Government &Tax Policies in 2-Period CE Model

Government Expenditures

Ricardian Equivalence

Capital Market Imperfections

Social Security

2-Period Model w/ Government

• Recall effect of taxes in one-period model: G = T• Consider two-period CE model w/ exogenous income.• Government Budget Constraint

Period 1:

Period 2:

Government’s Lifetime (Intertemporal) BC:

PDV of Government Expenditures = PDV of TaxesGG

rT

T

r12

12

1 1

BTG 11

22 )1( TBrG

Households Budget Constraint:

Period 1:

Period 2:

Lifetime BC:

we = Present Discounted Value of C

yy

rT

T

rc

c

r12

12

12

1 1 1

scTY 111

222 )1( cTrsY

• Optimal Consumption: MRSc1,c2 = (1+r)

• Note: For a given interest rate r, only changes in we will affect consumption and welfare.

• Market Clearing: B = s

y1 = c1 + G1

y2 = c2 + G2

• Remark – Consistency between BC and Market Clearing.

Effects of Government Expenditures

• Government BC changes in PDV of G must be balanced by PDV of T.

• Household BC PDV of G creates income effects.

• Increase in G1 (temp) Higher equilibrium r

• Increase in G2 (future) Lower equilibrium r

• Permanent increase in G Small effects on r.

Effects of Permanent Changes in Government Expenditures

• Permanent changes in G: Historical growth in size of government.

1930 1990

G/GDP 8% 20%

Gov Spend/GDP 10% 33%

Real Interest Rate 4.5% 5%

Government Spending Shocks and Interest Rates

Taxes

Ricardian Equivalence Proposition:• Financing a given amount of G by T or B are

equivalent.• For a given level of G, a current tax cut (which

increases BD) has no effect on equilibrium consumption, interest rates, or welfare.

• Result also holds with labor market & production under lump-sum taxation.

Application: G.H.W. Bush and the 1992-93 Tax Withholding Reduction

• Beginning of 1992 - $25 billion withholding reduction. No overall tax reduction

for 1993.

• No evidence that real consumption increased between 1992:Q1 and 1993:Q1.

• Supports Ricardian Equivalence.

Figure 8.25 Real Consumption of

Services, 1991–1993

• Evidence (Mixed)

(i) Temporary tax rebates do little to affect aggregate consumption. (supports)

(ii) Public is aware of “burdens” of national debt on future generations. (supports)

(iii) Large Tax cuts (even temporary) do tend to stimulate consumption and lead to higher long-term interest rates. (conflicts)

(iv) Large budget deficits in 1980s and economic expansion conflicts with Ricardian Equivalence. (conflicts)

• Ricardian Equivalence says that tax policies by themselves are irrelevant (only G matters).

• Problems with Ricardian Equivalence:

(1) Unequal Tax Burdens – redistributes income.

(2) Taxes are NOT lump-sum – may have substitution effects. (Need production & labor market in model).

(3) Intergenerational Transfers

(4) Capital Market Imperfections

Capital Market Imperfections

• How do individuals react to tax cuts when they face different borrowing and lending rates?

• Lending rate = r < rH = borrowing rate• Consumer is lender (s > 0):

• Consumer is borrower (s < 0)

yy

rT

T

rc

c

rH H H12

12

12

1 1 1

r

cc

r

TT

r

yy

1112

12

12

1

• Graphically, there’s a “kink” in the budget constraint.

• Government borrows at r < rH.

• Example: T1 = -1 and T2 = (1+r)

• Lender Ricardian Equivalence• Borrower Ricardian Equivalence fails! • Tax cuts for “constrained” borrowers work like a

low interest loan. Hence we > 0 and increases current consumption.

Intergenerational Transfers

• Two types of Social Security Programs

(1) Pay-As-You-Go

Benefits to old generation financed by taxing current young generation.

(2) Fully Funded

Government sponsored saving accounts which are retained until retirement.

Pay-As-You-Go

• Two period “overlapping generations” model• Definitions:

NY = young population

NO = old population

n = population growth rate

NY = (1+n)NO

S = social security tax paid by each young.

B = social security benefits paid to each old.

• Two Period Overlapping Generations:

Period 1 Young (“Y”)

Period 2 Old (“O”)• Assume in each period (except initial) G = 0 and

there are zero net taxes T = 0.• Zero Net Taxes: Total SS Taxes = Total SS

Benefits:

SNY = BNO S = B/(1+n)

Question: Can such a pure transfer (no net change in taxes) affect consumption and welfare?

Initial Generation:

subject to

• Anticipated Program:

B > 0 increases (each by less than B) and unambiguously welfare.

),(max 21 ccu

scy 11

22 )1( cBrsy

r

cc

r

Byywe

11

21

21

**, 21 cc

• Unanticipated Program:

constant

increases by B

Welfare unambiguously increases (but by less than anticipated program).

*1c

*2c

Figure 8.17 Pay-As-You-Go Social Security for Current Old

Future Generations:

subject to

• Lifetime BC:

• Effect of B > 0:

),(max 21 ccu

scSy 11

22 )1( cBrsy

r

cc

r

BS

r

yywe

1112

12

1

rnifccand

rnifccand

rnifccand

we

0,0

0,0

0,0

21

21

21

Figure 8.18 Pay-As-You-Go Social Security for Future Generation

US Population Growth: 1820-1997

US Real Interest Rates: 1930-2005

• Remarks:(1) Population growth has been declining.(2) Low (real) interest rate policies benefit the

PAYG system.(3) Less restrictive immigration policy may allow

PAYG system to be Pareto improving.(4) PAYG system discourages private saving.

Fully Funded SS• A fully funded program that simply sets aside a

required level of sg.• Consumer’s Problem:

subject to

• FF program only improves welfare relative to pay-as-you-go if n < r.

• In theory, FF program can do no better than “free market” choices.

• Practical issue – FF can only improve welfare relative if government can do better than individuals (“free market”) at choosing sg.

),(max 21 ccu

)(11gsscy

22 )1)(( crssy g

• Even if n < r, there are other issues when transitioning from PAYG to FF:(1) Benefits current young generation but

hurts current old.(2) Current old benefits can be financed by running budget deficits and taxing future generations. Possibly Pareto improving.