Macroeconomics
Chamberlin and Yueh
Chapter 4
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Government Spending, Taxation
and Debt
•
•
•
•
Deficits and debt
Fiscal policy and national income
Keynesian cross model
The Ricardian Model: Fiscal Policy with
Forward-Looking Consumers
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
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Learning objectives
• Understand the nature of government
spending and taxation
• Differentiate between government deficits
and national debt
• Appreciate the implications of fiscal
policy
• Using the Keynesian cross model
• Work through the theory of Ricardian
Equivalence
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Government
• The macroeconomic perspective is focused on the
role the government may play in regulating the
economy through their central position in the
circular flow of income.
• Government spending is an injection into the
circular flow of income.
• Government policies relating to taxes and spending
are known as fiscal policy.
• The government through its policies may have
scope to influence aggregate demand and the level
of income. This scope, though, is open to debate.
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Fiscal Policy
• Viewed from two perspectives:
• The first is the Keynesian view, which makes the case that
governments can play a major role in determining the level
of national income.
• The alternative is the Ricardian view, which argues the level
of aggregate demand is essentially neutral to government
policy.
• The effectiveness of fiscal policy will therefore depend very
much on which view of the world persists.
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Deficits and Debts
• Government spending is an injection, and
taxes are a leakage, into the circular flow of
income.
• The stance of fiscal policy, whether it is
expansionary or contractionary, will depend
on the difference between the two.
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Budget balance
• The current government budget balance is
the difference between its spending and its
receipts.
Bt  Gt  Tt
where Bt is the balance at time t; Gt and Tt are
the respective levels of government spending
and tax revenue, also at time t.
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UK budget surplus/deficit
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Cyclical pattern of budget position
• The cyclical path of the budget deficit is accounted for by:
• When the economy is in a recession, tax revenues fall and
government spending on transfer payments, such as
unemployment insurance, tend to rise. This moves the
government balance towards deficit.
• When the economy is growing strongly, unemployment
tends to fall, boosting tax revenues, and reducing the need
for government spending on income-related benefits. For
this reason, the budget deficit can behave as an automatic
stabiliser for the economy.
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Structural budget balance
• Due to the cyclical nature of the current balance, it is hard
to judge the true stance of fiscal policy, that is, whether it is
generally expansive or contractionary.
• For this purpose, the structural or cyclically adjusted
balance, which is also plotted, may be useful. This takes
the cyclical movement of the economy into consideration
by simply reflecting what the government’s balance would
be if the economy were on its trend growth path. In this
way, it gives a much clearer indication of the fiscal stance
taken by a government.
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National debt/surplus
• The government or national debt/surplus is the accumulated
total of all its deficits and surpluses. However, this is not
all.
• If the country is running a net debt, it is funded by
borrowing on which interest must be paid. Likewise, if the
country is running surpluses, it is effectively a net lender
and will receive an interest payments.
• Therefore, over time, the dynamics of the national debt are
not just accumulated deficits and surpluses from the
government’s budget, but also include the associated
interest payments involved in servicing the debt/surplus.
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National debt/surplus
• The current level of debt is equal to last
period’s debt level plus all the interest which
is accrued and the current budget balance.
Dt  1  r Dt 1  Bt
• Therefore, the national debt will evolve as
follows:
Dt  1  r Dt 1  Gt  Tt
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UK national debt
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Keynesian vs. Ricardian Views
• The difference between the Keynesian and the Ricardian
views comes down to the type of consumption function.
• In the Keynesian model, unsurprisingly the Keynesian
consumption function is prominent. People decide how
much to consume on the basis of their current disposable
income, which is influenced by fiscal policy.
• In the Ricardian view, the Permanent Income Hypothesis is
central. Consumers are forward-looking and base their
decisions on a longer run view of income. Households will
only change consumption plans if they believe their
permanent income has changed. If it accepted that the
government must ultimately balance its books, all deficits
must be offset by surpluses. In this case, permanent
income, consumption, aggregate demand and the level of
national income will all be neutral with respect to fiscal
policy.
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Keynesian Cross Model
• From the circular flow of income, the economy is
clearly in equilibrium when income or output is equal
to planned expenditures.
• In a closed economy (no exports or imports), planned
expenditures are just the sum of consumption,
investment and government spending.
E C  I G
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Keynesian Cross Model
• Consumption is determined by a
simple linear function of
disposable income. Disposable
income is actual income with the
deduction of net taxes, which we
assume are administered in a
lump sum fashion:
• In the Keynesian model,
investment, government
spending and taxes are
considered to be exogenous:
C  a  cY  T 
II
G G
T T
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Planned expenditure
• Aggregate planned expenditure can be found by substituting
for these components:
E  a  cY  T   I  G
• The slope of this expenditure function is given by the
marginal propensity to consume (mpc) or c. This is because
consumption only depends on income, so changes in
income will affect planned expenditures to the extent that
consumption changes. This is in turn determined by the
mpc, which usually takes a value between 0 and 1.
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Planned expenditure
• The intercept of the planned expenditure function is:
a  I  G  cT
• This represents all planned expenditures which are
undertaken independently of income. These include
autonomous consumption, investment and government
spending.
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Planned expenditure function
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Keynesian Cross Model
• National income/output equilibrium will be
where actual income or output is equal to
planned expenditures:
Y E
• This is a 45 degree line so it has a slope
equal to unity; every point on it represents a
position where actual income or output is
equal to planned expenditures.
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Keynesian Cross Model
• The equilibrium level of income is
determined by where the equilibrium and
planned expenditure functions cross:


Y  a  c Y T  I  G
• Rearranging,

1
Y 
a  I  G  cT
1 c

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
Equilibrium in the Keynesian Cross Model
• At income levels below Y*, planned expenditures exceed
income or output. In this case, firms will find that their
stocks are being run down as demand exceeds supply.
Firms will increase output, and in doing so, hire more
labour so income will also rise.
• At income levels above Y*, planned expenditures at clearly
below actual output, in which case firms will begin to build
up stocks of unsold goods and inventories. As supply
exceeds demand, firms will be encouraged to cut output.
Less labour will be hired so income will also fall. It is only
at the level of income where there is no pressure on output
to change. This is where demand is equal to supply.
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Government Spending in the
Keynesian Cross Model
• Suppose there was an increase in
government spending.
• Planned expenditures will now be higher at
every level of income, so the planned
expenditure function will shift upwards.
This is seen as a movement from E1 to E2.
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Increase in government spending in
the Keynesian Cross Model
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Government Spending in the
Keynesian Cross Model
• What will happen to equilibrium output?
– Expenditure initially rises by the change in government spending;
this is shown as the vertical distance between E1 and E2.
– From the circular flow, income will also rise by this amount.
– However, this initial increase in income will lead to an increase in
disposable income and therefore consumption, so aggregate
expenditure will rise even further.
– As expenditure rises, income will also increase further.
– This process then repeats itself, higher expenditure generating
higher income, higher disposable income, higher consumption and
so on.
– However, because the marginal propensity to consume is less than
one, the increase in expenditure each time gets smaller and smaller,
so income will eventually converge to a new value rather than keep
rising in an unbounded way.
– This process is shown by the path of arrows. The total change in
equilibrium income is shown as a movement from Y1* to Y2*.
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Government spending multiplier
• This total change in income is a multiple of
the initial change in government spending.
It is the change in government spending,
plus all the subsequent changes in
consumption brought about by increasing
income. Therefore, the total change in
income can be written as:
Y  G  cG  c G  c G  ...............
2
3
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Government spending multiplier
• or Y  kG
• where the multiplier is
k  1  c  c  c  .......
2
3
• As 0<c<1, the value of the multiplier can be
found by using the sum to infinity:
1
k
1 c
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Government spending multiplier
• Therefore, the total change in income resulting from a
change in government spending is:
1
Y 
G
1 c
• It should be intuitively clear that the size of the multiplier
increases as the marginal propensity to consume increases.
If the mpc is higher, then every increase in income brought
about by the initial increase in expenditure will proceed to
generate larger further increases in expenditure. As a result,
the overall effect on national income will be higher.
• So, in conclusion, an increase in government spending will
produce a multiplied increase in equilibrium output.
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Taxes in the Keynesian Cross Model
• Where taxes are levied in a lump sum
fashion, an increase in the level of this tax
will lead to a downward shift in the
expenditure function. The tax rise will lower
disposable income resulting in autonomous
consumption and thus planned expenditure
being lower by an amount equal to cT .
This is shown as a movement from E1 to E2.
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Increase in tax in the Keynesian Cross Model
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Tax multiplier
• The fall in expenditure will have a multiplied effect on the
level of national income. Falling consumption leads to
lower income, which in turn leads to lower consumption
and so on. The overall effect of the tax rise on national
income would be:
c
Y  
T
1 c
• This consists of the initial fall in expenditure and the
multiplier.
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Tax multiplier
• A rise in the marginal propensity to consume will
have two effects here.
• First, the initial fall in consumption following the
tax cut will be larger, as consumption is more
responsive to changes in disposable income.
• Second, the multiplier will be larger.
• In both cases, the negative consequences for
equilibrium income will be more severe following
a tax rise.
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The Balanced Budget Multiplier
• It is argued that if the government raises government
spending and taxes by the same amount, then the effect on
income will be zero.
• The government is adding to the circular flow of income
with one hand, whilst taking an equal amount away from it
at the same time with the other.
• This, though, is not always true. Tax financed government
spending can still have a significant effect on the level of
national income.
• This is a powerful result; the government can use policy to
expand the economy without incurring any additional debt.
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The Balanced Budget Multiplier
• A tax financed increase in government
spending implies that:
G  T
• The rise in spending as we have seen will
lead to an upward shift in the expenditure
function and the rise in taxes a
corresponding downward shift. What will
be the overall consequence for the
equilibrium level of national income?
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The Balanced Budget Multiplier
• The increase in government spending shifts
the expenditure function upwards, whereas
the increase in taxes moves it downward.
• The equilibrium level of national income
would rise as a result, simply because the
upward shift in the expenditure function is
greater than the downward shift.
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The Balanced Budget Multiplier
• The logic here is fairly simple.
• Even though G  T , the change in
expenditure from an increase in government
spending exceeds the fall in expenditure
from the rise in taxes. The net change in
expenditure is E  1  cG, and this will be
positive so as long as the mpc is less than
one .
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The Balanced Budget Multiplier
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The Balanced Budget Multiplier
• The only situation where this does not hold true is
where the marginal propensity to consume is equal
to 1. In this case, there is no saving, so any
increase in tax financed government spending will
lead to an equal fall in consumption and no change
in overall expenditures.
• The effect on equilibrium income/output is clearly
positive. The economy moves from Y1 to Y3 via Y2.
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The Balanced Budget Multiplier
• The combined effect of the increases in
government spending and taxes is:
1
c
Y 
G 
T
1 c
1 c
• Knowing that G  T leaves us with:
Y  G
which is the balanced budget multiplier.
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The Ricardian Model: Fiscal Policy
with Forward-Looking Consumers
• In the simple Keynesian model, changes in
government spending or taxes will only affect
consumers to the extent that their disposable
income changes.
• On the other hand, forward-looking and rational
utility maximising consumers must take a much
more complicated decision. This is because a
government’s current tax and spending policies
may influence its future tax and spending policies,
and therefore have repercussions for a household’s
future disposable income.
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Optimal Consumers
• A rational consumer will choose consumption to maximise
total lifetime utility subject to the constraint:
C2
Y2
C1 
 Y1 
1  r 
1  r 
• This constraint simply implies that the present discounted
value of consumption cannot exceed the present discounted
value of income.
• The solution to the maximisation problem is where the
indifference curve formed by the consumer’s preferences is
tangential to the budget constraint.
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Optimal Consumers
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Optimal Consumers
• The optimal pattern of consumption is given
by:
C ,C 

1

2
• This will only change if there are changes in
the factors that shift or pivot the budget
constraint.
• Is this something that can be achieved by
fiscal policy?
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The Government Debt
• The government can effectively borrow large
sums for a long period of time, but is it
subject to any constraints?
• Although the government does not have to
balance its budget in every period, it is
assumed that the government must
ultimately balance its books.
• That is, at the end of time, the government’s
national debt must be zero.
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The Government Debt
• In the two period model, that we have been using, the end
of time is effectively at the end of the second period.
Therefore, the evolution of the government’s debt must be
as follows:
0  1  r G1  T1   G2  T2 
• Rewriting,
G2  T2 
0  G1  T1  
1  r 
• The government’s constraint is that the present discounted
value of the sum of deficits and surpluses must sum to zero.
This constraint simply means that any deficit or surplus
would have to be eventually reversed in present value
terms.
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Ricardian Equivalence
• The forward-looking rational consumer will know
this. Therefore, when faced with a change in taxes
or government spending, their anticipation would
be that the policy will eventually be reversed in
present value terms. In that case, they shouldn’t
view their lifetime resources as being any different,
and therefore there is no need to change
consumption.
• Under these conditions, fiscal policy will have no
effect on the economy – a proposition known as
Ricardian Equivalence.
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Does the timing of taxes matter for
consumption?
• The government delivers an immediate tax cut.
How should the household respond?
• According to the predictions of the Permanent
Income Hypothesis, consumption will only change
if lifetime resources change.
• Consumption will be constrained by the following
budget constraint:
C2
Y2  T2
C1 
 Y1  T1 
1 r
1 r
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Does the timing of taxes matter for
consumption?
• In this case, the present discounted value of
all consumption cannot exceed the present
discounted value of all disposable income.
• Ignoring government spending and starting
from a position of no debt, the tax cut will
then create a deficit of T1 .
• Effectively, this is the amount that the
government is giving to each household.
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Does the timing of taxes matter for
consumption?
• However, the government must have no
deficit at the end of period 2, implying:
0  1  r T1  T2
• The government constraint then states that in
present value terms the current tax reduction
must be offset in present value terms with a
future tax increase.
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Does the timing of taxes matter for
consumption?
T2  1  r T1
• Substituting this result into the budget
constraint gives:
C2
Y2  1  r T1
C1 
 Y1  T1 
1 r
1 r
C2
Y2
C1 
 Y1 
1 r
1 r
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Does the timing of taxes matter for
consumption?
• The tax policy does not change the intertemporal budget
constraint.
• As long as the government runs a balanced budget, the
timing of taxes is irrelevant and will have no impact on the
intertemporal budget constraint, and therefore consumption.
• When the government cuts taxes in period 1, a household
would experience a rise in their disposable income. Under
the auspices of the Keynesian model, consumption would
rise. However, the predications of the PIH are all together
different. Knowing that future taxes will be higher,
households will smooth their consumption by saving the tax
cut this period to pay for the higher taxes next period.
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The Neutrality of Government Spending
• Will an increase in government spending have any
effect on output? The answer is again no.
• The best way to view this is to assume that
government spending is just consumption that the
government undertakes on behalf of households.
• The government is essentially purchasing goods
and services and distributing them to households
for consumption.
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The Neutrality of Government Spending
• Suppose the government were to increase
government spending in period 1 and to
finance it by borrowing. In this case, the
budget constraint would appear as follows:
C1  G1  
C2
Y  T2
 Y1  2
1  r 
1  r 
• As before, the government budget constraint
implies that future taxes will have to rise by:
T2  1  r G1
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The Neutrality of Government Spending
• Substituting in this expression for the change
in future taxes, we will once again see that
nothing has happened to the intertemporal
budget constraint faced by households:
C2
Y2
C1  G1  
 Y1  G1 
1  r 
1  r 
• In this case, C1  G1  C1
• So, G1  C1
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The Neutrality of Government Spending
• An increase in government spending raises household
consumption in the first period, but the households know
that they will face a higher tax bill in the second period.
• As a result, the increase in consumption in the first period
will be offset by extra saving. All that has happened is that
government consumption has replaced private consumption.
Instead of households choosing their own consumption, the
government is doing it for them.
• As government spending crowds out household spending on
a one-to-one basis, there will be no change to aggregate
demand. Fiscal policy is once again neutral.
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Theoretical Debates on Ricardian Equivalence
• In stating the neutrality of fiscal policy, the theory
of Ricardian Equivalence argues that the
government has little role to play in the
macroeconomy.
• This summation, though, is only valid if we can be
sure that Ricardian Equivalence holds in its
entirety. This has led to further debate, and many
reasons have subsequently been forwarded arguing
the case for a more non-Ricardian view on fiscal
policy.
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Discounting
• Future tax increases will only matter if consumers are
sufficiently forward-looking. If households do not place much
weight on future utility, they will not worry so much about
future tax rises.
• One of the most logical reasons why a household might
discount the future is because human mortality means there is a
positive probability of death. However, a famous counterargument is put forward by Robert Barro. The reason is that
we care about the utility of our children and we would save
more so that we could increase bequests to our offspring.
• This is a controversial debate. Although there is ample
evidence that bequests are left, for this to maintain the
predictions of Ricardian Equivalence would require each
household to be treated as a dynasty. There will also be a large
number of possible exceptions to this rule, such as households
that have no children.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Borrowing constraints
• If households were permanent income consumers,
consumption would tend to be tied to current disposable
income. The household would ideally like to increase
current consumption, but cannot borrow against future
income. Therefore, consumption can only change when
current income changes.
• The government by cutting taxes can increase current
disposable income, which would lead to a rise in
consumption. Alternatively, the government could purchase
goods and services for households, enabling an increase of
consumption towards its desired level.
• In both cases, fiscal policy will have not neutral but positive
consequences for aggregate demand. Effectively, the credit
constraints are being circumvented through fiscal policy as
the government is just borrowing on behalf on households.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Interest rate effects
• Most households are likely to be net borrowers. Changes in
the interest rate will thus have income effects that work in
the same direction.
• Government may be able to borrow at a lower rate of
interest than individual households because it can always
raise taxes to fund its borrowing, lowering the chances of a
default.
• Therefore, by funding a cut in taxes or an increase in
government spending by borrowing, this reduces the
amount that credit constrained consumers need to borrow;
the government is really just borrowing on their behalf.
However, because the rate of interest the government pays
is lower, households are effectively swapping high interest
for low interest borrowing. This will be expected to
generate a positive income effect, increasing current
consumption and aggregate demand.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Global Applications 4.1
• Interest Rate Subsidies
• Changes in taxes can have
non-Ricardian effects
when the government can
borrow at a lower interest
rate than individual
households.
• Why is this the case?
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Distortionary taxes
• Non-lump sum taxes may create distortions which lead to
the failure of Ricardian Equivalence.
• Lower taxes might encourage more work, meaning that
income rises. Higher taxes may have the opposite effect.
• As the budget constraint will shift with changes in income,
we can no longer expect consumption to remain unchanged
in the face of fiscal policy changes.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• In this chapter, we have explored the nature of government
spending and taxation.
• We analysed the differences between government deficits
and national debt
• Then, we worked through the implications of fiscal policy
• Using the Keynesian cross model, we analysed planned and
actual expenditure functions.
• Finally, we analysed the theory of Ricardian Equivalence
with forward-looking consumers.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning