Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 2 pptx
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 2 pptx
... (2. 4 .25 )
Population regression 51
0 10 20 30
0
0 .2
0.4
0.6
0.8
1
impulse response
0 1 2 3
10
0
10
1
10
2
spectrum
−15 −10 −5 0 5 10 15
2. 2
2. 4
2. 6
2. 8
3
3 .2
covariogram
20 40 60 80
−3
2. 5
2
−1.5
−1
−0.5
0
0.5
sample ... c
t
+(1−β) U
y
(I − βA
22
)
−1
C
2
w
t+1
(2. 6.18a)
b
t
= U
y
(I −βA
22
)
−1
z
t
−
1
1 − β
c
t
(2. 6.18b)
y
t
= U
y
z
t
(2. 6.18c)
z
t+1
= A...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 8 pptx
... the state-contingent consumption to-
day and the promised discounted utility tomorrow are functions of the initial
promised discounted utility levels.
Define v as the expected discounted utility ... extensive cross-history
and cross-time consumption smoothing. The constant-fractions-of-consumption
characterization comes from these two aspects of the theory: (1) complete mar-
kets, and (2) a ho...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 14 pptx
... is simpli ed to one where
utility function (14 .2. 1) is maximized subject to resource constraint (14.6 .2)
with quantities of intermediate inputs given by equation (14.6. 12) . The first-
order condition ... (14 .2. 5a)
F
2
(K, X)=
∂Xf(K/X)
∂X
= f
ˆ
K
− f
ˆ
K
ˆ
K. (14 .2. 5b)
14 .2. 1. Balanced growth path
We seek additional technological assumptions to generate market outcomes...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 1 potx
... insured away. Higher
present-value-of-endowment consumers will have permanently higher consump-
tion than lower present-value-of-endowment consumers, so that there is a non-
degenerate cross-section ... section
6
See Diaz-Gim´enez,Quadrini, and Rıios-Rull (1997), Krueger and Perri (20 03a,
20 03b), Rodriguez, D´ıiaz-Gim´enez, Quadrini, nd R´ıos-Rull (20 02) and Davies
and Shorrocks (20 00)....
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 3 docx
... 1isnotknownatt.Thatis,
t+1
is realized at (t +1), after u
t
has been chosen at t.Inproblem(3 .2. 1)–
(3 .2. 2), uncertainty is injected by assuming that x
t
follows a random difference
equation.
Problem (3 .2. 1)–(3 .2. 2) continues ... cycles.
3 .2. Stochastic control problems
We now consider a modification of problem (3.1.1) to permit uncertainty. Es-
sentially, we add some well-placed shoc...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 4 ppt
... that
m = 2. The vectors [v
1
,v
2
]obey
v
1
v
2
=
r
1
r
2
+
βP
11
J
1
βP
12
J
1
βP
21
J
2
βP
22
J
2
v
1
v
2
.
Then
v
1
v
2
=
I − β
P
11
J
1
P
12
J
1
P
21
J
2
P
22
J
2
−1
r
1
r
2
. ... T ([v
1
,v
2
]) that maps a pair of vectors [v
1
,v
2
]intoapairof
vectors [tv
1
,tv
2
]:
2
tv
1
=max{R
1
+ βP
11
1v
1
+ βP
12
1v
2...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 5 doc
... implies
µ
t
= −
V
22
−1
V
21
x
t
. (5.5.10)
Butnoticethatbecause(V
21
V
22
) is the second row block of the inverse of V ,
V
21
V
22
V
11
V
21
=0
which implies
V
21
V
11
+ V
22
V
21
=0.
Therefore
−
V
22
−1
V
21
= ... y
0
is evidently
y
t+1
= V
W
t
11
W
12, t
0 W
t
22
V
−1
y
0
(5.5.8)
where W
12, t
for t ≥ 1 obeys the recursion
W
12, t
= W
t−1
1...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 6 docx
... =
µ
i
n
h=ρ(1)
µ
h
.
Then
γ
2
(j)=Prob{w
2
=˜w
j
| w
1
≥ w
1
} =
n
i=ρ(1)
P
1
(i, j) δ
1
(i) .
For i ≥ ρ (2) , define
δ
2
(i)=Prob{w
2
=˜w
i
| w
2
≥ w
2
∩ w
1
≥ w
1
}
or
δ
2
(i)=
γ
2
(i)
n
h=ρ (2)
γ
2
(h)
.
Then
γ
3
(j)=Prob{w
3
=˜w
j
| ... w
1
}
or
δ
2
(i)=
γ
2
(i)
n
h=ρ (2)
γ
2
(h)
.
Then
γ
3
(j)=Prob{w
3
=˜w
j
| w
2
≥ w
2
∩ w
1
≥ w
1
}
=
n
i=ρ (2)
P...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 7 pdf
... ×k
1
; b
2
is n × k
2
; r
1
is n × n; r
2
is n × n; q
1
is k
1
×k
1
; q
2
is k
2
×k
2
; s
1
is k
2
× k
2
; s
2
is k
1
× k
1
; w
1
is n ×k
1
; w
2
is n ×k
2
; m
1
is k
2
× k
1
;andm
2
is k
1
× k
2
. ... P
2t
1
=0:
P
2t
=(A
t
− B
1t
F
1t
)
T
P
2t+1
(A
t
− B
1t
F
1t
)+
R
2
+ F
T
1t
S
2
F
1t
− (A
t
− B
1t
F
1t
)
T
P
2t+1
B
2t
B
T
2t
P
2t+1
B
2t
+ Q
2
−1
B...
Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 9 pdf
... issued by the government. We
can also think of them as being issued by a private bank.
Time-0 trading 26 5
Offer curve
Feasibility line
c
t
t+1
c
t-1
t
y
t
t
cc
c
c
c
y
t
t+1
1
1
2
2
2
3
2
1
0
1
,
c
t
t
Figure ... these equilibria is credible, in the sense of subgame perfection, to be studied
extensively in chapter 22 .
Narayana Kocherlakota (1998) has compared gift-giving and monet...
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