Deficit Financing, Debt Dynamics and
Ricardian Equivalence
1
• Define the primary deficit:
The total deficit is the primary deficit plus the interest
payments on government debt.
Here B is the nominal supply of short term bonds, i is the
short term nominal interest rate, and Dtp is the nominal
primary deficit.
2
• The annual evolution of nominal
government debt:
We assume that bonds are very short maturity just to keep things
simple: that way there is no change in value of government debt
when the interest rate changes.
We begin with a flow version of the government budget
constraint:
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set ∆M = 0
4
• The primary deficit is the reported deficit
less the governments net interest
payments.
• The total deficit is therefore itBt + Dtp
To keep things simple we have assume that bonds have a
maturity of one period.1
Also for simplicity, we assume that the interest rate is a constant.
5
• The result is an equation that links the evolution
of the bond supply to its past value: a difference
equation.
• Difference equations: the past of a state
variable determines its future values.
• Difference equations allow us to represent
dynamics.
6
• our basic debt accumulation equation:
This equation embodies our basic debt dynamics: the
accumulation of debt over time.
This says that debt grows due to the primary deficit and due
to interest rate payments on outstanding debt.
7
• Recall Dtp is the primary deficit: the difference
between
non-interest government outlays and government
revenues (Tx).
• Non-interest government outlays include
• Government expenditures G plus non-interest
transfer payments.
• The primary deficit differs from the reported
deficit by the amount of the interest payments
on government debt.
8
• We can also write this as
We now rewrite this as a fraction of GDP:
9
10
11
• This version of our debt dynamics equation also
says that
• Debt grows due to the primary deficit and due
to interest rate payments on outstanding debt,
• but since we are looking at the debt-to-gdp ratio
one additional factor enters:
• the rate of growth of GDP.
12
• Since we are focusing now on the
• debt-to-GDP ratio, when GDP grows this ratio
shrinks and we need to account for that.
13
• At this point is is very useful to think about a special
case:
• d = 0.
• In this case we see that the debt-to-GDP ratio grows if
• i > ^ Y N but shrinks if i < ^ Y N.
• That is, borrowing to make our interest payments
adds to the debt, but this can be offset by GDP
growth. On this observation hinges the entire question
of
• whether budget policy is sustainable.
14
• If the debt-to-GDP ratio grows unbounded,
• eventually the interest payments on the debt
will exceed the entire GDP.
• At this point (and obviously far before this) a
government can be considered bankrupt:
• its tax base can no longer provide the
revenues to meet its
• current interest obligations.
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16
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•
•
•
•
The solution to a difference equation tells us
the value of the state variable
(in this case, the debt-to-gdp ratio)
at each point in time.
• We can illustrate the evolution of the
• debt-to-gdp ratio graphically.
19
• In figure we show how a graph can be used to
analyze debt dynamics.
• Note that both axes measure debt, but at different
points in time.
• The horizontal axis is labeled bt and the
• vertical axis is bt+1.
• The graph includes a 45 deg line, along which bt+1 = bt
.
• That is, along this line the debt-to-GDP ratio is not
changing.
• We will refer to this as the steady-state locus.
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• The graph also includes another line,
• which represents our debt dynamics.
• For any current level of debt bt , the height of
the line is the debt next period.
• So given an initial level b0 of
• the debt-to-GDP ratio,
• we can follow the evolution over time in this
economy.
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Stability by Period: Farmer's Results
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• Recall that our debt dynamics were laid out in
equation (10),
• which we repeat here for convenience.
Again we simplify by holding constant the primary deficit-to-GDP
ratio, the interest rate, and the growth rate of GDP. So
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• In the steady state, the debt-to-GDP ratio is not
changing.
• If the economy is at the steady state, it stays
there.
Solving for the steady-state value of b we get
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We now ask if the steady state is stable. That is, if we are
near the steady state, will me move toward it?
Let us approach that question by subtracting the steady state
value of b from both sides of equation 15 to get
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Unstable Debt Dynamics
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Ricardian Equivalence Theorem: Questions
• Should government finance public budget deficit by
borrowing or by raising taxes?
• is it possible to cut tax rates without a cut in public
spending?
• David Ricardo. British economist, who wrote about 180
years ago that it is not.
• Ricardian Equivalence Theorem states that borrowing
more from private sector or taxing more have equivalent
outcome.
29
Ricardian Equivalence
Robert J. Barro, “Are Government Bonds Net Wealth?”
Journal of Political Economy (1974), 1095-1117.
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Assumptions
1.
2.
3.
4.
5.
6.
7.
8.
Agents are rational and farsighted.
Agents either live forever, or care about their progeny as
much as they care about themselves.
 This implies that agents are linked to the past and the
future (by immortality or bequests), and have an infinite
time horizon.
The belief that current budget deficits imply future taxes is
correct.
Taxes are lump sum.
The availability of the deficit spending does not alter the
political process.
No distributional effects. Households are homogeneous, so
that a representative agent model can be used.
No liquidity constraints.
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Capital markets are perfect.
The Argument (1)
• Question: Does it matter whether government
finances current spending through taxes or
debt?
• Assume the govt decreases lump-sum taxes in
the current period and finances the change with
debt:
 T  B
32
The Argument (2)
• According to Keynesian theory, AD should rise
because current disposable income increases.
• According to portfolio selection theory, the result is
due to an increase in the net wealth of the private
sector.
– Households own govt bonds, which they view as an asset,
hence they feel richer.
– Therefore, households increase consumption. This is a form
of fiscal illusion.
33
The Argument (3)
• The New Classical Economists argue that agents are
not fooled. They recognize that:
– In future periods, govt will have to pay interest on the
additional debt, and
– Govt will eventually have to repay the debt (assuming it does
not have an infinite maturity).
– For a given level of govt expenditures, the govt will have to
increase future taxes to pay the debt service and repay the
debt.
34
The Argument (4)
• Therefore, households will not view the bonds
as an increase in net wealth.
• They will subtract the present value of the
future taxes from it.
• For simplicity, let’s consider a bond of infinite
duration:
Tt  r  B; t  1, ..., 
35
The Argument (5)
• If the bonds and other assets are perfect substitutes, then the
subjective discount factor (for time preference in the PV) is
equal to the interest rate, and the present value of the tax
burden is:


Tt
r  B
T0  

 B
t
t
t 1 (1  r )
t 1 (1  r )
• It turns out that the present value of the additional taxes is
equal to the debt.
• Hence there is no difference between tax and debt finance in
terms of the effect on the economy. Govt borrowing is not
perceived as an increase in private wealth, and consumption
demand is not stimulated.
36
The Argument (6)
• Agents increase saving in anticipation of future tax
increases.
• This causes a reduction in private sector spending that
is exactly equal to the increase in government
spending.
• Deficit spending is not stimulative. It has no effect
whatsoever. Thus fiscal policy is useless at best.
Activist policy cannot work!
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The Opposing View
• Tobin and Buiter (1980) argue that the assumptions
are unrealistic, and that if the assumptions are
relaxed, then the Keynesian view is supported.
• Additionally, suppose that the bonds were sold entirely
to the central bank. (The new debt was fully
accommodated.)
– The money supply would be increased to finance the debt.
– Inflation would ensue. This is referred to as an inflation tax. If
wages move with prices, then there would be no real effect.
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The Opposing View (2)
• More from Tobin and Buiter:
– The inflation tax will fall only on those who hold the new
money
– Any individual can reduce their inflation tax by reducing
monetary holdings. Hence it is not a lump-sum tax.
– With an infinite horizon, the increase in money supply would
not cause an increase in the price level. How can this be
right?
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Barro’s Response
• In his later work, Barro makes it clear that he
views the “equivalence result” as a
benchmark—an extreme case that makes it
clear that the effects of deficit spending are
not as clear-cut nor as large as Keynesians
had suggested.
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Basic Proposition of the Ricardian Equivalence
Tax or Borrowing Does not Make Any Difference
Tomorrow
C2
Before Borrowing
Budget Constraint
After borrowing
budget constraint
C1 
C1 
C2
 w2 
 w1   

1 r
1 r 
C2
 
 w
 w1   1    2  2 
1 r
1 r 1 r 
C1
Today
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Ricardian Equivalence: Main Proposition
• It does not matter whether public deficit is financed by
raising tax rates or by borrowing from the private sector.
• More Borrowing now means higher rates of tax in the
future for repayment of debt.
• With higher amount of public debt now private
households save more in anticipation of higher taxes in
the future that government will impose on them to repay
the debt.
• Private households optimise intertemporally and
completely internalise public policy.
• Borrowing now or raising tax now are equivalent
strategies if both the government and household honour42
their own inter temporal budget constraints.
Limitations of Ricardian Equivalence Theorem
• Why was there a big concern on accumulation of public debt in 1970
and early 1980s? Also to debt accumulation in many developing
economies?
• By Ricardian Equivalence private saving rises against an increase in
the public sector deficit.
• If private sector saving compensates for public sector deficit then
there is no alteration in national saving in response to public debt.
• There is no crowding out between public and private sector.
• This does not hold when private agents face inter generational
borrowing-lending constraint or if it takes long time for government
to increase taxes to repay debt.
• By choosing deficit financing by borrowing government is promoting
inter generational transfers because current debts may be paid by
taxing people in the far distant future generation.
• Main issue in this intergenerational transfer is that how many people
save for their children, grand children or grand-grand children? 43