curve. In the limiting cases of (i) the so-called ‘classical range’ (where the
demand for money is perfectly interest-inelastic) and (ii) the liquidity trap
(where the demand for money is perfectly elastic with respect to the rate of
interest) the LM curve will be vertical and horizontal respectively.
Finally, it is important to remember that the LM curve is drawn for a given
money supply, price level and expectations, so that expansionary monetary
policy (that is, an increase in the supply of money) shifts the LM curve
downwards to the right, and vice versa. Following an increase in the money
supply, and a given income elasticity of the demand for money, any given
level of income must be associated with a lower interest rate to maintain
equilibrium in the money market. The extent to which the LM curve shifts
depends on the interest elasticity of the demand for money. A given increase
in the supply of money will cause a small/large shift in the LM curve where
the demand for money is relatively interest-elastic/inelastic as equilibrium in
the money market will be restored by a small/large fall in the interest rate.
Readers should verify this for themselves.
The complete model and the role of fiscal and monetary policy
Equilibrium in both the goods and money markets is simultaneously attained
where the IS and LM curves intersect, that is, at reYe in Figure 3.2. Two points
are worth emphasizing. First, the intersection of the two curves in Figure 3.2
represents the only value of the rate of interest and income which is consistent
with equilibrium in both markets. Second, if the level of income is below
that of full employment, then both fiscal and monetary policy have a potentially
important role to play in stabilizing the economy. We now briefly
review what determines the relative effectiveness of fiscal and monetary
policy in influencing aggregate demand and therefore the level of output and
employment.
In Figure 3.3, the economy is initially in equilibrium at r0Y0 (the intersection
of IS0 and LM) at less than full employment. Expansionary fiscal policy
(for example, an increase in government expenditure) shifts the IS curve
outwards to the right, from IS0 to IS1, and results in an increase in both the
equilibrium rate of interest (from r0 to r1) and the equilibrium level of income
(from Y0 to Y1). As spending and income increase, the transactions and precautionary
demand for money increase, which, with a fixed money supply,
results in an increase in the rate of interest. The rise in the rate of interest in
turn leads to a reduction in private sector investment spending, the extent of
which depends on the interest elasticity of investment. Readers should verify
for themselves that fiscal policy will be more effective in influencing aggregate
demand and therefore the level of output and employment (i) the more
interest-elastic is the demand for money; that is, the flatter is the LM curve,
and (ii) the less interest-elastic is investment; that is, the steeper is the IS
curve. In the limiting cases of (i) a vertical LM curve (classical range) fiscal
expansion will have no effect on income, as the rise in the rate of interest will
reduce private investment by an amount identical to the increase in government
expenditure; that is, complete (100 per cent) crowding out or the so-called
‘Treasury View’; and (ii) a horizontal LM curve (liquidity trap) fiscal expansion
will result in the full multiplier effect of the simple Keynesian 45° or
cross model.
In Figure 3.4, the economy is again initially in equilibrium at r0Y0 (the
intersection of LM0 and IS) at less than full employment. Expansionary
monetary policy shifts the LM curve downwards to the right, from LM0 to
LM1, and results in a fall in the equilibrium rate of interest (from r0 to r1) and
an increase in the equilibrium level of income (from Y0 to Y1). Within the
orthodox Keynesian transmission mechanism the strength of monetary policy
depends on (i) the degree to which the rate of interest falls following an
increase in the money supply; (ii) the degree to which investment responds to
a fall in the rate of interest; and (iii) the size of the multiplier. Readers should
verify for themselves that monetary policy will be more effective in influenc
ing aggregate demand and therefore the level of output and employment (i)
the more interest-inelastic is the demand for money; that is, the steeper is the
LM curve, and (ii) the more interest-elastic is investment; that is, the flatter is
the IS curve. In the limiting (extreme Keynesian) cases of either (i) a horizontal
LM curve (liquidity trap) or (ii) a vertical IS curve (that is, where investment
is completely interest-inelastic) the transmission mechanism breaks down
and monetary policy will have no effect on the level of income.
From the above discussion it should be evident that, while both fiscal and
monetary policy can, in normal circumstances, be used to influence the level
of output and employment, the relative effectiveness of these two policy
instruments depends on the structural parameters of the model, that is, the
relative slopes of the IS and LM curves. Within the orthodox Keynesian
approach, the demand for money has traditionally been viewed as being
highly responsive to changes in the rate of interest (generating a relatively flat
LM curve), while investment has been taken as being fairly unresponsive to
changes in the rate of interest (generating a relatively steep IS curve). Indeed,
there was early empirical support for orthodox Keynesianism associated with
the elasticities of the IS and LM curves, with Klein referring to its ‘solid
empirical basis’ (see Klein, 1968, pp. 65–6, pp. 71–2) – a basis, we hasten to
add, which became increasingly questionable in the early 1960s. In these
circumstances disturbances from the real side of the economy (that is,
stochastic shifts in the IS curve) tend to dominate changes in income. Furthermore,
fiscal policy is generally preferred as it is relatively powerful,
while monetary policy is relatively weak. At this point the reader should note
that by the end of the 1950s the belief in the efficacy of fiscal policy relative
to monetary policy was much stronger among British as compared to American
Keynesians.
This analysis can also be summarized in algebraic terms. In what follows it
is assumed that the price level is fixed when the economy is at less than full
employment. Aggregate real expenditure (E) is equal to an autonomous component
(A), a component dependent on real income (cY) and an interest-sensitive
component (ar).
E = A + cY − ar (3.1)
Equilibrium in the goods market occurs where the aggregate demand for and
aggregate supply of goods are equal.
E = Y (3.2)
Turning to the money market, the demand for real money balances (M/P) has
a component dependent on real income (mY) and an interest-sensitive component
(br).
M
P
= mY − br (3.3)
The supply of nominal money balances is assumed to be exogenously determined
(Ms ). Equilibrium in the money market occurs where the demand for
and supply of money are equal.
Within this framework, orthodox Keynesians can be characterized as low a
and high b people. Reference to equation (3.5) reveals that, where the ratio
a/b is small, (i) disturbances from the real side of the economy tend to
dominate changes in income, and (ii) fiscal policy is relatively powerful with
the autonomous expenditure multiplier tending to 1/1 – c, while monetary
policy is relatively weak with the money multiplier tending to zero. These
central distinguishing beliefs of orthodox Keynesians were noted earlier, in
section 3.2.
The orthodox Keynesian faith in the effectiveness of fiscal policy has been
challenged by, among others, monetarists who typically argue that in the long
run ‘pure’ fiscal expansion (that is, expansion without any accommodating
changes in the money supply) will result in the crowding out or replacement
of components of private expenditure with relatively minor effects on aggregate
demand, the level of income and employment. A number of reasons as to
why crowding out can occur in the IS–LM framework have been put forward
in the literature, which do not rely on the demand for money being perfectly
interest-inelastic (a vertically sloped LM curve), including expectations and
wealth effects (see Carlson and Spencer, 1975). In what follows we outline
the Keynesian response which reasserted the importance of fiscal policy (see
Blinder and Solow, 1973) focusing on the wealth effects of a bond-financed
increase in government expenditure. This analysis involves an extended version
of the Keynesian IS–LM model incorporating the government budget
constraint.
The top panel of Figure 3.5 depicts the conventional IS–LM model and the
lower panel the government budget position determined by the relationship
between government expenditure (G), which is assumed to be independent of
income, and tax receipts (T), which are endogenous to the level of income. At
Y0 (the intersection of IS0 and LM) both the goods and money markets are in
equilibrium and the government budget is balanced (G0 = T); that is, a stable
equilibrium position prevails. Suppose the authorities now seek to raise the
level of income and employment by increasing their expenditure. An increase
in government expenditure shifts the IS curve outwards to the right, from IS0
to IS1, and the government expenditure function downwards, from G0 to G1.
At Y1 (the intersection of IS1 and LM) there is a budget deficit equal to AB. As
long as the deficit persists, the authorities will have to issue more bonds,
which will lead to an increase in private sector wealth (owing to increased
bond holdings) and an increase in private consumption expenditure and the
demand for money. If the wealth effect on consumption (which shifts the IS
curve further outwards to the right, as indicated by the arrows) outweighs that
on the demand for money (which shifts the LM curve upwards to the left),
then in the long run bond-financed fiscal expansion will result in income
increasing to Y2, where the deficit will be removed; that is, crowding out will
be absent. Furthermore, if increased interest payments arising from bond
finance are taken into account (shifting the government expenditure function
downwards beyond G1), income will have to rise above Y2 in order to balance
the government budget. It is evident therefore that incorporating wealth
effects and the government budget constraint into the IS–LM model makes a
bond-financed increase in government expenditure potentially very effective
in raising the level of income and employment.
One particular objection to the predictions of this analysis concerning the
efficacy of fiscal policy worth commenting on is that which derives from
what has come to be known as the Ricardian debt equivalence theorem (see,
for example, Buchanan, 1976; Dimand, 2002a). In short, this theorem states
that the burden of government expenditure on the private sector is equivalent
whether it is financed by an increase in taxation or by bond sales. The sale of
government bonds places a burden on the private sector involving a future tax
liability in order to meet interest payments on and, where the bonds are not
perpetuities, redemption of the bonds. Assuming the private sector takes this
future tax liability fully into account, government bonds will be not regarded
as net wealth. Future tax liabilities will be discounted and their present value
will be perceived to exactly offset the value of the bonds sold. Barro’s (1974)
influential paper presents an elegant exposition of the controversial view that
government bonds should not be regarded as net wealth. In these circumstances
it would make no difference whether the government sold bonds or
raised taxes to finance expenditure, as selling bonds will not affect the private
sector’s wealth. The private sector would merely react to a bond-financed
increase in government expenditure by saving more in the present period in
order to meet future tax liabilities. In other words the effect of an increase in
government expenditure will be the same whether it is financed by increased
taxation or bond sales, in line with the so-called ‘balanced-budget’ multiplier
(see Shaw, 2002). A bond-financed increase in government expenditure will
only be more effective than a tax-financed increase in expenditure if government
bonds are regarded as net wealth.
Several arguments have been raised against the Ricardian debt equivalence
theorem and in what follows we briefly mention two of the main criticisms of
it. The reader is referred to Tobin (1980a) and Feldstein (1982) for accessible
and critical discussions of the Ricardian doctrine and its implications, and to
Barro (1989b) for a spirited defence against the main theoretical objections
that have been raised to the approach. First, if the future tax liability arising
out of bond-financed fiscal expansion falls on a future generation, then it can
be argued that the present generation will be wealthier. Barro has argued,
however, that the existence of bequests implies that the present generation
will raise their saving so as to increase their bequests to their children in
order to pay for the future tax liability. Barro’s argument that the existence of
bequests implies concern by parents about the tax burden their children will
face has itself been subjected to a number of criticisms. For example, it is
open to debate as to whether or not all parents will be so far-sighted, or
concerned enough, to take into account the expected tax liability of their
children. Second, given imperfect capital markets, government bonds may be
regarded as net wealth. The rate of interest the government pays on bonds
establishes the magnitude of the future tax liability. If, as a result of the
government having more favourable access to capital markets than individuals,
the rate of interest is less than the discount rate appropriate to the private
sector when estimating the present value of the future tax liability, government
bonds will be regarded as net wealth. In this situation a bond-financed
increase in government expenditure will increase private sector wealth and
consumption, and be more expansionary that a tax-financed increase in government
expenditure.
Before moving on and making use of the IS–LM framework to discuss the
Keynes v. Classics debate on the issue of ‘underemployment equilibrium’,
we should note that over the years the IS–LM model has stirred up a considerable
amount of controversy. Reflecting on the theoretical developments of
the early post-war period, Modigliani (1986) has identified the ‘Keynesian
system’ as resting on four building-blocks: the consumption function; the
investment function; the demand for and supply of money; and the mechanisms
for determining the movement of prices and wages. Following Hicks’s
(1937) effort to model the first three of Modigliani’s ‘building blocks’, other
major contributions to our understanding were made in the 1940s and 1950s
by Keynesian economists, including those by Modigliani (1944), Modigliani
and Brumberg (1954), Patinkin (1956), Phillips (1958) and Tobin (1958). By
the early 1960s, following the publication of Phillips’s (1958) influential
article, the mainstream macroeconomic model was one which could be described
as a Hicks (1937)–Hansen (1949) IS–LM model, augmented by a
Phillips curve relationship. The MPS–FMP macroeconometric model (based
on an extended IS–LM model) constructed by Modigliani and his associates
in the 1960s is probably the best practical example of the consensus position
during this era (Beaud and Dostaler, 1997; Blaug, 1997).
While a majority of economists (see, for example, Patinkin, 1990a; and the
Tobin interview at the end of this chapter) accepted the Hicksian inspired IS–
LM model as an accurate representation of the essence of Keynes’s thinking
in the General Theory, a vocal minority of ‘Keynesians’ view the IS–LM
model as a distortion or ‘bastardization’ of Keynes’s ideas (see Leijonhufvud,
1968; Robinson, 1975; Davidson, 1994). Interestingly, Dimand (2004) has
recently shown, using evidence from Keynes’s lecture notes compiled by
Rymes (1989) that Keynes himself used a similar IS–LM type of general
equilibrium system of equations to express his new ideas in his lectures
during Michaelmas Term of 1933 as well as a 1934 draft of the General
Theory. Monetarists such as Friedman, Brunner and Meltzer also ‘dislike’ the
IS–LM framework. Bordo and Schwartz (2003) attribute this negative view
to the model’s narrow definition of investment and its narrow view of monetary
influences. Nevertheless, even if the IS–LM model no longer forms the
foundation of graduate macro courses (now dominated by dynamic general
equilibrium theorizing), as it did until the mid-1970s, the model still forms a
major input into most mainstream intermediate macroeconomics textbooks
such as Blanchard (2003), Dornbusch et al. (2004), Gordon (2000a) and
Mankiw (2003). Readers interested in recent controversies and discussions
surrounding the origin, development and persistence of the IS–LM model
should consult King (1993), Young (1987), Young and Zilberfarb (2000),
Young and Darity (2004), Barens and Caspari (1999), De Vroey (2000),
Backhouse (2004), Colander (2004), Dimand (2004), and Snowdon (2004a).
We now turn to consider the Keynesian belief that the economy can take a
long time to return to full employment after being subjected to some disturbance.
This involves a discussion of the debate on underemployment
equilibrium and in what follows we examine the circumstances under which
the IS–LM model will fail to self-equilibrate at full employment.
The orthodox Keynesian model which has had such an important bearing on
the development of macroeconomics, right through to the present day, initially
stemmed from Hicks’s (1937) famous article entitled ‘Mr. Keynes and
the “Classics”: A Suggested Interpretation’. This Hicksian model was subsequently
elaborated upon by Modigliani (1944) and was popularized in the
USA by Hansen (1949, 1953). Indeed, over the next half-century the Hicksian
IS–LM model became the established model for macroeconomic theorizing
and it had a tremendous influence on the direction of macroeconomic policy
right up to the mid-1960s.
It is assumed that most readers will at least be familiar with the derivation
of the IS–LM model, so that in what follows initially we merely review the
main features of the model for a closed economy, in particular the way the
model integrates real and monetary factors in determining aggregate demand
The orthodox Keynesian school 103
and therefore the level of output and employment. Those readers who are
unfamiliar with the derivation of the model (or the extension of the model to
an open economy) should refer to any standard macroeconomics text, such as
Dornbusch et al. (2004). We begin our review with the goods market and the
IS curve.
The goods market and the IS curve
Equilibrium in the goods market occurs where the aggregate demand for and
aggregate supply of goods are equal. In the orthodox Keynesian model the
level of output and employment is assumed to be determined entirely by
aggregate demand; that is, supply constraints are ignored. In a closed economy
aggregate demand comprises the sum of consumption, government expenditure
and investment. In order to simplify the analysis, consumption expenditure
is held to depend positively on disposable income, government expenditure is
taken as being exogenously determined, while investment is treated as being
inversely related to the rate of interest, a variable determined within the
model by the interaction of the goods and money markets.
The IS curve traces out a locus of combinations of interest rates and
income associated with equilibrium in the goods market. The IS curve
derives its name from the equilibrium condition in the goods market where,
in a closed economy with no government sector, investment (I) equals
savings (S). Given the assumption that investment is inversely related to the
rate of interest, the IS curve is downward-sloping (see Figure 3.2). Ceteris
paribus, as the rate of interest falls, investment increases, resulting in a
higher level of income. The slope of the IS curve depends on the interest
elasticity of investment expenditure and the value of the multiplier (see
Chapter 2, section 2.8). The IS curve will be steeper (flatter) the less (more)
investment responds to a change in the rate of interest and the smaller
(greater) is the value of the multiplier. For example, ceteris paribus, the
less investment increases for a given fall in the rate of interest, the less
income will increase, generating a steeper IS curve. Similarly, the smaller
the value of the multiplier, the less income will increase following a given
increase in investment, and hence the steeper the IS curve will be. In the
limiting (extreme Keynesian) case where investment is perfectly interestinelastic,
the IS curve will be vertical.
Finally, it is important to remember that the IS curve is drawn for a given
level of government expenditure, taxation and expectations, so that expansionary
fiscal policy (that is, an increase in government expenditure and/or a
reduction in taxation, or a more optimistic business outlook) shifts the IS
curve outwards to the right, and vice versa. For example, an increase in
government expenditure will be associated with a higher level of income at
any given level of the rate of interest, the outward shift of the IS curve being
equal to the increase in government expenditure times the value of the multiplier.
We now turn to the money market and the LM curve.
The money market and the LM curve
Equilibrium in the money market occurs where the demand for and supply of
money are equal. The money supply is assumed to be exogenously determined
by the authorities. Within the model three main motives for holding
money are identified: the transactions, the precautionary and the speculative
motives. The demand for transactions and precautionary balances is assumed
to vary positively with income. The demand for speculative or idle balances
depends on the current level of the rate of interest relative to the normal rate
of interest. By assuming that different people have different expectations
about the future course of the rate of interest, it is possible to postulate that
the demand for speculative balances will vary inversely with the rate of
interest (see Figure 3.1). The higher the current level of the rate of interest
(relative to the level regarded as normal), the greater the number of individuals
who expect future reductions in the rate of interest (and therefore rising
bond prices) and the less speculative balances demanded, and vice versa. Of
particular importance is the theoretical possibility that, at low interest rates,
which would be expected to prevail in conditions of underemployment equilibrium,
the demand for money could become perfectly elastic with respect to
the rate of interest. This is illustrated by the horizontal section of the curve at
r* in Figure 3.1. At r* expectations converge as everyone expects that the only
future course of the rate of interest is upwards, so that the demand for money
becomes perfectly interest-elastic: the so-called ‘liquidity trap’. With regard
to the liquidity trap, it is interesting to note that Keynes put it forward only as
a theoretical possibility and even commented that he was not aware of it ever
having been operative in practice (see Keynes, 1936, p. 207). Nevertheless,
as we will discuss in section 3.4.2, it became especially important to the
analysis of underemployment equilibrium in the orthodox Keynesian model.
The LM curve traces out a locus of combinations of interest rates and income
associated with equilibrium in the money market. The LM curve derives its
name from the equilibrium condition in the money market where the demand
for money, or what Keynes called liquidity preference (L), equals the supply of
money (M). Given the assumption that the demand for money is positively/
negatively related to income/interest rate, the LM curve is upward-sloping (see
Figure 3.2). Ceteris paribus, as income rises the transactions and precautionary
demand for money increase, which, given the supply of money, necessitates a
higher rate of interest to reduce the speculative demand for money and maintain
equilibrium in the money market. The slope of the LM curve depends on
the income elasticity and the interest elasticity of the demand for money. The
LM curve will be steeper (flatter) the higher (smaller) the income elasticity and
the smaller (greater) the interest elasticity of the demand for money. For example,
ceteris paribus, the more the demand for money increases following a
given increase in income, the larger will be the rise in the rate of interest
required to maintain equilibrium in the money market, generating a steeper LM
curve. In the limiting cases of (i) the so-called ‘classical range’ (where the
demand for money is perfectly interest-inelastic) and (ii) the liquidity trap
(where the demand for money is perfectly elastic with respect to the rate of
interest) the LM curve will be vertical and horizontal respectively.
Finally, it is important to remember that the LM curve is drawn for a given
money supply, price level and expectations, so that expansionary monetary
policy (that is, an increase in the supply of money) shifts the LM curve
downwards to the right, and vice versa. Following an increase in the money
supply, and a given income elasticity of the demand for money, any given
level of income must be associated with a lower interest rate to maintain
equilibrium in the money market. The extent to which the LM curve shifts
depends on the interest elasticity of the demand for money. A given increase
in the supply of money will cause a small/large shift in the LM curve where
the demand for money is relatively interest-elastic/inelastic as equilibrium in
the money market will be restored by a small/large fall in the interest rate.
Readers should verify this for themselves.
The complete model and the role of fiscal and monetary policy
Equilibrium in both the goods and money markets is simultaneously attained
where the IS and LM curves intersect, that is, at reYe in Figure 3.2. Two points
are worth emphasizing. First, the intersection of the two curves in Figure 3.2
represents the only value of the rate of interest and income which is consistent
with equilibrium in both markets. Second, if the level of income is below
that of full employment, then both fiscal and monetary policy have a potentially
important role to play in stabilizing the economy. We now briefly
review what determines the relative effectiveness of fiscal and monetary
policy in influencing aggregate demand and therefore the level of output and
employment.
In Figure 3.3, the economy is initially in equilibrium at r0Y0 (the intersection
of IS0 and LM) at less than full employment. Expansionary fiscal policy
(for example, an increase in government expenditure) shifts the IS curve
outwards to the right, from IS0 to IS1, and results in an increase in both the
equilibrium rate of interest (from r0 to r1) and the equilibrium level of income
(from Y0 to Y1). As spending and income increase, the transactions and precautionary
demand for money increase, which, with a fixed money supply,
results in an increase in the rate of interest. The rise in the rate of interest in
turn leads to a reduction in private sector investment spending, the extent of
which depends on the interest elasticity of investment. Readers should verify
for themselves that fiscal policy will be more effective in influencing aggregate
demand and therefore the level of output and employment (i) the more
interest-elastic is the demand for money; that is, the flatter is the LM curve,
and (ii) the less interest-elastic is investment; that is, the steeper is the IS
curve. In the limiting cases of (i) a vertical LM curve (classical range) fiscal
expansion will have no effect on income, as the rise in the rate of interest will
reduce private investment by an amount identical to the increase in government
expenditure; that is, complete (100 per cent) crowding out or the so-called
‘Treasury View’; and (ii) a horizontal LM curve (liquidity trap) fiscal expansion
will result in the full multiplier effect of the simple Keynesian 45° or
cross model.
In Figure 3.4, the economy is again initially in equilibrium at r0Y0 (the
intersection of LM0 and IS) at less than full employment. Expansionary
monetary policy shifts the LM curve downwards to the right, from LM0 to
LM1, and results in a fall in the equilibrium rate of interest (from r0 to r1) and
an increase in the equilibrium level of income (from Y0 to Y1). Within the
orthodox Keynesian transmission mechanism the strength of monetary policy
depends on (i) the degree to which the rate of interest falls following an
increase in the money supply; (ii) the degree to which investment responds to
a fall in the rate of interest; and (iii) the size of the multiplier. Readers should
verify for themselves that monetary policy will be more effective in influenc
ing aggregate demand and therefore the level of output and employment (i)
the more interest-inelastic is the demand for money; that is, the steeper is the
LM curve, and (ii) the more interest-elastic is investment; that is, the flatter is
the IS curve. In the limiting (extreme Keynesian) cases of either (i) a horizontal
LM curve (liquidity trap) or (ii) a vertical IS curve (that is, where investment
is completely interest-inelastic) the transmission mechanism breaks down
and monetary policy will have no effect on the level of income.
From the above discussion it should be evident that, while both fiscal and
monetary policy can, in normal circumstances, be used to influence the level
of output and employment, the relative effectiveness of these two policy
instruments depends on the structural parameters of the model, that is, the
relative slopes of the IS and LM curves. Within the orthodox Keynesian
approach, the demand for money has traditionally been viewed as being
highly responsive to changes in the rate of interest (generating a relatively flat
LM curve), while investment has been taken as being fairly unresponsive to
changes in the rate of interest (generating a relatively steep IS curve). Indeed,
there was early empirical support for orthodox Keynesianism associated with
the elasticities of the IS and LM curves, with Klein referring to its ‘solid
empirical basis’ (see Klein, 1968, pp. 65–6, pp. 71–2) – a basis, we hasten to
add, which became increasingly questionable in the early 1960s. In these
circumstances disturbances from the real side of the economy (that is,
stochastic shifts in the IS curve) tend to dominate changes in income. Furthermore,
fiscal policy is generally preferred as it is relatively powerful,
while monetary policy is relatively weak. At this point the reader should note
that by the end of the 1950s the belief in the efficacy of fiscal policy relative
to monetary policy was much stronger among British as compared to American
Keynesians.
This analysis can also be summarized in algebraic terms. In what follows it
is assumed that the price level is fixed when the economy is at less than full
employment. Aggregate real expenditure (E) is equal to an autonomous component
(A), a component dependent on real income (cY) and an interest-sensitive
component (ar).
E = A + cY − ar (3.1)
Equilibrium in the goods market occurs where the aggregate demand for and
aggregate supply of goods are equal.
E = Y (3.2)
Turning to the money market, the demand for real money balances (M/P) has
a component dependent on real income (mY) and an interest-sensitive component
(br).
M
P
= mY − br (3.3)
The supply of nominal money balances is assumed to be exogenously determined
(Ms ). Equilibrium in the money market occurs where the demand for
and supply of money are equal.
Within this framework, orthodox Keynesians can be characterized as low a
and high b people. Reference to equation (3.5) reveals that, where the ratio
a/b is small, (i) disturbances from the real side of the economy tend to
dominate changes in income, and (ii) fiscal policy is relatively powerful with
the autonomous expenditure multiplier tending to 1/1 – c, while monetary
policy is relatively weak with the money multiplier tending to zero. These
central distinguishing beliefs of orthodox Keynesians were noted earlier, in
section 3.2.
The orthodox Keynesian faith in the effectiveness of fiscal policy has been
challenged by, among others, monetarists who typically argue that in the long
run ‘pure’ fiscal expansion (that is, expansion without any accommodating
changes in the money supply) will result in the crowding out or replacement
of components of private expenditure with relatively minor effects on aggregate
demand, the level of income and employment. A number of reasons as to
why crowding out can occur in the IS–LM framework have been put forward
in the literature, which do not rely on the demand for money being perfectly
interest-inelastic (a vertically sloped LM curve), including expectations and
wealth effects (see Carlson and Spencer, 1975). In what follows we outline
the Keynesian response which reasserted the importance of fiscal policy (see
Blinder and Solow, 1973) focusing on the wealth effects of a bond-financed
increase in government expenditure. This analysis involves an extended version
of the Keynesian IS–LM model incorporating the government budget
constraint.
The top panel of Figure 3.5 depicts the conventional IS–LM model and the
lower panel the government budget position determined by the relationship
between government expenditure (G), which is assumed to be independent of
income, and tax receipts (T), which are endogenous to the level of income. At
Y0 (the intersection of IS0 and LM) both the goods and money markets are in
equilibrium and the government budget is balanced (G0 = T); that is, a stable
equilibrium position prevails. Suppose the authorities now seek to raise the
level of income and employment by increasing their expenditure. An increase
in government expenditure shifts the IS curve outwards to the right, from IS0
to IS1, and the government expenditure function downwards, from G0 to G1.
At Y1 (the intersection of IS1 and LM) there is a budget deficit equal to AB. As
long as the deficit persists, the authorities will have to issue more bonds,
which will lead to an increase in private sector wealth (owing to increased
bond holdings) and an increase in private consumption expenditure and the
demand for money. If the wealth effect on consumption (which shifts the IS
curve further outwards to the right, as indicated by the arrows) outweighs that
on the demand for money (which shifts the LM curve upwards to the left),
then in the long run bond-financed fiscal expansion will result in income
increasing to Y2, where the deficit will be removed; that is, crowding out will
be absent. Furthermore, if increased interest payments arising from bond
finance are taken into account (shifting the government expenditure function
downwards beyond G1), income will have to rise above Y2 in order to balance
the government budget. It is evident therefore that incorporating wealth
effects and the government budget constraint into the IS–LM model makes a
bond-financed increase in government expenditure potentially very effective
in raising the level of income and employment.
One particular objection to the predictions of this analysis concerning the
efficacy of fiscal policy worth commenting on is that which derives from
what has come to be known as the Ricardian debt equivalence theorem (see,
for example, Buchanan, 1976; Dimand, 2002a). In short, this theorem states
that the burden of government expenditure on the private sector is equivalent
whether it is financed by an increase in taxation or by bond sales. The sale of
government bonds places a burden on the private sector involving a future tax
liability in order to meet interest payments on and, where the bonds are not
perpetuities, redemption of the bonds. Assuming the private sector takes this
future tax liability fully into account, government bonds will be not regarded
as net wealth. Future tax liabilities will be discounted and their present value
will be perceived to exactly offset the value of the bonds sold. Barro’s (1974)
influential paper presents an elegant exposition of the controversial view that
government bonds should not be regarded as net wealth. In these circumstances
it would make no difference whether the government sold bonds or
raised taxes to finance expenditure, as selling bonds will not affect the private
sector’s wealth. The private sector would merely react to a bond-financed
increase in government expenditure by saving more in the present period in
order to meet future tax liabilities. In other words the effect of an increase in
government expenditure will be the same whether it is financed by increased
taxation or bond sales, in line with the so-called ‘balanced-budget’ multiplier
(see Shaw, 2002). A bond-financed increase in government expenditure will
only be more effective than a tax-financed increase in expenditure if government
bonds are regarded as net wealth.
Several arguments have been raised against the Ricardian debt equivalence
theorem and in what follows we briefly mention two of the main criticisms of
it. The reader is referred to Tobin (1980a) and Feldstein (1982) for accessible
and critical discussions of the Ricardian doctrine and its implications, and to
Barro (1989b) for a spirited defence against the main theoretical objections
that have been raised to the approach. First, if the future tax liability arising
out of bond-financed fiscal expansion falls on a future generation, then it can
be argued that the present generation will be wealthier. Barro has argued,
however, that the existence of bequests implies that the present generation
will raise their saving so as to increase their bequests to their children in
order to pay for the future tax liability. Barro’s argument that the existence of
bequests implies concern by parents about the tax burden their children will
face has itself been subjected to a number of criticisms. For example, it is
open to debate as to whether or not all parents will be so far-sighted, or
concerned enough, to take into account the expected tax liability of their
children. Second, given imperfect capital markets, government bonds may be
regarded as net wealth. The rate of interest the government pays on bonds
establishes the magnitude of the future tax liability. If, as a result of the
government having more favourable access to capital markets than individuals,
the rate of interest is less than the discount rate appropriate to the private
sector when estimating the present value of the future tax liability, government
bonds will be regarded as net wealth. In this situation a bond-financed
increase in government expenditure will increase private sector wealth and
consumption, and be more expansionary that a tax-financed increase in government
expenditure.
Before moving on and making use of the IS–LM framework to discuss the
Keynes v. Classics debate on the issue of ‘underemployment equilibrium’,
we should note that over the years the IS–LM model has stirred up a considerable
amount of controversy. Reflecting on the theoretical developments of
the early post-war period, Modigliani (1986) has identified the ‘Keynesian
system’ as resting on four building-blocks: the consumption function; the
investment function; the demand for and supply of money; and the mechanisms
for determining the movement of prices and wages. Following Hicks’s
(1937) effort to model the first three of Modigliani’s ‘building blocks’, other
major contributions to our understanding were made in the 1940s and 1950s
by Keynesian economists, including those by Modigliani (1944), Modigliani
and Brumberg (1954), Patinkin (1956), Phillips (1958) and Tobin (1958). By
the early 1960s, following the publication of Phillips’s (1958) influential
article, the mainstream macroeconomic model was one which could be described
as a Hicks (1937)–Hansen (1949) IS–LM model, augmented by a
Phillips curve relationship. The MPS–FMP macroeconometric model (based
on an extended IS–LM model) constructed by Modigliani and his associates
in the 1960s is probably the best practical example of the consensus position
during this era (Beaud and Dostaler, 1997; Blaug, 1997).
While a majority of economists (see, for example, Patinkin, 1990a; and the
Tobin interview at the end of this chapter) accepted the Hicksian inspired IS–
LM model as an accurate representation of the essence of Keynes’s thinking
in the General Theory, a vocal minority of ‘Keynesians’ view the IS–LM
model as a distortion or ‘bastardization’ of Keynes’s ideas (see Leijonhufvud,
1968; Robinson, 1975; Davidson, 1994). Interestingly, Dimand (2004) has
recently shown, using evidence from Keynes’s lecture notes compiled by
Rymes (1989) that Keynes himself used a similar IS–LM type of general
equilibrium system of equations to express his new ideas in his lectures
during Michaelmas Term of 1933 as well as a 1934 draft of the General
Theory. Monetarists such as Friedman, Brunner and Meltzer also ‘dislike’ the
IS–LM framework. Bordo and Schwartz (2003) attribute this negative view
to the model’s narrow definition of investment and its narrow view of monetary
influences. Nevertheless, even if the IS–LM model no longer forms the
foundation of graduate macro courses (now dominated by dynamic general
equilibrium theorizing), as it did until the mid-1970s, the model still forms a
major input into most mainstream intermediate macroeconomics textbooks
such as Blanchard (2003), Dornbusch et al. (2004), Gordon (2000a) and
Mankiw (2003). Readers interested in recent controversies and discussions
surrounding the origin, development and persistence of the IS–LM model
should consult King (1993), Young (1987), Young and Zilberfarb (2000),
Young and Darity (2004), Barens and Caspari (1999), De Vroey (2000),
Backhouse (2004), Colander (2004), Dimand (2004), and Snowdon (2004a).
We now turn to consider the Keynesian belief that the economy can take a
long time to return to full employment after being subjected to some disturbance.
This involves a discussion of the debate on underemployment
equilibrium and in what follows we examine the circumstances under which
the IS–LM model will fail to self-equilibrate at full employment.
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