Transcript Government Sector and Fiscal Policy

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:
G 1  T1  B
Period 2:
G 2  (1  r ) B  T 2
Government’s Lifetime (Intertemporal) BC:
G1 
G2
1 r
 T1 
T2
1 r
PDV of Government Expenditures = PDV of Taxes
Households Budget Constraint:
Period 1: Y1  T1  c1  s
Period 2: Y 2  s (1  r )  T 2  c 2
Lifetime BC:
T2 
c2

y1 
  T1 
  c1 
1 r 
1 r 
1 r
y2
we = Present Discounted Value of C
• 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):
T2 
c2

y1 
 T1 
  c1 
1 r 
1 r 
1 r
y2
• Consumer is borrower (s < 0)
y1 
y2
1 r
H
T2 
c2

  T1 
H   c1 
H
1

r
1 r


• Graphically, there’s a “kink” in the budget
constraint.
• Government borrows at r < rH.
• Example: DT1 = -1 and DT2 = (1+r)
• Lender  Ricardian Equivalence
• Borrower  Ricardian Equivalence fails!
• Tax cuts for “constrained” borrowers work like a
low interest loan. Hence Dwe > 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
max u ( c1 , c 2 )
y 1  c1  s
• Anticipated Program:
we  y1 
y2  B
1 r
y 2  s (1  r )  B  c 2
 c1 
c2
1 r
 DB > 0  increases c1 *, c 2 * (each by less
than B) and unambiguously welfare.
• Unanticipated Program:
c1 *
constant
c2 *
increases by B
Welfare unambiguously increases (but by less
than anticipated program).
Figure 8.17 Pay-As-You-Go Social
Security for Current Old
Future Generations:
subject to
y 1  S  c1  s
y 2  s (1  r )  B  c 2
• Lifetime BC:
we  y1 
max u ( c1 , c 2 )
y2
1 r
S
B
1 r
 c1 
c2
1 r
• Effect of B > 0:
  0 and D c1 , D c 2  0 if n  r 


D we   0 and D c1 , D c 2  0 if n  r 
  0 and D c , D c  0 if n  r 
1
2


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:
max u ( c1 , c 2 )
subject to
g
y1  c1  ( s  s )
y 2  ( s  s )(1  r )  c 2
g
• 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.
• 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.