ISLM AnalysisPart I: The Real Sector

The Keynesian Framework According to John Hicks and Alvin Hansen

Roger W. Garrison 2008

(1 – b)

Y

I

I

S S

Macroeconomic equilibrium for a wholly private economy requires that saving equal investment. That is, “S = I” is an equilibrium condition. According to Keynes, saving depends upon income and income alone.In particular, S = – a + (1 – b)Y, where a > 0 and 0 < b < 1.In Keynes’s vision, investment depends primarily on “animal spirts.”But investment also depends, if only to a minor extent, on the rate of interest.The demand for investment funds in highly interest inelastic.

i

With “animal spirits” in play, the whole curve moves around on its own.

-a

1

1

1

How much borrowing and investment would the business community be willing to undertake?

How much income would people have to earn to be willing to save this amount? Y

Y

i

I

I

S S

i

So far, we have one equilibrium condition (in orange) and two behavioral relationships (in blue). Together, these three relationships imply a particular relationship between the interest rate and the economy’s total income.

This relationship is revealed by tracing out the implications of a low interest rate, a high interest rate, and a middling interest rate.

Suppose the interest rate is relatively low.

iLOW

How much saving is required to finance this level of investment?

How much

So, now we have one possible combination of the interest rate and total income.

How much income would people have to earn to be willing to save this amount? Y

Y

i

I

I

S S

i

So far, we have one equilibrium condition (in orange) and two behavioral relationships (in blue). Together, these three relationships imply a particular relationship between the interest rate and the economy’s total income.

This relationship is revealed by tracing out the implications of a low interest rate, a high interest rate, and a middling interest rate.

Suppose the interest rate is relatively high.

iLOW

How much borrowing and investment would the business community be willing to undertake?

How much saving is required to finance this level of investment?

How much

Now we have another possible combination of the interest rate and total income.

iHIGH

This relationship is revealed by tracing out the implications of a low interest rate, a high interest rate, and a middling interest rate.

How much borrowing and investment would the business community be willing to undertake?

How much saving is required to finance this level of investment?

How much income would people have to earn to be willing to save this amount?

Accordingly, we call this line the IS curve. (All along this curve, I = S.)

A line passing through these three points (two would have been enough) represents all combinations of the interest rate and total income that are consistent with the equality of investment and saving, given the relationships that describe investment behavior and saving behavior.

Y

Y

i

I

I

S S

IS

i

So far, we have one equilibrium condition (in orange) and two behavioral relationships (in blue). Together, these three relationships imply a particular relationship between the interest rate and the economy’s total income.

Suppose the interest rate is a middling rate.

iLOW

How much

Now we have a third possible combination of the interest rate and total income.

iHIGH

iMID

Y

Y

i

I

I

S S

IS

i

WARNING: “Equilibrium” in income-expenditure analysis means only that income gets spent---or, equivalently (for a wholly private economy), saving gets invested. It does not mean that the work force is fully employed or that the economy’s potential output is being realized. Keynes believed that some “unemployment equilibrium” was the norm for a wholly private economy.

If the middling rate of interest just happens to be the equilibrium rate, the level of total income that corresponds to that rate is the equilibrium level of income.

iLOW

iHIGH

iMID

Equilibrium levels of saving and investment are similarly identified.

ieq

Yeq Ieq

Seq

Marshall would observe that the wage rate has adjusted to the prevailing supply-and-demand for labor. Keynes would observe that, give the supply of labor and the going wage rate, the current level of expenditures just happens to be high enough to cause the resulting demand for labor to clear the labor market.

Wholly dismissive of the classical economists’ theorizing about the distribution of income among the factors of production, Keynes assumed a “fixed structure of industry” whose level of utilization varies directly with the employment of labor. And with the wage rate given, changes in total income are directly proportional to changes in the employment of labor.

But Keynes’s supply-and-demand reckoning of the labor market differs importantly from Alfred Marshall’s.

Keynes assumed that movements in total income faithfully reflect the movements in the level of employment.

ieq

Y

Y

i

I

I

S S

IS

i

If the income-expenditure equilibrium just happens to be consistent with full employment, then the labor force will be experiencing a supply-and-demand equilibrium.

Yeq Ieq

Seq

N

W

S

DLABOR

INCOME

(1 – b) ΔI

And note that with an unchanged rate of interest, the equilibrium level of income also changes in accordance with the simple Keynesian multiplier.Note that the interest rate, If only by assumption, remains unchanged.

With the change in investment behavior, the IS curve shifts to the left.The economy experiences a downturn in which lower levels of income, investment, and saving are established.

The magnitude of the shift in the IS curve is a multiple of the magnitude of the shift in the demand for investment funds. Here, the simple Keynesian multiplier is in play.

1(1 – b)ΔY =

ΔIΔY

ieq

Y

Y I

I

S S

IS

i

According to Keynes, the demand for investment funds is subject to a sudden, unpredictable collapse. The collapse (the leftward shift in the demand curve) upsets both the labor market’s supply-and-demand equilibrium and the macroeconomy’s income-expenditure equilibrium. Yeq Ieq

Seq

i

S'eq

Y'eq I'eq

ΔI

N

W

S

D

Finally, we note that the decrease in income reflects a corresponding decrease in the demand for labor. And with the going wage rate persisting, the labor market is experiencing a persistent (Marshallian) disequilibrium. Keynes would call it “unemployment equilibrium.”

1

The greater volume of saving would be borrowed by the business community only if the rate of interest were lower.If the old equilibrium rate of interest still prevails, then the economy’s reaction to increased saving is a fall income.

−1(1 – b)

ΔThrift

ΔY =ΔY

ieq

Y

Y I

I

S S

IS

i

According to Keynes, people’s saving behavior is unlikely to change. And fortunately so. In the Keynesian framework, increased saving has bad consequences.

A decision to save more is represented by an upward shift in the saving function. Yeq Ieq

Seq

i

Y'eq

ΔThrift

N

W

S

D

And whatever the eventual consequences of the increased saving, the old IS curve is no longer valid. The new one lies to its left. If we call an upward shift of the saving relationship a change in thrift, then the corresponding shift in the IS curve is given by the thrift multiplier---which is simply the negative of the spending multiplier. (Thrift means not spending.)

Finally, we note that the decrease in income reflects a corresponding decrease in the demand for labor. As happened in the case of a fall in investment demand, an increase in thrift reduces spending and causes the labor market to experience a persistent (Marshallian) disequilibrium.

ISLM AnalysisPart II: The Monetary Sector

The Keynesian Framework According to John Hicks and Alvin Hansen

Roger W. Garrison 2008

Keynes had once considered himself to be a “classical” economist. With Marshall, he believed that

1. the interest rate is determined in the loanable-funds market

and 2. money is to be analyzed in terms of the equation of exchange.

He later concluded that the interest rate wasn’t doing its job—because saving was not affected by the interest rate and investment was governed exclusively (or, at least, primarily) by psychological factors.

He also concluded that the equation of exchange should be jettisoned (or, at least, should have greatly diminished significance)—because it stood in the way of our recognizing the impact that monetary disturbances can have on the economy’s real sector.

Keynes had once considered himself to be a “classical” economist. With Marshall, he believed that

1. the interest rate is determined in the loanable-funds market

and 2. money is to be analyzed in terms of the equation of exchange.

Keynes was left with puzzles:

1. What job is the interest rate doing?

and 2. What replaces the equation of exchange?

Keynes’s then had s Road to Damascus conversion:

There is a single answer to both questions:

The supply and demand for money are brought into balance by adjustments in the interest rate!

C = a + bY

S = -a + (1-b)Y

According to Keynes, the interest rate has little or no influence on people’s willingness to save. But it has a great influence, he claims, on the preferred form of saving. Do people put their savings at interest (e.g. by buying bonds) or do they keep their savings liquid (by holding money)?

KEYNES’S LIQUIDITY-PREFERENCE THEORY OF INTEREST

Income alone determines consumption behavior.

Y B (if i is expected to fall)

M (if i is expected to rise)

Then, the interest rate (or rather, the expected direction of movement in the interest rate) affects the relative attractiveness of money and bonds.

Suppose that a Railroad issues a 6%, 30 year, $1,000 bond in 1872.

The bond, which sells for $1,000, has 60 coupons attached, These coupons are redeemable for $30 each at six-month intervals.

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

When the last coupon is redeemed, the $1,000 is returned to the bond holder.

So, the buyer pays $1,000 in 1872.

He gets back $1,000 in 1902.

And he gets $30 biannually for 30 years.

He can sell the bond any time he wants.

But the selling price might be less than, more than, or equal to $1,000. How so?

Suppose that a few years after you bought this bond, market rates of interest are significantly lower than 6%.

At that point, the $1,000-bond rate might be as low as 4% or 3%. These bonds would have a six-month coupon value of $20 or $15, respectively.

You could easily sell your 6% bond, and you would be able to sell it at a price considerably higher than $1,000.

Suppose that a few years after you bought this bond, market rates of interest are significantly higher than 6%.

At that point, someone might be able to buy a 9% bond or a 12% bond. These $1,000 bonds would have a coupon value of $45 and $60, respectively.

You could still sell your 6% bond, but you would have to offer it at a price considerably less than $1,000.

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

$30 $30 $30 $30 $30 $30

From a 1993 OECD OUTLOOK:

In the United States, long-term railroad-bond yields fell

gradually from about 5 per cent in 1880 to 4 per cent at the turn of the century then rose slightly.

i

MSPEC

Keynes portrayed each saver as facing a choice between holding his savings liquid or holding long-term bonds. The savers’ preferences in this regard determine both the demand for money (liquidity) and the demand for earning assets (bonds).

The choices (between money and bonds) hinge critically on beliefs about future movements in the interest rate.

In this connection, the demand for money is a speculative demand (MSPEC) whose magnitude is related, if only loosely, to the current rate of interest.

i

MSPEC

Keynes believed that the demand for money holdings, i.e., for liquidity, is fairly interest-rate elastic.

If a high current rate of interest implies that rates are likely to fall and a low current rate implies that they are likely to rise, then we get a downward-sloping demand for speculative money holdings.

If the current rate is sufficiently high, savers will lock themselves into high long-term bond rate and there will be no speculative holdings of money.

If the current rate is sufficiently low, savers will abstain from buying bonds and will hold all their savings liquid. The elasticity of money demand becomes infinite.

At rates of interest so high that virtually no one believes they are likely to go still higher, the speculative demand for money is perfectly inelastic and is co-incident with the vertical axis. This is the “classical region,” so named because in the classical theory, there is no speculative demand for money.

At rates of interest so low that virtually no one believes they are likely to go still lower, the speculative demand for money becomes perfectly elastic. In this “extreme Keynesian region,” all additions to the money supply are simply hoarded.

i

MSPEC

This special demand curve is non-linear and has three identifiable regions:

The speculative demand for money is unique to Keynesian macroeconomics and, according to some, is the sine qua non of Keynesianism. CLASSICAL

REGION

EXTREME KEYNESIAN

REGION

In the “intermediate region,” the quantity of money holdings demanded varies inversely with the rate of interest.

INTERM

EDIATE

REGION

i

MSPEC

Complicating matters, the demand for money holdings, like the demand for investment funds, is unstable. While investment is governed by “animal spirits,” hoarding money is rooted in a “fetish of liquidity.”

Expectations about which direction the interest rate is likely to move are not at all well-founded. The shifting and drifting expectational winds can send the demand for money holdings right and left or up and down.

i

MSPEC

If the demand for money holdings stays put for the time being, we can note the inverse relationship between the interest rate and the demand for money holdings.

To determine the particular rate of interest that actually prevails, we take into account the money supply, which is set by the central bank.

MS

ieq The rate of interest adjusts to its equilibrium value (ieq), where the preferred level of money holdings is equal to the money supply. This the hard-drawn Keynesian view, where “forces of a different kind” (and not the loanable-funds market) determine the market-clearing rate of interest.

i

MSPEC

If the demand for money holdings stays put for the time being, we can note the inverse relationship between the interest rate and the demand for money holdings.

To determine the particular rate of interest that actually prevails, we take into account the money supply, which is set by the central bank.

MS

ieq The rate of interest adjusts to its equilibrium value (ieq), where the preferred level of money holdings is equal to the money supply. This the hard-drawn Keynesian view, where “forces of a different kind” (and not the loanable-funds market) determine the market-clearing rate of interest.

Dennis Robertson (1890−1963)

According to Keynes:

“The interest rate is what it is because it is expected to be other than what it is. If it isn’t expected to be other than what it is, there is nothing to tell us why it is what it is. The organ that secretes it has been amputated and yet somehow it still exists, the grin without the cat.”

MSPEC

ieq

MSi

Suppose that people’s propensity to hoard strengthens—meaning that their demand for money to hold increases.

Note that the increased demand is not automatically accommodated by an increase in the money supply. Instead, the rate of interest rises until people are content to hold the existing money supply.

However, if the central bank wants to re-establish the pre-existing rate of interest, it can increase the money supply, moving the money holders along their money-demand curves.

i’eq

MSPEC

ieq

MSi

With an economy performing at full-employment without inflation, Keynes argued that changes in money demand be accommodated by corresponding changes in the money supply. He did not want increased money demand to be choked off by an increase in the rate of interest.

If the central bank could synchronize movements in the money supply with movements in money demand, the interest rate would not need to change.

Note that successful synchronization effectively transforms a perfectly inelastic money supply into a perfectly elastic money supply.

MS

ΔI

ieq

Y

Y

i

I

I

S S

IS

i

Yeq Ieq

Seq

N

W

S

D

MSPEC

ieq

MSi

ΔY

1(1 – b)

ΔY = ΔI

i’eq

So, why does it matter that the interest rate increases with a strengthening of hoarding propensities?

It matters because a change in the interest rate has an impact on the real sector of the economy.

Suppose the economy is in an income-expenditure equilibrium and is performing at full employment without inflation. That is, labor demand is just strong enough to clear the labor market at the going wage

An increase in money demand raises the rate of interest and takes this fully-employed economy into recession.

An accommodating increase in the money supply undoes the damage.

By continuously manipulating the money supply so as to keep the interest rate from changing, the central bank can nip in the bud any recession (or inflation) that would otherwise be associated with the unstable demand for money.

People behave fetishistically toward money, sometimes wanting to hoard it. If the central bank matches their hoarding propensities by supplying additional quantities of money, the economy will be spared from spiraling into depression.

ieq

Y

Y

i

I

I

S S

IS

i

Yeq Ieq

Seq

MSPEC

ieq

MSi

MS

i

MSPEC

ieq

Y

Y

i

I

I

S S

IS

i

Yeq Ieq

Seq

N

W

S

D

MS

ieq

We begin again with the economy in an income-expenditure equilibrium and performing at full employment without inflation. We assume away the problem of hoarding and show how monetary policy can counter a waning of animal spirits.

With the change in investment behavior, the IS curve shifts to the left.The magnitude of the shift in the IS curve is a multiple of the magnitude of the shift in the demand for investment funds. Here, the simple Keynesian multiplier is in play.

Finally, note that the decrease in income reflects a corresponding decrease in the demand for labor. And with the going wage rate persisting, the labor market is experiencing a persistent (Marshallian) disequilibrium. Keynes would call it “unemployment equilibrium.” And note that with an unchanged rate of interest, the equilibrium level of income also changes in accordance with the simple Keynesian multiplier.Note that the interest rate, which continues to match the money supply to the speculative demand for money, remains unchanged.

The economy has experienced a downturn in which lower levels of income, investment, and saving are established.

1(1 – b)ΔY =

ΔIΔY

ieq

Y

Y I

I

S S

IS

i

Suppose the animal spirits are on the wane, causing investors to cut back on their borrowing of investment funds.

Yeq Ieq

Seq

i

S'eq

Y'eq I'eq

ΔI

N

W

S

D

i

MSPEC

ieq

MS

ieq

N

W

S

D

In the absence of any fiscal-policy levers, the recession can be countered by monetary policy. Though strictly limited by the shape of the demand for money, an increase in the money supply can lower the rate of interest and move the economy down along the IS curve.

But Keynes did recognize another component of the demand for money. The transactions demand for money (MT) depends primarily on income and not so much on the interest rate. It is this component (MTRANS—or simply MT) that can be analyzed in terms of the equation of exchange.

Keynes’s hard-drawn version of the monetary sector gives no play to the equation of exchange. The whole story is about the supply of money and the speculative demand for money. The interest rate, which balances supply against demand is a purely monetary phenomenon.

Keynes recognized that the transactions velocity of money, like the velocity of money in the classical formulation, is fairly stable. VT is more or less constant.

This means that MT is linearly related to Y. MT = Y / VT graphs as a straight line that emanates from the origin and has a slope of 1/ VT.

The classical economists wrote:

MV = PQ, where Q also represents real income—i.e., Q = Y/P.

Since Q = Y/P, then PQ = Y.

So, we can write MV = Y, which applies, Keynes insisted, only to the transactions demand for money.

And so, MTVT = Y or MT = Y / VT

Y

MT

1

VT

MT is one component of the demand for money. The other component is MSPEC.

Y

MT

The monetary sector is in equilibrium when money supply equals money demand.

Simply written: MS = MD.

So, MS = MSPEC + MT, where MS is controlled by the central bank.

i

MSPEC

MSPEC

MT

Keynes took the two components to be additive. That is, the total demand for money (MD) is equal to MSPEC plus MT. [Or simply: MD = MSPEC + MT]

MS

MS

This equilibrium condition graphs as a straight line with a vertical intercept of MS, a horizontal intercept of MS and a slope of negative one.

1

1

The two (additive) demands for money together with the equilibrium condition imply possible combinations of income and the interest rate that are consistent with equilibrium in the monetary sector.

Y

MT

The line connecting the possible equilibrium points is named the LM curve—with L (liquidity) representing the demand for money and M representing the money supply.

i

Y

i

MSPEC

MSPEC

MT

LM

The two (additive) demands for money together with the equilibrium condition imply possible combinations of income and the interest rate that are consistent with equilibrium in the monetary sector.

Y

MT

The line connecting the possible equilibrium points is named the LM curve—with L (liquidity) representing the demand for money and M representing the money supply.

i

Y

i

MSPEC

MSPEC

MT

LM

LM

ieq

Y

Y

i

I

I

S S

IS

i

Yeq Ieq

Seq

N

W

S

DLABOR

INCOME

i

Y

MSPEC

MSPEC

MTMT

The Keynesian Framework According to John Hicksand Alvin Hansen

This is the Hicks-Hansen, fixed-price, eight-quadrant diagrammatical exposition of Keynesian Macroeconomics.

ieq

ISLM AnalysisPart I: The Real Sector

The Keynesian Framework According to John Hicks and Alvin Hansen

Roger W. Garrison 2008