**Unformatted text preview: **Lecture 11 Extensions to the Baseline IS/MP/AS Model:
Fiscal Policy and Investment
Mark Gertler
NYU
Intermediate Macro Theory
Spring 2018 0 Fiscal Policy
We …rst introduce government spending Gt …nanced by lump sum taxes Tt
– Resource constraint
Yt = Ct + Gt – Government budget constraint
Gt = Tt
Gt exogenous Assume capital market perfect ! Ricardian Equivalence holds
– i.e., only present value of taxes a¤ects consumpton spending - not timing
– present value of taxes = present value of government expenditures Adding Fiscal Policy to Aggregate Demand Sector
Resource constraint
Yt = Ct + Gt Consumption demand
Ct = Pt
n
(Rt+1
)
Pt+1 Fiscal Policy Gt = Gt Ct+1Dt IS Curve with Fiscal Policy
Combining equations
Pt
n
(Rt+1
)
Pt+1 Yt Gt = Yt = Pt
n
(Rt+1
)
Pt+1 (Yt+1 Gt+1)Dt IS Curve (Yt+1 Gt+1)Dt + Gt Gt " ! IS curve shifts " (direct impact on demand)
Gt+1 " ! IS curve shifts down (households save in anticipation of higher taxes) Loglinear Model
bt
Let x log Xt log X ; X steady state value of Xt Start with Yt = Ct + Gt Linear approximation
dYt = dCt + dGt
dYt
dCt
dGt
Y
=C
+G
Y
C
G t
(=Given dX
X b t for small changes) ! loglinear approximation
x Y ybt = C cbt + G gbt Loglinear Model (con’t) Y ybt = C cbt + G gbt ! Loglinear resource constraint ybt = C
G
cbt + gbt
Y
Y Consumption demand Fiscal policy cbt = (rtn t+1 r ) + cbt+1 + dt gbt = gbt IS Curve with Fiscal Policy
b
cbt = Y
C yt Gg
b
C t IS curve ybt = c(rtn t+1 G b
r ) + ybt+1 + (g t
Y gb C
t+1 ) + dt
Y IS/MP/AS
given adpative expectations ( t+1 = t 1 and t= t 1) IS ybt = c(rtn t 1 G (g
b
rn ) + ybt+1 + Y
t MP
rtn = r + AS t + y (ybt ybt ) Cd
gbt+1) + Y
t t = (ybt ybt ) + t 1 LRAS bt
ybt = a (since yt = at + x, y = a + x and ybt = yt y ) Flexible Price Benchmark
Resource constraint
ybt = C
G
cbt + gbt
Y
Y IS curve
ybt = (rt G b
r ) + ybt+1 + (g t
Y LRAS gbt " ! cbt # with no e¤ect on ybt bt
ybt = a cbt = Y
ybt
C Gb
g
C gb C
t+1 ) + dt
Y Intuitively: economy on production possibility frontier. gbt " ! rt "! cbt #. Sticky Price Case
IS ybt = c(rtn t 1 G (g
b
rn ) + ybt+1 + Y
t MP
rtn = r + t + y (ybt AS t = (ybt ybt ) + t 1 ybt ) Cd
gbt+1) + Y
t Holding constant rtn; gbt " ! ybt " dybt = G b
dg t
Y Intuitively, output demand determined in short turn. Fiscal policy a¤ects demand. Fiscal Muliplier
Fiscal multplier dYt
dGt – i.e. the e¤ect of a one dollar increase in Gt on Yt (holding rtn constant)
We know
dyt = where yt Since dyt log Yt and gt
dYt
Y and dgt G
dgt
Y log Gt
dGt
G : dYt
G dGt
=
Y
Y G ! …scal multiplier of unity
dYt
=1
dGt Fiscal Policy with Liquidity-Constrained Consumers
2009 Fiscal stimulus package justi…ed on the basis of a multiplier between 1:5
and 2
– Need a fraction of consumers to face borrowing constraints to get a multiplier
this high Let Ctu
consumption by "unconstrained" households; Ctc
"Constrained" households consumption by Ct = Ctu + Ctc – Unconstrained households obey standard consumption/saving behavior – Constrained households consume equal to their disposable income
Ctu = Ytu Ttu Loglinear Consumption with Liquidity-Constrained Consumers
Aggregate consumption c cbc !
C cbt = C u cbu
+
C
t
t where Cc
C cbt = (1 c
b
)cbu
+
c
t
t Consumption by constrained households – Assume Ytc = Yt and Ttc = Tt and given C c = C
Ctc =
C c cbct = Yt Tt ! Y ybt
T bt !
Y
T
bt
cbct =
ybt
Ct
C Loglinear Consumption (Con’t)
Aggregate consumption
cbt = (1 c
)cbu
t + cbt Consumption of unconstrained households (assuming dt = 0)
cbu
t = cbu
t = (rtn
1
X t+1
n
(rt+i r ) + cbu
t+1 t+1+i i=0 Consumption by constrained households
cbct = Y
ybt
Ct T
bt
C r ) IS Curve with Liquidity-Constrained Households
Aggregate demand
C
G
cbt + gbt
Y
Y
c
cbt = (1
)cbu
t + cbt ybt =
cbu
t = cct = 1
X n
(rt+i ybt = (1 ) [ i=0 r ) i=0 Y
yt
C T
t
C Combine to form IS curve (and recalling
1
X t+1+i n
(rt+i C)
=Y t+1+i r )] + [ybt T
Gb
b t] + g
t
Y
Y IS Curve con’t
IS curve ybt = (1 ) 1
X n
[(rt+i t+1+i ) i=0 r ] + [ybt T
Gb
b t] + g
t
Y
Y bt implies feedback e¤ect: ybt depends on ybt
Senstitivity of cbu
t to y We can solve out for this e¤ect
ybt = 1
X i=0 n
[(rt+i t+1+i ) r ]+ 1
1 Gb
gt
Y 1 T
bt
Y Multiplier
IS curve
ybt = 1
X n
[(rt+i t+1+i ) r ]+ i=0 1
1 Multiplier = 1 1 > 1
dybt = 1
1 dYt
1
=
Y
1
1
dYt =
1 Estimates of :4 ! 1 1 1:7 G b
dg t !
Y
G dGt
!
Y G
dGt Gb
gt
Y 1 T
bt
Y Tax Multiplier
IS Curve
ybt = 1
X n
[(rt+i t+1+i ) r ]+ i=0 1
1 Gb
gt
Y 1 T
bt
Y Tax Multiplier
dYt = 1 dTt Note that the absolute value of the tax multiplier is less than the expenditure multiplier.
Only constrained households respond directly to the tax cut.
One can maximize the e¤ectiveness of the tax cut by targeting it toward constrained
households. The 2009 …scal stimulus did this by targeting bene…ts toward lower income households
and the unemployed. ...

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