The impact of Expectations on Consumption and Investment and

the IS/LM Expectations Model

IntroductionIntroductionThe purpose of this Lecture is three-fold:

i. The role expectations play in determining consumption decisions. We will show that they depend not only on current income but also on expected future income and financial wealth;

ii. The role expectations play in determining investment decisions. We will show that they depend on current and expected profit and current and expected real interest rates;

iii. Derive the Expectations IS/LM model and reconsider the short-run effects on output of changes in monetary and fiscal policies.

We have considered the role of expectations in financial markets.

Now we have to consider the role of expectations in determining consumption and investment (the two main components of aggregate demand)

Once this is done we will have the main foundations for the expanded IS/LM model which we will call the expectations IS/LM model.

Recall that the basic IS curve assumes that: 1. people determine how much to consume and save on

the basis of current income.2. Investment depends on current nominal interest rate

and the current level of sales

These are unsatisfactory assumptions! We have already argued that investment decisions

depend not on the nominal interest rate but on the real interest rate. However we have to extend the analysis to reflect that investment depends not only on the current real interest rate and current sales but also on the expectations of future real interest rates and future sales!

Consumption also does not simply depend on current income but should also depend upon expectations of future income.

Expectations and Expectations and ConsumptionConsumption Consumption function that underpins the basic IS/LM model

is: C = C0 + C1YD

Where C1 is 0 < MPC < 1 and YD is current disposable income.

Our aim to develop a more realistic consumption function that takes into account expected future income as well.

To do this we will develop a consumption function that relies on the “Permanent income theory of consumption” (Friedman) and “life-cycle theory of consumption” (Modigliani)

The components of The components of consumptionconsumption The consumption profile for an individual depends upon his

total wealth accumulated over his lifetime Total Wealth = Human Wealth + Non Human Wealth Human Wealth is his present value of expected after-tax income NonHuman Wealth is the sum of his financial wealth and

housing wealth Therefore the consumer has to decide how much to spend out of

his total wealth at each point in time. We generally assume that consumers would like to spend a

proportion of total wealth to maintain a similar level of consumption each year throughout his life, X.

Therefore if X is higher than current income the consumer will borrow (to smooth consumption)

If X is lower than current income the consumer will save.

Consider a consumption function that depends completely on total wealth:

Ct = C(total wealtht)Thus consumption at time t depends upon

the sum of nonhuman wealth and human wealth (expected present value of current and future disposable income) at time t.

Example: 21 year-old student starting a 3 year university course. The retirement age is 60 and taxes are 25% of your income.

Expect a real wage of £40,000 once you finish university and to increase 3% p.a. in real terms.

Assume for simplicity that nonhuman wealth is zero and real interest rate is zero

Expected present value is:V(YeLt – Te

t) = (£40,000)(0.75)[1 + (1.03) + (1.03)2 +….+ (1.03)36] = £1,986,000.

If you expect to live to the age 76 then you have 56 years of expected life (76 – 21) in which to smooth consumption as thus the constant level of consumption per year is £35,464.

Thus you should borrow £35,464 x 3 = £106, 392 over next 3 years while you are a student and save when you start working!

Thus the problem with this consumption function is that is does not take into account the direct restrictions that you face given your current income.

So the consumption function we will use is:

Ct = C(total wealtht, YLt – Tt )

Consumption is an increasing function of total wealth and also an increasing function of current disposable income.

Total wealth component captures the consumers expectations about future income

Revised consumption function implies:1. Expectations affect consumption directly through

human wealth since human wealth is computed by the consumer forming expectations of future labour income, real interest rates and taxes:

– For example consider how expectations of higher output in the future affect consumption today:

Increase in expected future output;Increase in expected labour income;Increase in Human Wealth;Increase in Consumption today.

2. Expectations affect consumption indirectly through nonhuman wealth (bonds and stocks!!)

Consumers take the value of these assets as given (i.e. they don’t compute their values as this has already been done for them by financial markets).

However we know from earlier that the price of bonds and stocks, depend upon expectations of future interest rates and dividends.

Consider how expectations of higher output in the future affect consumption todayIncrease in expected future output;Increase in expected future dividends;Increase in stock prices;Increase in nonhuman wealth;Increase in consumption today

Therefore the dependence of consumption on expectations has two main implications for the relationship between consumption and income.

The response of consumption to changes in income depends on whether consumers perceive such changes as transitory (temporary) or permanent

Consumption may change even if current income does not change.

Expectations and InvestmentExpectations and Investment

Investment function that underpins the basic IS/LM model is:

I = I (Y, i ) i.e. Investment demand I is positively related to

current output Y and negatively related to the current nominal interest rate i.

Our aim to develop a more realistic investment equation not only depends upon the real interest rate but also takes into account expected future output as well.

Consider a firm who has to decide whether to make a new investment e.g. buy a new machine.

The decision to buy a machine depends on the present value of the profits the firm can expect from having this machine versus the cost of buying it.

Present value > costs; then the firm should buy the machine.

In order to compute the present value of expected profits for this investment, the firm must estimate how long the machine will last

The rate of depreciation, , measures how much usefulness the machine loses from one year to the next.

e.g. Reasonable values for are between 4% and 15% for machines, and between 2% and 4% for buildings and factories.

Buy the machine in year t, the machine makes its first expected profit in year t+1, e

t+1;

The present value of this expected profit is

We use real interest rate since we are measuring profits in real terms.

Expected profit in year t+2 is (1 – ) et+2 the

present value being:

1

11+ +rt

et

€

1

(1+ rt )(1+ rt+1e )

(1−δ)Π t+2e

Therefore the present value of expected profits from buying the machine in year t, V(e

t) is:

Therefore aggregate investment for the whole economy can be expressed as:

It = I (V(et) )

where It is aggregate investment and t is profit per unit of capital for the whole economy.

Investment depends positively on the expected present value of future profits (per unit of capital):

The higher current or expected profit, the higher is V(et) and thus the

higher the level of investment. The higher current or expected real interest rates, the lower is V(e

t) and thus the lower the level of investment.

( ) ...)1()1)(1(

1

1

12

11 +Π−

+++Π

+=Π +

++

ete

tt

et

t

et rrr

V δ

To see the intuition behind these results more clearly lets assume firms operate under static expectations i.e. they expect the future to be like the present.

Then the present value of expected profits is the ratio of the profit per unit of capital to the sum of the real interest rate and the depreciation rate

tet

et === ++ ....21

te

te

t rrr === ++ ....21

( )+

=

t

tet r

V

And the investment equation is thus:

The denominator rt + is the rental cost of capital Investment depends on the ratio of profit to the

rental cost of capital The higher the profit, the higher the level of

investment The higher the real interest rate, the higher the

rental cost of capital, the lower the level of investment

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

=t

tt r

II

Note the similarity between the present value computation of the firm and the fundamental value of a stock:

A firm’s investment decision depends on expected profit. Stock Price depends on expected dividends (which are paid

from firms profits) . Therefore investment decisions and stock market prices

depend on the same factors: expected future profits and expected future real interest rates.

( ) ...)1()1)(1(

1

1

12

11 +Π−

+++Π

+=Π +

++

ete

tt

et

t

et rrr

V δ

....)1)(1()1( 1

21 +++

++

=+

++ett

et

t

et

t rrD

rD

Q

qq Theory of Investment Theory of Investment

A firm can raise the financing it needs to pay for an investment by issuing shares.

Investors buying the shares expect to earn a return from dividends.

Stock prices tend to be high when the firm has many opportunities for profitable investment, because these profit opportunities mean higher future income for shareholders. Thus, stock prices reflect the incentives to invest. i.e. the stock price, in effect tells the firm how much the stock market values each unit of capital already in place.

James Tobin proposed that firms base their investment decisions on the following ratio:

q > 1 then stock market values installed capital at more than its replacement cost, so a firm can raise the market value of its stock by buying more capital

There is a strong relationship between Tobin’ q and investment thus highlighting the fact that investment decisions and stock market prices depend on similar factors.

capitalinstalledofcosttreplacemen

capitalinstalledofvaluemarket=q

Tobin’s q Versus the Ratio of Investment to Capital—Annual Rates of Change, 1960-1999

There is a tight relation between investment and the value of the stock market.

IItt = I (V( = I (V(eett) )) )

So far we have constructed a new investment condition that depends solely on expected future profits.

However empirical evidence also suggests that current profit also plays an important role in determining whether a firm invests.

Why? Firms may be reluctant to borrow if current profit is low. But if current profit is high, the firm may not need to borrow to finance its investments. It does not need to convince potential lenders.

Therefore Investment depends upon two factors:Profitability vs Cash Flow

Profitability is the expected present discounted value of profits Cashflow is current profit. Both profitability and cash flow are important for investment

decisions, and are likely to move together.

Changes in Investment and Changes in Profit in the United States, 1960-2000

Investment and profit move very much together.

Therefore the Investment Equation we will use is:

Investment decisions depend both on expected present value of profits and on the current level of profits!

I I Vte

t t= ( ( ), )

If investment depends on both current and expected profit, what determines profit?

1. Level of sales;2. Existing capital stock If sales are low relative to the capital stock,

profits per unit of capital are likely to be low as well

Assume that sales and output are the same (there is no inventory investment)

Profit per unit of capital , is an increasing function of the ratio of output (sales) Y, to the capital stock K.

For a given capital stock, the higher the output the higher the profit.

For a given level of output, the higher the capital stock the lower the profit.

Thus we have a link between current output, expected future output and investment.

Current output affects current profit; expected future output affects expected future profit; and current and expected future profits in turn affect investment!

⎟⎟⎠

⎞⎜⎜⎝

⎛=

t

tt K

Y

Derivation of the Expectations Derivation of the Expectations IS/LM model;IS/LM model;We have shown over the last two weeks that: Expectations affect bond and stock prices; Expectations affect consumption and investment

decisions;We are now ready to consider how the incorporation of such expectations into the IS/LM model impact on the effectiveness of monetary and fiscal policy (in the short-run!)

Consumption

An increase in current and expected future real disposable income, or a decrease in current and expected future real interest rates increases human wealth and leads to an increase in consumption today;

An increase in current and expected real dividends, or a decrease in current and expected future real interest rates increases nonhuman wealth and leads to an increase in consumption today;

A decrease in current and expected future nominal interest rates leads to an increase in bond prices which leads to an increase in nonhuman wealth and leads to an increase in consumption today;

Investment

An increase in current and expected future real profits, or a decrease in current and expected future real interest rates, increase the present value of real profits and leads to an increase in investment today.

Expectations and Spending: The Channels

Expectations affect consumption and investment decisions, both directly and through asset prices.

IS Curve RevisitedIS Curve Revisited

Since expectations affect consumption and investment it is clear that the IS curve will have to be amended.

Recall that the IS curve simply shows goods market equilibrium.

Since expectations involve the consideration of current and future periods we will simply the analysis by assuming that there is only two periods.

1. A current period (or current year)2. A future period (all future years collectively) This means that we don’t have to keep track of

expectations about each future year.

Recall that the basic IS curve is given by:Y = C(Y – T) + I(Y, i) + G

Since investment depends on the real interest rate we can amend this equation to get:

Y = C(Y – T) + I(Y, r) + G To introduce expectations we proceed in 2 steps:Step 1: Define aggregate private spending

And rewrite the IS equation as:A Y T r C Y T I Y r( , , ) ( ) ( , )≡ − +

Y A Y T r G= +( , , )

Note: nothing intuitively has changed. The properties of aggregate private spending A, follow from the standard properties of C and I

Aggregate private spending is an increasing function of income Y: Higher income increases consumption and investment

Aggregate private spending is a decreasing function of taxes T: Higher taxes decrease consumption

Aggregate private spending is a decreasing function of the real interest rate r: Higher r decreases investment

Y A Y T r Ge e e= +( , , , ' , ' ' ) T r Y( , , )+ −− − − , +,

* Primes denote future values, and * Primes denote future values, and e’e’ss expected values. expected values.

Y or Y e' A↑ → ↑

T or T e' A↑ → ↑r or r e' A↑ → ↓

The positive and negative signs explain how:The positive and negative signs explain how:

Step 2:Step 2: Incorporate expectations by allowing spending to Incorporate expectations by allowing spending to depend not only on current variables but also on their depend not only on current variables but also on their expected values in the future period.expected values in the future period.

Expectations and the Expectations and the ISIS Curve Curve

The New IS Curve

tt

t

Y

K=

⎛

⎝⎜

⎞

⎠⎟

Given expectations, a decrease in the real interest rate leads to a small increase in output: The IS curve is steeply downward sloping. Increases in government spending, or in expected future output, shift the IS curve to the right. Increases in taxes, in expected future taxes, or in the expected future real interest rate shift the IS curve to the left.

Notice that the new IS curve is still depicted by taking all variables as given except current output Y and current real interest rate r.

The IS curve is still downward-sloping. Why? A decrease in the current real interest rate leads to an increase in spending, which through the multiplier effect leads to an increase in output.

However, this revised IS curve is much steeper that the original, which means that a large decrease in the current interest rate is likely to have only a small effect on equilibrium output. Why?

1. A decrease in the current real interest rate does not have much effect on spending if future expected rates are not likely to be lower as well.

2. The multiplier is likely to be small. If changes in income are not expected to last, they will have a limited effect on consumption and investment.

Shifts in the IS curve arise through changes in all variable except current Y and current r.

a. Increase in current taxes or future taxes shift the IS curve to the left (consumption falls)

b. Increase in expected future output or a decrease in expected future real interest rate shift the IS curve to the right (consumption increases as consumers feel wealthier and investment increases as profits increase)

c. Increase in government spending shifts the IS curve to the right.

LMLM Curve Revisited Curve Revisited The LM relation is not modified because the

opportunity cost of holding money today depends on the current nominal interest rate, not on the expected nominal interest rate one year from now.

M

PYL i= ( )

The interest rate that enters the LM relation is the The interest rate that enters the LM relation is the current nominal interest rate.current nominal interest rate.

Monetary Policy, Expectations and Monetary Policy, Expectations and OutputOutput Expansionary Monetary Policy: Increase in the money

supply results in a fall in the nominal interest rate. In the baseline IS/LM model there was only one interest

rate, the nominal interest rate i, which entered both equations.

Now however we have many interest rates!1. Nominal interest rate which enters the LM equation;2. Real interest rate which enters the IS equation;

Current and expected future real interest rates which enter the IS equation.

Need to consider the link between changes in the nominal interest rate and changes in current and expected future real interest rates

Recall the Fisher Equationr = i – πe

Thus the expected future real interest rate is equal to the expected future nominal interest rate minus expected future inflation

r’e = I’e – π’e

The effect on current and expected future real interests to a change in the nominal interest rate depends upon:– How financial markets revise their expectations of the

future nominal interest rate, i’e.– How financial markets revise their expectations of

both current inflation, e, and future inflation, ’e.

To simply the analysis, assume that expected current inflation and expected future inflation are zero.

Therefore both current and expected future nominal and real interest rates are the same.

IS A Y T r Y T r Ge e e: ( , , , ' , ' , ' ) Y = +

LMM

PYL r: ( ) =

The New IS-LM

The IS curve is steeply downward sloping: Other things equal, a change in the current interest rate has a small effect on output. The LM curve is upward sloping. The equilibrium is at the intersection of the IS and LM curves.

Suppose that the economy is in a recession and the monetary authority adopts an expansionary monetary policy

Money supply increases, the LM curve shifts downwards and the current interest rate falls. A B.

If expectations remain unchanged then the effect of this policy is a small increase in output

However if expectations change as a result of this change in monetary policy then what happens?

Suppose that in response to the decrease in current interest rates, financial markets anticipate lower interest rates in the future and higher output in the future. Then the IS curve shifts to the right and we get a much larger increase in output!

The Effects of an Expansionary Monetary Policy

The effects of monetary policy on output depend very much on whether and how monetary policy affects expectations.

Therefore the impact of monetary policy on output depend crucially on its effects on expectations

The effect of monetary policy on output depends on whether and how changes in the short-term nominal interest rate lead to changes in the current and the expected future real interest rate.

Note the similarity with the effects of monetary policy on the stock market which we considered before. If changes in monetary policy is expected, investors, firms and consumers do not change their expectations and consequently there is little or no effect on output.

If however policy changes are unexpected then there can be potentially large effects on output as expectations of future interest rates come down, stock prices rise, and output increases.

Fiscal Policy, Expectations and Fiscal Policy, Expectations and OutputOutput Maintain the same assumptions as before, such

that nominal and real interest rates are the same. We want to consider the short-run impact of a

reduction in the budget deficit (i.e. a fall in government spending with taxes unchanged)

(G – T) Assume that taxes in both current period and

future period are unchanged and that government spending falls in both periods.

What will happen to current output?

To motivate the results that we get later, recall the implications of this policy under the basic IS/LM model which you consider in the autumn term.

Short-run: IS curve shifts to the left which results in lower output

Medium-run: deficit reduction has no effect on output which returns to its natural rate, but leads to a lower interest rate and higher investment. Why? Lower government spending with output unchanged implies that investment must have offset the decrease in public expenditure. Thus the interest rates must be lower for investment to have increased.

Long-run: Higher investment leads to a higher capital stock and thus a higher level of output.

Clearly in our new expectations IS/LM model we will get the same short-run results if expectations do not change.

However what should happen to expectations? Assume agents have Rational Expectations

i.e. expectations are formed in a forward-looking manner. Individuals, firms and investors form expectations about the future by assessing the likely course of future expected policy and then working out the implications of future activity.

The assumption of rational expectations is one of the most important (if not the most important!) developments in macroeconomics in the last 25 years. Designing a policy on the assumption that people make systematic mistakes in responding to it would be unwise!

Assume that the future period consists of the medium-run and the long-run. If people, firms and financial market participants have rational expectations then in response to the announcement of a reduction in the budget deficit they will expect that in the future output will return to its natural rate in the medium-run and increase in the long-run and future interest rates to fall.

Thus they will revise their expectation of future output up and their expectation of future interest rates down, which results in a shift of the IS curve to the right!

The Effects of a Deficit Reduction on Current Output

When account is taken of its effect on expectations, the decrease in government spending need not lead to a decrease in output.

Net effect is ambiguous. Expectations of higher consumption and investment may

offset the decrease in government spending. Also highlights the difficulties of using fiscal policy for

demand-management purposes. What we can say is the following: The smaller the

decrease in government spending today the smaller the adverse effect on output today.

The larger the decrease in government spending in the future period, the larger the effect on expected future output and interest rates, thus the larger the favourable effect on spending today.

Therefore, small cuts in government spending today and large expected cuts in the future will cause output to increase more in the current period—a concept known as backloading.

Backloading —leaving most of the reduction for the future, not the present, however, may lead to a problem with the credibility of the deficit reduction policy.

To summarize, the short-run impact on output of a particular fiscal policy crucially depends on:– The credibility of the program

i.e will spending be cut or taxes increased in the future as announced?

– The timing of the programi.e How large are the spending cuts today relative to the future?

– The composition of the programi.e. Does the policy remove some distortions in the economy?

– The state of government finances in the first place.i.e. What state are they in? What will happen to them if the policy fails?