數學代寫 - ECON6008: International Money & Finance

時間：2020-11-14

1 The model (equations and variables)
1.1 The model in brief
The model you will analyze is a simplied 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 simplied 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 bct 1 + 1
1 + h Etbct+1
1 1
1 +
hh hbit Etbt+1i +
g^t (1)
Goods-market clearing condition:
byt = (1 )bct + ybt + (2 )Sbt (2)
The link between terms of trade and real exchange rate:
bqt = (1 )Sbt (3)
Changes (growth rate) of the terms of trade:
Sbt Sbt 1 = bF;t bH;t (4)
1
Domestic-price in
ation (the "Phillips curve"):
(bH;t H ^H;t 1) = Et (bH;t+1 H ^H;t) + (1 H)(1 H) H cmct (5)
The real marginal cost:
cmct = 'ybt + Sbt + bct + ^"s;t (6)
The wedge between CPI- and PPI-in
ation:
bt = bH;t + Sbt Sbt 1
(7)
The uncovered interest-parity (UIP) condition:
bit bit = Etebct+1 bat + Etbt+1
(8)
The net-foreign-assets position (the current account):
byt bct = bat 1bat 1 +
(1 )qbt (9)
Imported-good in
ation (based on the law of one price):
bF;t = ebct + bt
(10)
Monetary-policy (Taylor) rule:
bit = ibit 1 + bt + ybyt + yybt + eebct "m;t (11)
Evolution of risk premium:
bt = bt 1 + ";t (12)
Evolution of foreign output:
byt = y ybt 1 + "y;t (13)
Evolution of foreign in
ation:
bt = bt 1 + ";t (14)
Evolution of foreign interest rate:
bit = ibit 1 + "i;t (15)
Evolution of preference shock:
^gt = gg^t 1 + "g;t (16)
Evolution of labor-supply shock:
^"s;t = s^"s;t 1 + s;t (17)
2
Denition 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 rate
bt CPI in
ation
byt output
bSt terms of trade (price of exports in terms of imports)
qbt real exchange rate
bH;t domestic-goods (PPI) in
ation
bF;t imported-goods in
ation
cmct real marginal cost
bat domestic-households' holding of foreign assets
bect domestic-currency depreciation rate (% change in the exchange rate)
byt
foreign output
bt
foreign in
ation
bit
foreign interest rate
bt
relative risk premium
bgt 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
4
Denition of parameters and their calibration
Parameters Denition Value
inverse intertemporal elasticity of substitution 1 openness parameter 0.25
elasticity of substitution between domestic and imported goods 0.80
subjective discount factor 0.99
H probability of price xity for domestic goods 0.70
risk-premium parameter 0.01
' inverse Frisch labor-supply elasticity 1.26
h degree of habit formation 0.25
consumption elasticity of preference shock 0.12
H degree of price indexation 0.20
i Taylor-rule interest smoothness 0.75
Taylor-rule response to in
ation 1.90
y Taylor-rule response to output 0.08
y Taylor-rule response to output growth 0.67
e Taylor-rule response to exchange-rate
uctuations 0 AR(1) coecient of risk-premium shock 0.95
y AR(1) coecient of foreign-output shock 0.55
AR(1) coecient of foreign-in
ation shock 0.50
i AR(1) coecient of foreign interest-rate shock 0.50
g AR(1) coecient of preference shock 0.65
s AR(1) coecient of labor-supply shock 0.70
m, , y , , i , g; s standard deviations of shocks 1
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 output ("y;t).
Analyze (i.e. explain the dynamics) and plot the eect of each of these shocks to
domestic output (ybt), consumption (bct), interest rate (bit), in
ation (bt), domestic-currency
nominal depreciation (ebct
), and the "shocked" variable (e.g. if it's a foreign output shock,
plot ybt
). 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 dierent assumptions on the central bank's monetary and exchange-rate policies.
Here, the COVID-19 pandemic "shocks" are proxied by a combination of negative labor
supply and negative preference shocks. The preference (or consumer-spending) shock in
the model is a type of demand 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. A negative
labor supply shock captures an aggregate supply reduction due to supply-chain disruptions
and large-scale social and economic restrictions (lockdowns).
In particular, assume that the economy starts at period 0 (2019.Q4) at the steady
state. Assume that the pandemic "shocks" occur for 4 periods or quarters, from periods
1-4 (2020.Q1-2020.Q4) with the following magnitudes:
Period
(Quarter)
1
(2020.Q1)
2
(2020.Q2)
3
(2020.Q3)
4
(2020.Q4)
Labor supply (s;t) 5% 7% 3% 2%
Preference ("g;t) 3% 3% 2% 3%
5
There are positive labor supply and preference shocks in period 4, perhaps in response to
the expectations that an eective COVID-19 vaccine is imminent and about to be approved
and rolled out to the public.
(a) Analyze the eect of these pandemic shocks under the current policy rule with i = 0:75, = 1:9, y = 0:08, y = 0:67, and e = 0. Plot the responses of ybt, bct, bit, bt, ebct
in one (3x2) gure. Explain their dynamics. In another (2x1) gure, plot the
evolution of exogenous labor supply variable ^"s;t and consumer preference variable bgt.
Is this combination of shocks a realistic representation of the COVID-19 pandemic
shocks? Why?
(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 = 0:65 > 0
The rest of policy rule coecients are unchanged. Analyze the eect of the pandemic
shocks under this new assumption, in comparison to the eect in part (a). Plot
the responses of byt, bct, bit, bt, ebct
in one (3x2) gure. Is this policy more eective in
terms of mitigating the eect of the pandemic shocks on byt, bt
, and bect
? Explain.
(c) Now assume that the central bank is operating under a xed exchange-rate regime.
Specically, the monetary policy rule in equation (11) is replaced with the following
policy rule:
bect = 0
This policy rule eectively (and credibly) xes the nominal exchange rate at a speci-
ed level. Redo questions 2(a). Your answer and analysis should be in comparison
to the
oating exchange-rate regime (both when e = 0 and e = 0:65).
[Notes: (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)].
[Extra points: plot the variables under the three policies in one gure, e.g. the plot
for ybt should include three dierent 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.

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