Quantitative Group Project
ECON6008 International Money & Finance
Semester 2 (Int. August-September) 2025
Due date: Sunday 19 October, 11:59pm
1 The model (equations and variables)
1.1 The model in brief
The model that you need to analyse is a modiÖed version of the New-Keynesian small
open-economy (SOE) model in Justiniano and Preston (2010, henceforth JP), which in
turn is based on the model in Monacelli (2005) and Gali and Monacelli (2005). Compared
to the JP model, our modiÖed 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
foreign economy is also modeled di§erently than in the paper (see below for further details),
although we still assume that the foreign economy is essentially a closed economy. There
is also a cost-push shock that enters the domestic-price Phillips curve.
Aggregate áuctuations in the model are driven by 7 exogenous shocks. Four of these
shocks are domestic shocks: preference (consumer spending), risk premium, monetary
policy (interest rate), and cost-push shocks. Three of the shocks are foreign or external
shocks: foreign output, foreign ináation, and foreign interest rate shocks. These shocks
a§ect the domestic economy through their ináuence on the foreign economyís output,
ináation, and nominal interest rate. The model can be derived from the ground up with
micro-foundations, based on optimizing households, domestic Örms and importers, etc.,
resulting in a set of non-linear equations. We will instead work directly with the log
linearized equilibrium equations, listed below.
1.2 The log-linearized equations
Consumption Euler-equation (the IS equation):
Goods-market clearing condition:
The link between terms of trade and real exchange rate:
Changes (growth rate) of the terms of trade:
Domestic-price ináation (the "Phillips curve"):
The real marginal cost:
The wedge between CPI- and PPI-ináation:
The uncovered interest-parity (UIP) condition:
The net-foreign-assets position (the current account):
Imported-good ináation (based on the law of one price):
Monetary-policy (Taylor) rule:
Evolution of risk premium:
Evolution of preference shock:
Evolution of cost-push shock:
The monetary policy (interest rate) shock ^"m;t is assumed to be i.i.d. (with zero mean
and a constant variance). ;t, z;t, and H;t are i.i.d. risk-premium shock, preference
shock, and cost-push shock, respectively.
The foreign economy
We will treat the foreign economy as essentially a closed economy,
i.e. we can think of it as the "rest of the world" and as a large economy, much larger in
size compared to the domestic economy. In the benchmark speciÖcation, letís assume an
exogenous foreign economy, in a sense that each of foreign output, foreign ináation, and
foreign nominal interest rate is assumed to follow an AR(1) process:
where y
;t,
;t, and i
;t are i.i.d. foreign-output shock, foreign-ináation shock, and
foreign interest-rate shock, respectively.
In the alternative speciÖcation, letís assume that the foreign economy is represented by
a standard closed-economy New Keynesian model (in its log-linearized form):
Under this specÖcation, i
now denotes the degree of interest-rate smoothing in the foreign
economyís monetary policy (Taylor) rule. Also, "y
;t, " ;t, and "i
;t can be interpreted
as a foreign preference (consumer spending) shock, foreign cost-push shock, and foreign
monetary policy shock, respectively, assumed to follow
Here, as in the benchmark speciÖcation, y
;t,
;t, and i
;t are i.i.d. shocks.
DeÖnition of variables and shocks
NOTE: all hatted variables are in terms of log or
percentage deviation from the steady-state value, except for
b
it
, b
t
, b
H;t
, b
F;t
, b
t
, and
b
i
t
,
which are in terms of level deviation from the steady state (e.g. bit it
The Questions
___
1. Solve the model described above using Dynare, assuming the benchmark foreign
economy speciÖcation (equations (16.A)-(18.A)). Obtain the impulse response for 12 peri
ods to a one-time positive 1% shock to
(a) money supply or the domestic interest-rate shock ("m;t);
(b) preference shock ( z;t);
(c) risk premium shock ( ;t);
(d) foreign interest rate shock ( i
;t).
Analyse (i.e. explain the dynamics) and plot the e§ect of each of these shocks to
domestic output (yb
t
), consumption (bct), interest rate (
b
it), ináation (b
t
), domestic-currency
nominal depreciation (eb
c
t
), the "shocked" variable (e.g. if itís a foreign interest rate shock,
plot b
t
), the level of the nominal exchange rate, and the current account. Plot these eight
variables in one 4x2 Ögure (with 4 rows and 2 columns). Relate your analysis to
what you have learned in the Örst half of the course on the qualitative AA-DD model (e.g.
how are they the same and/or di§erent). For the money supply or the domestic
interest-rate shock, do you observe an overshooting of the nominal exchange rate? Explain
your answer.
2. Now assume that the foreign economy is represented by a closed-economy New
Keynesian model, i.e. equations (16.B)-(18.B) and (19)-(21). Redo question 1(d), i.e. a
one-time 1% foreign-interest rate shock. Relate and compare your responses to both
that under the qualitative AA-DD model and the responses under 1(c) (where the foreign
interest rate follows an AR(1) process). How and why are they di§erent (or the same)?
3. GFC-like shocks and exchange rate policies
Letís analyse the impact of a GFC-like shock in the foreign economy on the domestic
economy. For simplicity, assume that the foreign economy follows the benchmark speciÖ-
cation in (16.A)-(18.A). First, letís assume that there is a GFC-like event in the foreign
economy at time t = 0 that decreases the level of foreign output by 5%, i.e. assuming
an AR(1) process for foreign output, we have a negative 5% foreign output shock y
;t at
t = 0. After this period, there is no more shock and yb
t
simply follows an AR(1) process in
(16.A). E§ectively, under this assumption, we assume that the exposure of the GFC-like
event in the foreign economy to the domestic economy is through its e§ect on the cur
rent account (since yb
t
in the model directly ináuences the foreign economyís demand for
domestic products, i.e. domestic economyís exports).
(a) Analyze the e§ect of this GFC-like shock under the current policy rule with i = 0:75,
= 1:90, y = 0:05, y = 0:55, and e = 0. Plot the responses of yb
t
, bct
,
b
it
, b
t
,
b
e
c
t
,
b
yt
, the level of nominal exchange, and the current account in one (4x2) Ögure for
the Örst 12 periods. Explain their dynamics and relate your analysis to that under
the qualitative AA-DD model.
Now assume that in addition to the exposure to the domestic economy through the
current account, there is an added exposure through domestic householdsíholding of foreign
assets. In our model, this can be represented by a further negative consumer-spending
shock (just like the how we incorporate the spillover e§ect of the GFC in the AA-DD
model in class). Letís assume that this added exposure is equivalent to a negative 3%
consumer preference shock ( z;t) at t = 0; after this period, there is no more shock and
the preference level (^"z;t) simply follows an AR(1) process in equation (13). Hence, at
t = 0, we have two shocks: a negative 5% foreign output shock ( y
;t) and a negative 3%
consumer preference or spending shock ( z;t).
(b) Redo part (a) above under this two-shock assumption. How and why they are di§er
ent (or the same) compared to part (a)?
(c) In part (a) and (b) above, we assume a fully-áexible (áoating) exchange rate regime.
Suppose that the domestic central bank also directly intervenes in the foreign ex
change market, i.e. itís operating under a managed áoating exchange rate regime.
This policy can be analyzed within our model by assuming that
e = 0:80 > 0
The rest of policy rule coe¢ cients are unchanged. Redo part (b) above, where we
assume that the spillover from the GFC-like event in the foreign economy is repre
sented by two combined shocks (negative y
;t and z;t shocks). Analyze the e§ect in
comparison to the e§ect in part (b) (under the fully-áexible, áoating exchange rate
regime). Plot the same (4x2) Ögure as in part (b). Is this policy more e§ective in
terms of mitigating the e§ect of the spillover of the GFC-like shocks on yb
t
, b
t
, and
eb
c
t
than the fully-áoating exchange rate policy? Explain.
(d) Now assume that the central bank is operating under a Öxed exchange-rate regime.
SpeciÖcally, the monetary policy rule in equation (11) is replaced with the following
policy rule:
eb
c
t = 0
This policy rule e§ectively (and credibly) Öxes the nominal exchange rate at a spec
iÖed level. Redo question 3(b) (GFC event with two shocks). Your answer and
analysis should be in comparison to the freely-áoating exchange-rate regime ( e = 0
under the original policy rule) and managed-áoating regime ( e = 0:85 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 Önd bit = bi
t under the
Öxed-exchange rate regime, unless = 0), (iii) to solve the model under the Öxed regime
in 2(d), you should remove monetary-policy shock "m;t from the list of shocks in your .mod
Öle, as this shock now does not enter any of the equations.]
[Extra points: plot the variables under the three policies in the two-shock case (parts
(b), (c), (d)) in one (4x2) Ögure as described above, e.g. the plot for yb
t
in the (4x2) Ögure
should include three di§erent impulse responses.]
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.
