Handout on CashInAdvance Models of Money
•
Christiano and Eichenbaum (1992) “Liquidity E
f
ects and the Monetary
Transmission Mechanism”, AER, p. 346353.
1
Environment
•
Prefs:
E
0
∞
X
t
=0
β
t
[
u
(
c
t
)
−
v
(
n
s
t
)]
where
n
s
t
∈
[0
,
1] is labor supply,
c
t
≥
0 is consumption,
β
∈
(0
,
1)
,u
is strictly increasing, concave, and di
f
erentiable,
v
is strictly increasing,
convex, and di
f
erentiable with
v
0
(0) = 0 and
v
0
(1) =
∞
.
•
Techn:
y
t
=
θn
d
t
.
•
Govt. Budget Constraint is given by
P
t
τ
t
=
M
s
t
+1
−
M
s
t
where
M
s
t
is
the nominal money supply,
P
t
is the price level, and
τ
t
are real lump
sum taxes or transfers. The money supply evolves according to
M
s
t
+1
=
(1 +
µ
)
M
s
t
+
ε
t
where
µ
is the growth rate of the money supply and
unanticipated money shocks
ε
t
are mean zero and i.i.d.
•
Hhs can also buy or sell private nominal discount (noncontingent) bonds.
•
Timing:
—
(i) hh enters with
M
t
units of money and
B
t
units of money from its
prior bond activity;
—
(ii) Shock realized and lump sum taxes/transfers are paid;
—
(iii) the bond market opens, past bond holdings redeemed, hh pur
chases/sells
B
t
+1
at money price
Q
t
;
—
(iv) the hh separates: worker supplies labor to the
f
rm (receiving
W
t
n
s
t
units of money for her services) and the shopper purchases
consumption goods at price
P
t
;
—
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 Spring '07
 CORBAE
 Inflation, Trigraph, Mts, Pt ct

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