Quantitative Group Project
ECON6008 International Money & Finance, Semester 1 2023
School of Economics, The University of Sydney
Instructor: Denny Lie
Due date: Friday 2 June, 11:59pm  — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —
1 The model (equations and variables)
1.1 The model in brief
The model you will analyze is a simpli…ed version of the New-Keynesian small open-
economy (SOE) model in Justiniano and Preston (2010), which in turn is based on the
model in Monacelli (2005) and Gali and Monacelli (2005). Compared to Justiniano and
Preston’s model, our simpli…ed model assumes that the law of one price (LoP) holds for
all imported retail goods and there is no price indexation for these imported goods. The
model is also extended to include labor-supply shocks, which could be used as a proxy
for the supply-side disruption of the COVID-19 pandemic. Aggregate ‡uctuations in our
model model are driven by 7 exogenous shocks: risk premium, monetary policy (money
supply), preference (consumer spending), labor supply, foreign in‡ation, foreign output,
and foreign interest rate.
The model can be derived from the ground up with micro-foundations, based on op-
timizing households, domestic …rms and importers, etc., resulting in a set of non-linear
equations. We will instead work directly with the log-linearized equilibrium equa-
tions, listed below.
1.2 The log-linearized equations
Consumption Euler-equation (the IS equation):
bct = h
1 + h
bct1 + 1
1 + h
Etbct+1 1
1 h
1 + h
hbit Etbt+1i+ g^t (1)
Goods-market clearing condition:
byt = (1 )bct + byt + (2 )bSt (2)
The link between terms of trade and real exchange rate:
bqt = (1 )bSt (3)
Changes (growth rate) of the terms of trade:bSt bSt1 = bF;t bH;t (4)
1
Domestic-price in‡ation (the "Phillips curve"):
(bH;t H ^H;t1) = Et (bH;t+1 H ^H;t) + (1 H)(1 H)
H
cmct (5)
The real marginal cost: cmct = 'byt + bSt + bct "^s;t (6)
The wedge between CPI- and PPI-in‡ation:
bt = bH;t + bSt bSt1 (7)
The uncovered interest-parity (UIP) condition:
bit bit = Etbect+1 bat + Etbt+1 (8)
The net-foreign-assets position (the current account):
byt bct = bat 1bat1 +
(1 )bqt (9)
Imported-good in‡ation (based on the law of one price):bF;t = bect + bt (10)
Monetary-policy (Taylor) rule:bit = ibit1 + bt + ybyt + ybyt + ebect "m;t (11)
Evolution of risk premium: bt = bt1 + ";t (12)
Evolution of foreign output: byt = ybyt1 + "y;t (13)
Evolution of foreign in‡ation: bt = bt1 + ";t (14)
Evolution of foreign interest rate:bit = ibit1 + "i;t (15)
Evolution of preference shock:
g^t = g g^t1 + "g;t (16)
Evolution of labor-supply shock:
"^s;t = s"^s;t1 + s;t (17)
2
De…nition of variables and shocks NOTE: all hatted variables are in terms of log or
percentage deviation from the steady-state value, except for bit, bt, bH;t, bF;t, bt , and bit ,
which are in terms of level deviation from the steady state (e.g. bit it i).
bct consumption (per capita)bit nominal interest ratebt CPI in‡ationbyt outputbSt terms of trade (price of exports in terms of imports)bqt real exchange ratebH;t domestic-goods (PPI) in‡ationbF;t imported-goods in‡ationcmct real marginal costbat domestic-households’holding of foreign assetsbect domestic-currency depreciation rate (% change in the exchange rate)byt foreign outputbt foreign in‡ationbit foreign interest ratebt relative risk premiumbgt consumer preference
"^s;t exogenous labor-supply disruption
"m;t monetary-policy shock (i.i.d.)
";t risk-premium shock (i.i.d.)
"y;t foreign-output shock (i.i.d.)
";t foreign-in‡ation shock (i.i.d.)
"i;t foreign interest-rate shock (i.i.d.)
"g;t preference shock (i.i.d.)
s;t labor-supply shock (i.i.d.)
3
D
e…
n
it
io
n
of
p
ar
am
et
er
s
an
d
th
ei
r
ca
li
b
ra
ti
on
P
ar
am
et
er
s
D
e…
ni
ti
on
V
al
ue

in
ve
rs
e
in
te
rt
em
p
or
al
el
as
ti
ci
ty
of
su
bs
ti
tu
ti
on
1

op
en
ne
ss
pa
ra
m
et
er
0.
22

el
as
ti
ci
ty
of
su
bs
ti
tu
ti
on
b
et
w
ee
n
do
m
es
ti
c
an
d
im
p
or
te
d
go
od
s
0.
85

su
b
je
ct
iv
e
di
sc
ou
nt
fa
ct
or
0.
99
H
pr
ob
ab
ili
ty
of
pr
ic
e
…x
it
y
fo
r
do
m
es
ti
c
go
od
s
0.
70

ri
sk
-p
re
m
iu
m
pa
ra
m
et
er
0.
01
'
in
ve
rs
e
Fr
is
ch
la
b
or
-s
up
pl
y
el
as
ti
ci
ty
1.
26
h
de
gr
ee
of
ha
bi
t
fo
rm
at
io
n
0.
30

co
ns
um
pt
io
n
el
as
ti
ci
ty
of
pr
ef
er
en
ce
sh
oc
k
0.
12
H
de
gr
ee
of
pr
ic
e
in
de
xa
ti
on
0.
25

i
T
ay
lo
r-
ru
le
in
te
re
st
sm
oo
th
ne
ss
0.
75


T
ay
lo
r-
ru
le
re
sp
on
se
to
in
‡a
ti
on
1.
85

y
T
ay
lo
r-
ru
le
re
sp
on
se
to
ou
tp
ut
0.
05


y
T
ay
lo
r-
ru
le
re
sp
on
se
to
ou
tp
ut
gr
ow
th
0.
70

e
T
ay
lo
r-
ru
le
re
sp
on
se
to
ex
ch
an
ge
-r
at
e
‡u
ct
ua
ti
on
s
0


A
R
(1
)
co
e¢
ci
en
t
of
ri
sk
-p
re
m
iu
m
sh
oc
k
0.
95

y

A
R
(1
)
co
e¢
ci
en
t
of
fo
re
ig
n-
ou
tp
ut
sh
oc
k
0.
55



A
R
(1
)
co
e¢
ci
en
t
of
fo
re
ig
n-
in
‡a
ti
on
sh
oc
k
0.
50

i
A
R
(1
)
co
e¢
ci
en
t
of
fo
re
ig
n
in
te
re
st
-r
at
e
sh
oc
k
0.
50

g
A
R
(1
)
co
e¢
ci
en
t
of
pr
ef
er
en
ce
sh
oc
k
0.
70

s
A
R
(1
)
co
e¢
ci
en
t
of
la
b
or
-s
up
pl
y
sh
oc
k
0.
65

m
,


,

y
,


,

i
,

g
;
s
st
an
da
rd
de
vi
at
io
ns
of
sh
oc
ks
1
4
The Questions
___
1. Solve the model described above using Dynare. Obtain the impulse response for 10
periods to a one-time 1% shock to
(a) money supply or the domestic interest-rate shock ("m;t);
(b) preference ("g;t);
(c) labor supply (s;t);
(d) foreign interest rate shock ("i;t).
Analyze (i.e. explain the dynamics) and plot the e¤ect of each of these shocks to
domestic output (byt), consumption (bct), interest rate (bit), in‡ation (bt), domestic-currency
nominal depreciation (bect), and the "shocked" variable (e.g. if it’s a foreign output shock,
plot byt ). Plot these six variables in one 3x2 …gure or plot (with 3 rows and 2
columns). Relate your analysis to what you have learned in the …rst half of the course
(the qualitative AA-DD model). For the money supply or the domestic interest-rate shock,
do you observe an overshooting of the nominal exchange rate?
[Extra points: plot the evolution of the level of nominal exchange rate and the current
account in a separate …gure and explain the dynamics.]
2. COVID-19 pandemic and monetary and exchange-rate policies.
Let’s analyze the economic impact of the COVID-19 pandemic using this model, with
several di¤erent assumptions on the central bank’s monetary and exchange-rate policies.
Here, assume that the COVID-19 pandemic "shock" is simply proxied by a one-time 15%
negative preference (consumer-spending) shock at period 1 (2020.Q1):
Period
(Quarter)
1
(2020.Q1)
Preference shock ("g;t) 15%
Note that this simple representation cannot fully capture the e¤ect of the COVID-19
pandemic as the actual pandemic shocks a¤ect both the supply-side and the demand-side
of the economy. The preference shock considered here is a demand shock — hence, we can
only capture the demand-side e¤ect of the pandemic.1 Nevertheless, we could still analyze
1The preference shock in the model is a shock that in‡uences household intertemporal consumption-
saving decisions. A negative preference shock thus serves as a proxy for a reduction in aggregate demand
during the pandemic, e.g. due to lost labor income or an increase in household income uncertainty which
leads to a precautionary saving behaviour.
5
the impact of the pandemic on several key macroeconomic variables under several di¤erent
central bank policies.
(a) Analyze the e¤ect of this pandemic shock under the current policy rule with i = 0:75,
= 1:85, y = 0:05, y = 0:70, and e = 0. Plot the responses of byt, bct, bit, bt,bect , and bgt in one (3x2) …gure. Explain their dynamics. In another (2x1) …gure, plot
the evolution of the level of nominal exchange rate and the current account. How
are the responses here di¤erent (or the same) compared to question 1(b) (where
the shock size is 1%)?
(b) In the model above, we assume a fully-‡exible (‡oating) exchange rate regime. Sup-
pose that the central bank also directly intervenes in the foreign exchange market, i.e.
it’s operating under a managed ‡oating exchange rate. This policy can be analyzed
within our model by assuming that
e = 0:75 > 0
The rest of policy rule coe¢ cients are unchanged. Analyze the e¤ect of the pandemic
shock under this new assumption, in comparison to the e¤ect in part (a). Plot
the same (3x2) …gure and (2x1) …gure as in part (a) above. Is this policy more
e¤ective in terms of mitigating the e¤ect of the pandemic shock on byt, bt, and bect
than the fully-‡oating exchange rate policy? Explain.
(c) Now assume that the central bank is operating under a …xed exchange-rate regime.
Speci…cally, the monetary policy rule in equation (11) is replaced with the following
policy rule: bect = 0
This policy rule e¤ectively (and credibly) …xes the nominal exchange rate at a speci-
…ed level. Redo question 2(b). Your answer and analysis should be in comparison
to the freely-‡oating exchange-rate regime ( e = 0 under the original policy rule)
and managed-‡oating regime ( e = 0:75 under the original policy rule).
[Notes/tips: (i) Dynare does not plot the impulse response of a variable if that variable
is always constant (zero deviation from the steady state), (ii) since the foreign-debt holding,bat, enters the UIP condition in equation (8), you will generally not …nd bit = bit under the
…xed-exchange rate regime, unless = 0), (iii) to solve the model under the …xed regime
in 2(c), you should remove monetary-policy shock "m;t from the list of shocks in your .mod
…le, as this shock now does not enter any of the equations.]
[Extra points: plot the variables under the three policies in one (3x2) …gure and one
(2x1) …gure as described above, e.g. the plot for byt in the (3x2) …gure should include three
di¤erent impulse responses.]
6
References
[1] Gali, J. and T. Monacelli. 2005. "Monetary policy and exchange rate volatility in a
small open economy". Review of Economic Studies 72: 707-734.
[2] Justiniano, A. and B. Preston. 2010. "Monetary policy and uncertainty in an empirical
small open-economy model". Journal of Applied Econometrics 25: 93-128.
[3] Monacelli, T. 2005. "Monetary policy in a low pass-through environment". Journal of
Money, Credit, and Banking 37(6): 1019-1045.