Lecture 15 1

Macroeconomic Analysis 2003

Fiscal Policy 2: Ricardian Equivalence Theorem

And Inflation Tax

Lecture 15 2

Contents• Main point of the Ricardian Equivalence Theorem

(RET)• Graphical and Algebraic Illustration of RET• Numerical Example of RET• Limitations of RET• Deficit financing by printing money:Seigniorage• Optimal Inflation tax rate• Why governments like inflation tax?• Dangers of excessive inflation

Lecture 15 3

Ricardian Equivalence: Main Proposition

• How important is a tax cut? • Should government finance deficit by borrowing

or by raising taxes?• Ricardian Equivalence Theorem is after David

Ricardo.• British economist, who wrote about 180 years ago

that it does not matter whether government finances its deficit by

• borrowing or • taxes.

Lecture 15 4

Ricardian Equivalence: Main Proposition

• If it borrows now it raises tax in future for repayment of its debt.

• With more current debt 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 only or tax only strategy does not matter if both the government and household honour their own inter temporal budget constraints.

Lecture 15 5

Basic Proposition of the Ricardian EquivalenceTax or Borrowing Does not Make Any Difference

r

ww

r

CC

112

12

1

rr

ww

r

CC

11122

112

1

C1

C2

Before Borrowing Budget Constraint

After borrowing budget constraint

Today

Tomorrow

Lecture 15 6

Preference of households:

2121 lnln, CCCCU

Endowments: 21 ,ww

Government policy: BGG ,,,, 2121 Budget constraint for N identical households (in real terms)

Period 1: 111 wbC

Period 2: 22 1 rbC Budget constraint for the Government:

Period 1: 11 NBG

Period 2: 22 1 NrBG

Model Economy for Ricardian Equivalence Theorem

Lecture 15 7

Tax Spending and Borrowing StrategiesInter-temporal budget constraint for the government:

r

NN

r

GG

112

12

1

Two strategies of financing fixed amount of 1G and 2G

(i) Taxes only strategy: 0,,,, 2121 BGG

(ii) Borrowing strategy BGG ,,0,, 2121 Market clearing for goods in period 1 and 2:

111 NwGNC

222 NwGNC

Lecture 15 8

Optimisation for Ricardian Equivalence Theorem Inter temporal budget constraint for individuals

r

T

r

wTw

r

CC

11122

112

1 (2)

where 11 NT 22 NT

r

T

r

WTW

r

CCCCL

1

2

1

211

1

212ln1ln

First order condition for optimisation:

rC

C1

1

1

2

=> 12 1 CrC

Using it in the intertemporal budget constraint:

r

T

r

WTWC

1

2

1

2111

11

Lecture 15 9

Given that number of households remains N The strategy 1 gives solution to consumption as above. There is no borrowing but only taxes in both periods.

Per Capita Consumption 11*1 gwc ; 22

*2 gwc .

In strategy 2 government cuts taxes to 0 in the first period and borrows to finance services and pays back by paying higher taxes in period 2. These two financing scheme are equivalent. Because if

government borrows 1 now, it has to pay back r1 in

period 2. Tax also has to increase by r1 in period 2. People anticipate higher taxes in future and save more in period 1 to be able to pay in period 2. These two effects offset each other.Both strategies of financing public deficit yields the same result.

Conclusion of the Ricardian Equivalence Theorem

Lecture 15 10

Numerical Proof of Ricardian Equivalence Theorem -1 Tax only Strategy

Endowments: 100,100, 21 ww Interest rate 5% Lump Sum Taxes in periods 1 and 2

1 = 20 ; 2 = 20 Thus the government is committed to provide services

05.1

1002.01002.0R = 39.04

Using these information in consumption function for period

05.1

8080

9.1

1

1

1

1

2

1

2111

r

T

r

WTWC

=82.2

Consumption in period 2

12 1 CrC = 0.9(1.05)(82.2) = 77.8

Lecture 15 11

2T = ? if 1T = 0 (it will certainly be higher)

Fix the consumption level as before at 1c = 82.2

05.01

2

05.01

100100

9.01

11

TC

05.01

2

05.01

100100

9.01

12.82

T

1.4105.1

1001009.12.8205.12

T

Thus taxes in period 2 has risen to 41.1.

Loan repayment 05.1301 rB = 31.5;

12 1 crc = 2.8205.19.0 = 77.68 Since households know that they have to pay so much of taxes in period 2, they increase their saving in period 1 in anticipation of higher taxes in period 2.

Borrowing strategy: period 1 borrowing of 30

Lecture 15 12

Limitations of Ricardian Equivalence TheoremWhy 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?

Lecture 15 13

Nominal Deficit: MTG (1)

Real deficit : P

MS

(2)

By multiplying and dividing by M: P

M

M

MS

(3)

Steady state inflation rate equals growth rate of money supply:

M

Me (4)

Thus segniorage depends upon growth rate of money supply and real money balances. Including demand for real money balances:

M

MrLY

M

MrLY

M

M

P

M

M

MS e (5)

Segniorage increases with growth rate of money supply but money demand decreases with higher rate of expected inflation.

Deficit Financing by Printing Money

Lecture 15 14

Start from real money balances equal to 1000 and use eight different inflation rates from 0% to 50%. In the steady state, the inflation rate equals to the growth rate of money supply. Revenue from inflation tax equals the product of inflation rate and the real money balances which in the base for the inflation tax. Seigniorage is highest when the inflation rate is 10 percent.

Table 4 Inflation rate, real balances and seigniorage (revenue from inflation tax )

0% 1% 2% 5% 10% 20% 25% 50%

Real balances (M/P)

1000 905 819 607 368 135 82 7

Revenue from inflation tax

0 9.05 16.38 30.35 36.8 27 20.5 3.5

Inflation Tax: A Numerical Example

Lecture 15 15

Seigniorage

0

10

20

30

40

00.

010.

020.

05 0.1

0.2

0.25 0.

5

Inflation

Sei

gn

iora

ge

reve

nu

e

Series2

Laffer Curve For Seigniorage

Lecture 15 16

Seigniorage as Percentage of GDP, 1997-98

(Miles and Scott Figure 12.10)

Lecture 15 17

Exercises

• Does it make difference if the deficit if financed by more taxes or by more borrowing?

• Proof of Ricardian Equivalence

• Household utility with and without public goods

• Implications of borrowing from the private sector or the central bank

• How does inflation tax reduce the debt burden for governments?