Expectations and our IS-LM model
• In this lecture we will examine how expectations
about the future will impact investment and
consumption today.
• We will introduce some new ways of thinking
about how people make the choice about how
much to consume today.
• We will then return to our IS-LM framework. We
will show how expectations about the future can
affect output and interest rates through changes
in consumption and investment decisions.
New investment function
• Last week we showed that the share value of a
firm must be equal to the present value of the
stream of future dividends of the firm.
Pt = det+1/(1+it) + det+2/(1+iet+1)(1+it) + …
• But the dividends can only come out of profits,
either profits today or delayed past profits that
were reinvested in the firm.
• Any profit that is reinvested into the firm must
earn at least an it return on the profit, or the
share price will drop.
Investment function
• In this case we can also think of share price as:
Pt = Profitset+1/(1+it) + Profitset+2/(1+iet+1)(1+it) + …
• The share price is the present value of the
expected stream of future profits.
• In the simple case where expected profits are
constant and the expected interest rate was
constant, this simplified to:
Pt = Profitse/ie
• The higher is Pt the greater is the incentive to
invest.
Investment function
• Our investment function can be imagined to be:
It = I(Profitse/ie)
• The book’s derivation uses similar logic in real
values instead of nominal values which we are
using here to derive:
It = I(Real Profitse/(re+δ))
• Where δ is the rate of depreciation of capital
over time, ie. wearing out.
• Since i and r are related through the Fisher
equation, the forms of these two functions will be
similar.
Understanding consumption
• Our consumption decision has been modelled
as
Ct = c0 + c1 Yt
• So we have assumed that the amount of
resources consumed today is a linear function of
today’s income.
• How reasonable an assumption is this?
• The aggregate consumption of an economy
must be nothing more than the sum of the
individual consumption choices of all the
households in an economy.
Household consumption
• Can we learn anything about the behaviour of
aggregate consumption by understanding how
individual households make consumption
choices?
• How do individuals/households plan their
consumption?
• Fact 1: Consumption choices are constrained by
people’s incomes.
• Households can borrow money to pay for
consumption, but any borrowings must be
matched by a later repayment. Borrowings can
not increase wealth of a household.
Time profile of income
• Fact 2: Over a lifetime,
people generally make
little money in their 20s,
income increases in 30s
and 40s, peaks in their
mid 50s and they earn
nothing after 65.
• Consumption could
match income in every
year, but then you would
live poorly while young
and starve to death after
65.
Income
40000
35000
30000
25000
20000
15000
10000
5000
0
20
30
40
50
60
70
Time profile of consumption
• Most people would prefer
a flatter “time profile” of
consumption.
• This could be achieved
by borrowing while
young, repaying the
borrowings and
accumulating some
savings while middleaged and then living off
savings when retired.
40000
35000
30000
25000
20000
15000
10000
5000
0
20
30
40
Income
50
60
Consumption
70
80
Time profile of net assets
• To do this households
would accumulate
debt while young
(mortgages etc),
repay the debt and
accumulate savings in
middle aged and then
live off savings while
old. Perhaps leaving
some savings to
children.
Assets
30000
25000
20000
15000
10000
5000
0
20
30
40
50
-5000
Assets
60
70
80
Human wealth
• What matters then for the time profile of a household’s
consumption are the total assets of the household.
• Where assets here mean financial wealth like savings
accounts, housing wealth like mortgages and human
wealth which is the present value of after-tax future
income.
• What is my human wealth?
Ht = (1-t)Yt+1e /(1+it) + (1-t)Yt+2e /(1+it+1e ) + …
• Where t is the share of your income taken by the
government.
• My human wealth is discounted present value.
Household consumption plan
• My consumption decision is a matter of choosing
how to allocate my household’s resources to
consumption over time.
• Your consumption plan can change for many
reasons.
• A change is likely to affect consumption in every
year, and not just this year’s consumption.
– One of the household may need expensive medical
treatment, so you have to pay for the treatment out of
wealth and lower consumption at all times.
Changes in plans
• An expected change in the future will likely have an
impact on consumption today.
– If I know that I will be wealthier in the future (a rich aunt puts the
family in her will), I may choose to increase consumption today.
• A change that is permanent will have a larger impact
than a temporary change.
• A tax cut of $1,000 for this year only will increase
consumption slightly as it only raises household wealth
by $1,000.
• A permanent tax increase of $1,000 raises household
wealth by the discounted present value of $1,000 for the
number of working years remaining for household.
Temporary versus permanent
• A permanent tax cut raises current income by $1,000
and raises human wealth by:
$1,000 /(1+it) + $1,000 /(1+it+1e ) + …
• Which for young households will be close to $1,000/i.
• So for a temporary tax cut, we might not expect
consumption to rise very much as households will
spread the $1,000 in new wealth over their whole
consumption plan.
• But for a permanent tax cut of $1,000, households can
raise their consumption in each year by almost $1,000
and still remain within their budgets.
Temporary versus permanent
• In our model of aggregate consumption, we had:
Ct = c0 + c1 Yt
• For a temporary tax cut, c1 would be low as
households do not consume much of the tax cut
today.
• For a permanent tax cut, c1 would be high as
households consume almost all of the tax cut
today.
• This means that we can not represent
aggregate consumption in this linear form.
New consumption function
• We have to adopt a new form
Ct = C(Yt , Wt )
• Where Wt is our household wealth, which will be
the sum of our financial and housing assets, At ,
plus our human wealth, Ht .
Wt = At + Ht
• A simple example might be something like:
Ct = c0 + c1 Yt + c2 Wt
• A temporary tax cut of $1 raises consumption by
c1 but a permanent tax cut raises consumption
by close to c1 + c2/i.
Back to our IS-LM model
• We have adjusted our IS equation to allow for
expectations of the future.
• Our new consumption function
Ct = C(Yt, Tt, Wt )
• Allows for the fact that consumption will be
affected by changes in household wealth.
• Our new investment function
It = I(Real Profitse/(re+δ))
• Allows for the fact that investment depends on
expectations of future profits and interest rates.
Present versus future
• One way to analyse effects is to think of
changes that affect variables today and/or
variables tomorrow.
• We have already been thinking this way when
we think of temporary versus permanent tax
cuts.
• We can arbitrarily divide our variables into
present income (Y) and future income (Ye),
present taxes (T) and future taxes (Te), present
real interest rates (r) and future real interest
rates (re).
Deriving a new IS equation
• Wealth (and so also consumption) will be
affected by Ye, re and Te. The effect of Ye and Te
on wealth is obvious, but what about re?
• Real assets of a household change from year to
year by:
At = (1 + rt-1) [At-1 + Yt-1 – Ct-1]
• We assume that left-over real assets are
invested.
• So a higher re will increase the wealth of people
who has positive assets and reduce the wealth
of people with negative assets.
Deriving a new IS equation
• A higher re will also reduce human wealth.
The net result on net wealth is ambiguous,
so we ignore the effect of re on wealth.
• A higher re will have a negative effect on
investment through the investment
function. We assume future profits (and
so also investment) will be affected
positively by future income and negatively
by future taxes.
Deriving a new IS equation
• Our new IS equation becomes:
Y = C(Y, T, W(Ye, Te)) + I(Profits(Ye, Te), r, re) + G
• Avoiding the book’s ugly notation, let’s just use
IS for the right-hand side.
Y = IS(Y, T, r, Ye, Te, re, G)
(+, -, -, +, -, -, +)
• Where IS = A + G in the book’s notation and the
+/- are the relationships between and increase in
the independent variable and Y.
Deriving a new IS equation
• What is important to remember here are the
channels through which the right-hand side
variables affect the IS equation, ie. an increase
in Ye raises C because wealth rises and raises I
because future profits rise.
• Example: Imagine the government increases G
without raising taxes today- issuing debt instead.
But people know that this new debt will have to
be paid off with future taxes, so Te rises.
Example: deficit spending
• The increase in G will
shift the IS curve to the
right. This would be
where our analysis would
end without expectations.
• However now we know
that Te rises, so future
wealth falls and present
consumption drops.
• The net effect on the IS
curve is ambiguous.
• Deficit spending
r
Te
G
IS
Y